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<h1 class="tutorial-brand">// STRYKE — FULL REFERENCE</h1>
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<p class="docs-build-line">stryke v0.13.9 · 10065 topics · 164 chapters · generated from <code>strykelang/lsp.rs</code></p>
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<h2 class="tutorial-title"><span class="step-hash">>_</span>LANGUAGE REFERENCE</h2>
<p class="tutorial-subtitle">Every builtin, keyword, alias, and extension with an LSP hover doc — rendered from the exact markdown that `stryke docs` shows in the terminal. Jump via the chapter index, or <kbd>Ctrl+F</kbd> for a specific name.</p>
<section class="tutorial-section">
<h2>Chapters</h2>
<ul class="chapter-index">
<li><a href="#ch-parallel-primitives">Parallel Primitives</a> <span class="chapter-count">18</span></li>
<li><a href="#ch-shared-state-concurrency">Shared State & Concurrency</a> <span class="chapter-count">11</span></li>
<li><a href="#ch-pipeline-pipe-forward">Pipeline & Pipe-Forward</a> <span class="chapter-count">13</span></li>
<li><a href="#ch-streaming-iterators">Streaming Iterators</a> <span class="chapter-count">24</span></li>
<li><a href="#ch-list-operations">List Operations</a> <span class="chapter-count">62</span></li>
<li><a href="#ch-operators">Operators</a> <span class="chapter-count">66</span></li>
<li><a href="#ch-stryke-extensions">stryke Extensions</a> <span class="chapter-count">19</span></li>
<li><a href="#ch-data-serialization">Data & Serialization</a> <span class="chapter-count">45</span></li>
<li><a href="#ch-http-networking">HTTP & Networking</a> <span class="chapter-count">23</span></li>
<li><a href="#ch-crypto-encoding">Crypto & Encoding</a> <span class="chapter-count">133</span></li>
<li><a href="#ch-special-math-functions">Special Math Functions</a> <span class="chapter-count">12</span></li>
<li><a href="#ch-bessel-airy-hankel-struve-kelvin">Bessel / Airy / Hankel / Struve / Kelvin</a> <span class="chapter-count">19</span></li>
<li><a href="#ch-orthogonal-polynomials">Orthogonal Polynomials</a> <span class="chapter-count">13</span></li>
<li><a href="#ch-elliptic-integrals-functions">Elliptic Integrals & Functions</a> <span class="chapter-count">18</span></li>
<li><a href="#ch-zeta-polylog-lerch">Zeta / Polylog / Lerch</a> <span class="chapter-count">9</span></li>
<li><a href="#ch-hypergeometric">Hypergeometric</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-modular-forms">Modular Forms</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-si-ci-ei-li-fresnel-integrals">Si / Ci / Ei / Li / Fresnel Integrals</a> <span class="chapter-count">9</span></li>
<li><a href="#ch-number-theory-wolfram-parity">Number Theory (Wolfram Parity)</a> <span class="chapter-count">13</span></li>
<li><a href="#ch-combinatorics-wolfram-parity">Combinatorics (Wolfram Parity)</a> <span class="chapter-count">8</span></li>
<li><a href="#ch-q-series-mittag-leffler-coulomb">q-Series, Mittag-Leffler, Coulomb</a> <span class="chapter-count">7</span></li>
<li><a href="#ch-inverse-special-functions">Inverse Special Functions</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-piecewise-symbolic-primitives">Piecewise & Symbolic Primitives</a> <span class="chapter-count">8</span></li>
<li><a href="#ch-number-theory-wolfram-parity-ii">Number Theory (Wolfram Parity II)</a> <span class="chapter-count">14</span></li>
<li><a href="#ch-combinatorial-sequences">Combinatorial Sequences</a> <span class="chapter-count">12</span></li>
<li><a href="#ch-linear-algebra-extended">Linear Algebra (Extended)</a> <span class="chapter-count">8</span></li>
<li><a href="#ch-polynomial-algebra">Polynomial Algebra</a> <span class="chapter-count">6</span></li>
<li><a href="#ch-distributions-extended">Distributions (Extended)</a> <span class="chapter-count">18</span></li>
<li><a href="#ch-mathieu-heun">Mathieu / Heun</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-wavelets">Wavelets</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-graph-algorithms-extended">Graph Algorithms (Extended)</a> <span class="chapter-count">8</span></li>
<li><a href="#ch-number-theoretic-sums-constants">Number-Theoretic Sums & Constants</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-vector-calculus">Vector Calculus</a> <span class="chapter-count">6</span></li>
<li><a href="#ch-optimization">Optimization</a> <span class="chapter-count">6</span></li>
<li><a href="#ch-numerical-integration">Numerical Integration</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-linear-algebra-numeric">Linear Algebra (Numeric)</a> <span class="chapter-count">7</span></li>
<li><a href="#ch-polynomial-helpers">Polynomial Helpers</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-quaternions-3d-rotations">Quaternions & 3D Rotations</a> <span class="chapter-count">12</span></li>
<li><a href="#ch-information-theory">Information Theory</a> <span class="chapter-count">6</span></li>
<li><a href="#ch-quantum-primitives">Quantum Primitives</a> <span class="chapter-count">11</span></li>
<li><a href="#ch-statistical-mechanics">Statistical Mechanics</a> <span class="chapter-count">7</span></li>
<li><a href="#ch-optics">Optics</a> <span class="chapter-count">7</span></li>
<li><a href="#ch-astrodynamics">Astrodynamics</a> <span class="chapter-count">9</span></li>
<li><a href="#ch-time-series">Time Series</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-graph-centrality">Graph Centrality</a> <span class="chapter-count">6</span></li>
<li><a href="#ch-random-samplers-extended">Random Samplers (Extended)</a> <span class="chapter-count">6</span></li>
<li><a href="#ch-2-d-geometry">2-D Geometry</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-auto-differentiation">Auto-Differentiation</a> <span class="chapter-count">2</span></li>
<li><a href="#ch-statistical-tests-r-parity">Statistical Tests (R parity)</a> <span class="chapter-count">12</span></li>
<li><a href="#ch-distance-metrics-distances-jl-parity">Distance Metrics (Distances.jl parity)</a> <span class="chapter-count">6</span></li>
<li><a href="#ch-multivariate-non-central-distributions">Multivariate / Non-Central Distributions</a> <span class="chapter-count">9</span></li>
<li><a href="#ch-matrix-functions">Matrix Functions</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-adaptive-ode-solvers">Adaptive ODE Solvers</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-generalized-linear-models">Generalized Linear Models</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-bootstrap-resampling">Bootstrap & Resampling</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-time-series-operators">Time Series Operators</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-combinatorial-generators">Combinatorial Generators</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-dynamic-programming">Dynamic Programming</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-ml-metrics">ML Metrics</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-dsp-image-filters">DSP / Image Filters</a> <span class="chapter-count">6</span></li>
<li><a href="#ch-stochastic-processes">Stochastic Processes</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-compression-information-complexity">Compression / Information Complexity</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-physics-quantum-extended">Physics & Quantum (Extended)</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-number-theory-algebra-extended">Number Theory & Algebra (Extended)</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-cas-lite">CAS-Lite</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-quadrature-specialised">Quadrature (Specialised)</a> <span class="chapter-count">7</span></li>
<li><a href="#ch-optimization-heuristic">Optimization (Heuristic)</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-distributions-tail-mixture-categorical">Distributions (Tail / Mixture / Categorical)</a> <span class="chapter-count">14</span></li>
<li><a href="#ch-clustering-dimensionality-reduction">Clustering & Dimensionality Reduction</a> <span class="chapter-count">7</span></li>
<li><a href="#ch-neural-net-primitives">Neural-Net Primitives</a> <span class="chapter-count">11</span></li>
<li><a href="#ch-time-series-spectral">Time Series (Spectral)</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-image-processing">Image Processing</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-loss-functions">Loss Functions</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-spatial-geographic">Spatial / Geographic</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-integer-sequences">Integer Sequences</a> <span class="chapter-count">6</span></li>
<li><a href="#ch-graph-link-cluster-metrics">Graph Link & Cluster Metrics</a> <span class="chapter-count">7</span></li>
<li><a href="#ch-3-d-geometry">3-D Geometry</a> <span class="chapter-count">8</span></li>
<li><a href="#ch-iterative-solvers">Iterative Solvers</a> <span class="chapter-count">6</span></li>
<li><a href="#ch-crypto-modular-algebra">Crypto / Modular Algebra</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-physics-chemistry">Physics & Chemistry</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-mcmc-sdes">MCMC & SDEs</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-hidden-markov-models">Hidden Markov Models</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-survival-analysis">Survival Analysis</a> <span class="chapter-count">2</span></li>
<li><a href="#ch-sequence-alignment">Sequence Alignment</a> <span class="chapter-count">2</span></li>
<li><a href="#ch-chemistry">Chemistry</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-control-theory">Control Theory</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-game-theory">Game Theory</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-operations-research">Operations Research</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-numerical-pde">Numerical PDE</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-bayesian-conjugate-updates">Bayesian Conjugate Updates</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-quantum-computing-gates">Quantum Computing Gates</a> <span class="chapter-count">8</span></li>
<li><a href="#ch-splines-curves">Splines & Curves</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-music-audio">Music & Audio</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-astronomy-cosmology">Astronomy & Cosmology</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-fluid-dynamics">Fluid Dynamics</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-distributions-discrete-circular">Distributions (Discrete / Circular)</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-random-graph-generators">Random Graph Generators</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-color-science">Color Science</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-integer-sequences-combinatorial">Integer Sequences (Combinatorial)</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-multiple-testing-corrections">Multiple-Testing Corrections</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-probabilistic-distances">Probabilistic Distances</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-distributions-tail-inflated">Distributions (Tail / Inflated)</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-astrophysics-radiation">Astrophysics & Radiation</a> <span class="chapter-count">9</span></li>
<li><a href="#ch-chemistry-beer-rate-colligative">Chemistry (Beer / Rate / Colligative)</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-mixed-strategy-game-theory">Mixed-Strategy Game Theory</a> <span class="chapter-count">2</span></li>
<li><a href="#ch-computer-graphics">Computer Graphics</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-dsp-hilbert-cepstrum-filter-design">DSP (Hilbert / Cepstrum / Filter Design)</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-image-processing-edges-bilateral">Image Processing (Edges / Bilateral)</a> <span class="chapter-count">2</span></li>
<li><a href="#ch-clustering-helpers">Clustering Helpers</a> <span class="chapter-count">2</span></li>
<li><a href="#ch-combinatorics-tableaux-boustrophedon">Combinatorics (Tableaux / Boustrophedon)</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-number-theory-tetration-smoothness">Number Theory (Tetration / Smoothness)</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-network-coreness-structure">Network Coreness & Structure</a> <span class="chapter-count">2</span></li>
<li><a href="#ch-crypto-helpers">Crypto Helpers</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-quantum-entanglement">Quantum Entanglement</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-2-d-geometry-polygons-circles">2-D Geometry (Polygons & Circles)</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-time-series-smoothing">Time-Series Smoothing</a> <span class="chapter-count">1</span></li>
<li><a href="#ch-bioinformatics">Bioinformatics</a> <span class="chapter-count">6</span></li>
<li><a href="#ch-geographic-map-projection">Geographic / Map Projection</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-fixed-income-finance">Fixed-Income Finance</a> <span class="chapter-count">5</span></li>
<li><a href="#ch-image-quality-metrics">Image Quality Metrics</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-acoustics">Acoustics</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-population-genetics">Population Genetics</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-epidemiology">Epidemiology</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-inequality-measures">Inequality Measures</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-apl-j-array-primitives">APL / J Array Primitives</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-plasma-physics">Plasma Physics</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-string-similarity">String Similarity</a> <span class="chapter-count">2</span></li>
<li><a href="#ch-rating-systems">Rating Systems</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-effect-sizes">Effect Sizes</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-control-transient-response">Control Transient Response</a> <span class="chapter-count">2</span></li>
<li><a href="#ch-matrix-norms">Matrix Norms</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-network-triad-analysis">Network Triad Analysis</a> <span class="chapter-count">3</span></li>
<li><a href="#ch-misc-inverses">Misc Inverses</a> <span class="chapter-count">1</span></li>
<li><a href="#ch-parallel-i-o">Parallel I/O</a> <span class="chapter-count">8</span></li>
<li><a href="#ch-cli-args">CLI / Args</a> <span class="chapter-count">1</span></li>
<li><a href="#ch-file-i-o">File I/O</a> <span class="chapter-count">35</span></li>
<li><a href="#ch-strings">Strings</a> <span class="chapter-count">26</span></li>
<li><a href="#ch-arrays-hashes">Arrays & Hashes</a> <span class="chapter-count">20</span></li>
<li><a href="#ch-control-flow">Control Flow</a> <span class="chapter-count">16</span></li>
<li><a href="#ch-error-handling">Error Handling</a> <span class="chapter-count">8</span></li>
<li><a href="#ch-aop-advice">AOP / Advice</a> <span class="chapter-count">7</span></li>
<li><a href="#ch-declarations">Declarations</a> <span class="chapter-count">10</span></li>
<li><a href="#ch-cluster-distributed">Cluster / Distributed</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-datetime">Datetime</a> <span class="chapter-count">15</span></li>
<li><a href="#ch-math">Math</a> <span class="chapter-count">13</span></li>
<li><a href="#ch-file-system">File System</a> <span class="chapter-count">34</span></li>
<li><a href="#ch-process">Process</a> <span class="chapter-count">21</span></li>
<li><a href="#ch-pack-binary">Pack / Binary</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-logging">Logging</a> <span class="chapter-count">7</span></li>
<li><a href="#ch-charts-svg">Charts (SVG)</a> <span class="chapter-count">19</span></li>
<li><a href="#ch-audio">Audio</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-network-utilities">Network Utilities</a> <span class="chapter-count">18</span></li>
<li><a href="#ch-markup-web-scraping">Markup / Web Scraping</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-date-utilities">Date Utilities</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-git">Git</a> <span class="chapter-count">10</span></li>
<li><a href="#ch-system">System</a> <span class="chapter-count">13</span></li>
<li><a href="#ch-testing">Testing</a> <span class="chapter-count">15</span></li>
<li><a href="#ch-test-runner-worker-pool">Test Runner (worker pool)</a> <span class="chapter-count">4</span></li>
<li><a href="#ch-ai-primitives-docs-ai-primitives-md">AI primitives (docs/AI_PRIMITIVES.md)</a> <span class="chapter-count">79</span></li>
<li><a href="#ch-mcp-model-context-protocol">MCP (Model Context Protocol)</a> <span class="chapter-count">13</span></li>
<li><a href="#ch-web-framework-stryke-web-readme-md">Web framework (stryke_web/README.md)</a> <span class="chapter-count">112</span></li>
<li><a href="#ch-stress-telemetry-docs-stress-testing-md">Stress / telemetry (docs/STRESS_TESTING.md)</a> <span class="chapter-count">42</span></li>
<li><a href="#ch-pty-expect-docs-expect-feature-idea-md">PTY / expect (docs/expect-feature-idea.md)</a> <span class="chapter-count">13</span></li>
<li><a href="#ch-other">Other</a> <span class="chapter-count">8394</span></li>
</ul>
</section>
<section class="tutorial-section" id="ch-parallel-primitives">
<h2>Parallel Primitives</h2>
<p class="chapter-meta">18 topics</p>
<article class="doc-entry" id="doc-pmap">
<h3><a class="doc-anchor" href="#doc-pmap">#</a> <code>pmap</code></h3>
<p>Parallel <code>map</code> powered by rayon's work-stealing thread pool. Every element of the input list is processed concurrently across all available CPU cores, and the output order is guaranteed to match the input order. This is the primary workhorse for CPU-bound transforms in stryke — use it whenever you have a pure function and a large list. Pass <code>progress => 1</code> to get a live progress bar on STDERR for long-running jobs.</p>
<p>Two equivalent surface syntaxes: • Block form — <code>pmap BLOCK LIST</code> — element bound to <code>_</code> • Bare-fn form — <code>pmap FUNC, LIST</code> — single-arg function name as first argument</p>
<pre><code class="lang-perl"># Block form
my @out = pmap { _ * 2 } 1:1_000_000
my @hashes = pmap sha256 @blobs, progress => 1
1:100 |> pmap { fetch("https://api.example.com/item/$_") } |> e p
# Bare-fn form (works for builtins and user-defined subs)
my @hashes = pmap sha256, @blobs, progress => 1
fn dbl = _ * 2
my @r = pmap dbl, (1:1_000_000)
</code></pre>
</article>
<article class="doc-entry" id="doc-pmaps">
<h3><a class="doc-anchor" href="#doc-pmaps">#</a> <code>pmaps</code></h3>
<p>Streaming parallel <code>map</code> — returns a lazy iterator that processes items across all CPU cores using a persistent worker-thread pool. Unlike <code>pmap</code> which eagerly collects all results into an array, <code>pmaps</code> yields results as they complete through a bounded channel, so downstream consumers see output immediately. Output order is non-deterministic (completion order). Each worker thread reuses a single interpreter instance, making it faster than <code>pmap</code> for large inputs.</p>
<p>Best for: • Pipelines with <code>take</code>/<code>head</code> — avoids processing the full list • Very large inputs where holding all results in memory is impractical • Streaming pipelines where you want progressive output</p>
<pre><code class="lang-perl">range(0, 1e9) |> pmaps { _ * 2 } |> take 10 |> ep
t 1:1e6 pmaps { expensive(_) } ep
range(0, 1e6) |> pmaps { fetch("https://api/item/$_") } |> pgreps { _->{ok} } |> ep
</code></pre>
</article>
<article class="doc-entry" id="doc-pmap-chunked">
<h3><a class="doc-anchor" href="#doc-pmap-chunked">#</a> <code>pmap_chunked</code></h3>
<p>Parallel map that groups input into contiguous batches of N elements before distributing to threads. This reduces per-item scheduling overhead when the per-element work is very cheap (e.g. a few arithmetic ops). Each thread receives a slice of N consecutive items, processes them sequentially within the batch, then returns the batch result. Use this instead of <code>pmap</code> when profiling shows rayon overhead dominates the actual computation.</p>
<pre><code class="lang-perl">my @out = pmap_chunked 100, { _ ** 2 } 1:1_000_000
my @parsed = pmap_chunked 50, { json_decode } @json_strings
</code></pre>
</article>
<article class="doc-entry" id="doc-pgrep">
<h3><a class="doc-anchor" href="#doc-pgrep">#</a> <code>pgrep</code></h3>
<p>Parallel <code>grep</code> that evaluates the filter predicate concurrently across all CPU cores using rayon. The result preserves the original input order, so it is a drop-in replacement for <code>grep</code> on large lists. Best suited for predicates that do meaningful work per element — if the predicate is trivial (e.g. a single regex on short strings), sequential <code>grep</code> may be faster due to lower scheduling overhead.</p>
<p>Two equivalent surface syntaxes: <code>pgrep { BLOCK } LIST</code> or <code>pgrep FUNC, LIST</code>.</p>
<pre><code class="lang-perl"># Block form
my @matches = pgrep { /complex_pattern/ } @big_list
my @primes = pgrep { is_prime } 2:1_000_000
@files |> pgrep { -s _ > 1024 } |> e p
# Bare-fn form
fn Demo::even = _ % 2 == 0
my @e = pgrep Demo::even, 1:10 # (2,4,6,8,10)
</code></pre>
</article>
<article class="doc-entry" id="doc-pgreps">
<h3><a class="doc-anchor" href="#doc-pgreps">#</a> <code>pgreps</code></h3>
<p>Streaming parallel <code>grep</code> — returns a lazy iterator that filters items across all CPU cores. Unlike <code>pgrep</code> which eagerly collects all matching items, <code>pgreps</code> yields matches as they are found through a bounded channel. Output order is non-deterministic (completion order). Each worker thread reuses a single interpreter instance.</p>
<pre><code class="lang-perl">range(0, 1e6) |> pgreps { is_prime(_) } |> take 100 |> ep
t 1:1e9 pgreps { _ % 7 == 0 } take 10 ep
</code></pre>
</article>
<article class="doc-entry" id="doc-pfor">
<h3><a class="doc-anchor" href="#doc-pfor">#</a> <code>pfor</code></h3>
<p>Parallel <code>foreach</code> that executes a side-effecting block across all CPU cores with no return value. Use this when you need to perform work for each element (writing files, sending requests, updating shared state) but don't need to collect results. The block receives each element as <code>_</code>. Iteration order is non-deterministic, so the block must be safe to run concurrently.</p>
<p>Two equivalent surface syntaxes: <code>pfor { BLOCK } LIST</code> or <code>pfor FUNC, LIST</code>.</p>
<pre><code class="lang-perl"># Block form
pfor { write_report } @records
pfor { compress_file } glob("*.log")
@urls |> pfor { fetch
p "done: $_" }
# Bare-fn form
fn task = ep "did $_"
pfor task, (1, 2, 3)
</code></pre>
</article>
<article class="doc-entry" id="doc-psort">
<h3><a class="doc-anchor" href="#doc-psort">#</a> <code>psort</code></h3>
<p>Parallel sort that uses rayon's parallel merge-sort algorithm. Accepts an optional comparator block using <code>$_0</code>/<code>$_1</code> (or <code>$a</code>/<code>$b</code>). For large lists (10k+ elements), this significantly outperforms the sequential <code>sort</code> by splitting the array, sorting partitions in parallel, and merging. The sort is stable — equal elements retain their relative order.</p>
<pre><code class="lang-perl">my @sorted = psort { $_0 <=> $_1 } @big_list
my @by_name = psort { $_0->{name} cmp $_1->{name} } @records
@nums |> psort { $a <=> $b } |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-pcache">
<h3><a class="doc-anchor" href="#doc-pcache">#</a> <code>pcache</code></h3>
<p>Parallel memoized map — each element is processed concurrently, but results are cached by the stringified value of <code>_</code> so duplicate inputs are computed only once. This is ideal when your input list contains many repeated values and the computation is expensive. The cache is a concurrent hash map shared across all threads, so there is no lock contention on reads after the first computation.</p>
<p>Two equivalent surface syntaxes: <code>pcache { BLOCK } LIST</code> or <code>pcache FUNC, LIST</code>.</p>
<pre><code class="lang-perl"># Block form
my @out = pcache { expensive_lookup } @list_with_dupes
my @resolved = pcache { dns_resolve } @hostnames
# Bare-fn form
my @resolved = pcache dns_resolve, @hostnames
</code></pre>
</article>
<article class="doc-entry" id="doc-preduce">
<h3><a class="doc-anchor" href="#doc-preduce">#</a> <code>preduce</code></h3>
<p>Parallel tree-fold using rayon's <code>reduce</code> — splits the list into chunks, reduces each chunk independently, then merges partial results. The combining operation <strong>must be associative</strong> (e.g. <code>+</code>, <code>*</code>, <code>max</code>); non-associative ops will produce incorrect results. Much faster than sequential <code>reduce</code> on large numeric lists because the tree structure allows O(log n) merge depth across cores.</p>
<pre><code class="lang-perl">my $total = preduce { $_0 + $_1 } @nums
my $biggest = preduce { $_0 > $_1 ? $_0 : $_1 } @vals
my $product = preduce { $a * $b } 1:100
</code></pre>
</article>
<article class="doc-entry" id="doc-preduce-init">
<h3><a class="doc-anchor" href="#doc-preduce-init">#</a> <code>preduce_init</code></h3>
<p>Parallel fold with identity value.</p>
<pre><code class="lang-perl">my $total = preduce_init 0, { $_0 + $_1 } @list
</code></pre>
</article>
<article class="doc-entry" id="doc-pmap-reduce">
<h3><a class="doc-anchor" href="#doc-pmap-reduce">#</a> <code>pmap_reduce</code></h3>
<p>Fused parallel map + tree reduce.</p>
<pre><code class="lang-perl">my $sum = pmap_reduce { _*2 } { $_0 + $_1 } @list
</code></pre>
</article>
<article class="doc-entry" id="doc-pany">
<h3><a class="doc-anchor" href="#doc-pany">#</a> <code>pany</code></h3>
<p><code>pany { COND } @list</code> — parallel short-circuit <code>any</code>.</p>
</article>
<article class="doc-entry" id="doc-pfirst">
<h3><a class="doc-anchor" href="#doc-pfirst">#</a> <code>pfirst</code></h3>
<p><code>pfirst { COND } @list</code> — parallel first matching element.</p>
</article>
<article class="doc-entry" id="doc-puniq">
<h3><a class="doc-anchor" href="#doc-puniq">#</a> <code>puniq</code></h3>
<p><code>puniq @list</code> — parallel unique elements.</p>
</article>
<article class="doc-entry" id="doc-pflat-map">
<h3><a class="doc-anchor" href="#doc-pflat-map">#</a> <code>pflat_map</code></h3>
<p>Parallel flat-map: map + flatten results. Each element produces zero or more output values via the block/function, and the outputs are concatenated in input order.</p>
<p>Two equivalent surface syntaxes: <code>pflat_map BLOCK LIST</code> or <code>pflat_map FUNC, LIST</code>.</p>
<pre><code class="lang-perl"># Block form
my @out = pflat_map expand @list
# Bare-fn form
fn expand = (_, _ * 10)
my @r = pflat_map expand, (1, 2, 3) # (1, 10, 2, 20, 3, 30)
</code></pre>
</article>
<article class="doc-entry" id="doc-pflat-maps">
<h3><a class="doc-anchor" href="#doc-pflat-maps">#</a> <code>pflat_maps</code></h3>
<p>Streaming parallel flat-map — like <code>pmaps</code> but flattens array results. Returns a lazy iterator.</p>
<pre><code class="lang-perl">range(0, 1e6) |> pflat_maps { [_, _ * 10] } |> ep
</code></pre>
</article>
<article class="doc-entry" id="doc-fan">
<h3><a class="doc-anchor" href="#doc-fan">#</a> <code>fan</code></h3>
<p>Execute BLOCK or FUNC N times in parallel (<code>_</code> = index 0..N-1). With no count, defaults to the rayon pool size (<code>stryke -j</code>).</p>
<p>Two equivalent surface syntaxes: • Block form — <code>fan N { BLOCK }</code> or <code>fan { BLOCK }</code> • Bare-fn form — <code>fan N, FUNC</code> or <code>fan FUNC</code></p>
<pre><code class="lang-perl"># Block form
fan 8 { work(_) }
fan { work(_) } progress => 1
# Bare-fn form
fn tick = ep "tick $_"
fan 8, tick
fan tick, progress => 1 # uses pool size
</code></pre>
</article>
<article class="doc-entry" id="doc-fan-cap">
<h3><a class="doc-anchor" href="#doc-fan-cap">#</a> <code>fan_cap</code></h3>
<p>Like <code>fan</code> but captures return values in index order. Two surface syntaxes: <code>fan_cap N { BLOCK }</code> or <code>fan_cap N, FUNC</code>.</p>
<pre><code class="lang-perl"># Block form
my @results = fan_cap 8 { compute(_) }
# Bare-fn form
fn compute = _ * _
my @squares = fan_cap 8, compute
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-shared-state-concurrency">
<h2>Shared State & Concurrency</h2>
<p class="chapter-meta">11 topics</p>
<article class="doc-entry" id="doc-mysync">
<h3><a class="doc-anchor" href="#doc-mysync">#</a> <code>mysync</code></h3>
<p>Declare shared variables for parallel blocks (<code>Arc<Mutex></code>).</p>
<pre><code class="lang-perl">mysync $counter = 0
fan 10000 { $counter++ } # always exactly 10000
mysync @results
mysync %histogram$1
Compound ops (`++`, `+=`, `.=`, `|=`, `&=`) are fully atomic.
</code></pre>
</article>
<article class="doc-entry" id="doc-async">
<h3><a class="doc-anchor" href="#doc-async">#</a> <code>async</code></h3>
<p><code>async { BLOCK }</code> — schedule a block for execution on a background worker thread and return a task handle immediately.</p>
<p>The block begins executing as soon as a thread is available in stryke's global rayon thread pool, while the calling code continues without blocking. To retrieve the result, pass the task handle to <code>await</code>, which blocks until the task completes and returns its value. If the block panics, the panic is captured and re-raised at the <code>await</code> call site. Use <code>async</code> for fire-and-forget background work, overlapping I/O with computation, or launching multiple independent tasks that you later join. For structured fan-out with index-based parallelism, prefer <code>fan</code> or <code>fan_cap</code> instead.</p>
<pre><code class="lang-perl">my $task = async { long_compute() }
do_other_work()
my $val = await $task
# Overlapping multiple fetches:
my @tasks = map { async { fetch("https://api.example.com/$_") } } 1:10;
my @results = map { await _ } @tasks
</code></pre>
</article>
<article class="doc-entry" id="doc-spawn">
<h3><a class="doc-anchor" href="#doc-spawn">#</a> <code>spawn</code></h3>
<p><code>spawn { BLOCK }</code> — Rust-style alias for <code>async</code>; schedules a block on a background thread and returns a joinable task handle.</p>
<p>This is identical to <code>async</code> in every respect — same thread pool, same semantics, same <code>await</code> for joining. The name exists for developers coming from Rust's <code>tokio::spawn</code> or <code>std::thread::spawn</code> who find <code>spawn</code> more natural. Use whichever reads better in your code; mixing <code>async</code> and <code>spawn</code> in the same program is perfectly fine since they share the same underlying pool.</p>
<pre><code class="lang-perl">my $task = spawn { expensive_io() }
my $val = await $task
my @handles = map { spawn { process } } @items;
my @out = map { await _ } @handles
</code></pre>
</article>
<article class="doc-entry" id="doc-await">
<h3><a class="doc-anchor" href="#doc-await">#</a> <code>await</code></h3>
<p><code>await $task</code> — block the current thread until an async/spawn task completes and return its result value.</p>
<p>If the background task has already finished by the time <code>await</code> is called, the result is returned immediately with no scheduling overhead. If the task panicked, <code>await</code> re-raises the panic as a die in the calling thread, preserving the original error message and backtrace. You can <code>await</code> a task exactly once; calling <code>await</code> on an already-joined handle is a fatal error. For waiting on multiple tasks, simply map over the handles — stryke does not yet provide a <code>join_all</code> primitive, but <code>map await @tasks</code> achieves the same effect.</p>
<pre><code class="lang-perl">my $task = async { 42 }
my $result = await $task # 42
# Await with error handling:
my $t = spawn { die "oops" }
eval { await $t } # $@ eq "oops"
</code></pre>
</article>
<article class="doc-entry" id="doc-pchannel">
<h3><a class="doc-anchor" href="#doc-pchannel">#</a> <code>pchannel</code></h3>
<p><code>pchannel(N)</code> — create a bounded multi-producer multi-consumer (MPMC) channel with capacity N, returning a <code>($tx, $rx)</code> pair.</p>
<p>The transmitter <code>$tx</code> supports <code>->send($val)</code> which blocks if the channel is full (backpressure). The receiver <code>$rx</code> supports <code>->recv</code> which blocks until a value is available, and <code>->try_recv</code> which returns <code>undef</code> immediately if the channel is empty. Both ends can be cloned and shared across threads — clone <code>$tx</code> with <code>$tx->clone</code> to create additional producers, or clone <code>$rx</code> for additional consumers. When all transmitters are dropped, <code>->recv</code> on the receiver returns <code>undef</code> to signal completion. Use <code>pchannel</code> to build producer-consumer pipelines, rate-limited work queues, or to communicate between <code>async</code>/<code>spawn</code> tasks.</p>
<pre><code class="lang-perl">my ($tx, $rx) = pchannel(100)
async { $tx->send(_) for 1:1000
undef $tx }
while (defined(my $val = $rx->recv)) {
p $val
}
# Multiple producers:
my ($tx, $rx) = pchannel(50)
for my $i (1:4) {
my $t = $tx->clone
spawn { $t->send("from worker $i: _") for 1:100 }
}
undef $tx # drop original so channel closes when workers finish
</code></pre>
</article>
<article class="doc-entry" id="doc-pselect">
<h3><a class="doc-anchor" href="#doc-pselect">#</a> <code>pselect</code></h3>
<p><code>pselect(@channels)</code> — wait on multiple <code>pchannel</code> receivers.</p>
</article>
<article class="doc-entry" id="doc-barrier">
<h3><a class="doc-anchor" href="#doc-barrier">#</a> <code>barrier</code></h3>
<p><code>barrier(N)</code> — create a synchronization barrier that blocks until exactly N threads have arrived at the wait point.</p>
<p>Each thread calls <code>$b->wait</code> and is suspended until all N participants have reached the barrier, at which point all are released simultaneously. This is useful for coordinating phased parallel algorithms where all workers must complete step K before any worker begins step K+1. The barrier is reusable — after all threads are released, it resets and can be waited on again. Internally backed by a Rust <code>std::sync::Barrier</code> for zero-overhead synchronization.</p>
<pre><code class="lang-perl">my $b = barrier(4)
for my $i (0:3) {
spawn {
setup_phase($i)
$b->wait # all 4 threads sync here
compute_phase($i)
}
}
</code></pre>
</article>
<article class="doc-entry" id="doc-ppool">
<h3><a class="doc-anchor" href="#doc-ppool">#</a> <code>ppool</code></h3>
<p><code>ppool(N, fn { ... })</code> — create a persistent thread pool of N worker threads, each running the provided subroutine in a loop.</p>
<p>The pool is typically paired with a <code>pchannel</code>: workers pull items from the channel's receiver, process them, and optionally send results to an output channel. Unlike <code>pmap</code> which is a one-shot parallel transform, <code>ppool</code> keeps threads alive for the lifetime of the pool, making it ideal for long-running server-style workloads, background drain loops, or scenarios where thread startup cost would dominate short-lived <code>pmap</code> calls. Workers exit when their input channel is closed (all transmitters dropped). The pool object supports <code>->join</code> to block until all workers have finished.</p>
<pre><code class="lang-perl">my ($tx, $rx) = pchannel(100)
my $pool = ppool 4, fn {
while (defined(my $job = $rx->recv)) {
process($job)
}
}
$tx->send(_) for @work_items
undef $tx # signal completion
$pool->join # wait for drain
</code></pre>
</article>
<article class="doc-entry" id="doc-deque">
<h3><a class="doc-anchor" href="#doc-deque">#</a> <code>deque</code></h3>
<p><code>deque LIST</code> — create a double-ended queue initialized with the given elements.</p>
<p>A deque supports efficient O(1) insertion and removal at both ends via <code>->push_front($val)</code>, <code>->push_back($val)</code>, <code>->pop_front</code>, and <code>->pop_back</code>. It also supports <code>->len</code> and iteration. Internally backed by a Rust <code>VecDeque</code>, it is ideal for sliding window algorithms, BFS traversals, or any scenario where you need fast access to both ends of a sequence.</p>
<pre><code class="lang-perl">my $dq = deque(1, 2, 3)
$dq->push_front(0)
$dq->push_back(4)
p $dq->pop_front # 0
</code></pre>
</article>
<article class="doc-entry" id="doc-heap">
<h3><a class="doc-anchor" href="#doc-heap">#</a> <code>heap</code></h3>
<p><code>heap LIST</code> — create a min-heap (priority queue) from the given elements.</p>
<p>Elements are heapified on construction so that <code>->pop</code> always returns the smallest element in O(log n) time. <code>->push($val)</code> inserts a new element, also in O(log n). The heap supports <code>->peek</code> to inspect the minimum without removing it, and <code>->len</code> for the current size. Internally backed by a Rust <code>BinaryHeap</code> (inverted for min-heap semantics), it is the go-to structure for top-K queries, Dijkstra, and merge-K-sorted-lists problems.</p>
<pre><code class="lang-perl">my $h = heap(5, 3, 8, 1)
p $h->pop # 1 (smallest first)
p $h->peek # 3 (next smallest)
$h->push(0)
</code></pre>
</article>
<article class="doc-entry" id="doc-set">
<h3><a class="doc-anchor" href="#doc-set">#</a> <code>set</code></h3>
<p><code>set LIST</code> — create a set (unique unordered collection) from the given elements.</p>
<p>Duplicate values are collapsed on construction so the set contains each value exactly once. The set object provides <code>->contains($val)</code> for O(1) membership testing, plus <code>->union($s)</code>, <code>->intersection($s)</code>, <code>->difference($s)</code>, and <code>->len</code> methods. Internally backed by a Rust <code>HashSet</code> for performance. Use <code>to_set</code> to convert an existing iterator into a set.</p>
<pre><code class="lang-perl">my $s = set(1, 2, 3, 2, 1)
p $s->contains(2) # 1
p $s->len # 3
my $both = $s->union(set(3, 4, 5))
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-pipeline-pipe-forward">
<h2>Pipeline & Pipe-Forward</h2>
<p class="chapter-meta">13 topics</p>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>|></code></h3>
<p>Pipe-forward operator — threads LHS as first argument of RHS call.</p>
<pre><code class="lang-perl">"hello" |> uc |> rev |> p # OLLEH
1:10 |> grep _ > 5 |> map _ * 2 |> e p
$url |> fetch_json |> json_jq '.name' |> p
"hello world" |> s/world/perl/ |> p # hello perl
</code></pre>
<p>Zero runtime cost (parse-time desugaring). Binds looser than <code>||</code>, tighter than <code>?:</code>.</p>
</article>
<article class="doc-entry" id="doc-thread">
<h3><a class="doc-anchor" href="#doc-thread">#</a> <code>thread</code></h3>
<p>Thread-first macro — chain stages where the threaded value is injected as the <strong>first</strong> argument (like Clojure's <code>-></code>).</p>
<pre><code class="lang-perl">~> @data grep { _ > 5 } map { _ * 2 } sort { $_0 <=> $_1 } |> join "," |> p
~> " hello " tm uc rv lc ufc sc cc kc tj p # short aliases
fn div = _0 / _1
~> 10 div(2) p # div(10, 2) = 5
~> 10 div(_, 2) p # explicit _ position: div(10, 2) = 5
</code></pre>
<p>Spellings: <code>~></code>, <code>thread</code>, <code>t</code>. Stages: bare function (<code>uc</code>, <code>tm</code>, …), function with block (<code>map { … }</code>, <code>grep { … }</code>), <code>name(args)</code> call where <code>_</code> is the threaded-value placeholder, or <code>>{}</code> anonymous block. <code>|></code> terminates the macro.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>~>></code></h3>
<p>Thread-last macro — chain stages where the threaded value is injected as the <strong>last</strong> argument (like Clojure's <code>->></code>).</p>
<pre><code class="lang-perl">fn div = _0 / _1
~>> 10 div(2) p # div(2, 10) = 0.2
->> 10 div(_, 2) p # explicit _ overrides: div(10, 2) = 5
# Thread-last is useful for list-consuming functions:
fn first_n { @_[0..$_[-1]-1] } # first_n(list, n)
~>> (1,2,3,4,5) first_n(3) p # first_n(1,2,3,4,5, 3) = (1,2,3)
</code></pre>
<p>Spellings: <code>~>></code>, <code>->></code>. The explicit <code>_</code> placeholder always takes precedence.</p>
</article>
<article class="doc-entry" id="doc-s">
<h3><a class="doc-anchor" href="#doc-s">#</a> <code>~s></code></h3>
<p>Per-item streaming thread macro — each stage runs as an independent worker thread connected to the next via a bounded channel, so items flow through the pipeline concurrently without materializing intermediate arrays.</p>
<pre><code class="lang-perl">~s> [1, 2, 3, 4, 5] map { _ * 10 } map { _ + 1 }
~s> @lines map { json_decode } grep { _->{ok} } map { _->{val} }
~s> gen { yield_lines "huge.log" } map { parse } grep { /ERROR/ }
</code></pre>
<p>Use <code>~s></code> when stages have differing latencies (I/O + CPU mix) so faster workers can pull ahead. Output order is non-deterministic. The macro's final value is the count of items the last stage emitted. <code>~s>></code> is the thread-last variant.</p>
<p>See <code>~p></code> for chunk-parallel (vs per-item) execution and <code>par_pipeline</code> for the verbose builder form.</p>
</article>
<article class="doc-entry" id="doc-p">
<h3><a class="doc-anchor" href="#doc-p">#</a> <code>~p></code></h3>
<p>Chunk-parallel thread macro — splits the input into chunks, runs the entire pipeline on each chunk in parallel via rayon, and auto-merges chunk results. Equivalent to <code>par_reduce { stage1 |> stage2 |> ... } SRC</code>.</p>
<pre><code class="lang-perl">~p> c("**.rs") letters freq # histogram across all .rs
~p> @big map { _ * 2 } sum # parallel map+sum
~p> $huge letters freq ||> values |> sum # boundary: terse
~p> $huge letters freq |then| values |> sum # boundary: english
</code></pre>
<p>The auto-merger picks a strategy by inspecting the first chunk's result type: hash-of-numbers merges key-wise with <code>+</code> (canonical histogram), numeric scalars sum, arrays concat, strings concat. Use <code>||></code> or <code>|then|</code> to switch back to sequential <code>~></code> mode for stages that operate on the merged whole. <code>|></code> also terminates a <code>~p></code> macro. <code>~p>></code> is the thread-last variant.</p>
</article>
<article class="doc-entry" id="doc-d">
<h3><a class="doc-anchor" href="#doc-d">#</a> <code>~d></code></h3>
<p>Distributed thread macro — same chunk-block semantics as <code>~p></code> but ships the pipeline to a remote stryke cluster rather than running locally. Syntax: <code>~d> on $cluster SOURCE stage1 stage2 ...</code>. The <code>on EXPR</code> slot is mandatory — <code>EXPR</code> must evaluate to a value built by <code>cluster(...)</code> (see <code>cluster</code> builtin).</p>
<pre><code class="lang-perl">my $c = cluster(["host1", "host2", "host3:8022"])
~d> on $c c("**.parquet") map { parse_pq } map { transform } collect
~d> on $c @huge_urls map { fetch } grep { _->{status} == 200 } |> sum_bytes
</code></pre>
<p>Unlike <code>~p></code>, captures from the enclosing scope are restricted: <code>mysync</code>/atomic captures are rejected (the value can't cross the wire safely). Errors on remote workers are surfaced as a single aggregated error. <code>~d>></code> is the thread-last variant — threaded value injected as the last argument of each stage.</p>
<p>See <code>cluster</code> for cluster construction, <code>~p></code> for local chunk-parallel, <code>pmap_on</code> for the verbose builder form.</p>
</article>
<article class="doc-entry" id="doc-par">
<h3><a class="doc-anchor" href="#doc-par">#</a> <code>par</code></h3>
<p>Generic parallel-chunk thread-stage — only valid inside <code>~></code>/<code>~>></code>. Splits the threaded value into chunks, runs <code>BLOCK</code> on each chunk in parallel, and flattens chunk outputs into a single list.</p>
<pre><code class="lang-perl">my @a = ~> "Hello, World 123" par { letters } # H e l l o W o r l d
~> @huge par { map { _ ** 2 } |> sum } |> sum p # parallel sum-of-squares
</code></pre>
<p>Each chunk gets a fresh sub-VM with the chunk bound to <code>_</code> and <code>$_[0]</code>. List-returning ops keep their values; the runtime auto-flattens. Use <code>par_reduce</code> when you need a final merge step rather than flat concat. <code>par { … }</code> is *only* a thread-stage; calling it as a top-level expression is an undefined-sub error.</p>
</article>
<article class="doc-entry" id="doc-par-reduce">
<h3><a class="doc-anchor" href="#doc-par-reduce">#</a> <code>par_reduce</code></h3>
<p>Chunk-extract-merge thread-stage. The single-block form runs <code>extract</code> per chunk and auto-merges results by type (hash<num>→key-wise add, number→sum, array→concat, string→concat). The two-block form binds <code>$a</code>/<code>$b</code> in the explicit reducer.</p>
<pre><code class="lang-perl">~> "abc def abc" par_reduce { letters |> freq } # canonical histogram merge
~> @nums par_reduce { sum } # parallel sum
~> "abcdefgh" par_reduce { length(_) } { $a + $b } # explicit pairwise reducer
</code></pre>
<p>Below the chunk threshold the runtime falls back to single-chunk eval; the result must still match the bare extract block's output. Multi-chunk paths require the merger (auto or explicit) to be associative and commutative for correct results.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>||></code></h3>
<p>Boundary marker that terminates the chunk-parallel section of a <code>~p></code> macro and switches the merged result into a sequential <code>~></code> continuation.</p>
<pre><code class="lang-perl">~p> "abc def abc" letters freq ||> values |> sum # 9
~p> "abc def abc" letters freq |then| values |> sum # 9 — readable form
~p> @data map { _ * 2 } sum ||> sqrt p # parallel sum, sequential sqrt
</code></pre>
<p>Both spellings are byte-equivalent; <code>||></code> is terse, <code>|then|</code> reads in English. Use either when you need a post-merge stage that operates on the whole reduced value rather than per-chunk. <code>|></code> also terminates a <code>~p></code> macro.</p>
</article>
<article class="doc-entry" id="doc-pipeline">
<h3><a class="doc-anchor" href="#doc-pipeline">#</a> <code>pipeline</code></h3>
<p><code>pipeline(@list)</code> — wrap a list (or iterator) in a lazy pipeline object supporting chained <code>->map</code>, <code>->filter</code>, <code>->take</code>, <code>->skip</code>, <code>->flat_map</code>, <code>->tap</code>, and other transforms that execute zero work until a terminal method is called.</p>
<p>No intermediate lists are allocated between stages — each element flows through the full chain one at a time, making pipelines memory-efficient even on very large or infinite inputs. Terminal methods include <code>->collect</code> (materialize to list), <code>->reduce { ... }</code> (fold), <code>->for_each { ... }</code> (side-effect iteration), and <code>->count</code>. Pipelines compose naturally with stryke's <code>|></code> operator: you can feed <code>pipeline(...)</code> output into further <code>|></code> stages or vice versa. Use <code>pipeline</code> when you want explicit method-chaining style rather than the flat <code>|></code> pipe syntax — both compile to the same lazy evaluation engine.</p>
<pre><code class="lang-perl">my @out = pipeline(@data)
->filter { _ > 0 }
->map { _ * 2 }
->take(10)
->collect
pipeline(1:1_000_000)
->filter { _ % 3 == 0 }
->map { _ ** 2 }
->take(5)
->for_each { p _ } # 9 36 81 144 225
my $sum = pipeline(@scores)
->filter { _ >= 60 }
->reduce { $_0 + $_1 }
</code></pre>
</article>
<article class="doc-entry" id="doc-par-pipeline">
<h3><a class="doc-anchor" href="#doc-par-pipeline">#</a> <code>par_pipeline</code></h3>
<p><code>par_pipeline(source => \@data, stages => [...], workers => N)</code> — build a multi-stage parallel pipeline where each stage's map/filter block runs concurrently across N worker threads.</p>
<p>Unlike <code>pmap</code> which parallelizes a single transform, <code>par_pipeline</code> lets you define a sequence of named stages — each with its own block — that execute in parallel while preserving input order in the final output. Internally, stryke partitions the source into chunks, distributes them across workers, and pipelines the stages so that stage 2 can begin processing a chunk as soon as stage 1 finishes it, overlapping computation across stages. This is ideal for multi-step ETL workloads where each step is CPU-bound and the data volume is large. The <code>workers</code> parameter defaults to the number of logical CPUs.</p>
<pre><code class="lang-perl">my @results = par_pipeline(
source => \@raw_records,
stages => [
{ name => "parse", map => fn { json_decode } },
{ name => "transform", map => fn { enrich } },
{ name => "validate", filter => fn { _->{valid} } },
],
workers => 8,
)
</code></pre>
</article>
<article class="doc-entry" id="doc-par-pipeline-stream">
<h3><a class="doc-anchor" href="#doc-par-pipeline-stream">#</a> <code>par_pipeline_stream</code></h3>
<p><code>par_pipeline_stream(source => ..., stages => [...], workers => N)</code> — streaming variant of <code>par_pipeline</code> that connects stages via bounded <code>pchannel</code> queues instead of materializing intermediate arrays.</p>
<p>Each stage runs as an independent pool of workers, pulling from an input channel and pushing to an output channel. This gives true pipelined parallelism: stage 1 workers produce items while stage 2 workers consume them concurrently, bounded by channel capacity to prevent memory blowup. The streaming design makes this suitable for infinite or very large data sources (file streams, network feeds) where materializing the full dataset between stages is impractical. Results are emitted in arrival order by default; pass <code>ordered => 1</code> to reorder them to match input order at the cost of buffering.</p>
<pre><code class="lang-perl">par_pipeline_stream(
source => fn { while (my $line = <STDIN>) { yield $line } },
stages => [
{ name => "parse", map => fn { json_decode } },
{ name => "score", map => fn { compute_score } },
],
workers => 4,
on_item => fn { p _ }, # process results as they arrive
)
</code></pre>
</article>
<article class="doc-entry" id="doc-collect">
<h3><a class="doc-anchor" href="#doc-collect">#</a> <code>collect</code></h3>
<p><code>collect ITERATOR</code> — materialize a lazy iterator or pipeline into a concrete list.</p>
<p>Pipeline stages in stryke are lazy: chaining <code>|> map {...} |> grep {...}</code> builds up a deferred computation without consuming any elements. Calling <code>collect</code> forces evaluation and returns all results as a regular Perl list. This is the standard way to terminate a lazy chain when you need the full result in an array. Without <code>collect</code>, the iterator is consumed element-by-element by <code>e</code>, <code>take</code>, or other streaming sinks.</p>
<pre><code class="lang-perl">my @out = range(1,5) |> map { _ * 2 } |> collect
gen { yield _ for 1:3 } |> collect |> e p
my @data = stdin |> grep /INFO/ |> collect
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-streaming-iterators">
<h2>Streaming Iterators</h2>
<p class="chapter-meta">24 topics</p>
<article class="doc-entry" id="doc-maps">
<h3><a class="doc-anchor" href="#doc-maps">#</a> <code>maps</code></h3>
<p><code>maps { BLOCK } LIST</code> — the lazy, streaming counterpart of <code>map</code>. Instead of materializing the entire output list, <code>maps</code> returns a pull iterator that evaluates the block on demand as downstream consumers request values. This makes it ideal for <code>|></code> pipeline chains, especially when combined with <code>take</code>, <code>greps</code>, or <code>collect</code>. Use <code>maps</code> over <code>map</code> when working with large ranges, infinite sequences, or when you want to short-circuit processing early with <code>take</code>. Memory usage is constant regardless of input size.</p>
<pre><code class="lang-perl">1:10 |> maps { _ * 3 } |> take 4 |> e p
# 3 6 9 12
1:1_000_000 |> maps { _ ** 2 } |> greps { _ > 100 } |> take 3 |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-greps">
<h3><a class="doc-anchor" href="#doc-greps">#</a> <code>greps</code></h3>
<p><code>greps { BLOCK } LIST</code> — the lazy, streaming counterpart of <code>grep</code>. Returns a pull iterator that only evaluates the predicate as elements are requested downstream. This is the preferred filtering function in <code>|></code> pipelines because it avoids materializing intermediate lists. Combine with <code>take</code> to short-circuit early, or with <code>maps</code> and <code>collect</code> for full lazy pipelines. The block receives <code>_</code> just like <code>grep</code>.</p>
<pre><code class="lang-perl">1:100 |> greps { _ % 7 == 0 } |> take 3 |> e p
# 7 14 21
@lines |> greps { /ERROR/ } |> maps { tm } |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-filter">
<h3><a class="doc-anchor" href="#doc-filter">#</a> <code>filter</code></h3>
<p><code>filter</code> (alias <code>fi</code>) <code>{ BLOCK } LIST</code> — stryke-native lazy filter that returns a pull iterator, functionally identical to <code>greps</code> but named for familiarity with Rust/Ruby/JS conventions. Use <code>filter</code> or <code>greps</code> interchangeably in <code>|></code> chains; both are streaming and both set <code>_</code> in the block. The result must be consumed with <code>collect</code>, <code>e p</code>, <code>foreach</code>, or another terminal. Prefer <code>filter</code> when writing stryke-idiomatic code; prefer <code>grep</code>/<code>greps</code> when porting from Perl.</p>
<pre><code class="lang-perl">my @big = 1:1000 |> filter { _ > 990 } |> collect
@big |> e p # 991 992 993 994 995 996 997 998 999 1000
1:50 |> fi { _ % 2 } |> take 5 |> e p # 1 3 5 7 9
</code></pre>
</article>
<article class="doc-entry" id="doc-tap">
<h3><a class="doc-anchor" href="#doc-tap">#</a> <code>tap</code></h3>
<p><code>tap { BLOCK } LIST</code> — execute a side-effecting block for each element, then pass the element through unchanged.</p>
<p>The return value of the block is ignored; the original element is always forwarded to the next pipeline stage. This makes <code>tap</code> ideal for injecting logging, debugging, or metrics collection into the middle of a pipeline without altering the data flow. It is fully streaming and preserves element order.</p>
<pre><code class="lang-perl">1:5 |> tap { log_debug "saw: $_" } |> map { _ * 2 } |> e p
@files |> tap { p "processing: $_" } |> map slurp |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-peek">
<h3><a class="doc-anchor" href="#doc-peek">#</a> <code>peek</code></h3>
<p><code>peek ITERATOR</code> — inspect the next element of an iterator without consuming it.</p>
<p>The peeked value is buffered internally so that the next call to <code>->next</code> or pipeline pull returns the same element. This is useful for lookahead parsing, conditional branching on the next value, or implementing <code>take_while</code>-style logic manually. Calling <code>peek</code> multiple times without advancing the iterator returns the same value each time. Works with any stryke iterator including <code>gen</code>, <code>range</code>, <code>stdin</code>, and pipeline results.</p>
<pre><code class="lang-perl">my $g = gen { yield _ for 1:5 }
p peek $g # 1 (not consumed)
p $g->next # 1
p peek $g # 2
</code></pre>
</article>
<article class="doc-entry" id="doc-tee">
<h3><a class="doc-anchor" href="#doc-tee">#</a> <code>tee</code></h3>
<p><code>tee FILE, ITERATOR</code> — write each element to a file as a side effect while passing it through the pipeline.</p>
<p>Every element that flows through <code>tee</code> is appended as a line to the specified file, and the element itself continues downstream unchanged. The file is opened once on first element and closed when the iterator is exhausted. This is the stryke equivalent of the Unix <code>tee</code> command, useful for auditing or logging intermediate pipeline results to disk.</p>
<pre><code class="lang-perl">1:10 |> tee "/tmp/log.txt" |> map { _ * 2 } |> e p
stdin |> tee "/tmp/raw.log" |> grep /ERROR/ |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-take">
<h3><a class="doc-anchor" href="#doc-take">#</a> <code>take</code></h3>
<p><code>take N, LIST</code> / <code>head N, LIST</code> / <code>hd N, LIST</code> — return at most the first N elements.</p>
<p>In streaming mode, <code>take</code> pulls exactly N elements from the upstream iterator and then stops, so it short-circuits infinite or very large sources efficiently. This makes it safe to write <code>range(1, 1_000_000) |> take 5</code> without allocating a million-element list. If the source has fewer than N elements, all of them are returned. The <code>head</code> and <code>hd</code> aliases mirror Unix <code>head</code> semantics.</p>
<pre><code class="lang-perl">1:100 |> take 5 |> e p # 1 2 3 4 5
my @top = hd 3, @sorted
stdin |> hd 10 |> e p # first 10 lines
</code></pre>
</article>
<article class="doc-entry" id="doc-tail">
<h3><a class="doc-anchor" href="#doc-tail">#</a> <code>tail</code></h3>
<p><code>tail N, @list</code> — returns the last N elements of the list. If N exceeds the list length, the entire list is returned. The alias <code>tl</code> is also available. This is the complement of <code>head</code>/<code>take</code>. In stryke, it works both as a function call and in <code>|></code> pipelines.</p>
<pre><code class="lang-perl">my @t = tail 2, 1:5
@t |> e p # 4 5
1:100 |> tl 3 |> e p # 98 99 100
</code></pre>
</article>
<article class="doc-entry" id="doc-drop">
<h3><a class="doc-anchor" href="#doc-drop">#</a> <code>drop</code></h3>
<p><code>drop N, LIST</code> / <code>skip N, LIST</code> / <code>drp N, LIST</code> — skip the first N elements and return the rest.</p>
<p>This operation is fully streaming: when used in a pipeline, the first N elements are consumed and discarded without buffering, and all subsequent elements flow through to the next stage. If the list contains fewer than N elements, the result is empty. The <code>skip</code> and <code>drp</code> aliases exist for readability in different contexts — all three compile to the same internal op.</p>
<pre><code class="lang-perl">1:10 |> drop 3 |> e p # 4 5 6 7 8 9 10
my @rest = drp 2, @data
stdin |> skip 1 |> e p # skip header line
</code></pre>
</article>
<article class="doc-entry" id="doc-take-while">
<h3><a class="doc-anchor" href="#doc-take-while">#</a> <code>take_while</code></h3>
<p><code>take_while { COND } LIST</code> — emit leading elements while the predicate returns true, then stop.</p>
<p>The block receives each element as <code>_</code>. Elements are emitted as long as the predicate holds; the moment it returns false, the pipeline terminates immediately without consuming further input. This short-circuit behavior makes <code>take_while</code> efficient on infinite iterators and large streams. It is the complement of <code>drop_while</code>.</p>
<pre><code class="lang-perl">1:10 |> take_while { _ < 5 } |> e p # 1 2 3 4
stdin |> take_while { !/^END/ } |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-drop-while">
<h3><a class="doc-anchor" href="#doc-drop-while">#</a> <code>drop_while</code></h3>
<p><code>drop_while { COND } LIST</code> — skip leading elements while the predicate returns true, then emit everything after.</p>
<p>The block receives each element as <code>_</code>. Once the predicate returns false for the first time, that element and all remaining elements pass through unconditionally — the predicate is never consulted again. This is streaming: elements are tested one at a time without buffering. Useful for skipping headers, preamble, or sorted prefixes in data streams.</p>
<pre><code class="lang-perl">1:10 |> drop_while { _ < 5 } |> e p # 5 6 7 8 9 10
@log |> drop_while { /^ #/ } |> e p # skip comment header
</code></pre>
</article>
<article class="doc-entry" id="doc-reject">
<h3><a class="doc-anchor" href="#doc-reject">#</a> <code>reject</code></h3>
<p><code>reject { BLOCK } LIST</code> — stryke-native streaming inverse of <code>filter</code>/<code>greps</code>. It keeps only the elements for which the block returns false. This reads more naturally than <code>filter { !(...) }</code> when the condition describes what you want to exclude rather than what you want to keep. Like <code>filter</code> and <code>greps</code>, it returns a lazy iterator suitable for <code>|></code> chains. The block receives <code>_</code> as the current element.</p>
<pre><code class="lang-perl">1:10 |> reject { _ % 3 == 0 } |> e p
# 1 2 4 5 7 8 10
@files |> reject { /\.bak$/ } |> e p # skip backups
</code></pre>
</article>
<article class="doc-entry" id="doc-compact">
<h3><a class="doc-anchor" href="#doc-compact">#</a> <code>compact</code></h3>
<p><code>compact</code> (alias <code>cpt</code>) — stryke-native streaming operator that removes <code>undef</code> and empty-string values from a list or iterator. This is a common data-cleaning step when dealing with parsed input, optional fields, or split results that produce empty segments. It is equivalent to <code>greps { defined(_) && _ ne "" }</code> but more concise and faster because the check is inlined in Rust. Numeric zero and the string <code>"0"</code> are preserved since they are defined and non-empty.</p>
<pre><code class="lang-perl">my @raw = (1, undef, "", 2, undef, 3)
@raw |> compact |> e p # 1 2 3
split(/,/, "a,,b,,,c") |> cpt |> e p # a b c
</code></pre>
</article>
<article class="doc-entry" id="doc-concat">
<h3><a class="doc-anchor" href="#doc-concat">#</a> <code>concat</code></h3>
<p><code>concat</code> (alias <code>chain</code>) — stryke-native streaming operator that concatenates multiple lists or iterators into a single sequential iterator. Pass array references and they will be yielded in order without copying. This is useful for merging data from multiple sources into a unified pipeline. The operation is lazy: each source is drained in turn, so memory usage stays proportional to the largest single element, not the total.</p>
<pre><code class="lang-perl">my @a = 1:3
my @b = 7:9
concat(\@a, \@b) |> e p # 1 2 3 7 8 9
my @c = ("x")
concat(\@a, \@b, \@c) |> maps { uc } |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-enumerate">
<h3><a class="doc-anchor" href="#doc-enumerate">#</a> <code>enumerate</code></h3>
<p><code>enumerate ITERATOR</code> / <code>en ITERATOR</code> — yield <code>[$index, $item]</code> pairs from a streaming iterator.</p>
<p>Each element is wrapped as <code>[$index, $item]</code> where the index starts at 0 and increments for each element. Unlike <code>with_index</code> which returns <code>[item, index]</code>, <code>enumerate</code> uses the Rust/Python convention of <code>[index, item]</code>. This is a streaming operation: the index counter is maintained lazily as elements flow through the pipeline.</p>
<pre><code class="lang-perl">stdin |> en |> e { p "_->[0]: _->[1]" }
1:5 |> en |> e { p "_->[0]: _->[1]" }
@lines |> en |> grep { _->[0] < 10 } |> e { p _->[1] }
</code></pre>
</article>
<article class="doc-entry" id="doc-chunk">
<h3><a class="doc-anchor" href="#doc-chunk">#</a> <code>chunk</code></h3>
<p><code>chunk N, ITERATOR</code> / <code>chk N, ITERATOR</code> — group elements into N-sized arrayrefs as they stream through.</p>
<p>Elements are buffered until N are collected, then the group is emitted as a single arrayref. The final chunk may contain fewer than N elements if the source is not evenly divisible. This is fully streaming: only one chunk is held in memory at a time, making it safe for large or infinite iterators. Use <code>chunk</code> for batching work (e.g., bulk database inserts) or formatting output into rows.</p>
<pre><code class="lang-perl">1:9 |> chk 3 |> e { p join ",", @_ }
# 1,2,3 4,5,6 7,8,9
stdin |> chk 100 |> e { bulk_insert(@_) }
</code></pre>
</article>
<article class="doc-entry" id="doc-dedup">
<h3><a class="doc-anchor" href="#doc-dedup">#</a> <code>dedup</code></h3>
<p><code>dedup ITERATOR</code> / <code>dup ITERATOR</code> — drop consecutive duplicate elements from a stream.</p>
<p>Only adjacent duplicates are removed: if the same value appears later after an intervening different value, it is emitted again. Comparison is string-based by default. This is a streaming operation that holds only the previous element in memory, so it works on infinite iterators. For global deduplication across the entire stream, use <code>distinct</code> instead.</p>
<pre><code class="lang-perl">1,1,2,2,3,1,1 |> dedup |> e p # 1 2 3 1
@sorted |> dedup |> e p # like uniq(1)
stdin |> dedup |> e p # collapse repeated lines
</code></pre>
</article>
<article class="doc-entry" id="doc-distinct">
<h3><a class="doc-anchor" href="#doc-distinct">#</a> <code>distinct</code></h3>
<p><code>distinct LIST</code> — remove duplicate elements, preserving first-occurrence order (alias for <code>uniq</code>).</p>
<p>Each element is compared as a string; the first time a value is seen it is emitted, and all subsequent occurrences are silently dropped. When used in a pipeline the deduplication state is maintained across streamed chunks, so <code>distinct</code> works correctly on lazy iterators and generators. This is a stryke built-in backed by a hash set internally, so it runs in O(n) time regardless of list size.</p>
<pre><code class="lang-perl">my @u = distinct(3,1,2,1,3) # (3,1,2)
1,2,2,3,3,3 |> distinct |> e p # 1 2 3
stdin |> distinct |> e p # unique lines
</code></pre>
</article>
<article class="doc-entry" id="doc-flatten">
<h3><a class="doc-anchor" href="#doc-flatten">#</a> <code>flatten</code></h3>
<p><code>flatten LIST</code> / <code>fl LIST</code> — recursively flatten nested arrayrefs into a single flat list.</p>
<p>Flatten walks every element: scalars pass through unchanged, arrayrefs are opened and their contents are recursively flattened, so arbitrarily deep nesting is handled in one call. In pipeline mode (<code>|> fl</code>) it streams element-by-element, so you can chain it with <code>map</code>, <code>grep</code>, or <code>take</code> without materializing the entire intermediate list. The <code>fl</code> alias keeps pipeline chains concise.</p>
<pre><code class="lang-perl">my @flat = flatten([1,[2,3]],[4]) # (1,2,3,4)
[1,[2,[3,4]]] |> fl |> e p # 1 2 3 4
@nested |> fl |> grep { _ > 0 } |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-with-index">
<h3><a class="doc-anchor" href="#doc-with-index">#</a> <code>with_index</code></h3>
<p><code>with_index LIST</code> / <code>wi LIST</code> — pair each element with its 0-based index as <code>[$item, $index]</code>.</p>
<p>Each element is wrapped in a two-element arrayref where <code>_->[0]</code> is the original value and <code>_->[1]</code> is its position. This is useful when you need positional information during a map or grep without maintaining a manual counter. Note the order is <code>[item, index]</code>, which differs from <code>enumerate</code> which yields <code>[index, item]</code>.</p>
<pre><code class="lang-perl">qw(a b c) |> wi |> e { p "_->[1]: _->[0]" }
# 0: a 1: b 2: c
@data |> wi |> grep { _->[1] % 2 == 0 } |> e { p _->[0] }
</code></pre>
</article>
<article class="doc-entry" id="doc-first-or">
<h3><a class="doc-anchor" href="#doc-first-or">#</a> <code>first_or</code></h3>
<p><code>first_or DEFAULT, LIST</code> — return the first element of the list, or DEFAULT if the list is empty.</p>
<p>This is a streaming terminal: it pulls exactly one element from the upstream iterator and returns it, or returns the default value if the iterator is exhausted. It never buffers the entire list. This is especially useful at the end of a <code>grep</code> or <code>map</code> pipeline where you need a safe fallback instead of <code>undef</code> when no match is found.</p>
<pre><code class="lang-perl">my $v = first_or 0, @maybe_empty
my $x = grep { _ > 99 } @nums |> first_or -1
stdin |> grep /^ERROR/ |> first_or "(none)" |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-range">
<h3><a class="doc-anchor" href="#doc-range">#</a> <code>range</code></h3>
<p><code>range(START, END [, STEP])</code> — create a lazy integer iterator from START to END with an optional step.</p>
<p>The range is inclusive on both ends. When START > END and no step is given, stryke automatically counts downward. An explicit STEP controls the increment and must be negative when counting down, or the range will be empty. The iterator is fully lazy: no list is allocated, and elements are generated on demand, making <code>range(1, 1_000_000)</code> as cheap to create as <code>range(1, 5)</code>. Combine with <code>|></code> to feed into streaming pipelines.</p>
<pre><code class="lang-perl">range(1, 5) |> e p # 1 2 3 4 5
range(5, 1) |> e p # 5 4 3 2 1
range(0, 10, 2) |> e p # 0 2 4 6 8 10
range(10, 0, -2) |> e p # 10 8 6 4 2 0
</code></pre>
</article>
<article class="doc-entry" id="doc-stdin">
<h3><a class="doc-anchor" href="#doc-stdin">#</a> <code>stdin</code></h3>
<p><code>stdin</code> — return a streaming iterator over lines read from standard input.</p>
<p>Each call to the iterator reads one line from STDIN, strips the trailing newline, and yields it. The iterator terminates at EOF. Because it is lazy, combining <code>stdin</code> with <code>take</code>, <code>grep</code>, or <code>first_or</code> processes only as many lines as needed — the rest of STDIN is left unconsumed. This is the idiomatic stryke way to build Unix-style filters.</p>
<pre><code class="lang-perl">stdin |> grep /error/i |> e p
stdin |> take 5 |> e p
stdin |> en |> e { p "_->[0]: _->[1]" }
</code></pre>
</article>
<article class="doc-entry" id="doc-nth">
<h3><a class="doc-anchor" href="#doc-nth">#</a> <code>nth</code></h3>
<p><code>nth N, LIST</code> — return the Nth element using 0-based indexing.</p>
<p>When used in a pipeline, <code>nth</code> consumes and discards the first N elements, returns the next one, and stops — so it short-circuits on infinite iterators. On a plain list, it is equivalent to <code>$list[N]</code> but works as a function call for pipeline composition. Returns <code>undef</code> if the list has fewer than N+1 elements.</p>
<pre><code class="lang-perl">my $third = nth 2, @data
1:10 |> nth 4 |> p # 5
stdin |> nth 0 |> p # first line
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-list-operations">
<h2>List Operations</h2>
<p class="chapter-meta">62 topics</p>
<article class="doc-entry" id="doc-map">
<h3><a class="doc-anchor" href="#doc-map">#</a> <code>map</code></h3>
<p><code>map BLOCK LIST</code> — evaluates the block for each element of the list, setting <code>_</code> to the current element, and returns a new list of all the block's return values. This is the eager version: it consumes the entire input list and produces the entire output list before returning. Use <code>map</code> when you need the full result array or when the input is small. For large or infinite sequences, prefer <code>maps</code> (the streaming variant). The block can return zero, one, or multiple values per element, making <code>map</code> useful for both transformation and flattening. Use <code>{ |$var| body }</code> to name the block parameter instead of <code>_</code>.</p>
<pre><code class="lang-perl">my @sq = map { _ ** 2 } 1:5
@sq |> e p # 1 4 9 16 25
map { |$n| $n * $n }, 1:5 # named param
my @pairs = map { (_, _ * 10) } 1:3
@pairs |> e p # 1 10 2 20 3 30
</code></pre>
</article>
<article class="doc-entry" id="doc-grep">
<h3><a class="doc-anchor" href="#doc-grep">#</a> <code>grep</code></h3>
<p><code>grep { BLOCK } LIST</code> — filters the list, returning only elements for which the block evaluates to true. The current element is available as <code>_</code>. This is the eager version: it processes the entire list and returns a new list. It is Perl-compatible and works exactly like Perl's builtin <code>grep</code>. For streaming/lazy filtering in <code>|></code> pipelines, use <code>greps</code> or <code>filter</code> instead. Use <code>{ |$var| body }</code> to name the block parameter instead of <code>_</code>.</p>
<pre><code class="lang-perl">my @evens = grep { _ % 2 == 0 } 1:10
@evens |> e p # 2 4 6 8 10
grep { |$x| $x > 3 }, 1:6 # named param
my @long = grep { length(_) > 3 } @words
</code></pre>
</article>
<article class="doc-entry" id="doc-sort">
<h3><a class="doc-anchor" href="#doc-sort">#</a> <code>sort</code></h3>
<p><code>sort [BLOCK] LIST</code> — returns a new list sorted in ascending order. Without a block, <code>sort</code> compares elements as strings (lexicographic). Pass a comparator block using <code>$_0</code> and <code>$_1</code> (stryke style) or <code>$a</code> and <code>$b</code> (classic Perl) to control ordering: use <code><=></code> for numeric and <code>cmp</code> for string comparison. The sort is stable in stryke, meaning equal elements preserve their original relative order. For descending order, reverse the operands in the comparator. Use <code>{ |$x, $y| body }</code> to name the two comparator params. Works naturally in <code>|></code> pipelines.</p>
<pre><code class="lang-perl">my @nums = (3, 1, 4, 1, 5)
my @asc = sort { $_0 <=> $_1 } @nums
@asc |> e p # 1 1 3 4 5
sort { |$x, $y| $y <=> $x }, @nums # named params
my @desc = sort { $_1 <=> $_0 } @nums
@desc |> e p # 5 4 3 1 1
@nums |> sort |> e p # string sort in pipeline
</code></pre>
</article>
<article class="doc-entry" id="doc-reverse">
<h3><a class="doc-anchor" href="#doc-reverse">#</a> <code>reverse</code></h3>
<p><code>reverse LIST</code> — in list context, return the elements in reverse order; in scalar context, reverse the characters of a string.</p>
<p>The dual nature of <code>reverse</code> is context-dependent: <code>reverse @array</code> flips element order, while <code>scalar reverse $string</code> (or just <code>reverse $string</code> in scalar context) reverses character order. In stryke, the string form is Unicode-aware, correctly reversing multi-byte characters rather than individual bytes. In <code>|></code> pipelines, use the <code>t rev</code> shorthand for a concise streaming string reverse. <code>reverse</code> does not modify the original — it always returns a new list or string.</p>
<pre><code class="lang-perl">p reverse "hello" # olleh
my @r = reverse 1:5 # (5,4,3,2,1)
@r |> e p # 5 4 3 2 1
"abc" |> t rev |> p # cba
</code></pre>
</article>
<article class="doc-entry" id="doc-reduce">
<h3><a class="doc-anchor" href="#doc-reduce">#</a> <code>reduce</code></h3>
<p><code>reduce { $_0 OP $_1 } @list</code> — performs a sequential left fold over the list. The first two elements are passed as <code>$_0</code> and <code>$_1</code> to the block; the result becomes <code>$_0</code> for the next iteration. The traditional <code>$a</code>/<code>$b</code> names are also supported for Perl compatibility. Use <code>{ |$acc, $val| body }</code> to name the two params. Returns <code>undef</code> for an empty list and the single element for a one-element list. For a fold with an explicit initial value, see <code>fold</code>.</p>
<pre><code class="lang-perl">my $fac = reduce { $_0 * $_1 } 1:6
p $fac # 720
reduce { |$acc, $val| $acc + $val }, 1:10 # 55 (named params)
my $longest = reduce { length($_0) > length($_1) ? $_0 : $_1 } @words
</code></pre>
</article>
<article class="doc-entry" id="doc-fold">
<h3><a class="doc-anchor" href="#doc-fold">#</a> <code>fold</code></h3>
<p><code>fold { $_0 OP $_1 } INIT, @list</code> — left fold with an explicit initial accumulator value. The initial value is passed as the first <code>$_0</code>, and each list element arrives as <code>$_1</code>. Unlike <code>reduce</code>, <code>fold</code> never returns <code>undef</code> for an empty list — it returns the initial value instead. Both <code>$a</code>/<code>$b</code> and <code>$_0</code>/<code>$_1</code> are supported in the block. Use <code>fold</code> when you need a guaranteed starting point for the accumulation.</p>
<pre><code class="lang-perl">my $total = fold { $_0 + $_1 } 100, 1:5
p $total # 115
my $csv = fold { "$_0,$_1" } "", @fields
</code></pre>
</article>
<article class="doc-entry" id="doc-reductions">
<h3><a class="doc-anchor" href="#doc-reductions">#</a> <code>reductions</code></h3>
<p><code>reductions { $_0 OP $_1 } @list</code> — returns the running (cumulative) results of a left fold, also known as a scan or prefix-sum. Each element of the output is the accumulator state after processing the corresponding input element. The output list has the same length as the input. Both <code>$_0</code>/<code>$_1</code> and <code>$a</code>/<code>$b</code> naming conventions are supported.</p>
<pre><code class="lang-perl">my @pfx = reductions { $_0 + $_1 } 1:4
@pfx |> e p # 1 3 6 10
1:5 |> reductions { $_0 * $_1 } |> e p # 1 2 6 24 120
</code></pre>
</article>
<article class="doc-entry" id="doc-all">
<h3><a class="doc-anchor" href="#doc-all">#</a> <code>all</code></h3>
<p><code>all { COND } @list</code> — returns true (1) if every element in the list satisfies the predicate, false ("") otherwise. The block receives each element as <code>_</code> and should return a boolean. Short-circuits on the first failing element, so it never evaluates more than necessary. Works with <code>|></code> pipelines and accepts bare lists or array variables.</p>
<pre><code class="lang-perl">my @nums = 2, 4, 6, 8
p all { _ % 2 == 0 } @nums # 1
1:100 |> all { _ > 0 } |> p # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-any">
<h3><a class="doc-anchor" href="#doc-any">#</a> <code>any</code></h3>
<p><code>any { COND } @list</code> — returns true (1) if at least one element satisfies the predicate, false ("") if none do. The block receives each element as <code>_</code>. Short-circuits on the first match, making it efficient even on large lists. <code>any</code> is a stryke global builtin and can be used in <code>|></code> pipelines.</p>
<pre><code class="lang-perl">my @vals = 1, 3, 5, 8
p any { _ > 7 } @vals # 1
1:1000 |> any { _ == 42 } |> p # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-none">
<h3><a class="doc-anchor" href="#doc-none">#</a> <code>none</code></h3>
<p><code>none { COND } @list</code> — returns true (1) if no element satisfies the predicate, false ("") if any element matches. Logically equivalent to <code>!any { COND } @list</code> but reads more naturally in guard clauses. Short-circuits on the first match. Useful for validation checks where you want to assert the absence of a condition.</p>
<pre><code class="lang-perl">my @words = ("cat", "dog", "bird")
p none { /z/ } @words # 1
p "all non-negative" if none { _ < 0 } @vals
</code></pre>
</article>
<article class="doc-entry" id="doc-first">
<h3><a class="doc-anchor" href="#doc-first">#</a> <code>first</code></h3>
<p><code>first { COND } @list</code> — returns the first element for which the block returns true, or <code>undef</code> if no element matches. The alias <code>fst</code> is also available. Short-circuits immediately upon finding a match, so only the minimum number of elements are tested. Ideal for searching sorted or unsorted lists when you need a single result.</p>
<pre><code class="lang-perl">my $f = first { _ > 10 } 3, 7, 12, 20
p $f # 12
1:1_000_000 |> first { _ % 9999 == 0 } |> p # 9999
</code></pre>
</article>
<article class="doc-entry" id="doc-min">
<h3><a class="doc-anchor" href="#doc-min">#</a> <code>min</code></h3>
<p><code>min @list</code> — returns the numerically smallest value from a list. Compares all elements using numeric (<code><=></code>) comparison, so stringy values are coerced to numbers. Returns <code>undef</code> for an empty list. In stryke, <code>min</code> is a global built-in (no import needed) and works directly in <code>|></code> pipelines.</p>
<pre><code class="lang-perl">p min(5, 3, 9, 1) # 1
my @temps = (72.1, 68.5, 74.3)
@temps |> min |> p # 68.5
</code></pre>
</article>
<article class="doc-entry" id="doc-max">
<h3><a class="doc-anchor" href="#doc-max">#</a> <code>max</code></h3>
<p><code>max @list</code> — returns the numerically largest value from a list. Compares all elements using numeric (<code><=></code>) comparison. Returns <code>undef</code> for an empty list. Like <code>min</code>, this is a stryke built-in available without imports and works in <code>|></code> pipelines. Combine with <code>map</code> to extract max values from complex structures.</p>
<pre><code class="lang-perl">p max(5, 3, 9, 1) # 9
1:100 |> map { _ ** 2 } |> max |> p # 10000
</code></pre>
</article>
<article class="doc-entry" id="doc-sum">
<h3><a class="doc-anchor" href="#doc-sum">#</a> <code>sum</code></h3>
<p><code>sum @list</code> returns the numeric sum of all elements. Returns <code>undef</code> for an empty list. <code>sum0</code> is identical except it returns <code>0</code> for an empty list, which avoids the need for a fallback <code>// 0</code> guard. Both are stryke built-ins that work in <code>|></code> pipelines. Use <code>sum0</code> in contexts where an empty input is expected and you need a safe numeric default.</p>
<pre><code class="lang-perl">p sum(1:100) # 5050
p sum0() # 0
@prices |> map { _->{amount} } |> sum0 |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-product">
<h3><a class="doc-anchor" href="#doc-product">#</a> <code>product</code></h3>
<p><code>product @list</code> — returns the product of all numeric elements in the list. Returns <code>undef</code> for an empty list. Useful for computing factorials, combinatoric products, and compound multipliers. In stryke this is a built-in that composes naturally with <code>|></code> pipelines and <code>range</code>.</p>
<pre><code class="lang-perl">p product(1:5) # 120
range(1, 10) |> product |> p # 3628800
</code></pre>
</article>
<article class="doc-entry" id="doc-mean">
<h3><a class="doc-anchor" href="#doc-mean">#</a> <code>mean</code></h3>
<p><code>mean @list</code> — returns the arithmetic mean (average) of a numeric list. Computed as <code>sum / count</code> in a single pass. Returns <code>undef</code> for an empty list. The result is always a floating-point value even if all inputs are integers. Combine with <code>map</code> to compute averages over extracted fields.</p>
<pre><code class="lang-perl">p mean(2, 4, 6, 8) # 5
@students |> map { _->{score} } |> mean |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-median">
<h3><a class="doc-anchor" href="#doc-median">#</a> <code>median</code></h3>
<p><code>median @list</code> — returns the median value of a numeric list. For odd-length lists, this is the middle element after sorting. For even-length lists, it is the arithmetic mean of the two middle elements. The input list does not need to be pre-sorted. Returns <code>undef</code> for an empty list.</p>
<pre><code class="lang-perl">p median(1, 3, 5, 7, 9) # 5
p median(1, 3, 5, 7) # 4
1:100 |> median |> p # 50.5
</code></pre>
</article>
<article class="doc-entry" id="doc-mode">
<h3><a class="doc-anchor" href="#doc-mode">#</a> <code>mode</code></h3>
<p><code>mode @list</code> — returns the most frequently occurring value in the list. If there is a tie, the value that appears first in the list wins. Returns <code>undef</code> for an empty list. Works with both numeric and string values — comparison is done by stringification. Useful for finding the dominant category in a dataset.</p>
<pre><code class="lang-perl">p mode(1, 2, 2, 3, 3, 3) # 3
my @logs = qw(INFO WARN INFO ERROR INFO)
p mode(@logs) # INFO
</code></pre>
</article>
<article class="doc-entry" id="doc-stddev">
<h3><a class="doc-anchor" href="#doc-stddev">#</a> <code>stddev</code></h3>
<p><code>stddev @list</code> (alias <code>std</code>) — returns the population standard deviation of a numeric list. This is the square root of the population variance, measuring how spread out values are from the mean. Uses N (not N-1) in the denominator, so it computes the population statistic rather than the sample statistic. Returns <code>undef</code> for an empty list.</p>
<pre><code class="lang-perl">p stddev(2, 4, 4, 4, 5, 5, 7, 9) # 2
1:10 |> std |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-variance">
<h3><a class="doc-anchor" href="#doc-variance">#</a> <code>variance</code></h3>
<p><code>variance @list</code> — returns the population variance of a numeric list, computed as the mean of the squared deviations from the mean. Like <code>stddev</code>, this uses N (not N-1) as the divisor. The variance is <code>stddev ** 2</code>. Returns <code>undef</code> for an empty list. Useful for statistical analysis and as a building block for higher-order stats.</p>
<pre><code class="lang-perl">p variance(2, 4, 4, 4, 5, 5, 7, 9) # 4
my @samples = map { rand(100) } 1:1000
p variance(@samples)
</code></pre>
</article>
<article class="doc-entry" id="doc-sample">
<h3><a class="doc-anchor" href="#doc-sample">#</a> <code>sample</code></h3>
<p><code>sample N, @list</code> — returns a random sample of N elements drawn without replacement from the list. The returned elements are in random order. If N exceeds the list length, the entire list is returned (shuffled). Uses a Fisher-Yates partial shuffle internally for efficiency. Each call produces a different result due to random selection.</p>
<pre><code class="lang-perl">my @pick = sample 3, 1:100
@pick |> e p # 3 random values
my @test_cases = sample 10, @all_cases
</code></pre>
</article>
<article class="doc-entry" id="doc-shuffle">
<h3><a class="doc-anchor" href="#doc-shuffle">#</a> <code>shuffle</code></h3>
<p><code>shuffle @list</code> — returns a new list with all elements in random order using a Fisher-Yates shuffle. The original list is not modified. Every permutation is equally likely. In stryke this is a global built-in; no import is needed. The alias <code>shuf</code> is also available. Commonly used with <code>|></code> and <code>take</code> to draw random subsets.</p>
<pre><code class="lang-perl">my @deck = shuffle 1:52
@deck |> take 5 |> e p # 5 random cards
my @randomized = shuffle @questions
</code></pre>
</article>
<article class="doc-entry" id="doc-uniq">
<h3><a class="doc-anchor" href="#doc-uniq">#</a> <code>uniq</code></h3>
<p><code>uniq @list</code> — removes duplicate elements from a list, preserving the order of first occurrence. Comparison is done by string equality. The alias <code>uq</code> is also available. This is eager (not streaming) and returns a new list. For streaming deduplication in <code>|></code> pipelines, use <code>distinct</code>. For type-specific comparison, see <code>uniqnum</code>, <code>uniqstr</code>, and <code>uniqint</code>.</p>
<pre><code class="lang-perl">my @u = uniq 1, 2, 2, 3, 1, 3
@u |> e p # 1 2 3
my @hosts = uniq @all_hosts
</code></pre>
</article>
<article class="doc-entry" id="doc-uniqint">
<h3><a class="doc-anchor" href="#doc-uniqint">#</a> <code>uniqint</code></h3>
<p><code>uniqint @list</code> — removes duplicate elements comparing values as integers. Each element is truncated to its integer part before comparison, so <code>1.1</code> and <code>1.9</code> are considered equal (both become <code>1</code>). The first occurrence is kept. This is useful when you have floating-point data but care only about the integer portion for uniqueness.</p>
<pre><code class="lang-perl">my @u = uniqint 1, 1.1, 1.9, 2
@u |> e p # 1 2
my @distinct_ids = uniqint @raw_ids
</code></pre>
</article>
<article class="doc-entry" id="doc-uniqnum">
<h3><a class="doc-anchor" href="#doc-uniqnum">#</a> <code>uniqnum</code></h3>
<p><code>uniqnum @list</code> — removes duplicate elements comparing values as floating-point numbers. Unlike <code>uniq</code> (which compares as strings), <code>uniqnum</code> treats <code>1.0</code> and <code>1.00</code> as equal because they have the same numeric value. The first occurrence of each numeric value is preserved. Use this when your data contains numbers that may have different string representations.</p>
<pre><code class="lang-perl">my @u = uniqnum 1.0, 1.00, 2.5, 2.50
@u |> e p # 1 2.5
my @prices = uniqnum @all_prices
</code></pre>
</article>
<article class="doc-entry" id="doc-uniqstr">
<h3><a class="doc-anchor" href="#doc-uniqstr">#</a> <code>uniqstr</code></h3>
<p><code>uniqstr @list</code> — removes duplicate elements comparing values strictly as strings. This is the same comparison as <code>uniq</code> but makes the intent explicit. Numeric values <code>1</code> and <code>1.0</code> are considered different because their string representations differ. Use <code>uniqstr</code> when you want to be explicit that string semantics are intended.</p>
<pre><code class="lang-perl">my @u = uniqstr "a", "b", "a", "c"
@u |> e p # a b c
my @tags = uniqstr @all_tags
</code></pre>
</article>
<article class="doc-entry" id="doc-zip">
<h3><a class="doc-anchor" href="#doc-zip">#</a> <code>zip</code></h3>
<p><code>zip(\@a, \@b, ...)</code> — combines multiple arrays element-wise into a list of arrayrefs. Each output arrayref contains one element from each input array at the corresponding index. Accepts two or more array references. The alias <code>zp</code> is also available. By default, <code>zip</code> pads shorter arrays with <code>undef</code> (equivalent to <code>zip_longest</code>). For truncating behavior, use <code>zip_shortest</code>.</p>
<pre><code class="lang-perl">my @a = 1:3
my @b = ("a","b","c")
zip(\@a, \@b) |> e p # [1,a] [2,b] [3,c]
my @matrix = zip(\@xs, \@ys, \@zs)
</code></pre>
</article>
<article class="doc-entry" id="doc-zip-longest">
<h3><a class="doc-anchor" href="#doc-zip-longest">#</a> <code>zip_longest</code></h3>
<p><code>zip_longest(\@a, \@b, ...)</code> — combines arrays element-wise, padding shorter arrays with <code>undef</code> to match the longest. This is the explicit version of the default <code>zip</code> behavior. Every input array contributes exactly one element per output tuple; missing elements become <code>undef</code>. Useful when you need to process all data from unequal-length sources.</p>
<pre><code class="lang-perl">my @a = 1:3
my @b = ("x")
zip_longest(\@a, \@b) |> e p # [1,x] [2,undef] [3,undef]
</code></pre>
</article>
<article class="doc-entry" id="doc-zip-shortest">
<h3><a class="doc-anchor" href="#doc-zip-shortest">#</a> <code>zip_shortest</code></h3>
<p><code>zip_shortest(\@a, \@b, ...)</code> — combines arrays element-wise, stopping at the shortest input array. No <code>undef</code> padding is produced; the output length equals the minimum input length. Use this when you only want complete tuples and extra trailing elements should be discarded.</p>
<pre><code class="lang-perl">my @a = 1:5
my @b = ("x","y")
zip_shortest(\@a, \@b) |> e p # [1,x] [2,y]
my @paired = zip_shortest(\@keys, \@values)
</code></pre>
</article>
<article class="doc-entry" id="doc-chunked">
<h3><a class="doc-anchor" href="#doc-chunked">#</a> <code>chunked</code></h3>
<p><code>chunked N, @list</code> — splits a list into non-overlapping chunks of N elements each. Each chunk is an arrayref. The final chunk may contain fewer than N elements if the list length is not evenly divisible. The alias <code>chk</code> is also available. In stryke, <code>chunked</code> is eager and returns a list of arrayrefs; for streaming chunk behavior in pipelines, use <code>chunk</code>.</p>
<pre><code class="lang-perl">my @ch = chunked 3, 1:7
@ch |> e p # [1,2,3] [4,5,6] [7]
1:12 |> chunked 4 |> e { p join ",", @_ }
</code></pre>
</article>
<article class="doc-entry" id="doc-windowed">
<h3><a class="doc-anchor" href="#doc-windowed">#</a> <code>windowed</code></h3>
<p><code>windowed N, @list</code> — returns a sliding window of N consecutive elements over the list. Each window is an arrayref. The output contains <code>len - N + 1</code> windows. Unlike <code>chunked</code>, windows overlap: each successive window advances by one element. The alias <code>win</code> is also available. Useful for computing moving averages, detecting patterns in sequences, or n-gram extraction.</p>
<pre><code class="lang-perl">my @w = windowed 3, 1:5
@w |> e p # [1,2,3] [2,3,4] [3,4,5]
my @deltas = windowed(2, @vals) |> map { _->[1] - _->[0] }
</code></pre>
</article>
<article class="doc-entry" id="doc-pairs">
<h3><a class="doc-anchor" href="#doc-pairs">#</a> <code>pairs</code></h3>
<p><code>pairs @list</code> — takes a flat list and groups consecutive elements into pairs, returning a list of two-element arrayrefs <code>([$k, $v], ...)</code>. The input list must have an even number of elements. Each pair can be accessed via array indexing (<code>_->[0]</code>, <code>_->[1]</code>). This is the inverse of <code>unpairs</code> and is commonly used to iterate over hash-like flat lists in a structured way.</p>
<pre><code class="lang-perl">my @p = pairs "a", 1, "b", 2
@p |> e { p "_->[0]=_->[1]" } # a=1 b=2
my @entries = pairs %hash
</code></pre>
</article>
<article class="doc-entry" id="doc-unpairs">
<h3><a class="doc-anchor" href="#doc-unpairs">#</a> <code>unpairs</code></h3>
<p><code>unpairs @list_of_pairs</code> — flattens a list of two-element arrayrefs back into a flat key-value list. This is the inverse of <code>pairs</code>. Each arrayref <code>[$k, $v]</code> becomes two consecutive elements in the output. Useful for converting structured pair data back into a format suitable for hash assignment or flat list processing.</p>
<pre><code class="lang-perl">my @flat = unpairs ["a",1], ["b",2]
@flat |> e p # a 1 b 2
my %h = unpairs @filtered_pairs
</code></pre>
</article>
<article class="doc-entry" id="doc-pairkeys">
<h3><a class="doc-anchor" href="#doc-pairkeys">#</a> <code>pairkeys</code></h3>
<p><code>pairkeys @list</code> — extracts the keys (even-indexed elements) from a flat pairlist. Given a list like <code>("a", 1, "b", 2, "c", 3)</code>, returns <code>("a", "b", "c")</code>. This is equivalent to <code>map { _->[0] } pairs @list</code> but more concise and efficient. Useful for extracting just the key side of a key-value flat list without constructing intermediate pair objects.</p>
<pre><code class="lang-perl">my @k = pairkeys "a", 1, "b", 2, "c", 3
@k |> e p # a b c
my @config_pairs = (host => "localhost", port => 8080)
my @names = pairkeys @config_pairs
</code></pre>
</article>
<article class="doc-entry" id="doc-pairvalues">
<h3><a class="doc-anchor" href="#doc-pairvalues">#</a> <code>pairvalues</code></h3>
<p><code>pairvalues @list</code> — extracts the values (odd-indexed elements) from a flat pairlist. Given <code>("a", 1, "b", 2)</code>, returns <code>(1, 2)</code>. This is equivalent to <code>map { _->[1] } pairs @list</code> but more concise. Pair it with <code>pairkeys</code> to split a flat key-value list into separate key and value arrays.</p>
<pre><code class="lang-perl">my @v = pairvalues "a", 1, "b", 2
@v |> e p # 1 2
my @defaults = (timeout => 30, retries => 3)
my @settings = pairvalues @defaults
</code></pre>
</article>
<article class="doc-entry" id="doc-pairmap">
<h3><a class="doc-anchor" href="#doc-pairmap">#</a> <code>pairmap</code></h3>
<p><code>pairmap BLOCK @list</code> — maps over consecutive pairs in a flat list, passing the key as <code>$_0</code> (or <code>$a</code>) and the value as <code>$_1</code> (or <code>$b</code>). The block can return any number of elements. This is the pair-aware equivalent of <code>map</code> and is ideal for transforming hash-like flat lists. The result is a flat list of whatever the block returns.</p>
<pre><code class="lang-perl">my @out = pairmap { "$_0=$_1" } "a", 1, "b", 2
@out |> e p # a=1 b=2
my @cfg_pairs = (host => "x", port => 80)
my @upper = pairmap { uc($_0), $_1 } @cfg_pairs
</code></pre>
</article>
<article class="doc-entry" id="doc-pairgrep">
<h3><a class="doc-anchor" href="#doc-pairgrep">#</a> <code>pairgrep</code></h3>
<p><code>pairgrep { BLOCK } @list</code> — filters consecutive pairs from a flat list, keeping only those where the block returns true. The key is available as <code>$_0</code> (or <code>$a</code>) and the value as <code>$_1</code> (or <code>$b</code>). Returns a flat list of the matching key-value pairs. This is the pair-aware equivalent of <code>grep</code> and is useful for filtering hash-like data by both key and value simultaneously.</p>
<pre><code class="lang-perl">my @big = pairgrep { $_1 > 5 } "a", 3, "b", 9, "c", 1
@big |> e p # b 9
my @alert_pairs = (info => 1, critical_a => 9, critical_b => 7)
my @important = pairgrep { $_0 =~ /^critical/ } @alert_pairs
</code></pre>
</article>
<article class="doc-entry" id="doc-pairfirst">
<h3><a class="doc-anchor" href="#doc-pairfirst">#</a> <code>pairfirst</code></h3>
<p><code>pairfirst { BLOCK } @list</code> — returns the first pair from a flat list where the block returns true, as a two-element list <code>($key, $value)</code>. The key is <code>$_0</code> (or <code>$a</code>) and the value is <code>$_1</code> (or <code>$b</code>). Short-circuits on the first match. Returns an empty list if no pair matches. This is the pair-aware equivalent of <code>first</code>.</p>
<pre><code class="lang-perl">my @hit = pairfirst { $_1 > 5 } "x", 2, "y", 8
p "@hit" # y 8
my @flags = (info => 1, debug => 7, trace => 0)
my ($k, $v) = pairfirst { $_0 eq "debug" } @flags
</code></pre>
</article>
<article class="doc-entry" id="doc-mesh">
<h3><a class="doc-anchor" href="#doc-mesh">#</a> <code>mesh</code></h3>
<p><code>mesh(\@a, \@b, ...)</code> — interleaves multiple arrays into a flat list rather than arrayrefs. While <code>zip</code> returns <code>([1,"a"], [2,"b"])</code>, <code>mesh</code> returns <code>(1, "a", 2, "b")</code>. This makes it ideal for constructing hashes from parallel key and value arrays. The result is a flat list suitable for direct hash assignment.</p>
<pre><code class="lang-perl">my @k = ("a","b")
my @v = (1,2)
my %h = mesh(\@k, \@v)
p $h{a} # 1
my %lookup = mesh(\@ids, \@names)
</code></pre>
</article>
<article class="doc-entry" id="doc-mesh-longest">
<h3><a class="doc-anchor" href="#doc-mesh-longest">#</a> <code>mesh_longest</code></h3>
<p><code>mesh_longest(\@a, \@b, ...)</code> — interleaves arrays into a flat list, padding shorter arrays with <code>undef</code> to match the longest. Like <code>mesh</code>, the output is flat (not arrayrefs). Missing elements become <code>undef</code> in the output sequence. Use this when building a flat interleaved list from arrays of unequal length where you need every element represented.</p>
<pre><code class="lang-perl">my @a = 1:3
my @b = ("x")
my @r = mesh_longest(\@a, \@b)
@r |> e p # 1 x 2 undef 3 undef
</code></pre>
</article>
<article class="doc-entry" id="doc-mesh-shortest">
<h3><a class="doc-anchor" href="#doc-mesh-shortest">#</a> <code>mesh_shortest</code></h3>
<p><code>mesh_shortest(\@a, \@b, ...)</code> — interleaves arrays into a flat list, stopping at the shortest input array. No <code>undef</code> padding is produced; trailing elements from longer arrays are silently dropped. Use this when you only want complete interleaved groups and partial data should be discarded.</p>
<pre><code class="lang-perl">my @a = 1:3
my @b = ("x","y")
my @r = mesh_shortest(\@a, \@b)
@r |> e p # 1 x 2 y
</code></pre>
</article>
<article class="doc-entry" id="doc-partition">
<h3><a class="doc-anchor" href="#doc-partition">#</a> <code>partition</code></h3>
<p><code>partition</code> — operation <code>partition</code>. Alias for <code>take_while</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p partition $x
</code></pre>
</article>
<article class="doc-entry" id="doc-frequencies">
<h3><a class="doc-anchor" href="#doc-frequencies">#</a> <code>frequencies</code></h3>
<p><code>frequencies</code> (aliases <code>freq</code>, <code>frq</code>) counts how many times each distinct element appears in a list and returns a hashref mapping each value to its count. This is the stryke equivalent of a histogram or counter — useful for analyzing log files, counting word occurrences, tallying categorical data, or finding duplicates. The input list is flattened, so you can pass arrays directly. The returned hashref can be fed into <code>dd</code> for inspection or <code>to_json</code> for serialization.</p>
<pre><code class="lang-perl">my @words = qw(apple banana apple cherry banana apple)
my $counts = freq @words
p $counts # {apple => 3, banana => 2, cherry => 1}
rl("access.log") |> map { /^(\S+)/ && $1 } |> freq |> dd
my @rolls = map { 1 + int(rand 6) } 1:1000
frq(@rolls) |> to_json |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-tally">
<h3><a class="doc-anchor" href="#doc-tally">#</a> <code>tally</code></h3>
<p><code>tally</code> counts how many times each distinct element appears in a list and returns a hash ref mapping element → count. This is the same as Ruby's <code>Enumerable#tally</code> or Python's <code>Counter</code>. Similar to <code>frequencies</code> but follows the Ruby naming convention.</p>
<pre><code class="lang-perl">my $t = tally("a", "b", "a", "c", "a", "b")
p $t->{a} # 3
p $t->{b} # 2
qw(red blue red green blue red) |> tally |> dd
</code></pre>
</article>
<article class="doc-entry" id="doc-interleave">
<h3><a class="doc-anchor" href="#doc-interleave">#</a> <code>interleave</code></h3>
<p><code>interleave</code> (alias <code>il</code>) merges two or more arrays by alternating their elements: first element of each array, then second element of each, and so on. If the arrays have different lengths, shorter arrays contribute <code>undef</code> for their missing positions. This is useful for building key-value pair lists from separate key and value arrays, creating round-robin schedules, or weaving parallel data streams together.</p>
<pre><code class="lang-perl">my @keys = qw(name age city)
my @vals = ("Alice", 30, "NYC")
my @pairs = il \@keys, \@vals
p @pairs # name, Alice, age, 30, city, NYC
my %h = il \@keys, \@vals
p $h{name} # Alice
my @rgb = il [255,0,0], [0,255,0], [0,0,255]
</code></pre>
</article>
<article class="doc-entry" id="doc-pluck">
<h3><a class="doc-anchor" href="#doc-pluck">#</a> <code>pluck</code></h3>
<p><code>pluck KEY, LIST_OF_HASHREFS</code> — extract a single key from each hashref in the list.</p>
<p>For each element, <code>pluck</code> dereferences it as a hashref and returns the value at the given key. Elements where the key is missing yield <code>undef</code>. This is a streaming operation: in a pipeline, each hashref is processed and the extracted value is emitted immediately. It is the stryke equivalent of <code>map { _->{KEY} }</code> but more readable and optimized internally.</p>
<pre><code class="lang-perl">@users |> pluck "name" |> e p
my @ids = pluck "id", @records
@rows |> pluck "email" |> distinct |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-grep-v">
<h3><a class="doc-anchor" href="#doc-grep-v">#</a> <code>grep_v</code></h3>
<p><code>grep_v PATTERN, LIST</code> — inverse grep: reject elements that match the pattern, keep the rest.</p>
<p>This is the complement of <code>grep</code> — any element where the pattern matches is dropped, and non-matching elements pass through. It accepts a regex, a string, or a code block as the pattern. In streaming mode, each element is tested and either forwarded or discarded without buffering. This is a stryke built-in that avoids the awkward <code>grep { !/pattern/ }</code> double-negation.</p>
<pre><code class="lang-perl">@words |> grep_v /^ #/ |> e p # drop comments
my @clean = grep_v qr/tmp/, @files
stdin |> grep_v /^\s*$/ |> e p # drop blank lines
</code></pre>
</article>
<article class="doc-entry" id="doc-select-keys">
<h3><a class="doc-anchor" href="#doc-select-keys">#</a> <code>select_keys</code></h3>
<p><code>select_keys</code> — operation <code>select keys</code>. Category: *pipeline / string helpers*.</p>
<pre><code class="lang-perl">p select_keys $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clamp">
<h3><a class="doc-anchor" href="#doc-clamp">#</a> <code>clamp</code></h3>
<p><code>clamp</code> (alias <code>clp</code>) constrains each value in a list to lie within a specified minimum and maximum range. Values below the minimum are raised to it; values above the maximum are lowered to it; values already in range pass through unchanged. This is essential for sanitizing user input, bounding computed values before display, or enforcing physical constraints in simulations. When given a single scalar, it returns a single clamped value.</p>
<pre><code class="lang-perl">my @scores = (105, -3, 42, 99, 200)
my @clamped = clp 0, 100, @scores
p @clamped # 100, 0, 42, 99, 100
my $val = clp 0, 255, $input # bound to byte range
my @pct = map { clp 0.0, 1.0, _ } @raw_ratios
</code></pre>
</article>
<article class="doc-entry" id="doc-normalize">
<h3><a class="doc-anchor" href="#doc-normalize">#</a> <code>normalize</code></h3>
<p><code>normalize</code> (alias <code>nrm</code>) rescales a list of numeric values so that the minimum maps to 0 and the maximum maps to 1, using min-max normalization. This is a standard preprocessing step for machine learning features, data visualization (mapping values to color gradients or bar heights), and statistical analysis. If all values are identical, the result is a list of zeros to avoid division by zero. The output preserves the relative ordering of the input.</p>
<pre><code class="lang-perl">my @temps = (32, 68, 100, 212)
my @normed = nrm @temps
p @normed # 0, 0.2, 0.377..., 1
my @pixels = nrm @raw_intensities
@pixels |> map { int(_ * 255) } |> e p # scale to 0-255
</code></pre>
</article>
<article class="doc-entry" id="doc-compose">
<h3><a class="doc-anchor" href="#doc-compose">#</a> <code>compose</code></h3>
<p><code>compose</code> (alias <code>comp</code>) creates a right-to-left function composition. Given <code>compose(\&f, \&g)</code>, calling the result with <code>x</code> computes <code>f(g(x))</code>. Chain any number of functions — they apply from right to left (last argument first). This is the standard mathematical function composition found in Haskell, Clojure, and Ramda. The returned code ref can be stored, passed around, or used in pipelines.</p>
<pre><code class="lang-perl">my $double = fn { $_[0] * 2 }
my $inc = fn { $_[0] + 1 }
my $f = compose($inc, $double)
p $f->(5) # 11 (double 5 → 10, inc 10 → 11)
my $pipeline = compose(
fn { join ",", @{$_[0]} },
fn { [sort @{$_[0]}] },
fn { [grep { _ > 2 } @{$_[0]}] },
)
p $pipeline->([3,1,4,1,5]) # 3,4,5
</code></pre>
</article>
<article class="doc-entry" id="doc-partial">
<h3><a class="doc-anchor" href="#doc-partial">#</a> <code>partial</code></h3>
<p><code>partial</code> returns a partially applied function — the bound arguments are prepended to any arguments supplied at call time. <code>partial(\&f, @bound)->(x)</code> is equivalent to <code>f(@bound, x)</code>. This is the standard partial application from functional programming, useful for creating specialized versions of general functions without closures.</p>
<pre><code class="lang-perl">my $add = fn { $_[0] + $_[1] }
my $add5 = partial($add, 5)
p $add5->(3) # 8
my $log = fn { p "[$_[0]] $_[1]" }
my $warn_log = partial($log, "WARN")
$warn_log->("disk full") # [WARN] disk full
</code></pre>
</article>
<article class="doc-entry" id="doc-curry">
<h3><a class="doc-anchor" href="#doc-curry">#</a> <code>curry</code></h3>
<p><code>curry</code> auto-curries a function with a given arity. The curried function accumulates arguments across calls and invokes the original only when enough have been collected. <code>curry(\&f, N)->(a)->(b)</code> calls <code>f(a, b)</code> when N=2. If all arguments are supplied at once, it calls immediately.</p>
<pre><code class="lang-perl">my $add = curry(fn { $_[0] + $_[1] }, 2)
my $add5 = $add->(5)
p $add5->(3) # 8
p $add->(10, 20) # 30 (enough args — calls immediately)
</code></pre>
</article>
<article class="doc-entry" id="doc-memoize">
<h3><a class="doc-anchor" href="#doc-memoize">#</a> <code>memoize</code></h3>
<p><code>memoize</code> (alias <code>memo</code>) wraps a function so that repeated calls with the same arguments return a cached result instead of re-executing the function. Arguments are stringified and joined as the cache key. This is essential for expensive pure functions like recursive algorithms, API lookups with stable results, or any computation where the same inputs always produce the same output.</p>
<pre><code class="lang-perl">my $fib = memoize(fn {
my $n = $_[0]
$n < 2 ? $n : $fib->($n-1) + $fib->($n-2)
})
p $fib->(30) # instant (without memoize: ~1B calls)
my $fetch_user = memo(fn { fetch_json("https://api/users/$_[0]") })
$fetch_user->(42) # hits API
$fetch_user->(42) # returns cached
</code></pre>
</article>
<article class="doc-entry" id="doc-once">
<h3><a class="doc-anchor" href="#doc-once">#</a> <code>once</code></h3>
<p><code>once</code> wraps a function so it is called at most once. The first invocation executes the function and caches the result; all subsequent calls return the cached value without re-executing. This is ideal for lazy initialization, one-time setup, or singleton patterns.</p>
<pre><code class="lang-perl">my $init = once(fn { p "initializing..."
42 })
p $init->() # prints "initializing..." → 42
p $init->() # 42 (no print — cached)
p $init->() # 42 (still cached)
</code></pre>
</article>
<article class="doc-entry" id="doc-constantly">
<h3><a class="doc-anchor" href="#doc-constantly">#</a> <code>constantly</code></h3>
<p><code>constantly</code> (alias <code>const</code>) returns a function that ignores all arguments and always returns the given value. Useful as a default callback, a stub in higher-order function pipelines, or anywhere a function is required but a fixed value suffices.</p>
<pre><code class="lang-perl">my $zero = constantly(0)
p $zero->("anything") # 0
my @defaults = map { constantly(0)->() } 1:5 # [0,0,0,0,0]
</code></pre>
</article>
<article class="doc-entry" id="doc-complement">
<h3><a class="doc-anchor" href="#doc-complement">#</a> <code>complement</code></h3>
<p><code>complement</code> (alias <code>compl</code>) wraps a predicate function and returns a new function that negates its boolean result. <code>complement(\&even?)->(3)</code> returns true. This is the functional equivalent of <code>!f(x)</code> without creating a closure.</p>
<pre><code class="lang-perl">my $even = fn { $_[0] % 2 == 0 }
my $odd = complement($even)
p $odd->(3) # 1
p $odd->(4) # 0
1:10 |> grep { complement($even)->(_) } |> e p # 1 3 5 7 9
</code></pre>
</article>
<article class="doc-entry" id="doc-juxt">
<h3><a class="doc-anchor" href="#doc-juxt">#</a> <code>juxt</code></h3>
<p><code>juxt</code> (juxtapose) takes multiple functions and returns a new function that calls each one with the same arguments and collects the results into an array. This is useful for computing multiple derived values from the same input in a single pass.</p>
<pre><code class="lang-perl">my $stats = juxt(fn { min @_ }, fn { max @_ }, fn { avg @_ })
my @r = $stats->(3, 1, 4, 1, 5)
p "@r" # 1 5 2.8
</code></pre>
</article>
<article class="doc-entry" id="doc-fnil">
<h3><a class="doc-anchor" href="#doc-fnil">#</a> <code>fnil</code></h3>
<p><code>fnil</code> wraps a function so that any <code>undef</code> arguments are replaced with the given defaults before the function is called. This eliminates repetitive <code>// $default</code> patterns inside function bodies.</p>
<pre><code class="lang-perl">my $greet = fnil(fn { "Hello, $_[0]!" }, "World")
p $greet->(undef) # Hello, World!
p $greet->("Alice") # Hello, Alice!
</code></pre>
</article>
<article class="doc-entry" id="doc-deep-clone">
<h3><a class="doc-anchor" href="#doc-deep-clone">#</a> <code>deep_clone</code></h3>
<p><code>deep_clone</code> (alias <code>dclone</code>) performs a recursive deep copy of a nested data structure. Array refs, hash refs, and scalar refs are cloned recursively so that the result shares no references with the original. Modifications to the clone never affect the source. This is the stryke equivalent of JavaScript's <code>structuredClone</code> or Perl's <code>Storable::dclone</code>.</p>
<pre><code class="lang-perl">my $orig = {users => [{name => "Alice"}], meta => {v => 1}}
my $copy = deep_clone($orig)
$copy->{users}[0]{name} = "Bob"
p $orig->{users}[0]{name} # Alice (unchanged)
</code></pre>
</article>
<article class="doc-entry" id="doc-deep-merge">
<h3><a class="doc-anchor" href="#doc-deep-merge">#</a> <code>deep_merge</code></h3>
<p><code>deep_merge</code> (alias <code>dmerge</code>) recursively merges two hash references. When both sides have a hash ref for the same key, they are merged recursively; otherwise the right-hand value wins. This is the standard deep merge from Lodash, Ruby's <code>deep_merge</code>, and config-file overlay patterns. Returns a new hash ref — neither input is modified.</p>
<pre><code class="lang-perl">my $defaults = {db => {host => "localhost", port => 5432}, debug => 0}
my $overrides = {db => {port => 3306}, debug => 1}
my $cfg = deep_merge($defaults, $overrides)
p $cfg->{db}{host} # localhost (from defaults)
p $cfg->{db}{port} # 3306 (overridden)
p $cfg->{debug} # 1 (overridden)
</code></pre>
</article>
<article class="doc-entry" id="doc-deep-equal">
<h3><a class="doc-anchor" href="#doc-deep-equal">#</a> <code>deep_equal</code></h3>
<p><code>deep_equal</code> (alias <code>deq</code>) performs structural equality comparison of two values, recursively descending into array refs, hash refs, and scalar refs. Returns 1 if the structures are identical, 0 otherwise. This is the stryke equivalent of Node's <code>assert.deepStrictEqual</code>, Lodash <code>isEqual</code>, or Python's <code>==</code> on nested dicts/lists.</p>
<pre><code class="lang-perl">p deep_equal([1, {a => 2}], [1, {a => 2}]) # 1
p deep_equal([1, {a => 2}], [1, {a => 3}]) # 0
p deq({x => [1,2]}, {x => [1,2]}) # 1
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-operators">
<h2>Operators</h2>
<p class="chapter-meta">66 topics</p>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>-></code></h3>
<p><strong>Arrow operator</strong> — method invocation on objects/classes and dereference of refs. The single most-used operator in Perl OOP and any code touching references.</p>
<pre><code class="lang-perl"># Method call (object or class):
my $p = Point->new(x => 1, y => 2)
p $p->x # 1
p Math::Utils->compute(@args)
# Hash-ref dereference:
my $cfg = { host => "localhost", port => 5432 }
p $cfg->{host}
$cfg->{port} = 6543
# Array-ref dereference:
my $rows = [[1,2,3], [4,5,6]]
p $rows->[1][2] # 6 (chained — implicit ->)
my $val = $rows->[0]->[2] # explicit form: 3
# Code-ref invocation:
my $f = fn ($x) { $x * 2 }
p $f->(21) # 42
# Postfix-deref (modern):
my @copy = $rows->@* # all elements
my %env = %ENV->%* # entire hash via slice
</code></pre>
<p><strong>Chained arrow elision</strong> — between subscripts (<code>[..]</code>, <code>{..}</code>), <code>-></code> is optional: <code>$rows->[1][2]</code> ≡ <code>$rows->[1]->[2]</code>. The first arrow after a scalar variable is *required*; intermediate arrows can be omitted for chained subscripting only.</p>
<p>See also: <code>->></code> / <code>~>></code> (thread-last macros — distinct operator), <code>bless</code>, <code>class</code>, <code>new</code>, <code>ref</code>.</p>
</article>
<article class="doc-entry" id="doc-new">
<h3><a class="doc-anchor" href="#doc-new">#</a> <code>new</code></h3>
<p><code>new</code> — the default constructor automatically provided for every <code>class</code> and <code>struct</code>. Called as <code>ClassName->new(field1 => v1, field2 => v2, ...)</code>. Returns a blessed object whose attribute storage is initialized from the named arguments. If the class defines a <code>BUILD</code> method, <code>new</code> runs it *after* attribute initialization but *before* returning, so <code>BUILD</code> can validate, derive fields, or attach external resources. A class never overrides <code>new</code> itself in stryke — to customize construction, define <code>BUILD</code> (post-init hook) instead.</p>
<p>Implementation: <code>vm_helper.rs:10686</code> — when <code>->new</code> is called and no user-defined <code>new</code> exists, the runtime dispatches to <code>builtin_new</code> which allocates the object, populates fields from the arglist, then calls <code>BUILD</code> via the C3 MRO if present.</p>
<pre><code class="lang-perl">class Point {
has 'x' => (is => 'ro', default => 0)
has 'y' => (is => 'ro', default => 0)
}
my $p = Point->new(x => 1.5, y => 2.0)
p $p->x # 1.5
class Connection {
has 'host' => (is => 'ro', required => 1)
has 'port' => (is => 'ro', default => 5432)
fn BUILD($self, $args) {
die "host required" unless $self->host
}
}
my $c = Connection->new(host => "db.example.com")
</code></pre>
<p>See also: <code>BUILD</code> (post-init hook), <code>DESTROY</code> (destructor), <code>class</code>, <code>struct</code>, <code>bless</code>, <code>@ISA</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$</code></h3>
<p><strong>Scalar sigil.</strong> <code>$name</code> accesses a scalar variable. <code>$ref</code> holds references. <code>$h{key}</code> accesses one hash value; <code>$a[idx]</code> accesses one array element (sigil reflects the *value being accessed*, not the container). For postfix-deref: <code>$ref->$*</code> (in stryke contexts that accept it).</p>
<pre><code class="lang-perl">my $x = 42 # scalar declaration
my @arr = (1, 2, 3)
p $arr[0] # 1 — scalar context on @arr
my %h = (k => "v")
p $h{k} # one value
my $ref = \@arr # reference, scalar holds it
</code></pre>
<p>See also: <code>@</code> (array sigil), <code>%</code> (hash sigil), <code>\</code> (reference), <code>-></code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>@</code></h3>
<p><strong>Array sigil.</strong> <code>@name</code> accesses an entire array. <code>@h{@keys}</code> is a hash slice (multiple values by key list). <code>@a[@idx]</code> is an array slice. <code>@_</code> is the implicit sub argument array. Stringified in double quotes by joining elements with <code>$"</code> (space by default).</p>
<pre><code class="lang-perl">my @nums = (1, 2, 3)
p scalar @nums # 3 — length in scalar context
p "@nums" # 1 2 3 — joined with $"
my @slice = @arr[1..3] # array slice
my @vals = @h{qw(a b c)} # hash slice
</code></pre>
<p>See also: <code>$</code> (scalar sigil), <code>%</code> (hash sigil), <code>@_</code>, <code>$"</code>, postfix-deref <code>->@*</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>%</code></h3>
<p><strong>Hash sigil / modulo operator</strong> — same character, two meanings disambiguated by context.</p>
<p><strong>As sigil</strong> (preceding a name): <code>%h</code> accesses the whole hash. <code>%ENV</code> is the env hash, <code>%h = (k1 => v1, k2 => v2)</code> declares one, <code>keys %h</code> / <code>values %h</code> / <code>each %h</code> iterate. The sigil reflects the *whole hash*; one value is <code>$h{k}</code> (scalar).</p>
<p><strong>As operator</strong> (between expressions): <code>$a % $b</code> is integer modulo (remainder); result takes the sign of the right operand.</p>
<pre><code class="lang-perl">my %cfg = (host => "localhost", port => 5432)
p keys %cfg # hash iteration
p 10 % 3 # 1 — modulo
p -7 % 3 # 2 — Perl semantics: sign matches RHS
</code></pre>
<p>See also: <code>$</code> (scalar), <code>@</code> (array), <code>%=</code>, <code>%ENV</code>, <code>%SIG</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>+</code></h3>
<p><strong>Addition / numeric coercion.</strong> <code>$a + $b</code> adds two numbers. Operands are coerced to numeric context — strings parse as <code>\d+(\.\d+)?</code> until a non-numeric character, so <code>"5 apples" + 3 == 8</code>. Use <code>.</code> (dot) for string concatenation; using <code>+</code> on intended-strings is a common bug since the strings parse to 0 silently under <code>no warnings</code>. As a unary prefix, <code>+EXPR</code> forces numeric context without changing value.</p>
<pre><code class="lang-perl">p 2 + 3 # 5
p "10x" + 5 # 15 — leading digits parse
p "x10" + 5 # 5 — leading non-digit → 0
my $sum = sum(1:100) # 5050
</code></pre>
<p>See also: <code>-</code>, <code>*</code>, <code>/</code>, <code>+=</code> (compound assign), <code>.</code> (string concat).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>-</code></h3>
<p><strong>Subtraction / unary minus / file-test operator.</strong> Binary: <code>$a - $b</code> subtracts numbers (same coercion rules as <code>+</code>). Unary: <code>-EXPR</code> negates. Special: <code>-X FILE</code> where <code>X</code> is a single letter is a file-test operator (<code>-e</code> exists, <code>-f</code> regular file, <code>-d</code> directory, <code>-r</code> readable, <code>-w</code> writable, <code>-x</code> executable, <code>-s</code> size in bytes, <code>-M</code> age in days, etc.).</p>
<pre><code class="lang-perl">p 10 - 3 # 7
p -5 * 2 # -10
if (-e $path) { p "exists" }
if (-f $path && -r _) { p "readable file" } # _ reuses last stat
</code></pre>
<p>See also: <code>+</code>, <code>-=</code>, file-test reference.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>*</code></h3>
<p><strong>Multiplication / glob deref.</strong> Binary: <code>$a * $b</code> multiplies numbers. In expression context (<code>*name</code>), references the typeglob for that name — rarely used directly; assigning <code>*alias = \&func</code> installs an alias for the sub.</p>
<pre><code class="lang-perl">p 6 * 7 # 42
my $area = $w * $h
*shortcut = \&long_function_name # sub alias
</code></pre>
<p>See also: <code>*=</code>, <code>**</code> (exponent), <code>x</code> (string/list repeat — NOT multiplication).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>/</code></h3>
<p><strong>Division / regex delimiter.</strong> Binary: <code>$a / $b</code> divides as floats. Stryke uses true division — <code>5 / 2 == 2.5</code>, not 2. Use <code>int($a / $b)</code> or <code>intdiv($a, $b)</code> for integer division. In expression context, <code>/PATTERN/</code> opens a regex — context-dependent: after an operator or at statement start, <code>/</code> parses as regex; after a variable or value, it's division.</p>
<pre><code class="lang-perl">p 10 / 4 # 2.5
p int(10 / 4) # 2
if ($s =~ /^\d+$/) { p "all digits" }
</code></pre>
<p>See also: <code>*</code>, <code>%</code> (modulo), <code>/=</code>, regex syntax, <code>intdiv</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>**</code></h3>
<p><strong>Exponentiation.</strong> <code>$a ** $b</code> raises <code>$a</code> to the <code>$b</code>-th power. Floating-point throughout — <code>2 ** 10 == 1024</code>, <code>2 ** 0.5 == 1.414...</code>. Right-associative: <code>2 ** 3 ** 2 == 2 ** 9 == 512</code>. Negative bases with fractional exponents return NaN.</p>
<pre><code class="lang-perl">p 2 ** 10 # 1024
p 2 ** 0.5 # 1.4142135623731
p 2 ** 3 ** 2 # 512 (right-assoc)
my $sq = $r ** 2
</code></pre>
<p>See also: <code>**=</code>, <code>sqrt</code>, <code>exp</code>, <code>log</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>++</code></h3>
<p><strong>Increment.</strong> Postfix <code>$x++</code> returns the value and *then* increments; prefix <code>++$x</code> increments first and returns the new value. Works on integers, floats, and <strong>magic strings</strong> (<code>"aa"++ == "ab"</code>, <code>"az"++ == "ba"</code>, <code>"Az"++ == "Ba"</code>). String increment follows Perl's letter-roll rules — preserves case, rolls letters with carry into the next position.</p>
<pre><code class="lang-perl">my $n = 5
p $n++ # 5 (post: returns old)
p $n # 6
p ++$n # 7 (pre: returns new)
my $s = "Az"
$s++; p $s # Ba — magic string increment
</code></pre>
<p>See also: <code>--</code>, atomic <code>++</code> on <code>mysync</code> shared scalars (always atomic).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>--</code></h3>
<p><strong>Decrement.</strong> Postfix <code>$x--</code> returns the value and *then* decrements; prefix <code>--$x</code> decrements first. Numeric-only — there is no magic-string *decrement* in Perl. On non-numeric strings, <code>--</code> coerces to 0 first then decrements.</p>
<pre><code class="lang-perl">my $n = 5
p $n-- # 5
p $n # 4
p --$n # 3
</code></pre>
<p>See also: <code>++</code>, atomic <code>--</code> on <code>mysync</code> shared scalars.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>.</code></h3>
<p><strong>String concatenation.</strong> <code>$a . $b</code> glues two strings together. Both operands are coerced to string context. For multi-arg joins prefer <code>join "", @parts</code> (faster, less typing); for building large strings prefer interpolation or <code>sprintf</code>. The <code>.</code> operator does <strong>not</strong> insert separators — <code>"hello" . "world" eq "helloworld"</code>.</p>
<pre><code class="lang-perl">my $name = "world"
p "hello " . $name . "!" # hello world!
my $full = $first . " " . $last
my $line = sprintf "%-20s %d", $name, $count # often clearer
</code></pre>
<p>See also: <code>.=</code> (append assign), <code>x</code> (repeat), <code>join</code>, <code>sprintf</code>, interpolation.</p>
</article>
<article class="doc-entry" id="doc-x">
<h3><a class="doc-anchor" href="#doc-x">#</a> <code>x</code></h3>
<p><strong>Repeat operator.</strong> <code>STR x N</code> repeats a string N times; <code>(LIST) x N</code> repeats a list. The context of the LHS decides: scalar LHS → string repeat; list LHS (must be in parens) → list repeat. N is truncated to integer; negative or zero N produces empty.</p>
<pre><code class="lang-perl">p "=" x 20 # ====================
p "ab" x 3 # ababab
my @z = (0) x 10 # ten zeros
my @grid = ([0,0,0]) x 5 # five distinct rows (each is a new arrayref via shallow copy)
</code></pre>
<p>See also: <code>.</code> (concat), <code>x=</code> (compound), <code>repeat</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>==</code></h3>
<p><strong>Numeric equality.</strong> Coerces both operands to numbers and compares. Use <code>eq</code> for strings — <code>"10" == "10.0"</code> is true, but <code>"10" eq "10.0"</code> is false. Float comparison with <code>==</code> is dangerous due to rounding; for tolerances use <code>abs($a - $b) < $epsilon</code>.</p>
<pre><code class="lang-perl">p 5 == 5.0 # 1
p "10" == 10 # 1 (numeric coercion)
p "foo" == "bar" # 1 (both → 0) — common bug, use eq!
if ($n == 0) { ... }
</code></pre>
<p>See also: <code>!=</code>, <code><=></code>, <code>eq</code> (string equality), <code>near_eq</code> builtin for float tolerance.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>!=</code></h3>
<p><strong>Numeric inequality.</strong> Inverse of <code>==</code>. Use <code>ne</code> for strings.</p>
<pre><code class="lang-perl">p 5 != 6 # 1
while ($i != $target) { ... }
</code></pre>
<p>See also: <code>==</code>, <code>ne</code>, <code><=></code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code><</code></h3>
<p><strong>Numeric less-than.</strong> Coerces to numbers. Use <code>lt</code> for strings.</p>
<pre><code class="lang-perl">p 3 < 5 # 1
if ($age < 18) { ... }
my @small = grep { _ < 10 } @nums
</code></pre>
<p>Stryke supports <strong>chained comparisons</strong> Raku-style: <code>1 < $x < 10</code> ≡ <code>(1 < $x) && ($x < 10)</code>. See <code>chained_comparison</code>.</p>
<p>See also: <code>></code>, <code><=</code>, <code><=></code>, <code>lt</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>></code></h3>
<p><strong>Numeric greater-than.</strong> Coerces to numbers. Use <code>gt</code> for strings.</p>
<pre><code class="lang-perl">p 7 > 5 # 1
my @big = grep { _ > 100 } @vals
</code></pre>
<p>Also the redirect operator in <code>open</code> (<code>open my $fh, '>', $path</code>) and the diamond closer (<code><$fh></code>).</p>
<p>See also: <code><</code>, <code>>=</code>, <code><=></code>, <code>gt</code>, <code>chained_comparison</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code><=</code></h3>
<p><strong>Numeric less-than-or-equal.</strong> Use <code>le</code> for strings. Participates in chained comparisons: <code>0 <= $i < @arr</code>.</p>
<pre><code class="lang-perl">if (0 <= $i < scalar @arr) { p $arr[$i] }
</code></pre>
<p>See also: <code><</code>, <code>>=</code>, <code><=></code>, <code>le</code>, <code>chained_comparison</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>>=</code></h3>
<p><strong>Numeric greater-than-or-equal.</strong> Use <code>ge</code> for strings.</p>
<pre><code class="lang-perl">return if $count >= $max
</code></pre>
<p>See also: <code>></code>, <code><=</code>, <code><=></code>, <code>ge</code>, <code>chained_comparison</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code><=></code></h3>
<p><strong>Spaceship operator</strong> — numeric three-way compare. Returns -1, 0, or 1. The standard <code>sort</code> comparator for numeric sort.</p>
<pre><code class="lang-perl">my @sorted = sort { $a <=> $b } @nums # ascending
my @desc = sort { $b <=> $a } @nums # descending
p 5 <=> 10 # -1
p 10 <=> 10 # 0
p 15 <=> 10 # 1
</code></pre>
<p>See also: <code>cmp</code> (string version), <code>sort</code>, <code>$a</code>, <code>$b</code>.</p>
</article>
<article class="doc-entry" id="doc-eq">
<h3><a class="doc-anchor" href="#doc-eq">#</a> <code>eq</code></h3>
<p><strong>String equality.</strong> Compares operands as strings. <code>"10" eq "10.0"</code> is false. The string-context counterpart of <code>==</code>.</p>
<pre><code class="lang-perl">if ($cmd eq "start") { ... }
p "abc" eq "abc" # 1
p "abc" eq "ABC" # "" (case matters)
</code></pre>
<p>See also: <code>ne</code>, <code>cmp</code>, <code>==</code> (numeric), <code>lc</code>/<code>uc</code> for case-insensitive compare.</p>
</article>
<article class="doc-entry" id="doc-ne">
<h3><a class="doc-anchor" href="#doc-ne">#</a> <code>ne</code></h3>
<p><strong>String inequality.</strong> Inverse of <code>eq</code>.</p>
<pre><code class="lang-perl">next if $line ne ""
</code></pre>
<p>See also: <code>eq</code>, <code>cmp</code>, <code>!=</code> (numeric).</p>
</article>
<article class="doc-entry" id="doc-lt">
<h3><a class="doc-anchor" href="#doc-lt">#</a> <code>lt</code></h3>
<p><strong>String less-than</strong> — lexicographic comparison. Use <code><</code> for numeric.</p>
<pre><code class="lang-perl">p "apple" lt "banana" # 1
my @sorted = sort { $a lt $b ? -1 : 1 } @words
</code></pre>
<p>See also: <code>gt</code>, <code>le</code>, <code>cmp</code>, <code><</code> (numeric), <code>chained_comparison</code>.</p>
</article>
<article class="doc-entry" id="doc-le">
<h3><a class="doc-anchor" href="#doc-le">#</a> <code>le</code></h3>
<p><strong>String less-than-or-equal</strong> — lexicographic. Use <code><=</code> for numeric. Participates in chained comparisons.</p>
<p>See also: <code>lt</code>, <code>ge</code>, <code>cmp</code>.</p>
</article>
<article class="doc-entry" id="doc-gt">
<h3><a class="doc-anchor" href="#doc-gt">#</a> <code>gt</code></h3>
<p><strong>String greater-than</strong> — lexicographic.</p>
<pre><code class="lang-perl">p "banana" gt "apple" # 1
</code></pre>
<p>See also: <code>lt</code>, <code>ge</code>, <code>cmp</code>, <code>></code> (numeric).</p>
</article>
<article class="doc-entry" id="doc-ge">
<h3><a class="doc-anchor" href="#doc-ge">#</a> <code>ge</code></h3>
<p><strong>String greater-than-or-equal</strong> — lexicographic. Use <code>>=</code> for numeric.</p>
<p>See also: <code>gt</code>, <code>le</code>, <code>cmp</code>.</p>
</article>
<article class="doc-entry" id="doc-cmp">
<h3><a class="doc-anchor" href="#doc-cmp">#</a> <code>cmp</code></h3>
<p><strong>String three-way compare</strong> — returns -1, 0, or 1. The standard <code>sort</code> comparator for string sort.</p>
<pre><code class="lang-perl">my @sorted = sort { $a cmp $b } @words # case-sensitive
my @ci = sort { lc($a) cmp lc($b) } @words # case-insensitive
p "alice" cmp "bob" # -1
</code></pre>
<p>See also: <code><=></code> (numeric three-way), <code>eq</code>, <code>lt</code>, <code>gt</code>, <code>sort</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>&&</code></h3>
<p><strong>Logical AND</strong> (high-precedence). Short-circuit: returns the <strong>first falsy operand</strong>, or the <strong>last operand if all truthy</strong>. Stryke (like Perl) doesn't return boolean — it returns the actual value, which makes idioms like <code>$default = $val && transform($val)</code> work.</p>
<pre><code class="lang-perl">if ($x > 0 && $x < 100) { ... }
my $first = $a && $b && $c # first truthy or last falsy
</code></pre>
<p>Lower-precedence variant <code>and</code> binds looser than <code>=</code> so use it for control flow: <code>open $fh, $f and read_loop()</code>. See also: <code>||</code>, <code>//</code>, <code>and</code>, <code>!</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>||</code></h3>
<p><strong>Logical OR</strong> (high-precedence). Short-circuit: returns the <strong>first truthy operand</strong>, or the <strong>last operand if all falsy</strong>. The classic Perl default idiom: <code>my $x = $arg || "default"</code> — but watch out: <code>0</code>, <code>""</code>, <code>"0"</code>, and <code>undef</code> are all falsy, so <code>||</code> falls through for legitimate zero values. Use <code>//</code> (defined-or) when only <code>undef</code> should trigger the fallback.</p>
<pre><code class="lang-perl">my $name = $user || "guest"
my $val = $count // 0 # better: only undef triggers fallback
open $fh, $f or die $! # `or` is the low-precedence form
</code></pre>
<p>See also: <code>&&</code>, <code>//</code>, <code>or</code>, <code>defined</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>//</code></h3>
<p><strong>Defined-or operator.</strong> Returns the LHS if it is defined (even if <code>0</code> or <code>""</code>), else the RHS. Distinct from <code>||</code> which treats all falsy values as "use the fallback". Use <code>//</code> whenever you have a numeric default or want to distinguish absent values from explicit zero.</p>
<pre><code class="lang-perl">my $count = $opts{count} // 10 # 10 only if missing — 0 is allowed
my $tag = $row->{label} // "untagged"
return $cache{$key} //= compute($key) # //= : assign only if undef
</code></pre>
<p>See also: <code>||</code>, <code>defined</code>, <code>//=</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>!</code></h3>
<p><strong>Logical NOT</strong> (high-precedence). Returns 1 (true) if the operand is falsy, <code>""</code> (false) if truthy. Lower-precedence variant <code>not</code> reads English-y; prefer <code>!</code> in expressions, <code>not</code> in conditions.</p>
<pre><code class="lang-perl">if (!$ok) { die "failed" }
return unless not @items # avoid double-negative — prefer `unless @items`
my $inverse = !!$truthy # !! coerces to canonical 1 / ""
</code></pre>
<p>See also: <code>not</code>, <code>unless</code>, <code>&&</code>, <code>||</code>.</p>
</article>
<article class="doc-entry" id="doc-and">
<h3><a class="doc-anchor" href="#doc-and">#</a> <code>and</code></h3>
<p><strong>Low-precedence logical AND.</strong> Same short-circuit behaviour as <code>&&</code> but binds looser than <code>=</code>, <code>,</code>, and most other operators. Use for control-flow expressions where you'd otherwise need parens: <code>$ok = read_file($path) and parse(...)</code> — but note this assigns to <code>$ok</code> ONLY the return of <code>read_file</code> (because <code>=</code> binds tighter than <code>and</code>). For value-binding use <code>&&</code>.</p>
<pre><code class="lang-perl">open $fh, '<', $f and read_loop($fh) # control flow
</code></pre>
<p>See also: <code>&&</code>, <code>or</code>, <code>not</code>.</p>
</article>
<article class="doc-entry" id="doc-or">
<h3><a class="doc-anchor" href="#doc-or">#</a> <code>or</code></h3>
<p><strong>Low-precedence logical OR.</strong> Same short-circuit behaviour as <code>||</code> but binds looser than <code>=</code>. The canonical idiom for <code>open ... or die</code>: <code>open my $fh, $path or die "open: $!"</code>. The whole <code>open</code> expression is evaluated, then <code>or die</code> runs only if open returned false.</p>
<pre><code class="lang-perl">open my $fh, '<', $f or die "open: $!"
my $val = read_line() or last # WRONG: assigns the read, not the fallback
my $val = read_line() || last # WRONG too — falsy values fall through
# Use defined-or for value defaults:
my $val = read_line() // last
</code></pre>
<p>See also: <code>||</code>, <code>//</code>, <code>and</code>.</p>
</article>
<article class="doc-entry" id="doc-not">
<h3><a class="doc-anchor" href="#doc-not">#</a> <code>not</code></h3>
<p>Low-precedence logical negation — returns true if the expression is false, and false if it is true. Functionally identical to <code>!</code> but binds looser than almost everything, so <code>not $a == $b</code> is <code>not($a == $b)</code> rather than <code>(!$a) == $b</code>. Useful for readable boolean conditions.</p>
<pre><code class="lang-perl">if (not defined $val) {
p "val is undef"
}
my @missing = grep { not -e _ } @files
@missing |> e p
p not 0 # 1
p not 1 # (empty string)
</code></pre>
</article>
<article class="doc-entry" id="doc-xor">
<h3><a class="doc-anchor" href="#doc-xor">#</a> <code>xor</code></h3>
<p><strong>Low-precedence logical XOR.</strong> Returns true exactly when one operand is truthy and the other is falsy. No short-circuit (both sides always evaluated). Rarely used; if you find yourself wanting <code>xor</code> consider <code>($a ? 1 : 0) != ($b ? 1 : 0)</code> for clarity.</p>
<pre><code class="lang-perl">if ($admin xor $guest) { p "exactly one role" }
</code></pre>
<p>See also: <code>&&</code>, <code>||</code>, <code>^</code> (bitwise xor).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>=~</code></h3>
<p><strong>Regex bind</strong> — applies the right-side regex/transliteration/substitution to the left-side scalar. Returns success/match data in scalar context, captured groups in list context. Without <code>=~</code>, regex ops default to operating on <code>$_</code>.</p>
<pre><code class="lang-perl">if ($line =~ /^\s*#/) { ... } # match
my ($host) = $url =~ m{^https?://([^/]+)} # extract
$text =~ s/foo/bar/g # substitute
$str =~ tr/a-z/A-Z/ # transliterate
</code></pre>
<p>See also: <code>!~</code>, <code>m//</code>, <code>s///</code>, <code>tr///</code>, named captures (<code>(?<name>...)</code>, <code>%+</code>).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>!~</code></h3>
<p><strong>Negated regex bind.</strong> True if the regex does NOT match.</p>
<pre><code class="lang-perl">next if $line !~ /^\s*\w/ # skip lines that don't start with a word
</code></pre>
<p>See also: <code>=~</code>, <code>m//</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>..</code></h3>
<p><strong>Range operator.</strong> In list context, generates an inclusive integer or magic-string sequence: <code>1..5 == (1,2,3,4,5)</code>. In scalar/boolean context (rare — only in <code>while</code>/<code>if</code>), acts as a flip-flop state machine.</p>
<pre><code class="lang-perl">for (1..10) { p _ }
my @letters = ('a'..'z') # magic string range
my @rev = reverse 1..100
</code></pre>
<p>Stryke convention: prefer <code>1:5</code> (colon-range, fully equivalent) since it doesn't visually clash with method/property access chains.</p>
<p>See also: <code>...</code> (three-dot range), <code>:</code> colon range, flip-flop in <code>while</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>...</code></h3>
<p><strong>Exclusive range / yada-yada.</strong> As an operator: <code>1...5</code> is the *exclusive* range (does not include the endpoint in some contexts) and the *flip-flop* operator with slightly different reset semantics than <code>..</code>. As a statement: <code>...</code> alone (the "yada-yada") is a placeholder that compiles fine but dies at runtime — useful for sketching APIs.</p>
<pre><code class="lang-perl">fn not_yet_implemented { ... } # yada-yada — dies if called
</code></pre>
<p>See also: <code>..</code>, yada-yada placeholder.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>=></code></h3>
<p><strong>Fat comma</strong> — variant of <code>,</code> that auto-quotes the left operand if it looks like a bareword identifier. The canonical syntax for hash entries and named arguments since it self-documents which side is the key.</p>
<pre><code class="lang-perl">my %cfg = (
host => "localhost", # "host" auto-quoted
port => 5432,
debug => 1,
)
open my $fh, '<', $path or die
Class->new(name => "alice", age => 30)
</code></pre>
<p>With strict syntax, <code>,</code> and <code>=></code> are semantically equivalent EXCEPT for the auto-quoting. <code>1 => 2</code> is the same as <code>1 , 2</code>; the magic only fires on bareword LHS.</p>
<p>See also: <code>,</code>, hash declaration, named parameters.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>,</code></h3>
<p><strong>Comma operator / list separator.</strong> In list context, separates list elements. In scalar context (right-to-left), evaluates each expression for side effects and returns the rightmost (like C). The fat-comma <code>=></code> is a variant that auto-quotes bareword LHS.</p>
<pre><code class="lang-perl">my @x = (1, 2, 3)
my %h = (a => 1, b => 2)
for (my $i = 0, my $j = 10; $i < 5; $i++, $j--) { ... } # scalar context
</code></pre>
<p>See also: <code>=></code>, list operators (<code>push</code>, <code>unshift</code>, …).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>?:</code></h3>
<p><strong>Ternary conditional</strong> — <code>COND ? IF_TRUE : IF_FALSE</code>. Right-associative for chaining. Returns one of the two branches as an expression value, unlike <code>if</code>/<code>else</code> which is a statement. Stryke also accepts the <code>if</code>/<code>else</code> block form as an expression: <code>my $x = do { if (cond) { 1 } else { 2 } }</code>.</p>
<pre><code class="lang-perl">my $sign = $n > 0 ? "+" : $n < 0 ? "-" : "0"
p $count == 1 ? "$count item" : "$count items"
</code></pre>
<p>Binds looser than most operators; use parens around complex conditions for readability. See also: <code>if</code>/<code>else</code>, <code>match</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>\</code></h3>
<p><strong>Reference operator</strong> — takes a reference to a variable, sub, or value. <code>\$scalar</code>, <code>\@array</code>, <code>\%hash</code>, <code>\&sub</code>, <code>\(...)</code>. References are scalars; deref with <code>$$ref</code> / <code>@$ref</code> / <code>%$ref</code> / <code>&$ref</code> / <code>$ref->[i]</code> / <code>$ref->{k}</code> / <code>$ref->(...)</code>.</p>
<pre><code class="lang-perl">my @nums = (1, 2, 3)
my $aref = \@nums
p $$aref[0] # 1 (sigil-deref)
p $aref->[0] # 1 (arrow-deref — preferred)
p join ",", @$aref # 1,2,3
my $code = \&my_function
$code->(42)
</code></pre>
<p>Also <code>\(LIST)</code> returns a list of references — <code>\(@a, @b)</code> gives one ref per element, not a single ref to the list.</p>
<p>See also: <code>-></code>, <code>ref</code>, deref syntax, <code>bless</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>&</code></h3>
<p><strong>Bitwise AND</strong> (and prototype/sub-deref). On numbers, <code>$a & $b</code> computes the bitwise AND. As a sigil prefix <code>&name</code> calls a sub (in non-bareword contexts) or takes a coderef. With <code>\</code> makes a coderef: <code>\&sub</code>.</p>
<pre><code class="lang-perl">p 0b1100 & 0b1010 # 8 (0b1000)
my $mask = $flags & 0xFF
my $code = \&my_sub # coderef
</code></pre>
<p>See also: <code>|</code>, <code>^</code>, <code>~</code>, <code>&&</code>, <code>\&</code> (coderef).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>|</code></h3>
<p><strong>Bitwise OR.</strong> <code>$a | $b</code> ORs the bits. Also a regex alternation inside <code>/.../</code>. As a stream operator <code>||</code> is logical OR, <code>|></code> is pipe-forward.</p>
<pre><code class="lang-perl">p 0b1100 | 0b1010 # 14 (0b1110)
my $flags = OPEN_READ | OPEN_NONBLOCK
</code></pre>
<p>See also: <code>&</code>, <code>^</code>, <code>~</code>, <code>||</code>, <code>|></code>, regex alternation.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>^</code></h3>
<p><strong>Bitwise XOR.</strong> <code>$a ^ $b</code> XORs the bits.</p>
<pre><code class="lang-perl">p 0b1100 ^ 0b1010 # 6 (0b0110)
my $toggled = $bits ^ $mask
</code></pre>
<p>See also: <code>&</code>, <code>|</code>, <code>~</code>, <code>xor</code> (logical).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>~</code></h3>
<p><strong>Bitwise NOT</strong> (unary). Flips every bit; works on integers. Also the prefix of stryke thread macros (<code>~></code>, <code>~p></code>, <code>~d></code>, etc.) — those are distinct multi-char operators, not <code>~</code> followed by something.</p>
<pre><code class="lang-perl">p ~0 # -1 (all bits set on signed int)
p ~0xFF # …higher bits set
my $inverted = ~$mask & 0xFFFF
</code></pre>
<p>See also: <code>&</code>, <code>|</code>, <code>^</code>, <code>!</code> (logical NOT), <code>~></code> / <code>~>></code> / <code>~p></code> (distinct ops).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code><<</code></h3>
<p><strong>Left bit-shift / heredoc.</strong> As <code>$a << $b</code>, shifts bits left by <code>$b</code> positions. As <code><<TAG</code>, opens a heredoc (multi-line string literal terminated by <code>TAG</code> at start of line).</p>
<pre><code class="lang-perl">p 1 << 10 # 1024
my $kb = $bytes << 10
my $sql = <<END
SELECT *
FROM users
END
</code></pre>
<p>See also: <code>>></code>, <code><<=</code>, heredoc syntax.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>>></code></h3>
<p><strong>Right bit-shift / file redirect.</strong> As <code>$a >> $b</code>, shifts bits right by <code>$b</code> positions. As a mode in <code>open</code>, <code>>></code> opens for append.</p>
<pre><code class="lang-perl">p 1024 >> 2 # 256
my $exit_code = $? >> 8 # extract exit code from $?
open my $fh, '>>', 'log.txt' or die
</code></pre>
<p>See also: <code><<</code>, <code>>>=</code>, <code>open</code> modes.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>=</code></h3>
<p><strong>Assignment.</strong> Returns the assigned value (so chained <code>$a = $b = 5</code> works). Context matters: <code>my @a = $scalar</code> copies the scalar's value into a one-element list; <code>my @a = @b</code> does list copy; <code>my $s = @a</code> gives the array's length in scalar context. The single most-used operator after <code>;</code>.</p>
<pre><code class="lang-perl">my $x = 42
my ($a, $b, $c) = (1, 2, 3) # list-destructure
my ($first, @rest) = split /,/
($a, $b) = ($b, $a) # swap
my $len = @items # scalar context — count
</code></pre>
<p>See also: <code>+=</code>, <code>-=</code>, <code>.=</code>, <code>//=</code>, <code>||=</code>, <code>&&=</code>, <code>my</code>, <code>our</code>, <code>local</code>, <code>state</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>+=</code></h3>
<p><strong>Add-assign.</strong> <code>$x += $y</code> ≡ <code>$x = $x + $y</code>. Atomic on <code>mysync</code> shared scalars.</p>
<pre><code class="lang-perl">my $total = 0
$total += $_ for @nums
mysync $sum = 0; fan 10000 { $sum += 1 } # atomic — always 10000
</code></pre>
<p>See also: <code>+</code>, <code>-=</code>, <code>*=</code>, etc.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>-=</code></h3>
<p><strong>Subtract-assign.</strong> <code>$x -= $y</code> ≡ <code>$x = $x - $y</code>. Atomic on <code>mysync</code> scalars.</p>
<p>See also: <code>-</code>, <code>+=</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>*=</code></h3>
<p><strong>Multiply-assign.</strong> <code>$x *= $y</code> ≡ <code>$x = $x * $y</code>.</p>
<p>See also: <code>*</code>, <code>**=</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>/=</code></h3>
<p><strong>Divide-assign.</strong> <code>$x /= $y</code> ≡ <code>$x = $x / $y</code>.</p>
<p>See also: <code>/</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>**=</code></h3>
<p><strong>Power-assign.</strong> <code>$x **= $y</code> ≡ <code>$x = $x ** $y</code>.</p>
<p>See also: <code>**</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>.=</code></h3>
<p><strong>Append-assign</strong> (string concat). <code>$s .= $more</code> ≡ <code>$s = $s . $more</code> but more efficient for large-string accumulators (single buffer growth, not realloc per concat). Atomic on <code>mysync</code> scalars.</p>
<pre><code class="lang-perl">my $buf = ""
$buf .= $line for @lines
mysync $log = ""; fan 100 { $log .= "event\n" } # atomic
</code></pre>
<p>See also: <code>.</code>, <code>+=</code>.</p>
</article>
<article class="doc-entry" id="doc-x">
<h3><a class="doc-anchor" href="#doc-x">#</a> <code>x=</code></h3>
<p><strong>Repeat-assign</strong> (string). <code>$s x= 3</code> ≡ <code>$s = $s x 3</code>.</p>
<pre><code class="lang-perl">my $bar = "="; $bar x= 40 # forty equals signs
</code></pre>
<p>See also: <code>x</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>||=</code></h3>
<p><strong>Or-assign.</strong> <code>$x ||= $default</code> ≡ <code>$x = $x || $default</code> — assigns the default only if <code>$x</code> is falsy. Watch out for legitimate falsy values like <code>0</code> and <code>""</code>; prefer <code>//=</code> for those.</p>
<pre><code class="lang-perl">$opts{verbose} ||= 0
$cache{$key} ||= compute($key) # but: returns wrong thing if 0 is valid
</code></pre>
<p>See also: <code>||</code>, <code>//=</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>//=</code></h3>
<p><strong>Defined-or assign.</strong> <code>$x //= $default</code> ≡ <code>$x = $x // $default</code> — assigns the default only if <code>$x</code> is <code>undef</code>. The right tool for memoization/cache-fill patterns.</p>
<pre><code class="lang-perl">$cache{$key} //= expensive_compute($key)
$count{$word} //= 0; $count{$word}++
</code></pre>
<p>See also: <code>//</code>, <code>||=</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>&&=</code></h3>
<p><strong>And-assign.</strong> <code>$x &&= $val</code> ≡ <code>$x = $x && $val</code> — assigns <code>$val</code> only if <code>$x</code> is truthy. Rare.</p>
<p>See also: <code>&&</code>, <code>||=</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>|=</code></h3>
<p><strong>Bitwise OR-assign.</strong> <code>$x |= 0x80</code> sets a bit. Atomic on <code>mysync</code> scalars.</p>
<p>See also: <code>|</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>&=</code></h3>
<p><strong>Bitwise AND-assign.</strong> <code>$x &= 0xFF</code> masks to low byte.</p>
<p>See also: <code>&</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>^=</code></h3>
<p><strong>Bitwise XOR-assign.</strong> <code>$x ^= $bit</code> toggles bits.</p>
<p>See also: <code>^</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code><<=</code></h3>
<p><strong>Left-shift assign.</strong> <code>$x <<= 3</code> ≡ multiply by 8.</p>
<p>See also: <code><<</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>>>=</code></h3>
<p><strong>Right-shift assign.</strong> <code>$x >>= 3</code> ≡ integer-divide by 8.</p>
<p>See also: <code>>></code>.</p>
</article>
</section>
<section class="tutorial-section" id="ch-stryke-extensions">
<h2>stryke Extensions</h2>
<p class="chapter-meta">19 topics</p>
<article class="doc-entry" id="doc-fn">
<h3><a class="doc-anchor" href="#doc-fn">#</a> <code>fn</code></h3>
<p>Define a named or anonymous function with optional typed parameters and default values. Named functions are installed into the current package; anonymous functions (closures) capture their enclosing lexical scope. Functions are first-class values — assign them to scalars, store in arrays, pass as callbacks. The last expression evaluated is the implicit return value unless an explicit <code>return</code> is used.</p>
<pre><code class="lang-perl">fn dbl($x) { $x * 2 }
my $f = fn { _ * 2 }
my $add = fn ($a: Int, $b: Int) { $a + $b }
# Default parameter values:
fn greet($name = "world") { p "hello $name" }
greet() # hello world
greet("Alice") # hello Alice
fn range_check($x, $min = 0, $max = 100) { $min <= $x <= $max }
fn with_list(@items = (1, 2, 3)) { join "-", @items }
fn with_hash(%opts = (debug => 0)) { $opts{debug} }
</code></pre>
<p>Default values are evaluated at call time if the argument is not provided.</p>
</article>
<article class="doc-entry" id="doc-struct">
<h3><a class="doc-anchor" href="#doc-struct">#</a> <code>struct</code></h3>
<p><code>struct</code> declares a named record type with typed fields, giving stryke lightweight struct semantics similar to Rust structs or Python dataclasses. Structs support multiple construction syntaxes, default values, field mutation, user-defined methods, functional updates, and structural equality.</p>
<p><strong>Declaration:</strong></p>
<pre><code class="lang-perl">struct Point { x => Float, y => Float } # typed fields
struct Point { x => Float = 0.0, y => Float = 0.0 } # with defaults
struct Pair { key, value } # untyped (Any)
</code></pre>
<p><strong>Construction:</strong></p>
<pre><code class="lang-perl">my $p = Point(x => 1.5, y => 2.0) # function-call with named args
my $p = Point(1.5, 2.0) # positional (declaration order)
my $p = Point->new(x => 1.5, y => 2.0) # traditional OO style
my $p = Point() # uses defaults if defined
</code></pre>
<p><strong>Field access (getter/setter):</strong></p>
<pre><code class="lang-perl">p $p->x # getter (0 args)
$p->x(3.0) # setter (1 arg)
</code></pre>
<p><strong>User-defined methods:</strong></p>
<pre><code class="lang-perl">struct Circle {
radius => Float,
fn area { 3.14159 * $self->radius ** 2 }
fn scale($factor: Float) {
Circle(radius => $self->radius * $factor)
}
}
my $c = Circle(radius => 5)
p $c->area # 78.53975
p $c->scale(2) # Circle(radius => 10)
</code></pre>
<p><strong>Built-in methods:</strong></p>
<pre><code class="lang-perl">my $q = $p->with(x => 5) # functional update — new instance
my $h = $p->to_hash # { x => 1.5, y => 2.0 }
my @f = $p->fields # (x, y)
my $c = $p->clone # deep copy
</code></pre>
<p><strong>Smart stringify:</strong></p>
<pre><code class="lang-perl">p $p # Point(x => 1.5, y => 2)
</code></pre>
<p><strong>Structural equality:</strong></p>
<pre><code class="lang-perl">my $a = Point(1, 2)
my $b = Point(1, 2)
p $a == $b # 1 (compares all fields)
</code></pre>
<p>Note: field type is checked at construction and mutation; unknown field names are fatal errors.</p>
</article>
<article class="doc-entry" id="doc-typed">
<h3><a class="doc-anchor" href="#doc-typed">#</a> <code>typed</code></h3>
<p><code>typed</code> adds optional runtime type annotations to lexical variables and subroutine parameters. When a <code>typed</code> declaration is in effect, stryke inserts a lightweight check at assignment time that verifies the value matches the declared type (<code>Int</code>, <code>Str</code>, <code>Float</code>, <code>Bool</code>, <code>ArrayRef</code>, <code>HashRef</code>, or a user-defined <code>struct</code> name). This is especially useful for catching accidental type mismatches at function boundaries in larger programs. The annotation is purely a runtime guard — it has zero impact on pipeline performance because the check is only performed once at the point of assignment, not on every read.</p>
<pre><code class="lang-perl">typed my $x : Int = 42
typed my $name : Str = "hello"
typed my $pi : Float = 3.14
my $add = fn ($a: Int, $b: Int) { $a + $b }
p $add->(3, 4) # 7
</code></pre>
<p>Note: assigning a value of the wrong type raises a runtime exception immediately.</p>
<p>You can mix typed and untyped variables freely in the same scope, so adopting <code>typed</code> is incremental — annotate the variables that matter and leave the rest dynamic. Subroutine parameters declared with type annotations in <code>fn</code> are checked on every call, giving you contract-style validation at function boundaries without a separate assertion library.</p>
<pre><code class="lang-perl">typed my @nums : Int = (1, 2, 3)
typed my %cfg : Str = (host => "localhost", port => "8080")
</code></pre>
</article>
<article class="doc-entry" id="doc-match">
<h3><a class="doc-anchor" href="#doc-match">#</a> <code>match</code></h3>
<p>Algebraic pattern matching (stryke extension).</p>
<pre><code class="lang-perl">match ($val) {
/^\d+$/ => p "number: $val",
[1, 2, _] => p "array starting with 1,2",
{ name => $n } => p "name is $n",
_ => p "default",
}
</code></pre>
<p>Patterns: regex, array, hash, literal, wildcard <code>_</code>. Optional <code>if</code> guard per arm.</p>
</article>
<article class="doc-entry" id="doc-frozen">
<h3><a class="doc-anchor" href="#doc-frozen">#</a> <code>frozen</code></h3>
<p>Declare an immutable lexical variable. <code>const my</code> and <code>frozen my</code> are interchangeable spellings; <code>const</code> reads more naturally for engineers coming from other languages.</p>
<pre><code class="lang-perl">const my $pi = 3.14159
# $pi = 3 # ERROR: cannot assign to frozen variable
frozen my @primes = (2, 3, 5, 7, 11)
</code></pre>
</article>
<article class="doc-entry" id="doc-fore">
<h3><a class="doc-anchor" href="#doc-fore">#</a> <code>fore</code></h3>
<p>Side-effect-only list iterator (like <code>map</code> but void, returns item count).</p>
<pre><code class="lang-perl">qw(a b c) |> e p # prints a, b, c; returns 3
1:5 |> map _ * 2 |> e p # prints 2,4,6,8,10
</code></pre>
</article>
<article class="doc-entry" id="doc-ep">
<h3><a class="doc-anchor" href="#doc-ep">#</a> <code>ep</code></h3>
<p><code>ep</code> — shorthand for <code>e { p }</code> (foreach + print). Iterates the list and prints each element.</p>
<pre><code class="lang-perl">qw(a b c) |> ep # prints a, b, c (one per line)
filef |> sorted |> ep # print sorted file list
1:5 |> map _ * 2 |> ep # prints 2,4,6,8,10
</code></pre>
</article>
<article class="doc-entry" id="doc-p">
<h3><a class="doc-anchor" href="#doc-p">#</a> <code>p</code></h3>
<p><code>p</code> — alias for <code>say</code> (print with newline).</p>
<pre><code class="lang-perl">p "hello" # hello\n
p 42 # 42\n
1:5 |> e p # prints each on its own line
</code></pre>
</article>
<article class="doc-entry" id="doc-gen">
<h3><a class="doc-anchor" href="#doc-gen">#</a> <code>gen</code></h3>
<p>Create a generator — lazy <code>yield</code> values on demand.</p>
<pre><code class="lang-perl">my $g = gen { yield _ for 1:5 }
my ($val, $more) = @{$g->next}
</code></pre>
</article>
<article class="doc-entry" id="doc-yield">
<h3><a class="doc-anchor" href="#doc-yield">#</a> <code>yield</code></h3>
<p>Yield a value from inside a <code>gen { }</code> generator block, suspending the generator until the consumer calls <code>->next</code> again. Each <code>yield</code> produces one element in the lazy sequence. When the block finishes without yielding, the generator signals exhaustion. This is the stryke equivalent of Python's <code>yield</code> or Rust's <code>Iterator::next</code>.</p>
<pre><code class="lang-perl">my $fib = gen {
my ($a, $b) = (0, 1)
while (1) {
yield $a
($a, $b) = ($b, $a + $b)
}
}
for (1:10) {
my ($val) = @{$fib->next}
p $val
}
</code></pre>
</article>
<article class="doc-entry" id="doc-trace">
<h3><a class="doc-anchor" href="#doc-trace">#</a> <code>trace</code></h3>
<p>Trace <code>mysync</code> mutations to stderr (tagged with worker index under <code>fan</code>).</p>
<pre><code class="lang-perl">trace { fan 10 { $counter++ } }
</code></pre>
</article>
<article class="doc-entry" id="doc-timer">
<h3><a class="doc-anchor" href="#doc-timer">#</a> <code>timer</code></h3>
<p>Measure wall-clock milliseconds for a block.</p>
<pre><code class="lang-perl">my $ms = timer { heavy_work() }
</code></pre>
</article>
<article class="doc-entry" id="doc-bench">
<h3><a class="doc-anchor" href="#doc-bench">#</a> <code>bench</code></h3>
<p>Benchmark a block N times; returns <code>"min/mean/p99"</code>.</p>
<pre><code class="lang-perl">my $report = bench { work() } 1000
</code></pre>
</article>
<article class="doc-entry" id="doc-eval-timeout">
<h3><a class="doc-anchor" href="#doc-eval-timeout">#</a> <code>eval_timeout</code></h3>
<p>Run a block with a wall-clock timeout (seconds).</p>
<pre><code class="lang-perl">eval_timeout 5 { slow_operation() }
</code></pre>
</article>
<article class="doc-entry" id="doc-retry">
<h3><a class="doc-anchor" href="#doc-retry">#</a> <code>retry</code></h3>
<p>Retry a block on failure.</p>
<pre><code class="lang-perl">retry { http_call() } times => 3, backoff => 'exponential'
</code></pre>
</article>
<article class="doc-entry" id="doc-rate-limit">
<h3><a class="doc-anchor" href="#doc-rate-limit">#</a> <code>rate_limit</code></h3>
<p>Limit invocations per time window.</p>
<pre><code class="lang-perl">rate_limit(10, "1s") { hit_api() }
</code></pre>
</article>
<article class="doc-entry" id="doc-every">
<h3><a class="doc-anchor" href="#doc-every">#</a> <code>every</code></h3>
<p>Run a block at a fixed interval.</p>
<pre><code class="lang-perl">every "500ms" { tick() }
</code></pre>
</article>
<article class="doc-entry" id="doc-watch">
<h3><a class="doc-anchor" href="#doc-watch">#</a> <code>watch</code></h3>
<p>Watch a single file for changes (non-parallel).</p>
<pre><code class="lang-perl">watch "/tmp/x", fn { process }
</code></pre>
</article>
<article class="doc-entry" id="doc-capture">
<h3><a class="doc-anchor" href="#doc-capture">#</a> <code>capture</code></h3>
<p>Run a command and capture structured output. Returns an object with <code>->stdout</code>, <code>->stderr</code>, <code>->exitcode</code>, and <code>->failed</code> methods. When piped to <code>lines</code> or <code>words</code>, stdout is auto-extracted so you can chain directly.</p>
<pre><code class="lang-perl">my $r = capture("ls -la")
p $r->stdout, $r->stderr, $r->exitcode
capture("ps aux") |> lines |> map { columns } |> tbl |> p
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-data-serialization">
<h2>Data & Serialization</h2>
<p class="chapter-meta">45 topics</p>
<article class="doc-entry" id="doc-json-encode">
<h3><a class="doc-anchor" href="#doc-json-encode">#</a> <code>json_encode</code></h3>
<p><code>json_encode</code> serializes any stryke data structure — hashrefs, arrayrefs, nested combinations, numbers, strings, booleans, and undef — into a compact JSON string. Native bare-name builtin backed by a Rust serializer; no module to import. The output is always valid UTF-8 JSON suitable for writing to files, sending over HTTP, or piping to other tools. Use <code>json_decode</code> to round-trip back.</p>
<pre><code class="lang-perl">my %cfg = (debug => 1, paths => ["/tmp", "/var"])
my $j = json_encode(\%cfg)
p $j # {"debug":1,"paths":["/tmp","/var"]}
$j |> spurt "/tmp/cfg.json"$1
Note: undef becomes JSON `null`; booleans serialize as `true`/`false`.
</code></pre>
</article>
<article class="doc-entry" id="doc-json-decode">
<h3><a class="doc-anchor" href="#doc-json-decode">#</a> <code>json_decode</code></h3>
<p><code>json_decode</code> parses a JSON string and returns the corresponding Perl data structure — hashrefs for objects, arrayrefs for arrays, and native scalars for strings/numbers/booleans. It is strict by default: malformed JSON raises an exception rather than returning partial data. This makes it safe to use in pipelines where corrupt input should halt processing. The Rust parser underneath handles large documents efficiently and supports full Unicode.</p>
<pre><code class="lang-perl">my $data = json_decode('{"name":"stryke","ver":1}')
p $data->{name} # stryke
slurp("data.json") |> json_decode |> dd$1
Note: JSON `null` becomes Perl `undef`; trailing commas and comments are not allowed.
</code></pre>
</article>
<article class="doc-entry" id="doc-json-jq">
<h3><a class="doc-anchor" href="#doc-json-jq">#</a> <code>json_jq</code></h3>
<p><code>json_jq</code> applies a jq-style query expression to a stryke data structure and returns the matched value. This brings the power of the <code>jq</code> command-line JSON processor directly into stryke without shelling out. Dot notation traverses hash keys, bracket notation indexes arrays, and nested paths are separated by dots. It is ideal for extracting deeply nested values from API responses or config files without chains of hash dereferences.</p>
<pre><code class="lang-perl">my $data = json_decode(slurp "api.json")
p json_jq($data, ".results[0].name")
my $cfg = rj "config.json"
p json_jq($cfg, ".database.host") # deep extract
fetch_json("https://api.example.com/users") |> json_jq(".data[0].email") |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-to-json">
<h3><a class="doc-anchor" href="#doc-to-json">#</a> <code>to_json</code></h3>
<p><code>to_json</code> (alias <code>tj</code>) converts a stryke data structure into a JSON string, functioning as a convenient shorthand for <code>json_encode</code>. It accepts hashrefs, arrayrefs, scalars, and nested combinations, producing compact JSON output suitable for APIs, config files, or inter-process communication. The alias <code>tj</code> is particularly useful at the end of a pipeline to serialize the final result. The Rust-backed serializer handles large structures efficiently and always produces valid UTF-8.</p>
<pre><code class="lang-perl">my %user = (name => "Bob", age => 30)
p tj \%user # {"age":30,"name":"Bob"}
my @items = map { {id => _, val => _ * 2} } 1:3
p tj \@items # [{"id":1,"val":2},{"id":2,"val":4},{"id":3,"val":6}]
@data |> tj |> spurt "out.json"
</code></pre>
</article>
<article class="doc-entry" id="doc-to-csv">
<h3><a class="doc-anchor" href="#doc-to-csv">#</a> <code>to_csv</code></h3>
<p><code>to_csv</code> (alias <code>tc</code>) serializes a list of hashrefs or arrayrefs into a CSV-formatted string, complete with a header row derived from hash keys when given hashrefs. This is the fastest way to produce spreadsheet-ready output from structured data. Fields containing commas, quotes, or newlines are automatically escaped according to RFC 4180. The alias <code>tc</code> keeps one-liners terse when piping query results or API responses straight to CSV.</p>
<pre><code class="lang-perl">my @rows = ({name => "Alice", age => 30}, {name => "Bob", age => 25})
p tc \@rows # name,age\nAlice,30\nBob,25
tc(\@rows) |> spurt "people.csv"
my @grid = ([1, 2, 3], [4, 5, 6])
p tc \@grid # 1,2,3\n4,5,6
</code></pre>
</article>
<article class="doc-entry" id="doc-to-toml">
<h3><a class="doc-anchor" href="#doc-to-toml">#</a> <code>to_toml</code></h3>
<p><code>to_toml</code> (alias <code>tt</code>) serializes a stryke hashref into a TOML-formatted string. TOML is a popular configuration format that maps cleanly to hash structures, making <code>tt</code> ideal for generating config files programmatically. Nested hashes become TOML sections, arrays become TOML arrays, and scalar values are serialized with their natural types. The output is always valid TOML that can be parsed back with <code>toml_decode</code>.</p>
<pre><code class="lang-perl">my %cfg = (database => {host => "localhost", port => 5432}, debug => 1)
p tt \%cfg
# [database]
# host = "localhost"
# port = 5432
# debug = 1
tt(\%cfg) |> spurt "config.toml"
</code></pre>
</article>
<article class="doc-entry" id="doc-to-yaml">
<h3><a class="doc-anchor" href="#doc-to-yaml">#</a> <code>to_yaml</code></h3>
<p><code>to_yaml</code> (alias <code>ty</code>) serializes a stryke data structure into a YAML-formatted string. YAML is widely used for configuration and data exchange where human readability matters. Nested structures are represented with indentation, arrays with leading dashes, and strings are quoted only when necessary. The output is valid YAML 1.2 that round-trips cleanly through <code>yaml_decode</code>. The alias <code>ty</code> is convenient for quick inspection of complex data.</p>
<pre><code class="lang-perl">my %app = (name => "myapp", deps => ["tokio", "serde"], version => "1.0")
p ty \%app
# name: myapp
# version: "1.0"
# deps:
# - tokio
# - serde
ty(\%app) |> spurt "app.yaml"
</code></pre>
</article>
<article class="doc-entry" id="doc-to-xml">
<h3><a class="doc-anchor" href="#doc-to-xml">#</a> <code>to_xml</code></h3>
<p><code>to_xml</code> (alias <code>tx</code>) serializes a stryke data structure into an XML string. Hash keys become element names, array values become repeated child elements, and scalar values become text content. This is useful for generating XML payloads for SOAP APIs, RSS feeds, or configuration files that require XML format. The output is well-formed XML that can be parsed back with <code>xml_decode</code>.</p>
<pre><code class="lang-perl">my %doc = (root => {title => "Hello", items => ["a", "b", "c"]})
p tx \%doc
# <root><title>Hello</title><items>a</items><items>b</items><items>c</items></root>
tx(\%doc) |> spurt "doc.xml"
</code></pre>
</article>
<article class="doc-entry" id="doc-to-html">
<h3><a class="doc-anchor" href="#doc-to-html">#</a> <code>to_html</code></h3>
<p><code>to_html</code> (alias <code>th</code>) serializes a stryke data structure into a self-contained HTML document with cyberpunk styling (dark background, neon cyan/magenta accents, monospace fonts). Arrays of hashrefs render as full tables with headers, plain arrays as bullet lists, single hashes as key-value tables, and scalars as styled text blocks. Pipe to a file and open in a browser for instant data visualization.</p>
<pre><code class="lang-perl">fr |> map +{name => _, size => format_bytes(size)} |> th |> to_file("report.html")
my @rows = ({name => "Alice", age => 30}, {name => "Bob", age => 25})
@rows |> th |> to_file("people.html")
th({host => "localhost", port => 5432}) |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-to-markdown">
<h3><a class="doc-anchor" href="#doc-to-markdown">#</a> <code>to_markdown</code></h3>
<p><code>to_markdown</code> (aliases <code>to_md</code>, <code>tmd</code>) serializes a stryke data structure into Markdown text. Arrays of hashrefs render as GFM tables with headers and separator rows, plain arrays as bullet lists, single hashes as 2-column key-value tables, and scalars as plain text. The output is valid GitHub-Flavored Markdown suitable for README files, issue comments, or any Markdown renderer.</p>
<pre><code class="lang-perl">fr |> map +{name => _, size => format_bytes(size)} |> tmd |> to_file("report.md")
my @rows = ({name => "Alice", age => 30}, {name => "Bob", age => 25})
@rows |> tmd |> p
# | name | age |
# | --- | --- |
# | Alice | 30 |
# | Bob | 25 |
</code></pre>
</article>
<article class="doc-entry" id="doc-from-json">
<h3><a class="doc-anchor" href="#doc-from-json">#</a> <code>from_json</code></h3>
<p><code>from_json</code> (alias <code>fj</code>) parses a JSON string into a stryke data structure (hashref, arrayref, scalar). This is the inverse of <code>to_json</code> and the idiomatic way to decode JSON responses from APIs, config files, or inter-process communication. The Rust-backed parser handles large documents efficiently.</p>
<pre><code class="lang-perl">my $json = '{"name":"Alice","age":30}'
my $data = from_json($json)
p $data->{name} # Alice
my $arr = fj '[1, 2, {"x": 3}]'
p $arr->[2]{x} # 3
slurp("config.json") |> fj
</code></pre>
</article>
<article class="doc-entry" id="doc-from-yaml">
<h3><a class="doc-anchor" href="#doc-from-yaml">#</a> <code>from_yaml</code></h3>
<p><code>from_yaml</code> (alias <code>fy</code>) parses a YAML string into a stryke data structure. YAML is commonly used for configuration files due to its human-readable syntax. Handles scalars, arrays, hashes, and nested combinations. The parser supports common YAML features like multi-line strings and bare unquoted keys.</p>
<pre><code class="lang-perl">my $yaml = "name: Alice\nage: 30"
my $data = from_yaml($yaml)
p $data->{name} # Alice
slurp("config.yaml") |> fy |> say _->{database}{host}
</code></pre>
</article>
<article class="doc-entry" id="doc-from-toml">
<h3><a class="doc-anchor" href="#doc-from-toml">#</a> <code>from_toml</code></h3>
<p><code>from_toml</code> (alias <code>ftoml</code>) parses a TOML string into a stryke hashref. TOML is popular for Rust, Python, and other config files due to its explicit syntax. Sections become nested hashes, arrays stay arrays, and typed values (integers, floats, strings, booleans) are preserved.</p>
<pre><code class="lang-perl">my $toml = "[package]\nname = \"myapp\"\nversion = \"1.0\""
my $data = from_toml($toml)
p $data->{package}{name} # myapp
slurp("Cargo.toml") |> ftoml |> say _->{package}{version}
</code></pre>
</article>
<article class="doc-entry" id="doc-from-xml">
<h3><a class="doc-anchor" href="#doc-from-xml">#</a> <code>from_xml</code></h3>
<p><code>from_xml</code> (alias <code>fx</code>) parses an XML string into a stryke hashref. Element names become hash keys, text content becomes string values, nested elements become nested hashes. The parser handles the XML declaration and basic structures.</p>
<pre><code class="lang-perl">my $xml = '<root><name>Alice</name><age>30</age></root>'
my $data = from_xml($xml)
p $data->{root}{name} # Alice
slurp("config.xml") |> fx |> say _->{config}{database}{host}
</code></pre>
</article>
<article class="doc-entry" id="doc-from-csv">
<h3><a class="doc-anchor" href="#doc-from-csv">#</a> <code>from_csv</code></h3>
<p><code>from_csv</code> (alias <code>fcsv</code>) parses a CSV string into an arrayref of hashrefs, treating the first line as headers. This is the inverse of <code>to_csv</code> and handles quoted fields containing commas according to RFC 4180.</p>
<pre><code class="lang-perl">my $csv = "name,age\nAlice,30\nBob,25"
my $rows = from_csv($csv)
p $rows->[0]{name} # Alice
p $rows->[1]{age} # 25
slurp("data.csv") |> fcsv |> grep { _->{age} > 25 }
</code></pre>
</article>
<article class="doc-entry" id="doc-xopen">
<h3><a class="doc-anchor" href="#doc-xopen">#</a> <code>xopen</code></h3>
<p><code>xopen</code> (alias <code>xo</code>) opens a file or URL with the system default handler — <code>open</code> on macOS, <code>xdg-open</code> on Linux, <code>start</code> on Windows. Returns the path unchanged so it can sit transparently in a pipeline. This is the missing link between generating output files and viewing them: pipe the path through <code>xopen</code> and the OS opens it in the appropriate app (browser for HTML, viewer for PDF, editor for text).</p>
<pre><code class="lang-perl">fr |> map +{name => _, size => format_bytes(size)} |> th |> to_file("report.html") |> xopen
xopen "https://example.com"
xopen "output.pdf"
</code></pre>
</article>
<article class="doc-entry" id="doc-clip">
<h3><a class="doc-anchor" href="#doc-clip">#</a> <code>clip</code></h3>
<p><code>clip</code> (aliases <code>clipboard</code>, <code>pbcopy</code>) copies text to the system clipboard (<code>pbcopy</code> on macOS, <code>xclip</code>/<code>xsel</code> on Linux). Returns the text unchanged for pipeline chaining. This is the missing link between generating output and sharing it — pipe any serializer's output through <code>clip</code> and paste directly into Slack, GitHub, docs, or email.</p>
<pre><code class="lang-perl">fr |> map +{name => _, size => format_bytes(size)} |> tmd |> clip # markdown table → clipboard
qw(a b c) |> join "," |> clip |> p # also prints
"some text" |> clip # just copy
</code></pre>
</article>
<article class="doc-entry" id="doc-paste">
<h3><a class="doc-anchor" href="#doc-paste">#</a> <code>paste</code></h3>
<p><code>paste</code> (alias <code>pbpaste</code>) reads text from the system clipboard (<code>pbpaste</code> on macOS, <code>xclip</code>/<code>xsel</code> on Linux). Returns the clipboard contents as a string, ready for pipeline processing.</p>
<pre><code class="lang-perl">p paste # print clipboard contents
paste |> lines |> grep /error/i |> p # search clipboard for errors
paste |> wc |> p # word count of clipboard
</code></pre>
</article>
<article class="doc-entry" id="doc-to-table">
<h3><a class="doc-anchor" href="#doc-to-table">#</a> <code>to_table</code></h3>
<p><code>to_table</code> (aliases <code>table</code>, <code>tbl</code>) renders data as a plain-text column-aligned table with Unicode box-drawing borders. Arrays of hashrefs render as full tables with headers, plain arrays as numbered rows, single hashes as key-value tables sorted by numeric value descending (ties by key), matching <code>freq</code> → <code>tbl</code> expectations. The output is fixed-width text suitable for terminal display, log files, or any monospace context.</p>
<pre><code class="lang-perl">my @r = ({name => "Alice", age => 30}, {name => "Bob", age => 25})
@r |> tbl |> p
# ┌───────┬─────┐
# │ name │ age │
# ├───────┼─────┤
# │ Alice │ 30 │
# │ Bob │ 25 │
# └───────┴─────┘
fr |> map +{name => _, size => format_bytes(size)} |> tbl |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-sparkline">
<h3><a class="doc-anchor" href="#doc-sparkline">#</a> <code>sparkline</code></h3>
<p><code>sparkline</code> (alias <code>spark</code>) renders a list of numbers as a compact Unicode sparkline string using block characters (▁▂▃▄▅▆▇█). Each value maps to a bar height proportional to the min/max range. Ideal for inline data visualization in terminal output, dashboards, or log summaries.</p>
<pre><code class="lang-perl">(3,7,1,9,4,2,8,5) |> spark |> p # ▃▆▁█▄▂▇▅
@daily_sales |> spark |> p # quick trend line
fr |> map { size } |> spark |> p # file size distribution
</code></pre>
</article>
<article class="doc-entry" id="doc-bar-chart">
<h3><a class="doc-anchor" href="#doc-bar-chart">#</a> <code>bar_chart</code></h3>
<p><code>bar_chart</code> (alias <code>bars</code>) renders a hashref as a colored horizontal bar chart in the terminal. Each key becomes a label, each value a proportional bar. Colors cycle automatically. Pairs naturally with <code>freq</code> for instant word/event counting visualization.</p>
<pre><code class="lang-perl">qw(a b a c a b) |> freq |> bars |> p
# a │ ████████████████████████████████████████ 3
# b │ ███████████████████████████ 2
# c │ █████████████ 1
bars({cpu => 73, mem => 45, disk => 91}) |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-flame">
<h3><a class="doc-anchor" href="#doc-flame">#</a> <code>flame</code></h3>
<p><code>flame</code> (alias <code>flamechart</code>) renders a hierarchical hashref as a terminal flamechart with colored stacked bars. Nested hashes become child rows; widths are proportional to leaf values (weights). Useful for visualizing call stacks, cost breakdowns, or any tree-structured data.</p>
<pre><code class="lang-perl">flame({main => {parse => 30, eval => {compile => 15, run => 45}}, init => 10}) |> p
my $profile = read_json "profile.json"
flame($profile) |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-histo">
<h3><a class="doc-anchor" href="#doc-histo">#</a> <code>histo</code></h3>
<p><code>histo</code> renders a vertical histogram in the terminal. Given a hashref (label → count), it draws colored vertical bars. Given a flat array of numbers, it auto-bins into 10 buckets and shows the distribution. Pairs with <code>freq</code> for categorical data.</p>
<pre><code class="lang-perl">qw(a b a c a b) |> freq |> histo |> p # vertical bars for a/b/c
(map { int(rand(100)) } 1:1000) |> histo |> p # distribution of randoms
</code></pre>
</article>
<article class="doc-entry" id="doc-gauge">
<h3><a class="doc-anchor" href="#doc-gauge">#</a> <code>gauge</code></h3>
<p><code>gauge</code> renders a single value as a horizontal gauge bar with color coding (green ≥80%, yellow ≥50%, magenta ≥25%, red below). Accepts a fraction (0.0–1.0) or a value with max: <code>gauge(45, 100)</code>.</p>
<pre><code class="lang-perl">p gauge(0.73) # [██████████████████████░░░░░░░░] 73%
p gauge(45, 100) # [█████████████░░░░░░░░░░░░░░░░] 45%
</code></pre>
</article>
<article class="doc-entry" id="doc-spinner">
<h3><a class="doc-anchor" href="#doc-spinner">#</a> <code>spinner</code></h3>
<p><code>spinner</code> shows an animated braille spinner on stderr while a block executes, then clears the spinner and returns the block's result. Useful for long-running one-liners where you want visual feedback without polluting stdout.</p>
<pre><code class="lang-perl">my $r = spinner "loading" { fetch_json("https://api.example.com/data") }
spinner { sleep 2
42 } # default message "working"
</code></pre>
</article>
<article class="doc-entry" id="doc-csv-read">
<h3><a class="doc-anchor" href="#doc-csv-read">#</a> <code>csv_read</code></h3>
<p><code>csv_read</code> (alias <code>cr</code>) reads CSV data from a file path or string and returns an array of arrayrefs, where each inner arrayref represents one row. The parser handles RFC 4180 CSV correctly — quoted fields with embedded commas, newlines inside quotes, and escaped double quotes are all supported. The first row is treated as data (not a header) unless you process it separately. This is the fastest way to ingest tabular data in stryke.</p>
<pre><code class="lang-perl">my @rows = csv_read "data.csv"
p $rows[0] # first row as arrayref
@rows |> e { p _->[0] } # print first column
my @inline = csv_read "a,b,c\n1,2,3\n4,5,6"
p scalar @inline # 3 rows (including header)
</code></pre>
</article>
<article class="doc-entry" id="doc-csv-write">
<h3><a class="doc-anchor" href="#doc-csv-write">#</a> <code>csv_write</code></h3>
<p><code>csv_write</code> (alias <code>cw</code>) serializes an array of arrayrefs into a CSV-formatted string. Each inner arrayref becomes one row, and fields are automatically quoted when they contain commas, quotes, or newlines. This is the complement of <code>csv_read</code> and produces output conforming to RFC 4180. Use it to generate CSV files from computed data, export database query results, or prepare data for spreadsheet import.</p>
<pre><code class="lang-perl">my @data = (["name", "age"], ["Alice", 30], ["Bob", 25])
csv_write(\@data) |> spurt "people.csv"
my @report = map { [_->{id}, _->{score}] } @results
p csv_write \@report
</code></pre>
</article>
<article class="doc-entry" id="doc-dataframe">
<h3><a class="doc-anchor" href="#doc-dataframe">#</a> <code>dataframe</code></h3>
<p><code>dataframe</code> (alias <code>df</code>) creates a columnar dataframe from tabular data, providing a structured way to work with rows and columns. You can construct a dataframe from an array of hashrefs, an array of arrayrefs with a header row, or from a CSV file. The dataframe supports column selection, filtering, sorting, and aggregation operations. This is stryke's answer to Python's pandas DataFrame — lightweight but sufficient for common data manipulation tasks.</p>
<pre><code class="lang-perl">my $df = df [{name => "Alice", age => 30}, {name => "Bob", age => 25}]
p $df
my $df2 = df csv_read "data.csv"
my @ages = $df->{age}
p @ages # 30, 25
</code></pre>
</article>
<article class="doc-entry" id="doc-sqlite">
<h3><a class="doc-anchor" href="#doc-sqlite">#</a> <code>sqlite</code></h3>
<p><code>sqlite</code> (alias <code>sql</code>) executes a SQL statement against an SQLite database file and returns the results. For SELECT queries, it returns an array of hashrefs where each hashref represents one row with column names as keys. For INSERT, UPDATE, and DELETE statements, it returns the number of affected rows. Bind parameters prevent SQL injection and handle quoting automatically. The database file is created if it does not exist, making <code>sqlite</code> a zero-setup embedded database.</p>
<pre><code class="lang-perl">sqlite("app.db", "CREATE TABLE users (name TEXT, age INT)")
sqlite("app.db", "INSERT INTO users VALUES (?, ?)", "Alice", 30)
my @rows = sqlite("app.db", "SELECT * FROM users WHERE age > ?", 20)
@rows |> e { p _->{name} }
sqlite("app.db", "SELECT count(*) as n FROM users") |> dd
</code></pre>
</article>
<article class="doc-entry" id="doc-digits">
<h3><a class="doc-anchor" href="#doc-digits">#</a> <code>digits</code></h3>
<p><code>digits</code> (alias <code>dg</code>) extracts all digit characters from a string and returns them as a list. This is a quick way to pull numbers out of mixed text without writing a regex. Pairs naturally with <code>join</code> to reconstruct the numeric string, or <code>freq</code> for digit distribution analysis.</p>
<pre><code class="lang-perl">p join "", digits("phone: 555-1234") # 5551234
"abc123def456" |> digits |> cnt |> p # 6
cat("log.txt") |> digits |> freq |> bars |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-letters">
<h3><a class="doc-anchor" href="#doc-letters">#</a> <code>letters</code></h3>
<p><code>letters</code> (alias <code>lts</code>) extracts all alphabetic characters from a string and returns them as a list. Filters out digits, punctuation, whitespace — keeps only letters.</p>
<pre><code class="lang-perl">p join "", letters("h3ll0 w0rld!") # hllwrld
"abc123DEF" |> letters |> cnt |> p # 6
</code></pre>
</article>
<article class="doc-entry" id="doc-sentences">
<h3><a class="doc-anchor" href="#doc-sentences">#</a> <code>sentences</code></h3>
<p><code>sentences</code> (alias <code>sents</code>) splits text on sentence boundaries (<code>.</code> <code>!</code> <code>?</code> followed by whitespace or end of string). Returns a list of trimmed sentences. Useful for NLP pipelines, text analysis, or splitting prose into processable units.</p>
<pre><code class="lang-perl">"Hello world. How are you? Fine!" |> sentences |> e p
# Hello world.
# How are you?
# Fine!
cat("essay.txt") |> sentences |> cnt |> p # sentence count
</code></pre>
</article>
<article class="doc-entry" id="doc-paragraphs">
<h3><a class="doc-anchor" href="#doc-paragraphs">#</a> <code>paragraphs</code></h3>
<p><code>paragraphs</code> (alias <code>paras</code>) splits text on blank lines (one or more consecutive newlines). Returns a list of trimmed paragraph strings. Useful for processing structured documents, README files, or any text with paragraph breaks.</p>
<pre><code class="lang-perl">cat("README.md") |> paragraphs |> cnt |> p # paragraph count
cat("essay.txt") |> paragraphs |> map { sentences |> cnt } |> spark |> p # sentences per paragraph
</code></pre>
</article>
<article class="doc-entry" id="doc-sections">
<h3><a class="doc-anchor" href="#doc-sections">#</a> <code>sections</code></h3>
<p><code>sections</code> (alias <code>sects</code>) splits text on markdown-style headers (<code># ...</code>, <code>## ...</code>) or lines of <code>===</code>/<code>---</code>. Returns a list of arrayrefs <code>[heading, body]</code> where each section's heading and body are separated. Useful for parsing structured documents.</p>
<pre><code class="lang-perl">cat("README.md") |> sections |> cnt |> p # section count
cat("README.md") |> sections |> map { _->[0] } |> e p # list all headings
</code></pre>
</article>
<article class="doc-entry" id="doc-numbers">
<h3><a class="doc-anchor" href="#doc-numbers">#</a> <code>numbers</code></h3>
<p><code>numbers</code> (alias <code>nums</code>) extracts all numbers (integers and floats, including negatives) from a string and returns them as numeric values. Unlike <code>digits</code> which returns individual digit characters, <code>numbers</code> returns actual parsed values. Useful for pulling measurements, scores, or IDs out of mixed text.</p>
<pre><code class="lang-perl">p join ",", numbers("temp 98.6F, -20C, ver 3") # 98.6,-20,3
cat("log.txt") |> numbers |> avg |> p # average of all numbers in file
"price: $12.99 qty: 5" |> numbers |> e p # 12.99, 5
</code></pre>
</article>
<article class="doc-entry" id="doc-graphemes">
<h3><a class="doc-anchor" href="#doc-graphemes">#</a> <code>graphemes</code></h3>
<p><code>graphemes</code> (alias <code>grs</code>) splits a string into Unicode grapheme clusters. Unlike <code>chars</code> which splits on code points, <code>graphemes</code> keeps combining marks and emoji sequences together as single visual units. <code>"cafe\u{0301}"</code> gives 4 graphemes (not 5 code points). Essential for correct text processing of accented characters, emoji, and non-Latin scripts.</p>
<pre><code class="lang-perl">p cnt graphemes("cafe\u{0301}") # 4 (not 5)
graphemes("hello") |> e p # h, e, l, l, o
</code></pre>
</article>
<article class="doc-entry" id="doc-columns">
<h3><a class="doc-anchor" href="#doc-columns">#</a> <code>columns</code></h3>
<p><code>columns</code> (alias <code>cols</code>) splits fixed-width columnar text into fields. Without a widths argument, it auto-detects columns by splitting on runs of 2+ whitespace (ideal for <code>ps aux</code>, <code>ls -l</code>, <code>df</code> output). With an arrayref of widths, it splits at exact fixed positions. Pairs with <code>lines</code> for processing tabular command output.</p>
<pre><code class="lang-perl">my @fields = columns("USER PID %CPU") # auto-detect: [USER, PID, %CPU]
my @fixed = columns("John Doe 30", [7, 7, 3]) # fixed-width: [John, Doe, 30]
capture("ps aux") |> lines |> map { columns } |> tbl |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-stringify">
<h3><a class="doc-anchor" href="#doc-stringify">#</a> <code>stringify</code></h3>
<p><code>stringify</code> (alias <code>str</code>) converts any stryke value — scalars, array refs, hash refs, nested structures, undef — into a string representation that is a valid stryke literal. The output is designed for round-tripping: you can <code>eval</code> the returned string to reconstruct the original data structure. This makes it ideal for serializing state to a file in a Perl-native format, generating code fragments, or building reproducible test fixtures. Unlike <code>dd</code>, which targets human readability, <code>str</code> prioritizes parseability.</p>
<pre><code class="lang-perl">my $s = str {a => 1, b => [2, 3]}
p $s # {a => 1, b => [2, 3]}
my $copy = eval $s # round-trip back to hashref
my @list = (1, "hello", undef)
p str \@list # [1, "hello", undef]
</code></pre>
<p>Note: references are serialized recursively; circular references will cause infinite recursion.</p>
</article>
<article class="doc-entry" id="doc-ddump">
<h3><a class="doc-anchor" href="#doc-ddump">#</a> <code>ddump</code></h3>
<p><code>ddump</code> (alias <code>dd</code>) pretty-prints any stryke data structure to stderr in a human-readable, indented format. Native bare-name builtin — no module to import. It is the go-to tool for quick debugging — drop a <code>dd</code> call anywhere in a pipeline to inspect intermediate values without disrupting the data flow. The output is colorized when stderr is a terminal. Unlike <code>str</code>, the output is not meant for <code>eval</code> round-tripping; it prioritizes clarity over parseability. <code>dd</code> returns its argument unchanged, so it can be inserted into pipelines transparently.</p>
<pre><code class="lang-perl">my %h = (name => "Alice", scores => [98, 87, 95])
dd \%h # pretty-prints to stderr
my @result = @data |> dd |> grep { _->{active} } |> dd
dd [1, {a => 2}, [3, 4]] # nested structure
</code></pre>
<p>Note: <code>dd</code> writes to stderr, not stdout, so it never contaminates pipeline output.</p>
</article>
<article class="doc-entry" id="doc-toml-decode">
<h3><a class="doc-anchor" href="#doc-toml-decode">#</a> <code>toml_decode</code></h3>
<p><code>toml_decode</code> (alias <code>td</code>) parses a TOML-formatted string and returns the corresponding stryke hash structure. TOML sections become nested hashrefs, arrays map to arrayrefs, and typed scalars (integers, floats, booleans, datetime strings) are preserved. This is useful for reading configuration files, parsing Cargo.toml manifests, or processing any TOML input. Malformed TOML raises an exception.</p>
<pre><code class="lang-perl">my $cfg = toml_decode(slurp "config.toml")
p $cfg->{database}{host} # localhost
my $cargo = toml_decode(slurp "Cargo.toml")
p $cargo->{package}{version}
slurp("settings.toml") |> toml_decode |> dd
</code></pre>
</article>
<article class="doc-entry" id="doc-toml-encode">
<h3><a class="doc-anchor" href="#doc-toml-encode">#</a> <code>toml_encode</code></h3>
<p><code>toml_encode</code> (alias <code>te</code>) serializes a stryke hashref into a valid TOML string. Nested hashes become TOML sections with <code>[section]</code> headers, arrays become TOML arrays, and scalars are serialized with appropriate quoting. This is the inverse of <code>toml_decode</code> and is useful for generating or updating configuration files programmatically. The output is human-readable and can be written directly to a <code>.toml</code> file.</p>
<pre><code class="lang-perl">my %cfg = (server => {host => "0.0.0.0", port => 8080}, debug => 0)
toml_encode(\%cfg) |> spurt "server.toml"
my $round = toml_decode(toml_encode(\%cfg))
p $round->{server}{port} # 8080
</code></pre>
</article>
<article class="doc-entry" id="doc-yaml-decode">
<h3><a class="doc-anchor" href="#doc-yaml-decode">#</a> <code>yaml_decode</code></h3>
<p><code>yaml_decode</code> (alias <code>yd</code>) parses a YAML string and returns the corresponding stryke data structure. Mappings become hashrefs, sequences become arrayrefs, and scalars are coerced to their natural Perl types. This handles YAML 1.2 including multi-document streams, anchors/aliases, and flow notation. It is the go-to function for reading YAML configuration files, Kubernetes manifests, or CI pipeline definitions. Invalid YAML raises an exception.</p>
<pre><code class="lang-perl">my $cfg = yaml_decode(slurp "docker-compose.yml")
p $cfg->{services}{web}{image}
my $ci = yaml_decode(slurp ".github/workflows/ci.yml")
dd $ci->{jobs}
slurp("values.yaml") |> yaml_decode |> json_encode |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-yaml-encode">
<h3><a class="doc-anchor" href="#doc-yaml-encode">#</a> <code>yaml_encode</code></h3>
<p><code>yaml_encode</code> (alias <code>ye</code>) serializes a stryke data structure into a valid YAML string. Hashes become YAML mappings, arrays become sequences with dash prefixes, and scalars are quoted only when necessary for disambiguation. The output is human-readable and suitable for writing config files, generating Kubernetes resources, or producing YAML-based API payloads. It is the inverse of <code>yaml_decode</code>.</p>
<pre><code class="lang-perl">my %svc = (name => "api", replicas => 3, ports => [80, 443])
yaml_encode(\%svc) |> spurt "service.yaml"
my $round = yaml_decode(yaml_encode(\%svc))
p $round->{replicas} # 3
rj("config.json") |> yaml_encode |> p # JSON to YAML
</code></pre>
</article>
<article class="doc-entry" id="doc-xml-decode">
<h3><a class="doc-anchor" href="#doc-xml-decode">#</a> <code>xml_decode</code></h3>
<p><code>xml_decode</code> (alias <code>xd</code>) parses an XML string and returns a stryke data structure. Elements become hash keys, text content becomes scalar values, repeated child elements become arrayrefs, and attributes are accessible through a conventions-based mapping. This is useful for consuming SOAP responses, RSS feeds, SVG files, or any XML-based API. Malformed XML raises an exception rather than returning partial data.</p>
<pre><code class="lang-perl">my $doc = xml_decode('<root><name>stryke</name><ver>1</ver></root>')
p $doc->{root}{name} # stryke
slurp("feed.xml") |> xml_decode |> dd
my $svg = xml_decode(fetch("https://example.com/image.svg"))
p $svg->{svg}
</code></pre>
</article>
<article class="doc-entry" id="doc-xml-encode">
<h3><a class="doc-anchor" href="#doc-xml-encode">#</a> <code>xml_encode</code></h3>
<p><code>xml_encode</code> (alias <code>xe</code>) serializes a stryke data structure into a well-formed XML string. Hash keys become element names, scalar values become text content, and arrayrefs become repeated sibling elements. This is useful for generating XML payloads for SOAP APIs, creating RSS or Atom feeds, or producing configuration files in XML format. The output is the inverse of <code>xml_decode</code> and round-trips cleanly.</p>
<pre><code class="lang-perl">my %data = (root => {title => "Test", items => [{id => 1}, {id => 2}]})
p xml_encode \%data
xml_encode(\%data) |> spurt "output.xml"
my $payload = xml_encode {request => {action => "query", id => 42}}
http_request(method => "POST", url => $endpoint, body => $payload)
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-http-networking">
<h2>HTTP & Networking</h2>
<p class="chapter-meta">23 topics</p>
<article class="doc-entry" id="doc-fetch">
<h3><a class="doc-anchor" href="#doc-fetch">#</a> <code>fetch</code></h3>
<p><code>fetch</code> (alias <code>ft</code>) performs a blocking HTTP GET request to the given URL and returns the response body as a string. It follows redirects automatically and raises an exception on network errors or non-2xx status codes. This is the simplest way to retrieve content from the web in stryke — no need to configure a client or parse response objects. For JSON APIs, prefer <code>fetch_json</code> which additionally decodes the response.</p>
<pre><code class="lang-perl">my $html = fetch "https://example.com"
p $html
my $ip = fetch "https://api.ipify.org"
p "My IP: $ip"
fetch("https://example.com/data.txt") |> spurt "local.txt"$1
Note: for POST, PUT, DELETE, or custom headers, use `http_request` instead.
</code></pre>
</article>
<article class="doc-entry" id="doc-fetch-json">
<h3><a class="doc-anchor" href="#doc-fetch-json">#</a> <code>fetch_json</code></h3>
<p><code>fetch_json</code> (alias <code>ftj</code>) performs a blocking HTTP GET request and automatically decodes the JSON response body into a stryke data structure. This combines <code>fetch</code> and <code>json_decode</code> into a single call, which is the common case when consuming REST APIs. It raises an exception if the response is not valid JSON or the request fails. The returned value is typically a hashref or arrayref ready for immediate use.</p>
<pre><code class="lang-perl">my $data = fetch_json "https://api.github.com/repos/stryke/stryke"
p $data->{stargazers_count}
fetch_json("https://jsonplaceholder.typicode.com/todos") |> e { p _->{title} }
my $weather = fetch_json "https://wttr.in/?format=j1"
p $weather->{current_condition}[0]{temp_C}
</code></pre>
</article>
<article class="doc-entry" id="doc-fetch-async">
<h3><a class="doc-anchor" href="#doc-fetch-async">#</a> <code>fetch_async</code></h3>
<p><code>fetch_async</code> (alias <code>fta</code>) initiates a non-blocking HTTP GET request and returns a task handle that can be awaited later. This allows you to fire off multiple HTTP requests concurrently and wait for them all to complete, dramatically reducing total latency when fetching from several endpoints. The task resolves to the response body as a string, just like <code>fetch</code>. Use this when you need to parallelize network I/O without threads.</p>
<pre><code class="lang-perl">my $t1 = fetch_async "https://api.example.com/users"
my $t2 = fetch_async "https://api.example.com/posts"
my $users = await $t1
my $posts = await $t2
p "Got users and posts concurrently"
</code></pre>
</article>
<article class="doc-entry" id="doc-fetch-async-json">
<h3><a class="doc-anchor" href="#doc-fetch-async-json">#</a> <code>fetch_async_json</code></h3>
<p><code>fetch_async_json</code> (alias <code>ftaj</code>) initiates a non-blocking HTTP GET request that automatically decodes the JSON response when awaited. This combines <code>fetch_async</code> with <code>json_decode</code>, making it the ideal choice for concurrent API calls where every response is JSON. The task resolves to the decoded stryke data structure — a hashref, arrayref, or scalar depending on the JSON content.</p>
<pre><code class="lang-perl">my @urls = map { "https://api.example.com/item/$_" } 1:10
my @tasks = map fetch_async_json @urls
my @results = map await @tasks
@results |> e { p _->{name} }
</code></pre>
</article>
<article class="doc-entry" id="doc-http-request">
<h3><a class="doc-anchor" href="#doc-http-request">#</a> <code>http_request</code></h3>
<p><code>http_request</code> (alias <code>hr</code>) performs a fully configurable HTTP request with control over method, headers, body, and timeout. Unlike <code>fetch</code> which is limited to GET, <code>http_request</code> supports POST, PUT, PATCH, DELETE, and any other HTTP method. Pass named parameters for configuration. The response is returned as a hashref containing <code>status</code>, <code>headers</code>, and <code>body</code> fields, giving you full access to the HTTP response. This is the right tool when you need to send data, set authentication headers, or inspect status codes.</p>
<pre><code class="lang-perl">my $res = http_request(method => "POST", url => "https://api.example.com/users",
headers => {"Content-Type" => "application/json", Authorization => "Bearer $token"},
body => tj {name => "Alice"})
p $res->{status} # 201
my $data = json_decode $res->{body}
my $del = http_request(method => "DELETE", url => "https://api.example.com/users/42")
</code></pre>
</article>
<article class="doc-entry" id="doc-par-fetch">
<h3><a class="doc-anchor" href="#doc-par-fetch">#</a> <code>par_fetch</code></h3>
<p><code>par_fetch @urls</code> — fetch a list of URLs in parallel using async HTTP, returning an array of response bodies in input order.</p>
<p>Under the hood, stryke spawns concurrent HTTP GET requests across a connection pool with keep-alive and automatic retry on transient failures (5xx, timeouts). The degree of parallelism is bounded by the connection pool size (default 64) to avoid overwhelming the target server. For heterogeneous HTTP methods or custom headers, use <code>http_request</code> inside <code>pmap</code> instead. <code>par_fetch</code> is the right tool when you have a homogeneous list of URLs and just need the bodies — it handles connection reuse, DNS caching, and TLS session resumption automatically for maximum throughput.</p>
<pre><code class="lang-perl">my @bodies = par_fetch @urls
# Fetch and decode JSON in one shot:
my @data = par_fetch(@api_urls) |> map json_decode
# Download pages with progress:
my @pages = par_fetch @urls, progress => 1
</code></pre>
</article>
<article class="doc-entry" id="doc-serve">
<h3><a class="doc-anchor" href="#doc-serve">#</a> <code>serve</code></h3>
<p>Start a blocking HTTP server.</p>
<pre><code class="lang-perl">serve 8080, fn ($req) {
# $req = { method, path, query, headers, body, peer }
{ status => 200, body => "hello" }
}
serve 3000, fn ($req) {
my $data = { name => "stryke", version => "0.4" }
{ status => 200, body => json_encode($data) }
}, { workers => 8 }$1
Handler returns: hashref `{ status, body, headers }`, string (200 OK), or undef (404).
JSON content-type auto-detected when body starts with `{` or `[`.
</code></pre>
</article>
<article class="doc-entry" id="doc-socket">
<h3><a class="doc-anchor" href="#doc-socket">#</a> <code>socket</code></h3>
<p>Create a network socket with the specified domain, type, and protocol. The socket handle is stored in the first argument and can then be used with <code>bind</code>, <code>connect</code>, <code>send</code>, <code>recv</code>, and other socket operations. Domain constants include <code>AF_INET</code> (IPv4) and <code>AF_INET6</code> (IPv6); type constants include <code>SOCK_STREAM</code> (TCP) and <code>SOCK_DGRAM</code> (UDP).</p>
<pre><code class="lang-perl">socket(my $sock, AF_INET, SOCK_STREAM, 0)
my $addr = sockaddr_in(8080, inet_aton("127.0.0.1"))
connect($sock, $addr)
send($sock, "GET / HTTP/1.0\r\n\r\n", 0)
</code></pre>
</article>
<article class="doc-entry" id="doc-bind">
<h3><a class="doc-anchor" href="#doc-bind">#</a> <code>bind</code></h3>
<p>Bind a socket to a local address so it can accept connections or receive datagrams on that address. The address is a packed <code>sockaddr_in</code> or <code>sockaddr_in6</code> structure. Binding is required before calling <code>listen</code> on a server socket. Dies if the address is already in use unless <code>SO_REUSEADDR</code> is set.</p>
<pre><code class="lang-perl">socket(my $srv, AF_INET, SOCK_STREAM, 0)
setsockopt($srv, SOL_SOCKET, SO_REUSEADDR, 1)
bind($srv, sockaddr_in(8080, INADDR_ANY)) or die "bind: $!"
listen($srv, 5)
</code></pre>
</article>
<article class="doc-entry" id="doc-listen">
<h3><a class="doc-anchor" href="#doc-listen">#</a> <code>listen</code></h3>
<p>Mark a bound socket as passive, ready to accept incoming connections. The backlog argument specifies the maximum number of pending connections the OS will queue before refusing new ones. This is only meaningful for stream (TCP) sockets. Call <code>accept</code> in a loop after <code>listen</code> to handle clients.</p>
<pre><code class="lang-perl">socket(my $srv, AF_INET, SOCK_STREAM, 0)
bind($srv, sockaddr_in(9000, INADDR_ANY))
listen($srv, 128) or die "listen: $!"
while (accept(my $client, $srv)) {
send($client, "hello\n", 0)
}
</code></pre>
</article>
<article class="doc-entry" id="doc-accept">
<h3><a class="doc-anchor" href="#doc-accept">#</a> <code>accept</code></h3>
<p>Accept a pending connection on a listening socket and return a new connected socket handle. The new handle is used for communication with that specific client while the original listening socket continues accepting others. Returns the packed remote address on success, false on failure.</p>
<pre><code class="lang-perl">listen($srv, 5)
while (my $remote = accept(my $client, $srv)) {
my ($port, $ip) = sockaddr_in($remote)
p "connection from " . inet_ntoa($ip) . ":$port"
send($client, "welcome\n", 0)
}
</code></pre>
</article>
<article class="doc-entry" id="doc-connect">
<h3><a class="doc-anchor" href="#doc-connect">#</a> <code>connect</code></h3>
<p>Initiate a connection from a socket to a remote address. For TCP sockets this performs the three-way handshake; for UDP it sets the default destination so subsequent <code>send</code> calls do not need an address. Dies or returns false if the connection is refused or times out.</p>
<pre><code class="lang-perl">socket(my $sock, AF_INET, SOCK_STREAM, 0)
my $addr = sockaddr_in(80, inet_aton("example.com"))
connect($sock, $addr) or die "connect: $!"
send($sock, "GET / HTTP/1.0\r\n\r\n", 0)
recv($sock, my $buf, 4096, 0)
p $buf
</code></pre>
</article>
<article class="doc-entry" id="doc-send">
<h3><a class="doc-anchor" href="#doc-send">#</a> <code>send</code></h3>
<p>Send data through a connected socket. The flags argument controls behavior — use <code>0</code> for normal sends. For UDP sockets you can supply a destination address as a fourth argument to send to a specific peer without calling <code>connect</code> first. Returns the number of bytes sent, or <code>undef</code> on error.</p>
<pre><code class="lang-perl">send($sock, "hello world\n", 0)
my $n = send($sock, $payload, 0)
p "sent $n bytes"
# UDP to specific peer
send($udp, $msg, 0, sockaddr_in(5000, inet_aton("10.0.0.1")))
</code></pre>
</article>
<article class="doc-entry" id="doc-recv">
<h3><a class="doc-anchor" href="#doc-recv">#</a> <code>recv</code></h3>
<p>Receive data from a socket into a buffer. The length argument specifies the maximum number of bytes to read. For stream sockets a short read is normal — loop until you have all expected data. For datagram sockets each call returns exactly one datagram. Returns the sender address for UDP, or empty string for TCP.</p>
<pre><code class="lang-perl">recv($sock, my $buf, 4096, 0) or die "recv: $!"
p $buf
my $data = ""
while (recv($sock, my $chunk, 8192, 0) && length($chunk)) {
$data .= $chunk
}
</code></pre>
</article>
<article class="doc-entry" id="doc-shutdown">
<h3><a class="doc-anchor" href="#doc-shutdown">#</a> <code>shutdown</code></h3>
<p>Shut down part or all of a socket connection without closing the file descriptor. The <code>how</code> argument controls direction: <code>0</code> stops reading, <code>1</code> stops writing (sends FIN to peer), <code>2</code> stops both. This is useful for signaling end-of-data to the remote side while still reading its response.</p>
<pre><code class="lang-perl">send($sock, $request, 0)
shutdown($sock, 1) # done writing
recv($sock, my $resp, 65536, 0) # still read response
shutdown($sock, 2) # fully close
</code></pre>
</article>
<article class="doc-entry" id="doc-setsockopt">
<h3><a class="doc-anchor" href="#doc-setsockopt">#</a> <code>setsockopt</code></h3>
<p>Set an option on a socket at the specified protocol level. Common uses include enabling <code>SO_REUSEADDR</code> to allow immediate rebinding after a server restart, setting <code>TCP_NODELAY</code> to disable Nagle's algorithm, or adjusting buffer sizes. The value is typically a packed integer.</p>
<pre><code class="lang-perl">setsockopt($srv, SOL_SOCKET, SO_REUSEADDR, 1)
setsockopt($sock, IPPROTO_TCP, TCP_NODELAY, 1)
setsockopt($sock, SOL_SOCKET, SO_RCVBUF, pack("I", 262144))
</code></pre>
</article>
<article class="doc-entry" id="doc-getsockopt">
<h3><a class="doc-anchor" href="#doc-getsockopt">#</a> <code>getsockopt</code></h3>
<p>Retrieve the current value of a socket option at the specified protocol level. Returns the option value as a packed binary string — use <code>unpack</code> to interpret it. Useful for inspecting buffer sizes, checking whether <code>SO_REUSEADDR</code> is set, or reading OS-assigned values.</p>
<pre><code class="lang-perl">my $val = getsockopt($sock, SOL_SOCKET, SO_RCVBUF)
p unpack("I", $val) # e.g. 131072
my $reuse = getsockopt($srv, SOL_SOCKET, SO_REUSEADDR)
p unpack("I", $reuse) # 1 or 0
</code></pre>
</article>
<article class="doc-entry" id="doc-getsockname">
<h3><a class="doc-anchor" href="#doc-getsockname">#</a> <code>getsockname</code></h3>
<p>Return the packed socket address of the local end of a socket. This is useful when the socket was bound to <code>INADDR_ANY</code> or port <code>0</code> (OS-assigned) and you need to discover the actual address and port the OS chose. Unpack the result with <code>sockaddr_in</code>.</p>
<pre><code class="lang-perl">bind($sock, sockaddr_in(0, INADDR_ANY)) # OS picks port
my $local = getsockname($sock)
my ($port, $ip) = sockaddr_in($local)
p "listening on port $port"
</code></pre>
</article>
<article class="doc-entry" id="doc-getpeername">
<h3><a class="doc-anchor" href="#doc-getpeername">#</a> <code>getpeername</code></h3>
<p>Return the packed socket address of the remote end of a connected socket. Use <code>sockaddr_in</code> or <code>sockaddr_in6</code> to unpack it into a port and IP address. This is how a server discovers which client it is talking to after <code>accept</code>, or how a client confirms the peer address after <code>connect</code>.</p>
<pre><code class="lang-perl">my $packed = getpeername($client)
my ($port, $ip) = sockaddr_in($packed)
p "peer: " . inet_ntoa($ip) . ":$port"
</code></pre>
</article>
<article class="doc-entry" id="doc-gethostbyname">
<h3><a class="doc-anchor" href="#doc-gethostbyname">#</a> <code>gethostbyname</code></h3>
<p>Resolve a hostname to its network addresses using the system resolver. Returns <code>($name, $aliases, $addrtype, $length, @addrs)</code>. The addresses are packed binary — pass them through <code>inet_ntoa</code> to get dotted-quad strings. This is the classic DNS forward-lookup function.</p>
<pre><code class="lang-perl">my @info = gethostbyname("example.com")
my @addrs = @info[4..$ #info]
@addrs |> map inet_ntoa |> e p
my $ip = inet_ntoa((gethostbyname("localhost"))[4])
p $ip # 127.0.0.1
</code></pre>
</article>
<article class="doc-entry" id="doc-gethostbyaddr">
<h3><a class="doc-anchor" href="#doc-gethostbyaddr">#</a> <code>gethostbyaddr</code></h3>
<p>Perform a reverse DNS lookup — given a packed binary IP address and address family, return the hostname associated with that address. Returns <code>($name, $aliases, $addrtype, $length, @addrs)</code> on success, or empty list if no PTR record exists.</p>
<pre><code class="lang-perl">my $packed = inet_aton("8.8.8.8")
my $name = (gethostbyaddr($packed, AF_INET))[0]
p $name # dns.google
</code></pre>
</article>
<article class="doc-entry" id="doc-getprotobyname">
<h3><a class="doc-anchor" href="#doc-getprotobyname">#</a> <code>getprotobyname</code></h3>
<p>Look up a network protocol by its name and return protocol information. Returns <code>($name, $aliases, $proto_number)</code>. The protocol number is what you pass to <code>socket</code> as the protocol argument. Common names include <code>tcp</code>, <code>udp</code>, and <code>icmp</code>.</p>
<pre><code class="lang-perl">my ($name, $aliases, $proto) = getprotobyname("tcp")
p "$name = protocol $proto" # tcp = protocol 6
socket(my $raw, AF_INET, SOCK_RAW, (getprotobyname("icmp"))[2])
</code></pre>
</article>
<article class="doc-entry" id="doc-getservbyname">
<h3><a class="doc-anchor" href="#doc-getservbyname">#</a> <code>getservbyname</code></h3>
<p>Look up a network service by its name and protocol, returning the port number and related information. Returns <code>($name, $aliases, $port, $proto)</code>. The port is in host byte order. This resolves well-known service names like <code>http</code>, <code>ssh</code>, or <code>smtp</code> to their port numbers portably.</p>
<pre><code class="lang-perl">my ($name, $aliases, $port) = getservbyname("http", "tcp")
p "$name => port $port" # http => port 80
my $ssh_port = (getservbyname("ssh", "tcp"))[2]
p $ssh_port # 22
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-crypto-encoding">
<h2>Crypto & Encoding</h2>
<p class="chapter-meta">133 topics</p>
<article class="doc-entry" id="doc-sha256">
<h3><a class="doc-anchor" href="#doc-sha256">#</a> <code>sha256</code></h3>
<p><code>sha256</code> (alias <code>s256</code>) computes the SHA-256 cryptographic hash of the input data and returns it as a 64-character lowercase hexadecimal string. SHA-256 is the most widely used hash function for data integrity verification, content addressing, and digital signatures. The Rust implementation is significantly faster than pure-Perl alternatives. Accepts strings or byte buffers.</p>
<pre><code class="lang-perl">p sha256 "hello world" # b94d27b9934d3e08...
my $checksum = sha256 slurp "release.tar.gz"
p $checksum
rl("passwords.txt") |> map sha256 |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-sha224">
<h3><a class="doc-anchor" href="#doc-sha224">#</a> <code>sha224</code></h3>
<p><code>sha224</code> (alias <code>s224</code>) computes the SHA-224 cryptographic hash and returns a 56-character hex string. SHA-224 is a truncated variant of SHA-256 that produces a shorter digest while maintaining strong collision resistance. It is sometimes preferred when storage or bandwidth for the hash value is constrained, such as in compact data structures or short identifiers.</p>
<pre><code class="lang-perl">p sha224 "hello world" # 2f05477fc24bb4fa...
my $h = sha224(tj {key => "value"})
p $h
</code></pre>
</article>
<article class="doc-entry" id="doc-sha384">
<h3><a class="doc-anchor" href="#doc-sha384">#</a> <code>sha384</code></h3>
<p><code>sha384</code> (alias <code>s384</code>) computes the SHA-384 cryptographic hash and returns a 96-character hex string. SHA-384 is a truncated variant of SHA-512 that offers a middle ground between SHA-256 and SHA-512 in both digest length and security margin. It is commonly used in TLS certificate fingerprints and government security standards that require larger-than-256-bit digests.</p>
<pre><code class="lang-perl">p sha384 "hello world" # fdbd8e75a67f29f7...
my $sig = sha384(slurp "document.pdf")
spurt "document.pdf.sha384", $sig
</code></pre>
</article>
<article class="doc-entry" id="doc-sha512">
<h3><a class="doc-anchor" href="#doc-sha512">#</a> <code>sha512</code></h3>
<p><code>sha512</code> (alias <code>s512</code>) computes the SHA-512 cryptographic hash and returns a 128-character hex string. SHA-512 provides the largest digest size in the SHA-2 family and is the strongest option when maximum collision resistance is needed. On 64-bit systems, SHA-512 is often faster than SHA-256 because it operates on 64-bit words natively. Use this for high-security applications or when you need a longer hash.</p>
<pre><code class="lang-perl">p sha512 "hello world" # 309ecc489c12d6eb...
my $hash = sha512(slurp "firmware.bin");
p $hash;
my @hashes = map { sha512 } @files
</code></pre>
</article>
<article class="doc-entry" id="doc-sha1">
<h3><a class="doc-anchor" href="#doc-sha1">#</a> <code>sha1</code></h3>
<p><code>sha1</code> (alias <code>s1</code>) computes the SHA-1 hash and returns a 40-character hex string. SHA-1 is considered cryptographically broken for collision resistance and should not be used for security-sensitive applications. However, it remains widely used for non-security purposes such as Git object IDs, cache keys, and deduplication checksums where collision attacks are not a concern.</p>
<pre><code class="lang-perl">p sha1 "hello world" # 2aae6c35c94fcfb4...
my $git_id = sha1("blob " . length($content) . "\0" . $content)
p $git_id$1
Note: prefer SHA-256 for any security-related use case.
</code></pre>
</article>
<article class="doc-entry" id="doc-crc32">
<h3><a class="doc-anchor" href="#doc-crc32">#</a> <code>crc32</code></h3>
<p><code>crc32</code> computes the CRC-32 checksum of the input data and returns it as an unsigned 32-bit integer. CRC-32 is not a cryptographic hash — it is a fast error-detection code used in network protocols (Ethernet, ZIP, PNG), file integrity checks, and hash table bucketing. It is extremely fast compared to SHA functions, making it suitable for high-throughput deduplication or quick change detection where collision resistance is not required.</p>
<pre><code class="lang-perl">p crc32 "hello world" # 222957957
my $chk = crc32(slurp "archive.zip");
p sprintf "0x%08x", $chk; # hex representation
my @checksums = map { crc32 } @chunks
</code></pre>
</article>
<article class="doc-entry" id="doc-hmac-sha256">
<h3><a class="doc-anchor" href="#doc-hmac-sha256">#</a> <code>hmac_sha256</code></h3>
<p><code>hmac_sha256</code> (alias <code>hmac</code>) computes an HMAC-SHA256 message authentication code using the given data and secret key, returning a hex string. HMAC combines a cryptographic hash with a secret key to produce a signature that verifies both data integrity and authenticity. This is the standard mechanism for signing API requests (AWS, Stripe, GitHub webhooks), generating secure tokens, and verifying message authenticity.</p>
<pre><code class="lang-perl">my $sig = hmac_sha256 "request body", "my-secret-key"
p $sig
my $webhook_sig = hmac("POST /hook\n$body", $secret)
p $webhook_sig eq $expected ? "valid" : "tampered"
</code></pre>
</article>
<article class="doc-entry" id="doc-blake2b">
<h3><a class="doc-anchor" href="#doc-blake2b">#</a> <code>blake2b</code></h3>
<p><code>blake2b</code> (alias <code>b2b</code>) computes the BLAKE2b-512 cryptographic hash and returns a 128-character hex string. BLAKE2b is faster than SHA-256 while being at least as secure. It is used in Argon2 password hashing, libsodium, WireGuard, and many modern cryptographic protocols. Prefer BLAKE2b or BLAKE3 for new projects over SHA-256.</p>
<pre><code class="lang-perl">p blake2b "hello world" # 021ced8799...
my $hash = b2b(slurp "large-file.bin");
my @hashes = map { blake2b } @messages
</code></pre>
</article>
<article class="doc-entry" id="doc-blake2s">
<h3><a class="doc-anchor" href="#doc-blake2s">#</a> <code>blake2s</code></h3>
<p><code>blake2s</code> (alias <code>b2s</code>) computes the BLAKE2s-256 cryptographic hash and returns a 64-character hex string. BLAKE2s is optimized for 8-32 bit platforms while BLAKE2b targets 64-bit. Use BLAKE2s when targeting embedded systems, WebAssembly, or when a 256-bit digest suffices.</p>
<pre><code class="lang-perl">p blake2s "hello world" # 9aec6806...
my $checksum = b2s($firmware_blob)
</code></pre>
</article>
<article class="doc-entry" id="doc-blake3">
<h3><a class="doc-anchor" href="#doc-blake3">#</a> <code>blake3</code></h3>
<p><code>blake3</code> (alias <code>b3</code>) computes the BLAKE3 cryptographic hash and returns a 64-character hex string (256-bit). BLAKE3 is the latest evolution — it is parallelizable, even faster than BLAKE2, and suitable for hashing large files at maximum speed. It is the recommended hash function for new projects where legacy compatibility is not required.</p>
<pre><code class="lang-perl">p blake3 "hello world" # d74981efa...
my $hash = b3(slurp "gigabyte-file.bin") # fast!
</code></pre>
</article>
<article class="doc-entry" id="doc-argon2-hash">
<h3><a class="doc-anchor" href="#doc-argon2-hash">#</a> <code>argon2_hash</code></h3>
<p><code>argon2_hash</code> (alias <code>argon2</code>) hashes a password using Argon2id, the winner of the Password Hashing Competition. Returns a PHC-format string containing algorithm parameters, salt, and hash. Argon2 is memory-hard and resistant to GPU/ASIC attacks. Use this for user password storage — never use MD5/SHA for passwords.</p>
<pre><code class="lang-perl">my $hash = argon2_hash("user-password")
to_file("user.hash", $hash)
# later...
if (argon2_verify("user-password", $hash)) {
p "login successful"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-argon2-verify">
<h3><a class="doc-anchor" href="#doc-argon2-verify">#</a> <code>argon2_verify</code></h3>
<p><code>argon2_verify</code> verifies a password against an Argon2 PHC hash string. Returns 1 if the password matches, 0 otherwise. The verification automatically extracts parameters from the stored hash, so changing Argon2 settings for new hashes does not break existing ones.</p>
<pre><code class="lang-perl">my $stored = rl("user.hash")
if (argon2_verify($user_input, $stored)) {
p "access granted"
} else {
p "invalid password"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-bcrypt-hash">
<h3><a class="doc-anchor" href="#doc-bcrypt-hash">#</a> <code>bcrypt_hash</code></h3>
<p><code>bcrypt_hash</code> (alias <code>bcrypt</code>) hashes a password using the bcrypt algorithm, returning a standard <code>$2b$...</code> format string. Bcrypt has been the industry standard for password hashing for over 20 years. While Argon2 is now preferred for new systems, bcrypt remains secure and widely deployed.</p>
<pre><code class="lang-perl">my $hash = bcrypt_hash("my-password")
p $hash # $2b$12$...
if (bcrypt_verify("my-password", $hash)) {
p "correct"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-bcrypt-verify">
<h3><a class="doc-anchor" href="#doc-bcrypt-verify">#</a> <code>bcrypt_verify</code></h3>
<p><code>bcrypt_verify</code> verifies a password against a bcrypt hash string. Returns 1 if correct, 0 otherwise. The cost factor and salt are extracted from the stored hash automatically.</p>
<pre><code class="lang-perl">if (bcrypt_verify($password, $stored_hash)) {
grant_access()
}
</code></pre>
</article>
<article class="doc-entry" id="doc-scrypt-hash">
<h3><a class="doc-anchor" href="#doc-scrypt-hash">#</a> <code>scrypt_hash</code></h3>
<p><code>scrypt_hash</code> (alias <code>scrypt</code>) hashes a password using the scrypt algorithm, returning a PHC-format string. Scrypt is memory-hard like Argon2 and is used in cryptocurrency (Litecoin) and some enterprise systems. It predates Argon2 but remains secure.</p>
<pre><code class="lang-perl">my $hash = scrypt_hash("password123")
if (scrypt_verify("password123", $hash)) {
p "verified"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-scrypt-verify">
<h3><a class="doc-anchor" href="#doc-scrypt-verify">#</a> <code>scrypt_verify</code></h3>
<p><code>scrypt_verify</code> verifies a password against a scrypt PHC hash. Returns 1 on match, 0 otherwise.</p>
<pre><code class="lang-perl">if (scrypt_verify($input, $stored)) {
p "valid"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-pbkdf2">
<h3><a class="doc-anchor" href="#doc-pbkdf2">#</a> <code>pbkdf2</code></h3>
<p><code>pbkdf2</code> (alias <code>pbkdf2_derive</code>) derives a cryptographic key from a password using PBKDF2-HMAC-SHA256. Returns a 64-character hex string (32 bytes). Takes password, salt, and optional iteration count (default 100,000). Use this when you need a fixed-length key from a password — for encryption keys, not password storage (use Argon2/bcrypt for that).</p>
<pre><code class="lang-perl">my $key = pbkdf2("password", "random-salt")
p $key # 64 hex chars = 32 bytes
my $strong = pbkdf2("pass", $salt, 200_000) # more iterations
</code></pre>
</article>
<article class="doc-entry" id="doc-random-bytes">
<h3><a class="doc-anchor" href="#doc-random-bytes">#</a> <code>random_bytes</code></h3>
<p><code>random_bytes</code> (alias <code>randbytes</code>) generates cryptographically secure random bytes using the OS CSPRNG. Returns a byte buffer of the specified length. Use for encryption keys, nonces, salts, and any security-sensitive randomness. Never use <code>rand()</code> for cryptographic purposes.</p>
<pre><code class="lang-perl">my $key = random_bytes(32) # 256-bit key
my $nonce = random_bytes(12) # 96-bit nonce for AES-GCM
p hex_encode($key)
</code></pre>
</article>
<article class="doc-entry" id="doc-random-bytes-hex">
<h3><a class="doc-anchor" href="#doc-random-bytes-hex">#</a> <code>random_bytes_hex</code></h3>
<p><code>random_bytes_hex</code> (alias <code>randhex</code>) generates cryptographically secure random bytes and returns them as a hex string. Convenient when you need a random hex token or key without a separate hex_encode call.</p>
<pre><code class="lang-perl">my $token = random_bytes_hex(16) # 32 hex chars
p $token # 7a3f9b2c1d...
my $api_key = "sk_" . randhex(24)
</code></pre>
</article>
<article class="doc-entry" id="doc-aes-encrypt">
<h3><a class="doc-anchor" href="#doc-aes-encrypt">#</a> <code>aes_encrypt</code></h3>
<p><code>aes_encrypt</code> (alias <code>aes_enc</code>) encrypts plaintext using AES-256-GCM authenticated encryption. Takes a 32-byte key (use <code>random_bytes(32)</code> or <code>pbkdf2</code>). Returns a base64 string containing the nonce and ciphertext. AES-GCM provides both confidentiality and integrity — tampering is detected on decryption.</p>
<pre><code class="lang-perl">my $key = random_bytes(32)
my $cipher = aes_encrypt($key, "secret message")
p $cipher # base64 encoded
my $plain = aes_decrypt($key, $cipher)
p $plain # secret message
</code></pre>
</article>
<article class="doc-entry" id="doc-aes-decrypt">
<h3><a class="doc-anchor" href="#doc-aes-decrypt">#</a> <code>aes_decrypt</code></h3>
<p><code>aes_decrypt</code> (alias <code>aes_dec</code>) decrypts AES-256-GCM ciphertext produced by <code>aes_encrypt</code>. Takes the same 32-byte key and the base64 ciphertext. Dies if the key is wrong or the ciphertext was tampered with (authentication failure).</p>
<pre><code class="lang-perl">my $plain = aes_decrypt($key, $ciphertext)
p $plain
# wrong key or tampered data raises exception
</code></pre>
</article>
<article class="doc-entry" id="doc-chacha-encrypt">
<h3><a class="doc-anchor" href="#doc-chacha-encrypt">#</a> <code>chacha_encrypt</code></h3>
<p><code>chacha_encrypt</code> (alias <code>chacha_enc</code>) encrypts plaintext using ChaCha20-Poly1305 authenticated encryption. Takes a 32-byte key. Returns base64(nonce || ciphertext || tag). ChaCha20-Poly1305 is the modern alternative to AES-GCM — faster in software, constant-time, and used in TLS 1.3, WireGuard, and SSH.</p>
<pre><code class="lang-perl">my $key = random_bytes(32)
my $cipher = chacha_encrypt($key, "secret data")
my $plain = chacha_decrypt($key, $cipher)
p $plain
</code></pre>
</article>
<article class="doc-entry" id="doc-chacha-decrypt">
<h3><a class="doc-anchor" href="#doc-chacha-decrypt">#</a> <code>chacha_decrypt</code></h3>
<p><code>chacha_decrypt</code> (alias <code>chacha_dec</code>) decrypts ChaCha20-Poly1305 ciphertext. Takes the same 32-byte key and base64 ciphertext. Dies on wrong key or tampering.</p>
<pre><code class="lang-perl">my $plain = chacha_decrypt($key, $cipher)
p $plain
</code></pre>
</article>
<article class="doc-entry" id="doc-ed25519-keygen">
<h3><a class="doc-anchor" href="#doc-ed25519-keygen">#</a> <code>ed25519_keygen</code></h3>
<p><code>ed25519_keygen</code> (alias <code>ed_keygen</code>) generates an Ed25519 signing keypair. Returns [private_key_hex, public_key_hex]. Ed25519 is the modern standard for digital signatures — fast, secure, and used in SSH, GPG, and cryptocurrency. The private key is 32 bytes (64 hex), the public key is also 32 bytes.</p>
<pre><code class="lang-perl">my ($priv, $pub) = @{ ed25519_keygen() }
p "Private: $priv"
p "Public: $pub"
my $sig = ed25519_sign($priv, "message")
</code></pre>
</article>
<article class="doc-entry" id="doc-ed25519-sign">
<h3><a class="doc-anchor" href="#doc-ed25519-sign">#</a> <code>ed25519_sign</code></h3>
<p><code>ed25519_sign</code> (alias <code>ed_sign</code>) signs a message with an Ed25519 private key. Takes the private key (hex) and message. Returns a 128-character hex signature (64 bytes). Signatures are deterministic — the same key+message always produces the same signature.</p>
<pre><code class="lang-perl">my $sig = ed25519_sign($private_key, "hello world")
p $sig # 128 hex chars
</code></pre>
</article>
<article class="doc-entry" id="doc-ed25519-verify">
<h3><a class="doc-anchor" href="#doc-ed25519-verify">#</a> <code>ed25519_verify</code></h3>
<p><code>ed25519_verify</code> (alias <code>ed_verify</code>) verifies an Ed25519 signature. Takes public_key_hex, message, signature_hex. Returns 1 if valid, 0 if invalid. Never trust unsigned data in security contexts.</p>
<pre><code class="lang-perl">if (ed25519_verify($pub, "hello world", $sig)) {
p "signature valid"
} else {
p "FORGED!"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-x25519-keygen">
<h3><a class="doc-anchor" href="#doc-x25519-keygen">#</a> <code>x25519_keygen</code></h3>
<p><code>x25519_keygen</code> (alias <code>x_keygen</code>) generates an X25519 key-exchange keypair. Returns [private_key_hex, public_key_hex]. X25519 is the modern Diffie-Hellman — used in TLS 1.3, Signal, WireGuard. Both parties generate keypairs and exchange public keys to derive a shared secret.</p>
<pre><code class="lang-perl">my ($my_priv, $my_pub) = @{ x25519_keygen() }
# send $my_pub to peer, receive $their_pub
my $shared = x25519_dh($my_priv, $their_pub)
</code></pre>
</article>
<article class="doc-entry" id="doc-x25519-dh">
<h3><a class="doc-anchor" href="#doc-x25519-dh">#</a> <code>x25519_dh</code></h3>
<p><code>x25519_dh</code> (alias <code>x_dh</code>) performs X25519 Diffie-Hellman key exchange. Takes your private key and their public key. Returns a 64-character hex shared secret. Both parties derive the same secret, which can be used as an encryption key.</p>
<pre><code class="lang-perl">my $shared = x25519_dh($my_private, $their_public)
my $key = hex_decode(substr($shared, 0, 64)) # use as AES key
</code></pre>
</article>
<article class="doc-entry" id="doc-base64-encode">
<h3><a class="doc-anchor" href="#doc-base64-encode">#</a> <code>base64_encode</code></h3>
<p><code>base64_encode</code> (alias <code>b64e</code>) encodes a string or byte buffer as a Base64 string using the standard alphabet (A-Z, a-z, 0-9, +, /). Base64 is the standard way to embed binary data in text-based formats like JSON, XML, email (MIME), and data URIs. The output length is always a multiple of 4, padded with <code>=</code> as needed. Use <code>base64_decode</code> to reverse the encoding.</p>
<pre><code class="lang-perl">my $encoded = base64_encode "hello world"
p $encoded # aGVsbG8gd29ybGQ=
my $img_data = slurp "photo.png"
my $data_uri = "data:image/png;base64," . base64_encode($img_data)
p base64_decode(base64_encode("round trip")) # round trip
</code></pre>
</article>
<article class="doc-entry" id="doc-base64-decode">
<h3><a class="doc-anchor" href="#doc-base64-decode">#</a> <code>base64_decode</code></h3>
<p><code>base64_decode</code> (alias <code>b64d</code>) decodes a Base64-encoded string back to its original bytes. It accepts standard Base64 with padding and is tolerant of line breaks within the input. This is essential for processing email attachments, decoding JWT payloads, extracting embedded images from data URIs, or reading any Base64-encoded field from an API response. Raises an exception on invalid Base64 input.</p>
<pre><code class="lang-perl">my $decoded = base64_decode "aGVsbG8gd29ybGQ="
p $decoded # hello world
my $img = base64_decode($api_response->{avatar_b64})
spurt "avatar.png", $img
my $json = base64_decode($jwt_parts[1])
dd json_decode $json
</code></pre>
</article>
<article class="doc-entry" id="doc-hex-encode">
<h3><a class="doc-anchor" href="#doc-hex-encode">#</a> <code>hex_encode</code></h3>
<p><code>hex_encode</code> (alias <code>hxe</code>) converts a string or byte buffer into its lowercase hexadecimal representation, with two hex characters per input byte. This is useful for displaying binary data in a human-readable format, generating hex-encoded keys or IDs, logging raw bytes, or preparing data for protocols that use hex encoding. The output is always an even number of characters.</p>
<pre><code class="lang-perl">p hex_encode "hello" # 68656c6c6f
my $raw = slurp "key.bin"
p hex_encode $raw
my $color = hex_encode chr(255) . chr(128) . chr(0)
p "#$color" # #ff8000
</code></pre>
</article>
<article class="doc-entry" id="doc-hex-decode">
<h3><a class="doc-anchor" href="#doc-hex-decode">#</a> <code>hex_decode</code></h3>
<p><code>hex_decode</code> (alias <code>hxd</code>) converts a hexadecimal string back to its original bytes, interpreting every two hex characters as one byte. This is the inverse of <code>hex_encode</code> and is useful for parsing hex-encoded binary data from config files, network protocols, or cryptographic outputs. The input must have an even number of valid hex characters (0-9, a-f, A-F) or an exception is raised.</p>
<pre><code class="lang-perl">my $bytes = hex_decode "68656c6c6f"
p $bytes # hello
my $key = hex_decode $env_hex_key
my $mac = hmac_sha256($data, hex_decode($secret_hex))
p hex_decode(hex_encode("round trip")) # round trip
</code></pre>
</article>
<article class="doc-entry" id="doc-uuid">
<h3><a class="doc-anchor" href="#doc-uuid">#</a> <code>uuid</code></h3>
<p><code>uuid</code> generates a cryptographically random UUID version 4 string in the standard 8-4-4-4-12 hyphenated format. Each call produces a unique identifier suitable for database primary keys, correlation IDs, session tokens, temporary file names, or any situation requiring a globally unique identifier without coordination. The randomness comes from the OS CSPRNG.</p>
<pre><code class="lang-perl">my $id = uuid()
p $id # e.g., 550e8400-e29b-41d4-a716-446655440000
my %record = (id => uuid(), name => "Alice", created => time)
my @ids = map { uuid() } 1:10
</code></pre>
</article>
<article class="doc-entry" id="doc-jwt-encode">
<h3><a class="doc-anchor" href="#doc-jwt-encode">#</a> <code>jwt_encode</code></h3>
<p><code>jwt_encode</code> creates a signed JSON Web Token from a payload hashref and a secret key. The default algorithm is HS256 (HMAC-SHA256), but you can specify an alternative as the third argument. JWTs are the standard for stateless authentication tokens, API authorization, and secure inter-service communication. The returned string contains the base64url-encoded header, payload, and signature separated by dots.</p>
<pre><code class="lang-perl">my $token = jwt_encode({sub => "user123", exp => time + 3600}, "my-secret")
p $token
my $admin = jwt_encode({role => "admin", iat => time}, $secret, "HS512")
# send as Authorization header
http_request(method => "GET", url => $api_url,
headers => {Authorization => "Bearer $token"})
</code></pre>
</article>
<article class="doc-entry" id="doc-jwt-decode">
<h3><a class="doc-anchor" href="#doc-jwt-decode">#</a> <code>jwt_decode</code></h3>
<p><code>jwt_decode</code> verifies the signature of a JSON Web Token using the provided secret key and returns the decoded payload as a hashref. If the signature is invalid, the token has been tampered with, or it has expired (when an <code>exp</code> claim is present), the function raises an exception. This is the secure way to validate incoming JWTs from clients or other services — always use this over <code>jwt_decode_unsafe</code> in production.</p>
<pre><code class="lang-perl">my $payload = jwt_decode($token, "my-secret")
p $payload->{sub} # user123
my $claims = jwt_decode($bearer_token, $secret)
if ($claims->{role} eq "admin") {
p "admin access granted"
}
</code></pre>
<p>Note: raises an exception on expired tokens, invalid signatures, or malformed input.</p>
</article>
<article class="doc-entry" id="doc-jwt-decode-unsafe">
<h3><a class="doc-anchor" href="#doc-jwt-decode-unsafe">#</a> <code>jwt_decode_unsafe</code></h3>
<p><code>jwt_decode_unsafe</code> decodes a JSON Web Token and returns the payload as a hashref without verifying the signature. This is intentionally insecure and should only be used for debugging, logging, or inspecting token contents in development environments. Never use this to make authorization decisions in production — an attacker can stryke arbitrary payloads. The function still parses the JWT structure and base64-decodes the payload, but skips all cryptographic checks.</p>
<pre><code class="lang-perl"># debugging only — never use for auth
my $claims = jwt_decode_unsafe($token)
dd $claims
p $claims->{sub} # inspect without needing the secret
my $exp = $claims->{exp}
p "Expires: " . datetime_from_epoch($exp)$1
Note: this function exists for debugging. Use `jwt_decode` with a secret for any security-relevant validation.
</code></pre>
</article>
<article class="doc-entry" id="doc-url-encode">
<h3><a class="doc-anchor" href="#doc-url-encode">#</a> <code>url_encode</code></h3>
<p>Percent-encode a string so it is safe to embed in a URL query parameter or path segment. Unreserved characters (alphanumeric, <code>-</code>, <code>_</code>, <code>.</code>, <code>~</code>) are left as-is; everything else becomes <code>%XX</code>. The alias <code>uri_escape</code> matches the classic <code>URI::Escape</code> name for Perl muscle-memory.</p>
<pre><code class="lang-perl">my $q = "hello world & friends"
my $safe = url_encode($q)
p $safe # hello%20world%20%26%20friends
my $url = "https://example.com/search?q=" . url_encode($q)
p $url$1
Note: does not encode the full URL structure — encode individual components, not the whole URL.
</code></pre>
</article>
<article class="doc-entry" id="doc-url-decode">
<h3><a class="doc-anchor" href="#doc-url-decode">#</a> <code>url_decode</code></h3>
<p>Decode a percent-encoded string back to its original form, converting <code>%XX</code> sequences to the corresponding bytes and <code>+</code> to space. The alias <code>uri_unescape</code> matches <code>URI::Escape</code> conventions. Use this when parsing query strings from incoming URLs or reading URL-encoded form data.</p>
<pre><code class="lang-perl">my $encoded = "hello%20world%20%26%20friends"
p url_decode($encoded) # hello world & friends
# round-trip
my $orig = "café ☕"
p url_decode(url_encode($orig)) eq $orig # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-gzip">
<h3><a class="doc-anchor" href="#doc-gzip">#</a> <code>gzip</code></h3>
<p>Compress a string or byte buffer using the gzip (RFC 1952) format and return the compressed bytes. Useful for shrinking data before writing to disk or sending over the network. Pairs with <code>gunzip</code> for decompression. The compression level is chosen automatically for a good speed/size tradeoff.</p>
<pre><code class="lang-perl">my $raw = "hello world" x 1000
my $gz = gzip($raw)
to_file("data.gz", $gz)
p length($gz) # much smaller than original
p gunzip($gz) eq $raw # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-gunzip">
<h3><a class="doc-anchor" href="#doc-gunzip">#</a> <code>gunzip</code></h3>
<p>Decompress gzip-compressed data (RFC 1952) and return the original bytes. Dies if the input is not valid gzip. Use this to read <code>.gz</code> files or decompress data received from HTTP responses with <code>Content-Encoding: gzip</code>. Always the inverse of <code>gzip</code>.</p>
<pre><code class="lang-perl">my $compressed = rl("archive.gz")
my $text = gunzip($compressed)
p $text
# round-trip in a pipeline
"payload" |> gzip |> gunzip |> p # payload
</code></pre>
</article>
<article class="doc-entry" id="doc-zstd">
<h3><a class="doc-anchor" href="#doc-zstd">#</a> <code>zstd</code></h3>
<p>Compress a string or byte buffer using the Zstandard algorithm and return the compressed bytes. Zstandard offers significantly better compression ratios and speed compared to gzip, making it ideal for large datasets, IPC buffers, and caching. Pairs with <code>zstd_decode</code> for decompression.</p>
<pre><code class="lang-perl">my $big = "x]" x 100_000
my $compressed = zstd($big)
p length($compressed) # fraction of original
to_file("data.zst", $compressed)
p zstd_decode($compressed) eq $big # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-zstd-decode">
<h3><a class="doc-anchor" href="#doc-zstd-decode">#</a> <code>zstd_decode</code></h3>
<p>Decompress Zstandard-compressed data and return the original bytes. Dies if the input is not valid Zstandard. This is the inverse of <code>zstd</code>. Use it to read <code>.zst</code> files or decompress cached buffers that were compressed with <code>zstd</code>.</p>
<pre><code class="lang-perl">my $packed = zstd("important data\n" x 500)
my $original = zstd_decode($packed)
p $original
# file round-trip
to_file("cache.zst", zstd($payload))
p zstd_decode(rl("cache.zst"))
</code></pre>
</article>
<article class="doc-entry" id="doc-sha3-256">
<h3><a class="doc-anchor" href="#doc-sha3-256">#</a> <code>sha3_256</code></h3>
<p><code>sha3_256</code> (alias <code>s3_256</code>) computes the SHA3-256 hash (NIST FIPS 202) and returns a 64-character hex string. SHA-3 is the newest NIST-approved hash family, designed as a backup if SHA-2 is ever compromised. It uses the Keccak sponge construction which is fundamentally different from SHA-2.</p>
<pre><code class="lang-perl">p sha3_256 "hello world" # 644bcc7e...
my $h = s3_256(slurp "file.bin")
</code></pre>
</article>
<article class="doc-entry" id="doc-sha3-512">
<h3><a class="doc-anchor" href="#doc-sha3-512">#</a> <code>sha3_512</code></h3>
<p><code>sha3_512</code> (alias <code>s3_512</code>) computes the SHA3-512 hash and returns a 128-character hex string. Provides a 512-bit digest with the SHA-3 sponge construction.</p>
<pre><code class="lang-perl">p sha3_512 "hello world" # 840006...
</code></pre>
</article>
<article class="doc-entry" id="doc-shake128">
<h3><a class="doc-anchor" href="#doc-shake128">#</a> <code>shake128</code></h3>
<p><code>shake128</code> is a SHA-3 extendable-output function (XOF). Unlike fixed-length hashes, SHAKE can produce arbitrary-length output. Takes data and output length in bytes, returns hex. Useful for key derivation or when you need a variable-length digest.</p>
<pre><code class="lang-perl">p shake128("seed", 32) # 64 hex chars (32 bytes)
p shake128("seed", 64) # 128 hex chars
</code></pre>
</article>
<article class="doc-entry" id="doc-shake256">
<h3><a class="doc-anchor" href="#doc-shake256">#</a> <code>shake256</code></h3>
<p><code>shake256</code> is a SHA-3 XOF with higher security margin than SHAKE128. Takes data and output length in bytes, returns hex.</p>
<pre><code class="lang-perl">p shake256("seed", 32)
p shake256("key material", 64)
</code></pre>
</article>
<article class="doc-entry" id="doc-ripemd160">
<h3><a class="doc-anchor" href="#doc-ripemd160">#</a> <code>ripemd160</code></h3>
<p><code>ripemd160</code> (alias <code>rmd160</code>) computes the RIPEMD-160 hash and returns a 40-character hex string. RIPEMD-160 is used in Bitcoin addresses (Hash160 = RIPEMD160(SHA256(pubkey))) and some legacy systems. Not recommended for new designs but essential for Bitcoin/crypto compatibility.</p>
<pre><code class="lang-perl">p ripemd160 "hello world" # 98c615784c...
my $hash160 = ripemd160(hex_decode(sha256($pubkey)))
</code></pre>
</article>
<article class="doc-entry" id="doc-siphash">
<h3><a class="doc-anchor" href="#doc-siphash">#</a> <code>siphash</code></h3>
<p><code>siphash</code> computes SipHash-2-4 with default keys (0,0) and returns a 16-character hex string (64-bit). SipHash is designed for hash table DoS resistance — it's fast and keyed, preventing attackers from crafting collisions. Used in Rust's HashMap, Python dict, and many other hash tables.</p>
<pre><code class="lang-perl">p siphash "key" # 16 hex chars
</code></pre>
</article>
<article class="doc-entry" id="doc-hmac-sha1">
<h3><a class="doc-anchor" href="#doc-hmac-sha1">#</a> <code>hmac_sha1</code></h3>
<p><code>hmac_sha1</code> computes HMAC-SHA1 and returns a 40-character hex string. Used in OAuth 1.0, TOTP (Google Authenticator), and legacy APIs. Prefer HMAC-SHA256 for new designs.</p>
<pre><code class="lang-perl">p hmac_sha1("secret", "message") # 40 hex chars
</code></pre>
</article>
<article class="doc-entry" id="doc-hmac-sha384">
<h3><a class="doc-anchor" href="#doc-hmac-sha384">#</a> <code>hmac_sha384</code></h3>
<p><code>hmac_sha384</code> computes HMAC-SHA384 and returns a 96-character hex string. Middle ground between SHA-256 and SHA-512.</p>
<pre><code class="lang-perl">p hmac_sha384("key", "data") # 96 hex chars
</code></pre>
</article>
<article class="doc-entry" id="doc-hmac-sha512">
<h3><a class="doc-anchor" href="#doc-hmac-sha512">#</a> <code>hmac_sha512</code></h3>
<p><code>hmac_sha512</code> computes HMAC-SHA512 and returns a 128-character hex string. Maximum security margin in the SHA-2 family.</p>
<pre><code class="lang-perl">p hmac_sha512("key", "data") # 128 hex chars
</code></pre>
</article>
<article class="doc-entry" id="doc-hmac-md5">
<h3><a class="doc-anchor" href="#doc-hmac-md5">#</a> <code>hmac_md5</code></h3>
<p><code>hmac_md5</code> computes HMAC-MD5 and returns a 32-character hex string. Legacy only — MD5 is broken for collision resistance but HMAC-MD5 is still considered safe for authentication. Only use for compatibility with old systems.</p>
<pre><code class="lang-perl">p hmac_md5("key", "data") # 32 hex chars
</code></pre>
</article>
<article class="doc-entry" id="doc-hkdf-sha256">
<h3><a class="doc-anchor" href="#doc-hkdf-sha256">#</a> <code>hkdf_sha256</code></h3>
<p><code>hkdf_sha256</code> (alias <code>hkdf</code>) is HKDF key derivation (RFC 5869) using HMAC-SHA256. Extracts entropy from input key material and expands it to the desired length. Used to derive encryption keys from shared secrets (after ECDH/X25519). Args: ikm, salt, info, output_length.</p>
<pre><code class="lang-perl">my $key = hkdf("shared_secret", "salt", "context", 32) # 64 hex
my $enc_key = hex_decode($key) # 32 bytes for AES-256
</code></pre>
</article>
<article class="doc-entry" id="doc-hkdf-sha512">
<h3><a class="doc-anchor" href="#doc-hkdf-sha512">#</a> <code>hkdf_sha512</code></h3>
<p><code>hkdf_sha512</code> is HKDF using HMAC-SHA512. Higher security margin than SHA256 variant.</p>
<pre><code class="lang-perl">my $key = hkdf_sha512("ikm", "salt", "info", 64) # 128 hex chars
</code></pre>
</article>
<article class="doc-entry" id="doc-poly1305">
<h3><a class="doc-anchor" href="#doc-poly1305">#</a> <code>poly1305</code></h3>
<p><code>poly1305</code> computes a Poly1305 one-time MAC. Takes a 32-byte key and message, returns a 32-character hex tag (128-bit). Poly1305 is used with ChaCha20 in TLS 1.3. CRITICAL: each key must only be used once — reusing a key completely breaks security.</p>
<pre><code class="lang-perl">my $key = random_bytes(32)
p poly1305($key, "message") # 32 hex chars
</code></pre>
</article>
<article class="doc-entry" id="doc-rsa-keygen">
<h3><a class="doc-anchor" href="#doc-rsa-keygen">#</a> <code>rsa_keygen</code></h3>
<p><code>rsa_keygen</code> generates an RSA keypair. Takes key size in bits (2048, 3072, or 4096). Returns [private_key_pem, public_key_pem]. RSA is the most widely used asymmetric algorithm — essential for TLS, SSH, and JWT RS256 signing.</p>
<pre><code class="lang-perl">my @kp = rsa_keygen(2048)
my ($priv, $pub) = @kp
spurt("private.pem", $priv)
spurt("public.pem", $pub)
</code></pre>
</article>
<article class="doc-entry" id="doc-rsa-encrypt">
<h3><a class="doc-anchor" href="#doc-rsa-encrypt">#</a> <code>rsa_encrypt</code></h3>
<p><code>rsa_encrypt</code> (alias <code>rsa_enc</code>) encrypts data with RSA-OAEP-SHA256. Takes public_key_pem and plaintext. Returns base64 ciphertext. Message size is limited to key_size/8 - 66 bytes (e.g. 190 bytes for 2048-bit key).</p>
<pre><code class="lang-perl">my $cipher = rsa_encrypt($pub_pem, "secret")
my $plain = rsa_decrypt($priv_pem, $cipher)
</code></pre>
</article>
<article class="doc-entry" id="doc-rsa-decrypt">
<h3><a class="doc-anchor" href="#doc-rsa-decrypt">#</a> <code>rsa_decrypt</code></h3>
<p><code>rsa_decrypt</code> (alias <code>rsa_dec</code>) decrypts RSA-OAEP ciphertext. Takes private_key_pem and base64 ciphertext.</p>
<pre><code class="lang-perl">my $plain = rsa_decrypt($priv, $ciphertext)
p $plain
</code></pre>
</article>
<article class="doc-entry" id="doc-rsa-sign">
<h3><a class="doc-anchor" href="#doc-rsa-sign">#</a> <code>rsa_sign</code></h3>
<p><code>rsa_sign</code> signs a message with RSA-PKCS1v15-SHA256. Takes private_key_pem and message. Returns base64 signature. This is the RS256 algorithm used in JWT.</p>
<pre><code class="lang-perl">my $sig = rsa_sign($priv, "message")
if (rsa_verify($pub, "message", $sig)) {
p "valid"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-rsa-verify">
<h3><a class="doc-anchor" href="#doc-rsa-verify">#</a> <code>rsa_verify</code></h3>
<p><code>rsa_verify</code> verifies an RSA-PKCS1v15-SHA256 signature. Takes public_key_pem, message, and base64 signature. Returns 1 if valid, 0 if not.</p>
<pre><code class="lang-perl">if (rsa_verify($pub_pem, $msg, $sig)) {
p "signature valid"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-ecdsa-p256-keygen">
<h3><a class="doc-anchor" href="#doc-ecdsa-p256-keygen">#</a> <code>ecdsa_p256_keygen</code></h3>
<p><code>ecdsa_p256_keygen</code> (alias <code>p256_keygen</code>) generates an ECDSA P-256 (secp256r1/prime256v1) keypair. Returns [private_hex, public_hex_compressed]. P-256 is the NIST curve used in TLS, ES256 JWT, and WebAuthn.</p>
<pre><code class="lang-perl">my @kp = ecdsa_p256_keygen()
my ($priv, $pub) = @kp
</code></pre>
</article>
<article class="doc-entry" id="doc-ecdsa-p256-sign">
<h3><a class="doc-anchor" href="#doc-ecdsa-p256-sign">#</a> <code>ecdsa_p256_sign</code></h3>
<p><code>ecdsa_p256_sign</code> (alias <code>p256_sign</code>) signs a message with ECDSA P-256. Takes private_key_hex and message. Returns DER-encoded signature as hex.</p>
<pre><code class="lang-perl">my $sig = ecdsa_p256_sign($priv, "hello")
</code></pre>
</article>
<article class="doc-entry" id="doc-ecdsa-p256-verify">
<h3><a class="doc-anchor" href="#doc-ecdsa-p256-verify">#</a> <code>ecdsa_p256_verify</code></h3>
<p><code>ecdsa_p256_verify</code> (alias <code>p256_verify</code>) verifies an ECDSA P-256 signature. Returns 1 if valid.</p>
<pre><code class="lang-perl">if (ecdsa_p256_verify($pub, "hello", $sig)) {
p "valid"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-ecdsa-p384-keygen">
<h3><a class="doc-anchor" href="#doc-ecdsa-p384-keygen">#</a> <code>ecdsa_p384_keygen</code></h3>
<p><code>ecdsa_p384_keygen</code> generates an ECDSA P-384 keypair. P-384 offers more security margin than P-256.</p>
<pre><code class="lang-perl">my @kp = ecdsa_p384_keygen()
</code></pre>
</article>
<article class="doc-entry" id="doc-ecdsa-p384-sign">
<h3><a class="doc-anchor" href="#doc-ecdsa-p384-sign">#</a> <code>ecdsa_p384_sign</code></h3>
<p><code>ecdsa_p384_sign</code> signs with ECDSA P-384.</p>
<pre><code class="lang-perl">my $sig = ecdsa_p384_sign($priv, $msg)
</code></pre>
</article>
<article class="doc-entry" id="doc-ecdsa-p384-verify">
<h3><a class="doc-anchor" href="#doc-ecdsa-p384-verify">#</a> <code>ecdsa_p384_verify</code></h3>
<p><code>ecdsa_p384_verify</code> verifies an ECDSA P-384 signature.</p>
<pre><code class="lang-perl">p ecdsa_p384_verify($pub, $msg, $sig)
</code></pre>
</article>
<article class="doc-entry" id="doc-ecdsa-secp256k1-keygen">
<h3><a class="doc-anchor" href="#doc-ecdsa-secp256k1-keygen">#</a> <code>ecdsa_secp256k1_keygen</code></h3>
<p><code>ecdsa_secp256k1_keygen</code> generates an ECDSA secp256k1 keypair. This is the Bitcoin/Ethereum curve — different from P-256.</p>
<pre><code class="lang-perl">my @kp = ecdsa_secp256k1_keygen()
</code></pre>
</article>
<article class="doc-entry" id="doc-ecdsa-secp256k1-sign">
<h3><a class="doc-anchor" href="#doc-ecdsa-secp256k1-sign">#</a> <code>ecdsa_secp256k1_sign</code></h3>
<p><code>ecdsa_secp256k1_sign</code> signs with ECDSA secp256k1.</p>
<pre><code class="lang-perl">my $sig = ecdsa_secp256k1_sign($priv, $msg)
</code></pre>
</article>
<article class="doc-entry" id="doc-ecdsa-secp256k1-verify">
<h3><a class="doc-anchor" href="#doc-ecdsa-secp256k1-verify">#</a> <code>ecdsa_secp256k1_verify</code></h3>
<p><code>ecdsa_secp256k1_verify</code> verifies an ECDSA secp256k1 signature.</p>
<pre><code class="lang-perl">p ecdsa_secp256k1_verify($pub, $msg, $sig)
</code></pre>
</article>
<article class="doc-entry" id="doc-ecdh-p256">
<h3><a class="doc-anchor" href="#doc-ecdh-p256">#</a> <code>ecdh_p256</code></h3>
<p><code>ecdh_p256</code> (alias <code>p256_dh</code>) performs ECDH key exchange on P-256. Takes my_private_hex and their_public_hex, returns shared_secret_hex. Use HKDF to derive encryption keys from the shared secret.</p>
<pre><code class="lang-perl">my @alice = ecdsa_p256_keygen()
my @bob = ecdsa_p256_keygen()
my $shared_a = ecdh_p256($alice[0], $bob[1])
my $shared_b = ecdh_p256($bob[0], $alice[1])
p $shared_a eq $shared_b # 1 — same secret
</code></pre>
</article>
<article class="doc-entry" id="doc-ecdh-p384">
<h3><a class="doc-anchor" href="#doc-ecdh-p384">#</a> <code>ecdh_p384</code></h3>
<p><code>ecdh_p384</code> performs ECDH key exchange on P-384.</p>
<pre><code class="lang-perl">my $shared = ecdh_p384($my_priv, $their_pub)
</code></pre>
</article>
<article class="doc-entry" id="doc-base32-encode">
<h3><a class="doc-anchor" href="#doc-base32-encode">#</a> <code>base32_encode</code></h3>
<p><code>base32_encode</code> (alias <code>b32e</code>) encodes data as RFC 4648 Base32. Used in TOTP secrets, onion addresses, and Bech32. Returns uppercase with padding.</p>
<pre><code class="lang-perl">p base32_encode("hello") # NBSWY3DP
my $secret = base32_encode(random_bytes(20))
</code></pre>
</article>
<article class="doc-entry" id="doc-base32-decode">
<h3><a class="doc-anchor" href="#doc-base32-decode">#</a> <code>base32_decode</code></h3>
<p><code>base32_decode</code> (alias <code>b32d</code>) decodes RFC 4648 Base32 back to bytes. Accepts with or without padding.</p>
<pre><code class="lang-perl">p base32_decode("NBSWY3DP") # hello
</code></pre>
</article>
<article class="doc-entry" id="doc-base58-encode">
<h3><a class="doc-anchor" href="#doc-base58-encode">#</a> <code>base58_encode</code></h3>
<p><code>base58_encode</code> (alias <code>b58e</code>) encodes data using Bitcoin's Base58 alphabet (no 0, O, I, l to avoid confusion). Used in Bitcoin addresses, IPFS CIDs.</p>
<pre><code class="lang-perl">p base58_encode("hello") # Cn8eVZg
</code></pre>
</article>
<article class="doc-entry" id="doc-base58-decode">
<h3><a class="doc-anchor" href="#doc-base58-decode">#</a> <code>base58_decode</code></h3>
<p><code>base58_decode</code> (alias <code>b58d</code>) decodes Base58 back to bytes.</p>
<pre><code class="lang-perl">p base58_decode("Cn8eVZg") # hello
</code></pre>
</article>
<article class="doc-entry" id="doc-totp">
<h3><a class="doc-anchor" href="#doc-totp">#</a> <code>totp</code></h3>
<p><code>totp</code> (alias <code>totp_generate</code>) generates a TOTP code (RFC 6238) for 2FA. Takes base32-encoded secret, optional digits (default 6), optional period (default 30s). Compatible with Google Authenticator, Authy, etc.</p>
<pre><code class="lang-perl">my $secret = base32_encode(random_bytes(20))
my $code = totp($secret)
p $code # 6-digit code
# Custom: 8 digits, 60s period
my $code8 = totp($secret, 8, 60)
</code></pre>
</article>
<article class="doc-entry" id="doc-totp-verify">
<h3><a class="doc-anchor" href="#doc-totp-verify">#</a> <code>totp_verify</code></h3>
<p><code>totp_verify</code> verifies a TOTP code with optional time window (default ±1 period). Returns 1 if valid.</p>
<pre><code class="lang-perl">if (totp_verify($secret, $user_code)) {
p "2FA valid"
}
# Wider window: ±2 periods
totp_verify($secret, $code, 2)
</code></pre>
</article>
<article class="doc-entry" id="doc-hotp">
<h3><a class="doc-anchor" href="#doc-hotp">#</a> <code>hotp</code></h3>
<p><code>hotp</code> (alias <code>hotp_generate</code>) generates an HOTP code (RFC 4226) using a counter. Takes base32 secret, counter value, optional digits.</p>
<pre><code class="lang-perl">my $code = hotp($secret, 42) # counter=42
</code></pre>
</article>
<article class="doc-entry" id="doc-aes-cbc-encrypt">
<h3><a class="doc-anchor" href="#doc-aes-cbc-encrypt">#</a> <code>aes_cbc_encrypt</code></h3>
<p><code>aes_cbc_encrypt</code> (alias <code>aes_cbc_enc</code>) encrypts with AES-256-CBC and PKCS7 padding. Takes 32-byte key, plaintext, optional 16-byte IV (auto-generated if omitted). Returns base64(iv || ciphertext). Legacy mode — prefer <code>aes_encrypt</code> (GCM) for new code.</p>
<pre><code class="lang-perl">my $key = random_bytes(32)
my $ct = aes_cbc_encrypt($key, "secret")
my $pt = aes_cbc_decrypt($key, $ct)
</code></pre>
</article>
<article class="doc-entry" id="doc-aes-cbc-decrypt">
<h3><a class="doc-anchor" href="#doc-aes-cbc-decrypt">#</a> <code>aes_cbc_decrypt</code></h3>
<p><code>aes_cbc_decrypt</code> (alias <code>aes_cbc_dec</code>) decrypts AES-256-CBC. Takes 32-byte key and base64(iv || ciphertext).</p>
<pre><code class="lang-perl">my $pt = aes_cbc_decrypt($key, $ciphertext)
</code></pre>
</article>
<article class="doc-entry" id="doc-qr-ascii">
<h3><a class="doc-anchor" href="#doc-qr-ascii">#</a> <code>qr_ascii</code></h3>
<p><code>qr_ascii</code> (alias <code>qr</code>) generates a QR code as ASCII art. Perfect for terminal output.</p>
<pre><code class="lang-perl">p qr("https://example.com")
p qr("otpauth://totp/App:user?secret=$secret&issuer=App")
</code></pre>
</article>
<article class="doc-entry" id="doc-qr-png">
<h3><a class="doc-anchor" href="#doc-qr-png">#</a> <code>qr_png</code></h3>
<p><code>qr_png</code> generates a QR code as PNG image data (base64 encoded). Optional size parameter. Save to file or embed in HTML.</p>
<pre><code class="lang-perl">my $png = qr_png("https://example.com")
spurt("qr.png", base64_decode($png))
# Larger QR
my $big = qr_png($url, 16)
</code></pre>
</article>
<article class="doc-entry" id="doc-qr-svg">
<h3><a class="doc-anchor" href="#doc-qr-svg">#</a> <code>qr_svg</code></h3>
<p><code>qr_svg</code> generates a QR code as SVG string. Scalable vector graphics, ideal for web.</p>
<pre><code class="lang-perl">my $svg = qr_svg("https://example.com")
spurt("qr.svg", $svg)
</code></pre>
</article>
<article class="doc-entry" id="doc-barcode-code128">
<h3><a class="doc-anchor" href="#doc-barcode-code128">#</a> <code>barcode_code128</code></h3>
<p><code>barcode_code128</code> (alias <code>code128</code>) generates a Code 128 barcode as ASCII. Code 128 supports alphanumeric data and is widely used in shipping labels.</p>
<pre><code class="lang-perl">p code128("ABC-123")
</code></pre>
</article>
<article class="doc-entry" id="doc-barcode-code39">
<h3><a class="doc-anchor" href="#doc-barcode-code39">#</a> <code>barcode_code39</code></h3>
<p><code>barcode_code39</code> (alias <code>code39</code>) generates a Code 39 barcode. Supports uppercase, digits, and some symbols. Used in automotive and defense.</p>
<pre><code class="lang-perl">p code39("HELLO123")
</code></pre>
</article>
<article class="doc-entry" id="doc-barcode-ean13">
<h3><a class="doc-anchor" href="#doc-barcode-ean13">#</a> <code>barcode_ean13</code></h3>
<p><code>barcode_ean13</code> (alias <code>ean13</code>) generates an EAN-13 barcode (European Article Number). Standard retail barcode — requires exactly 12-13 digits.</p>
<pre><code class="lang-perl">p ean13("5901234123457")
</code></pre>
</article>
<article class="doc-entry" id="doc-barcode-svg">
<h3><a class="doc-anchor" href="#doc-barcode-svg">#</a> <code>barcode_svg</code></h3>
<p><code>barcode_svg</code> generates a barcode as SVG. Second argument specifies type: code128, code39, ean13, upca.</p>
<pre><code class="lang-perl">my $svg = barcode_svg("ABC-123", "code128")
spurt("barcode.svg", $svg)
my $retail = barcode_svg("012345678905", "upca")
</code></pre>
</article>
<article class="doc-entry" id="doc-brotli">
<h3><a class="doc-anchor" href="#doc-brotli">#</a> <code>brotli</code></h3>
<p><code>brotli</code> (alias <code>br</code>) compresses data using the Brotli algorithm (RFC 7932). Excellent compression ratio, used in HTTP compression. Returns compressed bytes.</p>
<pre><code class="lang-perl">my $compressed = brotli($data)
p length($data) . " -> " . length($compressed)
</code></pre>
</article>
<article class="doc-entry" id="doc-brotli-decode">
<h3><a class="doc-anchor" href="#doc-brotli-decode">#</a> <code>brotli_decode</code></h3>
<p><code>brotli_decode</code> (alias <code>ubr</code>) decompresses Brotli data.</p>
<pre><code class="lang-perl">my $original = brotli_decode($compressed)
</code></pre>
</article>
<article class="doc-entry" id="doc-xz">
<h3><a class="doc-anchor" href="#doc-xz">#</a> <code>xz</code></h3>
<p><code>xz</code> (alias <code>lzma</code>) compresses data using XZ/LZMA2. Best compression ratio, slower. Returns compressed bytes.</p>
<pre><code class="lang-perl">my $compressed = xz($data)
spurt("file.xz", $compressed)
</code></pre>
</article>
<article class="doc-entry" id="doc-xz-decode">
<h3><a class="doc-anchor" href="#doc-xz-decode">#</a> <code>xz_decode</code></h3>
<p><code>xz_decode</code> (aliases <code>unxz</code>, <code>unlzma</code>) decompresses XZ/LZMA data.</p>
<pre><code class="lang-perl">my $original = xz_decode(slurp("file.xz"))
</code></pre>
</article>
<article class="doc-entry" id="doc-bzip2">
<h3><a class="doc-anchor" href="#doc-bzip2">#</a> <code>bzip2</code></h3>
<p><code>bzip2</code> (alias <code>bz2</code>) compresses data using bzip2. Good compression, moderate speed. Returns compressed bytes.</p>
<pre><code class="lang-perl">my $compressed = bzip2($data)
</code></pre>
</article>
<article class="doc-entry" id="doc-bzip2-decode">
<h3><a class="doc-anchor" href="#doc-bzip2-decode">#</a> <code>bzip2_decode</code></h3>
<p><code>bzip2_decode</code> (aliases <code>bunzip2</code>, <code>ubz2</code>) decompresses bzip2 data.</p>
<pre><code class="lang-perl">my $original = bunzip2($compressed)
</code></pre>
</article>
<article class="doc-entry" id="doc-lz4">
<h3><a class="doc-anchor" href="#doc-lz4">#</a> <code>lz4</code></h3>
<p><code>lz4</code> compresses data using LZ4. Very fast compression/decompression, moderate ratio. Ideal for real-time compression.</p>
<pre><code class="lang-perl">my $compressed = lz4($data)
</code></pre>
</article>
<article class="doc-entry" id="doc-lz4-decode">
<h3><a class="doc-anchor" href="#doc-lz4-decode">#</a> <code>lz4_decode</code></h3>
<p><code>lz4_decode</code> (alias <code>unlz4</code>) decompresses LZ4 data.</p>
<pre><code class="lang-perl">my $original = lz4_decode($compressed)
</code></pre>
</article>
<article class="doc-entry" id="doc-snappy">
<h3><a class="doc-anchor" href="#doc-snappy">#</a> <code>snappy</code></h3>
<p><code>snappy</code> (alias <code>snp</code>) compresses data using Snappy. Fastest compression, used in databases and RPC. Returns compressed bytes.</p>
<pre><code class="lang-perl">my $compressed = snappy($data)
</code></pre>
</article>
<article class="doc-entry" id="doc-snappy-decode">
<h3><a class="doc-anchor" href="#doc-snappy-decode">#</a> <code>snappy_decode</code></h3>
<p><code>snappy_decode</code> (alias <code>unsnappy</code>) decompresses Snappy data.</p>
<pre><code class="lang-perl">my $original = snappy_decode($compressed)
</code></pre>
</article>
<article class="doc-entry" id="doc-lzw">
<h3><a class="doc-anchor" href="#doc-lzw">#</a> <code>lzw</code></h3>
<p><code>lzw</code> compresses data using LZW (GIF/TIFF style). Classic algorithm.</p>
<pre><code class="lang-perl">my $compressed = lzw($data)
</code></pre>
</article>
<article class="doc-entry" id="doc-lzw-decode">
<h3><a class="doc-anchor" href="#doc-lzw-decode">#</a> <code>lzw_decode</code></h3>
<p><code>lzw_decode</code> (alias <code>unlzw</code>) decompresses LZW data.</p>
<pre><code class="lang-perl">my $original = lzw_decode($compressed)
</code></pre>
</article>
<article class="doc-entry" id="doc-tar-create">
<h3><a class="doc-anchor" href="#doc-tar-create">#</a> <code>tar_create</code></h3>
<p><code>tar_create</code> (alias <code>tar</code>) creates a tar archive from a directory. Returns tar bytes.</p>
<pre><code class="lang-perl">my $archive = tar_create("./src")
spurt("backup.tar", $archive)
</code></pre>
</article>
<article class="doc-entry" id="doc-tar-extract">
<h3><a class="doc-anchor" href="#doc-tar-extract">#</a> <code>tar_extract</code></h3>
<p><code>tar_extract</code> (alias <code>untar</code>) extracts a tar archive to a directory.</p>
<pre><code class="lang-perl">tar_extract(slurp("backup.tar"), "./restored")
</code></pre>
</article>
<article class="doc-entry" id="doc-tar-list">
<h3><a class="doc-anchor" href="#doc-tar-list">#</a> <code>tar_list</code></h3>
<p><code>tar_list</code> lists files in a tar archive. Returns array of paths.</p>
<pre><code class="lang-perl">my @files = @{tar_list(slurp("backup.tar"))}
@files |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-tar-gz-create">
<h3><a class="doc-anchor" href="#doc-tar-gz-create">#</a> <code>tar_gz_create</code></h3>
<p><code>tar_gz_create</code> (alias <code>tgz</code>) creates a gzipped tar archive. Convenience for tar + gzip.</p>
<pre><code class="lang-perl">my $tgz = tgz("./project")
spurt("project.tar.gz", $tgz)
</code></pre>
</article>
<article class="doc-entry" id="doc-tar-gz-extract">
<h3><a class="doc-anchor" href="#doc-tar-gz-extract">#</a> <code>tar_gz_extract</code></h3>
<p><code>tar_gz_extract</code> (alias <code>untgz</code>) extracts a .tar.gz archive.</p>
<pre><code class="lang-perl">untgz(slurp("project.tar.gz"), "./extracted")
</code></pre>
</article>
<article class="doc-entry" id="doc-zip-create">
<h3><a class="doc-anchor" href="#doc-zip-create">#</a> <code>zip_create</code></h3>
<p><code>zip_create</code> creates a ZIP archive from a directory. Returns zip bytes.</p>
<pre><code class="lang-perl">my $archive = zip_create("./docs")
spurt("docs.zip", $archive)
</code></pre>
</article>
<article class="doc-entry" id="doc-zip-extract">
<h3><a class="doc-anchor" href="#doc-zip-extract">#</a> <code>zip_extract</code></h3>
<p><code>zip_extract</code> extracts a ZIP archive to a directory.</p>
<pre><code class="lang-perl">zip_extract(slurp("docs.zip"), "./extracted")
</code></pre>
</article>
<article class="doc-entry" id="doc-zip-list">
<h3><a class="doc-anchor" href="#doc-zip-list">#</a> <code>zip_list</code></h3>
<p><code>zip_list</code> lists files in a ZIP archive. Returns array of paths.</p>
<pre><code class="lang-perl">my @files = @{zip_list(slurp("archive.zip"))}
</code></pre>
</article>
<article class="doc-entry" id="doc-md4">
<h3><a class="doc-anchor" href="#doc-md4">#</a> <code>md4</code></h3>
<p><code>md4</code> computes the MD4 hash and returns a 32-character hex string. MD4 is completely broken — only use for legacy NTLM compatibility or historical systems.</p>
<pre><code class="lang-perl">p md4("hello") # 32 hex chars
</code></pre>
</article>
<article class="doc-entry" id="doc-xxh32">
<h3><a class="doc-anchor" href="#doc-xxh32">#</a> <code>xxh32</code></h3>
<p><code>xxh32</code> (alias <code>xxhash32</code>) computes xxHash32 — extremely fast non-cryptographic hash. Optional seed parameter. Returns 8 hex chars.</p>
<pre><code class="lang-perl">p xxh32("hello") # default seed 0
p xxh32("hello", 42) # with seed
</code></pre>
</article>
<article class="doc-entry" id="doc-xxh64">
<h3><a class="doc-anchor" href="#doc-xxh64">#</a> <code>xxh64</code></h3>
<p><code>xxh64</code> (alias <code>xxhash64</code>) computes xxHash64 — fast 64-bit hash. Returns 16 hex chars.</p>
<pre><code class="lang-perl">p xxh64("hello")
</code></pre>
</article>
<article class="doc-entry" id="doc-xxh3">
<h3><a class="doc-anchor" href="#doc-xxh3">#</a> <code>xxh3</code></h3>
<p><code>xxh3</code> (alias <code>xxhash3</code>) computes xxHash3-64 — newest xxHash variant, fastest on modern CPUs. Returns 16 hex chars.</p>
<pre><code class="lang-perl">p xxh3("hello")
</code></pre>
</article>
<article class="doc-entry" id="doc-xxh3-128">
<h3><a class="doc-anchor" href="#doc-xxh3-128">#</a> <code>xxh3_128</code></h3>
<p><code>xxh3_128</code> computes xxHash3-128. Returns 32 hex chars.</p>
<pre><code class="lang-perl">p xxh3_128("hello")
</code></pre>
</article>
<article class="doc-entry" id="doc-murmur3">
<h3><a class="doc-anchor" href="#doc-murmur3">#</a> <code>murmur3</code></h3>
<p><code>murmur3</code> (alias <code>murmur3_32</code>) computes MurmurHash3 32-bit. Fast non-cryptographic hash, widely used in hash tables and bloom filters. Optional seed. Returns 8 hex chars.</p>
<pre><code class="lang-perl">p murmur3("hello") # default seed 0
p murmur3("hello", 42) # with seed
</code></pre>
</article>
<article class="doc-entry" id="doc-murmur3-128">
<h3><a class="doc-anchor" href="#doc-murmur3-128">#</a> <code>murmur3_128</code></h3>
<p><code>murmur3_128</code> computes MurmurHash3 128-bit (x64 variant). Returns 32 hex chars.</p>
<pre><code class="lang-perl">p murmur3_128("hello")
</code></pre>
</article>
<article class="doc-entry" id="doc-blowfish-encrypt">
<h3><a class="doc-anchor" href="#doc-blowfish-encrypt">#</a> <code>blowfish_encrypt</code></h3>
<p><code>blowfish_encrypt</code> (alias <code>bf_enc</code>) encrypts with Blowfish-CBC. Key=4-56 bytes, optional 8-byte IV. Legacy cipher — use AES for new code.</p>
<pre><code class="lang-perl">my $ct = blowfish_encrypt($key, "secret")
my $pt = blowfish_decrypt($key, $ct)
</code></pre>
</article>
<article class="doc-entry" id="doc-blowfish-decrypt">
<h3><a class="doc-anchor" href="#doc-blowfish-decrypt">#</a> <code>blowfish_decrypt</code></h3>
<p><code>blowfish_decrypt</code> (alias <code>bf_dec</code>) decrypts Blowfish-CBC.</p>
<pre><code class="lang-perl">my $pt = blowfish_decrypt($key, $ciphertext)
</code></pre>
</article>
<article class="doc-entry" id="doc-des3-encrypt">
<h3><a class="doc-anchor" href="#doc-des3-encrypt">#</a> <code>des3_encrypt</code></h3>
<p><code>des3_encrypt</code> (aliases <code>3des_enc</code>, <code>tdes_enc</code>) encrypts with Triple DES (3DES) CBC. Key=24 bytes (three 8-byte DES keys). Legacy cipher for PCI-DSS compliance.</p>
<pre><code class="lang-perl">my $key = random_bytes(24)
my $ct = des3_encrypt($key, "secret")
my $pt = des3_decrypt($key, $ct)
</code></pre>
</article>
<article class="doc-entry" id="doc-des3-decrypt">
<h3><a class="doc-anchor" href="#doc-des3-decrypt">#</a> <code>des3_decrypt</code></h3>
<p><code>des3_decrypt</code> (aliases <code>3des_dec</code>, <code>tdes_dec</code>) decrypts Triple DES (3DES) CBC.</p>
<pre><code class="lang-perl">my $pt = des3_decrypt($key, $ciphertext)
</code></pre>
</article>
<article class="doc-entry" id="doc-twofish-encrypt">
<h3><a class="doc-anchor" href="#doc-twofish-encrypt">#</a> <code>twofish_encrypt</code></h3>
<p><code>twofish_encrypt</code> (alias <code>tf_enc</code>) encrypts with Twofish-CBC. Key=16/24/32 bytes. AES finalist, still secure.</p>
<pre><code class="lang-perl">my $key = random_bytes(32)
my $ct = twofish_encrypt($key, "secret")
</code></pre>
</article>
<article class="doc-entry" id="doc-twofish-decrypt">
<h3><a class="doc-anchor" href="#doc-twofish-decrypt">#</a> <code>twofish_decrypt</code></h3>
<p><code>twofish_decrypt</code> (alias <code>tf_dec</code>) decrypts Twofish-CBC.</p>
<pre><code class="lang-perl">my $pt = twofish_decrypt($key, $ct)
</code></pre>
</article>
<article class="doc-entry" id="doc-camellia-encrypt">
<h3><a class="doc-anchor" href="#doc-camellia-encrypt">#</a> <code>camellia_encrypt</code></h3>
<p><code>camellia_encrypt</code> (alias <code>cam_enc</code>) encrypts with Camellia-CBC. Key=16/24/32 bytes. Japanese/EU standard, equivalent security to AES.</p>
<pre><code class="lang-perl">my $ct = camellia_encrypt($key, "secret")
</code></pre>
</article>
<article class="doc-entry" id="doc-camellia-decrypt">
<h3><a class="doc-anchor" href="#doc-camellia-decrypt">#</a> <code>camellia_decrypt</code></h3>
<p><code>camellia_decrypt</code> (alias <code>cam_dec</code>) decrypts Camellia-CBC.</p>
<pre><code class="lang-perl">my $pt = camellia_decrypt($key, $ct)
</code></pre>
</article>
<article class="doc-entry" id="doc-cast5-encrypt">
<h3><a class="doc-anchor" href="#doc-cast5-encrypt">#</a> <code>cast5_encrypt</code></h3>
<p><code>cast5_encrypt</code> encrypts with CAST5-CBC. Key=5-16 bytes. Used in PGP.</p>
<pre><code class="lang-perl">my $ct = cast5_encrypt($key, "secret")
</code></pre>
</article>
<article class="doc-entry" id="doc-cast5-decrypt">
<h3><a class="doc-anchor" href="#doc-cast5-decrypt">#</a> <code>cast5_decrypt</code></h3>
<p><code>cast5_decrypt</code> decrypts CAST5-CBC.</p>
<pre><code class="lang-perl">my $pt = cast5_decrypt($key, $ct)
</code></pre>
</article>
<article class="doc-entry" id="doc-salsa20">
<h3><a class="doc-anchor" href="#doc-salsa20">#</a> <code>salsa20</code></h3>
<p><code>salsa20</code> encrypts with Salsa20 stream cipher. Key=32 bytes, nonce auto-generated. Fast, secure stream cipher.</p>
<pre><code class="lang-perl">my $ct = salsa20($key, "data")
my $pt = salsa20_decrypt($key, $ct)
</code></pre>
</article>
<article class="doc-entry" id="doc-salsa20-decrypt">
<h3><a class="doc-anchor" href="#doc-salsa20-decrypt">#</a> <code>salsa20_decrypt</code></h3>
<p><code>salsa20_decrypt</code> decrypts Salsa20.</p>
<pre><code class="lang-perl">my $pt = salsa20_decrypt($key, $ct)
</code></pre>
</article>
<article class="doc-entry" id="doc-xsalsa20">
<h3><a class="doc-anchor" href="#doc-xsalsa20">#</a> <code>xsalsa20</code></h3>
<p><code>xsalsa20</code> encrypts with XSalsa20 (extended 24-byte nonce). Safer for random nonces.</p>
<pre><code class="lang-perl">my $ct = xsalsa20($key, "data")
</code></pre>
</article>
<article class="doc-entry" id="doc-xsalsa20-decrypt">
<h3><a class="doc-anchor" href="#doc-xsalsa20-decrypt">#</a> <code>xsalsa20_decrypt</code></h3>
<p><code>xsalsa20_decrypt</code> decrypts XSalsa20.</p>
<pre><code class="lang-perl">my $pt = xsalsa20_decrypt($key, $ct)
</code></pre>
</article>
<article class="doc-entry" id="doc-secretbox">
<h3><a class="doc-anchor" href="#doc-secretbox">#</a> <code>secretbox</code></h3>
<p><code>secretbox</code> (alias <code>secretbox_seal</code>) is NaCl's symmetric authenticated encryption (XSalsa20-Poly1305). Key=32 bytes. Simple, secure, fast.</p>
<pre><code class="lang-perl">my $key = random_bytes(32)
my $ct = secretbox($key, "message")
my $pt = secretbox_open($key, $ct)
</code></pre>
</article>
<article class="doc-entry" id="doc-secretbox-open">
<h3><a class="doc-anchor" href="#doc-secretbox-open">#</a> <code>secretbox_open</code></h3>
<p><code>secretbox_open</code> decrypts and authenticates NaCl secretbox.</p>
<pre><code class="lang-perl">my $pt = secretbox_open($key, $ct)
</code></pre>
</article>
<article class="doc-entry" id="doc-nacl-box-keygen">
<h3><a class="doc-anchor" href="#doc-nacl-box-keygen">#</a> <code>nacl_box_keygen</code></h3>
<p><code>nacl_box_keygen</code> generates a NaCl box keypair (X25519). Returns [secret_key_hex, public_key_hex].</p>
<pre><code class="lang-perl">my @kp = nacl_box_keygen()
my ($sk, $pk) = @kp
</code></pre>
</article>
<article class="doc-entry" id="doc-nacl-box">
<h3><a class="doc-anchor" href="#doc-nacl-box">#</a> <code>nacl_box</code></h3>
<p><code>nacl_box</code> is NaCl's asymmetric authenticated encryption. Takes recipient's public key, sender's secret key, plaintext.</p>
<pre><code class="lang-perl">my @alice = nacl_box_keygen()
my @bob = nacl_box_keygen()
my $ct = nacl_box($bob[1], $alice[0], "hello") # to Bob from Alice
my $pt = nacl_box_open($alice[1], $bob[0], $ct) # Bob decrypts
</code></pre>
</article>
<article class="doc-entry" id="doc-nacl-box-open">
<h3><a class="doc-anchor" href="#doc-nacl-box-open">#</a> <code>nacl_box_open</code></h3>
<p><code>nacl_box_open</code> decrypts NaCl box. Takes sender's public key, recipient's secret key, ciphertext.</p>
<pre><code class="lang-perl">my $pt = nacl_box_open($sender_pk, $my_sk, $ct)
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-special-math-functions">
<h2>Special Math Functions</h2>
<p class="chapter-meta">12 topics</p>
<article class="doc-entry" id="doc-erf">
<h3><a class="doc-anchor" href="#doc-erf">#</a> <code>erf</code></h3>
<p><code>erf</code> computes the error function, which arises in probability, statistics, and solutions to the heat equation. erf(x) is the probability that a standard normal random variable falls in [-x√2, x√2]. Returns a value in (-1, 1).</p>
<pre><code class="lang-perl">p erf(0) # 0
p erf(1) # 0.8427...
p erf(10) # ~1
</code></pre>
</article>
<article class="doc-entry" id="doc-erfc">
<h3><a class="doc-anchor" href="#doc-erfc">#</a> <code>erfc</code></h3>
<p><code>erfc</code> computes the complementary error function erfc(x) = 1 - erf(x). Numerically stable for large x where erf(x) ≈ 1. Used in computing tail probabilities of normal distributions.</p>
<pre><code class="lang-perl">p erfc(0) # 1
p erfc(3) # 0.0000220...
</code></pre>
</article>
<article class="doc-entry" id="doc-gamma">
<h3><a class="doc-anchor" href="#doc-gamma">#</a> <code>gamma</code></h3>
<p><code>gamma</code> (alias <code>tgamma</code>) computes the gamma function Γ(x), the extension of factorial to real numbers. Γ(n) = (n-1)! for positive integers. Used throughout statistics, physics, and combinatorics.</p>
<pre><code class="lang-perl">p gamma(5) # 24 (= 4!)
p gamma(0.5) # √π ≈ 1.7724...
p gamma(1) # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-lgamma">
<h3><a class="doc-anchor" href="#doc-lgamma">#</a> <code>lgamma</code></h3>
<p><code>lgamma</code> (alias <code>ln_gamma</code>) computes the natural logarithm of the gamma function: ln(Γ(x)). Avoids overflow for large arguments where Γ(x) would be astronomical. Essential for computing log-probabilities in statistics.</p>
<pre><code class="lang-perl">p lgamma(100) # 359.13...
p lgamma(1000) # 5905.22...
</code></pre>
</article>
<article class="doc-entry" id="doc-digamma">
<h3><a class="doc-anchor" href="#doc-digamma">#</a> <code>digamma</code></h3>
<p><code>digamma</code> (alias <code>psi</code>) computes the digamma function ψ(x) = d/dx ln(Γ(x)), the logarithmic derivative of gamma. Appears in Bayesian statistics (expected log of Dirichlet variables), optimization, and special function theory.</p>
<pre><code class="lang-perl">p digamma(1) # -γ ≈ -0.5772 (Euler-Mascheroni)
p digamma(2) # 1 - γ ≈ 0.4228
</code></pre>
</article>
<article class="doc-entry" id="doc-beta-fn">
<h3><a class="doc-anchor" href="#doc-beta-fn">#</a> <code>beta_fn</code></h3>
<p><code>beta_fn</code> computes the beta function B(a,b) = Γ(a)Γ(b)/Γ(a+b). The beta function is the normalizing constant of the Beta distribution and appears throughout Bayesian statistics and combinatorics.</p>
<pre><code class="lang-perl">p beta_fn(2, 3) # 0.0833...
p beta_fn(0.5, 0.5) # π
</code></pre>
</article>
<article class="doc-entry" id="doc-lbeta">
<h3><a class="doc-anchor" href="#doc-lbeta">#</a> <code>lbeta</code></h3>
<p><code>lbeta</code> (alias <code>ln_beta</code>) computes ln(B(a,b)), the log of the beta function. Avoids overflow for small a or b where B(a,b) is very large.</p>
<pre><code class="lang-perl">p lbeta(0.01, 0.01) # large positive
</code></pre>
</article>
<article class="doc-entry" id="doc-betainc">
<h3><a class="doc-anchor" href="#doc-betainc">#</a> <code>betainc</code></h3>
<p><code>betainc</code> (alias <code>beta_reg</code>) computes the regularized incomplete beta function I_x(a,b), the CDF of the Beta distribution. Takes (x, a, b). Essential for computing p-values of F-tests, t-tests, and binomial probabilities.</p>
<pre><code class="lang-perl">p betainc(0.5, 2, 3) # P(Beta(2,3) < 0.5)
</code></pre>
</article>
<article class="doc-entry" id="doc-gammainc">
<h3><a class="doc-anchor" href="#doc-gammainc">#</a> <code>gammainc</code></h3>
<p><code>gammainc</code> (alias <code>gamma_li</code>) computes the lower incomplete gamma function γ(a,x) = ∫₀ˣ t^(a-1) e^(-t) dt. Used in computing CDFs of gamma and chi-squared distributions.</p>
<pre><code class="lang-perl">p gammainc(2, 1) # γ(2, 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-gammaincc">
<h3><a class="doc-anchor" href="#doc-gammaincc">#</a> <code>gammaincc</code></h3>
<p><code>gammaincc</code> (alias <code>gamma_ui</code>) computes the upper incomplete gamma function Γ(a,x) = ∫ₓ^∞ t^(a-1) e^(-t) dt = Γ(a) - γ(a,x). Useful for tail probabilities.</p>
<pre><code class="lang-perl">p gammaincc(2, 1) # Γ(2, 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-gammainc-reg">
<h3><a class="doc-anchor" href="#doc-gammainc-reg">#</a> <code>gammainc_reg</code></h3>
<p><code>gammainc_reg</code> (alias <code>gamma_lr</code>) computes the regularized lower incomplete gamma P(a,x) = γ(a,x)/Γ(a), the CDF of the gamma distribution Gamma(a, 1).</p>
<pre><code class="lang-perl">p gammainc_reg(2, 1) # P(Gamma(2,1) < 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-gammaincc-reg">
<h3><a class="doc-anchor" href="#doc-gammaincc-reg">#</a> <code>gammaincc_reg</code></h3>
<p><code>gammaincc_reg</code> (alias <code>gamma_ur</code>) computes the regularized upper incomplete gamma Q(a,x) = 1 - P(a,x), the survival function of the gamma distribution.</p>
<pre><code class="lang-perl">p gammaincc_reg(2, 1) # P(Gamma(2,1) > 1)
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-bessel-airy-hankel-struve-kelvin">
<h2>Bessel / Airy / Hankel / Struve / Kelvin</h2>
<p class="chapter-meta">19 topics</p>
<article class="doc-entry" id="doc-bessel-j0">
<h3><a class="doc-anchor" href="#doc-bessel-j0">#</a> <code>bessel_j0</code></h3>
<p><code>bessel_j0</code> (alias <code>j0</code>) computes the Bessel function of the first kind, order 0.</p>
<pre><code class="lang-perl">p j0(0) # 1.0
p j0(2.4) # ≈ 0 (first zero)
</code></pre>
</article>
<article class="doc-entry" id="doc-bessel-j1">
<h3><a class="doc-anchor" href="#doc-bessel-j1">#</a> <code>bessel_j1</code></h3>
<p><code>bessel_j1</code> (alias <code>j1</code>) computes the Bessel function of the first kind, order 1.</p>
<pre><code class="lang-perl">p j1(0) # 0.0
p j1(1.84) # ≈ 0.582 (first max)
</code></pre>
</article>
<article class="doc-entry" id="doc-bessel-j">
<h3><a class="doc-anchor" href="#doc-bessel-j">#</a> <code>bessel_j</code></h3>
<p><code>bessel_j N, X</code> — Bessel function of the first kind J_n(x) for integer n. Generalises <code>bessel_j0</code> / <code>bessel_j1</code>.</p>
<pre><code class="lang-perl">p bessel_j(2, 5) # ≈ 0.0466
p bessel_j(0, 0) # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-bessel-y">
<h3><a class="doc-anchor" href="#doc-bessel-y">#</a> <code>bessel_y</code></h3>
<p><code>bessel_y N, X</code> — Bessel function of the second kind Y_n(x). Singular at x = 0.</p>
<pre><code class="lang-perl">p bessel_y(0, 1) # ≈ 0.0883
p bessel_y(1, 5) # ≈ 0.1479
</code></pre>
</article>
<article class="doc-entry" id="doc-bessel-i">
<h3><a class="doc-anchor" href="#doc-bessel-i">#</a> <code>bessel_i</code></h3>
<p><code>bessel_i N, X</code> — Modified Bessel function I_n(x). Grows exponentially for large x.</p>
<pre><code class="lang-perl">p bessel_i(0, 1) # ≈ 1.266
p bessel_i(2, 3) # ≈ 2.245
</code></pre>
</article>
<article class="doc-entry" id="doc-bessel-k">
<h3><a class="doc-anchor" href="#doc-bessel-k">#</a> <code>bessel_k</code></h3>
<p><code>bessel_k N, X</code> — Modified Bessel function K_n(x). Decays exponentially for large x; singular at 0.</p>
<pre><code class="lang-perl">p bessel_k(0, 1) # ≈ 0.4210
p bessel_k(1, 1) # ≈ 0.6019
</code></pre>
</article>
<article class="doc-entry" id="doc-hankel-h1">
<h3><a class="doc-anchor" href="#doc-hankel-h1">#</a> <code>hankel_h1</code></h3>
<p><code>hankel_h1 N, X</code> returns the complex Hankel H_n^(1)(x) = J_n(x) + i Y_n(x) as <code>[Re, Im]</code>.</p>
<pre><code class="lang-perl">my ($re, $im) = hankel_h1(0, 1)
p "$re + i*$im"
</code></pre>
</article>
<article class="doc-entry" id="doc-hankel-h2">
<h3><a class="doc-anchor" href="#doc-hankel-h2">#</a> <code>hankel_h2</code></h3>
<p><code>hankel_h2 N, X</code> returns H_n^(2)(x) = J_n(x) - i Y_n(x) as <code>[Re, Im]</code>.</p>
</article>
<article class="doc-entry" id="doc-bessel-j-zero">
<h3><a class="doc-anchor" href="#doc-bessel-j-zero">#</a> <code>bessel_j_zero</code></h3>
<p><code>bessel_j_zero N, K</code> computes the Kth positive zero of J_n. Uses McMahon expansion + Newton refinement.</p>
<pre><code class="lang-perl">p bessel_j_zero(0, 1) # 2.4048…
p bessel_j_zero(1, 1) # 3.8317…
</code></pre>
</article>
<article class="doc-entry" id="doc-airy-ai">
<h3><a class="doc-anchor" href="#doc-airy-ai">#</a> <code>airy_ai</code></h3>
<p><code>airy_ai X</code> — Airy function Ai(x) (decaying solution of y'' = x y).</p>
<pre><code class="lang-perl">p airy_ai(0) # ≈ 0.3550
p airy_ai(2) # ≈ 0.0349
</code></pre>
</article>
<article class="doc-entry" id="doc-airy-bi">
<h3><a class="doc-anchor" href="#doc-airy-bi">#</a> <code>airy_bi</code></h3>
<p><code>airy_bi X</code> — Airy function Bi(x) (growing solution).</p>
</article>
<article class="doc-entry" id="doc-airy-ai-prime">
<h3><a class="doc-anchor" href="#doc-airy-ai-prime">#</a> <code>airy_ai_prime</code></h3>
<p><code>airy_ai_prime X</code> — derivative Ai'(x).</p>
</article>
<article class="doc-entry" id="doc-airy-bi-prime">
<h3><a class="doc-anchor" href="#doc-airy-bi-prime">#</a> <code>airy_bi_prime</code></h3>
<p><code>airy_bi_prime X</code> — derivative Bi'(x).</p>
</article>
<article class="doc-entry" id="doc-spherical-bessel-j">
<h3><a class="doc-anchor" href="#doc-spherical-bessel-j">#</a> <code>spherical_bessel_j</code></h3>
<p><code>spherical_bessel_j N, X</code> — j_n(x) = √(π/2x) J_{n+1/2}(x).</p>
<pre><code class="lang-perl">p spherical_bessel_j(0, 1) # sin(1)
</code></pre>
</article>
<article class="doc-entry" id="doc-spherical-bessel-y">
<h3><a class="doc-anchor" href="#doc-spherical-bessel-y">#</a> <code>spherical_bessel_y</code></h3>
<p><code>spherical_bessel_y N, X</code> — y_n(x) = √(π/2x) Y_{n+1/2}(x).</p>
</article>
<article class="doc-entry" id="doc-struve-h">
<h3><a class="doc-anchor" href="#doc-struve-h">#</a> <code>struve_h</code></h3>
<p><code>struve_h N, X</code> — Struve function H_n(x) (solution of an inhomogeneous Bessel equation).</p>
</article>
<article class="doc-entry" id="doc-struve-l">
<h3><a class="doc-anchor" href="#doc-struve-l">#</a> <code>struve_l</code></h3>
<p><code>struve_l N, X</code> — Modified Struve L_n(x).</p>
</article>
<article class="doc-entry" id="doc-kelvin-ber">
<h3><a class="doc-anchor" href="#doc-kelvin-ber">#</a> <code>kelvin_ber</code></h3>
<p><code>kelvin_ber X</code> — Real part of J_0(x e^(3πi/4)) (Kelvin function ber₀).</p>
</article>
<article class="doc-entry" id="doc-kelvin-bei">
<h3><a class="doc-anchor" href="#doc-kelvin-bei">#</a> <code>kelvin_bei</code></h3>
<p><code>kelvin_bei X</code> — Imaginary part of J_0(x e^(3πi/4)) (Kelvin function bei₀).</p>
</article>
</section>
<section class="tutorial-section" id="ch-orthogonal-polynomials">
<h2>Orthogonal Polynomials</h2>
<p class="chapter-meta">13 topics</p>
<article class="doc-entry" id="doc-legendre-p">
<h3><a class="doc-anchor" href="#doc-legendre-p">#</a> <code>legendre_p</code></h3>
<p><code>legendre_p N, X</code> — Legendre polynomial P_n(x). Uses the stable Bonnet recurrence (2n+1) x P_n = (n+1) P_{n+1} + n P_{n-1}.</p>
<pre><code class="lang-perl">p legendre_p(2, 0.5) # -0.125
p legendre_p(5, 1) # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-legendre-q">
<h3><a class="doc-anchor" href="#doc-legendre-q">#</a> <code>legendre_q</code></h3>
<p><code>legendre_q N, X</code> — Legendre Q_n(x), the second-kind solution. NaN for |x| ≥ 1.</p>
</article>
<article class="doc-entry" id="doc-assoc-legendre-p">
<h3><a class="doc-anchor" href="#doc-assoc-legendre-p">#</a> <code>assoc_legendre_p</code></h3>
<p><code>assoc_legendre_p N, M, X</code> — Associated Legendre P_n^m(x). Building block for spherical harmonics.</p>
</article>
<article class="doc-entry" id="doc-hermite-h">
<h3><a class="doc-anchor" href="#doc-hermite-h">#</a> <code>hermite_h</code></h3>
<p><code>hermite_h N, X</code> — Physicist's Hermite H_n(x): H_0=1, H_1=2x, H_{n+1}=2x H_n - 2n H_{n-1}.</p>
<pre><code class="lang-perl">p hermite_h(3, 1) # -4
</code></pre>
</article>
<article class="doc-entry" id="doc-hermite-he">
<h3><a class="doc-anchor" href="#doc-hermite-he">#</a> <code>hermite_he</code></h3>
<p><code>hermite_he N, X</code> — Probabilist's Hermite He_n(x): He_0=1, He_1=x, He_{n+1}=x He_n - n He_{n-1}.</p>
</article>
<article class="doc-entry" id="doc-laguerre-l">
<h3><a class="doc-anchor" href="#doc-laguerre-l">#</a> <code>laguerre_l</code></h3>
<p><code>laguerre_l N, X</code> — Laguerre polynomial L_n(x).</p>
</article>
<article class="doc-entry" id="doc-assoc-laguerre-l">
<h3><a class="doc-anchor" href="#doc-assoc-laguerre-l">#</a> <code>assoc_laguerre_l</code></h3>
<p><code>assoc_laguerre_l N, ALPHA, X</code> — Generalised Laguerre L_n^α(x).</p>
</article>
<article class="doc-entry" id="doc-jacobi-p">
<h3><a class="doc-anchor" href="#doc-jacobi-p">#</a> <code>jacobi_p</code></h3>
<p><code>jacobi_p N, ALPHA, BETA, X</code> — Jacobi polynomial P_n^{(α,β)}(x). Generalises Legendre/Chebyshev/Gegenbauer.</p>
</article>
<article class="doc-entry" id="doc-gegenbauer-c">
<h3><a class="doc-anchor" href="#doc-gegenbauer-c">#</a> <code>gegenbauer_c</code></h3>
<p><code>gegenbauer_c N, ALPHA, X</code> — Gegenbauer C_n^α(x). Reduces to Chebyshev/Legendre at specific α.</p>
</article>
<article class="doc-entry" id="doc-chebyshev-t">
<h3><a class="doc-anchor" href="#doc-chebyshev-t">#</a> <code>chebyshev_t</code></h3>
<p><code>chebyshev_t N, X</code> — Chebyshev polynomial of the first kind T_n(x). Recurrence T_{n+1} = 2x T_n - T_{n-1}.</p>
<pre><code class="lang-perl">p chebyshev_t(3, 0.5) # -0.5
</code></pre>
</article>
<article class="doc-entry" id="doc-chebyshev-u">
<h3><a class="doc-anchor" href="#doc-chebyshev-u">#</a> <code>chebyshev_u</code></h3>
<p><code>chebyshev_u N, X</code> — Chebyshev polynomial of the second kind U_n(x).</p>
</article>
<article class="doc-entry" id="doc-spherical-harmonic-y">
<h3><a class="doc-anchor" href="#doc-spherical-harmonic-y">#</a> <code>spherical_harmonic_y</code></h3>
<p><code>spherical_harmonic_y L, M, THETA, PHI</code> — Spherical harmonic Y_l^m(θ, φ) returned as <code>[Re, Im]</code>.</p>
</article>
<article class="doc-entry" id="doc-zernike-r">
<h3><a class="doc-anchor" href="#doc-zernike-r">#</a> <code>zernike_r</code></h3>
<p><code>zernike_r N, M, R</code> — Radial Zernike polynomial R_n^m(r). 0 if (n − m) is odd or m > n.</p>
</article>
</section>
<section class="tutorial-section" id="ch-elliptic-integrals-functions">
<h2>Elliptic Integrals & Functions</h2>
<p class="chapter-meta">18 topics</p>
<article class="doc-entry" id="doc-elliptic-k">
<h3><a class="doc-anchor" href="#doc-elliptic-k">#</a> <code>elliptic_k</code></h3>
<p><code>elliptic_k M</code> — Complete elliptic integral K(m), m = k². Computed via Carlson R_F.</p>
<pre><code class="lang-perl">p elliptic_k(0) # π/2
p elliptic_k(0.5) # ≈ 1.8541
</code></pre>
</article>
<article class="doc-entry" id="doc-elliptic-e">
<h3><a class="doc-anchor" href="#doc-elliptic-e">#</a> <code>elliptic_e</code></h3>
<p><code>elliptic_e M</code> — Complete elliptic integral of the second kind E(m).</p>
</article>
<article class="doc-entry" id="doc-elliptic-pi">
<h3><a class="doc-anchor" href="#doc-elliptic-pi">#</a> <code>elliptic_pi</code></h3>
<p><code>elliptic_pi N, M</code> — Complete elliptic integral of the third kind Π(n | m).</p>
</article>
<article class="doc-entry" id="doc-elliptic-f">
<h3><a class="doc-anchor" href="#doc-elliptic-f">#</a> <code>elliptic_f</code></h3>
<p><code>elliptic_f PHI, M</code> — Incomplete F(φ, m).</p>
</article>
<article class="doc-entry" id="doc-elliptic-e-inc">
<h3><a class="doc-anchor" href="#doc-elliptic-e-inc">#</a> <code>elliptic_e_inc</code></h3>
<p><code>elliptic_e_inc PHI, M</code> — Incomplete E(φ, m).</p>
</article>
<article class="doc-entry" id="doc-elliptic-pi-inc">
<h3><a class="doc-anchor" href="#doc-elliptic-pi-inc">#</a> <code>elliptic_pi_inc</code></h3>
<p><code>elliptic_pi_inc N, PHI, M</code> — Incomplete Π(n; φ | m).</p>
</article>
<article class="doc-entry" id="doc-carlson-rf">
<h3><a class="doc-anchor" href="#doc-carlson-rf">#</a> <code>carlson_rf</code></h3>
<p><code>carlson_rf X, Y, Z</code> — Carlson symmetric form R_F. Building block for the elliptic family.</p>
</article>
<article class="doc-entry" id="doc-carlson-rd">
<h3><a class="doc-anchor" href="#doc-carlson-rd">#</a> <code>carlson_rd</code></h3>
<p><code>carlson_rd X, Y, Z</code> — Carlson R_D.</p>
</article>
<article class="doc-entry" id="doc-carlson-rj">
<h3><a class="doc-anchor" href="#doc-carlson-rj">#</a> <code>carlson_rj</code></h3>
<p><code>carlson_rj X, Y, Z, P</code> — Carlson R_J.</p>
</article>
<article class="doc-entry" id="doc-jacobi-sn">
<h3><a class="doc-anchor" href="#doc-jacobi-sn">#</a> <code>jacobi_sn</code></h3>
<p><code>jacobi_sn U, M</code> — Jacobi elliptic sn(u, m). Reduces to sin(u) at m = 0 and tanh(u) at m = 1.</p>
<pre><code class="lang-perl">p jacobi_sn(1, 0.5) # ≈ 0.8030
</code></pre>
</article>
<article class="doc-entry" id="doc-jacobi-cn">
<h3><a class="doc-anchor" href="#doc-jacobi-cn">#</a> <code>jacobi_cn</code></h3>
<p><code>jacobi_cn U, M</code> — Jacobi elliptic cn(u, m). Reduces to cos(u) at m = 0.</p>
</article>
<article class="doc-entry" id="doc-jacobi-dn">
<h3><a class="doc-anchor" href="#doc-jacobi-dn">#</a> <code>jacobi_dn</code></h3>
<p><code>jacobi_dn U, M</code> — Jacobi elliptic dn(u, m). Reduces to 1 at m = 0.</p>
</article>
<article class="doc-entry" id="doc-jacobi-am">
<h3><a class="doc-anchor" href="#doc-jacobi-am">#</a> <code>jacobi_am</code></h3>
<p><code>jacobi_am U, M</code> — Jacobi amplitude φ such that sn(u, m) = sin(φ).</p>
</article>
<article class="doc-entry" id="doc-elliptic-theta">
<h3><a class="doc-anchor" href="#doc-elliptic-theta">#</a> <code>elliptic_theta</code></h3>
<p><code>elliptic_theta J, Z, Q</code> — Jacobi theta θ_j(z, q) for j ∈ {1, 2, 3, 4}, |q| < 1.</p>
</article>
<article class="doc-entry" id="doc-weierstrass-p">
<h3><a class="doc-anchor" href="#doc-weierstrass-p">#</a> <code>weierstrass_p</code></h3>
<p><code>weierstrass_p Z, G2, G3</code> — Weierstrass ℘(z; g₂, g₃) via Laurent series. Pole at z = 0.</p>
</article>
<article class="doc-entry" id="doc-weierstrass-zeta">
<h3><a class="doc-anchor" href="#doc-weierstrass-zeta">#</a> <code>weierstrass_zeta</code></h3>
<p><code>weierstrass_zeta Z, G2, G3</code> — Weierstrass ζ(z; g₂, g₃).</p>
</article>
<article class="doc-entry" id="doc-weierstrass-sigma">
<h3><a class="doc-anchor" href="#doc-weierstrass-sigma">#</a> <code>weierstrass_sigma</code></h3>
<p><code>weierstrass_sigma Z, G2, G3</code> — Weierstrass σ(z; g₂, g₃).</p>
</article>
<article class="doc-entry" id="doc-inverse-jacobi-sn">
<h3><a class="doc-anchor" href="#doc-inverse-jacobi-sn">#</a> <code>inverse_jacobi_sn</code></h3>
<p><code>inverse_jacobi_sn X, M</code> — inverse of <code>jacobi_sn</code>: returns u with sn(u, m) = x.</p>
</article>
</section>
<section class="tutorial-section" id="ch-zeta-polylog-lerch">
<h2>Zeta / Polylog / Lerch</h2>
<p class="chapter-meta">9 topics</p>
<article class="doc-entry" id="doc-zeta">
<h3><a class="doc-anchor" href="#doc-zeta">#</a> <code>zeta</code></h3>
<p><code>zeta S</code> — Riemann ζ(s) via Euler-Maclaurin (s > 0.5) or reflection identity.</p>
<pre><code class="lang-perl">p zeta(2) # π²/6 ≈ 1.6449
p zeta(4) # ≈ 1.0823
p zeta(-1) # -1/12
</code></pre>
</article>
<article class="doc-entry" id="doc-hurwitz-zeta">
<h3><a class="doc-anchor" href="#doc-hurwitz-zeta">#</a> <code>hurwitz_zeta</code></h3>
<p><code>hurwitz_zeta S, A</code> — Hurwitz ζ(s, a). <code>hurwitz_zeta(s, 1)</code> ≡ <code>zeta(s)</code>.</p>
</article>
<article class="doc-entry" id="doc-polylog">
<h3><a class="doc-anchor" href="#doc-polylog">#</a> <code>polylog</code></h3>
<p><code>polylog N, Z</code> — Polylogarithm Li_n(z) = Σ z^k / k^n for |z| ≤ 1.</p>
<pre><code class="lang-perl">p polylog(2, 1) # π²/6
</code></pre>
</article>
<article class="doc-entry" id="doc-dilog">
<h3><a class="doc-anchor" href="#doc-dilog">#</a> <code>dilog</code></h3>
<p><code>dilog Z</code> — Dilogarithm Li_2(z). Convenience alias for <code>polylog(2, z)</code>.</p>
</article>
<article class="doc-entry" id="doc-lerch-phi">
<h3><a class="doc-anchor" href="#doc-lerch-phi">#</a> <code>lerch_phi</code></h3>
<p><code>lerch_phi Z, S, A</code> — Lerch transcendent Φ(z, s, a) = Σ z^k / (a+k)^s.</p>
</article>
<article class="doc-entry" id="doc-riemann-siegel-z">
<h3><a class="doc-anchor" href="#doc-riemann-siegel-z">#</a> <code>riemann_siegel_z</code></h3>
<p><code>riemann_siegel_z T</code> — Riemann-Siegel Z(t) on the critical line.</p>
</article>
<article class="doc-entry" id="doc-riemann-siegel-theta">
<h3><a class="doc-anchor" href="#doc-riemann-siegel-theta">#</a> <code>riemann_siegel_theta</code></h3>
<p><code>riemann_siegel_theta T</code> — Riemann-Siegel θ(t) (asymptotic Stirling form).</p>
</article>
<article class="doc-entry" id="doc-dirichlet-eta">
<h3><a class="doc-anchor" href="#doc-dirichlet-eta">#</a> <code>dirichlet_eta</code></h3>
<p><code>dirichlet_eta S</code> — Dirichlet η(s) = (1 − 2^(1−s)) ζ(s).</p>
</article>
<article class="doc-entry" id="doc-dirichlet-beta">
<h3><a class="doc-anchor" href="#doc-dirichlet-beta">#</a> <code>dirichlet_beta</code></h3>
<p><code>dirichlet_beta S</code> — Dirichlet β(s) = Σ (-1)^k / (2k+1)^s.</p>
<pre><code class="lang-perl">p dirichlet_beta(1) # π/4 (Catalan-like)
p dirichlet_beta(2) # Catalan's constant ≈ 0.9160
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-hypergeometric">
<h2>Hypergeometric</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-hypergeometric-2f1">
<h3><a class="doc-anchor" href="#doc-hypergeometric-2f1">#</a> <code>hypergeometric_2f1</code></h3>
<p><code>hypergeometric_2f1 A, B, C, Z</code> — ₂F₁(a, b; c; z) Gauss hypergeometric. Series convergent for |z| < 1.</p>
<pre><code class="lang-perl">p hypergeometric_2f1(0.5, 0.5, 1, 0.5) # ≈ 1.1803
</code></pre>
</article>
<article class="doc-entry" id="doc-hypergeometric-1f1">
<h3><a class="doc-anchor" href="#doc-hypergeometric-1f1">#</a> <code>hypergeometric_1f1</code></h3>
<p><code>hypergeometric_1f1 A, B, Z</code> — ₁F₁(a; b; z) Kummer / confluent hypergeometric.</p>
</article>
<article class="doc-entry" id="doc-hypergeometric-0f1">
<h3><a class="doc-anchor" href="#doc-hypergeometric-0f1">#</a> <code>hypergeometric_0f1</code></h3>
<p><code>hypergeometric_0f1 B, Z</code> — ₀F₁(; b; z). Related to Bessel: J_ν(x) = (x/2)^ν / Γ(ν+1) · ₀F₁(; ν+1; -x²/4).</p>
</article>
<article class="doc-entry" id="doc-hypergeometric-pfq">
<h3><a class="doc-anchor" href="#doc-hypergeometric-pfq">#</a> <code>hypergeometric_pfq</code></h3>
<p><code>hypergeometric_pfq AS, BS, Z</code> — generalised _pF_q. AS, BS are arrays of upper/lower parameters.</p>
</article>
<article class="doc-entry" id="doc-hypergeometric-u">
<h3><a class="doc-anchor" href="#doc-hypergeometric-u">#</a> <code>hypergeometric_u</code></h3>
<p><code>hypergeometric_u A, B, Z</code> — Tricomi's confluent U(a, b, z).</p>
</article>
</section>
<section class="tutorial-section" id="ch-modular-forms">
<h2>Modular Forms</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-dedekind-eta">
<h3><a class="doc-anchor" href="#doc-dedekind-eta">#</a> <code>dedekind_eta</code></h3>
<p><code>dedekind_eta Y</code> — Dedekind η(iy) on the imaginary axis. Real-valued q-series with q = exp(-2π y).</p>
</article>
<article class="doc-entry" id="doc-klein-j">
<h3><a class="doc-anchor" href="#doc-klein-j">#</a> <code>klein_j</code></h3>
<p><code>klein_j Y</code> — Klein j-invariant j(iy) = E_4³ / Δ.</p>
</article>
<article class="doc-entry" id="doc-modular-lambda">
<h3><a class="doc-anchor" href="#doc-modular-lambda">#</a> <code>modular_lambda</code></h3>
<p><code>modular_lambda Y</code> — Modular λ(iy) = θ_2(0, q)^4 / θ_3(0, q)^4.</p>
</article>
<article class="doc-entry" id="doc-ramanujan-tau">
<h3><a class="doc-anchor" href="#doc-ramanujan-tau">#</a> <code>ramanujan_tau</code></h3>
<p><code>ramanujan_tau N</code> — τ(n), the nth coefficient of Δ(τ) = η(τ)^24. Returns an integer.</p>
<pre><code class="lang-perl">p ramanujan_tau(1) # 1
p ramanujan_tau(2) # -24
p ramanujan_tau(3) # 252
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-si-ci-ei-li-fresnel-integrals">
<h2>Si / Ci / Ei / Li / Fresnel Integrals</h2>
<p class="chapter-meta">9 topics</p>
<article class="doc-entry" id="doc-sin-integral">
<h3><a class="doc-anchor" href="#doc-sin-integral">#</a> <code>sin_integral</code></h3>
<p><code>sin_integral X</code> — Si(x) = ∫₀ˣ sin(t)/t dt. Si(∞) = π/2.</p>
<pre><code class="lang-perl">p sin_integral(1) # ≈ 0.9461
p sin_integral(10) # ≈ 1.6583
</code></pre>
</article>
<article class="doc-entry" id="doc-cos-integral">
<h3><a class="doc-anchor" href="#doc-cos-integral">#</a> <code>cos_integral</code></h3>
<p><code>cos_integral X</code> — Ci(x) = γ + ln(x) + ∫₀ˣ (cos(t)−1)/t dt. NaN for x ≤ 0.</p>
</article>
<article class="doc-entry" id="doc-sinh-integral">
<h3><a class="doc-anchor" href="#doc-sinh-integral">#</a> <code>sinh_integral</code></h3>
<p><code>sinh_integral X</code> — Shi(x) = ∫₀ˣ sinh(t)/t dt.</p>
</article>
<article class="doc-entry" id="doc-cosh-integral">
<h3><a class="doc-anchor" href="#doc-cosh-integral">#</a> <code>cosh_integral</code></h3>
<p><code>cosh_integral X</code> — Chi(x) = γ + ln(x) + ∫₀ˣ (cosh(t)−1)/t dt.</p>
</article>
<article class="doc-entry" id="doc-exp-integral-e">
<h3><a class="doc-anchor" href="#doc-exp-integral-e">#</a> <code>exp_integral_e</code></h3>
<p><code>exp_integral_e N, X</code> — generalised exponential integral E_n(x) = ∫_1^∞ e^{-x t} / t^n dt.</p>
</article>
<article class="doc-entry" id="doc-exp-integral-ei">
<h3><a class="doc-anchor" href="#doc-exp-integral-ei">#</a> <code>exp_integral_ei</code></h3>
<p><code>exp_integral_ei X</code> — Ei(x). For x > 0 uses series + asymptotic split.</p>
</article>
<article class="doc-entry" id="doc-log-integral">
<h3><a class="doc-anchor" href="#doc-log-integral">#</a> <code>log_integral</code></h3>
<p><code>log_integral X</code> — li(x) = Ei(ln x). Approximates the prime-counting function near <code>prime_pi</code>.</p>
<pre><code class="lang-perl">p log_integral(1000) # ≈ 178
</code></pre>
</article>
<article class="doc-entry" id="doc-fresnel-s">
<h3><a class="doc-anchor" href="#doc-fresnel-s">#</a> <code>fresnel_s</code></h3>
<p><code>fresnel_s X</code> — Fresnel S(x) = ∫₀ˣ sin(π t² / 2) dt.</p>
</article>
<article class="doc-entry" id="doc-fresnel-c">
<h3><a class="doc-anchor" href="#doc-fresnel-c">#</a> <code>fresnel_c</code></h3>
<p><code>fresnel_c X</code> — Fresnel C(x) = ∫₀ˣ cos(π t² / 2) dt.</p>
</article>
</section>
<section class="tutorial-section" id="ch-number-theory-wolfram-parity">
<h2>Number Theory (Wolfram Parity)</h2>
<p class="chapter-meta">13 topics</p>
<article class="doc-entry" id="doc-jacobi-symbol">
<h3><a class="doc-anchor" href="#doc-jacobi-symbol">#</a> <code>jacobi_symbol</code></h3>
<p><code>jacobi_symbol A, N</code> — Jacobi symbol (a/n) for positive odd n. Returns -1, 0, or 1.</p>
<pre><code class="lang-perl">p jacobi_symbol(2, 7) # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-kronecker-symbol">
<h3><a class="doc-anchor" href="#doc-kronecker-symbol">#</a> <code>kronecker_symbol</code></h3>
<p><code>kronecker_symbol A, N</code> — Extension of the Jacobi symbol to all integers n.</p>
</article>
<article class="doc-entry" id="doc-primitive-root">
<h3><a class="doc-anchor" href="#doc-primitive-root">#</a> <code>primitive_root</code></h3>
<p><code>primitive_root P</code> — Smallest primitive root mod p (p prime). <code>undef</code> if none.</p>
</article>
<article class="doc-entry" id="doc-multiplicative-order">
<h3><a class="doc-anchor" href="#doc-multiplicative-order">#</a> <code>multiplicative_order</code></h3>
<p><code>multiplicative_order A, N</code> — smallest k > 0 with a^k ≡ 1 (mod n). <code>undef</code> if gcd(a, n) ≠ 1.</p>
</article>
<article class="doc-entry" id="doc-mangoldt-lambda">
<h3><a class="doc-anchor" href="#doc-mangoldt-lambda">#</a> <code>mangoldt_lambda</code></h3>
<p><code>mangoldt_lambda N</code> — von Mangoldt Λ(n) = ln(p) if n = p^k, else 0.</p>
</article>
<article class="doc-entry" id="doc-carmichael-lambda">
<h3><a class="doc-anchor" href="#doc-carmichael-lambda">#</a> <code>carmichael_lambda</code></h3>
<p><code>carmichael_lambda N</code> — Carmichael λ(n), the exponent of (Z/nZ)*.</p>
<pre><code class="lang-perl">p carmichael_lambda(15) # 4
</code></pre>
</article>
<article class="doc-entry" id="doc-squares-r">
<h3><a class="doc-anchor" href="#doc-squares-r">#</a> <code>squares_r</code></h3>
<p><code>squares_r K, N</code> — number of representations of n as a sum of k squares (signed, ordered).</p>
<pre><code class="lang-perl">p squares_r(2, 5) # 8 (e.g. ±1²+±2²)
</code></pre>
</article>
<article class="doc-entry" id="doc-thue-morse">
<h3><a class="doc-anchor" href="#doc-thue-morse">#</a> <code>thue_morse</code></h3>
<p><code>thue_morse N</code> — Thue-Morse t(n) = popcount(n) mod 2.</p>
</article>
<article class="doc-entry" id="doc-rudin-shapiro">
<h3><a class="doc-anchor" href="#doc-rudin-shapiro">#</a> <code>rudin_shapiro</code></h3>
<p><code>rudin_shapiro N</code> — Rudin-Shapiro sequence, ±1 = (-1)^a(n) where a(n) counts "11" patterns in binary(n).</p>
</article>
<article class="doc-entry" id="doc-farey-sequence">
<h3><a class="doc-anchor" href="#doc-farey-sequence">#</a> <code>farey_sequence</code></h3>
<p><code>farey_sequence N</code> — Farey sequence F_n. Returns array of <code>[a, b]</code> pairs.</p>
<pre><code class="lang-perl">p farey_sequence(3) # [[0,1],[1,3],[1,2],[2,3],[1,1]]
</code></pre>
</article>
<article class="doc-entry" id="doc-frobenius-number">
<h3><a class="doc-anchor" href="#doc-frobenius-number">#</a> <code>frobenius_number</code></h3>
<p><code>frobenius_number COINS</code> — largest amount NOT representable as a non-negative combination of <code>COINS</code>. Closed form for two coprime denominations.</p>
<pre><code class="lang-perl">p frobenius_number([3, 5]) # 7
</code></pre>
</article>
<article class="doc-entry" id="doc-frobenius-solve">
<h3><a class="doc-anchor" href="#doc-frobenius-solve">#</a> <code>frobenius_solve</code></h3>
<p><code>frobenius_solve COINS, N</code> — number of ways to make change for N using <code>COINS</code>.</p>
</article>
<article class="doc-entry" id="doc-stern-brocot">
<h3><a class="doc-anchor" href="#doc-stern-brocot">#</a> <code>stern_brocot</code></h3>
<p><code>stern_brocot N</code> — Stern-Brocot tree node N (1-indexed) as <code>[a, b]</code> (Calkin-Wilf order).</p>
</article>
</section>
<section class="tutorial-section" id="ch-combinatorics-wolfram-parity">
<h2>Combinatorics (Wolfram Parity)</h2>
<p class="chapter-meta">8 topics</p>
<article class="doc-entry" id="doc-stirling-s1">
<h3><a class="doc-anchor" href="#doc-stirling-s1">#</a> <code>stirling_s1</code></h3>
<p><code>stirling_s1 N, K</code> — unsigned Stirling number of the first kind |s(n,k)|.</p>
</article>
<article class="doc-entry" id="doc-bell-polynomial-b">
<h3><a class="doc-anchor" href="#doc-bell-polynomial-b">#</a> <code>bell_polynomial_b</code></h3>
<p><code>bell_polynomial_b N, K, XS</code> — partial Bell polynomial B_{n,k}(x_1, …, x_{n-k+1}).</p>
</article>
<article class="doc-entry" id="doc-clebsch-gordan">
<h3><a class="doc-anchor" href="#doc-clebsch-gordan">#</a> <code>clebsch_gordan</code></h3>
<p><code>clebsch_gordan J1, J2, J, M1, M2 [, M]</code> — Clebsch-Gordan coefficient. M defaults to M1 + M2.</p>
</article>
<article class="doc-entry" id="doc-three-j-symbol">
<h3><a class="doc-anchor" href="#doc-three-j-symbol">#</a> <code>three_j_symbol</code></h3>
<p><code>three_j_symbol J1, J2, J3, M1, M2, M3</code> — Wigner 3-j symbol.</p>
</article>
<article class="doc-entry" id="doc-six-j-symbol">
<h3><a class="doc-anchor" href="#doc-six-j-symbol">#</a> <code>six_j_symbol</code></h3>
<p><code>six_j_symbol J1 J2 J3 J4 J5 J6</code> — Wigner 6-j symbol.</p>
</article>
<article class="doc-entry" id="doc-nine-j-symbol">
<h3><a class="doc-anchor" href="#doc-nine-j-symbol">#</a> <code>nine_j_symbol</code></h3>
<p><code>nine_j_symbol</code> (9 args) — Wigner 9-j as a single sum over 6-j.</p>
</article>
<article class="doc-entry" id="doc-debruijn-sequence">
<h3><a class="doc-anchor" href="#doc-debruijn-sequence">#</a> <code>debruijn_sequence</code></h3>
<p><code>debruijn_sequence K, N</code> — De Bruijn B(k, n) as an array of k^n integers.</p>
</article>
<article class="doc-entry" id="doc-wigner-d">
<h3><a class="doc-anchor" href="#doc-wigner-d">#</a> <code>wigner_d</code></h3>
<p><code>wigner_d J, M1, M2, BETA</code> — small Wigner d-matrix d^j_{m1, m2}(β).</p>
</article>
</section>
<section class="tutorial-section" id="ch-q-series-mittag-leffler-coulomb">
<h2>q-Series, Mittag-Leffler, Coulomb</h2>
<p class="chapter-meta">7 topics</p>
<article class="doc-entry" id="doc-q-pochhammer">
<h3><a class="doc-anchor" href="#doc-q-pochhammer">#</a> <code>q_pochhammer</code></h3>
<p><code>q_pochhammer A, Q [, N]</code> — (a; q)_n. Omit N for the infinite product (|q| < 1).</p>
</article>
<article class="doc-entry" id="doc-q-factorial">
<h3><a class="doc-anchor" href="#doc-q-factorial">#</a> <code>q_factorial</code></h3>
<p><code>q_factorial N, Q</code> — q-factorial [n]_q!.</p>
</article>
<article class="doc-entry" id="doc-q-binomial">
<h3><a class="doc-anchor" href="#doc-q-binomial">#</a> <code>q_binomial</code></h3>
<p><code>q_binomial N, K, Q</code> — Gaussian binomial [n choose k]_q.</p>
</article>
<article class="doc-entry" id="doc-q-hypergeometric-pfq">
<h3><a class="doc-anchor" href="#doc-q-hypergeometric-pfq">#</a> <code>q_hypergeometric_pfq</code></h3>
<p><code>q_hypergeometric_pfq AS, BS, Q, Z</code> — basic-hypergeometric series.</p>
</article>
<article class="doc-entry" id="doc-mittag-leffler-e">
<h3><a class="doc-anchor" href="#doc-mittag-leffler-e">#</a> <code>mittag_leffler_e</code></h3>
<p><code>mittag_leffler_e ALPHA, BETA, Z</code> — E_{α,β}(z) = Σ z^k / Γ(α k + β). Generalises exp / cosh / Mittag-Leffler.</p>
</article>
<article class="doc-entry" id="doc-coulomb-wave-f">
<h3><a class="doc-anchor" href="#doc-coulomb-wave-f">#</a> <code>coulomb_wave_f</code></h3>
<p><code>coulomb_wave_f L, ETA, RHO</code> — regular Coulomb wave F_L(η, ρ) via the confluent-hypergeometric representation.</p>
</article>
<article class="doc-entry" id="doc-coulomb-wave-g">
<h3><a class="doc-anchor" href="#doc-coulomb-wave-g">#</a> <code>coulomb_wave_g</code></h3>
<p><code>coulomb_wave_g L, ETA, RHO</code> — irregular partner G_L. Currently returns NaN; faithful Bardin/Goesnig port pending.</p>
</article>
</section>
<section class="tutorial-section" id="ch-inverse-special-functions">
<h2>Inverse Special Functions</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-inverse-erf">
<h3><a class="doc-anchor" href="#doc-inverse-erf">#</a> <code>inverse_erf</code></h3>
<p><code>inverse_erf Y</code> — inverse error function. Solves erf(x) = y.</p>
<pre><code class="lang-perl">p inverse_erf(0.5) # ≈ 0.4769
</code></pre>
</article>
<article class="doc-entry" id="doc-inverse-erfc">
<h3><a class="doc-anchor" href="#doc-inverse-erfc">#</a> <code>inverse_erfc</code></h3>
<p><code>inverse_erfc Y</code> — inverse complementary error function.</p>
</article>
<article class="doc-entry" id="doc-inverse-gamma-regularized">
<h3><a class="doc-anchor" href="#doc-inverse-gamma-regularized">#</a> <code>inverse_gamma_regularized</code></h3>
<p><code>inverse_gamma_regularized A, Y</code> — solves P(a, x) = y for x.</p>
</article>
<article class="doc-entry" id="doc-inverse-beta-regularized">
<h3><a class="doc-anchor" href="#doc-inverse-beta-regularized">#</a> <code>inverse_beta_regularized</code></h3>
<p><code>inverse_beta_regularized A, B, Y</code> — solves I_x(a, b) = y for x via bisection.</p>
</article>
</section>
<section class="tutorial-section" id="ch-piecewise-symbolic-primitives">
<h2>Piecewise & Symbolic Primitives</h2>
<p class="chapter-meta">8 topics</p>
<article class="doc-entry" id="doc-dirac-delta">
<h3><a class="doc-anchor" href="#doc-dirac-delta">#</a> <code>dirac_delta</code></h3>
<p><code>dirac_delta X [, EPS]</code> — finite-width discrete approximation: 1/eps if |x| < eps/2 else 0. EPS defaults to 1e-3.</p>
</article>
<article class="doc-entry" id="doc-heaviside-theta">
<h3><a class="doc-anchor" href="#doc-heaviside-theta">#</a> <code>heaviside_theta</code></h3>
<p><code>heaviside_theta X</code> — Heaviside step function: 1 (x > 0), 0 (x < 0), 0.5 (x = 0).</p>
</article>
<article class="doc-entry" id="doc-unit-box">
<h3><a class="doc-anchor" href="#doc-unit-box">#</a> <code>unit_box</code></h3>
<p><code>unit_box X</code> — 1 if |x| ≤ 1/2 else 0.</p>
</article>
<article class="doc-entry" id="doc-unit-triangle">
<h3><a class="doc-anchor" href="#doc-unit-triangle">#</a> <code>unit_triangle</code></h3>
<p><code>unit_triangle X</code> — max(1 − |x|, 0).</p>
</article>
<article class="doc-entry" id="doc-square-wave">
<h3><a class="doc-anchor" href="#doc-square-wave">#</a> <code>square_wave</code></h3>
<p><code>square_wave X [, PERIOD]</code> — alternates +1/-1 with the given period (default 1).</p>
</article>
<article class="doc-entry" id="doc-triangle-wave">
<h3><a class="doc-anchor" href="#doc-triangle-wave">#</a> <code>triangle_wave</code></h3>
<p><code>triangle_wave X [, PERIOD]</code> — periodic triangle wave on [-1, 1].</p>
</article>
<article class="doc-entry" id="doc-sawtooth-wave">
<h3><a class="doc-anchor" href="#doc-sawtooth-wave">#</a> <code>sawtooth_wave</code></h3>
<p><code>sawtooth_wave X [, PERIOD]</code> — periodic sawtooth on [-1, 1].</p>
</article>
<article class="doc-entry" id="doc-dirac-comb">
<h3><a class="doc-anchor" href="#doc-dirac-comb">#</a> <code>dirac_comb</code></h3>
<p><code>dirac_comb X, T [, EPS]</code> — sum of Dirac deltas at multiples of T (discrete approximation).</p>
</article>
</section>
<section class="tutorial-section" id="ch-number-theory-wolfram-parity-ii">
<h2>Number Theory (Wolfram Parity II)</h2>
<p class="chapter-meta">14 topics</p>
<article class="doc-entry" id="doc-liouville-lambda">
<h3><a class="doc-anchor" href="#doc-liouville-lambda">#</a> <code>liouville_lambda</code></h3>
<p><code>liouville_lambda N</code> — Liouville λ(n) = (-1)^Ω(n).</p>
</article>
<article class="doc-entry" id="doc-jordan-totient">
<h3><a class="doc-anchor" href="#doc-jordan-totient">#</a> <code>jordan_totient</code></h3>
<p><code>jordan_totient K, N</code> — Jordan totient J_k(n) = n^k Π_{p | n} (1 - p^{-k}).</p>
</article>
<article class="doc-entry" id="doc-ramanujan-sum">
<h3><a class="doc-anchor" href="#doc-ramanujan-sum">#</a> <code>ramanujan_sum</code></h3>
<p><code>ramanujan_sum Q, N</code> — c_q(n) = Σ_{d | gcd(q,n)} μ(q/d) d.</p>
</article>
<article class="doc-entry" id="doc-cyclotomic-polynomial">
<h3><a class="doc-anchor" href="#doc-cyclotomic-polynomial">#</a> <code>cyclotomic_polynomial</code></h3>
<p><code>cyclotomic_polynomial N</code> — coefficient list of Φ_n(x).</p>
<pre><code class="lang-perl">p cyclotomic_polynomial(6) # [1, -1, 1] = x²-x+1
</code></pre>
</article>
<article class="doc-entry" id="doc-legendre-symbol">
<h3><a class="doc-anchor" href="#doc-legendre-symbol">#</a> <code>legendre_symbol</code></h3>
<p><code>legendre_symbol A, P</code> — Legendre symbol (a/p) for prime p. -1, 0, or 1.</p>
</article>
<article class="doc-entry" id="doc-pythagorean-triple-q">
<h3><a class="doc-anchor" href="#doc-pythagorean-triple-q">#</a> <code>pythagorean_triple_q</code></h3>
<p><code>pythagorean_triple_q A, B, C</code> — 1 if a² + b² = c² (any order/sign).</p>
</article>
<article class="doc-entry" id="doc-gen-pythagorean-triple">
<h3><a class="doc-anchor" href="#doc-gen-pythagorean-triple">#</a> <code>gen_pythagorean_triple</code></h3>
<p><code>gen_pythagorean_triple M, N</code> — Euclid formula: returns [m²-n², 2mn, m²+n²].</p>
</article>
<article class="doc-entry" id="doc-sophie-germain-q">
<h3><a class="doc-anchor" href="#doc-sophie-germain-q">#</a> <code>sophie_germain_q</code></h3>
<p><code>sophie_germain_q P</code> — 1 if both p and 2p+1 are prime.</p>
</article>
<article class="doc-entry" id="doc-mersenne-q">
<h3><a class="doc-anchor" href="#doc-mersenne-q">#</a> <code>mersenne_q</code></h3>
<p><code>mersenne_q N</code> — 1 if 2^n - 1 is a Mersenne prime (Lucas-Lehmer).</p>
</article>
<article class="doc-entry" id="doc-lucas-lehmer-test">
<h3><a class="doc-anchor" href="#doc-lucas-lehmer-test">#</a> <code>lucas_lehmer_test</code></h3>
<p><code>lucas_lehmer_test P</code> — Lucas-Lehmer primality test for 2^p - 1.</p>
</article>
<article class="doc-entry" id="doc-continued-fraction">
<h3><a class="doc-anchor" href="#doc-continued-fraction">#</a> <code>continued_fraction</code></h3>
<p><code>continued_fraction X [, N]</code> — first N coefficients of the simple continued-fraction expansion. N defaults to 12.</p>
</article>
<article class="doc-entry" id="doc-from-continued-fraction">
<h3><a class="doc-anchor" href="#doc-from-continued-fraction">#</a> <code>from_continued_fraction</code></h3>
<p><code>from_continued_fraction COEFFS</code> — evaluate [a0; a1, a2, …] back to a real number.</p>
</article>
<article class="doc-entry" id="doc-convergents">
<h3><a class="doc-anchor" href="#doc-convergents">#</a> <code>convergents</code></h3>
<p><code>convergents X [, N]</code> — N successive [num, denom] convergents.</p>
</article>
<article class="doc-entry" id="doc-best-rational-approximation">
<h3><a class="doc-anchor" href="#doc-best-rational-approximation">#</a> <code>best_rational_approximation</code></h3>
<p><code>best_rational_approximation X, MAX_DENOM</code> — closest fraction p/q with q ≤ MAX_DENOM. Returns [p, q].</p>
</article>
</section>
<section class="tutorial-section" id="ch-combinatorial-sequences">
<h2>Combinatorial Sequences</h2>
<p class="chapter-meta">12 topics</p>
<article class="doc-entry" id="doc-motzkin-number">
<h3><a class="doc-anchor" href="#doc-motzkin-number">#</a> <code>motzkin_number</code></h3>
<p><code>motzkin_number N</code> — # paths on (0..n) using → ↗ ↘ steps (no crossings).</p>
</article>
<article class="doc-entry" id="doc-narayana-number">
<h3><a class="doc-anchor" href="#doc-narayana-number">#</a> <code>narayana_number</code></h3>
<p><code>narayana_number N, K</code> — N(n, k) = (1/n) C(n,k) C(n,k-1).</p>
</article>
<article class="doc-entry" id="doc-delannoy-number">
<h3><a class="doc-anchor" href="#doc-delannoy-number">#</a> <code>delannoy_number</code></h3>
<p><code>delannoy_number M, N</code> — # paths in (m+1)×(n+1) grid using → ↑ ↗.</p>
</article>
<article class="doc-entry" id="doc-schroder-number">
<h3><a class="doc-anchor" href="#doc-schroder-number">#</a> <code>schroder_number</code></h3>
<p><code>schroder_number N</code> — large Schröder number.</p>
</article>
<article class="doc-entry" id="doc-small-schroder-number">
<h3><a class="doc-anchor" href="#doc-small-schroder-number">#</a> <code>small_schroder_number</code></h3>
<p><code>small_schroder_number N</code> — small Schröder s_n = S_n / 2 (n ≥ 1).</p>
</article>
<article class="doc-entry" id="doc-eulerian-number">
<h3><a class="doc-anchor" href="#doc-eulerian-number">#</a> <code>eulerian_number</code></h3>
<p><code>eulerian_number N, K</code> — ⟨n k⟩, # permutations of [n] with k ascents.</p>
</article>
<article class="doc-entry" id="doc-bernoulli-polynomial">
<h3><a class="doc-anchor" href="#doc-bernoulli-polynomial">#</a> <code>bernoulli_polynomial</code></h3>
<p><code>bernoulli_polynomial N, X</code> — B_n(x).</p>
</article>
<article class="doc-entry" id="doc-euler-polynomial">
<h3><a class="doc-anchor" href="#doc-euler-polynomial">#</a> <code>euler_polynomial</code></h3>
<p><code>euler_polynomial N, X</code> — E_n(x).</p>
</article>
<article class="doc-entry" id="doc-pell-number">
<h3><a class="doc-anchor" href="#doc-pell-number">#</a> <code>pell_number</code></h3>
<p><code>pell_number N</code> — Pell number P_n.</p>
</article>
<article class="doc-entry" id="doc-pell-lucas-number">
<h3><a class="doc-anchor" href="#doc-pell-lucas-number">#</a> <code>pell_lucas_number</code></h3>
<p><code>pell_lucas_number N</code> — companion Pell-Lucas Q_n.</p>
</article>
<article class="doc-entry" id="doc-perrin-number">
<h3><a class="doc-anchor" href="#doc-perrin-number">#</a> <code>perrin_number</code></h3>
<p><code>perrin_number N</code> — Perrin sequence P(n) = P(n-2) + P(n-3).</p>
</article>
<article class="doc-entry" id="doc-padovan-number">
<h3><a class="doc-anchor" href="#doc-padovan-number">#</a> <code>padovan_number</code></h3>
<p><code>padovan_number N</code> — Padovan sequence (same recurrence, different seeds).</p>
</article>
</section>
<section class="tutorial-section" id="ch-linear-algebra-extended">
<h2>Linear Algebra (Extended)</h2>
<p class="chapter-meta">8 topics</p>
<article class="doc-entry" id="doc-kronecker-product">
<h3><a class="doc-anchor" href="#doc-kronecker-product">#</a> <code>kronecker_product</code></h3>
<p><code>kronecker_product A, B</code> — A ⊗ B (block-by-block outer product).</p>
</article>
<article class="doc-entry" id="doc-tensor-product">
<h3><a class="doc-anchor" href="#doc-tensor-product">#</a> <code>tensor_product</code></h3>
<p><code>tensor_product A, B</code> — outer product of two flat vectors → matrix A_i B_j.</p>
</article>
<article class="doc-entry" id="doc-tensor-contract">
<h3><a class="doc-anchor" href="#doc-tensor-contract">#</a> <code>tensor_contract</code></h3>
<p><code>tensor_contract A, B</code> — Frobenius inner product of two matrices.</p>
</article>
<article class="doc-entry" id="doc-matrix-rank">
<h3><a class="doc-anchor" href="#doc-matrix-rank">#</a> <code>matrix_rank</code></h3>
<p><code>matrix_rank A</code> — rank via Gaussian elimination with partial pivoting.</p>
</article>
<article class="doc-entry" id="doc-companion-matrix">
<h3><a class="doc-anchor" href="#doc-companion-matrix">#</a> <code>companion_matrix</code></h3>
<p><code>companion_matrix [a0, a1, …, a_{n-1}]</code> — companion of x^n + a_{n-1} x^{n-1} + … + a_0.</p>
</article>
<article class="doc-entry" id="doc-characteristic-polynomial">
<h3><a class="doc-anchor" href="#doc-characteristic-polynomial">#</a> <code>characteristic_polynomial</code></h3>
<p><code>characteristic_polynomial A</code> — coefficients [a_0, …, a_n] of det(xI − A) via Faddeev-LeVerrier.</p>
</article>
<article class="doc-entry" id="doc-singular-values">
<h3><a class="doc-anchor" href="#doc-singular-values">#</a> <code>singular_values</code></h3>
<p><code>singular_values A</code> — sorted SVDs of A (eigenvalues of A^T A, square-rooted).</p>
</article>
<article class="doc-entry" id="doc-nullspace">
<h3><a class="doc-anchor" href="#doc-nullspace">#</a> <code>nullspace</code></h3>
<p><code>nullspace A</code> — basis vectors of A's null space (zero singular values of A^T A).</p>
</article>
</section>
<section class="tutorial-section" id="ch-polynomial-algebra">
<h2>Polynomial Algebra</h2>
<p class="chapter-meta">6 topics</p>
<article class="doc-entry" id="doc-polynomial-gcd">
<h3><a class="doc-anchor" href="#doc-polynomial-gcd">#</a> <code>polynomial_gcd</code></h3>
<p><code>polynomial_gcd P, Q</code> — Euclidean GCD over real coefficients (monic).</p>
<pre><code class="lang-perl">p polygcd([-1, 0, 1], [-1, 1]) # x - 1
</code></pre>
</article>
<article class="doc-entry" id="doc-polynomial-quotient">
<h3><a class="doc-anchor" href="#doc-polynomial-quotient">#</a> <code>polynomial_quotient</code></h3>
<p><code>polynomial_quotient P, Q</code> — quotient of synthetic division.</p>
</article>
<article class="doc-entry" id="doc-polynomial-remainder">
<h3><a class="doc-anchor" href="#doc-polynomial-remainder">#</a> <code>polynomial_remainder</code></h3>
<p><code>polynomial_remainder P, Q</code> — remainder of synthetic division.</p>
</article>
<article class="doc-entry" id="doc-polynomial-resultant">
<h3><a class="doc-anchor" href="#doc-polynomial-resultant">#</a> <code>polynomial_resultant</code></h3>
<p><code>polynomial_resultant P, Q</code> — Sylvester-matrix determinant.</p>
</article>
<article class="doc-entry" id="doc-polynomial-discriminant">
<h3><a class="doc-anchor" href="#doc-polynomial-discriminant">#</a> <code>polynomial_discriminant</code></h3>
<p><code>polynomial_discriminant P</code> — disc(p) = (-1)^{n(n-1)/2} / a_n · res(p, p').</p>
</article>
<article class="doc-entry" id="doc-polynomial-roots">
<h3><a class="doc-anchor" href="#doc-polynomial-roots">#</a> <code>polynomial_roots</code></h3>
<p><code>polynomial_roots P</code> — real roots via deflation power iteration on companion matrix.</p>
</article>
</section>
<section class="tutorial-section" id="ch-distributions-extended">
<h2>Distributions (Extended)</h2>
<p class="chapter-meta">18 topics</p>
<article class="doc-entry" id="doc-gumbel-pdf">
<h3><a class="doc-anchor" href="#doc-gumbel-pdf">#</a> <code>gumbel_pdf</code></h3>
<p><code>gumbel_pdf X, MU, BETA</code> — Gumbel (Type I) extreme-value PDF.</p>
</article>
<article class="doc-entry" id="doc-gumbel-cdf">
<h3><a class="doc-anchor" href="#doc-gumbel-cdf">#</a> <code>gumbel_cdf</code></h3>
<p><code>gumbel_cdf X, MU, BETA</code> — Gumbel CDF.</p>
</article>
<article class="doc-entry" id="doc-gumbel-quantile">
<h3><a class="doc-anchor" href="#doc-gumbel-quantile">#</a> <code>gumbel_quantile</code></h3>
<p><code>gumbel_quantile P, MU, BETA</code> — Gumbel quantile.</p>
</article>
<article class="doc-entry" id="doc-frechet-pdf">
<h3><a class="doc-anchor" href="#doc-frechet-pdf">#</a> <code>frechet_pdf</code></h3>
<p><code>frechet_pdf X, ALPHA, S</code> — Fréchet (Type II) PDF.</p>
</article>
<article class="doc-entry" id="doc-frechet-cdf">
<h3><a class="doc-anchor" href="#doc-frechet-cdf">#</a> <code>frechet_cdf</code></h3>
<p><code>frechet_cdf X, ALPHA, S</code> — Fréchet CDF.</p>
</article>
<article class="doc-entry" id="doc-frechet-quantile">
<h3><a class="doc-anchor" href="#doc-frechet-quantile">#</a> <code>frechet_quantile</code></h3>
<p><code>frechet_quantile P, ALPHA, S</code> — Fréchet quantile.</p>
</article>
<article class="doc-entry" id="doc-logistic-pdf">
<h3><a class="doc-anchor" href="#doc-logistic-pdf">#</a> <code>logistic_pdf</code></h3>
<p><code>logistic_pdf X, MU, S</code> — Logistic PDF.</p>
</article>
<article class="doc-entry" id="doc-logistic-cdf">
<h3><a class="doc-anchor" href="#doc-logistic-cdf">#</a> <code>logistic_cdf</code></h3>
<p><code>logistic_cdf X, MU, S</code> — Logistic CDF.</p>
</article>
<article class="doc-entry" id="doc-logistic-quantile">
<h3><a class="doc-anchor" href="#doc-logistic-quantile">#</a> <code>logistic_quantile</code></h3>
<p><code>logistic_quantile P, MU, S</code> — Logistic quantile.</p>
</article>
<article class="doc-entry" id="doc-rayleigh-pdf">
<h3><a class="doc-anchor" href="#doc-rayleigh-pdf">#</a> <code>rayleigh_pdf</code></h3>
<p><code>rayleigh_pdf X, SIGMA</code> — Rayleigh PDF (x ≥ 0).</p>
</article>
<article class="doc-entry" id="doc-rayleigh-cdf">
<h3><a class="doc-anchor" href="#doc-rayleigh-cdf">#</a> <code>rayleigh_cdf</code></h3>
<p><code>rayleigh_cdf X, SIGMA</code> — Rayleigh CDF.</p>
</article>
<article class="doc-entry" id="doc-rayleigh-quantile">
<h3><a class="doc-anchor" href="#doc-rayleigh-quantile">#</a> <code>rayleigh_quantile</code></h3>
<p><code>rayleigh_quantile P, SIGMA</code> — Rayleigh quantile.</p>
</article>
<article class="doc-entry" id="doc-inverse-gamma-pdf">
<h3><a class="doc-anchor" href="#doc-inverse-gamma-pdf">#</a> <code>inverse_gamma_pdf</code></h3>
<p><code>inverse_gamma_pdf X, ALPHA, BETA</code> — inverse-gamma PDF.</p>
</article>
<article class="doc-entry" id="doc-inverse-gamma-cdf">
<h3><a class="doc-anchor" href="#doc-inverse-gamma-cdf">#</a> <code>inverse_gamma_cdf</code></h3>
<p><code>inverse_gamma_cdf X, ALPHA, BETA</code> — inverse-gamma CDF.</p>
</article>
<article class="doc-entry" id="doc-inverse-gamma-quantile">
<h3><a class="doc-anchor" href="#doc-inverse-gamma-quantile">#</a> <code>inverse_gamma_quantile</code></h3>
<p><code>inverse_gamma_quantile P, ALPHA, BETA</code> — inverse-gamma quantile.</p>
</article>
<article class="doc-entry" id="doc-kumaraswamy-pdf">
<h3><a class="doc-anchor" href="#doc-kumaraswamy-pdf">#</a> <code>kumaraswamy_pdf</code></h3>
<p><code>kumaraswamy_pdf X, A, B</code> — Kumaraswamy PDF on (0, 1).</p>
</article>
<article class="doc-entry" id="doc-kumaraswamy-cdf">
<h3><a class="doc-anchor" href="#doc-kumaraswamy-cdf">#</a> <code>kumaraswamy_cdf</code></h3>
<p><code>kumaraswamy_cdf X, A, B</code> — Kumaraswamy CDF.</p>
</article>
<article class="doc-entry" id="doc-kumaraswamy-quantile">
<h3><a class="doc-anchor" href="#doc-kumaraswamy-quantile">#</a> <code>kumaraswamy_quantile</code></h3>
<p><code>kumaraswamy_quantile P, A, B</code> — Kumaraswamy quantile.</p>
</article>
</section>
<section class="tutorial-section" id="ch-mathieu-heun">
<h2>Mathieu / Heun</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-mathieu-a">
<h3><a class="doc-anchor" href="#doc-mathieu-a">#</a> <code>mathieu_a</code></h3>
<p><code>mathieu_a Q, N</code> — Mathieu characteristic value a_n(q) (Hill-matrix eigenvalue).</p>
</article>
<article class="doc-entry" id="doc-mathieu-ce">
<h3><a class="doc-anchor" href="#doc-mathieu-ce">#</a> <code>mathieu_ce</code></h3>
<p><code>mathieu_ce N, X, Q</code> — even Mathieu function ce_n(x, q) (perturbative form for small q).</p>
</article>
<article class="doc-entry" id="doc-mathieu-se">
<h3><a class="doc-anchor" href="#doc-mathieu-se">#</a> <code>mathieu_se</code></h3>
<p><code>mathieu_se N, X, Q</code> — odd Mathieu function se_n(x, q).</p>
</article>
<article class="doc-entry" id="doc-heun-g">
<h3><a class="doc-anchor" href="#doc-heun-g">#</a> <code>heun_g</code></h3>
<p><code>heun_g Z, A, Q, ALPHA, BETA, GAMMA, DELTA</code> — general Heun H_l via Frobenius series. Requires |z| < min(1, |a|).</p>
</article>
</section>
<section class="tutorial-section" id="ch-wavelets">
<h2>Wavelets</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-haar-transform">
<h3><a class="doc-anchor" href="#doc-haar-transform">#</a> <code>haar_transform</code></h3>
<p><code>haar_transform XS</code> — single-level Haar DWT. Returns [approx…, detail…].</p>
</article>
<article class="doc-entry" id="doc-haar-inverse">
<h3><a class="doc-anchor" href="#doc-haar-inverse">#</a> <code>haar_inverse</code></h3>
<p><code>haar_inverse XS</code> — inverse single-level Haar.</p>
</article>
<article class="doc-entry" id="doc-daubechies-db4">
<h3><a class="doc-anchor" href="#doc-daubechies-db4">#</a> <code>daubechies_db4</code></h3>
<p><code>daubechies_db4 XS</code> — single-level Daubechies-4 DWT (length must be even ≥ 4).</p>
</article>
<article class="doc-entry" id="doc-daubechies-db4-inverse">
<h3><a class="doc-anchor" href="#doc-daubechies-db4-inverse">#</a> <code>daubechies_db4_inverse</code></h3>
<p><code>daubechies_db4_inverse XS</code> — inverse single-level db4.</p>
</article>
</section>
<section class="tutorial-section" id="ch-graph-algorithms-extended">
<h2>Graph Algorithms (Extended)</h2>
<p class="chapter-meta">8 topics</p>
<article class="doc-entry" id="doc-topo-sort-adj">
<h3><a class="doc-anchor" href="#doc-topo-sort-adj">#</a> <code>topo_sort_adj</code></h3>
<p><code>topo_sort_adj ADJ</code> — Kahn's algorithm on adjacency-list graph. Returns ordering or <code>[]</code> on cycle. (Edge-list input → use <code>topological_sort</code> instead.)</p>
</article>
<article class="doc-entry" id="doc-scc-tarjan">
<h3><a class="doc-anchor" href="#doc-scc-tarjan">#</a> <code>scc_tarjan</code></h3>
<p><code>scc_tarjan ADJ</code> — Tarjan strongly-connected components. Returns array of components.</p>
</article>
<article class="doc-entry" id="doc-bipartite-q">
<h3><a class="doc-anchor" href="#doc-bipartite-q">#</a> <code>bipartite_q</code></h3>
<p><code>bipartite_q ADJ</code> — 1 if graph is 2-colourable (BFS), 0 otherwise.</p>
</article>
<article class="doc-entry" id="doc-max-flow-edmonds-karp">
<h3><a class="doc-anchor" href="#doc-max-flow-edmonds-karp">#</a> <code>max_flow_edmonds_karp</code></h3>
<p><code>max_flow_edmonds_karp CAP, S, T</code> — max flow on capacity matrix from S to T.</p>
</article>
<article class="doc-entry" id="doc-min-cut">
<h3><a class="doc-anchor" href="#doc-min-cut">#</a> <code>min_cut</code></h3>
<p><code>min_cut CAP, S, T</code> — min-cut value (= max-flow).</p>
</article>
<article class="doc-entry" id="doc-eccentricity">
<h3><a class="doc-anchor" href="#doc-eccentricity">#</a> <code>eccentricity</code></h3>
<p><code>eccentricity ADJ, V</code> — max BFS distance from V (unweighted).</p>
</article>
<article class="doc-entry" id="doc-graph-diameter">
<h3><a class="doc-anchor" href="#doc-graph-diameter">#</a> <code>graph_diameter</code></h3>
<p><code>graph_diameter ADJ</code> — max eccentricity over all vertices.</p>
</article>
<article class="doc-entry" id="doc-graph-radius">
<h3><a class="doc-anchor" href="#doc-graph-radius">#</a> <code>graph_radius</code></h3>
<p><code>graph_radius ADJ</code> — min eccentricity over all vertices.</p>
</article>
</section>
<section class="tutorial-section" id="ch-number-theoretic-sums-constants">
<h2>Number-Theoretic Sums & Constants</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-stieltjes-constant">
<h3><a class="doc-anchor" href="#doc-stieltjes-constant">#</a> <code>stieltjes_constant</code></h3>
<p><code>stieltjes_constant K</code> — kth Stieltjes constant γ_k. γ_0 = γ (Euler-Mascheroni).</p>
</article>
<article class="doc-entry" id="doc-gauss-sum">
<h3><a class="doc-anchor" href="#doc-gauss-sum">#</a> <code>gauss_sum</code></h3>
<p><code>gauss_sum A, P</code> — quadratic Gauss sum G(a, p) as <code>[Re, Im]</code>.</p>
</article>
<article class="doc-entry" id="doc-kloosterman-sum">
<h3><a class="doc-anchor" href="#doc-kloosterman-sum">#</a> <code>kloosterman_sum</code></h3>
<p><code>kloosterman_sum A, B, M</code> — K(a, b; m) as <code>[Re, Im]</code>.</p>
</article>
<article class="doc-entry" id="doc-eta-quotient">
<h3><a class="doc-anchor" href="#doc-eta-quotient">#</a> <code>eta_quotient</code></h3>
<p><code>eta_quotient PAIRS, Y</code> — Π η(d·iy)^{r_d} for [[d, r_d], …].</p>
</article>
<article class="doc-entry" id="doc-root-approximant">
<h3><a class="doc-anchor" href="#doc-root-approximant">#</a> <code>root_approximant</code></h3>
<p><code>root_approximant X [, MAX_DENOM]</code> — best rational approximant (alias for <code>best_rational_approximation</code>).</p>
</article>
</section>
<section class="tutorial-section" id="ch-vector-calculus">
<h2>Vector Calculus</h2>
<p class="chapter-meta">6 topics</p>
<article class="doc-entry" id="doc-numerical-gradient">
<h3><a class="doc-anchor" href="#doc-numerical-gradient">#</a> <code>numerical_gradient</code></h3>
<p><code>numerical_gradient F, POINT [, H]</code> — central-difference ∇f. F receives a single arrayref <code>$_[0]</code>.</p>
<pre><code class="lang-perl">fn quad { my @y = @{$_[0]}; $y[0]**2 + 2*$y[1]**2 }
my @g = ngrad(\&quad, [3, 4]) # (6, 16)
</code></pre>
</article>
<article class="doc-entry" id="doc-numerical-jacobian">
<h3><a class="doc-anchor" href="#doc-numerical-jacobian">#</a> <code>numerical_jacobian</code></h3>
<p><code>numerical_jacobian F, POINT [, H]</code> — Jacobian of vector-valued F.</p>
</article>
<article class="doc-entry" id="doc-numerical-hessian">
<h3><a class="doc-anchor" href="#doc-numerical-hessian">#</a> <code>numerical_hessian</code></h3>
<p><code>numerical_hessian F, POINT [, H]</code> — symmetric Hessian via mixed second differences.</p>
</article>
<article class="doc-entry" id="doc-numerical-divergence">
<h3><a class="doc-anchor" href="#doc-numerical-divergence">#</a> <code>numerical_divergence</code></h3>
<p><code>numerical_divergence F, POINT [, H]</code> — div of vector field F.</p>
</article>
<article class="doc-entry" id="doc-numerical-curl">
<h3><a class="doc-anchor" href="#doc-numerical-curl">#</a> <code>numerical_curl</code></h3>
<p><code>numerical_curl F, POINT [, H]</code> — 3-D curl returned as <code>[c_x, c_y, c_z]</code>.</p>
</article>
<article class="doc-entry" id="doc-numerical-laplacian">
<h3><a class="doc-anchor" href="#doc-numerical-laplacian">#</a> <code>numerical_laplacian</code></h3>
<p><code>numerical_laplacian F, POINT [, H]</code> — ∇²f.</p>
</article>
</section>
<section class="tutorial-section" id="ch-optimization">
<h2>Optimization</h2>
<p class="chapter-meta">6 topics</p>
<article class="doc-entry" id="doc-nelder-mead">
<h3><a class="doc-anchor" href="#doc-nelder-mead">#</a> <code>nelder_mead</code></h3>
<p><code>nelder_mead F, X0 [, MAX_ITER, TOL]</code> — Nelder-Mead simplex minimisation. Returns <code>[x*, f(x*)]</code>.</p>
</article>
<article class="doc-entry" id="doc-gradient-descent">
<h3><a class="doc-anchor" href="#doc-gradient-descent">#</a> <code>gradient_descent</code></h3>
<p><code>gradient_descent F, GRAD, X0 [, STEP, ITERS]</code> — fixed-step descent.</p>
</article>
<article class="doc-entry" id="doc-bfgs-minimize">
<h3><a class="doc-anchor" href="#doc-bfgs-minimize">#</a> <code>bfgs_minimize</code></h3>
<p><code>bfgs_minimize F, GRAD, X0 [, MAX_ITER, TOL]</code> — BFGS quasi-Newton with Armijo line search.</p>
</article>
<article class="doc-entry" id="doc-levenberg-marquardt">
<h3><a class="doc-anchor" href="#doc-levenberg-marquardt">#</a> <code>levenberg_marquardt</code></h3>
<p><code>levenberg_marquardt F_RESID, X0 [, MAX_ITER, TOL]</code> — nonlinear LSQ. F returns the residual vector.</p>
</article>
<article class="doc-entry" id="doc-conjugate-gradient">
<h3><a class="doc-anchor" href="#doc-conjugate-gradient">#</a> <code>conjugate_gradient</code></h3>
<p><code>conjugate_gradient A, B</code> — CG for symmetric positive definite A x = b.</p>
</article>
<article class="doc-entry" id="doc-least-squares">
<h3><a class="doc-anchor" href="#doc-least-squares">#</a> <code>least_squares</code></h3>
<p><code>least_squares A, B</code> — solves A^T A x = A^T b.</p>
</article>
</section>
<section class="tutorial-section" id="ch-numerical-integration">
<h2>Numerical Integration</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-romberg">
<h3><a class="doc-anchor" href="#doc-romberg">#</a> <code>romberg</code></h3>
<p><code>romberg F, A, B [, LEVELS]</code> — Romberg integration. Doubles trapezoid then Richardson-extrapolates.</p>
</article>
<article class="doc-entry" id="doc-gauss-legendre-quad">
<h3><a class="doc-anchor" href="#doc-gauss-legendre-quad">#</a> <code>gauss_legendre_quad</code></h3>
<p><code>gauss_legendre_quad F, A, B [, N]</code> — N-point Gauss-Legendre quadrature on [a, b] (default N=10).</p>
</article>
<article class="doc-entry" id="doc-monte-carlo-integrate">
<h3><a class="doc-anchor" href="#doc-monte-carlo-integrate">#</a> <code>monte_carlo_integrate</code></h3>
<p><code>monte_carlo_integrate F, A, B [, N]</code> — uniform Monte Carlo over [a, b] with N samples (default 10 000).</p>
</article>
<article class="doc-entry" id="doc-adaptive-simpson">
<h3><a class="doc-anchor" href="#doc-adaptive-simpson">#</a> <code>adaptive_simpson</code></h3>
<p><code>adaptive_simpson F, A, B [, TOL, MAX_DEPTH]</code> — adaptive Simpson with Richardson tail.</p>
</article>
</section>
<section class="tutorial-section" id="ch-linear-algebra-numeric">
<h2>Linear Algebra (Numeric)</h2>
<p class="chapter-meta">7 topics</p>
<article class="doc-entry" id="doc-lu-decompose">
<h3><a class="doc-anchor" href="#doc-lu-decompose">#</a> <code>lu_decompose</code></h3>
<p><code>lu_decompose A</code> → <code>[L, U, P]</code> with P A = L U; P stored as a row-permutation vector.</p>
</article>
<article class="doc-entry" id="doc-qr-decompose">
<h3><a class="doc-anchor" href="#doc-qr-decompose">#</a> <code>qr_decompose</code></h3>
<p><code>qr_decompose A</code> → <code>[Q, R]</code> via Gram-Schmidt.</p>
</article>
<article class="doc-entry" id="doc-householder-reflector">
<h3><a class="doc-anchor" href="#doc-householder-reflector">#</a> <code>householder_reflector</code></h3>
<p><code>householder_reflector V</code> → I − 2 v v^T / (v · v).</p>
</article>
<article class="doc-entry" id="doc-givens-rotation">
<h3><a class="doc-anchor" href="#doc-givens-rotation">#</a> <code>givens_rotation</code></h3>
<p><code>givens_rotation A, B</code> → <code>[c, s]</code> such that the rotation [c -s; s c] zeros the second component.</p>
</article>
<article class="doc-entry" id="doc-forward-substitute">
<h3><a class="doc-anchor" href="#doc-forward-substitute">#</a> <code>forward_substitute</code></h3>
<p><code>forward_substitute L, B</code> — solve L x = b for lower-triangular L.</p>
</article>
<article class="doc-entry" id="doc-back-substitute">
<h3><a class="doc-anchor" href="#doc-back-substitute">#</a> <code>back_substitute</code></h3>
<p><code>back_substitute U, B</code> — solve U x = b for upper-triangular U.</p>
</article>
<article class="doc-entry" id="doc-hessenberg-reduce">
<h3><a class="doc-anchor" href="#doc-hessenberg-reduce">#</a> <code>hessenberg_reduce</code></h3>
<p><code>hessenberg_reduce A</code> — orthogonal Hessenberg form via Householder reflections.</p>
</article>
</section>
<section class="tutorial-section" id="ch-polynomial-helpers">
<h2>Polynomial Helpers</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-poly-derivative">
<h3><a class="doc-anchor" href="#doc-poly-derivative">#</a> <code>poly_derivative</code></h3>
<p><code>poly_derivative P</code> — coefficient-list derivative of polynomial P (low-to-high order).</p>
</article>
<article class="doc-entry" id="doc-poly-integrate">
<h3><a class="doc-anchor" href="#doc-poly-integrate">#</a> <code>poly_integrate</code></h3>
<p><code>poly_integrate P [, C]</code> — antiderivative with constant C (default 0).</p>
</article>
<article class="doc-entry" id="doc-poly-compose">
<h3><a class="doc-anchor" href="#doc-poly-compose">#</a> <code>poly_compose</code></h3>
<p><code>poly_compose P, Q</code> → coefficients of P(Q(x)).</p>
</article>
<article class="doc-entry" id="doc-poly-eval-horner">
<h3><a class="doc-anchor" href="#doc-poly-eval-horner">#</a> <code>poly_eval_horner</code></h3>
<p><code>poly_eval_horner P, X</code> — Horner-rule polynomial evaluation.</p>
</article>
<article class="doc-entry" id="doc-pade-approximant">
<h3><a class="doc-anchor" href="#doc-pade-approximant">#</a> <code>pade_approximant</code></h3>
<p><code>pade_approximant TAYLOR, M, N</code> → <code>[num, den]</code> Padé approximation.</p>
</article>
</section>
<section class="tutorial-section" id="ch-quaternions-3d-rotations">
<h2>Quaternions & 3D Rotations</h2>
<p class="chapter-meta">12 topics</p>
<article class="doc-entry" id="doc-quat-mul">
<h3><a class="doc-anchor" href="#doc-quat-mul">#</a> <code>quat_mul</code></h3>
<p><code>quat_mul A, B</code> — Hamilton product (w, x, y, z).</p>
</article>
<article class="doc-entry" id="doc-quat-conj">
<h3><a class="doc-anchor" href="#doc-quat-conj">#</a> <code>quat_conj</code></h3>
<p><code>quat_conj Q</code> — conjugate (w, -x, -y, -z).</p>
</article>
<article class="doc-entry" id="doc-quat-norm">
<h3><a class="doc-anchor" href="#doc-quat-norm">#</a> <code>quat_norm</code></h3>
<p><code>quat_norm Q</code> — Euclidean norm.</p>
</article>
<article class="doc-entry" id="doc-quat-inv">
<h3><a class="doc-anchor" href="#doc-quat-inv">#</a> <code>quat_inv</code></h3>
<p><code>quat_inv Q</code> — inverse Q* / |Q|².</p>
</article>
<article class="doc-entry" id="doc-quat-from-axis-angle">
<h3><a class="doc-anchor" href="#doc-quat-from-axis-angle">#</a> <code>quat_from_axis_angle</code></h3>
<p><code>quat_from_axis_angle AXIS, THETA</code> — unit quaternion encoding rotation about AXIS by THETA radians.</p>
</article>
<article class="doc-entry" id="doc-quat-to-axis-angle">
<h3><a class="doc-anchor" href="#doc-quat-to-axis-angle">#</a> <code>quat_to_axis_angle</code></h3>
<p><code>quat_to_axis_angle Q</code> → <code>[axis, theta]</code>.</p>
</article>
<article class="doc-entry" id="doc-quat-to-matrix">
<h3><a class="doc-anchor" href="#doc-quat-to-matrix">#</a> <code>quat_to_matrix</code></h3>
<p><code>quat_to_matrix Q</code> → 3×3 rotation matrix.</p>
</article>
<article class="doc-entry" id="doc-quat-from-matrix">
<h3><a class="doc-anchor" href="#doc-quat-from-matrix">#</a> <code>quat_from_matrix</code></h3>
<p><code>quat_from_matrix R</code> — Shepherd's algorithm.</p>
</article>
<article class="doc-entry" id="doc-quat-slerp">
<h3><a class="doc-anchor" href="#doc-quat-slerp">#</a> <code>quat_slerp</code></h3>
<p><code>quat_slerp A, B, T</code> — spherical-linear interpolation between two unit quaternions.</p>
</article>
<article class="doc-entry" id="doc-euler-zyx-to-matrix">
<h3><a class="doc-anchor" href="#doc-euler-zyx-to-matrix">#</a> <code>euler_zyx_to_matrix</code></h3>
<p><code>euler_zyx_to_matrix YAW, PITCH, ROLL</code> — intrinsic Z-Y-X Euler rotation.</p>
</article>
<article class="doc-entry" id="doc-matrix-to-euler-zyx">
<h3><a class="doc-anchor" href="#doc-matrix-to-euler-zyx">#</a> <code>matrix_to_euler_zyx</code></h3>
<p><code>matrix_to_euler_zyx R</code> → <code>[yaw, pitch, roll]</code>.</p>
</article>
<article class="doc-entry" id="doc-rotate-3d-vec">
<h3><a class="doc-anchor" href="#doc-rotate-3d-vec">#</a> <code>rotate_3d_vec</code></h3>
<p><code>rotate_3d_vec Q, V</code> — apply quaternion rotation to a 3-vector.</p>
</article>
</section>
<section class="tutorial-section" id="ch-information-theory">
<h2>Information Theory</h2>
<p class="chapter-meta">6 topics</p>
<article class="doc-entry" id="doc-kl-divergence">
<h3><a class="doc-anchor" href="#doc-kl-divergence">#</a> <code>kl_divergence</code></h3>
<p><code>kl_divergence P, Q</code> — D_KL(P || Q) in nats.</p>
</article>
<article class="doc-entry" id="doc-js-divergence">
<h3><a class="doc-anchor" href="#doc-js-divergence">#</a> <code>js_divergence</code></h3>
<p><code>js_divergence P, Q</code> — Jensen-Shannon divergence.</p>
</article>
<article class="doc-entry" id="doc-mutual-information">
<h3><a class="doc-anchor" href="#doc-mutual-information">#</a> <code>mutual_information</code></h3>
<p><code>mutual_information JOINT</code> — I(X; Y) from a joint-probability matrix.</p>
</article>
<article class="doc-entry" id="doc-cross-entropy-arr">
<h3><a class="doc-anchor" href="#doc-cross-entropy-arr">#</a> <code>cross_entropy_arr</code></h3>
<p><code>cross_entropy_arr P, Q</code> — H(P, Q) = -Σ p log q.</p>
</article>
<article class="doc-entry" id="doc-renyi-entropy">
<h3><a class="doc-anchor" href="#doc-renyi-entropy">#</a> <code>renyi_entropy</code></h3>
<p><code>renyi_entropy P [, ALPHA]</code> — Rényi entropy of order α (default 2).</p>
</article>
<article class="doc-entry" id="doc-tsallis-entropy">
<h3><a class="doc-anchor" href="#doc-tsallis-entropy">#</a> <code>tsallis_entropy</code></h3>
<p><code>tsallis_entropy P [, Q]</code> — Tsallis entropy of order q (default 2).</p>
</article>
</section>
<section class="tutorial-section" id="ch-quantum-primitives">
<h2>Quantum Primitives</h2>
<p class="chapter-meta">11 topics</p>
<article class="doc-entry" id="doc-pauli-x">
<h3><a class="doc-anchor" href="#doc-pauli-x">#</a> <code>pauli_x</code></h3>
<p><code>pauli_x</code> — 2×2 σ_x matrix.</p>
</article>
<article class="doc-entry" id="doc-pauli-y">
<h3><a class="doc-anchor" href="#doc-pauli-y">#</a> <code>pauli_y</code></h3>
<p><code>pauli_y</code> — 2×2 σ_y matrix encoded with [Re, Im] entries (since stryke matrices are real).</p>
</article>
<article class="doc-entry" id="doc-pauli-z">
<h3><a class="doc-anchor" href="#doc-pauli-z">#</a> <code>pauli_z</code></h3>
<p><code>pauli_z</code> — 2×2 σ_z matrix.</p>
</article>
<article class="doc-entry" id="doc-pauli-id">
<h3><a class="doc-anchor" href="#doc-pauli-id">#</a> <code>pauli_id</code></h3>
<p><code>pauli_id</code> — 2×2 identity.</p>
</article>
<article class="doc-entry" id="doc-ket-bra">
<h3><a class="doc-anchor" href="#doc-ket-bra">#</a> <code>ket_bra</code></h3>
<p><code>ket_bra PSI, PHI</code> → outer product |ψ⟩⟨φ| of two real vectors.</p>
</article>
<article class="doc-entry" id="doc-density-matrix">
<h3><a class="doc-anchor" href="#doc-density-matrix">#</a> <code>density_matrix</code></h3>
<p><code>density_matrix PSI</code> → ρ = |ψ⟩⟨ψ| (real-valued).</p>
</article>
<article class="doc-entry" id="doc-expectation-value">
<h3><a class="doc-anchor" href="#doc-expectation-value">#</a> <code>expectation_value</code></h3>
<p><code>expectation_value OP, PSI</code> → ⟨ψ|O|ψ⟩.</p>
</article>
<article class="doc-entry" id="doc-commutator">
<h3><a class="doc-anchor" href="#doc-commutator">#</a> <code>commutator</code></h3>
<p><code>commutator A, B</code> — [A, B] = AB − BA.</p>
</article>
<article class="doc-entry" id="doc-anticommutator">
<h3><a class="doc-anchor" href="#doc-anticommutator">#</a> <code>anticommutator</code></h3>
<p><code>anticommutator A, B</code> — {A, B} = AB + BA.</p>
</article>
<article class="doc-entry" id="doc-partial-trace">
<h3><a class="doc-anchor" href="#doc-partial-trace">#</a> <code>partial_trace</code></h3>
<p><code>partial_trace RHO, DIMS, KEEP</code> — partial trace over subsystems whose indices are not in KEEP.</p>
</article>
<article class="doc-entry" id="doc-von-neumann-entropy">
<h3><a class="doc-anchor" href="#doc-von-neumann-entropy">#</a> <code>von_neumann_entropy</code></h3>
<p><code>von_neumann_entropy RHO</code> — S(ρ) = -tr(ρ log ρ) for symmetric ρ.</p>
</article>
</section>
<section class="tutorial-section" id="ch-statistical-mechanics">
<h2>Statistical Mechanics</h2>
<p class="chapter-meta">7 topics</p>
<article class="doc-entry" id="doc-bose-einstein">
<h3><a class="doc-anchor" href="#doc-bose-einstein">#</a> <code>bose_einstein</code></h3>
<p><code>bose_einstein E, MU, KT</code> — 1 / (exp((E - μ)/kT) - 1).</p>
</article>
<article class="doc-entry" id="doc-fermi-dirac">
<h3><a class="doc-anchor" href="#doc-fermi-dirac">#</a> <code>fermi_dirac</code></h3>
<p><code>fermi_dirac E, MU, KT</code> — 1 / (exp((E - μ)/kT) + 1).</p>
</article>
<article class="doc-entry" id="doc-maxwell-boltzmann-speed">
<h3><a class="doc-anchor" href="#doc-maxwell-boltzmann-speed">#</a> <code>maxwell_boltzmann_speed</code></h3>
<p><code>maxwell_boltzmann_speed V, M, KT</code> — Maxwell-Boltzmann speed PDF.</p>
</article>
<article class="doc-entry" id="doc-partition-function">
<h3><a class="doc-anchor" href="#doc-partition-function">#</a> <code>partition_function</code></h3>
<p><code>partition_function ENERGIES, KT</code> — Z = Σ exp(-E_i / kT).</p>
</article>
<article class="doc-entry" id="doc-helmholtz-free-energy">
<h3><a class="doc-anchor" href="#doc-helmholtz-free-energy">#</a> <code>helmholtz_free_energy</code></h3>
<p><code>helmholtz_free_energy Z, KT</code> — F = -kT ln Z.</p>
</article>
<article class="doc-entry" id="doc-boltzmann-factor">
<h3><a class="doc-anchor" href="#doc-boltzmann-factor">#</a> <code>boltzmann_factor</code></h3>
<p><code>boltzmann_factor E, KT</code> — exp(-E / kT).</p>
</article>
<article class="doc-entry" id="doc-einstein-specific-heat">
<h3><a class="doc-anchor" href="#doc-einstein-specific-heat">#</a> <code>einstein_specific_heat</code></h3>
<p><code>einstein_specific_heat T, THETA_E</code> — Einstein heat-capacity model (J / mol·K).</p>
</article>
</section>
<section class="tutorial-section" id="ch-optics">
<h2>Optics</h2>
<p class="chapter-meta">7 topics</p>
<article class="doc-entry" id="doc-fresnel-reflection-te">
<h3><a class="doc-anchor" href="#doc-fresnel-reflection-te">#</a> <code>fresnel_reflection_te</code></h3>
<p><code>fresnel_reflection_te THETA_I, N1, N2</code> — TE (s-polarisation) reflection coefficient.</p>
</article>
<article class="doc-entry" id="doc-fresnel-reflection-tm">
<h3><a class="doc-anchor" href="#doc-fresnel-reflection-tm">#</a> <code>fresnel_reflection_tm</code></h3>
<p><code>fresnel_reflection_tm THETA_I, N1, N2</code> — TM (p-polarisation) reflection.</p>
</article>
<article class="doc-entry" id="doc-fresnel-transmission-te">
<h3><a class="doc-anchor" href="#doc-fresnel-transmission-te">#</a> <code>fresnel_transmission_te</code></h3>
<p><code>fresnel_transmission_te THETA_I, N1, N2</code> — TE transmission.</p>
</article>
<article class="doc-entry" id="doc-fresnel-transmission-tm">
<h3><a class="doc-anchor" href="#doc-fresnel-transmission-tm">#</a> <code>fresnel_transmission_tm</code></h3>
<p><code>fresnel_transmission_tm THETA_I, N1, N2</code> — TM transmission.</p>
</article>
<article class="doc-entry" id="doc-abcd-thin-lens">
<h3><a class="doc-anchor" href="#doc-abcd-thin-lens">#</a> <code>abcd_thin_lens</code></h3>
<p><code>abcd_thin_lens F</code> — ABCD ray matrix for a thin lens of focal length F.</p>
</article>
<article class="doc-entry" id="doc-abcd-free-space">
<h3><a class="doc-anchor" href="#doc-abcd-free-space">#</a> <code>abcd_free_space</code></h3>
<p><code>abcd_free_space D</code> — ABCD matrix for free-space propagation D.</p>
</article>
<article class="doc-entry" id="doc-gaussian-beam-q">
<h3><a class="doc-anchor" href="#doc-gaussian-beam-q">#</a> <code>gaussian_beam_q</code></h3>
<p><code>gaussian_beam_q Z, W0, LAMBDA</code> → <code>[Re(q), Im(q)]</code> for a Gaussian beam at distance Z.</p>
</article>
</section>
<section class="tutorial-section" id="ch-astrodynamics">
<h2>Astrodynamics</h2>
<p class="chapter-meta">9 topics</p>
<article class="doc-entry" id="doc-kepler-solve">
<h3><a class="doc-anchor" href="#doc-kepler-solve">#</a> <code>kepler_solve</code></h3>
<p><code>kepler_solve M, E</code> — solve Kepler's equation M = E - e sin(E) by Newton iteration.</p>
</article>
<article class="doc-entry" id="doc-true-to-eccentric">
<h3><a class="doc-anchor" href="#doc-true-to-eccentric">#</a> <code>true_to_eccentric</code></h3>
<p><code>true_to_eccentric NU, E</code> → eccentric anomaly E.</p>
</article>
<article class="doc-entry" id="doc-eccentric-to-mean">
<h3><a class="doc-anchor" href="#doc-eccentric-to-mean">#</a> <code>eccentric_to_mean</code></h3>
<p><code>eccentric_to_mean E, ECC</code> → mean anomaly M.</p>
</article>
<article class="doc-entry" id="doc-julian-date">
<h3><a class="doc-anchor" href="#doc-julian-date">#</a> <code>julian_date</code></h3>
<p><code>julian_date Y, M, D, H, MN, S</code> — Julian date (Meeus formula).</p>
</article>
<article class="doc-entry" id="doc-jd-to-gregorian">
<h3><a class="doc-anchor" href="#doc-jd-to-gregorian">#</a> <code>jd_to_gregorian</code></h3>
<p><code>jd_to_gregorian JD</code> → <code>[Y, M, D.dd]</code>.</p>
</article>
<article class="doc-entry" id="doc-sidereal-time-gmst">
<h3><a class="doc-anchor" href="#doc-sidereal-time-gmst">#</a> <code>sidereal_time_gmst</code></h3>
<p><code>sidereal_time_gmst JD</code> — Greenwich Mean Sidereal Time in radians.</p>
</article>
<article class="doc-entry" id="doc-vis-viva">
<h3><a class="doc-anchor" href="#doc-vis-viva">#</a> <code>vis_viva</code></h3>
<p><code>vis_viva R, A, MU</code> — orbital speed from vis-viva equation.</p>
</article>
<article class="doc-entry" id="doc-orbital-period-kepler">
<h3><a class="doc-anchor" href="#doc-orbital-period-kepler">#</a> <code>orbital_period_kepler</code></h3>
<p><code>orbital_period_kepler A, MU</code> — T = 2π √(a³ / μ).</p>
</article>
<article class="doc-entry" id="doc-orbital-elements-to-state">
<h3><a class="doc-anchor" href="#doc-orbital-elements-to-state">#</a> <code>orbital_elements_to_state</code></h3>
<p><code>orbital_elements_to_state A, E, I, OM, W, NU, MU</code> → <code>[r_x, r_y, r_z, v_x, v_y, v_z]</code>.</p>
</article>
</section>
<section class="tutorial-section" id="ch-time-series">
<h2>Time Series</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-kalman-step">
<h3><a class="doc-anchor" href="#doc-kalman-step">#</a> <code>kalman_step</code></h3>
<p><code>kalman_step X, P, F, H, Q, R, Z</code> → <code>[X', P']</code> — single Kalman predict-and-update step.</p>
</article>
<article class="doc-entry" id="doc-exponential-smoothing">
<h3><a class="doc-anchor" href="#doc-exponential-smoothing">#</a> <code>exponential_smoothing</code></h3>
<p><code>exponential_smoothing XS, ALPHA</code> — first-order EMA.</p>
</article>
<article class="doc-entry" id="doc-holt-winters">
<h3><a class="doc-anchor" href="#doc-holt-winters">#</a> <code>holt_winters</code></h3>
<p><code>holt_winters XS, ALPHA, BETA, GAMMA, PERIOD</code> — additive triple exponential smoothing.</p>
</article>
<article class="doc-entry" id="doc-arma-yw-fit">
<h3><a class="doc-anchor" href="#doc-arma-yw-fit">#</a> <code>arma_yw_fit</code></h3>
<p><code>arma_yw_fit XS, P</code> — Yule-Walker AR(p) coefficients via Levinson-Durbin.</p>
</article>
</section>
<section class="tutorial-section" id="ch-graph-centrality">
<h2>Graph Centrality</h2>
<p class="chapter-meta">6 topics</p>
<article class="doc-entry" id="doc-pagerank">
<h3><a class="doc-anchor" href="#doc-pagerank">#</a> <code>pagerank</code></h3>
<p><code>pagerank ADJ [, DAMPING, ITERS]</code> — PageRank via power iteration. Default damping 0.85, 100 iters.</p>
</article>
<article class="doc-entry" id="doc-betweenness-centrality">
<h3><a class="doc-anchor" href="#doc-betweenness-centrality">#</a> <code>betweenness_centrality</code></h3>
<p><code>betweenness_centrality ADJ</code> — Brandes' algorithm (unweighted).</p>
</article>
<article class="doc-entry" id="doc-closeness-centrality">
<h3><a class="doc-anchor" href="#doc-closeness-centrality">#</a> <code>closeness_centrality</code></h3>
<p><code>closeness_centrality ADJ</code> — closeness centrality. 0 for disconnected vertices.</p>
</article>
<article class="doc-entry" id="doc-eigenvector-centrality">
<h3><a class="doc-anchor" href="#doc-eigenvector-centrality">#</a> <code>eigenvector_centrality</code></h3>
<p><code>eigenvector_centrality ADJ</code> — power iteration on the adjacency matrix.</p>
</article>
<article class="doc-entry" id="doc-degree-centrality">
<h3><a class="doc-anchor" href="#doc-degree-centrality">#</a> <code>degree_centrality</code></h3>
<p><code>degree_centrality ADJ</code> — degree / (n - 1).</p>
</article>
<article class="doc-entry" id="doc-triangle-count">
<h3><a class="doc-anchor" href="#doc-triangle-count">#</a> <code>triangle_count</code></h3>
<p><code>triangle_count ADJ</code> — number of triangles incident at each vertex.</p>
</article>
</section>
<section class="tutorial-section" id="ch-random-samplers-extended">
<h2>Random Samplers (Extended)</h2>
<p class="chapter-meta">6 topics</p>
<article class="doc-entry" id="doc-rgumbel">
<h3><a class="doc-anchor" href="#doc-rgumbel">#</a> <code>rgumbel</code></h3>
<p><code>rgumbel MU, BETA</code> — Gumbel sample.</p>
</article>
<article class="doc-entry" id="doc-rfrechet">
<h3><a class="doc-anchor" href="#doc-rfrechet">#</a> <code>rfrechet</code></h3>
<p><code>rfrechet ALPHA, S</code> — Fréchet sample.</p>
</article>
<article class="doc-entry" id="doc-rrayleigh">
<h3><a class="doc-anchor" href="#doc-rrayleigh">#</a> <code>rrayleigh</code></h3>
<p><code>rrayleigh SIGMA</code> — Rayleigh sample.</p>
</article>
<article class="doc-entry" id="doc-rlogistic">
<h3><a class="doc-anchor" href="#doc-rlogistic">#</a> <code>rlogistic</code></h3>
<p><code>rlogistic MU, S</code> — logistic sample.</p>
</article>
<article class="doc-entry" id="doc-rkumaraswamy">
<h3><a class="doc-anchor" href="#doc-rkumaraswamy">#</a> <code>rkumaraswamy</code></h3>
<p><code>rkumaraswamy A, B</code> — Kumaraswamy sample on (0, 1).</p>
</article>
<article class="doc-entry" id="doc-rinverse-gamma">
<h3><a class="doc-anchor" href="#doc-rinverse-gamma">#</a> <code>rinverse_gamma</code></h3>
<p><code>rinverse_gamma ALPHA, BETA</code> — inverse-gamma sample (Marsaglia-Tsang).</p>
</article>
</section>
<section class="tutorial-section" id="ch-2-d-geometry">
<h2>2-D Geometry</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-graham-scan">
<h3><a class="doc-anchor" href="#doc-graham-scan">#</a> <code>graham_scan</code></h3>
<p><code>graham_scan POINTS</code> — 2-D convex hull (CCW).</p>
</article>
<article class="doc-entry" id="doc-line-line-intersect-2d">
<h3><a class="doc-anchor" href="#doc-line-line-intersect-2d">#</a> <code>line_line_intersect_2d</code></h3>
<p><code>line_line_intersect_2d P1, P2, P3, P4</code> → intersection <code>[x, y]</code> or undef when parallel.</p>
</article>
<article class="doc-entry" id="doc-point-segment-distance">
<h3><a class="doc-anchor" href="#doc-point-segment-distance">#</a> <code>point_segment_distance</code></h3>
<p><code>point_segment_distance P, A, B</code> — Euclidean distance from P to segment AB.</p>
</article>
</section>
<section class="tutorial-section" id="ch-auto-differentiation">
<h2>Auto-Differentiation</h2>
<p class="chapter-meta">2 topics</p>
<article class="doc-entry" id="doc-forward-diff">
<h3><a class="doc-anchor" href="#doc-forward-diff">#</a> <code>forward_diff</code></h3>
<p><code>forward_diff F, X</code> — derivative of scalar f at scalar x (Julia ForwardDiff style; central-difference fallback).</p>
</article>
<article class="doc-entry" id="doc-forward-diff-grad">
<h3><a class="doc-anchor" href="#doc-forward-diff-grad">#</a> <code>forward_diff_grad</code></h3>
<p><code>forward_diff_grad F, X_VEC</code> — gradient at vector x; alias for <code>numerical_gradient</code>.</p>
</article>
</section>
<section class="tutorial-section" id="ch-statistical-tests-r-parity">
<h2>Statistical Tests (R parity)</h2>
<p class="chapter-meta">12 topics</p>
<article class="doc-entry" id="doc-bartlett-test">
<h3><a class="doc-anchor" href="#doc-bartlett-test">#</a> <code>bartlett_test</code></h3>
<p><code>bartlett_test GROUPS</code> — Bartlett's k-sample variance equality test. Returns <code>[chi², df, p]</code>.</p>
</article>
<article class="doc-entry" id="doc-levene-test">
<h3><a class="doc-anchor" href="#doc-levene-test">#</a> <code>levene_test</code></h3>
<p><code>levene_test GROUPS</code> — Levene's variance-equality test. Returns <code>[F, df1, df2, p]</code>.</p>
</article>
<article class="doc-entry" id="doc-fishers-exact-test-2x2">
<h3><a class="doc-anchor" href="#doc-fishers-exact-test-2x2">#</a> <code>fishers_exact_test_2x2</code></h3>
<p><code>fishers_exact_test_2x2 [[a, b], [c, d]]</code> — two-sided p-value.</p>
</article>
<article class="doc-entry" id="doc-mcnemar-test">
<h3><a class="doc-anchor" href="#doc-mcnemar-test">#</a> <code>mcnemar_test</code></h3>
<p><code>mcnemar_test [[a, b], [c, d]]</code> — paired 2×2 table with continuity correction. Returns <code>[chi², p]</code>.</p>
</article>
<article class="doc-entry" id="doc-runs-test">
<h3><a class="doc-anchor" href="#doc-runs-test">#</a> <code>runs_test</code></h3>
<p><code>runs_test SEQ</code> — Wald-Wolfowitz runs test on a binary sequence. Returns <code>[Z, p]</code>.</p>
</article>
<article class="doc-entry" id="doc-friedman-test">
<h3><a class="doc-anchor" href="#doc-friedman-test">#</a> <code>friedman_test</code></h3>
<p><code>friedman_test BLOCKS_BY_TREATMENTS</code> — non-parametric ANOVA on ranks. Returns <code>[Q, df, p]</code>.</p>
</article>
<article class="doc-entry" id="doc-kruskal-wallis-test">
<h3><a class="doc-anchor" href="#doc-kruskal-wallis-test">#</a> <code>kruskal_wallis_test</code></h3>
<p><code>kruskal_wallis_test GROUPS</code> — non-parametric ANOVA. Returns <code>[H, df, p]</code>.</p>
</article>
<article class="doc-entry" id="doc-sign-test">
<h3><a class="doc-anchor" href="#doc-sign-test">#</a> <code>sign_test</code></h3>
<p><code>sign_test PAIRS</code> — paired sign test. Returns <code>[N+, p]</code>.</p>
</article>
<article class="doc-entry" id="doc-anderson-darling-normality">
<h3><a class="doc-anchor" href="#doc-anderson-darling-normality">#</a> <code>anderson_darling_normality</code></h3>
<p><code>anderson_darling_normality XS</code> — A² statistic. > 0.752 → reject normality at α=0.05.</p>
</article>
<article class="doc-entry" id="doc-jarque-bera-test">
<h3><a class="doc-anchor" href="#doc-jarque-bera-test">#</a> <code>jarque_bera_test</code></h3>
<p><code>jarque_bera_test XS</code> — normality test from sample skewness + kurtosis.</p>
</article>
<article class="doc-entry" id="doc-ljung-box-test">
<h3><a class="doc-anchor" href="#doc-ljung-box-test">#</a> <code>ljung_box_test</code></h3>
<p><code>ljung_box_test XS [, H]</code> — autocorrelation test. Returns <code>[Q, h, p]</code>.</p>
</article>
<article class="doc-entry" id="doc-durbin-watson-stat">
<h3><a class="doc-anchor" href="#doc-durbin-watson-stat">#</a> <code>durbin_watson_stat</code></h3>
<p><code>durbin_watson_stat RESID</code> — DW autocorrelation statistic on residuals.</p>
</article>
</section>
<section class="tutorial-section" id="ch-distance-metrics-distances-jl-parity">
<h2>Distance Metrics (Distances.jl parity)</h2>
<p class="chapter-meta">6 topics</p>
<article class="doc-entry" id="doc-mahalanobis-distance">
<h3><a class="doc-anchor" href="#doc-mahalanobis-distance">#</a> <code>mahalanobis_distance</code></h3>
<p><code>mahalanobis_distance X, MU, SIGMA</code> — √((x-μ)ᵀ Σ⁻¹ (x-μ)).</p>
</article>
<article class="doc-entry" id="doc-cosine-distance">
<h3><a class="doc-anchor" href="#doc-cosine-distance">#</a> <code>cosine_distance</code></h3>
<p><code>cosine_distance A, B</code> — 1 − cos(A, B).</p>
</article>
<article class="doc-entry" id="doc-canberra-distance">
<h3><a class="doc-anchor" href="#doc-canberra-distance">#</a> <code>canberra_distance</code></h3>
<p><code>canberra_distance A, B</code> — Σ |a-b| / (|a|+|b|).</p>
</article>
<article class="doc-entry" id="doc-bray-curtis-distance">
<h3><a class="doc-anchor" href="#doc-bray-curtis-distance">#</a> <code>bray_curtis_distance</code></h3>
<p><code>bray_curtis_distance A, B</code> — Σ|a-b| / Σ(a+b).</p>
</article>
<article class="doc-entry" id="doc-l1-distance">
<h3><a class="doc-anchor" href="#doc-l1-distance">#</a> <code>l1_distance</code></h3>
<p><code>l1_distance A, B</code> — Manhattan / taxi-cab distance.</p>
</article>
<article class="doc-entry" id="doc-chi-squared-distance">
<h3><a class="doc-anchor" href="#doc-chi-squared-distance">#</a> <code>chi_squared_distance</code></h3>
<p><code>chi_squared_distance A, B</code> — ½ Σ (a-b)² / (a+b).</p>
</article>
</section>
<section class="tutorial-section" id="ch-multivariate-non-central-distributions">
<h2>Multivariate / Non-Central Distributions</h2>
<p class="chapter-meta">9 topics</p>
<article class="doc-entry" id="doc-multivariate-normal-pdf">
<h3><a class="doc-anchor" href="#doc-multivariate-normal-pdf">#</a> <code>multivariate_normal_pdf</code></h3>
<p><code>multivariate_normal_pdf X, MU, SIGMA</code> — multivariate Gaussian PDF.</p>
</article>
<article class="doc-entry" id="doc-multivariate-normal-sample">
<h3><a class="doc-anchor" href="#doc-multivariate-normal-sample">#</a> <code>multivariate_normal_sample</code></h3>
<p><code>multivariate_normal_sample MU, SIGMA</code> — sample from MVN via Cholesky.</p>
</article>
<article class="doc-entry" id="doc-dirichlet-pdf">
<h3><a class="doc-anchor" href="#doc-dirichlet-pdf">#</a> <code>dirichlet_pdf</code></h3>
<p><code>dirichlet_pdf X, ALPHA</code> — Dirichlet PDF on the simplex.</p>
</article>
<article class="doc-entry" id="doc-dirichlet-sample">
<h3><a class="doc-anchor" href="#doc-dirichlet-sample">#</a> <code>dirichlet_sample</code></h3>
<p><code>dirichlet_sample ALPHA</code> — sample via independent Gamma draws.</p>
</article>
<article class="doc-entry" id="doc-skellam-pmf">
<h3><a class="doc-anchor" href="#doc-skellam-pmf">#</a> <code>skellam_pmf</code></h3>
<p><code>skellam_pmf K, MU1, MU2</code> — difference of two independent Poisson(μ) variates.</p>
</article>
<article class="doc-entry" id="doc-inverse-gaussian-pdf">
<h3><a class="doc-anchor" href="#doc-inverse-gaussian-pdf">#</a> <code>inverse_gaussian_pdf</code></h3>
<p><code>inverse_gaussian_pdf X, MU, LAMBDA</code> — Wald PDF.</p>
</article>
<article class="doc-entry" id="doc-inverse-gaussian-cdf">
<h3><a class="doc-anchor" href="#doc-inverse-gaussian-cdf">#</a> <code>inverse_gaussian_cdf</code></h3>
<p><code>inverse_gaussian_cdf X, MU, LAMBDA</code> — Wald CDF.</p>
</article>
<article class="doc-entry" id="doc-inverse-gaussian-sample">
<h3><a class="doc-anchor" href="#doc-inverse-gaussian-sample">#</a> <code>inverse_gaussian_sample</code></h3>
<p><code>inverse_gaussian_sample MU, LAMBDA</code> — Michael-Schucany-Haas.</p>
</article>
<article class="doc-entry" id="doc-non-central-chi2-pdf">
<h3><a class="doc-anchor" href="#doc-non-central-chi2-pdf">#</a> <code>non_central_chi2_pdf</code></h3>
<p><code>non_central_chi2_pdf X, K, LAMBDA</code> — Series-form non-central χ² PDF.</p>
</article>
</section>
<section class="tutorial-section" id="ch-matrix-functions">
<h2>Matrix Functions</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-matrix-exp">
<h3><a class="doc-anchor" href="#doc-matrix-exp">#</a> <code>matrix_exp</code></h3>
<p><code>matrix_exp A</code> — e^A via 13-term Padé + scaling-and-squaring.</p>
</article>
<article class="doc-entry" id="doc-matrix-log">
<h3><a class="doc-anchor" href="#doc-matrix-log">#</a> <code>matrix_log</code></h3>
<p><code>matrix_log A</code> — ln A via inverse scaling (Denman-Beavers SQRT) + Padé log.</p>
</article>
<article class="doc-entry" id="doc-matrix-sqrt">
<h3><a class="doc-anchor" href="#doc-matrix-sqrt">#</a> <code>matrix_sqrt</code></h3>
<p><code>matrix_sqrt A</code> — A^(1/2) via Denman-Beavers iteration.</p>
</article>
<article class="doc-entry" id="doc-matrix-sin">
<h3><a class="doc-anchor" href="#doc-matrix-sin">#</a> <code>matrix_sin</code></h3>
<p><code>matrix_sin A</code> — series form Σ (-1)^k A^(2k+1) / (2k+1)!.</p>
</article>
<article class="doc-entry" id="doc-matrix-cos">
<h3><a class="doc-anchor" href="#doc-matrix-cos">#</a> <code>matrix_cos</code></h3>
<p><code>matrix_cos A</code> — series form Σ (-1)^k A^(2k) / (2k)!.</p>
</article>
</section>
<section class="tutorial-section" id="ch-adaptive-ode-solvers">
<h2>Adaptive ODE Solvers</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-rk45-dormand-prince">
<h3><a class="doc-anchor" href="#doc-rk45-dormand-prince">#</a> <code>rk45_dormand_prince</code></h3>
<p><code>rk45_dormand_prince F, Y0, T0, T1, H0 [, TOL]</code> — adaptive Dormand-Prince. F receives <code>[t, y0, …]</code>.</p>
</article>
<article class="doc-entry" id="doc-midpoint-step">
<h3><a class="doc-anchor" href="#doc-midpoint-step">#</a> <code>midpoint_step</code></h3>
<p><code>midpoint_step F, Y, T, H</code> — single explicit-midpoint step.</p>
</article>
<article class="doc-entry" id="doc-heun-step">
<h3><a class="doc-anchor" href="#doc-heun-step">#</a> <code>heun_step</code></h3>
<p><code>heun_step F, Y, T, H</code> — improved-Euler / Heun step.</p>
</article>
<article class="doc-entry" id="doc-verlet-step">
<h3><a class="doc-anchor" href="#doc-verlet-step">#</a> <code>verlet_step</code></h3>
<p><code>verlet_step ACCEL, Q, P, T, H</code> — velocity-Verlet symplectic step.</p>
</article>
</section>
<section class="tutorial-section" id="ch-generalized-linear-models">
<h2>Generalized Linear Models</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-logistic-regression">
<h3><a class="doc-anchor" href="#doc-logistic-regression">#</a> <code>logistic_regression</code></h3>
<p><code>logistic_regression X, Y</code> — IRLS (no intercept added — supply column of ones).</p>
</article>
<article class="doc-entry" id="doc-poisson-regression">
<h3><a class="doc-anchor" href="#doc-poisson-regression">#</a> <code>poisson_regression</code></h3>
<p><code>poisson_regression X, Y</code> — IRLS with log link.</p>
</article>
<article class="doc-entry" id="doc-ridge-regression">
<h3><a class="doc-anchor" href="#doc-ridge-regression">#</a> <code>ridge_regression</code></h3>
<p><code>ridge_regression X, Y [, LAMBDA]</code> — Tikhonov-regularised LSQ.</p>
</article>
<article class="doc-entry" id="doc-lasso-coord">
<h3><a class="doc-anchor" href="#doc-lasso-coord">#</a> <code>lasso_coord</code></h3>
<p><code>lasso_coord X, Y [, LAMBDA, MAX_ITER]</code> — coordinate-descent LASSO.</p>
</article>
</section>
<section class="tutorial-section" id="ch-bootstrap-resampling">
<h2>Bootstrap & Resampling</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-bootstrap-mean-ci">
<h3><a class="doc-anchor" href="#doc-bootstrap-mean-ci">#</a> <code>bootstrap_mean_ci</code></h3>
<p><code>bootstrap_mean_ci DATA [, B, ALPHA]</code> — percentile CI for the mean.</p>
</article>
<article class="doc-entry" id="doc-jackknife-estimate">
<h3><a class="doc-anchor" href="#doc-jackknife-estimate">#</a> <code>jackknife_estimate</code></h3>
<p><code>jackknife_estimate DATA</code> — leave-one-out SE of the mean.</p>
</article>
<article class="doc-entry" id="doc-permutation-test-diff">
<h3><a class="doc-anchor" href="#doc-permutation-test-diff">#</a> <code>permutation_test_diff</code></h3>
<p><code>permutation_test_diff A, B [, N_ITER]</code> — two-sided p of mean difference.</p>
</article>
</section>
<section class="tutorial-section" id="ch-time-series-operators">
<h2>Time Series Operators</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-acf-at-lag">
<h3><a class="doc-anchor" href="#doc-acf-at-lag">#</a> <code>acf_at_lag</code></h3>
<p><code>acf_at_lag XS, LAG</code> — autocorrelation at one lag.</p>
</article>
<article class="doc-entry" id="doc-diff-op">
<h3><a class="doc-anchor" href="#doc-diff-op">#</a> <code>diff_op</code></h3>
<p><code>diff_op XS [, LAG]</code> — y_t − y_{t-lag}.</p>
</article>
<article class="doc-entry" id="doc-lag-op">
<h3><a class="doc-anchor" href="#doc-lag-op">#</a> <code>lag_op</code></h3>
<p><code>lag_op XS [, K]</code> — shift by k (NaN-pad).</p>
</article>
<article class="doc-entry" id="doc-decompose-classical">
<h3><a class="doc-anchor" href="#doc-decompose-classical">#</a> <code>decompose_classical</code></h3>
<p><code>decompose_classical XS [, PERIOD]</code> — additive [trend, season, residual].</p>
</article>
</section>
<section class="tutorial-section" id="ch-combinatorial-generators">
<h2>Combinatorial Generators</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-combinations-list">
<h3><a class="doc-anchor" href="#doc-combinations-list">#</a> <code>combinations_list</code></h3>
<p><code>combinations_list N, K</code> — all k-subsets of 0..n in lex order.</p>
</article>
<article class="doc-entry" id="doc-permutations-list">
<h3><a class="doc-anchor" href="#doc-permutations-list">#</a> <code>permutations_list</code></h3>
<p><code>permutations_list N</code> — all permutations of 0..n via Heap's algorithm.</p>
</article>
<article class="doc-entry" id="doc-cyclic-permutations">
<h3><a class="doc-anchor" href="#doc-cyclic-permutations">#</a> <code>cyclic_permutations</code></h3>
<p><code>cyclic_permutations ARR</code> — all rotations.</p>
</article>
<article class="doc-entry" id="doc-subsets-of-size">
<h3><a class="doc-anchor" href="#doc-subsets-of-size">#</a> <code>subsets_of_size</code></h3>
<p><code>subsets_of_size ARR, K</code> — all k-subsets of an arbitrary array.</p>
</article>
</section>
<section class="tutorial-section" id="ch-dynamic-programming">
<h2>Dynamic Programming</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-longest-increasing-subseq">
<h3><a class="doc-anchor" href="#doc-longest-increasing-subseq">#</a> <code>longest_increasing_subseq</code></h3>
<p><code>longest_increasing_subseq XS</code> — length only (O(n log n)).</p>
</article>
<article class="doc-entry" id="doc-knapsack-01">
<h3><a class="doc-anchor" href="#doc-knapsack-01">#</a> <code>knapsack_01</code></h3>
<p><code>knapsack_01 ITEMS, CAPACITY</code> — items as <code>[[w, v], …]</code>.</p>
</article>
<article class="doc-entry" id="doc-subset-sum-target">
<h3><a class="doc-anchor" href="#doc-subset-sum-target">#</a> <code>subset_sum_target</code></h3>
<p><code>subset_sum_target ARR, T</code> — 1 if any subset sums to T.</p>
</article>
<article class="doc-entry" id="doc-coin-change-min">
<h3><a class="doc-anchor" href="#doc-coin-change-min">#</a> <code>coin_change_min</code></h3>
<p><code>coin_change_min COINS, N</code> — min number of coins to make N (-1 if impossible).</p>
</article>
<article class="doc-entry" id="doc-edit-distance-levenshtein">
<h3><a class="doc-anchor" href="#doc-edit-distance-levenshtein">#</a> <code>edit_distance_levenshtein</code></h3>
<p><code>edit_distance A, B</code> — Levenshtein distance.</p>
</article>
</section>
<section class="tutorial-section" id="ch-ml-metrics">
<h2>ML Metrics</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-one-hot-encode">
<h3><a class="doc-anchor" href="#doc-one-hot-encode">#</a> <code>one_hot_encode</code></h3>
<p><code>one_hot_encode LABELS [, N_CLASSES]</code> → n×K matrix.</p>
</article>
<article class="doc-entry" id="doc-label-encode">
<h3><a class="doc-anchor" href="#doc-label-encode">#</a> <code>label_encode</code></h3>
<p><code>label_encode ARR</code> → <code>[indices, classes]</code>.</p>
</article>
<article class="doc-entry" id="doc-categorical-cross-entropy">
<h3><a class="doc-anchor" href="#doc-categorical-cross-entropy">#</a> <code>categorical_cross_entropy</code></h3>
<p><code>categorical_cross_entropy Y_TRUE, Y_PRED</code> — averaged over batch.</p>
</article>
<article class="doc-entry" id="doc-classification-metrics">
<h3><a class="doc-anchor" href="#doc-classification-metrics">#</a> <code>classification_metrics</code></h3>
<p><code>classification_metrics TP, FP, FN, TN</code> → <code>[acc, prec, recall, f1]</code>.</p>
</article>
<article class="doc-entry" id="doc-roc-auc">
<h3><a class="doc-anchor" href="#doc-roc-auc">#</a> <code>roc_auc</code></h3>
<p><code>roc_auc SCORES, LABELS</code> — Mann-Whitney U / (n+ n−).</p>
</article>
</section>
<section class="tutorial-section" id="ch-dsp-image-filters">
<h2>DSP / Image Filters</h2>
<p class="chapter-meta">6 topics</p>
<article class="doc-entry" id="doc-gaussian-blur-kernel">
<h3><a class="doc-anchor" href="#doc-gaussian-blur-kernel">#</a> <code>gaussian_blur_kernel</code></h3>
<p><code>gaussian_blur_kernel SIGMA [, RADIUS]</code> — 1-D normalized kernel.</p>
</article>
<article class="doc-entry" id="doc-sobel-x">
<h3><a class="doc-anchor" href="#doc-sobel-x">#</a> <code>sobel_x</code></h3>
<p><code>sobel_x</code> — horizontal Sobel kernel.</p>
</article>
<article class="doc-entry" id="doc-sobel-y">
<h3><a class="doc-anchor" href="#doc-sobel-y">#</a> <code>sobel_y</code></h3>
<p><code>sobel_y</code> — vertical Sobel kernel.</p>
</article>
<article class="doc-entry" id="doc-prewitt-x">
<h3><a class="doc-anchor" href="#doc-prewitt-x">#</a> <code>prewitt_x</code></h3>
<p><code>prewitt_x</code> — horizontal Prewitt.</p>
</article>
<article class="doc-entry" id="doc-prewitt-y">
<h3><a class="doc-anchor" href="#doc-prewitt-y">#</a> <code>prewitt_y</code></h3>
<p><code>prewitt_y</code> — vertical Prewitt.</p>
</article>
<article class="doc-entry" id="doc-laplacian-of-gaussian">
<h3><a class="doc-anchor" href="#doc-laplacian-of-gaussian">#</a> <code>laplacian_of_gaussian</code></h3>
<p><code>laplacian_of_gaussian SIGMA</code> — 2-D LoG kernel.</p>
</article>
</section>
<section class="tutorial-section" id="ch-stochastic-processes">
<h2>Stochastic Processes</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-brownian-path">
<h3><a class="doc-anchor" href="#doc-brownian-path">#</a> <code>brownian_path</code></h3>
<p><code>brownian_path T, N</code> — discrete Wiener path on [0, T].</p>
</article>
<article class="doc-entry" id="doc-geometric-brownian-path">
<h3><a class="doc-anchor" href="#doc-geometric-brownian-path">#</a> <code>geometric_brownian_path</code></h3>
<p><code>geometric_brownian_path S0, MU, SIGMA, T, N</code> — GBM sample path.</p>
</article>
<article class="doc-entry" id="doc-poisson-process">
<h3><a class="doc-anchor" href="#doc-poisson-process">#</a> <code>poisson_process</code></h3>
<p><code>poisson_process LAMBDA, T</code> — homogeneous Poisson arrival times.</p>
</article>
<article class="doc-entry" id="doc-random-walk-1d">
<h3><a class="doc-anchor" href="#doc-random-walk-1d">#</a> <code>random_walk_1d</code></h3>
<p><code>random_walk_1d N [, P]</code> — ±1 walk over N steps.</p>
</article>
</section>
<section class="tutorial-section" id="ch-compression-information-complexity">
<h2>Compression / Information Complexity</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-lempel-ziv-complexity">
<h3><a class="doc-anchor" href="#doc-lempel-ziv-complexity">#</a> <code>lempel_ziv_complexity</code></h3>
<p><code>lempel_ziv_complexity SEQ</code> — LZ76 production count.</p>
</article>
<article class="doc-entry" id="doc-huffman-code-lengths">
<h3><a class="doc-anchor" href="#doc-huffman-code-lengths">#</a> <code>huffman_code_lengths</code></h3>
<p><code>huffman_code_lengths FREQS</code> — code-length per symbol.</p>
</article>
<article class="doc-entry" id="doc-shannon-entropy-rate">
<h3><a class="doc-anchor" href="#doc-shannon-entropy-rate">#</a> <code>shannon_entropy_rate</code></h3>
<p><code>shannon_entropy_rate SEQ [, M]</code> — H_m − H_{m-1} block estimate.</p>
</article>
</section>
<section class="tutorial-section" id="ch-physics-quantum-extended">
<h2>Physics & Quantum (Extended)</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-planck-blackbody">
<h3><a class="doc-anchor" href="#doc-planck-blackbody">#</a> <code>planck_blackbody</code></h3>
<p><code>planck_blackbody LAMBDA, T</code> — spectral radiance B(λ, T).</p>
</article>
<article class="doc-entry" id="doc-rayleigh-jeans">
<h3><a class="doc-anchor" href="#doc-rayleigh-jeans">#</a> <code>rayleigh_jeans</code></h3>
<p><code>rayleigh_jeans LAMBDA, T</code> — long-wavelength approx.</p>
</article>
<article class="doc-entry" id="doc-compton-shift">
<h3><a class="doc-anchor" href="#doc-compton-shift">#</a> <code>compton_shift</code></h3>
<p><code>compton_shift THETA</code> — photon wavelength shift Δλ = (h/m_e c)(1-cosθ).</p>
</article>
<article class="doc-entry" id="doc-rydberg-energy">
<h3><a class="doc-anchor" href="#doc-rydberg-energy">#</a> <code>rydberg_energy</code></h3>
<p><code>rydberg_energy N</code> — hydrogen level energy −13.605693/n² eV.</p>
</article>
<article class="doc-entry" id="doc-hydrogen-radial-wavefunction">
<h3><a class="doc-anchor" href="#doc-hydrogen-radial-wavefunction">#</a> <code>hydrogen_radial_wavefunction</code></h3>
<p><code>hydrogen_radial_wavefunction N, L, R</code> — atomic-units R_{n,l}(r).</p>
</article>
</section>
<section class="tutorial-section" id="ch-number-theory-algebra-extended">
<h2>Number Theory & Algebra (Extended)</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-integer-log">
<h3><a class="doc-anchor" href="#doc-integer-log">#</a> <code>integer_log</code></h3>
<p><code>integer_log N [, BASE]</code> — largest k with base^k ≤ n.</p>
</article>
<article class="doc-entry" id="doc-aks-primality">
<h3><a class="doc-anchor" href="#doc-aks-primality">#</a> <code>aks_primality</code></h3>
<p><code>aks_primality N</code> — deterministic primality (perfect-power + small-factor + Miller-Rabin fallback).</p>
</article>
<article class="doc-entry" id="doc-elliptic-curve-add">
<h3><a class="doc-anchor" href="#doc-elliptic-curve-add">#</a> <code>elliptic_curve_add</code></h3>
<p><code>elliptic_curve_add P, Q, A, B</code> — group law on y² = x³ + a x + b. Identity = <code>[NaN, NaN]</code>.</p>
</article>
<article class="doc-entry" id="doc-berlekamp-massey">
<h3><a class="doc-anchor" href="#doc-berlekamp-massey">#</a> <code>berlekamp_massey</code></h3>
<p><code>berlekamp_massey SEQ</code> — minimal-LFSR connection-polynomial coefficients.</p>
</article>
<article class="doc-entry" id="doc-bezout-coefficients">
<h3><a class="doc-anchor" href="#doc-bezout-coefficients">#</a> <code>bezout_coefficients</code></h3>
<p><code>bezout_coefficients A, B</code> → <code>[gcd, x, y]</code> with a x + b y = gcd.</p>
</article>
</section>
<section class="tutorial-section" id="ch-cas-lite">
<h2>CAS-Lite</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-factor-quadratic">
<h3><a class="doc-anchor" href="#doc-factor-quadratic">#</a> <code>factor_quadratic</code></h3>
<p><code>factor_quadratic A, B, C</code> — real roots of a x² + b x + c = 0.</p>
</article>
<article class="doc-entry" id="doc-complete-square">
<h3><a class="doc-anchor" href="#doc-complete-square">#</a> <code>complete_square</code></h3>
<p><code>complete_square A, B, C</code> → <code>[h, k]</code> for a (x-h)² + k.</p>
</article>
<article class="doc-entry" id="doc-partial-fraction-simple">
<h3><a class="doc-anchor" href="#doc-partial-fraction-simple">#</a> <code>partial_fraction_simple</code></h3>
<p><code>partial_fraction_simple NUM, ROOTS</code> — Heaviside cover-up residues.</p>
</article>
</section>
<section class="tutorial-section" id="ch-quadrature-specialised">
<h2>Quadrature (Specialised)</h2>
<p class="chapter-meta">7 topics</p>
<article class="doc-entry" id="doc-gauss-chebyshev-quad">
<h3><a class="doc-anchor" href="#doc-gauss-chebyshev-quad">#</a> <code>gauss_chebyshev_quad</code></h3>
<p><code>gauss_chebyshev_quad F [, N]</code> — ∫_{-1}^1 f(x)/√(1-x²) dx (default N=16).</p>
</article>
<article class="doc-entry" id="doc-gauss-hermite-quad">
<h3><a class="doc-anchor" href="#doc-gauss-hermite-quad">#</a> <code>gauss_hermite_quad</code></h3>
<p><code>gauss_hermite_quad F [, N]</code> — ∫_{-∞}^∞ f(x) e^{-x²} dx (default N=20).</p>
</article>
<article class="doc-entry" id="doc-gauss-laguerre-quad">
<h3><a class="doc-anchor" href="#doc-gauss-laguerre-quad">#</a> <code>gauss_laguerre_quad</code></h3>
<p><code>gauss_laguerre_quad F [, N]</code> — ∫_0^∞ f(x) e^{-x} dx (default N=20).</p>
</article>
<article class="doc-entry" id="doc-clenshaw-curtis-quad">
<h3><a class="doc-anchor" href="#doc-clenshaw-curtis-quad">#</a> <code>clenshaw_curtis_quad</code></h3>
<p><code>clenshaw_curtis_quad F, A, B [, N]</code> — Chebyshev-node quadrature.</p>
</article>
<article class="doc-entry" id="doc-tanh-sinh-quad">
<h3><a class="doc-anchor" href="#doc-tanh-sinh-quad">#</a> <code>tanh_sinh_quad</code></h3>
<p><code>tanh_sinh_quad F, A, B [, LEVELS]</code> — double-exponential quadrature.</p>
</article>
<article class="doc-entry" id="doc-gauss-legendre-2d">
<h3><a class="doc-anchor" href="#doc-gauss-legendre-2d">#</a> <code>gauss_legendre_2d</code></h3>
<p><code>gauss_legendre_2d F, AX, BX, AY, BY [, N]</code> — Cartesian-product GL.</p>
</article>
<article class="doc-entry" id="doc-monte-carlo-2d">
<h3><a class="doc-anchor" href="#doc-monte-carlo-2d">#</a> <code>monte_carlo_2d</code></h3>
<p><code>monte_carlo_2d F, AX, BX, AY, BY [, N]</code> — uniform Monte Carlo on a rectangle.</p>
</article>
</section>
<section class="tutorial-section" id="ch-optimization-heuristic">
<h2>Optimization (Heuristic)</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-simulated-annealing">
<h3><a class="doc-anchor" href="#doc-simulated-annealing">#</a> <code>simulated_annealing</code></h3>
<p><code>simulated_annealing F, X0 [, T0, COOL, ITERS, STEP]</code> — Metropolis-Hastings minimisation.</p>
</article>
<article class="doc-entry" id="doc-simplex-lp">
<h3><a class="doc-anchor" href="#doc-simplex-lp">#</a> <code>simplex_lp</code></h3>
<p><code>simplex_lp C, A, B</code> — max cᵀx s.t. Ax ≤ b, x ≥ 0. Returns <code>[x, value]</code>.</p>
</article>
<article class="doc-entry" id="doc-particle-swarm">
<h3><a class="doc-anchor" href="#doc-particle-swarm">#</a> <code>particle_swarm</code></h3>
<p><code>particle_swarm F, BOUNDS, SWARM, ITERS</code> — constriction-coefficient PSO.</p>
</article>
</section>
<section class="tutorial-section" id="ch-distributions-tail-mixture-categorical">
<h2>Distributions (Tail / Mixture / Categorical)</h2>
<p class="chapter-meta">14 topics</p>
<article class="doc-entry" id="doc-gev-pdf">
<h3><a class="doc-anchor" href="#doc-gev-pdf">#</a> <code>gev_pdf</code></h3>
<p><code>gev_pdf X, MU, SIGMA, XI</code> — Generalised Extreme Value PDF.</p>
</article>
<article class="doc-entry" id="doc-gev-cdf">
<h3><a class="doc-anchor" href="#doc-gev-cdf">#</a> <code>gev_cdf</code></h3>
<p><code>gev_cdf X, MU, SIGMA, XI</code> — GEV CDF.</p>
</article>
<article class="doc-entry" id="doc-gev-sample">
<h3><a class="doc-anchor" href="#doc-gev-sample">#</a> <code>gev_sample</code></h3>
<p><code>gev_sample MU, SIGMA, XI</code> — GEV sample.</p>
</article>
<article class="doc-entry" id="doc-gen-pareto-pdf">
<h3><a class="doc-anchor" href="#doc-gen-pareto-pdf">#</a> <code>gen_pareto_pdf</code></h3>
<p><code>gen_pareto_pdf X, MU, SIGMA, XI</code> — Generalised Pareto PDF.</p>
</article>
<article class="doc-entry" id="doc-gen-pareto-cdf">
<h3><a class="doc-anchor" href="#doc-gen-pareto-cdf">#</a> <code>gen_pareto_cdf</code></h3>
<p><code>gen_pareto_cdf X, MU, SIGMA, XI</code> — GP CDF.</p>
</article>
<article class="doc-entry" id="doc-gen-pareto-sample">
<h3><a class="doc-anchor" href="#doc-gen-pareto-sample">#</a> <code>gen_pareto_sample</code></h3>
<p><code>gen_pareto_sample MU, SIGMA, XI</code> — GP sample.</p>
</article>
<article class="doc-entry" id="doc-skew-normal-pdf">
<h3><a class="doc-anchor" href="#doc-skew-normal-pdf">#</a> <code>skew_normal_pdf</code></h3>
<p><code>skew_normal_pdf X, XI, OMEGA, ALPHA</code> — Azzalini skew-normal PDF.</p>
</article>
<article class="doc-entry" id="doc-skew-normal-cdf">
<h3><a class="doc-anchor" href="#doc-skew-normal-cdf">#</a> <code>skew_normal_cdf</code></h3>
<p><code>skew_normal_cdf X, XI, OMEGA, ALPHA</code> — skew-normal CDF (numeric integration).</p>
</article>
<article class="doc-entry" id="doc-mixture-normal-pdf">
<h3><a class="doc-anchor" href="#doc-mixture-normal-pdf">#</a> <code>mixture_normal_pdf</code></h3>
<p><code>mixture_normal_pdf X, WEIGHTS, MEANS, STDS</code> — Gaussian-mixture PDF.</p>
</article>
<article class="doc-entry" id="doc-categorical-sample">
<h3><a class="doc-anchor" href="#doc-categorical-sample">#</a> <code>categorical_sample</code></h3>
<p><code>categorical_sample PROBS</code> — sample category index.</p>
</article>
<article class="doc-entry" id="doc-multinomial-pmf">
<h3><a class="doc-anchor" href="#doc-multinomial-pmf">#</a> <code>multinomial_pmf</code></h3>
<p><code>multinomial_pmf COUNTS, PROBS</code> — multinomial PMF.</p>
</article>
<article class="doc-entry" id="doc-multinomial-sample">
<h3><a class="doc-anchor" href="#doc-multinomial-sample">#</a> <code>multinomial_sample</code></h3>
<p><code>multinomial_sample N, PROBS</code> — multinomial counts vector.</p>
</article>
<article class="doc-entry" id="doc-truncated-normal-pdf">
<h3><a class="doc-anchor" href="#doc-truncated-normal-pdf">#</a> <code>truncated_normal_pdf</code></h3>
<p><code>truncated_normal_pdf X, MU, SIGMA, LO, HI</code> — truncated-normal PDF.</p>
</article>
<article class="doc-entry" id="doc-truncated-normal-sample">
<h3><a class="doc-anchor" href="#doc-truncated-normal-sample">#</a> <code>truncated_normal_sample</code></h3>
<p><code>truncated_normal_sample MU, SIGMA, LO, HI</code> — rejection sampler.</p>
</article>
</section>
<section class="tutorial-section" id="ch-clustering-dimensionality-reduction">
<h2>Clustering & Dimensionality Reduction</h2>
<p class="chapter-meta">7 topics</p>
<article class="doc-entry" id="doc-dbscan">
<h3><a class="doc-anchor" href="#doc-dbscan">#</a> <code>dbscan</code></h3>
<p><code>dbscan POINTS, EPS, MIN_PTS</code> — density-based clustering. Returns label per point (-1 = noise).</p>
</article>
<article class="doc-entry" id="doc-gmm-em-1d">
<h3><a class="doc-anchor" href="#doc-gmm-em-1d">#</a> <code>gmm_em_1d</code></h3>
<p><code>gmm_em_1d DATA, K [, MAX_ITER]</code> — 1-D Gaussian-mixture EM. Returns <code>[π, μ, σ]</code>.</p>
</article>
<article class="doc-entry" id="doc-silhouette-score">
<h3><a class="doc-anchor" href="#doc-silhouette-score">#</a> <code>silhouette_score</code></h3>
<p><code>silhouette_score POINTS, LABELS</code> — mean silhouette coefficient.</p>
</article>
<article class="doc-entry" id="doc-davies-bouldin-index">
<h3><a class="doc-anchor" href="#doc-davies-bouldin-index">#</a> <code>davies_bouldin_index</code></h3>
<p><code>davies_bouldin_index POINTS, LABELS</code> — lower is better.</p>
</article>
<article class="doc-entry" id="doc-calinski-harabasz-index">
<h3><a class="doc-anchor" href="#doc-calinski-harabasz-index">#</a> <code>calinski_harabasz_index</code></h3>
<p><code>calinski_harabasz_index POINTS, LABELS</code> — higher is better.</p>
</article>
<article class="doc-entry" id="doc-mds-2d">
<h3><a class="doc-anchor" href="#doc-mds-2d">#</a> <code>mds_2d</code></h3>
<p><code>mds_2d D</code> — classical multidimensional scaling on a distance matrix → 2-D coords.</p>
</article>
<article class="doc-entry" id="doc-mean-shift">
<h3><a class="doc-anchor" href="#doc-mean-shift">#</a> <code>mean_shift</code></h3>
<p><code>mean_shift POINTS [, BANDWIDTH, MAX_ITER]</code> — non-parametric mode-seeking.</p>
</article>
</section>
<section class="tutorial-section" id="ch-neural-net-primitives">
<h2>Neural-Net Primitives</h2>
<p class="chapter-meta">11 topics</p>
<article class="doc-entry" id="doc-batch-norm">
<h3><a class="doc-anchor" href="#doc-batch-norm">#</a> <code>batch_norm</code></h3>
<p><code>batch_norm XS [, EPS]</code> — zero-mean unit-variance normalisation.</p>
</article>
<article class="doc-entry" id="doc-layer-norm">
<h3><a class="doc-anchor" href="#doc-layer-norm">#</a> <code>layer_norm</code></h3>
<p><code>layer_norm XS [, EPS]</code> — alias for batch_norm (per-sample reuse).</p>
</article>
<article class="doc-entry" id="doc-dropout-mask">
<h3><a class="doc-anchor" href="#doc-dropout-mask">#</a> <code>dropout_mask</code></h3>
<p><code>dropout_mask N [, P]</code> — Bernoulli dropout mask scaled by 1/(1−p).</p>
</article>
<article class="doc-entry" id="doc-max-pool-1d">
<h3><a class="doc-anchor" href="#doc-max-pool-1d">#</a> <code>max_pool_1d</code></h3>
<p><code>max_pool_1d XS [, WIN]</code> — non-overlapping max-pool.</p>
</article>
<article class="doc-entry" id="doc-avg-pool-1d">
<h3><a class="doc-anchor" href="#doc-avg-pool-1d">#</a> <code>avg_pool_1d</code></h3>
<p><code>avg_pool_1d XS [, WIN]</code> — non-overlapping average-pool.</p>
</article>
<article class="doc-entry" id="doc-attention-softmax">
<h3><a class="doc-anchor" href="#doc-attention-softmax">#</a> <code>attention_softmax</code></h3>
<p><code>attention_softmax XS</code> — numerically stable softmax.</p>
</article>
<article class="doc-entry" id="doc-positional-encoding">
<h3><a class="doc-anchor" href="#doc-positional-encoding">#</a> <code>positional_encoding</code></h3>
<p><code>positional_encoding LENGTH, D_MODEL</code> — sinusoidal Transformer encoding.</p>
</article>
<article class="doc-entry" id="doc-glorot-init">
<h3><a class="doc-anchor" href="#doc-glorot-init">#</a> <code>glorot_init</code></h3>
<p><code>glorot_init FAN_IN, FAN_OUT</code> — Glorot uniform.</p>
</article>
<article class="doc-entry" id="doc-he-init">
<h3><a class="doc-anchor" href="#doc-he-init">#</a> <code>he_init</code></h3>
<p><code>he_init FAN_IN, FAN_OUT</code> — Gaussian (std = √(2/fan_in)).</p>
</article>
<article class="doc-entry" id="doc-adam-step">
<h3><a class="doc-anchor" href="#doc-adam-step">#</a> <code>adam_step</code></h3>
<p><code>adam_step PARAM, GRAD, M, V, LR, B1, B2, EPS, T</code> → <code>[param', m', v']</code>.</p>
</article>
<article class="doc-entry" id="doc-rmsprop-step">
<h3><a class="doc-anchor" href="#doc-rmsprop-step">#</a> <code>rmsprop_step</code></h3>
<p><code>rmsprop_step PARAM, GRAD, V, LR, DECAY, EPS</code> → <code>[param', v']</code>.</p>
</article>
</section>
<section class="tutorial-section" id="ch-time-series-spectral">
<h2>Time Series (Spectral)</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-ewma">
<h3><a class="doc-anchor" href="#doc-ewma">#</a> <code>ewma</code></h3>
<p><code>ewma XS [, ALPHA]</code> — exponentially-weighted moving average.</p>
</article>
<article class="doc-entry" id="doc-ccf">
<h3><a class="doc-anchor" href="#doc-ccf">#</a> <code>ccf</code></h3>
<p><code>ccf XS, YS [, MAX_LAG]</code> — sample cross-correlation function over -L..L lags.</p>
</article>
<article class="doc-entry" id="doc-periodogram">
<h3><a class="doc-anchor" href="#doc-periodogram">#</a> <code>periodogram</code></h3>
<p><code>periodogram XS</code> — squared-magnitude DFT / N (one-sided spectrum).</p>
</article>
<article class="doc-entry" id="doc-welch-psd">
<h3><a class="doc-anchor" href="#doc-welch-psd">#</a> <code>welch_psd</code></h3>
<p><code>welch_psd XS [, SEG_LEN, OVERLAP]</code> — Welch's PSD via Hann segments.</p>
</article>
<article class="doc-entry" id="doc-lag-features">
<h3><a class="doc-anchor" href="#doc-lag-features">#</a> <code>lag_features</code></h3>
<p><code>lag_features XS, P</code> — design matrix of P lagged features.</p>
</article>
</section>
<section class="tutorial-section" id="ch-image-processing">
<h2>Image Processing</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-median-filter-2d">
<h3><a class="doc-anchor" href="#doc-median-filter-2d">#</a> <code>median_filter_2d</code></h3>
<p><code>median_filter_2d IMG [, RADIUS]</code> — denoising median filter.</p>
</article>
<article class="doc-entry" id="doc-threshold-otsu">
<h3><a class="doc-anchor" href="#doc-threshold-otsu">#</a> <code>threshold_otsu</code></h3>
<p><code>threshold_otsu IMG</code> — Otsu's optimal threshold for 0..255 grayscale.</p>
</article>
<article class="doc-entry" id="doc-histogram-equalize">
<h3><a class="doc-anchor" href="#doc-histogram-equalize">#</a> <code>histogram_equalize</code></h3>
<p><code>histogram_equalize IMG</code> — global histogram equalisation.</p>
</article>
<article class="doc-entry" id="doc-erode-2d">
<h3><a class="doc-anchor" href="#doc-erode-2d">#</a> <code>erode_2d</code></h3>
<p><code>erode_2d IMG [, RADIUS]</code> — morphological erosion (square structuring element).</p>
</article>
<article class="doc-entry" id="doc-dilate-2d">
<h3><a class="doc-anchor" href="#doc-dilate-2d">#</a> <code>dilate_2d</code></h3>
<p><code>dilate_2d IMG [, RADIUS]</code> — morphological dilation.</p>
</article>
</section>
<section class="tutorial-section" id="ch-loss-functions">
<h2>Loss Functions</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-mse-loss">
<h3><a class="doc-anchor" href="#doc-mse-loss">#</a> <code>mse_loss</code></h3>
<p><code>mse_loss A, B</code> — mean-squared error.</p>
</article>
<article class="doc-entry" id="doc-mae-loss">
<h3><a class="doc-anchor" href="#doc-mae-loss">#</a> <code>mae_loss</code></h3>
<p><code>mae_loss A, B</code> — mean-absolute error.</p>
</article>
<article class="doc-entry" id="doc-huber-loss">
<h3><a class="doc-anchor" href="#doc-huber-loss">#</a> <code>huber_loss</code></h3>
<p><code>huber_loss A, B [, DELTA]</code> — Huber loss (default δ=1).</p>
</article>
</section>
<section class="tutorial-section" id="ch-spatial-geographic">
<h2>Spatial / Geographic</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-vincenty-distance">
<h3><a class="doc-anchor" href="#doc-vincenty-distance">#</a> <code>vincenty_distance</code></h3>
<p><code>vincenty_distance LAT1, LON1, LAT2, LON2</code> — geodesic distance on WGS-84.</p>
</article>
<article class="doc-entry" id="doc-mercator-project">
<h3><a class="doc-anchor" href="#doc-mercator-project">#</a> <code>mercator_project</code></h3>
<p><code>mercator_project LAT, LON [, R]</code> → <code>[x, y]</code> Mercator metres.</p>
</article>
<article class="doc-entry" id="doc-destination-from-bearing">
<h3><a class="doc-anchor" href="#doc-destination-from-bearing">#</a> <code>destination_from_bearing</code></h3>
<p><code>destination_from_bearing LAT, LON, BEARING_DEG, DIST_M [, R]</code> — spherical great-circle target.</p>
</article>
</section>
<section class="tutorial-section" id="ch-integer-sequences">
<h2>Integer Sequences</h2>
<p class="chapter-meta">6 topics</p>
<article class="doc-entry" id="doc-recaman">
<h3><a class="doc-anchor" href="#doc-recaman">#</a> <code>recaman</code></h3>
<p><code>recaman N</code> — first N terms of Recamán's sequence.</p>
</article>
<article class="doc-entry" id="doc-sylvester">
<h3><a class="doc-anchor" href="#doc-sylvester">#</a> <code>sylvester</code></h3>
<p><code>sylvester N</code> — Sylvester's sequence (a_n = a_{n-1}² − a_{n-1} + 1).</p>
</article>
<article class="doc-entry" id="doc-happy-q">
<h3><a class="doc-anchor" href="#doc-happy-q">#</a> <code>happy_q</code></h3>
<p><code>happy_q N</code> — 1 if N is a happy number.</p>
</article>
<article class="doc-entry" id="doc-amicable-pair-q">
<h3><a class="doc-anchor" href="#doc-amicable-pair-q">#</a> <code>amicable_pair_q</code></h3>
<p><code>amicable_pair_q A, B</code> — 1 if (a, b) is an amicable pair.</p>
</article>
<article class="doc-entry" id="doc-aliquot-sequence">
<h3><a class="doc-anchor" href="#doc-aliquot-sequence">#</a> <code>aliquot_sequence</code></h3>
<p><code>aliquot_sequence N [, MAX_STEPS]</code> — sum-of-proper-divisors trajectory.</p>
</article>
<article class="doc-entry" id="doc-magic-constant">
<h3><a class="doc-anchor" href="#doc-magic-constant">#</a> <code>magic_constant</code></h3>
<p><code>magic_constant N</code> — n(n²+1)/2 (sum of any line of an n×n magic square).</p>
</article>
</section>
<section class="tutorial-section" id="ch-graph-link-cluster-metrics">
<h2>Graph Link & Cluster Metrics</h2>
<p class="chapter-meta">7 topics</p>
<article class="doc-entry" id="doc-clustering-coefficient-local">
<h3><a class="doc-anchor" href="#doc-clustering-coefficient-local">#</a> <code>clustering_coefficient_local</code></h3>
<p><code>clustering_coefficient_local ADJ</code> — local CC per vertex.</p>
</article>
<article class="doc-entry" id="doc-clustering-coefficient-global">
<h3><a class="doc-anchor" href="#doc-clustering-coefficient-global">#</a> <code>clustering_coefficient_global</code></h3>
<p><code>clustering_coefficient_global ADJ</code> — mean local CC.</p>
</article>
<article class="doc-entry" id="doc-assortativity">
<h3><a class="doc-anchor" href="#doc-assortativity">#</a> <code>assortativity</code></h3>
<p><code>assortativity ADJ</code> — degree-degree correlation coefficient.</p>
</article>
<article class="doc-entry" id="doc-common-neighbors">
<h3><a class="doc-anchor" href="#doc-common-neighbors">#</a> <code>common_neighbors</code></h3>
<p><code>common_neighbors ADJ, U, V</code> — count.</p>
</article>
<article class="doc-entry" id="doc-jaccard-neighbors">
<h3><a class="doc-anchor" href="#doc-jaccard-neighbors">#</a> <code>jaccard_neighbors</code></h3>
<p><code>jaccard_neighbors ADJ, U, V</code> — |Γ(u) ∩ Γ(v)| / |Γ(u) ∪ Γ(v)|.</p>
</article>
<article class="doc-entry" id="doc-adamic-adar">
<h3><a class="doc-anchor" href="#doc-adamic-adar">#</a> <code>adamic_adar</code></h3>
<p><code>adamic_adar ADJ, U, V</code> — Σ 1/log(deg(w)) over common neighbours w.</p>
</article>
<article class="doc-entry" id="doc-preferential-attachment-score">
<h3><a class="doc-anchor" href="#doc-preferential-attachment-score">#</a> <code>preferential_attachment_score</code></h3>
<p><code>preferential_attachment_score ADJ, U, V</code> — deg(u)·deg(v).</p>
</article>
</section>
<section class="tutorial-section" id="ch-3-d-geometry">
<h2>3-D Geometry</h2>
<p class="chapter-meta">8 topics</p>
<article class="doc-entry" id="doc-triangle-3d-normal">
<h3><a class="doc-anchor" href="#doc-triangle-3d-normal">#</a> <code>triangle_3d_normal</code></h3>
<p><code>triangle_3d_normal P1, P2, P3</code> — unit normal.</p>
</article>
<article class="doc-entry" id="doc-triangle-3d-area">
<h3><a class="doc-anchor" href="#doc-triangle-3d-area">#</a> <code>triangle_3d_area</code></h3>
<p><code>triangle_3d_area P1, P2, P3</code> — area via cross product.</p>
</article>
<article class="doc-entry" id="doc-tetrahedron-volume">
<h3><a class="doc-anchor" href="#doc-tetrahedron-volume">#</a> <code>tetrahedron_volume</code></h3>
<p><code>tetrahedron_volume A, B, C, D</code> — |det(B-A, C-A, D-A)|/6.</p>
</article>
<article class="doc-entry" id="doc-plane-from-3-points">
<h3><a class="doc-anchor" href="#doc-plane-from-3-points">#</a> <code>plane_from_3_points</code></h3>
<p><code>plane_from_3_points P1, P2, P3</code> → <code>[a, b, c, d]</code> (a x + b y + c z + d = 0).</p>
</article>
<article class="doc-entry" id="doc-point-to-plane-distance">
<h3><a class="doc-anchor" href="#doc-point-to-plane-distance">#</a> <code>point_to_plane_distance</code></h3>
<p><code>point_to_plane_distance P, [a, b, c, d]</code>.</p>
</article>
<article class="doc-entry" id="doc-ray-triangle-intersect">
<h3><a class="doc-anchor" href="#doc-ray-triangle-intersect">#</a> <code>ray_triangle_intersect</code></h3>
<p><code>ray_triangle_intersect O, D, A, B, C</code> — Möller-Trumbore. Returns t or NaN.</p>
</article>
<article class="doc-entry" id="doc-ray-sphere-intersect">
<h3><a class="doc-anchor" href="#doc-ray-sphere-intersect">#</a> <code>ray_sphere_intersect</code></h3>
<p><code>ray_sphere_intersect O, D, CENTER, RADIUS</code> — nearest non-negative t.</p>
</article>
<article class="doc-entry" id="doc-aabb-overlap">
<h3><a class="doc-anchor" href="#doc-aabb-overlap">#</a> <code>aabb_overlap</code></h3>
<p><code>aabb_overlap A_MIN, A_MAX, B_MIN, B_MAX</code> — 1 if 3-D AABBs overlap.</p>
</article>
</section>
<section class="tutorial-section" id="ch-iterative-solvers">
<h2>Iterative Solvers</h2>
<p class="chapter-meta">6 topics</p>
<article class="doc-entry" id="doc-gauss-seidel">
<h3><a class="doc-anchor" href="#doc-gauss-seidel">#</a> <code>gauss_seidel</code></h3>
<p><code>gauss_seidel A, B [, MAX_ITER, TOL]</code> — Gauss-Seidel iterative solver.</p>
</article>
<article class="doc-entry" id="doc-jacobi-iteration">
<h3><a class="doc-anchor" href="#doc-jacobi-iteration">#</a> <code>jacobi_iteration</code></h3>
<p><code>jacobi_iteration A, B [, MAX_ITER, TOL]</code> — Jacobi iteration.</p>
</article>
<article class="doc-entry" id="doc-sor-solve">
<h3><a class="doc-anchor" href="#doc-sor-solve">#</a> <code>sor_solve</code></h3>
<p><code>sor_solve A, B [, OMEGA, MAX_ITER, TOL]</code> — Successive Over-Relaxation.</p>
</article>
<article class="doc-entry" id="doc-thomas-tridiag-solve">
<h3><a class="doc-anchor" href="#doc-thomas-tridiag-solve">#</a> <code>thomas_tridiag_solve</code></h3>
<p><code>thomas_tridiag_solve A_SUB, B_MAIN, C_SUP, D</code> — tridiagonal direct solve.</p>
</article>
<article class="doc-entry" id="doc-richardson-extrapolation">
<h3><a class="doc-anchor" href="#doc-richardson-extrapolation">#</a> <code>richardson_extrapolation</code></h3>
<p><code>richardson_extrapolation F, H0 [, LEVELS]</code> — Romberg-style extrapolation.</p>
</article>
<article class="doc-entry" id="doc-finite-difference-5pt">
<h3><a class="doc-anchor" href="#doc-finite-difference-5pt">#</a> <code>finite_difference_5pt</code></h3>
<p><code>finite_difference_5pt F, X [, H]</code> — five-point central derivative.</p>
</article>
</section>
<section class="tutorial-section" id="ch-crypto-modular-algebra">
<h2>Crypto / Modular Algebra</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-tonelli-shanks-sqrt">
<h3><a class="doc-anchor" href="#doc-tonelli-shanks-sqrt">#</a> <code>tonelli_shanks_sqrt</code></h3>
<p><code>tonelli_shanks_sqrt N, P</code> — modular square root mod prime p.</p>
</article>
<article class="doc-entry" id="doc-baby-step-giant-step">
<h3><a class="doc-anchor" href="#doc-baby-step-giant-step">#</a> <code>baby_step_giant_step</code></h3>
<p><code>baby_step_giant_step G, H, P</code> — discrete logarithm mod p.</p>
</article>
<article class="doc-entry" id="doc-pollard-rho-factor">
<h3><a class="doc-anchor" href="#doc-pollard-rho-factor">#</a> <code>pollard_rho_factor</code></h3>
<p><code>pollard_rho_factor N</code> — return a non-trivial factor of N.</p>
</article>
<article class="doc-entry" id="doc-modular-lcm">
<h3><a class="doc-anchor" href="#doc-modular-lcm">#</a> <code>modular_lcm</code></h3>
<p><code>modular_lcm XS</code> — LCM via gcd.</p>
</article>
<article class="doc-entry" id="doc-crt-general">
<h3><a class="doc-anchor" href="#doc-crt-general">#</a> <code>crt_general</code></h3>
<p><code>crt_general REMAINDERS, MODULI</code> — CRT over arbitrary (not coprime) moduli; -1 if infeasible.</p>
</article>
</section>
<section class="tutorial-section" id="ch-physics-chemistry">
<h2>Physics & Chemistry</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-van-der-waals-p">
<h3><a class="doc-anchor" href="#doc-van-der-waals-p">#</a> <code>van_der_waals_p</code></h3>
<p><code>van_der_waals_p N, T, V, A, B</code> — pressure from Van der Waals equation.</p>
</article>
<article class="doc-entry" id="doc-nernst-equation">
<h3><a class="doc-anchor" href="#doc-nernst-equation">#</a> <code>nernst_equation</code></h3>
<p><code>nernst_equation E0, N, T, Q</code> — half-cell potential.</p>
</article>
<article class="doc-entry" id="doc-arrhenius-rate">
<h3><a class="doc-anchor" href="#doc-arrhenius-rate">#</a> <code>arrhenius_rate</code></h3>
<p><code>arrhenius_rate A, EA, T</code> — k = A exp(-Ea / RT).</p>
</article>
<article class="doc-entry" id="doc-reduced-mass">
<h3><a class="doc-anchor" href="#doc-reduced-mass">#</a> <code>reduced_mass</code></h3>
<p><code>reduced_mass M1, M2</code> — μ = m1 m2 / (m1 + m2).</p>
</article>
<article class="doc-entry" id="doc-ph-to-concentration">
<h3><a class="doc-anchor" href="#doc-ph-to-concentration">#</a> <code>ph_to_concentration</code></h3>
<p><code>ph_to_concentration PH</code> — [H⁺] = 10^{-pH}.</p>
</article>
</section>
<section class="tutorial-section" id="ch-mcmc-sdes">
<h2>MCMC & SDEs</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-metropolis-hastings">
<h3><a class="doc-anchor" href="#doc-metropolis-hastings">#</a> <code>metropolis_hastings</code></h3>
<p><code>metropolis_hastings LOG_PI, X0, SIGMA, ITERS [, BURN_IN]</code> — random-walk MH.</p>
</article>
<article class="doc-entry" id="doc-gibbs-sampler-step">
<h3><a class="doc-anchor" href="#doc-gibbs-sampler-step">#</a> <code>gibbs_sampler_step</code></h3>
<p><code>gibbs_sampler_step COND_SAMPLERS, X</code> — one Gibbs sweep over coordinates.</p>
</article>
<article class="doc-entry" id="doc-euler-maruyama">
<h3><a class="doc-anchor" href="#doc-euler-maruyama">#</a> <code>euler_maruyama</code></h3>
<p><code>euler_maruyama MU, SIGMA, X0, T0, T_END, N_STEPS</code> — Euler-Maruyama SDE integrator.</p>
</article>
<article class="doc-entry" id="doc-milstein">
<h3><a class="doc-anchor" href="#doc-milstein">#</a> <code>milstein</code></h3>
<p><code>milstein MU, SIGMA, SIGMA_X, X0, T0, T_END, N_STEPS</code> — Milstein scheme.</p>
</article>
<article class="doc-entry" id="doc-ornstein-uhlenbeck-path">
<h3><a class="doc-anchor" href="#doc-ornstein-uhlenbeck-path">#</a> <code>ornstein_uhlenbeck_path</code></h3>
<p><code>ornstein_uhlenbeck_path THETA, MU, SIGMA, X0, T, N</code> — exact OU sample path.</p>
</article>
</section>
<section class="tutorial-section" id="ch-hidden-markov-models">
<h2>Hidden Markov Models</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-hmm-forward">
<h3><a class="doc-anchor" href="#doc-hmm-forward">#</a> <code>hmm_forward</code></h3>
<p><code>hmm_forward PI, A, B, OBS</code> — log P(O | λ).</p>
</article>
<article class="doc-entry" id="doc-hmm-viterbi">
<h3><a class="doc-anchor" href="#doc-hmm-viterbi">#</a> <code>hmm_viterbi</code></h3>
<p><code>hmm_viterbi PI, A, B, OBS</code> — most-likely state path.</p>
</article>
<article class="doc-entry" id="doc-hmm-backward">
<h3><a class="doc-anchor" href="#doc-hmm-backward">#</a> <code>hmm_backward</code></h3>
<p><code>hmm_backward PI, A, B, OBS</code> — backward β matrix.</p>
</article>
</section>
<section class="tutorial-section" id="ch-survival-analysis">
<h2>Survival Analysis</h2>
<p class="chapter-meta">2 topics</p>
<article class="doc-entry" id="doc-kaplan-meier">
<h3><a class="doc-anchor" href="#doc-kaplan-meier">#</a> <code>kaplan_meier</code></h3>
<p><code>kaplan_meier TIMES, EVENTS</code> → matrix of [t, S(t)].</p>
</article>
<article class="doc-entry" id="doc-log-rank-test">
<h3><a class="doc-anchor" href="#doc-log-rank-test">#</a> <code>log_rank_test</code></h3>
<p><code>log_rank_test T1, E1, T2, E2</code> → <code>[chi², p]</code>.</p>
</article>
</section>
<section class="tutorial-section" id="ch-sequence-alignment">
<h2>Sequence Alignment</h2>
<p class="chapter-meta">2 topics</p>
<article class="doc-entry" id="doc-needleman-wunsch">
<h3><a class="doc-anchor" href="#doc-needleman-wunsch">#</a> <code>needleman_wunsch</code></h3>
<p><code>needleman_wunsch A, B [, MATCH, MISMATCH, GAP]</code> — global alignment score.</p>
</article>
<article class="doc-entry" id="doc-smith-waterman">
<h3><a class="doc-anchor" href="#doc-smith-waterman">#</a> <code>smith_waterman</code></h3>
<p><code>smith_waterman A, B [, MATCH, MISMATCH, GAP]</code> — best local-alignment score.</p>
</article>
</section>
<section class="tutorial-section" id="ch-chemistry">
<h2>Chemistry</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-gibbs-free-energy">
<h3><a class="doc-anchor" href="#doc-gibbs-free-energy">#</a> <code>gibbs_free_energy</code></h3>
<p><code>gibbs_free_energy DH [, T, DS]</code> — ΔG = ΔH − TΔS.</p>
</article>
<article class="doc-entry" id="doc-henderson-hasselbalch">
<h3><a class="doc-anchor" href="#doc-henderson-hasselbalch">#</a> <code>henderson_hasselbalch</code></h3>
<p><code>henderson_hasselbalch PKA, A_CONJ, HA</code> — pH = pKa + log10([A⁻]/[HA]).</p>
</article>
<article class="doc-entry" id="doc-radioactive-decay">
<h3><a class="doc-anchor" href="#doc-radioactive-decay">#</a> <code>radioactive_decay</code></h3>
<p><code>radioactive_decay N0, LAMBDA, T</code> — N(t) = N₀ e^{-λt}.</p>
</article>
<article class="doc-entry" id="doc-half-life-to-constant">
<h3><a class="doc-anchor" href="#doc-half-life-to-constant">#</a> <code>half_life_to_constant</code></h3>
<p><code>half_life_to_constant T_HALF</code> — λ = ln 2 / t_½.</p>
</article>
</section>
<section class="tutorial-section" id="ch-control-theory">
<h2>Control Theory</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-pid-step">
<h3><a class="doc-anchor" href="#doc-pid-step">#</a> <code>pid_step</code></h3>
<p><code>pid_step STATE, KP, KI, KD, E, DT</code> → <code>[new_state, u]</code> (PID controller).</p>
</article>
<article class="doc-entry" id="doc-transfer-function-eval">
<h3><a class="doc-anchor" href="#doc-transfer-function-eval">#</a> <code>transfer_function_eval</code></h3>
<p><code>transfer_function_eval NUM, DEN, OMEGA</code> → <code>[Re, Im]</code> of H(jω).</p>
</article>
<article class="doc-entry" id="doc-bode-magnitude-db">
<h3><a class="doc-anchor" href="#doc-bode-magnitude-db">#</a> <code>bode_magnitude_db</code></h3>
<p><code>bode_magnitude_db NUM, DEN, OMEGA</code> — 20 log₁₀ |H(jω)|.</p>
</article>
<article class="doc-entry" id="doc-bode-phase-deg">
<h3><a class="doc-anchor" href="#doc-bode-phase-deg">#</a> <code>bode_phase_deg</code></h3>
<p><code>bode_phase_deg NUM, DEN, OMEGA</code> — phase of H(jω) in degrees.</p>
</article>
<article class="doc-entry" id="doc-lqr-2x2">
<h3><a class="doc-anchor" href="#doc-lqr-2x2">#</a> <code>lqr_2x2</code></h3>
<p><code>lqr_2x2 A, B, Q, R</code> — closed-form 2×2 continuous LQR. Returns <code>[K, P]</code>.</p>
</article>
</section>
<section class="tutorial-section" id="ch-game-theory">
<h2>Game Theory</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-nash-eq-2x2">
<h3><a class="doc-anchor" href="#doc-nash-eq-2x2">#</a> <code>nash_eq_2x2</code></h3>
<p><code>nash_eq_2x2 P1, P2</code> — pure Nash equilibria of a 2×2 bimatrix game.</p>
</article>
<article class="doc-entry" id="doc-shapley-value">
<h3><a class="doc-anchor" href="#doc-shapley-value">#</a> <code>shapley_value</code></h3>
<p><code>shapley_value N, V_TABLE</code> — Shapley values from characteristic-function vector.</p>
</article>
<article class="doc-entry" id="doc-expected-utility">
<h3><a class="doc-anchor" href="#doc-expected-utility">#</a> <code>expected_utility</code></h3>
<p><code>expected_utility PROBS, PAYOFFS</code> — Σ p·u.</p>
</article>
</section>
<section class="tutorial-section" id="ch-operations-research">
<h2>Operations Research</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-hungarian-assignment">
<h3><a class="doc-anchor" href="#doc-hungarian-assignment">#</a> <code>hungarian_assignment</code></h3>
<p><code>hungarian_assignment COST_MATRIX</code> — assignment + total cost. (Greedy heuristic; reduces to Hungarian for small instances.)</p>
</article>
<article class="doc-entry" id="doc-tsp-nearest-neighbor">
<h3><a class="doc-anchor" href="#doc-tsp-nearest-neighbor">#</a> <code>tsp_nearest_neighbor</code></h3>
<p><code>tsp_nearest_neighbor DIST_MATRIX</code> → <code>[tour, length]</code>.</p>
</article>
<article class="doc-entry" id="doc-vertex-cover-2approx">
<h3><a class="doc-anchor" href="#doc-vertex-cover-2approx">#</a> <code>vertex_cover_2approx</code></h3>
<p><code>vertex_cover_2approx ADJ</code> — 2-approximation greedy.</p>
</article>
</section>
<section class="tutorial-section" id="ch-numerical-pde">
<h2>Numerical PDE</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-heat-eq-1d">
<h3><a class="doc-anchor" href="#doc-heat-eq-1d">#</a> <code>heat_eq_1d</code></h3>
<p><code>heat_eq_1d F, A, B, NX, T, NT, ALPHA</code> — explicit FTCS heat-equation solver.</p>
</article>
<article class="doc-entry" id="doc-wave-eq-1d">
<h3><a class="doc-anchor" href="#doc-wave-eq-1d">#</a> <code>wave_eq_1d</code></h3>
<p><code>wave_eq_1d F, A, B, NX, T, NT, C</code> — explicit wave-equation solver.</p>
</article>
<article class="doc-entry" id="doc-laplace-2d-jacobi">
<h3><a class="doc-anchor" href="#doc-laplace-2d-jacobi">#</a> <code>laplace_2d_jacobi</code></h3>
<p><code>laplace_2d_jacobi GRID [, MAX_ITER, TOL]</code> — Jacobi smoother on a Dirichlet grid.</p>
</article>
</section>
<section class="tutorial-section" id="ch-bayesian-conjugate-updates">
<h2>Bayesian Conjugate Updates</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-beta-binomial-update">
<h3><a class="doc-anchor" href="#doc-beta-binomial-update">#</a> <code>beta_binomial_update</code></h3>
<p><code>beta_binomial_update ALPHA, BETA, N, K</code> → posterior <code>[α', β']</code>.</p>
</article>
<article class="doc-entry" id="doc-normal-normal-update">
<h3><a class="doc-anchor" href="#doc-normal-normal-update">#</a> <code>normal_normal_update</code></h3>
<p><code>normal_normal_update MU0, VAR0, N, YBAR, VAR_DATA</code> → <code>[μ_post, σ²_post]</code>.</p>
</article>
<article class="doc-entry" id="doc-gamma-poisson-update">
<h3><a class="doc-anchor" href="#doc-gamma-poisson-update">#</a> <code>gamma_poisson_update</code></h3>
<p><code>gamma_poisson_update ALPHA, BETA, N, TOTAL_EVENTS</code> → <code>[α', β']</code>.</p>
</article>
<article class="doc-entry" id="doc-dirichlet-multinomial-update">
<h3><a class="doc-anchor" href="#doc-dirichlet-multinomial-update">#</a> <code>dirichlet_multinomial_update</code></h3>
<p><code>dirichlet_multinomial_update ALPHA, COUNTS</code> → α + counts.</p>
</article>
</section>
<section class="tutorial-section" id="ch-quantum-computing-gates">
<h2>Quantum Computing Gates</h2>
<p class="chapter-meta">8 topics</p>
<article class="doc-entry" id="doc-hadamard-gate">
<h3><a class="doc-anchor" href="#doc-hadamard-gate">#</a> <code>hadamard_gate</code></h3>
<p><code>hadamard_gate</code> — 2×2 Hadamard.</p>
</article>
<article class="doc-entry" id="doc-cnot-gate">
<h3><a class="doc-anchor" href="#doc-cnot-gate">#</a> <code>cnot_gate</code></h3>
<p><code>cnot_gate</code> — 4×4 controlled-NOT.</p>
</article>
<article class="doc-entry" id="doc-swap-gate">
<h3><a class="doc-anchor" href="#doc-swap-gate">#</a> <code>swap_gate</code></h3>
<p><code>swap_gate</code> — 4×4 SWAP.</p>
</article>
<article class="doc-entry" id="doc-cz-gate">
<h3><a class="doc-anchor" href="#doc-cz-gate">#</a> <code>cz_gate</code></h3>
<p><code>cz_gate</code> — 4×4 controlled-Z.</p>
</article>
<article class="doc-entry" id="doc-qft-matrix">
<h3><a class="doc-anchor" href="#doc-qft-matrix">#</a> <code>qft_matrix</code></h3>
<p><code>qft_matrix N</code> → <code>[Re, Im]</code> of N×N QFT matrix.</p>
</article>
<article class="doc-entry" id="doc-phase-gate">
<h3><a class="doc-anchor" href="#doc-phase-gate">#</a> <code>phase_gate</code></h3>
<p><code>phase_gate PHI</code> → <code>[Re, Im]</code> of diag(1, e^iφ).</p>
</article>
<article class="doc-entry" id="doc-s-gate">
<h3><a class="doc-anchor" href="#doc-s-gate">#</a> <code>s_gate</code></h3>
<p><code>s_gate</code> — phase(π/2).</p>
</article>
<article class="doc-entry" id="doc-t-gate">
<h3><a class="doc-anchor" href="#doc-t-gate">#</a> <code>t_gate</code></h3>
<p><code>t_gate</code> — phase(π/4).</p>
</article>
</section>
<section class="tutorial-section" id="ch-splines-curves">
<h2>Splines & Curves</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-bezier-eval">
<h3><a class="doc-anchor" href="#doc-bezier-eval">#</a> <code>bezier_eval</code></h3>
<p><code>bezier_eval CONTROL_PTS, T</code> — de Casteljau evaluation.</p>
</article>
<article class="doc-entry" id="doc-catmull-rom-eval">
<h3><a class="doc-anchor" href="#doc-catmull-rom-eval">#</a> <code>catmull_rom_eval</code></h3>
<p><code>catmull_rom_eval P0, P1, P2, P3, T</code> — uniform Catmull-Rom.</p>
</article>
<article class="doc-entry" id="doc-cubic-hermite-eval">
<h3><a class="doc-anchor" href="#doc-cubic-hermite-eval">#</a> <code>cubic_hermite_eval</code></h3>
<p><code>cubic_hermite_eval P0, M0, P1, M1, T</code> — Hermite basis interpolation.</p>
</article>
<article class="doc-entry" id="doc-bspline-basis">
<h3><a class="doc-anchor" href="#doc-bspline-basis">#</a> <code>bspline_basis</code></h3>
<p><code>bspline_basis I, K, T, KNOTS</code> — Cox-de Boor B-spline basis.</p>
</article>
</section>
<section class="tutorial-section" id="ch-music-audio">
<h2>Music & Audio</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-freq-to-midi">
<h3><a class="doc-anchor" href="#doc-freq-to-midi">#</a> <code>freq_to_midi</code></h3>
<p><code>freq_to_midi F</code> — MIDI note number from frequency.</p>
</article>
<article class="doc-entry" id="doc-midi-to-freq">
<h3><a class="doc-anchor" href="#doc-midi-to-freq">#</a> <code>midi_to_freq</code></h3>
<p><code>midi_to_freq M</code> — frequency from MIDI note.</p>
</article>
<article class="doc-entry" id="doc-equal-temperament-freq">
<h3><a class="doc-anchor" href="#doc-equal-temperament-freq">#</a> <code>equal_temperament_freq</code></h3>
<p><code>equal_temperament_freq SEMITONES_ABOVE_A4</code> — 12-TET frequency.</p>
</article>
<article class="doc-entry" id="doc-cents-difference">
<h3><a class="doc-anchor" href="#doc-cents-difference">#</a> <code>cents_difference</code></h3>
<p><code>cents_difference F1, F2</code> — 1200 log₂(F2/F1).</p>
</article>
</section>
<section class="tutorial-section" id="ch-astronomy-cosmology">
<h2>Astronomy & Cosmology</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-redshift-z">
<h3><a class="doc-anchor" href="#doc-redshift-z">#</a> <code>redshift_z</code></h3>
<p><code>redshift_z LAMBDA_OBS, LAMBDA_EMIT</code> — z = λ_obs/λ_emit − 1.</p>
</article>
<article class="doc-entry" id="doc-hubble-distance">
<h3><a class="doc-anchor" href="#doc-hubble-distance">#</a> <code>hubble_distance</code></h3>
<p><code>hubble_distance H0</code> — c / H₀ in Mpc.</p>
</article>
<article class="doc-entry" id="doc-luminosity-distance">
<h3><a class="doc-anchor" href="#doc-luminosity-distance">#</a> <code>luminosity_distance</code></h3>
<p><code>luminosity_distance Z, H0, OMEGA_M, OMEGA_L</code> — flat ΛCDM (numeric).</p>
</article>
</section>
<section class="tutorial-section" id="ch-fluid-dynamics">
<h2>Fluid Dynamics</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-reynolds-number">
<h3><a class="doc-anchor" href="#doc-reynolds-number">#</a> <code>reynolds_number</code></h3>
<p><code>reynolds_number RHO, U, L, MU</code> — ρ U L / μ.</p>
</article>
<article class="doc-entry" id="doc-mach-number">
<h3><a class="doc-anchor" href="#doc-mach-number">#</a> <code>mach_number</code></h3>
<p><code>mach_number U, C</code> — U / c.</p>
</article>
<article class="doc-entry" id="doc-prandtl-number">
<h3><a class="doc-anchor" href="#doc-prandtl-number">#</a> <code>prandtl_number</code></h3>
<p><code>prandtl_number CP, MU, K</code> — c_p μ / k.</p>
</article>
<article class="doc-entry" id="doc-bernoulli-velocity">
<h3><a class="doc-anchor" href="#doc-bernoulli-velocity">#</a> <code>bernoulli_velocity</code></h3>
<p><code>bernoulli_velocity P1, P2, RHO</code> — √(2(p₁ − p₂)/ρ).</p>
</article>
</section>
<section class="tutorial-section" id="ch-distributions-discrete-circular">
<h2>Distributions (Discrete / Circular)</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-negative-binomial-pmf">
<h3><a class="doc-anchor" href="#doc-negative-binomial-pmf">#</a> <code>negative_binomial_pmf</code></h3>
<p><code>negative_binomial_pmf K, R, P</code> — failures-before-rth-success PMF.</p>
</article>
<article class="doc-entry" id="doc-hypergeometric-pmf">
<h3><a class="doc-anchor" href="#doc-hypergeometric-pmf">#</a> <code>hypergeometric_pmf</code></h3>
<p><code>hypergeometric_pmf N, K_POP, N_DRAWS, K_OBS</code> — finite-population PMF.</p>
</article>
<article class="doc-entry" id="doc-beta-binomial-pmf">
<h3><a class="doc-anchor" href="#doc-beta-binomial-pmf">#</a> <code>beta_binomial_pmf</code></h3>
<p><code>beta_binomial_pmf K, N, ALPHA, BETA</code> — beta-binomial PMF.</p>
</article>
<article class="doc-entry" id="doc-von-mises-pdf">
<h3><a class="doc-anchor" href="#doc-von-mises-pdf">#</a> <code>von_mises_pdf</code></h3>
<p><code>von_mises_pdf THETA, MU, KAPPA</code> — circular Gaussian.</p>
</article>
</section>
<section class="tutorial-section" id="ch-random-graph-generators">
<h2>Random Graph Generators</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-erdos-renyi-random">
<h3><a class="doc-anchor" href="#doc-erdos-renyi-random">#</a> <code>erdos_renyi_random</code></h3>
<p><code>erdos_renyi_random N, P</code> — G(n, p) Bernoulli edge model.</p>
</article>
<article class="doc-entry" id="doc-barabasi-albert-random">
<h3><a class="doc-anchor" href="#doc-barabasi-albert-random">#</a> <code>barabasi_albert_random</code></h3>
<p><code>barabasi_albert_random N, M</code> — preferential-attachment model.</p>
</article>
<article class="doc-entry" id="doc-watts-strogatz-random">
<h3><a class="doc-anchor" href="#doc-watts-strogatz-random">#</a> <code>watts_strogatz_random</code></h3>
<p><code>watts_strogatz_random N, K, P</code> — small-world rewiring.</p>
</article>
</section>
<section class="tutorial-section" id="ch-color-science">
<h2>Color Science</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-rgb-to-lab">
<h3><a class="doc-anchor" href="#doc-rgb-to-lab">#</a> <code>rgb_to_lab</code></h3>
<p><code>rgb_to_lab R, G, B</code> — sRGB → CIE Lab.</p>
</article>
<article class="doc-entry" id="doc-lab-to-rgb">
<h3><a class="doc-anchor" href="#doc-lab-to-rgb">#</a> <code>lab_to_rgb</code></h3>
<p><code>lab_to_rgb L, A, B</code> — CIE Lab → sRGB.</p>
</article>
<article class="doc-entry" id="doc-kelvin-to-rgb">
<h3><a class="doc-anchor" href="#doc-kelvin-to-rgb">#</a> <code>kelvin_to_rgb</code></h3>
<p><code>kelvin_to_rgb K</code> — black-body sRGB approximation (Tanner Helland).</p>
</article>
</section>
<section class="tutorial-section" id="ch-integer-sequences-combinatorial">
<h2>Integer Sequences (Combinatorial)</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-bell-triangle">
<h3><a class="doc-anchor" href="#doc-bell-triangle">#</a> <code>bell_triangle</code></h3>
<p><code>bell_triangle N</code> — first N+1 rows of the Bell / Aitken triangle.</p>
</article>
<article class="doc-entry" id="doc-surjection-count">
<h3><a class="doc-anchor" href="#doc-surjection-count">#</a> <code>surjection_count</code></h3>
<p><code>surjection_count N, K</code> — k! · S(n, k).</p>
</article>
<article class="doc-entry" id="doc-distinct-partition-count">
<h3><a class="doc-anchor" href="#doc-distinct-partition-count">#</a> <code>distinct_partition_count</code></h3>
<p><code>distinct_partition_count N</code> — partitions of N into distinct parts.</p>
</article>
<article class="doc-entry" id="doc-fibonacci-q">
<h3><a class="doc-anchor" href="#doc-fibonacci-q">#</a> <code>fibonacci_q</code></h3>
<p><code>fibonacci_q N</code> — 1 if N is a Fibonacci number.</p>
</article>
</section>
<section class="tutorial-section" id="ch-multiple-testing-corrections">
<h2>Multiple-Testing Corrections</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-bonferroni-correction">
<h3><a class="doc-anchor" href="#doc-bonferroni-correction">#</a> <code>bonferroni_correction</code></h3>
<p><code>bonferroni_correction PVALS</code> — Bonferroni-adjusted p-values (capped at 1).</p>
</article>
<article class="doc-entry" id="doc-benjamini-hochberg">
<h3><a class="doc-anchor" href="#doc-benjamini-hochberg">#</a> <code>benjamini_hochberg</code></h3>
<p><code>benjamini_hochberg PVALS</code> — BH FDR q-values.</p>
</article>
<article class="doc-entry" id="doc-tukey-hsd">
<h3><a class="doc-anchor" href="#doc-tukey-hsd">#</a> <code>tukey_hsd</code></h3>
<p><code>tukey_hsd ALPHA, K, DF, MSE, N</code> — Tukey honestly-significant-difference critical bound.</p>
</article>
</section>
<section class="tutorial-section" id="ch-probabilistic-distances">
<h2>Probabilistic Distances</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-hellinger-distance">
<h3><a class="doc-anchor" href="#doc-hellinger-distance">#</a> <code>hellinger_distance</code></h3>
<p><code>hellinger_distance P, Q</code> — √(½ Σ (√p − √q)²).</p>
</article>
<article class="doc-entry" id="doc-wasserstein-1d">
<h3><a class="doc-anchor" href="#doc-wasserstein-1d">#</a> <code>wasserstein_1d</code></h3>
<p><code>wasserstein_1d A, B</code> — earth-mover distance for sorted samples.</p>
</article>
<article class="doc-entry" id="doc-chi-squared-divergence">
<h3><a class="doc-anchor" href="#doc-chi-squared-divergence">#</a> <code>chi_squared_divergence</code></h3>
<p><code>chi_squared_divergence P, Q</code> — Σ (p − q)² / q.</p>
</article>
</section>
<section class="tutorial-section" id="ch-distributions-tail-inflated">
<h2>Distributions (Tail / Inflated)</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-beta-geometric-pmf">
<h3><a class="doc-anchor" href="#doc-beta-geometric-pmf">#</a> <code>beta_geometric_pmf</code></h3>
<p><code>beta_geometric_pmf K, ALPHA, BETA</code> — beta-geometric PMF.</p>
</article>
<article class="doc-entry" id="doc-generalized-gamma-pdf">
<h3><a class="doc-anchor" href="#doc-generalized-gamma-pdf">#</a> <code>generalized_gamma_pdf</code></h3>
<p><code>generalized_gamma_pdf X, A, D, P</code> — generalised-gamma PDF.</p>
</article>
<article class="doc-entry" id="doc-zip-pmf">
<h3><a class="doc-anchor" href="#doc-zip-pmf">#</a> <code>zip_pmf</code></h3>
<p><code>zip_pmf K, PI, LAMBDA</code> — zero-inflated Poisson.</p>
</article>
</section>
<section class="tutorial-section" id="ch-astrophysics-radiation">
<h2>Astrophysics & Radiation</h2>
<p class="chapter-meta">9 topics</p>
<article class="doc-entry" id="doc-stefan-boltzmann-luminosity">
<h3><a class="doc-anchor" href="#doc-stefan-boltzmann-luminosity">#</a> <code>stefan_boltzmann_luminosity</code></h3>
<p><code>stefan_boltzmann_luminosity R, T</code> — L = 4π R² σ T⁴.</p>
</article>
<article class="doc-entry" id="doc-photon-momentum">
<h3><a class="doc-anchor" href="#doc-photon-momentum">#</a> <code>photon_momentum</code></h3>
<p><code>photon_momentum LAMBDA</code> — h / λ.</p>
</article>
<article class="doc-entry" id="doc-photon-energy-ev">
<h3><a class="doc-anchor" href="#doc-photon-energy-ev">#</a> <code>photon_energy_ev</code></h3>
<p><code>photon_energy_ev LAMBDA</code> — hc / λ in eV.</p>
</article>
<article class="doc-entry" id="doc-dipole-radiation-power">
<h3><a class="doc-anchor" href="#doc-dipole-radiation-power">#</a> <code>dipole_radiation_power</code></h3>
<p><code>dipole_radiation_power Q, A</code> — Larmor formula.</p>
</article>
<article class="doc-entry" id="doc-parallax-to-distance">
<h3><a class="doc-anchor" href="#doc-parallax-to-distance">#</a> <code>parallax_to_distance</code></h3>
<p><code>parallax_to_distance P_ARCSEC</code> — parsecs from arcseconds.</p>
</article>
<article class="doc-entry" id="doc-hawking-temperature">
<h3><a class="doc-anchor" href="#doc-hawking-temperature">#</a> <code>hawking_temperature</code></h3>
<p><code>hawking_temperature M_KG</code> — black-hole temperature.</p>
</article>
<article class="doc-entry" id="doc-roche-limit">
<h3><a class="doc-anchor" href="#doc-roche-limit">#</a> <code>roche_limit</code></h3>
<p><code>roche_limit R, RHO_PRIMARY, RHO_SAT</code> — rigid-body Roche limit.</p>
</article>
<article class="doc-entry" id="doc-apparent-magnitude">
<h3><a class="doc-anchor" href="#doc-apparent-magnitude">#</a> <code>apparent_magnitude</code></h3>
<p><code>apparent_magnitude ABS_M, D_PC</code> — m = M + 5 log₁₀(d/10).</p>
</article>
<article class="doc-entry" id="doc-distance-modulus">
<h3><a class="doc-anchor" href="#doc-distance-modulus">#</a> <code>distance_modulus</code></h3>
<p><code>distance_modulus D_PC</code> — μ = 5 log d − 5.</p>
</article>
</section>
<section class="tutorial-section" id="ch-chemistry-beer-rate-colligative">
<h2>Chemistry (Beer / Rate / Colligative)</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-beer-lambert">
<h3><a class="doc-anchor" href="#doc-beer-lambert">#</a> <code>beer_lambert</code></h3>
<p><code>beer_lambert EPSILON, L, C</code> — A = ε·l·c.</p>
</article>
<article class="doc-entry" id="doc-rate-law-n">
<h3><a class="doc-anchor" href="#doc-rate-law-n">#</a> <code>rate_law_n</code></h3>
<p><code>rate_law_n A0, K, T, N</code> — concentration after time t for nth-order reaction.</p>
</article>
<article class="doc-entry" id="doc-freezing-point-depression">
<h3><a class="doc-anchor" href="#doc-freezing-point-depression">#</a> <code>freezing_point_depression</code></h3>
<p><code>freezing_point_depression KF, MOLALITY, I</code> — ΔT = K_f m i.</p>
</article>
</section>
<section class="tutorial-section" id="ch-mixed-strategy-game-theory">
<h2>Mixed-Strategy Game Theory</h2>
<p class="chapter-meta">2 topics</p>
<article class="doc-entry" id="doc-mixed-nash-2x2">
<h3><a class="doc-anchor" href="#doc-mixed-nash-2x2">#</a> <code>mixed_nash_2x2</code></h3>
<p><code>mixed_nash_2x2 P1, P2</code> → <code>[p, q]</code> mixed-strategy probabilities.</p>
</article>
<article class="doc-entry" id="doc-minimax-2x2">
<h3><a class="doc-anchor" href="#doc-minimax-2x2">#</a> <code>minimax_2x2</code></h3>
<p><code>minimax_2x2 M</code> — security level for the row player.</p>
</article>
</section>
<section class="tutorial-section" id="ch-computer-graphics">
<h2>Computer Graphics</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-barycentric-coords-2d">
<h3><a class="doc-anchor" href="#doc-barycentric-coords-2d">#</a> <code>barycentric_coords_2d</code></h3>
<p><code>barycentric_coords_2d P, A, B, C</code> → <code>[u, v, w]</code>.</p>
</article>
<article class="doc-entry" id="doc-bresenham-line">
<h3><a class="doc-anchor" href="#doc-bresenham-line">#</a> <code>bresenham_line</code></h3>
<p><code>bresenham_line X0, Y0, X1, Y1</code> → array of integer pixels.</p>
</article>
<article class="doc-entry" id="doc-bilinear-interp-2d">
<h3><a class="doc-anchor" href="#doc-bilinear-interp-2d">#</a> <code>bilinear_interp_2d</code></h3>
<p><code>bilinear_interp_2d F00, F10, F01, F11, U, V</code> — unit-square bilinear.</p>
</article>
<article class="doc-entry" id="doc-point-in-polygon-2d">
<h3><a class="doc-anchor" href="#doc-point-in-polygon-2d">#</a> <code>point_in_polygon_2d</code></h3>
<p><code>point_in_polygon_2d P, POLY</code> — ray-casting test.</p>
</article>
</section>
<section class="tutorial-section" id="ch-dsp-hilbert-cepstrum-filter-design">
<h2>DSP (Hilbert / Cepstrum / Filter Design)</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-hilbert-transform">
<h3><a class="doc-anchor" href="#doc-hilbert-transform">#</a> <code>hilbert_transform</code></h3>
<p><code>hilbert_transform XS</code> — discrete Hilbert via DFT.</p>
</article>
<article class="doc-entry" id="doc-cepstrum">
<h3><a class="doc-anchor" href="#doc-cepstrum">#</a> <code>cepstrum</code></h3>
<p><code>cepstrum XS</code> — real cepstrum ifft(log|fft|).</p>
</article>
<article class="doc-entry" id="doc-butterworth-lowpass-coeffs">
<h3><a class="doc-anchor" href="#doc-butterworth-lowpass-coeffs">#</a> <code>butterworth_lowpass_coeffs</code></h3>
<p><code>butterworth_lowpass_coeffs ORDER, CUTOFF</code> → <code>[b, a]</code> digital biquad-cascade.</p>
</article>
<article class="doc-entry" id="doc-savitzky-golay-coeffs">
<h3><a class="doc-anchor" href="#doc-savitzky-golay-coeffs">#</a> <code>savitzky_golay_coeffs</code></h3>
<p><code>savitzky_golay_coeffs NL, NR, M</code> — SG filter coefficients.</p>
</article>
<article class="doc-entry" id="doc-savitzky-golay-filter">
<h3><a class="doc-anchor" href="#doc-savitzky-golay-filter">#</a> <code>savitzky_golay_filter</code></h3>
<p><code>savitzky_golay_filter XS, COEFFS</code> — apply pre-computed SG coefficients.</p>
</article>
</section>
<section class="tutorial-section" id="ch-image-processing-edges-bilateral">
<h2>Image Processing (Edges / Bilateral)</h2>
<p class="chapter-meta">2 topics</p>
<article class="doc-entry" id="doc-canny-edge-intensity">
<h3><a class="doc-anchor" href="#doc-canny-edge-intensity">#</a> <code>canny_edge_intensity</code></h3>
<p><code>canny_edge_intensity IMG</code> — Sobel-magnitude edge map (caller thresholds).</p>
</article>
<article class="doc-entry" id="doc-bilateral-filter-basic">
<h3><a class="doc-anchor" href="#doc-bilateral-filter-basic">#</a> <code>bilateral_filter_basic</code></h3>
<p><code>bilateral_filter_basic IMG, RADIUS, SIGMA_S, SIGMA_R</code> — edge-preserving smoother.</p>
</article>
</section>
<section class="tutorial-section" id="ch-clustering-helpers">
<h2>Clustering Helpers</h2>
<p class="chapter-meta">2 topics</p>
<article class="doc-entry" id="doc-kmeans-pp-init">
<h3><a class="doc-anchor" href="#doc-kmeans-pp-init">#</a> <code>kmeans_pp_init</code></h3>
<p><code>kmeans_pp_init POINTS, K</code> — k-means++ seed centroids.</p>
</article>
<article class="doc-entry" id="doc-elbow-score">
<h3><a class="doc-anchor" href="#doc-elbow-score">#</a> <code>elbow_score</code></h3>
<p><code>elbow_score POINTS, LABELS</code> — within-cluster sum of squares.</p>
</article>
</section>
<section class="tutorial-section" id="ch-combinatorics-tableaux-boustrophedon">
<h2>Combinatorics (Tableaux / Boustrophedon)</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-young-tableaux-count">
<h3><a class="doc-anchor" href="#doc-young-tableaux-count">#</a> <code>young_tableaux_count</code></h3>
<p><code>young_tableaux_count LAMBDA</code> — hook-length formula.</p>
</article>
<article class="doc-entry" id="doc-euler-alt-permutation">
<h3><a class="doc-anchor" href="#doc-euler-alt-permutation">#</a> <code>euler_alt_permutation</code></h3>
<p><code>euler_alt_permutation N</code> — Euler / zigzag number A000111.</p>
</article>
<article class="doc-entry" id="doc-genocchi-number">
<h3><a class="doc-anchor" href="#doc-genocchi-number">#</a> <code>genocchi_number</code></h3>
<p><code>genocchi_number N</code> — G_n via Bernoulli identity.</p>
</article>
<article class="doc-entry" id="doc-lattice-paths-count">
<h3><a class="doc-anchor" href="#doc-lattice-paths-count">#</a> <code>lattice_paths_count</code></h3>
<p><code>lattice_paths_count M, N</code> — C(m+n, n) east/north paths.</p>
</article>
</section>
<section class="tutorial-section" id="ch-number-theory-tetration-smoothness">
<h2>Number Theory (Tetration / Smoothness)</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-tetration">
<h3><a class="doc-anchor" href="#doc-tetration">#</a> <code>tetration</code></h3>
<p><code>tetration A, N</code> — N-fold a-tower (overflow → ∞).</p>
</article>
<article class="doc-entry" id="doc-ackermann-limited">
<h3><a class="doc-anchor" href="#doc-ackermann-limited">#</a> <code>ackermann_limited</code></h3>
<p><code>ackermann_limited M, N</code> — depth-limited Ackermann (refuses past M=3 N=14).</p>
</article>
<article class="doc-entry" id="doc-perfect-power-q">
<h3><a class="doc-anchor" href="#doc-perfect-power-q">#</a> <code>perfect_power_q</code></h3>
<p><code>perfect_power_q N</code> — 1 if N = a^b for integers a, b ≥ 2.</p>
</article>
<article class="doc-entry" id="doc-b-smooth-q">
<h3><a class="doc-anchor" href="#doc-b-smooth-q">#</a> <code>b_smooth_q</code></h3>
<p><code>b_smooth_q N, B</code> — 1 if every prime factor of N is ≤ B.</p>
</article>
</section>
<section class="tutorial-section" id="ch-network-coreness-structure">
<h2>Network Coreness & Structure</h2>
<p class="chapter-meta">2 topics</p>
<article class="doc-entry" id="doc-k-core">
<h3><a class="doc-anchor" href="#doc-k-core">#</a> <code>k_core</code></h3>
<p><code>k_core ADJ</code> — vertex coreness.</p>
</article>
<article class="doc-entry" id="doc-rich-club-coefficient">
<h3><a class="doc-anchor" href="#doc-rich-club-coefficient">#</a> <code>rich_club_coefficient</code></h3>
<p><code>rich_club_coefficient ADJ, K</code> — fraction of edges among nodes with deg > k.</p>
</article>
</section>
<section class="tutorial-section" id="ch-crypto-helpers">
<h2>Crypto Helpers</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-rsa-basic-encrypt">
<h3><a class="doc-anchor" href="#doc-rsa-basic-encrypt">#</a> <code>rsa_basic_encrypt</code></h3>
<p><code>rsa_basic_encrypt M, E, N</code> — m^e mod n.</p>
</article>
<article class="doc-entry" id="doc-rsa-basic-decrypt">
<h3><a class="doc-anchor" href="#doc-rsa-basic-decrypt">#</a> <code>rsa_basic_decrypt</code></h3>
<p><code>rsa_basic_decrypt C, D, N</code> — c^d mod n.</p>
</article>
<article class="doc-entry" id="doc-dh-shared-secret">
<h3><a class="doc-anchor" href="#doc-dh-shared-secret">#</a> <code>dh_shared_secret</code></h3>
<p><code>dh_shared_secret PEER_PUB, PRIVATE, P</code> — Diffie-Hellman.</p>
</article>
</section>
<section class="tutorial-section" id="ch-quantum-entanglement">
<h2>Quantum Entanglement</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-bell-state-phi-plus">
<h3><a class="doc-anchor" href="#doc-bell-state-phi-plus">#</a> <code>bell_state_phi_plus</code></h3>
<p><code>bell_state_phi_plus</code> — Bell state (|00⟩+|11⟩)/√2.</p>
</article>
<article class="doc-entry" id="doc-bell-state-psi-minus">
<h3><a class="doc-anchor" href="#doc-bell-state-psi-minus">#</a> <code>bell_state_psi_minus</code></h3>
<p><code>bell_state_psi_minus</code> — singlet (|01⟩-|10⟩)/√2.</p>
</article>
<article class="doc-entry" id="doc-density-matrix-purity">
<h3><a class="doc-anchor" href="#doc-density-matrix-purity">#</a> <code>density_matrix_purity</code></h3>
<p><code>density_matrix_purity RHO</code> — tr(ρ²).</p>
</article>
<article class="doc-entry" id="doc-concurrence-2qubit">
<h3><a class="doc-anchor" href="#doc-concurrence-2qubit">#</a> <code>concurrence_2qubit</code></h3>
<p><code>concurrence_2qubit PSI</code> — 2|ad − bc| in real basis.</p>
</article>
</section>
<section class="tutorial-section" id="ch-2-d-geometry-polygons-circles">
<h2>2-D Geometry (Polygons & Circles)</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-point-in-circle">
<h3><a class="doc-anchor" href="#doc-point-in-circle">#</a> <code>point_in_circle</code></h3>
<p><code>point_in_circle P, CENTER, R</code> — 1 if inside.</p>
</article>
<article class="doc-entry" id="doc-circle-circle-intersect-2d">
<h3><a class="doc-anchor" href="#doc-circle-circle-intersect-2d">#</a> <code>circle_circle_intersect_2d</code></h3>
<p><code>circle_circle_intersect_2d C1, R1, C2, R2</code> — 0/1/2 intersection points.</p>
</article>
<article class="doc-entry" id="doc-polygon-centroid">
<h3><a class="doc-anchor" href="#doc-polygon-centroid">#</a> <code>polygon_centroid</code></h3>
<p><code>polygon_centroid POLY</code> — area-weighted centroid.</p>
</article>
<article class="doc-entry" id="doc-sutherland-hodgman-clip">
<h3><a class="doc-anchor" href="#doc-sutherland-hodgman-clip">#</a> <code>sutherland_hodgman_clip</code></h3>
<p><code>sutherland_hodgman_clip SUBJECT, CLIP</code> — clip against convex CCW polygon.</p>
</article>
</section>
<section class="tutorial-section" id="ch-time-series-smoothing">
<h2>Time-Series Smoothing</h2>
<p class="chapter-meta">1 topics</p>
<article class="doc-entry" id="doc-kalman-rts-smoother">
<h3><a class="doc-anchor" href="#doc-kalman-rts-smoother">#</a> <code>kalman_rts_smoother</code></h3>
<p><code>kalman_rts_smoother X_HAT, P, X_PRED, P_PRED, F</code> — RTS smoothed means.</p>
</article>
</section>
<section class="tutorial-section" id="ch-bioinformatics">
<h2>Bioinformatics</h2>
<p class="chapter-meta">6 topics</p>
<article class="doc-entry" id="doc-gc-content">
<h3><a class="doc-anchor" href="#doc-gc-content">#</a> <code>gc_content</code></h3>
<p><code>gc_content SEQ</code> — fraction of G + C in DNA / RNA string.</p>
</article>
<article class="doc-entry" id="doc-codon-to-aa">
<h3><a class="doc-anchor" href="#doc-codon-to-aa">#</a> <code>codon_to_aa</code></h3>
<p><code>codon_to_aa CODON</code> — single-letter amino-acid (or '*' / 'X').</p>
</article>
<article class="doc-entry" id="doc-reverse-complement-dna">
<h3><a class="doc-anchor" href="#doc-reverse-complement-dna">#</a> <code>reverse_complement_dna</code></h3>
<p><code>reverse_complement_dna SEQ</code> — DNA reverse complement.</p>
</article>
<article class="doc-entry" id="doc-hamming-dna">
<h3><a class="doc-anchor" href="#doc-hamming-dna">#</a> <code>hamming_dna</code></h3>
<p><code>hamming_dna A, B</code> — case-insensitive Hamming distance.</p>
</article>
<article class="doc-entry" id="doc-blosum62-pair-score">
<h3><a class="doc-anchor" href="#doc-blosum62-pair-score">#</a> <code>blosum62_pair_score</code></h3>
<p><code>blosum62_pair_score A, B</code> — BLOSUM62 substitution score.</p>
</article>
<article class="doc-entry" id="doc-kmer-count">
<h3><a class="doc-anchor" href="#doc-kmer-count">#</a> <code>kmer_count</code></h3>
<p><code>kmer_count SEQ, K</code> — total count of length-K windows.</p>
</article>
</section>
<section class="tutorial-section" id="ch-geographic-map-projection">
<h2>Geographic / Map Projection</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-great-circle-bearing">
<h3><a class="doc-anchor" href="#doc-great-circle-bearing">#</a> <code>great_circle_bearing</code></h3>
<p><code>great_circle_bearing LAT1, LON1, LAT2, LON2</code> — initial bearing in degrees.</p>
</article>
<article class="doc-entry" id="doc-midpoint-lat-lon">
<h3><a class="doc-anchor" href="#doc-midpoint-lat-lon">#</a> <code>midpoint_lat_lon</code></h3>
<p><code>midpoint_lat_lon LAT1, LON1, LAT2, LON2</code> — great-circle midpoint.</p>
</article>
<article class="doc-entry" id="doc-utm-zone-for">
<h3><a class="doc-anchor" href="#doc-utm-zone-for">#</a> <code>utm_zone_for</code></h3>
<p><code>utm_zone_for LON</code> — UTM zone (1..60).</p>
</article>
<article class="doc-entry" id="doc-area-polygon-lat-lon">
<h3><a class="doc-anchor" href="#doc-area-polygon-lat-lon">#</a> <code>area_polygon_lat_lon</code></h3>
<p><code>area_polygon_lat_lon POLY [, R]</code> — spherical-excess polygon area in m².</p>
</article>
</section>
<section class="tutorial-section" id="ch-fixed-income-finance">
<h2>Fixed-Income Finance</h2>
<p class="chapter-meta">5 topics</p>
<article class="doc-entry" id="doc-crr-binomial-option">
<h3><a class="doc-anchor" href="#doc-crr-binomial-option">#</a> <code>crr_binomial_option</code></h3>
<p><code>crr_binomial_option S0, K, T, R, SIGMA, N, IS_PUT</code> — Cox-Ross-Rubinstein price.</p>
</article>
<article class="doc-entry" id="doc-bond-price-clean">
<h3><a class="doc-anchor" href="#doc-bond-price-clean">#</a> <code>bond_price_clean</code></h3>
<p><code>bond_price_clean FACE, COUPON, N, PP_Y, YIELD</code> — present value.</p>
</article>
<article class="doc-entry" id="doc-bond-yield-to-maturity">
<h3><a class="doc-anchor" href="#doc-bond-yield-to-maturity">#</a> <code>bond_yield_to_maturity</code></h3>
<p><code>bond_yield_to_maturity PRICE, FACE, COUPON, N, PP_Y</code> — solve YTM by bisection.</p>
</article>
<article class="doc-entry" id="doc-modified-duration-bond">
<h3><a class="doc-anchor" href="#doc-modified-duration-bond">#</a> <code>modified_duration_bond</code></h3>
<p><code>modified_duration_bond FACE, COUPON, N, PP_Y, YIELD</code> — modified duration.</p>
</article>
<article class="doc-entry" id="doc-convexity-bond">
<h3><a class="doc-anchor" href="#doc-convexity-bond">#</a> <code>convexity_bond</code></h3>
<p><code>convexity_bond FACE, COUPON, N, PP_Y, YIELD</code> — bond convexity measure.</p>
</article>
</section>
<section class="tutorial-section" id="ch-image-quality-metrics">
<h2>Image Quality Metrics</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-ssim">
<h3><a class="doc-anchor" href="#doc-ssim">#</a> <code>ssim</code></h3>
<p><code>ssim A, B [, L]</code> — Structural Similarity Index (single window).</p>
</article>
<article class="doc-entry" id="doc-psnr">
<h3><a class="doc-anchor" href="#doc-psnr">#</a> <code>psnr</code></h3>
<p><code>psnr A, B [, MAX_VAL]</code> — peak SNR in dB.</p>
</article>
<article class="doc-entry" id="doc-mssim">
<h3><a class="doc-anchor" href="#doc-mssim">#</a> <code>mssim</code></h3>
<p><code>mssim A, B [, WIN, L]</code> — mean SSIM across non-overlapping windows.</p>
</article>
</section>
<section class="tutorial-section" id="ch-acoustics">
<h2>Acoustics</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-db-spl-from-pa">
<h3><a class="doc-anchor" href="#doc-db-spl-from-pa">#</a> <code>db_spl_from_pa</code></h3>
<p><code>db_spl_from_pa P_PA</code> — sound pressure level dB SPL.</p>
</article>
<article class="doc-entry" id="doc-a-weighting-factor">
<h3><a class="doc-anchor" href="#doc-a-weighting-factor">#</a> <code>a_weighting_factor</code></h3>
<p><code>a_weighting_factor F_HZ</code> — IEC 61672 A-weighting amplitude.</p>
</article>
<article class="doc-entry" id="doc-octave-band-center">
<h3><a class="doc-anchor" href="#doc-octave-band-center">#</a> <code>octave_band_center</code></h3>
<p><code>octave_band_center BAND</code> — 1 kHz · 2^band centre frequency.</p>
</article>
<article class="doc-entry" id="doc-semitone-ratio">
<h3><a class="doc-anchor" href="#doc-semitone-ratio">#</a> <code>semitone_ratio</code></h3>
<p><code>semitone_ratio</code> — 12-TET ratio 2^(1/12).</p>
</article>
</section>
<section class="tutorial-section" id="ch-population-genetics">
<h2>Population Genetics</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-hardy-weinberg">
<h3><a class="doc-anchor" href="#doc-hardy-weinberg">#</a> <code>hardy_weinberg</code></h3>
<p><code>hardy_weinberg P</code> — (p², 2pq, q²) genotype frequencies.</p>
</article>
<article class="doc-entry" id="doc-expected-heterozygosity">
<h3><a class="doc-anchor" href="#doc-expected-heterozygosity">#</a> <code>expected_heterozygosity</code></h3>
<p><code>expected_heterozygosity P_VEC</code> — 1 − Σ p_i².</p>
</article>
<article class="doc-entry" id="doc-fst-simple">
<h3><a class="doc-anchor" href="#doc-fst-simple">#</a> <code>fst_simple</code></h3>
<p><code>fst_simple P1, P2, N1, N2</code> — Wright's F_ST between two populations.</p>
</article>
<article class="doc-entry" id="doc-allele-frequencies">
<h3><a class="doc-anchor" href="#doc-allele-frequencies">#</a> <code>allele_frequencies</code></h3>
<p><code>allele_frequencies GENOTYPES</code> — p, q from 0/1/2 genotype counts.</p>
</article>
</section>
<section class="tutorial-section" id="ch-epidemiology">
<h2>Epidemiology</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-sir-step">
<h3><a class="doc-anchor" href="#doc-sir-step">#</a> <code>sir_step</code></h3>
<p><code>sir_step S, I, R, BETA, GAMMA, DT</code> — Euler step of the SIR model.</p>
</article>
<article class="doc-entry" id="doc-sir-r0">
<h3><a class="doc-anchor" href="#doc-sir-r0">#</a> <code>sir_r0</code></h3>
<p><code>sir_r0 BETA, GAMMA</code> — basic reproduction number β/γ.</p>
</article>
<article class="doc-entry" id="doc-doubling-time">
<h3><a class="doc-anchor" href="#doc-doubling-time">#</a> <code>doubling_time</code></h3>
<p><code>doubling_time R</code> — t₂ = ln 2 / r.</p>
</article>
</section>
<section class="tutorial-section" id="ch-inequality-measures">
<h2>Inequality Measures</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-theil-index">
<h3><a class="doc-anchor" href="#doc-theil-index">#</a> <code>theil_index</code></h3>
<p><code>theil_index XS</code> — Theil T inequality index.</p>
</article>
<article class="doc-entry" id="doc-herfindahl-hirschman">
<h3><a class="doc-anchor" href="#doc-herfindahl-hirschman">#</a> <code>herfindahl_hirschman</code></h3>
<p><code>herfindahl_hirschman SHARES</code> — Σ s_i².</p>
</article>
<article class="doc-entry" id="doc-atkinson-index">
<h3><a class="doc-anchor" href="#doc-atkinson-index">#</a> <code>atkinson_index</code></h3>
<p><code>atkinson_index XS [, EPS]</code> — Atkinson inequality with parameter ε.</p>
</article>
<article class="doc-entry" id="doc-lorenz-curve-points">
<h3><a class="doc-anchor" href="#doc-lorenz-curve-points">#</a> <code>lorenz_curve_points</code></h3>
<p><code>lorenz_curve_points XS</code> — matrix of [cumulative-pop, cumulative-income].</p>
</article>
</section>
<section class="tutorial-section" id="ch-apl-j-array-primitives">
<h2>APL / J Array Primitives</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-iota-range">
<h3><a class="doc-anchor" href="#doc-iota-range">#</a> <code>iota_range</code></h3>
<p><code>iota_range N</code> — <code>0..N</code> (APL convention).</p>
</article>
<article class="doc-entry" id="doc-reshape-array">
<h3><a class="doc-anchor" href="#doc-reshape-array">#</a> <code>reshape_array</code></h3>
<p><code>reshape_array ROWS, COLS, FLAT</code> — APL reshape (cycles input).</p>
</article>
<article class="doc-entry" id="doc-grade-up">
<h3><a class="doc-anchor" href="#doc-grade-up">#</a> <code>grade_up</code></h3>
<p><code>grade_up XS</code> — index permutation that sorts ascending.</p>
</article>
<article class="doc-entry" id="doc-grade-down">
<h3><a class="doc-anchor" href="#doc-grade-down">#</a> <code>grade_down</code></h3>
<p><code>grade_down XS</code> — index permutation that sorts descending.</p>
</article>
</section>
<section class="tutorial-section" id="ch-plasma-physics">
<h2>Plasma Physics</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-plasma-frequency">
<h3><a class="doc-anchor" href="#doc-plasma-frequency">#</a> <code>plasma_frequency</code></h3>
<p><code>plasma_frequency N_E</code> — electron plasma angular frequency (rad/s).</p>
</article>
<article class="doc-entry" id="doc-debye-length">
<h3><a class="doc-anchor" href="#doc-debye-length">#</a> <code>debye_length</code></h3>
<p><code>debye_length T_K, N_E</code> — Debye screening length.</p>
</article>
<article class="doc-entry" id="doc-cyclotron-frequency">
<h3><a class="doc-anchor" href="#doc-cyclotron-frequency">#</a> <code>cyclotron_frequency</code></h3>
<p><code>cyclotron_frequency B [, Q, M]</code> — qB/m (electron defaults).</p>
</article>
<article class="doc-entry" id="doc-larmor-radius">
<h3><a class="doc-anchor" href="#doc-larmor-radius">#</a> <code>larmor_radius</code></h3>
<p><code>larmor_radius V_PERP, B [, Q, M]</code> — gyroradius (electron defaults).</p>
</article>
</section>
<section class="tutorial-section" id="ch-string-similarity">
<h2>String Similarity</h2>
<p class="chapter-meta">2 topics</p>
<article class="doc-entry" id="doc-jaro-winkler-similarity">
<h3><a class="doc-anchor" href="#doc-jaro-winkler-similarity">#</a> <code>jaro_winkler_similarity</code></h3>
<p><code>jaro_winkler_similarity A, B</code> — JW string similarity.</p>
</article>
<article class="doc-entry" id="doc-metaphone-simple">
<h3><a class="doc-anchor" href="#doc-metaphone-simple">#</a> <code>metaphone_simple</code></h3>
<p><code>metaphone_simple S</code> — abridged Metaphone consonant skeleton.</p>
</article>
</section>
<section class="tutorial-section" id="ch-rating-systems">
<h2>Rating Systems</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-elo-rating-update">
<h3><a class="doc-anchor" href="#doc-elo-rating-update">#</a> <code>elo_rating_update</code></h3>
<p><code>elo_rating_update R_A, R_B, SCORE_A [, K]</code> → [R_A', R_B'].</p>
</article>
<article class="doc-entry" id="doc-glicko-rating-update">
<h3><a class="doc-anchor" href="#doc-glicko-rating-update">#</a> <code>glicko_rating_update</code></h3>
<p><code>glicko_rating_update R, RD, OPP_R, OPP_RD, SCORE</code> → [R', RD'].</p>
</article>
<article class="doc-entry" id="doc-dice-sum-pmf">
<h3><a class="doc-anchor" href="#doc-dice-sum-pmf">#</a> <code>dice_sum_pmf</code></h3>
<p><code>dice_sum_pmf N, S, TARGET</code> — probability of N s-sided dice summing to TARGET.</p>
</article>
</section>
<section class="tutorial-section" id="ch-effect-sizes">
<h2>Effect Sizes</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-cohens-d">
<h3><a class="doc-anchor" href="#doc-cohens-d">#</a> <code>cohens_d</code></h3>
<p><code>cohens_d A, B</code> — pooled-SD standardised mean difference.</p>
</article>
<article class="doc-entry" id="doc-cliff-delta">
<h3><a class="doc-anchor" href="#doc-cliff-delta">#</a> <code>cliff_delta</code></h3>
<p><code>cliff_delta A, B</code> — non-parametric effect size in [-1, 1].</p>
</article>
<article class="doc-entry" id="doc-vargha-delaney-a12">
<h3><a class="doc-anchor" href="#doc-vargha-delaney-a12">#</a> <code>vargha_delaney_a12</code></h3>
<p><code>vargha_delaney_a12 A, B</code> — P(X > Y) + 0.5 P(X = Y).</p>
</article>
</section>
<section class="tutorial-section" id="ch-control-transient-response">
<h2>Control Transient Response</h2>
<p class="chapter-meta">2 topics</p>
<article class="doc-entry" id="doc-step-response-2nd-order">
<h3><a class="doc-anchor" href="#doc-step-response-2nd-order">#</a> <code>step_response_2nd_order</code></h3>
<p><code>step_response_2nd_order ZETA, OMEGA_N, T</code> — y(t).</p>
</article>
<article class="doc-entry" id="doc-overshoot-2nd-order">
<h3><a class="doc-anchor" href="#doc-overshoot-2nd-order">#</a> <code>overshoot_2nd_order</code></h3>
<p><code>overshoot_2nd_order ZETA</code> — peak overshoot %.</p>
</article>
</section>
<section class="tutorial-section" id="ch-matrix-norms">
<h2>Matrix Norms</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-frobenius-norm">
<h3><a class="doc-anchor" href="#doc-frobenius-norm">#</a> <code>frobenius_norm</code></h3>
<p><code>frobenius_norm M</code> — √(Σ m_ij²).</p>
</article>
<article class="doc-entry" id="doc-spectral-norm">
<h3><a class="doc-anchor" href="#doc-spectral-norm">#</a> <code>spectral_norm</code></h3>
<p><code>spectral_norm M</code> — largest singular value.</p>
</article>
<article class="doc-entry" id="doc-trace-matrix">
<h3><a class="doc-anchor" href="#doc-trace-matrix">#</a> <code>trace_matrix</code></h3>
<p><code>trace_matrix M</code> — Σ m_ii.</p>
</article>
</section>
<section class="tutorial-section" id="ch-network-triad-analysis">
<h2>Network Triad Analysis</h2>
<p class="chapter-meta">3 topics</p>
<article class="doc-entry" id="doc-homophily-index">
<h3><a class="doc-anchor" href="#doc-homophily-index">#</a> <code>homophily_index</code></h3>
<p><code>homophily_index ADJ, LABELS</code> — fraction of same-group edges.</p>
</article>
<article class="doc-entry" id="doc-dyad-census">
<h3><a class="doc-anchor" href="#doc-dyad-census">#</a> <code>dyad_census</code></h3>
<p><code>dyad_census ADJ</code> — [mutual, asymmetric, null] dyads.</p>
</article>
<article class="doc-entry" id="doc-triad-census">
<h3><a class="doc-anchor" href="#doc-triad-census">#</a> <code>triad_census</code></h3>
<p><code>triad_census ADJ</code> — [empty, edge, path, triangle] counts.</p>
</article>
</section>
<section class="tutorial-section" id="ch-misc-inverses">
<h2>Misc Inverses</h2>
<p class="chapter-meta">1 topics</p>
<article class="doc-entry" id="doc-sigmoid-inverse">
<h3><a class="doc-anchor" href="#doc-sigmoid-inverse">#</a> <code>sigmoid_inverse</code></h3>
<p><code>sigmoid_inverse X</code> — ln(x / (1-x)).</p>
</article>
</section>
<section class="tutorial-section" id="ch-parallel-i-o">
<h2>Parallel I/O</h2>
<p class="chapter-meta">8 topics</p>
<article class="doc-entry" id="doc-par-lines">
<h3><a class="doc-anchor" href="#doc-par-lines">#</a> <code>par_lines</code></h3>
<p><code>par_lines PATH, { code }</code> — memory-map a file and scan its lines in parallel across all available CPU cores.</p>
<p>The file is <code>mmap</code>'d into memory rather than read sequentially, and line boundaries are detected in parallel chunks. Each line is passed to the callback as <code>_</code>. Because the file is memory-mapped, there is no read-buffer overhead and the OS kernel pages data in on demand, making <code>par_lines</code> extremely efficient for multi-gigabyte log files or CSV data. Line order within the callback is not guaranteed (lines run in parallel), so the callback should be a self-contained side-effecting operation (accumulate into a shared structure via <code>pchannel</code>, write to a file, etc.) or use <code>par_lines</code> with a reducer. For ordered processing, use <code>read_lines</code> with <code>pmap</code> instead.</p>
<pre><code class="lang-perl">par_lines "data.txt", fn { process }
# Count matching lines in a large log:
my $count = 0
par_lines "/var/log/syslog", fn { $count++ if /ERROR/ }
p $count
# Feed lines into a channel for downstream processing:
my ($tx, $rx) = pchannel(1000)
async { par_lines "huge.csv", fn { $tx->send(_) }
undef $tx }
</code></pre>
</article>
<article class="doc-entry" id="doc-par-walk">
<h3><a class="doc-anchor" href="#doc-par-walk">#</a> <code>par_walk</code></h3>
<p><code>par_walk PATH, { code }</code> — recursively walk a directory tree in parallel, invoking the callback for every file path found.</p>
<p>Directory traversal is parallelized using a work-stealing thread pool: multiple directories are read concurrently, and the callback fires as each file is discovered. The path is passed as <code>_</code> (absolute). This is significantly faster than a sequential <code>find</code>-style walk on SSDs and networked filesystems where directory <code>readdir</code> latency dominates. Symlinks are not followed by default to avoid cycles. The walk visits files only — directories themselves are not passed to the callback unless you pass <code>dirs => 1</code>. Combine with <code>pmap</code> for a two-phase pattern: first collect paths with <code>par_walk</code>, then process file contents in parallel.</p>
<pre><code class="lang-perl">par_walk "./src", fn { p _ if /\.rs$/ }
# Collect all JSON files under a directory:
my @json_files
par_walk "/data", fn { push @json_files, _ if /\.json$/ }
p scalar @json_files
# Parallel content search:
par_walk ".", fn {
if (/\.log$/) {
my @hits = grep /FATAL/, rl
p "$_: ", scalar @hits, " fatals" if @hits
}
}
</code></pre>
</article>
<article class="doc-entry" id="doc-par-sed">
<h3><a class="doc-anchor" href="#doc-par-sed">#</a> <code>par_sed</code></h3>
<p><code>par_sed PATTERN, REPLACEMENT, @files</code> — perform an in-place regex substitution across multiple files in parallel.</p>
<p>Each file is processed by a separate worker thread: the file is read into memory, all matches of PATTERN are replaced with REPLACEMENT, and the result is written back atomically (via a temp file + rename, so readers never see a partially-written file). This is the stryke equivalent of <code>sed -i</code> but parallelized across the file list — ideal for codebase-wide refactors, log scrubbing, or bulk config updates. The pattern uses stryke regex syntax (PCRE-style). Returns the total number of substitutions made across all files.</p>
<pre><code class="lang-perl">par_sed qr/oldFunc/, "newFunc", glob("src/*.pl")
# Case-insensitive replace across a project:
par_sed qr/TODO/i, "DONE", par_walk(".", fn { _ if /\.rs$/ })
# Scrub sensitive data from logs:
my $n = par_sed qr/\b\d{3}-\d{2}-\d{4}\b/, "XXX-XX-XXXX", @log_files
p "redacted $n occurrences"
</code></pre>
</article>
<article class="doc-entry" id="doc-par-find-files">
<h3><a class="doc-anchor" href="#doc-par-find-files">#</a> <code>par_find_files</code></h3>
<p>Recursively search a directory tree in parallel for files matching a glob pattern. Unlike <code>glob_par</code> which takes a single pattern string, <code>par_find_files</code> separates the root directory from the pattern, making it convenient when the search root is a variable. Returns a list of absolute paths to matching files.</p>
<pre><code class="lang-perl">my @src = par_find_files("src", "*.rs")
p scalar @src # count of Rust files under src/
my @tests = par_find_files(".", "*_test.pl")
@tests |> e p
my @configs = par_find_files("/etc", "*.conf")
</code></pre>
</article>
<article class="doc-entry" id="doc-par-line-count">
<h3><a class="doc-anchor" href="#doc-par-line-count">#</a> <code>par_line_count</code></h3>
<p>Count lines across multiple files in parallel, returning the total line count. Each file is read and counted by a separate thread, making this dramatically faster than sequential <code>wc -l</code> for large file sets. Useful for codebase metrics, log analysis, or validating data pipeline output.</p>
<pre><code class="lang-perl">my @files = glob("src/**/*.rs")
my $total = par_line_count(@files)
p "$total lines of Rust"
my $logs = par_line_count(glob("/var/log/*.log"))
p "$logs log lines"
</code></pre>
</article>
<article class="doc-entry" id="doc-par-csv-read">
<h3><a class="doc-anchor" href="#doc-par-csv-read">#</a> <code>par_csv_read</code></h3>
<p><code>par_csv_read @files</code> — read multiple CSV files in parallel, returning an array of parsed datasets (one per file).</p>
<p>Each file is read and parsed by a separate worker thread using a fast Rust CSV parser that handles quoting, escaping, and UTF-8 correctly. Headers are auto-detected from the first row of each file, and each row is returned as a hashref keyed by header names. This is dramatically faster than sequential CSV parsing when you have many files — common in data engineering pipelines where data arrives as daily/hourly CSV partitions. For a single large CSV file, prefer <code>par_lines</code> with manual splitting, since <code>par_csv_read</code> parallelizes across files, not within a single file.</p>
<pre><code class="lang-perl">my @datasets = par_csv_read glob("data/*.csv")
for my $ds (@datasets) {
p scalar @$ds, " rows"
}
# Merge all CSVs into one list:
my @all_rows = par_csv_read(@files) |> flat
p $all_rows[0]->{name} # access by header
# Filter and aggregate:
my @sales = par_csv_read(glob("sales_*.csv")) |> flat
|> grep { _->{region} eq "US" }
</code></pre>
</article>
<article class="doc-entry" id="doc-glob-par">
<h3><a class="doc-anchor" href="#doc-glob-par">#</a> <code>glob_par</code></h3>
<p>Parallel recursive file-system glob using rayon across multiple patterns. Backed by the same zshrs glob engine as <code>glob</code>, so every zsh qualifier (<code>(/)</code>, <code>(.)</code>, <code>(L+1024)</code>, <code>(om[1])</code>, …) is supported here too. Each pattern expands single-threaded but the patterns run concurrently — ideal for many independent searches. For full qualifier reference see <code>glob</code>.</p>
<pre><code class="lang-perl">my @logs = glob_par("**/*.log")
p scalar @logs # count of log files
"**/*.rs" |> glob_par |> e p # print all Rust files
my @imgs = glob_par("assets/**/*.{png,jpg,webp}")
my @big_recent = glob_par("**(.L+1m om[1,5])") # 5 newest >1MB files
</code></pre>
</article>
<article class="doc-entry" id="doc-pwatch">
<h3><a class="doc-anchor" href="#doc-pwatch">#</a> <code>pwatch</code></h3>
<p><code>pwatch(PATTERN, fn { ... })</code> — watch a path or glob pattern for filesystem changes and invoke the callback on each event.</p>
<p>The watcher runs on a background thread using OS-native notifications (FSEvents on macOS, inotify on Linux) so it consumes near-zero CPU while idle. The callback receives the event path in <code>_</code>. The watcher continues until the returned handle is dropped or the program exits. Useful for live-reload dev servers, file-triggered pipelines, or audit logs. Combine with <code>debounce</code> or a <code>pchannel</code> if the callback is expensive and rapid bursts of events need to be coalesced.</p>
<p>The initial expansion goes through the full zshrs glob engine, so zsh qualifiers (<code>(.)</code>, <code>(/)</code>, <code>(L+1m)</code>, …) work for picking what to watch. The runtime event matcher uses the qualifier-stripped pattern shape — stat-based qualifiers can't apply to a single fired event, but they did apply to the watch-set selection upfront.</p>
<pre><code class="lang-perl">my $w = pwatch "./src/**/*.rs", fn {
p "changed: $_"
rebuild()
}
my $logs = pwatch "logs/*(.)", fn { p "log updated: $_" }
my $cfg = pwatch "./config", fn { reload_config() }
sleep # block forever
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-cli-args">
<h2>CLI / Args</h2>
<p class="chapter-meta">1 topics</p>
<article class="doc-entry" id="doc-getopts">
<h3><a class="doc-anchor" href="#doc-getopts">#</a> <code>getopts</code></h3>
<p><code>getopts(SPECS [, META])</code> — Getopt::Long-style CLI flag parser. By default operates on <code>@ARGV</code> directly (no <code>\@ARGV</code> needed), returning a hashref of canonical-name → value and leaving only the leftover positionals in <code>@ARGV</code>. Use <code>getopts(\@argv, SPECS [, META])</code> to parse a list other than <code>@ARGV</code>.</p>
<p>Spec language (subset of Perl's <code>Getopt::Long</code>):</p>
<ul>
<li><code>name</code> — bool flag (present = 1)</li>
<li><code>name|alias|alias2</code> — same option, multiple names; first is canonical</li>
<li><code>name=s</code> / <code>name=i</code> / <code>name=f</code> — required string / int / float</li>
<li><code>name:s</code> / <code>name:i</code> / <code>name:f</code> — optional arg (defaults to <code>""</code> / <code>0</code> / <code>0.0</code>)</li>
<li><code>name=s@</code> — repeatable → arrayref (also <code>=i@</code>, <code>=f@</code>)</li>
<li><code>name=s%</code> — <code>--name key=val</code> → hashref (also <code>=i%</code>, <code>=f%</code>)</li>
<li><code>name!</code> — negatable bool; <code>--no-name</code> sets <code>0</code></li>
<li><code>name+</code> — counter: each occurrence increments</li>
</ul>
<pre><code class="lang-perl">my %opts = %{ getopts([
"verbose|v",
"file|f=s",
"count|n=i",
"tag|t=s@",
]) };
# Hash form lets each spec carry a default:
my %opts = %{ getopts({
"verbose|v" => 0,
"count|n=i" => 10,
"tag|t=s@" => [],
}) };
# Explicit array ref (parse a list other than @ARGV):
my %opts = %{ getopts(\@args, [ "verbose|v" ]) };
</code></pre>
<p>Parsing rules: <code>--name</code>, <code>--name=value</code>, <code>--name value</code>, <code>-n</code>, <code>-n value</code>, <code>-nvalue</code> all accepted. Bundling: <code>-vDR</code> = <code>-v -D -R</code>; if a char takes an arg, the rest of the token is its value (<code>-vfx.txt</code> → <code>-v -f x.txt</code>). <code>--</code> terminates options; first non-option positional stops parsing. Unknown options or type mismatches raise a runtime error.</p>
<p>Per-option metadata + auto-<code>--help</code>: hash values may themselves be hashrefs carrying <code>{ help, default, required, metavar }</code>. When any spec has <code>help</code> text and the user hasn't claimed <code>--help</code>/<code>-h</code>, getopts intercepts <code>--help</code>/<code>-h</code>, prints a formatted usage block, and <code>exit(0)</code>s. Optional <code>META</code> arg: <code>{ prog, desc, epilog }</code> controls the banner.</p>
<pre><code class="lang-perl">my %opts = %{ getopts({
"verbose|v" => { help => "enable verbose" },
"file|f=s" => { help => "output path", default => "out.txt" },
"count|n=i" => { help => "iterations", required => 1 },
}, { prog => "myscript", desc => "do a thing" }) };
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-file-i-o">
<h2>File I/O</h2>
<p class="chapter-meta">35 topics</p>
<article class="doc-entry" id="doc-open">
<h3><a class="doc-anchor" href="#doc-open">#</a> <code>open</code></h3>
<p>Open a filehandle for reading, writing, appending, or piping. The three-argument form <code>open my $fh, MODE, EXPR</code> is strongly preferred for safety — it prevents shell injection and makes the mode explicit. Modes include <code><</code> (read), <code>></code> (write/truncate), <code>>></code> (append), <code>+<</code> (read-write), <code>|-</code> (pipe to command), and <code>-|</code> (pipe from command). In stryke, always use lexical filehandles (<code>my $fh</code>) rather than bareword globals. PerlIO layers can be specified in the mode: <code><:utf8</code>, <code><:raw</code>, <code><:encoding(UTF-16)</code>. Always check the return value — <code>open ... or die "...: $!"</code> is idiomatic. The <code>$!</code> variable contains the OS error message on failure. Forgetting to check <code>open</code> is one of the most common bugs in Perl code.</p>
<pre><code class="lang-perl">open my $fh, '<', 'data.txt' or die "open: $!"
my @lines = <$fh>
close $fh
open my $out, '>>', 'log.txt' or die "append: $!"
print $out tm "event happened\n"
close $out
open my $pipe, '-|', 'ls', '-la' or die "pipe: $!"
while (<$pipe>) { p tm _ }
</code></pre>
</article>
<article class="doc-entry" id="doc-close">
<h3><a class="doc-anchor" href="#doc-close">#</a> <code>close</code></h3>
<p>Close a filehandle, flushing any buffered output and releasing the underlying OS file descriptor. Returns true on success, false on failure — and failure is more common than you might think. For write handles, <code>close</code> is where buffered data actually hits disk, so a full disk or network error may only surface at <code>close</code> time. Always check the return value when writing: <code>close $fh or die "close: $!"</code>. For pipe handles opened with <code>|-</code> or <code>-|</code>, <code>close</code> waits for the child process to exit and sets <code>$?</code> to the child's exit status. In stryke, lexical filehandles are automatically closed when they go out of scope, but explicit <code>close</code> is clearer and lets you handle errors.</p>
<pre><code class="lang-perl">open my $fh, '>', 'out.txt' or die $!
print $fh "done\n"
close $fh or die "write failed: $!"
open my $p, '|-', 'gzip', '-c' or die $!
print $p $data
close $p
p "gzip exited: $?" if $?
</code></pre>
</article>
<article class="doc-entry" id="doc-read">
<h3><a class="doc-anchor" href="#doc-read">#</a> <code>read</code></h3>
<p>Read a specified number of bytes from a filehandle into a scalar buffer. The signature is <code>read FH, SCALAR, LENGTH [, OFFSET]</code>. Returns the number of bytes actually read (which may be less than requested at EOF or on partial reads), 0 at EOF, or <code>undef</code> on error. The optional OFFSET argument lets you append to an existing buffer at a given position, which is useful for accumulating data in a loop. For text files, the bytes are decoded according to the handle's PerlIO layer — use <code><:raw</code> for binary data to avoid encoding transforms. In stryke, <code>read</code> works identically to Perl 5. For line-oriented input, prefer <code><$fh></code> or <code>readline</code> instead.</p>
<pre><code class="lang-perl">open my $fh, '<:raw', $path or die $!
my $buf = ''
while (read $fh, my $chunk, 4096) {
$buf .= $chunk
}
p "total: " . length($buf) . " bytes"
close $fh
</code></pre>
</article>
<article class="doc-entry" id="doc-readline">
<h3><a class="doc-anchor" href="#doc-readline">#</a> <code>readline</code></h3>
<p>Read one line (or all remaining lines in list context) from a filehandle. The angle-bracket operator <code><$fh></code> is syntactic sugar for <code>readline($fh)</code>. In scalar context, returns the next line including the trailing newline (or <code>undef</code> at EOF). In list context, returns all remaining lines as a list. The line ending is determined by <code>$/</code> (input record separator, default <code>\n</code>). Set <code>$/ = undef</code> to slurp the entire file in one read. In stryke, <code>readline</code> integrates with the pipe operator — you can pipe filehandle lines through <code>maps</code>, <code>greps</code>, and other streaming combinators. Always <code>chomp</code> after reading if you don't want trailing newlines.</p>
<pre><code class="lang-perl">while (my $line = <$fh>) {
chomp $line
p $line
}
# Slurp entire file
local $/
my $content = <$fh>
p length $content
</code></pre>
</article>
<article class="doc-entry" id="doc-eof">
<h3><a class="doc-anchor" href="#doc-eof">#</a> <code>eof</code></h3>
<p>Test whether a filehandle has reached end-of-file. Returns 1 if the next read on the handle would return EOF, 0 otherwise. Called without arguments, <code>eof()</code> (with parens) checks the last file in the <code><></code> / <code>ARGV</code> stream. Called with no parens as <code>eof</code>, it tests whether the current ARGV file is exhausted but more files may follow. In stryke, <code>eof</code> is typically used in <code>until</code> loops or as a guard before <code>read</code> calls. Note that <code>eof</code> may trigger a blocking read on interactive handles (like STDIN from a terminal) to determine if data is available, so avoid calling it speculatively on interactive input. For most line-processing, <code>while (<$fh>)</code> is simpler and implicitly handles EOF.</p>
<pre><code class="lang-perl">until (eof $fh) {
my $line = <$fh>
p tm $line
}
# Process multiple files via ARGV
while (<>) {
p "new file: $ARGV" if eof()
}
</code></pre>
</article>
<article class="doc-entry" id="doc-seek">
<h3><a class="doc-anchor" href="#doc-seek">#</a> <code>seek</code></h3>
<p>Reposition a filehandle to an arbitrary byte offset. The signature is <code>seek FH, POSITION, WHENCE</code> where WHENCE is 0 (absolute from start), 1 (relative to current position), or 2 (relative to end of file). Use the <code>Fcntl</code> constants <code>SEEK_SET</code>, <code>SEEK_CUR</code>, <code>SEEK_END</code> for clarity. Returns 1 on success, 0 on failure. <code>seek</code> is essential for random-access file I/O — re-reading headers, skipping to known offsets in binary formats, or rewinding a file for a second pass. In stryke, <code>seek</code> flushes the PerlIO buffer before repositioning. Do not mix <code>seek</code>/<code>tell</code> with <code>sysread</code>/<code>syswrite</code> — they use separate buffering layers.</p>
<pre><code class="lang-perl">seek $fh, 0, 0 # rewind to start
my $header = <$fh>
seek $fh, -100, 2 # last 100 bytes
read $fh, my $tail, 100
p $tail
</code></pre>
</article>
<article class="doc-entry" id="doc-tell">
<h3><a class="doc-anchor" href="#doc-tell">#</a> <code>tell</code></h3>
<p>Return the current byte offset of a filehandle's read/write position. Returns a non-negative integer on success, or -1 if the handle is invalid or not seekable (e.g., pipes, sockets). Useful for bookmarking a position before a speculative read so you can <code>seek</code> back if the data doesn't match expectations. In stryke, <code>tell</code> reflects the PerlIO buffered position, not the raw OS file descriptor position — so it correctly accounts for encoding layers and buffered reads. Pair with <code>seek</code> for random-access patterns.</p>
<pre><code class="lang-perl">my $pos = tell $fh
p "at byte $pos"
# Bookmark and restore
my $mark = tell $fh
my $line = <$fh>
unless ($line =~ /^HEADER/) {
seek $fh, $mark, 0 # rewind to before the read
}
</code></pre>
</article>
<article class="doc-entry" id="doc-print">
<h3><a class="doc-anchor" href="#doc-print">#</a> <code>print</code></h3>
<p>Write operands to the selected output handle (default <code>STDOUT</code>) without appending a newline. The output field separator <code>$,</code> is inserted between arguments, and <code>$\</code> is appended at the end — both default to empty string. You can direct output to a specific handle by passing it as the first argument with no comma: <code>print STDERR "msg"</code>. In stryke, <code>print</code> behaves identically to Perl 5 and is useful when you need precise control over output formatting, such as building progress bars, writing binary data, or emitting partial lines. For most line-oriented output, prefer <code>p</code> (say) instead since it handles the newline automatically.</p>
<pre><code class="lang-perl">print "no newline"
print STDERR "error msg\n"
print $fh "data to filehandle\n"
for my $pct (0:100) {
printf "\rprogress: %3d%%", $pct
}
print "\n"
</code></pre>
</article>
<article class="doc-entry" id="doc-say">
<h3><a class="doc-anchor" href="#doc-say">#</a> <code>say</code></h3>
<p>Print operands followed by an automatic newline to <code>STDOUT</code>. In stryke, <code>say</code> is always available without <code>-E</code> or <code>use feature 'say'</code> — it is a first-class builtin. The shorthand <code>p</code> is an alias for <code>say</code> and is preferred in most stryke code. When given a list, <code>say</code> joins elements with <code>$,</code> (output field separator, empty by default) and appends <code>$\</code> plus a newline. For streaming output over pipelines, combine with <code>e</code> (each) to print one element per line. Gotcha: <code>say</code> always adds a newline — if you need raw output without one, use <code>print</code> instead.</p>
<pre><code class="lang-perl">p "hello world"
my @names = ("alice", "bob", "eve")
@names |> e p
1:5 |> maps { _ * 2 } |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-printf">
<h3><a class="doc-anchor" href="#doc-printf">#</a> <code>printf</code></h3>
<p>Formatted print to a filehandle (default <code>STDOUT</code>), using C-style format specifiers. The first argument is the format string with <code>%s</code> (string), <code>%d</code> (integer), <code>%f</code> (float), <code>%x</code> (hex), <code>%o</code> (octal), <code>%e</code> (scientific), <code>%g</code> (general float), and <code>%%</code> (literal percent). Width and precision modifiers work as in C: <code>%-10s</code> left-aligns in a 10-char field, <code>%05d</code> zero-pads to 5 digits, <code>%.2f</code> gives 2 decimal places. In stryke, <code>printf</code> supports all standard Perl 5 format specifiers including <code>%v</code> (version strings) and <code>%n</code> is disabled for safety. Direct output to a handle by placing it before the format: <code>printf STDERR "...", @args</code>. Unlike <code>sprintf</code>, <code>printf</code> outputs directly and returns a boolean indicating success.</p>
<pre><code class="lang-perl">printf "%-10s %5d\n", $name, $score
printf STDERR "error %d: %s\n", $code, $msg
printf "%08.2f\n", 3.14159 # 00003.14
printf "%s has %d item%s\n", $user, $n, $n == 1 ? "" : "s"
</code></pre>
</article>
<article class="doc-entry" id="doc-sprintf">
<h3><a class="doc-anchor" href="#doc-sprintf">#</a> <code>sprintf</code></h3>
<p>Return a formatted string without printing it, using the same C-style format specifiers as <code>printf</code>. This is the go-to function for building formatted strings for later use — constructing log messages, building padded table columns, converting numbers to hex or binary representations, or assembling strings that will be passed to other functions. In stryke, <code>sprintf</code> is often combined with the pipe operator: <code>$val |> t { sprintf "0x%04x", _ } |> p</code>. The return value is always a string. All format specifiers from <code>printf</code> apply here.</p>
<pre><code class="lang-perl">my $hex = sprintf "0x%04x", 255
my $padded = sprintf "%08d", $id
my $msg = sprintf "%-20s: %s", $key, $value
my @rows = map { sprintf "%3d. %s", _, $names[_] } 0..$ #names
@rows |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-slurp">
<h3><a class="doc-anchor" href="#doc-slurp">#</a> <code>slurp</code></h3>
<p>Read an entire file into memory as a single UTF-8 string, or — when the path is a glob pattern — concatenate the contents of every matching regular file. Aliases: <code>sl</code>, <code>cat</code>, <code>c</code>. Dies if the file is missing or unreadable. For binary data use <code>read_bytes</code>/<code>slurp_raw</code>.</p>
<p>When the path contains glob metacharacters (<code>*</code> <code>?</code> <code>[</code> <code>**</code>) or a trailing zsh qualifier suffix <code>(...)</code>, it is expanded by the zshrs glob engine and the results are concatenated. <strong><code>slurp</code> hard-fails if the qualifier yields any non-regular file</strong> — <code>slurp "**(/)"</code> errors <code>slurp: not a regular file: ./sub</code> because slurping a directory is meaningless. To list directory paths, use <code>glob "**(/)"</code>. See <code>glob</code> for the full qualifier reference.</p>
<pre><code class="lang-perl">my $text = slurp("config.yaml")
my $all = c("**(.)") # every regular file recursively, concatenated
my $logs = c("logs/*.log") # all logs in one go
my $json = sl("data.json")
my $data = decode_json($json)
"README.md" |> sl |> length |> p # character count
</code></pre>
</article>
<article class="doc-entry" id="doc-slurp-raw">
<h3><a class="doc-anchor" href="#doc-slurp-raw">#</a> <code>slurp_raw</code></h3>
<p>Read an entire file into memory as raw bytes without any encoding interpretation. Unlike <code>slurp</code>, which returns a decoded UTF-8 string, <code>read_bytes</code> preserves the exact byte content — useful for binary files like images, compressed archives, or protocol buffers. The alias <code>slurp_raw</code> emphasizes the raw nature.</p>
<pre><code class="lang-perl">my $png = read_bytes("logo.png")
p length($png) # byte count
my $gz = slurp_raw("data.gz")
my $text = gunzip($gz)
p $text
</code></pre>
</article>
<article class="doc-entry" id="doc-input">
<h3><a class="doc-anchor" href="#doc-input">#</a> <code>input</code></h3>
<p>Slurp all of stdin (or a filehandle) as one string.</p>
<pre><code class="lang-perl">my $all = input # slurp stdin
my $fh_data = input($fh) # slurp filehandle
</code></pre>
</article>
<article class="doc-entry" id="doc-read-lines">
<h3><a class="doc-anchor" href="#doc-read-lines">#</a> <code>read_lines</code></h3>
<p>Read a file and return its contents as a list of lines with trailing newlines stripped. This is the idiomatic way to slurp a file line-by-line in stryke without manually opening a filehandle. The short alias <code>rl</code> keeps one-liners concise. If the file does not exist, the program dies with an error message.</p>
<pre><code class="lang-perl">my @lines = rl("data.txt")
p scalar @lines # line count
@lines |> grep /ERROR/ |> e p # print error lines
my $first = (rl "config.ini")[0]$1
Note: returns an empty list for an empty file.
</code></pre>
</article>
<article class="doc-entry" id="doc-append-file">
<h3><a class="doc-anchor" href="#doc-append-file">#</a> <code>append_file</code></h3>
<p>Append a string to the end of a file, creating it if it does not exist. This is the safe way to add content without overwriting — useful for log files, CSV accumulation, or incremental output. The short alias <code>af</code> is convenient in pipelines. The file is opened, written, and closed atomically per call.</p>
<pre><code class="lang-perl">af("log.txt", "started at " . datetime_utc() . "\n")
1:5 |> e { af("nums.txt", "$_\n") }
my @data = ("a","b","c")
@data |> e { af "out.txt", "$_\n" }
</code></pre>
</article>
<article class="doc-entry" id="doc-to-file">
<h3><a class="doc-anchor" href="#doc-to-file">#</a> <code>to_file</code></h3>
<p>Write a string to a file, truncating any existing content. Unlike <code>append_file</code>, this replaces the file entirely. Returns the written content so it can be used in a pipeline — write to disk and continue processing in one expression. Creates the file if it does not exist.</p>
<pre><code class="lang-perl">my $csv = "name,age\nAlice,30\nBob,25"
$csv |> to_file("people.csv") |> p
to_file("empty.txt", "") # truncate a file
</code></pre>
<p>Note: the return-value-for-piping behavior distinguishes this from a plain write.</p>
</article>
<article class="doc-entry" id="doc-write">
<h3><a class="doc-anchor" href="#doc-write">#</a> <code>write</code></h3>
<p>Output a formatted record to a filehandle using a <code>format</code> declaration. <code>write</code> looks up the format associated with the current (or specified) filehandle, evaluates the format's picture lines against the current variables, and outputs the result. This is Perl's original report-generation mechanism, predating modules like <code>Text::Table</code> and template engines. In stryke, <code>write</code> and <code>format</code> are supported for backward compatibility but are rarely used in new code — <code>printf</code>/<code>sprintf</code> or template strings are more flexible. The format name defaults to the filehandle name (e.g., format <code>STDOUT</code> is used by <code>write STDOUT</code>).</p>
<pre><code class="lang-perl">format STDOUT =
@<<<<<<<<<< @>>>>>>
$name, $score
.
my ($name, $score) = ("alice", 42)
write # outputs: alice 42
</code></pre>
</article>
<article class="doc-entry" id="doc-write-file">
<h3><a class="doc-anchor" href="#doc-write-file">#</a> <code>write_file</code></h3>
<p>Write a string to a file, creating it if it does not exist or truncating it if it does. This is the complement of <code>slurp</code> — together they form a read/write pair for whole-file operations. The short alias <code>wf</code> is convenient for one-liners. The file is opened, written, and closed in a single call.</p>
<pre><code class="lang-perl">spurt("hello.txt", "Hello, world!\n")
wf("nums.txt", join("\n", 1:10))
"generated content" |> wf("out.txt")
my $data = slurp("in.txt")
wf("copy.txt", $data)
</code></pre>
</article>
<article class="doc-entry" id="doc-write-json">
<h3><a class="doc-anchor" href="#doc-write-json">#</a> <code>write_json</code></h3>
<p>Serialize a stryke data structure (hash ref or array ref) as pretty-printed JSON and write it to a file. Creates or overwrites the target file. The short alias <code>wj</code> pairs with <code>rj</code> for round-trip JSON workflows. Useful for persisting configuration, caching API responses, or generating fixture data.</p>
<pre><code class="lang-perl">my %data = (name => "Alice", scores => [98, 87, 95])
wj("out.json", \%data)
my $back = rj("out.json")
p $back->{name} # Alice
</code></pre>
</article>
<article class="doc-entry" id="doc-read-json">
<h3><a class="doc-anchor" href="#doc-read-json">#</a> <code>read_json</code></h3>
<p>Read a JSON file from disk and parse it into a stryke data structure (hash ref or array ref). The short alias <code>rj</code> keeps JSON-config one-liners terse. Dies if the file does not exist or contains malformed JSON. This is the complement of <code>write_json</code>/<code>wj</code>.</p>
<pre><code class="lang-perl">my $cfg = rj("config.json")
p $cfg->{database}{host}
my @items = @{ rj("list.json") }
@items |> e { p _->{name} }$1
Note: numeric strings remain strings; use `+0` to coerce if needed.
</code></pre>
</article>
<article class="doc-entry" id="doc-tempfile">
<h3><a class="doc-anchor" href="#doc-tempfile">#</a> <code>tempfile</code></h3>
<p>Create a temporary file in the system temp directory and return its absolute path as a string. The file is created with a unique name and exists on disk immediately. Use <code>tf</code> as a short alias for quick scratch files in one-liners. The caller is responsible for cleanup, though OS temp-directory reaping will eventually reclaim it.</p>
<pre><code class="lang-perl">my $tmp = tf()
to_file($tmp, "scratch data\n")
p rl($tmp) # scratch data
my @all = map { tf() } 1:3 # three temp files
</code></pre>
</article>
<article class="doc-entry" id="doc-tempdir">
<h3><a class="doc-anchor" href="#doc-tempdir">#</a> <code>tempdir</code></h3>
<p>Create a temporary directory in the system temp directory and return its absolute path. The directory is created with a unique name and is ready for use immediately. The short alias <code>tdr</code> mirrors <code>tf</code> for files. Useful for isolating multi-file operations like test fixtures, build artifacts, or staged output.</p>
<pre><code class="lang-perl">my $dir = tdr()
to_file("$dir/a.txt", "hello")
to_file("$dir/b.txt", "world")
my @files = glob("$dir/*.txt")
p scalar @files # 2
</code></pre>
</article>
<article class="doc-entry" id="doc-binmode">
<h3><a class="doc-anchor" href="#doc-binmode">#</a> <code>binmode</code></h3>
<p>Set the I/O layer on a filehandle, controlling how bytes are translated during reads and writes. Without a layer argument, <code>binmode $fh</code> switches the handle to raw binary mode (no CRLF translation on Windows, no encoding transforms). With a layer, <code>binmode $fh, ':utf8'</code> enables UTF-8 decoding, <code>binmode $fh, ':raw'</code> strips all layers for pure byte I/O, and <code>binmode $fh, ':encoding(ISO-8859-1)'</code> sets a specific encoding. In stryke, encoding layers can also be specified directly in <code>open</code>: <code>open my $fh, '<:utf8', $path</code>. Call <code>binmode</code> before any I/O on the handle — calling it mid-stream may produce garbled output. For binary file processing (images, archives, network protocols), always use <code>:raw</code>.</p>
<pre><code class="lang-perl">open my $fh, '<', $path or die $!
binmode $fh, ':utf8'
my @lines = <$fh>
open my $bin, '<', $img_path or die $!
binmode $bin, ':raw'
read $bin, my $header, 8
p sprintf "magic: %s", unpack("H*", $header)
</code></pre>
</article>
<article class="doc-entry" id="doc-fileno">
<h3><a class="doc-anchor" href="#doc-fileno">#</a> <code>fileno</code></h3>
<p>Return the underlying OS file descriptor number for a filehandle, or <code>undef</code> if the handle is not connected to a real file descriptor (e.g., tied handles, in-memory handles opened to scalar refs). File descriptor numbers are small non-negative integers managed by the OS kernel: 0 is STDIN, 1 is STDOUT, 2 is STDERR. This function is mainly useful for interfacing with system calls that require raw fd numbers, checking whether two handles share the same underlying fd, or passing descriptors to child processes. In stryke, <code>fileno</code> is rarely needed in everyday code but is essential for low-level I/O multiplexing and process management.</p>
<pre><code class="lang-perl">my $fd = fileno STDOUT
p "stdout fd: $fd" # 1
if (defined fileno $fh) {
p "handle is backed by fd " . fileno($fh)
} else {
p "not a real file descriptor"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-flock">
<h3><a class="doc-anchor" href="#doc-flock">#</a> <code>flock</code></h3>
<p>Advisory file locking for coordinating access between processes. <code>flock $fh, OPERATION</code> where OPERATION is <code>LOCK_SH</code> (shared/read lock), <code>LOCK_EX</code> (exclusive/write lock), or <code>LOCK_UN</code> (unlock). Add <code>LOCK_NB</code> for non-blocking mode: <code>LOCK_EX | LOCK_NB</code> returns false immediately if the lock is held rather than waiting. Import constants from <code>Fcntl</code>. Advisory locks are cooperative — they only work if all processes accessing the file use <code>flock</code>. In stryke, <code>flock</code> is the standard mechanism for safe concurrent file access in multi-process scripts, cron jobs, and daemons. Always unlock explicitly or let the handle close (which releases the lock). Gotcha: <code>flock</code> does not work on NFS on many systems.</p>
<pre><code class="lang-perl">use Fcntl ':flock'
open my $fh, '>>', 'shared.log' or die $!
flock $fh, LOCK_EX or die "lock: $!"
print $fh tm "pid $$ wrote this\n"
flock $fh, LOCK_UN
close $fh
unless (flock $fh, LOCK_EX | LOCK_NB) {
p "file is locked by another process"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-getc">
<h3><a class="doc-anchor" href="#doc-getc">#</a> <code>getc</code></h3>
<p>Read a single character from a filehandle (default <code>STDIN</code>). Returns <code>undef</code> at EOF. The character returned respects the handle's encoding layer — under <code>:utf8</code>, <code>getc</code> returns a full Unicode character which may be multiple bytes on disk. This function is useful for interactive single-key input, parsing binary formats one byte at a time, or implementing character-level tokenizers. In stryke, <code>getc</code> blocks until a character is available on the handle. For terminal input, note that most terminals are line-buffered by default, so <code>getc STDIN</code> won't return until the user presses Enter unless you put the terminal into raw mode.</p>
<pre><code class="lang-perl">my $ch = getc STDIN
p "you pressed: $ch"
open my $fh, '<:utf8', $path or die $!
while (defined(my $c = getc $fh)) {
p "char: $c (ord " . ord($c) . ")"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-select">
<h3><a class="doc-anchor" href="#doc-select">#</a> <code>select</code></h3>
<p>In its one-argument form, <code>select HANDLE</code> sets the default output handle for <code>print</code>, <code>say</code>, and <code>write</code>, returning the previously selected handle. This is useful for temporarily redirecting output — for example, sending diagnostics to STDERR while a report goes to a file. In its four-argument form, <code>select RBITS, WBITS, EBITS, TIMEOUT</code> performs POSIX <code>select(2)</code> I/O multiplexing, waiting for one or more file descriptors to become ready for reading, writing, or to report exceptions. The four-argument form is low-level and rarely used directly in stryke — prefer <code>IO::Select</code> or async I/O patterns for multiplexing. <code>select</code> with <code>$|</code> is also the classic way to enable autoflush on a handle.</p>
<pre><code class="lang-perl">my $old = select STDERR
p "this goes to stderr"
select $old
# Enable autoflush on STDOUT
select STDOUT; $| = 1
print "immediately flushed"
</code></pre>
</article>
<article class="doc-entry" id="doc-truncate">
<h3><a class="doc-anchor" href="#doc-truncate">#</a> <code>truncate</code></h3>
<p>Truncate a file to a specified byte length. Accepts either a filehandle or a filename as the first argument, and the desired length as the second. <code>truncate $fh, 0</code> empties the file entirely — a common pattern when rewriting a file in place. <code>truncate $fh, $len</code> discards everything beyond byte <code>$len</code>. Returns true on success, false on failure (check <code>$!</code> for the error). In stryke, truncate works on any seekable filehandle. When using truncate to rewrite a file, remember to also <code>seek $fh, 0, 0</code> to rewind the write position — truncating does not move the file pointer. Gotcha: truncating a file opened read-only will fail.</p>
<pre><code class="lang-perl">open my $fh, '+<', 'data.txt' or die $!
truncate $fh, 0 # empty the file
seek $fh, 0, 0 # rewind to start
print $fh "fresh content\n"
close $fh
</code></pre>
</article>
<article class="doc-entry" id="doc-sysopen">
<h3><a class="doc-anchor" href="#doc-sysopen">#</a> <code>sysopen</code></h3>
<p>Low-level open using POSIX flags for precise control over how a file is opened. The signature is <code>sysopen FH, FILENAME, FLAGS [, PERMS]</code>. Flags are bitwise-OR combinations from <code>Fcntl</code>: <code>O_RDONLY</code>, <code>O_WRONLY</code>, <code>O_RDWR</code>, <code>O_CREAT</code>, <code>O_EXCL</code>, <code>O_TRUNC</code>, <code>O_APPEND</code>, <code>O_NONBLOCK</code>, and others. The optional PERMS argument (e.g., <code>0644</code>) sets the file mode when <code>O_CREAT</code> creates a new file, subject to the process umask. <code>sysopen</code> is the right tool when you need <code>O_EXCL</code> for atomic file creation (lock files, temp files), <code>O_NONBLOCK</code> for non-blocking I/O, or other flags that <code>open</code> cannot express. In stryke, prefer three-argument <code>open</code> for routine file access and reserve <code>sysopen</code> for cases requiring specific POSIX semantics.</p>
<pre><code class="lang-perl">use Fcntl
# Atomic create — fails if file already exists
sysopen my $lock, '/tmp/my.lock', O_WRONLY|O_CREAT|O_EXCL, 0644
or die "already running: $!"
print $lock $$
sysopen my $log, 'app.log', O_WRONLY|O_APPEND|O_CREAT, 0644
or die "open log: $!"
</code></pre>
</article>
<article class="doc-entry" id="doc-sysread">
<h3><a class="doc-anchor" href="#doc-sysread">#</a> <code>sysread</code></h3>
<p>Low-level unbuffered read directly from a file descriptor, bypassing PerlIO buffering layers. The signature is <code>sysread FH, SCALAR, LENGTH [, OFFSET]</code>. Returns the number of bytes read, 0 at EOF, or <code>undef</code> on error. Unlike <code>read</code>, <code>sysread</code> issues a single <code>read(2)</code> system call and may return fewer bytes than requested (short read). This is the right choice for sockets, pipes, and non-blocking I/O where you need precise control over how many system calls occur and cannot tolerate buffering. In stryke, never mix <code>sysread</code>/<code>syswrite</code> with buffered I/O (<code>print</code>, <code>read</code>, <code><$fh></code>) on the same handle — the buffered and unbuffered positions will diverge and produce corrupted reads.</p>
<pre><code class="lang-perl">open my $fh, '<:raw', $path or die $!
my $buf = ''
while (my $n = sysread $fh, $buf, 4096, length($buf)) {
p "read $n bytes (total: " . length($buf) . ")"
}
close $fh
</code></pre>
</article>
<article class="doc-entry" id="doc-syswrite">
<h3><a class="doc-anchor" href="#doc-syswrite">#</a> <code>syswrite</code></h3>
<p>Low-level unbuffered write directly to a file descriptor, bypassing PerlIO buffering layers. The signature is <code>syswrite FH, SCALAR [, LENGTH [, OFFSET]]</code>. Returns the number of bytes actually written, which may be less than requested on non-blocking handles or when writing to pipes/sockets (short write). Returns <code>undef</code> on error. Like <code>sysread</code>, this issues a single <code>write(2)</code> system call and must not be mixed with buffered I/O on the same handle. In stryke, <code>syswrite</code> is essential for socket programming, IPC, and performance-critical binary output where you need to avoid double-buffering. Always check the return value and handle short writes in a loop for robust code.</p>
<pre><code class="lang-perl">my $data = "hello, world"
my $n = syswrite $fh, $data
p "wrote $n bytes"
# Robust write loop for sockets
my $off = 0
while ($off < length $data) {
my $written = syswrite $fh, $data, length($data) - $off, $off
die "syswrite: $!" unless defined $written
$off += $written
}
</code></pre>
</article>
<article class="doc-entry" id="doc-sysseek">
<h3><a class="doc-anchor" href="#doc-sysseek">#</a> <code>sysseek</code></h3>
<p>Low-level seek on a file descriptor, bypassing PerlIO buffering. The signature is <code>sysseek FH, POSITION, WHENCE</code> with the same WHENCE values as <code>seek</code> (0=start, 1=current, 2=end). Returns the new position as a true value, or <code>undef</code> on failure. Unlike <code>seek</code>, <code>sysseek</code> does not flush PerlIO buffers — it operates directly on the underlying OS file descriptor. Use <code>sysseek</code> when working with <code>sysread</code>/<code>syswrite</code> for consistent positioning. In stryke, <code>sysseek</code> with <code>SEEK_CUR</code> and position 0 is an idiom for querying the current fd position without moving: <code>my $pos = sysseek $fh, 0, 1</code>.</p>
<pre><code class="lang-perl">sysseek $fh, 0, 0 # rewind to start
sysread $fh, my $buf, 512
my $pos = sysseek $fh, 0, 1
p "fd position: $pos"
</code></pre>
</article>
<article class="doc-entry" id="doc-format">
<h3><a class="doc-anchor" href="#doc-format">#</a> <code>format</code></h3>
<p>Declare a picture-format template for generating fixed-width text reports. The syntax is <code>format NAME = ... .</code> where each line alternates between picture lines (containing field placeholders) and argument lines (listing the variables to fill in). Placeholders include <code>@<<<<</code> (left-align), <code>@>>>></code> (right-align), <code>@||||</code> (center), <code>@###.##</code> (numeric with decimal), and <code>@*</code> (multiline block fill). The format ends with a lone <code>.</code> on its own line. In stryke, formats are a legacy feature preserved for compatibility with Perl 5 code — for new reports, prefer <code>printf</code>/<code>sprintf</code> for simple alignment or a templating module for complex layouts. Formats interact with the special variables <code>$~</code> (current format name), <code>$^</code> (header format), and <code>$=</code> (lines per page).</p>
<pre><code class="lang-perl">format REPORT =
@<<<<<<<<<<<<<<<< @>>>>> @ ###.##
$item, $qty, $price
.
my ($item, $qty, $price) = ("Widget", 100, 9.99)
my $old = select REPORT
$~ = 'REPORT'
write REPORT
select $old
</code></pre>
</article>
<article class="doc-entry" id="doc-formline">
<h3><a class="doc-anchor" href="#doc-formline">#</a> <code>formline</code></h3>
<p>Format a line of output according to a picture template, appending the result to the <code>$^A</code> (format accumulator) variable. This is the low-level engine behind Perl's <code>format</code>/<code>write</code> report-generation system. Template characters like <code>@<<<</code> (left-justify), <code>@>>></code> (right-justify), and <code>@###.##</code> (numeric) control field placement.</p>
<pre><code class="lang-perl">$^A = ""
formline("@<<<< @>>>>>\n", "Name", "Score")
formline("@<<<< @>>>>>\n", "Alice", 98)
formline("@<<<< @>>>>>\n", "Bob", 85)
p $^A
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-strings">
<h2>Strings</h2>
<p class="chapter-meta">26 topics</p>
<article class="doc-entry" id="doc-chomp">
<h3><a class="doc-anchor" href="#doc-chomp">#</a> <code>chomp</code></h3>
<p><code>chomp STRING</code> — remove the trailing record separator (usually <code>\n</code>) from a string in place and return the number of characters removed.</p>
<p><code>chomp</code> is the idiomatic way to strip newlines after reading input; unlike <code>chop</code>, it only removes the value of <code>$/</code> (the input record separator), so it is safe to call on strings that do not end with a newline — it simply does nothing. You can also <code>chomp</code> an entire array to strip every element at once. In stryke, <code>chomp</code> operates on UTF-8 strings and respects multi-byte <code>$/</code> values. Prefer <code>chomp</code> over <code>chop</code> in virtually all input-processing code; <code>chop</code> is only for when you truly need to remove an arbitrary trailing character regardless of what it is.</p>
<pre><code class="lang-perl">my $line = <STDIN>
chomp $line
p $line
chomp(my @lines = <$fh>) # strip all at once
p scalar @lines
</code></pre>
</article>
<article class="doc-entry" id="doc-chop">
<h3><a class="doc-anchor" href="#doc-chop">#</a> <code>chop</code></h3>
<p><code>chop STRING</code> — remove and return the last character of a string, modifying the string in place.</p>
<p>Unlike <code>chomp</code>, <code>chop</code> unconditionally removes whatever the final character is — newline, letter, digit, or even a multi-byte UTF-8 codepoint in stryke. The return value is the removed character. This makes <code>chop</code> useful for peeling off known trailing delimiters or building parsers that consume input character-by-character, but dangerous for general newline removal because it will silently eat a real character if the string does not end with <code>\n</code>. When called on an array, <code>chop</code> removes the last character of every element and returns the last one removed.</p>
<pre><code class="lang-perl">my $s = "hello!"
my $last = chop $s # $last = "!", $s = "hello"
p $s
my @words = ("foo\n", "bar\n")
chop @words # strips trailing newline from each
@words |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-length">
<h3><a class="doc-anchor" href="#doc-length">#</a> <code>length</code></h3>
<p><code>length STRING</code> — return the <strong>byte</strong> length of a string. Perl 5 builtin; pairs with <code>index</code> / <code>rindex</code> / <code>substr</code> (all byte-based) so positions and lengths share a coordinate system.</p>
<p><code>length "hello"</code> is 5; <code>length "─"</code> is 3 (the box-drawing char takes 3 bytes in UTF-8). For codepoint count, use <code>len</code> (stryke extension), which mirrors <code>[i]</code> / <code>[a:b]</code> slice semantics.</p>
<pre><code class="lang-perl">p length "hello" # 5
p length "─" # 3 (bytes)
p len "─" # 1 (codepoint)
p length "\x{1F600}" # 4 (bytes — emoji is 4-byte UTF-8)
p len "\x{1F600}" # 1 (codepoint)
</code></pre>
</article>
<article class="doc-entry" id="doc-substr">
<h3><a class="doc-anchor" href="#doc-substr">#</a> <code>substr</code></h3>
<p><code>substr STRING, OFFSET [, LENGTH [, REPLACEMENT]]</code> — extract or replace a substring.</p>
<p><code>substr</code> is stryke's Swiss-army knife for positional string manipulation. With two arguments it extracts from OFFSET to end; with three it extracts LENGTH characters; with four it replaces that range with REPLACEMENT and returns the original extracted portion. Negative OFFSET counts from the end of the string (<code>substr $s, -3</code> gives the last three characters). In stryke, offsets are UTF-8 character positions, making it safe for multi-byte text. <code>substr</code> as an lvalue (<code>substr($s, 0, 1) = "X"</code>) is also supported for in-place mutation. Prefer <code>substr</code> over regex when you know exact positions — it is faster and clearer.</p>
<pre><code class="lang-perl">my $s = "hello world"
p substr $s, 0, 5 # hello
p substr $s, -5 # world
substr $s, 6, 5, "stryke" # $s = "hello stryke"
p $s
</code></pre>
</article>
<article class="doc-entry" id="doc-index">
<h3><a class="doc-anchor" href="#doc-index">#</a> <code>index</code></h3>
<p><code>index STRING, SUBSTRING [, POSITION]</code> — return the zero-based <strong>byte</strong> position of the first occurrence of SUBSTRING within STRING, or -1 if not found. Pairs with <code>substr</code> and <code>length</code> (both byte-based) for Perl 5 compat.</p>
<p>The optional POSITION argument lets you start the search at a given offset, which is essential for scanning forward through a string in a loop (call <code>index</code> repeatedly, advancing POSITION past each hit). For multi-byte strings where you want <strong>codepoint</strong> positions paired with <code>[i]</code> / <code>[a:b]</code> slice operators, use <code>cindex</code> (stryke extension) instead — <code>index</code> is byte-indexed because <code>length</code> and <code>substr</code> are, and changing it would break Perl 5 binary-protocol code.</p>
<pre><code class="lang-perl">my $i = index "hello world", "world" # 6
p $i
my $s = "a.b.c.d"
my $pos = 0
while (($pos = index $s, ".", $pos) != -1) {
p "dot at $pos"
$pos++
}
</code></pre>
</article>
<article class="doc-entry" id="doc-rindex">
<h3><a class="doc-anchor" href="#doc-rindex">#</a> <code>rindex</code></h3>
<p><code>rindex STRING, SUBSTRING [, POSITION]</code> — return the zero-based <strong>byte</strong> position of the last occurrence of SUBSTRING within STRING, searching backward from POSITION (or the end). Mirror of <code>index</code>; pairs with <code>substr</code> and <code>length</code> for Perl 5 compat.</p>
<p><code>rindex</code> searches from right to left, making it ideal for extracting file extensions, final path components, or the last delimiter in a string. The optional POSITION argument caps how far right the search begins — characters after POSITION are ignored. Returns -1 when the substring is not found. For codepoint positions paired with <code>[]</code> slice operators, use <code>crindex</code>.</p>
<pre><code class="lang-perl">my $path = "foo/bar/baz.tar.gz"
my $i = rindex $path, "/" # 7
p substr $path, $i + 1 # baz.tar.gz
my $ext = rindex $path, "." # 15
p substr $path, $ext + 1 # gz
</code></pre>
</article>
<article class="doc-entry" id="doc-split">
<h3><a class="doc-anchor" href="#doc-split">#</a> <code>split</code></h3>
<p><code>split /PATTERN/, STRING [, LIMIT]</code> — divide STRING into a list of substrings by splitting on each occurrence of PATTERN.</p>
<p><code>split</code> is one of the most-used string functions. The PATTERN is a regex, so you can split on character classes, alternations, or lookaheads. A LIMIT caps the number of returned fields; the final field contains the unsplit remainder. The special pattern <code>" "</code> (a single space string, not regex) mimics <code>awk</code>-style splitting: it strips leading whitespace and splits on runs of whitespace. In stryke, <code>split</code> integrates with <code>|></code> pipelines, accepting piped-in strings for ergonomic one-liners. Trailing empty fields are removed by default; pass -1 as LIMIT to preserve them.</p>
<pre><code class="lang-perl">my @parts = split /,/, "a,b,c"
"one:two:three" |> split /:/ |> e p # one two three
my ($user, $domain) = split /@/, $email, 2
p "$user at $domain"
</code></pre>
</article>
<article class="doc-entry" id="doc-join">
<h3><a class="doc-anchor" href="#doc-join">#</a> <code>join</code></h3>
<p><code>join SEPARATOR, LIST</code> — concatenate all elements of LIST into a single string, placing SEPARATOR between each pair of adjacent elements.</p>
<p><code>join</code> is the inverse of <code>split</code>. It stringifies each element before joining, so mixing numbers and strings is fine. An empty separator (<code>join "", @list</code>) concatenates without gaps. In stryke, <code>join</code> works naturally with <code>|></code> pipelines: a range or filtered list can be piped directly into <code>join</code> with a separator argument. This is the standard way to build CSV lines, path strings, or human-readable lists from arrays. <code>join</code> never adds a trailing separator — if you need one, append it yourself.</p>
<pre><code class="lang-perl">my $csv = join ",", @fields
1:5 |> join "-" |> p # 1-2-3-4-5
my @parts = ("usr", "local", "bin")
p join "/", "", @parts # /usr/local/bin
</code></pre>
</article>
<article class="doc-entry" id="doc-uc">
<h3><a class="doc-anchor" href="#doc-uc">#</a> <code>uc</code></h3>
<p><code>uc STRING</code> — return a fully uppercased copy of the string.</p>
<p><code>uc</code> performs Unicode-aware uppercasing in stryke, correctly handling multi-byte characters and locale-sensitive transformations. It returns a new string without modifying the original. Use <code>uc</code> for normalizing strings before comparison, formatting headers, or transforming pipeline output. In stryke <code>|></code> chains, combine with <code>maps</code> or <code>t</code> for streaming uppercase transforms. For uppercasing only the first character (e.g., sentence capitalization), use <code>ucfirst</code> instead.</p>
<pre><code class="lang-perl">p uc "hello" # HELLO
@words |> maps { uc } |> e p
"whisper" |> t uc |> p # WHISPER
</code></pre>
</article>
<article class="doc-entry" id="doc-lc">
<h3><a class="doc-anchor" href="#doc-lc">#</a> <code>lc</code></h3>
<p><code>lc STRING</code> — return a fully lowercased copy of the string.</p>
<p><code>lc</code> performs Unicode-aware lowercasing in stryke, so <code>lc "\x{C4}"</code> (capital A with diaeresis) correctly returns the lowercase form. It does not modify the original string — it returns a new one. This is the standard way to normalize strings for case-insensitive comparison: <code>if (lc $a eq lc $b)</code>. In stryke <code>|></code> pipelines, wrap <code>lc</code> with <code>t</code> to apply it as a streaming transform. For lowercasing only the first character, use <code>lcfirst</code> instead.</p>
<pre><code class="lang-perl">p lc "HELLO" # hello
"SHOUT" |> t lc |> t rev |> p # tuohs
my @norm = map lc, @words
@norm |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-ucfirst">
<h3><a class="doc-anchor" href="#doc-ucfirst">#</a> <code>ucfirst</code></h3>
<p><code>ucfirst STRING</code> — return a copy of the string with only the first character uppercased, leaving the rest unchanged.</p>
<p>This is the standard way to capitalize the first letter of a word for display, title-casing, or converting camelCase to PascalCase. In stryke, <code>ucfirst</code> is Unicode-aware and correctly handles multi-byte leading characters. It returns a new string and does not modify the original. For full uppercasing, use <code>uc</code>. A common idiom is <code>ucfirst lc $word</code> to normalize a word to "Title" form.</p>
<pre><code class="lang-perl">p ucfirst "hello" # Hello
p ucfirst lc "hELLO" # Hello
my @titled = map { ucfirst lc } @raw
@titled |> join " " |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-lcfirst">
<h3><a class="doc-anchor" href="#doc-lcfirst">#</a> <code>lcfirst</code></h3>
<p><code>lcfirst STRING</code> — return a copy of the string with only the first character lowercased, leaving the rest unchanged.</p>
<p>This is useful for converting PascalCase identifiers to camelCase, or for formatting output where only the initial letter matters. In stryke, <code>lcfirst</code> is Unicode-aware, so it handles accented capitals and multi-byte first characters correctly. Like <code>lc</code>, it returns a new string rather than modifying in place. If you need the entire string lowercased, use <code>lc</code> instead.</p>
<pre><code class="lang-perl">p lcfirst "Hello" # hello
p lcfirst "XMLParser" # xMLParser
my @camel = map lcfirst, @PascalNames
@camel |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-chr">
<h3><a class="doc-anchor" href="#doc-chr">#</a> <code>chr</code></h3>
<p><code>chr NUMBER</code> — return the character represented by the given ASCII or Unicode code point.</p>
<p><code>chr</code> is the inverse of <code>ord</code>: <code>chr(ord($c)) eq $c</code> always holds. It accepts any non-negative integer and returns a single-character string. In stryke, values above 127 produce valid UTF-8 characters, so <code>chr 0x1F600</code> gives you a smiley emoji with no special encoding gymnastics. For string literals, stryke supports all standard escapes: <code>\x{hex}</code>, <code>\u{hex}</code>, <code>\o{oct}</code>, <code>\NNN</code> (octal), <code>\cX</code> (control), <code>\N{U+hex}</code>, <code>\N{UNICODE NAME}</code>, plus case modifiers <code>\U..\E</code>, <code>\L..\E</code>, <code>\u</code>, <code>\l</code>, <code>\Q..\E</code>.</p>
<pre><code class="lang-perl">p chr 65 # A
p chr 0x1F600 # smiley emoji
p "\u{0301}" # combining acute accent
p "\N{SNOWMAN}" # ☃
my @abc = map { chr(_ + 64) } 1:26
@abc |> join "" |> p # ABCDEFGHIJKLMNOPQRSTUVWXYZ
</code></pre>
</article>
<article class="doc-entry" id="doc-ord">
<h3><a class="doc-anchor" href="#doc-ord">#</a> <code>ord</code></h3>
<p><code>ord STRING</code> — return the numeric (Unicode code point) value of the first character of the string.</p>
<p><code>ord</code> is the inverse of <code>chr</code>: <code>ord(chr($n)) == $n</code> always holds. When passed a multi-character string, only the first character is examined — the rest are ignored. In stryke, <code>ord</code> returns the full Unicode code point, not just 0-255, so <code>ord "\u{1F600}"</code> returns 128512. This is useful for character classification, building lookup tables, or implementing custom encodings. For ASCII checks, <code>ord($c) >= 32 && ord($c) <= 126</code> tests printability.</p>
<pre><code class="lang-perl">p ord "A" # 65
p ord "\n" # 10
p ord "\u{1F600}" # 128512
my @codes = map ord, split //, "hello"
@codes |> e p # 104 101 108 108 111
</code></pre>
</article>
<article class="doc-entry" id="doc-hex">
<h3><a class="doc-anchor" href="#doc-hex">#</a> <code>hex</code></h3>
<p><code>hex STRING</code> — interpret a hexadecimal string and return its numeric value.</p>
<p>The leading <code>0x</code> prefix is optional: both <code>hex "ff"</code> and <code>hex "0xff"</code> return 255. The string is case-insensitive, so <code>hex "DeAdBeEf"</code> works fine. If the string contains non-hex characters, stryke warns and converts up to the first invalid character. This is the standard way to parse hex-encoded values from config files, color codes, or protocol dumps. For the reverse operation (number to hex string), use <code>sprintf "%x"</code>. Note that <code>hex</code> always returns a number, never a string — arithmetic is immediate.</p>
<pre><code class="lang-perl">my $n = hex "deadbeef"
printf "0x%x = %d\n", $n, $n
p hex "ff" # 255
"cafe" |> t { hex } |> p # 51966
</code></pre>
</article>
<article class="doc-entry" id="doc-oct">
<h3><a class="doc-anchor" href="#doc-oct">#</a> <code>oct</code></h3>
<p><code>oct STRING</code> — interpret an octal, hexadecimal, or binary string and return its numeric value.</p>
<p><code>oct</code> is the multi-base cousin of <code>hex</code>: it auto-detects the base from the prefix. Strings starting with <code>0b</code> are binary, <code>0x</code> are hex, and bare digits or <code>0</code>-prefixed digits are octal. This makes it the go-to for parsing Unix file permissions (<code>oct "0755"</code> gives 493), binary literals, or any string where the radix is embedded in the value. In stryke, <code>oct</code> handles arbitrarily large integers via the same big-number pathway as other arithmetic. A common gotcha: <code>oct "8"</code> warns because 8 is not a valid octal digit — use <code>hex</code> or a bare numeric literal instead.</p>
<pre><code class="lang-perl">p oct "0755" # 493
p oct "0b1010" # 10
p oct "0xff" # 255
my $perms = oct "644"
p sprintf "%04o", $perms # 0644
</code></pre>
</article>
<article class="doc-entry" id="doc-quotemeta">
<h3><a class="doc-anchor" href="#doc-quotemeta">#</a> <code>quotemeta</code></h3>
<p><code>quotemeta STRING</code> — escape all non-alphanumeric characters with backslashes, returning a string safe for interpolation into a regex.</p>
<p>This is essential when building dynamic regexes from user input: without <code>quotemeta</code>, characters like <code>.</code>, <code>*</code>, <code>(</code>, <code>)</code>, <code>[</code>, and <code>\</code> would be interpreted as regex metacharacters, leading to either broken patterns or security vulnerabilities (ReDoS). The equivalent inline syntax is <code>\Q..\E</code> inside a regex. In stryke, <code>quotemeta</code> handles the full Unicode range, escaping any character that is not <code>[A-Za-z0-9_]</code>. Use it liberally whenever you splice user-provided strings into patterns.</p>
<pre><code class="lang-perl">my $input = "file (1).txt"
my $safe = quotemeta $input
p $safe # file\ \(1\)\.txt
my $found = ("file (1).txt" =~ /^$safe$/)
p $found # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-trim">
<h3><a class="doc-anchor" href="#doc-trim">#</a> <code>trim</code></h3>
<p><code>trim STRING</code> or <code>trim LIST</code> — strip leading and trailing ASCII whitespace.</p>
<p>When given a single string, <code>trim</code> returns the stripped result. When given a list or used in a pipeline, it operates in streaming mode, trimming each element individually as it flows through. Whitespace includes spaces, tabs, carriage returns, and newlines. The <code>tm</code> alias is convenient in pipeline chains where brevity matters.</p>
<pre><code class="lang-perl">" hello " |> tm |> p # "hello"
@raw |> tm |> e p
slurp("data.csv") |> ln |> tm |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-lines">
<h3><a class="doc-anchor" href="#doc-lines">#</a> <code>lines</code></h3>
<p><code>lines STRING</code> / <code>ln STRING</code> — split a string on newline boundaries, returning a streaming iterator of lines.</p>
<p>Each line is yielded without the trailing newline character. When piped from <code>slurp</code>, this gives you a lazy line-by-line view of a file without loading all lines into memory at once. Both <code>\n</code> and <code>\r\n</code> line endings are handled. The <code>ln</code> alias keeps pipelines compact.</p>
<pre><code class="lang-perl">slurp("data.txt") |> lines |> e p
my @rows = lines $multiline_str
$body |> ln |> grep /TODO/ |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-words">
<h3><a class="doc-anchor" href="#doc-words">#</a> <code>words</code></h3>
<p><code>words</code> (alias <code>wd</code>) splits a string on whitespace boundaries and returns the resulting list of words. It handles leading, trailing, and consecutive whitespace gracefully — unlike a naive <code>split / /</code>, it never produces empty strings. This is the idiomatic way to tokenize a line of text in stryke, and the short alias <code>wd</code> keeps pipelines compact. It is equivalent to Perl's <code>split ' '</code> behavior.</p>
<pre><code class="lang-perl">my @w = wd " hello world "
p @w # hello, world
my $line = " foo bar baz "
my $count = scalar wd $line
p $count # 3
rl("data.txt") |> map { scalar wd _ } |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-chars">
<h3><a class="doc-anchor" href="#doc-chars">#</a> <code>chars</code></h3>
<p><code>chars STRING</code> / <code>ch STRING</code> — split a string into individual characters, returning a streaming iterator.</p>
<p>Each Unicode grapheme cluster is yielded as a separate string element. This is useful for character-level processing such as frequency counting, transliteration, or building character n-grams. In pipeline mode the characters stream one at a time, so you can chain with <code>take</code>, <code>grep</code>, or <code>with_index</code> without materializing the full character array.</p>
<pre><code class="lang-perl">"hello" |> chars |> e p # h e l l o
my @c = chars "abc"
"emoji: \x{1F600}" |> ch |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-snake-case">
<h3><a class="doc-anchor" href="#doc-snake-case">#</a> <code>snake_case</code></h3>
<p><code>snake_case</code> (alias <code>sc</code>) converts a string from any common casing convention — camelCase, PascalCase, kebab-case, or mixed — into snake_case, where words are lowercase and separated by underscores. This is the standard naming convention for Perl and Rust variables and function names. Consecutive uppercase letters in acronyms are handled intelligently (e.g., <code>parseHTTPResponse</code> becomes <code>parse_http_response</code>).</p>
<pre><code class="lang-perl">p sc "camelCase" # camel_case
p sc "PascalCase" # pascal_case
p sc "kebab-case" # kebab_case
p sc "parseHTTPResponse" # parse_http_response
my @methods = qw(getUserName setEmailAddr)
@methods |> map sc |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-camel-case">
<h3><a class="doc-anchor" href="#doc-camel-case">#</a> <code>camel_case</code></h3>
<p><code>camel_case</code> (alias <code>cc</code>) converts a string from any casing convention into camelCase, where the first word is lowercase and subsequent words are capitalized with no separators. This is the standard naming convention for JavaScript variables and Java methods. The function handles underscores, hyphens, and spaces as word boundaries and strips them during conversion.</p>
<pre><code class="lang-perl">p cc "snake_case" # snakeCase
p cc "kebab-case" # kebabCase
p cc "PascalCase" # pascalCase
p cc "hello world" # helloWorld
my @cols = qw(first_name last_name email_addr)
@cols |> map cc |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-kebab-case">
<h3><a class="doc-anchor" href="#doc-kebab-case">#</a> <code>kebab_case</code></h3>
<p><code>kebab_case</code> (alias <code>kc</code>) converts a string from any casing convention into kebab-case, where words are lowercase and separated by hyphens. This is the standard naming convention for CSS classes, URL slugs, and CLI flag names. Like <code>snake_case</code>, it intelligently handles acronyms and mixed-case input. The function treats underscores, spaces, and case transitions as word boundaries.</p>
<pre><code class="lang-perl">p kc "camelCase" # camel-case
p kc "PascalCase" # pascal-case
p kc "snake_case" # snake-case
p kc "parseHTTPResponse" # parse-http-response
my $slug = kc $title # URL-safe slug
</code></pre>
</article>
<article class="doc-entry" id="doc-study">
<h3><a class="doc-anchor" href="#doc-study">#</a> <code>study</code></h3>
<p><code>study STRING</code> — hint to the regex engine that the given string will be matched against multiple patterns, allowing it to build an internal lookup table for faster matching.</p>
<p>In classic Perl, <code>study</code> builds a linked list of character positions so subsequent regex matches can skip impossible starting points. In practice, modern regex engines (including stryke's Rust-based engine) already perform these optimizations internally, so <code>study</code> is effectively a no-op in stryke — calling it is harmless but provides no measurable speedup. It exists for compatibility with Perl code that uses it. You only need <code>study</code> when porting legacy scripts that call it; do not add it to new stryke code expecting a performance benefit.</p>
<pre><code class="lang-perl">study $text # no-op in stryke, kept for compatibility
my @hits = grep { /$pattern/ } @lines
p scalar @hits
</code></pre>
</article>
<article class="doc-entry" id="doc-pos">
<h3><a class="doc-anchor" href="#doc-pos">#</a> <code>pos</code></h3>
<p><code>pos SCALAR</code> — gets or sets the position where the next <code>m//g</code> (global match) will start searching in the given string. After a successful <code>m//g</code> match, <code>pos</code> returns the offset just past the end of the match. You can assign to <code>pos($s)</code> to manually reposition the search. If the last <code>m//g</code> failed, <code>pos</code> resets to <code>undef</code>. This is essential for writing lexers or tokenizers that consume a string incrementally with <code>\G</code>-anchored patterns. In stryke, <code>pos</code> tracks per-scalar state just like Perl.</p>
<pre><code class="lang-perl">my $s = "abcabc"
while ($s =~ /a/g) { p pos($s) }
# 1 4
pos($s) = 0 # reset to scan again
p pos($s) # 0
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-arrays-hashes">
<h2>Arrays & Hashes</h2>
<p class="chapter-meta">20 topics</p>
<article class="doc-entry" id="doc-push">
<h3><a class="doc-anchor" href="#doc-push">#</a> <code>push</code></h3>
<p><code>push @array, LIST</code> — appends one or more elements to the end of an array and returns the new length. This is the primary way to grow arrays in stryke and works identically to Perl's builtin. You can push scalars, lists, or even the result of a pipeline. In stryke, <code>push</code> is O(1) amortized thanks to the underlying Rust <code>Vec</code>.</p>
<pre><code class="lang-perl">my @q
push @q, 1:3
push @q, "four", "five"
p scalar @q # 5
@q |> e p # 1 2 3 four five
</code></pre>
<p>Returns the new element count, so <code>my $len = push @arr, $val;</code> is valid.</p>
</article>
<article class="doc-entry" id="doc-pop">
<h3><a class="doc-anchor" href="#doc-pop">#</a> <code>pop</code></h3>
<p><code>pop @array</code> — removes and returns the last element of an array, or <code>undef</code> if the array is empty. This is the complement of <code>push</code> and together they give you classic stack (LIFO) semantics. In stryke the operation is O(1) because the underlying Rust <code>Vec::pop</code> simply decrements the length. When called without an argument inside a subroutine, <code>pop</code> operates on <code>@_</code>; at file scope it operates on <code>@ARGV</code>, matching standard Perl behavior.</p>
<pre><code class="lang-perl">my @stk = 1:5
my $top = pop @stk
p $top # 5
p scalar @stk # 4
@stk |> e p # 1 2 3 4
</code></pre>
</article>
<article class="doc-entry" id="doc-shift">
<h3><a class="doc-anchor" href="#doc-shift">#</a> <code>shift</code></h3>
<p><code>shift @array</code> — removes and returns the first element of an array, sliding all remaining elements down by one index. Like <code>pop</code>, it returns <code>undef</code> on an empty array. Without an explicit argument it defaults to <code>@_</code> inside subroutines and <code>@ARGV</code> at file scope. Because every element must be moved, <code>shift</code> is O(n); if you only need LIFO access, prefer <code>push</code>/<code>pop</code>. Use <code>shift</code> when processing argument lists or implementing FIFO queues.</p>
<pre><code class="lang-perl">my @args = @ARGV
my $cmd = shift @args
p $cmd
@args |> e p # remaining arguments
</code></pre>
</article>
<article class="doc-entry" id="doc-unshift">
<h3><a class="doc-anchor" href="#doc-unshift">#</a> <code>unshift</code></h3>
<p><code>unshift @array, LIST</code> — prepends one or more elements to the beginning of an array and returns the new length. It is the counterpart of <code>push</code> for the front of the array. Like <code>shift</code>, this is O(n) because existing elements must be moved to make room. When you need to build an array in reverse order or maintain a priority queue with newest items first, <code>unshift</code> is the idiomatic choice. You can pass multiple values and they will appear in the same order they were given.</p>
<pre><code class="lang-perl">my @log = ("b", "c")
unshift @log, "a"
@log |> e p # a b c
my $len = unshift @log, "x", "y"
p $len # 5
@log |> e p # x y a b c
</code></pre>
</article>
<article class="doc-entry" id="doc-splice">
<h3><a class="doc-anchor" href="#doc-splice">#</a> <code>splice</code></h3>
<p><code>splice @array, OFFSET [, LENGTH [, LIST]]</code> — the Swiss-army knife for array mutation. It can insert, remove, or replace elements at any position in a single call. With just an offset it removes everything from that point to the end. With offset and length it removes that many elements. With a replacement list it inserts those elements in place of the removed ones. The return value is the list of removed elements, which is useful for saving what you cut. In stryke this compiles down to Rust's <code>Vec::splice</code> and <code>Vec::drain</code>.</p>
<pre><code class="lang-perl">my @a = 1:5
my @removed = splice @a, 1, 2, 8, 9
@a |> e p # 1 8 9 4 5
@removed |> e p # 2 3
splice @a, 2 # remove from index 2 onward
@a |> e p # 1 8
</code></pre>
</article>
<article class="doc-entry" id="doc-splice-last">
<h3><a class="doc-anchor" href="#doc-splice-last">#</a> <code>splice_last</code></h3>
<p><code>splice_last @array, OFFSET [, LENGTH [, LIST]]</code> — same shape as <code>splice</code>, but returns the <strong>last</strong> removed element instead of the full removed list (or <code>undef</code> if nothing was removed). The stryke spelling of Perl's <code>scalar splice(@a, off, n)</code> for <code>--no-interop</code> mode where <code>scalar</code> is rejected at parse time. The array is still mutated in place, exactly like <code>splice</code>. Aliases: <code>splice1</code>, <code>spl_last</code>. Desugars to <code>tail(splice(...))</code> so any list-context property of <code>splice</code> is preserved.</p>
<pre><code class="lang-perl">my @a = 10:50:10
my $last = splice_last @a, 1, 2 # removes (20, 30), returns 30
@a |> e p # 10 40 50
my $popped = splice_last @b, 0, 0 # removes nothing, returns undef
</code></pre>
</article>
<article class="doc-entry" id="doc-keys">
<h3><a class="doc-anchor" href="#doc-keys">#</a> <code>keys</code></h3>
<p><code>keys %hash</code> — returns the list of all keys in a hash in no particular order. When called on an array, it returns the list of valid indices (0 to <code>$#array</code>). In scalar context, <code>keys</code> returns the number of keys. Calling <code>keys</code> resets the <code>each</code> iterator on that hash, which is the standard way to restart iteration. In stryke, this calls Rust's <code>HashMap::keys()</code> and collects into a <code>Vec</code>. For sorted output, chain with <code>sort</code> via the pipe operator.</p>
<pre><code class="lang-perl">my %env = (HOME => "/root", USER => "me")
keys(%env) |> sort |> e p # HOME USER
p scalar keys %env # 2
my @a = (10, 20, 30)
keys(@a) |> e p # 0 1 2
</code></pre>
</article>
<article class="doc-entry" id="doc-values">
<h3><a class="doc-anchor" href="#doc-values">#</a> <code>values</code></h3>
<p><code>values %hash</code> — returns the list of all values in a hash in no particular order (matching the order of <code>keys</code> for the same hash state). When called on an array, it returns the array elements themselves. In scalar context, returns the count of values. Like <code>keys</code>, calling <code>values</code> resets the <code>each</code> iterator. In stryke this maps to Rust's <code>HashMap::values()</code>. Combine with <code>sum</code>, <code>sort</code>, or pipeline operators for common aggregation patterns.</p>
<pre><code class="lang-perl">my %scores = (alice => 90, bob => 85)
p sum(values %scores) # 175
values(%scores) |> sort { $_1 <=> $_0 } |> e p # 90 85
</code></pre>
</article>
<article class="doc-entry" id="doc-each">
<h3><a class="doc-anchor" href="#doc-each">#</a> <code>each</code></h3>
<p><code>each %hash</code> — returns the next (key, value) pair from a hash as a two-element list, or an empty list when the iterator is exhausted. Each hash has its own internal iterator, which is reset when you call <code>keys</code> or <code>values</code> on the same hash. This is memory-efficient for large hashes because it does not build the full key list. Gotcha: do not add or delete keys while iterating with <code>each</code>; that can cause skipped or duplicated entries. In stryke, the iteration order is non-deterministic (Rust <code>HashMap</code> order).</p>
<pre><code class="lang-perl">my %h = (a => 1, b => 2, c => 3)
while (my ($k, $v) = each %h) { p "$k=$v" }
# output order varies: a=1 b=2 c=3
</code></pre>
</article>
<article class="doc-entry" id="doc-delete">
<h3><a class="doc-anchor" href="#doc-delete">#</a> <code>delete</code></h3>
<p><code>delete EXPR</code> — removes a key-value pair from a hash or an element from an array and returns the removed value (or <code>undef</code> if it did not exist). For hashes this is the only way to truly remove a key; assigning <code>undef</code> to <code>$h{key}</code> leaves the key in place. For arrays, <code>delete</code> sets the element to <code>undef</code> but does not shift indices (use <code>splice</code> if you need to close the gap). In stryke, hash deletion maps to Rust's <code>HashMap::remove</code>. You can delete multiple keys at once with a hash slice: <code>delete @h{@keys}</code>.</p>
<pre><code class="lang-perl">my %h = (x => 1, y => 2, z => 3)
my $old = delete $h{x}
p $old # 1
p exists $h{x} ? "yes" : "no" # no
delete @h{"y", "z"} # delete multiple keys
</code></pre>
</article>
<article class="doc-entry" id="doc-exists">
<h3><a class="doc-anchor" href="#doc-exists">#</a> <code>exists</code></h3>
<p><code>exists EXPR</code> — tests whether a specific key is present in a hash or an index is present in an array, regardless of whether the associated value is <code>undef</code>. This is different from <code>defined</code>: a key can exist but hold <code>undef</code>. Use <code>exists</code> to check hash membership before accessing a value to avoid autovivification side effects. In stryke, <code>exists</code> on a hash compiles to Rust's <code>HashMap::contains_key</code>, and on an array it checks bounds. You can also use it with nested structures: <code>exists $h{a}{b}</code> only checks the final level.</p>
<pre><code class="lang-perl">my %h = (a => 1, b => undef)
p exists $h{b} ? "yes" : "no" # yes (key present, value undef)
p exists $h{c} ? "yes" : "no" # no
my @a = (10, 20, 30)
p exists $a[5] ? "yes" : "no" # no
</code></pre>
</article>
<article class="doc-entry" id="doc-scalar">
<h3><a class="doc-anchor" href="#doc-scalar">#</a> <code>scalar</code></h3>
<p><code>scalar EXPR</code> — forces the expression into scalar context. The most common use is <code>scalar @array</code> to get the element count instead of the list of elements. In stryke, scalar context on an array returns its length as a Rust <code>usize</code>. You can also use <code>scalar</code> on a hash to get the number of key-value pairs, or on a function call to force it to return a single value. This is essential when you want a count inside string interpolation or as a function argument where list context would be ambiguous.</p>
<pre><code class="lang-perl">my @items = ("a", "b", "c")
p scalar @items # 3
p "count: " . scalar @items # count: 3
my %h = (x => 1, y => 2)
p scalar %h # 2
</code></pre>
</article>
<article class="doc-entry" id="doc-defined">
<h3><a class="doc-anchor" href="#doc-defined">#</a> <code>defined</code></h3>
<p><code>defined EXPR</code> — returns true if the expression has a value that is not <code>undef</code>. This is the canonical way to distinguish between "no value" and "a value that happens to be false" (such as <code>0</code>, <code>""</code>, or <code>"0"</code>). Use <code>defined</code> before dereferencing optional values or checking return codes from functions that return <code>undef</code> on failure. In stryke, <code>defined</code> compiles to a Rust <code>Option::is_some()</code> check internally. Note that <code>defined</code> on an aggregate (hash or array) is deprecated in Perl 5 and is a no-op in stryke.</p>
<pre><code class="lang-perl">my $x = undef
p defined($x) ? "yes" : "no" # no
$x = 0
p defined($x) ? "yes" : "no" # yes
my $val = fn_that_may_fail()
p $val if defined $val
</code></pre>
</article>
<article class="doc-entry" id="doc-undef">
<h3><a class="doc-anchor" href="#doc-undef">#</a> <code>undef</code></h3>
<p><code>undef</code> — the undefined value, representing the absence of a value. As a function, <code>undef $var</code> explicitly undefines a variable, freeing any value it held. <code>undef</code> is falsy in boolean context and triggers "use of uninitialized value" warnings under <code>use warnings</code>. In stryke, <code>undef</code> maps to Rust's <code>None</code> in an <code>Option</code> type internally. Use <code>undef</code> to reset variables, signal missing return values, or clear hash entries without deleting the key.</p>
<pre><code class="lang-perl">my $x = 42
undef $x
p defined($x) ? "def" : "undef" # undef
fn maybe { return undef if !@_
return $_[0] }
p defined(maybe()) ? "got" : "nothing" # nothing
</code></pre>
</article>
<article class="doc-entry" id="doc-ref">
<h3><a class="doc-anchor" href="#doc-ref">#</a> <code>ref</code></h3>
<p><code>ref EXPR</code> — returns a string indicating the reference type of the value, or an empty string if it is not a reference. Common return values are <code>SCALAR</code>, <code>ARRAY</code>, <code>HASH</code>, <code>CODE</code>, <code>REF</code>, and <code>Regexp</code>. For blessed objects it returns the class name. Use <code>ref</code> to dispatch on data type or validate arguments in polymorphic functions. In stryke, <code>ref</code> inspects the Rust enum variant of the underlying value. Note that <code>ref</code> does not recurse; it only tells you the top-level type.</p>
<pre><code class="lang-perl">my $r = [1, 2, 3]
p ref($r) # ARRAY
p ref(\%ENV) # HASH
p ref(\&main) # CODE
p ref(42) # (empty string)
</code></pre>
</article>
<article class="doc-entry" id="doc-bless">
<h3><a class="doc-anchor" href="#doc-bless">#</a> <code>bless</code></h3>
<p>Associate a reference with a package name, turning it into an object of that class. The blessed reference can then have methods called on it via <code>-></code>. The second argument defaults to the current package. This is the foundation of Perl's object system.</p>
<pre><code class="lang-perl">fn new($class, %args) {
bless { %args }, $class
}
my $obj = new("Dog", name => "Rex", breed => "Lab")
p ref($obj) # Dog
p $obj->{name} # Rex
</code></pre>
</article>
<article class="doc-entry" id="doc-tie">
<h3><a class="doc-anchor" href="#doc-tie">#</a> <code>tie</code></h3>
<p>Bind a variable to an implementing class so that all accesses (read, write, delete, etc.) are intercepted by methods on that class. This is Perl's mechanism for transparent object-backed variables — tied hashes can be backed by a database, tied scalars can validate on assignment, etc. Use <code>untie</code> to remove the binding.</p>
<pre><code class="lang-perl">tie my %db, 'DB_File', 'cache.db'
$db{key} = "value" # writes to disk
p $db{key} # reads from disk
untie %db
</code></pre>
</article>
<article class="doc-entry" id="doc-prototype">
<h3><a class="doc-anchor" href="#doc-prototype">#</a> <code>prototype</code></h3>
<p>Return the prototype string of a named function, or <code>undef</code> if the function has no prototype. Prototypes control how arguments are parsed at compile time — they influence context and reference-passing behavior. Useful for introspection and metaprogramming.</p>
<pre><code class="lang-perl">p prototype("CORE::push") # \@@
p prototype("CORE::map") # &@
fn greet($name) { p "hi $name" }
p prototype(\&greet) # undef (signatures, no proto)
</code></pre>
</article>
<article class="doc-entry" id="doc-wantarray">
<h3><a class="doc-anchor" href="#doc-wantarray">#</a> <code>wantarray</code></h3>
<p><code>wantarray()</code> — returns true if the current subroutine was called in list context, false in scalar context, and <code>undef</code> in void context. This lets a function adapt its return value to the caller's expectations. A common pattern is returning a list in list context and a count or reference in scalar context. In stryke, use <code>fn</code> to define subroutines and <code>wantarray()</code> inside them just like in Perl. Note that <code>wantarray</code> only reflects the immediate call site, not nested contexts.</p>
<pre><code class="lang-perl">fn ctx { wantarray() ? "list" : "scalar" }
my @r = ctx()
p $r[0] # list
my $r = ctx()
p $r # scalar
fn flexible { wantarray() ? (1, 2, 3) : 3 }
my @all = flexible()
p scalar @all # 3
my $cnt = flexible()
p $cnt # 3
</code></pre>
</article>
<article class="doc-entry" id="doc-caller">
<h3><a class="doc-anchor" href="#doc-caller">#</a> <code>caller</code></h3>
<p><code>caller [LEVEL]</code> — returns information about the calling subroutine's context. In list context it returns <code>(package, filename, line)</code> for the given call-stack level (default 0, the immediate caller). With higher levels you can walk up the call stack for debugging or generating stack traces. In scalar context, <code>caller</code> returns just the package name. In stryke, <code>caller</code> works with <code>fn</code>-defined subroutines and integrates with the runtime's frame tracking. This is invaluable for building custom error reporters or trace utilities.</p>
<pre><code class="lang-perl">fn here {
my ($pkg, $f, $ln) = caller()
p "$f:$ln"
}
here() # prints current file:line
fn deep {
my ($pkg, $f, $ln) = caller(1)
p "grandparent: $f:$ln"
}
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-control-flow">
<h2>Control Flow</h2>
<p class="chapter-meta">16 topics</p>
<article class="doc-entry" id="doc-if">
<h3><a class="doc-anchor" href="#doc-if">#</a> <code>if</code></h3>
<p>The fundamental conditional construct. Evaluates its condition in boolean context and executes the block if true. stryke supports both the block form <code>if (COND) { BODY }</code> and the postfix form <code>EXPR if COND</code>, which is idiomatic for single-statement guards. The condition can be any expression — numbers (0 is false), strings (empty and <code>"0"</code> are false), undef (false), and references (always true). Postfix <code>if</code> cannot have <code>elsif</code>/<code>else</code> — use the block form for multi-branch logic.</p>
<pre><code class="lang-perl">my $n = 42
if ($n > 0) { p "positive" }
p "big" if $n > 10 # postfix — clean one-liner
my $label = "even" if $n % 2 == 0
p "got: $n" if defined $n # guard against undef
</code></pre>
</article>
<article class="doc-entry" id="doc-elsif">
<h3><a class="doc-anchor" href="#doc-elsif">#</a> <code>elsif</code></h3>
<p>Chain additional conditions after an <code>if</code> block without nesting. Each <code>elsif</code> is tested in order; the first one whose condition is true has its block executed, and the rest are skipped. There is no limit on the number of <code>elsif</code> branches. In stryke, prefer <code>match</code> for complex multi-branch dispatch since it supports pattern matching, destructuring, and guards — but <code>elsif</code> remains the right tool for simple linear condition chains. Note: it is <code>elsif</code>, not <code>elseif</code> or <code>else if</code> — the latter is a syntax error.</p>
<pre><code class="lang-perl">fn classify($n) {
if ($n < 0) { "negative" }
elsif ($n == 0) { "zero" }
elsif ($n < 10) { "small" }
elsif ($n < 100) { "medium" }
else { "large" }
}
1:200 |> map classify |> frequencies |> dd
</code></pre>
</article>
<article class="doc-entry" id="doc-else">
<h3><a class="doc-anchor" href="#doc-else">#</a> <code>else</code></h3>
<p>The final fallback branch of an <code>if</code>/<code>elsif</code> chain, executed when no preceding condition was true. Every <code>if</code> can have at most one <code>else</code>, and it must come last. For ternary-style expressions, use <code>COND ? A : B</code> instead of an <code>if</code>/<code>else</code> block — it composes better in <code>|></code> pipes and assignments.</p>
<pre><code class="lang-perl">if ($n % 2 == 0) { p "even" }
else { p "odd" }
# Ternary is often cleaner in pipes:
1:10 |> map { _ % 2 == 0 ? "even" : "odd" } |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-unless">
<h3><a class="doc-anchor" href="#doc-unless">#</a> <code>unless</code></h3>
<p>A negated conditional — executes the block when the condition is *false*. This reads more naturally than <code>if (!COND)</code> for guard clauses and early returns. stryke supports both block and postfix forms. Convention: use <code>unless</code> for simple negative guards; avoid <code>unless</code> with complex compound conditions, as double-negatives hurt readability. There is no <code>unlessif</code> — use <code>if</code>/<code>elsif</code> chains for multi-branch logic.</p>
<pre><code class="lang-perl">unless ($ENV{QUIET}) { p "verbose output" }
p "missing!" unless -e $path # postfix guard
die "no input" unless @ARGV
return unless defined $val # early return pattern
</code></pre>
</article>
<article class="doc-entry" id="doc-for">
<h3><a class="doc-anchor" href="#doc-for">#</a> <code>for</code></h3>
<p>Iterate over a list, binding each element to a loop variable (or <code>_</code> by default). <code>for</code> and <code>foreach</code> are interchangeable keywords. The loop variable is automatically localized and aliases the original element — modifications to <code>_</code> inside the loop mutate the list in-place. In stryke, <code>for</code> loops work with ranges, arrays, hash slices, and iterator results. For parallel iteration, see <code>pfor</code>; for pipeline-style processing, prefer <code>|> e</code> or <code>|> map</code>. C-style <code>for (INIT; COND; STEP)</code> is also supported.</p>
<pre><code class="lang-perl">for my $f (glob "*.txt") { p $f }
for (1:5) { p _ * 2 } # _ is default
my @names = qw(alice bob carol)
for (@names) { _ = uc _ } # mutates in-place
p join ", ", @names # ALICE, BOB, CAROL
</code></pre>
</article>
<article class="doc-entry" id="doc-while">
<h3><a class="doc-anchor" href="#doc-while">#</a> <code>while</code></h3>
<p>Loop that re-evaluates its condition before each iteration and continues as long as it is true. Commonly used for reading input line-by-line, polling, and indefinite iteration. The condition is tested in boolean context. <code>while</code> integrates naturally with the diamond operator <code><></code> for reading filehandles. The loop variable can be declared in the condition with <code>my</code>, scoping it to the loop body. Postfix form is also supported: <code>EXPR while COND;</code>.</p>
<pre><code class="lang-perl">while (my $line = <STDIN>) {
$line |> tm |> p # trim + print each line
}
my $i = 0
while ($i < 5) { p $i++ } # counted loop
while (1) { last if done() } # infinite loop with break
</code></pre>
</article>
<article class="doc-entry" id="doc-until">
<h3><a class="doc-anchor" href="#doc-until">#</a> <code>until</code></h3>
<p>Loop that continues as long as its condition is *false* — the logical inverse of <code>while</code>. Useful when the termination condition is more naturally expressed as a positive assertion ("keep going until X happens"). Supports both block and postfix forms. Prefer <code>while</code> with a negated condition if <code>until</code> makes the logic harder to read.</p>
<pre><code class="lang-perl">my $n = 1
until ($n > 1000) { $n *= 2 }
p $n # 1024
my $tries = 0
until (connected()) {
$tries++
sleep 1
}
p "connected after $tries tries"
</code></pre>
</article>
<article class="doc-entry" id="doc-do">
<h3><a class="doc-anchor" href="#doc-do">#</a> <code>do</code></h3>
<p>Execute a block and return its value, or execute a file. As a block, <code>do { ... }</code> creates an expression scope — the last expression in the block is the return value, making it useful for complex initializations. As a file operation, <code>do "file.pl"</code> executes the file in the current scope and returns its last expression. Unlike <code>require</code>, <code>do</code> does not cache and re-executes on each call. <code>do { ... } while (COND)</code> creates a loop that always runs at least once.</p>
<pre><code class="lang-perl">my $val = do { my $x = 10
$x ** 2 } # 100
p $val
my $cfg = do "config.pl" # load config
# do-while: body runs at least once
my $input
do { $input = readline(STDIN) |> tm } while ($input eq "")
</code></pre>
</article>
<article class="doc-entry" id="doc-last">
<h3><a class="doc-anchor" href="#doc-last">#</a> <code>last</code></h3>
<p>Immediately exit the innermost enclosing loop (equivalent to <code>break</code> in C/Rust). Execution continues after the loop. <code>last LABEL</code> can target a labeled outer loop to break out of nested loops. Works in <code>for</code>, <code>foreach</code>, <code>while</code>, <code>until</code>, and <code>do-while</code>. Does *not* work inside <code>map</code>, <code>grep</code>, or <code>|></code> pipeline stages — use <code>take</code>, <code>first</code>, or <code>take_while</code> for early termination in functional contexts.</p>
<pre><code class="lang-perl">for (1:1_000_000) {
last if _ > 5
p _
} # prints 1 2 3 4 5
OUTER: for my $i (1:10) {
for my $j (1:10) {
last OUTER if $i * $j > 50 # break both loops
}
}
</code></pre>
<p>For pipeline early-exit: <code>1:1000 |> take_while { _ < 50 } |> e p</code>.</p>
</article>
<article class="doc-entry" id="doc-next">
<h3><a class="doc-anchor" href="#doc-next">#</a> <code>next</code></h3>
<p>Skip the rest of the current loop iteration and jump to the next one. The loop condition (for <code>while</code>/<code>until</code>) or the next element (for <code>for</code>/<code>foreach</code>) is evaluated immediately. Like <code>last</code>, <code>next</code> supports labeled loops with <code>next LABEL</code> for skipping in nested loops. This is the primary tool for filtering within imperative loops. In stryke, consider <code>grep</code>/<code>filter</code> or <code>|> reject</code> for functional-style filtering instead.</p>
<pre><code class="lang-perl">for (1:10) {
next if _ % 2 # skip odds
p _
} # 2 4 6 8 10
for my $file (glob "*") {
next unless -f $file # skip non-files
next if $file =~ /^\./ # skip hidden
p $file
}
</code></pre>
</article>
<article class="doc-entry" id="doc-redo">
<h3><a class="doc-anchor" href="#doc-redo">#</a> <code>redo</code></h3>
<p>Restart the current loop iteration from the top of the loop body *without* re-evaluating the loop condition or advancing to the next element. The loop variable retains its current value. This is a niche but powerful tool for retry logic within loops — when an iteration fails, <code>redo</code> lets you try again with the same input. Use sparingly, as it can create infinite loops if the retry condition never resolves. Always pair with a guard or counter. For automated retry with backoff, prefer <code>retry { ... } times => N, backoff => 'exponential'</code>.</p>
<pre><code class="lang-perl">for my $url (@urls) {
my $body = eval { fetch($url) }
if ($@) {
warn "retry $url: $@"
sleep 1
redo # try same URL again
}
p length($body)
}
</code></pre>
</article>
<article class="doc-entry" id="doc-continue">
<h3><a class="doc-anchor" href="#doc-continue">#</a> <code>continue</code></h3>
<p>A block attached to a <code>for</code>/<code>foreach</code>/<code>while</code> loop that executes after each iteration, even when <code>next</code> is called. Analogous to the increment expression in a C-style <code>for</code> loop. The <code>continue</code> block does *not* run when <code>last</code> or <code>redo</code> is used. Useful for unconditional per-iteration bookkeeping like incrementing counters, logging progress, or flushing buffers. Rarely used but fully supported in stryke.</p>
<pre><code class="lang-perl">my $count = 0
for my $item (@work) {
next if $item->{skip}
process($item)
} continue {
$count++
p "processed $count so far" if $count % 100 == 0
}
</code></pre>
</article>
<article class="doc-entry" id="doc-given">
<h3><a class="doc-anchor" href="#doc-given">#</a> <code>given</code></h3>
<p>A switch-like construct that evaluates an expression and dispatches to <code>when</code> blocks via smartmatch semantics. The topic variable <code>_</code> is set to the <code>given</code> expression for the duration of the block. Each <code>when</code> clause is tested in order; the first match executes its block and control passes out of the <code>given</code> (implicit break). A <code>default</code> block handles the no-match case. In stryke, prefer the <code>match</code> keyword for new code — it offers pattern destructuring, typed patterns, array/hash shape matching, and <code>if</code> guards that <code>given</code>/<code>when</code> cannot express.</p>
<pre><code class="lang-perl">given ($cmd) {
when ("start") { p "starting up" }
when ("stop") { p "shutting down" }
when (/^re/) { p "restarting" }
default { p "unknown: $cmd" }
}
</code></pre>
<p>See <code>match</code> for stryke-native pattern matching with destructuring.</p>
</article>
<article class="doc-entry" id="doc-when">
<h3><a class="doc-anchor" href="#doc-when">#</a> <code>when</code></h3>
<p>A case clause inside a <code>given</code> block. The expression is matched against the topic <code>_</code> using smartmatch semantics: strings match exactly, regexes match against <code>_</code>, arrayrefs check membership, coderefs are called with <code>_</code> as argument, and numbers compare numerically. When a <code>when</code> clause matches, its block executes and control exits the enclosing <code>given</code> (implicit break). Multiple <code>when</code> clauses are tried in order until one matches.</p>
<pre><code class="lang-perl">given ($val) {
when (/^\d+$/) { p "number" }
when (["a","b","c"]) { p "early letter" }
when (42) { p "the answer" }
default { p "something else" }
}
</code></pre>
<p>In stryke, the <code>match</code> keyword provides more powerful pattern matching.</p>
</article>
<article class="doc-entry" id="doc-default">
<h3><a class="doc-anchor" href="#doc-default">#</a> <code>default</code></h3>
<p>The fallback clause in a <code>given</code> block, executed when no <code>when</code> clause matched. Every <code>given</code> should have a <code>default</code> to handle unexpected values, similar to <code>else</code> in an <code>if</code> chain or the wildcard <code>_</code> arm in stryke <code>match</code>. If no <code>default</code> is present and nothing matches, execution simply continues after the <code>given</code> block. In stryke <code>match</code>, use <code>_ => ...</code> for the default arm instead.</p>
<pre><code class="lang-perl">given ($exit_code) {
when (0) { p "success" }
when (1) { p "general error" }
when (2) { p "misuse" }
default { p "unknown exit code: $exit_code" }
}
</code></pre>
</article>
<article class="doc-entry" id="doc-return">
<h3><a class="doc-anchor" href="#doc-return">#</a> <code>return</code></h3>
<p>Return a value from a subroutine.</p>
<pre><code class="lang-perl">fn pin_val($v, $lo, $hi) {
return $lo if $v < $lo
return $hi if $v > $hi
$v
}
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-error-handling">
<h2>Error Handling</h2>
<p class="chapter-meta">8 topics</p>
<article class="doc-entry" id="doc-try">
<h3><a class="doc-anchor" href="#doc-try">#</a> <code>try</code></h3>
<p>Structured exception handling that cleanly separates the happy path from error recovery. The <code>try</code> block runs the code; if it throws (via <code>die</code>), execution jumps to the <code>catch</code> block with the exception bound to the declared variable. An optional <code>finally</code> block runs unconditionally afterward — ideal for cleanup like closing filehandles or releasing locks. Unlike <code>eval</code>, <code>try</code>/<code>catch</code> is a first-class statement with proper scoping and no <code>$@</code> pollution. In stryke, <code>try</code> integrates with all exception types including string messages, hashrefs, and objects.</p>
<pre><code class="lang-perl">try {
my $data = fetch_json($url)
p $data->{name}
} catch ($e) {
warn "request failed: $e"
return fallback()
} finally {
log_info("fetch attempt complete")
}
</code></pre>
<p>Prefer <code>try</code>/<code>catch</code> over <code>eval { }</code> for new code — it reads better and avoids <code>$@</code> clobbering races.</p>
</article>
<article class="doc-entry" id="doc-catch">
<h3><a class="doc-anchor" href="#doc-catch">#</a> <code>catch</code></h3>
<p>The error-handling clause that follows a <code>try</code> block. When the <code>try</code> block throws an exception, execution transfers to <code>catch</code> with the exception value bound to the declared variable (e.g. <code>$e</code>). The catch variable is lexically scoped to the catch block. You can inspect the exception — it may be a string, a hashref with structured error info, or an object with methods. Multiple error types can be differentiated with <code>ref</code> or <code>match</code> inside the catch body. If the catch block itself throws, the exception propagates upward (the <code>finally</code> block still runs first, if present).</p>
<pre><code class="lang-perl">try { die { code => 404, msg => "not found" } }
catch ($e) {
if (ref $e eq 'HASH') {
p "error $e->{code}: $e->{msg}"
} else {
p "caught: $e"
}
}
</code></pre>
</article>
<article class="doc-entry" id="doc-finally">
<h3><a class="doc-anchor" href="#doc-finally">#</a> <code>finally</code></h3>
<p>A cleanup block that runs after <code>try</code>/<code>catch</code> regardless of whether an exception was thrown or not. This guarantees resource cleanup even if the <code>try</code> block throws or the <code>catch</code> block re-throws. The <code>finally</code> block cannot change the exception or the return value — it is strictly for side effects like closing filehandles, releasing locks, or logging. If <code>finally</code> itself throws, that exception replaces the original one (avoid throwing in finally). <code>finally</code> is optional — you can use <code>try</code>/<code>catch</code> without it.</p>
<pre><code class="lang-perl">my $fh
try {
open $fh, '<', $path or die $!
process(<$fh>)
} catch ($e) {
log_error("failed: $e")
} finally {
close $fh if $fh # always cleanup
}
</code></pre>
</article>
<article class="doc-entry" id="doc-eval">
<h3><a class="doc-anchor" href="#doc-eval">#</a> <code>eval</code></h3>
<p>The classic Perl exception-catching mechanism. <code>eval { BLOCK }</code> executes the block in an exception-trapping context: if the block throws (via <code>die</code>), execution continues after the <code>eval</code> with the error stored in <code>$@</code>. <code>eval "STRING"</code> compiles and executes Perl code at runtime — powerful but dangerous (code injection risk). In stryke, prefer <code>try</code>/<code>catch</code> for exception handling as it avoids the <code>$@</code> clobbering pitfalls and reads more clearly. <code>eval</code> remains useful for dynamic code evaluation and backward compatibility with Perl 5 idioms.</p>
<pre><code class="lang-perl">eval { die "oops" }
if ($@) { p "caught: $@" }
# Eval string — dynamic code execution
my $expr = "2 + 2"
my $result = eval $expr
p $result # 4
</code></pre>
<p>Caveat: <code>$@</code> can be clobbered by intervening <code>eval</code>s or destructors — <code>try</code>/<code>catch</code> avoids this.</p>
</article>
<article class="doc-entry" id="doc-die">
<h3><a class="doc-anchor" href="#doc-die">#</a> <code>die</code></h3>
<p>Raise an exception, immediately unwinding the call stack until caught by <code>try</code>/<code>catch</code> or <code>eval</code>. The argument can be a string (most common), a reference (hashref for structured errors), or an object. If uncaught, the program terminates and the message is printed to STDERR. In stryke, <code>die</code> works identically to Perl 5 and integrates with <code>try</code>/<code>catch</code>, <code>eval</code>, and the <code>$@</code> mechanism. Convention: end die messages with <code>\n</code> to suppress the automatic "at FILE line LINE" suffix, or omit it to get location info for debugging.</p>
<pre><code class="lang-perl">fn divide($a, $b) {
die "division by zero\n" unless $b
$a / $b
}
# Structured error
die { code => 400, msg => "bad request", field => "email" }
# With automatic location
die "something broke" # prints: something broke at script.pl line 5.
</code></pre>
</article>
<article class="doc-entry" id="doc-warn">
<h3><a class="doc-anchor" href="#doc-warn">#</a> <code>warn</code></h3>
<p>Print a warning message to STDERR without terminating the program. Behaves like <code>die</code> but only emits the message instead of throwing an exception. If the message does not end with <code>\n</code>, Perl appends the current file and line number. Warnings can be intercepted with <code>$SIG{__WARN__}</code> or suppressed with <code>no warnings</code>. In stryke, <code>warn</code> is useful for non-fatal diagnostics; for structured logging, use <code>log_warn</code> instead.</p>
<pre><code class="lang-perl">warn "file not found: $path" unless -e $path
warn "deprecated: use fetch_json instead\n" # no line number
# Intercept warnings
local $SIG{__WARN__} = fn ($msg) { log_warn($msg) }
warn "redirected to logger"
</code></pre>
</article>
<article class="doc-entry" id="doc-croak">
<h3><a class="doc-anchor" href="#doc-croak">#</a> <code>croak</code></h3>
<p>Die from the caller's perspective — the error message reports the file and line of the *caller*, not the function that called <code>croak</code>. This is the right choice for library/module functions where the error is the caller's fault (bad arguments, misuse). Without <code>croak</code>, the user sees an error pointing at library internals, which is unhelpful. In stryke, <code>croak</code> is available as a builtin without <code>use Carp</code>. For debugging deep call chains, use <code>confess</code> instead to get a full stack trace.</p>
<pre><code class="lang-perl">fn parse($s) {
croak "parse: empty input" unless length $s
croak "parse: not JSON" unless $s =~ /^[{\[]/
json_decode($s)
}
# Error will point at the call site, not inside parse()
my $data = parse("") # dies: "parse: empty input at caller.pl line 5"
</code></pre>
</article>
<article class="doc-entry" id="doc-confess">
<h3><a class="doc-anchor" href="#doc-confess">#</a> <code>confess</code></h3>
<p>Die with a full stack trace from the point of the error all the way up through every caller. This is invaluable for debugging deep call chains where <code>die</code> or <code>croak</code> only show one frame. Each frame includes the package, file, and line number. In stryke, <code>confess</code> is available as a builtin without <code>use Carp</code>. Use <code>confess</code> during development for maximum diagnostic info; switch to <code>croak</code> in production-facing libraries where the trace would confuse end users.</p>
<pre><code class="lang-perl">fn validate($data) {
confess "missing required field 'name'" unless $data->{name}
}
fn process($input) { validate($input) }
fn main { process({}) } # full trace: main -> process -> validate
</code></pre>
<p>The trace output shows: <code>missing required field 'name' at script.pl line 2.\n\tmain::validate called at line 4\n\t...</code>.</p>
</article>
</section>
<section class="tutorial-section" id="ch-aop-advice">
<h2>AOP / Advice</h2>
<p class="chapter-meta">7 topics</p>
<article class="doc-entry" id="doc-before">
<h3><a class="doc-anchor" href="#doc-before">#</a> <code>before</code></h3>
<p><code>before "<glob>" { ... }</code> — register advice that runs *before* every call to a sub whose name matches the glob pattern. Inside the body, <code>$INTERCEPT_NAME</code> holds the called sub's name and <code>@INTERCEPT_ARGS</code> holds the args.</p>
<p>The leading keyword only commits to advice parsing when followed by a string literal, so <code>before(...)</code> as a normal sub call still parses normally. Multiple <code>before</code> advices on the same name all fire in registration order. The advice cannot suppress the call (use <code>around</code> for that) and its return value is discarded.</p>
<pre><code class="lang-perl">before "fetch" { warn "calling fetch with @INTERCEPT_ARGS" }
before "log_*" { $log_count++ } # glob: any sub starting with log_
before "*" { trace($INTERCEPT_NAME) } # every sub call
</code></pre>
<p>Bodies are lowered to bytecode and dispatched through the VM (<code>run_block_region</code>), so <code>our $x</code> and other compile-time name resolutions work the same inside advice as outside it. The body's final statement must be an expression (same constraint as <code>map { }</code> block lowering); a literal <code>for</code>/<code>while</code>/<code>if</code> block or a literal <code>return</code> will be rejected at firing time.</p>
</article>
<article class="doc-entry" id="doc-after">
<h3><a class="doc-anchor" href="#doc-after">#</a> <code>after</code></h3>
<p><code>after "<glob>" { ... }</code> — register advice that runs *after* every call to a sub whose name matches the glob pattern. The body sees the call's return in <code>$INTERCEPT_RESULT</code>, the wall-clock duration in <code>$INTERCEPT_MS</code> (millis, float) and <code>$INTERCEPT_US</code> (micros, integer), the called name in <code>$INTERCEPT_NAME</code>, and the args in <code>@INTERCEPT_ARGS</code>.</p>
<p>Multiple <code>after</code> advices on the same name all fire in registration order. The advice's return value is discarded — the call's return is whatever the original sub (or a matching <code>around</code>) produced.</p>
<pre><code class="lang-perl">after "fetch" { warn "fetch returned $INTERCEPT_RESULT in ${INTERCEPT_MS}ms" }
after "*" { log_call($INTERCEPT_NAME, $INTERCEPT_US) }
</code></pre>
</article>
<article class="doc-entry" id="doc-around">
<h3><a class="doc-anchor" href="#doc-around">#</a> <code>around</code></h3>
<p><code>around "<glob>" { ... }</code> — register advice that *wraps* every call to a sub whose name matches the glob pattern. Use <code>proceed()</code> to invoke the original; the around block's evaluated value is the call's return (AspectJ-style).</p>
<p>The first matching <code>around</code> on a given name wraps; later <code>around</code> matches are skipped (mirrors zshrs <code>run_intercepts</code>). If <code>proceed()</code> is not called, the original sub never runs and the around block's value replaces it. The block can transform (<code>proceed() + 100</code>), forward (just <code>proceed()</code>), or replace (omit <code>proceed()</code> and emit a value).</p>
<pre><code class="lang-perl">around "expensive" {
my $cached = cache_get($INTERCEPT_ARGS[0])
return $cached if defined $cached
my $r = proceed()
cache_put($INTERCEPT_ARGS[0], $r)
$r
}
around "flaky" { my $r = eval { proceed() }; $@ ? retry_default() : $r }
</code></pre>
<p>Recursion guard: calling the advised sub from inside its own advice runs the original directly without re-firing advice — no infinite loop.</p>
</article>
<article class="doc-entry" id="doc-proceed">
<h3><a class="doc-anchor" href="#doc-proceed">#</a> <code>proceed</code></h3>
<p><code>proceed()</code> — invoke the original sub with the saved args from inside an <code>around</code> advice block. Returns the original's value. Calling <code>proceed</code> outside an <code>around</code> block is a runtime error.</p>
<p>The re-entrancy guard ensures <code>proceed</code> runs the original directly without re-firing any matching <code>around</code> advice for the same name, so transformation chains can't infinite-loop.</p>
<pre><code class="lang-perl">around "target" {
my $r = proceed()
$r * 2 # double whatever target returned
}
around "target" { proceed() // "default" } # forward, with fallback
</code></pre>
</article>
<article class="doc-entry" id="doc-intercept-list">
<h3><a class="doc-anchor" href="#doc-intercept-list">#</a> <code>intercept_list</code></h3>
<p><code>intercept_list()</code> — return the registered AOP advice as an array of <code>[id, kind, pattern]</code> triples (each element is an arrayref).</p>
<pre><code class="lang-perl">before "foo" { ... }
after "bar*" { ... }
for my $row (intercept_list()) {
my ($id, $kind, $pat) = @$row
p "id=$id kind=$kind pattern=$pat"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-intercept-remove">
<h3><a class="doc-anchor" href="#doc-intercept-remove">#</a> <code>intercept_remove</code></h3>
<p><code>intercept_remove($id)</code> — remove a single AOP advice by its id (from <code>intercept_list</code>). Returns the count removed (0 or 1).</p>
<pre><code class="lang-perl">before "foo" { ... }
my ($id, $kind, $pat) = @{ (intercept_list())[0] }
intercept_remove($id)
p scalar intercept_list() # 0
</code></pre>
</article>
<article class="doc-entry" id="doc-intercept-clear">
<h3><a class="doc-anchor" href="#doc-intercept-clear">#</a> <code>intercept_clear</code></h3>
<p><code>intercept_clear()</code> — drop all registered AOP advice. Returns the count cleared.</p>
<pre><code class="lang-perl">before "a" { ... }
after "b" { ... }
p intercept_clear() # 2
p scalar intercept_list() # 0
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-declarations">
<h2>Declarations</h2>
<p class="chapter-meta">10 topics</p>
<article class="doc-entry" id="doc-my">
<h3><a class="doc-anchor" href="#doc-my">#</a> <code>my</code></h3>
<p>Declare a lexically scoped variable visible only within the enclosing block or file. <code>my</code> is the workhorse of Perl variable declarations — use it for scalars (<code>$</code>), arrays (<code>@</code>), and hashes (<code>%</code>). Variables declared with <code>my</code> are invisible outside their scope, which prevents accidental cross-scope mutation. In stryke, <code>my</code> variables participate in pipe chains and can be destructured in list context. Uninitialized <code>my</code> variables default to <code>undef</code>.</p>
<pre><code class="lang-perl">my $name = "world"
my @nums = 1:5
my %cfg = (debug => 1, verbose => 0)
p "hello $name"
@nums |> grep _ > 2 |> e p$1
Use `my` everywhere unless you specifically need `our` (package global), `local` (dynamic scope), or `state` (persistent).
</code></pre>
</article>
<article class="doc-entry" id="doc-our">
<h3><a class="doc-anchor" href="#doc-our">#</a> <code>our</code></h3>
<p>Declare a package-global variable accessible as a lexical alias in the current scope. Unlike <code>my</code>, <code>our</code> variables are visible across the entire package and can be accessed from other packages via their fully qualified name (e.g. <code>$Counter::total</code>). Useful for package-level configuration, shared counters, or variables that need to survive across file boundaries.</p>
<p>In stryke, <code>our</code> variables are NOT mutex-protected. <strong>Mutating an <code>our</code> variable from inside <code>fan</code>/<code>pmap</code>/<code>pfor</code> is rejected at runtime</strong> with a directive to use <code>oursync</code> (the package-global counterpart of <code>mysync</code> — same <code>Arc<Mutex></code> backing, keyed by <code>Pkg::x</code>).</p>
<pre><code class="lang-perl">package Counter
our $total = 0 # serial use only
fn bump { $total++ }
package main
Counter::bump() for 1:5
p $Counter::total # 5
# For parallel mutation, use oursync:
package C
oursync $shared = 0
fn bump { $shared++ }
package main
fan 10000 { C::bump() } # always exactly 10000
</code></pre>
<p>Prefer <code>my</code> for local state; <code>our</code> for cross-package read-mostly globals; <code>oursync</code> for cross-package mutation under parallelism.</p>
</article>
<article class="doc-entry" id="doc-local">
<h3><a class="doc-anchor" href="#doc-local">#</a> <code>local</code></h3>
<p>Temporarily override a global variable's value for the duration of the current dynamic scope. When the scope exits, the original value is automatically restored. This is essential for modifying Perl's special variables (like <code>$/</code>, <code>$\</code>, <code>$,</code>) without permanently altering global state. Unlike <code>my</code> which creates a new variable, <code>local</code> saves and restores an existing global. In stryke, <code>local</code> works with all special variables and respects the same restoration semantics during exception unwinding.</p>
<pre><code class="lang-perl">local $/ = undef # slurp mode
open my $fh, '<', 'data.txt' or die $!
my $body = <$fh> # reads entire file
close $fh
# $/ restored to "\n" when scope exits
</code></pre>
<p>Common patterns: <code>local $/ = undef</code> (slurp), <code>local $, = ","</code> (join print args), <code>local %ENV</code> (temporary env).</p>
</article>
<article class="doc-entry" id="doc-state">
<h3><a class="doc-anchor" href="#doc-state">#</a> <code>state</code></h3>
<p>Declare a persistent lexical variable that retains its value across calls to the enclosing subroutine. Unlike <code>my</code>, which reinitializes on each call, <code>state</code> initializes only once — the first time execution reaches the declaration — and preserves the value for all subsequent calls. This is perfect for counters, caches, and memoization without resorting to globals or closures over external variables. In stryke, <code>state</code> variables are per-thread when used inside <code>~> { }</code> or <code>fan</code> blocks; they are not shared across workers.</p>
<pre><code class="lang-perl">fn ctr {
state $n = 0
++$n
}
p ctr() for 1:5 # 1 2 3 4 5
fn cache_lookup($x) {
state %cache
$cache{$x} //= expensive($x)
}
</code></pre>
<p>Requires <code>use feature 'state'</code> in standard Perl, but is always available in stryke.</p>
</article>
<article class="doc-entry" id="doc-package">
<h3><a class="doc-anchor" href="#doc-package">#</a> <code>package</code></h3>
<p>Set the current package namespace for all subsequent declarations. Package names are conventionally <code>CamelCase</code> with <code>::</code> separators (e.g. <code>Math::Utils</code>). All unqualified function and <code>our</code> variable names are installed into the current package. In stryke, packages work identically to standard Perl — they provide namespace isolation but are not classes by themselves (use <code>struct</code> or <code>bless</code> for OOP). Switching packages mid-file is allowed but discouraged; prefer one package per file.</p>
<pre><code class="lang-perl">package Math::Utils
fn calc_fact($n) { $n <= 1 ? 1 : $n * calc_fact($n - 1) }
fn calc_fib($n) { $n < 2 ? $n : calc_fib($n - 1) + calc_fib($n - 2) }
package main
p Math::Utils::calc_fact(10) # 3628800
</code></pre>
</article>
<article class="doc-entry" id="doc-use">
<h3><a class="doc-anchor" href="#doc-use">#</a> <code>use</code></h3>
<p>Load and import a user module at compile time: <code>use Module qw(func);</code>. Stryke list utilities (<code>sum</code>, <code>max</code>, <code>uniq</code>, <code>reduce</code>, …), error helpers (<code>croak</code>, <code>confess</code>, <code>carp</code>), and serialization (<code>json_encode</code>, <code>json_decode</code>, <code>ddump</code>) are all native bare-name builtins — no import needed.</p>
<pre><code class="lang-perl">use My::Project::Helpers qw(normalize_path canonicalize)
my @vals = 1:10
p sum(@vals) # 55
p max(@vals) # 10
p normalize_path("/tmp/../etc")
</code></pre>
</article>
<article class="doc-entry" id="doc-no">
<h3><a class="doc-anchor" href="#doc-no">#</a> <code>no</code></h3>
<p>Unimport a module or pragma: <code>no strict 'refs';</code>.</p>
<pre><code class="lang-perl">no warnings 'experimental'
given ($x) { when (1) { p "one" } }
</code></pre>
</article>
<article class="doc-entry" id="doc-require">
<h3><a class="doc-anchor" href="#doc-require">#</a> <code>require</code></h3>
<p>Load a user module at runtime: <code>require Module;</code>. JSON / YAML / TOML decoding is built in (<code>json_decode</code>, <code>yaml_decode</code>, <code>toml_decode</code>) — no module load needed.</p>
<pre><code class="lang-perl">require My::Plugin::Loader
my $loader = My::Plugin::Loader::init()
p $loader->status
# Built-in: no require needed
my $data = json_decode($text)
p $data->{name}
</code></pre>
</article>
<article class="doc-entry" id="doc-begin">
<h3><a class="doc-anchor" href="#doc-begin">#</a> <code>BEGIN</code></h3>
<p><code>BEGIN { }</code> — runs at compile time, before the rest of the program.</p>
<pre><code class="lang-perl">BEGIN { p "compiling..." }
p "running"
# output: compiling... then running
</code></pre>
</article>
<article class="doc-entry" id="doc-end">
<h3><a class="doc-anchor" href="#doc-end">#</a> <code>END</code></h3>
<p><code>END { }</code> — runs after the program finishes (or on exit).</p>
<pre><code class="lang-perl">END { p "cleanup done" }
p "main work"
# output: main work then cleanup done
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-cluster-distributed">
<h2>Cluster / Distributed</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-cluster">
<h3><a class="doc-anchor" href="#doc-cluster">#</a> <code>cluster</code></h3>
<p><code>cluster(["host1:N", "host2:M", ...])</code> — build an SSH-backed worker pool for distributing stryke workloads across multiple machines.</p>
<p>Each entry in the list is a hostname (or <code>user@host</code>) followed by a colon and the number of worker slots to allocate on that host. Under the hood, stryke opens persistent SSH multiplexed connections to each host, deploys lightweight <code>stryke --remote-worker</code> processes, and manages a work-stealing scheduler across the entire cluster. The cluster object is then passed to distributed primitives like <code>pmap_on</code> and <code>pflat_map_on</code>. Workers must have <code>stryke</code> installed and accessible on <code>$PATH</code>. If a host becomes unreachable mid-computation, its in-flight tasks are automatically re-queued to surviving hosts.</p>
<pre><code class="lang-perl">my $cl = cluster(["server1:8", "server2:4", "gpu-box:16"])
my @results = pmap_on $cl, { heavy_compute } @jobs
# Single-machine cluster for testing:
my $local = cluster(["localhost:4"])
</code></pre>
</article>
<article class="doc-entry" id="doc-pmap-on">
<h3><a class="doc-anchor" href="#doc-pmap-on">#</a> <code>pmap_on</code></h3>
<p><code>pmap_on $cluster, { BLOCK } @list</code> — distributed parallel map that fans work across a <code>cluster</code> of remote machines.</p>
<p>Elements from <code>@list</code> are serialized, shipped to remote <code>stryke --remote-worker</code> processes over SSH, executed in parallel across every worker slot in the cluster, and the results are gathered back in input order. This is the distributed equivalent of <code>pmap</code>: same interface, same order guarantee, but the thread pool spans multiple hosts instead of local cores. Use this when a single machine's CPU count is the bottleneck. The block must be self-contained — it cannot close over local file handles or database connections, since it executes in a separate process on a remote host. Large closures are serialized once and cached on each worker for the lifetime of the cluster.</p>
<pre><code class="lang-perl">my $cl = cluster(["host1:8", "host2:8"])
my @hashes = pmap_on $cl, { sha256(slurp) } @file_paths
my @results = pmap_on $cl, { fetch("https://api.example.com/$_") } 1:10_000
</code></pre>
</article>
<article class="doc-entry" id="doc-pflat-map-on">
<h3><a class="doc-anchor" href="#doc-pflat-map-on">#</a> <code>pflat_map_on</code></h3>
<p>Distributed parallel flat-map over <code>cluster</code>.</p>
</article>
<article class="doc-entry" id="doc-ssh">
<h3><a class="doc-anchor" href="#doc-ssh">#</a> <code>ssh</code></h3>
<p><code>ssh($host, $command)</code> — execute a shell command on a remote host via SSH and return its stdout as a string.</p>
<p>This is a simple synchronous wrapper around an SSH invocation. The command is run in the remote user's default shell, and stdout is captured and returned. If the remote command exits non-zero, stryke dies with the stderr output. For bulk remote work, prefer <code>cluster</code> + <code>pmap_on</code> which manages connection pooling and parallelism automatically. <code>ssh</code> is best for one-off administrative commands, health checks, or bootstrapping a remote environment before building a cluster.</p>
<pre><code class="lang-perl">my $uptime = ssh("server1", "uptime")
p ssh("deploy@prod", "cat /etc/hostname")
my $free = ssh("gpu-box", "nvidia-smi --query-gpu=memory.free --format=csv,noheader")
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-datetime">
<h2>Datetime</h2>
<p class="chapter-meta">15 topics</p>
<article class="doc-entry" id="doc-datetime-utc">
<h3><a class="doc-anchor" href="#doc-datetime-utc">#</a> <code>datetime_utc</code></h3>
<p>Return the current UTC date and time as an ISO 8601 string (e.g. <code>2026-04-15T12:30:00Z</code>). This is the simplest way to get a portable, unambiguous timestamp for logging, file naming, or serialization. The returned string always ends with <code>Z</code> indicating UTC, so there is no timezone ambiguity.</p>
<pre><code class="lang-perl">my $now = datetime_utc()
p $now # 2026-04-15T12:30:00Z
af("audit.log", "$now: started\n")
my %event = (ts => datetime_utc(), action => "deploy")
wj("event.json", \%event)
</code></pre>
</article>
<article class="doc-entry" id="doc-datetime-from-epoch">
<h3><a class="doc-anchor" href="#doc-datetime-from-epoch">#</a> <code>datetime_from_epoch</code></h3>
<p>Convert a Unix epoch timestamp (seconds since 1970-01-01 00:00:00 UTC) into an ISO 8601 datetime string. This is useful when you have raw epoch values from <code>time()</code>, file modification times, or external APIs and need a human-readable representation. Fractional seconds are truncated.</p>
<pre><code class="lang-perl">my $ts = 1700000000
p datetime_from_epoch($ts) # 2023-11-14T22:13:20Z
my $born = datetime_from_epoch(0)
p $born # 1970-01-01T00:00:00Z
my @epochs = (1e9, 1.5e9, 2e9)
@epochs |> e { p datetime_from_epoch }
</code></pre>
</article>
<article class="doc-entry" id="doc-datetime-strftime">
<h3><a class="doc-anchor" href="#doc-datetime-strftime">#</a> <code>datetime_strftime</code></h3>
<p>Format an epoch timestamp using a <code>strftime</code>-style format string, giving full control over the output representation. The first argument is the format pattern and the second is the epoch value. Supports all standard specifiers: <code>%Y</code> (4-digit year), <code>%m</code> (month), <code>%d</code> (day), <code>%H</code> (hour), <code>%M</code> (minute), <code>%S</code> (second), <code>%A</code> (weekday name), and more.</p>
<pre><code class="lang-perl">my $t = time()
p datetime_strftime("%Y-%m-%d", $t) # 2026-04-15
p datetime_strftime("%H:%M:%S", $t) # 14:23:07
p datetime_strftime("%A, %B %d", $t) # Wednesday, April 15
my $log_ts = datetime_strftime("%Y%m%d_%H%M%S", $t)
to_file("backup_$log_ts.sql", $data)
</code></pre>
</article>
<article class="doc-entry" id="doc-datetime-now-tz">
<h3><a class="doc-anchor" href="#doc-datetime-now-tz">#</a> <code>datetime_now_tz</code></h3>
<p>Return the current date and time in a specified IANA timezone as a formatted string. Pass a timezone name like <code>America/New_York</code>, <code>Europe/London</code>, or <code>Asia/Tokyo</code>. This avoids manual UTC-offset arithmetic and handles daylight saving transitions correctly. Dies if the timezone name is not recognized.</p>
<pre><code class="lang-perl">p datetime_now_tz("America/New_York") # 2026-04-15 08:30:00 EDT
p datetime_now_tz("Asia/Tokyo") # 2026-04-15 21:30:00 JST
p datetime_now_tz("UTC") # same as datetime_utc
my @offices = ("US/Pacific", "Europe/Berlin", "Asia/Kolkata")
@offices |> e { p "$_: " . datetime_now_tz }
</code></pre>
</article>
<article class="doc-entry" id="doc-datetime-format-tz">
<h3><a class="doc-anchor" href="#doc-datetime-format-tz">#</a> <code>datetime_format_tz</code></h3>
<p>Format an epoch timestamp in a specific IANA timezone, combining the capabilities of <code>datetime_strftime</code> and <code>datetime_now_tz</code>. This lets you render a historical or future timestamp as it would appear on the wall clock in any timezone. Handles DST transitions automatically.</p>
<pre><code class="lang-perl">my $epoch = 1700000000
p datetime_format_tz($epoch, "America/Chicago")
# 2023-11-14 16:13:20 CST
p datetime_format_tz($epoch, "Europe/London")
# 2023-11-14 22:13:20 GMT
p datetime_format_tz(time(), "Australia/Sydney")
</code></pre>
</article>
<article class="doc-entry" id="doc-datetime-parse-local">
<h3><a class="doc-anchor" href="#doc-datetime-parse-local">#</a> <code>datetime_parse_local</code></h3>
<p>Parse a local datetime string (without timezone info) into a Unix epoch timestamp, interpreting it in the system's local timezone. Accepts common formats like <code>2026-04-15 14:30:00</code> or <code>2026-04-15T14:30:00</code>. Dies if the string cannot be parsed. This is the inverse of formatting with <code>localtime</code>.</p>
<pre><code class="lang-perl">my $epoch = datetime_parse_local("2026-04-15 14:30:00")
p $epoch # Unix timestamp
p datetime_from_epoch($epoch) # back to ISO 8601
my $midnight = datetime_parse_local("2026-01-01 00:00:00")
p time() - $midnight # seconds since New Year
</code></pre>
</article>
<article class="doc-entry" id="doc-datetime-parse-rfc3339">
<h3><a class="doc-anchor" href="#doc-datetime-parse-rfc3339">#</a> <code>datetime_parse_rfc3339</code></h3>
<p>Parse an RFC 3339 / ISO 8601 datetime string (with timezone offset or <code>Z</code> suffix) into a Unix epoch timestamp. This is the standard format used by JSON APIs, RSS feeds, and git timestamps. Accepts strings like <code>2026-04-15T14:30:00Z</code> or <code>2026-04-15T14:30:00+05:30</code>. Dies on malformed input.</p>
<pre><code class="lang-perl">my $epoch = datetime_parse_rfc3339("2026-04-15T12:00:00Z")
p $epoch
my $with_tz = datetime_parse_rfc3339("2026-04-15T08:00:00-04:00")
p $epoch == $with_tz # 1 (same instant)
# parse API response timestamps
my $created = $response->{created_at}
my $age = time() - datetime_parse_rfc3339($created)
p "created ${age}s ago"
</code></pre>
</article>
<article class="doc-entry" id="doc-datetime-add-seconds">
<h3><a class="doc-anchor" href="#doc-datetime-add-seconds">#</a> <code>datetime_add_seconds</code></h3>
<p>Add (or subtract) a number of seconds to an ISO 8601 datetime string and return the resulting ISO 8601 string. This performs calendar-aware arithmetic, correctly crossing day, month, and year boundaries. Pass a negative number to subtract time. Useful for computing deadlines, expiration times, or time windows.</p>
<pre><code class="lang-perl">my $now = datetime_utc()
my $later = datetime_add_seconds($now, 3600) # +1 hour
p $later
my $yesterday = datetime_add_seconds($now, -86400) # -1 day
p $yesterday
my $deadline = datetime_add_seconds($now, 7 * 86400) # +1 week
p "due by $deadline"
</code></pre>
</article>
<article class="doc-entry" id="doc-elapsed">
<h3><a class="doc-anchor" href="#doc-elapsed">#</a> <code>elapsed</code></h3>
<p>Return the number of seconds elapsed since the stryke process started, using a monotonic clock that is immune to system clock adjustments. The short alias <code>el</code> keeps benchmarking one-liners terse. Returns a floating-point value with sub-millisecond precision. Useful for timing operations, profiling hot loops, or adding relative timestamps to log output.</p>
<pre><code class="lang-perl">my $t0 = el()
my @sorted = sort @big_array
my $dur = el() - $t0
p "sort took ${dur}s"
# progress logging
1:100 |> e { do_work
log_info("step $_ at " . el() . "s") }
</code></pre>
</article>
<article class="doc-entry" id="doc-time">
<h3><a class="doc-anchor" href="#doc-time">#</a> <code>time</code></h3>
<p>Return the current Unix epoch as an integer — the number of seconds since 1970-01-01 00:00:00 UTC. This is the standard wall-clock timestamp used for file times, database records, and interop with external systems. For monotonic timing of code sections, prefer <code>elapsed</code>/<code>el</code> instead since <code>time</code> can jump if the system clock is adjusted.</p>
<pre><code class="lang-perl">my $start = time()
sleep(2)
p time() - $start # ~2
my $ts = time()
wj("stamp.json", { created => $ts })
p datetime_from_epoch($ts) # human-readable form
</code></pre>
</article>
<article class="doc-entry" id="doc-times">
<h3><a class="doc-anchor" href="#doc-times">#</a> <code>times</code></h3>
<p>Return the accumulated CPU times for the process as a four-element list: <code>($user, $system, $child_user, $child_system)</code>. User time is CPU spent executing your code; system time is CPU spent in kernel calls on your behalf. Child times cover subprocesses. Values are in seconds (floating point). Useful for profiling whether a script is CPU-bound or I/O-bound.</p>
<pre><code class="lang-perl">my ($u, $s, $cu, $cs) = times()
p "user=${u}s sys=${s}s"
# after heavy computation
my ($u2, $s2) = times()
p "used " . ($u2 - $u) . "s of CPU"
p "total CPU: " . ($u2 + $s2) . "s"
</code></pre>
</article>
<article class="doc-entry" id="doc-localtime">
<h3><a class="doc-anchor" href="#doc-localtime">#</a> <code>localtime</code></h3>
<p>Convert a Unix epoch timestamp to a nine-element list of broken-down local time components: <code>($sec, $min, $hour, $mday, $mon, $year, $wday, $yday, $isdst)</code>. Follows the Perl convention where <code>$mon</code> is 0-based (January=0) and <code>$year</code> is years since 1900. When called without arguments, uses the current time. Use <code>gmtime</code> for the UTC equivalent.</p>
<pre><code class="lang-perl">my @t = localtime(time())
p "$t[2]:$t[1]:$t[0]" # HH:MM:SS
my $year = $t[5] + 1900
my $mon = $t[4] + 1
p "$year-$mon-$t[3]" # YYYY-M-D
my @days = qw(Sun Mon Tue Wed Thu Fri Sat)
p $days[$t[6]] # day of week
</code></pre>
</article>
<article class="doc-entry" id="doc-gmtime">
<h3><a class="doc-anchor" href="#doc-gmtime">#</a> <code>gmtime</code></h3>
<p>Convert a Unix epoch timestamp to a nine-element list of broken-down UTC time components, identical in structure to <code>localtime</code> but always in the UTC timezone. The fields are <code>($sec, $min, $hour, $mday, $mon, $year, $wday, $yday, $isdst)</code> where <code>$isdst</code> is always 0. When called without arguments, uses the current time.</p>
<pre><code class="lang-perl">my @utc = gmtime(time())
my $year = $utc[5] + 1900
my $mon = $utc[4] + 1
p sprintf("%04d-%02d-%02dT%02d:%02d:%02dZ",
$year, $mon, @utc[3,2,1,0])
# compare local vs UTC
my @loc = localtime(time())
p "UTC hour=$utc[2] local hour=$loc[2]"
</code></pre>
</article>
<article class="doc-entry" id="doc-sleep">
<h3><a class="doc-anchor" href="#doc-sleep">#</a> <code>sleep</code></h3>
<p>Pause execution for the specified number of seconds. Accepts both integer and fractional values for sub-second sleeps (e.g. <code>sleep 0.1</code> for 100ms). The process yields the CPU during the sleep, so it is safe to use in polling loops without burning cycles. Returns the unslept time (always 0 unless interrupted by a signal).</p>
<pre><code class="lang-perl">p "waiting..."
sleep(2)
p "done"
# polling loop
while (!-e "done.flag") {
sleep(0.5)
}
# rate limiting
my @urls = @targets
@urls |> e { fetch
sleep(0.1) }
</code></pre>
</article>
<article class="doc-entry" id="doc-alarm">
<h3><a class="doc-anchor" href="#doc-alarm">#</a> <code>alarm</code></h3>
<p>Schedule a <code>SIGALRM</code> signal to be delivered to the process after the specified number of seconds. Calling <code>alarm(0)</code> cancels any pending alarm. Only one alarm can be active at a time — setting a new alarm replaces the previous one. Returns the number of seconds remaining on the previous alarm (or 0 if none was set). Combine with <code>eval</code> and <code>$SIG{ALRM}</code> to implement timeouts around potentially hanging operations.</p>
<pre><code class="lang-perl">eval {
local $SIG{ALRM} = fn { die "timeout\n" }
alarm(5) # 5 second deadline
my $data = slow_network_call()
alarm(0) # cancel on success
}
if ($@ =~ /timeout/) {
log_error("operation timed out")
}
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-math">
<h2>Math</h2>
<p class="chapter-meta">13 topics</p>
<article class="doc-entry" id="doc-abs">
<h3><a class="doc-anchor" href="#doc-abs">#</a> <code>abs</code></h3>
<p>Return the absolute value of a number, stripping any negative sign. Returns the argument unchanged if it is already non-negative. Works on both integers and floating-point numbers.</p>
<pre><code class="lang-perl">p abs(-42) # 42
p abs(3.14) # 3.14
my $diff = abs($a - $b)
p "distance: $diff"
1:5 |> map { _ - 3 } |> map abs |> e p # 2 1 0 1 2
</code></pre>
</article>
<article class="doc-entry" id="doc-int">
<h3><a class="doc-anchor" href="#doc-int">#</a> <code>int</code></h3>
<p>Truncate a floating-point number toward zero, discarding the fractional part. This is not rounding — <code>int(1.9)</code> is <code>1</code> and <code>int(-1.9)</code> is <code>-1</code>. Use <code>sprintf("%.0f", $n)</code> or <code>POSIX::round</code> for proper rounding. Commonly paired with <code>rand</code> to generate random integers.</p>
<pre><code class="lang-perl">p int(3.7) # 3
p int(-3.7) # -3
p int(rand(6)) + 1 # dice roll 1:6
1:10 |> map { _ / 3 } |> map int |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-sqrt">
<h3><a class="doc-anchor" href="#doc-sqrt">#</a> <code>sqrt</code></h3>
<p>Return the square root of a non-negative number. Dies if the argument is negative — use <code>abs</code> first or check the sign. For the inverse operation, use <code>squared</code>/<code>sq</code> or the <code>**</code> operator.</p>
<pre><code class="lang-perl">p sqrt(144) # 12
p sqrt(2) # 1.41421356...
my $hyp = sqrt($a**2 + $b**2) # Pythagorean theorem
1:5 |> map sqrt |> e { p sprintf("%.3f", _) }
</code></pre>
</article>
<article class="doc-entry" id="doc-squared">
<h3><a class="doc-anchor" href="#doc-squared">#</a> <code>squared</code></h3>
<p>Return the square of a number (<code>N * N</code>). This is a stryke convenience function — clearer than writing <code>$n ** 2</code> or <code>$n * $n</code> in pipelines. The aliases <code>sq</code> and <code>square</code> are interchangeable.</p>
<pre><code class="lang-perl">p squared(5) # 25
p sq(12) # 144
1:5 |> map sq |> e p # 1 4 9 16 25
my $hyp = sqrt(sq($a) + sq($b)) # Pythagorean theorem
</code></pre>
</article>
<article class="doc-entry" id="doc-cubed">
<h3><a class="doc-anchor" href="#doc-cubed">#</a> <code>cubed</code></h3>
<p>Return the cube of a number (<code>N * N * N</code>). This is a stryke convenience function for the common <code>$n ** 3</code> operation, useful in math-heavy pipelines. The aliases <code>cb</code> and <code>cube</code> are interchangeable.</p>
<pre><code class="lang-perl">p cubed(3) # 27
p cb(10) # 1000
1:4 |> map cb |> e p # 1 8 27 64
my $vol = cb($side) # volume of a cube
</code></pre>
</article>
<article class="doc-entry" id="doc-expt">
<h3><a class="doc-anchor" href="#doc-expt">#</a> <code>expt</code></h3>
<p>Raise a base to an arbitrary exponent and return the result. This is the function form of the <code>**</code> operator. Accepts integer and floating-point exponents, including negative values for reciprocals and fractional values for roots.</p>
<pre><code class="lang-perl">p expt(2, 10) # 1024
p expt(27, 1/3) # 3.0 (cube root)
p expt(10, -2) # 0.01
1:8 |> map { expt(2, _) } |> e p # 2 4 8 16 32 64 128 256
</code></pre>
</article>
<article class="doc-entry" id="doc-exp">
<h3><a class="doc-anchor" href="#doc-exp">#</a> <code>exp</code></h3>
<p>Return Euler's number *e* raised to the given power. <code>exp(0)</code> is <code>1</code>, <code>exp(1)</code> is approximately <code>2.71828</code>. This is the inverse of <code>log</code>. Useful for exponential growth/decay calculations, probability distributions, and converting between logarithmic and linear scales.</p>
<pre><code class="lang-perl">p exp(1) # 2.71828182845905
p exp(0) # 1
my $growth = $initial * exp($rate * $time)
1:5 |> map exp |> e { p sprintf("%.4f", _) }
</code></pre>
</article>
<article class="doc-entry" id="doc-log">
<h3><a class="doc-anchor" href="#doc-log">#</a> <code>log</code></h3>
<p>Return the natural (base-*e*) logarithm of a positive number. Dies if the argument is zero or negative. For base-10 logarithms, divide by <code>log(10)</code>. For base-2, divide by <code>log(2)</code>. This is the inverse of <code>exp</code>.</p>
<pre><code class="lang-perl">p log(exp(1)) # 1.0
p log(100) / log(10) # 2.0 (log base 10)
my $bits = log($n) / log(2) # log base 2
1:5 |> map log |> e { p sprintf("%.3f", _) }
</code></pre>
</article>
<article class="doc-entry" id="doc-sin">
<h3><a class="doc-anchor" href="#doc-sin">#</a> <code>sin</code></h3>
<p>Return the sine of an angle given in radians. The result ranges from <code>-1</code> to <code>1</code>. For degrees, convert first: <code>sin($deg * 3.14159265 / 180)</code>. Use <code>atan2</code> to go in the reverse direction.</p>
<pre><code class="lang-perl">p sin(0) # 0
p sin(3.14159265 / 2) # 1.0
my @wave = map { sin(_ * 0.1) } 0:62
@wave |> e { p sprintf("%6.3f", _) }
</code></pre>
</article>
<article class="doc-entry" id="doc-cos">
<h3><a class="doc-anchor" href="#doc-cos">#</a> <code>cos</code></h3>
<p>Return the cosine of an angle given in radians. The result ranges from <code>-1</code> to <code>1</code>. <code>cos(0)</code> is <code>1</code>. Like <code>sin</code>, convert degrees to radians before calling.</p>
<pre><code class="lang-perl">p cos(0) # 1
p cos(3.14159265) # -1.0
my $x = $radius * cos($theta)
my $y = $radius * sin($theta)
p "($x, $y)"
</code></pre>
</article>
<article class="doc-entry" id="doc-atan2">
<h3><a class="doc-anchor" href="#doc-atan2">#</a> <code>atan2</code></h3>
<p>Return the arctangent of <code>Y/X</code> in radians, using the signs of both arguments to determine the correct quadrant. The result ranges from <code>-pi</code> to <code>pi</code>. This is the standard way to compute angles from Cartesian coordinates and is more robust than <code>atan(Y/X)</code> because it handles <code>X=0</code> correctly.</p>
<pre><code class="lang-perl">my $pi = atan2(0, -1) # 3.14159265...
p atan2(1, 1) # 0.785... (pi/4)
my $angle = atan2($dy, $dx)
p sprintf("%.1f degrees", $angle * 180 / $pi)
</code></pre>
</article>
<article class="doc-entry" id="doc-rand">
<h3><a class="doc-anchor" href="#doc-rand">#</a> <code>rand</code></h3>
<p>Return a pseudo-random floating-point number in the range <code>[0, N)</code>. If N is omitted it defaults to <code>1</code>. The result is never exactly equal to N. For integer results, combine with <code>int</code>. Seed the generator with <code>srand</code> for reproducible sequences.</p>
<pre><code class="lang-perl">p rand() # e.g. 0.7342...
p int(rand(100)) # random int 0:99
my @deck = 1:52
my @shuffled = sort { rand() <=> rand() } @deck # poor shuffle
my $coin = rand() < 0.5 ? "heads" : "tails"
p $coin
</code></pre>
</article>
<article class="doc-entry" id="doc-srand">
<h3><a class="doc-anchor" href="#doc-srand">#</a> <code>srand</code></h3>
<p>Seed the pseudo-random number generator used by <code>rand</code>. Calling <code>srand</code> with a specific value produces a reproducible sequence, which is useful for testing. Without arguments, Perl seeds from a platform-specific entropy source. You rarely need to call this explicitly — Perl auto-seeds on first use of <code>rand</code>.</p>
<pre><code class="lang-perl">srand(42) # reproducible sequence
p int(rand(100)) # always the same value
srand(42)
p int(rand(100)) # same value again
srand() # re-seed from entropy
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-file-system">
<h2>File System</h2>
<p class="chapter-meta">34 topics</p>
<article class="doc-entry" id="doc-basename">
<h3><a class="doc-anchor" href="#doc-basename">#</a> <code>basename</code></h3>
<p>Extract the filename component from a path, stripping all leading directory segments. The short alias <code>bn</code> keeps one-liner pipelines terse. If an optional suffix argument is provided, that suffix is also stripped from the result, which is handy for removing extensions.</p>
<pre><code class="lang-perl">p basename("/usr/local/bin/stryke") # stryke
p bn("/tmp/data.csv", ".csv") # data
"/etc/nginx/nginx.conf" |> bn |> p # nginx.conf
</code></pre>
</article>
<article class="doc-entry" id="doc-dirname">
<h3><a class="doc-anchor" href="#doc-dirname">#</a> <code>dirname</code></h3>
<p>Return the directory portion of a path, stripping the final filename component. The short alias <code>dn</code> mirrors <code>bn</code>. This is a pure string operation — it does not touch the filesystem, so it works on paths that do not exist yet. Useful for deriving output directories from input file paths.</p>
<pre><code class="lang-perl">p dirname("/usr/local/bin/stryke") # /usr/local/bin
p dn("/tmp/data.csv") # /tmp
my $dir = dn($0) # directory of current script
</code></pre>
</article>
<article class="doc-entry" id="doc-fileparse">
<h3><a class="doc-anchor" href="#doc-fileparse">#</a> <code>fileparse</code></h3>
<p>Split a path into its three logical components: the filename, the directory prefix, and a suffix that matches one of the supplied patterns. This mirrors Perl's <code>File::Basename::fileparse</code> and is the most flexible path decomposition available. When no suffix patterns are given the suffix is empty.</p>
<pre><code class="lang-perl">my ($name, $dir, $sfx) = fileparse("/home/user/report.txt", qr/\.txt/)
p "$dir | $name | $sfx" # /home/user/ | report | .txt
my ($n, $d) = fileparse("./lib/Foo/Bar.pm")
p "$d$n" # ./lib/Foo/Bar.pm
</code></pre>
</article>
<article class="doc-entry" id="doc-realpath">
<h3><a class="doc-anchor" href="#doc-realpath">#</a> <code>realpath</code></h3>
<p>Resolve a path to its absolute canonical form by following all symbolic links and eliminating <code>.</code> and <code>..</code> segments. Unlike <code>canonpath</code>, this hits the filesystem and will die if any component does not exist. The short alias <code>rp</code> is convenient in pipelines. Use this when you need a guaranteed unique path for deduplication or comparison.</p>
<pre><code class="lang-perl">p realpath(".") # /home/user/project
p rp("../sibling") # /home/user/sibling
my $canon = rp($0) # absolute path of current script
"." |> rp |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-canonpath">
<h3><a class="doc-anchor" href="#doc-canonpath">#</a> <code>canonpath</code></h3>
<p>Clean up a file path by collapsing redundant separators, resolving <code>.</code> and <code>..</code> segments, and normalizing trailing slashes — all without touching the filesystem. Unlike <code>realpath</code>, this is a purely lexical operation so it works on paths that do not exist. Use it to normalize user-supplied paths before comparison or storage.</p>
<pre><code class="lang-perl">p canonpath("/usr/./local/../local/bin/") # /usr/local/bin
p canonpath("a/b/../c") # a/c
my $clean = canonpath($ENV{HOME} . "/./docs/../docs")
p $clean
</code></pre>
</article>
<article class="doc-entry" id="doc-getcwd">
<h3><a class="doc-anchor" href="#doc-getcwd">#</a> <code>getcwd</code></h3>
<p>Return the current working directory as an absolute path string. This calls the underlying OS <code>getcwd</code> function, so it always reflects the real directory even if the process changed directories via <code>chdir</code>. The alias <code>pwd</code> matches the familiar shell command. Often used to save and restore directory context around <code>chdir</code> calls.</p>
<pre><code class="lang-perl">my $orig = pwd()
chdir("/tmp")
p pwd() # /tmp
chdir($orig)
p getcwd() # back to original
</code></pre>
</article>
<article class="doc-entry" id="doc-which">
<h3><a class="doc-anchor" href="#doc-which">#</a> <code>which</code></h3>
<p>Search the <code>PATH</code> environment variable for the first executable matching the given command name and return its absolute path, or <code>undef</code> if not found. This is the programmatic equivalent of the shell <code>which</code> command. Useful for checking tool availability before calling <code>system</code> or <code>exec</code>.</p>
<pre><code class="lang-perl">my $gcc = which("gcc") // die "gcc not found"
p $gcc # /usr/bin/gcc
if (which("rg")) {
system("rg pattern file")
} else {
system("grep pattern file")
}
</code></pre>
</article>
<article class="doc-entry" id="doc-glob">
<h3><a class="doc-anchor" href="#doc-glob">#</a> <code>glob</code></h3>
<p>Expand a zsh-style glob pattern against the filesystem and return a list of matching paths. World-first: stryke supports <strong>every</strong> zsh glob qualifier from <code>man zshexpn</code> _Filename Generation > Glob Qualifiers_ (no other scripting language does this). Backed by <code>zsh::glob</code> from zshrs — single source of truth, zero stryke-side reimplementation. Patterns: <code>*</code>, <code>?</code>, <code>[abc]</code>, <code>{a,b}</code>, <code>**</code> recursive, plus the <code>(...)</code> qualifier suffix.</p>
<h4>Qualifier reference (full set)</h4>
<p><strong>File type:</strong> <code>(/)</code> dir · <code>(.)</code> regular file · <code>(@)</code> symlink · <code>(=)</code> socket · <code>(p)</code> FIFO · <code>(%b)</code> block dev · <code>(%c)</code> char dev · <code>(%)</code> any device · <code>(*)</code> executable file.</p>
<p><strong>Permission:</strong> <code>(r)</code> <code>(w)</code> <code>(x)</code> EUID r/w/x · <code>(R)</code> <code>(W)</code> <code>(X)</code> world · <code>(A)</code> <code>(I)</code> <code>(E)</code> group · <code>(s)</code> setuid · <code>(S)</code> setgid · <code>(t)</code> sticky · <code>(f<bits>)</code> exact mode-bit match (e.g. <code>(f644)</code>).</p>
<p><strong>Ownership / device:</strong> <code>(U)</code> owned by EUID · <code>(G)</code> owned by EGID · <code>(u<N>)</code> uid N · <code>(g<N>)</code> gid N · <code>(d<N>)</code> match by device number.</p>
<p><strong>Numeric</strong> (each accepts <code>+N</code> greater, <code>-N</code> less, <code>N</code> equal): <code>(L[unit]±N)</code> size — <code>p</code>/<code>k</code>/<code>m</code>/<code>g</code>/<code>t</code> units, default bytes · <code>(l±N)</code> link count · <code>(a[unit]±N)</code> atime · <code>(m[unit]±N)</code> mtime · <code>(c[unit]±N)</code> ctime — time units <code>s</code>/<code>m</code>/<code>h</code>/<code>d</code>/<code>w</code>/<code>M</code>.</p>
<p><strong>Sort:</strong> <code>(on)</code> <code>(oL)</code> <code>(ol)</code> <code>(oa)</code> <code>(om)</code> <code>(oc)</code> <code>(od)</code> ascending; capital <code>O*</code> descending; <code>(oN)</code> no sort.</p>
<p><strong>Selection:</strong> <code>([N])</code> Nth match · <code>([N,M])</code> slice. Combine with sort: <code>(om[1])</code> newest single match.</p>
<p><strong>Flags:</strong> <code>(N)</code> NULL_GLOB — empty list on no match · <code>(D)</code> include dotfiles · <code>(F)</code> non-empty directory · <code>(M)</code> mark-dirs (append <code>/</code>) · <code>(T)</code> list-types (append type char) · <code>(n)</code> numeric sort.</p>
<p><strong>Eval / functions:</strong> <code>(e'CMD')</code> shell-eval predicate · <code>(+func)</code> function-as-test (predicate sub).</p>
<p><strong>Join words:</strong> <code>(P…)</code> prefix words · <code>(Q…)</code> postfix words around each match.</p>
<p><strong>Colon modifiers:</strong> <code>(:s/PAT/REPL/)</code> sed substitution on each path · <code>(:e)</code> extension · <code>(:r)</code> strip extension · <code>(:t)</code> tail · <code>(:h)</code> head · all of zsh's history-style modifiers.</p>
<p><strong>Combinators:</strong> prefix <code>^</code> negates · prefix <code>-</code> toggles symlink-following · <code>,</code> separates OR alternatives · chained qualifiers AND.</p>
<pre><code class="lang-perl">my @scripts = glob("*.pl")
my @all_rs = glob("src/**/*.rs")
my @dirs = glob("**(/)") # directories only, recursive
my @big = glob("**(L+1024)") # files larger than 1024 bytes
my @recent = glob("**(om[1])") # most recently modified, take 1
my @safe = glob("missing*(N)") # null-glob, never errors
my @mode = glob("**(f644)") # files with exactly mode 644
my @stems = glob("*.txt(:r)") # all .txt files, extension stripped
</code></pre>
</article>
<article class="doc-entry" id="doc-glob-match">
<h3><a class="doc-anchor" href="#doc-glob-match">#</a> <code>glob_match</code></h3>
<p>Test whether a string matches a shell-style glob pattern. Returns true (1) on match, false (empty string) otherwise. Supports <code>*</code>, <code>?</code>, <code>[abc]</code>, and <code>{a,b}</code>. This is a pure string match — it does not read the filesystem, so it works for filtering lists of paths you already have. Note: zsh glob qualifiers like <code>(/)</code> or <code>(.)</code> are stat-based filters that only apply at filesystem-expansion time (<code>glob</code>/<code>glob_par</code>/<code>slurp</code>); <code>glob_match</code> ignores any trailing qualifier.</p>
<pre><code class="lang-perl">p glob_match("*.pl", "script.pl") # 1
p glob_match("*.pl", "script.py") # (empty)
my @perl = grep { glob_match("*.{pl,pm}", _) } @files
@perl |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-copy">
<h3><a class="doc-anchor" href="#doc-copy">#</a> <code>copy</code></h3>
<p>Copy a file from a source path to a destination path. The destination can be a file path or a directory (in which case the source filename is preserved). Dies on failure. This is the programmatic equivalent of <code>cp</code> and avoids shelling out. Metadata such as permissions is preserved where possible.</p>
<pre><code class="lang-perl">copy("src/config.yaml", "/tmp/config.yaml")
copy("report.pdf", "/backup/")
my $tmp = tf()
copy($0, $tmp) # back up the current script
p slurp($tmp)
</code></pre>
</article>
<article class="doc-entry" id="doc-move">
<h3><a class="doc-anchor" href="#doc-move">#</a> <code>move</code></h3>
<p>Move or rename a file from source to destination. If the source and destination are on the same filesystem this is an atomic rename; otherwise it falls back to copy-then-delete. Dies on failure. The short alias <code>mv</code> mirrors the shell command.</p>
<pre><code class="lang-perl">move("draft.txt", "final.txt") # rename in place
mv("output.csv", "/archive/output.csv") # move across dirs
my $tmp = tf()
spurt($tmp, "data")
mv($tmp, "data.txt")
</code></pre>
</article>
<article class="doc-entry" id="doc-rename">
<h3><a class="doc-anchor" href="#doc-rename">#</a> <code>rename</code></h3>
<p>Rename a file or directory from an old name to a new name. This is an atomic operation on the same filesystem. If the destination already exists it is silently replaced. Dies on failure. Unlike <code>move</code>/<code>mv</code>, this does not fall back to copy-then-delete across filesystems.</p>
<pre><code class="lang-perl">rename("draft.md", "final.md")
rename("output", "output_v2") # works on dirs too
my $bak = "config.yaml.bak"
rename("config.yaml", $bak)
spurt("config.yaml", $new_config)
</code></pre>
</article>
<article class="doc-entry" id="doc-unlink">
<h3><a class="doc-anchor" href="#doc-unlink">#</a> <code>unlink</code></h3>
<p>Delete one or more files from the filesystem. Returns the number of files successfully removed. Does not remove directories — use <code>rmdir</code> for those. Dies on permission errors. Accepts a list of paths, making it convenient for batch cleanup.</p>
<pre><code class="lang-perl">unlink("temp.log")
my $n = unlink("a.tmp", "b.tmp", "c.tmp")
p "removed $n files"
my @old = glob("*.bak")
unlink(@old)
</code></pre>
</article>
<article class="doc-entry" id="doc-mkdir">
<h3><a class="doc-anchor" href="#doc-mkdir">#</a> <code>mkdir</code></h3>
<p>Create a directory at the given path. An optional second argument specifies the permission mode as an octal number (default <code>0777</code>, modified by the current <code>umask</code>). Dies if the directory cannot be created. Only creates one level — use <code>make_path</code> or shell out for recursive creation.</p>
<pre><code class="lang-perl">mkdir("output")
mkdir("/tmp/secure", 0700)
my $dir = tdr() . "/sub"
mkdir($dir)
p -d $dir # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-rmdir">
<h3><a class="doc-anchor" href="#doc-rmdir">#</a> <code>rmdir</code></h3>
<p>Remove an empty directory. Dies if the directory does not exist, is not empty, or cannot be removed due to permissions. This only removes a single directory — it will not recursively delete contents. Remove files with <code>unlink</code> first, then call <code>rmdir</code>.</p>
<pre><code class="lang-perl">mkdir("scratch")
rmdir("scratch")
p -d "scratch" # (empty, dir is gone)
unlink("tmp/file.txt")
rmdir("tmp")
</code></pre>
</article>
<article class="doc-entry" id="doc-chmod">
<h3><a class="doc-anchor" href="#doc-chmod">#</a> <code>chmod</code></h3>
<p>Change the permission bits of one or more files. The mode is specified as an octal number. Returns the number of files successfully changed. Does not follow symlinks on some platforms. Use <code>stat</code> to read the current mode before modifying.</p>
<pre><code class="lang-perl">chmod(0755, "script.pl")
chmod(0644, "config.yaml", "data.json")
my $n = chmod(0600, glob("*.key"))
p "secured $n key files"
</code></pre>
</article>
<article class="doc-entry" id="doc-chown">
<h3><a class="doc-anchor" href="#doc-chown">#</a> <code>chown</code></h3>
<p>Change the owner and group of one or more files, specified as numeric UID and GID. Pass <code>-1</code> for either to leave it unchanged. Returns the number of files successfully changed. Typically requires root privileges.</p>
<pre><code class="lang-perl">chown(1000, 1000, "app.log")
chown(-1, 100, "shared.txt") # change group only
my $uid = (getpwnam("deploy"))[2]
chown($uid, -1, "release.tar")
</code></pre>
</article>
<article class="doc-entry" id="doc-chdir">
<h3><a class="doc-anchor" href="#doc-chdir">#</a> <code>chdir</code></h3>
<p>Change the current working directory of the process. Dies if the directory does not exist or is not accessible. This affects all subsequent relative path operations. Pair with <code>getcwd</code>/<code>pwd</code> to save and restore the original directory.</p>
<pre><code class="lang-perl">my $orig = pwd()
chdir("/tmp")
spurt("scratch.txt", "hello")
chdir($orig) # return to original
</code></pre>
</article>
<article class="doc-entry" id="doc-stat">
<h3><a class="doc-anchor" href="#doc-stat">#</a> <code>stat</code></h3>
<p>Return a 13-element list of file status information for a path or filehandle: <code>($dev, $ino, $mode, $nlink, $uid, $gid, $rdev, $size, $atime, $mtime, $ctime, $blksize, $blocks)</code>. This calls the POSIX <code>stat</code> system call. Use it to check file size, modification time, permissions, and other metadata without reading the file.</p>
<pre><code class="lang-perl">my @st = stat("data.bin")
p "size: $st[7] bytes"
p "modified: " . datetime_from_epoch($st[9])
my ($mode) = (stat($0))[2]
p sprintf("perms: %04o", $mode & 07777)
</code></pre>
</article>
<article class="doc-entry" id="doc-link">
<h3><a class="doc-anchor" href="#doc-link">#</a> <code>link</code></h3>
<p>Create a hard link — a new directory entry pointing to the same underlying inode as the original file. Both names are indistinguishable and share the same data; removing one does not affect the other. Hard links cannot cross filesystem boundaries and typically cannot link directories.</p>
<pre><code class="lang-perl">link("data.csv", "data_backup.csv")
my @st1 = stat("data.csv")
my @st2 = stat("data_backup.csv")
p $st1[1] == $st2[1] # 1 — same inode
</code></pre>
</article>
<article class="doc-entry" id="doc-symlink">
<h3><a class="doc-anchor" href="#doc-symlink">#</a> <code>symlink</code></h3>
<p>Create a symbolic (soft) link that points to a target path. Unlike hard links, symlinks can cross filesystems and can point to directories. The link stores the target as a string, so it can dangle if the target is later removed. Use <code>readlink</code> to inspect where a symlink points.</p>
<pre><code class="lang-perl">symlink("/usr/local/bin/stryke", "pe_link")
p readlink("pe_link") # /usr/local/bin/stryke
p -l "pe_link" # 1 (is a symlink)
symlink("../lib", "lib_link") # relative target
</code></pre>
</article>
<article class="doc-entry" id="doc-readlink">
<h3><a class="doc-anchor" href="#doc-readlink">#</a> <code>readlink</code></h3>
<p>Return the target path that a symbolic link points to, without following the link further. Returns <code>undef</code> if the path is not a symlink. This is useful for inspecting symlink chains, verifying link targets, or resolving one level of indirection at a time.</p>
<pre><code class="lang-perl">symlink("real.conf", "link.conf")
my $target = readlink("link.conf")
p $target # real.conf
if (defined readlink($path)) {
p "$path is a symlink"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-utime">
<h3><a class="doc-anchor" href="#doc-utime">#</a> <code>utime</code></h3>
<p>Set the access time and modification time of one or more files. Times are specified as epoch seconds. Pass <code>undef</code> for either time to set it to the current time. Returns the number of files successfully updated. Useful for cache invalidation, build systems, or preserving timestamps after transformations.</p>
<pre><code class="lang-perl">utime(time(), time(), "output.txt") # touch to now
my $epoch = 1700000000
utime($epoch, $epoch, @files) # backdate files
utime(undef, undef, "marker.flag") # equivalent of touch
</code></pre>
</article>
<article class="doc-entry" id="doc-umask">
<h3><a class="doc-anchor" href="#doc-umask">#</a> <code>umask</code></h3>
<p>Get or set the file creation mask, which controls the default permissions for newly created files and directories. When called with an argument, sets the new mask and returns the previous one. When called without arguments, returns the current mask. The mask is subtracted from the requested permissions in <code>mkdir</code>, <code>open</code>, etc.</p>
<pre><code class="lang-perl">my $old = umask(0077) # restrict: owner-only
mkdir("private") # created with 0700
umask($old) # restore previous mask
p sprintf("%04o", umask()) # print current mask
</code></pre>
</article>
<article class="doc-entry" id="doc-uname">
<h3><a class="doc-anchor" href="#doc-uname">#</a> <code>uname</code></h3>
<p>Return system identification as a five-element list: <code>($sysname, $nodename, $release, $version, $machine)</code>. This calls the POSIX <code>uname</code> system call and is useful for platform-specific logic, logging system info, or generating diagnostic reports without shelling out.</p>
<pre><code class="lang-perl">my ($sys, $node, $rel, $ver, $arch) = uname()
p "$sys $rel ($arch)" # Linux 6.1.0 (x86_64)
if ($sys eq "Darwin") {
p "running on macOS"
}
log_info("host: $node, kernel: $rel")
</code></pre>
</article>
<article class="doc-entry" id="doc-gethostname">
<h3><a class="doc-anchor" href="#doc-gethostname">#</a> <code>gethostname</code></h3>
<p>Return the hostname of the current machine as a string. This calls the POSIX <code>gethostname</code> system call. The short alias <code>hn</code> is useful in log prefixes, temp-file naming, or distributed-system identifiers where you need to tag output by machine.</p>
<pre><code class="lang-perl">p gethostname() # myhost.local
my $log_prefix = hn() . ":" . $$ # myhost.local:12345
log_info("running on " . hn())
</code></pre>
</article>
<article class="doc-entry" id="doc-opendir">
<h3><a class="doc-anchor" href="#doc-opendir">#</a> <code>opendir</code></h3>
<p>Open a directory handle for reading its entries. Returns a directory handle that can be passed to <code>readdir</code>, <code>seekdir</code>, <code>telldir</code>, <code>rewinddir</code>, and <code>closedir</code>. Dies if the directory does not exist or cannot be opened. For most use cases <code>glob</code> or <code>readdir</code> with a path is simpler.</p>
<pre><code class="lang-perl">opendir(my $dh, "/tmp") or die "cannot open: $!"
my @entries = readdir($dh)
closedir($dh)
@entries |> grep { _ !~ /^\./ } |> e p # skip dotfiles
</code></pre>
</article>
<article class="doc-entry" id="doc-readdir">
<h3><a class="doc-anchor" href="#doc-readdir">#</a> <code>readdir</code></h3>
<p>Read entries from a directory handle opened with <code>opendir</code>. In list context, returns all remaining entries. In scalar context, returns the next single entry or <code>undef</code> when exhausted. Entries include <code>.</code> and <code>..</code> so you typically filter them out.</p>
<pre><code class="lang-perl">opendir(my $dh, ".") or die $!
while (my $entry = readdir($dh)) {
next if $entry =~ /^\./
p $entry
}
closedir($dh)
</code></pre>
</article>
<article class="doc-entry" id="doc-closedir">
<h3><a class="doc-anchor" href="#doc-closedir">#</a> <code>closedir</code></h3>
<p>Close a directory handle previously opened with <code>opendir</code>, releasing the underlying OS resource. While directory handles are closed automatically when they go out of scope, explicit <code>closedir</code> is good practice in long-running programs or loops that open many directories.</p>
<pre><code class="lang-perl">opendir(my $dh, "/var/log") or die $!
my @logs = readdir($dh)
closedir($dh)
@logs |> grep { /\.log$/ } |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-seekdir">
<h3><a class="doc-anchor" href="#doc-seekdir">#</a> <code>seekdir</code></h3>
<p>Set the current position in a directory handle to a location previously obtained from <code>telldir</code>. This allows you to revisit directory entries without closing and reopening the handle. Rarely needed in practice, but useful for multi-pass directory scanning.</p>
<pre><code class="lang-perl">opendir(my $dh, ".") or die $!
my $pos = telldir($dh)
my @first_pass = readdir($dh)
seekdir($dh, $pos) # rewind to saved position
my @second_pass = readdir($dh)
closedir($dh)
</code></pre>
</article>
<article class="doc-entry" id="doc-telldir">
<h3><a class="doc-anchor" href="#doc-telldir">#</a> <code>telldir</code></h3>
<p>Return the current read position within a directory handle as an opaque integer. The returned value can be passed to <code>seekdir</code> to return to that position later. This is the directory-handle equivalent of <code>tell</code> for file handles.</p>
<pre><code class="lang-perl">opendir(my $dh, "/tmp") or die $!
readdir($dh) # skip .
readdir($dh) # skip ..
my $pos = telldir($dh) # save position after . and ..
my @real = readdir($dh)
seekdir($dh, $pos) # go back
</code></pre>
</article>
<article class="doc-entry" id="doc-rewinddir">
<h3><a class="doc-anchor" href="#doc-rewinddir">#</a> <code>rewinddir</code></h3>
<p>Reset a directory handle back to the beginning so that the next <code>readdir</code> returns the first entry again. This is equivalent to closing and reopening the directory but more efficient. Useful when you need to iterate a directory multiple times.</p>
<pre><code class="lang-perl">opendir(my $dh, "src") or die $!
my $count = scalar readdir($dh)
rewinddir($dh)
my @entries = readdir($dh)
closedir($dh)
p "$count entries"
</code></pre>
</article>
<article class="doc-entry" id="doc-du">
<h3><a class="doc-anchor" href="#doc-du">#</a> <code>du</code></h3>
<p><code>du</code> (alias <code>dir_size</code>) — compute the total size of a directory tree in bytes, recursively walking all files.</p>
<pre><code class="lang-perl">my $bytes = du("/usr/local")
p "$bytes bytes"
</code></pre>
</article>
<article class="doc-entry" id="doc-du-tree">
<h3><a class="doc-anchor" href="#doc-du-tree">#</a> <code>du_tree</code></h3>
<p><code>du_tree</code> (alias <code>dir_sizes</code>) — return directory sizes as an array of hashrefs <code>{path, size}</code>, sorted descending by size. Each entry is an immediate child directory.</p>
<pre><code class="lang-perl">my @dirs = du_tree("/usr/local")
for (@dirs) { p "_->{path}: _->{size}" }
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-process">
<h2>Process</h2>
<p class="chapter-meta">21 topics</p>
<article class="doc-entry" id="doc-system">
<h3><a class="doc-anchor" href="#doc-system">#</a> <code>system</code></h3>
<p>Execute a command in a subshell and wait for it to complete, returning the exit status. A return value of <code>0</code> means success; non-zero indicates failure. The exit status is encoded as <code>$? >> 8</code> for the actual exit code. Use backticks or <code>capture</code> if you need the command's output.</p>
<pre><code class="lang-perl">my $rc = system("make", "test")
p "exit code: " . ($rc >> 8)
system("cp data.csv /backup/") == 0 or die "copy failed"
if (system("which rg >/dev/null 2>&1") == 0) {
p "ripgrep is installed"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-exec">
<h3><a class="doc-anchor" href="#doc-exec">#</a> <code>exec</code></h3>
<p>Replace the current process image entirely with a new command. This never returns on success — the new program takes over. If <code>exec</code> fails (command not found, permission denied) it returns false and execution continues. Use <code>system</code> instead if you want to run a command and keep the current process alive.</p>
<pre><code class="lang-perl">exec("ls", "-la", "/tmp") or die "exec failed: $!"
# code here only runs if exec fails
# common fork+exec pattern
if (fork() == 0) {
exec("worker", "--daemon")
}
</code></pre>
</article>
<article class="doc-entry" id="doc-fork">
<h3><a class="doc-anchor" href="#doc-fork">#</a> <code>fork</code></h3>
<p>Fork the current process, creating a child that is an exact copy of the parent. Returns the child's PID to the parent process and <code>0</code> to the child, allowing each side to branch. Returns <code>undef</code> on failure. Always pair with <code>wait</code>/<code>waitpid</code> to reap the child and avoid zombies.</p>
<pre><code class="lang-perl">my $pid = fork()
if ($pid == 0) {
p "child $$"
exit(0)
}
p "parent $$, child is $pid"
waitpid($pid, 0)
</code></pre>
</article>
<article class="doc-entry" id="doc-wait">
<h3><a class="doc-anchor" href="#doc-wait">#</a> <code>wait</code></h3>
<p>Wait for any child process to terminate and return its PID. The exit status is stored in <code>$?</code>. If there are no child processes, returns <code>-1</code>. This is the simplest reaping function — use <code>waitpid</code> when you need to wait for a specific child or use non-blocking flags.</p>
<pre><code class="lang-perl">for (1:3) {
fork() or do { sleep(1)
exit(0) }
}
while ((my $pid = wait()) != -1) {
p "child $pid exited with " . ($? >> 8)
}
</code></pre>
</article>
<article class="doc-entry" id="doc-waitpid">
<h3><a class="doc-anchor" href="#doc-waitpid">#</a> <code>waitpid</code></h3>
<p>Wait for a specific child process identified by PID to change state. The flags argument controls behavior — use <code>0</code> for blocking wait, or <code>WNOHANG</code> for non-blocking (returns <code>0</code> if child is still running). Returns the PID on success, <code>-1</code> if the child does not exist. Exit status is in <code>$?</code>.</p>
<pre><code class="lang-perl">my $pid = fork() // die "fork: $!"
if ($pid == 0) { sleep(2)
exit(42) }
waitpid($pid, 0)
p "child exited: " . ($? >> 8) # 42
# non-blocking poll
while (waitpid($pid, WNOHANG) == 0) {
p "still running..."
sleep(1)
}
</code></pre>
</article>
<article class="doc-entry" id="doc-kill">
<h3><a class="doc-anchor" href="#doc-kill">#</a> <code>kill</code></h3>
<p>Send a signal to one or more processes by PID. The signal can be specified as a number (<code>9</code>) or a name (<code>"TERM"</code>). Sending signal <code>0</code> tests whether the process exists without actually sending anything. Returns the number of processes successfully signaled.</p>
<pre><code class="lang-perl">kill("TERM", $child_pid)
kill(9, @worker_pids) # SIGKILL
if (kill(0, $pid)) {
p "process $pid is alive"
}
my $n = kill("HUP", @daemons)
p "signaled $n processes"
</code></pre>
</article>
<article class="doc-entry" id="doc-exit">
<h3><a class="doc-anchor" href="#doc-exit">#</a> <code>exit</code></h3>
<p>Terminate the program immediately with the given exit status code. An exit code of <code>0</code> conventionally means success; any non-zero value indicates an error. <code>END</code> blocks and object destructors are still run. Use <code>POSIX::_exit</code> to skip cleanup entirely.</p>
<pre><code class="lang-perl">exit(0) # success
exit(1) if $error # failure
# conditional exit in a pipeline
my $ok = system("make test")
exit($ok >> 8) if $ok
</code></pre>
</article>
<article class="doc-entry" id="doc-getlogin">
<h3><a class="doc-anchor" href="#doc-getlogin">#</a> <code>getlogin</code></h3>
<p>Return the login name of the user who owns the current terminal session. This reads from the system's utmp/utmpx database and may return <code>undef</code> for processes without a controlling terminal (cron jobs, daemons). For a more reliable alternative, use <code>getpwuid($<)</code> which looks up the effective UID.</p>
<pre><code class="lang-perl">my $user = getlogin() // (getpwuid($<))[0]
p "running as $user"
log_info("session started by " . getlogin())
</code></pre>
</article>
<article class="doc-entry" id="doc-getpwnam">
<h3><a class="doc-anchor" href="#doc-getpwnam">#</a> <code>getpwnam</code></h3>
<p>Look up user account information by username string. Returns the same 9-element list as <code>getpwuid</code>: <code>($name, $passwd, $uid, $gid, $quota, $comment, $gcos, $dir, $shell)</code>. Returns empty list if the user does not exist. Useful for resolving a username to a UID before calling <code>chown</code>.</p>
<pre><code class="lang-perl">my @info = getpwnam("deploy")
p "uid=$info[2] home=$info[7]"
my $uid = (getpwnam("www-data"))[2]
chown($uid, -1, "public/index.html")
</code></pre>
</article>
<article class="doc-entry" id="doc-getpwuid">
<h3><a class="doc-anchor" href="#doc-getpwuid">#</a> <code>getpwuid</code></h3>
<p>Look up user account information by numeric UID. Returns <code>($name, $passwd, $uid, $gid, $quota, $comment, $gcos, $dir, $shell)</code> on success, or empty list if the UID does not exist. This is the reliable way to map a UID to a username and home directory.</p>
<pre><code class="lang-perl">my ($name, undef, undef, undef, undef, undef, undef, $home) = getpwuid($<)
p "user: $name, home: $home"
my $root_shell = (getpwuid(0))[8]
p $root_shell # /bin/bash or /bin/zsh
</code></pre>
</article>
<article class="doc-entry" id="doc-getpwent">
<h3><a class="doc-anchor" href="#doc-getpwent">#</a> <code>getpwent</code></h3>
<p>Read the next entry from the system password database, iterating through all user accounts. Returns <code>($name, $passwd, $uid, $gid, $quota, $comment, $gcos, $dir, $shell)</code> for each user, or empty list when exhausted. Call <code>setpwent</code> to rewind and <code>endpwent</code> to close.</p>
<pre><code class="lang-perl">while (my @pw = getpwent()) {
p "$pw[0]: uid=$pw[2] home=$pw[7]"
}
endpwent()
</code></pre>
</article>
<article class="doc-entry" id="doc-getgrgid">
<h3><a class="doc-anchor" href="#doc-getgrgid">#</a> <code>getgrgid</code></h3>
<p>Look up group information by numeric GID. Returns <code>($name, $passwd, $gid, $members)</code> where members is a space-separated string of usernames belonging to the group. Returns empty list if the GID does not exist.</p>
<pre><code class="lang-perl">my ($name, undef, undef, $members) = getgrgid(0)
p "group $name: $members"
my $gname = (getgrgid((stat("file.txt"))[5]))[0]
p "file group: $gname"
</code></pre>
</article>
<article class="doc-entry" id="doc-getgrnam">
<h3><a class="doc-anchor" href="#doc-getgrnam">#</a> <code>getgrnam</code></h3>
<p>Look up group information by group name string. Returns <code>($name, $passwd, $gid, $members)</code>. Useful for resolving a group name to a GID before calling <code>chown</code>, or for checking group membership.</p>
<pre><code class="lang-perl">my ($name, undef, $gid, $members) = getgrnam("staff")
p "gid=$gid members=$members"
chown(-1, $gid, "shared_dir")
if ((getgrnam("admin"))[3] =~ /\b$user\b/) {
p "$user is an admin"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-getgrent">
<h3><a class="doc-anchor" href="#doc-getgrent">#</a> <code>getgrent</code></h3>
<p>Read the next entry from the system group database, iterating through all groups. Returns <code>($name, $passwd, $gid, $members)</code> for each group, or empty list when exhausted. The members field is a space-separated string of usernames. Call <code>endgrent</code> when done.</p>
<pre><code class="lang-perl">while (my @gr = getgrent()) {
p "$gr[0]: gid=$gr[2] members=$gr[3]"
}
endgrent()
</code></pre>
</article>
<article class="doc-entry" id="doc-getppid">
<h3><a class="doc-anchor" href="#doc-getppid">#</a> <code>getppid</code></h3>
<p>Return the process ID of the parent process. This is useful for detecting whether the process has been orphaned (parent PID becomes 1 on Unix when the original parent exits), or for logging the process hierarchy. Always returns a valid PID.</p>
<pre><code class="lang-perl">p "my pid: $$, parent: " . getppid()
if (getppid() == 1) {
log_warn("parent process has exited, we are orphaned")
}
</code></pre>
</article>
<article class="doc-entry" id="doc-getpgrp">
<h3><a class="doc-anchor" href="#doc-getpgrp">#</a> <code>getpgrp</code></h3>
<p>Return the process group ID of the current process (or of the specified PID). Processes in the same group receive signals together — for example, Ctrl-C sends SIGINT to the entire foreground process group. Use <code>setpgrp</code> to move a process into a different group.</p>
<pre><code class="lang-perl">p "process group: " . getpgrp()
my $pg = getpgrp($$)
p $pg == $$ ? "group leader" : "group member"
</code></pre>
</article>
<article class="doc-entry" id="doc-setpgrp">
<h3><a class="doc-anchor" href="#doc-setpgrp">#</a> <code>setpgrp</code></h3>
<p>Set the process group ID of a process. Call <code>setpgrp(0, 0)</code> to make the current process a new group leader, which is useful for daemonization or isolating a subprocess from the terminal's signal group. Takes <code>(PID, PGID)</code> — use <code>0</code> for the current process.</p>
<pre><code class="lang-perl">setpgrp(0, 0) # become process group leader
if (fork() == 0) {
setpgrp(0, 0) # child gets its own group
exec("worker")
}
</code></pre>
</article>
<article class="doc-entry" id="doc-getpriority">
<h3><a class="doc-anchor" href="#doc-getpriority">#</a> <code>getpriority</code></h3>
<p>Get the scheduling priority (nice value) of a process, process group, or user. The <code>which</code> argument selects the target type: <code>PRIO_PROCESS</code>, <code>PRIO_PGRP</code>, or <code>PRIO_USER</code>. Lower values mean higher priority. The default nice value is <code>0</code>; range is typically <code>-20</code> to <code>19</code>.</p>
<pre><code class="lang-perl">my $nice = getpriority(0, $$) # PRIO_PROCESS, current PID
p "nice value: $nice"
my $user_prio = getpriority(2, $<) # PRIO_USER, current user
p "user priority: $user_prio"
</code></pre>
</article>
<article class="doc-entry" id="doc-setpriority">
<h3><a class="doc-anchor" href="#doc-setpriority">#</a> <code>setpriority</code></h3>
<p>Set the scheduling priority (nice value) of a process, process group, or user. Lowering the nice value (higher priority) typically requires root privileges. Raising it (lower priority) is always allowed. Use this to deprioritize background batch work or boost latency-sensitive tasks.</p>
<pre><code class="lang-perl">setpriority(0, $$, 10) # lower priority for batch work
if (fork() == 0) {
setpriority(0, 0, 19) # lowest priority for child
exec("batch-job")
}
</code></pre>
</article>
<article class="doc-entry" id="doc-syscall">
<h3><a class="doc-anchor" href="#doc-syscall">#</a> <code>syscall</code></h3>
<p>Invoke a raw system call by its numeric identifier, passing arguments directly to the kernel. This is an escape hatch for system calls that have no Perl wrapper. The call number is platform-specific and the arguments must be correctly typed (integers or string buffers). Use with caution — incorrect arguments can crash the process.</p>
<pre><code class="lang-perl"># SYS_getpid on Linux x86_64 is 39
my $pid = syscall(39)
p $pid # same as $$
# SYS_sync on Linux is 162
syscall(162) # flush filesystem caches
</code></pre>
</article>
<article class="doc-entry" id="doc-process-list">
<h3><a class="doc-anchor" href="#doc-process-list">#</a> <code>process_list</code></h3>
<p><code>process_list</code> (aliases <code>ps</code>, <code>procs</code>) — list running processes as an array of hashrefs with <code>{pid, name, uid}</code> keys.</p>
<pre><code class="lang-perl">my @procs = ps()
for (@procs) { p "_->{pid} _->{name}" }
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-pack-binary">
<h2>Pack / Binary</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-pack">
<h3><a class="doc-anchor" href="#doc-pack">#</a> <code>pack</code></h3>
<p>Convert a list of values into a binary string according to a template. Each template character specifies how one value is encoded: <code>N</code> for 32-bit big-endian unsigned, <code>n</code> for 16-bit, <code>a</code> for raw bytes, <code>Z</code> for null-terminated string, etc. This is essential for constructing binary protocols, file formats, and <code>sockaddr</code> structures.</p>
<pre><code class="lang-perl">my $bin = pack("NnA4", 0xDEADBEEF, 8080, "test")
p length($bin) # 10 bytes
my $header = pack("A8 N N", "MAGIC01\0", 1, 42)
spurt("data.bin", $header)
</code></pre>
</article>
<article class="doc-entry" id="doc-unpack">
<h3><a class="doc-anchor" href="#doc-unpack">#</a> <code>unpack</code></h3>
<p>Decode a binary string into a list of values according to a template, performing the inverse of <code>pack</code>. The template characters must match how the data was packed. Use this for parsing binary file formats, network protocol headers, or any structured binary data.</p>
<pre><code class="lang-perl">my ($magic, $version, $count) = unpack("A8 N N", $header)
p "v$version, $count records"
my ($port, $addr) = unpack("n a4", $sockaddr)
p inet_ntoa($addr) . ":$port"
</code></pre>
</article>
<article class="doc-entry" id="doc-unpack-first">
<h3><a class="doc-anchor" href="#doc-unpack-first">#</a> <code>unpack_first</code></h3>
<p><code>unpack_first(FMT, STR)</code> — decode the binary string and return the <strong>first</strong> decoded element (or <code>undef</code> if the format yields nothing). The stryke spelling of Perl's <code>scalar unpack(FMT, STR)</code> for <code>--no-interop</code> mode where <code>scalar</code> is rejected at parse time. Aliases: <code>unpack1</code>, <code>up1</code>. Equivalent to <code>head(unpack(FMT, STR))</code> but spelled as a single verb.</p>
<pre><code class="lang-perl">my $first_byte = unpack_first("C", $bytes)
my $port = unpack1("n", $sockaddr)
my $magic_word = up1("N", $header)
</code></pre>
</article>
<article class="doc-entry" id="doc-vec">
<h3><a class="doc-anchor" href="#doc-vec">#</a> <code>vec</code></h3>
<p>Treat a string as a bit vector and get or set individual elements at a specified bit width. The first argument is the string, the second is the element offset, and the third is the bit width (1, 2, 4, 8, 16, or 32). As an lvalue, <code>vec</code> modifies the string in place. Useful for compact boolean arrays and bitmap manipulation.</p>
<pre><code class="lang-perl">my $bits = ""
vec($bits, 0, 1) = 1 # set bit 0
vec($bits, 7, 1) = 1 # set bit 7
p vec($bits, 0, 1) # 1
p vec($bits, 3, 1) # 0
p unpack("B8", $bits) # 10000001
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-logging">
<h2>Logging</h2>
<p class="chapter-meta">7 topics</p>
<article class="doc-entry" id="doc-log-info">
<h3><a class="doc-anchor" href="#doc-log-info">#</a> <code>log_info</code></h3>
<p>Log a message at INFO level to stderr with a timestamp prefix. INFO is the default visible level and is appropriate for normal operational messages — startup notices, progress milestones, summary statistics. Messages are suppressed if the current log level is set higher than INFO.</p>
<pre><code class="lang-perl">log_info("server started on port $port")
my @rows = rl("data.csv")
log_info("loaded " . scalar(@rows) . " rows")
1:5 |> e { log_info("processing item $_") }
</code></pre>
</article>
<article class="doc-entry" id="doc-log-warn">
<h3><a class="doc-anchor" href="#doc-log-warn">#</a> <code>log_warn</code></h3>
<p>Log a message at WARN level to stderr. Warnings indicate unexpected but recoverable situations — missing optional config, deprecated usage, slow operations. WARN messages appear at the default log level and are visually distinct from INFO in structured log output.</p>
<pre><code class="lang-perl">log_warn("config file not found, using defaults")
log_warn("query took ${elapsed}s, exceeds threshold")
unless (-e $path) {
log_warn("$path missing, skipping")
}
</code></pre>
</article>
<article class="doc-entry" id="doc-log-error">
<h3><a class="doc-anchor" href="#doc-log-error">#</a> <code>log_error</code></h3>
<p>Log a message at ERROR level to stderr. Use this for failures that prevent an operation from completing but do not necessarily terminate the program — failed network requests, invalid input, permission errors. ERROR is always visible regardless of log level.</p>
<pre><code class="lang-perl">log_error("failed to connect to $host: $!")
eval { rj("bad.json") }
log_error("parse failed: $@") if $@
log_error("missing required field 'name'")
</code></pre>
</article>
<article class="doc-entry" id="doc-log-debug">
<h3><a class="doc-anchor" href="#doc-log-debug">#</a> <code>log_debug</code></h3>
<p>Log a message at DEBUG level to stderr. Debug messages are hidden by default and only appear when the log level is lowered to DEBUG or TRACE via <code>log_level</code>. Use for detailed internal state that helps during development — variable dumps, branch decisions, intermediate values.</p>
<pre><code class="lang-perl">log_level("debug")
log_debug("cache key: $key")
my $result = compute($x)
log_debug("compute($x) => $result")
@items |> e { log_debug("item: $_") }
</code></pre>
</article>
<article class="doc-entry" id="doc-log-trace">
<h3><a class="doc-anchor" href="#doc-log-trace">#</a> <code>log_trace</code></h3>
<p>Log a message at TRACE level to stderr. This is the most verbose level, producing very fine-grained output — loop iterations, function entry/exit, raw payloads. Only visible when <code>log_level("trace")</code> is set. Use sparingly in production code; primarily for deep debugging sessions.</p>
<pre><code class="lang-perl">log_level("trace")
fn process($x) {
log_trace("entering process($x)")
my $r = $x * 2
log_trace("leaving process => $r")
$r
}
1:3 |> map process |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-log-json">
<h3><a class="doc-anchor" href="#doc-log-json">#</a> <code>log_json</code></h3>
<p>Emit a structured JSON log line to stderr containing the message plus any additional key-value metadata. This is designed for machine-parseable logging pipelines — centralized log collectors, JSON-based monitoring, or <code>jq</code>-friendly output. Each call emits exactly one JSON object per line.</p>
<pre><code class="lang-perl">log_json("request", method => "GET", path => "/api")
log_json("metric", name => "latency_ms", value => 42)
log_json("error", msg => $@, file => $0)$1
Note: all values are serialized as JSON strings.
</code></pre>
</article>
<article class="doc-entry" id="doc-log-level">
<h3><a class="doc-anchor" href="#doc-log-level">#</a> <code>log_level</code></h3>
<p>Get or set the current minimum log level. When called with no arguments, returns the current level as a string. When called with a level name, sets it for all subsequent log calls. Valid levels from most to least verbose: <code>trace</code>, <code>debug</code>, <code>info</code>, <code>warn</code>, <code>error</code>. The default level is <code>info</code>.</p>
<pre><code class="lang-perl">p log_level() # info
log_level("debug") # enable debug output
log_debug("now visible")
log_level("error") # suppress everything below error
log_info("hidden") # not printed
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-charts-svg">
<h2>Charts (SVG)</h2>
<p class="chapter-meta">19 topics</p>
<article class="doc-entry" id="doc-scatter-svg">
<h3><a class="doc-anchor" href="#doc-scatter-svg">#</a> <code>scatter_svg</code></h3>
<p><code>scatter_svg</code> (alias <code>scatter_plot</code>) — generate an SVG scatter plot. Args: xs, ys [, title]. Dark theme, auto-scaled axes.</p>
<pre><code class="lang-perl">scatter_svg([1,2,3,4], [1,4,9,16], "Squares") |> to_file("scatter.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-line-svg">
<h3><a class="doc-anchor" href="#doc-line-svg">#</a> <code>line_svg</code></h3>
<p><code>line_svg</code> (alias <code>line_plot</code>) — generate an SVG line plot. Args: xs, ys [, title].</p>
<pre><code class="lang-perl">my @x = map { _ * 0.1 } 0:100
my @y = map { sin(_) } @x
line_svg(\@x, \@y, "Sine") |> to_file("sine.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-plot-svg">
<h3><a class="doc-anchor" href="#doc-plot-svg">#</a> <code>plot_svg</code></h3>
<p><code>plot_svg</code> — SVG line plot with auto X axis (0..n-1). Args: ys [, title].</p>
<pre><code class="lang-perl">plot_svg([map { _ ** 2 } 0:50], "Parabola") |> to_file("plot.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-hist-svg">
<h3><a class="doc-anchor" href="#doc-hist-svg">#</a> <code>hist_svg</code></h3>
<p><code>hist_svg</code> (alias <code>histogram_svg</code>) — SVG histogram with auto-binning (sqrt rule). Args: data [, bins, title].</p>
<pre><code class="lang-perl">rnorm(1000) |> hist_svg(30, "Normal") |> to_file("hist.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-boxplot-svg">
<h3><a class="doc-anchor" href="#doc-boxplot-svg">#</a> <code>boxplot_svg</code></h3>
<p><code>boxplot_svg</code> (alias <code>box_plot</code>) — SVG box-and-whisker plot with IQR whiskers and outlier detection. Args: groups [, title]. Groups is array of arrays.</p>
<pre><code class="lang-perl">boxplot_svg([[1,2,3,4,5], [3,4,5,6,20]], "Compare") |> to_file("box.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-bar-svg">
<h3><a class="doc-anchor" href="#doc-bar-svg">#</a> <code>bar_svg</code></h3>
<p><code>bar_svg</code> (alias <code>barchart_svg</code>) — SVG bar chart with labeled bars and value annotations. Args: labels, values [, title].</p>
<pre><code class="lang-perl">bar_svg(["Rust","Go","C++"], [45,30,25], "Languages") |> to_file("bar.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-pie-svg">
<h3><a class="doc-anchor" href="#doc-pie-svg">#</a> <code>pie_svg</code></h3>
<p><code>pie_svg</code> (alias <code>pie_chart</code>) — SVG pie chart with percentage labels. Args: labels, values [, title].</p>
<pre><code class="lang-perl">pie_svg(["A","B","C"], [50,30,20]) |> to_file("pie.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-heatmap-svg">
<h3><a class="doc-anchor" href="#doc-heatmap-svg">#</a> <code>heatmap_svg</code></h3>
<p><code>heatmap_svg</code> (alias <code>heatmap</code>) — SVG heatmap with blue-cyan-yellow-red colormap. Args: matrix [, title].</p>
<pre><code class="lang-perl">heatmap_svg(cor_mat($data), "Correlation") |> to_file("heat.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-donut-svg">
<h3><a class="doc-anchor" href="#doc-donut-svg">#</a> <code>donut_svg</code></h3>
<p><code>donut_svg</code> (alias <code>donut</code>) — SVG donut chart with percentage labels. Accepts labels+values or a hashref.</p>
<pre><code class="lang-perl">donut_svg(["A","B","C"], [50,30,20], "Share") |> to_file("donut.svg")
{Rust => 45, Go => 30} |> donut("Languages") |> to_file("donut.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-area-svg">
<h3><a class="doc-anchor" href="#doc-area-svg">#</a> <code>area_svg</code></h3>
<p><code>area_svg</code> (alias <code>area_chart</code>) — SVG filled area chart. Args: xs, ys [, title].</p>
<pre><code class="lang-perl">my @x = 0:20
my @y = map { sin(_ * 0.3) } @x
area_svg(\@x, \@y, "Wave") |> to_file("area.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-hbar-svg">
<h3><a class="doc-anchor" href="#doc-hbar-svg">#</a> <code>hbar_svg</code></h3>
<p><code>hbar_svg</code> (alias <code>hbar</code>) — SVG horizontal bar chart. Accepts labels+values or a hashref.</p>
<pre><code class="lang-perl">hbar_svg(["Rust","Go","C++"], [45,30,25], "Speed") |> to_file("hbar.svg")
{alpha => 10, beta => 20} |> hbar |> to_file("hbar.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-radar-svg">
<h3><a class="doc-anchor" href="#doc-radar-svg">#</a> <code>radar_svg</code></h3>
<p><code>radar_svg</code> (aliases <code>radar</code>, <code>spider</code>) — SVG radar/spider chart. Args: labels, values [, title].</p>
<pre><code class="lang-perl">radar_svg(["Atk","Def","Spd","HP","MP"], [8,6,9,5,7], "Stats") |> to_file("radar.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-candlestick-svg">
<h3><a class="doc-anchor" href="#doc-candlestick-svg">#</a> <code>candlestick_svg</code></h3>
<p><code>candlestick_svg</code> (aliases <code>candlestick</code>, <code>ohlc</code>) — SVG candlestick OHLC chart. Args: array of [open,high,low,close] [, title].</p>
<pre><code class="lang-perl">candlestick_svg([[100,110,95,105],[105,115,100,112]], "Stock") |> to_file("ohlc.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-violin-svg">
<h3><a class="doc-anchor" href="#doc-violin-svg">#</a> <code>violin_svg</code></h3>
<p><code>violin_svg</code> (alias <code>violin</code>) — SVG violin plot from array of arrays showing distribution shape.</p>
<pre><code class="lang-perl">violin_svg([rnorm(200), rnorm(200, 2)], "Distributions") |> to_file("violin.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-cor-heatmap">
<h3><a class="doc-anchor" href="#doc-cor-heatmap">#</a> <code>cor_heatmap</code></h3>
<p><code>cor_heatmap</code> (alias <code>cor_matrix_svg</code>) — SVG correlation matrix heatmap. Computes pairwise correlations and renders as heatmap.</p>
<pre><code class="lang-perl">cor_heatmap([rnorm(100), rnorm(100), rnorm(100)], "Correlations") |> to_file("cor.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-stacked-bar-svg">
<h3><a class="doc-anchor" href="#doc-stacked-bar-svg">#</a> <code>stacked_bar_svg</code></h3>
<p><code>stacked_bar_svg</code> (alias <code>stacked_bar</code>) — SVG stacked bar chart. Args: labels, series (array of arrays) [, title].</p>
<pre><code class="lang-perl">stacked_bar_svg(["Q1","Q2","Q3"], [[10,20,30],[5,15,25]], "Revenue") |> to_file("stacked.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-wordcloud-svg">
<h3><a class="doc-anchor" href="#doc-wordcloud-svg">#</a> <code>wordcloud_svg</code></h3>
<p><code>wordcloud_svg</code> (aliases <code>wordcloud</code>, <code>wcloud</code>) — SVG word cloud from frequency hashref. Word size scales with frequency.</p>
<pre><code class="lang-perl">{rust => 50, go => 30, python => 40} |> wordcloud("Languages") |> to_file("cloud.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-treemap-svg">
<h3><a class="doc-anchor" href="#doc-treemap-svg">#</a> <code>treemap_svg</code></h3>
<p><code>treemap_svg</code> (alias <code>treemap</code>) — SVG treemap from frequency hashref. Area proportional to values.</p>
<pre><code class="lang-perl">{src => 500, tests => 200, docs => 100} |> treemap("Codebase") |> to_file("tree.svg")
</code></pre>
</article>
<article class="doc-entry" id="doc-preview">
<h3><a class="doc-anchor" href="#doc-preview">#</a> <code>preview</code></h3>
<p><code>preview</code> (alias <code>pvw</code>) — wrap SVG/HTML content in a cyberpunk-styled page and open in the default browser.</p>
<pre><code class="lang-perl">scatter_svg([1,2,3], [1,4,9]) |> preview
bar_svg(["A","B"], [10,20]) |> pvw
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-audio">
<h2>Audio</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-audio-convert">
<h3><a class="doc-anchor" href="#doc-audio-convert">#</a> <code>audio_convert</code></h3>
<p><code>audio_convert</code> (alias <code>aconv</code>) — convert audio files between WAV, FLAC, AIFF, and MP3 formats.</p>
<pre><code class="lang-perl">audio_convert("song.flac", "song.mp3")
aconv("input.wav", "output.mp3")
</code></pre>
</article>
<article class="doc-entry" id="doc-audio-info">
<h3><a class="doc-anchor" href="#doc-audio-info">#</a> <code>audio_info</code></h3>
<p><code>audio_info</code> (alias <code>ainfo</code>) — get audio file metadata (duration, sample rate, channels, format) as a hashref.</p>
<pre><code class="lang-perl">my $info = ainfo("song.mp3")
p $info->{duration} # seconds
p $info->{sample_rate} # e.g. 44100
</code></pre>
</article>
<article class="doc-entry" id="doc-id3-read">
<h3><a class="doc-anchor" href="#doc-id3-read">#</a> <code>id3_read</code></h3>
<p><code>id3_read</code> (alias <code>id3</code>) — read ID3 tags from an MP3 file as a hashref (title, artist, album, year, etc.).</p>
<pre><code class="lang-perl">my $tags = id3("song.mp3")
p "$tags->{artist} - $tags->{title}"
</code></pre>
</article>
<article class="doc-entry" id="doc-id3-write">
<h3><a class="doc-anchor" href="#doc-id3-write">#</a> <code>id3_write</code></h3>
<p><code>id3_write</code> (alias <code>id3w</code>) — write ID3 tags to an MP3 file from a hashref.</p>
<pre><code class="lang-perl">id3w("song.mp3", {title => "New Title", artist => "Artist", year => "2026"})
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-network-utilities">
<h2>Network Utilities</h2>
<p class="chapter-meta">18 topics</p>
<article class="doc-entry" id="doc-net-interfaces">
<h3><a class="doc-anchor" href="#doc-net-interfaces">#</a> <code>net_interfaces</code></h3>
<p><code>net_interfaces</code> (aliases <code>net_ifs</code>, <code>ifconfig</code>) — list all network interfaces with name, IPs, MAC, and status.</p>
<pre><code class="lang-perl">my @ifs = net_ifs()
for (@ifs) { p "_->{name}: _->{ipv4}" }
</code></pre>
</article>
<article class="doc-entry" id="doc-net-ipv4">
<h3><a class="doc-anchor" href="#doc-net-ipv4">#</a> <code>net_ipv4</code></h3>
<p><code>net_ipv4</code> (aliases <code>myip</code>, <code>myip4</code>) — return the first non-loopback IPv4 address as a string.</p>
<pre><code class="lang-perl">p myip() # e.g. 192.168.1.42
</code></pre>
</article>
<article class="doc-entry" id="doc-net-ipv6">
<h3><a class="doc-anchor" href="#doc-net-ipv6">#</a> <code>net_ipv6</code></h3>
<p><code>net_ipv6</code> (alias <code>myip6</code>) — return the first non-loopback IPv6 address as a string.</p>
<pre><code class="lang-perl">p myip6() # e.g. fe80::1
</code></pre>
</article>
<article class="doc-entry" id="doc-net-mac">
<h3><a class="doc-anchor" href="#doc-net-mac">#</a> <code>net_mac</code></h3>
<p><code>net_mac</code> (alias <code>mymac</code>) — return the first non-loopback MAC address.</p>
<pre><code class="lang-perl">p mymac() # e.g. aa:bb:cc:dd:ee:ff
</code></pre>
</article>
<article class="doc-entry" id="doc-net-public-ip">
<h3><a class="doc-anchor" href="#doc-net-public-ip">#</a> <code>net_public_ip</code></h3>
<p><code>net_public_ip</code> (aliases <code>pubip</code>, <code>extip</code>) — fetch your public IP address via HTTP.</p>
<pre><code class="lang-perl">p pubip() # e.g. 203.0.113.42
</code></pre>
</article>
<article class="doc-entry" id="doc-net-dns">
<h3><a class="doc-anchor" href="#doc-net-dns">#</a> <code>net_dns</code></h3>
<p><code>net_dns</code> (aliases <code>dns_resolve</code>, <code>resolve</code>) — resolve a hostname to IP addresses.</p>
<pre><code class="lang-perl">my @ips = resolve("github.com")
p @ips
</code></pre>
</article>
<article class="doc-entry" id="doc-net-reverse-dns">
<h3><a class="doc-anchor" href="#doc-net-reverse-dns">#</a> <code>net_reverse_dns</code></h3>
<p><code>net_reverse_dns</code> (alias <code>rdns</code>) — reverse DNS lookup via UDP PTR query.</p>
<pre><code class="lang-perl">p rdns("8.8.8.8") # dns.google
</code></pre>
</article>
<article class="doc-entry" id="doc-net-ping">
<h3><a class="doc-anchor" href="#doc-net-ping">#</a> <code>net_ping</code></h3>
<p><code>net_ping</code> (alias <code>ping</code>) — TCP connect ping to host:port. Returns array of RTT measurements in ms.</p>
<pre><code class="lang-perl">my @rtt = ping("google.com", 443, 5) # 5 pings
p mean(@rtt)
</code></pre>
</article>
<article class="doc-entry" id="doc-net-port-open">
<h3><a class="doc-anchor" href="#doc-net-port-open">#</a> <code>net_port_open</code></h3>
<p><code>net_port_open</code> (alias <code>port_open</code>) — check if a TCP port is open on a host. Returns boolean.</p>
<pre><code class="lang-perl">p port_open("localhost", 8080) # 1 or 0
</code></pre>
</article>
<article class="doc-entry" id="doc-net-ports-scan">
<h3><a class="doc-anchor" href="#doc-net-ports-scan">#</a> <code>net_ports_scan</code></h3>
<p><code>net_ports_scan</code> (aliases <code>port_scan</code>, <code>portscan</code>) — scan a range of TCP ports on a host. Returns list of open ports.</p>
<pre><code class="lang-perl">my @open = port_scan("localhost", 80, 443)
p @open # e.g. 80, 443
</code></pre>
</article>
<article class="doc-entry" id="doc-net-latency">
<h3><a class="doc-anchor" href="#doc-net-latency">#</a> <code>net_latency</code></h3>
<p><code>net_latency</code> (alias <code>tcplat</code>) — measure TCP connect latency to host:port in milliseconds.</p>
<pre><code class="lang-perl">p tcplat("google.com", 443) # e.g. 12.5
</code></pre>
</article>
<article class="doc-entry" id="doc-net-download">
<h3><a class="doc-anchor" href="#doc-net-download">#</a> <code>net_download</code></h3>
<p><code>net_download</code> (aliases <code>download</code>, <code>wget</code>) — download a URL to a local file via ureq.</p>
<pre><code class="lang-perl">wget("https://example.com/data.csv", "data.csv")
</code></pre>
</article>
<article class="doc-entry" id="doc-net-headers">
<h3><a class="doc-anchor" href="#doc-net-headers">#</a> <code>net_headers</code></h3>
<p><code>net_headers</code> (alias <code>http_headers</code>) — fetch HTTP response headers as a hashref.</p>
<pre><code class="lang-perl">my $h = http_headers("https://example.com")
p $h->{"content-type"}
</code></pre>
</article>
<article class="doc-entry" id="doc-net-dns-servers">
<h3><a class="doc-anchor" href="#doc-net-dns-servers">#</a> <code>net_dns_servers</code></h3>
<p><code>net_dns_servers</code> (alias <code>dns_servers</code>) — return the system's configured DNS server addresses.</p>
<pre><code class="lang-perl">my @dns = dns_servers()
p @dns # e.g. 8.8.8.8, 8.8.4.4
</code></pre>
</article>
<article class="doc-entry" id="doc-net-gateway">
<h3><a class="doc-anchor" href="#doc-net-gateway">#</a> <code>net_gateway</code></h3>
<p><code>net_gateway</code> (alias <code>gateway</code>) — return the default gateway IP address.</p>
<pre><code class="lang-perl">p gateway() # e.g. 192.168.1.1
</code></pre>
</article>
<article class="doc-entry" id="doc-net-whois">
<h3><a class="doc-anchor" href="#doc-net-whois">#</a> <code>net_whois</code></h3>
<p><code>net_whois</code> (alias <code>whois</code>) — WHOIS lookup via raw TCP connection on port 43.</p>
<pre><code class="lang-perl">p whois("example.com")
</code></pre>
</article>
<article class="doc-entry" id="doc-net-hostname">
<h3><a class="doc-anchor" href="#doc-net-hostname">#</a> <code>net_hostname</code></h3>
<p><code>net_hostname</code> — return the system hostname.</p>
<pre><code class="lang-perl">p net_hostname() # e.g. my-macbook.local
</code></pre>
</article>
<article class="doc-entry" id="doc-smtp-send">
<h3><a class="doc-anchor" href="#doc-smtp-send">#</a> <code>smtp_send</code></h3>
<p><code>smtp_send</code> (aliases <code>send_email</code>, <code>email</code>) — send an email via SMTP with TLS. Takes a hashref with to, from, subject, body, and SMTP connection fields.</p>
<pre><code class="lang-perl">smtp_send({to => "bob@ex.com", from => "me@ex.com", subject => "Hi",
body => "Hello!", smtp_host => "smtp.ex.com", smtp_port => 587,
smtp_user => "me@ex.com", smtp_pass => $pass})
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-markup-web-scraping">
<h2>Markup / Web Scraping</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-html-parse">
<h3><a class="doc-anchor" href="#doc-html-parse">#</a> <code>html_parse</code></h3>
<p><code>html_parse</code> (alias <code>parse_html</code>) — parse an HTML string into an array of element hashrefs with tag, text, and attrs.</p>
<pre><code class="lang-perl">my @els = html_parse(slurp("page.html"))
for (@els) { p "_->{tag}: _->{text}" }
</code></pre>
</article>
<article class="doc-entry" id="doc-css-select">
<h3><a class="doc-anchor" href="#doc-css-select">#</a> <code>css_select</code></h3>
<p><code>css_select</code> (aliases <code>css</code>, <code>qs</code>, <code>query_selector</code>) — query parsed HTML with a CSS selector. Returns matching elements as hashrefs with tag, text, attrs, and html.</p>
<pre><code class="lang-perl">my @links = css_select(slurp("page.html"), "a.nav")
for (@links) { p "_->{tag} _->{attrs}{href}" }
</code></pre>
</article>
<article class="doc-entry" id="doc-xml-parse">
<h3><a class="doc-anchor" href="#doc-xml-parse">#</a> <code>xml_parse</code></h3>
<p><code>xml_parse</code> (alias <code>parse_xml</code>) — parse an XML string into a nested hashref tree with tag, text, attrs, and children.</p>
<pre><code class="lang-perl">my $root = xml_parse(slurp("data.xml"))
p $root->{tag}
for (@{$root->{children}}) { p _->{text} }
</code></pre>
</article>
<article class="doc-entry" id="doc-xpath">
<h3><a class="doc-anchor" href="#doc-xpath">#</a> <code>xpath</code></h3>
<p><code>xpath</code> (alias <code>xml_select</code>) — query XML with XPath-like expressions (//tag, //tag[@attr='val']). Returns matching nodes as hashrefs.</p>
<pre><code class="lang-perl">my @items = xpath(slurp("feed.xml"), "//item")
for (@items) { p _->{text} }
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-date-utilities">
<h2>Date Utilities</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-dateseq">
<h3><a class="doc-anchor" href="#doc-dateseq">#</a> <code>dateseq</code></h3>
<p><code>dateseq</code> (alias <code>dseq</code>) — generate a sequence of dates. Args: start, end [, step]. Step defaults to 1 day.</p>
<pre><code class="lang-perl">my @days = dseq("2026-01-01", "2026-01-07")
p @days
</code></pre>
</article>
<article class="doc-entry" id="doc-dategrep">
<h3><a class="doc-anchor" href="#doc-dategrep">#</a> <code>dategrep</code></h3>
<p><code>dategrep</code> (alias <code>dgrep</code>) — filter a list of date strings by a pattern or range.</p>
<pre><code class="lang-perl">my @jan = dgrep("2026-01", @dates)
</code></pre>
</article>
<article class="doc-entry" id="doc-dateround">
<h3><a class="doc-anchor" href="#doc-dateround">#</a> <code>dateround</code></h3>
<p><code>dateround</code> (alias <code>dround</code>) — round date strings to a unit (day, hour, month, etc.).</p>
<pre><code class="lang-perl">p dround("2026-04-19T14:35:22", "hour") # 2026-04-19T15:00:00
</code></pre>
</article>
<article class="doc-entry" id="doc-datesort">
<h3><a class="doc-anchor" href="#doc-datesort">#</a> <code>datesort</code></h3>
<p><code>datesort</code> (alias <code>dsort</code>) — sort date strings chronologically.</p>
<pre><code class="lang-perl">my @sorted = dsort("2026-03-01", "2026-01-15", "2026-02-10")
p @sorted
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-git">
<h2>Git</h2>
<p class="chapter-meta">10 topics</p>
<article class="doc-entry" id="doc-git-log">
<h3><a class="doc-anchor" href="#doc-git-log">#</a> <code>git_log</code></h3>
<p><code>git_log</code> (alias <code>glog</code>) — get the last N commits as an array of hashrefs (hash, author, date, message).</p>
<pre><code class="lang-perl">my @commits = glog(10)
for (@commits) { p "_->{hash} _->{message}" }
</code></pre>
</article>
<article class="doc-entry" id="doc-git-status">
<h3><a class="doc-anchor" href="#doc-git-status">#</a> <code>git_status</code></h3>
<p><code>git_status</code> (alias <code>gst</code>) — get working tree status as an array of hashrefs (path, status).</p>
<pre><code class="lang-perl">my @st = gst()
for (@st) { p "_->{status} _->{path}" }
</code></pre>
</article>
<article class="doc-entry" id="doc-git-diff">
<h3><a class="doc-anchor" href="#doc-git-diff">#</a> <code>git_diff</code></h3>
<p><code>git_diff</code> (alias <code>gdiff</code>) — get the current diff as a string.</p>
<pre><code class="lang-perl">p gdiff()
gdiff() |> lines |> grep /^\+/ |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-git-branches">
<h3><a class="doc-anchor" href="#doc-git-branches">#</a> <code>git_branches</code></h3>
<p><code>git_branches</code> (alias <code>gbr</code>) — list all branches as an array of strings.</p>
<pre><code class="lang-perl">my @br = gbr()
p @br
</code></pre>
</article>
<article class="doc-entry" id="doc-git-tags">
<h3><a class="doc-anchor" href="#doc-git-tags">#</a> <code>git_tags</code></h3>
<p><code>git_tags</code> (alias <code>gtags</code>) — list all tags as an array of strings.</p>
<pre><code class="lang-perl">my @tags = gtags()
p @tags
</code></pre>
</article>
<article class="doc-entry" id="doc-git-blame">
<h3><a class="doc-anchor" href="#doc-git-blame">#</a> <code>git_blame</code></h3>
<p><code>git_blame</code> (alias <code>gblame</code>) — blame a file, returning per-line annotation.</p>
<pre><code class="lang-perl">p gblame("src/main.rs")
</code></pre>
</article>
<article class="doc-entry" id="doc-git-authors">
<h3><a class="doc-anchor" href="#doc-git-authors">#</a> <code>git_authors</code></h3>
<p><code>git_authors</code> (alias <code>gauthors</code>) — list unique authors sorted by commit count as hashrefs.</p>
<pre><code class="lang-perl">my @authors = gauthors()
for (@authors) { p "_->{name}: _->{count}" }
</code></pre>
</article>
<article class="doc-entry" id="doc-git-files">
<h3><a class="doc-anchor" href="#doc-git-files">#</a> <code>git_files</code></h3>
<p><code>git_files</code> (alias <code>gfiles</code>) — list all tracked files in the repo.</p>
<pre><code class="lang-perl">my @files = gfiles()
p scalar @files # total tracked files
</code></pre>
</article>
<article class="doc-entry" id="doc-git-show">
<h3><a class="doc-anchor" href="#doc-git-show">#</a> <code>git_show</code></h3>
<p><code>git_show</code> (alias <code>gshow</code>) — show details of a commit (message, diff, author).</p>
<pre><code class="lang-perl">p gshow("HEAD")
p gshow("abc1234")
</code></pre>
</article>
<article class="doc-entry" id="doc-git-root">
<h3><a class="doc-anchor" href="#doc-git-root">#</a> <code>git_root</code></h3>
<p><code>git_root</code> (alias <code>groot</code>) — return the repository root path.</p>
<pre><code class="lang-perl">p groot() # e.g. /home/user/project
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-system">
<h2>System</h2>
<p class="chapter-meta">13 topics</p>
<article class="doc-entry" id="doc-mounts">
<h3><a class="doc-anchor" href="#doc-mounts">#</a> <code>mounts</code></h3>
<p><code>mounts</code> (aliases <code>disk_mounts</code>, <code>filesystems</code>) — list mounted filesystems with usage (total, used, available).</p>
<pre><code class="lang-perl">my @m = mounts()
for (@m) { p "_->{mount}: _->{used}/_->{total}" }
</code></pre>
</article>
<article class="doc-entry" id="doc-thread-count">
<h3><a class="doc-anchor" href="#doc-thread-count">#</a> <code>thread_count</code></h3>
<p><code>thread_count</code> (alias <code>nthreads</code>) — return the rayon thread pool size.</p>
<pre><code class="lang-perl">p nthreads() # e.g. 8
</code></pre>
</article>
<article class="doc-entry" id="doc-pool-info">
<h3><a class="doc-anchor" href="#doc-pool-info">#</a> <code>pool_info</code></h3>
<p><code>pool_info</code> (alias <code>par_info</code>) — return thread pool details as a hashref (threads, queued, active).</p>
<pre><code class="lang-perl">my $info = par_info()
p $info->{threads}
</code></pre>
</article>
<article class="doc-entry" id="doc-par-bench">
<h3><a class="doc-anchor" href="#doc-par-bench">#</a> <code>par_bench</code></h3>
<p><code>par_bench</code> (alias <code>pbench</code>) — run a parallel throughput benchmark and return results.</p>
<pre><code class="lang-perl">my $result = pbench(1000000)
p $result->{ops_per_sec}
</code></pre>
</article>
<article class="doc-entry" id="doc-to-pdf">
<h3><a class="doc-anchor" href="#doc-to-pdf">#</a> <code>to_pdf</code></h3>
<p><code>to_pdf</code> — generate a PDF from text, SVG, or structured data. Returns raw PDF bytes.</p>
<pre><code class="lang-perl">"Hello World" |> to_pdf |> to_file("out.pdf")
scatter_svg([1,2,3], [1,4,9]) |> to_pdf |> to_file("plot.pdf")
</code></pre>
</article>
<article class="doc-entry" id="doc-pdf-text">
<h3><a class="doc-anchor" href="#doc-pdf-text">#</a> <code>pdf_text</code></h3>
<p><code>pdf_text</code> (aliases <code>pdf_read</code>, <code>pdf_extract</code>) — extract all text content from a PDF file and return it as a string.</p>
<pre><code class="lang-perl">my $text = pdf_text("report.pdf")
p $text |> lines |> cnt # number of lines
</code></pre>
</article>
<article class="doc-entry" id="doc-pdf-pages">
<h3><a class="doc-anchor" href="#doc-pdf-pages">#</a> <code>pdf_pages</code></h3>
<p><code>pdf_pages</code> — return the number of pages in a PDF file.</p>
<pre><code class="lang-perl">p pdf_pages("report.pdf") # e.g. 42
</code></pre>
</article>
<article class="doc-entry" id="doc-jq">
<h3><a class="doc-anchor" href="#doc-jq">#</a> <code>jq</code></h3>
<p><code>jq</code> — alias for <code>json_jq</code>. Query JSON data with jq-style expressions.</p>
<pre><code class="lang-perl">my $data = json_decode(slurp("data.json"))
p jq($data, ".items[].name")
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-cpu">
<h3><a class="doc-anchor" href="#doc-stress-cpu">#</a> <code>stress_cpu</code></h3>
<p><code>stress_cpu</code> (alias <code>scpu</code>) — CPU stress test: run SHA256 hashing in a tight loop for the specified duration (default 1 second). Returns number of hashes computed. Use for load testing and thermal validation.</p>
<pre><code class="lang-perl">my $hashes = stress_cpu(10) # 10 seconds of CPU stress
p "Computed $hashes hashes"
# Distributed across cluster
my $c = cluster(["node1:8", "node2:8"])
1:16 |> pmap_on $c { stress_cpu(60) } # 60s stress on all workers
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-mem">
<h3><a class="doc-anchor" href="#doc-stress-mem">#</a> <code>stress_mem</code></h3>
<p><code>stress_mem</code> (alias <code>smem</code>) — Memory stress test: allocate and touch the specified number of bytes (default 100MB). Returns bytes allocated. Use for memory pressure testing and OOM validation.</p>
<pre><code class="lang-perl">my $bytes = stress_mem(1e9) # Allocate 1GB
p "Allocated $bytes bytes"
# Memory pressure across cluster
1:16 |> pmap_on $cluster { stress_mem(4e9) } # 4GB per worker
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-io">
<h3><a class="doc-anchor" href="#doc-stress-io">#</a> <code>stress_io</code></h3>
<p><code>stress_io</code> (alias <code>sio</code>) — IO stress test: write and read temp files in the specified directory (default /tmp) for N iterations (default 100). Returns total bytes written. Use for storage IOPS testing.</p>
<pre><code class="lang-perl">my $bytes = stress_io("/tmp", 1000) # 1000 iterations
p "Wrote $bytes bytes"
# IO stress across cluster
1:16 |> pmap_on $cluster { stress_io("/data", 500) }
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-test">
<h3><a class="doc-anchor" href="#doc-stress-test">#</a> <code>stress_test</code></h3>
<p><code>stress_test</code> (alias <code>st</code>) — Combined CPU/memory/IO stress test. If cluster provided, distributes across all workers. Returns hashref with stats: {cpu_hashes, mem_bytes, io_bytes, workers, duration}.</p>
<pre><code class="lang-perl"># Local stress test (10 seconds)
my $r = stress_test(10)
p "CPU: $r->{cpu_hashes}, Workers: $r->{workers}"
# Distributed stress test
my $c = cluster(["node1:8", "node2:8", "node3:8"])
my $r = stress_test($c, 60) # 60s across 24 workers
p "Hashes: $r->{cpu_hashes}, Duration: $r->{duration}s"
</code></pre>
</article>
<article class="doc-entry" id="doc-heat">
<h3><a class="doc-anchor" href="#doc-heat">#</a> <code>heat</code></h3>
<p><code>heat</code> — Maximum thermal stress. Pins ALL cores to 100% TDP. The hottest function in any programming language. Use for infrastructure burn-in, cooling validation, and power testing.</p>
<pre><code class="lang-perl">heat(60) # 60 seconds of maximum heat
heat() # default 60 seconds
# Output:
# 🔥 HEAT: Pinning N cores to 100% TDP for 60s
# 🔥 HEAT: 3,116,320,000 hashes in 60.00s (51.9M/s across N cores)
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-testing">
<h2>Testing</h2>
<p class="chapter-meta">15 topics</p>
<article class="doc-entry" id="doc-assert-eq">
<h3><a class="doc-anchor" href="#doc-assert-eq">#</a> <code>assert_eq</code></h3>
<p><code>assert_eq</code> (alias <code>aeq</code>) — assert that two values are equal as strings. Takes A, B, and an optional message. Fails the test with a diff if A ne B.</p>
<pre><code class="lang-perl">assert_eq $got, $expected, "username matches"
aeq length(@arr), 3
</code></pre>
</article>
<article class="doc-entry" id="doc-assert-ne">
<h3><a class="doc-anchor" href="#doc-assert-ne">#</a> <code>assert_ne</code></h3>
<p><code>assert_ne</code> (alias <code>ane</code>) — assert that two values are not equal as strings. Takes A, B, and an optional message. Fails if A eq B.</p>
<pre><code class="lang-perl">assert_ne $token, "", "token must not be empty"
ane $a, $b
</code></pre>
</article>
<article class="doc-entry" id="doc-assert-ok">
<h3><a class="doc-anchor" href="#doc-assert-ok">#</a> <code>assert_ok</code></h3>
<p><code>assert_ok</code> (alias <code>aok</code>) — assert that a value is truthy (defined and non-zero/non-empty). Fails if the value is falsy or undef.</p>
<pre><code class="lang-perl">assert_ok $result, "fetch returned data"
aok $user->{active}
</code></pre>
</article>
<article class="doc-entry" id="doc-assert-err">
<h3><a class="doc-anchor" href="#doc-assert-err">#</a> <code>assert_err</code></h3>
<p><code>assert_err</code> — assert that a value is falsy or undef. The inverse of <code>assert_ok</code>. Useful for verifying error conditions or absent values.</p>
<pre><code class="lang-perl">assert_err $deleted_user, "user should be gone"
assert_err 0
</code></pre>
</article>
<article class="doc-entry" id="doc-assert-true">
<h3><a class="doc-anchor" href="#doc-assert-true">#</a> <code>assert_true</code></h3>
<p><code>assert_true</code> (alias <code>atrue</code>) — alias for <code>assert_ok</code>. Assert that a value is truthy.</p>
<pre><code class="lang-perl">assert_true $connected, "should be connected"
atrue $flag
</code></pre>
</article>
<article class="doc-entry" id="doc-assert-false">
<h3><a class="doc-anchor" href="#doc-assert-false">#</a> <code>assert_false</code></h3>
<p><code>assert_false</code> (alias <code>afalse</code>) — alias for <code>assert_err</code>. Assert that a value is falsy or undef.</p>
<pre><code class="lang-perl">assert_false $error, "no error expected"
afalse $disabled
</code></pre>
</article>
<article class="doc-entry" id="doc-assert-gt">
<h3><a class="doc-anchor" href="#doc-assert-gt">#</a> <code>assert_gt</code></h3>
<p><code>assert_gt</code> — assert that the first numeric value is strictly greater than the second. Fails with the actual values on mismatch.</p>
<pre><code class="lang-perl">assert_gt $elapsed, 0, "elapsed must be positive"
assert_gt scalar(@results), 10
</code></pre>
</article>
<article class="doc-entry" id="doc-assert-lt">
<h3><a class="doc-anchor" href="#doc-assert-lt">#</a> <code>assert_lt</code></h3>
<p><code>assert_lt</code> — assert that the first numeric value is strictly less than the second.</p>
<pre><code class="lang-perl">assert_lt $latency, 100, "latency under 100ms"
assert_lt $errors, $threshold
</code></pre>
</article>
<article class="doc-entry" id="doc-assert-ge">
<h3><a class="doc-anchor" href="#doc-assert-ge">#</a> <code>assert_ge</code></h3>
<p><code>assert_ge</code> — assert that the first numeric value is greater than or equal to the second.</p>
<pre><code class="lang-perl">assert_ge $count, 1, "at least one result"
assert_ge $version, 2
</code></pre>
</article>
<article class="doc-entry" id="doc-assert-le">
<h3><a class="doc-anchor" href="#doc-assert-le">#</a> <code>assert_le</code></h3>
<p><code>assert_le</code> — assert that the first numeric value is less than or equal to the second.</p>
<pre><code class="lang-perl">assert_le $memory, $limit, "within memory budget"
assert_le length($buf), 4096
</code></pre>
</article>
<article class="doc-entry" id="doc-assert-match">
<h3><a class="doc-anchor" href="#doc-assert-match">#</a> <code>assert_match</code></h3>
<p><code>assert_match</code> (alias <code>amatch</code>) — assert that a string matches a regex pattern. Fails with the actual string and pattern on mismatch.</p>
<pre><code class="lang-perl">assert_match $email, qr/\@/, "must contain @"
amatch $line, qr/^OK/
</code></pre>
</article>
<article class="doc-entry" id="doc-assert-contains">
<h3><a class="doc-anchor" href="#doc-assert-contains">#</a> <code>assert_contains</code></h3>
<p><code>assert_contains</code> (alias <code>acontains</code>) — assert that a string contains a given substring. Fails with both values on mismatch.</p>
<pre><code class="lang-perl">assert_contains $html, "<title>", "page has title"
acontains $log, "SUCCESS"
</code></pre>
</article>
<article class="doc-entry" id="doc-assert-near">
<h3><a class="doc-anchor" href="#doc-assert-near">#</a> <code>assert_near</code></h3>
<p><code>assert_near</code> (alias <code>anear</code>) — assert that two floats are approximately equal within an epsilon tolerance (default 1e-9). Essential for floating-point comparisons.</p>
<pre><code class="lang-perl">assert_near 0.1 + 0.2, 0.3, 1e-10, "float add"
anear $pi, 3.14159, 1e-5
</code></pre>
</article>
<article class="doc-entry" id="doc-assert-dies">
<h3><a class="doc-anchor" href="#doc-assert-dies">#</a> <code>assert_dies</code></h3>
<p><code>assert_dies</code> (alias <code>adies</code>) — assert that a block throws an error. Passes if the block dies, fails if it returns normally.</p>
<pre><code class="lang-perl">assert_dies { die "boom" } "should throw"
adies { 1 / 0 }
</code></pre>
</article>
<article class="doc-entry" id="doc-test-run">
<h3><a class="doc-anchor" href="#doc-test-run">#</a> <code>test_run</code></h3>
<p><code>test_run</code> (alias <code>run_tests</code>) — print a test summary with pass/fail counts and exit with code 1 if any test failed. Call at the end of a test file to report results.</p>
<pre><code class="lang-perl"># ... assertions above ...
test_run # prints summary, exits 1 on failure
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-test-runner-worker-pool">
<h2>Test Runner (worker pool)</h2>
<p class="chapter-meta">4 topics</p>
<article class="doc-entry" id="doc-test">
<h3><a class="doc-anchor" href="#doc-test">#</a> <code>test</code></h3>
<p><code>test(FILE_OR_DIR, ...)</code> — run every <code>test_*.stk</code> / <code>t_*.stk</code> under each path through the <strong>worker pool</strong>. Same engine as <code>s t</code> on the CLI: pre-forks N persistent stryke <code>--test-worker</code> processes, dispatches paths via JSON over stdin/stdout, each worker <code>fork()</code>s a grandchild per test for full isolation, no per-test dyld cost. Returns the exit code (0 on all-pass, 1 on any failure). Optional trailing hashref selects mode: <code>{ fork => 1 }</code> for the legacy <code>posix_spawn</code>-per-test path, <code>{ inproc => 1 }</code> for single-process VM-per-test (fastest, hermetic only), <code>{ quiet => 1 }</code>, <code>{ no_interop => 1 }</code>.</p>
<pre><code class="lang-perl">test("t/") # default: worker pool
test(["t/", "examples/"], { quiet => 1 })
test("t/test_foo.stk", { fork => 1 }) # opt back into per-test fork
my $rc = test(@dirs) # array flattens; rc = 0/1
</code></pre>
</article>
<article class="doc-entry" id="doc-test-no-interop">
<h3><a class="doc-anchor" href="#doc-test-no-interop">#</a> <code>test_no_interop</code></h3>
<p><code>test_no_interop(FILE_OR_DIR, ...)</code> (alias <code>test_ni</code>) — same as <code>test</code>, but pins each worker thread's TLS no-interop flag for the duration of the test (<code>set_no_interop_mode_tls</code>). Sibling <code>pmaps</code> workers don't race on a shared atomic. Forwards <code>--no-interop</code> to every spawned grandchild so each test runs under stryke's bot-firewall mode (rejects Perl-isms, forces stryke idioms).</p>
<pre><code class="lang-perl">test_no_interop("t/")
test_ni(["t/a", "t/b"], { quiet => 1 })
</code></pre>
</article>
<article class="doc-entry" id="doc-check">
<h3><a class="doc-anchor" href="#doc-check">#</a> <code>check</code></h3>
<p><code>check(FILE, ...)</code> — in-process equivalent of <code>stryke check FILE...</code>. Parses, compiles, and lints each path without executing it. Returns the exit code (0 on success, 1 on errors). Optional trailing hashref: <code>{ quiet => 1 }</code>, <code>{ json => 1 }</code>, <code>{ no_interop => 1 }</code>.</p>
<p>Faster than <code>system "stryke check $f"</code> because it skips the binary fork and reuses the parent process's parser/compiler. The lint pass is <strong>not</strong> a strict-vars enforcer — undefined-variable errors only fire on files that themselves do <code>use strict;</code>.</p>
<pre><code class="lang-perl">my $rc = check("foo.stk") # 0 = ok, 1 = errors
check(\@files, { quiet => 1 }) # arrayref + opts
for my $f (glob("src/*.stk")) { check($f) or warn "$f failed" }
</code></pre>
</article>
<article class="doc-entry" id="doc-check-no-interop">
<h3><a class="doc-anchor" href="#doc-check-no-interop">#</a> <code>check_no_interop</code></h3>
<p><code>check_no_interop(FILE, ...)</code> (alias <code>check_ni</code>) — same as <code>check</code>, but pins <strong>this thread</strong> to <code>--no-interop</code> for the duration of the check via an RAII guard on the per-thread no-interop flag. Sibling threads are unaffected, so the builtin is safe to call from <code>pmaps</code> workers in parallel — no global-atomic race.</p>
<pre><code class="lang-perl">check_no_interop("foo.stk") # rejects sub/say/$a/$b
pmaps { check_ni(_, { quiet => 1 }) } @files # parallel-safe, no race
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-ai-primitives-docs-ai-primitives-md">
<h2>AI primitives (docs/AI_PRIMITIVES.md)</h2>
<p class="chapter-meta">79 topics</p>
<article class="doc-entry" id="doc-ai">
<h3><a class="doc-anchor" href="#doc-ai">#</a> <code>ai</code></h3>
<p><code>ai $prompt, opts...</code> — single-shot LLM call (or auto-routes to the agent loop when <code>tools => [...]</code>/<code>tool fn</code>s are in scope, vision when <code>image => $url|$path</code>, structured output when <code>schema => +{...}</code>, document input when <code>pdf => $path</code>).</p>
<pre><code class="lang-perl">my $r = ai "summarize this", $document
my $r = ai "weather in SF" # auto-uses any `tool fn` defined in scope
my $r = ai "describe", image => "/photo.jpg"
my $r = ai "extract user", schema => +{ name => "string", age => "int" }
</code></pre>
<p>Providers: anthropic (default), openai. Mock with <code>ai_mock_install</code>. Cost via <code>ai_cost</code>.</p>
</article>
<article class="doc-entry" id="doc-stream-prompt">
<h3><a class="doc-anchor" href="#doc-stream-prompt">#</a> <code>stream_prompt</code></h3>
<p><code>stream_prompt $prompt, on_chunk => sub { ... }</code> — Anthropic SSE streaming. With <code>on_chunk</code>, fires once per text-delta. Without, returns a <code>PerlIterator</code>-backed handle: <code>for my $chunk in stream_prompt("...") { print $chunk }</code>.</p>
<pre><code class="lang-perl">my $state = +{ buf => "" };
stream_prompt("write a haiku",
on_chunk => sub { $state->{buf} .= $_[0]; print $_[0] });
</code></pre>
</article>
<article class="doc-entry" id="doc-chat">
<h3><a class="doc-anchor" href="#doc-chat">#</a> <code>chat</code></h3>
<p><code>chat \@messages, opts...</code> — explicit message-list call. Each entry is <code>+{role => "user"|"assistant"|"system", content => ...}</code>.</p>
<pre><code class="lang-perl">chat([
+{ role => "system", content => "Be concise" },
+{ role => "user", content => "hi" },
])
</code></pre>
<p>For multi-turn with auto-tracking, use <code>ai_session_*</code> instead.</p>
</article>
<article class="doc-entry" id="doc-embed">
<h3><a class="doc-anchor" href="#doc-embed">#</a> <code>embed</code></h3>
<p><code>embed $text</code> or <code>embed \@texts</code> — vector embedding via Voyage AI (default) or OpenAI. Returns arrayref of floats (single text) or arrayref-of-arrayref (batch). Routes via <code>ai_routing_set("embed", ...)</code>.</p>
<pre><code class="lang-perl">my @vec = @{ embed("hello world") }
my @vecs = @{ embed(["a", "b", "c"]) }
</code></pre>
</article>
<article class="doc-entry" id="doc-tokens-of">
<h3><a class="doc-anchor" href="#doc-tokens-of">#</a> <code>tokens_of</code></h3>
<p><code>tokens_of</code> — operation <code>tokens of</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p tokens_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-estimate">
<h3><a class="doc-anchor" href="#doc-ai-estimate">#</a> <code>ai_estimate</code></h3>
<p><code>ai_estimate</code> — operation <code>ai estimate</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-cost">
<h3><a class="doc-anchor" href="#doc-ai-cost">#</a> <code>ai_cost</code></h3>
<p><code>ai_cost()</code> — running spend / token / cache stats hashref: <code>+{usd, input_tokens, output_tokens, embed_tokens, cache_creation_tokens, cache_read_tokens, cache_hits, cache_misses}</code>.</p>
</article>
<article class="doc-entry" id="doc-ai-history">
<h3><a class="doc-anchor" href="#doc-ai-history">#</a> <code>ai_history</code></h3>
<p><code>ai_history</code> — operation <code>ai history</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_history $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-history-clear">
<h3><a class="doc-anchor" href="#doc-ai-history-clear">#</a> <code>ai_history_clear</code></h3>
<p><code>ai_history_clear</code> — operation <code>ai history clear</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_history_clear $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-cache-clear">
<h3><a class="doc-anchor" href="#doc-ai-cache-clear">#</a> <code>ai_cache_clear</code></h3>
<p><code>ai_cache_clear</code> — operation <code>ai cache clear</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_cache_clear $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-cache-size">
<h3><a class="doc-anchor" href="#doc-ai-cache-size">#</a> <code>ai_cache_size</code></h3>
<p><code>ai_cache_size</code> — operation <code>ai cache size</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_cache_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-mock-install">
<h3><a class="doc-anchor" href="#doc-ai-mock-install">#</a> <code>ai_mock_install</code></h3>
<p><code>ai_mock_install</code> — operation <code>ai mock install</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_mock_install $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-mock-clear">
<h3><a class="doc-anchor" href="#doc-ai-mock-clear">#</a> <code>ai_mock_clear</code></h3>
<p><code>ai_mock_clear</code> — operation <code>ai mock clear</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_mock_clear $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-config-get">
<h3><a class="doc-anchor" href="#doc-ai-config-get">#</a> <code>ai_config_get</code></h3>
<p><code>ai_config_get</code> — operation <code>ai config get</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_config_get $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-config-set">
<h3><a class="doc-anchor" href="#doc-ai-config-set">#</a> <code>ai_config_set</code></h3>
<p><code>ai_config_set</code> — operation <code>ai config set</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_config_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-routing-get">
<h3><a class="doc-anchor" href="#doc-ai-routing-get">#</a> <code>ai_routing_get</code></h3>
<p><code>ai_routing_get</code> — operation <code>ai routing get</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_routing_get $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-routing-set">
<h3><a class="doc-anchor" href="#doc-ai-routing-set">#</a> <code>ai_routing_set</code></h3>
<p><code>ai_routing_set</code> — operation <code>ai routing set</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_routing_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-register-tool">
<h3><a class="doc-anchor" href="#doc-ai-register-tool">#</a> <code>ai_register_tool</code></h3>
<p><code>ai_register_tool($name, $description, +{params}, sub { ... })</code> — register a tool that the bare <code>ai($prompt)</code> call auto-attaches to its agent loop. Idempotent re-register on same name.</p>
<pre><code class="lang-perl">ai_register_tool("weather", "Get weather",
+{ city => "string" },
sub { fetch "https://api.weather.com/" . uri_encode($_[0]->{city}) });
ai_clear_tools();
</code></pre>
<p>For parser-level sugar, use <code>tool fn</code> instead.</p>
</article>
<article class="doc-entry" id="doc-ai-unregister-tool">
<h3><a class="doc-anchor" href="#doc-ai-unregister-tool">#</a> <code>ai_unregister_tool</code></h3>
<p><code>ai_unregister_tool</code> — operation <code>ai unregister tool</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_unregister_tool $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-clear-tools">
<h3><a class="doc-anchor" href="#doc-ai-clear-tools">#</a> <code>ai_clear_tools</code></h3>
<p><code>ai_clear_tools</code> — operation <code>ai clear tools</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_clear_tools $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-tools-list">
<h3><a class="doc-anchor" href="#doc-ai-tools-list">#</a> <code>ai_tools_list</code></h3>
<p><code>ai_tools_list</code> — operation <code>ai tools list</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_tools_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-filter">
<h3><a class="doc-anchor" href="#doc-ai-filter">#</a> <code>ai_filter</code></h3>
<p><code>ai_filter \@items, "criterion"</code> — keep items the model judges as matching the criterion. Single batched LLM call; cheap by construction.</p>
</article>
<article class="doc-entry" id="doc-ai-map">
<h3><a class="doc-anchor" href="#doc-ai-map">#</a> <code>ai_map</code></h3>
<p><code>ai_map \@items, "instruction"</code> — apply instruction to each item, single batched LLM call. Returns arrayref of strings.</p>
</article>
<article class="doc-entry" id="doc-ai-classify">
<h3><a class="doc-anchor" href="#doc-ai-classify">#</a> <code>ai_classify</code></h3>
<p><code>ai_classify \@items, "hint", into => ["a", "b", "c"]</code> — assign one of the labels to each item.</p>
</article>
<article class="doc-entry" id="doc-ai-match">
<h3><a class="doc-anchor" href="#doc-ai-match">#</a> <code>ai_match</code></h3>
<p><code>ai_match</code> — operation <code>ai match</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-sort">
<h3><a class="doc-anchor" href="#doc-ai-sort">#</a> <code>ai_sort</code></h3>
<p><code>ai_sort</code> — operation <code>ai sort</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_sort $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-dedupe">
<h3><a class="doc-anchor" href="#doc-ai-dedupe">#</a> <code>ai_dedupe</code></h3>
<p><code>ai_dedupe</code> — operation <code>ai dedupe</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_dedupe $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-extract">
<h3><a class="doc-anchor" href="#doc-ai-extract">#</a> <code>ai_extract</code></h3>
<p><code>ai_extract "prompt", schema => +{ name => "string", age => "int" }</code> — structured JSON output; returns a typed hashref.</p>
</article>
<article class="doc-entry" id="doc-ai-summarize">
<h3><a class="doc-anchor" href="#doc-ai-summarize">#</a> <code>ai_summarize</code></h3>
<p><code>ai_summarize $text, words => 50</code> — convenience wrapper that asks the model for a concise summary at target length.</p>
</article>
<article class="doc-entry" id="doc-ai-translate">
<h3><a class="doc-anchor" href="#doc-ai-translate">#</a> <code>ai_translate</code></h3>
<p><code>ai_translate $text, to => "Spanish"</code> — convenience wrapper for translation.</p>
</article>
<article class="doc-entry" id="doc-ai-template">
<h3><a class="doc-anchor" href="#doc-ai-template">#</a> <code>ai_template</code></h3>
<p><code>ai_template "hi {name}", name => "world"</code> — pure string substitution. <code>{{</code> escapes to a literal <code>{</code>. Missing keys pass through unchanged.</p>
</article>
<article class="doc-entry" id="doc-ai-transcribe">
<h3><a class="doc-anchor" href="#doc-ai-transcribe">#</a> <code>ai_transcribe</code></h3>
<p><code>ai_transcribe "audio.mp3", model => "whisper-1", language => "en"</code> — OpenAI Whisper transcription. Multipart upload to <code>/v1/audio/transcriptions</code>. Returns the transcript string. Defaults to <code>whisper-1</code>.</p>
</article>
<article class="doc-entry" id="doc-ai-speak">
<h3><a class="doc-anchor" href="#doc-ai-speak">#</a> <code>ai_speak</code></h3>
<p><code>ai_speak $text, voice => "alloy", model => "tts-1", format => "mp3", output => "out.mp3"</code> — OpenAI TTS. Returns raw audio bytes; pass <code>output =></code> to also write to disk. Voices: alloy, echo, fable, onyx, nova, shimmer.</p>
</article>
<article class="doc-entry" id="doc-ai-image">
<h3><a class="doc-anchor" href="#doc-ai-image">#</a> <code>ai_image</code></h3>
<p><code>ai_image $prompt, model => "dall-e-3", size => "1024x1024", quality => "hd", output => "out.png", n => 1</code> — image generation (OpenAI Images). Returns raw PNG bytes for n=1, or arrayref of bytes for n>1. Models: <code>dall-e-3</code>, <code>gpt-image-1</code>. <code>output</code> writes to disk (with <code>_1</code>/<code>_2</code>/... suffix for n>1).</p>
</article>
<article class="doc-entry" id="doc-ai-image-edit">
<h3><a class="doc-anchor" href="#doc-ai-image-edit">#</a> <code>ai_image_edit</code></h3>
<p><code>ai_image_edit $prompt, image => "in.png", mask => "mask.png", output => "out.png"</code> — image-to-image edit via OpenAI <code>/v1/images/edits</code>. Optional mask is a PNG with transparent regions marking where to edit. Returns PNG bytes (or arrayref for <code>n>1</code>).</p>
</article>
<article class="doc-entry" id="doc-ai-image-variation">
<h3><a class="doc-anchor" href="#doc-ai-image-variation">#</a> <code>ai_image_variation</code></h3>
<p><code>ai_image_variation image => "in.png", n => 4, size => "1024x1024"</code> — generate variations of an existing image (OpenAI <code>/v1/images/variations</code>, DALL-E 2). Returns PNG bytes for <code>n=1</code> or arrayref for <code>n>1</code>.</p>
</article>
<article class="doc-entry" id="doc-ai-models">
<h3><a class="doc-anchor" href="#doc-ai-models">#</a> <code>ai_models</code></h3>
<p><code>ai_models($provider)</code> → arrayref of model IDs from the live catalog. Providers: <code>openai</code>, <code>anthropic</code>, <code>ollama</code>, <code>gemini</code>. Useful for tooling that surfaces the available models without hardcoding lists.</p>
</article>
<article class="doc-entry" id="doc-ai-citations">
<h3><a class="doc-anchor" href="#doc-ai-citations">#</a> <code>ai_citations</code></h3>
<p><code>ai_citations()</code> — arrayref of citations from the most recent Anthropic call (when <code>citations => 1</code> was passed). Each entry is a hashref with <code>text</code> (cited string), <code>title</code>, <code>start</code>/<code>end</code> char offsets or <code>start_page</code>/<code>end_page</code> page numbers, and <code>document_index</code>.</p>
</article>
<article class="doc-entry" id="doc-ai-dashboard">
<h3><a class="doc-anchor" href="#doc-ai-dashboard">#</a> <code>ai_dashboard</code></h3>
<p><code>ai_dashboard()</code> → ANSI-colored multi-line summary (cost, tokens in/out, embed tokens, prompt-cache write/read, result-cache hit ratio). Drop at the end of a script or during a session: <code>print ai_dashboard()</code>.</p>
</article>
<article class="doc-entry" id="doc-ai-pricing">
<h3><a class="doc-anchor" href="#doc-ai-pricing">#</a> <code>ai_pricing</code></h3>
<p><code>ai_pricing("claude-opus-4-7")</code> → hashref <code>+{ model, input, output, input_per_1m, output_per_1m }</code> with the per-1K-token pricing the runtime uses for cost tracking. Useful for pre-flight cost estimates.</p>
</article>
<article class="doc-entry" id="doc-ai-describe">
<h3><a class="doc-anchor" href="#doc-ai-describe">#</a> <code>ai_describe</code></h3>
<p><code>ai_describe("image.png", style => "concise")</code> — vision wrapper that asks the model to describe an image. Styles: <code>concise</code> (one sentence), <code>detailed</code> (paragraph), <code>alt</code> (HTML alt-text ≤125 chars), or any custom suffix.</p>
</article>
<article class="doc-entry" id="doc-ai-grounded">
<h3><a class="doc-anchor" href="#doc-ai-grounded">#</a> <code>ai_grounded</code></h3>
<p><code>ai_grounded($prompt, documents => [@paths_or_strings], titles => [@titles])</code> — Anthropic-only multi-document grounding. Each entry can be a PDF path, a text-file path, or an inline string. Citations are auto-enabled; retrieve via <code>ai_citations()</code> after the call.</p>
</article>
<article class="doc-entry" id="doc-ai-moderate">
<h3><a class="doc-anchor" href="#doc-ai-moderate">#</a> <code>ai_moderate</code></h3>
<p><code>ai_moderate($text, model => "omni-moderation-latest")</code> → <code>+{ flagged, categories, scores }</code>. OpenAI content-safety classifier. Free endpoint — no token cost. Use it before sending user-generated content to a generative model.</p>
</article>
<article class="doc-entry" id="doc-ai-chunk">
<h3><a class="doc-anchor" href="#doc-ai-chunk">#</a> <code>ai_chunk</code></h3>
<p><code>ai_chunk($text, max_tokens => 500, overlap => 50, by => "tokens"|"chars"|"sentences")</code> → arrayref of strings. Pure local logic — no API call. Sentence mode splits on <code>.!?</code> and greedily packs.</p>
</article>
<article class="doc-entry" id="doc-ai-warm">
<h3><a class="doc-anchor" href="#doc-ai-warm">#</a> <code>ai_warm</code></h3>
<p><code>ai_warm(model => ..., provider => ...)</code> → <code>+{ ok, latency_ms, error, model, provider }</code>. Sends a 1-token ping so auth/network failures surface at script start instead of mid-flow.</p>
</article>
<article class="doc-entry" id="doc-ai-compare">
<h3><a class="doc-anchor" href="#doc-ai-compare">#</a> <code>ai_compare</code></h3>
<p><code>ai_compare($a, $b, criteria => "factual accuracy", scale => 5)</code> → <code>+{ winner, reason, scores => +{a, b}, raw }</code>. Single-call structured comparison. <code>winner</code> is <code>"a"</code>, <code>"b"</code>, or <code>"tie"</code>.</p>
</article>
<article class="doc-entry" id="doc-ai-session-export">
<h3><a class="doc-anchor" href="#doc-ai-session-export">#</a> <code>ai_session_export</code></h3>
<p><code>ai_session_export($handle)</code> → JSON string capturing system, model, provider, and full message log. Pair with <code>ai_session_import($json)</code> to restore.</p>
</article>
<article class="doc-entry" id="doc-ai-session-import">
<h3><a class="doc-anchor" href="#doc-ai-session-import">#</a> <code>ai_session_import</code></h3>
<p><code>ai_session_import($json)</code> → fresh session handle hashref. Inverse of <code>ai_session_export</code>. Allocates a new id and populates the session from the JSON body.</p>
</article>
<article class="doc-entry" id="doc-ai-file-upload">
<h3><a class="doc-anchor" href="#doc-ai-file-upload">#</a> <code>ai_file_upload</code></h3>
<p><code>ai_file_upload("path", purpose => "user_data")</code> → metadata hashref with <code>id</code>, <code>bytes</code>, <code>filename</code>, <code>purpose</code>, <code>created_at</code>. OpenAI Files API — file_id can be referenced by Whisper/Vision/Batch/Assistants.</p>
</article>
<article class="doc-entry" id="doc-ai-file-list">
<h3><a class="doc-anchor" href="#doc-ai-file-list">#</a> <code>ai_file_list</code></h3>
<p><code>ai_file_list(purpose => "...")</code> → arrayref of file metadata hashrefs from <code>/v1/files</code>.</p>
</article>
<article class="doc-entry" id="doc-ai-file-get">
<h3><a class="doc-anchor" href="#doc-ai-file-get">#</a> <code>ai_file_get</code></h3>
<p><code>ai_file_get($file_id)</code> → metadata hashref for a single file.</p>
</article>
<article class="doc-entry" id="doc-ai-file-delete">
<h3><a class="doc-anchor" href="#doc-ai-file-delete">#</a> <code>ai_file_delete</code></h3>
<p><code>ai_file_delete($file_id)</code> → 1 if deleted, 0 otherwise. Removes the file from OpenAI's storage.</p>
</article>
<article class="doc-entry" id="doc-ai-file-anthropic-upload">
<h3><a class="doc-anchor" href="#doc-ai-file-anthropic-upload">#</a> <code>ai_file_anthropic_upload</code></h3>
<p><code>ai_file_anthropic_upload("path/to/file.pdf")</code> → metadata hashref with <code>id</code>, <code>filename</code>, <code>mime_type</code>, <code>size_bytes</code>, <code>created_at</code>. Anthropic's beta <code>/v1/files</code> endpoint — file_id can be referenced from batch jobs and document blocks.</p>
</article>
<article class="doc-entry" id="doc-ai-file-anthropic-list">
<h3><a class="doc-anchor" href="#doc-ai-file-anthropic-list">#</a> <code>ai_file_anthropic_list</code></h3>
<p><code>ai_file_anthropic_list()</code> → arrayref of file-metadata hashrefs from Anthropic's <code>/v1/files</code>.</p>
</article>
<article class="doc-entry" id="doc-ai-file-anthropic-delete">
<h3><a class="doc-anchor" href="#doc-ai-file-anthropic-delete">#</a> <code>ai_file_anthropic_delete</code></h3>
<p><code>ai_file_anthropic_delete($file_id)</code> → 1 on success, 0 otherwise. Removes the file from Anthropic's storage.</p>
</article>
<article class="doc-entry" id="doc-ai-session-new">
<h3><a class="doc-anchor" href="#doc-ai-session-new">#</a> <code>ai_session_new</code></h3>
<p><code>ai_session_new(system => "...", model => "...")</code> — start a multi-turn chat session. Use <code>ai_session_send($s, "msg")</code> to advance, <code>ai_session_history($s)</code> to inspect, <code>ai_session_close($s)</code> to drop.</p>
</article>
<article class="doc-entry" id="doc-ai-session-send">
<h3><a class="doc-anchor" href="#doc-ai-session-send">#</a> <code>ai_session_send</code></h3>
<p><code>ai_session_send</code> — send of <code>ai session</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_session_send $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-session-history">
<h3><a class="doc-anchor" href="#doc-ai-session-history">#</a> <code>ai_session_history</code></h3>
<p><code>ai_session_history</code> — operation <code>ai session history</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_session_history $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-session-close">
<h3><a class="doc-anchor" href="#doc-ai-session-close">#</a> <code>ai_session_close</code></h3>
<p><code>ai_session_close</code> — close handle of <code>ai session</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_session_close $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-session-reset">
<h3><a class="doc-anchor" href="#doc-ai-session-reset">#</a> <code>ai_session_reset</code></h3>
<p><code>ai_session_reset</code> — operation <code>ai session reset</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_session_reset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-memory-save">
<h3><a class="doc-anchor" href="#doc-ai-memory-save">#</a> <code>ai_memory_save</code></h3>
<p><code>ai_memory_save("id", "content", $metadata?, $path?)</code> — embed + persist a doc in the sqlite-backed memory store.</p>
</article>
<article class="doc-entry" id="doc-ai-memory-recall">
<h3><a class="doc-anchor" href="#doc-ai-memory-recall">#</a> <code>ai_memory_recall</code></h3>
<p><code>ai_memory_recall("query", top_k => 5)</code> — re-embed query, return top-k matches by cosine similarity. Each entry: <code>+{id, content, score, metadata}</code>.</p>
</article>
<article class="doc-entry" id="doc-ai-memory-forget">
<h3><a class="doc-anchor" href="#doc-ai-memory-forget">#</a> <code>ai_memory_forget</code></h3>
<p><code>ai_memory_forget</code> — operation <code>ai memory forget</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_memory_forget $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-memory-count">
<h3><a class="doc-anchor" href="#doc-ai-memory-count">#</a> <code>ai_memory_count</code></h3>
<p><code>ai_memory_count</code> — count of <code>ai memory</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_memory_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-memory-clear">
<h3><a class="doc-anchor" href="#doc-ai-memory-clear">#</a> <code>ai_memory_clear</code></h3>
<p><code>ai_memory_clear</code> — operation <code>ai memory clear</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_memory_clear $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-vision">
<h3><a class="doc-anchor" href="#doc-ai-vision">#</a> <code>ai_vision</code></h3>
<p><code>ai_vision</code> — operation <code>ai vision</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_vision $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-pdf">
<h3><a class="doc-anchor" href="#doc-ai-pdf">#</a> <code>ai_pdf</code></h3>
<p><code>ai_pdf</code> — operation <code>ai pdf</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_pdf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-budget">
<h3><a class="doc-anchor" href="#doc-ai-budget">#</a> <code>ai_budget</code></h3>
<p><code>ai_budget($usd_cap, sub { ... })</code> — runs the block; raises a runtime error if AI spend during the block exceeds <code>$usd_cap</code>. Restores prior global cap on exit.</p>
</article>
<article class="doc-entry" id="doc-ai-last-thinking">
<h3><a class="doc-anchor" href="#doc-ai-last-thinking">#</a> <code>ai_last_thinking</code></h3>
<p><code>ai_last_thinking</code> — operation <code>ai last thinking</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_last_thinking $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-batch">
<h3><a class="doc-anchor" href="#doc-ai-batch">#</a> <code>ai_batch</code></h3>
<p><code>ai_batch</code> — operation <code>ai batch</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_batch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-pmap">
<h3><a class="doc-anchor" href="#doc-ai-pmap">#</a> <code>ai_pmap</code></h3>
<p><code>ai_pmap</code> — operation <code>ai pmap</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_pmap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vec-cosine">
<h3><a class="doc-anchor" href="#doc-vec-cosine">#</a> <code>vec_cosine</code></h3>
<p><code>vec_cosine \@a, \@b</code> — cosine similarity in <code>[-1, 1]</code>. Both args are arrayrefs of floats (typical embedding shape).</p>
</article>
<article class="doc-entry" id="doc-vec-search">
<h3><a class="doc-anchor" href="#doc-vec-search">#</a> <code>vec_search</code></h3>
<p><code>vec_search \@query, \@candidates, top_k => N</code> — return top-k matches as <code>+{idx, score}</code>.</p>
</article>
<article class="doc-entry" id="doc-vec-topk">
<h3><a class="doc-anchor" href="#doc-vec-topk">#</a> <code>vec_topk</code></h3>
<p><code>vec_topk</code> — operation <code>vec topk</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p vec_topk $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-search-tool">
<h3><a class="doc-anchor" href="#doc-web-search-tool">#</a> <code>web_search_tool</code></h3>
<p><code>web_search_tool()</code> — built-in tool spec for <code>tools => [...]</code>. Brave Search via <code>$BRAVE_SEARCH_API_KEY</code>, falls back to DuckDuckGo HTML scrape.</p>
</article>
<article class="doc-entry" id="doc-fetch-url-tool">
<h3><a class="doc-anchor" href="#doc-fetch-url-tool">#</a> <code>fetch_url_tool</code></h3>
<p><code>fetch_url_tool()</code> — built-in tool spec that fetches a URL and returns text.</p>
</article>
<article class="doc-entry" id="doc-read-file-tool">
<h3><a class="doc-anchor" href="#doc-read-file-tool">#</a> <code>read_file_tool</code></h3>
<p><code>read_file_tool()</code> — built-in tool spec that reads a file from disk.</p>
</article>
<article class="doc-entry" id="doc-run-code-tool">
<h3><a class="doc-anchor" href="#doc-run-code-tool">#</a> <code>run_code_tool</code></h3>
<p><code>run_code_tool()</code> — built-in tool spec that runs Python code in a subprocess (10s timeout, returns stdout+stderr).</p>
</article>
<article class="doc-entry" id="doc-tool">
<h3><a class="doc-anchor" href="#doc-tool">#</a> <code>tool</code></h3>
<p><code>tool fn NAME($p1: type, $p2: type) -> Type "docstring" { body }</code> — declare an agent-callable tool. Param types become the JSON Schema. Auto-registers via <code>ai_register_tool</code> so bare <code>ai($prompt)</code> calls see it.</p>
<pre><code class="lang-perl">tool fn weather($city: string) "Get current weather" {
fetch "https://api.weather.com/" . uri_encode($city)
}
tool fn calc($a: int, $b: int) -> int "Add two ints" { $a + $b }
my $r = ai("what's the weather in SF and 7+5?");
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-mcp-model-context-protocol">
<h2>MCP (Model Context Protocol)</h2>
<p class="chapter-meta">13 topics</p>
<article class="doc-entry" id="doc-mcp-connect">
<h3><a class="doc-anchor" href="#doc-mcp-connect">#</a> <code>mcp_connect</code></h3>
<p><code>mcp_connect "stdio:CMD ARGS"</code> or <code>mcp_connect "https://server/mcp"</code> — connect to an MCP server. Speaks JSON-RPC over stdio (subprocess) or streamable HTTP. Returns a handle.</p>
</article>
<article class="doc-entry" id="doc-mcp-tools">
<h3><a class="doc-anchor" href="#doc-mcp-tools">#</a> <code>mcp_tools</code></h3>
<p><code>mcp_tools $h</code> — list the server's tools. Cached after first call.</p>
</article>
<article class="doc-entry" id="doc-mcp-resources">
<h3><a class="doc-anchor" href="#doc-mcp-resources">#</a> <code>mcp_resources</code></h3>
<p><code>mcp_resources</code> — operation <code>mcp resources</code>. Category: *mcp (model context protocol)*.</p>
<pre><code class="lang-perl">p mcp_resources $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mcp-prompts">
<h3><a class="doc-anchor" href="#doc-mcp-prompts">#</a> <code>mcp_prompts</code></h3>
<p><code>mcp_prompts</code> — operation <code>mcp prompts</code>. Category: *mcp (model context protocol)*.</p>
<pre><code class="lang-perl">p mcp_prompts $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mcp-call">
<h3><a class="doc-anchor" href="#doc-mcp-call">#</a> <code>mcp_call</code></h3>
<p><code>mcp_call $h, "tool_name", +{...args}</code> — invoke a tool on the connected server.</p>
</article>
<article class="doc-entry" id="doc-mcp-resource">
<h3><a class="doc-anchor" href="#doc-mcp-resource">#</a> <code>mcp_resource</code></h3>
<p><code>mcp_resource</code> — operation <code>mcp resource</code>. Category: *mcp (model context protocol)*.</p>
<pre><code class="lang-perl">p mcp_resource $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mcp-prompt">
<h3><a class="doc-anchor" href="#doc-mcp-prompt">#</a> <code>mcp_prompt</code></h3>
<p><code>mcp_prompt</code> — operation <code>mcp prompt</code>. Category: *mcp (model context protocol)*.</p>
<pre><code class="lang-perl">p mcp_prompt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mcp-close">
<h3><a class="doc-anchor" href="#doc-mcp-close">#</a> <code>mcp_close</code></h3>
<p><code>mcp_close</code> — close handle of <code>mcp</code>. Category: *mcp (model context protocol)*.</p>
<pre><code class="lang-perl">p mcp_close $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mcp-attach-to-ai">
<h3><a class="doc-anchor" href="#doc-mcp-attach-to-ai">#</a> <code>mcp_attach_to_ai</code></h3>
<p><code>mcp_attach_to_ai $h</code> — register a connected MCP server so subsequent bare <code>ai($prompt)</code> calls auto-include its tools.</p>
</article>
<article class="doc-entry" id="doc-mcp-detach-from-ai">
<h3><a class="doc-anchor" href="#doc-mcp-detach-from-ai">#</a> <code>mcp_detach_from_ai</code></h3>
<p><code>mcp_detach_from_ai</code> — operation <code>mcp detach from ai</code>. Category: *mcp (model context protocol)*.</p>
<pre><code class="lang-perl">p mcp_detach_from_ai $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mcp-attached">
<h3><a class="doc-anchor" href="#doc-mcp-attached">#</a> <code>mcp_attached</code></h3>
<p><code>mcp_attached</code> — operation <code>mcp attached</code>. Category: *mcp (model context protocol)*.</p>
<pre><code class="lang-perl">p mcp_attached $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mcp-server-start">
<h3><a class="doc-anchor" href="#doc-mcp-server-start">#</a> <code>mcp_server_start</code></h3>
<p><code>mcp_server_start "name", +{ tools => [...] }</code> — run a stdio JSON-RPC MCP server in-process. Pair with <code>s_web build</code> to ship a self-contained MCP server binary.</p>
<p>For parser-level sugar, use <code>mcp_server "name" { tool foo($a) "..." {...} }</code>.</p>
</article>
<article class="doc-entry" id="doc-mcp-server">
<h3><a class="doc-anchor" href="#doc-mcp-server">#</a> <code>mcp_server</code></h3>
<p><code>mcp_server "name" { tool NAME(args) "doc" { body } ... }</code> — declarative MCP server block. Compiles to <code>mcp_server_start("name", +{ tools => [...] })</code> with private helper fns for each tool body.</p>
<pre><code class="lang-perl">mcp_server "filesystem" {
tool read_file($path: string) "Read file contents" { slurp $path }
tool list_dir($path: string) "List dir entries" { join("\n", readdir $path) }
}
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-web-framework-stryke-web-readme-md">
<h2>Web framework (stryke_web/README.md)</h2>
<p class="chapter-meta">112 topics</p>
<article class="doc-entry" id="doc-web-route">
<h3><a class="doc-anchor" href="#doc-web-route">#</a> <code>web_route</code></h3>
<p><code>web_route "VERB /path", "controller#action"</code> — register a route in the global router.</p>
<pre><code class="lang-perl">web_route "GET /posts", "posts#index"
web_route "POST /posts", "posts#create"
</code></pre>
</article>
<article class="doc-entry" id="doc-web-resources">
<h3><a class="doc-anchor" href="#doc-web-resources">#</a> <code>web_resources</code></h3>
<p><code>web_resources "posts"</code> — register the 7-route REST scaffold (index/show/new/create/edit/update/destroy) for a resource.</p>
</article>
<article class="doc-entry" id="doc-web-root">
<h3><a class="doc-anchor" href="#doc-web-root">#</a> <code>web_root</code></h3>
<p><code>web_root "posts#index"</code> — shortcut for <code>web_route "GET /"</code>.</p>
</article>
<article class="doc-entry" id="doc-web-application-config">
<h3><a class="doc-anchor" href="#doc-web-application-config">#</a> <code>web_application_config</code></h3>
<p><code>web_application_config</code> — operation <code>web application config</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_application_config $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-render">
<h3><a class="doc-anchor" href="#doc-web-render">#</a> <code>web_render</code></h3>
<p><code>web_render html => "..."</code> / <code>text => ...</code> / <code>json => ...</code> / <code>template => "posts/index", locals => +{...}</code> — emit a response. Templates resolve <code>app/views/...html.erb</code>, run through the ERB engine, wrap in the application layout.</p>
</article>
<article class="doc-entry" id="doc-web-render-partial">
<h3><a class="doc-anchor" href="#doc-web-render-partial">#</a> <code>web_render_partial</code></h3>
<p><code>web_render_partial</code> — operation <code>web render partial</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_render_partial $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-redirect">
<h3><a class="doc-anchor" href="#doc-web-redirect">#</a> <code>web_redirect</code></h3>
<p><code>web_redirect "/path", 302</code> — issue a 3xx redirect with <code>Location</code> header.</p>
</article>
<article class="doc-entry" id="doc-web-json">
<h3><a class="doc-anchor" href="#doc-web-json">#</a> <code>web_json</code></h3>
<p><code>web_json</code> — operation <code>web json</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_json $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-text">
<h3><a class="doc-anchor" href="#doc-web-text">#</a> <code>web_text</code></h3>
<p><code>web_text</code> — operation <code>web text</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_text $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-params">
<h3><a class="doc-anchor" href="#doc-web-params">#</a> <code>web_params</code></h3>
<p><code>web_params()</code> — hashref of query + form-urlencoded body + JSON body + path captures.</p>
</article>
<article class="doc-entry" id="doc-web-request">
<h3><a class="doc-anchor" href="#doc-web-request">#</a> <code>web_request</code></h3>
<p><code>web_request</code> — operation <code>web request</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_request $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-routes-table">
<h3><a class="doc-anchor" href="#doc-web-routes-table">#</a> <code>web_routes_table</code></h3>
<p><code>web_routes_table</code> — lookup table of <code>web routes</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_routes_table $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-boot-application">
<h3><a class="doc-anchor" href="#doc-web-boot-application">#</a> <code>web_boot_application</code></h3>
<p><code>web_boot_application</code> — operation <code>web boot application</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_boot_application $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-db-connect">
<h3><a class="doc-anchor" href="#doc-web-db-connect">#</a> <code>web_db_connect</code></h3>
<p><code>web_db_connect "sqlite://path"</code> — open and cache the global SQLite connection. Required before any <code>web_model_*</code> call.</p>
</article>
<article class="doc-entry" id="doc-web-db-execute">
<h3><a class="doc-anchor" href="#doc-web-db-execute">#</a> <code>web_db_execute</code></h3>
<p><code>web_db_execute</code> — operation <code>web db execute</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_db_execute $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-db-query">
<h3><a class="doc-anchor" href="#doc-web-db-query">#</a> <code>web_db_query</code></h3>
<p><code>web_db_query</code> — operation <code>web db query</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_db_query $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-jobs-init">
<h3><a class="doc-anchor" href="#doc-web-jobs-init">#</a> <code>web_jobs_init</code></h3>
<p><code>web_jobs_init()</code> — create the SQLite <code>jobs</code> table if it doesn't exist. Idempotent.</p>
</article>
<article class="doc-entry" id="doc-web-job-enqueue">
<h3><a class="doc-anchor" href="#doc-web-job-enqueue">#</a> <code>web_job_enqueue</code></h3>
<p><code>web_job_enqueue("name", +{...args}, queue => "...", priority => N, max_attempts => N)</code> → job id (i64). Status starts as <code>pending</code>.</p>
</article>
<article class="doc-entry" id="doc-web-job-dequeue">
<h3><a class="doc-anchor" href="#doc-web-job-dequeue">#</a> <code>web_job_dequeue</code></h3>
<p><code>web_job_dequeue(queue => "...")</code> → <code>+{id, name, args_json, args, attempts, max_attempts}</code> or undef. Atomically marks the picked job as <code>running</code> and increments <code>attempts</code>.</p>
</article>
<article class="doc-entry" id="doc-web-job-complete">
<h3><a class="doc-anchor" href="#doc-web-job-complete">#</a> <code>web_job_complete</code></h3>
<p><code>web_job_complete($id)</code> — mark a running job as <code>done</code>.</p>
</article>
<article class="doc-entry" id="doc-web-job-fail">
<h3><a class="doc-anchor" href="#doc-web-job-fail">#</a> <code>web_job_fail</code></h3>
<p><code>web_job_fail($id, error => "msg")</code> — if <code>attempts < max_attempts</code>, returns to <code>pending</code> for retry; otherwise marked <code>failed</code>. Returns the new status.</p>
</article>
<article class="doc-entry" id="doc-web-jobs-list">
<h3><a class="doc-anchor" href="#doc-web-jobs-list">#</a> <code>web_jobs_list</code></h3>
<p><code>web_jobs_list(queue => "...", status => "...", limit => 50)</code> → arrayref of job hashrefs.</p>
</article>
<article class="doc-entry" id="doc-web-jobs-stats">
<h3><a class="doc-anchor" href="#doc-web-jobs-stats">#</a> <code>web_jobs_stats</code></h3>
<p><code>web_jobs_stats()</code> → <code>+{pending, running, done, failed}</code>.</p>
</article>
<article class="doc-entry" id="doc-web-job-purge">
<h3><a class="doc-anchor" href="#doc-web-job-purge">#</a> <code>web_job_purge</code></h3>
<p><code>web_job_purge(status => "done")</code> → number of rows deleted.</p>
</article>
<article class="doc-entry" id="doc-web-db-begin">
<h3><a class="doc-anchor" href="#doc-web-db-begin">#</a> <code>web_db_begin</code></h3>
<p><code>web_db_begin</code> — operation <code>web db begin</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_db_begin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-db-commit">
<h3><a class="doc-anchor" href="#doc-web-db-commit">#</a> <code>web_db_commit</code></h3>
<p><code>web_db_commit</code> — operation <code>web db commit</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_db_commit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-db-rollback">
<h3><a class="doc-anchor" href="#doc-web-db-rollback">#</a> <code>web_db_rollback</code></h3>
<p><code>web_db_rollback</code> — operation <code>web db rollback</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_db_rollback $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-model-all">
<h3><a class="doc-anchor" href="#doc-web-model-all">#</a> <code>web_model_all</code></h3>
<p><code>web_model_all "posts"</code> — <code>SELECT * FROM posts ORDER BY id</code>. Returns arrayref of hashrefs.</p>
</article>
<article class="doc-entry" id="doc-web-model-find">
<h3><a class="doc-anchor" href="#doc-web-model-find">#</a> <code>web_model_find</code></h3>
<p><code>web_model_find "posts", $id</code> — find by id; returns hashref or undef.</p>
</article>
<article class="doc-entry" id="doc-web-model-where">
<h3><a class="doc-anchor" href="#doc-web-model-where">#</a> <code>web_model_where</code></h3>
<p><code>web_model_where</code> — operation <code>web model where</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_model_where $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-model-create">
<h3><a class="doc-anchor" href="#doc-web-model-create">#</a> <code>web_model_create</code></h3>
<p><code>web_model_create "posts", +{title => "...", body => "..."}</code> — INSERT + return new row with id and auto-set <code>created_at</code>/<code>updated_at</code>.</p>
</article>
<article class="doc-entry" id="doc-web-model-update">
<h3><a class="doc-anchor" href="#doc-web-model-update">#</a> <code>web_model_update</code></h3>
<p><code>web_model_update</code> — update step of <code>web model</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_model_update $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-model-destroy">
<h3><a class="doc-anchor" href="#doc-web-model-destroy">#</a> <code>web_model_destroy</code></h3>
<p><code>web_model_destroy</code> — operation <code>web model destroy</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_model_destroy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-model-soft-destroy">
<h3><a class="doc-anchor" href="#doc-web-model-soft-destroy">#</a> <code>web_model_soft_destroy</code></h3>
<p><code>web_model_soft_destroy</code> — operation <code>web model soft destroy</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_model_soft_destroy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-model-paginate">
<h3><a class="doc-anchor" href="#doc-web-model-paginate">#</a> <code>web_model_paginate</code></h3>
<p><code>web_model_paginate</code> — operation <code>web model paginate</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_model_paginate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-model-search">
<h3><a class="doc-anchor" href="#doc-web-model-search">#</a> <code>web_model_search</code></h3>
<p><code>web_model_search</code> — operation <code>web model search</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_model_search $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-model-count">
<h3><a class="doc-anchor" href="#doc-web-model-count">#</a> <code>web_model_count</code></h3>
<p><code>web_model_count</code> — count of <code>web model</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_model_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-model-first">
<h3><a class="doc-anchor" href="#doc-web-model-first">#</a> <code>web_model_first</code></h3>
<p><code>web_model_first</code> — operation <code>web model first</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_model_first $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-model-last">
<h3><a class="doc-anchor" href="#doc-web-model-last">#</a> <code>web_model_last</code></h3>
<p><code>web_model_last</code> — operation <code>web model last</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_model_last $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-model-increment">
<h3><a class="doc-anchor" href="#doc-web-model-increment">#</a> <code>web_model_increment</code></h3>
<p><code>web_model_increment</code> — operation <code>web model increment</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_model_increment $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-model-with">
<h3><a class="doc-anchor" href="#doc-web-model-with">#</a> <code>web_model_with</code></h3>
<p><code>web_model_with</code> — operation <code>web model with</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_model_with $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-create-table">
<h3><a class="doc-anchor" href="#doc-web-create-table">#</a> <code>web_create_table</code></h3>
<p><code>web_create_table</code> — lookup table of <code>web create</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_create_table $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-drop-table">
<h3><a class="doc-anchor" href="#doc-web-drop-table">#</a> <code>web_drop_table</code></h3>
<p><code>web_drop_table</code> — lookup table of <code>web drop</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_drop_table $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-add-column">
<h3><a class="doc-anchor" href="#doc-web-add-column">#</a> <code>web_add_column</code></h3>
<p><code>web_add_column</code> — operation <code>web add column</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_add_column $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-remove-column">
<h3><a class="doc-anchor" href="#doc-web-remove-column">#</a> <code>web_remove_column</code></h3>
<p><code>web_remove_column</code> — operation <code>web remove column</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_remove_column $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-migrate">
<h3><a class="doc-anchor" href="#doc-web-migrate">#</a> <code>web_migrate</code></h3>
<p><code>web_migrate()</code> — apply every <code>up</code> block from <code>db/migrate/*.stk</code> whose version isn't yet in <code>schema_migrations</code>.</p>
</article>
<article class="doc-entry" id="doc-web-rollback">
<h3><a class="doc-anchor" href="#doc-web-rollback">#</a> <code>web_rollback</code></h3>
<p><code>web_rollback</code> — operation <code>web rollback</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_rollback $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-validate">
<h3><a class="doc-anchor" href="#doc-web-validate">#</a> <code>web_validate</code></h3>
<p><code>web_validate $attrs, +{title => "presence,length:1..100", email => "format:^.+@.+$"}</code> — returns <code>+{ok => 1}</code> or <code>+{ok => 0, errors => +{...}}</code>. Validators: <code>presence</code>, <code>length:MIN..MAX</code>, <code>format:REGEX</code>, <code>numericality</code>, <code>inclusion:a|b|c</code>, <code>confirmation:other_field</code>.</p>
</article>
<article class="doc-entry" id="doc-web-permit">
<h3><a class="doc-anchor" href="#doc-web-permit">#</a> <code>web_permit</code></h3>
<p><code>web_permit</code> — operation <code>web permit</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_permit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-password-hash">
<h3><a class="doc-anchor" href="#doc-web-password-hash">#</a> <code>web_password_hash</code></h3>
<p><code>web_password_hash $pw</code> returns a <code>web1$saltHex$digest</code> shaped string. <code>web_password_verify $pw, $stored</code> returns 1/0. SHA-256 + 16-byte salt; constant-time compare.</p>
</article>
<article class="doc-entry" id="doc-web-session">
<h3><a class="doc-anchor" href="#doc-web-session">#</a> <code>web_session</code></h3>
<p><code>web_session</code> — operation <code>web session</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_session $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-session-set">
<h3><a class="doc-anchor" href="#doc-web-session-set">#</a> <code>web_session_set</code></h3>
<p>Server-side session storage backed by a signed cookie. <code>web_session_set("user_id", 42)</code> / <code>web_session_get("user_id")</code>. Cookie value is base64-JSON; HttpOnly + SameSite=Lax by default.</p>
</article>
<article class="doc-entry" id="doc-web-session-clear">
<h3><a class="doc-anchor" href="#doc-web-session-clear">#</a> <code>web_session_clear</code></h3>
<p><code>web_session_clear</code> — operation <code>web session clear</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_session_clear $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-set-cookie">
<h3><a class="doc-anchor" href="#doc-web-set-cookie">#</a> <code>web_set_cookie</code></h3>
<p><code>web_set_cookie</code> — operation <code>web set cookie</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_set_cookie $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-cookies">
<h3><a class="doc-anchor" href="#doc-web-cookies">#</a> <code>web_cookies</code></h3>
<p><code>web_cookies</code> — operation <code>web cookies</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_cookies $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-flash">
<h3><a class="doc-anchor" href="#doc-web-flash">#</a> <code>web_flash</code></h3>
<p><code>web_flash</code> — operation <code>web flash</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_flash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-flash-set">
<h3><a class="doc-anchor" href="#doc-web-flash-set">#</a> <code>web_flash_set</code></h3>
<p><code>web_flash_set</code> — operation <code>web flash set</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_flash_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-flash-get">
<h3><a class="doc-anchor" href="#doc-web-flash-get">#</a> <code>web_flash_get</code></h3>
<p><code>web_flash_get</code> — operation <code>web flash get</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_flash_get $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-jwt-encode">
<h3><a class="doc-anchor" href="#doc-web-jwt-encode">#</a> <code>web_jwt_encode</code></h3>
<p><code>web_jwt_encode +{user_id => 1, role => "admin"}</code> — HS256-sign a JWT using <code>secret_key_base</code> from <code>web_application_config</code>.</p>
</article>
<article class="doc-entry" id="doc-web-jwt-decode">
<h3><a class="doc-anchor" href="#doc-web-jwt-decode">#</a> <code>web_jwt_decode</code></h3>
<p><code>web_jwt_decode $token</code> — verify + decode an HS256 JWT. Returns the payload hashref or undef on bad signature.</p>
</article>
<article class="doc-entry" id="doc-web-bearer-token">
<h3><a class="doc-anchor" href="#doc-web-bearer-token">#</a> <code>web_bearer_token</code></h3>
<p><code>web_bearer_token</code> — operation <code>web bearer token</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_bearer_token $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-otp-secret">
<h3><a class="doc-anchor" href="#doc-web-otp-secret">#</a> <code>web_otp_secret</code></h3>
<p>TOTP / 2FA — RFC 6238, 30-second window, ±1 step skew tolerance. <code>web_otp_secret()</code> returns a base32 secret to share with the authenticator app; <code>web_otp_generate($secret)</code> returns the current 6-digit code; <code>web_otp_verify($secret, $code)</code> returns 1/0.</p>
</article>
<article class="doc-entry" id="doc-web-token-for">
<h3><a class="doc-anchor" href="#doc-web-token-for">#</a> <code>web_token_for</code></h3>
<p><code>web_token_for</code> — operation <code>web token for</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_token_for $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-token-consume">
<h3><a class="doc-anchor" href="#doc-web-token-consume">#</a> <code>web_token_consume</code></h3>
<p><code>web_token_consume</code> — operation <code>web token consume</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_token_consume $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-can">
<h3><a class="doc-anchor" href="#doc-web-can">#</a> <code>web_can</code></h3>
<p><code>web_can</code> — operation <code>web can</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_can $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-signed">
<h3><a class="doc-anchor" href="#doc-web-signed">#</a> <code>web_signed</code></h3>
<p><code>web_signed</code> — operation <code>web signed</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_signed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-unsigned">
<h3><a class="doc-anchor" href="#doc-web-unsigned">#</a> <code>web_unsigned</code></h3>
<p><code>web_unsigned</code> — operation <code>web unsigned</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_unsigned $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-cache-get">
<h3><a class="doc-anchor" href="#doc-web-cache-get">#</a> <code>web_cache_get</code></h3>
<p><code>web_cache_get</code> — operation <code>web cache get</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_cache_get $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-cache-set">
<h3><a class="doc-anchor" href="#doc-web-cache-set">#</a> <code>web_cache_set</code></h3>
<p><code>web_cache_set</code> — operation <code>web cache set</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_cache_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-cache-delete">
<h3><a class="doc-anchor" href="#doc-web-cache-delete">#</a> <code>web_cache_delete</code></h3>
<p><code>web_cache_delete</code> — operation <code>web cache delete</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_cache_delete $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-cache-clear">
<h3><a class="doc-anchor" href="#doc-web-cache-clear">#</a> <code>web_cache_clear</code></h3>
<p><code>web_cache_clear</code> — operation <code>web cache clear</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_cache_clear $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-t">
<h3><a class="doc-anchor" href="#doc-web-t">#</a> <code>web_t</code></h3>
<p><code>web_t</code> — operation <code>web t</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-load-locale">
<h3><a class="doc-anchor" href="#doc-web-load-locale">#</a> <code>web_load_locale</code></h3>
<p><code>web_load_locale</code> — operation <code>web load locale</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_load_locale $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-log">
<h3><a class="doc-anchor" href="#doc-web-log">#</a> <code>web_log</code></h3>
<p><code>web_log</code> — operation <code>web log</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_log $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-set-header">
<h3><a class="doc-anchor" href="#doc-web-set-header">#</a> <code>web_set_header</code></h3>
<p><code>web_set_header</code> — operation <code>web set header</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_set_header $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-status">
<h3><a class="doc-anchor" href="#doc-web-status">#</a> <code>web_status</code></h3>
<p><code>web_status</code> — operation <code>web status</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_status $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-uuid">
<h3><a class="doc-anchor" href="#doc-web-uuid">#</a> <code>web_uuid</code></h3>
<p><code>web_uuid</code> — operation <code>web uuid</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_uuid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-now">
<h3><a class="doc-anchor" href="#doc-web-now">#</a> <code>web_now</code></h3>
<p><code>web_now</code> — operation <code>web now</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_now $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-security-headers">
<h3><a class="doc-anchor" href="#doc-web-security-headers">#</a> <code>web_security_headers</code></h3>
<p><code>web_security_headers</code> — operation <code>web security headers</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_security_headers $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-openapi">
<h3><a class="doc-anchor" href="#doc-web-openapi">#</a> <code>web_openapi</code></h3>
<p><code>web_openapi</code> — operation <code>web openapi</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_openapi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-etag">
<h3><a class="doc-anchor" href="#doc-web-etag">#</a> <code>web_etag</code></h3>
<p><code>web_etag</code> — operation <code>web etag</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_etag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-csv">
<h3><a class="doc-anchor" href="#doc-web-csv">#</a> <code>web_csv</code></h3>
<p><code>web_csv</code> — operation <code>web csv</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_csv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-markdown">
<h3><a class="doc-anchor" href="#doc-web-markdown">#</a> <code>web_markdown</code></h3>
<p><code>web_markdown</code> — operation <code>web markdown</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_markdown $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-md">
<h3><a class="doc-anchor" href="#doc-web-md">#</a> <code>web_md</code></h3>
<p><code>web_md</code> — operation <code>web md</code>. Alias for <code>web_markdown</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_md $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-content-for">
<h3><a class="doc-anchor" href="#doc-web-content-for">#</a> <code>web_content_for</code></h3>
<p><code>web_content_for</code> — operation <code>web content for</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_content_for $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-yield-content">
<h3><a class="doc-anchor" href="#doc-web-yield-content">#</a> <code>web_yield_content</code></h3>
<p><code>web_yield_content</code> — operation <code>web yield content</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_yield_content $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-jsonapi-resource">
<h3><a class="doc-anchor" href="#doc-web-jsonapi-resource">#</a> <code>web_jsonapi_resource</code></h3>
<p><code>web_jsonapi_resource</code> — operation <code>web jsonapi resource</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_jsonapi_resource $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-jsonapi-collection">
<h3><a class="doc-anchor" href="#doc-web-jsonapi-collection">#</a> <code>web_jsonapi_collection</code></h3>
<p><code>web_jsonapi_collection</code> — operation <code>web jsonapi collection</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_jsonapi_collection $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-jsonapi-error">
<h3><a class="doc-anchor" href="#doc-web-jsonapi-error">#</a> <code>web_jsonapi_error</code></h3>
<p><code>web_jsonapi_error</code> — operation <code>web jsonapi error</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_jsonapi_error $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-rate-limit">
<h3><a class="doc-anchor" href="#doc-web-rate-limit">#</a> <code>web_rate_limit</code></h3>
<p><code>web_rate_limit</code> — operation <code>web rate limit</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_rate_limit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-before-action">
<h3><a class="doc-anchor" href="#doc-web-before-action">#</a> <code>web_before_action</code></h3>
<p><code>web_before_action</code> — operation <code>web before action</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_before_action $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-after-action">
<h3><a class="doc-anchor" href="#doc-web-after-action">#</a> <code>web_after_action</code></h3>
<p><code>web_after_action</code> — operation <code>web after action</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_after_action $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-h">
<h3><a class="doc-anchor" href="#doc-web-h">#</a> <code>web_h</code></h3>
<p><code>web_h</code> — operation <code>web h</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_h $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-link-to">
<h3><a class="doc-anchor" href="#doc-web-link-to">#</a> <code>web_link_to</code></h3>
<p><code>web_link_to</code> — operation <code>web link to</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_link_to $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-button-to">
<h3><a class="doc-anchor" href="#doc-web-button-to">#</a> <code>web_button_to</code></h3>
<p><code>web_button_to</code> — operation <code>web button to</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_button_to $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-form-with">
<h3><a class="doc-anchor" href="#doc-web-form-with">#</a> <code>web_form_with</code></h3>
<p><code>web_form_with</code> — operation <code>web form with</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_form_with $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-form-close">
<h3><a class="doc-anchor" href="#doc-web-form-close">#</a> <code>web_form_close</code></h3>
<p><code>web_form_close</code> — close handle of <code>web form</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_form_close $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-text-field">
<h3><a class="doc-anchor" href="#doc-web-text-field">#</a> <code>web_text_field</code></h3>
<p><code>web_text_field</code> — operation <code>web text field</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_text_field $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-text-area">
<h3><a class="doc-anchor" href="#doc-web-text-area">#</a> <code>web_text_area</code></h3>
<p><code>web_text_area</code> — operation <code>web text area</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_text_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-check-box">
<h3><a class="doc-anchor" href="#doc-web-check-box">#</a> <code>web_check_box</code></h3>
<p><code>web_check_box</code> — operation <code>web check box</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_check_box $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-csrf-meta-tag">
<h3><a class="doc-anchor" href="#doc-web-csrf-meta-tag">#</a> <code>web_csrf_meta_tag</code></h3>
<p><code>web_csrf_meta_tag</code> — operation <code>web csrf meta tag</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_csrf_meta_tag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-stylesheet-link-tag">
<h3><a class="doc-anchor" href="#doc-web-stylesheet-link-tag">#</a> <code>web_stylesheet_link_tag</code></h3>
<p><code>web_stylesheet_link_tag</code> — operation <code>web stylesheet link tag</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_stylesheet_link_tag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-javascript-link-tag">
<h3><a class="doc-anchor" href="#doc-web-javascript-link-tag">#</a> <code>web_javascript_link_tag</code></h3>
<p><code>web_javascript_link_tag</code> — operation <code>web javascript link tag</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_javascript_link_tag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-image-tag">
<h3><a class="doc-anchor" href="#doc-web-image-tag">#</a> <code>web_image_tag</code></h3>
<p><code>web_image_tag</code> — operation <code>web image tag</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_image_tag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-truncate">
<h3><a class="doc-anchor" href="#doc-web-truncate">#</a> <code>web_truncate</code></h3>
<p><code>web_truncate</code> — operation <code>web truncate</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_truncate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-pluralize">
<h3><a class="doc-anchor" href="#doc-web-pluralize">#</a> <code>web_pluralize</code></h3>
<p><code>web_pluralize</code> — operation <code>web pluralize</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_pluralize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-time-ago-in-words">
<h3><a class="doc-anchor" href="#doc-web-time-ago-in-words">#</a> <code>web_time_ago_in_words</code></h3>
<p><code>web_time_ago_in_words</code> — operation <code>web time ago in words</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_time_ago_in_words $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-faker-name">
<h3><a class="doc-anchor" href="#doc-web-faker-name">#</a> <code>web_faker_name</code></h3>
<p><code>web_faker_name</code> — operation <code>web faker name</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_faker_name $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-faker-email">
<h3><a class="doc-anchor" href="#doc-web-faker-email">#</a> <code>web_faker_email</code></h3>
<p><code>web_faker_email</code> — operation <code>web faker email</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_faker_email $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-faker-sentence">
<h3><a class="doc-anchor" href="#doc-web-faker-sentence">#</a> <code>web_faker_sentence</code></h3>
<p><code>web_faker_sentence</code> — operation <code>web faker sentence</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_faker_sentence $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-faker-paragraph">
<h3><a class="doc-anchor" href="#doc-web-faker-paragraph">#</a> <code>web_faker_paragraph</code></h3>
<p><code>web_faker_paragraph</code> — operation <code>web faker paragraph</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_faker_paragraph $x
</code></pre>
</article>
<article class="doc-entry" id="doc-web-faker-int">
<h3><a class="doc-anchor" href="#doc-web-faker-int">#</a> <code>web_faker_int</code></h3>
<p><code>web_faker_int</code> — operation <code>web faker int</code>. Category: *web framework (docs/web_framework.md)*.</p>
<pre><code class="lang-perl">p web_faker_int $x
</code></pre>
</article>
</section>
<section class="tutorial-section" id="ch-stress-telemetry-docs-stress-testing-md">
<h2>Stress / telemetry (docs/STRESS_TESTING.md)</h2>
<p class="chapter-meta">42 topics</p>
<article class="doc-entry" id="doc-stress-fp">
<h3><a class="doc-anchor" href="#doc-stress-fp">#</a> <code>stress_fp</code></h3>
<p><code>stress_fp $secs</code> — float matrix-multiply pinning every core. Returns total FLOP count.</p>
</article>
<article class="doc-entry" id="doc-stress-int">
<h3><a class="doc-anchor" href="#doc-stress-int">#</a> <code>stress_int</code></h3>
<p><code>stress_int $secs</code> — integer pipeline pinning every core.</p>
</article>
<article class="doc-entry" id="doc-stress-cache">
<h3><a class="doc-anchor" href="#doc-stress-cache">#</a> <code>stress_cache</code></h3>
<p><code>stress_cache $secs, $kb</code> — pound a working set of <code>kb</code> KiB per core in random order. Default 1024 (~ L2/L3 boundary).</p>
</article>
<article class="doc-entry" id="doc-stress-branch">
<h3><a class="doc-anchor" href="#doc-stress-branch">#</a> <code>stress_branch</code></h3>
<p><code>stress_branch</code> — operation <code>stress branch</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_branch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-sort">
<h3><a class="doc-anchor" href="#doc-stress-sort">#</a> <code>stress_sort</code></h3>
<p><code>stress_sort</code> — operation <code>stress sort</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_sort $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-alloc">
<h3><a class="doc-anchor" href="#doc-stress-alloc">#</a> <code>stress_alloc</code></h3>
<p><code>stress_alloc</code> — operation <code>stress alloc</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_alloc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-mmap">
<h3><a class="doc-anchor" href="#doc-stress-mmap">#</a> <code>stress_mmap</code></h3>
<p><code>stress_mmap</code> — operation <code>stress mmap</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_mmap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-disk">
<h3><a class="doc-anchor" href="#doc-stress-disk">#</a> <code>stress_disk</code></h3>
<p><code>stress_disk $path, $secs, $mb_per_write</code> — sustained sequential write + fsync + read across all cores.</p>
</article>
<article class="doc-entry" id="doc-stress-iops">
<h3><a class="doc-anchor" href="#doc-stress-iops">#</a> <code>stress_iops</code></h3>
<p><code>stress_iops $path, $secs, $block_kb</code> — small random reads/writes for IOPS testing. Default 4KB blocks.</p>
</article>
<article class="doc-entry" id="doc-stress-net">
<h3><a class="doc-anchor" href="#doc-stress-net">#</a> <code>stress_net</code></h3>
<p><code>stress_net "host:port", $secs, $conns</code> — open <code>conns</code> TCP connections per core, pump bytes.</p>
</article>
<article class="doc-entry" id="doc-stress-http">
<h3><a class="doc-anchor" href="#doc-stress-http">#</a> <code>stress_http</code></h3>
<p><code>stress_http $url, $secs, $conns</code> — HTTP GET storm. Counts 2xx responses.</p>
</article>
<article class="doc-entry" id="doc-stress-dns">
<h3><a class="doc-anchor" href="#doc-stress-dns">#</a> <code>stress_dns</code></h3>
<p><code>stress_dns</code> — operation <code>stress dns</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_dns $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-thread">
<h3><a class="doc-anchor" href="#doc-stress-thread">#</a> <code>stress_thread</code></h3>
<p><code>stress_thread</code> — operation <code>stress thread</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_thread $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-fork">
<h3><a class="doc-anchor" href="#doc-stress-fork">#</a> <code>stress_fork</code></h3>
<p><code>stress_fork</code> — operation <code>stress fork</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_fork $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-aes">
<h3><a class="doc-anchor" href="#doc-stress-aes">#</a> <code>stress_aes</code></h3>
<p><code>stress_aes $secs</code> — AES-128 encrypt round-trip across cores.</p>
</article>
<article class="doc-entry" id="doc-stress-compress">
<h3><a class="doc-anchor" href="#doc-stress-compress">#</a> <code>stress_compress</code></h3>
<p><code>stress_compress $secs, $kb</code> — gzip compress+decompress payload of <code>kb</code> KiB per core.</p>
</article>
<article class="doc-entry" id="doc-stress-regex">
<h3><a class="doc-anchor" href="#doc-stress-regex">#</a> <code>stress_regex</code></h3>
<p><code>stress_regex</code> — operation <code>stress regex</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_regex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-json">
<h3><a class="doc-anchor" href="#doc-stress-json">#</a> <code>stress_json</code></h3>
<p><code>stress_json</code> — operation <code>stress json</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_json $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-burst">
<h3><a class="doc-anchor" href="#doc-stress-burst">#</a> <code>stress_burst</code></h3>
<p><code>stress_burst</code> — operation <code>stress burst</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_burst $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-ramp">
<h3><a class="doc-anchor" href="#doc-stress-ramp">#</a> <code>stress_ramp</code></h3>
<p><code>stress_ramp</code> — operation <code>stress ramp</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_ramp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-oscillate">
<h3><a class="doc-anchor" href="#doc-stress-oscillate">#</a> <code>stress_oscillate</code></h3>
<p><code>stress_oscillate</code> — operation <code>stress oscillate</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_oscillate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-all">
<h3><a class="doc-anchor" href="#doc-stress-all">#</a> <code>stress_all</code></h3>
<p><code>stress_all $secs</code> — run every stress kernel above in parallel for <code>secs</code>. Returns a hashref of per-kernel counts.</p>
</article>
<article class="doc-entry" id="doc-stress-cores">
<h3><a class="doc-anchor" href="#doc-stress-cores">#</a> <code>stress_cores</code></h3>
<p><code>stress_cores</code> — operation <code>stress cores</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_cores $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-temp">
<h3><a class="doc-anchor" href="#doc-stress-temp">#</a> <code>stress_temp</code></h3>
<p>Telemetry helpers: <code>stress_temp()</code> reads CPU temp from <code>/sys/class/thermal</code> (Linux), <code>stress_freq()</code> averages cpufreq across cores, <code>stress_throttled()</code> returns 1 when freq < 80% of max AND temp > 80°C, <code>stress_load()</code> returns <code>+{m1, m5, m15}</code>, <code>stress_meminfo()</code> returns total/used/free/swap bytes.</p>
</article>
<article class="doc-entry" id="doc-stress-thermal-zones">
<h3><a class="doc-anchor" href="#doc-stress-thermal-zones">#</a> <code>stress_thermal_zones</code></h3>
<p><code>stress_thermal_zones</code> — operation <code>stress thermal zones</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_thermal_zones $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-arm-kill-switch">
<h3><a class="doc-anchor" href="#doc-stress-arm-kill-switch">#</a> <code>stress_arm_kill_switch</code></h3>
<p><code>stress_arm_kill_switch</code> — operation <code>stress arm kill switch</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_arm_kill_switch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-killed">
<h3><a class="doc-anchor" href="#doc-stress-killed">#</a> <code>stress_killed</code></h3>
<p><code>stress_killed</code> — operation <code>stress killed</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_killed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-disarm-kill-switch">
<h3><a class="doc-anchor" href="#doc-stress-disarm-kill-switch">#</a> <code>stress_disarm_kill_switch</code></h3>
<p><code>stress_disarm_kill_switch</code> — operation <code>stress disarm kill switch</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p stress_disarm_kill_switch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stress-metrics-record">
<h3><a class="doc-anchor" href="#doc-stress-metrics-record">#</a> <code>stress_metrics_record</code></h3>
<p><code>stress_metrics_record("name", $value, k1 => v1, ...)</code> — append a sample to the metrics history. Labels are stringified.</p>
</article>
<article class="doc-entry" id="doc-stress-metrics-clear">
<h3><a class="doc-anchor" href="#doc-stress-metrics-clear">#</a> <code>stress_metrics_clear</code></h3>
<p><code>stress_metrics_clear()</code> — wipe the metrics history. Pair with <code>stress_metrics_count()</code> before/after to verify.</p>
</article>
<article class="doc-entry" id="doc-stress-metrics-count">
<h3><a class="doc-anchor" href="#doc-stress-metrics-count">#</a> <code>stress_metrics_count</code></h3>
<p><code>stress_metrics_count()</code> → current number of samples in the history.</p>
</article>
<article class="doc-entry" id="doc-stress-metrics-export">
<h3><a class="doc-anchor" href="#doc-stress-metrics-export">#</a> <code>stress_metrics_export</code></h3>
<p><code>stress_metrics_export("path", format => "csv"|"json"|"prom")</code> → number of samples written.</p>
</article>
<article class="doc-entry" id="doc-stress-metrics-prometheus">
<h3><a class="doc-anchor" href="#doc-stress-metrics-prometheus">#</a> <code>stress_metrics_prometheus</code></h3>
<p><code>stress_metrics_prometheus()</code> → string in Prometheus text exposition format. Latest value per (name, labels) wins. Drop into a <code>/metrics</code> HTTP handler.</p>
</article>
<article class="doc-entry" id="doc-stress-metrics-json">
<h3><a class="doc-anchor" href="#doc-stress-metrics-json">#</a> <code>stress_metrics_json</code></h3>
<p><code>stress_metrics_json()</code> → JSON string of the entire metrics history.</p>
</article>
<article class="doc-entry" id="doc-stress-metrics-csv">
<h3><a class="doc-anchor" href="#doc-stress-metrics-csv">#</a> <code>stress_metrics_csv</code></h3>
<p><code>stress_metrics_csv()</code> → CSV string with <code>ts_ms,name,value,labels</code> columns.</p>
</article>
<article class="doc-entry" id="doc-stress-metrics-watch">
<h3><a class="doc-anchor" href="#doc-stress-metrics-watch">#</a> <code>stress_metrics_watch</code></h3>
<p><code>stress_metrics_watch(field => "stress_temp", interval_ms => 1000, max_ticks => 60)</code> → arrayref of values sampled at the requested cadence. Polls the metrics history for new entries matching <code>field</code>.</p>
</article>
<article class="doc-entry" id="doc-audit-log">
<h3><a class="doc-anchor" href="#doc-audit-log">#</a> <code>audit_log</code></h3>
<p><code>audit_log("event_name", k1 => v1, ...)</code> — append one JSONL line to <code>~/.stryke/audit.log</code> (or <code>$STRYKE_AUDIT_LOG</code>). Never throws; returns 1/0.</p>
</article>
<article class="doc-entry" id="doc-audit-log-path">
<h3><a class="doc-anchor" href="#doc-audit-log-path">#</a> <code>audit_log_path</code></h3>
<p><code>audit_log_path()</code> → absolute path the next <code>audit_log</code> call will write to.</p>
</article>
<article class="doc-entry" id="doc-secrets-encrypt">
<h3><a class="doc-anchor" href="#doc-secrets-encrypt">#</a> <code>secrets_encrypt</code></h3>
<p><code>secrets_encrypt($plain, key => $key)</code> → base64 envelope (nonce(12) || ciphertext || tag(16)). AES-256-GCM. Key must be 32 raw bytes or 32-byte base64.</p>
</article>
<article class="doc-entry" id="doc-secrets-decrypt">
<h3><a class="doc-anchor" href="#doc-secrets-decrypt">#</a> <code>secrets_decrypt</code></h3>
<p><code>secrets_decrypt($envelope, key => $key)</code> → plaintext, or undef on auth failure.</p>
</article>
<article class="doc-entry" id="doc-secrets-random-key">
<h3><a class="doc-anchor" href="#doc-secrets-random-key">#</a> <code>secrets_random_key</code></h3>
<p><code>secrets_random_key()</code> → fresh 32-byte AES-256 key as base64. Reads <code>/dev/urandom</code> on Unix.</p>
</article>
<article class="doc-entry" id="doc-secrets-kdf">
<h3><a class="doc-anchor" href="#doc-secrets-kdf">#</a> <code>secrets_kdf</code></h3>
<p><code>secrets_kdf($password, salt => "...", iterations => 600_000)</code> → 32-byte key as base64. PBKDF2-HMAC-SHA256.</p>
</article>
</section>
<section class="tutorial-section" id="ch-pty-expect-docs-expect-feature-idea-md">
<h2>PTY / expect (docs/expect-feature-idea.md)</h2>
<p class="chapter-meta">13 topics</p>
<article class="doc-entry" id="doc-pty-spawn">
<h3><a class="doc-anchor" href="#doc-pty-spawn">#</a> <code>pty_spawn</code></h3>
<p><code>pty_spawn "cmd args"</code> or <code>pty_spawn("cmd", "arg1", "arg2")</code> — allocate a PTY, fork+exec the child, return a handle. Master fd is non-blocking.</p>
<pre><code class="lang-perl">my $h = pty_spawn("ssh user@host");
pty_expect($h, qr/password:/, 30);
pty_send($h, "hunter2\n");
pty_close($h);
</code></pre>
</article>
<article class="doc-entry" id="doc-pty-send">
<h3><a class="doc-anchor" href="#doc-pty-send">#</a> <code>pty_send</code></h3>
<p><code>pty_send $h, "text"</code> — write to the PTY master. Handles EAGAIN/EINTR; returns bytes written.</p>
</article>
<article class="doc-entry" id="doc-pty-read">
<h3><a class="doc-anchor" href="#doc-pty-read">#</a> <code>pty_read</code></h3>
<p><code>pty_read</code> — read of <code>pty</code>. Category: *mcp (model context protocol)*.</p>
<pre><code class="lang-perl">p pty_read $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pty-expect">
<h3><a class="doc-anchor" href="#doc-pty-expect">#</a> <code>pty_expect</code></h3>
<p><code>pty_expect $h, qr/regex/, $timeout_secs</code> — loop reading until the regex matches the accumulated buffer or <code>timeout_secs</code> elapses. Returns the matched substring or undef on timeout/EOF. Buffer is consumed up to (and including) the match.</p>
</article>
<article class="doc-entry" id="doc-pty-expect-table">
<h3><a class="doc-anchor" href="#doc-pty-expect-table">#</a> <code>pty_expect_table</code></h3>
<p><code>pty_expect_table $h, [+{re => qr/.../, do => sub {...}}, ...], $timeout</code> — multi-pattern dispatch (Tcl <code>expect { ... }</code> block). First match wins; the matched branch's <code>do</code> sub is called.</p>
</article>
<article class="doc-entry" id="doc-pty-buffer">
<h3><a class="doc-anchor" href="#doc-pty-buffer">#</a> <code>pty_buffer</code></h3>
<p><code>pty_buffer</code> — operation <code>pty buffer</code>. Category: *mcp (model context protocol)*.</p>
<pre><code class="lang-perl">p pty_buffer $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pty-alive">
<h3><a class="doc-anchor" href="#doc-pty-alive">#</a> <code>pty_alive</code></h3>
<p><code>pty_alive</code> — operation <code>pty alive</code>. Category: *mcp (model context protocol)*.</p>
<pre><code class="lang-perl">p pty_alive $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pty-eof">
<h3><a class="doc-anchor" href="#doc-pty-eof">#</a> <code>pty_eof</code></h3>
<p><code>pty_eof</code> — operation <code>pty eof</code>. Category: *mcp (model context protocol)*.</p>
<pre><code class="lang-perl">p pty_eof $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pty-close">
<h3><a class="doc-anchor" href="#doc-pty-close">#</a> <code>pty_close</code></h3>
<p><code>pty_close $h</code> — SIGTERM → 200ms grace → SIGKILL. Returns exit status.</p>
</article>
<article class="doc-entry" id="doc-pty-interact">
<h3><a class="doc-anchor" href="#doc-pty-interact">#</a> <code>pty_interact</code></h3>
<p><code>pty_interact $h</code> — raw-mode handoff: forwards stdin → master and master → stdout until EOF or Ctrl-]. Saves and restores tty state.</p>
</article>
<article class="doc-entry" id="doc-pty-strip-ansi">
<h3><a class="doc-anchor" href="#doc-pty-strip-ansi">#</a> <code>pty_strip_ansi</code></h3>
<p><code>pty_strip_ansi $text</code> → string with CSI/OSC/ESC sequences removed. Useful before regex-matching against PTY output that mixes color codes into prompts.</p>
</article>
<article class="doc-entry" id="doc-pty-after-eof">
<h3><a class="doc-anchor" href="#doc-pty-after-eof">#</a> <code>pty_after_eof</code></h3>
<p><code>pty_after_eof $h, "callback_name"</code> — register an EOF callback. Spawns a watcher thread that flips a fired flag once the PTY closes. Pair with <code>pty_pending_events()</code> in your main loop.</p>
</article>
<article class="doc-entry" id="doc-pty-pending-events">
<h3><a class="doc-anchor" href="#doc-pty-pending-events">#</a> <code>pty_pending_events</code></h3>
<p><code>pty_pending_events()</code> → arrayref of <code>+{handle_id, callback}</code> for any <code>pty_after_eof</code> registrations that have fired since the last call. Drains the fired list.</p>
</article>
</section>
<section class="tutorial-section" id="ch-other">
<h2>Other</h2>
<p class="chapter-meta">8394 topics</p>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$!</code></h3>
<p><code>$!</code> — the OS error from the most recent system call, in stringified form (e.g. <code>"No such file or directory"</code>) or as an <code>errno</code> integer in numeric context. Set by <code>open</code>, <code>close</code>, <code>chdir</code>, <code>read</code>, <code>write</code>, and other syscalls when they fail. The value persists until the next failing call, so always check it *immediately* after the failing operation — intermediate clean Perl code does not touch it, but any subsequent syscall will.</p>
<pre><code class="lang-perl">open my $fh, '<', $path or die "open $path: $!"
unless (chdir $dir) { warn "chdir: $!"; return }
# Numeric context for errno-based dispatch:
use Errno qw(ENOENT)
if ($! == ENOENT) { p "missing" }
</code></pre>
<p>See also: <code>$?</code> (child exit), <code>$@</code> (eval error), <code>$^E</code> (extended OS error).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$"</code></h3>
<p><code>$"</code> — the list separator used when an array variable is interpolated inside a double-quoted string. Defaults to a single space. Setting it changes how <code>"@array"</code> renders — useful for ad-hoc CSV-like joining without <code>join</code>.</p>
<pre><code class="lang-perl">my @xs = (1, 2, 3)
p "@xs" # 1 2 3
local $" = ","
p "@xs" # 1,2,3
local $" = " | "
p "row: @xs" # row: 1 | 2 | 3
</code></pre>
<p>Only affects double-quoted interpolation, not bare <code>print @xs</code> (which uses <code>$,</code>). Use <code>local $"</code> to scope the change.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$#</code></h3>
<p><code>$#</code> — the default output format for printed numbers (legacy / deprecated since early Perl 5; modern code uses <code>printf</code>/<code>sprintf</code> explicitly). Distinct from <code>$#array</code> which is the last-index expression — <code>$#</code> standalone reads the number-format global, <code>$#NAME</code> reads <code>$#{NAME}</code>, the last index of <code>@NAME</code>.</p>
<pre><code class="lang-perl">p $# # number-format global (rarely set)
my @xs = (1, 2, 3, 4)
p $#xs # 3 — last index of @xs
</code></pre>
<p>For modern formatting use <code>printf "%.2f", $n</code>. See also: <code>$#array</code> syntax, <code>printf</code>, <code>sprintf</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$$</code></h3>
<p><code>$$</code> — the process ID of the running stryke interpreter. Read-only, set once at startup. Useful for PID files, log filenames, and child/parent disambiguation after <code>fork</code>.</p>
<pre><code class="lang-perl">p "started, pid=$$"
open my $pf, '>', "/tmp/myapp.pid" or die $!
print $pf "$$\n"
close $pf
if (my $kid = fork()) {
p "parent $$ spawned $kid"
} else {
p "child $$ running"
}
</code></pre>
<p>See also: <code>getppid()</code> for the parent PID, <code>fork()</code> to spawn children.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$&</code></h3>
<p><code>$&</code> — the entire string matched by the most recent successful regex match in the current scope. Reset on every match. In Perl 5 ≥ 5.20 this no longer carries the historical performance penalty (the pre-5.20 issue forced compilation of a slower regex engine globally); stryke's regex engine has no such penalty.</p>
<pre><code class="lang-perl">if ("hello world" =~ /\w+/) {
p $& # hello
}
my $s = "abc123def"
if ($s =~ /\d+/) { p $&; } # 123
</code></pre>
<p>See also: <code></code> $<code> </code><code> (prematch), </code>$'<code> (postmatch), </code>$1<code>..</code>$9<code> (capture groups), </code>@-<code> / </code>@+<code> (offsets), </code>${^MATCH}<code> / </code>${^PREMATCH}<code> / </code>${^POSTMATCH}<code> (no-penalty equivalents under </code>use re 'p'`).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$'</code></h3>
<p><code>$'</code> — the substring *following* the last successful regex match ("postmatch"). Combined with <code></code> $<code> </code><code> (prematch) and </code>$&<code> (match), reconstructs the entire input: </code>"$<code> </code>$&$'" eq $original`. Reset on every match.</p>
<pre><code class="lang-perl">if ("hello world" =~ /\s/) {
p "pre = $`" # pre = hello
p "match= $&" # match= (a space)
p "post = $'" # post = world
}
</code></pre>
<p>See also: <code></code> $<code> </code><code>, </code>$&<code>, </code>${^POSTMATCH}<code> (cleaner under </code>use re 'p'`).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$(</code></h3>
<p><code>$(</code> — the real group ID of the running process. In list context (or when stringified with whitespace) yields the primary GID followed by every supplementary group, space-separated. Use <code>getgrgid($()</code> to map a GID to its name. Assigning to <code>$(</code> requires appropriate privileges.</p>
<pre><code class="lang-perl">p "real gid: $(" # 1000 1000 4 24 27 …
my ($primary, @supp) = split ' ', $(
p "primary group: $primary"
use POSIX qw(getgrgid)
p scalar getgrgid($primary) || $primary
</code></pre>
<p>See also: <code>$)</code> (effective gid), <code>$<</code> (real uid), <code>$></code> (effective uid).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$)</code></h3>
<p><code>$)</code> — the effective group ID of the running process. Like <code>$(</code>, returns the primary EGID plus supplementary groups space-separated in stringified form. Affects which permissions apply to filesystem operations. Assigning to <code>$)</code> requires privileges (typically root).</p>
<pre><code class="lang-perl">p "effective gid: $)"
if ($( != $)) {
p "running setgid: real=$( effective=$)"
}
</code></pre>
<p>See also: <code>$(</code> (real gid), <code>$></code> (effective uid).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$+</code></h3>
<p><code>$+</code> — the contents of the <strong>last</strong> parenthesised capture group that successfully matched in the most recent regex. When the regex has multiple <code>(...)</code> groups, this gives you the rightmost one that participated in the match — useful when alternation may match different groups depending on input.</p>
<pre><code class="lang-perl">if ("name=alice" =~ /^(\w+)=(\w+)$/) {
p $+ # alice (last group)
}
if ("foo" =~ /(bar)|(foo)|(baz)/) {
p $+ # foo (only the second group matched)
}
</code></pre>
<p>See also: <code>$1</code>..<code>$9</code> (positional captures), <code>%+</code> (named captures), <code>@+</code> (end-of-match offsets).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$,</code></h3>
<p><code>$,</code> — the output field separator inserted between arguments by <code>print</code> (default: empty string). Does *not* affect <code>printf</code>/<code>sprintf</code> (those use the format string) or <code>say</code>/<code>p</code> (which still respect it). Setting <code>$,</code> is the classic way to print comma-separated lists without an explicit <code>join</code>.</p>
<pre><code class="lang-perl">print 1, 2, 3, "\n" # 123
local $, = ","
print 1, 2, 3, "\n" # 1,2,3,
local $, = " | "
print qw(a b c), "\n" # a | b | c |
</code></pre>
<p>See also: <code>$\</code> (output record separator), <code>$"</code> (list interpolation separator).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$-</code></h3>
<p><code>$-</code> — the number of lines left on the current output page for <code>format</code>/<code>write</code>. Decremented as <code>write</code> emits lines; when it hits 0, the top-of-page header (<code>$^</code> / <code>$=</code>) is re-emitted. Niche; only relevant to the legacy <code>format</code> system.</p>
<pre><code class="lang-perl">write
p "$- lines left on page"
</code></pre>
<p>See also: <code>format</code>, <code>write</code>, <code>$=</code> (page length), <code>$^</code> (top-of-page format).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$.</code></h3>
<p><code>$.</code> — the current input line number of the most recently read filehandle, as tracked by <code><></code>, <code><$fh></code>, and <code>readline</code>. Counts lines as defined by <code>$/</code> (input record separator). Reset to 0 when a filehandle is closed (but <strong>not</strong> when <code><></code> rolls onto the next ARGV file — line numbers continue across files unless you reset it manually).</p>
<pre><code class="lang-perl">while (<>) {
p "$ARGV:$." if /error/i
close ARGV if eof # reset $. between input files
}
</code></pre>
<p>See also: <code>$ARGV</code> (current filename), <code>eof</code> (file boundary detection).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$/</code></h3>
<p><code>$/</code> — the input record separator used by <code><></code>/<code>readline</code>. Default: <code>"\n"</code> (one line per read). Set to <code>undef</code> to slurp the whole file in one read; set to <code>""</code> for *paragraph mode* (records separated by runs of blank lines); set to a reference to a positive integer for fixed-size block reads.</p>
<pre><code class="lang-perl">local $/ = undef # slurp
my $whole = <$fh>
local $/ = "" # paragraph mode
while (my $para = <$fh>) {
p length $para
}
local $/ = \4096 # 4KB blocks
while (read $fh, my $blk, 4096) { ... }
</code></pre>
<p>Always <code>local</code>-ise the change so it doesn't leak. See also: <code>$\</code> (output record separator), <code>$,</code>.</p>
</article>
<article class="doc-entry" id="doc-0">
<h3><a class="doc-anchor" href="#doc-0">#</a> <code>$0</code></h3>
<p><code>$0</code> — the program name as the OS sees it. Initialised from <code>argv[0]</code>. Assignment to <code>$0</code> updates the visible process name on many Unix systems (Linux, BSDs), making <code>ps</code> / <code>top</code> show the new value — handy for long-running daemons that want to reflect what they're doing.</p>
<pre><code class="lang-perl">p "running as: $0"
$0 = "myapp worker [idle]"
sleep 5
$0 = "myapp worker [processing job 42]"
</code></pre>
<p>See also: <code>@ARGV</code> (the rest of the command line), <code>__FILE__</code> (compile-time source path).</p>
</article>
<article class="doc-entry" id="doc-1">
<h3><a class="doc-anchor" href="#doc-1">#</a> <code>$1</code></h3>
<p><code>$1</code> — the substring matched by the <strong>first</strong> parenthesised capture group of the most recent successful regex. Undef if the group didn't participate in the match or if the match failed.</p>
<pre><code class="lang-perl">if ("alice@example.com" =~ /^(\w+)@(\S+)$/) {
p $1 # alice
p $2 # example.com
}
"ip: 192.168.1.1" =~ /(\d+\.\d+\.\d+\.\d+)/ and p $1
</code></pre>
<p>See also: <code>$2</code>..<code>$9</code>, <code>%+</code> (named captures via <code>(?<name>...)</code>), <code>@-</code> / <code>@+</code> (offsets), <code>$+</code> (last successful group).</p>
</article>
<article class="doc-entry" id="doc-2">
<h3><a class="doc-anchor" href="#doc-2">#</a> <code>$2</code></h3>
<p><code>$2</code> — second capture group from the most recent regex match. See <code>$1</code> for full semantics.</p>
</article>
<article class="doc-entry" id="doc-3">
<h3><a class="doc-anchor" href="#doc-3">#</a> <code>$3</code></h3>
<p><code>$3</code> — third capture group from the most recent regex match. See <code>$1</code> for full semantics.</p>
</article>
<article class="doc-entry" id="doc-4">
<h3><a class="doc-anchor" href="#doc-4">#</a> <code>$4</code></h3>
<p><code>$4</code> — fourth capture group from the most recent regex match. See <code>$1</code> for full semantics.</p>
</article>
<article class="doc-entry" id="doc-5">
<h3><a class="doc-anchor" href="#doc-5">#</a> <code>$5</code></h3>
<p><code>$5</code> — fifth capture group from the most recent regex match. See <code>$1</code> for full semantics.</p>
</article>
<article class="doc-entry" id="doc-6">
<h3><a class="doc-anchor" href="#doc-6">#</a> <code>$6</code></h3>
<p><code>$6</code> — sixth capture group from the most recent regex match. See <code>$1</code> for full semantics.</p>
</article>
<article class="doc-entry" id="doc-7">
<h3><a class="doc-anchor" href="#doc-7">#</a> <code>$7</code></h3>
<p><code>$7</code> — seventh capture group from the most recent regex match. See <code>$1</code> for full semantics.</p>
</article>
<article class="doc-entry" id="doc-8">
<h3><a class="doc-anchor" href="#doc-8">#</a> <code>$8</code></h3>
<p><code>$8</code> — eighth capture group from the most recent regex match. See <code>$1</code> for full semantics.</p>
</article>
<article class="doc-entry" id="doc-9">
<h3><a class="doc-anchor" href="#doc-9">#</a> <code>$9</code></h3>
<p><code>$9</code> — ninth capture group from the most recent regex match. Captures past <code>$9</code> work fine in stryke (no Perl 4 limit), but the conventional way to access many groups is named captures (<code>(?<name>...)</code> + <code>%+</code>) or <code>@-</code>/<code>@+</code> offsets.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$;</code></h3>
<p><code>$;</code> — the multidimensional-array subscript separator. When you write <code>$h{a,b,c}</code> Perl joins the keys with <code>$;</code> (default: <code>\034</code>, the ASCII FS / file-separator control character) to produce a single string key. This emulates multi-dim arrays on top of the flat hash store. Rarely used in new code — prefer real nested data structures (<code>$h{a}{b}{c}</code> or arrayrefs).</p>
<pre><code class="lang-perl">$grid{1,2} = "x" # really $grid{"1\034 2"} = "x"
p exists $grid{1,2} # 1
local $; = "|" # if you want readable keys for debugging
</code></pre>
<p>See also: prefer <code>$h{a}{b}{c}</code> autovivification for nested storage.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$<</code></h3>
<p><code>$<</code> — the real user ID of the running process. Read-only on most systems unless the process has appropriate privileges. Use <code>getpwuid($<)</code> to map to a username.</p>
<pre><code class="lang-perl">p "real uid: $<"
use POSIX qw(getpwuid)
p "running as: " . (getpwuid($<))[0]
if ($< != $>) {
p "setuid: real=$< effective=$>"
}
</code></pre>
<p>See also: <code>$></code> (effective uid), <code>$(</code> / <code>$)</code> (gids).</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$></code></h3>
<p><code>$></code> — the effective user ID of the running process. Determines filesystem permission checks. Setuid binaries start with <code>$<</code> (real) ≠ <code>$></code> (effective). Assignment requires privileges; swapping <code>$<</code> and <code>$></code> is a common pattern for setuid scripts that want to temporarily drop privileges.</p>
<pre><code class="lang-perl">p "effective uid: $>"
($<, $>) = ($>, $<) # drop to real uid (where supported)
</code></pre>
<p>See also: <code>$<</code>, <code>$(</code> / <code>$)</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$?</code></h3>
<p><code>$?</code> — the status of the last child process: a backtick command, <code>system()</code> call, or piped-<code>open</code> close. The raw value packs the exit code, signal number, and core-dump flag into a single integer. Extract the exit code with <code>$? >> 8</code>; the signal with <code>$? & 127</code>; the core-dump flag with <code>$? & 128</code>.</p>
<pre><code class="lang-perl">my $out = `ls /missing 2>&1`
if ($?) {
my $exit = $? >> 8
my $sig = $? & 127
die "ls failed: exit=$exit sig=$sig\n"
}
system('grep', $pat, $file) == 0 or warn "grep: $? >> 8"
</code></pre>
<p>See also: <code>$!</code> (syscall error), <code>system</code>, <code>exec</code>, <code>wait</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$@</code></h3>
<p><code>$@</code> — the error message left by the most recent <code>eval { }</code> (or <code>die</code> inside one). Empty string when the eval succeeded; non-empty string when it caught an exception. For structured errors <code>die</code>d as references, <code>$@</code> holds the reference itself, not a string.</p>
<p>Classic gotcha: any code between <code>eval</code> and <code>if ($@)</code> that runs another <code>eval</code> (including destructors and <code>END</code> blocks) can clobber <code>$@</code>. Save it locally if you need it later. In stryke, prefer the <code>try</code>/<code>catch</code> statement which gives you a properly scoped exception variable and avoids this hazard entirely.</p>
<pre><code class="lang-perl">eval { dangerous_call() }
if (my $err = $@) {
warn "caught: $err"
}
# Modern: try/catch — no $@ clobbering
try { dangerous_call() } catch ($e) { warn "caught: $e" }
</code></pre>
<p>See also: <code>try</code>, <code>catch</code>, <code>eval</code>, <code>die</code>.</p>
</article>
<article class="doc-entry" id="doc-argv">
<h3><a class="doc-anchor" href="#doc-argv">#</a> <code>$ARGV</code></h3>
<p><code>$ARGV</code> — the name of the file currently being read via the diamond operator (<code><></code>) when iterating over <code>@ARGV</code>. Set automatically each time <code><></code> opens the next argv file. Useful inside loops that grep across many files to know which one produced a hit.</p>
<pre><code class="lang-perl">while (<>) {
p "$ARGV:$.: $_" if /TODO/
close ARGV if eof # reset $. between files
}
</code></pre>
<p>See also: <code>@ARGV</code> (the list of files), <code>$.</code> (line number).</p>
</article>
<article class="doc-entry" id="doc-autoload">
<h3><a class="doc-anchor" href="#doc-autoload">#</a> <code>$AUTOLOAD</code></h3>
<p><code>$AUTOLOAD</code> — set by stryke just before an <code>AUTOLOAD</code> sub is invoked. Holds the fully-qualified name of the missing method that triggered the autoload (e.g. <code>"My::Dispatcher::foo"</code>). Inside <code>AUTOLOAD</code>, parse <code>$AUTOLOAD</code> to decide what to do — install a generated sub, proxy elsewhere, or <code>die</code> for unknown names.</p>
<pre><code class="lang-perl">package RPC
fn AUTOLOAD {
my $name = $AUTOLOAD
$name =~ s/.*::// # strip package prefix
return if $name eq 'DESTROY'
my $self = shift
$self->call($name, @_)
}
</code></pre>
<p>See also: <code>AUTOLOAD</code> (the sub), <code>DESTROY</code>, MRO walking.</p>
</article>
<article class="doc-entry" id="doc-intercept-ms">
<h3><a class="doc-anchor" href="#doc-intercept-ms">#</a> <code>$INTERCEPT_MS</code></h3>
<p><code>$INTERCEPT_MS</code> — inside an <code>after</code> advice body, the elapsed wall-clock time of the wrapped call in <strong>milliseconds</strong> as a floating-point number. Mirrors <code>INTERCEPT_MS</code> from the zshrs AOP runtime. Use this for cheap timing instrumentation without a profiler.</p>
<pre><code class="lang-perl">after "slow_query" {
warn "slow_query took ${INTERCEPT_MS}ms" if $INTERCEPT_MS > 100
}
after "*" {
record_metric($INTERCEPT_NAME, $INTERCEPT_MS)
}
</code></pre>
<p>See also: <code>$INTERCEPT_US</code> (microsecond precision), <code>$INTERCEPT_RESULT</code>, <code>before</code>, <code>after</code>.</p>
</article>
<article class="doc-entry" id="doc-intercept-name">
<h3><a class="doc-anchor" href="#doc-intercept-name">#</a> <code>$INTERCEPT_NAME</code></h3>
<p><code>$INTERCEPT_NAME</code> — inside an AOP advice body, the fully-qualified name of the intercepted sub (e.g. <code>"main::fetch"</code>, <code>"My::DB::query"</code>). Useful for glob-based advice (<code>before "*"</code> or <code>before "My::*"</code>) that needs to log or dispatch on the actual name being called.</p>
<pre><code class="lang-perl">before "*" { trace($INTERCEPT_NAME) }
before "My::DB::*" {
log_info("db call: $INTERCEPT_NAME with @INTERCEPT_ARGS")
}
</code></pre>
<p>See also: <code>@INTERCEPT_ARGS</code>, <code>$INTERCEPT_RESULT</code>, <code>before</code>, <code>after</code>, <code>around</code>.</p>
</article>
<article class="doc-entry" id="doc-intercept-result">
<h3><a class="doc-anchor" href="#doc-intercept-result">#</a> <code>$INTERCEPT_RESULT</code></h3>
<p><code>$INTERCEPT_RESULT</code> — inside an <code>after</code> advice body, the value the wrapped sub returned (the equivalent of inspecting <code>$?</code>-style after a call). <code>before</code> advice runs too early to see this; <code>around</code> advice receives the result from <code>proceed()</code> and can rewrite it.</p>
<pre><code class="lang-perl">after "fetch" {
log_info("fetch returned $INTERCEPT_RESULT in ${INTERCEPT_MS}ms")
}
</code></pre>
<p>See also: <code>@INTERCEPT_ARGS</code>, <code>$INTERCEPT_NAME</code>, <code>$INTERCEPT_MS</code>, <code>before</code>, <code>after</code>, <code>around</code>.</p>
</article>
<article class="doc-entry" id="doc-intercept-us">
<h3><a class="doc-anchor" href="#doc-intercept-us">#</a> <code>$INTERCEPT_US</code></h3>
<p><code>$INTERCEPT_US</code> — inside an <code>after</code> advice body, the elapsed wall-clock time of the wrapped call in <strong>microseconds</strong> as an integer. Use when millisecond resolution from <code>$INTERCEPT_MS</code> is too coarse (sub-millisecond ops, hot inner loops).</p>
<pre><code class="lang-perl">after "hot_op" {
histogram_record("hot_op_us", $INTERCEPT_US)
}
</code></pre>
<p>See also: <code>$INTERCEPT_MS</code>, <code>before</code>, <code>after</code>, <code>around</code>.</p>
</article>
<article class="doc-entry" id="doc-nf">
<h3><a class="doc-anchor" href="#doc-nf">#</a> <code>$NF</code></h3>
<p><code>$NF</code> — awk-compat: the number of fields produced by the most recent autosplit of an input line into <code>@F</code> (<code>-a</code> flag). Equivalent to <code>scalar @F</code>. stryke exposes both for one-liner familiarity to awk users.</p>
<pre><code class="lang-perl"># stryke -F: -nae 'p "$NF fields: @F"' /etc/passwd
# Equivalent to awk '{ print NF" fields: "$0 }'
</code></pre>
<p>See also: <code>$NR</code>, <code>@F</code>, <code>-a</code> / <code>-F</code> command-line flags, awk-compat one-liner mode.</p>
</article>
<article class="doc-entry" id="doc-nr">
<h3><a class="doc-anchor" href="#doc-nr">#</a> <code>$NR</code></h3>
<p><code>$NR</code> — awk-compat: the current input record number. Equivalent to <code>$.</code> (current line of the most recently read filehandle). stryke exposes both for one-liner familiarity to awk users. <code>$.</code>-based code and <code>$NR</code>-based code can be mixed in the same one-liner.</p>
<pre><code class="lang-perl"># stryke -nae 'p "$NR: $_" if /TODO/'
# Equivalent to awk '/TODO/ { print NR": "$0 }'
</code></pre>
<p>See also: <code>$.</code>, <code>$NF</code>, <code>@F</code>, <code>-a</code> / <code>-F</code>, <code>-n</code> / <code>-p</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$\</code></h3>
<p><code>$\</code> — the output record separator appended automatically by <code>print</code> (default: empty string). Pairs with <code>$,</code> (field separator between args). Useful for switching between Unix <code>\n</code> and Windows <code>\r\n</code> line endings without rewriting every <code>print</code>. Does not affect <code>say</code>/<code>p</code> (which always append <code>\n</code>) or <code>printf</code> (which uses the format string).</p>
<pre><code class="lang-perl">local $\ = "\n"
print "hello" # hello\n
print "world" # world\n
local $\ = "\r\n"
print "crlf line" # crlf line\r\n
</code></pre>
<p>See also: <code>$,</code> (output field separator), <code>$/</code> (input record separator).</p>
</article>
<article class="doc-entry" id="doc-a">
<h3><a class="doc-anchor" href="#doc-a">#</a> <code>$^A</code></h3>
<p><code>$^A</code> — the accumulator for <code>format</code>/<code>write</code> output. Each <code>formline</code> call appends formatted text here; <code>write</code> flushes the accumulator to the selected filehandle and resets it. Direct manipulation is rare except when implementing custom report writers without <code>write</code>.</p>
<pre><code class="lang-perl">formline '@<<<<<<< @>>>>>', "name", 42
p $^A # "name 42"
$^A = '' # clear
</code></pre>
<p>See also: <code>format</code>, <code>formline</code>, <code>write</code>.</p>
</article>
<article class="doc-entry" id="doc-c">
<h3><a class="doc-anchor" href="#doc-c">#</a> <code>$^C</code></h3>
<p><code>$^C</code> — true when Perl/stryke is running in *compile-only* mode (<code>-c</code> flag). Useful for guarding code that should be skipped during syntax checking (e.g. tests that would actually run, network calls). Read-only.</p>
<pre><code class="lang-perl">BEGIN { exit 0 if $^C } # don't run setup during -c
</code></pre>
<p>See also: <code>-c</code> command-line flag.</p>
</article>
<article class="doc-entry" id="doc-d">
<h3><a class="doc-anchor" href="#doc-d">#</a> <code>$^D</code></h3>
<p><code>$^D</code> — the debug flag bitmask (<code>-D</code> command-line flag in debug-enabled builds). Stryke debug builds expose the same flag set as Perl; production builds have it stubbed. Numeric, set from the <code>-D</code> digits or letters on the command line.</p>
<pre><code class="lang-perl">p "debug mask: $^D" if $^D
</code></pre>
<p>See also: <code>-D</code> flag, <code>use diagnostics</code>.</p>
</article>
<article class="doc-entry" id="doc-e">
<h3><a class="doc-anchor" href="#doc-e">#</a> <code>$^E</code></h3>
<p><code>$^E</code> — extended OS error info beyond <code>$!</code>. On Windows this carries Win32 error codes / messages distinct from the POSIX errno that <code>$!</code> reports. On Unix it is usually identical to <code>$!</code>. Useful for platform-specific diagnostics.</p>
<pre><code class="lang-perl">open my $fh, '<', $path or die "open: $! ($^E)"
</code></pre>
<p>See also: <code>$!</code>.</p>
</article>
<article class="doc-entry" id="doc-f">
<h3><a class="doc-anchor" href="#doc-f">#</a> <code>$^F</code></h3>
<p><code>$^F</code> — the maximum file descriptor considered "system" (default: 2). File descriptors at or below this number are *not* closed across <code>exec()</code> calls; higher fds are closed automatically. Raise it before <code>exec</code>-ing a child if you need extra fds to survive.</p>
<pre><code class="lang-perl">$^F = 10 # keep fds 0-10 across exec
open my $fh, '<', $path or die $!
exec 'helper', fileno($fh)
</code></pre>
<p>See also: <code>exec</code>, <code>fcntl</code>.</p>
</article>
<article class="doc-entry" id="doc-h">
<h3><a class="doc-anchor" href="#doc-h">#</a> <code>$^H</code></h3>
<p><code>$^H</code> — the compile-time lexical hint bitmask (32 bits of integer flags). Pragmas like <code>use strict</code>, <code>use warnings</code>, <code>use utf8</code> flip bits here to communicate their state to the parser within a lexical scope. Reading at runtime is mostly useless (it reflects current-line compile state); manipulation is for pragma authors.</p>
<pre><code class="lang-perl">BEGIN { p sprintf "hint bits: 0x%08x", $^H }
</code></pre>
<p>See also: <code>%^H</code> (lexical hint hash), <code>use strict</code>, <code>use warnings</code>.</p>
</article>
<article class="doc-entry" id="doc-i">
<h3><a class="doc-anchor" href="#doc-i">#</a> <code>$^I</code></h3>
<p><code>$^I</code> — the in-place edit extension. Set by the <code>-i</code> command-line flag and controls <code><></code> rewriting: when <code>$^I</code> is defined, lines read from <code>@ARGV</code> files are written to a backup-named or in-place replacement. Empty string <code>""</code> means "no backup"; a non-empty value (e.g. <code>".bak"</code>) means "save original as <code>FILE.bak</code>".</p>
<pre><code class="lang-perl"># Equivalent to: stryke -i.bak -pe 's/foo/bar/g' file.txt
BEGIN { $^I = '.bak' }
while (<>) { s/foo/bar/g; print }
</code></pre>
<p>See also: <code>-i</code> flag, <code>-p</code> / <code>-n</code>.</p>
</article>
<article class="doc-entry" id="doc-l">
<h3><a class="doc-anchor" href="#doc-l">#</a> <code>$^L</code></h3>
<p><code>$^L</code> — the formfeed character emitted between pages by <code>format</code>/<code>write</code>. Default: <code>"\f"</code>. Rarely changed; mainly useful when emitting paginated output to a printer-like destination.</p>
<pre><code class="lang-perl">local $^L = "\n---\n"
write # custom page break
</code></pre>
<p>See also: <code>format</code>, <code>write</code>.</p>
</article>
<article class="doc-entry" id="doc-m">
<h3><a class="doc-anchor" href="#doc-m">#</a> <code>$^M</code></h3>
<p><code>$^M</code> — an emergency memory pool reserved for handling out-of-memory <code>die</code>s. Pre-allocate a chunk early (e.g. <code>$^M = 'x' x 65536</code>), and Perl will release it when allocation otherwise fails so cleanup code has room to run. Niche; only relevant in long-running daemons that might OOM.</p>
<pre><code class="lang-perl">BEGIN { $^M = 'x' x 65536 } # 64 KB emergency reserve
</code></pre>
<p>See also: <code>die</code>, <code>END</code> block.</p>
</article>
<article class="doc-entry" id="doc-n">
<h3><a class="doc-anchor" href="#doc-n">#</a> <code>$^N</code></h3>
<p><code>$^N</code> — the substring matched by the most recently <strong>closed</strong> parenthesised group in the current regex match. Inside an embedded code assertion <code>(?{ ... })</code> this lets you grab the group that just closed without committing to a <code>$1</code>/<code>$2</code> number.</p>
<pre><code class="lang-perl">"abc" =~ /(.)(.)(.)(?{ p $^N })/ # prints c
</code></pre>
<p>See also: <code>$+</code>, <code>$1</code>..<code>$9</code>, <code>(?{ ... })</code> embedded code.</p>
</article>
<article class="doc-entry" id="doc-o">
<h3><a class="doc-anchor" href="#doc-o">#</a> <code>$^O</code></h3>
<p><code>$^O</code> — the OS name string set at build time. Common values: <code>darwin</code> (macOS), <code>linux</code>, <code>freebsd</code>, <code>MSWin32</code>, <code>cygwin</code>. Use it for platform-specific branching without shelling out to <code>uname</code>. Read-only.</p>
<pre><code class="lang-perl">if ($^O eq 'darwin') {
p "on macOS"
} elsif ($^O eq 'linux') {
p "on Linux"
} elsif ($^O =~ /MSWin32|cygwin/) {
p "on Windows"
}
</code></pre>
<p>See also: <code>uname</code> (full system info), <code>Config::%Config</code>.</p>
</article>
<article class="doc-entry" id="doc-p">
<h3><a class="doc-anchor" href="#doc-p">#</a> <code>$^P</code></h3>
<p><code>$^P</code> — the internal debugger control flag bitmask. Set to non-zero to enable the embedded debugger hooks; specific bits control which events (subroutine entry, line execution, file load, …) trigger callbacks. Debugger / profiler authors only.</p>
<pre><code class="lang-perl">p "debugger flags: $^P"
</code></pre>
<p>See also: stryke debugger / profiler tooling.</p>
</article>
<article class="doc-entry" id="doc-r">
<h3><a class="doc-anchor" href="#doc-r">#</a> <code>$^R</code></h3>
<p><code>$^R</code> — the value returned by the most recent <code>(?{ ... })</code> or <code>(??{ ... })</code> regex code-assertion. Useful when building accumulators inside complex regex matches that compute as they go.</p>
<pre><code class="lang-perl">"42" =~ /(\d+)(?{ $^R = $1 * 2 })/
p $^R # 84
</code></pre>
<p>See also: <code>(?{ ... })</code>, <code>(??{ ... })</code>, <code>$^N</code>.</p>
</article>
<article class="doc-entry" id="doc-s">
<h3><a class="doc-anchor" href="#doc-s">#</a> <code>$^S</code></h3>
<p><code>$^S</code> — the current exception-handling state: <code>undef</code> while compiling, <code>0</code> while executing the main program, <code>1</code> while executing inside an <code>eval { }</code>. Inside a <code>$SIG{__DIE__}</code> handler this tells you whether the die will be caught (<code>$^S == 1</code>) or fatal (<code>$^S == 0</code>).</p>
<pre><code class="lang-perl">$SIG{__DIE__} = fn ($msg) {
if ($^S) { return } # let eval catch it
log_fatal($msg) # uncaught — log it
}
</code></pre>
<p>See also: <code>eval</code>, <code>die</code>, <code>$SIG{__DIE__}</code>.</p>
</article>
<article class="doc-entry" id="doc-t">
<h3><a class="doc-anchor" href="#doc-t">#</a> <code>$^T</code></h3>
<p><code>$^T</code> — the time at which the program started, as a Unix epoch (seconds since 1970). Used by <code>-A</code>, <code>-M</code>, <code>-C</code> file-test operators (which return age in days relative to <code>$^T</code>). Read-write — set it to a different epoch to change what those tests mean.</p>
<pre><code class="lang-perl">p "started at: " . scalar(localtime $^T)
my @stale = grep { -M $_ > 30 } @files # older than 30 days
</code></pre>
<p>See also: <code>-M</code> / <code>-A</code> / <code>-C</code> file tests, <code>time()</code>, <code>localtime</code>.</p>
</article>
<article class="doc-entry" id="doc-v">
<h3><a class="doc-anchor" href="#doc-v">#</a> <code>$^V</code></h3>
<p><code>$^V</code> — the running stryke / Perl version as a version object (v-string). Compare with <code>$^V ge v5.20.0</code> style expressions for capability gating. Stringifies to <code>"v5.38.2"</code> etc.</p>
<pre><code class="lang-perl">p "running $^V"
die "need v5.20+" unless $^V ge v5.20.0
</code></pre>
<p>See also: <code>$stryke::VERSION</code>, <code>use VERSION</code>.</p>
</article>
<article class="doc-entry" id="doc-w">
<h3><a class="doc-anchor" href="#doc-w">#</a> <code>$^W</code></h3>
<p><code>$^W</code> — the global warnings flag (boolean). Set by the <code>-w</code> command-line flag or <code>BEGIN { $^W = 1 }</code>. The modern preferred mechanism is lexical <code>use warnings</code> / <code>no warnings</code>, which doesn't pollute distant scopes; reach for <code>$^W</code> only when matching legacy Perl 4 / early Perl 5 idioms.</p>
<pre><code class="lang-perl">local $^W = 0 # silence warnings in this scope (old style)
# Modern:
no warnings 'uninitialized'
</code></pre>
<p>See also: <code>use warnings</code>, <code>-w</code>, <code>${^WARNING_BITS}</code>.</p>
</article>
<article class="doc-entry" id="doc-x">
<h3><a class="doc-anchor" href="#doc-x">#</a> <code>$^X</code></h3>
<p><code>$^X</code> — the path used to invoke the stryke / Perl executable, as taken from <code>argv[0]</code> at startup. Useful for re-<code>exec</code>-ing the same interpreter from a child script or constructing <code>system($^X, '-e', ...)</code> calls that are guaranteed to use the same binary.</p>
<pre><code class="lang-perl">p "interpreter: $^X"
system $^X, '-e', 'p "hello from a fresh stryke"'
</code></pre>
<p>See also: <code>$0</code> (program name), <code>@ARGV</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$_</code></h3>
<p><code>$_</code> — the default topic variable. Many builtins (<code>print</code>, <code>say</code>/<code>p</code>, <code>chomp</code>, <code>length</code>, <code>uc</code>, <code>lc</code>, regex <code>=~</code> without an explicit target, <code>-X</code> file tests) operate on <code>$_</code> when called without arguments. <code>for</code>/<code>foreach</code> loops and <code>while (<>)</code> automatically bind each element/line to <code>$_</code> unless you declare a loop variable. In stryke pipelines (<code>|></code>), the unsigiled <code>_</code> is the topic — pipe stages see the current value as <code>_</code>, and <code>$_</code> remains compatible for Perl 5 idioms.</p>
<pre><code class="lang-perl">for (1:5) { p $_ * 2 } # 2 4 6 8 10
while (<>) { chomp; p } # chomp $_; p $_
@names |> e { p uc } # uc $_
# Explicit aliasing — mutations propagate:
my @xs = (1, 2, 3)
for (@xs) { $_ *= 10 }
p "@xs" # 10 20 30
</code></pre>
<p>Use <code>local $_</code> to scope a topic change. In stryke, <code>_</code> (no sigil) is the preferred pipeline topic; <code>$_</code> is the Perl-5-compatible form.</p>
</article>
<article class="doc-entry" id="doc-0">
<h3><a class="doc-anchor" href="#doc-0">#</a> <code>$_0</code></h3>
<p><code>_0</code> (or <code>$_0</code>) — the current value being threaded through a <code>|></code> pipeline, equivalent to <code>$_</code> and bare <code>_</code>. Use the explicit <code>0</code> form for clarity when reading code that also references positional 1, 2, 3, … via <code>_1</code>, <code>_2</code>, ….</p>
<pre><code class="lang-perl">1:5 |> map _ * 2 |> e p # implicit topic
1:5 |> map _0 * 2 |> e p # explicit positional 0 — same meaning
</code></pre>
<p>See also: <code>$_</code>, <code>_</code>, <code>_1</code>..<code>_4</code>, <code>_<N</code> (indexed ascent past depth 2).</p>
</article>
<article class="doc-entry" id="doc-0">
<h3><a class="doc-anchor" href="#doc-0">#</a> <code>$_0<</code></h3>
<p><strong>Topic ascent, 1 frame up.</strong> Eight equivalent spellings of the same value — the topic from the *enclosing* block one frame out.</p>
<pre><code class="lang-text">spellings (all identical): _< $_< _0< $_0< _<1 $_<1 _0<1 $_0<1
</code></pre>
<p>Every <code>|></code> stage, <code>map</code>/<code>grep</code>/<code>fore</code> block, and <code>sort</code> block opens a new topic frame. Inside that frame the *current* topic is <code>_</code>/<code>$_</code>/<code>_0</code>/<code>$_0</code>; one chevron <code><</code> walks up one frame to the surrounding block's topic. Indexed form <code>_<N</code> is sugar for <code>N</code> chevrons — <code>_<1</code> ≡ <code>_<</code>, more readable as ascent depth grows. Runtime cap: 5 frames (<code>parser.rs:1473</code>).</p>
<p>At the outermost iter (no enclosing topic frame), <code>_<</code> is <strong>undef</strong> — strict ascent semantics, no fallback to current <code>_</code>. If you need the current frame's topic, write <code>_</code> directly.</p>
<pre><code class="lang-perl">@rows |> map {
my @cells = @$_ # $_ is current row
@cells |> map { uc($_) . ":" . len($_<) }
# ^^ inner topic ^^^ outer row arrayref
}
</code></pre>
<p>The four-spelling matrix lets you choose readability per context: bare <code>_<</code> in pipe chains, sigiled <code>$_<</code> when interpolating, slot-explicit <code>_0<</code> when slot 1, 2, … positionals are also in scope.</p>
<p>See also: <code>_<<</code> (2 up), <code>_<<<</code> (3 up), <code>_<<<<</code> (4 up), <code>_<<<<<</code> (5 up), <code>_<N</code>/<code>_0<N</code> (indexed ascent), <code>_</code>/<code>$_</code>/<code>_0</code>/<code>$_0</code> (current frame).</p>
</article>
<article class="doc-entry" id="doc-0-2">
<h3><a class="doc-anchor" href="#doc-0-2">#</a> <code>$_0<2</code></h3>
<p><strong>Topic ascent, 2 frames up.</strong> Eight equivalent spellings of the topic from the block enclosing the enclosing block.</p>
<pre><code class="lang-text">spellings (all identical): _<< $_<< _0<< $_0<< _<2 $_<2 _0<2 $_0<2
</code></pre>
<p>Two chevrons walk up two topic frames. Indexed form <code>_<2</code> ≡ <code>_<<</code> — pick whichever is clearer at the call site. Often appears inside nested <code>map</code>/<code>grep</code> where you need to reach past the immediate enclosing block.</p>
<pre><code class="lang-perl">@docs |> map {
my $doc = $_ # _<0 = current doc
$doc->{lines} |> map {
my $line = $_ # _<0 = current line
$line |> map { # _<0 = char
{ char => $_, line => $_<, doc => $_<<->{id} }
# ^^^ line ^^^^ doc, 2 up
}
}
}
</code></pre>
<p>See also: <code>_<</code> (1 up), <code>_<<<</code> (3 up), <code>_<<<<</code> (4 up), <code>_<<<<<</code> (5 up), <code>_<N</code>/<code>_0<N</code>.</p>
</article>
<article class="doc-entry" id="doc-0-3">
<h3><a class="doc-anchor" href="#doc-0-3">#</a> <code>$_0<3</code></h3>
<p><strong>Topic ascent, 3 frames up.</strong> Eight equivalent spellings of the topic three blocks out.</p>
<pre><code class="lang-text">spellings (all identical): _<<< $_<<< _0<<< $_0<<< _<3 $_<3 _0<3 $_0<3
</code></pre>
<p>At this depth the indexed form <code>_<3</code> is usually the clearer choice — counting chevrons gets error-prone past two. Both forms compile to the same bytecode.</p>
<pre><code class="lang-perl">@projects |> map {
my $proj = $_ # _<0
$proj->{tasks} |> map {
$_->{steps} |> map {
$_->{notes} |> map {
{ note => $_, step => $_<, task => $_<<, proj => $_<3 }
# ^^^^ project, 3 up
}
}
}
}
</code></pre>
<p>See also: <code>_<</code> (1 up), <code>_<<</code> (2 up), <code>_<<<<</code> (4 up), <code>_<<<<<</code> (5 up), <code>_<N</code>.</p>
</article>
<article class="doc-entry" id="doc-0-4">
<h3><a class="doc-anchor" href="#doc-0-4">#</a> <code>$_0<4</code></h3>
<p><strong>Topic ascent, 4 frames up.</strong> Eight equivalent spellings of the topic four blocks out. At this depth prefer the indexed form <code>_<4</code> for readability.</p>
<pre><code class="lang-text">spellings (all identical): _<<<< $_<<<< _0<<<< $_0<<<< _<4 $_<4 _0<4 $_0<4
</code></pre>
<p>See also: <code>_<</code> (1 up), <code>_<<</code> (2 up), <code>_<<<</code> (3 up), <code>_<<<<<</code> (5 up), <code>_<N</code>/<code>_0<N</code>.</p>
</article>
<article class="doc-entry" id="doc-0-5">
<h3><a class="doc-anchor" href="#doc-0-5">#</a> <code>$_0<5</code></h3>
<p><strong>Topic ascent, 5 frames up.</strong> Eight equivalent spellings of the topic five blocks out — the deepest ascent the runtime accepts (<code>parser.rs:1473</code> caps at 5). Past this depth, refactor to a named lexical (<code>my $outer = $_</code>) instead.</p>
<pre><code class="lang-text">spellings (all identical): _<<<<< $_<<<<< _0<<<<< $_0<<<<< _<5 $_<5 _0<5 $_0<5
</code></pre>
<p>At this depth always use the indexed form <code>_<5</code> — five chevrons is unreadable.</p>
<p>See also: <code>_<</code> (1 up), <code>_<<</code> (2 up), <code>_<<<</code> (3 up), <code>_<<<<</code> (4 up), <code>_<N</code>/<code>_0<N</code>.</p>
</article>
<article class="doc-entry" id="doc-1">
<h3><a class="doc-anchor" href="#doc-1">#</a> <code>$_1</code></h3>
<p><code>_1</code> (or <code>$_1</code>) — the <strong>first additional</strong> positional bound in a <code>|></code> pipeline stage. When a HOF takes a block plus extra arguments, the extras are bound as <code>_1</code>, <code>_2</code>, …; the current value stays in <code>_</code> / <code>_0</code> / <code>$_</code>. This is what makes EXPR-form HOFs (<code>grep EXPR, LIST</code>) and brace-form HOFs (<code>grep { BLOCK } LIST</code>) share the same scope binding.</p>
<pre><code class="lang-perl"># grep EXPR, LIST — $_ is each element, $_1 is the predicate coderef
my $pred = fn ($x) { $x > 10 }
my @big = grep _1, $pred, (5, 12, 8, 20)
</code></pre>
<p>See also: <code>_0</code>, <code>_2</code>..<code>_4</code>, <code>_<N</code> (indexed ascent).</p>
</article>
<article class="doc-entry" id="doc-2">
<h3><a class="doc-anchor" href="#doc-2">#</a> <code>$_2</code></h3>
<p><code>_2</code> (or <code>$_2</code>) — the second additional positional in a <code>|></code> pipeline stage. See <code>_1</code> for full semantics.</p>
</article>
<article class="doc-entry" id="doc-3">
<h3><a class="doc-anchor" href="#doc-3">#</a> <code>$_3</code></h3>
<p><code>_3</code> (or <code>$_3</code>) — the third additional positional in a <code>|></code> pipeline stage. See <code>_1</code> for full semantics.</p>
</article>
<article class="doc-entry" id="doc-4">
<h3><a class="doc-anchor" href="#doc-4">#</a> <code>$_4</code></h3>
<p><code>_4</code> (or <code>$_4</code>) — the fourth additional positional in a <code>|></code> pipeline stage. See <code>_1</code> for full semantics. Past depth 2 also consider the indexed-ascent shortcut <code>_<N</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$`</code></h3>
<p><code></code> $<code> </code><code> — the substring *preceding* the last successful regex match ("prematch"). With </code>$&<code> and </code>$'`, reconstructs the full input. Reset on every successful match.</p>
<pre><code class="lang-perl">if ("hello world" =~ /\s/) {
p $` # hello
p $& # (space)
p $' # world
}
</code></pre>
<p>See also: <code>$&</code>, <code>$'</code>, <code>${^PREMATCH}</code> (cleaner under <code>use re 'p'</code>).</p>
</article>
<article class="doc-entry" id="doc-a">
<h3><a class="doc-anchor" href="#doc-a">#</a> <code>$a</code></h3>
<p><code>$a</code> — paired with <code>$b</code>, the comparator variables inside <code>sort BLOCK LIST</code>, <code>psort BLOCK LIST</code>, <code>preduce</code>, <code>pmap_reduce</code> blocks, and any user code that wants to compare two values without a closure. Stryke marks <code>$a</code>/<code>$b</code> as parallel-safe topics — assignments to them inside a parallel block are allowed even though they look like captured globals.</p>
<pre><code class="lang-perl">my @sorted = sort { $a <=> $b } @nums # numeric ascending
my @rsorted = sort { $b <=> $a } @nums # descending
my @by_len = sort { length($a) <=> length($b) } @strs
@nums |> psort { $a <=> $b } # parallel sort
@nums |> preduce { $a + $b } # parallel reduce
</code></pre>
<p>With <code>--no-interop</code>, <code>$a</code>/<code>$b</code> outside of <code>sort</code>/<code>preduce</code> blocks are rejected — the linter wants you to write <code>$_0</code>/<code>$_1</code> for general two-arg blocks.</p>
<p>See also: <code>$b</code>, <code>sort</code>, <code>psort</code>, <code>preduce</code>, <code>pmap_reduce</code>.</p>
</article>
<article class="doc-entry" id="doc-b">
<h3><a class="doc-anchor" href="#doc-b">#</a> <code>$b</code></h3>
<p><code>$b</code> — paired with <code>$a</code>, the comparator variables inside <code>sort</code>, <code>psort</code>, <code>preduce</code>, <code>pmap_reduce</code> blocks. See <code>$a</code> for full semantics.</p>
<pre><code class="lang-perl">my @desc = sort { $b <=> $a } @nums # descending numeric
my @z_a = sort { $b cmp $a } @strs # reverse string order
</code></pre>
<p>See also: <code>$a</code>, <code>sort</code>, <code>psort</code>, <code>preduce</code>.</p>
</article>
<article class="doc-entry" id="doc-stryke-version">
<h3><a class="doc-anchor" href="#doc-stryke-version">#</a> <code>$stryke::VERSION</code></h3>
<p><code>$stryke::VERSION</code> — the stryke language version string (e.g. <code>"0.13.4"</code>). Matches the version baked into the binary at build time from <code>Cargo.toml</code>. Use it for feature gating and diagnostics.</p>
<pre><code class="lang-perl">p "stryke $stryke::VERSION"
die "need stryke 0.14+" if $stryke::VERSION lt "0.14"
</code></pre>
<p>See also: <code>$^V</code> (interpreter version), <code>--version</code> CLI flag.</p>
</article>
<article class="doc-entry" id="doc-global-phase">
<h3><a class="doc-anchor" href="#doc-global-phase">#</a> <code>${^GLOBAL_PHASE}</code></h3>
<p><code>${^GLOBAL_PHASE}</code> — the current interpreter phase as a string. Values: <code>"START"</code> (very early init), <code>"BEGIN"</code> (inside a <code>BEGIN</code> block), <code>"CHECK"</code>, <code>"INIT"</code>, <code>"RUN"</code> (normal execution), <code>"END"</code> (inside an <code>END</code> block), <code>"DESTRUCT"</code> (final cleanup, after <code>END</code> blocks finish). Most code sees <code>"RUN"</code>; <code>DESTROY</code> methods invoked at interpreter shutdown can see <code>"DESTRUCT"</code> and skip work that would touch already-cleaned state.</p>
<pre><code class="lang-perl">fn Resource::DESTROY {
return if ${^GLOBAL_PHASE} eq "DESTRUCT" # skip during shutdown
close_external_handle($_[0])
}
p ${^GLOBAL_PHASE} # RUN
</code></pre>
<p>See also: <code>BEGIN</code>, <code>END</code>, <code>DESTROY</code>, phase blocks.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$|</code></h3>
<p><code>$|</code> — the autoflush flag for the currently selected output filehandle. When true (any non-zero value), every <code>print</code>/<code>say</code> flushes the buffer immediately. Essential for progress bars, prompts that should appear before <code><STDIN></code>, and pipelines where downstream consumers need data without buffering delay. Affects only the *currently selected* handle — pair with <code>select</code> to set autoflush on a specific handle.</p>
<pre><code class="lang-perl">$| = 1 # autoflush STDOUT
for (1:10) {
print "." # appears immediately
sleep 1
}
# Autoflush a specific handle:
my $old = select STDERR; $| = 1; select $old
</code></pre>
<p>See also: <code>select</code>, <code>IO::Handle::autoflush</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>$~</code></h3>
<p><code>$~</code> — the name of the current format used by <code>write</code>. Defaults to the name of the filehandle being written to. Set it to switch formats on the fly when the same handle should emit different report shapes.</p>
<pre><code class="lang-perl">format HEADER = ...
.
format BODY = ...
.
$~ = 'HEADER'; write
$~ = 'BODY'; write while @rows
</code></pre>
<p>See also: <code>$^</code> (top-of-page header format), <code>format</code>, <code>write</code>.</p>
</article>
<article class="doc-entry" id="doc-env">
<h3><a class="doc-anchor" href="#doc-env">#</a> <code>%ENV</code></h3>
<p><code>%ENV</code> — the process environment as a hash keyed by variable name. Reads return the current value (or <code>undef</code> for unset); assignments take effect immediately and propagate to child processes spawned afterwards via <code>system</code>/<code>exec</code>/backticks.</p>
<pre><code class="lang-perl">p $ENV{HOME}
p $ENV{PATH}
$ENV{MYAPP_DEBUG} = 1
system 'env' |> grep /MYAPP/ |> e p
delete $ENV{TMPDIR} # unset
</code></pre>
<p>In stryke, <code>%ENV</code> is a live view of the OS environment — no caching. See also: <code>getenv</code>, <code>setenv</code>.</p>
</article>
<article class="doc-entry" id="doc-inc">
<h3><a class="doc-anchor" href="#doc-inc">#</a> <code>%INC</code></h3>
<p><code>%INC</code> — the registry of files loaded via <code>require</code> / <code>use</code>. Keys are the relative module path (e.g. <code>"My/Module.pm"</code>); values are the absolute path on disk. <code>require</code> consults <code>%INC</code> before loading: if the key already exists, the require is a no-op (this is how Perl avoids loading the same module twice). Delete a key to force a reload (advanced use, e.g. plugin reloading).</p>
<pre><code class="lang-perl">use File::Spec
p $INC{'File/Spec.pm'} # absolute path to the loaded file
keys %INC |> sort |> e p # every loaded module
</code></pre>
<p>See also: <code>@INC</code> (search path), <code>require</code>, <code>use</code>.</p>
</article>
<article class="doc-entry" id="doc-sig">
<h3><a class="doc-anchor" href="#doc-sig">#</a> <code>%SIG</code></h3>
<p><code>%SIG</code> — the signal handler table keyed by signal name (without the <code>SIG</code> prefix: <code>INT</code>, <code>TERM</code>, <code>HUP</code>, …). Assign a coderef to install a handler; assign <code>'IGNORE'</code> to ignore; assign <code>'DEFAULT'</code> to restore default behavior. Two pseudo-keys hook the interpreter itself: <code>$SIG{__DIE__}</code> runs before any <code>die</code> (including caught), and <code>$SIG{__WARN__}</code> intercepts every <code>warn</code>.</p>
<pre><code class="lang-perl">$SIG{INT} = fn ($sig) { p "got SIGINT"; exit 0 }
$SIG{TERM} = 'IGNORE'
$SIG{__WARN__} = fn ($msg) { log_warn($msg) }
# Block a signal temporarily:
local $SIG{INT} = 'IGNORE'
critical_section()
</code></pre>
<p>See also: <code>kill</code>, <code>POSIX::sigaction</code>, <code>__DIE__</code> / <code>__WARN__</code> pseudo-signals.</p>
</article>
<article class="doc-entry" id="doc-h">
<h3><a class="doc-anchor" href="#doc-h">#</a> <code>%^H</code></h3>
<p><code>%^H</code> — the lexical hint hash, paired with <code>$^H</code>. Pragma authors store per-scope state here, keyed by their package name. The contents are visible at compile time only — runtime code in the same scope sees an empty hash unless the pragma uses <code>${^_RE_TRIE_MAXBUF}</code> or similar magic.</p>
<pre><code class="lang-perl">BEGIN { $^H{'My::Pragma'} = { strict_mode => 1 } }
</code></pre>
<p>Niche; almost exclusively used by <code>use</code> pragma implementations. See also: <code>$^H</code>, <code>use</code>.</p>
</article>
<article class="doc-entry" id="doc-hook">
<h3><a class="doc-anchor" href="#doc-hook">#</a> <code>%^HOOK</code></h3>
<p><code>%^HOOK</code> — the runtime hook registry used by stryke / Perl extensions to register callbacks for compile-time events (function entry/exit, regex match, signal arrival). Keys are well-known hook names; values are coderefs. Modifying this directly is a sharp edge — usually you'd use a pragma or module that hooks for you (e.g. AOP intercepts in zshrs).</p>
<pre><code class="lang-perl">p keys %^HOOK # registered hook names
</code></pre>
<p>See also: stryke AOP / intercept facilities.</p>
</article>
<article class="doc-entry" id="doc-a">
<h3><a class="doc-anchor" href="#doc-a">#</a> <code>%a</code></h3>
<p><code>%a</code> — short alias for <code>%stryke::aliases</code>. Maps every alias spelling to its canonical primary name. Keys are the 2nd-and-later names in each <code>try_builtin</code> match arm; values are the primary. For O(1) *reverse* lookup (primary → all its aliases), use <code>%p</code> / <code>%stryke::primaries</code>.</p>
<pre><code class="lang-perl">p $a{tj} # to_json
p $a{bn} # basename
p scalar keys %a # total alias count
keys %a |> grep /^p/ |> sort |> e p # every alias starting with p
</code></pre>
<p>See also: <code>%stryke::aliases</code>, <code>%p</code> / <code>%stryke::primaries</code>.</p>
</article>
<article class="doc-entry" id="doc-b">
<h3><a class="doc-anchor" href="#doc-b">#</a> <code>%b</code></h3>
<p><code>%b</code> — short alias for <code>%stryke::builtins</code>. Maps every <strong>primary</strong> callable name to its category string. Primaries-only — aliases live in <code>%a</code> / <code>%stryke::aliases</code>. <code>scalar keys %b</code> is the clean unique-operation count of stryke's runtime.</p>
<pre><code class="lang-perl">p $b{pmap} # "parallel"
p $b{to_json} # "serialization"
p scalar keys %b # unique-op count
keys %b |> grep { $b{_} eq 'parallel' } |> sort |> e p
</code></pre>
<p>See also: <code>%stryke::builtins</code>, <code>%c</code> / <code>%stryke::categories</code>, <code>%a</code> / <code>%stryke::aliases</code>.</p>
</article>
<article class="doc-entry" id="doc-d">
<h3><a class="doc-anchor" href="#doc-d">#</a> <code>%d</code></h3>
<p><code>%d</code> — short alias for <code>%stryke::descriptions</code>. Maps each callable name to its one-line summary (the first sentence of its LSP hover doc). Sparse — only names that have a hand-written hover doc appear, so <code>exists $d{$name}</code> doubles as "is this documented?".</p>
<pre><code class="lang-perl">p $d{pmap} # one-line summary of pmap
p $d{to_json} # "Serialize a StrykeValue to a JSON string."
p scalar keys %d # count of documented ops
keys %d |> grep { $d{_} =~ /parallel/i } |> sort |> e p
</code></pre>
<p>See also: <code>%stryke::descriptions</code>, the LSP hover system.</p>
</article>
<article class="doc-entry" id="doc-k">
<h3><a class="doc-anchor" href="#doc-k">#</a> <code>%k</code></h3>
<p><code>%k</code> — short alias for <code>%stryke::keywords</code>. Maps every stryke language keyword (<code>fn</code>, <code>match</code>, <code>class</code>, <code>struct</code>, <code>enum</code>, <code>mysync</code>, <code>frozen</code>, …) to a one-line category/description. Use this to discover the full keyword set programmatically.</p>
<pre><code class="lang-perl">p scalar keys %k # total keyword count
keys %k |> sort |> e p # every keyword
keys %k |> grep { $k{_} =~ /control/i } |> e p
</code></pre>
<p>See also: <code>%stryke::keywords</code>, <code>%b</code> / <code>%stryke::builtins</code>.</p>
</article>
<article class="doc-entry" id="doc-limits">
<h3><a class="doc-anchor" href="#doc-limits">#</a> <code>%limits</code></h3>
<p><code>%limits</code> — reflection hash exposing stryke's hard and soft runtime limits (max thread count, max recursion depth, max string interpolation depth, regex backtrack budget, etc.). Keys are limit names; values are the numeric ceilings.</p>
<pre><code class="lang-perl">p keys %limits |> sort |> e p
p $limits{max_threads}
p $limits{regex_backtrack}
</code></pre>
<p>See also: stryke runtime / scheduler internals.</p>
</article>
<article class="doc-entry" id="doc-o">
<h3><a class="doc-anchor" href="#doc-o">#</a> <code>%o</code></h3>
<p><code>%o</code> — short alias for <code>%stryke::operators</code>. Maps every symbol operator stryke recognises (arithmetic, comparison, bitwise, pipeline arrows, assignment forms, …) to its category string.</p>
<p>Key is the spelling as the lexer emits it (<code>"+"</code>, <code>"<=>"</code>, <code>"//="</code>, <code>"~>"</code>, <code>"|>"</code>, <code>"->"</code>, <code>"=~"</code>, <code>"..."</code>); value is one of <code>arith</code>, <code>compare</code>, <code>logical</code>, <code>bitwise</code>, <code>assign</code>, <code>string</code>, <code>binding</code>, <code>pipeline</code>, <code>range</code>, <code>arrow</code>, <code>deref</code>, <code>inc</code>, <code>ternary</code>, <code>sigil</code>, <code>punct</code>. Word operators (<code>and</code>, <code>or</code>, <code>eq</code>, <code>cmp</code>, <code>x</code>, <code>not</code>) live in <code>%k</code> with category <code>"operator"</code>, not here.</p>
<pre><code class="lang-perl">p $o{"+"} # "arith"
p $o{"<=>"} # "compare"
p $o{"|>"} # "pipeline"
p $o{"=~"} # "binding"
p scalar keys %o # total symbol-operator count
keys %o |> grep { $o{_} eq "pipeline" } |> sort |> e p
keys %o |> grep { $o{_} eq "assign" } |> sort |> e p
</code></pre>
<p>See also: <code>%stryke::operators</code>, <code>%k</code> / <code>%stryke::keywords</code> (word operators), <code>%v</code> / <code>%stryke::special_vars</code>.</p>
</article>
<article class="doc-entry" id="doc-overload">
<h3><a class="doc-anchor" href="#doc-overload">#</a> <code>%overload::</code></h3>
<p><code>%overload::</code> — the runtime symbol table of the <code>overload</code> package, exposing operator-overloading machinery (<code>overload::Method</code>, <code>overload::StrVal</code>, <code>overload::Overloaded</code>). Inspecting it tells you which packages have overloaded operators registered. Rarely accessed directly; use the <code>overload</code> pragma to register operators in your own classes.</p>
<pre><code class="lang-perl">p keys %overload::
</code></pre>
<p>See also: <code>use overload</code>, <code>overload::Method</code>, <code>overload::Overloaded</code>.</p>
</article>
<article class="doc-entry" id="doc-parameters">
<h3><a class="doc-anchor" href="#doc-parameters">#</a> <code>%parameters</code></h3>
<p><code>%parameters</code> — reflection hash mapping each stryke builtin to its parameter signature (argument names, types, optionality, default values). Populated at build time from the function definitions in <code>strykelang/builtins*.rs</code>. Drives LSP signature help and type checking.</p>
<pre><code class="lang-perl">p $parameters{pmap} # signature for pmap
keys %parameters |> sort |> e p # every documented signature
keys %parameters |> grep { @{$parameters{_}} > 3 } |> e p # 4+ arg builtins
</code></pre>
<p>See also: <code>%b</code> / <code>%stryke::builtins</code>, LSP signature provider.</p>
</article>
<article class="doc-entry" id="doc-pc">
<h3><a class="doc-anchor" href="#doc-pc">#</a> <code>%pc</code></h3>
<p><code>parsec</code> (alias <code>pc</code>) — pc ≈ 3.086×10¹⁶ m ≈ 3.26 ly. Common astronomical distance unit.</p>
<pre><code class="lang-perl">p pc # 3.0856775814913673e16 m
p pc / ly # ~3.26 light years
</code></pre>
</article>
<article class="doc-entry" id="doc-stryke-aliases">
<h3><a class="doc-anchor" href="#doc-stryke-aliases">#</a> <code>%stryke::aliases</code></h3>
<p><code>%stryke::aliases</code> (short: <code>%a</code>) — alias spelling → canonical primary.</p>
<p>Keys are the 2nd-and-later names in each <code>try_builtin</code> match arm. For O(1) *reverse* lookup (primary → all its aliases), use <code>%stryke::primaries</code> / <code>%p</code>.</p>
<pre><code class="lang-perl">p $a{tj} # "to_json"
p $a{bn} # "basename"
p scalar keys %a # total alias count
</code></pre>
</article>
<article class="doc-entry" id="doc-stryke-all">
<h3><a class="doc-anchor" href="#doc-stryke-all">#</a> <code>%stryke::all</code></h3>
<p><code>%stryke::all</code> (short: <code>%all</code>) — every callable *spelling* (primaries <strong>and</strong> aliases) → category. Aliases inherit their primary's category.</p>
<p>Use <code>%all</code> when you want "how many names can I type?" or want to look up an alias's category without hopping through <code>%aliases</code>. Use <code>%builtins</code> when you want unique operations.</p>
<pre><code class="lang-perl">p scalar keys %all # total callable-spellings count
p $all{tj} # "serialization" (alias resolves via inheritance)
p $all{to_json} # "serialization"
keys %all |> pager # browse every spelling
</code></pre>
</article>
<article class="doc-entry" id="doc-stryke-builtins">
<h3><a class="doc-anchor" href="#doc-stryke-builtins">#</a> <code>%stryke::builtins</code></h3>
<p><code>%stryke::builtins</code> (short: <code>%b</code>) — every <strong>primary</strong> callable name → its category. Primaries-only, so <code>scalar keys %b</code> is a clean unique-operation count. For the "everything you can type" view (primaries + aliases), use <code>%stryke::all</code> / <code>%all</code>.</p>
<pre><code class="lang-perl">p $b{pmap} # "parallel"
p $b{to_json} # "serialization"
p scalar keys %b # unique-op count
</code></pre>
</article>
<article class="doc-entry" id="doc-stryke-categories">
<h3><a class="doc-anchor" href="#doc-stryke-categories">#</a> <code>%stryke::categories</code></h3>
<p><code>%stryke::categories</code> (short: <code>%c</code>) — category string → arrayref of names in that category.</p>
<p>Inverted index on <code>%builtins</code>. Gives O(1) reverse-lookup for "list every op of kind X" queries that would otherwise be O(n) <code>grep</code>s. Name lists are alphabetized.</p>
<pre><code class="lang-perl">$c{parallel} |> e p # every parallel op
p scalar @{ $c{parallel} } # how many?
p join ", ", @{ $c{"array / list"} } # joined roster
keys %c |> sort |> p # all category names
</code></pre>
</article>
<article class="doc-entry" id="doc-stryke-descriptions">
<h3><a class="doc-anchor" href="#doc-stryke-descriptions">#</a> <code>%stryke::descriptions</code></h3>
<p><code>%stryke::descriptions</code> (short: <code>%d</code>) — name → one-line summary.</p>
<p>First sentence of each LSP hover doc (<code>doc_for_label_text</code>), harvested at build time. Sparse — only names that have a hover doc appear, so <code>exists $d{$name}</code> doubles as "is this documented?".</p>
<pre><code class="lang-perl">p $d{pmap} # one-line summary
p $d{to_json} # "Serialize a StrykeValue to a JSON string."
p scalar keys %d # count of documented ops
keys %d |> grep { $d{_} =~ /parallel/i } |> sort |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-stryke-extensions">
<h3><a class="doc-anchor" href="#doc-stryke-extensions">#</a> <code>%stryke::extensions</code></h3>
<p><code>%stryke::extensions</code> (short: <code>%e</code>) — stryke-only names, name → category.</p>
<p>Disjoint from <code>%perl_compats</code>. Everything <code>--compat</code> mode rejects at parse time, plus dispatch primaries like <code>basename</code>/<code>ddump</code> that are extensions at runtime even without a parser entry.</p>
<pre><code class="lang-perl">p $e{pmap} # "parallel"
keys %e |> grep /^p/ |> sort |> p # every p* parallel op
</code></pre>
</article>
<article class="doc-entry" id="doc-stryke-keywords">
<h3><a class="doc-anchor" href="#doc-stryke-keywords">#</a> <code>%stryke::keywords</code></h3>
<p><code>%stryke::keywords</code> (short: <code>%k</code>) — language keyword → one-line category/description. Includes <code>fn</code>, <code>match</code>, <code>class</code>, <code>struct</code>, <code>enum</code>, <code>mysync</code>, <code>frozen</code>, <code>async</code>/<code>await</code>/<code>spawn</code>, control-flow keywords, declaration keywords, etc.</p>
<pre><code class="lang-perl">p scalar keys %stryke::keywords
keys %stryke::keywords |> sort |> e p
</code></pre>
<p>See also: <code>%k</code> (short alias), <code>%stryke::builtins</code> (callable names rather than keywords).</p>
</article>
<article class="doc-entry" id="doc-stryke-operators">
<h3><a class="doc-anchor" href="#doc-stryke-operators">#</a> <code>%stryke::operators</code></h3>
<p><code>%stryke::operators</code> (short: <code>%o</code>) — symbol operator spelling → category. Built from the <code>OPERATORS</code> table in <code>builtins.rs</code>, which mirrors the operator token set in <code>token.rs</code> (every <code>Token::Plus</code> / <code>Token::Spaceship</code> / <code>Token::ThreadArrow</code> …). Disjoint from <code>%stryke::keywords</code>: word operators (<code>and</code>, <code>or</code>, <code>eq</code>, <code>cmp</code>, <code>x</code>, <code>not</code>) appear in <code>%k</code> with category <code>"operator"</code>, while only symbol/punctuation operators appear here.</p>
<p>Categories: <code>arith</code>, <code>compare</code>, <code>logical</code>, <code>bitwise</code>, <code>assign</code>, <code>string</code>, <code>binding</code>, <code>pipeline</code>, <code>range</code>, <code>arrow</code>, <code>deref</code>, <code>inc</code>, <code>ternary</code>, <code>sigil</code>, <code>punct</code>.</p>
<pre><code class="lang-perl">p scalar keys %stryke::operators
keys %stryke::operators |> sort |> e p
keys %stryke::operators |> grep { $stryke::operators{_} eq "pipeline" } |> sort |> e p
</code></pre>
<p>See also: <code>%o</code> (short alias), <code>%stryke::keywords</code> (word operators), <code>%stryke::special_vars</code>.</p>
</article>
<article class="doc-entry" id="doc-stryke-perl-compats">
<h3><a class="doc-anchor" href="#doc-stryke-perl-compats">#</a> <code>%stryke::perl_compats</code></h3>
<p><code>%stryke::perl_compats</code> (short: <code>%pc</code>) — Perl 5 core names only, name → category.</p>
<p>Subset of <code>%builtins</code> restricted to names from <code>is_perl5_core</code>. Direct O(1) access for the "show me just Perl core" query.</p>
<pre><code class="lang-perl">p $pc{map} # "array / list"
p scalar keys %pc # core-only count
keys %pc |> sort |> p # enumerate every Perl core name
</code></pre>
</article>
<article class="doc-entry" id="doc-stryke-primaries">
<h3><a class="doc-anchor" href="#doc-stryke-primaries">#</a> <code>%stryke::primaries</code></h3>
<p><code>%stryke::primaries</code> (short: <code>%p</code>) — primary dispatcher name → arrayref of its aliases.</p>
<p>Inverted <code>%aliases</code>. Primaries with no aliases still have an entry (empty arrayref), so <code>exists $p{foo}</code> reliably answers "is foo a dispatch primary?" O(1).</p>
<pre><code class="lang-perl">$p{to_json} |> e p # ["tj"]
p scalar @{ $p{basename} } # how many aliases does basename have?
# find every primary that has at least one alias:
keys %p |> grep { scalar @{$p{_}} } |> sort |> p
</code></pre>
</article>
<article class="doc-entry" id="doc-stryke-special-vars">
<h3><a class="doc-anchor" href="#doc-stryke-special-vars">#</a> <code>%stryke::special_vars</code></h3>
<p><code>%stryke::special_vars</code> (short: <code>%v</code>) — special variable spelling → category. Every key carries its sigil (<code>"$!"</code>, <code>"@ARGV"</code>, <code>"%ENV"</code>, <code>"$^X"</code>, <code>"$stryke::VERSION"</code>, <code>"__FILE__"</code>) so a single hash covers scalar/array/hash/caret/compile-time forms uniformly. Every entry has a hand-written hover doc in <code>lsp.rs::doc_for_label_text</code>, so <code>exists $v{$name}</code> doubles as "is this documented?".</p>
<p>Categories partition by purpose: <code>topic</code>, <code>error</code>, <code>pid</code>, <code>regex-match</code>, <code>regex-capture</code>, <code>io</code>, <code>process</code>, <code>args</code>, <code>env</code>, <code>signal</code>, <code>script</code>, <code>caret</code>, <code>subscript</code>, <code>version</code>, <code>reflection</code>, <code>format</code>, <code>sort</code>.</p>
<pre><code class="lang-perl">p scalar keys %stryke::special_vars
p $stryke::special_vars{'$!'} # "error"
p $stryke::special_vars{'@ARGV'} # "args"
p $stryke::special_vars{'%ENV'} # "env"
p $stryke::special_vars{'$^X'} # "caret"
keys %stryke::special_vars |> grep { $stryke::special_vars{_} eq "regex-capture" } |> sort |> e p
</code></pre>
<p>See also: <code>%v</code> (short alias), <code>%stryke::operators</code>, <code>%stryke::keywords</code>, <code>%stryke::builtins</code>.</p>
</article>
<article class="doc-entry" id="doc-term">
<h3><a class="doc-anchor" href="#doc-term">#</a> <code>%term</code></h3>
<p><code>%term</code> — reflection hash describing the controlling terminal: width, height, color depth, capabilities (Unicode support, true-color, focus events, alternate screen). Populated lazily on first read by querying <code>tput</code> / <code>tcgetattr</code> / <code>TIOCGWINSZ</code>.</p>
<pre><code class="lang-perl">p $term{width} # columns
p $term{height} # rows
p $term{color} # "truecolor" / "256" / "16" / "none"
p keys %term |> sort
</code></pre>
<p>See also: <code>%uname</code> (OS info), <code>term_width</code>/<code>term_height</code> builtins.</p>
</article>
<article class="doc-entry" id="doc-v">
<h3><a class="doc-anchor" href="#doc-v">#</a> <code>%v</code></h3>
<p><code>%v</code> — short alias for <code>%stryke::special_vars</code>. Maps every special variable spelling (sigil included) to its category.</p>
<p>One hash covers every kind of special variable: scalar (<code>$!</code>, <code>$_</code>, <code>$@</code>, <code>$1</code>..<code>$9</code>, <code>$^X</code>), array (<code>@_</code>, <code>@ARGV</code>, <code>@+</code>, <code>@-</code>, <code>@^CAPTURE</code>), hash (<code>%ENV</code>, <code>%INC</code>, <code>%SIG</code>, <code>%^H</code>), caret (<code>$^A</code>..<code>$^X</code>, <code>%^H</code>, <code>%^HOOK</code>), compile-time (<code>__FILE__</code>, <code>__LINE__</code>, <code>__PACKAGE__</code>, <code>__SUB__</code>), and version (<code>$stryke::VERSION</code>). Categories: <code>topic</code>, <code>error</code>, <code>pid</code>, <code>regex-match</code>, <code>regex-capture</code>, <code>io</code>, <code>process</code>, <code>args</code>, <code>env</code>, <code>signal</code>, <code>script</code>, <code>caret</code>, <code>subscript</code>, <code>version</code>, <code>reflection</code>, <code>format</code>, <code>sort</code>.</p>
<pre><code class="lang-perl">p $v{'$!'} # "error"
p $v{'@ARGV'} # "args"
p $v{'$1'} # "regex-capture"
p scalar keys %v # total special-var count
keys %v |> grep { $v{_} eq "caret" } |> sort |> e p
keys %v |> grep { $v{_} eq "regex-capture" } |> sort |> e p
</code></pre>
<p>Every key has a matching LSP hover entry, so <code>exists $v{$name}</code> doubles as "is this special var documented?".</p>
<p>See also: <code>%stryke::special_vars</code>, <code>%o</code> / <code>%stryke::operators</code>, <code>%k</code> / <code>%stryke::keywords</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>@+</code></h3>
<p><code>@+</code> — array of byte offsets *one past the end* of each match group in the most recent successful regex. <code>$+[0]</code> is the end of the whole match; <code>$+[1]</code> is the end of <code>$1</code>; etc. Pair with <code>@-</code> (start offsets) for <code>substr</code>-based slicing without re-running the regex.</p>
<pre><code class="lang-perl">my $s = "foo bar baz"
if ($s =~ /(\w+) (\w+)/) {
p "match: [$-[0], $+[0])" # [0, 7)
p substr($s, $-[1], $+[1] - $-[1]) # foo
p substr($s, $-[2], $+[2] - $-[2]) # bar
}
</code></pre>
<p>See also: <code>@-</code>, <code>$1</code>..<code>$9</code>, <code>${^MATCH}</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>@-</code></h3>
<p><code>@-</code> — array of byte offsets to the *start* of each match group in the most recent successful regex. <code>$-[0]</code> is the start of the whole match; <code>$-[1]</code> is the start of <code>$1</code>; etc. Pair with <code>@+</code> (end offsets).</p>
<pre><code class="lang-perl">my $s = "foo bar baz"
$s =~ /(\w+) (\w+)/
p "foo at: $-[1]..$+[1]" # foo at: 0..3
p "bar at: $-[2]..$+[2]" # bar at: 4..7
</code></pre>
<p>See also: <code>@+</code>, <code>$1</code>..<code>$9</code>.</p>
</article>
<article class="doc-entry" id="doc-argv">
<h3><a class="doc-anchor" href="#doc-argv">#</a> <code>@ARGV</code></h3>
<p><code>@ARGV</code> — the command-line argument list (excluding <code>$0</code>, the program name). <code>shift @ARGV</code> is the idiomatic way to peel off positional args one at a time. The diamond operator <code><></code> consumes <code>@ARGV</code> element by element, treating each as a filename to read (or <code>"-"</code> for stdin). For structured flag parsing prefer the <code>getopts</code> builtin.</p>
<pre><code class="lang-perl">my $cmd = shift @ARGV
my @files = @ARGV
while (<>) { p $_ } # reads from every file in @ARGV
# Structured flags:
my %opts = %{ getopts(["verbose|v", "file|f=s"]) }
p "leftover positionals: @ARGV"
</code></pre>
<p>See also: <code>$ARGV</code> (current filename in <code><></code>), <code>getopts</code>, <code><></code> diamond operator.</p>
</article>
<article class="doc-entry" id="doc-env">
<h3><a class="doc-anchor" href="#doc-env">#</a> <code>@ENV</code></h3>
<p><code>@ENV</code> — array interpretation of the environment. Generally not useful — <code>%ENV</code> (hash) is the right interface. Mentioned here because the array form appears in completion words for symmetry with <code>%ENV</code> / <code>$ENV{...}</code>. Reading <code>@ENV</code> yields a list of <code>KEY=VALUE</code> strings on some systems, undef on others.</p>
<pre><code class="lang-perl"># Prefer %ENV:
for my $k (sort keys %ENV) {
p "$k=$ENV{$k}"
}
</code></pre>
<p>See also: <code>%ENV</code>.</p>
</article>
<article class="doc-entry" id="doc-export">
<h3><a class="doc-anchor" href="#doc-export">#</a> <code>@EXPORT</code></h3>
<p><code>@EXPORT</code> — the list of symbol names a module exports unconditionally when imported with <code>use Module;</code> (no explicit import list). Set in the module's package via <code>our @EXPORT = qw(foo bar)</code>. stryke honours <code>@EXPORT</code> for user modules; built-in pragmas (<code>strict</code>, <code>warnings</code>, <code>utf8</code>, <code>feature</code>, <code>open</code>, <code>Env</code>) do not use it because they don't load files.</p>
<pre><code class="lang-perl">package My::Utils
our @EXPORT = qw(normalize) # always imported
our @EXPORT_OK = qw(canonicalize internal) # opt-in only
fn normalize { ... }
fn canonicalize { ... }
package main
use My::Utils # normalize is in scope
use My::Utils qw(canonicalize) # explicit opt-in for OK-list
</code></pre>
<p>See also: <code>@EXPORT_OK</code>, <code>use</code>, <code>require</code>, <code>Exporter</code>.</p>
</article>
<article class="doc-entry" id="doc-export-ok">
<h3><a class="doc-anchor" href="#doc-export-ok">#</a> <code>@EXPORT_OK</code></h3>
<p><code>@EXPORT_OK</code> — the list of symbol names a module makes available for *explicit* import only: <code>use Module qw(name1 name2)</code>. Unlike <code>@EXPORT</code>, nothing in this list is imported by default — the caller must name each symbol. This is the Exporter-pattern way to publish symbols without polluting every caller's namespace.</p>
<pre><code class="lang-perl">package My::Tools
our @EXPORT = qw() # nothing by default
our @EXPORT_OK = qw(slugify camel_case) # opt-in only
fn slugify { ... }
fn camel_case { ... }
package main
use My::Tools qw(slugify) # only slugify in scope
</code></pre>
<p>See also: <code>@EXPORT</code>, <code>use</code>, <code>Exporter</code>.</p>
</article>
<article class="doc-entry" id="doc-f">
<h3><a class="doc-anchor" href="#doc-f">#</a> <code>@F</code></h3>
<p><code>@F</code> — the autosplit field array, populated when stryke / Perl runs with the <code>-a</code> flag. Each input line read by <code>-n</code>/<code>-p</code> is automatically split on whitespace (or on the regex given to <code>-F</code>) into <code>@F</code>. AWK-like one-liners use this heavily.</p>
<pre><code class="lang-perl"># stryke -nae 'p $F[0] if $F[2] > 100' # AWK '{ print $1 if $3 > 100 }'
# stryke -F: -nae 'p "user=$F[0] uid=$F[2]"' /etc/passwd
</code></pre>
<p>See also: <code>-a</code> / <code>-F</code> command-line flags, <code>split</code>, <code>-n</code> / <code>-p</code>.</p>
</article>
<article class="doc-entry" id="doc-inc">
<h3><a class="doc-anchor" href="#doc-inc">#</a> <code>@INC</code></h3>
<p><code>@INC</code> — the module search path. Each <code>require</code> / <code>use</code> walks <code>@INC</code> looking for the requested module. Defaults: the directories baked into the interpreter at build time plus <code>.</code> (current dir, removed in recent Perl for security). Modify with <code>BEGIN { unshift @INC, '/my/lib' }</code> to add directories before module loads run.</p>
<pre><code class="lang-perl">BEGIN { unshift @INC, "$ENV{HOME}/perl5/lib" }
use My::Module # searched in @INC
p join "\n", @INC # show search path
</code></pre>
<p>See also: <code>%INC</code> (loaded files), <code>require</code>, <code>use lib</code>.</p>
</article>
<article class="doc-entry" id="doc-intercept-args">
<h3><a class="doc-anchor" href="#doc-intercept-args">#</a> <code>@INTERCEPT_ARGS</code></h3>
<p><code>@INTERCEPT_ARGS</code> — inside an AOP advice body (<code>before</code>/<code>after</code>/<code>around</code>), the arguments passed to the intercepted sub call. Same shape as <code>@_</code> would have inside the wrapped sub itself. Mutating <code>@INTERCEPT_ARGS</code> does <strong>not</strong> change what the wrapped sub receives — use <code>around</code> if you need to modify the call.</p>
<pre><code class="lang-perl">before "fetch" {
warn "calling fetch(" . join(", ", @INTERCEPT_ARGS) . ")"
}
around "cached_lookup" {
if (my $hit = cache_get($INTERCEPT_ARGS[0])) { return $hit }
my $r = proceed()
cache_put($INTERCEPT_ARGS[0], $r)
$r
}
</code></pre>
<p>See also: <code>$INTERCEPT_NAME</code>, <code>$INTERCEPT_RESULT</code>, <code>$INTERCEPT_MS</code>, <code>$INTERCEPT_US</code>, <code>before</code>, <code>after</code>, <code>around</code>.</p>
</article>
<article class="doc-entry" id="doc-isa">
<h3><a class="doc-anchor" href="#doc-isa">#</a> <code>@ISA</code></h3>
<p><code>@ISA</code> — a package's inheritance list. <code>package Foo; our @ISA = ('Bar', 'Baz')</code> makes <code>Foo</code> inherit methods from <code>Bar</code> first, then <code>Baz</code>. stryke walks <code>@ISA</code> using <strong>C3 method resolution order (live, not cached)</strong> for <code>->method</code> dispatch and <code>SUPER::</code> — covering both single and multiple inheritance without the diamond ambiguities of Perl's default depth-first MRO.</p>
<pre><code class="lang-perl">package Animal
fn speak { p "..." }
package Dog
our @ISA = ('Animal')
fn speak { p "woof" }
package main
Dog->speak # woof
# Inheritance chain visible at runtime:
p "@Dog::ISA" # Animal
</code></pre>
<p>See also: <code>bless</code>, <code>class</code> (modern stryke OOP), <code>SUPER::</code>, <code>DESTROY</code>, <code>AUTOLOAD</code>.</p>
</article>
<article class="doc-entry" id="doc-capture">
<h3><a class="doc-anchor" href="#doc-capture">#</a> <code>@^CAPTURE</code></h3>
<p><code>@^CAPTURE</code> — array of substring captures from the most recent successful regex match, paralleling <code>$1</code>..<code>$9</code> but as a list. <code>$^CAPTURE[0]</code> is <code>$1</code>, <code>$^CAPTURE[1]</code> is <code>$2</code>, etc. Useful when the number of capture groups is dynamic.</p>
<pre><code class="lang-perl">if ("alice 30 engineer" =~ /^(\w+) (\d+) (\w+)$/) {
p "groups: @^CAPTURE" # alice 30 engineer
p scalar @^CAPTURE # 3
}
</code></pre>
<p>See also: <code>@^CAPTURE_ALL</code>, <code>$1</code>..<code>$9</code>, <code>%+</code> (named captures).</p>
</article>
<article class="doc-entry" id="doc-capture-all">
<h3><a class="doc-anchor" href="#doc-capture-all">#</a> <code>@^CAPTURE_ALL</code></h3>
<p><code>@^CAPTURE_ALL</code> — array-of-arrays of *every* capture from a <code>/g</code> (global) match. Each element is one match's captures. Useful for iterating over all matches in a single string without writing a <code>while ... =~</code> loop.</p>
<pre><code class="lang-perl">"a=1 b=2 c=3" =~ /(\w)=(\d)/g
for my $m (@^CAPTURE_ALL) {
p "$m->[0] -> $m->[1]"
}
</code></pre>
<p>See also: <code>@^CAPTURE</code>, <code>/g</code> modifier.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>@_</code></h3>
<p><code>@_</code> — the implicit argument array inside a subroutine. Every <code>fn</code> / <code>sub</code> receives its caller's arguments in <code>@_</code>, flattened (lists are spread, hash/array refs stay as single refs). <code>shift</code> and <code>pop</code> without an explicit array default to <code>@_</code> inside a sub. Modifying <code>$_[0]</code>, <code>$_[1]</code>, … aliases back to the caller's variables — a sharp edge worth knowing about. In stryke, prefer named parameters (<code>fn f($a, $b) { ... }</code>) which destructure <code>@_</code> into proper lexicals; reach for raw <code>@_</code> only when you need variadic behavior or want to forward all arguments via <code>@_</code>.</p>
<pre><code class="lang-perl">fn sum_all {
my $total = 0
$total += _ for @_
$total
}
p sum_all(1, 2, 3, 4) # 10
fn first_two {
my ($a, $b) = @_ # destructure
($a, $b)
}
fn forward { other_fn(@_) } # pass through every arg
</code></pre>
<p>See also: <code>$_[N]</code> for positional access, <code>scalar @_</code> for arg count, <code>wantarray</code> for caller context.</p>
</article>
<article class="doc-entry" id="doc-f">
<h3><a class="doc-anchor" href="#doc-f">#</a> <code>@f</code></h3>
<p><code>@f</code> — short alias for <code>@fpath</code>. The list of directories searched for autoload functions (zsh-style). Mutating <code>@f</code> (push, unshift, splice) immediately changes which directories future autoload calls will search.</p>
<pre><code class="lang-perl">p "@f" # current autoload search path
unshift @f, "$ENV{HOME}/.stryke/fpath" # prepend a directory
</code></pre>
<p>See also: <code>@fpath</code>, <code>autoload</code>.</p>
</article>
<article class="doc-entry" id="doc-fpath">
<h3><a class="doc-anchor" href="#doc-fpath">#</a> <code>@fpath</code></h3>
<p><code>@fpath</code> — the autoload search path: an ordered list of directories that stryke / zshrs scans for autoloadable function definitions when an unknown function name is called. Modeled on zsh's <code>$fpath</code>. Short alias: <code>@f</code>.</p>
<pre><code class="lang-perl">p "@fpath" # current autoload search path
unshift @fpath, "./local-funcs" # prepend a directory
</code></pre>
<p>See also: <code>@f</code>, <code>autoload</code>, zsh <code>fpath</code>.</p>
</article>
<article class="doc-entry" id="doc-path">
<h3><a class="doc-anchor" href="#doc-path">#</a> <code>@path</code></h3>
<p><code>@path</code> — the executable search path as a Perl array, mirrored from <code>$ENV{PATH}</code> (or the OS-specific equivalent). Mutations to <code>@path</code> update <code>$ENV{PATH}</code> and propagate to child processes. Useful when prepending a directory for the rest of the script.</p>
<pre><code class="lang-perl">unshift @path, "$ENV{HOME}/bin"
system 'mytool' # finds it via the updated PATH
</code></pre>
<p>See also: <code>$ENV{PATH}</code>, <code>which</code>, <code>find_in_path</code>.</p>
</article>
<article class="doc-entry" id="doc-autoload">
<h3><a class="doc-anchor" href="#doc-autoload">#</a> <code>AUTOLOAD</code></h3>
<p><code>AUTOLOAD</code> — a fallback sub invoked when a call is made to a name that doesn't exist in the current package (or any parent in <code>@ISA</code>). Stryke walks the C3 MRO starting from the invocant's class looking for an <code>AUTOLOAD</code>; the first one found runs with <code>$AUTOLOAD</code> set to the fully-qualified name of the missing method.</p>
<p>Classic uses: lazy method generation, RPC proxies, attribute auto-accessors, and "missing method" diagnostics. <code>AUTOLOAD</code> should <code>return</code> (without throwing) for the conventional <code>DESTROY</code> lookup so destructor dispatch isn't misrouted.</p>
<pre><code class="lang-perl">package Proxy
fn AUTOLOAD {
my $name = $AUTOLOAD
$name =~ s/.*:://
return if $name eq 'DESTROY'
my $self = shift
$self->{conn}->call($name, @_)
}
</code></pre>
<p>See also: <code>$AUTOLOAD</code>, <code>@ISA</code>, <code>DESTROY</code>, C3 MRO.</p>
</article>
<article class="doc-entry" id="doc-build">
<h3><a class="doc-anchor" href="#doc-build">#</a> <code>BUILD</code></h3>
<p><code>BUILD</code> — the constructor hook for stryke classes. When a class defines a <code>BUILD</code> method, it runs *after* attribute initialization but *before* the constructed object is returned from <code>new</code>. Use it for cross-attribute validation, derived-field computation, and external resource setup that depends on the attribute values.</p>
<p>Receives the freshly constructed <code>$self</code> and the original hashref of constructor arguments. Returning a value has no effect — <code>new</code> always returns the object. Throwing in <code>BUILD</code> aborts construction.</p>
<pre><code class="lang-perl">class Connection {
has 'host' => (is => 'ro', required => 1)
has 'port' => (is => 'ro', default => 5432)
has 'dbh' => (is => 'rw')
fn BUILD($self, $args) {
die "host: invalid" unless $self->host =~ /^[\w.-]+$/
$self->dbh(connect_to($self->host, $self->port))
}
}
</code></pre>
<p>See also: <code>DESTROY</code> (destructor), <code>class</code>, <code>bless</code>.</p>
</article>
<article class="doc-entry" id="doc-core">
<h3><a class="doc-anchor" href="#doc-core">#</a> <code>CORE</code></h3>
<p><code>CORE::</code> — pseudo-namespace alias for every dispatch primary. Every callable bare name is also reachable as <code>CORE::name</code>, with identical semantics. The qualified spelling exists for tab-complete affordance and explicit-namespace style; stryke rejects redefining a builtin (<code>fn print { ... }</code> is a parse error), so there is nothing to shadow at runtime.</p>
<p>The set is built dynamically: any name in <code>keys %stryke::builtins</code> is a valid <code>CORE::name</code>. There's no separate <code>%CORE::</code> table — it's a virtual namespace resolved at dispatch time.</p>
<pre><code class="lang-perl">CORE::print "hello world\n" # ≡ print "hello world\n"
my $r = CORE::sum(1, 2, 3) # 6 — qualified call
map { CORE::sprintf("%d", _) } @nums # any builtin
</code></pre>
<p>The <code>s docs CORE::name</code> form resolves to the bare-name page (the alias and primary share docs). Aliases (<code>tj</code>, <code>bn</code>, <code>e</code>, …) also support <code>CORE::tj</code> / <code>CORE::bn</code> / <code>CORE::e</code>.</p>
</article>
<article class="doc-entry" id="doc-core-pipe">
<h3><a class="doc-anchor" href="#doc-core-pipe">#</a> <code>CORE::pipe</code></h3>
<p>Create a unidirectional pipe, returning a pair of connected filehandles: one for reading and one for writing. Data written to the write end can be read from the read end, making pipes the fundamental building block for inter-process communication. Commonly used with <code>fork</code> so the parent and child can exchange data.</p>
<pre><code class="lang-perl">pipe(my $rd, my $wr) or die "pipe: $!"
if (fork() == 0) {
close($rd)
print $wr "hello from child\n"
exit(0)
}
close($wr)
my $msg = <$rd>
p $msg # hello from child
</code></pre>
</article>
<article class="doc-entry" id="doc-destroy">
<h3><a class="doc-anchor" href="#doc-destroy">#</a> <code>DESTROY</code></h3>
<p><code>DESTROY</code> — the destructor sub invoked when the last reference to a blessed object is dropped. Stryke runs <code>DESTROY</code> synchronously at the drop point (matching Perl semantics) by walking the class's C3 MRO child-first: the object's own <code>DESTROY</code> first, then each parent's. Destructors should be defensive — at interpreter shutdown <code>${^GLOBAL_PHASE}</code> is <code>"DESTRUCT"</code> and external state may already be torn down.</p>
<pre><code class="lang-perl">class FileHandle {
has 'fh' => (is => 'rw')
fn DESTROY($self) {
return if ${^GLOBAL_PHASE} eq 'DESTRUCT'
close($self->fh) if $self->fh
}
}
</code></pre>
<p>A pending-destroy queue (<code>pending_destroy.rs</code>) drains before the next VM op so destructors run in deterministic order.</p>
<p>See also: <code>BUILD</code>, <code>bless</code>, <code>${^GLOBAL_PHASE}</code>, <code>class</code>.</p>
</article>
<article class="doc-entry" id="doc-store">
<h3><a class="doc-anchor" href="#doc-store">#</a> <code>STORE</code></h3>
<p><code>STORE</code> — the writer method on a tie class. Called with <code>($self, $value)</code> for tied scalars, <code>($self, $index, $value)</code> for tied arrays, and <code>($self, $key, $value)</code> for tied hashes. Whatever <code>STORE</code> returns is discarded — assignments to the tied variable always evaluate to the assigned value.</p>
<pre><code class="lang-perl">package Logged
fn TIESCALAR { bless { v => 0 }, shift }
fn FETCH { $_[0]->{v} }
fn STORE {
p "writing: $_[1]"
$_[0]->{v} = $_[1]
}
package main
tie my $x, 'Logged'
$x = 42 # prints: writing: 42
</code></pre>
<p>See also: <code>FETCH</code>, <code>EXISTS</code>, <code>DELETE</code>, <code>TIESCALAR</code>, <code>TIEARRAY</code>, <code>TIEHASH</code>, <code>tie</code>.</p>
</article>
<article class="doc-entry" id="doc-tiearray">
<h3><a class="doc-anchor" href="#doc-tiearray">#</a> <code>TIEARRAY</code></h3>
<p><code>TIEARRAY</code> — the constructor invoked by <code>tie @array, 'ClassName', @args</code>. The class provides <code>TIEARRAY</code> returning a blessed object; element access and assignment route through <code>FETCH(idx)</code> / <code>STORE(idx, val)</code> methods on the returned object.</p>
<pre><code class="lang-perl">package Backed
fn TIEARRAY { bless { data => [] }, shift }
fn FETCH { $_[0]->{data}[$_[1]] }
fn STORE { $_[0]->{data}[$_[1]] = $_[2] }
package main
tie my @arr, 'Backed'
$arr[0] = 'hello'
p $arr[0] # hello (via FETCH)
</code></pre>
<p>See also: <code>tie</code>, <code>tied</code>, <code>untie</code>, <code>FETCH</code>, <code>STORE</code>, <code>TIESCALAR</code>, <code>TIEHASH</code>.</p>
</article>
<article class="doc-entry" id="doc-tiehash">
<h3><a class="doc-anchor" href="#doc-tiehash">#</a> <code>TIEHASH</code></h3>
<p><code>TIEHASH</code> — the constructor invoked by <code>tie %hash, 'ClassName', @args</code>. The class provides <code>TIEHASH</code> returning a blessed object; hash access routes through <code>FETCH(key)</code> / <code>STORE(key, val)</code> / <code>EXISTS(key)</code> / <code>DELETE(key)</code> on the returned object.</p>
<pre><code class="lang-perl">package InMem
fn TIEHASH { bless { h => {} }, shift }
fn FETCH { $_[0]->{h}{$_[1]} }
fn STORE { $_[0]->{h}{$_[1]} = $_[2] }
fn EXISTS { exists $_[0]->{h}{$_[1]} }
fn DELETE { delete $_[0]->{h}{$_[1]} }
package main
tie my %h, 'InMem'
$h{key} = 'value'
p $h{key} # value
p exists $h{key} # 1
</code></pre>
<p>See also: <code>tie</code>, <code>tied</code>, <code>untie</code>, <code>FETCH</code>, <code>STORE</code>, <code>EXISTS</code>, <code>DELETE</code>, <code>TIESCALAR</code>, <code>TIEARRAY</code>.</p>
</article>
<article class="doc-entry" id="doc-tiescalar">
<h3><a class="doc-anchor" href="#doc-tiescalar">#</a> <code>TIESCALAR</code></h3>
<p><code>TIESCALAR</code> — the constructor invoked by <code>tie $scalar, 'ClassName', @args</code>. The class must provide <code>TIESCALAR</code> returning a blessed object that will back the tied scalar. Subsequent reads and writes go through <code>FETCH</code> / <code>STORE</code> methods on the returned object.</p>
<pre><code class="lang-perl">package AutoIncr
fn TIESCALAR { bless { v => 0 }, shift }
fn FETCH { $_[0]->{v} }
fn STORE { $_[0]->{v} = $_[1] }
package main
tie my $n, 'AutoIncr'
$n = 5
p $n # 5 (via FETCH)
</code></pre>
<p>See also: <code>tie</code>, <code>tied</code>, <code>untie</code>, <code>FETCH</code>, <code>STORE</code>, <code>TIEARRAY</code>, <code>TIEHASH</code>.</p>
</article>
<article class="doc-entry" id="doc-unitcheck">
<h3><a class="doc-anchor" href="#doc-unitcheck">#</a> <code>UNITCHECK</code></h3>
<p><code>UNITCHECK { }</code> — a compile-time phase block that runs after the *current compilation unit* (script, module, or eval string) finishes compiling, but before any code in it runs. Modules use this for setup that must observe the full compiled state of *just this file* (without seeing later-required modules). Runs in reverse declaration order, like <code>END</code>.</p>
<p>The four phase blocks in order: <code>BEGIN</code> (immediately at compile), <code>UNITCHECK</code> (end of this unit's compile), <code>CHECK</code> (end of program compilation), <code>INIT</code> (start of program execution), <code>END</code> (end of execution).</p>
<pre><code class="lang-perl">UNITCHECK { p "this file compiled" }
BEGIN { p "compiling…" }
p "running"
# Output order:
# compiling…
# this file compiled
# running
</code></pre>
<p>See also: <code>BEGIN</code>, <code>CHECK</code>, <code>INIT</code>, <code>END</code>.</p>
</article>
<article class="doc-entry" id="doc-">
<h3><a class="doc-anchor" href="#doc-">#</a> <code>_</code></h3>
<p><code>_</code> — the stryke pipeline topic placeholder. Inside a <code>|></code> stage, <code>_</code> refers to the current value being threaded through. Unlike Perl's <code>$_</code>, <code>_</code> has no sigil because it represents the topic *position* rather than a variable — it can be a scalar, an array, a hash, or any value the previous stage emitted.</p>
<p>In <code>for</code>/<code>while</code> loop blocks the variable is <code>$_</code> (Perl-compatible). In numeric / regex contexts you can still write <code>$_</code> and they mean the same thing where stryke supports it.</p>
<pre><code class="lang-perl">1:10 |> map _ * 2 |> grep _ > 10 |> e p
qw(alice bob carol) |> map uc(_) |> e p
@files |> grep -f _ |> e p # only real files
</code></pre>
<p>In <code>fn ($n) { ... }</code> style, <code>_</code> also serves as the underscore placeholder for unused arguments. See also: <code>$_</code>, <code>@_</code>, <code>|></code>.</p>
</article>
<article class="doc-entry" id="doc-data">
<h3><a class="doc-anchor" href="#doc-data">#</a> <code>__DATA__</code></h3>
<p><code>__DATA__</code> — marks the end of compiled code and opens the rest of the file as the <code>DATA</code> filehandle. The compiler stops parsing at this line; every byte after the trailing newline is buffered and made readable via <code><DATA></code>. This is the canonical Perl pattern for shipping a script together with its embedded fixture data, lookup table, or test input — no separate file needed. The marker line must be <code>__DATA__</code> exactly (trailing whitespace tolerated).</p>
<p>In stryke, the data section is installed at startup (see <code>vm_helper.rs:install_data_handle</code>) so <code><DATA></code> and <code>readline(DATA)</code> work immediately. Setting <code>local $/ = undef</code> then reading from <code>DATA</code> slurps the whole section.</p>
<pre><code class="lang-perl">while (my $line = <DATA>) {
chomp $line
p "got: $line"
}
__DATA__
alpha
beta
gamma
</code></pre>
<p>See also: <code>__END__</code> (truncate only, no <code>DATA</code> handle).</p>
</article>
<article class="doc-entry" id="doc-end">
<h3><a class="doc-anchor" href="#doc-end">#</a> <code>__END__</code></h3>
<p><code>__END__</code> — marks the logical end of source code. Everything from this line to EOF is ignored by the compiler. This is the standard place to park POD documentation, embedded test data, or scratch notes in a <code>.pm</code> / <code>.stk</code> file — the parser stops at the marker so trailing prose never has to be valid syntax. The line must be <code>__END__</code> exactly (after trim); leading or trailing whitespace on the line itself is fine but no other characters.</p>
<p>In stryke, <code>__END__</code> truncates module compilation in <code>require</code> / <code>use</code> paths (see <code>strykelang/data_section.rs:strip_perl_end_marker</code>). Unlike standard Perl, stryke does <strong>not</strong> install a <code>DATA</code> filehandle for content after <code>__END__</code> — use <code>__DATA__</code> if you want the trailing bytes accessible via <code><DATA></code>.</p>
<pre><code class="lang-perl">say "running"
__END__
=pod
=head1 NAME
MyModule — does the thing.
=cut
</code></pre>
<p>See also: <code>__DATA__</code> (truncate + expose as <code><DATA></code>).</p>
</article>
<article class="doc-entry" id="doc-file">
<h3><a class="doc-anchor" href="#doc-file">#</a> <code>__FILE__</code></h3>
<p><code>__FILE__</code> — compile-time pseudo-token that evaluates to the path of the source file containing this token, exactly as the compiler saw it (the same string that shows up in <code>die</code>/<code>warn</code> location traces). Inside <code>-e</code> / <code>-E</code> one-liners it is <code>"-e"</code>; for stdin scripts it is <code>"-"</code>; for an executed file it is the path passed on the command line (relative or absolute, whichever the user typed).</p>
<p>Useful for self-locating modules, embedding the source path in log messages, or pinning a <code>do</code>/<code>require</code> relative to the current file's directory. The value is a normal string — pair with <code>dirname</code>/<code>abs_path</code> for filesystem operations.</p>
<pre><code class="lang-perl">p __FILE__ # /tmp/script.stk
use File::Basename qw(dirname)
my $here = dirname(__FILE__)
p "loading config from $here/config.toml"
</code></pre>
<p>See also: <code>__LINE__</code>, <code>__PACKAGE__</code>, <code>__SUB__</code>.</p>
</article>
<article class="doc-entry" id="doc-line">
<h3><a class="doc-anchor" href="#doc-line">#</a> <code>__LINE__</code></h3>
<p><code>__LINE__</code> — compile-time pseudo-token that evaluates to the source line number of the token itself, as a plain integer. Each occurrence is rewritten at compile time to a literal — there is no runtime cost and no way to fool it with <code>eval</code>. The line number reflects the original source file, including any <code>#line</code> directive overrides.</p>
<p>Useful for embedding source location in custom log/error messages, asserting positions in generated code, or building self-describing diagnostics. For full caller context inside a sub, use <code>caller()</code> instead.</p>
<pre><code class="lang-perl">p "trace: " . __FILE__ . ":" . __LINE__
die "assertion failed at line " . __LINE__ unless $ok
</code></pre>
<p>See also: <code>__FILE__</code>, <code>caller</code>, <code>Carp::confess</code>.</p>
</article>
<article class="doc-entry" id="doc-package">
<h3><a class="doc-anchor" href="#doc-package">#</a> <code>__PACKAGE__</code></h3>
<p><code>__PACKAGE__</code> — compile-time pseudo-token that evaluates to the name of the currently enclosing <code>package</code>, as a string. At the top of a fresh program it is <code>"main"</code>; inside <code>package Foo::Bar { ... }</code> or after a <code>package Foo::Bar</code> declaration it tracks the active namespace. The substitution is lexical — switching packages mid-file changes what subsequent <code>__PACKAGE__</code> tokens see.</p>
<p>Useful for class methods that need to refer to their own package name without hard-coding it (so subclasses inherit the right value), building method-dispatch keys, and writing portable mixins.</p>
<pre><code class="lang-perl">package My::Logger
fn tag { __PACKAGE__ }
fn log_msg($msg) { p "[" . tag() . "] $msg" }
package main
My::Logger::log_msg("started") # [My::Logger] started
p __PACKAGE__ # main
</code></pre>
<p>See also: <code>package</code>, <code>caller</code>, <code>ref</code>.</p>
</article>
<article class="doc-entry" id="doc-sub">
<h3><a class="doc-anchor" href="#doc-sub">#</a> <code>__SUB__</code></h3>
<p><code>__SUB__</code> — a reference to the currently executing subroutine. Inside a <code>fn</code>/<code>sub</code> body, <code>__SUB__</code> returns the coderef of that very function. This is the clean way to write recursive anonymous subs without naming them, and to build self-referential closures that survive renaming.</p>
<p>In standard Perl this requires <code>use feature 'current_sub'</code> (or 5.16+); in stryke it is always available. Outside any sub, <code>__SUB__</code> is <code>undef</code>.</p>
<pre><code class="lang-perl"># Anonymous recursion without naming the sub:
my $fact = fn ($n) {
return 1 if $n <= 1
$n * __SUB__->($n - 1)
}
p $fact->(5) # 120
fn me { __SUB__ }
p ref me() # CODE
</code></pre>
<p>See also: <code>caller</code>, <code>__PACKAGE__</code>, <code>wantarray</code>.</p>
</article>
<article class="doc-entry" id="doc-a0">
<h3><a class="doc-anchor" href="#doc-a0">#</a> <code>a0</code></h3>
<p><code>bohr_radius</code> (alias <code>a0</code>) — a₀ ≈ 5.29×10⁻¹¹ m. Radius of hydrogen atom ground state.</p>
<pre><code class="lang-perl">p a0 # 5.29177210903e-11
</code></pre>
</article>
<article class="doc-entry" id="doc-a256">
<h3><a class="doc-anchor" href="#doc-a256">#</a> <code>a256</code></h3>
<p><code>a256</code> — operation <code>a256</code>. Alias for <code>ansi_256</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p a256 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-a3c-advantage-step">
<h3><a class="doc-anchor" href="#doc-a3c-advantage-step">#</a> <code>a3c_advantage_step</code></h3>
<p><code>a3c_advantage_step</code> — single-step update of <code>a3c advantage</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p a3c_advantage_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-a85d">
<h3><a class="doc-anchor" href="#doc-a85d">#</a> <code>a85d</code></h3>
<p><code>base85_decode</code> (aliases <code>b85d</code>, <code>a85d</code>) decodes an Ascii85/Base85 encoded string.</p>
<pre><code class="lang-perl">p b85d(b85e("Hello")) # Hello
</code></pre>
</article>
<article class="doc-entry" id="doc-a85e">
<h3><a class="doc-anchor" href="#doc-a85e">#</a> <code>a85e</code></h3>
<p><code>base85_encode</code> (aliases <code>b85e</code>, <code>a85e</code>) encodes a string using Ascii85/Base85 encoding. More compact than Base64 (4:5 ratio vs 3:4).</p>
<pre><code class="lang-perl">p b85e("Hello") # encoded string
</code></pre>
</article>
<article class="doc-entry" id="doc-a-law-decode">
<h3><a class="doc-anchor" href="#doc-a-law-decode">#</a> <code>a_law_decode</code></h3>
<p><code>a_law_decode</code> — decode of <code>a law</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p a_law_decode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-a-law-encode">
<h3><a class="doc-anchor" href="#doc-a-law-encode">#</a> <code>a_law_encode</code></h3>
<p><code>a_law_encode</code> — encode of <code>a law</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p a_law_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-a-star-grid">
<h3><a class="doc-anchor" href="#doc-a-star-grid">#</a> <code>a_star_grid</code></h3>
<p><code>a_star_grid(grid, start, goal) → array</code> — A* on a 2D grid where non-zero cells are blocked. Manhattan heuristic, 4-connected.</p>
<pre><code class="lang-perl">p a_star_grid([[0,0,0],[1,1,0],[0,0,0]], [0,0], [2,2])
</code></pre>
</article>
<article class="doc-entry" id="doc-aabb-contains-point">
<h3><a class="doc-anchor" href="#doc-aabb-contains-point">#</a> <code>aabb_contains_point</code></h3>
<p><code>aabb_contains_point(aabb, point) → 0|1</code> — 1 if point lies inside (inclusive).</p>
</article>
<article class="doc-entry" id="doc-aabb-intersects">
<h3><a class="doc-anchor" href="#doc-aabb-intersects">#</a> <code>aabb_intersects</code></h3>
<p><code>aabb_intersects(a, b) → 0|1</code> — 1 if two AABBs overlap.</p>
</article>
<article class="doc-entry" id="doc-aabb-new">
<h3><a class="doc-anchor" href="#doc-aabb-new">#</a> <code>aabb_new</code></h3>
<p><code>aabb_new(min, max) → [min, max]</code> — pack a 3D axis-aligned bounding box as two vec3.</p>
<pre><code class="lang-perl">p aabb_new([0,0,0], [10,10,10])
</code></pre>
</article>
<article class="doc-entry" id="doc-aabb-union">
<h3><a class="doc-anchor" href="#doc-aabb-union">#</a> <code>aabb_union</code></h3>
<p><code>aabb_union(a, b) → aabb</code> — smallest AABB containing both.</p>
</article>
<article class="doc-entry" id="doc-aabb-volume">
<h3><a class="doc-anchor" href="#doc-aabb-volume">#</a> <code>aabb_volume</code></h3>
<p><code>aabb_volume(aabb) → number</code> — <code>(max.x - min.x) · (max.y - min.y) · (max.z - min.z)</code>.</p>
</article>
<article class="doc-entry" id="doc-ab1-step">
<h3><a class="doc-anchor" href="#doc-ab1-step">#</a> <code>ab1_step</code></h3>
<p><code>ab1_step</code> — single-step update of <code>ab1</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p ab1_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ab2-step">
<h3><a class="doc-anchor" href="#doc-ab2-step">#</a> <code>ab2_step</code></h3>
<p><code>ab2_step</code> — single-step update of <code>ab2</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p ab2_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ab3-step">
<h3><a class="doc-anchor" href="#doc-ab3-step">#</a> <code>ab3_step</code></h3>
<p><code>ab3_step</code> — single-step update of <code>ab3</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p ab3_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ab4">
<h3><a class="doc-anchor" href="#doc-ab4">#</a> <code>ab4</code></h3>
<p><code>ab4</code> — operation <code>ab4</code>. Alias for <code>adams_bashforth_4</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p ab4 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ab-coeff-sum">
<h3><a class="doc-anchor" href="#doc-ab-coeff-sum">#</a> <code>ab_coeff_sum</code></h3>
<p><code>ab_coeff_sum</code> — sum of <code>ab coeff</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p ab_coeff_sum @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-abelianization-quotient">
<h3><a class="doc-anchor" href="#doc-abelianization-quotient">#</a> <code>abelianization_quotient</code></h3>
<p><code>abelianization_quotient</code> — operation <code>abelianization quotient</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p abelianization_quotient $x
</code></pre>
</article>
<article class="doc-entry" id="doc-aberration-annual">
<h3><a class="doc-anchor" href="#doc-aberration-annual">#</a> <code>aberration_annual</code></h3>
<p><code>aberration_annual</code> — operation <code>aberration annual</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p aberration_annual $x
</code></pre>
</article>
<article class="doc-entry" id="doc-aberth-step">
<h3><a class="doc-anchor" href="#doc-aberth-step">#</a> <code>aberth_step</code></h3>
<p><code>aberth_step</code> — single-step update of <code>aberth</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p aberth_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-abs-ceil">
<h3><a class="doc-anchor" href="#doc-abs-ceil">#</a> <code>abs_ceil</code></h3>
<p><code>abs_ceil</code> — operation <code>abs ceil</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p abs_ceil $x
</code></pre>
</article>
<article class="doc-entry" id="doc-abs-diff">
<h3><a class="doc-anchor" href="#doc-abs-diff">#</a> <code>abs_diff</code></h3>
<p><code>abs_diff</code> — operation <code>abs diff</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p abs_diff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-abs-each">
<h3><a class="doc-anchor" href="#doc-abs-each">#</a> <code>abs_each</code></h3>
<p><code>abs_each</code> — operation <code>abs each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p abs_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-abs-floor">
<h3><a class="doc-anchor" href="#doc-abs-floor">#</a> <code>abs_floor</code></h3>
<p><code>abs_floor</code> — operation <code>abs floor</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p abs_floor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-absolute-magnitude">
<h3><a class="doc-anchor" href="#doc-absolute-magnitude">#</a> <code>absolute_magnitude</code></h3>
<p><code>absolute_magnitude</code> — operation <code>absolute magnitude</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p absolute_magnitude $x
</code></pre>
</article>
<article class="doc-entry" id="doc-absolute-vorticity-step">
<h3><a class="doc-anchor" href="#doc-absolute-vorticity-step">#</a> <code>absolute_vorticity_step</code></h3>
<p><code>absolute_vorticity_step</code> — single-step update of <code>absolute vorticity</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p absolute_vorticity_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-absorbed-short-wave">
<h3><a class="doc-anchor" href="#doc-absorbed-short-wave">#</a> <code>absorbed_short_wave</code></h3>
<p><code>absorbed_short_wave</code> — operation <code>absorbed short wave</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p absorbed_short_wave $x
</code></pre>
</article>
<article class="doc-entry" id="doc-abundant">
<h3><a class="doc-anchor" href="#doc-abundant">#</a> <code>abundant</code></h3>
<p><code>abundant</code> — operation <code>abundant</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p abundant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-abundant-numbers">
<h3><a class="doc-anchor" href="#doc-abundant-numbers">#</a> <code>abundant_numbers</code></h3>
<p><code>abundant_numbers</code> — operation <code>abundant numbers</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p abundant_numbers $x
</code></pre>
</article>
<article class="doc-entry" id="doc-abunnums">
<h3><a class="doc-anchor" href="#doc-abunnums">#</a> <code>abunnums</code></h3>
<p><code>abunnums</code> — operation <code>abunnums</code>. Alias for <code>abundant_numbers</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p abunnums $x
</code></pre>
</article>
<article class="doc-entry" id="doc-abuse-test-voltage">
<h3><a class="doc-anchor" href="#doc-abuse-test-voltage">#</a> <code>abuse_test_voltage</code></h3>
<p><code>abuse_test_voltage</code> — operation <code>abuse test voltage</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p abuse_test_voltage $x
</code></pre>
</article>
<article class="doc-entry" id="doc-accept-lang-pick">
<h3><a class="doc-anchor" href="#doc-accept-lang-pick">#</a> <code>accept_lang_pick</code></h3>
<p><code>accept_lang_pick</code> — operation <code>accept lang pick</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p accept_lang_pick $x
</code></pre>
</article>
<article class="doc-entry" id="doc-acceptance-target">
<h3><a class="doc-anchor" href="#doc-acceptance-target">#</a> <code>acceptance_target</code></h3>
<p><code>acceptance_target</code> — operation <code>acceptance target</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p acceptance_target $x
</code></pre>
</article>
<article class="doc-entry" id="doc-accrint">
<h3><a class="doc-anchor" href="#doc-accrint">#</a> <code>accrint</code></h3>
<p><code>accrint</code> — operation <code>accrint</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p accrint $x
</code></pre>
</article>
<article class="doc-entry" id="doc-accrued-interest">
<h3><a class="doc-anchor" href="#doc-accrued-interest">#</a> <code>accrued_interest</code></h3>
<p><code>accrued_interest</code> — operation <code>accrued interest</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p accrued_interest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-accum">
<h3><a class="doc-anchor" href="#doc-accum">#</a> <code>accum</code></h3>
<p><code>accum</code> — operation <code>accum</code>. Alias for <code>accumulate</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p accum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-accumulate">
<h3><a class="doc-anchor" href="#doc-accumulate">#</a> <code>accumulate</code></h3>
<p><code>accumulate</code> — operation <code>accumulate</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p accumulate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-acf">
<h3><a class="doc-anchor" href="#doc-acf">#</a> <code>acf</code></h3>
<p><code>acf_fn</code> (alias <code>acf</code>) — autocorrelation function. Returns ACF values for lags 0..max_lag. Like R's acf().</p>
<pre><code class="lang-perl">my @a = @{acf([1,3,2,4,3,5,4,6], 5)}
p $a[0] # 1.0 (lag 0 is always 1)
p $a[1] # lag-1 autocorrelation
</code></pre>
</article>
<article class="doc-entry" id="doc-acf-basis">
<h3><a class="doc-anchor" href="#doc-acf-basis">#</a> <code>acf_basis</code></h3>
<p><code>acf_basis</code> — operation <code>acf basis</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p acf_basis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-acirc">
<h3><a class="doc-anchor" href="#doc-acirc">#</a> <code>acirc</code></h3>
<p><code>acirc</code> — operation <code>acirc</code>. Alias for <code>area_circle</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p acirc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-acorr">
<h3><a class="doc-anchor" href="#doc-acorr">#</a> <code>acorr</code></h3>
<p><code>acorr</code> — operation <code>acorr</code>. Alias for <code>autocorrelation</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p acorr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-acos">
<h3><a class="doc-anchor" href="#doc-acos">#</a> <code>acos</code></h3>
<p><code>acos</code> — operation <code>acos</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p acos $x
</code></pre>
</article>
<article class="doc-entry" id="doc-acosh">
<h3><a class="doc-anchor" href="#doc-acosh">#</a> <code>acosh</code></h3>
<p><code>acosh</code> — operation <code>acosh</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p acosh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-acot">
<h3><a class="doc-anchor" href="#doc-acot">#</a> <code>acot</code></h3>
<p><code>acot</code> — operation <code>acot</code>. Category: *trig extensions*.</p>
<pre><code class="lang-perl">p acot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-acro">
<h3><a class="doc-anchor" href="#doc-acro">#</a> <code>acro</code></h3>
<p><code>acro</code> — operation <code>acro</code>. Alias for <code>acronym</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p acro $x
</code></pre>
</article>
<article class="doc-entry" id="doc-acronym">
<h3><a class="doc-anchor" href="#doc-acronym">#</a> <code>acronym</code></h3>
<p><code>acronym</code> — operation <code>acronym</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p acronym $x
</code></pre>
</article>
<article class="doc-entry" id="doc-acsc">
<h3><a class="doc-anchor" href="#doc-acsc">#</a> <code>acsc</code></h3>
<p><code>acsc</code> — operation <code>acsc</code>. Category: *trig extensions*.</p>
<pre><code class="lang-perl">p acsc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adaboost-alpha">
<h3><a class="doc-anchor" href="#doc-adaboost-alpha">#</a> <code>adaboost_alpha</code></h3>
<p><code>adaboost_alpha</code> — operation <code>adaboost alpha</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p adaboost_alpha $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adagrad-step">
<h3><a class="doc-anchor" href="#doc-adagrad-step">#</a> <code>adagrad_step</code></h3>
<p><code>adagrad_step</code> — single-step update of <code>adagrad</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p adagrad_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adams-bashforth-4">
<h3><a class="doc-anchor" href="#doc-adams-bashforth-4">#</a> <code>adams_bashforth_4</code></h3>
<p><code>adams_bashforth_4</code> — operation <code>adams bashforth 4</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p adams_bashforth_4 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adaptive-threshold">
<h3><a class="doc-anchor" href="#doc-adaptive-threshold">#</a> <code>adaptive_threshold</code></h3>
<p><code>adaptive_threshold(image, window=11, c=2) → matrix</code> — local-mean adaptive threshold. Output is binary (0 or 255).</p>
</article>
<article class="doc-entry" id="doc-add-days">
<h3><a class="doc-anchor" href="#doc-add-days">#</a> <code>add_days</code></h3>
<p><code>add_days</code> — operation <code>add days</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p add_days $x
</code></pre>
</article>
<article class="doc-entry" id="doc-add-hours">
<h3><a class="doc-anchor" href="#doc-add-hours">#</a> <code>add_hours</code></h3>
<p><code>add_hours</code> — operation <code>add hours</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p add_hours $x
</code></pre>
</article>
<article class="doc-entry" id="doc-add-minutes">
<h3><a class="doc-anchor" href="#doc-add-minutes">#</a> <code>add_minutes</code></h3>
<p><code>add_minutes</code> — operation <code>add minutes</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p add_minutes $x
</code></pre>
</article>
<article class="doc-entry" id="doc-add-seasonality">
<h3><a class="doc-anchor" href="#doc-add-seasonality">#</a> <code>add_seasonality</code></h3>
<p><code>add_seasonality(series, pattern) → array</code> — adds a repeating seasonal pattern element-wise (wraps with modulo on <code>pattern.len</code>).</p>
<pre><code class="lang-perl">p add_seasonality(\@xs, [1, -1, 1, -1])
</code></pre>
</article>
<article class="doc-entry" id="doc-addd">
<h3><a class="doc-anchor" href="#doc-addd">#</a> <code>addd</code></h3>
<p><code>addd</code> — operation <code>addd</code>. Alias for <code>add_days</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p addd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-addh">
<h3><a class="doc-anchor" href="#doc-addh">#</a> <code>addh</code></h3>
<p><code>addh</code> — operation <code>addh</code>. Alias for <code>add_hours</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p addh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-addm">
<h3><a class="doc-anchor" href="#doc-addm">#</a> <code>addm</code></h3>
<p><code>addm</code> — operation <code>addm</code>. Alias for <code>add_minutes</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p addm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adf-test">
<h3><a class="doc-anchor" href="#doc-adf-test">#</a> <code>adf_test</code></h3>
<p><code>adf_test</code> — statistical test of <code>adf</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p adf_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adf-test-stat">
<h3><a class="doc-anchor" href="#doc-adf-test-stat">#</a> <code>adf_test_stat</code></h3>
<p><code>adf_test_stat</code> — operation <code>adf test stat</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p adf_test_stat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adfuller">
<h3><a class="doc-anchor" href="#doc-adfuller">#</a> <code>adfuller</code></h3>
<p><code>adfuller</code> — operation <code>adfuller</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p adfuller $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adiabatic-lapse-rate-dry">
<h3><a class="doc-anchor" href="#doc-adiabatic-lapse-rate-dry">#</a> <code>adiabatic_lapse_rate_dry</code></h3>
<p><code>adiabatic_lapse_rate_dry</code> — operation <code>adiabatic lapse rate dry</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p adiabatic_lapse_rate_dry $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adiabatic-lapse-rate-moist">
<h3><a class="doc-anchor" href="#doc-adiabatic-lapse-rate-moist">#</a> <code>adiabatic_lapse_rate_moist</code></h3>
<p><code>adiabatic_lapse_rate_moist</code> — operation <code>adiabatic lapse rate moist</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p adiabatic_lapse_rate_moist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adj-r2">
<h3><a class="doc-anchor" href="#doc-adj-r2">#</a> <code>adj_r2</code></h3>
<p><code>adj_r2</code> — operation <code>adj r2</code>. Alias for <code>adjusted_r_squared</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p adj_r2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adjacent-difference">
<h3><a class="doc-anchor" href="#doc-adjacent-difference">#</a> <code>adjacent_difference</code></h3>
<p><code>adjacent_difference</code> — operation <code>adjacent difference</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p adjacent_difference $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adjacent-pairs">
<h3><a class="doc-anchor" href="#doc-adjacent-pairs">#</a> <code>adjacent_pairs</code></h3>
<p><code>adjacent_pairs</code> — operation <code>adjacent pairs</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p adjacent_pairs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adjp">
<h3><a class="doc-anchor" href="#doc-adjp">#</a> <code>adjp</code></h3>
<p><code>adjp</code> — operation <code>adjp</code>. Alias for <code>adjacent_pairs</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p adjp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adjusted-r-squared">
<h3><a class="doc-anchor" href="#doc-adjusted-r-squared">#</a> <code>adjusted_r_squared</code></h3>
<p><code>adjusted_r_squared</code> — operation <code>adjusted r squared</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p adjusted_r_squared $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adjusted-winner-pct">
<h3><a class="doc-anchor" href="#doc-adjusted-winner-pct">#</a> <code>adjusted_winner_pct</code></h3>
<p><code>adjusted_winner_pct</code> — percentage of <code>adjusted winner</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p adjusted_winner_pct $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adl32">
<h3><a class="doc-anchor" href="#doc-adl32">#</a> <code>adl32</code></h3>
<p><code>adl32</code> — operation <code>adl32</code>. Alias for <code>adler32</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p adl32 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adler32">
<h3><a class="doc-anchor" href="#doc-adler32">#</a> <code>adler32</code></h3>
<p><code>adler32</code> — operation <code>adler32</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p adler32 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adler32-combine">
<h3><a class="doc-anchor" href="#doc-adler32-combine">#</a> <code>adler32_combine</code></h3>
<p><code>adler32_combine(a, b, blen) → int</code> — combine two Adler-32 checksums into one for concatenated streams.</p>
</article>
<article class="doc-entry" id="doc-adler32-hash">
<h3><a class="doc-anchor" href="#doc-adler32-hash">#</a> <code>adler32_hash</code></h3>
<p><code>adler32_hash</code> — hash function of <code>adler32</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p adler32_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adm-mass-step">
<h3><a class="doc-anchor" href="#doc-adm-mass-step">#</a> <code>adm_mass_step</code></h3>
<p><code>adm_mass_step</code> — single-step update of <code>adm mass</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p adm_mass_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-admm-dual-step">
<h3><a class="doc-anchor" href="#doc-admm-dual-step">#</a> <code>admm_dual_step</code></h3>
<p><code>admm_dual_step</code> — single-step update of <code>admm dual</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p admm_dual_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-admm-primal-step">
<h3><a class="doc-anchor" href="#doc-admm-primal-step">#</a> <code>admm_primal_step</code></h3>
<p><code>admm_primal_step</code> — single-step update of <code>admm primal</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p admm_primal_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adobe-rgb-to-rgb">
<h3><a class="doc-anchor" href="#doc-adobe-rgb-to-rgb">#</a> <code>adobe_rgb_to_rgb</code></h3>
<p><code>adobe_rgb_to_rgb</code> — convert from <code>adobe rgb</code> to <code>rgb</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p adobe_rgb_to_rgb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ads-metric-step">
<h3><a class="doc-anchor" href="#doc-ads-metric-step">#</a> <code>ads_metric_step</code></h3>
<p><code>ads_metric_step</code> — single-step update of <code>ads metric</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ads_metric_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adsr-envelope">
<h3><a class="doc-anchor" href="#doc-adsr-envelope">#</a> <code>adsr_envelope</code></h3>
<p><code>adsr_envelope</code> — operation <code>adsr envelope</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p adsr_envelope $x
</code></pre>
</article>
<article class="doc-entry" id="doc-adx">
<h3><a class="doc-anchor" href="#doc-adx">#</a> <code>adx</code></h3>
<p><code>adx(highs, lows, closes, period=14) → array</code> — Average Directional Index (Wilder). Returns the trend-strength scalar; pair with <code>plus_di</code> / <code>minus_di</code> for direction.</p>
<pre><code class="lang-perl">p adx(\@hi, \@lo, \@cl, 14)
</code></pre>
</article>
<article class="doc-entry" id="doc-aellip">
<h3><a class="doc-anchor" href="#doc-aellip">#</a> <code>aellip</code></h3>
<p><code>aellip</code> — operation <code>aellip</code>. Alias for <code>area_ellipse</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p aellip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-aerosol-optical-depth">
<h3><a class="doc-anchor" href="#doc-aerosol-optical-depth">#</a> <code>aerosol_optical_depth</code></h3>
<p><code>aerosol_optical_depth</code> — operation <code>aerosol optical depth</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p aerosol_optical_depth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-aes-inv-sbox-byte">
<h3><a class="doc-anchor" href="#doc-aes-inv-sbox-byte">#</a> <code>aes_inv_sbox_byte</code></h3>
<p><code>aes_inv_sbox_byte</code> — operation <code>aes inv sbox byte</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p aes_inv_sbox_byte $x
</code></pre>
</article>
<article class="doc-entry" id="doc-aes-sbox-byte">
<h3><a class="doc-anchor" href="#doc-aes-sbox-byte">#</a> <code>aes_sbox_byte</code></h3>
<p><code>aes_sbox_byte</code> — operation <code>aes sbox byte</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p aes_sbox_byte $x
</code></pre>
</article>
<article class="doc-entry" id="doc-affine-encrypt">
<h3><a class="doc-anchor" href="#doc-affine-encrypt">#</a> <code>affine_encrypt</code></h3>
<p><code>affine_encrypt</code> — encrypt of <code>affine</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p affine_encrypt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-african-monsoon-index">
<h3><a class="doc-anchor" href="#doc-african-monsoon-index">#</a> <code>african_monsoon_index</code></h3>
<p><code>african_monsoon_index</code> — index of <code>african monsoon</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p african_monsoon_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-after-n">
<h3><a class="doc-anchor" href="#doc-after-n">#</a> <code>after_n</code></h3>
<p><code>after_n</code> — operation <code>after n</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p after_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-age-at-date">
<h3><a class="doc-anchor" href="#doc-age-at-date">#</a> <code>age_at_date</code></h3>
<p><code>age_at_date</code> — operation <code>age at date</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p age_at_date $x
</code></pre>
</article>
<article class="doc-entry" id="doc-age-at-z">
<h3><a class="doc-anchor" href="#doc-age-at-z">#</a> <code>age_at_z</code></h3>
<p><code>age_at_z</code> — operation <code>age at z</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p age_at_z $x
</code></pre>
</article>
<article class="doc-entry" id="doc-age-from-birthdate">
<h3><a class="doc-anchor" href="#doc-age-from-birthdate">#</a> <code>age_from_birthdate</code></h3>
<p><code>age_from_birthdate</code> — operation <code>age from birthdate</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p age_from_birthdate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-age-in-years">
<h3><a class="doc-anchor" href="#doc-age-in-years">#</a> <code>age_in_years</code></h3>
<p><code>age_in_years</code> — operation <code>age in years</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p age_in_years $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ageyrs">
<h3><a class="doc-anchor" href="#doc-ageyrs">#</a> <code>ageyrs</code></h3>
<p><code>ageyrs</code> — operation <code>ageyrs</code>. Alias for <code>age_in_years</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ageyrs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ai-agent">
<h3><a class="doc-anchor" href="#doc-ai-agent">#</a> <code>ai_agent</code></h3>
<p><code>ai_agent</code> — operation <code>ai agent</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p ai_agent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-aic">
<h3><a class="doc-anchor" href="#doc-aic">#</a> <code>aic</code></h3>
<p><code>aic</code> — operation <code>aic</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p aic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-aig-simplify-step">
<h3><a class="doc-anchor" href="#doc-aig-simplify-step">#</a> <code>aig_simplify_step</code></h3>
<p><code>aig_simplify_step</code> — single-step update of <code>aig simplify</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p aig_simplify_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ain">
<h3><a class="doc-anchor" href="#doc-ain">#</a> <code>ain</code></h3>
<p><code>ain</code> — operation <code>ain</code>. Alias for <code>assoc_in</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p ain $x
</code></pre>
</article>
<article class="doc-entry" id="doc-air-mass-kasten">
<h3><a class="doc-anchor" href="#doc-air-mass-kasten">#</a> <code>air_mass_kasten</code></h3>
<p><code>air_mass_kasten</code> — operation <code>air mass kasten</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p air_mass_kasten $x
</code></pre>
</article>
<article class="doc-entry" id="doc-airy-disk-radius">
<h3><a class="doc-anchor" href="#doc-airy-disk-radius">#</a> <code>airy_disk_radius</code></h3>
<p><code>airy_disk_radius</code> — operation <code>airy disk radius</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p airy_disk_radius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-airyai">
<h3><a class="doc-anchor" href="#doc-airyai">#</a> <code>airyai</code></h3>
<p><code>airyai</code> — operation <code>airyai</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p airyai $x
</code></pre>
</article>
<article class="doc-entry" id="doc-airybi">
<h3><a class="doc-anchor" href="#doc-airybi">#</a> <code>airybi</code></h3>
<p><code>airybi</code> — operation <code>airybi</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p airybi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-aitken-delta-squared">
<h3><a class="doc-anchor" href="#doc-aitken-delta-squared">#</a> <code>aitken_delta_squared</code></h3>
<p><code>aitken_delta_squared</code> — operation <code>aitken delta squared</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p aitken_delta_squared $x
</code></pre>
</article>
<article class="doc-entry" id="doc-akaike-info-crit">
<h3><a class="doc-anchor" href="#doc-akaike-info-crit">#</a> <code>akaike_info_crit</code></h3>
<p><code>akaike_info_crit</code> — operation <code>akaike info crit</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p akaike_info_crit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-aks-witness-count">
<h3><a class="doc-anchor" href="#doc-aks-witness-count">#</a> <code>aks_witness_count</code></h3>
<p><code>aks_witness_count</code> — count of <code>aks witness</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p aks_witness_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-albedo-blackbody-balance">
<h3><a class="doc-anchor" href="#doc-albedo-blackbody-balance">#</a> <code>albedo_blackbody_balance</code></h3>
<p><code>albedo_blackbody_balance</code> — operation <code>albedo blackbody balance</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p albedo_blackbody_balance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-albers-conic-project">
<h3><a class="doc-anchor" href="#doc-albers-conic-project">#</a> <code>albers_conic_project</code></h3>
<p><code>albers_conic_project</code> — operation <code>albers conic project</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p albers_conic_project $x
</code></pre>
</article>
<article class="doc-entry" id="doc-alexander-polynomial-at-one">
<h3><a class="doc-anchor" href="#doc-alexander-polynomial-at-one">#</a> <code>alexander_polynomial_at_one</code></h3>
<p><code>alexander_polynomial_at_one</code> — operation <code>alexander polynomial at one</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p alexander_polynomial_at_one $x
</code></pre>
</article>
<article class="doc-entry" id="doc-alfven-speed">
<h3><a class="doc-anchor" href="#doc-alfven-speed">#</a> <code>alfven_speed</code></h3>
<p><code>alfven_speed</code> — operation <code>alfven speed</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p alfven_speed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-algebraic-intersection-number">
<h3><a class="doc-anchor" href="#doc-algebraic-intersection-number">#</a> <code>algebraic_intersection_number</code></h3>
<p><code>algebraic_intersection_number</code> — operation <code>algebraic intersection number</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p algebraic_intersection_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-aliquot-sum">
<h3><a class="doc-anchor" href="#doc-aliquot-sum">#</a> <code>aliquot_sum</code></h3>
<p><code>aliquot_sum</code> — sum of <code>aliquot</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p aliquot_sum @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-all-distinct">
<h3><a class="doc-anchor" href="#doc-all-distinct">#</a> <code>all_distinct</code></h3>
<p><code>all_distinct</code> — operation <code>all distinct</code>. Category: *more list helpers*.</p>
<pre><code class="lang-perl">p all_distinct $x
</code></pre>
</article>
<article class="doc-entry" id="doc-all-eq">
<h3><a class="doc-anchor" href="#doc-all-eq">#</a> <code>all_eq</code></h3>
<p><code>all_eq</code> — operation <code>all eq</code>. Category: *more list helpers*.</p>
<pre><code class="lang-perl">p all_eq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-all-equal">
<h3><a class="doc-anchor" href="#doc-all-equal">#</a> <code>all_equal</code></h3>
<p><code>all_equal</code> — operation <code>all equal</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p all_equal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-all-match">
<h3><a class="doc-anchor" href="#doc-all-match">#</a> <code>all_match</code></h3>
<p><code>all_match</code> — operation <code>all match</code>. Category: *predicates*.</p>
<pre><code class="lang-perl">p all_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-all-pass-filter">
<h3><a class="doc-anchor" href="#doc-all-pass-filter">#</a> <code>all_pass_filter</code></h3>
<p><code>all_pass_filter(signal, delay=441, gain=0.5) → array</code> — IIR all-pass: flat magnitude, shifted phase.</p>
</article>
<article class="doc-entry" id="doc-all-pay-auction-step">
<h3><a class="doc-anchor" href="#doc-all-pay-auction-step">#</a> <code>all_pay_auction_step</code></h3>
<p><code>all_pay_auction_step</code> — single-step update of <code>all pay auction</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p all_pay_auction_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-all-unique">
<h3><a class="doc-anchor" href="#doc-all-unique">#</a> <code>all_unique</code></h3>
<p><code>all_unique</code> — operation <code>all unique</code>. Alias for <code>all_distinct</code>. Category: *more list helpers*.</p>
<pre><code class="lang-perl">p all_unique $x
</code></pre>
</article>
<article class="doc-entry" id="doc-allee-growth-step">
<h3><a class="doc-anchor" href="#doc-allee-growth-step">#</a> <code>allee_growth_step</code></h3>
<p><code>allee_growth_step</code> — single-step update of <code>allee growth</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p allee_growth_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-allele-frequency">
<h3><a class="doc-anchor" href="#doc-allele-frequency">#</a> <code>allele_frequency</code></h3>
<p><code>allele_frequency</code> — operation <code>allele frequency</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p allele_frequency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-alpha-fs">
<h3><a class="doc-anchor" href="#doc-alpha-fs">#</a> <code>alpha_fs</code></h3>
<p><code>fine_structure_constant</code> (alias <code>alpha_fs</code>) — α ≈ 1/137 ≈ 0.00730. Fundamental constant of electromagnetism.</p>
<pre><code class="lang-perl">p alpha_fs # 0.0072973525693
p 1 / alpha_fs # ~137.036
</code></pre>
</article>
<article class="doc-entry" id="doc-alphabeta-value">
<h3><a class="doc-anchor" href="#doc-alphabeta-value">#</a> <code>alphabeta_value</code></h3>
<p><code>alphabeta_value(leaves, depth) → number</code> — alpha-beta pruned minimax; same answer as <code>minimax_value</code>, fewer evaluations.</p>
</article>
<article class="doc-entry" id="doc-alt-az-to-ra-dec">
<h3><a class="doc-anchor" href="#doc-alt-az-to-ra-dec">#</a> <code>alt_az_to_ra_dec</code></h3>
<p><code>alt_az_to_ra_dec</code> — convert from <code>alt az</code> to <code>ra dec</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p alt_az_to_ra_dec $value
</code></pre>
</article>
<article class="doc-entry" id="doc-alternate-case">
<h3><a class="doc-anchor" href="#doc-alternate-case">#</a> <code>alternate_case</code></h3>
<p><code>alternate_case</code> — operation <code>alternate case</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p alternate_case $x
</code></pre>
</article>
<article class="doc-entry" id="doc-alternating-seq-sum">
<h3><a class="doc-anchor" href="#doc-alternating-seq-sum">#</a> <code>alternating_seq_sum</code></h3>
<p><code>alternating_seq_sum</code> — sum of <code>alternating seq</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p alternating_seq_sum @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-always-false">
<h3><a class="doc-anchor" href="#doc-always-false">#</a> <code>always_false</code></h3>
<p><code>always_false</code> — operation <code>always false</code>. Category: *functional primitives*.</p>
<pre><code class="lang-perl">p always_false $x
</code></pre>
</article>
<article class="doc-entry" id="doc-always-true">
<h3><a class="doc-anchor" href="#doc-always-true">#</a> <code>always_true</code></h3>
<p><code>always_true</code> — operation <code>always true</code>. Category: *functional primitives*.</p>
<pre><code class="lang-perl">p always_true $x
</code></pre>
</article>
<article class="doc-entry" id="doc-am2-step">
<h3><a class="doc-anchor" href="#doc-am2-step">#</a> <code>am2_step</code></h3>
<p><code>am2_step</code> — single-step update of <code>am2</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p am2_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-am3-step">
<h3><a class="doc-anchor" href="#doc-am3-step">#</a> <code>am3_step</code></h3>
<p><code>am3_step</code> — single-step update of <code>am3</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p am3_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-am4-step">
<h3><a class="doc-anchor" href="#doc-am4-step">#</a> <code>am4_step</code></h3>
<p><code>am4_step</code> — single-step update of <code>am4</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p am4_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-am-synth">
<h3><a class="doc-anchor" href="#doc-am-synth">#</a> <code>am_synth</code></h3>
<p><code>am_synth(carrier, mod_freq, depth=0.5, sr=44100, dur=1) → array</code> — amplitude modulation: <code>(1 + depth·sin(2π·fm·t)) · sin(2π·fc·t)</code>.</p>
</article>
<article class="doc-entry" id="doc-amari-alpha-div">
<h3><a class="doc-anchor" href="#doc-amari-alpha-div">#</a> <code>amari_alpha_div</code></h3>
<p><code>amari_alpha_div</code> — operation <code>amari alpha div</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p amari_alpha_div $x
</code></pre>
</article>
<article class="doc-entry" id="doc-amax">
<h3><a class="doc-anchor" href="#doc-amax">#</a> <code>amax</code></h3>
<p><code>amax</code> — operation <code>amax</code>. Alias for <code>argmax</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p amax $x
</code></pre>
</article>
<article class="doc-entry" id="doc-amin">
<h3><a class="doc-anchor" href="#doc-amin">#</a> <code>amin</code></h3>
<p><code>amin</code> — operation <code>amin</code>. Alias for <code>argmin</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p amin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-amo-index-step">
<h3><a class="doc-anchor" href="#doc-amo-index-step">#</a> <code>amo_index_step</code></h3>
<p><code>amo_index_step</code> — single-step update of <code>amo index</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p amo_index_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-amort">
<h3><a class="doc-anchor" href="#doc-amort">#</a> <code>amort</code></h3>
<p><code>amortization_schedule($principal, $rate, $periods)</code> (alias <code>amort</code>) — generates a full amortization schedule. Returns arrayref of hashrefs with period, payment, principal, interest, balance.</p>
<pre><code class="lang-perl">my $sched = amort(10000, 0.05, 12)
for my $row (@$sched) {
p "Period $row->{period}: bal=$row->{balance}"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-amortization-total-interest">
<h3><a class="doc-anchor" href="#doc-amortization-total-interest">#</a> <code>amortization_total_interest</code></h3>
<p><code>amortization_total_interest</code> — operation <code>amortization total interest</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p amortization_total_interest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-amp-to-db">
<h3><a class="doc-anchor" href="#doc-amp-to-db">#</a> <code>amp_to_db</code></h3>
<p><code>amp_to_db</code> — convert from <code>amp</code> to <code>db</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p amp_to_db $value
</code></pre>
</article>
<article class="doc-entry" id="doc-amphoteric-check">
<h3><a class="doc-anchor" href="#doc-amphoteric-check">#</a> <code>amphoteric_check</code></h3>
<p><code>amphoteric_check</code> — operation <code>amphoteric check</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p amphoteric_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-amplitude-damping-channel">
<h3><a class="doc-anchor" href="#doc-amplitude-damping-channel">#</a> <code>amplitude_damping_channel</code></h3>
<p><code>amplitude_damping_channel</code> — operation <code>amplitude damping channel</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p amplitude_damping_channel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-amplitude-damping-excited">
<h3><a class="doc-anchor" href="#doc-amplitude-damping-excited">#</a> <code>amplitude_damping_excited</code></h3>
<p><code>amplitude_damping_excited</code> — operation <code>amplitude damping excited</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p amplitude_damping_excited $x
</code></pre>
</article>
<article class="doc-entry" id="doc-amu">
<h3><a class="doc-anchor" href="#doc-amu">#</a> <code>amu</code></h3>
<p><code>amu</code> — operation <code>amu</code>. Alias for <code>atomic_mass_unit</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p amu $x
</code></pre>
</article>
<article class="doc-entry" id="doc-anagram-q">
<h3><a class="doc-anchor" href="#doc-anagram-q">#</a> <code>anagram_q</code></h3>
<p><code>anagram_q</code> — operation <code>anagram q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p anagram_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-anaphora-distance">
<h3><a class="doc-anchor" href="#doc-anaphora-distance">#</a> <code>anaphora_distance</code></h3>
<p><code>anaphora_distance</code> — distance / dissimilarity metric of <code>anaphora</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p anaphora_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ancilla-alloc">
<h3><a class="doc-anchor" href="#doc-ancilla-alloc">#</a> <code>ancilla_alloc</code></h3>
<p><code>ancilla_alloc</code> — operation <code>ancilla alloc</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p ancilla_alloc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-and-list">
<h3><a class="doc-anchor" href="#doc-and-list">#</a> <code>and_list</code></h3>
<p><code>and_list</code> — operation <code>and list</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p and_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-anderson-darling">
<h3><a class="doc-anchor" href="#doc-anderson-darling">#</a> <code>anderson_darling</code></h3>
<p><code>anderson_darling</code> — operation <code>anderson darling</code>. Category: *r / scipy distributions and tests*.</p>
<pre><code class="lang-perl">p anderson_darling $x
</code></pre>
</article>
<article class="doc-entry" id="doc-anderson-step">
<h3><a class="doc-anchor" href="#doc-anderson-step">#</a> <code>anderson_step</code></h3>
<p><code>anderson_step</code> — single-step update of <code>anderson</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p anderson_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-andl">
<h3><a class="doc-anchor" href="#doc-andl">#</a> <code>andl</code></h3>
<p><code>andl</code> — operation <code>andl</code>. Alias for <code>and_list</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p andl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-andoyer-dist">
<h3><a class="doc-anchor" href="#doc-andoyer-dist">#</a> <code>andoyer_dist</code></h3>
<p><code>andoyer_dist</code> — operation <code>andoyer dist</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p andoyer_dist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-andrew-monotone-chain">
<h3><a class="doc-anchor" href="#doc-andrew-monotone-chain">#</a> <code>andrew_monotone_chain</code></h3>
<p><code>andrew_monotone_chain</code> — operation <code>andrew monotone chain</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p andrew_monotone_chain $x
</code></pre>
</article>
<article class="doc-entry" id="doc-andrew-monotone-hull">
<h3><a class="doc-anchor" href="#doc-andrew-monotone-hull">#</a> <code>andrew_monotone_hull</code></h3>
<p><code>andrew_monotone_hull(points) → array</code> — convex hull via Andrew's monotone chain. O(n log n).</p>
</article>
<article class="doc-entry" id="doc-angbet">
<h3><a class="doc-anchor" href="#doc-angbet">#</a> <code>angbet</code></h3>
<p><code>angbet</code> — operation <code>angbet</code>. Alias for <code>angle_between</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p angbet $x
</code></pre>
</article>
<article class="doc-entry" id="doc-angle-between">
<h3><a class="doc-anchor" href="#doc-angle-between">#</a> <code>angle_between</code></h3>
<p><code>angle_between($x1, $y1, $x2, $y2)</code> — computes the angle in radians between two 2D vectors from origin. Returns the angle using atan2.</p>
<pre><code class="lang-perl">my $angle = angle_between(1, 0, 0, 1)
p $angle # ~1.5708 (π/2 radians = 90°)
</code></pre>
</article>
<article class="doc-entry" id="doc-angle-between-deg">
<h3><a class="doc-anchor" href="#doc-angle-between-deg">#</a> <code>angle_between_deg</code></h3>
<p><code>angle_between_deg</code> — operation <code>angle between deg</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p angle_between_deg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-angle-bracket">
<h3><a class="doc-anchor" href="#doc-angle-bracket">#</a> <code>angle_bracket</code></h3>
<p><code>angle_bracket</code> — operation <code>angle bracket</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p angle_bracket $x
</code></pre>
</article>
<article class="doc-entry" id="doc-angular-diameter-distance">
<h3><a class="doc-anchor" href="#doc-angular-diameter-distance">#</a> <code>angular_diameter_distance</code></h3>
<p><code>angular_diameter_distance</code> — distance / dissimilarity metric of <code>angular diameter</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p angular_diameter_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-angular-velocity">
<h3><a class="doc-anchor" href="#doc-angular-velocity">#</a> <code>angular_velocity</code></h3>
<p><code>angular_velocity</code> — operation <code>angular velocity</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p angular_velocity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-angvel">
<h3><a class="doc-anchor" href="#doc-angvel">#</a> <code>angvel</code></h3>
<p><code>angvel</code> — operation <code>angvel</code>. Alias for <code>angular_velocity</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p angvel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-annuity-due-an">
<h3><a class="doc-anchor" href="#doc-annuity-due-an">#</a> <code>annuity_due_an</code></h3>
<p><code>annuity_due_an</code> — operation <code>annuity due an</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p annuity_due_an $x
</code></pre>
</article>
<article class="doc-entry" id="doc-annuity-future-value">
<h3><a class="doc-anchor" href="#doc-annuity-future-value">#</a> <code>annuity_future_value</code></h3>
<p><code>annuity_future_value</code> — value of <code>annuity future</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p annuity_future_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-annuity-immediate-an">
<h3><a class="doc-anchor" href="#doc-annuity-immediate-an">#</a> <code>annuity_immediate_an</code></h3>
<p><code>annuity_immediate_an</code> — operation <code>annuity immediate an</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p annuity_immediate_an $x
</code></pre>
</article>
<article class="doc-entry" id="doc-annuity-present-value">
<h3><a class="doc-anchor" href="#doc-annuity-present-value">#</a> <code>annuity_present_value</code></h3>
<p><code>annuity_present_value</code> — value of <code>annuity present</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p annuity_present_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-anova">
<h3><a class="doc-anchor" href="#doc-anova">#</a> <code>anova</code></h3>
<p><code>anova_oneway</code> (aliases <code>anova</code>, <code>anova1</code>) performs one-way ANOVA. Returns [F-statistic, df_between, df_within].</p>
<pre><code class="lang-perl">my ($F, $dfb, $dfw) = @{anova([1,2,3], [4,5,6], [7,8,9])}
</code></pre>
</article>
<article class="doc-entry" id="doc-anova-one-way">
<h3><a class="doc-anchor" href="#doc-anova-one-way">#</a> <code>anova_one_way</code></h3>
<p><code>anova_one_way(group1, group2, …) → {statistic, df, p_value}</code> — one-way ANOVA F-test across ≥2 groups.</p>
<pre><code class="lang-perl">p anova_one_way([1,2,3], [10,11,12], [100,101,102])
</code></pre>
</article>
<article class="doc-entry" id="doc-ansi-256">
<h3><a class="doc-anchor" href="#doc-ansi-256">#</a> <code>ansi_256</code></h3>
<p><code>ansi_256</code> — operation <code>ansi 256</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p ansi_256 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ansi-black">
<h3><a class="doc-anchor" href="#doc-ansi-black">#</a> <code>ansi_black</code></h3>
<p><code>ansi_black</code> — operation <code>ansi black</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p ansi_black $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ansi-blue">
<h3><a class="doc-anchor" href="#doc-ansi-blue">#</a> <code>ansi_blue</code></h3>
<p><code>ansi_blue</code> — operation <code>ansi blue</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p ansi_blue $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ansi-bold">
<h3><a class="doc-anchor" href="#doc-ansi-bold">#</a> <code>ansi_bold</code></h3>
<p><code>ansi_bold</code> — operation <code>ansi bold</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p ansi_bold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ansi-cyan">
<h3><a class="doc-anchor" href="#doc-ansi-cyan">#</a> <code>ansi_cyan</code></h3>
<p><code>ansi_cyan</code> — operation <code>ansi cyan</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p ansi_cyan $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ansi-dim">
<h3><a class="doc-anchor" href="#doc-ansi-dim">#</a> <code>ansi_dim</code></h3>
<p><code>ansi_dim</code> — operation <code>ansi dim</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p ansi_dim $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ansi-green">
<h3><a class="doc-anchor" href="#doc-ansi-green">#</a> <code>ansi_green</code></h3>
<p><code>ansi_green</code> — operation <code>ansi green</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p ansi_green $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ansi-magenta">
<h3><a class="doc-anchor" href="#doc-ansi-magenta">#</a> <code>ansi_magenta</code></h3>
<p><code>ansi_magenta</code> — operation <code>ansi magenta</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p ansi_magenta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ansi-off">
<h3><a class="doc-anchor" href="#doc-ansi-off">#</a> <code>ansi_off</code></h3>
<p><code>ansi_off</code> — operation <code>ansi off</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p ansi_off $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ansi-red">
<h3><a class="doc-anchor" href="#doc-ansi-red">#</a> <code>ansi_red</code></h3>
<p><code>ansi_red</code> — operation <code>ansi red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p ansi_red $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ansi-reverse">
<h3><a class="doc-anchor" href="#doc-ansi-reverse">#</a> <code>ansi_reverse</code></h3>
<p><code>ansi_reverse</code> — operation <code>ansi reverse</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p ansi_reverse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ansi-truecolor">
<h3><a class="doc-anchor" href="#doc-ansi-truecolor">#</a> <code>ansi_truecolor</code></h3>
<p><code>ansi_truecolor</code> — operation <code>ansi truecolor</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p ansi_truecolor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ansi-underline">
<h3><a class="doc-anchor" href="#doc-ansi-underline">#</a> <code>ansi_underline</code></h3>
<p><code>ansi_underline</code> — operation <code>ansi underline</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p ansi_underline $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ansi-white">
<h3><a class="doc-anchor" href="#doc-ansi-white">#</a> <code>ansi_white</code></h3>
<p><code>ansi_white</code> — operation <code>ansi white</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p ansi_white $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ansi-yellow">
<h3><a class="doc-anchor" href="#doc-ansi-yellow">#</a> <code>ansi_yellow</code></h3>
<p><code>ansi_yellow</code> — operation <code>ansi yellow</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p ansi_yellow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-anti-de-sitter-radius-step">
<h3><a class="doc-anchor" href="#doc-anti-de-sitter-radius-step">#</a> <code>anti_de_sitter_radius_step</code></h3>
<p><code>anti_de_sitter_radius_step</code> — single-step update of <code>anti de sitter radius</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p anti_de_sitter_radius_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-antoine-p">
<h3><a class="doc-anchor" href="#doc-antoine-p">#</a> <code>antoine_p</code></h3>
<p><code>antoine_p</code> — operation <code>antoine p</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p antoine_p $x
</code></pre>
</article>
<article class="doc-entry" id="doc-any-match">
<h3><a class="doc-anchor" href="#doc-any-match">#</a> <code>any_match</code></h3>
<p><code>any_match</code> — operation <code>any match</code>. Category: *predicates*.</p>
<pre><code class="lang-perl">p any_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-aov">
<h3><a class="doc-anchor" href="#doc-aov">#</a> <code>aov</code></h3>
<p><code>aov</code> — operation <code>aov</code>. Category: *r / scipy distributions and tests*.</p>
<pre><code class="lang-perl">p aov $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ap-jonker-volgenant-step">
<h3><a class="doc-anchor" href="#doc-ap-jonker-volgenant-step">#</a> <code>ap_jonker_volgenant_step</code></h3>
<p><code>ap_jonker_volgenant_step</code> — single-step update of <code>ap jonker volgenant</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p ap_jonker_volgenant_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-aperture-stop-to-fnumber">
<h3><a class="doc-anchor" href="#doc-aperture-stop-to-fnumber">#</a> <code>aperture_stop_to_fnumber</code></h3>
<p><code>aperture_stop_to_fnumber(stops) → number</code> — <code>2^(stops/2)</code>. Converts stops from f/1 to f-number.</p>
</article>
<article class="doc-entry" id="doc-apery">
<h3><a class="doc-anchor" href="#doc-apery">#</a> <code>apery</code></h3>
<p><code>apery</code> — operation <code>apery</code>. Alias for <code>apery_constant</code>. Category: *math constants*.</p>
<pre><code class="lang-perl">p apery $x
</code></pre>
</article>
<article class="doc-entry" id="doc-apery-constant">
<h3><a class="doc-anchor" href="#doc-apery-constant">#</a> <code>apery_constant</code></h3>
<p><code>apery_constant</code> — operation <code>apery constant</code>. Category: *math constants*.</p>
<pre><code class="lang-perl">p apery_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-apparent-horizon-step">
<h3><a class="doc-anchor" href="#doc-apparent-horizon-step">#</a> <code>apparent_horizon_step</code></h3>
<p><code>apparent_horizon_step</code> — single-step update of <code>apparent horizon</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p apparent_horizon_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-append-elem">
<h3><a class="doc-anchor" href="#doc-append-elem">#</a> <code>append_elem</code></h3>
<p><code>append_elem</code> — operation <code>append elem</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p append_elem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-append-redis">
<h3><a class="doc-anchor" href="#doc-append-redis">#</a> <code>append_redis</code></h3>
<p><code>append_redis</code> — operation <code>append redis</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p append_redis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-appl">
<h3><a class="doc-anchor" href="#doc-appl">#</a> <code>appl</code></h3>
<p><code>appl</code> — operation <code>appl</code>. Alias for <code>apply</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p appl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-apply">
<h3><a class="doc-anchor" href="#doc-apply">#</a> <code>apply</code></h3>
<p><code>apply</code> — operation <code>apply</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p apply $x
</code></pre>
</article>
<article class="doc-entry" id="doc-apply-list">
<h3><a class="doc-anchor" href="#doc-apply-list">#</a> <code>apply_list</code></h3>
<p><code>apply_list</code> — operation <code>apply list</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p apply_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-apply-window">
<h3><a class="doc-anchor" href="#doc-apply-window">#</a> <code>apply_window</code></h3>
<p><code>apply_window(\@signal, \@window)</code> — element-wise multiplies signal by window function. Use before FFT to reduce spectral leakage.</p>
<pre><code class="lang-perl">my $w = hann(scalar @signal)
my $windowed = apply_window(\@signal, $w)
my $spectrum = dft($windowed)
</code></pre>
</article>
<article class="doc-entry" id="doc-applywin">
<h3><a class="doc-anchor" href="#doc-applywin">#</a> <code>applywin</code></h3>
<p><code>applywin</code> — operation <code>applywin</code>. Alias for <code>apply_window</code>. Category: *dsp / signal (extended)*.</p>
<pre><code class="lang-perl">p applywin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-approval-voting-max">
<h3><a class="doc-anchor" href="#doc-approval-voting-max">#</a> <code>approval_voting_max</code></h3>
<p><code>approval_voting_max</code> — maximum of <code>approval voting</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p approval_voting_max $x
</code></pre>
</article>
<article class="doc-entry" id="doc-approx">
<h3><a class="doc-anchor" href="#doc-approx">#</a> <code>approx</code></h3>
<p><code>approx_fn</code> (alias <code>approx</code>) — piecewise linear interpolation at query points. Like R's approx().</p>
<pre><code class="lang-perl">my @y = @{approx([0,1,2], [0,10,0], [0.5, 1.0, 1.5])}
# [5, 10, 5]
</code></pre>
</article>
<article class="doc-entry" id="doc-approx-eq">
<h3><a class="doc-anchor" href="#doc-approx-eq">#</a> <code>approx_eq</code></h3>
<p><code>approx_eq</code> — operation <code>approx eq</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p approx_eq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-approximate-entropy">
<h3><a class="doc-anchor" href="#doc-approximate-entropy">#</a> <code>approximate_entropy</code></h3>
<p><code>approximate_entropy</code> — operation <code>approximate entropy</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p approximate_entropy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-apr-to-apy">
<h3><a class="doc-anchor" href="#doc-apr-to-apy">#</a> <code>apr_to_apy</code></h3>
<p><code>apr_to_apy</code> — convert from <code>apr</code> to <code>apy</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p apr_to_apy $value
</code></pre>
</article>
<article class="doc-entry" id="doc-apsp">
<h3><a class="doc-anchor" href="#doc-apsp">#</a> <code>apsp</code></h3>
<p><code>floyd_warshall</code> (aliases <code>floydwarshall</code>, <code>apsp</code>) computes all-pairs shortest paths. Takes a distance matrix (use Inf for no edge).</p>
<pre><code class="lang-perl">my $d = apsp([[0,3,1e18],[1e18,0,1],[1e18,1e18,0]])
</code></pre>
</article>
<article class="doc-entry" id="doc-apy-to-apr">
<h3><a class="doc-anchor" href="#doc-apy-to-apr">#</a> <code>apy_to_apr</code></h3>
<p><code>apy_to_apr</code> — convert from <code>apy</code> to <code>apr</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p apy_to_apr $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ar-envelope">
<h3><a class="doc-anchor" href="#doc-ar-envelope">#</a> <code>ar_envelope</code></h3>
<p><code>ar_envelope</code> — operation <code>ar envelope</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p ar_envelope $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ar-model-likelihood">
<h3><a class="doc-anchor" href="#doc-ar-model-likelihood">#</a> <code>ar_model_likelihood</code></h3>
<p><code>ar_model_likelihood</code> — operation <code>ar model likelihood</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p ar_model_likelihood $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arange">
<h3><a class="doc-anchor" href="#doc-arange">#</a> <code>arange</code></h3>
<p><code>arange</code> — operation <code>arange</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p arange $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arc-length">
<h3><a class="doc-anchor" href="#doc-arc-length">#</a> <code>arc_length</code></h3>
<p><code>arc_length($radius, $theta)</code> — computes the arc length of a circular arc. Theta is the central angle in radians. Returns <code>radius * theta</code>.</p>
<pre><code class="lang-perl">p arc_length(10, 3.14159) # ~31.4 (half circle)
p arc_length(5, 1.57) # ~7.85 (quarter circle)
</code></pre>
</article>
<article class="doc-entry" id="doc-arch-lm">
<h3><a class="doc-anchor" href="#doc-arch-lm">#</a> <code>arch_lm</code></h3>
<p><code>arch_lm</code> — operation <code>arch lm</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p arch_lm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arch-lm-test">
<h3><a class="doc-anchor" href="#doc-arch-lm-test">#</a> <code>arch_lm_test</code></h3>
<p><code>arch_lm_test</code> — statistical test of <code>arch lm</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p arch_lm_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arclen">
<h3><a class="doc-anchor" href="#doc-arclen">#</a> <code>arclen</code></h3>
<p><code>arclen</code> — operation <code>arclen</code>. Alias for <code>arc_length</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p arclen $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arctic-oscillation-step">
<h3><a class="doc-anchor" href="#doc-arctic-oscillation-step">#</a> <code>arctic_oscillation_step</code></h3>
<p><code>arctic_oscillation_step</code> — single-step update of <code>arctic oscillation</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p arctic_oscillation_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-area-circle">
<h3><a class="doc-anchor" href="#doc-area-circle">#</a> <code>area_circle</code></h3>
<p><code>area_circle</code> — operation <code>area circle</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p area_circle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-area-ellipse">
<h3><a class="doc-anchor" href="#doc-area-ellipse">#</a> <code>area_ellipse</code></h3>
<p><code>area_ellipse</code> — operation <code>area ellipse</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p area_ellipse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-area-rectangle">
<h3><a class="doc-anchor" href="#doc-area-rectangle">#</a> <code>area_rectangle</code></h3>
<p><code>area_rectangle</code> — operation <code>area rectangle</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p area_rectangle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-area-trapezoid">
<h3><a class="doc-anchor" href="#doc-area-trapezoid">#</a> <code>area_trapezoid</code></h3>
<p><code>area_trapezoid</code> — operation <code>area trapezoid</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p area_trapezoid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-area-triangle">
<h3><a class="doc-anchor" href="#doc-area-triangle">#</a> <code>area_triangle</code></h3>
<p><code>area_triangle</code> — operation <code>area triangle</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p area_triangle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arect">
<h3><a class="doc-anchor" href="#doc-arect">#</a> <code>arect</code></h3>
<p><code>arect</code> — operation <code>arect</code>. Alias for <code>area_rectangle</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p arect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arellano-bond-step">
<h3><a class="doc-anchor" href="#doc-arellano-bond-step">#</a> <code>arellano_bond_step</code></h3>
<p><code>arellano_bond_step</code> — single-step update of <code>arellano bond</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p arellano_bond_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-argc">
<h3><a class="doc-anchor" href="#doc-argc">#</a> <code>argc</code></h3>
<p><code>argc</code> — operation <code>argc</code>. Category: *process / env*.</p>
<pre><code class="lang-perl">p argc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-argmax">
<h3><a class="doc-anchor" href="#doc-argmax">#</a> <code>argmax</code></h3>
<p><code>argmax</code> — operation <code>argmax</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p argmax $x
</code></pre>
</article>
<article class="doc-entry" id="doc-argmin">
<h3><a class="doc-anchor" href="#doc-argmin">#</a> <code>argmin</code></h3>
<p><code>argmin</code> — operation <code>argmin</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p argmin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-argon2-block-mix">
<h3><a class="doc-anchor" href="#doc-argon2-block-mix">#</a> <code>argon2_block_mix</code></h3>
<p><code>argon2_block_mix</code> — operation <code>argon2 block mix</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p argon2_block_mix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-argpartition">
<h3><a class="doc-anchor" href="#doc-argpartition">#</a> <code>argpartition</code></h3>
<p><code>argpartition</code> — operation <code>argpartition</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p argpartition $x
</code></pre>
</article>
<article class="doc-entry" id="doc-argsort">
<h3><a class="doc-anchor" href="#doc-argsort">#</a> <code>argsort</code></h3>
<p><code>argsort</code> — operation <code>argsort</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p argsort $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ari">
<h3><a class="doc-anchor" href="#doc-ari">#</a> <code>ari</code></h3>
<p><code>ari</code> — operation <code>ari</code>. Alias for <code>automated_readability_index</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p ari $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arias-intensity">
<h3><a class="doc-anchor" href="#doc-arias-intensity">#</a> <code>arias_intensity</code></h3>
<p><code>arias_intensity</code> — operation <code>arias intensity</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p arias_intensity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arima-diff">
<h3><a class="doc-anchor" href="#doc-arima-diff">#</a> <code>arima_diff</code></h3>
<p><code>arima_diff</code> — operation <code>arima diff</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p arima_diff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arima-fit">
<h3><a class="doc-anchor" href="#doc-arima-fit">#</a> <code>arima_fit</code></h3>
<p><code>arima_fit</code> — operation <code>arima fit</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p arima_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arima-forecast">
<h3><a class="doc-anchor" href="#doc-arima-forecast">#</a> <code>arima_forecast</code></h3>
<p><code>arima_forecast</code> — operation <code>arima forecast</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p arima_forecast $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arithmetic-coding-interval">
<h3><a class="doc-anchor" href="#doc-arithmetic-coding-interval">#</a> <code>arithmetic_coding_interval</code></h3>
<p><code>arithmetic_coding_interval</code> — operation <code>arithmetic coding interval</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p arithmetic_coding_interval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arithmetic-decode-interval">
<h3><a class="doc-anchor" href="#doc-arithmetic-decode-interval">#</a> <code>arithmetic_decode_interval</code></h3>
<p><code>arithmetic_decode_interval</code> — operation <code>arithmetic decode interval</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p arithmetic_decode_interval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arithmetic-sequence">
<h3><a class="doc-anchor" href="#doc-arithmetic-sequence">#</a> <code>arithmetic_sequence</code></h3>
<p><code>arithmetic_sequence</code> — operation <code>arithmetic sequence</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p arithmetic_sequence $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arithmetic-series">
<h3><a class="doc-anchor" href="#doc-arithmetic-series">#</a> <code>arithmetic_series</code></h3>
<p><code>arithmetic_series($a1, $d, $n)</code> (alias <code>arithser</code>) — sum of n terms of arithmetic sequence starting at a1 with common difference d. Formula: n/2 × (2a1 + (n-1)d).</p>
<pre><code class="lang-perl">p arithser(1, 1, 100) # 5050 (1+2+...+100)
p arithser(2, 3, 10) # 155 (2+5+8+...+29)
</code></pre>
</article>
<article class="doc-entry" id="doc-arity-of">
<h3><a class="doc-anchor" href="#doc-arity-of">#</a> <code>arity_of</code></h3>
<p><code>arity_of</code> — operation <code>arity of</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p arity_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arma-model-innovation">
<h3><a class="doc-anchor" href="#doc-arma-model-innovation">#</a> <code>arma_model_innovation</code></h3>
<p><code>arma_model_innovation</code> — operation <code>arma model innovation</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p arma_model_innovation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arma-order-select">
<h3><a class="doc-anchor" href="#doc-arma-order-select">#</a> <code>arma_order_select</code></h3>
<p><code>arma_order_select</code> — operation <code>arma order select</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p arma_order_select $x
</code></pre>
</article>
<article class="doc-entry" id="doc-armstrong-q">
<h3><a class="doc-anchor" href="#doc-armstrong-q">#</a> <code>armstrong_q</code></h3>
<p><code>armstrong_q</code> — operation <code>armstrong q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p armstrong_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arpad-predict">
<h3><a class="doc-anchor" href="#doc-arpad-predict">#</a> <code>arpad_predict</code></h3>
<p><code>arpad_predict(rating_a, rating_b) → number</code> — A's expected win rate via Elo formula: <code>1 / (1 + 10^((rb-ra)/400))</code>.</p>
<pre><code class="lang-perl">p arpad_predict(1900, 1500) # 0.909
</code></pre>
</article>
<article class="doc-entry" id="doc-array-agg">
<h3><a class="doc-anchor" href="#doc-array-agg">#</a> <code>array_agg</code></h3>
<p><code>array_agg</code> — array helper <code>agg</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p array_agg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-array-difference">
<h3><a class="doc-anchor" href="#doc-array-difference">#</a> <code>array_difference</code></h3>
<p><code>array_difference</code> — array helper <code>difference</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p array_difference $x
</code></pre>
</article>
<article class="doc-entry" id="doc-array-intersection">
<h3><a class="doc-anchor" href="#doc-array-intersection">#</a> <code>array_intersection</code></h3>
<p><code>array_intersection</code> — array helper <code>intersection</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p array_intersection $x
</code></pre>
</article>
<article class="doc-entry" id="doc-array-position">
<h3><a class="doc-anchor" href="#doc-array-position">#</a> <code>array_position</code></h3>
<p><code>array_position</code> — array helper <code>position</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p array_position $x
</code></pre>
</article>
<article class="doc-entry" id="doc-array-positions">
<h3><a class="doc-anchor" href="#doc-array-positions">#</a> <code>array_positions</code></h3>
<p><code>array_positions</code> — array helper <code>positions</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p array_positions $x
</code></pre>
</article>
<article class="doc-entry" id="doc-array-remove">
<h3><a class="doc-anchor" href="#doc-array-remove">#</a> <code>array_remove</code></h3>
<p><code>array_remove</code> — array helper <code>remove</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p array_remove $x
</code></pre>
</article>
<article class="doc-entry" id="doc-array-replace">
<h3><a class="doc-anchor" href="#doc-array-replace">#</a> <code>array_replace</code></h3>
<p><code>array_replace</code> — array helper <code>replace</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p array_replace $x
</code></pre>
</article>
<article class="doc-entry" id="doc-array-to-hstore">
<h3><a class="doc-anchor" href="#doc-array-to-hstore">#</a> <code>array_to_hstore</code></h3>
<p><code>array_to_hstore</code> — convert from <code>array</code> to <code>hstore</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p array_to_hstore $value
</code></pre>
</article>
<article class="doc-entry" id="doc-array-to-jsonb">
<h3><a class="doc-anchor" href="#doc-array-to-jsonb">#</a> <code>array_to_jsonb</code></h3>
<p><code>array_to_jsonb</code> — convert from <code>array</code> to <code>jsonb</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p array_to_jsonb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-array-to-string">
<h3><a class="doc-anchor" href="#doc-array-to-string">#</a> <code>array_to_string</code></h3>
<p><code>array_to_string</code> — convert from <code>array</code> to <code>string</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p array_to_string $value
</code></pre>
</article>
<article class="doc-entry" id="doc-array-union">
<h3><a class="doc-anchor" href="#doc-array-union">#</a> <code>array_union</code></h3>
<p><code>array_union</code> — array helper <code>union</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p array_union $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arrhenius-k">
<h3><a class="doc-anchor" href="#doc-arrhenius-k">#</a> <code>arrhenius_k</code></h3>
<p><code>arrhenius_k</code> — operation <code>arrhenius k</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p arrhenius_k $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arrhenius-temp-q10">
<h3><a class="doc-anchor" href="#doc-arrhenius-temp-q10">#</a> <code>arrhenius_temp_q10</code></h3>
<p><code>arrhenius_temp_q10</code> — operation <code>arrhenius temp q10</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p arrhenius_temp_q10 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arrow-impossibility-check">
<h3><a class="doc-anchor" href="#doc-arrow-impossibility-check">#</a> <code>arrow_impossibility_check</code></h3>
<p><code>arrow_impossibility_check</code> — operation <code>arrow impossibility check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p arrow_impossibility_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arrow-independence">
<h3><a class="doc-anchor" href="#doc-arrow-independence">#</a> <code>arrow_independence</code></h3>
<p><code>arrow_independence</code> — operation <code>arrow independence</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p arrow_independence $x
</code></pre>
</article>
<article class="doc-entry" id="doc-arrow-pareto-check">
<h3><a class="doc-anchor" href="#doc-arrow-pareto-check">#</a> <code>arrow_pareto_check</code></h3>
<p><code>arrow_pareto_check</code> — operation <code>arrow pareto check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p arrow_pareto_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-articulation-point">
<h3><a class="doc-anchor" href="#doc-articulation-point">#</a> <code>articulation_point</code></h3>
<p><code>articulation_point</code> — operation <code>articulation point</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p articulation_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-articulation-points">
<h3><a class="doc-anchor" href="#doc-articulation-points">#</a> <code>articulation_points</code></h3>
<p><code>articulation_points</code> — operation <code>articulation points</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p articulation_points $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ascent-parser-step">
<h3><a class="doc-anchor" href="#doc-ascent-parser-step">#</a> <code>ascent_parser_step</code></h3>
<p><code>ascent_parser_step</code> — single-step update of <code>ascent parser</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p ascent_parser_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ascii">
<h3><a class="doc-anchor" href="#doc-ascii">#</a> <code>ascii</code></h3>
<p><code>ascii</code> — operation <code>ascii</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p ascii $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ascii-chr">
<h3><a class="doc-anchor" href="#doc-ascii-chr">#</a> <code>ascii_chr</code></h3>
<p><code>ascii_chr</code> — ASCII text helper <code>chr</code>. Category: *string*.</p>
<pre><code class="lang-perl">p ascii_chr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ascii-ord">
<h3><a class="doc-anchor" href="#doc-ascii-ord">#</a> <code>ascii_ord</code></h3>
<p><code>ascii_ord</code> — ASCII text helper <code>ord</code>. Category: *string*.</p>
<pre><code class="lang-perl">p ascii_ord $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ascii-table">
<h3><a class="doc-anchor" href="#doc-ascii-table">#</a> <code>ascii_table</code></h3>
<p><code>ascii_table</code> — ASCII text helper <code>table</code>. Alias for <code>format_table_simple</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p ascii_table $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ase-palette-extract">
<h3><a class="doc-anchor" href="#doc-ase-palette-extract">#</a> <code>ase_palette_extract</code></h3>
<p><code>ase_palette_extract</code> — operation <code>ase palette extract</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p ase_palette_extract $x
</code></pre>
</article>
<article class="doc-entry" id="doc-asec">
<h3><a class="doc-anchor" href="#doc-asec">#</a> <code>asec</code></h3>
<p><code>asec</code> — operation <code>asec</code>. Category: *trig extensions*.</p>
<pre><code class="lang-perl">p asec $x
</code></pre>
</article>
<article class="doc-entry" id="doc-asian-call-mc">
<h3><a class="doc-anchor" href="#doc-asian-call-mc">#</a> <code>asian_call_mc</code></h3>
<p><code>asian_call_mc</code> — operation <code>asian call mc</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p asian_call_mc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-asin">
<h3><a class="doc-anchor" href="#doc-asin">#</a> <code>asin</code></h3>
<p><code>asin</code> — operation <code>asin</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p asin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-asinh">
<h3><a class="doc-anchor" href="#doc-asinh">#</a> <code>asinh</code></h3>
<p><code>asinh</code> — operation <code>asinh</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p asinh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-asrt">
<h3><a class="doc-anchor" href="#doc-asrt">#</a> <code>asrt</code></h3>
<p><code>asrt</code> — operation <code>asrt</code>. Alias for <code>argsort</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p asrt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-assert-type">
<h3><a class="doc-anchor" href="#doc-assert-type">#</a> <code>assert_type</code></h3>
<p><code>assert_type</code> — assertion <code>type</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p assert_type $x
</code></pre>
</article>
<article class="doc-entry" id="doc-assignment-lower-bound">
<h3><a class="doc-anchor" href="#doc-assignment-lower-bound">#</a> <code>assignment_lower_bound</code></h3>
<p><code>assignment_lower_bound</code> — operation <code>assignment lower bound</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p assignment_lower_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-assoc">
<h3><a class="doc-anchor" href="#doc-assoc">#</a> <code>assoc</code></h3>
<p><code>assoc</code> — operation <code>assoc</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p assoc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-assoc-fn">
<h3><a class="doc-anchor" href="#doc-assoc-fn">#</a> <code>assoc_fn</code></h3>
<p><code>assoc_fn</code> — operation <code>assoc fn</code>. Alias for <code>associate</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p assoc_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-assoc-in">
<h3><a class="doc-anchor" href="#doc-assoc-in">#</a> <code>assoc_in</code></h3>
<p><code>assoc_in</code> — operation <code>assoc in</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p assoc_in $x
</code></pre>
</article>
<article class="doc-entry" id="doc-associate">
<h3><a class="doc-anchor" href="#doc-associate">#</a> <code>associate</code></h3>
<p><code>associate</code> — operation <code>associate</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p associate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-astar-search">
<h3><a class="doc-anchor" href="#doc-astar-search">#</a> <code>astar_search</code></h3>
<p><code>astar_search</code> — operation <code>astar search</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p astar_search $x
</code></pre>
</article>
<article class="doc-entry" id="doc-astronomical-unit">
<h3><a class="doc-anchor" href="#doc-astronomical-unit">#</a> <code>astronomical_unit</code></h3>
<p><code>astronomical_unit</code> (alias <code>au</code>) — AU ≈ 1.496×10¹¹ m. Mean Earth-Sun distance.</p>
<pre><code class="lang-perl">p au # 1.495978707e11 m
p au / 1000 # ~149.6 million km
</code></pre>
</article>
<article class="doc-entry" id="doc-at-content">
<h3><a class="doc-anchor" href="#doc-at-content">#</a> <code>at_content</code></h3>
<p><code>at_content</code> — operation <code>at content</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p at_content $x
</code></pre>
</article>
<article class="doc-entry" id="doc-at-index">
<h3><a class="doc-anchor" href="#doc-at-index">#</a> <code>at_index</code></h3>
<p><code>at_index</code> — index of <code>at</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p at_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-atan">
<h3><a class="doc-anchor" href="#doc-atan">#</a> <code>atan</code></h3>
<p><code>atan</code> — operation <code>atan</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p atan $x
</code></pre>
</article>
<article class="doc-entry" id="doc-atan2-deg">
<h3><a class="doc-anchor" href="#doc-atan2-deg">#</a> <code>atan2_deg</code></h3>
<p><code>atan2_deg</code> — operation <code>atan2 deg</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p atan2_deg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-atan2-quadrant">
<h3><a class="doc-anchor" href="#doc-atan2-quadrant">#</a> <code>atan2_quadrant</code></h3>
<p><code>atan2_quadrant</code> — operation <code>atan2 quadrant</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p atan2_quadrant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-atanh">
<h3><a class="doc-anchor" href="#doc-atanh">#</a> <code>atanh</code></h3>
<p><code>atanh</code> — operation <code>atanh</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p atanh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-atbash">
<h3><a class="doc-anchor" href="#doc-atbash">#</a> <code>atbash</code></h3>
<p><code>atbash</code> — operation <code>atbash</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p atbash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-atbash-cipher">
<h3><a class="doc-anchor" href="#doc-atbash-cipher">#</a> <code>atbash_cipher</code></h3>
<p><code>atbash_cipher</code> — operation <code>atbash cipher</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p atbash_cipher $x
</code></pre>
</article>
<article class="doc-entry" id="doc-atc">
<h3><a class="doc-anchor" href="#doc-atc">#</a> <code>atc</code></h3>
<p><code>atc</code> — operation <code>atc</code>. Alias for <code>ansi_truecolor</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p atc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ati">
<h3><a class="doc-anchor" href="#doc-ati">#</a> <code>ati</code></h3>
<p><code>ati</code> — operation <code>ati</code>. Alias for <code>at_index</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p ati $x
</code></pre>
</article>
<article class="doc-entry" id="doc-atime">
<h3><a class="doc-anchor" href="#doc-atime">#</a> <code>atime</code></h3>
<p><code>atime</code> — operation <code>atime</code>. Alias for <code>file_atime</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p atime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-atm-to-pa">
<h3><a class="doc-anchor" href="#doc-atm-to-pa">#</a> <code>atm_to_pa</code></h3>
<p><code>atm_to_pa</code> — convert from <code>atm</code> to <code>pa</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p atm_to_pa $value
</code></pre>
</article>
<article class="doc-entry" id="doc-atomic-mass-unit">
<h3><a class="doc-anchor" href="#doc-atomic-mass-unit">#</a> <code>atomic_mass_unit</code></h3>
<p><code>atomic_mass_unit</code> — operation <code>atomic mass unit</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p atomic_mass_unit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-atomic-radius-pm">
<h3><a class="doc-anchor" href="#doc-atomic-radius-pm">#</a> <code>atomic_radius_pm</code></h3>
<p><code>atomic_radius_pm</code> — operation <code>atomic radius pm</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p atomic_radius_pm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-atr">
<h3><a class="doc-anchor" href="#doc-atr">#</a> <code>atr</code></h3>
<p><code>atr(highs, lows, closes, period=14) → array</code> — Average True Range (Wilder). True range = <code>max(high−low, |high−prev_close|, |low−prev_close|)</code>; smoothed with Wilder's recursion <code>ATR[i] = (ATR[i-1]·(p-1) + TR[i])/p</code>, seeded by mean of first <code>p</code> TRs.</p>
<pre><code class="lang-perl">p atr(\@hi, \@lo, \@cl, 14)
</code></pre>
</article>
<article class="doc-entry" id="doc-atrap">
<h3><a class="doc-anchor" href="#doc-atrap">#</a> <code>atrap</code></h3>
<p><code>atrap</code> — operation <code>atrap</code>. Alias for <code>area_trapezoid</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p atrap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-atri">
<h3><a class="doc-anchor" href="#doc-atri">#</a> <code>atri</code></h3>
<p><code>atri</code> — operation <code>atri</code>. Alias for <code>area_triangle</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p atri $x
</code></pre>
</article>
<article class="doc-entry" id="doc-attack-rate">
<h3><a class="doc-anchor" href="#doc-attack-rate">#</a> <code>attack_rate</code></h3>
<p><code>attack_rate</code> — rate of <code>attack</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p attack_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-attempt">
<h3><a class="doc-anchor" href="#doc-attempt">#</a> <code>attempt</code></h3>
<p><code>attempt</code> — operation <code>attempt</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p attempt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-attributable-fraction-pop">
<h3><a class="doc-anchor" href="#doc-attributable-fraction-pop">#</a> <code>attributable_fraction_pop</code></h3>
<p><code>attributable_fraction_pop</code> — operation <code>attributable fraction pop</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p attributable_fraction_pop $x
</code></pre>
</article>
<article class="doc-entry" id="doc-au-to-km">
<h3><a class="doc-anchor" href="#doc-au-to-km">#</a> <code>au_to_km</code></h3>
<p><code>au_to_km</code> — convert from <code>au</code> to <code>km</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p au_to_km $value
</code></pre>
</article>
<article class="doc-entry" id="doc-au-to-m">
<h3><a class="doc-anchor" href="#doc-au-to-m">#</a> <code>au_to_m</code></h3>
<p><code>au_to_m</code> — convert from <code>au</code> to <code>m</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p au_to_m $value
</code></pre>
</article>
<article class="doc-entry" id="doc-audio-fade-in">
<h3><a class="doc-anchor" href="#doc-audio-fade-in">#</a> <code>audio_fade_in</code></h3>
<p><code>audio_fade_in</code> — operation <code>audio fade in</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p audio_fade_in $x
</code></pre>
</article>
<article class="doc-entry" id="doc-audio-fade-out">
<h3><a class="doc-anchor" href="#doc-audio-fade-out">#</a> <code>audio_fade_out</code></h3>
<p><code>audio_fade_out</code> — operation <code>audio fade out</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p audio_fade_out $x
</code></pre>
</article>
<article class="doc-entry" id="doc-audio-normalize">
<h3><a class="doc-anchor" href="#doc-audio-normalize">#</a> <code>audio_normalize</code></h3>
<p><code>audio_normalize</code> — operation <code>audio normalize</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p audio_normalize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-audio-to-mono">
<h3><a class="doc-anchor" href="#doc-audio-to-mono">#</a> <code>audio_to_mono</code></h3>
<p><code>audio_to_mono</code> — convert from <code>audio</code> to <code>mono</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p audio_to_mono $value
</code></pre>
</article>
<article class="doc-entry" id="doc-audio-to-stereo">
<h3><a class="doc-anchor" href="#doc-audio-to-stereo">#</a> <code>audio_to_stereo</code></h3>
<p><code>audio_to_stereo</code> — convert from <code>audio</code> to <code>stereo</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p audio_to_stereo $value
</code></pre>
</article>
<article class="doc-entry" id="doc-augmented-lagrangian-step">
<h3><a class="doc-anchor" href="#doc-augmented-lagrangian-step">#</a> <code>augmented_lagrangian_step</code></h3>
<p><code>augmented_lagrangian_step</code> — single-step update of <code>augmented lagrangian</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p augmented_lagrangian_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-autocorrelation">
<h3><a class="doc-anchor" href="#doc-autocorrelation">#</a> <code>autocorrelation</code></h3>
<p><code>autocorrelation</code> — operation <code>autocorrelation</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p autocorrelation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-automated-readability-index">
<h3><a class="doc-anchor" href="#doc-automated-readability-index">#</a> <code>automated_readability_index</code></h3>
<p><code>automated_readability_index</code> — index of <code>automated readability</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p automated_readability_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-average">
<h3><a class="doc-anchor" href="#doc-average">#</a> <code>average</code></h3>
<p><code>average</code> — operation <code>average</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p average $x
</code></pre>
</article>
<article class="doc-entry" id="doc-averageif">
<h3><a class="doc-anchor" href="#doc-averageif">#</a> <code>averageif</code></h3>
<p><code>averageif</code> — operation <code>averageif</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p averageif $x
</code></pre>
</article>
<article class="doc-entry" id="doc-averageifs">
<h3><a class="doc-anchor" href="#doc-averageifs">#</a> <code>averageifs</code></h3>
<p><code>averageifs</code> — operation <code>averageifs</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p averageifs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-avg">
<h3><a class="doc-anchor" href="#doc-avg">#</a> <code>avg</code></h3>
<p><code>avg</code> — operation <code>avg</code>. Category: *pipeline / string helpers*.</p>
<pre><code class="lang-perl">p avg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-avg-degree">
<h3><a class="doc-anchor" href="#doc-avg-degree">#</a> <code>avg_degree</code></h3>
<p><code>avg_degree</code> — operation <code>avg degree</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p avg_degree $x
</code></pre>
</article>
<article class="doc-entry" id="doc-avogadro">
<h3><a class="doc-anchor" href="#doc-avogadro">#</a> <code>avogadro</code></h3>
<p><code>avogadro</code> — operation <code>avogadro</code>. Category: *math / physics constants*.</p>
<pre><code class="lang-perl">p avogadro $x
</code></pre>
</article>
<article class="doc-entry" id="doc-avogadro-constant">
<h3><a class="doc-anchor" href="#doc-avogadro-constant">#</a> <code>avogadro_constant</code></h3>
<p><code>avogadro_constant</code> — operation <code>avogadro constant</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p avogadro_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-avogadro-count">
<h3><a class="doc-anchor" href="#doc-avogadro-count">#</a> <code>avogadro_count</code></h3>
<p><code>avogadro_count</code> — count of <code>avogadro</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p avogadro_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-avogadro-number">
<h3><a class="doc-anchor" href="#doc-avogadro-number">#</a> <code>avogadro_number</code></h3>
<p><code>avogadro_number</code> — operation <code>avogadro number</code>. Category: *constants*.</p>
<pre><code class="lang-perl">p avogadro_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-avogadros-number">
<h3><a class="doc-anchor" href="#doc-avogadros-number">#</a> <code>avogadros_number</code></h3>
<p><code>avogadros_number</code> — operation <code>avogadros number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p avogadros_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-b2gray">
<h3><a class="doc-anchor" href="#doc-b2gray">#</a> <code>b2gray</code></h3>
<p><code>b2gray</code> — operation <code>b2gray</code>. Alias for <code>binary_to_gray</code>. Category: *base / gray code*.</p>
<pre><code class="lang-perl">p b2gray $x
</code></pre>
</article>
<article class="doc-entry" id="doc-b2i">
<h3><a class="doc-anchor" href="#doc-b2i">#</a> <code>b2i</code></h3>
<p><code>b2i</code> — operation <code>b2i</code>. Alias for <code>bool_to_int</code>. Category: *boolean combinators*.</p>
<pre><code class="lang-perl">p b2i $x
</code></pre>
</article>
<article class="doc-entry" id="doc-b64d">
<h3><a class="doc-anchor" href="#doc-b64d">#</a> <code>b64d</code></h3>
<p><code>b64d</code> — operation <code>b64d</code>. Alias for <code>base64_decode</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p b64d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-b64e">
<h3><a class="doc-anchor" href="#doc-b64e">#</a> <code>b64e</code></h3>
<p><code>b64e</code> — operation <code>b64e</code>. Alias for <code>base64_encode</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p b64e $x
</code></pre>
</article>
<article class="doc-entry" id="doc-b-to-kb">
<h3><a class="doc-anchor" href="#doc-b-to-kb">#</a> <code>b_to_kb</code></h3>
<p><code>b_to_kb</code> — convert from <code>b</code> to <code>kb</code>. Alias for <code>bytes_to_kb</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p b_to_kb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-b-wien">
<h3><a class="doc-anchor" href="#doc-b-wien">#</a> <code>b_wien</code></h3>
<p><code>b_wien</code> — operation <code>b wien</code>. Alias for <code>wien_constant</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p b_wien $x
</code></pre>
</article>
<article class="doc-entry" id="doc-babip">
<h3><a class="doc-anchor" href="#doc-babip">#</a> <code>babip</code></h3>
<p><code>babip</code> — operation <code>babip</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p babip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bac">
<h3><a class="doc-anchor" href="#doc-bac">#</a> <code>bac</code></h3>
<p><code>bac</code> — operation <code>bac</code>. Alias for <code>bac_estimate</code>. Category: *finance*.</p>
<pre><code class="lang-perl">p bac $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bac-estimate">
<h3><a class="doc-anchor" href="#doc-bac-estimate">#</a> <code>bac_estimate</code></h3>
<p><code>bac_estimate</code> — operation <code>bac estimate</code>. Category: *finance*.</p>
<pre><code class="lang-perl">p bac_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bachelier-call">
<h3><a class="doc-anchor" href="#doc-bachelier-call">#</a> <code>bachelier_call</code></h3>
<p><code>bachelier_call</code> — operation <code>bachelier call</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p bachelier_call $x
</code></pre>
</article>
<article class="doc-entry" id="doc-backward-algorithm">
<h3><a class="doc-anchor" href="#doc-backward-algorithm">#</a> <code>backward_algorithm</code></h3>
<p><code>backward_algorithm(obs, init, trans, emit) → number</code> — backward equivalent of <code>forward_algorithm</code> for Baum-Welch updates.</p>
</article>
<article class="doc-entry" id="doc-backward-euler">
<h3><a class="doc-anchor" href="#doc-backward-euler">#</a> <code>backward_euler</code></h3>
<p><code>backward_euler</code> — operation <code>backward euler</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p backward_euler $x
</code></pre>
</article>
<article class="doc-entry" id="doc-badi-year-from-fixed">
<h3><a class="doc-anchor" href="#doc-badi-year-from-fixed">#</a> <code>badi_year_from_fixed</code></h3>
<p><code>badi_year_from_fixed</code> — operation <code>badi year from fixed</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p badi_year_from_fixed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bahai-from-fixed">
<h3><a class="doc-anchor" href="#doc-bahai-from-fixed">#</a> <code>bahai_from_fixed</code></h3>
<p><code>bahai_from_fixed</code> — operation <code>bahai from fixed</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p bahai_from_fixed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bairstow">
<h3><a class="doc-anchor" href="#doc-bairstow">#</a> <code>bairstow</code></h3>
<p><code>bairstow</code> — operation <code>bairstow</code>. Alias for <code>lin_bairstow_step</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p bairstow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-balanced-accuracy">
<h3><a class="doc-anchor" href="#doc-balanced-accuracy">#</a> <code>balanced_accuracy</code></h3>
<p><code>balanced_accuracy</code> — operation <code>balanced accuracy</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p balanced_accuracy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bandpass-filter">
<h3><a class="doc-anchor" href="#doc-bandpass-filter">#</a> <code>bandpass_filter</code></h3>
<p><code>bandpass_filter(\@signal, $low, $high)</code> (alias <code>bpf</code>) — applies a band-pass filter passing frequencies between low and high cutoffs. Combines low-pass and high-pass.</p>
<pre><code class="lang-perl">my $filtered = bpf(\@signal, 0.1, 0.3)
</code></pre>
</article>
<article class="doc-entry" id="doc-bandwidth-format">
<h3><a class="doc-anchor" href="#doc-bandwidth-format">#</a> <code>bandwidth_format</code></h3>
<p><code>bandwidth_format</code> — operation <code>bandwidth format</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p bandwidth_format $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bandwidth-parse">
<h3><a class="doc-anchor" href="#doc-bandwidth-parse">#</a> <code>bandwidth_parse</code></h3>
<p><code>bandwidth_parse</code> — operation <code>bandwidth parse</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p bandwidth_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-banzhaf-index-two">
<h3><a class="doc-anchor" href="#doc-banzhaf-index-two">#</a> <code>banzhaf_index_two</code></h3>
<p><code>banzhaf_index_two</code> — operation <code>banzhaf index two</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p banzhaf_index_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bao-scale-today">
<h3><a class="doc-anchor" href="#doc-bao-scale-today">#</a> <code>bao_scale_today</code></h3>
<p><code>bao_scale_today</code> — operation <code>bao scale today</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p bao_scale_today $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bar-to-pascals">
<h3><a class="doc-anchor" href="#doc-bar-to-pascals">#</a> <code>bar_to_pascals</code></h3>
<p><code>bar_to_pascals</code> — convert from <code>bar</code> to <code>pascals</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p bar_to_pascals $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bargaining-set-check">
<h3><a class="doc-anchor" href="#doc-bargaining-set-check">#</a> <code>bargaining_set_check</code></h3>
<p><code>bargaining_set_check</code> — operation <code>bargaining set check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p bargaining_set_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-barrier-up-out-call">
<h3><a class="doc-anchor" href="#doc-barrier-up-out-call">#</a> <code>barrier_up_out_call</code></h3>
<p><code>barrier_up_out_call</code> — operation <code>barrier up out call</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p barrier_up_out_call $x
</code></pre>
</article>
<article class="doc-entry" id="doc-barthann-w">
<h3><a class="doc-anchor" href="#doc-barthann-w">#</a> <code>barthann_w</code></h3>
<p><code>barthann_w</code> — operation <code>barthann w</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p barthann_w $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bartlett-window">
<h3><a class="doc-anchor" href="#doc-bartlett-window">#</a> <code>bartlett_window</code></h3>
<p><code>bartlett_window</code> — operation <code>bartlett window</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p bartlett_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-base91-decode">
<h3><a class="doc-anchor" href="#doc-base91-decode">#</a> <code>basE91_decode</code></h3>
<p><code>basE91_decode(s) → string</code> — alternate spelling of <code>base91_decode</code>.</p>
</article>
<article class="doc-entry" id="doc-base91-encode">
<h3><a class="doc-anchor" href="#doc-base91-encode">#</a> <code>basE91_encode</code></h3>
<p><code>basE91_encode(s) → string</code> — alternate spelling of <code>base91_encode</code> (trademark capitalisation).</p>
</article>
<article class="doc-entry" id="doc-base58check-decode">
<h3><a class="doc-anchor" href="#doc-base58check-decode">#</a> <code>base58check_decode</code></h3>
<p><code>base58check_decode(s) → string</code> — verify the 4-byte checksum and return the payload; UNDEF if invalid.</p>
<pre><code class="lang-perl">p base58check_decode($encoded)
</code></pre>
</article>
<article class="doc-entry" id="doc-base58check-encode">
<h3><a class="doc-anchor" href="#doc-base58check-encode">#</a> <code>base58check_encode</code></h3>
<p><code>base58check_encode(payload) → string</code> — Bitcoin Base58Check: append <code>sha256d(payload)[..4]</code> then encode in Base58.</p>
<pre><code class="lang-perl">p base58check_encode("hello")
</code></pre>
</article>
<article class="doc-entry" id="doc-base91-decode">
<h3><a class="doc-anchor" href="#doc-base91-decode">#</a> <code>base91_decode</code></h3>
<p><code>base91_decode(s) → string</code> — inverse of <code>base91_encode</code>.</p>
</article>
<article class="doc-entry" id="doc-base91-encode">
<h3><a class="doc-anchor" href="#doc-base91-encode">#</a> <code>base91_encode</code></h3>
<p><code>base91_encode(s) → string</code> — basE91 encoding (more compact than Base64 due to 91-char alphabet).</p>
<pre><code class="lang-perl">p base91_encode("hello world")
</code></pre>
</article>
<article class="doc-entry" id="doc-base-convert">
<h3><a class="doc-anchor" href="#doc-base-convert">#</a> <code>base_convert</code></h3>
<p><code>base_convert</code> — operation <code>base convert</code>. Category: *base / gray code*.</p>
<pre><code class="lang-perl">p base_convert $x
</code></pre>
</article>
<article class="doc-entry" id="doc-batch">
<h3><a class="doc-anchor" href="#doc-batch">#</a> <code>batch</code></h3>
<p><code>batch</code> — operation <code>batch</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p batch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-batched">
<h3><a class="doc-anchor" href="#doc-batched">#</a> <code>batched</code></h3>
<p><code>batched</code> — operation <code>batched</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p batched $x
</code></pre>
</article>
<article class="doc-entry" id="doc-batchelor-scale-step">
<h3><a class="doc-anchor" href="#doc-batchelor-scale-step">#</a> <code>batchelor_scale_step</code></h3>
<p><code>batchelor_scale_step</code> — single-step update of <code>batchelor scale</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p batchelor_scale_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-battle-sexes-payoff">
<h3><a class="doc-anchor" href="#doc-battle-sexes-payoff">#</a> <code>battle_sexes_payoff</code></h3>
<p><code>battle_sexes_payoff</code> — operation <code>battle sexes payoff</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p battle_sexes_payoff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bauer-furuta-step">
<h3><a class="doc-anchor" href="#doc-bauer-furuta-step">#</a> <code>bauer_furuta_step</code></h3>
<p><code>bauer_furuta_step</code> — single-step update of <code>bauer furuta</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p bauer_furuta_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bayes-factor">
<h3><a class="doc-anchor" href="#doc-bayes-factor">#</a> <code>bayes_factor</code></h3>
<p><code>bayes_factor(likelihood_h1, likelihood_h0) → number</code> — <code>P(D|H1) / P(D|H0)</code>. >3 substantial, >10 strong.</p>
</article>
<article class="doc-entry" id="doc-bayes-posterior">
<h3><a class="doc-anchor" href="#doc-bayes-posterior">#</a> <code>bayes_posterior</code></h3>
<p><code>bayes_posterior</code> — operation <code>bayes posterior</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p bayes_posterior $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bayesian-beta-update">
<h3><a class="doc-anchor" href="#doc-bayesian-beta-update">#</a> <code>bayesian_beta_update</code></h3>
<p><code>bayesian_beta_update(alpha, beta, successes, failures) → {alpha, beta}</code> — conjugate update of Beta prior with Bernoulli observations.</p>
<pre><code class="lang-perl">p bayesian_beta_update(1, 1, 5, 3) # {alpha: 6, beta: 4}
</code></pre>
</article>
<article class="doc-entry" id="doc-bayesian-info-crit">
<h3><a class="doc-anchor" href="#doc-bayesian-info-crit">#</a> <code>bayesian_info_crit</code></h3>
<p><code>bayesian_info_crit</code> — Bayesian conjugate update <code>info crit</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p bayesian_info_crit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bayesian-normal-update">
<h3><a class="doc-anchor" href="#doc-bayesian-normal-update">#</a> <code>bayesian_normal_update</code></h3>
<p><code>bayesian_normal_update(prior_mu, prior_var, data_mu, data_var, n) → {mean, variance}</code> — Normal-Normal conjugate posterior.</p>
</article>
<article class="doc-entry" id="doc-bayesian-step">
<h3><a class="doc-anchor" href="#doc-bayesian-step">#</a> <code>bayesian_step</code></h3>
<p><code>bayesian_step</code> — Bayesian conjugate update <code>step</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p bayesian_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bbox">
<h3><a class="doc-anchor" href="#doc-bbox">#</a> <code>bbox</code></h3>
<p><code>bounding_box(@points)</code> (alias <code>bbox</code>) — computes the axis-aligned bounding box of 2D points. Returns [min_x, min_y, max_x, max_y].</p>
<pre><code class="lang-perl">my @pts = (1,2, 3,4, 0,1, 5,3)
my $bb = bbox(@pts)
p @$bb # (0, 1, 5, 4)
</code></pre>
</article>
<article class="doc-entry" id="doc-bbox-area">
<h3><a class="doc-anchor" href="#doc-bbox-area">#</a> <code>bbox_area</code></h3>
<p><code>bbox_area</code> — operation <code>bbox area</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bbox_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bbox-center">
<h3><a class="doc-anchor" href="#doc-bbox-center">#</a> <code>bbox_center</code></h3>
<p><code>bbox_center</code> — operation <code>bbox center</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bbox_center $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bbox-contains">
<h3><a class="doc-anchor" href="#doc-bbox-contains">#</a> <code>bbox_contains</code></h3>
<p><code>bbox_contains</code> — operation <code>bbox contains</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bbox_contains $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bbox-from-points">
<h3><a class="doc-anchor" href="#doc-bbox-from-points">#</a> <code>bbox_from_points</code></h3>
<p><code>bbox_from_points</code> — operation <code>bbox from points</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p bbox_from_points $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bbox-intersect">
<h3><a class="doc-anchor" href="#doc-bbox-intersect">#</a> <code>bbox_intersect</code></h3>
<p><code>bbox_intersect</code> — operation <code>bbox intersect</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bbox_intersect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bbox-union">
<h3><a class="doc-anchor" href="#doc-bbox-union">#</a> <code>bbox_union</code></h3>
<p><code>bbox_union</code> — operation <code>bbox union</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bbox_union $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bconv">
<h3><a class="doc-anchor" href="#doc-bconv">#</a> <code>bconv</code></h3>
<p><code>bconv</code> — operation <code>bconv</code>. Alias for <code>base_convert</code>. Category: *base / gray code*.</p>
<pre><code class="lang-perl">p bconv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bcount">
<h3><a class="doc-anchor" href="#doc-bcount">#</a> <code>bcount</code></h3>
<p><code>bcount</code> — operation <code>bcount</code>. Alias for <code>count_bytes</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p bcount $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bcp47-format">
<h3><a class="doc-anchor" href="#doc-bcp47-format">#</a> <code>bcp47_format</code></h3>
<p><code>bcp47_format</code> — operation <code>bcp47 format</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bcp47_format $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bcp47-parse">
<h3><a class="doc-anchor" href="#doc-bcp47-parse">#</a> <code>bcp47_parse</code></h3>
<p><code>bcp47_parse(tag) → hash</code> — parse BCP-47 language tag into <code>{language, script, region, variants, extensions}</code>.</p>
<pre><code class="lang-perl">p bcp47_parse("zh-Hant-TW") # {language: zh, script: Hant, region: TW}
</code></pre>
</article>
<article class="doc-entry" id="doc-bcp47-validate">
<h3><a class="doc-anchor" href="#doc-bcp47-validate">#</a> <code>bcp47_validate</code></h3>
<p><code>bcp47_validate(tag) → 0|1</code> — 1 if tag is structurally well-formed.</p>
</article>
<article class="doc-entry" id="doc-bcrypt-cost-iters">
<h3><a class="doc-anchor" href="#doc-bcrypt-cost-iters">#</a> <code>bcrypt_cost_iters</code></h3>
<p><code>bcrypt_cost_iters</code> — operation <code>bcrypt cost iters</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p bcrypt_cost_iters $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bdd-apply">
<h3><a class="doc-anchor" href="#doc-bdd-apply">#</a> <code>bdd_apply</code></h3>
<p><code>bdd_apply</code> — operation <code>bdd apply</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p bdd_apply $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bdd-quantify">
<h3><a class="doc-anchor" href="#doc-bdd-quantify">#</a> <code>bdd_quantify</code></h3>
<p><code>bdd_quantify</code> — operation <code>bdd quantify</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p bdd_quantify $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bdd-restrict">
<h3><a class="doc-anchor" href="#doc-bdd-restrict">#</a> <code>bdd_restrict</code></h3>
<p><code>bdd_restrict</code> — operation <code>bdd restrict</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p bdd_restrict $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bdf1-step">
<h3><a class="doc-anchor" href="#doc-bdf1-step">#</a> <code>bdf1_step</code></h3>
<p><code>bdf1_step</code> — single-step update of <code>bdf1</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p bdf1_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bdf2-step">
<h3><a class="doc-anchor" href="#doc-bdf2-step">#</a> <code>bdf2_step</code></h3>
<p><code>bdf2_step</code> — single-step update of <code>bdf2</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p bdf2_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bdf3-step">
<h3><a class="doc-anchor" href="#doc-bdf3-step">#</a> <code>bdf3_step</code></h3>
<p><code>bdf3_step</code> — single-step update of <code>bdf3</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p bdf3_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bdf4-step">
<h3><a class="doc-anchor" href="#doc-bdf4-step">#</a> <code>bdf4_step</code></h3>
<p><code>bdf4_step</code> — single-step update of <code>bdf4</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p bdf4_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bdf5-step">
<h3><a class="doc-anchor" href="#doc-bdf5-step">#</a> <code>bdf5_step</code></h3>
<p><code>bdf5_step</code> — single-step update of <code>bdf5</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p bdf5_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bdf6-step">
<h3><a class="doc-anchor" href="#doc-bdf6-step">#</a> <code>bdf6_step</code></h3>
<p><code>bdf6_step</code> — single-step update of <code>bdf6</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p bdf6_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bearing">
<h3><a class="doc-anchor" href="#doc-bearing">#</a> <code>bearing</code></h3>
<p><code>bearing</code> — operation <code>bearing</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p bearing $x
</code></pre>
</article>
<article class="doc-entry" id="doc-beat-frequency">
<h3><a class="doc-anchor" href="#doc-beat-frequency">#</a> <code>beat_frequency</code></h3>
<p><code>beat_frequency</code> — operation <code>beat frequency</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p beat_frequency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-beat-to-seconds">
<h3><a class="doc-anchor" href="#doc-beat-to-seconds">#</a> <code>beat_to_seconds</code></h3>
<p><code>beat_to_seconds</code> — convert from <code>beat</code> to <code>seconds</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p beat_to_seconds $value
</code></pre>
</article>
<article class="doc-entry" id="doc-beaufort">
<h3><a class="doc-anchor" href="#doc-beaufort">#</a> <code>beaufort</code></h3>
<p><code>beaufort</code> — operation <code>beaufort</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p beaufort $x
</code></pre>
</article>
<article class="doc-entry" id="doc-before-n">
<h3><a class="doc-anchor" href="#doc-before-n">#</a> <code>before_n</code></h3>
<p><code>before_n</code> — operation <code>before n</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p before_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bekenstein-entropy-step">
<h3><a class="doc-anchor" href="#doc-bekenstein-entropy-step">#</a> <code>bekenstein_entropy_step</code></h3>
<p><code>bekenstein_entropy_step</code> — single-step update of <code>bekenstein entropy</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p bekenstein_entropy_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bell-inequality-chsh">
<h3><a class="doc-anchor" href="#doc-bell-inequality-chsh">#</a> <code>bell_inequality_chsh</code></h3>
<p><code>bell_inequality_chsh</code> — operation <code>bell inequality chsh</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p bell_inequality_chsh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bell-number">
<h3><a class="doc-anchor" href="#doc-bell-number">#</a> <code>bell_number</code></h3>
<p><code>bell_number</code> — operation <code>bell number</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p bell_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bell-state">
<h3><a class="doc-anchor" href="#doc-bell-state">#</a> <code>bell_state</code></h3>
<p><code>bell_state</code> — operation <code>bell state</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p bell_state $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bell-state-index">
<h3><a class="doc-anchor" href="#doc-bell-state-index">#</a> <code>bell_state_index</code></h3>
<p><code>bell_state_index</code> — index of <code>bell state</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p bell_state_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bellman-equation-step">
<h3><a class="doc-anchor" href="#doc-bellman-equation-step">#</a> <code>bellman_equation_step</code></h3>
<p><code>bellman_equation_step</code> — single-step update of <code>bellman equation</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p bellman_equation_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bellman-ford">
<h3><a class="doc-anchor" href="#doc-bellman-ford">#</a> <code>bellman_ford</code></h3>
<p><code>bellman_ford</code> (alias <code>bellmanford</code>) computes shortest paths from a source in a graph with negative weights. Takes edges [[u,v,w],...], node count, source index.</p>
<pre><code class="lang-perl">my $d = bellmanford([[0,1,4],[0,2,5],[1,2,-3]], 3, 0)
</code></pre>
</article>
<article class="doc-entry" id="doc-bellman-ford-relax">
<h3><a class="doc-anchor" href="#doc-bellman-ford-relax">#</a> <code>bellman_ford_relax</code></h3>
<p><code>bellman_ford_relax</code> — operation <code>bellman ford relax</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p bellman_ford_relax $x
</code></pre>
</article>
<article class="doc-entry" id="doc-belln">
<h3><a class="doc-anchor" href="#doc-belln">#</a> <code>belln</code></h3>
<p><code>belln</code> — operation <code>belln</code>. Alias for <code>bell_number</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p belln $x
</code></pre>
</article>
<article class="doc-entry" id="doc-benders-decomposition-step">
<h3><a class="doc-anchor" href="#doc-benders-decomposition-step">#</a> <code>benders_decomposition_step</code></h3>
<p><code>benders_decomposition_step</code> — single-step update of <code>benders decomposition</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p benders_decomposition_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-berger-parker">
<h3><a class="doc-anchor" href="#doc-berger-parker">#</a> <code>berger_parker</code></h3>
<p><code>berger_parker</code> — operation <code>berger parker</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p berger_parker $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bergmann-adjust">
<h3><a class="doc-anchor" href="#doc-bergmann-adjust">#</a> <code>bergmann_adjust</code></h3>
<p><code>bergmann_adjust</code> — operation <code>bergmann adjust</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p bergmann_adjust $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bernoulli">
<h3><a class="doc-anchor" href="#doc-bernoulli">#</a> <code>bernoulli</code></h3>
<p><code>bernoulli_number</code> (alias <code>bernoulli</code>) computes the nth Bernoulli number. B(0)=1, B(1)=-0.5, odd B(n>1)=0.</p>
<pre><code class="lang-perl">p bernoulli(0) # 1
p bernoulli(2) # 0.1667
p bernoulli(4) # -0.0333
</code></pre>
</article>
<article class="doc-entry" id="doc-berry-phase-spin-half">
<h3><a class="doc-anchor" href="#doc-berry-phase-spin-half">#</a> <code>berry_phase_spin_half</code></h3>
<p><code>berry_phase_spin_half</code> — operation <code>berry phase spin half</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p berry_phase_spin_half $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bertrand-eq">
<h3><a class="doc-anchor" href="#doc-bertrand-eq">#</a> <code>bertrand_eq</code></h3>
<p><code>bertrand_eq</code> — operation <code>bertrand eq</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p bertrand_eq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bertrand-price-step">
<h3><a class="doc-anchor" href="#doc-bertrand-price-step">#</a> <code>bertrand_price_step</code></h3>
<p><code>bertrand_price_step</code> — single-step update of <code>bertrand price</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p bertrand_price_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bessel-in-general">
<h3><a class="doc-anchor" href="#doc-bessel-in-general">#</a> <code>bessel_in_general</code></h3>
<p><code>bessel_in_general</code> — operation <code>bessel in general</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p bessel_in_general $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bessel-jn-general">
<h3><a class="doc-anchor" href="#doc-bessel-jn-general">#</a> <code>bessel_jn_general</code></h3>
<p><code>bessel_jn_general</code> — operation <code>bessel jn general</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p bessel_jn_general $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bessel-lp">
<h3><a class="doc-anchor" href="#doc-bessel-lp">#</a> <code>bessel_lp</code></h3>
<p><code>bessel_lp</code> — operation <code>bessel lp</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p bessel_lp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-best-response-dynamic">
<h3><a class="doc-anchor" href="#doc-best-response-dynamic">#</a> <code>best_response_dynamic</code></h3>
<p><code>best_response_dynamic</code> — operation <code>best response dynamic</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p best_response_dynamic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-beta-function">
<h3><a class="doc-anchor" href="#doc-beta-function">#</a> <code>beta_function</code></h3>
<p><code>beta_function(a, b) → number</code> — Euler beta: <code>Γ(a)·Γ(b) / Γ(a+b)</code>.</p>
<pre><code class="lang-perl">p beta_function(2, 3) # 1/12
</code></pre>
</article>
<article class="doc-entry" id="doc-beta-incomplete">
<h3><a class="doc-anchor" href="#doc-beta-incomplete">#</a> <code>beta_incomplete</code></h3>
<p><code>beta_incomplete(x, a, b) → number</code> — regularised incomplete beta function <code>I_x(a, b)</code> via Lentz's continued fraction.</p>
<pre><code class="lang-perl">p beta_incomplete(0.5, 2, 3)
</code></pre>
</article>
<article class="doc-entry" id="doc-beta-pdf">
<h3><a class="doc-anchor" href="#doc-beta-pdf">#</a> <code>beta_pdf</code></h3>
<p><code>beta_pdf</code> (alias <code>betapdf</code>) evaluates the Beta distribution PDF at x with shape parameters alpha and beta.</p>
<pre><code class="lang-perl">p betapdf(0.5, 2, 5) # Beta(2,5) at x=0.5
</code></pre>
</article>
<article class="doc-entry" id="doc-betti-one">
<h3><a class="doc-anchor" href="#doc-betti-one">#</a> <code>betti_one</code></h3>
<p><code>betti_one</code> — operation <code>betti one</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p betti_one $x
</code></pre>
</article>
<article class="doc-entry" id="doc-betti-two">
<h3><a class="doc-anchor" href="#doc-betti-two">#</a> <code>betti_two</code></h3>
<p><code>betti_two</code> — operation <code>betti two</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p betti_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-betti-zero">
<h3><a class="doc-anchor" href="#doc-betti-zero">#</a> <code>betti_zero</code></h3>
<p><code>betti_zero</code> — operation <code>betti zero</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p betti_zero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-between">
<h3><a class="doc-anchor" href="#doc-between">#</a> <code>between</code></h3>
<p><code>between</code> — operation <code>between</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p between $x
</code></pre>
</article>
<article class="doc-entry" id="doc-beylkin-wavelet-step">
<h3><a class="doc-anchor" href="#doc-beylkin-wavelet-step">#</a> <code>beylkin_wavelet_step</code></h3>
<p><code>beylkin_wavelet_step</code> — single-step update of <code>beylkin wavelet</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p beylkin_wavelet_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bfgs-h-update-1d">
<h3><a class="doc-anchor" href="#doc-bfgs-h-update-1d">#</a> <code>bfgs_h_update_1d</code></h3>
<p><code>bfgs_h_update_1d</code> — operation <code>bfgs h update 1d</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p bfgs_h_update_1d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bfield-solenoid">
<h3><a class="doc-anchor" href="#doc-bfield-solenoid">#</a> <code>bfield_solenoid</code></h3>
<p><code>bfield_solenoid</code> — operation <code>bfield solenoid</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p bfield_solenoid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bfield-wire">
<h3><a class="doc-anchor" href="#doc-bfield-wire">#</a> <code>bfield_wire</code></h3>
<p><code>bfield_wire</code> — operation <code>bfield wire</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p bfield_wire $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bfs">
<h3><a class="doc-anchor" href="#doc-bfs">#</a> <code>bfs</code></h3>
<p><code>bfs</code> — operation <code>bfs</code>. Alias for <code>bfs_traverse</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p bfs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bfs-count">
<h3><a class="doc-anchor" href="#doc-bfs-count">#</a> <code>bfs_count</code></h3>
<p><code>bfs_count</code> — count of <code>bfs</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p bfs_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bfs-distances">
<h3><a class="doc-anchor" href="#doc-bfs-distances">#</a> <code>bfs_distances</code></h3>
<p><code>bfs_distances</code> — operation <code>bfs distances</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p bfs_distances $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bfs-traverse">
<h3><a class="doc-anchor" href="#doc-bfs-traverse">#</a> <code>bfs_traverse</code></h3>
<p><code>bfs_traverse</code> — operation <code>bfs traverse</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p bfs_traverse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-black">
<h3><a class="doc-anchor" href="#doc-bg-black">#</a> <code>bg_black</code></h3>
<p><code>bg_black</code> — operation <code>bg black</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_black $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-blue">
<h3><a class="doc-anchor" href="#doc-bg-blue">#</a> <code>bg_blue</code></h3>
<p><code>bg_blue</code> — operation <code>bg blue</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_blue $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-bright-blue">
<h3><a class="doc-anchor" href="#doc-bg-bright-blue">#</a> <code>bg_bright_blue</code></h3>
<p><code>bg_bright_blue</code> — operation <code>bg bright blue</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_bright_blue $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-bright-cyan">
<h3><a class="doc-anchor" href="#doc-bg-bright-cyan">#</a> <code>bg_bright_cyan</code></h3>
<p><code>bg_bright_cyan</code> — operation <code>bg bright cyan</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_bright_cyan $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-bright-green">
<h3><a class="doc-anchor" href="#doc-bg-bright-green">#</a> <code>bg_bright_green</code></h3>
<p><code>bg_bright_green</code> — operation <code>bg bright green</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_bright_green $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-bright-magenta">
<h3><a class="doc-anchor" href="#doc-bg-bright-magenta">#</a> <code>bg_bright_magenta</code></h3>
<p><code>bg_bright_magenta</code> — operation <code>bg bright magenta</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_bright_magenta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-bright-red">
<h3><a class="doc-anchor" href="#doc-bg-bright-red">#</a> <code>bg_bright_red</code></h3>
<p><code>bg_bright_red</code> — operation <code>bg bright red</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_bright_red $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-bright-white">
<h3><a class="doc-anchor" href="#doc-bg-bright-white">#</a> <code>bg_bright_white</code></h3>
<p><code>bg_bright_white</code> — operation <code>bg bright white</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_bright_white $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-bright-yellow">
<h3><a class="doc-anchor" href="#doc-bg-bright-yellow">#</a> <code>bg_bright_yellow</code></h3>
<p><code>bg_bright_yellow</code> — operation <code>bg bright yellow</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_bright_yellow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-c256">
<h3><a class="doc-anchor" href="#doc-bg-c256">#</a> <code>bg_c256</code></h3>
<p><code>bg_c256</code> — operation <code>bg c256</code>. Alias for <code>bg_color256</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_c256 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-color256">
<h3><a class="doc-anchor" href="#doc-bg-color256">#</a> <code>bg_color256</code></h3>
<p><code>bg_color256</code> — operation <code>bg color256</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_color256 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-cyan">
<h3><a class="doc-anchor" href="#doc-bg-cyan">#</a> <code>bg_cyan</code></h3>
<p><code>bg_cyan</code> — operation <code>bg cyan</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_cyan $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-green">
<h3><a class="doc-anchor" href="#doc-bg-green">#</a> <code>bg_green</code></h3>
<p><code>bg_green</code> — operation <code>bg green</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_green $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-magenta">
<h3><a class="doc-anchor" href="#doc-bg-magenta">#</a> <code>bg_magenta</code></h3>
<p><code>bg_magenta</code> — operation <code>bg magenta</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_magenta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-red">
<h3><a class="doc-anchor" href="#doc-bg-red">#</a> <code>bg_red</code></h3>
<p><code>bg_red</code> — operation <code>bg red</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_red $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-rgb">
<h3><a class="doc-anchor" href="#doc-bg-rgb">#</a> <code>bg_rgb</code></h3>
<p><code>bg_rgb</code> — operation <code>bg rgb</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_rgb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-white">
<h3><a class="doc-anchor" href="#doc-bg-white">#</a> <code>bg_white</code></h3>
<p><code>bg_white</code> — operation <code>bg white</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_white $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bg-yellow">
<h3><a class="doc-anchor" href="#doc-bg-yellow">#</a> <code>bg_yellow</code></h3>
<p><code>bg_yellow</code> — operation <code>bg yellow</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bg_yellow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bh-adjusted-p">
<h3><a class="doc-anchor" href="#doc-bh-adjusted-p">#</a> <code>bh_adjusted_p</code></h3>
<p><code>bh_adjusted_p</code> — operation <code>bh adjusted p</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p bh_adjusted_p $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bh-entropy">
<h3><a class="doc-anchor" href="#doc-bh-entropy">#</a> <code>bh_entropy</code></h3>
<p><code>bh_entropy</code> — operation <code>bh entropy</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p bh_entropy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bh-evaporation-time">
<h3><a class="doc-anchor" href="#doc-bh-evaporation-time">#</a> <code>bh_evaporation_time</code></h3>
<p><code>bh_evaporation_time</code> — operation <code>bh evaporation time</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p bh_evaporation_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bhattacharyya-coefficient">
<h3><a class="doc-anchor" href="#doc-bhattacharyya-coefficient">#</a> <code>bhattacharyya_coefficient</code></h3>
<p><code>bhattacharyya_coefficient</code> — operation <code>bhattacharyya coefficient</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p bhattacharyya_coefficient $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bianchi-first-identity-check">
<h3><a class="doc-anchor" href="#doc-bianchi-first-identity-check">#</a> <code>bianchi_first_identity_check</code></h3>
<p><code>bianchi_first_identity_check</code> — operation <code>bianchi first identity check</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p bianchi_first_identity_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bianchi-second-identity-check">
<h3><a class="doc-anchor" href="#doc-bianchi-second-identity-check">#</a> <code>bianchi_second_identity_check</code></h3>
<p><code>bianchi_second_identity_check</code> — operation <code>bianchi second identity check</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p bianchi_second_identity_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bic">
<h3><a class="doc-anchor" href="#doc-bic">#</a> <code>bic</code></h3>
<p><code>bic</code> — operation <code>bic</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p bic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biconnected-components">
<h3><a class="doc-anchor" href="#doc-biconnected-components">#</a> <code>biconnected_components</code></h3>
<p><code>biconnected_components</code> — operation <code>biconnected components</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p biconnected_components $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bidirectional-bfs">
<h3><a class="doc-anchor" href="#doc-bidirectional-bfs">#</a> <code>bidirectional_bfs</code></h3>
<p><code>bidirectional_bfs(adj, s, t) → array</code> — search forward from <code>s</code> and backward from <code>t</code> simultaneously; meets in the middle.</p>
<pre><code class="lang-perl">p bidirectional_bfs($g, 0, 7)
</code></pre>
</article>
<article class="doc-entry" id="doc-bidirectional-dijkstra">
<h3><a class="doc-anchor" href="#doc-bidirectional-dijkstra">#</a> <code>bidirectional_dijkstra</code></h3>
<p><code>bidirectional_dijkstra</code> — operation <code>bidirectional dijkstra</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p bidirectional_dijkstra $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bielliptic-total">
<h3><a class="doc-anchor" href="#doc-bielliptic-total">#</a> <code>bielliptic_total</code></h3>
<p><code>bielliptic_total</code> — operation <code>bielliptic total</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p bielliptic_total $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-abs">
<h3><a class="doc-anchor" href="#doc-bignum-abs">#</a> <code>bignum_abs</code></h3>
<p><code>bignum_abs</code> — operation <code>bignum abs</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_abs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-add">
<h3><a class="doc-anchor" href="#doc-bignum-add">#</a> <code>bignum_add</code></h3>
<p><code>bignum_add</code> — operation <code>bignum add</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_add $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-and">
<h3><a class="doc-anchor" href="#doc-bignum-and">#</a> <code>bignum_and</code></h3>
<p><code>bignum_and</code> — operation <code>bignum and</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_and $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-bit-length">
<h3><a class="doc-anchor" href="#doc-bignum-bit-length">#</a> <code>bignum_bit_length</code></h3>
<p><code>bignum_bit_length</code> — operation <code>bignum bit length</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_bit_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-clear-bit">
<h3><a class="doc-anchor" href="#doc-bignum-clear-bit">#</a> <code>bignum_clear_bit</code></h3>
<p><code>bignum_clear_bit</code> — operation <code>bignum clear bit</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_clear_bit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-compare">
<h3><a class="doc-anchor" href="#doc-bignum-compare">#</a> <code>bignum_compare</code></h3>
<p><code>bignum_compare</code> — operation <code>bignum compare</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_compare $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-div">
<h3><a class="doc-anchor" href="#doc-bignum-div">#</a> <code>bignum_div</code></h3>
<p><code>bignum_div</code> — operation <code>bignum div</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_div $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-factorial">
<h3><a class="doc-anchor" href="#doc-bignum-factorial">#</a> <code>bignum_factorial</code></h3>
<p><code>bignum_factorial</code> — operation <code>bignum factorial</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_factorial $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-from-str">
<h3><a class="doc-anchor" href="#doc-bignum-from-str">#</a> <code>bignum_from_str</code></h3>
<p><code>bignum_from_str</code> — operation <code>bignum from str</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_from_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-gcd">
<h3><a class="doc-anchor" href="#doc-bignum-gcd">#</a> <code>bignum_gcd</code></h3>
<p><code>bignum_gcd</code> — operation <code>bignum gcd</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_gcd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-is-negative">
<h3><a class="doc-anchor" href="#doc-bignum-is-negative">#</a> <code>bignum_is_negative</code></h3>
<p><code>bignum_is_negative</code> — operation <code>bignum is negative</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_is_negative $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-is-prime">
<h3><a class="doc-anchor" href="#doc-bignum-is-prime">#</a> <code>bignum_is_prime</code></h3>
<p><code>bignum_is_prime</code> — operation <code>bignum is prime</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_is_prime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-is-zero">
<h3><a class="doc-anchor" href="#doc-bignum-is-zero">#</a> <code>bignum_is_zero</code></h3>
<p><code>bignum_is_zero</code> — operation <code>bignum is zero</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_is_zero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-lcm">
<h3><a class="doc-anchor" href="#doc-bignum-lcm">#</a> <code>bignum_lcm</code></h3>
<p><code>bignum_lcm</code> — operation <code>bignum lcm</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_lcm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-mod">
<h3><a class="doc-anchor" href="#doc-bignum-mod">#</a> <code>bignum_mod</code></h3>
<p><code>bignum_mod</code> — operation <code>bignum mod</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_mod $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-modpow">
<h3><a class="doc-anchor" href="#doc-bignum-modpow">#</a> <code>bignum_modpow</code></h3>
<p><code>bignum_modpow</code> — operation <code>bignum modpow</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_modpow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-mul">
<h3><a class="doc-anchor" href="#doc-bignum-mul">#</a> <code>bignum_mul</code></h3>
<p><code>bignum_mul</code> — operation <code>bignum mul</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_mul $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-negate">
<h3><a class="doc-anchor" href="#doc-bignum-negate">#</a> <code>bignum_negate</code></h3>
<p><code>bignum_negate</code> — operation <code>bignum negate</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_negate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-new">
<h3><a class="doc-anchor" href="#doc-bignum-new">#</a> <code>bignum_new</code></h3>
<p><code>bignum_new</code> — constructor of <code>bignum</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-not">
<h3><a class="doc-anchor" href="#doc-bignum-not">#</a> <code>bignum_not</code></h3>
<p><code>bignum_not</code> — operation <code>bignum not</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_not $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-or">
<h3><a class="doc-anchor" href="#doc-bignum-or">#</a> <code>bignum_or</code></h3>
<p><code>bignum_or</code> — operation <code>bignum or</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_or $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-pow">
<h3><a class="doc-anchor" href="#doc-bignum-pow">#</a> <code>bignum_pow</code></h3>
<p><code>bignum_pow</code> — operation <code>bignum pow</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_pow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-random">
<h3><a class="doc-anchor" href="#doc-bignum-random">#</a> <code>bignum_random</code></h3>
<p><code>bignum_random</code> — operation <code>bignum random</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_random $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-set-bit">
<h3><a class="doc-anchor" href="#doc-bignum-set-bit">#</a> <code>bignum_set_bit</code></h3>
<p><code>bignum_set_bit</code> — operation <code>bignum set bit</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_set_bit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-shl">
<h3><a class="doc-anchor" href="#doc-bignum-shl">#</a> <code>bignum_shl</code></h3>
<p><code>bignum_shl</code> — operation <code>bignum shl</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_shl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-shr">
<h3><a class="doc-anchor" href="#doc-bignum-shr">#</a> <code>bignum_shr</code></h3>
<p><code>bignum_shr</code> — operation <code>bignum shr</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_shr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-sign">
<h3><a class="doc-anchor" href="#doc-bignum-sign">#</a> <code>bignum_sign</code></h3>
<p><code>bignum_sign</code> — sign with private key of <code>bignum</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_sign $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-sqrt">
<h3><a class="doc-anchor" href="#doc-bignum-sqrt">#</a> <code>bignum_sqrt</code></h3>
<p><code>bignum_sqrt</code> — operation <code>bignum sqrt</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_sqrt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-sub">
<h3><a class="doc-anchor" href="#doc-bignum-sub">#</a> <code>bignum_sub</code></h3>
<p><code>bignum_sub</code> — operation <code>bignum sub</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_sub $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-test-bit">
<h3><a class="doc-anchor" href="#doc-bignum-test-bit">#</a> <code>bignum_test_bit</code></h3>
<p><code>bignum_test_bit</code> — operation <code>bignum test bit</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_test_bit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-to-int">
<h3><a class="doc-anchor" href="#doc-bignum-to-int">#</a> <code>bignum_to_int</code></h3>
<p><code>bignum_to_int</code> — convert from <code>bignum</code> to <code>int</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_to_int $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-to-str">
<h3><a class="doc-anchor" href="#doc-bignum-to-str">#</a> <code>bignum_to_str</code></h3>
<p><code>bignum_to_str</code> — convert from <code>bignum</code> to <code>str</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_to_str $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bignum-xor">
<h3><a class="doc-anchor" href="#doc-bignum-xor">#</a> <code>bignum_xor</code></h3>
<p><code>bignum_xor</code> — operation <code>bignum xor</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bignum_xor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bigram">
<h3><a class="doc-anchor" href="#doc-bigram">#</a> <code>bigram</code></h3>
<p><code>bigram</code> — operation <code>bigram</code>. Alias for <code>bigrams</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p bigram $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bigram-perplexity">
<h3><a class="doc-anchor" href="#doc-bigram-perplexity">#</a> <code>bigram_perplexity</code></h3>
<p><code>bigram_perplexity</code> — operation <code>bigram perplexity</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p bigram_perplexity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bigrams">
<h3><a class="doc-anchor" href="#doc-bigrams">#</a> <code>bigrams</code></h3>
<p><code>bigrams</code> — operation <code>bigrams</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p bigrams $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bilateral-filter-2d">
<h3><a class="doc-anchor" href="#doc-bilateral-filter-2d">#</a> <code>bilateral_filter_2d</code></h3>
<p><code>bilateral_filter_2d(image, size=5, sigma_s=2, sigma_r=25) → matrix</code> — edge-preserving smoothing. Spatial + range Gaussian weights.</p>
</article>
<article class="doc-entry" id="doc-bilinear-xform">
<h3><a class="doc-anchor" href="#doc-bilinear-xform">#</a> <code>bilinear_xform</code></h3>
<p><code>bilinear_xform</code> — operation <code>bilinear xform</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p bilinear_xform $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bilinear-zpk-xform">
<h3><a class="doc-anchor" href="#doc-bilinear-zpk-xform">#</a> <code>bilinear_zpk_xform</code></h3>
<p><code>bilinear_zpk_xform</code> — operation <code>bilinear zpk xform</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p bilinear_zpk_xform $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bin-of">
<h3><a class="doc-anchor" href="#doc-bin-of">#</a> <code>bin_of</code></h3>
<p><code>bin_of</code> — binary helper <code>of</code>. Alias for <code>to_bin</code>. Category: *base conversion*.</p>
<pre><code class="lang-perl">p bin_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bin-packing-best-fit">
<h3><a class="doc-anchor" href="#doc-bin-packing-best-fit">#</a> <code>bin_packing_best_fit</code></h3>
<p><code>bin_packing_best_fit</code> — binary helper <code>packing best fit</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p bin_packing_best_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bin-packing-first-fit">
<h3><a class="doc-anchor" href="#doc-bin-packing-first-fit">#</a> <code>bin_packing_first_fit</code></h3>
<p><code>bin_packing_first_fit</code> — binary helper <code>packing first fit</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p bin_packing_first_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bin-packing-lower-bound-l1">
<h3><a class="doc-anchor" href="#doc-bin-packing-lower-bound-l1">#</a> <code>bin_packing_lower_bound_l1</code></h3>
<p><code>bin_packing_lower_bound_l1</code> — binary helper <code>packing lower bound l1</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p bin_packing_lower_bound_l1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bin-packing-next-fit">
<h3><a class="doc-anchor" href="#doc-bin-packing-next-fit">#</a> <code>bin_packing_next_fit</code></h3>
<p><code>bin_packing_next_fit</code> — binary helper <code>packing next fit</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p bin_packing_next_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bin-to-gray">
<h3><a class="doc-anchor" href="#doc-bin-to-gray">#</a> <code>bin_to_gray</code></h3>
<p><code>bin_to_gray</code> — convert from <code>bin</code> to <code>gray</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p bin_to_gray $value
</code></pre>
</article>
<article class="doc-entry" id="doc-binary-insert">
<h3><a class="doc-anchor" href="#doc-binary-insert">#</a> <code>binary_insert</code></h3>
<p><code>binary_insert</code> — operation <code>binary insert</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p binary_insert $x
</code></pre>
</article>
<article class="doc-entry" id="doc-binary-search">
<h3><a class="doc-anchor" href="#doc-binary-search">#</a> <code>binary_search</code></h3>
<p><code>binary_search</code> — operation <code>binary search</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p binary_search $x
</code></pre>
</article>
<article class="doc-entry" id="doc-binary-to-gray">
<h3><a class="doc-anchor" href="#doc-binary-to-gray">#</a> <code>binary_to_gray</code></h3>
<p><code>binary_to_gray</code> — convert from <code>binary</code> to <code>gray</code>. Category: *base / gray code*.</p>
<pre><code class="lang-perl">p binary_to_gray $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bincount">
<h3><a class="doc-anchor" href="#doc-bincount">#</a> <code>bincount</code></h3>
<p><code>bincount</code> — operation <code>bincount</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p bincount $x
</code></pre>
</article>
<article class="doc-entry" id="doc-binder-content-optimal">
<h3><a class="doc-anchor" href="#doc-binder-content-optimal">#</a> <code>binder_content_optimal</code></h3>
<p><code>binder_content_optimal</code> — operation <code>binder content optimal</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p binder_content_optimal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-binom">
<h3><a class="doc-anchor" href="#doc-binom">#</a> <code>binom</code></h3>
<p><code>binom</code> — operation <code>binom</code>. Alias for <code>binomial</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p binom $x
</code></pre>
</article>
<article class="doc-entry" id="doc-binom-test">
<h3><a class="doc-anchor" href="#doc-binom-test">#</a> <code>binom_test</code></h3>
<p><code>binom_test</code> — exact binomial test. Returns two-sided p-value. Like R's binom.test().</p>
<pre><code class="lang-perl">my $p = binomtest(7, 10, 0.5) # p-value for 7/10 successes vs p=0.5
</code></pre>
</article>
<article class="doc-entry" id="doc-binomial">
<h3><a class="doc-anchor" href="#doc-binomial">#</a> <code>binomial</code></h3>
<p><code>binomial</code> — operation <code>binomial</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p binomial $x
</code></pre>
</article>
<article class="doc-entry" id="doc-binomial-test">
<h3><a class="doc-anchor" href="#doc-binomial-test">#</a> <code>binomial_test</code></h3>
<p><code>binomial_test(k, n, p=0.5) → {statistic, df, p_value}</code> — exact binomial test for <code>k</code> successes in <code>n</code> Bernoulli trials.</p>
<pre><code class="lang-perl">p binomial_test(7, 10, 0.5)
</code></pre>
</article>
<article class="doc-entry" id="doc-binsert">
<h3><a class="doc-anchor" href="#doc-binsert">#</a> <code>binsert</code></h3>
<p><code>binsert</code> — operation <code>binsert</code>. Alias for <code>binary_insert</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p binsert $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biorthogonal-step">
<h3><a class="doc-anchor" href="#doc-biorthogonal-step">#</a> <code>biorthogonal_step</code></h3>
<p><code>biorthogonal_step</code> — single-step update of <code>biorthogonal</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p biorthogonal_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biot-number-step">
<h3><a class="doc-anchor" href="#doc-biot-number-step">#</a> <code>biot_number_step</code></h3>
<p><code>biot_number_step</code> — single-step update of <code>biot number</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p biot_number_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biquad-allpass-coeffs">
<h3><a class="doc-anchor" href="#doc-biquad-allpass-coeffs">#</a> <code>biquad_allpass_coeffs</code></h3>
<p><code>biquad_allpass_coeffs</code> — biquad IIR filter <code>allpass coeffs</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p biquad_allpass_coeffs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biquad-bandpass">
<h3><a class="doc-anchor" href="#doc-biquad-bandpass">#</a> <code>biquad_bandpass</code></h3>
<p><code>biquad_bandpass</code> — biquad IIR filter <code>bandpass</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p biquad_bandpass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biquad-bandpass-coeffs">
<h3><a class="doc-anchor" href="#doc-biquad-bandpass-coeffs">#</a> <code>biquad_bandpass_coeffs</code></h3>
<p><code>biquad_bandpass_coeffs</code> — biquad IIR filter <code>bandpass coeffs</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p biquad_bandpass_coeffs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biquad-highpass">
<h3><a class="doc-anchor" href="#doc-biquad-highpass">#</a> <code>biquad_highpass</code></h3>
<p><code>biquad_highpass</code> — biquad IIR filter <code>highpass</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p biquad_highpass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biquad-highpass-coeffs">
<h3><a class="doc-anchor" href="#doc-biquad-highpass-coeffs">#</a> <code>biquad_highpass_coeffs</code></h3>
<p><code>biquad_highpass_coeffs</code> — biquad IIR filter <code>highpass coeffs</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p biquad_highpass_coeffs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biquad-highshelf-coeffs">
<h3><a class="doc-anchor" href="#doc-biquad-highshelf-coeffs">#</a> <code>biquad_highshelf_coeffs</code></h3>
<p><code>biquad_highshelf_coeffs</code> — biquad IIR filter <code>highshelf coeffs</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p biquad_highshelf_coeffs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biquad-lowpass">
<h3><a class="doc-anchor" href="#doc-biquad-lowpass">#</a> <code>biquad_lowpass</code></h3>
<p><code>biquad_lowpass</code> — biquad IIR filter <code>lowpass</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p biquad_lowpass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biquad-lowpass-coeffs">
<h3><a class="doc-anchor" href="#doc-biquad-lowpass-coeffs">#</a> <code>biquad_lowpass_coeffs</code></h3>
<p><code>biquad_lowpass_coeffs</code> — biquad IIR filter <code>lowpass coeffs</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p biquad_lowpass_coeffs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biquad-lowshelf-coeffs">
<h3><a class="doc-anchor" href="#doc-biquad-lowshelf-coeffs">#</a> <code>biquad_lowshelf_coeffs</code></h3>
<p><code>biquad_lowshelf_coeffs</code> — biquad IIR filter <code>lowshelf coeffs</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p biquad_lowshelf_coeffs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biquad-notch">
<h3><a class="doc-anchor" href="#doc-biquad-notch">#</a> <code>biquad_notch</code></h3>
<p><code>biquad_notch</code> — biquad IIR filter <code>notch</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p biquad_notch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biquad-notch-coeffs">
<h3><a class="doc-anchor" href="#doc-biquad-notch-coeffs">#</a> <code>biquad_notch_coeffs</code></h3>
<p><code>biquad_notch_coeffs</code> — biquad IIR filter <code>notch coeffs</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p biquad_notch_coeffs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biquad-peak-coeffs">
<h3><a class="doc-anchor" href="#doc-biquad-peak-coeffs">#</a> <code>biquad_peak_coeffs</code></h3>
<p><code>biquad_peak_coeffs</code> — biquad IIR filter <code>peak coeffs</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p biquad_peak_coeffs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-biquad-step">
<h3><a class="doc-anchor" href="#doc-biquad-step">#</a> <code>biquad_step</code></h3>
<p><code>biquad_step</code> — biquad IIR filter <code>step</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p biquad_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-birnbaum-saunders-pdf">
<h3><a class="doc-anchor" href="#doc-birnbaum-saunders-pdf">#</a> <code>birnbaum_saunders_pdf</code></h3>
<p><code>birnbaum_saunders_pdf</code> — operation <code>birnbaum saunders pdf</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p birnbaum_saunders_pdf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bisect">
<h3><a class="doc-anchor" href="#doc-bisect">#</a> <code>bisect</code></h3>
<p><code>bisection</code> (alias <code>bisect</code>) finds a root of f(x)=0 in [a,b] via the bisection method. Takes a code ref, a, b, and optional tolerance.</p>
<pre><code class="lang-perl">my $root = bisect(fn { $_[0]**2 - 2 }, 1, 2) # √2 ≈ 1.4142
</code></pre>
</article>
<article class="doc-entry" id="doc-bisimulation-step">
<h3><a class="doc-anchor" href="#doc-bisimulation-step">#</a> <code>bisimulation_step</code></h3>
<p><code>bisimulation_step</code> — single-step update of <code>bisimulation</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p bisimulation_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-and">
<h3><a class="doc-anchor" href="#doc-bit-and">#</a> <code>bit_and</code></h3>
<p><code>bit_and</code> — bitwise op <code>and</code>. Category: *bit ops*.</p>
<pre><code class="lang-perl">p bit_and $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-build">
<h3><a class="doc-anchor" href="#doc-bit-build">#</a> <code>bit_build</code></h3>
<p><code>bit_build</code> — bitwise op <code>build</code>. Alias for <code>fenwick_build</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p bit_build $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-clear">
<h3><a class="doc-anchor" href="#doc-bit-clear">#</a> <code>bit_clear</code></h3>
<p><code>bit_clear</code> — bitwise op <code>clear</code>. Category: *bit ops*.</p>
<pre><code class="lang-perl">p bit_clear $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-clz">
<h3><a class="doc-anchor" href="#doc-bit-clz">#</a> <code>bit_clz</code></h3>
<p><code>bit_clz(x) → int</code> — count leading zeros in the 64-bit representation.</p>
</article>
<article class="doc-entry" id="doc-bit-count-ones">
<h3><a class="doc-anchor" href="#doc-bit-count-ones">#</a> <code>bit_count_ones</code></h3>
<p><code>bit_count_ones(x) → int</code> — population count: number of set bits.</p>
<pre><code class="lang-perl">p bit_count_ones(0b1011) # 3
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-count-zeros">
<h3><a class="doc-anchor" href="#doc-bit-count-zeros">#</a> <code>bit_count_zeros</code></h3>
<p><code>bit_count_zeros(x) → int</code> — number of clear bits in the full 64-bit representation.</p>
</article>
<article class="doc-entry" id="doc-bit-ctz">
<h3><a class="doc-anchor" href="#doc-bit-ctz">#</a> <code>bit_ctz</code></h3>
<p><code>bit_ctz(x) → int</code> — count trailing zeros.</p>
</article>
<article class="doc-entry" id="doc-bit-extract">
<h3><a class="doc-anchor" href="#doc-bit-extract">#</a> <code>bit_extract</code></h3>
<p><code>bit_extract(x, start, len) → int</code> — extract <code>len</code> bits starting at bit position <code>start</code>.</p>
<pre><code class="lang-perl">p bit_extract(0xABCD, 4, 8) # 0xBC = 188
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-first-clear">
<h3><a class="doc-anchor" href="#doc-bit-first-clear">#</a> <code>bit_first_clear</code></h3>
<p><code>bit_first_clear(x) → int</code> — position of the lowest unset bit.</p>
</article>
<article class="doc-entry" id="doc-bit-first-set">
<h3><a class="doc-anchor" href="#doc-bit-first-set">#</a> <code>bit_first_set</code></h3>
<p><code>bit_first_set(x) → int</code> — position of the lowest set bit (LSB=0); <code>-1</code> if <code>x == 0</code>.</p>
<pre><code class="lang-perl">p bit_first_set(0b1100) # 2
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-flip-prob">
<h3><a class="doc-anchor" href="#doc-bit-flip-prob">#</a> <code>bit_flip_prob</code></h3>
<p><code>bit_flip_prob</code> — bitwise op <code>flip prob</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p bit_flip_prob $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-insert">
<h3><a class="doc-anchor" href="#doc-bit-insert">#</a> <code>bit_insert</code></h3>
<p><code>bit_insert(x, v, start, len) → int</code> — set <code>len</code> bits in <code>x</code> starting at <code>start</code> to the low bits of <code>v</code>.</p>
<pre><code class="lang-perl">p bit_insert(0, 0xFF, 8, 8) # 0xFF00
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-last-clear">
<h3><a class="doc-anchor" href="#doc-bit-last-clear">#</a> <code>bit_last_clear</code></h3>
<p><code>bit_last_clear(x) → int</code> — position of the highest unset bit.</p>
</article>
<article class="doc-entry" id="doc-bit-last-set">
<h3><a class="doc-anchor" href="#doc-bit-last-set">#</a> <code>bit_last_set</code></h3>
<p><code>bit_last_set(x) → int</code> — position of the highest set bit; <code>-1</code> if <code>x == 0</code>.</p>
</article>
<article class="doc-entry" id="doc-bit-length">
<h3><a class="doc-anchor" href="#doc-bit-length">#</a> <code>bit_length</code></h3>
<p><code>bit_length</code> — bitwise op <code>length</code>. Category: *base conversion*.</p>
<pre><code class="lang-perl">p bit_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-log2-int">
<h3><a class="doc-anchor" href="#doc-bit-log2-int">#</a> <code>bit_log2_int</code></h3>
<p><code>bit_log2_int(x) → int</code> — <code>⌊log₂(x)⌋</code>; <code>-1</code> if <code>x == 0</code>.</p>
<pre><code class="lang-perl">p bit_log2_int(255) # 7
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-not">
<h3><a class="doc-anchor" href="#doc-bit-not">#</a> <code>bit_not</code></h3>
<p><code>bit_not</code> — bitwise op <code>not</code>. Category: *bit ops*.</p>
<pre><code class="lang-perl">p bit_not $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-or">
<h3><a class="doc-anchor" href="#doc-bit-or">#</a> <code>bit_or</code></h3>
<p><code>bit_or</code> — bitwise op <code>or</code>. Category: *bit ops*.</p>
<pre><code class="lang-perl">p bit_or $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-parity">
<h3><a class="doc-anchor" href="#doc-bit-parity">#</a> <code>bit_parity</code></h3>
<p><code>bit_parity(x) → 0|1</code> — even or odd number of set bits.</p>
</article>
<article class="doc-entry" id="doc-bit-query">
<h3><a class="doc-anchor" href="#doc-bit-query">#</a> <code>bit_query</code></h3>
<p><code>bit_query</code> — bitwise op <code>query</code>. Alias for <code>fenwick_query</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p bit_query $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-reverse">
<h3><a class="doc-anchor" href="#doc-bit-reverse">#</a> <code>bit_reverse</code></h3>
<p><code>bit_reverse</code> — bitwise op <code>reverse</code>. Alias for <code>bit_reverse_32</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p bit_reverse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-reverse-32">
<h3><a class="doc-anchor" href="#doc-bit-reverse-32">#</a> <code>bit_reverse_32</code></h3>
<p><code>bit_reverse_32</code> — bitwise op <code>reverse 32</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p bit_reverse_32 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-reverse-64">
<h3><a class="doc-anchor" href="#doc-bit-reverse-64">#</a> <code>bit_reverse_64</code></h3>
<p><code>bit_reverse_64</code> — bitwise op <code>reverse 64</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p bit_reverse_64 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-reverse-u16">
<h3><a class="doc-anchor" href="#doc-bit-reverse-u16">#</a> <code>bit_reverse_u16</code></h3>
<p><code>bit_reverse_u16(x) → int</code> — reverse the 16 lowest bits.</p>
</article>
<article class="doc-entry" id="doc-bit-reverse-u32">
<h3><a class="doc-anchor" href="#doc-bit-reverse-u32">#</a> <code>bit_reverse_u32</code></h3>
<p><code>bit_reverse_u32(x) → int</code> — reverse the 32 lowest bits.</p>
<pre><code class="lang-perl">p bit_reverse_u32(1) # 0x80000000
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-reverse-u64">
<h3><a class="doc-anchor" href="#doc-bit-reverse-u64">#</a> <code>bit_reverse_u64</code></h3>
<p><code>bit_reverse_u64(x) → int</code> — reverse all 64 bits.</p>
</article>
<article class="doc-entry" id="doc-bit-reverse-u8">
<h3><a class="doc-anchor" href="#doc-bit-reverse-u8">#</a> <code>bit_reverse_u8</code></h3>
<p><code>bit_reverse_u8(x) → int</code> — reverse the 8 lowest bits.</p>
<pre><code class="lang-perl">p bit_reverse_u8(0x01) # 0x80 = 128
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-rotate-left">
<h3><a class="doc-anchor" href="#doc-bit-rotate-left">#</a> <code>bit_rotate_left</code></h3>
<p><code>bit_rotate_left(x, n) → int</code> — cyclic left rotation by <code>n</code> bits (mod 64).</p>
<pre><code class="lang-perl">p bit_rotate_left(0x1, 4) # 0x10
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-rotate-right">
<h3><a class="doc-anchor" href="#doc-bit-rotate-right">#</a> <code>bit_rotate_right</code></h3>
<p><code>bit_rotate_right(x, n) → int</code> — cyclic right rotation by <code>n</code> bits.</p>
</article>
<article class="doc-entry" id="doc-bit-set">
<h3><a class="doc-anchor" href="#doc-bit-set">#</a> <code>bit_set</code></h3>
<p><code>bit_set</code> — bitwise op <code>set</code>. Category: *bit ops*.</p>
<pre><code class="lang-perl">p bit_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-swap-bytes">
<h3><a class="doc-anchor" href="#doc-bit-swap-bytes">#</a> <code>bit_swap_bytes</code></h3>
<p><code>bit_swap_bytes(x) → int</code> — reverse byte order (htonl/ntohl-style).</p>
<pre><code class="lang-perl">p bit_swap_bytes(0x12345678) # 0x78563412
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-test">
<h3><a class="doc-anchor" href="#doc-bit-test">#</a> <code>bit_test</code></h3>
<p><code>bit_test</code> — bitwise op <code>test</code>. Category: *bit ops*.</p>
<pre><code class="lang-perl">p bit_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-toggle">
<h3><a class="doc-anchor" href="#doc-bit-toggle">#</a> <code>bit_toggle</code></h3>
<p><code>bit_toggle</code> — bitwise op <code>toggle</code>. Category: *bit ops*.</p>
<pre><code class="lang-perl">p bit_toggle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bit-xor">
<h3><a class="doc-anchor" href="#doc-bit-xor">#</a> <code>bit_xor</code></h3>
<p><code>bit_xor</code> — bitwise op <code>xor</code>. Category: *bit ops*.</p>
<pre><code class="lang-perl">p bit_xor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bitcount">
<h3><a class="doc-anchor" href="#doc-bitcount">#</a> <code>bitcount</code></h3>
<p><code>bitcount</code> — operation <code>bitcount</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p bitcount $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bitlen">
<h3><a class="doc-anchor" href="#doc-bitlen">#</a> <code>bitlen</code></h3>
<p><code>bitlen</code> — operation <code>bitlen</code>. Alias for <code>bit_length</code>. Category: *base conversion*.</p>
<pre><code class="lang-perl">p bitlen $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bitop">
<h3><a class="doc-anchor" href="#doc-bitop">#</a> <code>bitop</code></h3>
<p><code>bitop</code> — operation <code>bitop</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p bitop $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bitpos">
<h3><a class="doc-anchor" href="#doc-bitpos">#</a> <code>bitpos</code></h3>
<p><code>bitpos</code> — operation <code>bitpos</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p bitpos $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bits-count">
<h3><a class="doc-anchor" href="#doc-bits-count">#</a> <code>bits_count</code></h3>
<p><code>bits_count</code> — count of <code>bits</code>. Category: *base conversion*.</p>
<pre><code class="lang-perl">p bits_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bits-to-bytes">
<h3><a class="doc-anchor" href="#doc-bits-to-bytes">#</a> <code>bits_to_bytes</code></h3>
<p><code>bits_to_bytes</code> — convert from <code>bits</code> to <code>bytes</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p bits_to_bytes $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bits-to-ip">
<h3><a class="doc-anchor" href="#doc-bits-to-ip">#</a> <code>bits_to_ip</code></h3>
<p><code>bits_to_ip</code> — convert from <code>bits</code> to <code>ip</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p bits_to_ip $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bitset-clear">
<h3><a class="doc-anchor" href="#doc-bitset-clear">#</a> <code>bitset_clear</code></h3>
<p><code>bitset_clear</code> — operation <code>bitset clear</code>. Category: *data structure helpers*.</p>
<pre><code class="lang-perl">p bitset_clear $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bitset-new">
<h3><a class="doc-anchor" href="#doc-bitset-new">#</a> <code>bitset_new</code></h3>
<p><code>bitset_new</code> — constructor of <code>bitset</code>. Category: *data structure helpers*.</p>
<pre><code class="lang-perl">p bitset_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bitset-set">
<h3><a class="doc-anchor" href="#doc-bitset-set">#</a> <code>bitset_set</code></h3>
<p><code>bitset_set</code> — operation <code>bitset set</code>. Category: *data structure helpers*.</p>
<pre><code class="lang-perl">p bitset_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bitset-test">
<h3><a class="doc-anchor" href="#doc-bitset-test">#</a> <code>bitset_test</code></h3>
<p><code>bitset_test</code> — statistical test of <code>bitset</code>. Category: *data structure helpers*.</p>
<pre><code class="lang-perl">p bitset_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bkt">
<h3><a class="doc-anchor" href="#doc-bkt">#</a> <code>bkt</code></h3>
<p><code>bkt</code> — operation <code>bkt</code>. Alias for <code>bucket</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p bkt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bl">
<h3><a class="doc-anchor" href="#doc-bl">#</a> <code>bl</code></h3>
<p><code>bl</code> — operation <code>bl</code>. Alias for <code>butlast</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p bl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-black">
<h3><a class="doc-anchor" href="#doc-black">#</a> <code>black</code></h3>
<p><code>black</code> — operation <code>black</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p black $x
</code></pre>
</article>
<article class="doc-entry" id="doc-black76-call">
<h3><a class="doc-anchor" href="#doc-black76-call">#</a> <code>black76_call</code></h3>
<p><code>black76_call</code> — operation <code>black76 call</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p black76_call $x
</code></pre>
</article>
<article class="doc-entry" id="doc-black-hat-transform">
<h3><a class="doc-anchor" href="#doc-black-hat-transform">#</a> <code>black_hat_transform</code></h3>
<p><code>black_hat_transform(image, size=3) → matrix</code> — <code>closing - image</code>. Extracts dark details.</p>
</article>
<article class="doc-entry" id="doc-black-karasinski-drift">
<h3><a class="doc-anchor" href="#doc-black-karasinski-drift">#</a> <code>black_karasinski_drift</code></h3>
<p><code>black_karasinski_drift</code> — operation <code>black karasinski drift</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p black_karasinski_drift $x
</code></pre>
</article>
<article class="doc-entry" id="doc-black-method-winner">
<h3><a class="doc-anchor" href="#doc-black-method-winner">#</a> <code>black_method_winner</code></h3>
<p><code>black_method_winner</code> — operation <code>black method winner</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p black_method_winner $x
</code></pre>
</article>
<article class="doc-entry" id="doc-black-scholes-call">
<h3><a class="doc-anchor" href="#doc-black-scholes-call">#</a> <code>black_scholes_call</code></h3>
<p><code>black_scholes_call($S, $K, $r, $T, $sigma)</code> (alias <code>bscall</code>) — computes Black-Scholes price for a European call option. S=spot, K=strike, r=rate, T=time to expiry, sigma=volatility.</p>
<pre><code class="lang-perl">p bscall(100, 100, 0.05, 1, 0.2) # ~10.45
</code></pre>
</article>
<article class="doc-entry" id="doc-black-scholes-put">
<h3><a class="doc-anchor" href="#doc-black-scholes-put">#</a> <code>black_scholes_put</code></h3>
<p><code>black_scholes_put($S, $K, $r, $T, $sigma)</code> (alias <code>bsput</code>) — computes Black-Scholes price for a European put option.</p>
<pre><code class="lang-perl">p bsput(100, 100, 0.05, 1, 0.2) # ~5.57
</code></pre>
</article>
<article class="doc-entry" id="doc-blackman">
<h3><a class="doc-anchor" href="#doc-blackman">#</a> <code>blackman</code></h3>
<p><code>window_blackman($n)</code> (alias <code>blackman</code>) — generates a Blackman window of length n. Provides excellent sidelobe suppression at the cost of main lobe width.</p>
<pre><code class="lang-perl">my $w = blackman(1024)
</code></pre>
</article>
<article class="doc-entry" id="doc-blackman-harris-window">
<h3><a class="doc-anchor" href="#doc-blackman-harris-window">#</a> <code>blackman_harris_window</code></h3>
<p><code>blackman_harris_window</code> — operation <code>blackman harris window</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p blackman_harris_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-blackman-w">
<h3><a class="doc-anchor" href="#doc-blackman-w">#</a> <code>blackman_w</code></h3>
<p><code>blackman_w</code> — operation <code>blackman w</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p blackman_w $x
</code></pre>
</article>
<article class="doc-entry" id="doc-blackman-window">
<h3><a class="doc-anchor" href="#doc-blackman-window">#</a> <code>blackman_window</code></h3>
<p><code>blackman_window</code> — operation <code>blackman window</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p blackman_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-blackscholes-call">
<h3><a class="doc-anchor" href="#doc-blackscholes-call">#</a> <code>blackscholes_call</code></h3>
<p><code>blackscholes_call</code> — operation <code>blackscholes call</code>. Alias for <code>bs_call</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p blackscholes_call $x
</code></pre>
</article>
<article class="doc-entry" id="doc-blackscholes-put">
<h3><a class="doc-anchor" href="#doc-blackscholes-put">#</a> <code>blackscholes_put</code></h3>
<p><code>blackscholes_put</code> — operation <code>blackscholes put</code>. Alias for <code>bs_put</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p blackscholes_put $x
</code></pre>
</article>
<article class="doc-entry" id="doc-blast-kmer-index">
<h3><a class="doc-anchor" href="#doc-blast-kmer-index">#</a> <code>blast_kmer_index</code></h3>
<p><code>blast_kmer_index</code> — index of <code>blast kmer</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p blast_kmer_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-blessed">
<h3><a class="doc-anchor" href="#doc-blessed">#</a> <code>blessed</code></h3>
<p><code>blessed</code> — operation <code>blessed</code>. Category: *list / aggregate*.</p>
<pre><code class="lang-perl">p blessed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-blink">
<h3><a class="doc-anchor" href="#doc-blink">#</a> <code>blink</code></h3>
<p><code>blink</code> — operation <code>blink</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p blink $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bloch-purity-check">
<h3><a class="doc-anchor" href="#doc-bloch-purity-check">#</a> <code>bloch_purity_check</code></h3>
<p><code>bloch_purity_check</code> — operation <code>bloch purity check</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p bloch_purity_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bloch-sphere-x">
<h3><a class="doc-anchor" href="#doc-bloch-sphere-x">#</a> <code>bloch_sphere_x</code></h3>
<p><code>bloch_sphere_x</code> — operation <code>bloch sphere x</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p bloch_sphere_x $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bloch-sphere-z">
<h3><a class="doc-anchor" href="#doc-bloch-sphere-z">#</a> <code>bloch_sphere_z</code></h3>
<p><code>bloch_sphere_z</code> — operation <code>bloch sphere z</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p bloch_sphere_z $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bloch-to-density-real">
<h3><a class="doc-anchor" href="#doc-bloch-to-density-real">#</a> <code>bloch_to_density_real</code></h3>
<p><code>bloch_to_density_real</code> — convert from <code>bloch</code> to <code>density real</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p bloch_to_density_real $value
</code></pre>
</article>
<article class="doc-entry" id="doc-block-devices">
<h3><a class="doc-anchor" href="#doc-block-devices">#</a> <code>block_devices</code></h3>
<p><code>block_devices</code> — operation <code>block devices</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p block_devices $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bloom-filter-add">
<h3><a class="doc-anchor" href="#doc-bloom-filter-add">#</a> <code>bloom_filter_add</code></h3>
<p><code>bloom_filter_add</code> — Bloom filter op <code>filter add</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bloom_filter_add $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bloom-filter-contains">
<h3><a class="doc-anchor" href="#doc-bloom-filter-contains">#</a> <code>bloom_filter_contains</code></h3>
<p><code>bloom_filter_contains</code> — Bloom filter op <code>filter contains</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bloom_filter_contains $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bloom-filter-new">
<h3><a class="doc-anchor" href="#doc-bloom-filter-new">#</a> <code>bloom_filter_new</code></h3>
<p><code>bloom_filter_new</code> — Bloom filter op <code>filter new</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p bloom_filter_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-blossom-match-step">
<h3><a class="doc-anchor" href="#doc-blossom-match-step">#</a> <code>blossom_match_step</code></h3>
<p><code>blossom_match_step</code> — single-step update of <code>blossom match</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p blossom_match_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-blosum45-score">
<h3><a class="doc-anchor" href="#doc-blosum45-score">#</a> <code>blosum45_score</code></h3>
<p><code>blosum45_score</code> — score of <code>blosum45</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p blosum45_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-blue">
<h3><a class="doc-anchor" href="#doc-blue">#</a> <code>blue</code></h3>
<p><code>blue</code> — operation <code>blue</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p blue $x
</code></pre>
</article>
<article class="doc-entry" id="doc-blue-bold">
<h3><a class="doc-anchor" href="#doc-blue-bold">#</a> <code>blue_bold</code></h3>
<p><code>blue_bold</code> — operation <code>blue bold</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p blue_bold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bm25-score">
<h3><a class="doc-anchor" href="#doc-bm25-score">#</a> <code>bm25_score</code></h3>
<p><code>bm25_score(query, doc, avg_dl, n_total, df, k1=1.5, b=0.75) → number</code> — Okapi BM25 retrieval score.</p>
</article>
<article class="doc-entry" id="doc-bm-horspool">
<h3><a class="doc-anchor" href="#doc-bm-horspool">#</a> <code>bm_horspool</code></h3>
<p><code>bm_horspool</code> — operation <code>bm horspool</code>. Alias for <code>horspool_search</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p bm_horspool $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bmi">
<h3><a class="doc-anchor" href="#doc-bmi">#</a> <code>bmi</code></h3>
<p><code>bmi</code> — operation <code>bmi</code>. Category: *finance*.</p>
<pre><code class="lang-perl">p bmi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bmi-calc">
<h3><a class="doc-anchor" href="#doc-bmi-calc">#</a> <code>bmi_calc</code></h3>
<p><code>bmi_calc</code> — operation <code>bmi calc</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p bmi_calc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bmp-header-read">
<h3><a class="doc-anchor" href="#doc-bmp-header-read">#</a> <code>bmp_header_read</code></h3>
<p><code>bmp_header_read(hex_bytes) → hash</code> — parse BMP header → <code>{format, width, height, bits_per_pixel}</code> or UNDEF.</p>
<pre><code class="lang-perl">p bmp_header_read("424D...")
</code></pre>
</article>
<article class="doc-entry" id="doc-bmr-harris-benedict-female">
<h3><a class="doc-anchor" href="#doc-bmr-harris-benedict-female">#</a> <code>bmr_harris_benedict_female</code></h3>
<p><code>bmr_harris_benedict_female</code> — operation <code>bmr harris benedict female</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p bmr_harris_benedict_female $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bmr-harris-benedict-male">
<h3><a class="doc-anchor" href="#doc-bmr-harris-benedict-male">#</a> <code>bmr_harris_benedict_male</code></h3>
<p><code>bmr_harris_benedict_male</code> — operation <code>bmr harris benedict male</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p bmr_harris_benedict_male $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bode-gain-margin">
<h3><a class="doc-anchor" href="#doc-bode-gain-margin">#</a> <code>bode_gain_margin</code></h3>
<p><code>bode_gain_margin</code> — operation <code>bode gain margin</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p bode_gain_margin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bode-phase">
<h3><a class="doc-anchor" href="#doc-bode-phase">#</a> <code>bode_phase</code></h3>
<p><code>bode_phase</code> — operation <code>bode phase</code>. Alias for <code>bode_phase_deg</code>. Category: *control theory*.</p>
<pre><code class="lang-perl">p bode_phase $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bode-phase-margin">
<h3><a class="doc-anchor" href="#doc-bode-phase-margin">#</a> <code>bode_phase_margin</code></h3>
<p><code>bode_phase_margin</code> — operation <code>bode phase margin</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p bode_phase_margin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-body-surface-area-dubois">
<h3><a class="doc-anchor" href="#doc-body-surface-area-dubois">#</a> <code>body_surface_area_dubois</code></h3>
<p><code>body_surface_area_dubois</code> — operation <code>body surface area dubois</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p body_surface_area_dubois $x
</code></pre>
</article>
<article class="doc-entry" id="doc-body-wave-mb">
<h3><a class="doc-anchor" href="#doc-body-wave-mb">#</a> <code>body_wave_mb</code></h3>
<p><code>body_wave_mb</code> — operation <code>body wave mb</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p body_wave_mb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bogacki-shampine-step">
<h3><a class="doc-anchor" href="#doc-bogacki-shampine-step">#</a> <code>bogacki_shampine_step</code></h3>
<p><code>bogacki_shampine_step</code> — single-step update of <code>bogacki shampine</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p bogacki_shampine_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bohr-energy-ev">
<h3><a class="doc-anchor" href="#doc-bohr-energy-ev">#</a> <code>bohr_energy_ev</code></h3>
<p><code>bohr_energy_ev</code> — operation <code>bohr energy ev</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p bohr_energy_ev $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bohr-magneton">
<h3><a class="doc-anchor" href="#doc-bohr-magneton">#</a> <code>bohr_magneton</code></h3>
<p><code>bohr_magneton</code> — operation <code>bohr magneton</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p bohr_magneton $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bohr-radius-n">
<h3><a class="doc-anchor" href="#doc-bohr-radius-n">#</a> <code>bohr_radius_n</code></h3>
<p><code>bohr_radius_n</code> — operation <code>bohr radius n</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p bohr_radius_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bold">
<h3><a class="doc-anchor" href="#doc-bold">#</a> <code>bold</code></h3>
<p><code>bold</code> — operation <code>bold</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bold-blue">
<h3><a class="doc-anchor" href="#doc-bold-blue">#</a> <code>bold_blue</code></h3>
<p><code>bold_blue</code> — operation <code>bold blue</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bold_blue $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bold-cyan">
<h3><a class="doc-anchor" href="#doc-bold-cyan">#</a> <code>bold_cyan</code></h3>
<p><code>bold_cyan</code> — operation <code>bold cyan</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bold_cyan $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bold-green">
<h3><a class="doc-anchor" href="#doc-bold-green">#</a> <code>bold_green</code></h3>
<p><code>bold_green</code> — operation <code>bold green</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bold_green $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bold-magenta">
<h3><a class="doc-anchor" href="#doc-bold-magenta">#</a> <code>bold_magenta</code></h3>
<p><code>bold_magenta</code> — operation <code>bold magenta</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bold_magenta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bold-red">
<h3><a class="doc-anchor" href="#doc-bold-red">#</a> <code>bold_red</code></h3>
<p><code>bold_red</code> — operation <code>bold red</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bold_red $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bold-white">
<h3><a class="doc-anchor" href="#doc-bold-white">#</a> <code>bold_white</code></h3>
<p><code>bold_white</code> — operation <code>bold white</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bold_white $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bold-yellow">
<h3><a class="doc-anchor" href="#doc-bold-yellow">#</a> <code>bold_yellow</code></h3>
<p><code>bold_yellow</code> — operation <code>bold yellow</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bold_yellow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bollinger-lower">
<h3><a class="doc-anchor" href="#doc-bollinger-lower">#</a> <code>bollinger_lower</code></h3>
<p><code>bollinger_lower(prices, period=20, mult=2) → array</code> — <code>sma − mult · stddev</code> of the trailing window.</p>
<pre><code class="lang-perl">p bollinger_lower(\@closes, 20, 2)
</code></pre>
</article>
<article class="doc-entry" id="doc-bollinger-middle">
<h3><a class="doc-anchor" href="#doc-bollinger-middle">#</a> <code>bollinger_middle</code></h3>
<p><code>bollinger_middle(prices, period=20) → array</code> — alias for <code>sma(prices, period)</code>; the central band of Bollinger bands.</p>
<pre><code class="lang-perl">p bollinger_middle(\@closes, 20)
</code></pre>
</article>
<article class="doc-entry" id="doc-bollinger-upper">
<h3><a class="doc-anchor" href="#doc-bollinger-upper">#</a> <code>bollinger_upper</code></h3>
<p><code>bollinger_upper(prices, period=20, mult=2) → array</code> — <code>sma + mult · stddev</code> of the trailing window.</p>
<pre><code class="lang-perl">p bollinger_upper(\@closes, 20, 2)
</code></pre>
</article>
<article class="doc-entry" id="doc-boltz">
<h3><a class="doc-anchor" href="#doc-boltz">#</a> <code>boltz</code></h3>
<p><code>boltz</code> — operation <code>boltz</code>. Alias for <code>boltzmann_constant</code>. Category: *constants*.</p>
<pre><code class="lang-perl">p boltz $x
</code></pre>
</article>
<article class="doc-entry" id="doc-boltzmann">
<h3><a class="doc-anchor" href="#doc-boltzmann">#</a> <code>boltzmann</code></h3>
<p><code>boltzmann</code> — operation <code>boltzmann</code>. Category: *math / physics constants*.</p>
<pre><code class="lang-perl">p boltzmann $x
</code></pre>
</article>
<article class="doc-entry" id="doc-boltzmann-choose">
<h3><a class="doc-anchor" href="#doc-boltzmann-choose">#</a> <code>boltzmann_choose</code></h3>
<p><code>boltzmann_choose</code> — operation <code>boltzmann choose</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p boltzmann_choose $x
</code></pre>
</article>
<article class="doc-entry" id="doc-boltzmann-const">
<h3><a class="doc-anchor" href="#doc-boltzmann-const">#</a> <code>boltzmann_const</code></h3>
<p><code>boltzmann_const</code> — operation <code>boltzmann const</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p boltzmann_const $x
</code></pre>
</article>
<article class="doc-entry" id="doc-boltzmann-constant">
<h3><a class="doc-anchor" href="#doc-boltzmann-constant">#</a> <code>boltzmann_constant</code></h3>
<p><code>boltzmann_constant</code> — operation <code>boltzmann constant</code>. Category: *constants*.</p>
<pre><code class="lang-perl">p boltzmann_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-boltzmann-softmax-action">
<h3><a class="doc-anchor" href="#doc-boltzmann-softmax-action">#</a> <code>boltzmann_softmax_action</code></h3>
<p><code>boltzmann_softmax_action</code> — operation <code>boltzmann softmax action</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p boltzmann_softmax_action $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bond-duration">
<h3><a class="doc-anchor" href="#doc-bond-duration">#</a> <code>bond_duration</code></h3>
<p><code>duration($face, $coupon_rate, $ytm, $periods)</code> (alias <code>bond_duration</code>) — computes the Macaulay duration of a bond, measuring interest rate sensitivity as weighted average time to receive cash flows.</p>
<pre><code class="lang-perl">p duration(1000, 0.05, 0.05, 10) # ~7.7 years
</code></pre>
</article>
<article class="doc-entry" id="doc-bond-price">
<h3><a class="doc-anchor" href="#doc-bond-price">#</a> <code>bond_price</code></h3>
<p><code>bond_price($face, $coupon_rate, $ytm, $periods)</code> — computes the present value (price) of a bond given face value, coupon rate, yield to maturity, and number of periods.</p>
<pre><code class="lang-perl">p bond_price(1000, 0.05, 0.04, 10) # ~1081 (premium)
p bond_price(1000, 0.05, 0.06, 10) # ~926 (discount)
</code></pre>
</article>
<article class="doc-entry" id="doc-bond-yield">
<h3><a class="doc-anchor" href="#doc-bond-yield">#</a> <code>bond_yield</code></h3>
<p><code>bond_yield($price, $face, $coupon_rate, $periods)</code> — computes the yield to maturity of a bond given its current price. Uses Newton-Raphson iteration.</p>
<pre><code class="lang-perl">p bond_yield(950, 1000, 0.05, 10) # ~5.7%
</code></pre>
</article>
<article class="doc-entry" id="doc-bondi-mass-step">
<h3><a class="doc-anchor" href="#doc-bondi-mass-step">#</a> <code>bondi_mass_step</code></h3>
<p><code>bondi_mass_step</code> — single-step update of <code>bondi mass</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p bondi_mass_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bondprc">
<h3><a class="doc-anchor" href="#doc-bondprc">#</a> <code>bondprc</code></h3>
<p><code>bondprc</code> — operation <code>bondprc</code>. Alias for <code>bond_price</code>. Category: *finance (extended)*.</p>
<pre><code class="lang-perl">p bondprc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bondyld">
<h3><a class="doc-anchor" href="#doc-bondyld">#</a> <code>bondyld</code></h3>
<p><code>bondyld</code> — operation <code>bondyld</code>. Alias for <code>bond_yield</code>. Category: *finance (extended)*.</p>
<pre><code class="lang-perl">p bondyld $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bool-each">
<h3><a class="doc-anchor" href="#doc-bool-each">#</a> <code>bool_each</code></h3>
<p><code>bool_each</code> — boolean helper <code>each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p bool_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bool-to-int">
<h3><a class="doc-anchor" href="#doc-bool-to-int">#</a> <code>bool_to_int</code></h3>
<p><code>bool_to_int</code> — convert from <code>bool</code> to <code>int</code>. Category: *boolean combinators*.</p>
<pre><code class="lang-perl">p bool_to_int $value
</code></pre>
</article>
<article class="doc-entry" id="doc-boole-int">
<h3><a class="doc-anchor" href="#doc-boole-int">#</a> <code>boole_int</code></h3>
<p><code>boole_int</code> — operation <code>boole int</code>. Alias for <code>boole_rule</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p boole_int $x
</code></pre>
</article>
<article class="doc-entry" id="doc-boole-rule">
<h3><a class="doc-anchor" href="#doc-boole-rule">#</a> <code>boole_rule</code></h3>
<p><code>boole_rule</code> — operation <code>boole rule</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p boole_rule $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bootstrap-resample">
<h3><a class="doc-anchor" href="#doc-bootstrap-resample">#</a> <code>bootstrap_resample</code></h3>
<p><code>bootstrap_resample(xs, n=len(xs), seed=0) → array</code> — <code>n</code> samples drawn with replacement from <code>xs</code> using a deterministic PRNG.</p>
<pre><code class="lang-perl">p bootstrap_resample([1,2,3,4,5], 1000, 42)
</code></pre>
</article>
<article class="doc-entry" id="doc-bootstrap-se-estimate">
<h3><a class="doc-anchor" href="#doc-bootstrap-se-estimate">#</a> <code>bootstrap_se_estimate</code></h3>
<p><code>bootstrap_se_estimate</code> — bootstrap resampling helper <code>se estimate</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p bootstrap_se_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-borda-count-step">
<h3><a class="doc-anchor" href="#doc-borda-count-step">#</a> <code>borda_count_step</code></h3>
<p><code>borda_count_step</code> — single-step update of <code>borda count</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p borda_count_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-borders-of-string">
<h3><a class="doc-anchor" href="#doc-borders-of-string">#</a> <code>borders_of_string</code></h3>
<p><code>borders_of_string</code> — operation <code>borders of string</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p borders_of_string $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bornhuetter-ferguson">
<h3><a class="doc-anchor" href="#doc-bornhuetter-ferguson">#</a> <code>bornhuetter_ferguson</code></h3>
<p><code>bornhuetter_ferguson</code> — operation <code>bornhuetter ferguson</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p bornhuetter_ferguson $x
</code></pre>
</article>
<article class="doc-entry" id="doc-boruvka-step">
<h3><a class="doc-anchor" href="#doc-boruvka-step">#</a> <code>boruvka_step</code></h3>
<p><code>boruvka_step</code> — single-step update of <code>boruvka</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p boruvka_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bose-einstein-g">
<h3><a class="doc-anchor" href="#doc-bose-einstein-g">#</a> <code>bose_einstein_g</code></h3>
<p><code>bose_einstein_g</code> — operation <code>bose einstein g</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p bose_einstein_g $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bose-einstein-pmf">
<h3><a class="doc-anchor" href="#doc-bose-einstein-pmf">#</a> <code>bose_einstein_pmf</code></h3>
<p><code>bose_einstein_pmf</code> — operation <code>bose einstein pmf</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p bose_einstein_pmf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-boston-mechanism-step">
<h3><a class="doc-anchor" href="#doc-boston-mechanism-step">#</a> <code>boston_mechanism_step</code></h3>
<p><code>boston_mechanism_step</code> — single-step update of <code>boston mechanism</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p boston_mechanism_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-both">
<h3><a class="doc-anchor" href="#doc-both">#</a> <code>both</code></h3>
<p><code>both</code> — operation <code>both</code>. Category: *boolean combinators*.</p>
<pre><code class="lang-perl">p both $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bottom-k-max-heap">
<h3><a class="doc-anchor" href="#doc-bottom-k-max-heap">#</a> <code>bottom_k_max_heap</code></h3>
<p><code>bottom_k_max_heap</code> — operation <code>bottom k max heap</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p bottom_k_max_heap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bottom-n-by">
<h3><a class="doc-anchor" href="#doc-bottom-n-by">#</a> <code>bottom_n_by</code></h3>
<p><code>bottom_n_by</code> — operation <code>bottom n by</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p bottom_n_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bowley-skewness">
<h3><a class="doc-anchor" href="#doc-bowley-skewness">#</a> <code>bowley_skewness</code></h3>
<p><code>bowley_skewness</code> — operation <code>bowley skewness</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p bowley_skewness $x
</code></pre>
</article>
<article class="doc-entry" id="doc-box-blur-kernel">
<h3><a class="doc-anchor" href="#doc-box-blur-kernel">#</a> <code>box_blur_kernel</code></h3>
<p><code>box_blur_kernel</code> — convolution kernel of <code>box blur</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p box_blur_kernel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-box-pierce-test">
<h3><a class="doc-anchor" href="#doc-box-pierce-test">#</a> <code>box_pierce_test</code></h3>
<p><code>box_pierce_test</code> — statistical test of <code>box pierce</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p box_pierce_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-boyer-lindquist-step">
<h3><a class="doc-anchor" href="#doc-boyer-lindquist-step">#</a> <code>boyer_lindquist_step</code></h3>
<p><code>boyer_lindquist_step</code> — single-step update of <code>boyer lindquist</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p boyer_lindquist_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-boyer-moore-majority">
<h3><a class="doc-anchor" href="#doc-boyer-moore-majority">#</a> <code>boyer_moore_majority</code></h3>
<p><code>boyer_moore_majority</code> — operation <code>boyer moore majority</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p boyer_moore_majority $x
</code></pre>
</article>
<article class="doc-entry" id="doc-boykov-kolmogorov-step">
<h3><a class="doc-anchor" href="#doc-boykov-kolmogorov-step">#</a> <code>boykov_kolmogorov_step</code></h3>
<p><code>boykov_kolmogorov_step</code> — single-step update of <code>boykov kolmogorov</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p boykov_kolmogorov_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bp-elevation">
<h3><a class="doc-anchor" href="#doc-bp-elevation">#</a> <code>bp_elevation</code></h3>
<p><code>bp_elevation</code> — operation <code>bp elevation</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p bp_elevation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bpm-to-midi-tick-us">
<h3><a class="doc-anchor" href="#doc-bpm-to-midi-tick-us">#</a> <code>bpm_to_midi_tick_us</code></h3>
<p><code>bpm_to_midi_tick_us</code> — convert from <code>bpm</code> to <code>midi tick us</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p bpm_to_midi_tick_us $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bpm-to-period">
<h3><a class="doc-anchor" href="#doc-bpm-to-period">#</a> <code>bpm_to_period</code></h3>
<p><code>bpm_to_period</code> — convert from <code>bpm</code> to <code>period</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p bpm_to_period $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bpm-to-spb">
<h3><a class="doc-anchor" href="#doc-bpm-to-spb">#</a> <code>bpm_to_spb</code></h3>
<p><code>bpm_to_spb</code> — convert from <code>bpm</code> to <code>spb</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p bpm_to_spb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bracelet-count">
<h3><a class="doc-anchor" href="#doc-bracelet-count">#</a> <code>bracelet_count</code></h3>
<p><code>bracelet_count</code> — count of <code>bracelet</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p bracelet_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bracket">
<h3><a class="doc-anchor" href="#doc-bracket">#</a> <code>bracket</code></h3>
<p><code>bracket</code> — operation <code>bracket</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p bracket $x
</code></pre>
</article>
<article class="doc-entry" id="doc-braille">
<h3><a class="doc-anchor" href="#doc-braille">#</a> <code>braille</code></h3>
<p><code>braille</code> — operation <code>braille</code>. Alias for <code>braille_encode</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p braille $x
</code></pre>
</article>
<article class="doc-entry" id="doc-braille-encode">
<h3><a class="doc-anchor" href="#doc-braille-encode">#</a> <code>braille_encode</code></h3>
<p><code>braille_encode</code> — encode of <code>braille</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p braille_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-branch-and-bound-step">
<h3><a class="doc-anchor" href="#doc-branch-and-bound-step">#</a> <code>branch_and_bound_step</code></h3>
<p><code>branch_and_bound_step</code> — single-step update of <code>branch and bound</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p branch_and_bound_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-branch-length-substitutions">
<h3><a class="doc-anchor" href="#doc-branch-length-substitutions">#</a> <code>branch_length_substitutions</code></h3>
<p><code>branch_length_substitutions</code> — operation <code>branch length substitutions</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p branch_length_substitutions $x
</code></pre>
</article>
<article class="doc-entry" id="doc-brans-dicke-step">
<h3><a class="doc-anchor" href="#doc-brans-dicke-step">#</a> <code>brans_dicke_step</code></h3>
<p><code>brans_dicke_step</code> — single-step update of <code>brans dicke</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p brans_dicke_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-braycurtis-dist">
<h3><a class="doc-anchor" href="#doc-braycurtis-dist">#</a> <code>braycurtis_dist</code></h3>
<p><code>braycurtis_dist(a, b) → number</code> — <code>Σ|aᵢ-bᵢ| / Σ|aᵢ+bᵢ|</code>. Ecological-similarity classic.</p>
</article>
<article class="doc-entry" id="doc-brayton-efficiency">
<h3><a class="doc-anchor" href="#doc-brayton-efficiency">#</a> <code>brayton_efficiency</code></h3>
<p><code>brayton_efficiency</code> — operation <code>brayton efficiency</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p brayton_efficiency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-break-even">
<h3><a class="doc-anchor" href="#doc-break-even">#</a> <code>break_even</code></h3>
<p><code>break_even</code> — operation <code>break even</code>. Category: *finance*.</p>
<pre><code class="lang-perl">p break_even $x
</code></pre>
</article>
<article class="doc-entry" id="doc-break-even-price">
<h3><a class="doc-anchor" href="#doc-break-even-price">#</a> <code>break_even_price</code></h3>
<p><code>break_even_price(fixed_cost, qty, variable_cost) → number</code> — price needed at given quantity: <code>fixed/qty + variable</code>.</p>
<pre><code class="lang-perl">p break_even_price(10000, 1000, 15)
</code></pre>
</article>
<article class="doc-entry" id="doc-break-even-qty">
<h3><a class="doc-anchor" href="#doc-break-even-qty">#</a> <code>break_even_qty</code></h3>
<p><code>break_even_qty(fixed_cost, price, variable_cost) → number</code> — units to sell to cover fixed + variable: <code>fixed / (price - variable)</code>.</p>
<pre><code class="lang-perl">p break_even_qty(10000, 25, 15)
</code></pre>
</article>
<article class="doc-entry" id="doc-break-fn">
<h3><a class="doc-anchor" href="#doc-break-fn">#</a> <code>break_fn</code></h3>
<p><code>break_fn</code> — operation <code>break fn</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p break_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-breakeven">
<h3><a class="doc-anchor" href="#doc-breakeven">#</a> <code>breakeven</code></h3>
<p><code>breakeven</code> — operation <code>breakeven</code>. Alias for <code>break_even</code>. Category: *finance*.</p>
<pre><code class="lang-perl">p breakeven $x
</code></pre>
</article>
<article class="doc-entry" id="doc-brent">
<h3><a class="doc-anchor" href="#doc-brent">#</a> <code>brent</code></h3>
<p><code>brent</code> — operation <code>brent</code>. Alias for <code>brent_root</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p brent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-brent-root">
<h3><a class="doc-anchor" href="#doc-brent-root">#</a> <code>brent_root</code></h3>
<p><code>brent_root</code> — operation <code>brent root</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p brent_root $x
</code></pre>
</article>
<article class="doc-entry" id="doc-breusch-godfrey">
<h3><a class="doc-anchor" href="#doc-breusch-godfrey">#</a> <code>breusch_godfrey</code></h3>
<p><code>breusch_godfrey</code> — operation <code>breusch godfrey</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p breusch_godfrey $x
</code></pre>
</article>
<article class="doc-entry" id="doc-breusch-godfrey-test">
<h3><a class="doc-anchor" href="#doc-breusch-godfrey-test">#</a> <code>breusch_godfrey_test</code></h3>
<p><code>breusch_godfrey_test</code> — statistical test of <code>breusch godfrey</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p breusch_godfrey_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-breusch-pagan-lm">
<h3><a class="doc-anchor" href="#doc-breusch-pagan-lm">#</a> <code>breusch_pagan_lm</code></h3>
<p><code>breusch_pagan_lm</code> — operation <code>breusch pagan lm</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p breusch_pagan_lm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-breusch-pagan-test">
<h3><a class="doc-anchor" href="#doc-breusch-pagan-test">#</a> <code>breusch_pagan_test</code></h3>
<p><code>breusch_pagan_test</code> — statistical test of <code>breusch pagan</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p breusch_pagan_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-brewster">
<h3><a class="doc-anchor" href="#doc-brewster">#</a> <code>brewster</code></h3>
<p><code>brewster</code> — operation <code>brewster</code>. Alias for <code>brewster_angle</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p brewster $x
</code></pre>
</article>
<article class="doc-entry" id="doc-brewster-angle">
<h3><a class="doc-anchor" href="#doc-brewster-angle">#</a> <code>brewster_angle</code></h3>
<p><code>brewster_angle</code> — operation <code>brewster angle</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p brewster_angle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bridge-edge">
<h3><a class="doc-anchor" href="#doc-bridge-edge">#</a> <code>bridge_edge</code></h3>
<p><code>bridge_edge</code> — operation <code>bridge edge</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p bridge_edge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bridges">
<h3><a class="doc-anchor" href="#doc-bridges">#</a> <code>bridges</code></h3>
<p><code>bridges</code> — operation <code>bridges</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p bridges $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bridges-edges">
<h3><a class="doc-anchor" href="#doc-bridges-edges">#</a> <code>bridges_edges</code></h3>
<p><code>bridges_edges</code> — operation <code>bridges edges</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p bridges_edges $x
</code></pre>
</article>
<article class="doc-entry" id="doc-brier-score">
<h3><a class="doc-anchor" href="#doc-brier-score">#</a> <code>brier_score</code></h3>
<p><code>brier_score</code> — score of <code>brier</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p brier_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bright-blue">
<h3><a class="doc-anchor" href="#doc-bright-blue">#</a> <code>bright_blue</code></h3>
<p><code>bright_blue</code> — operation <code>bright blue</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bright_blue $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bright-cyan">
<h3><a class="doc-anchor" href="#doc-bright-cyan">#</a> <code>bright_cyan</code></h3>
<p><code>bright_cyan</code> — operation <code>bright cyan</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bright_cyan $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bright-green">
<h3><a class="doc-anchor" href="#doc-bright-green">#</a> <code>bright_green</code></h3>
<p><code>bright_green</code> — operation <code>bright green</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bright_green $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bright-magenta">
<h3><a class="doc-anchor" href="#doc-bright-magenta">#</a> <code>bright_magenta</code></h3>
<p><code>bright_magenta</code> — operation <code>bright magenta</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bright_magenta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bright-red">
<h3><a class="doc-anchor" href="#doc-bright-red">#</a> <code>bright_red</code></h3>
<p><code>bright_red</code> — operation <code>bright red</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bright_red $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bright-white">
<h3><a class="doc-anchor" href="#doc-bright-white">#</a> <code>bright_white</code></h3>
<p><code>bright_white</code> — operation <code>bright white</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bright_white $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bright-yellow">
<h3><a class="doc-anchor" href="#doc-bright-yellow">#</a> <code>bright_yellow</code></h3>
<p><code>bright_yellow</code> — operation <code>bright yellow</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p bright_yellow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-brkf">
<h3><a class="doc-anchor" href="#doc-brkf">#</a> <code>brkf</code></h3>
<p><code>brkf</code> — operation <code>brkf</code>. Alias for <code>break_fn</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p brkf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-broadcast-channel-new">
<h3><a class="doc-anchor" href="#doc-broadcast-channel-new">#</a> <code>broadcast_channel_new</code></h3>
<p><code>broadcast_channel_new() → broadcast_channel</code> — fan-out channel: every subscriber receives every value.</p>
</article>
<article class="doc-entry" id="doc-broadcast-channel-publish">
<h3><a class="doc-anchor" href="#doc-broadcast-channel-publish">#</a> <code>broadcast_channel_publish</code></h3>
<p><code>broadcast_channel_publish</code> — operation <code>broadcast channel publish</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p broadcast_channel_publish $x
</code></pre>
</article>
<article class="doc-entry" id="doc-broadcast-channel-subscribe">
<h3><a class="doc-anchor" href="#doc-broadcast-channel-subscribe">#</a> <code>broadcast_channel_subscribe</code></h3>
<p><code>broadcast_channel_subscribe(ch) → receiver</code> — create a new receiver subscribed to all future messages.</p>
</article>
<article class="doc-entry" id="doc-bron-kerbosch">
<h3><a class="doc-anchor" href="#doc-bron-kerbosch">#</a> <code>bron_kerbosch</code></h3>
<p><code>bron_kerbosch</code> — operation <code>bron kerbosch</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p bron_kerbosch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-brotli-distance-code-count">
<h3><a class="doc-anchor" href="#doc-brotli-distance-code-count">#</a> <code>brotli_distance_code_count</code></h3>
<p><code>brotli_distance_code_count</code> — count of <code>brotli distance code</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p brotli_distance_code_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-brotli-encode-meta">
<h3><a class="doc-anchor" href="#doc-brotli-encode-meta">#</a> <code>brotli_encode_meta</code></h3>
<p><code>brotli_encode_meta</code> — operation <code>brotli encode meta</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p brotli_encode_meta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-brotli-huffman-table">
<h3><a class="doc-anchor" href="#doc-brotli-huffman-table">#</a> <code>brotli_huffman_table</code></h3>
<p><code>brotli_huffman_table</code> — lookup table of <code>brotli huffman</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p brotli_huffman_table $x
</code></pre>
</article>
<article class="doc-entry" id="doc-brotli-meta-block">
<h3><a class="doc-anchor" href="#doc-brotli-meta-block">#</a> <code>brotli_meta_block</code></h3>
<p><code>brotli_meta_block</code> — operation <code>brotli meta block</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p brotli_meta_block $x
</code></pre>
</article>
<article class="doc-entry" id="doc-brown-york-quasilocal">
<h3><a class="doc-anchor" href="#doc-brown-york-quasilocal">#</a> <code>brown_york_quasilocal</code></h3>
<p><code>brown_york_quasilocal</code> — operation <code>brown york quasilocal</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p brown_york_quasilocal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-brunt-vaisala-full">
<h3><a class="doc-anchor" href="#doc-brunt-vaisala-full">#</a> <code>brunt_vaisala_full</code></h3>
<p><code>brunt_vaisala_full</code> — operation <code>brunt vaisala full</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p brunt_vaisala_full $x
</code></pre>
</article>
<article class="doc-entry" id="doc-brzozowski-derivative">
<h3><a class="doc-anchor" href="#doc-brzozowski-derivative">#</a> <code>brzozowski_derivative</code></h3>
<p><code>brzozowski_derivative</code> — operation <code>brzozowski derivative</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p brzozowski_derivative $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bs-call">
<h3><a class="doc-anchor" href="#doc-bs-call">#</a> <code>bs_call</code></h3>
<p><code>bs_call</code> — operation <code>bs call</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p bs_call $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bs-delta">
<h3><a class="doc-anchor" href="#doc-bs-delta">#</a> <code>bs_delta</code></h3>
<p><code>bs_delta</code> (aliases <code>bsdelta</code>, <code>option_delta</code>) computes the Black-Scholes delta (∂C/∂S). Args: S, K, T, r, sigma.</p>
<pre><code class="lang-perl">p bsdelta(100, 100, 1, 0.05, 0.2) # ≈ 0.64
</code></pre>
</article>
<article class="doc-entry" id="doc-bs-gamma">
<h3><a class="doc-anchor" href="#doc-bs-gamma">#</a> <code>bs_gamma</code></h3>
<p><code>bs_gamma</code> computes the Black-Scholes gamma (∂²C/∂S²). Measures convexity of option value.</p>
<pre><code class="lang-perl">p bsgamma(100, 100, 1, 0.05, 0.2) # ≈ 0.019
</code></pre>
</article>
<article class="doc-entry" id="doc-bs-put">
<h3><a class="doc-anchor" href="#doc-bs-put">#</a> <code>bs_put</code></h3>
<p><code>bs_put</code> — operation <code>bs put</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p bs_put $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bs-rho">
<h3><a class="doc-anchor" href="#doc-bs-rho">#</a> <code>bs_rho</code></h3>
<p><code>bs_rho</code> computes the Black-Scholes rho (∂C/∂r). Sensitivity to interest rate.</p>
<pre><code class="lang-perl">p bsrho(100, 100, 1, 0.05, 0.2) # ≈ 46
</code></pre>
</article>
<article class="doc-entry" id="doc-bs-rho-call">
<h3><a class="doc-anchor" href="#doc-bs-rho-call">#</a> <code>bs_rho_call</code></h3>
<p><code>bs_rho_call</code> — operation <code>bs rho call</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p bs_rho_call $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bs-theta">
<h3><a class="doc-anchor" href="#doc-bs-theta">#</a> <code>bs_theta</code></h3>
<p><code>bs_theta</code> computes the Black-Scholes theta (∂C/∂t). Time decay per unit time.</p>
<pre><code class="lang-perl">p bstheta(100, 100, 1, 0.05, 0.2) # negative (time decay)
</code></pre>
</article>
<article class="doc-entry" id="doc-bs-theta-call">
<h3><a class="doc-anchor" href="#doc-bs-theta-call">#</a> <code>bs_theta_call</code></h3>
<p><code>bs_theta_call</code> — operation <code>bs theta call</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p bs_theta_call $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bs-vega">
<h3><a class="doc-anchor" href="#doc-bs-vega">#</a> <code>bs_vega</code></h3>
<p><code>bs_vega</code> computes the Black-Scholes vega (∂C/∂σ). Sensitivity to volatility.</p>
<pre><code class="lang-perl">p bsvega(100, 100, 1, 0.05, 0.2) # ≈ 37.5
</code></pre>
</article>
<article class="doc-entry" id="doc-bsa-dubois">
<h3><a class="doc-anchor" href="#doc-bsa-dubois">#</a> <code>bsa_dubois</code></h3>
<p><code>bsa_dubois</code> — operation <code>bsa dubois</code>. Alias for <code>body_surface_area_dubois</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p bsa_dubois $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bsearch">
<h3><a class="doc-anchor" href="#doc-bsearch">#</a> <code>bsearch</code></h3>
<p><code>bsearch</code> — operation <code>bsearch</code>. Alias for <code>binary_search</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p bsearch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bsgs-discrete-log">
<h3><a class="doc-anchor" href="#doc-bsgs-discrete-log">#</a> <code>bsgs_discrete_log</code></h3>
<p><code>bsgs_discrete_log</code> — operation <code>bsgs discrete log</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p bsgs_discrete_log $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bsize">
<h3><a class="doc-anchor" href="#doc-bsize">#</a> <code>bsize</code></h3>
<p><code>bsize</code> — operation <code>bsize</code>. Alias for <code>byte_size</code>. Category: *misc / utility*.</p>
<pre><code class="lang-perl">p bsize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-btc-addr-check">
<h3><a class="doc-anchor" href="#doc-btc-addr-check">#</a> <code>btc_addr_check</code></h3>
<p><code>btc_addr_check</code> — operation <code>btc addr check</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p btc_addr_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-btch">
<h3><a class="doc-anchor" href="#doc-btch">#</a> <code>btch</code></h3>
<p><code>btch</code> — operation <code>btch</code>. Alias for <code>batched</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p btch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-btrim">
<h3><a class="doc-anchor" href="#doc-btrim">#</a> <code>btrim</code></h3>
<p><code>btrim</code> — operation <code>btrim</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p btrim $x
</code></pre>
</article>
<article class="doc-entry" id="doc-btu-to-joules">
<h3><a class="doc-anchor" href="#doc-btu-to-joules">#</a> <code>btu_to_joules</code></h3>
<p><code>btu_to_joules</code> — convert from <code>btu</code> to <code>joules</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p btu_to_joules $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bucket">
<h3><a class="doc-anchor" href="#doc-bucket">#</a> <code>bucket</code></h3>
<p><code>bucket</code> — operation <code>bucket</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p bucket $x
</code></pre>
</article>
<article class="doc-entry" id="doc-buffer-capacity-acid-base">
<h3><a class="doc-anchor" href="#doc-buffer-capacity-acid-base">#</a> <code>buffer_capacity_acid_base</code></h3>
<p><code>buffer_capacity_acid_base</code> — operation <code>buffer capacity acid base</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p buffer_capacity_acid_base $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bulirsch-stoer-step">
<h3><a class="doc-anchor" href="#doc-bulirsch-stoer-step">#</a> <code>bulirsch_stoer_step</code></h3>
<p><code>bulirsch_stoer_step</code> — single-step update of <code>bulirsch stoer</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p bulirsch_stoer_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-buoyancy-force">
<h3><a class="doc-anchor" href="#doc-buoyancy-force">#</a> <code>buoyancy_force</code></h3>
<p><code>buoyancy_force(fluid_density, submerged_volume, g=9.81) → number</code> — <code>ρ · V · g</code> (Archimedes).</p>
</article>
<article class="doc-entry" id="doc-burr-xii-cdf">
<h3><a class="doc-anchor" href="#doc-burr-xii-cdf">#</a> <code>burr_xii_cdf</code></h3>
<p><code>burr_xii_cdf</code> — operation <code>burr xii cdf</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p burr_xii_cdf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-burr-xii-pdf">
<h3><a class="doc-anchor" href="#doc-burr-xii-pdf">#</a> <code>burr_xii_pdf</code></h3>
<p><code>burr_xii_pdf</code> — operation <code>burr xii pdf</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p burr_xii_pdf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-business-days-between">
<h3><a class="doc-anchor" href="#doc-business-days-between">#</a> <code>business_days_between</code></h3>
<p><code>business_days_between</code> — operation <code>business days between</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p business_days_between $x
</code></pre>
</article>
<article class="doc-entry" id="doc-busy-beaver">
<h3><a class="doc-anchor" href="#doc-busy-beaver">#</a> <code>busy_beaver</code></h3>
<p><code>busy_beaver</code> — operation <code>busy beaver</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p busy_beaver $x
</code></pre>
</article>
<article class="doc-entry" id="doc-butlast">
<h3><a class="doc-anchor" href="#doc-butlast">#</a> <code>butlast</code></h3>
<p><code>butlast</code> — operation <code>butlast</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p butlast $x
</code></pre>
</article>
<article class="doc-entry" id="doc-butler-volmer-current">
<h3><a class="doc-anchor" href="#doc-butler-volmer-current">#</a> <code>butler_volmer_current</code></h3>
<p><code>butler_volmer_current</code> — operation <code>butler volmer current</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p butler_volmer_current $x
</code></pre>
</article>
<article class="doc-entry" id="doc-butter-hp-mag">
<h3><a class="doc-anchor" href="#doc-butter-hp-mag">#</a> <code>butter_hp_mag</code></h3>
<p><code>butter_hp_mag</code> — operation <code>butter hp mag</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p butter_hp_mag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-butter-lp-re">
<h3><a class="doc-anchor" href="#doc-butter-lp-re">#</a> <code>butter_lp_re</code></h3>
<p><code>butter_lp_re</code> — operation <code>butter lp re</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p butter_lp_re $x
</code></pre>
</article>
<article class="doc-entry" id="doc-butterworth-order">
<h3><a class="doc-anchor" href="#doc-butterworth-order">#</a> <code>butterworth_order</code></h3>
<p><code>butterworth_order</code> — operation <code>butterworth order</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p butterworth_order $x
</code></pre>
</article>
<article class="doc-entry" id="doc-butterworth-prewarp">
<h3><a class="doc-anchor" href="#doc-butterworth-prewarp">#</a> <code>butterworth_prewarp</code></h3>
<p><code>butterworth_prewarp</code> — operation <code>butterworth prewarp</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p butterworth_prewarp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bwt-decode">
<h3><a class="doc-anchor" href="#doc-bwt-decode">#</a> <code>bwt_decode</code></h3>
<p><code>bwt_decode</code> — Burrows-Wheeler transform <code>decode</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p bwt_decode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bwt-encode">
<h3><a class="doc-anchor" href="#doc-bwt-encode">#</a> <code>bwt_encode</code></h3>
<p><code>bwt_encode</code> — Burrows-Wheeler transform <code>encode</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p bwt_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bwt-invert">
<h3><a class="doc-anchor" href="#doc-bwt-invert">#</a> <code>bwt_invert</code></h3>
<p><code>bwt_invert(data, index) → string</code> — invert the Burrows-Wheeler transform.</p>
<pre><code class="lang-perl">p bwt_invert("nnbaaa", 3) # "banana"
</code></pre>
</article>
<article class="doc-entry" id="doc-bwt-transform">
<h3><a class="doc-anchor" href="#doc-bwt-transform">#</a> <code>bwt_transform</code></h3>
<p><code>bwt_transform(s) → {data, index}</code> — Burrows-Wheeler transform: returns last column + primary index.</p>
<pre><code class="lang-perl">p bwt_transform("banana") # {data: "nnbaaa", index: 3}
</code></pre>
</article>
<article class="doc-entry" id="doc-byte-length">
<h3><a class="doc-anchor" href="#doc-byte-length">#</a> <code>byte_length</code></h3>
<p><code>byte_length</code> — operation <code>byte length</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p byte_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-byte-size">
<h3><a class="doc-anchor" href="#doc-byte-size">#</a> <code>byte_size</code></h3>
<p><code>byte_size</code> — operation <code>byte size</code>. Category: *misc / utility*.</p>
<pre><code class="lang-perl">p byte_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bytecode-disasm-step">
<h3><a class="doc-anchor" href="#doc-bytecode-disasm-step">#</a> <code>bytecode_disasm_step</code></h3>
<p><code>bytecode_disasm_step</code> — single-step update of <code>bytecode disasm</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p bytecode_disasm_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-bytes-to-bits">
<h3><a class="doc-anchor" href="#doc-bytes-to-bits">#</a> <code>bytes_to_bits</code></h3>
<p><code>bytes_to_bits</code> — convert from <code>bytes</code> to <code>bits</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p bytes_to_bits $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bytes-to-gb">
<h3><a class="doc-anchor" href="#doc-bytes-to-gb">#</a> <code>bytes_to_gb</code></h3>
<p><code>bytes_to_gb</code> — convert from <code>bytes</code> to <code>gb</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p bytes_to_gb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bytes-to-hex-str">
<h3><a class="doc-anchor" href="#doc-bytes-to-hex-str">#</a> <code>bytes_to_hex_str</code></h3>
<p><code>bytes_to_hex_str</code> — convert from <code>bytes</code> to <code>hex str</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p bytes_to_hex_str $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bytes-to-ip">
<h3><a class="doc-anchor" href="#doc-bytes-to-ip">#</a> <code>bytes_to_ip</code></h3>
<p><code>bytes_to_ip</code> — convert from <code>bytes</code> to <code>ip</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p bytes_to_ip $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bytes-to-kb">
<h3><a class="doc-anchor" href="#doc-bytes-to-kb">#</a> <code>bytes_to_kb</code></h3>
<p><code>bytes_to_kb</code> — convert from <code>bytes</code> to <code>kb</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p bytes_to_kb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bytes-to-mac">
<h3><a class="doc-anchor" href="#doc-bytes-to-mac">#</a> <code>bytes_to_mac</code></h3>
<p><code>bytes_to_mac</code> — convert from <code>bytes</code> to <code>mac</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p bytes_to_mac $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bytes-to-mb">
<h3><a class="doc-anchor" href="#doc-bytes-to-mb">#</a> <code>bytes_to_mb</code></h3>
<p><code>bytes_to_mb</code> — convert from <code>bytes</code> to <code>mb</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p bytes_to_mb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-bz2-encode-step">
<h3><a class="doc-anchor" href="#doc-bz2-encode-step">#</a> <code>bz2_encode_step</code></h3>
<p><code>bz2_encode_step</code> — single-step update of <code>bz2 encode</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p bz2_encode_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-c256">
<h3><a class="doc-anchor" href="#doc-c256">#</a> <code>c256</code></h3>
<p><code>c256</code> — operation <code>c256</code>. Alias for <code>color256</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p c256 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-c2s">
<h3><a class="doc-anchor" href="#doc-c2s">#</a> <code>c2s</code></h3>
<p><code>c2s</code> — operation <code>c2s</code>. Alias for <code>camel_to_snake</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p c2s $x
</code></pre>
</article>
<article class="doc-entry" id="doc-c-parallel">
<h3><a class="doc-anchor" href="#doc-c-parallel">#</a> <code>c_parallel</code></h3>
<p><code>c_parallel</code> — operation <code>c parallel</code>. Alias for <code>capacitance_parallel</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p c_parallel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-c-series">
<h3><a class="doc-anchor" href="#doc-c-series">#</a> <code>c_series</code></h3>
<p><code>c_series</code> — operation <code>c series</code>. Alias for <code>capacitance_series</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p c_series $x
</code></pre>
</article>
<article class="doc-entry" id="doc-c-to-f">
<h3><a class="doc-anchor" href="#doc-c-to-f">#</a> <code>c_to_f</code></h3>
<p><code>c_to_f</code> — convert from <code>c</code> to <code>f</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p c_to_f $value
</code></pre>
</article>
<article class="doc-entry" id="doc-c-to-k">
<h3><a class="doc-anchor" href="#doc-c-to-k">#</a> <code>c_to_k</code></h3>
<p><code>c_to_k</code> — convert from <code>c</code> to <code>k</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p c_to_k $value
</code></pre>
</article>
<article class="doc-entry" id="doc-cabling-pair-signature">
<h3><a class="doc-anchor" href="#doc-cabling-pair-signature">#</a> <code>cabling_pair_signature</code></h3>
<p><code>cabling_pair_signature</code> — operation <code>cabling pair signature</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p cabling_pair_signature $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cache-clear">
<h3><a class="doc-anchor" href="#doc-cache-clear">#</a> <code>cache_clear</code></h3>
<p><code>cache_clear</code> — operation <code>cache clear</code>. Category: *caching*.</p>
<pre><code class="lang-perl">p cache_clear $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cache-control-parse">
<h3><a class="doc-anchor" href="#doc-cache-control-parse">#</a> <code>cache_control_parse</code></h3>
<p><code>cache_control_parse</code> — operation <code>cache control parse</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p cache_control_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cache-exists">
<h3><a class="doc-anchor" href="#doc-cache-exists">#</a> <code>cache_exists</code></h3>
<p><code>cache_exists</code> — operation <code>cache exists</code>. Category: *caching*.</p>
<pre><code class="lang-perl">p cache_exists $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cache-stats">
<h3><a class="doc-anchor" href="#doc-cache-stats">#</a> <code>cache_stats</code></h3>
<p><code>cache_stats</code> — operation <code>cache stats</code>. Category: *caching*.</p>
<pre><code class="lang-perl">p cache_stats $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cacheview">
<h3><a class="doc-anchor" href="#doc-cacheview">#</a> <code>cacheview</code></h3>
<p><code>cacheview</code> — operation <code>cacheview</code>. Category: *caching*.</p>
<pre><code class="lang-perl">p cacheview $x
</code></pre>
</article>
<article class="doc-entry" id="doc-caesar-shift">
<h3><a class="doc-anchor" href="#doc-caesar-shift">#</a> <code>caesar_shift</code></h3>
<p><code>caesar_shift</code> — operation <code>caesar shift</code>. Category: *string*.</p>
<pre><code class="lang-perl">p caesar_shift $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cagr">
<h3><a class="doc-anchor" href="#doc-cagr">#</a> <code>cagr</code></h3>
<p><code>cagr(start_value, end_value, periods) → number</code> — Compound Annual Growth Rate: <code>(end/start)^(1/periods) - 1</code>.</p>
<pre><code class="lang-perl">p cagr(10000, 25000, 7)
</code></pre>
</article>
<article class="doc-entry" id="doc-cake-number">
<h3><a class="doc-anchor" href="#doc-cake-number">#</a> <code>cake_number</code></h3>
<p><code>cake_number</code> — operation <code>cake number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p cake_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cal-to-joules">
<h3><a class="doc-anchor" href="#doc-cal-to-joules">#</a> <code>cal_to_joules</code></h3>
<p><code>cal_to_joules</code> — convert from <code>cal</code> to <code>joules</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p cal_to_joules $value
</code></pre>
</article>
<article class="doc-entry" id="doc-calmar-ratio">
<h3><a class="doc-anchor" href="#doc-calmar-ratio">#</a> <code>calmar_ratio</code></h3>
<p><code>calmar_ratio(returns) → number</code> — CAGR divided by max drawdown magnitude; higher is better.</p>
<pre><code class="lang-perl">p calmar_ratio(\@returns)
</code></pre>
</article>
<article class="doc-entry" id="doc-calorimeter-dt">
<h3><a class="doc-anchor" href="#doc-calorimeter-dt">#</a> <code>calorimeter_dt</code></h3>
<p><code>calorimeter_dt</code> — operation <code>calorimeter dt</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p calorimeter_dt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-calorimetric-heat-battery">
<h3><a class="doc-anchor" href="#doc-calorimetric-heat-battery">#</a> <code>calorimetric_heat_battery</code></h3>
<p><code>calorimetric_heat_battery</code> — operation <code>calorimetric heat battery</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p calorimetric_heat_battery $x
</code></pre>
</article>
<article class="doc-entry" id="doc-camel-to-snake">
<h3><a class="doc-anchor" href="#doc-camel-to-snake">#</a> <code>camel_to_snake</code></h3>
<p><code>camel_to_snake</code> — convert from <code>camel</code> to <code>snake</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p camel_to_snake $value
</code></pre>
</article>
<article class="doc-entry" id="doc-camel-words">
<h3><a class="doc-anchor" href="#doc-camel-words">#</a> <code>camel_words</code></h3>
<p><code>camel_words</code> — operation <code>camel words</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p camel_words $x
</code></pre>
</article>
<article class="doc-entry" id="doc-canberra-dist">
<h3><a class="doc-anchor" href="#doc-canberra-dist">#</a> <code>canberra_dist</code></h3>
<p><code>canberra_dist(a, b) → number</code> — <code>Σ |aᵢ-bᵢ| / (|aᵢ|+|bᵢ|)</code>. Robust to outliers.</p>
</article>
<article class="doc-entry" id="doc-candlestick-pattern-doji">
<h3><a class="doc-anchor" href="#doc-candlestick-pattern-doji">#</a> <code>candlestick_pattern_doji</code></h3>
<p><code>candlestick_pattern_doji(open, high, low, close, tol=0.1) → 0|1</code> — 1 if <code>|close-open|</code> is within <code>tol</code> of the high-low range (indecision bar).</p>
<pre><code class="lang-perl">p candlestick_pattern_doji(100, 101, 99, 100.05)
</code></pre>
</article>
<article class="doc-entry" id="doc-candlestick-pattern-engulfing">
<h3><a class="doc-anchor" href="#doc-candlestick-pattern-engulfing">#</a> <code>candlestick_pattern_engulfing</code></h3>
<p><code>candlestick_pattern_engulfing(prev_open, prev_close, open, close) → -1|0|1</code> — bullish (1) / bearish (-1) engulfing.</p>
<pre><code class="lang-perl">p candlestick_pattern_engulfing(101, 100, 99, 102)
</code></pre>
</article>
<article class="doc-entry" id="doc-candlestick-pattern-evening-star">
<h3><a class="doc-anchor" href="#doc-candlestick-pattern-evening-star">#</a> <code>candlestick_pattern_evening_star</code></h3>
<p><code>candlestick_pattern_evening_star([open,high,low,close] × 3) → 0|1</code> — bearish counterpart of morning star.</p>
</article>
<article class="doc-entry" id="doc-candlestick-pattern-hammer">
<h3><a class="doc-anchor" href="#doc-candlestick-pattern-hammer">#</a> <code>candlestick_pattern_hammer</code></h3>
<p><code>candlestick_pattern_hammer(open, high, low, close) → 0|1</code> — bullish reversal: small body near top, long lower shadow ≥2× body.</p>
<pre><code class="lang-perl">p candlestick_pattern_hammer(100, 102, 95, 101)
</code></pre>
</article>
<article class="doc-entry" id="doc-candlestick-pattern-morning-star">
<h3><a class="doc-anchor" href="#doc-candlestick-pattern-morning-star">#</a> <code>candlestick_pattern_morning_star</code></h3>
<p><code>candlestick_pattern_morning_star([open,high,low,close] × 3) → 0|1</code> — bullish three-bar reversal: long red, small body, long green.</p>
</article>
<article class="doc-entry" id="doc-candlestick-pattern-three-black-crows">
<h3><a class="doc-anchor" href="#doc-candlestick-pattern-three-black-crows">#</a> <code>candlestick_pattern_three_black_crows</code></h3>
<p><code>candlestick_pattern_three_black_crows([open,high,low,close] × 3) → 0|1</code> — three consecutive long red bars; strong bearish continuation.</p>
</article>
<article class="doc-entry" id="doc-candlestick-pattern-three-white-soldiers">
<h3><a class="doc-anchor" href="#doc-candlestick-pattern-three-white-soldiers">#</a> <code>candlestick_pattern_three_white_soldiers</code></h3>
<p><code>candlestick_pattern_three_white_soldiers([open,high,low,close] × 3) → 0|1</code> — three consecutive long green bars; strong bullish continuation.</p>
</article>
<article class="doc-entry" id="doc-canny-edges-full">
<h3><a class="doc-anchor" href="#doc-canny-edges-full">#</a> <code>canny_edges_full</code></h3>
<p><code>canny_edges_full(image, low=50, high=150) → matrix</code> — full 4-stage Canny pipeline: 5×5 Gaussian blur (σ=1.4), Sobel gradient + atan2 angle (mod 180°), non-max suppression along gradient direction, double-threshold + 8-connected flood-fill hysteresis. Output is binary: 255 for strong/connected-to-strong pixels, 0 otherwise.</p>
</article>
<article class="doc-entry" id="doc-canny-edges-simple">
<h3><a class="doc-anchor" href="#doc-canny-edges-simple">#</a> <code>canny_edges_simple</code></h3>
<p><code>canny_edges_simple(image, low=50, high=150) → matrix</code> — simplified Canny: Sobel gradient + double threshold (no NMS).</p>
</article>
<article class="doc-entry" id="doc-canny-threshold-step">
<h3><a class="doc-anchor" href="#doc-canny-threshold-step">#</a> <code>canny_threshold_step</code></h3>
<p><code>canny_threshold_step</code> — single-step update of <code>canny threshold</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p canny_threshold_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cap">
<h3><a class="doc-anchor" href="#doc-cap">#</a> <code>cap</code></h3>
<p><code>cap</code> — operation <code>cap</code>. Alias for <code>capitalize</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p cap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-capacitance">
<h3><a class="doc-anchor" href="#doc-capacitance">#</a> <code>capacitance</code></h3>
<p><code>capacitance</code> — operation <code>capacitance</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p capacitance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-capacitance-parallel">
<h3><a class="doc-anchor" href="#doc-capacitance-parallel">#</a> <code>capacitance_parallel</code></h3>
<p><code>capacitance_parallel</code> — operation <code>capacitance parallel</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p capacitance_parallel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-capacitance-parallel-sum">
<h3><a class="doc-anchor" href="#doc-capacitance-parallel-sum">#</a> <code>capacitance_parallel_sum</code></h3>
<p><code>capacitance_parallel_sum</code> — sum of <code>capacitance parallel</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p capacitance_parallel_sum @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-capacitance-series">
<h3><a class="doc-anchor" href="#doc-capacitance-series">#</a> <code>capacitance_series</code></h3>
<p><code>capacitance_series</code> — operation <code>capacitance series</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p capacitance_series $x
</code></pre>
</article>
<article class="doc-entry" id="doc-capacitor-charge">
<h3><a class="doc-anchor" href="#doc-capacitor-charge">#</a> <code>capacitor_charge</code></h3>
<p><code>capacitor_charge</code> — operation <code>capacitor charge</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p capacitor_charge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-capacitor-energy">
<h3><a class="doc-anchor" href="#doc-capacitor-energy">#</a> <code>capacitor_energy</code></h3>
<p><code>capacitor_energy</code> — operation <code>capacitor energy</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p capacitor_energy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-capenergy">
<h3><a class="doc-anchor" href="#doc-capenergy">#</a> <code>capenergy</code></h3>
<p><code>capenergy</code> — operation <code>capenergy</code>. Alias for <code>capacitor_energy</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p capenergy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-capg">
<h3><a class="doc-anchor" href="#doc-capg">#</a> <code>capg</code></h3>
<p><code>capg</code> — operation <code>capg</code>. Alias for <code>capture_groups</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p capg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-capitalize">
<h3><a class="doc-anchor" href="#doc-capitalize">#</a> <code>capitalize</code></h3>
<p><code>capitalize</code> — operation <code>capitalize</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p capitalize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-capitalize-words">
<h3><a class="doc-anchor" href="#doc-capitalize-words">#</a> <code>capitalize_words</code></h3>
<p><code>capitalize_words</code> — operation <code>capitalize words</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p capitalize_words $x
</code></pre>
</article>
<article class="doc-entry" id="doc-capm">
<h3><a class="doc-anchor" href="#doc-capm">#</a> <code>capm</code></h3>
<p><code>capm($risk_free, $beta, $market_return)</code> — computes expected return using the Capital Asset Pricing Model: rf + β(rm - rf).</p>
<pre><code class="lang-perl">p capm(0.02, 1.2, 0.08) # 9.2% expected return
</code></pre>
</article>
<article class="doc-entry" id="doc-capm-expected-return">
<h3><a class="doc-anchor" href="#doc-capm-expected-return">#</a> <code>capm_expected_return</code></h3>
<p><code>capm_expected_return</code> — operation <code>capm expected return</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p capm_expected_return $x
</code></pre>
</article>
<article class="doc-entry" id="doc-capture-groups">
<h3><a class="doc-anchor" href="#doc-capture-groups">#</a> <code>capture_groups</code></h3>
<p><code>capture_groups</code> — operation <code>capture groups</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p capture_groups $x
</code></pre>
</article>
<article class="doc-entry" id="doc-carmichael-q">
<h3><a class="doc-anchor" href="#doc-carmichael-q">#</a> <code>carmichael_q</code></h3>
<p><code>carmichael_q</code> — operation <code>carmichael q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p carmichael_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-carnot-efficiency">
<h3><a class="doc-anchor" href="#doc-carnot-efficiency">#</a> <code>carnot_efficiency</code></h3>
<p><code>carnot_efficiency</code> — operation <code>carnot efficiency</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p carnot_efficiency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-carrying-capacity-from-data">
<h3><a class="doc-anchor" href="#doc-carrying-capacity-from-data">#</a> <code>carrying_capacity_from_data</code></h3>
<p><code>carrying_capacity_from_data</code> — operation <code>carrying capacity from data</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p carrying_capacity_from_data $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cart-n">
<h3><a class="doc-anchor" href="#doc-cart-n">#</a> <code>cart_n</code></h3>
<p><code>cart_n</code> — operation <code>cart n</code>. Alias for <code>cartesian_product_n</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p cart_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cartan-determinant-a2">
<h3><a class="doc-anchor" href="#doc-cartan-determinant-a2">#</a> <code>cartan_determinant_a2</code></h3>
<p><code>cartan_determinant_a2</code> — operation <code>cartan determinant a2</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p cartan_determinant_a2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cartan-matrix-b2">
<h3><a class="doc-anchor" href="#doc-cartan-matrix-b2">#</a> <code>cartan_matrix_b2</code></h3>
<p><code>cartan_matrix_b2</code> — operation <code>cartan matrix b2</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p cartan_matrix_b2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cartesian-power">
<h3><a class="doc-anchor" href="#doc-cartesian-power">#</a> <code>cartesian_power</code></h3>
<p><code>cartesian_power</code> — operation <code>cartesian power</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p cartesian_power $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cartesian-product">
<h3><a class="doc-anchor" href="#doc-cartesian-product">#</a> <code>cartesian_product</code></h3>
<p><code>cartesian_product</code> — operation <code>cartesian product</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p cartesian_product $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cartesian-product-n">
<h3><a class="doc-anchor" href="#doc-cartesian-product-n">#</a> <code>cartesian_product_n</code></h3>
<p><code>cartesian_product_n</code> — operation <code>cartesian product n</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p cartesian_product_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cartesian-to-cylindrical">
<h3><a class="doc-anchor" href="#doc-cartesian-to-cylindrical">#</a> <code>cartesian_to_cylindrical</code></h3>
<p><code>cartesian_to_cylindrical</code> — convert from <code>cartesian</code> to <code>cylindrical</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p cartesian_to_cylindrical $value
</code></pre>
</article>
<article class="doc-entry" id="doc-cartesian-to-polar">
<h3><a class="doc-anchor" href="#doc-cartesian-to-polar">#</a> <code>cartesian_to_polar</code></h3>
<p><code>cartesian_to_polar</code> — convert from <code>cartesian</code> to <code>polar</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p cartesian_to_polar $value
</code></pre>
</article>
<article class="doc-entry" id="doc-cartesian-to-spherical">
<h3><a class="doc-anchor" href="#doc-cartesian-to-spherical">#</a> <code>cartesian_to_spherical</code></h3>
<p><code>cartesian_to_spherical</code> — convert from <code>cartesian</code> to <code>spherical</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p cartesian_to_spherical $value
</code></pre>
</article>
<article class="doc-entry" id="doc-cartpow">
<h3><a class="doc-anchor" href="#doc-cartpow">#</a> <code>cartpow</code></h3>
<p><code>cartpow</code> — operation <code>cartpow</code>. Alias for <code>cartesian_power</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p cartpow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-admm-lasso-step">
<h3><a class="doc-anchor" href="#doc-cas-admm-lasso-step">#</a> <code>cas_admm_lasso_step</code></h3>
<p><code>cas_admm_lasso_step</code> — single-step update of <code>cas admm lasso</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_admm_lasso_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-alternating-projection">
<h3><a class="doc-anchor" href="#doc-cas-alternating-projection">#</a> <code>cas_alternating_projection</code></h3>
<p><code>cas_alternating_projection</code> — operation <code>cas alternating projection</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_alternating_projection $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-arnoldi-iteration-step">
<h3><a class="doc-anchor" href="#doc-cas-arnoldi-iteration-step">#</a> <code>cas_arnoldi_iteration_step</code></h3>
<p><code>cas_arnoldi_iteration_step</code> — single-step update of <code>cas arnoldi iteration</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_arnoldi_iteration_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-basis-pursuit-step">
<h3><a class="doc-anchor" href="#doc-cas-basis-pursuit-step">#</a> <code>cas_basis_pursuit_step</code></h3>
<p><code>cas_basis_pursuit_step</code> — single-step update of <code>cas basis pursuit</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_basis_pursuit_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-block-lu-step">
<h3><a class="doc-anchor" href="#doc-cas-block-lu-step">#</a> <code>cas_block_lu_step</code></h3>
<p><code>cas_block_lu_step</code> — single-step update of <code>cas block lu</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_block_lu_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-buchberger-step">
<h3><a class="doc-anchor" href="#doc-cas-buchberger-step">#</a> <code>cas_buchberger_step</code></h3>
<p><code>cas_buchberger_step</code> — single-step update of <code>cas buchberger</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_buchberger_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-bunch-kaufman-step">
<h3><a class="doc-anchor" href="#doc-cas-bunch-kaufman-step">#</a> <code>cas_bunch_kaufman_step</code></h3>
<p><code>cas_bunch_kaufman_step</code> — single-step update of <code>cas bunch kaufman</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_bunch_kaufman_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-burnside-count-step">
<h3><a class="doc-anchor" href="#doc-cas-burnside-count-step">#</a> <code>cas_burnside_count_step</code></h3>
<p><code>cas_burnside_count_step</code> — single-step update of <code>cas burnside count</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_burnside_count_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-chebyshev-eval">
<h3><a class="doc-anchor" href="#doc-cas-chebyshev-eval">#</a> <code>cas_chebyshev_eval</code></h3>
<p><code>cas_chebyshev_eval</code> — operation <code>cas chebyshev eval</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_chebyshev_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-cholesky-step">
<h3><a class="doc-anchor" href="#doc-cas-cholesky-step">#</a> <code>cas_cholesky_step</code></h3>
<p><code>cas_cholesky_step</code> — single-step update of <code>cas cholesky</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_cholesky_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-classical-gram-schmidt">
<h3><a class="doc-anchor" href="#doc-cas-classical-gram-schmidt">#</a> <code>cas_classical_gram_schmidt</code></h3>
<p><code>cas_classical_gram_schmidt</code> — operation <code>cas classical gram schmidt</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_classical_gram_schmidt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-companion-matrix-root">
<h3><a class="doc-anchor" href="#doc-cas-companion-matrix-root">#</a> <code>cas_companion_matrix_root</code></h3>
<p><code>cas_companion_matrix_root</code> — operation <code>cas companion matrix root</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_companion_matrix_root $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-constrained-ls-step">
<h3><a class="doc-anchor" href="#doc-cas-constrained-ls-step">#</a> <code>cas_constrained_ls_step</code></h3>
<p><code>cas_constrained_ls_step</code> — single-step update of <code>cas constrained ls</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_constrained_ls_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-continued-fraction-step">
<h3><a class="doc-anchor" href="#doc-cas-continued-fraction-step">#</a> <code>cas_continued_fraction_step</code></h3>
<p><code>cas_continued_fraction_step</code> — single-step update of <code>cas continued fraction</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_continued_fraction_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-cosamp-step">
<h3><a class="doc-anchor" href="#doc-cas-cosamp-step">#</a> <code>cas_cosamp_step</code></h3>
<p><code>cas_cosamp_step</code> — single-step update of <code>cas cosamp</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_cosamp_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-descartes-rule-count">
<h3><a class="doc-anchor" href="#doc-cas-descartes-rule-count">#</a> <code>cas_descartes_rule_count</code></h3>
<p><code>cas_descartes_rule_count</code> — count of <code>cas descartes rule</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_descartes_rule_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-drazin-inverse-step">
<h3><a class="doc-anchor" href="#doc-cas-drazin-inverse-step">#</a> <code>cas_drazin_inverse_step</code></h3>
<p><code>cas_drazin_inverse_step</code> — single-step update of <code>cas drazin inverse</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_drazin_inverse_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-dykstra-step">
<h3><a class="doc-anchor" href="#doc-cas-dykstra-step">#</a> <code>cas_dykstra_step</code></h3>
<p><code>cas_dykstra_step</code> — single-step update of <code>cas dykstra</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_dykstra_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-eigenvalue-inverse-iteration">
<h3><a class="doc-anchor" href="#doc-cas-eigenvalue-inverse-iteration">#</a> <code>cas_eigenvalue_inverse_iteration</code></h3>
<p><code>cas_eigenvalue_inverse_iteration</code> — operation <code>cas eigenvalue inverse iteration</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_eigenvalue_inverse_iteration $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-elastic-net-step">
<h3><a class="doc-anchor" href="#doc-cas-elastic-net-step">#</a> <code>cas_elastic_net_step</code></h3>
<p><code>cas_elastic_net_step</code> — single-step update of <code>cas elastic net</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_elastic_net_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-expand-two-terms">
<h3><a class="doc-anchor" href="#doc-cas-expand-two-terms">#</a> <code>cas_expand_two_terms</code></h3>
<p><code>cas_expand_two_terms</code> — operation <code>cas expand two terms</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_expand_two_terms $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-extended-euclid-step">
<h3><a class="doc-anchor" href="#doc-cas-extended-euclid-step">#</a> <code>cas_extended_euclid_step</code></h3>
<p><code>cas_extended_euclid_step</code> — single-step update of <code>cas extended euclid</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_extended_euclid_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-factor-quadratic">
<h3><a class="doc-anchor" href="#doc-cas-factor-quadratic">#</a> <code>cas_factor_quadratic</code></h3>
<p><code>cas_factor_quadratic</code> — operation <code>cas factor quadratic</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_factor_quadratic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-gcd-polynomial-step">
<h3><a class="doc-anchor" href="#doc-cas-gcd-polynomial-step">#</a> <code>cas_gcd_polynomial_step</code></h3>
<p><code>cas_gcd_polynomial_step</code> — single-step update of <code>cas gcd polynomial</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_gcd_polynomial_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-gegenbauer-eval">
<h3><a class="doc-anchor" href="#doc-cas-gegenbauer-eval">#</a> <code>cas_gegenbauer_eval</code></h3>
<p><code>cas_gegenbauer_eval</code> — operation <code>cas gegenbauer eval</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_gegenbauer_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-generalized-eigen">
<h3><a class="doc-anchor" href="#doc-cas-generalized-eigen">#</a> <code>cas_generalized_eigen</code></h3>
<p><code>cas_generalized_eigen</code> — operation <code>cas generalized eigen</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_generalized_eigen $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-givens-rotation-apply">
<h3><a class="doc-anchor" href="#doc-cas-givens-rotation-apply">#</a> <code>cas_givens_rotation_apply</code></h3>
<p><code>cas_givens_rotation_apply</code> — operation <code>cas givens rotation apply</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_givens_rotation_apply $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-groebner-lt-step">
<h3><a class="doc-anchor" href="#doc-cas-groebner-lt-step">#</a> <code>cas_groebner_lt_step</code></h3>
<p><code>cas_groebner_lt_step</code> — single-step update of <code>cas groebner lt</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_groebner_lt_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-hermite-eval">
<h3><a class="doc-anchor" href="#doc-cas-hermite-eval">#</a> <code>cas_hermite_eval</code></h3>
<p><code>cas_hermite_eval</code> — operation <code>cas hermite eval</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_hermite_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-hermite-normal-step">
<h3><a class="doc-anchor" href="#doc-cas-hermite-normal-step">#</a> <code>cas_hermite_normal_step</code></h3>
<p><code>cas_hermite_normal_step</code> — single-step update of <code>cas hermite normal</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_hermite_normal_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-householder-reflection">
<h3><a class="doc-anchor" href="#doc-cas-householder-reflection">#</a> <code>cas_householder_reflection</code></h3>
<p><code>cas_householder_reflection</code> — operation <code>cas householder reflection</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_householder_reflection $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-iht-iteration">
<h3><a class="doc-anchor" href="#doc-cas-iht-iteration">#</a> <code>cas_iht_iteration</code></h3>
<p><code>cas_iht_iteration</code> — operation <code>cas iht iteration</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_iht_iteration $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-indicator-simplex-proj">
<h3><a class="doc-anchor" href="#doc-cas-indicator-simplex-proj">#</a> <code>cas_indicator_simplex_proj</code></h3>
<p><code>cas_indicator_simplex_proj</code> — operation <code>cas indicator simplex proj</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_indicator_simplex_proj $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-jacobi-eigen-step">
<h3><a class="doc-anchor" href="#doc-cas-jacobi-eigen-step">#</a> <code>cas_jacobi_eigen_step</code></h3>
<p><code>cas_jacobi_eigen_step</code> — single-step update of <code>cas jacobi eigen</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_jacobi_eigen_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-jacobi-eval">
<h3><a class="doc-anchor" href="#doc-cas-jacobi-eval">#</a> <code>cas_jacobi_eval</code></h3>
<p><code>cas_jacobi_eval</code> — operation <code>cas jacobi eval</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_jacobi_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-kronecker-product-step">
<h3><a class="doc-anchor" href="#doc-cas-kronecker-product-step">#</a> <code>cas_kronecker_product_step</code></h3>
<p><code>cas_kronecker_product_step</code> — single-step update of <code>cas kronecker product</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_kronecker_product_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-lagrange-interpolate">
<h3><a class="doc-anchor" href="#doc-cas-lagrange-interpolate">#</a> <code>cas_lagrange_interpolate</code></h3>
<p><code>cas_lagrange_interpolate</code> — operation <code>cas lagrange interpolate</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_lagrange_interpolate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-laguerre-eval">
<h3><a class="doc-anchor" href="#doc-cas-laguerre-eval">#</a> <code>cas_laguerre_eval</code></h3>
<p><code>cas_laguerre_eval</code> — operation <code>cas laguerre eval</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_laguerre_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-lanczos-iteration-step">
<h3><a class="doc-anchor" href="#doc-cas-lanczos-iteration-step">#</a> <code>cas_lanczos_iteration_step</code></h3>
<p><code>cas_lanczos_iteration_step</code> — single-step update of <code>cas lanczos iteration</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_lanczos_iteration_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-lasso-soft-threshold">
<h3><a class="doc-anchor" href="#doc-cas-lasso-soft-threshold">#</a> <code>cas_lasso_soft_threshold</code></h3>
<p><code>cas_lasso_soft_threshold</code> — operation <code>cas lasso soft threshold</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_lasso_soft_threshold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-ldlt-step">
<h3><a class="doc-anchor" href="#doc-cas-ldlt-step">#</a> <code>cas_ldlt_step</code></h3>
<p><code>cas_ldlt_step</code> — single-step update of <code>cas ldlt</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_ldlt_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-least-squares-solve">
<h3><a class="doc-anchor" href="#doc-cas-least-squares-solve">#</a> <code>cas_least_squares_solve</code></h3>
<p><code>cas_least_squares_solve</code> — operation <code>cas least squares solve</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_least_squares_solve $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-legendre-eval">
<h3><a class="doc-anchor" href="#doc-cas-legendre-eval">#</a> <code>cas_legendre_eval</code></h3>
<p><code>cas_legendre_eval</code> — operation <code>cas legendre eval</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_legendre_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-lyapunov-continuous-step">
<h3><a class="doc-anchor" href="#doc-cas-lyapunov-continuous-step">#</a> <code>cas_lyapunov_continuous_step</code></h3>
<p><code>cas_lyapunov_continuous_step</code> — single-step update of <code>cas lyapunov continuous</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_lyapunov_continuous_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-lyapunov-discrete-step">
<h3><a class="doc-anchor" href="#doc-cas-lyapunov-discrete-step">#</a> <code>cas_lyapunov_discrete_step</code></h3>
<p><code>cas_lyapunov_discrete_step</code> — single-step update of <code>cas lyapunov discrete</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_lyapunov_discrete_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-macaulay-matrix-step">
<h3><a class="doc-anchor" href="#doc-cas-macaulay-matrix-step">#</a> <code>cas_macaulay_matrix_step</code></h3>
<p><code>cas_macaulay_matrix_step</code> — single-step update of <code>cas macaulay matrix</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_macaulay_matrix_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-matrix-exp-pade">
<h3><a class="doc-anchor" href="#doc-cas-matrix-exp-pade">#</a> <code>cas_matrix_exp_pade</code></h3>
<p><code>cas_matrix_exp_pade</code> — operation <code>cas matrix exp pade</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_matrix_exp_pade $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-matrix-function-step">
<h3><a class="doc-anchor" href="#doc-cas-matrix-function-step">#</a> <code>cas_matrix_function_step</code></h3>
<p><code>cas_matrix_function_step</code> — single-step update of <code>cas matrix function</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_matrix_function_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-matrix-log-step">
<h3><a class="doc-anchor" href="#doc-cas-matrix-log-step">#</a> <code>cas_matrix_log_step</code></h3>
<p><code>cas_matrix_log_step</code> — single-step update of <code>cas matrix log</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_matrix_log_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-matrix-pencil-step">
<h3><a class="doc-anchor" href="#doc-cas-matrix-pencil-step">#</a> <code>cas_matrix_pencil_step</code></h3>
<p><code>cas_matrix_pencil_step</code> — single-step update of <code>cas matrix pencil</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_matrix_pencil_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-matrix-sqrt-step">
<h3><a class="doc-anchor" href="#doc-cas-matrix-sqrt-step">#</a> <code>cas_matrix_sqrt_step</code></h3>
<p><code>cas_matrix_sqrt_step</code> — single-step update of <code>cas matrix sqrt</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_matrix_sqrt_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-minimal-polynomial">
<h3><a class="doc-anchor" href="#doc-cas-minimal-polynomial">#</a> <code>cas_minimal_polynomial</code></h3>
<p><code>cas_minimal_polynomial</code> — operation <code>cas minimal polynomial</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_minimal_polynomial $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-modified-cholesky">
<h3><a class="doc-anchor" href="#doc-cas-modified-cholesky">#</a> <code>cas_modified_cholesky</code></h3>
<p><code>cas_modified_cholesky</code> — operation <code>cas modified cholesky</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_modified_cholesky $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-modified-gram-schmidt">
<h3><a class="doc-anchor" href="#doc-cas-modified-gram-schmidt">#</a> <code>cas_modified_gram_schmidt</code></h3>
<p><code>cas_modified_gram_schmidt</code> — operation <code>cas modified gram schmidt</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_modified_gram_schmidt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-modular-inverse">
<h3><a class="doc-anchor" href="#doc-cas-modular-inverse">#</a> <code>cas_modular_inverse</code></h3>
<p><code>cas_modular_inverse</code> — inverse of <code>cas modular</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_modular_inverse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-moore-penrose-step">
<h3><a class="doc-anchor" href="#doc-cas-moore-penrose-step">#</a> <code>cas_moore_penrose_step</code></h3>
<p><code>cas_moore_penrose_step</code> — single-step update of <code>cas moore penrose</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_moore_penrose_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-omp-step">
<h3><a class="doc-anchor" href="#doc-cas-omp-step">#</a> <code>cas_omp_step</code></h3>
<p><code>cas_omp_step</code> — single-step update of <code>cas omp</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_omp_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-partial-fraction-simple">
<h3><a class="doc-anchor" href="#doc-cas-partial-fraction-simple">#</a> <code>cas_partial_fraction_simple</code></h3>
<p><code>cas_partial_fraction_simple</code> — operation <code>cas partial fraction simple</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_partial_fraction_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-pivoted-lu-step">
<h3><a class="doc-anchor" href="#doc-cas-pivoted-lu-step">#</a> <code>cas_pivoted_lu_step</code></h3>
<p><code>cas_pivoted_lu_step</code> — single-step update of <code>cas pivoted lu</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_pivoted_lu_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-polar-decomposition">
<h3><a class="doc-anchor" href="#doc-cas-polar-decomposition">#</a> <code>cas_polar_decomposition</code></h3>
<p><code>cas_polar_decomposition</code> — operation <code>cas polar decomposition</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_polar_decomposition $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-polya-enumeration-step">
<h3><a class="doc-anchor" href="#doc-cas-polya-enumeration-step">#</a> <code>cas_polya_enumeration_step</code></h3>
<p><code>cas_polya_enumeration_step</code> — single-step update of <code>cas polya enumeration</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_polya_enumeration_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-polynomial-div-step">
<h3><a class="doc-anchor" href="#doc-cas-polynomial-div-step">#</a> <code>cas_polynomial_div_step</code></h3>
<p><code>cas_polynomial_div_step</code> — single-step update of <code>cas polynomial div</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_polynomial_div_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-polynomial-gcd-step">
<h3><a class="doc-anchor" href="#doc-cas-polynomial-gcd-step">#</a> <code>cas_polynomial_gcd_step</code></h3>
<p><code>cas_polynomial_gcd_step</code> — single-step update of <code>cas polynomial gcd</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_polynomial_gcd_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-polynomial-roots-kahan">
<h3><a class="doc-anchor" href="#doc-cas-polynomial-roots-kahan">#</a> <code>cas_polynomial_roots_kahan</code></h3>
<p><code>cas_polynomial_roots_kahan</code> — operation <code>cas polynomial roots kahan</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_polynomial_roots_kahan $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-proj-box">
<h3><a class="doc-anchor" href="#doc-cas-proj-box">#</a> <code>cas_proj_box</code></h3>
<p><code>cas_proj_box</code> — operation <code>cas proj box</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_proj_box $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-proj-exp-cone">
<h3><a class="doc-anchor" href="#doc-cas-proj-exp-cone">#</a> <code>cas_proj_exp_cone</code></h3>
<p><code>cas_proj_exp_cone</code> — operation <code>cas proj exp cone</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_proj_exp_cone $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-proj-l1-ball">
<h3><a class="doc-anchor" href="#doc-cas-proj-l1-ball">#</a> <code>cas_proj_l1_ball</code></h3>
<p><code>cas_proj_l1_ball</code> — operation <code>cas proj l1 ball</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_proj_l1_ball $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-proj-l2-ball">
<h3><a class="doc-anchor" href="#doc-cas-proj-l2-ball">#</a> <code>cas_proj_l2_ball</code></h3>
<p><code>cas_proj_l2_ball</code> — operation <code>cas proj l2 ball</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_proj_l2_ball $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-proj-psd-cone">
<h3><a class="doc-anchor" href="#doc-cas-proj-psd-cone">#</a> <code>cas_proj_psd_cone</code></h3>
<p><code>cas_proj_psd_cone</code> — operation <code>cas proj psd cone</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_proj_psd_cone $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-proj-soc-step">
<h3><a class="doc-anchor" href="#doc-cas-proj-soc-step">#</a> <code>cas_proj_soc_step</code></h3>
<p><code>cas_proj_soc_step</code> — single-step update of <code>cas proj soc</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_proj_soc_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-proximal-l1-step">
<h3><a class="doc-anchor" href="#doc-cas-proximal-l1-step">#</a> <code>cas_proximal_l1_step</code></h3>
<p><code>cas_proximal_l1_step</code> — single-step update of <code>cas proximal l1</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_proximal_l1_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-proximal-l2-step">
<h3><a class="doc-anchor" href="#doc-cas-proximal-l2-step">#</a> <code>cas_proximal_l2_step</code></h3>
<p><code>cas_proximal_l2_step</code> — single-step update of <code>cas proximal l2</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_proximal_l2_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-proximal-l-inf-step">
<h3><a class="doc-anchor" href="#doc-cas-proximal-l-inf-step">#</a> <code>cas_proximal_l_inf_step</code></h3>
<p><code>cas_proximal_l_inf_step</code> — single-step update of <code>cas proximal l inf</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_proximal_l_inf_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-pseudoinverse-step">
<h3><a class="doc-anchor" href="#doc-cas-pseudoinverse-step">#</a> <code>cas_pseudoinverse_step</code></h3>
<p><code>cas_pseudoinverse_step</code> — single-step update of <code>cas pseudoinverse</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_pseudoinverse_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-qr-iteration-step">
<h3><a class="doc-anchor" href="#doc-cas-qr-iteration-step">#</a> <code>cas_qr_iteration_step</code></h3>
<p><code>cas_qr_iteration_step</code> — single-step update of <code>cas qr iteration</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_qr_iteration_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-quasi-triangular">
<h3><a class="doc-anchor" href="#doc-cas-quasi-triangular">#</a> <code>cas_quasi_triangular</code></h3>
<p><code>cas_quasi_triangular</code> — operation <code>cas quasi triangular</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_quasi_triangular $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-radical-simplify">
<h3><a class="doc-anchor" href="#doc-cas-radical-simplify">#</a> <code>cas_radical_simplify</code></h3>
<p><code>cas_radical_simplify</code> — operation <code>cas radical simplify</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_radical_simplify $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-rank-revealing-qr">
<h3><a class="doc-anchor" href="#doc-cas-rank-revealing-qr">#</a> <code>cas_rank_revealing_qr</code></h3>
<p><code>cas_rank_revealing_qr</code> — operation <code>cas rank revealing qr</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_rank_revealing_qr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-regularized-lsq-tikhonov">
<h3><a class="doc-anchor" href="#doc-cas-regularized-lsq-tikhonov">#</a> <code>cas_regularized_lsq_tikhonov</code></h3>
<p><code>cas_regularized_lsq_tikhonov</code> — operation <code>cas regularized lsq tikhonov</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_regularized_lsq_tikhonov $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-resultant-two">
<h3><a class="doc-anchor" href="#doc-cas-resultant-two">#</a> <code>cas_resultant_two</code></h3>
<p><code>cas_resultant_two</code> — operation <code>cas resultant two</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_resultant_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-resultant-x-y">
<h3><a class="doc-anchor" href="#doc-cas-resultant-x-y">#</a> <code>cas_resultant_x_y</code></h3>
<p><code>cas_resultant_x_y</code> — operation <code>cas resultant x y</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_resultant_x_y $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-riccati-continuous-step">
<h3><a class="doc-anchor" href="#doc-cas-riccati-continuous-step">#</a> <code>cas_riccati_continuous_step</code></h3>
<p><code>cas_riccati_continuous_step</code> — single-step update of <code>cas riccati continuous</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_riccati_continuous_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-riccati-discrete-step">
<h3><a class="doc-anchor" href="#doc-cas-riccati-discrete-step">#</a> <code>cas_riccati_discrete_step</code></h3>
<p><code>cas_riccati_discrete_step</code> — single-step update of <code>cas riccati discrete</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_riccati_discrete_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-root-isolate-step">
<h3><a class="doc-anchor" href="#doc-cas-root-isolate-step">#</a> <code>cas_root_isolate_step</code></h3>
<p><code>cas_root_isolate_step</code> — single-step update of <code>cas root isolate</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_root_isolate_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-schur-decomposition-step">
<h3><a class="doc-anchor" href="#doc-cas-schur-decomposition-step">#</a> <code>cas_schur_decomposition_step</code></h3>
<p><code>cas_schur_decomposition_step</code> — single-step update of <code>cas schur decomposition</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_schur_decomposition_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-simplify-term">
<h3><a class="doc-anchor" href="#doc-cas-simplify-term">#</a> <code>cas_simplify_term</code></h3>
<p><code>cas_simplify_term</code> — operation <code>cas simplify term</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_simplify_term $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-singular-value-step">
<h3><a class="doc-anchor" href="#doc-cas-singular-value-step">#</a> <code>cas_singular_value_step</code></h3>
<p><code>cas_singular_value_step</code> — single-step update of <code>cas singular value</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_singular_value_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-smith-normal-step">
<h3><a class="doc-anchor" href="#doc-cas-smith-normal-step">#</a> <code>cas_smith_normal_step</code></h3>
<p><code>cas_smith_normal_step</code> — single-step update of <code>cas smith normal</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_smith_normal_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-solve-cubic">
<h3><a class="doc-anchor" href="#doc-cas-solve-cubic">#</a> <code>cas_solve_cubic</code></h3>
<p><code>cas_solve_cubic</code> — operation <code>cas solve cubic</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_solve_cubic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-solve-linear">
<h3><a class="doc-anchor" href="#doc-cas-solve-linear">#</a> <code>cas_solve_linear</code></h3>
<p><code>cas_solve_linear</code> — operation <code>cas solve linear</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_solve_linear $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-solve-polynomial-n">
<h3><a class="doc-anchor" href="#doc-cas-solve-polynomial-n">#</a> <code>cas_solve_polynomial_n</code></h3>
<p><code>cas_solve_polynomial_n</code> — operation <code>cas solve polynomial n</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_solve_polynomial_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-solve-quadratic">
<h3><a class="doc-anchor" href="#doc-cas-solve-quadratic">#</a> <code>cas_solve_quadratic</code></h3>
<p><code>cas_solve_quadratic</code> — operation <code>cas solve quadratic</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_solve_quadratic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-solve-quartic">
<h3><a class="doc-anchor" href="#doc-cas-solve-quartic">#</a> <code>cas_solve_quartic</code></h3>
<p><code>cas_solve_quartic</code> — operation <code>cas solve quartic</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_solve_quartic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-sturm-sequence-step">
<h3><a class="doc-anchor" href="#doc-cas-sturm-sequence-step">#</a> <code>cas_sturm_sequence_step</code></h3>
<p><code>cas_sturm_sequence_step</code> — single-step update of <code>cas sturm sequence</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_sturm_sequence_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-subresultant-two">
<h3><a class="doc-anchor" href="#doc-cas-subresultant-two">#</a> <code>cas_subresultant_two</code></h3>
<p><code>cas_subresultant_two</code> — operation <code>cas subresultant two</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_subresultant_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-sylvester-equation-step">
<h3><a class="doc-anchor" href="#doc-cas-sylvester-equation-step">#</a> <code>cas_sylvester_equation_step</code></h3>
<p><code>cas_sylvester_equation_step</code> — single-step update of <code>cas sylvester equation</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_sylvester_equation_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-taylor-coefficient">
<h3><a class="doc-anchor" href="#doc-cas-taylor-coefficient">#</a> <code>cas_taylor_coefficient</code></h3>
<p><code>cas_taylor_coefficient</code> — operation <code>cas taylor coefficient</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_taylor_coefficient $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-total-least-squares">
<h3><a class="doc-anchor" href="#doc-cas-total-least-squares">#</a> <code>cas_total_least_squares</code></h3>
<p><code>cas_total_least_squares</code> — operation <code>cas total least squares</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_total_least_squares $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-truncated-lsq">
<h3><a class="doc-anchor" href="#doc-cas-truncated-lsq">#</a> <code>cas_truncated_lsq</code></h3>
<p><code>cas_truncated_lsq</code> — operation <code>cas truncated lsq</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_truncated_lsq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-truncated-svd-value">
<h3><a class="doc-anchor" href="#doc-cas-truncated-svd-value">#</a> <code>cas_truncated_svd_value</code></h3>
<p><code>cas_truncated_svd_value</code> — value of <code>cas truncated svd</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_truncated_svd_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-vec-operator-step">
<h3><a class="doc-anchor" href="#doc-cas-vec-operator-step">#</a> <code>cas_vec_operator_step</code></h3>
<p><code>cas_vec_operator_step</code> — single-step update of <code>cas vec operator</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_vec_operator_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cas-woodbury-identity">
<h3><a class="doc-anchor" href="#doc-cas-woodbury-identity">#</a> <code>cas_woodbury_identity</code></h3>
<p><code>cas_woodbury_identity</code> — operation <code>cas woodbury identity</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cas_woodbury_identity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-case-alternating">
<h3><a class="doc-anchor" href="#doc-case-alternating">#</a> <code>case_alternating</code></h3>
<p><code>case_alternating(s) → string</code> — alternating case starting with lowercase.</p>
<pre><code class="lang-perl">p case_alternating("hello") # "hElLo"
</code></pre>
</article>
<article class="doc-entry" id="doc-case-constant">
<h3><a class="doc-anchor" href="#doc-case-constant">#</a> <code>case_constant</code></h3>
<p><code>case_constant(s) → string</code> — SCREAMING_SNAKE_CASE.</p>
<pre><code class="lang-perl">p case_constant("helloWorld") # "HELLO_WORLD"
</code></pre>
</article>
<article class="doc-entry" id="doc-case-dot">
<h3><a class="doc-anchor" href="#doc-case-dot">#</a> <code>case_dot</code></h3>
<p><code>case_dot(s) → string</code> — dot.case (lowercase, dot-separated).</p>
</article>
<article class="doc-entry" id="doc-case-pascal">
<h3><a class="doc-anchor" href="#doc-case-pascal">#</a> <code>case_pascal</code></h3>
<p><code>case_pascal(s) → string</code> — PascalCase: each word capitalised, no separators.</p>
<pre><code class="lang-perl">p case_pascal("hello_world") # "HelloWorld"
</code></pre>
</article>
<article class="doc-entry" id="doc-case-path">
<h3><a class="doc-anchor" href="#doc-case-path">#</a> <code>case_path</code></h3>
<p><code>case_path(s) → string</code> — lower/case/path/style.</p>
</article>
<article class="doc-entry" id="doc-case-sentence">
<h3><a class="doc-anchor" href="#doc-case-sentence">#</a> <code>case_sentence</code></h3>
<p><code>case_sentence(s) → string</code> — Sentence case (first word capitalised, rest lowercase).</p>
</article>
<article class="doc-entry" id="doc-case-swap">
<h3><a class="doc-anchor" href="#doc-case-swap">#</a> <code>case_swap</code></h3>
<p><code>case_swap(s) → string</code> — invert case of each ASCII letter.</p>
<pre><code class="lang-perl">p case_swap("Hello World") # "hELLO wORLD"
</code></pre>
</article>
<article class="doc-entry" id="doc-case-title-proper">
<h3><a class="doc-anchor" href="#doc-case-title-proper">#</a> <code>case_title_proper</code></h3>
<p><code>case_title_proper(s) → string</code> — Title Case with small-word exceptions (a/an/the/and/or/of/in/…).</p>
</article>
<article class="doc-entry" id="doc-case-train">
<h3><a class="doc-anchor" href="#doc-case-train">#</a> <code>case_train</code></h3>
<p><code>case_train(s) → string</code> — Train-Case (capitalised, hyphen-separated).</p>
</article>
<article class="doc-entry" id="doc-casimir-eigenvalue-su2">
<h3><a class="doc-anchor" href="#doc-casimir-eigenvalue-su2">#</a> <code>casimir_eigenvalue_su2</code></h3>
<p><code>casimir_eigenvalue_su2</code> — operation <code>casimir eigenvalue su2</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p casimir_eigenvalue_su2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-catalan">
<h3><a class="doc-anchor" href="#doc-catalan">#</a> <code>catalan</code></h3>
<p><code>catalan_constant</code> (alias <code>catalan</code>) — Catalan's constant G ≈ 0.9159. Appears in combinatorics and series.</p>
<pre><code class="lang-perl">p catalan # 0.9159655941772190
</code></pre>
</article>
<article class="doc-entry" id="doc-catalan-number">
<h3><a class="doc-anchor" href="#doc-catalan-number">#</a> <code>catalan_number</code></h3>
<p><code>catalan_number</code> — operation <code>catalan number</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p catalan_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-catn">
<h3><a class="doc-anchor" href="#doc-catn">#</a> <code>catn</code></h3>
<p><code>catn</code> — operation <code>catn</code>. Alias for <code>catalan</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p catn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cauchy-pdf">
<h3><a class="doc-anchor" href="#doc-cauchy-pdf">#</a> <code>cauchy_pdf</code></h3>
<p><code>cauchy_pdf</code> (alias <code>cauchypdf</code>) evaluates the Cauchy distribution PDF at x with location x0 and scale gamma.</p>
<pre><code class="lang-perl">p cauchypdf(0, 0, 1) # peak of standard Cauchy
</code></pre>
</article>
<article class="doc-entry" id="doc-caverphone">
<h3><a class="doc-anchor" href="#doc-caverphone">#</a> <code>caverphone</code></h3>
<p><code>caverphone(name) → string</code> — Caverphone 1.0 (6-char). Designed for matching New Zealand electoral roll names.</p>
<pre><code class="lang-perl">p caverphone("John")
</code></pre>
</article>
<article class="doc-entry" id="doc-caverphone2">
<h3><a class="doc-anchor" href="#doc-caverphone2">#</a> <code>caverphone2</code></h3>
<p><code>caverphone2(name) → string</code> — Caverphone 2.0 (10-char, padded with <code>1</code>).</p>
</article>
<article class="doc-entry" id="doc-caverphone-2">
<h3><a class="doc-anchor" href="#doc-caverphone-2">#</a> <code>caverphone_2</code></h3>
<p><code>caverphone_2</code> — operation <code>caverphone 2</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p caverphone_2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cbind">
<h3><a class="doc-anchor" href="#doc-cbind">#</a> <code>cbind</code></h3>
<p><code>cbind</code> — bind matrices by columns (horizontal join). Like R's cbind().</p>
<pre><code class="lang-perl">my $m = cbind([[1],[2]], [[3],[4]]) # [[1,3],[2,4]]
</code></pre>
</article>
<article class="doc-entry" id="doc-cblend">
<h3><a class="doc-anchor" href="#doc-cblend">#</a> <code>cblend</code></h3>
<p><code>cblend</code> — operation <code>cblend</code>. Alias for <code>color_blend</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p cblend $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cbor-encode-str">
<h3><a class="doc-anchor" href="#doc-cbor-encode-str">#</a> <code>cbor_encode_str</code></h3>
<p><code>cbor_encode_str</code> — operation <code>cbor encode str</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p cbor_encode_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cbor-encode-uint">
<h3><a class="doc-anchor" href="#doc-cbor-encode-uint">#</a> <code>cbor_encode_uint</code></h3>
<p><code>cbor_encode_uint</code> — operation <code>cbor encode uint</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p cbor_encode_uint $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cbrt">
<h3><a class="doc-anchor" href="#doc-cbrt">#</a> <code>cbrt</code></h3>
<p><code>cbrt</code> — operation <code>cbrt</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p cbrt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cc-count">
<h3><a class="doc-anchor" href="#doc-cc-count">#</a> <code>cc_count</code></h3>
<p><code>cc_count</code> — count of <code>cc</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p cc_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cc-labels">
<h3><a class="doc-anchor" href="#doc-cc-labels">#</a> <code>cc_labels</code></h3>
<p><code>cc_labels</code> — operation <code>cc labels</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p cc_labels $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ccgraph">
<h3><a class="doc-anchor" href="#doc-ccgraph">#</a> <code>ccgraph</code></h3>
<p><code>ccgraph</code> — operation <code>ccgraph</code>. Alias for <code>connected_components_graph</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ccgraph $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cci">
<h3><a class="doc-anchor" href="#doc-cci">#</a> <code>cci</code></h3>
<p><code>cci(highs, lows, closes, period=20) → array</code> — Commodity Channel Index: <code>(typical_price − sma) / (0.015 · mean_dev)</code>.</p>
<pre><code class="lang-perl">p cci(\@hi, \@lo, \@cl, 20)
</code></pre>
</article>
<article class="doc-entry" id="doc-ccompl">
<h3><a class="doc-anchor" href="#doc-ccompl">#</a> <code>ccompl</code></h3>
<p><code>ccompl</code> — operation <code>ccompl</code>. Alias for <code>color_complement</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p ccompl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ccount">
<h3><a class="doc-anchor" href="#doc-ccount">#</a> <code>ccount</code></h3>
<p><code>ccount</code> — operation <code>ccount</code>. Alias for <code>count_chars</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ccount $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ccx-gate">
<h3><a class="doc-anchor" href="#doc-ccx-gate">#</a> <code>ccx_gate</code></h3>
<p><code>ccx_gate</code> — operation <code>ccx gate</code>. Alias for <code>toffoli_gate</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p ccx_gate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cdarken">
<h3><a class="doc-anchor" href="#doc-cdarken">#</a> <code>cdarken</code></h3>
<p><code>cdarken</code> — operation <code>cdarken</code>. Alias for <code>color_darken</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p cdarken $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cdist">
<h3><a class="doc-anchor" href="#doc-cdist">#</a> <code>cdist</code></h3>
<p><code>cdist</code> — operation <code>cdist</code>. Alias for <code>color_distance</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p cdist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cds-upfront">
<h3><a class="doc-anchor" href="#doc-cds-upfront">#</a> <code>cds_upfront</code></h3>
<p><code>cds_upfront</code> — operation <code>cds upfront</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p cds_upfront $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cech-zero-cohomology">
<h3><a class="doc-anchor" href="#doc-cech-zero-cohomology">#</a> <code>cech_zero_cohomology</code></h3>
<p><code>cech_zero_cohomology</code> — operation <code>cech zero cohomology</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p cech_zero_cohomology $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ceil">
<h3><a class="doc-anchor" href="#doc-ceil">#</a> <code>ceil</code></h3>
<p><code>ceil</code> — operation <code>ceil</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p ceil $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ceil-div">
<h3><a class="doc-anchor" href="#doc-ceil-div">#</a> <code>ceil_div</code></h3>
<p><code>ceil_div</code> — operation <code>ceil div</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p ceil_div $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ceil-each">
<h3><a class="doc-anchor" href="#doc-ceil-each">#</a> <code>ceil_each</code></h3>
<p><code>ceil_each</code> — operation <code>ceil each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p ceil_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ceiling">
<h3><a class="doc-anchor" href="#doc-ceiling">#</a> <code>ceiling</code></h3>
<p><code>ceiling</code> — operation <code>ceiling</code>. Alias for <code>ceil</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p ceiling $x
</code></pre>
</article>
<article class="doc-entry" id="doc-center">
<h3><a class="doc-anchor" href="#doc-center">#</a> <code>center</code></h3>
<p><code>center</code> — operation <code>center</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p center $x
</code></pre>
</article>
<article class="doc-entry" id="doc-center-of-mass-2d">
<h3><a class="doc-anchor" href="#doc-center-of-mass-2d">#</a> <code>center_of_mass_2d</code></h3>
<p><code>center_of_mass_2d(masses, positions) → [x, y]</code> — mass-weighted centroid of point particles in 2D.</p>
</article>
<article class="doc-entry" id="doc-center-of-mass-3d">
<h3><a class="doc-anchor" href="#doc-center-of-mass-3d">#</a> <code>center_of_mass_3d</code></h3>
<p><code>center_of_mass_3d(masses, positions) → [x, y, z]</code> — same in 3D.</p>
</article>
<article class="doc-entry" id="doc-center-text">
<h3><a class="doc-anchor" href="#doc-center-text">#</a> <code>center_text</code></h3>
<p><code>center_text</code> — operation <code>center text</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p center_text $x
</code></pre>
</article>
<article class="doc-entry" id="doc-centered-hexagonal-number">
<h3><a class="doc-anchor" href="#doc-centered-hexagonal-number">#</a> <code>centered_hexagonal_number</code></h3>
<p><code>centered_hexagonal_number</code> — operation <code>centered hexagonal number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p centered_hexagonal_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-centered-pentagonal">
<h3><a class="doc-anchor" href="#doc-centered-pentagonal">#</a> <code>centered_pentagonal</code></h3>
<p><code>centered_pentagonal</code> — operation <code>centered pentagonal</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p centered_pentagonal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-centered-polygonal">
<h3><a class="doc-anchor" href="#doc-centered-polygonal">#</a> <code>centered_polygonal</code></h3>
<p><code>centered_polygonal(k, n) → int</code> — centered k-gonal number <code>1 + k·n·(n-1)/2</code>.</p>
</article>
<article class="doc-entry" id="doc-centered-square">
<h3><a class="doc-anchor" href="#doc-centered-square">#</a> <code>centered_square</code></h3>
<p><code>centered_square</code> — operation <code>centered square</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p centered_square $x
</code></pre>
</article>
<article class="doc-entry" id="doc-centered-triangular">
<h3><a class="doc-anchor" href="#doc-centered-triangular">#</a> <code>centered_triangular</code></h3>
<p><code>centered_triangular</code> — operation <code>centered triangular</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p centered_triangular $x
</code></pre>
</article>
<article class="doc-entry" id="doc-central-polygonal">
<h3><a class="doc-anchor" href="#doc-central-polygonal">#</a> <code>central_polygonal</code></h3>
<p><code>central_polygonal</code> — operation <code>central polygonal</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p central_polygonal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-centrality-betweenness">
<h3><a class="doc-anchor" href="#doc-centrality-betweenness">#</a> <code>centrality_betweenness</code></h3>
<p><code>centrality_betweenness</code> — operation <code>centrality betweenness</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p centrality_betweenness $x
</code></pre>
</article>
<article class="doc-entry" id="doc-centrality-closeness">
<h3><a class="doc-anchor" href="#doc-centrality-closeness">#</a> <code>centrality_closeness</code></h3>
<p><code>centrality_closeness</code> — operation <code>centrality closeness</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p centrality_closeness $x
</code></pre>
</article>
<article class="doc-entry" id="doc-centrality-degree">
<h3><a class="doc-anchor" href="#doc-centrality-degree">#</a> <code>centrality_degree</code></h3>
<p><code>centrality_degree</code> — operation <code>centrality degree</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p centrality_degree $x
</code></pre>
</article>
<article class="doc-entry" id="doc-centrality-eigenvector">
<h3><a class="doc-anchor" href="#doc-centrality-eigenvector">#</a> <code>centrality_eigenvector</code></h3>
<p><code>centrality_eigenvector</code> — operation <code>centrality eigenvector</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p centrality_eigenvector $x
</code></pre>
</article>
<article class="doc-entry" id="doc-centrality-katz">
<h3><a class="doc-anchor" href="#doc-centrality-katz">#</a> <code>centrality_katz</code></h3>
<p><code>centrality_katz</code> — operation <code>centrality katz</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p centrality_katz $x
</code></pre>
</article>
<article class="doc-entry" id="doc-centrip">
<h3><a class="doc-anchor" href="#doc-centrip">#</a> <code>centrip</code></h3>
<p><code>centripetal_force($mass, $velocity, $radius)</code> (alias <code>centrip</code>) — F = mv²/r for circular motion.</p>
<pre><code class="lang-perl">p centrip(1000, 20, 50) # 8000 N (car turning)
</code></pre>
</article>
<article class="doc-entry" id="doc-centripetal-accel">
<h3><a class="doc-anchor" href="#doc-centripetal-accel">#</a> <code>centripetal_accel</code></h3>
<p><code>centripetal_accel</code> — operation <code>centripetal accel</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p centripetal_accel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-centroid">
<h3><a class="doc-anchor" href="#doc-centroid">#</a> <code>centroid</code></h3>
<p><code>centroid(@points)</code> — computes the centroid (geometric center) of 2D points. Points as flat list [x1,y1,x2,y2,...]. Returns [$cx, $cy].</p>
<pre><code class="lang-perl">my @triangle = (0,0, 3,0, 0,3)
my $c = centroid(@triangle)
p @$c # (1, 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-centroid-nd">
<h3><a class="doc-anchor" href="#doc-centroid-nd">#</a> <code>centroid_nd</code></h3>
<p><code>centroid_nd</code> — operation <code>centroid nd</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p centroid_nd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cents-between">
<h3><a class="doc-anchor" href="#doc-cents-between">#</a> <code>cents_between</code></h3>
<p><code>cents_between</code> — operation <code>cents between</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p cents_between $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cents-between-freqs">
<h3><a class="doc-anchor" href="#doc-cents-between-freqs">#</a> <code>cents_between_freqs</code></h3>
<p><code>cents_between_freqs</code> — operation <code>cents between freqs</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p cents_between_freqs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ces-production">
<h3><a class="doc-anchor" href="#doc-ces-production">#</a> <code>ces_production</code></h3>
<p><code>ces_production</code> — operation <code>ces production</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p ces_production $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cfl-number">
<h3><a class="doc-anchor" href="#doc-cfl-number">#</a> <code>cfl_number</code></h3>
<p><code>cfl_number</code> — operation <code>cfl number</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p cfl_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cfr-case-fatality">
<h3><a class="doc-anchor" href="#doc-cfr-case-fatality">#</a> <code>cfr_case_fatality</code></h3>
<p><code>cfr_case_fatality</code> — operation <code>cfr case fatality</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p cfr_case_fatality $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cg-beta-fr">
<h3><a class="doc-anchor" href="#doc-cg-beta-fr">#</a> <code>cg_beta_fr</code></h3>
<p><code>cg_beta_fr</code> — operation <code>cg beta fr</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p cg_beta_fr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cg-beta-pr">
<h3><a class="doc-anchor" href="#doc-cg-beta-pr">#</a> <code>cg_beta_pr</code></h3>
<p><code>cg_beta_pr</code> — operation <code>cg beta pr</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p cg_beta_pr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cg-simple">
<h3><a class="doc-anchor" href="#doc-cg-simple">#</a> <code>cg_simple</code></h3>
<p><code>cg_simple</code> — operation <code>cg simple</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p cg_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cgemm">
<h3><a class="doc-anchor" href="#doc-cgemm">#</a> <code>cgemm</code></h3>
<p><code>cgemm</code> — operation <code>cgemm</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p cgemm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cgray">
<h3><a class="doc-anchor" href="#doc-cgray">#</a> <code>cgray</code></h3>
<p><code>cgray</code> — operation <code>cgray</code>. Alias for <code>color_grayscale</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p cgray $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chacha20-qround">
<h3><a class="doc-anchor" href="#doc-chacha20-qround">#</a> <code>chacha20_qround</code></h3>
<p><code>chacha20_qround</code> — operation <code>chacha20 qround</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p chacha20_qround $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chain-from">
<h3><a class="doc-anchor" href="#doc-chain-from">#</a> <code>chain_from</code></h3>
<p><code>chain_from</code> — operation <code>chain from</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p chain_from $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chain-ladder-step">
<h3><a class="doc-anchor" href="#doc-chain-ladder-step">#</a> <code>chain_ladder_step</code></h3>
<p><code>chain_ladder_step</code> — single-step update of <code>chain ladder</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p chain_ladder_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chain-rule-entropy">
<h3><a class="doc-anchor" href="#doc-chain-rule-entropy">#</a> <code>chain_rule_entropy</code></h3>
<p><code>chain_rule_entropy</code> — operation <code>chain rule entropy</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p chain_rule_entropy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chandrasekhar-mass">
<h3><a class="doc-anchor" href="#doc-chandrasekhar-mass">#</a> <code>chandrasekhar_mass</code></h3>
<p><code>chandrasekhar_mass</code> — operation <code>chandrasekhar mass</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p chandrasekhar_mass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-channel-bounded">
<h3><a class="doc-anchor" href="#doc-channel-bounded">#</a> <code>channel_bounded</code></h3>
<p><code>channel_bounded(capacity) → channel</code> — bounded channel; senders block when full.</p>
</article>
<article class="doc-entry" id="doc-channel-close">
<h3><a class="doc-anchor" href="#doc-channel-close">#</a> <code>channel_close</code></h3>
<p><code>channel_close(ch) → 0|1</code> — close channel; pending receivers get the channel-closed sentinel.</p>
</article>
<article class="doc-entry" id="doc-channel-drain">
<h3><a class="doc-anchor" href="#doc-channel-drain">#</a> <code>channel_drain</code></h3>
<p><code>channel_drain(ch) → array</code> — receive all pending values.</p>
</article>
<article class="doc-entry" id="doc-channel-is-closed">
<h3><a class="doc-anchor" href="#doc-channel-is-closed">#</a> <code>channel_is_closed</code></h3>
<p><code>channel_is_closed(ch) → 0|1</code> — 1 if channel has been closed.</p>
</article>
<article class="doc-entry" id="doc-channel-recv-timeout">
<h3><a class="doc-anchor" href="#doc-channel-recv-timeout">#</a> <code>channel_recv_timeout</code></h3>
<p><code>channel_recv_timeout(ch, ms) → value</code> — try to receive with timeout.</p>
</article>
<article class="doc-entry" id="doc-channel-send-timeout">
<h3><a class="doc-anchor" href="#doc-channel-send-timeout">#</a> <code>channel_send_timeout</code></h3>
<p><code>channel_send_timeout(ch, value, ms) → 0|1</code> — try to send with timeout.</p>
</article>
<article class="doc-entry" id="doc-channel-sync">
<h3><a class="doc-anchor" href="#doc-channel-sync">#</a> <code>channel_sync</code></h3>
<p><code>channel_sync() → channel</code> — rendezvous channel (capacity 0); send and recv complete in lockstep.</p>
</article>
<article class="doc-entry" id="doc-channel-try-recv">
<h3><a class="doc-anchor" href="#doc-channel-try-recv">#</a> <code>channel_try_recv</code></h3>
<p><code>channel_try_recv</code> — receive of <code>channel try</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p channel_try_recv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-channel-try-send">
<h3><a class="doc-anchor" href="#doc-channel-try-send">#</a> <code>channel_try_send</code></h3>
<p><code>channel_try_send</code> — send of <code>channel try</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p channel_try_send $x
</code></pre>
</article>
<article class="doc-entry" id="doc-channel-unbounded">
<h3><a class="doc-anchor" href="#doc-channel-unbounded">#</a> <code>channel_unbounded</code></h3>
<p><code>channel_unbounded() → channel</code> — create an unbounded multi-producer multi-consumer channel.</p>
</article>
<article class="doc-entry" id="doc-chapman-estimator">
<h3><a class="doc-anchor" href="#doc-chapman-estimator">#</a> <code>chapman_estimator</code></h3>
<p><code>chapman_estimator</code> — operation <code>chapman estimator</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p chapman_estimator $x
</code></pre>
</article>
<article class="doc-entry" id="doc-char-at">
<h3><a class="doc-anchor" href="#doc-char-at">#</a> <code>char_at</code></h3>
<p><code>char_at</code> — single-character helper <code>at</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p char_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-char-count">
<h3><a class="doc-anchor" href="#doc-char-count">#</a> <code>char_count</code></h3>
<p><code>char_count</code> — single-character helper <code>count</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p char_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-char-devices">
<h3><a class="doc-anchor" href="#doc-char-devices">#</a> <code>char_devices</code></h3>
<p><code>char_devices</code> — single-character helper <code>devices</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p char_devices $x
</code></pre>
</article>
<article class="doc-entry" id="doc-char-frequencies">
<h3><a class="doc-anchor" href="#doc-char-frequencies">#</a> <code>char_frequencies</code></h3>
<p><code>char_frequencies</code> — single-character helper <code>frequencies</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p char_frequencies $x
</code></pre>
</article>
<article class="doc-entry" id="doc-char-length">
<h3><a class="doc-anchor" href="#doc-char-length">#</a> <code>char_length</code></h3>
<p><code>char_length</code> — single-character helper <code>length</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p char_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-character-su2">
<h3><a class="doc-anchor" href="#doc-character-su2">#</a> <code>character_su2</code></h3>
<p><code>character_su2</code> — operation <code>character su2</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p character_su2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-character-sun">
<h3><a class="doc-anchor" href="#doc-character-sun">#</a> <code>character_sun</code></h3>
<p><code>character_sun</code> — operation <code>character sun</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p character_sun $x
</code></pre>
</article>
<article class="doc-entry" id="doc-characteristic-function">
<h3><a class="doc-anchor" href="#doc-characteristic-function">#</a> <code>characteristic_function</code></h3>
<p><code>characteristic_function</code> — operation <code>characteristic function</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p characteristic_function $x
</code></pre>
</article>
<article class="doc-entry" id="doc-charcodes-to-string">
<h3><a class="doc-anchor" href="#doc-charcodes-to-string">#</a> <code>charcodes_to_string</code></h3>
<p><code>charcodes_to_string</code> — convert from <code>charcodes</code> to <code>string</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p charcodes_to_string $value
</code></pre>
</article>
<article class="doc-entry" id="doc-charfreq">
<h3><a class="doc-anchor" href="#doc-charfreq">#</a> <code>charfreq</code></h3>
<p><code>charfreq</code> — operation <code>charfreq</code>. Alias for <code>char_frequencies</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p charfreq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-charge-capacity-battery">
<h3><a class="doc-anchor" href="#doc-charge-capacity-battery">#</a> <code>charge_capacity_battery</code></h3>
<p><code>charge_capacity_battery</code> — operation <code>charge capacity battery</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p charge_capacity_battery $x
</code></pre>
</article>
<article class="doc-entry" id="doc-charge-transfer-resistance">
<h3><a class="doc-anchor" href="#doc-charge-transfer-resistance">#</a> <code>charge_transfer_resistance</code></h3>
<p><code>charge_transfer_resistance</code> — operation <code>charge transfer resistance</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p charge_transfer_resistance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chars-to-string">
<h3><a class="doc-anchor" href="#doc-chars-to-string">#</a> <code>chars_to_string</code></h3>
<p><code>chars_to_string</code> — convert from <code>chars</code> to <code>string</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p chars_to_string $value
</code></pre>
</article>
<article class="doc-entry" id="doc-chc-bound-makespan">
<h3><a class="doc-anchor" href="#doc-chc-bound-makespan">#</a> <code>chc_bound_makespan</code></h3>
<p><code>chc_bound_makespan</code> — operation <code>chc bound makespan</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p chc_bound_makespan $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cheapest-insertion-step">
<h3><a class="doc-anchor" href="#doc-cheapest-insertion-step">#</a> <code>cheapest_insertion_step</code></h3>
<p><code>cheapest_insertion_step</code> — single-step update of <code>cheapest insertion</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p cheapest_insertion_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cheby1-lp">
<h3><a class="doc-anchor" href="#doc-cheby1-lp">#</a> <code>cheby1_lp</code></h3>
<p><code>cheby1_lp</code> — operation <code>cheby1 lp</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p cheby1_lp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cheby2-lp">
<h3><a class="doc-anchor" href="#doc-cheby2-lp">#</a> <code>cheby2_lp</code></h3>
<p><code>cheby2_lp</code> — operation <code>cheby2 lp</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p cheby2_lp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chebyshev-distance">
<h3><a class="doc-anchor" href="#doc-chebyshev-distance">#</a> <code>chebyshev_distance</code></h3>
<p><code>chebyshev_distance</code> — distance / dissimilarity metric of <code>chebyshev</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p chebyshev_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chebyshev-norm">
<h3><a class="doc-anchor" href="#doc-chebyshev-norm">#</a> <code>chebyshev_norm</code></h3>
<p><code>chebyshev_norm(v) → number</code> — L∞ norm <code>max |vᵢ|</code>.</p>
</article>
<article class="doc-entry" id="doc-chebyt">
<h3><a class="doc-anchor" href="#doc-chebyt">#</a> <code>chebyt</code></h3>
<p><code>chebyt</code> — operation <code>chebyt</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p chebyt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chebyu">
<h3><a class="doc-anchor" href="#doc-chebyu">#</a> <code>chebyu</code></h3>
<p><code>chebyu</code> — operation <code>chebyu</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p chebyu $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chem-arrhenius-k">
<h3><a class="doc-anchor" href="#doc-chem-arrhenius-k">#</a> <code>chem_arrhenius_k</code></h3>
<p><code>chem_arrhenius_k(A, Ea_J, T_K) → number</code> — <code>k = A · e^(-Ea / (R·T))</code>.</p>
</article>
<article class="doc-entry" id="doc-chem-avogadro">
<h3><a class="doc-anchor" href="#doc-chem-avogadro">#</a> <code>chem_avogadro</code></h3>
<p><code>chem_avogadro() → number</code> — Avogadro constant 6.022·10²³ mol⁻¹.</p>
</article>
<article class="doc-entry" id="doc-chem-balance-check">
<h3><a class="doc-anchor" href="#doc-chem-balance-check">#</a> <code>chem_balance_check</code></h3>
<p><code>chem_balance_check(lhs, rhs) → 0|1</code> — 1 if both sides have identical element counts.</p>
</article>
<article class="doc-entry" id="doc-chem-boiling-point-elevation">
<h3><a class="doc-anchor" href="#doc-chem-boiling-point-elevation">#</a> <code>chem_boiling_point_elevation</code></h3>
<p><code>chem_boiling_point_elevation(Kb, molality, i=1) → number</code> — <code>ΔTb = Kb · m · i</code>.</p>
</article>
<article class="doc-entry" id="doc-chem-buffer-capacity">
<h3><a class="doc-anchor" href="#doc-chem-buffer-capacity">#</a> <code>chem_buffer_capacity</code></h3>
<p><code>chem_buffer_capacity([H+], Ca, Ka) → number</code> — Van Slyke buffer capacity β.</p>
</article>
<article class="doc-entry" id="doc-chem-celsius-to-fahrenheit">
<h3><a class="doc-anchor" href="#doc-chem-celsius-to-fahrenheit">#</a> <code>chem_celsius_to_fahrenheit</code></h3>
<p><code>chem_celsius_to_fahrenheit(C) → number</code> — <code>C · 9/5 + 32</code>.</p>
</article>
<article class="doc-entry" id="doc-chem-celsius-to-kelvin">
<h3><a class="doc-anchor" href="#doc-chem-celsius-to-kelvin">#</a> <code>chem_celsius_to_kelvin</code></h3>
<p><code>chem_celsius_to_kelvin(C) → number</code> — <code>C + 273.15</code>.</p>
</article>
<article class="doc-entry" id="doc-chem-concentration-to-molarity">
<h3><a class="doc-anchor" href="#doc-chem-concentration-to-molarity">#</a> <code>chem_concentration_to_molarity</code></h3>
<p><code>chem_concentration_to_molarity(mass_g, molar_mass, volume_L) → number</code> — molarity = mass / (MM · V).</p>
</article>
<article class="doc-entry" id="doc-chem-dilution">
<h3><a class="doc-anchor" href="#doc-chem-dilution">#</a> <code>chem_dilution</code></h3>
<p><code>chem_dilution(C1, V1, C2) → number</code> — V2 such that C1V1 = C2V2.</p>
<pre><code class="lang-perl">p chem_dilution(1.0, 100, 0.1) # 1000
</code></pre>
</article>
<article class="doc-entry" id="doc-chem-fahrenheit-to-celsius">
<h3><a class="doc-anchor" href="#doc-chem-fahrenheit-to-celsius">#</a> <code>chem_fahrenheit_to_celsius</code></h3>
<p><code>chem_fahrenheit_to_celsius(F) → number</code> — <code>(F - 32) · 5/9</code>.</p>
</article>
<article class="doc-entry" id="doc-chem-fahrenheit-to-kelvin">
<h3><a class="doc-anchor" href="#doc-chem-fahrenheit-to-kelvin">#</a> <code>chem_fahrenheit_to_kelvin</code></h3>
<p><code>chem_fahrenheit_to_kelvin(F) → number</code> — chain via Celsius.</p>
</article>
<article class="doc-entry" id="doc-chem-formula-parse">
<h3><a class="doc-anchor" href="#doc-chem-formula-parse">#</a> <code>chem_formula_parse</code></h3>
<p><code>chem_formula_parse(formula) → array</code> — parse chemical formula into <code>[[element, count], …]</code>.</p>
<pre><code class="lang-perl">p chem_formula_parse("C6H12O6")
</code></pre>
</article>
<article class="doc-entry" id="doc-chem-freezing-point-depression">
<h3><a class="doc-anchor" href="#doc-chem-freezing-point-depression">#</a> <code>chem_freezing_point_depression</code></h3>
<p><code>chem_freezing_point_depression(Kf, molality, i=1) → number</code> — <code>ΔTf = Kf · m · i</code> (van't Hoff factor).</p>
</article>
<article class="doc-entry" id="doc-chem-h-from-ph">
<h3><a class="doc-anchor" href="#doc-chem-h-from-ph">#</a> <code>chem_h_from_ph</code></h3>
<p><code>chem_h_from_ph(pH) → number</code> — <code>[H+] = 10^-pH</code>.</p>
</article>
<article class="doc-entry" id="doc-chem-henderson-hasselbalch">
<h3><a class="doc-anchor" href="#doc-chem-henderson-hasselbalch">#</a> <code>chem_henderson_hasselbalch</code></h3>
<p><code>chem_henderson_hasselbalch(pKa, [A-], [HA]) → number</code> — <code>pH = pKa + log10([A-]/[HA])</code>.</p>
<pre><code class="lang-perl">p chem_henderson_hasselbalch(4.76, 10, 1) # 5.76
</code></pre>
</article>
<article class="doc-entry" id="doc-chem-ideal-gas-volume">
<h3><a class="doc-anchor" href="#doc-chem-ideal-gas-volume">#</a> <code>chem_ideal_gas_volume</code></h3>
<p><code>chem_ideal_gas_volume(moles, T_K=273.15, P_atm=1) → number</code> — volume in liters from <code>PV = nRT</code>.</p>
<pre><code class="lang-perl">p chem_ideal_gas_volume(1) # 22.41 (STP)
</code></pre>
</article>
<article class="doc-entry" id="doc-chem-isoelectric-estimate">
<h3><a class="doc-anchor" href="#doc-chem-isoelectric-estimate">#</a> <code>chem_isoelectric_estimate</code></h3>
<p><code>chem_isoelectric_estimate(pk1, pk2) → number</code> — <code>(pk1 + pk2) / 2</code>; classic pI estimate for simple amino acids.</p>
</article>
<article class="doc-entry" id="doc-chem-kelvin-to-celsius">
<h3><a class="doc-anchor" href="#doc-chem-kelvin-to-celsius">#</a> <code>chem_kelvin_to_celsius</code></h3>
<p><code>chem_kelvin_to_celsius(K) → number</code> — <code>K - 273.15</code>.</p>
</article>
<article class="doc-entry" id="doc-chem-kelvin-to-fahrenheit">
<h3><a class="doc-anchor" href="#doc-chem-kelvin-to-fahrenheit">#</a> <code>chem_kelvin_to_fahrenheit</code></h3>
<p><code>chem_kelvin_to_fahrenheit(K) → number</code> — chain via Celsius.</p>
</article>
<article class="doc-entry" id="doc-chem-kelvin-to-rankine">
<h3><a class="doc-anchor" href="#doc-chem-kelvin-to-rankine">#</a> <code>chem_kelvin_to_rankine</code></h3>
<p><code>chem_kelvin_to_rankine(K) → number</code> — <code>K · 9/5</code>.</p>
</article>
<article class="doc-entry" id="doc-chem-molality">
<h3><a class="doc-anchor" href="#doc-chem-molality">#</a> <code>chem_molality</code></h3>
<p><code>chem_molality(moles_solute, kg_solvent) → number</code> — moles per kg of solvent.</p>
</article>
<article class="doc-entry" id="doc-chem-molar-mass">
<h3><a class="doc-anchor" href="#doc-chem-molar-mass">#</a> <code>chem_molar_mass</code></h3>
<p><code>chem_molar_mass(formula) → number</code> — molar mass in g/mol using a built-in atomic weights table.</p>
<pre><code class="lang-perl">p chem_molar_mass("H2O") # 18.015
p chem_molar_mass("C6H12O6") # 180.156
</code></pre>
</article>
<article class="doc-entry" id="doc-chem-molarity-to-normality">
<h3><a class="doc-anchor" href="#doc-chem-molarity-to-normality">#</a> <code>chem_molarity_to_normality</code></h3>
<p><code>chem_molarity_to_normality(M, equiv_per_mole=1) → number</code> — <code>N = M · equiv_per_mole</code>.</p>
</article>
<article class="doc-entry" id="doc-chem-partial-pressure">
<h3><a class="doc-anchor" href="#doc-chem-partial-pressure">#</a> <code>chem_partial_pressure</code></h3>
<p><code>chem_partial_pressure(total, mole_fraction) → number</code> — <code>total · mole_fraction</code> (Dalton's law).</p>
</article>
<article class="doc-entry" id="doc-chem-ph-from-h">
<h3><a class="doc-anchor" href="#doc-chem-ph-from-h">#</a> <code>chem_ph_from_h</code></h3>
<p><code>chem_ph_from_h(h_concentration) → number</code> — <code>pH = -log10([H+])</code>.</p>
<pre><code class="lang-perl">p chem_ph_from_h(1e-7) # 7
</code></pre>
</article>
<article class="doc-entry" id="doc-chem-pka-lookup">
<h3><a class="doc-anchor" href="#doc-chem-pka-lookup">#</a> <code>chem_pka_lookup</code></h3>
<p><code>chem_pka_lookup(name) → number</code> — pKa for common acid/base names: HCl, H2SO4, HNO3, CH3COOH, NH4+, H2CO3, etc.</p>
<pre><code class="lang-perl">p chem_pka_lookup("CH3COOH") # 4.76
</code></pre>
</article>
<article class="doc-entry" id="doc-chem-rankine-to-kelvin">
<h3><a class="doc-anchor" href="#doc-chem-rankine-to-kelvin">#</a> <code>chem_rankine_to_kelvin</code></h3>
<p><code>chem_rankine_to_kelvin(R) → number</code> — <code>R · 5/9</code>.</p>
</article>
<article class="doc-entry" id="doc-chern-first-2d">
<h3><a class="doc-anchor" href="#doc-chern-first-2d">#</a> <code>chern_first_2d</code></h3>
<p><code>chern_first_2d</code> — operation <code>chern first 2d</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p chern_first_2d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chern-pontryagin-4d-step">
<h3><a class="doc-anchor" href="#doc-chern-pontryagin-4d-step">#</a> <code>chern_pontryagin_4d_step</code></h3>
<p><code>chern_pontryagin_4d_step</code> — single-step update of <code>chern pontryagin 4d</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p chern_pontryagin_4d_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chern-simons-action">
<h3><a class="doc-anchor" href="#doc-chern-simons-action">#</a> <code>chern_simons_action</code></h3>
<p><code>chern_simons_action</code> — operation <code>chern simons action</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p chern_simons_action $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chezy-velocity">
<h3><a class="doc-anchor" href="#doc-chezy-velocity">#</a> <code>chezy_velocity</code></h3>
<p><code>chezy_velocity</code> — operation <code>chezy velocity</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p chezy_velocity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chfr">
<h3><a class="doc-anchor" href="#doc-chfr">#</a> <code>chfr</code></h3>
<p><code>chfr</code> — operation <code>chfr</code>. Alias for <code>chain_from</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p chfr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chi2">
<h3><a class="doc-anchor" href="#doc-chi2">#</a> <code>chi2</code></h3>
<p><code>chi_square_stat(\@observed, \@expected)</code> (alias <code>chi2</code>) — computes the chi-squared test statistic comparing observed vs expected frequencies. Useful for goodness-of-fit tests. Returns the chi-squared value.</p>
<pre><code class="lang-perl">my @obs = (10, 20, 30)
my @exp = (15, 20, 25)
p chi2(\@obs, \@exp) # chi-squared statistic
</code></pre>
</article>
<article class="doc-entry" id="doc-chi2-pdf">
<h3><a class="doc-anchor" href="#doc-chi2-pdf">#</a> <code>chi2_pdf</code></h3>
<p><code>chi2_pdf</code> (alias <code>chi2pdf</code>) evaluates the chi-squared distribution PDF at x with k degrees of freedom.</p>
<pre><code class="lang-perl">p chi2pdf(3.84, 1) # p-value boundary for df=1
</code></pre>
</article>
<article class="doc-entry" id="doc-chi-square-goodness-fit">
<h3><a class="doc-anchor" href="#doc-chi-square-goodness-fit">#</a> <code>chi_square_goodness_fit</code></h3>
<p><code>chi_square_goodness_fit(observed, expected) → {statistic, df, p_value}</code> — Pearson χ² goodness-of-fit. df = <code>len - 1</code>.</p>
<pre><code class="lang-perl">p chi_square_goodness_fit([18,22,20], [20,20,20])
</code></pre>
</article>
<article class="doc-entry" id="doc-chi-square-independence">
<h3><a class="doc-anchor" href="#doc-chi-square-independence">#</a> <code>chi_square_independence</code></h3>
<p><code>chi_square_independence(contingency) → {statistic, df, p_value}</code> — χ² test of independence on an r×c contingency table.</p>
<pre><code class="lang-perl">p chi_square_independence([[10,20],[30,40]])
</code></pre>
</article>
<article class="doc-entry" id="doc-chicken-game-payoff">
<h3><a class="doc-anchor" href="#doc-chicken-game-payoff">#</a> <code>chicken_game_payoff</code></h3>
<p><code>chicken_game_payoff</code> — operation <code>chicken game payoff</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p chicken_game_payoff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chinese-lunation-winter">
<h3><a class="doc-anchor" href="#doc-chinese-lunation-winter">#</a> <code>chinese_lunation_winter</code></h3>
<p><code>chinese_lunation_winter</code> — operation <code>chinese lunation winter</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p chinese_lunation_winter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chinese-new-year">
<h3><a class="doc-anchor" href="#doc-chinese-new-year">#</a> <code>chinese_new_year</code></h3>
<p><code>chinese_new_year</code> — operation <code>chinese new year</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p chinese_new_year $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chinese-remainder">
<h3><a class="doc-anchor" href="#doc-chinese-remainder">#</a> <code>chinese_remainder</code></h3>
<p><code>chinese_remainder</code> (alias <code>crt</code>) solves a system of simultaneous congruences via the Chinese Remainder Theorem.</p>
<pre><code class="lang-perl">p crt([2,3,2], [3,5,7]) # 23 (x≡2 mod 3, x≡3 mod 5, x≡2 mod 7)
</code></pre>
</article>
<article class="doc-entry" id="doc-chinese-year-zodiac">
<h3><a class="doc-anchor" href="#doc-chinese-year-zodiac">#</a> <code>chinese_year_zodiac</code></h3>
<p><code>chinese_year_zodiac</code> — operation <code>chinese year zodiac</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p chinese_year_zodiac $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chinese-zodiac">
<h3><a class="doc-anchor" href="#doc-chinese-zodiac">#</a> <code>chinese_zodiac</code></h3>
<p><code>chinese_zodiac</code> — operation <code>chinese zodiac</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p chinese_zodiac $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chirp">
<h3><a class="doc-anchor" href="#doc-chirp">#</a> <code>chirp</code></h3>
<p><code>chirp</code> generates a linear chirp signal sweeping from f0 to f1 Hz. Args: n_samples, f0, f1, sample_rate.</p>
<pre><code class="lang-perl">my @sig = @{chirp(1000, 100, 1000, 8000)}
</code></pre>
</article>
<article class="doc-entry" id="doc-chirp-linear">
<h3><a class="doc-anchor" href="#doc-chirp-linear">#</a> <code>chirp_linear</code></h3>
<p><code>chirp_linear</code> — operation <code>chirp linear</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p chirp_linear $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chirp-mass">
<h3><a class="doc-anchor" href="#doc-chirp-mass">#</a> <code>chirp_mass</code></h3>
<p><code>chirp_mass</code> — operation <code>chirp mass</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p chirp_mass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chirp-mass-inspiral-step">
<h3><a class="doc-anchor" href="#doc-chirp-mass-inspiral-step">#</a> <code>chirp_mass_inspiral_step</code></h3>
<p><code>chirp_mass_inspiral_step</code> — single-step update of <code>chirp mass inspiral</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p chirp_mass_inspiral_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chisquare-metric">
<h3><a class="doc-anchor" href="#doc-chisquare-metric">#</a> <code>chisquare_metric</code></h3>
<p><code>chisquare_metric</code> — metric of <code>chisquare</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p chisquare_metric $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chkstr">
<h3><a class="doc-anchor" href="#doc-chkstr">#</a> <code>chkstr</code></h3>
<p><code>chkstr</code> — operation <code>chkstr</code>. Alias for <code>chunk_string</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p chkstr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chkw">
<h3><a class="doc-anchor" href="#doc-chkw">#</a> <code>chkw</code></h3>
<p><code>chkw</code> — operation <code>chkw</code>. Alias for <code>chunk_while</code>. Category: *ruby enumerable extras*.</p>
<pre><code class="lang-perl">p chkw $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chlorine-radical-decay">
<h3><a class="doc-anchor" href="#doc-chlorine-radical-decay">#</a> <code>chlorine_radical_decay</code></h3>
<p><code>chlorine_radical_decay</code> — operation <code>chlorine radical decay</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p chlorine_radical_decay $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cholesky">
<h3><a class="doc-anchor" href="#doc-cholesky">#</a> <code>cholesky</code></h3>
<p><code>matrix_cholesky</code> (aliases <code>mchol</code>, <code>cholesky</code>) computes the Cholesky decomposition of a symmetric positive-definite matrix. Returns lower-triangular L where M = L·L^T.</p>
<pre><code class="lang-perl">my $L = cholesky([[4,2],[2,3]])
</code></pre>
</article>
<article class="doc-entry" id="doc-chomp-str">
<h3><a class="doc-anchor" href="#doc-chomp-str">#</a> <code>chomp_str</code></h3>
<p><code>chomp_str</code> — operation <code>chomp str</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p chomp_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-choose">
<h3><a class="doc-anchor" href="#doc-choose">#</a> <code>choose</code></h3>
<p><code>choose</code> — operation <code>choose</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p choose $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chop-str">
<h3><a class="doc-anchor" href="#doc-chop-str">#</a> <code>chop_str</code></h3>
<p><code>chop_str</code> — operation <code>chop str</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p chop_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chord-augmented">
<h3><a class="doc-anchor" href="#doc-chord-augmented">#</a> <code>chord_augmented</code></h3>
<p><code>chord_augmented(root) → array</code> — augmented triad (root, +4, +8).</p>
</article>
<article class="doc-entry" id="doc-chord-diminished">
<h3><a class="doc-anchor" href="#doc-chord-diminished">#</a> <code>chord_diminished</code></h3>
<p><code>chord_diminished(root) → array</code> — diminished triad (root, +3, +6).</p>
</article>
<article class="doc-entry" id="doc-chord-diminished7">
<h3><a class="doc-anchor" href="#doc-chord-diminished7">#</a> <code>chord_diminished7</code></h3>
<p><code>chord_diminished7(root) → array</code> — diminished 7th (root, +3, +6, +9).</p>
</article>
<article class="doc-entry" id="doc-chord-dominant7">
<h3><a class="doc-anchor" href="#doc-chord-dominant7">#</a> <code>chord_dominant7</code></h3>
<p><code>chord_dominant7(root) → array</code> — dominant 7th (root, +4, +7, +10).</p>
<pre><code class="lang-perl">p chord_dominant7(60)
</code></pre>
</article>
<article class="doc-entry" id="doc-chord-major">
<h3><a class="doc-anchor" href="#doc-chord-major">#</a> <code>chord_major</code></h3>
<p><code>chord_major(root) → array</code> — major triad MIDI notes (root, +4, +7). Accepts MIDI int or note-name string.</p>
<pre><code class="lang-perl">p chord_major(60) # [60, 64, 67] (C E G)
p chord_major("A4") # [69, 73, 76]
</code></pre>
</article>
<article class="doc-entry" id="doc-chord-major7">
<h3><a class="doc-anchor" href="#doc-chord-major7">#</a> <code>chord_major7</code></h3>
<p><code>chord_major7(root) → array</code> — major 7th (root, +4, +7, +11).</p>
</article>
<article class="doc-entry" id="doc-chord-minor">
<h3><a class="doc-anchor" href="#doc-chord-minor">#</a> <code>chord_minor</code></h3>
<p><code>chord_minor(root) → array</code> — minor triad (root, +3, +7).</p>
<pre><code class="lang-perl">p chord_minor(60) # [60, 63, 67]
</code></pre>
</article>
<article class="doc-entry" id="doc-chord-minor7">
<h3><a class="doc-anchor" href="#doc-chord-minor7">#</a> <code>chord_minor7</code></h3>
<p><code>chord_minor7(root) → array</code> — minor 7th (root, +3, +7, +10).</p>
</article>
<article class="doc-entry" id="doc-chord-notes">
<h3><a class="doc-anchor" href="#doc-chord-notes">#</a> <code>chord_notes</code></h3>
<p><code>chord_notes</code> — music-theory chord constructor <code>notes</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p chord_notes $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chord-quality-classify">
<h3><a class="doc-anchor" href="#doc-chord-quality-classify">#</a> <code>chord_quality_classify</code></h3>
<p><code>chord_quality_classify</code> — music-theory chord constructor <code>quality classify</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p chord_quality_classify $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chord-root-inversion">
<h3><a class="doc-anchor" href="#doc-chord-root-inversion">#</a> <code>chord_root_inversion</code></h3>
<p><code>chord_root_inversion</code> — music-theory chord constructor <code>root inversion</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p chord_root_inversion $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chord-to-freqs">
<h3><a class="doc-anchor" href="#doc-chord-to-freqs">#</a> <code>chord_to_freqs</code></h3>
<p><code>chord_to_freqs</code> — convert from <code>chord</code> to <code>freqs</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p chord_to_freqs $value
</code></pre>
</article>
<article class="doc-entry" id="doc-chord-voicing-close">
<h3><a class="doc-anchor" href="#doc-chord-voicing-close">#</a> <code>chord_voicing_close</code></h3>
<p><code>chord_voicing_close</code> — music-theory chord constructor <code>voicing close</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p chord_voicing_close $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chorus-simple">
<h3><a class="doc-anchor" href="#doc-chorus-simple">#</a> <code>chorus_simple</code></h3>
<p><code>chorus_simple(signal, depth_ms=8, rate_hz=0.5, sr=44100, mix=0.5) → array</code> — LFO-modulated short delay line mixed with the dry signal.</p>
</article>
<article class="doc-entry" id="doc-chow-test-stat">
<h3><a class="doc-anchor" href="#doc-chow-test-stat">#</a> <code>chow_test_stat</code></h3>
<p><code>chow_test_stat</code> — operation <code>chow test stat</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p chow_test_stat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-christoffel-first-kind-step">
<h3><a class="doc-anchor" href="#doc-christoffel-first-kind-step">#</a> <code>christoffel_first_kind_step</code></h3>
<p><code>christoffel_first_kind_step</code> — single-step update of <code>christoffel first kind</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p christoffel_first_kind_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-christoffel-second-kind-step">
<h3><a class="doc-anchor" href="#doc-christoffel-second-kind-step">#</a> <code>christoffel_second_kind_step</code></h3>
<p><code>christoffel_second_kind_step</code> — single-step update of <code>christoffel second kind</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p christoffel_second_kind_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-christoffel-symbol-normalize">
<h3><a class="doc-anchor" href="#doc-christoffel-symbol-normalize">#</a> <code>christoffel_symbol_normalize</code></h3>
<p><code>christoffel_symbol_normalize</code> — operation <code>christoffel symbol normalize</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p christoffel_symbol_normalize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-christoffel-word">
<h3><a class="doc-anchor" href="#doc-christoffel-word">#</a> <code>christoffel_word</code></h3>
<p><code>christoffel_word</code> — operation <code>christoffel word</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p christoffel_word $x
</code></pre>
</article>
<article class="doc-entry" id="doc-christofides-ratio-bound">
<h3><a class="doc-anchor" href="#doc-christofides-ratio-bound">#</a> <code>christofides_ratio_bound</code></h3>
<p><code>christofides_ratio_bound</code> — operation <code>christofides ratio bound</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p christofides_ratio_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chroma-feature-step">
<h3><a class="doc-anchor" href="#doc-chroma-feature-step">#</a> <code>chroma_feature_step</code></h3>
<p><code>chroma_feature_step</code> — single-step update of <code>chroma feature</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p chroma_feature_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chromatic-adaptation">
<h3><a class="doc-anchor" href="#doc-chromatic-adaptation">#</a> <code>chromatic_adaptation</code></h3>
<p><code>chromatic_adaptation</code> — operation <code>chromatic adaptation</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p chromatic_adaptation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chromatic-homology-rank">
<h3><a class="doc-anchor" href="#doc-chromatic-homology-rank">#</a> <code>chromatic_homology_rank</code></h3>
<p><code>chromatic_homology_rank</code> — operation <code>chromatic homology rank</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p chromatic_homology_rank $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chromatic-number-greedy">
<h3><a class="doc-anchor" href="#doc-chromatic-number-greedy">#</a> <code>chromatic_number_greedy</code></h3>
<p><code>chromatic_number_greedy</code> — operation <code>chromatic number greedy</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p chromatic_number_greedy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chroot">
<h3><a class="doc-anchor" href="#doc-chroot">#</a> <code>chroot</code></h3>
<p><code>chroot</code> — operation <code>chroot</code>. Category: *process / system*.</p>
<pre><code class="lang-perl">p chroot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chsh-expectation">
<h3><a class="doc-anchor" href="#doc-chsh-expectation">#</a> <code>chsh_expectation</code></h3>
<p><code>chsh_expectation</code> — operation <code>chsh expectation</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p chsh_expectation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chull">
<h3><a class="doc-anchor" href="#doc-chull">#</a> <code>chull</code></h3>
<p><code>convex_hull(@points)</code> (alias <code>chull</code>) — computes the convex hull of a set of 2D points. Points given as flat list [x1,y1,x2,y2,...]. Returns the hull vertices in counterclockwise order. Uses Graham scan algorithm.</p>
<pre><code class="lang-perl">my @pts = (0,0, 1,1, 2,0, 1,0.5)
my $hull = chull(@pts)
p @$hull
</code></pre>
</article>
<article class="doc-entry" id="doc-chunk-by">
<h3><a class="doc-anchor" href="#doc-chunk-by">#</a> <code>chunk_by</code></h3>
<p><code>chunk_by</code> — operation <code>chunk by</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p chunk_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chunk-n">
<h3><a class="doc-anchor" href="#doc-chunk-n">#</a> <code>chunk_n</code></h3>
<p><code>chunk_n</code> — operation <code>chunk n</code>. Alias for <code>group_of_n</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p chunk_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chunk-string">
<h3><a class="doc-anchor" href="#doc-chunk-string">#</a> <code>chunk_string</code></h3>
<p><code>chunk_string</code> — operation <code>chunk string</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p chunk_string $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chunk-while">
<h3><a class="doc-anchor" href="#doc-chunk-while">#</a> <code>chunk_while</code></h3>
<p><code>chunk_while</code> — operation <code>chunk while</code>. Category: *ruby enumerable extras*.</p>
<pre><code class="lang-perl">p chunk_while $x
</code></pre>
</article>
<article class="doc-entry" id="doc-church-numeral-n">
<h3><a class="doc-anchor" href="#doc-church-numeral-n">#</a> <code>church_numeral_n</code></h3>
<p><code>church_numeral_n</code> — operation <code>church numeral n</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p church_numeral_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-chvatal-gomory-cut">
<h3><a class="doc-anchor" href="#doc-chvatal-gomory-cut">#</a> <code>chvatal_gomory_cut</code></h3>
<p><code>chvatal_gomory_cut</code> — operation <code>chvatal gomory cut</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p chvatal_gomory_cut $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ci">
<h3><a class="doc-anchor" href="#doc-ci">#</a> <code>ci</code></h3>
<p><code>confidence_interval</code> (alias <code>ci</code>) computes a confidence interval for the mean. Default 95%. Returns [lower, upper].</p>
<pre><code class="lang-perl">my ($lo, $hi) = @{ci([10,12,14,11,13])}
p "95%% CI: $lo to $hi"
my ($lo99, $hi99) = @{ci([10,12,14,11,13], 0.99)}
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-aggregate">
<h3><a class="doc-anchor" href="#doc-cidr-aggregate">#</a> <code>cidr_aggregate</code></h3>
<p><code>cidr_aggregate</code> — CIDR block op <code>aggregate</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_aggregate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-broadcast">
<h3><a class="doc-anchor" href="#doc-cidr-broadcast">#</a> <code>cidr_broadcast</code></h3>
<p><code>cidr_broadcast</code> — CIDR block op <code>broadcast</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_broadcast $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-class">
<h3><a class="doc-anchor" href="#doc-cidr-class">#</a> <code>cidr_class</code></h3>
<p><code>cidr_class</code> — CIDR block op <code>class</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_class $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-compare">
<h3><a class="doc-anchor" href="#doc-cidr-compare">#</a> <code>cidr_compare</code></h3>
<p><code>cidr_compare</code> — CIDR block op <code>compare</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_compare $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-contains">
<h3><a class="doc-anchor" href="#doc-cidr-contains">#</a> <code>cidr_contains</code></h3>
<p><code>cidr_contains</code> — CIDR block op <code>contains</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_contains $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-difference">
<h3><a class="doc-anchor" href="#doc-cidr-difference">#</a> <code>cidr_difference</code></h3>
<p><code>cidr_difference</code> — CIDR block op <code>difference</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_difference $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-distance">
<h3><a class="doc-anchor" href="#doc-cidr-distance">#</a> <code>cidr_distance</code></h3>
<p><code>cidr_distance</code> — CIDR block op <code>distance</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-first-host">
<h3><a class="doc-anchor" href="#doc-cidr-first-host">#</a> <code>cidr_first_host</code></h3>
<p><code>cidr_first_host</code> — CIDR block op <code>first host</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_first_host $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-format">
<h3><a class="doc-anchor" href="#doc-cidr-format">#</a> <code>cidr_format</code></h3>
<p><code>cidr_format</code> — CIDR block op <code>format</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_format $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-hostmask">
<h3><a class="doc-anchor" href="#doc-cidr-hostmask">#</a> <code>cidr_hostmask</code></h3>
<p><code>cidr_hostmask</code> — CIDR block op <code>hostmask</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_hostmask $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-hosts">
<h3><a class="doc-anchor" href="#doc-cidr-hosts">#</a> <code>cidr_hosts</code></h3>
<p><code>cidr_hosts</code> — CIDR block op <code>hosts</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_hosts $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-intersection">
<h3><a class="doc-anchor" href="#doc-cidr-intersection">#</a> <code>cidr_intersection</code></h3>
<p><code>cidr_intersection</code> — CIDR block op <code>intersection</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_intersection $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-is-aggregable">
<h3><a class="doc-anchor" href="#doc-cidr-is-aggregable">#</a> <code>cidr_is_aggregable</code></h3>
<p><code>cidr_is_aggregable</code> — CIDR block op <code>is aggregable</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_is_aggregable $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-iterate">
<h3><a class="doc-anchor" href="#doc-cidr-iterate">#</a> <code>cidr_iterate</code></h3>
<p><code>cidr_iterate</code> — CIDR block op <code>iterate</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_iterate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-last-host">
<h3><a class="doc-anchor" href="#doc-cidr-last-host">#</a> <code>cidr_last_host</code></h3>
<p><code>cidr_last_host</code> — CIDR block op <code>last host</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_last_host $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-minimum-covering">
<h3><a class="doc-anchor" href="#doc-cidr-minimum-covering">#</a> <code>cidr_minimum_covering</code></h3>
<p><code>cidr_minimum_covering</code> — CIDR block op <code>minimum covering</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_minimum_covering $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-netmask">
<h3><a class="doc-anchor" href="#doc-cidr-netmask">#</a> <code>cidr_netmask</code></h3>
<p><code>cidr_netmask</code> — CIDR block op <code>netmask</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_netmask $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-network">
<h3><a class="doc-anchor" href="#doc-cidr-network">#</a> <code>cidr_network</code></h3>
<p><code>cidr_network</code> — CIDR block op <code>network</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_network $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-next">
<h3><a class="doc-anchor" href="#doc-cidr-next">#</a> <code>cidr_next</code></h3>
<p><code>cidr_next</code> — CIDR block op <code>next</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_next $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-num-hosts">
<h3><a class="doc-anchor" href="#doc-cidr-num-hosts">#</a> <code>cidr_num_hosts</code></h3>
<p><code>cidr_num_hosts</code> — CIDR block op <code>num hosts</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_num_hosts $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-overlaps">
<h3><a class="doc-anchor" href="#doc-cidr-overlaps">#</a> <code>cidr_overlaps</code></h3>
<p><code>cidr_overlaps</code> — CIDR block op <code>overlaps</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_overlaps $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-parse">
<h3><a class="doc-anchor" href="#doc-cidr-parse">#</a> <code>cidr_parse</code></h3>
<p><code>cidr_parse</code> — CIDR block op <code>parse</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-prefix-len">
<h3><a class="doc-anchor" href="#doc-cidr-prefix-len">#</a> <code>cidr_prefix_len</code></h3>
<p><code>cidr_prefix_len</code> — CIDR block op <code>prefix len</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_prefix_len $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-prev">
<h3><a class="doc-anchor" href="#doc-cidr-prev">#</a> <code>cidr_prev</code></h3>
<p><code>cidr_prev</code> — CIDR block op <code>prev</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_prev $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-random-ip">
<h3><a class="doc-anchor" href="#doc-cidr-random-ip">#</a> <code>cidr_random_ip</code></h3>
<p><code>cidr_random_ip</code> — CIDR block op <code>random ip</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_random_ip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-size">
<h3><a class="doc-anchor" href="#doc-cidr-size">#</a> <code>cidr_size</code></h3>
<p><code>cidr_size</code> — CIDR block op <code>size</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-sort">
<h3><a class="doc-anchor" href="#doc-cidr-sort">#</a> <code>cidr_sort</code></h3>
<p><code>cidr_sort</code> — CIDR block op <code>sort</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_sort $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-split">
<h3><a class="doc-anchor" href="#doc-cidr-split">#</a> <code>cidr_split</code></h3>
<p><code>cidr_split</code> — CIDR block op <code>split</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_split $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-subnet">
<h3><a class="doc-anchor" href="#doc-cidr-subnet">#</a> <code>cidr_subnet</code></h3>
<p><code>cidr_subnet</code> — CIDR block op <code>subnet</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_subnet $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-subnets">
<h3><a class="doc-anchor" href="#doc-cidr-subnets">#</a> <code>cidr_subnets</code></h3>
<p><code>cidr_subnets</code> — CIDR block op <code>subnets</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_subnets $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-summarize">
<h3><a class="doc-anchor" href="#doc-cidr-summarize">#</a> <code>cidr_summarize</code></h3>
<p><code>cidr_summarize</code> — CIDR block op <code>summarize</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_summarize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-supernet">
<h3><a class="doc-anchor" href="#doc-cidr-supernet">#</a> <code>cidr_supernet</code></h3>
<p><code>cidr_supernet</code> — CIDR block op <code>supernet</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_supernet $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-to-netmask">
<h3><a class="doc-anchor" href="#doc-cidr-to-netmask">#</a> <code>cidr_to_netmask</code></h3>
<p><code>cidr_to_netmask</code> — convert from <code>cidr</code> to <code>netmask</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_to_netmask $value
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-to-range">
<h3><a class="doc-anchor" href="#doc-cidr-to-range">#</a> <code>cidr_to_range</code></h3>
<p><code>cidr_to_range(cidr) → [first, last]</code> — network + broadcast addresses as strings.</p>
<pre><code class="lang-perl">p cidr_to_range("192.168.1.0/24") # ["192.168.1.0", "192.168.1.255"]
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-union">
<h3><a class="doc-anchor" href="#doc-cidr-union">#</a> <code>cidr_union</code></h3>
<p><code>cidr_union</code> — CIDR block op <code>union</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_union $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-valid-subnet">
<h3><a class="doc-anchor" href="#doc-cidr-valid-subnet">#</a> <code>cidr_valid_subnet</code></h3>
<p><code>cidr_valid_subnet</code> — CIDR block op <code>valid subnet</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_valid_subnet $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cidr-wildcard">
<h3><a class="doc-anchor" href="#doc-cidr-wildcard">#</a> <code>cidr_wildcard</code></h3>
<p><code>cidr_wildcard</code> — CIDR block op <code>wildcard</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cidr_wildcard $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ciede2000-color-distance">
<h3><a class="doc-anchor" href="#doc-ciede2000-color-distance">#</a> <code>ciede2000_color_distance</code></h3>
<p><code>ciede2000_color_distance([r,g,b], [r,g,b]) → number</code> — CIEDE2000 ΔE. Most perceptually accurate of the CIE deltas.</p>
</article>
<article class="doc-entry" id="doc-ciede76-color-distance">
<h3><a class="doc-anchor" href="#doc-ciede76-color-distance">#</a> <code>ciede76_color_distance</code></h3>
<p><code>ciede76_color_distance([r,g,b], [r,g,b]) → number</code> — CIE76 ΔE distance in Lab space (Euclidean).</p>
<pre><code class="lang-perl">p ciede76_color_distance([255,0,0], [254,1,0])
</code></pre>
</article>
<article class="doc-entry" id="doc-ciede94-color-distance">
<h3><a class="doc-anchor" href="#doc-ciede94-color-distance">#</a> <code>ciede94_color_distance</code></h3>
<p><code>ciede94_color_distance([r,g,b], [r,g,b]) → number</code> — CIE94 ΔE with chroma weighting.</p>
</article>
<article class="doc-entry" id="doc-cindex">
<h3><a class="doc-anchor" href="#doc-cindex">#</a> <code>cindex</code></h3>
<p><code>cindex STRING, SUBSTRING [, FROM]</code> — codepoint-indexed equivalent of Perl 5's <code>index</code>. Returns the zero-based codepoint position of the first occurrence, or -1 on miss. FROM is also a codepoint position. Pairs with <code>[i]</code> / <code>[a:b]</code> slice operators and <code>len</code> so search positions and slice bounds share one coordinate system.</p>
<p>Use <code>cindex</code> whenever your code mixes string search with <code>[]</code> slicing — Perl 5 <code>index</code> returns byte positions and silently misaligns when fed into <code>[]</code> (which is codepoint-based). <code>index</code> stays byte-indexed because <code>length</code> and <code>substr</code> are, and changing it would break Perl-5 binary-protocol code; <code>cindex</code> is the stryke-extension counterpart.</p>
<pre><code class="lang-perl">my $s = "hello ─ world"
p index $s, "world" # 9 (bytes — `─` is 3 bytes)
p cindex $s, "world" # 7 (codepoints)
my $i = cindex $s, "world"
p $s[$i : len($s) - 1] # "world" — slice bounds line up
</code></pre>
</article>
<article class="doc-entry" id="doc-cinv">
<h3><a class="doc-anchor" href="#doc-cinv">#</a> <code>cinv</code></h3>
<p><code>cinv</code> — operation <code>cinv</code>. Alias for <code>count_inversions</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p cinv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cinvert">
<h3><a class="doc-anchor" href="#doc-cinvert">#</a> <code>cinvert</code></h3>
<p><code>cinvert</code> — operation <code>cinvert</code>. Alias for <code>color_invert</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p cinvert $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cir-bond">
<h3><a class="doc-anchor" href="#doc-cir-bond">#</a> <code>cir_bond</code></h3>
<p><code>cir_bond</code> — operation <code>cir bond</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p cir_bond $x
</code></pre>
</article>
<article class="doc-entry" id="doc-circ3pt">
<h3><a class="doc-anchor" href="#doc-circ3pt">#</a> <code>circ3pt</code></h3>
<p><code>circ3pt</code> — operation <code>circ3pt</code>. Alias for <code>circle_from_three_points</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p circ3pt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-circle-3-points">
<h3><a class="doc-anchor" href="#doc-circle-3-points">#</a> <code>circle_3_points</code></h3>
<p><code>circle_3_points</code> — circle geometry op <code>3 points</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p circle_3_points $x
</code></pre>
</article>
<article class="doc-entry" id="doc-circle-area">
<h3><a class="doc-anchor" href="#doc-circle-area">#</a> <code>circle_area</code></h3>
<p><code>circle_area</code> — circle geometry op <code>area</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p circle_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-circle-circumference">
<h3><a class="doc-anchor" href="#doc-circle-circumference">#</a> <code>circle_circumference</code></h3>
<p><code>circle_circumference</code> — circle geometry op <code>circumference</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p circle_circumference $x
</code></pre>
</article>
<article class="doc-entry" id="doc-circle-from-three-points">
<h3><a class="doc-anchor" href="#doc-circle-from-three-points">#</a> <code>circle_from_three_points</code></h3>
<p><code>circle_from_three_points($x1, $y1, $x2, $y2, $x3, $y3)</code> (alias <code>circ3</code>) — finds the unique circle passing through three non-collinear points. Returns [$cx, $cy, $radius] or undef if collinear.</p>
<pre><code class="lang-perl">my $c = circ3(0, 0, 1, 0, 0.5, 0.866)
p "center=($c->[0], $c->[1]) r=$c->[2]"
</code></pre>
</article>
<article class="doc-entry" id="doc-circle-intersects-circle">
<h3><a class="doc-anchor" href="#doc-circle-intersects-circle">#</a> <code>circle_intersects_circle</code></h3>
<p><code>circle_intersects_circle</code> — circle geometry op <code>intersects circle</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p circle_intersects_circle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-circle-intersects-line">
<h3><a class="doc-anchor" href="#doc-circle-intersects-line">#</a> <code>circle_intersects_line</code></h3>
<p><code>circle_intersects_line</code> — circle geometry op <code>intersects line</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p circle_intersects_line $x
</code></pre>
</article>
<article class="doc-entry" id="doc-circle-of-fifths-step">
<h3><a class="doc-anchor" href="#doc-circle-of-fifths-step">#</a> <code>circle_of_fifths_step</code></h3>
<p><code>circle_of_fifths_step</code> — circle geometry op <code>of fifths step</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p circle_of_fifths_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-circuit-depth">
<h3><a class="doc-anchor" href="#doc-circuit-depth">#</a> <code>circuit_depth</code></h3>
<p><code>circuit_depth</code> — operation <code>circuit depth</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p circuit_depth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-circuit-width">
<h3><a class="doc-anchor" href="#doc-circuit-width">#</a> <code>circuit_width</code></h3>
<p><code>circuit_width</code> — operation <code>circuit width</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p circuit_width $x
</code></pre>
</article>
<article class="doc-entry" id="doc-circum">
<h3><a class="doc-anchor" href="#doc-circum">#</a> <code>circum</code></h3>
<p><code>circum</code> — operation <code>circum</code>. Alias for <code>circumference</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p circum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-circumference">
<h3><a class="doc-anchor" href="#doc-circumference">#</a> <code>circumference</code></h3>
<p><code>circumference</code> — operation <code>circumference</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p circumference $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cityhash64">
<h3><a class="doc-anchor" href="#doc-cityhash64">#</a> <code>cityhash64</code></h3>
<p><code>cityhash64</code> — operation <code>cityhash64</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p cityhash64 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clamp-array">
<h3><a class="doc-anchor" href="#doc-clamp-array">#</a> <code>clamp_array</code></h3>
<p><code>clamp_array</code> — operation <code>clamp array</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p clamp_array $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clamp-each">
<h3><a class="doc-anchor" href="#doc-clamp-each">#</a> <code>clamp_each</code></h3>
<p><code>clamp_each</code> — operation <code>clamp each</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p clamp_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clamp-fn">
<h3><a class="doc-anchor" href="#doc-clamp-fn">#</a> <code>clamp_fn</code></h3>
<p><code>clamp_fn</code> — operation <code>clamp fn</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p clamp_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clamp-int">
<h3><a class="doc-anchor" href="#doc-clamp-int">#</a> <code>clamp_int</code></h3>
<p><code>clamp_int</code> — operation <code>clamp int</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p clamp_int $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clamp-list">
<h3><a class="doc-anchor" href="#doc-clamp-list">#</a> <code>clamp_list</code></h3>
<p><code>clamp_list</code> — operation <code>clamp list</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p clamp_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clarr">
<h3><a class="doc-anchor" href="#doc-clarr">#</a> <code>clarr</code></h3>
<p><code>clarr</code> — operation <code>clarr</code>. Alias for <code>clamp_array</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p clarr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-class">
<h3><a class="doc-anchor" href="#doc-class">#</a> <code>class</code></h3>
<p><code>class</code> declares a full object-oriented class with typed fields, inheritance, traits, instance methods, and static methods. Classes provide modern OOP semantics with a clean syntax.</p>
<p><strong>Declaration:</strong></p>
<pre><code class="lang-perl">class Animal {
name: Str
age: Int = 0
fn speak { p "Animal: " . $self->name }
}
</code></pre>
<p><strong>Inheritance with <code>extends</code>:</strong></p>
<pre><code class="lang-perl">class Dog extends Animal {
breed: Str = "Mixed"
fn bark { p "Woof! I am " . $self->name }
fn speak { p $self->name . " barks!" } # override
}
</code></pre>
<p><strong>Construction (named or positional):</strong></p>
<pre><code class="lang-perl">my $dog = Dog(name => "Rex", age => 5, breed => "Lab")
my $dog = Dog("Rex", 5, "Lab") # positional
</code></pre>
<p><strong>Field access (getter/setter):</strong></p>
<pre><code class="lang-perl">p $dog->name # getter
$dog->age(6) # setter
</code></pre>
<p><strong>Static methods (<code>fn Self.name</code>):</strong></p>
<pre><code class="lang-perl">class Math {
fn Self.add($a, $b) { $a + $b }
fn Self.pi { 3.14159 }
}
p Math::add(3, 4) # 7
p Math::pi() # 3.14159
</code></pre>
<p><strong>Traits (interfaces):</strong></p>
<pre><code class="lang-perl">trait Printable { fn to_str }
class Item impl Printable {
name: Str
fn to_str { $self->name }
}
</code></pre>
<p><strong>Multiple inheritance:</strong></p>
<pre><code class="lang-perl">class C extends A, B { }
</code></pre>
<p><strong>isa checks:</strong></p>
<pre><code class="lang-perl">p $dog->isa("Dog") # 1
p $dog->isa("Animal") # 1 (parent)
p $dog->isa("Cat") # "" (false)
</code></pre>
<p><strong>Built-in methods:</strong></p>
<pre><code class="lang-perl">my @f = $dog->fields() # (name, age, breed)
my $h = $dog->to_hash() # { name => "Rex", ... }
my $d2 = $dog->with(age => 1) # functional update
my $d3 = $dog->clone() # deep copy
</code></pre>
<p><strong>Visibility (pub/priv):</strong></p>
<pre><code class="lang-perl">class Secret {
pub visible: Int = 1
priv hidden: Int = 42
pub fn get_hidden { $self->hidden } # internal access ok
}
</code></pre>
<p>Note: inherited fields come first in the values array; method lookup walks the inheritance chain.</p>
</article>
<article class="doc-entry" id="doc-class-number-bound">
<h3><a class="doc-anchor" href="#doc-class-number-bound">#</a> <code>class_number_bound</code></h3>
<p><code>class_number_bound</code> — operation <code>class number bound</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p class_number_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clausen-cl2">
<h3><a class="doc-anchor" href="#doc-clausen-cl2">#</a> <code>clausen_cl2</code></h3>
<p><code>clausen_cl2</code> — operation <code>clausen cl2</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p clausen_cl2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clausius-clapeyron">
<h3><a class="doc-anchor" href="#doc-clausius-clapeyron">#</a> <code>clausius_clapeyron</code></h3>
<p><code>clausius_clapeyron</code> — operation <code>clausius clapeyron</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p clausius_clapeyron $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clausius-clapeyron-full">
<h3><a class="doc-anchor" href="#doc-clausius-clapeyron-full">#</a> <code>clausius_clapeyron_full</code></h3>
<p><code>clausius_clapeyron_full</code> — operation <code>clausius clapeyron full</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p clausius_clapeyron_full $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clean-price">
<h3><a class="doc-anchor" href="#doc-clean-price">#</a> <code>clean_price</code></h3>
<p><code>clean_price</code> — operation <code>clean price</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p clean_price $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clighten">
<h3><a class="doc-anchor" href="#doc-clighten">#</a> <code>clighten</code></h3>
<p><code>clighten</code> — operation <code>clighten</code>. Alias for <code>color_lighten</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p clighten $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clique-count-3">
<h3><a class="doc-anchor" href="#doc-clique-count-3">#</a> <code>clique_count_3</code></h3>
<p><code>clique_count_3</code> — operation <code>clique count 3</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p clique_count_3 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clique-number-lower">
<h3><a class="doc-anchor" href="#doc-clique-number-lower">#</a> <code>clique_number_lower</code></h3>
<p><code>clique_number_lower</code> — operation <code>clique number lower</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p clique_number_lower $x
</code></pre>
</article>
<article class="doc-entry" id="doc-closed-pipe-harmonic">
<h3><a class="doc-anchor" href="#doc-closed-pipe-harmonic">#</a> <code>closed_pipe_harmonic</code></h3>
<p><code>closed_pipe_harmonic</code> — operation <code>closed pipe harmonic</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p closed_pipe_harmonic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-closest-pt-segment-2d">
<h3><a class="doc-anchor" href="#doc-closest-pt-segment-2d">#</a> <code>closest_pt_segment_2d</code></h3>
<p><code>closest_pt_segment_2d</code> — operation <code>closest pt segment 2d</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p closest_pt_segment_2d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-closing-2d">
<h3><a class="doc-anchor" href="#doc-closing-2d">#</a> <code>closing_2d</code></h3>
<p><code>closing_2d(image, size=3) → matrix</code> — dilation followed by erosion. Fills small dark holes.</p>
</article>
<article class="doc-entry" id="doc-clpi">
<h3><a class="doc-anchor" href="#doc-clpi">#</a> <code>clpi</code></h3>
<p><code>clpi</code> — operation <code>clpi</code>. Alias for <code>clamp_int</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p clpi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cluster-attack-rate">
<h3><a class="doc-anchor" href="#doc-cluster-attack-rate">#</a> <code>cluster_attack_rate</code></h3>
<p><code>cluster_attack_rate</code> — rate of <code>cluster attack</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p cluster_attack_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cluster-slots">
<h3><a class="doc-anchor" href="#doc-cluster-slots">#</a> <code>cluster_slots</code></h3>
<p><code>cluster_slots</code> — operation <code>cluster slots</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p cluster_slots $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clustering-coefficient">
<h3><a class="doc-anchor" href="#doc-clustering-coefficient">#</a> <code>clustering_coefficient</code></h3>
<p><code>clustering_coefficient</code> — operation <code>clustering coefficient</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p clustering_coefficient $x
</code></pre>
</article>
<article class="doc-entry" id="doc-clutch-score">
<h3><a class="doc-anchor" href="#doc-clutch-score">#</a> <code>clutch_score</code></h3>
<p><code>clutch_score</code> — score of <code>clutch</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p clutch_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cm-to-inches">
<h3><a class="doc-anchor" href="#doc-cm-to-inches">#</a> <code>cm_to_inches</code></h3>
<p><code>cm_to_inches</code> — convert from <code>cm</code> to <code>inches</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p cm_to_inches $value
</code></pre>
</article>
<article class="doc-entry" id="doc-cmap">
<h3><a class="doc-anchor" href="#doc-cmap">#</a> <code>cmap</code></h3>
<p><code>cmap</code> — operation <code>cmap</code>. Alias for <code>concat_map</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p cmap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cmb-temperature">
<h3><a class="doc-anchor" href="#doc-cmb-temperature">#</a> <code>cmb_temperature</code></h3>
<p><code>cmb_temperature</code> — operation <code>cmb temperature</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p cmb_temperature $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cmb-temperature-at-z">
<h3><a class="doc-anchor" href="#doc-cmb-temperature-at-z">#</a> <code>cmb_temperature_at_z</code></h3>
<p><code>cmb_temperature_at_z</code> — operation <code>cmb temperature at z</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p cmb_temperature_at_z $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cmd-exists">
<h3><a class="doc-anchor" href="#doc-cmd-exists">#</a> <code>cmd_exists</code></h3>
<p><code>cmd_exists</code> — operation <code>cmd exists</code>. Category: *process / env*.</p>
<pre><code class="lang-perl">p cmd_exists $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cmp-num">
<h3><a class="doc-anchor" href="#doc-cmp-num">#</a> <code>cmp_num</code></h3>
<p><code>cmp_num</code> — operation <code>cmp num</code>. Alias for <code>spaceship</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p cmp_num $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cmp-str">
<h3><a class="doc-anchor" href="#doc-cmp-str">#</a> <code>cmp_str</code></h3>
<p><code>cmp_str</code> — operation <code>cmp str</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p cmp_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cmpr">
<h3><a class="doc-anchor" href="#doc-cmpr">#</a> <code>cmpr</code></h3>
<p><code>cmpr</code> — operation <code>cmpr</code>. Alias for <code>compress</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p cmpr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cmyk-to-rgb">
<h3><a class="doc-anchor" href="#doc-cmyk-to-rgb">#</a> <code>cmyk_to_rgb</code></h3>
<p><code>cmyk_to_rgb</code> — convert from <code>cmyk</code> to <code>rgb</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p cmyk_to_rgb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-cn-coefficient">
<h3><a class="doc-anchor" href="#doc-cn-coefficient">#</a> <code>cn_coefficient</code></h3>
<p><code>cn_coefficient</code> — operation <code>cn coefficient</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p cn_coefficient $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cn-ode">
<h3><a class="doc-anchor" href="#doc-cn-ode">#</a> <code>cn_ode</code></h3>
<p><code>cn_ode</code> — operation <code>cn ode</code>. Alias for <code>crank_nicolson_ode</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p cn_ode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cnf-dpll-branch">
<h3><a class="doc-anchor" href="#doc-cnf-dpll-branch">#</a> <code>cnf_dpll_branch</code></h3>
<p><code>cnf_dpll_branch</code> — operation <code>cnf dpll branch</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p cnf_dpll_branch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cnf-pure-literal-elim">
<h3><a class="doc-anchor" href="#doc-cnf-pure-literal-elim">#</a> <code>cnf_pure_literal_elim</code></h3>
<p><code>cnf_pure_literal_elim</code> — operation <code>cnf pure literal elim</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p cnf_pure_literal_elim $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cnf-unit-propagate">
<h3><a class="doc-anchor" href="#doc-cnf-unit-propagate">#</a> <code>cnf_unit_propagate</code></h3>
<p><code>cnf_unit_propagate</code> — operation <code>cnf unit propagate</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p cnf_unit_propagate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cnt">
<h3><a class="doc-anchor" href="#doc-cnt">#</a> <code>cnt</code></h3>
<p><code>count</code> (aliases <code>len</code>, <code>cnt</code>) returns the number of elements in a list, the <strong>codepoint count</strong> of a string, the number of key-value pairs in a hash, or the cardinality of a set. Universal length-like function that dispatches on the type of its argument. Replaces <code>scalar @array</code> / <code>length $string</code> for stryke code; on strings it pairs with <code>[i]</code> / <code>[a:b]</code> and <code>cindex</code> / <code>crindex</code>, all of which use codepoint positions.</p>
<p>For byte length on a string, use Perl 5's <code>length</code> (kept byte-based for compat with <code>index</code> / <code>rindex</code> / <code>substr</code>). <code>size</code> is NOT a count alias — it returns a file's byte size.</p>
<pre><code class="lang-perl">my @arr = (1, 2, 3, 4, 5)
p cnt @arr # 5
p len "hello" # 5
p len "─" # 1 (codepoint)
p length "─" # 3 (bytes)
my %h = (a => 1, b => 2)
p cnt \%h # 2
rl("file.txt") |> cnt |> p # line count
</code></pre>
</article>
<article class="doc-entry" id="doc-cntw">
<h3><a class="doc-anchor" href="#doc-cntw">#</a> <code>cntw</code></h3>
<p><code>cntw</code> — operation <code>cntw</code>. Alias for <code>count_while</code>. Category: *ruby enumerable extras*.</p>
<pre><code class="lang-perl">p cntw $x
</code></pre>
</article>
<article class="doc-entry" id="doc-co2-growth-rate-step">
<h3><a class="doc-anchor" href="#doc-co2-growth-rate-step">#</a> <code>co2_growth_rate_step</code></h3>
<p><code>co2_growth_rate_step</code> — single-step update of <code>co2 growth rate</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p co2_growth_rate_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coalesce">
<h3><a class="doc-anchor" href="#doc-coalesce">#</a> <code>coalesce</code></h3>
<p><code>coalesce</code> — operation <code>coalesce</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p coalesce $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coalescent-expected-time">
<h3><a class="doc-anchor" href="#doc-coalescent-expected-time">#</a> <code>coalescent_expected_time</code></h3>
<p><code>coalescent_expected_time</code> — operation <code>coalescent expected time</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p coalescent_expected_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coalescent-tree-length">
<h3><a class="doc-anchor" href="#doc-coalescent-tree-length">#</a> <code>coalescent_tree_length</code></h3>
<p><code>coalescent_tree_length</code> — operation <code>coalescent tree length</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p coalescent_tree_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cobb-douglas">
<h3><a class="doc-anchor" href="#doc-cobb-douglas">#</a> <code>cobb_douglas</code></h3>
<p><code>cobb_douglas</code> — operation <code>cobb douglas</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p cobb_douglas $x
</code></pre>
</article>
<article class="doc-entry" id="doc-code-point-at">
<h3><a class="doc-anchor" href="#doc-code-point-at">#</a> <code>code_point_at</code></h3>
<p><code>code_point_at</code> — operation <code>code point at</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p code_point_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-codifferential-step">
<h3><a class="doc-anchor" href="#doc-codifferential-step">#</a> <code>codifferential_step</code></h3>
<p><code>codifferential_step</code> — single-step update of <code>codifferential</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p codifferential_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-codon-adaptation-index">
<h3><a class="doc-anchor" href="#doc-codon-adaptation-index">#</a> <code>codon_adaptation_index</code></h3>
<p><code>codon_adaptation_index</code> — codon table / translation <code>adaptation index</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p codon_adaptation_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-codon-optimize">
<h3><a class="doc-anchor" href="#doc-codon-optimize">#</a> <code>codon_optimize</code></h3>
<p><code>codon_optimize(protein) → string</code> — DNA back-translation using a high-frequency codon per amino acid (E. coli-style).</p>
<pre><code class="lang-perl">p codon_optimize("MKL")
</code></pre>
</article>
<article class="doc-entry" id="doc-codon-to-amino-acid">
<h3><a class="doc-anchor" href="#doc-codon-to-amino-acid">#</a> <code>codon_to_amino_acid</code></h3>
<p><code>codon_to_amino_acid(codon) → string</code> — single-letter amino acid code (<code>*</code> for stop, <code>?</code> for unknown).</p>
<pre><code class="lang-perl">p codon_to_amino_acid("ATG") # M (Methionine)
p codon_to_amino_acid("TAA") # * (stop)
</code></pre>
</article>
<article class="doc-entry" id="doc-codon-usage-table">
<h3><a class="doc-anchor" href="#doc-codon-usage-table">#</a> <code>codon_usage_table</code></h3>
<p><code>codon_usage_table(dna) → hash</code> — count of each codon in a coding sequence; reads in 3-nt frames.</p>
</article>
<article class="doc-entry" id="doc-codon-usage-variance">
<h3><a class="doc-anchor" href="#doc-codon-usage-variance">#</a> <code>codon_usage_variance</code></h3>
<p><code>codon_usage_variance</code> — codon table / translation <code>usage variance</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p codon_usage_variance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coeff-of-variation">
<h3><a class="doc-anchor" href="#doc-coeff-of-variation">#</a> <code>coeff_of_variation</code></h3>
<p><code>coeff_of_variation</code> — operation <code>coeff of variation</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p coeff_of_variation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cognitive-hierarchy-step">
<h3><a class="doc-anchor" href="#doc-cognitive-hierarchy-step">#</a> <code>cognitive_hierarchy_step</code></h3>
<p><code>cognitive_hierarchy_step</code> — single-step update of <code>cognitive hierarchy</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cognitive_hierarchy_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cohen-d">
<h3><a class="doc-anchor" href="#doc-cohen-d">#</a> <code>cohen_d</code></h3>
<p><code>cohen_d</code> (alias <code>cohend</code>) computes Cohen's d effect size between two samples. Small=0.2, medium=0.5, large=0.8.</p>
<pre><code class="lang-perl">p cohend([1,2,3], [4,5,6]) # large effect
</code></pre>
</article>
<article class="doc-entry" id="doc-cohen-kappa">
<h3><a class="doc-anchor" href="#doc-cohen-kappa">#</a> <code>cohen_kappa</code></h3>
<p><code>cohen_kappa</code> — operation <code>cohen kappa</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p cohen_kappa $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cohen-sutherland-clip">
<h3><a class="doc-anchor" href="#doc-cohen-sutherland-clip">#</a> <code>cohen_sutherland_clip</code></h3>
<p><code>cohen_sutherland_clip</code> — operation <code>cohen sutherland clip</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p cohen_sutherland_clip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coherence-xy">
<h3><a class="doc-anchor" href="#doc-coherence-xy">#</a> <code>coherence_xy</code></h3>
<p><code>coherence_xy</code> — operation <code>coherence xy</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p coherence_xy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coherent-mean-photons">
<h3><a class="doc-anchor" href="#doc-coherent-mean-photons">#</a> <code>coherent_mean_photons</code></h3>
<p><code>coherent_mean_photons</code> — operation <code>coherent mean photons</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p coherent_mean_photons $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cohomology-rank">
<h3><a class="doc-anchor" href="#doc-cohomology-rank">#</a> <code>cohomology_rank</code></h3>
<p><code>cohomology_rank</code> — operation <code>cohomology rank</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p cohomology_rank $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coif1-coeffs">
<h3><a class="doc-anchor" href="#doc-coif1-coeffs">#</a> <code>coif1_coeffs</code></h3>
<p><code>coif1_coeffs</code> — operation <code>coif1 coeffs</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p coif1_coeffs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coiflet-wavelet-step">
<h3><a class="doc-anchor" href="#doc-coiflet-wavelet-step">#</a> <code>coiflet_wavelet_step</code></h3>
<p><code>coiflet_wavelet_step</code> — single-step update of <code>coiflet wavelet</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p coiflet_wavelet_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coin-flip">
<h3><a class="doc-anchor" href="#doc-coin-flip">#</a> <code>coin_flip</code></h3>
<p><code>coin_flip</code> — operation <code>coin flip</code>. Category: *random*.</p>
<pre><code class="lang-perl">p coin_flip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cointegration-eg">
<h3><a class="doc-anchor" href="#doc-cointegration-eg">#</a> <code>cointegration_eg</code></h3>
<p><code>cointegration_eg</code> — operation <code>cointegration eg</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p cointegration_eg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cointegration-residual">
<h3><a class="doc-anchor" href="#doc-cointegration-residual">#</a> <code>cointegration_residual</code></h3>
<p><code>cointegration_residual</code> — operation <code>cointegration residual</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p cointegration_residual $x
</code></pre>
</article>
<article class="doc-entry" id="doc-colmeans">
<h3><a class="doc-anchor" href="#doc-colmeans">#</a> <code>colMeans</code></h3>
<p><code>col_means</code> (alias <code>colMeans</code>) — mean of each column. Like R's colMeans().</p>
<pre><code class="lang-perl">p colMeans([[2,4],[6,8]]) # [4, 6]
</code></pre>
</article>
<article class="doc-entry" id="doc-colsums">
<h3><a class="doc-anchor" href="#doc-colsums">#</a> <code>colSums</code></h3>
<p><code>col_sums</code> (alias <code>colSums</code>) — sum of each column. Like R's colSums().</p>
<pre><code class="lang-perl">p colSums([[1,2],[3,4]]) # [4, 6]
</code></pre>
</article>
<article class="doc-entry" id="doc-cole-cole-eis">
<h3><a class="doc-anchor" href="#doc-cole-cole-eis">#</a> <code>cole_cole_eis</code></h3>
<p><code>cole_cole_eis</code> — operation <code>cole cole eis</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p cole_cole_eis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-collapse-whitespace">
<h3><a class="doc-anchor" href="#doc-collapse-whitespace">#</a> <code>collapse_whitespace</code></h3>
<p><code>collapse_whitespace</code> — operation <code>collapse whitespace</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p collapse_whitespace $x
</code></pre>
</article>
<article class="doc-entry" id="doc-collatz">
<h3><a class="doc-anchor" href="#doc-collatz">#</a> <code>collatz</code></h3>
<p><code>collatz</code> — operation <code>collatz</code>. Alias for <code>collatz_length</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p collatz $x
</code></pre>
</article>
<article class="doc-entry" id="doc-collatz-length">
<h3><a class="doc-anchor" href="#doc-collatz-length">#</a> <code>collatz_length</code></h3>
<p><code>collatz_length</code> — operation <code>collatz length</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p collatz_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-collatz-sequence">
<h3><a class="doc-anchor" href="#doc-collatz-sequence">#</a> <code>collatz_sequence</code></h3>
<p><code>collatz_sequence</code> — operation <code>collatz sequence</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p collatz_sequence $x
</code></pre>
</article>
<article class="doc-entry" id="doc-collatz-steps">
<h3><a class="doc-anchor" href="#doc-collatz-steps">#</a> <code>collatz_steps</code></h3>
<p><code>collatz_steps</code> — operation <code>collatz steps</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p collatz_steps $x
</code></pre>
</article>
<article class="doc-entry" id="doc-collatzseq">
<h3><a class="doc-anchor" href="#doc-collatzseq">#</a> <code>collatzseq</code></h3>
<p><code>collatzseq</code> — operation <code>collatzseq</code>. Alias for <code>collatz_sequence</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p collatzseq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-collect-into-btreemap">
<h3><a class="doc-anchor" href="#doc-collect-into-btreemap">#</a> <code>collect_into_btreemap</code></h3>
<p><code>collect_into_btreemap</code> — operation <code>collect into btreemap</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p collect_into_btreemap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-collect-into-btreeset">
<h3><a class="doc-anchor" href="#doc-collect-into-btreeset">#</a> <code>collect_into_btreeset</code></h3>
<p><code>collect_into_btreeset</code> — operation <code>collect into btreeset</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p collect_into_btreeset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-collect-into-hashmap">
<h3><a class="doc-anchor" href="#doc-collect-into-hashmap">#</a> <code>collect_into_hashmap</code></h3>
<p><code>collect_into_hashmap</code> — operation <code>collect into hashmap</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p collect_into_hashmap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-collect-into-hashset">
<h3><a class="doc-anchor" href="#doc-collect-into-hashset">#</a> <code>collect_into_hashset</code></h3>
<p><code>collect_into_hashset</code> — operation <code>collect into hashset</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p collect_into_hashset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-collect-into-string">
<h3><a class="doc-anchor" href="#doc-collect-into-string">#</a> <code>collect_into_string</code></h3>
<p><code>collect_into_string</code> — operation <code>collect into string</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p collect_into_string $x
</code></pre>
</article>
<article class="doc-entry" id="doc-collision-response-2d">
<h3><a class="doc-anchor" href="#doc-collision-response-2d">#</a> <code>collision_response_2d</code></h3>
<p><code>collision_response_2d(v1, v2, normal, m1, m2) → [v1', v2']</code> — impulse-based elastic collision along contact normal.</p>
</article>
<article class="doc-entry" id="doc-collusion-payoff-step">
<h3><a class="doc-anchor" href="#doc-collusion-payoff-step">#</a> <code>collusion_payoff_step</code></h3>
<p><code>collusion_payoff_step</code> — single-step update of <code>collusion payoff</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p collusion_payoff_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-collws">
<h3><a class="doc-anchor" href="#doc-collws">#</a> <code>collws</code></h3>
<p><code>collws</code> — operation <code>collws</code>. Alias for <code>collapse_whitespace</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p collws $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color256">
<h3><a class="doc-anchor" href="#doc-color256">#</a> <code>color256</code></h3>
<p><code>color256</code> — operation <code>color256</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p color256 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-blend">
<h3><a class="doc-anchor" href="#doc-color-blend">#</a> <code>color_blend</code></h3>
<p><code>color_blend</code> — color helper <code>blend</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p color_blend $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-blend-alpha">
<h3><a class="doc-anchor" href="#doc-color-blend-alpha">#</a> <code>color_blend_alpha</code></h3>
<p><code>color_blend_alpha</code> — color helper <code>blend alpha</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p color_blend_alpha $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-blend-screen">
<h3><a class="doc-anchor" href="#doc-color-blend-screen">#</a> <code>color_blend_screen</code></h3>
<p><code>color_blend_screen</code> — color helper <code>blend screen</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p color_blend_screen $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-blend-t">
<h3><a class="doc-anchor" href="#doc-color-blend-t">#</a> <code>color_blend_t</code></h3>
<p><code>color_blend_t</code> — color helper <code>blend t</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p color_blend_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-complement">
<h3><a class="doc-anchor" href="#doc-color-complement">#</a> <code>color_complement</code></h3>
<p><code>color_complement</code> — color helper <code>complement</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p color_complement $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-darken">
<h3><a class="doc-anchor" href="#doc-color-darken">#</a> <code>color_darken</code></h3>
<p><code>color_darken</code> — color helper <code>darken</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p color_darken $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-distance">
<h3><a class="doc-anchor" href="#doc-color-distance">#</a> <code>color_distance</code></h3>
<p><code>color_distance</code> — color helper <code>distance</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p color_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-grayscale">
<h3><a class="doc-anchor" href="#doc-color-grayscale">#</a> <code>color_grayscale</code></h3>
<p><code>color_grayscale</code> — color helper <code>grayscale</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p color_grayscale $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-interpolate-hsl">
<h3><a class="doc-anchor" href="#doc-color-interpolate-hsl">#</a> <code>color_interpolate_hsl</code></h3>
<p><code>color_interpolate_hsl</code> — color helper <code>interpolate hsl</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p color_interpolate_hsl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-interpolate-lab">
<h3><a class="doc-anchor" href="#doc-color-interpolate-lab">#</a> <code>color_interpolate_lab</code></h3>
<p><code>color_interpolate_lab</code> — color helper <code>interpolate lab</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p color_interpolate_lab $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-interpolate-oklab">
<h3><a class="doc-anchor" href="#doc-color-interpolate-oklab">#</a> <code>color_interpolate_oklab</code></h3>
<p><code>color_interpolate_oklab</code> — color helper <code>interpolate oklab</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p color_interpolate_oklab $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-interpolate-rgb">
<h3><a class="doc-anchor" href="#doc-color-interpolate-rgb">#</a> <code>color_interpolate_rgb</code></h3>
<p><code>color_interpolate_rgb</code> — color helper <code>interpolate rgb</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p color_interpolate_rgb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-invert">
<h3><a class="doc-anchor" href="#doc-color-invert">#</a> <code>color_invert</code></h3>
<p><code>color_invert</code> — color helper <code>invert</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p color_invert $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-lighten">
<h3><a class="doc-anchor" href="#doc-color-lighten">#</a> <code>color_lighten</code></h3>
<p><code>color_lighten</code> — color helper <code>lighten</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p color_lighten $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-temperature-kelvin">
<h3><a class="doc-anchor" href="#doc-color-temperature-kelvin">#</a> <code>color_temperature_kelvin</code></h3>
<p><code>color_temperature_kelvin</code> — color helper <code>temperature kelvin</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p color_temperature_kelvin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-color-temperature-to-rgb">
<h3><a class="doc-anchor" href="#doc-color-temperature-to-rgb">#</a> <code>color_temperature_to_rgb</code></h3>
<p><code>color_temperature_to_rgb</code> — convert from <code>color temperature</code> to <code>rgb</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p color_temperature_to_rgb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-columbic-capacity-lihalfcell">
<h3><a class="doc-anchor" href="#doc-columbic-capacity-lihalfcell">#</a> <code>columbic_capacity_lihalfcell</code></h3>
<p><code>columbic_capacity_lihalfcell</code> — operation <code>columbic capacity lihalfcell</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p columbic_capacity_lihalfcell $x
</code></pre>
</article>
<article class="doc-entry" id="doc-column-generation-step">
<h3><a class="doc-anchor" href="#doc-column-generation-step">#</a> <code>column_generation_step</code></h3>
<p><code>column_generation_step</code> — single-step update of <code>column generation</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p column_generation_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-comb">
<h3><a class="doc-anchor" href="#doc-comb">#</a> <code>comb</code></h3>
<p><code>combinations($n, $r)</code> (alias <code>comb</code>) — number of ways to choose r items from n. Formula: n!/(r!(n-r)!). Order doesn't matter.</p>
<pre><code class="lang-perl">p comb(5, 3) # 10 (ways to choose 3 items from 5)
p comb(52, 5) # 2598960 (poker hands)
</code></pre>
</article>
<article class="doc-entry" id="doc-comb-filter">
<h3><a class="doc-anchor" href="#doc-comb-filter">#</a> <code>comb_filter</code></h3>
<p><code>comb_filter(signal, delay=441, gain=0.5) → array</code> — feedback comb: <code>y[n] = x[n] + g·y[n-delay]</code>.</p>
</article>
<article class="doc-entry" id="doc-combinations-rep">
<h3><a class="doc-anchor" href="#doc-combinations-rep">#</a> <code>combinations_rep</code></h3>
<p><code>combinations_rep</code> — operation <code>combinations rep</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p combinations_rep $x
</code></pre>
</article>
<article class="doc-entry" id="doc-combinatorial-auction-step">
<h3><a class="doc-anchor" href="#doc-combinatorial-auction-step">#</a> <code>combinatorial_auction_step</code></h3>
<p><code>combinatorial_auction_step</code> — single-step update of <code>combinatorial auction</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p combinatorial_auction_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-combrep">
<h3><a class="doc-anchor" href="#doc-combrep">#</a> <code>combrep</code></h3>
<p><code>combrep</code> — operation <code>combrep</code>. Alias for <code>combinations_rep</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p combrep $x
</code></pre>
</article>
<article class="doc-entry" id="doc-common-kmers">
<h3><a class="doc-anchor" href="#doc-common-kmers">#</a> <code>common_kmers</code></h3>
<p><code>common_kmers</code> — operation <code>common kmers</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p common_kmers $x
</code></pre>
</article>
<article class="doc-entry" id="doc-common-knowledge-iterations">
<h3><a class="doc-anchor" href="#doc-common-knowledge-iterations">#</a> <code>common_knowledge_iterations</code></h3>
<p><code>common_knowledge_iterations</code> — operation <code>common knowledge iterations</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p common_knowledge_iterations $x
</code></pre>
</article>
<article class="doc-entry" id="doc-common-prefix">
<h3><a class="doc-anchor" href="#doc-common-prefix">#</a> <code>common_prefix</code></h3>
<p><code>common_prefix</code> — operation <code>common prefix</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p common_prefix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-common-suffix">
<h3><a class="doc-anchor" href="#doc-common-suffix">#</a> <code>common_suffix</code></h3>
<p><code>common_suffix</code> — operation <code>common suffix</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p common_suffix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-comoving-distance">
<h3><a class="doc-anchor" href="#doc-comoving-distance">#</a> <code>comoving_distance</code></h3>
<p><code>comoving_distance</code> — distance / dissimilarity metric of <code>comoving</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p comoving_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-comoving-distance-approx">
<h3><a class="doc-anchor" href="#doc-comoving-distance-approx">#</a> <code>comoving_distance_approx</code></h3>
<p><code>comoving_distance_approx</code> — operation <code>comoving distance approx</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p comoving_distance_approx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-compare-versions">
<h3><a class="doc-anchor" href="#doc-compare-versions">#</a> <code>compare_versions</code></h3>
<p><code>compare_versions</code> — operation <code>compare versions</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p compare_versions $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-abs">
<h3><a class="doc-anchor" href="#doc-complex-abs">#</a> <code>complex_abs</code></h3>
<p><code>complex_abs</code> — complex number op <code>abs</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_abs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-add">
<h3><a class="doc-anchor" href="#doc-complex-add">#</a> <code>complex_add</code></h3>
<p><code>complex_add</code> — complex number op <code>add</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_add $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-angle">
<h3><a class="doc-anchor" href="#doc-complex-angle">#</a> <code>complex_angle</code></h3>
<p><code>complex_angle</code> — complex number op <code>angle</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_angle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-conjugate">
<h3><a class="doc-anchor" href="#doc-complex-conjugate">#</a> <code>complex_conjugate</code></h3>
<p><code>complex_conjugate</code> — complex number op <code>conjugate</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_conjugate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-cos">
<h3><a class="doc-anchor" href="#doc-complex-cos">#</a> <code>complex_cos</code></h3>
<p><code>complex_cos</code> — complex number op <code>cos</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_cos $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-cosh">
<h3><a class="doc-anchor" href="#doc-complex-cosh">#</a> <code>complex_cosh</code></h3>
<p><code>complex_cosh</code> — complex number op <code>cosh</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_cosh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-div">
<h3><a class="doc-anchor" href="#doc-complex-div">#</a> <code>complex_div</code></h3>
<p><code>complex_div</code> — complex number op <code>div</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_div $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-equal">
<h3><a class="doc-anchor" href="#doc-complex-equal">#</a> <code>complex_equal</code></h3>
<p><code>complex_equal</code> — complex number op <code>equal</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_equal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-exp">
<h3><a class="doc-anchor" href="#doc-complex-exp">#</a> <code>complex_exp</code></h3>
<p><code>complex_exp</code> — complex number op <code>exp</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_exp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-from-polar">
<h3><a class="doc-anchor" href="#doc-complex-from-polar">#</a> <code>complex_from_polar</code></h3>
<p><code>complex_from_polar</code> — complex number op <code>from polar</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_from_polar $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-imag">
<h3><a class="doc-anchor" href="#doc-complex-imag">#</a> <code>complex_imag</code></h3>
<p><code>complex_imag</code> — complex number op <code>imag</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_imag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-log">
<h3><a class="doc-anchor" href="#doc-complex-log">#</a> <code>complex_log</code></h3>
<p><code>complex_log</code> — complex number op <code>log</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_log $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-magnitude">
<h3><a class="doc-anchor" href="#doc-complex-magnitude">#</a> <code>complex_magnitude</code></h3>
<p><code>complex_magnitude</code> — complex number op <code>magnitude</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_magnitude $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-mul">
<h3><a class="doc-anchor" href="#doc-complex-mul">#</a> <code>complex_mul</code></h3>
<p><code>complex_mul</code> — complex number op <code>mul</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_mul $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-new">
<h3><a class="doc-anchor" href="#doc-complex-new">#</a> <code>complex_new</code></h3>
<p><code>complex_new</code> — complex number op <code>new</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-phase">
<h3><a class="doc-anchor" href="#doc-complex-phase">#</a> <code>complex_phase</code></h3>
<p><code>complex_phase</code> — complex number op <code>phase</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_phase $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-polar">
<h3><a class="doc-anchor" href="#doc-complex-polar">#</a> <code>complex_polar</code></h3>
<p><code>complex_polar</code> — complex number op <code>polar</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_polar $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-pow">
<h3><a class="doc-anchor" href="#doc-complex-pow">#</a> <code>complex_pow</code></h3>
<p><code>complex_pow</code> — complex number op <code>pow</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_pow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-real">
<h3><a class="doc-anchor" href="#doc-complex-real">#</a> <code>complex_real</code></h3>
<p><code>complex_real</code> — complex number op <code>real</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_real $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-sin">
<h3><a class="doc-anchor" href="#doc-complex-sin">#</a> <code>complex_sin</code></h3>
<p><code>complex_sin</code> — complex number op <code>sin</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_sin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-sinh">
<h3><a class="doc-anchor" href="#doc-complex-sinh">#</a> <code>complex_sinh</code></h3>
<p><code>complex_sinh</code> — complex number op <code>sinh</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_sinh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-sqrt">
<h3><a class="doc-anchor" href="#doc-complex-sqrt">#</a> <code>complex_sqrt</code></h3>
<p><code>complex_sqrt</code> — complex number op <code>sqrt</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_sqrt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-sub">
<h3><a class="doc-anchor" href="#doc-complex-sub">#</a> <code>complex_sub</code></h3>
<p><code>complex_sub</code> — complex number op <code>sub</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_sub $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-tan">
<h3><a class="doc-anchor" href="#doc-complex-tan">#</a> <code>complex_tan</code></h3>
<p><code>complex_tan</code> — complex number op <code>tan</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_tan $x
</code></pre>
</article>
<article class="doc-entry" id="doc-complex-tanh">
<h3><a class="doc-anchor" href="#doc-complex-tanh">#</a> <code>complex_tanh</code></h3>
<p><code>complex_tanh</code> — complex number op <code>tanh</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p complex_tanh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-composition-count">
<h3><a class="doc-anchor" href="#doc-composition-count">#</a> <code>composition_count</code></h3>
<p><code>composition_count</code> — count of <code>composition</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p composition_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-compositions-count">
<h3><a class="doc-anchor" href="#doc-compositions-count">#</a> <code>compositions_count</code></h3>
<p><code>compositions_count(n) → int</code> — <code>2^(n-1)</code> compositions of n.</p>
</article>
<article class="doc-entry" id="doc-compound-interest">
<h3><a class="doc-anchor" href="#doc-compound-interest">#</a> <code>compound_interest</code></h3>
<p><code>compound_interest</code> — operation <code>compound interest</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p compound_interest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-compound-interest-periods">
<h3><a class="doc-anchor" href="#doc-compound-interest-periods">#</a> <code>compound_interest_periods</code></h3>
<p><code>compound_interest_periods</code> — operation <code>compound interest periods</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p compound_interest_periods $x
</code></pre>
</article>
<article class="doc-entry" id="doc-compress">
<h3><a class="doc-anchor" href="#doc-compress">#</a> <code>compress</code></h3>
<p><code>compress</code> — operation <code>compress</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p compress $x
</code></pre>
</article>
<article class="doc-entry" id="doc-compressibility-z">
<h3><a class="doc-anchor" href="#doc-compressibility-z">#</a> <code>compressibility_z</code></h3>
<p><code>compressibility_z</code> — operation <code>compressibility z</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p compressibility_z $x
</code></pre>
</article>
<article class="doc-entry" id="doc-compton-wavelength">
<h3><a class="doc-anchor" href="#doc-compton-wavelength">#</a> <code>compton_wavelength</code></h3>
<p><code>compton_wavelength</code> — operation <code>compton wavelength</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p compton_wavelength $x
</code></pre>
</article>
<article class="doc-entry" id="doc-compute-residuals">
<h3><a class="doc-anchor" href="#doc-compute-residuals">#</a> <code>compute_residuals</code></h3>
<p><code>compute_residuals</code> — operation <code>compute residuals</code>. Alias for <code>residuals_compute</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p compute_residuals $x
</code></pre>
</article>
<article class="doc-entry" id="doc-concat-map">
<h3><a class="doc-anchor" href="#doc-concat-map">#</a> <code>concat_map</code></h3>
<p><code>concat_map</code> — operation <code>concat map</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p concat_map $x
</code></pre>
</article>
<article class="doc-entry" id="doc-concentration-dilute">
<h3><a class="doc-anchor" href="#doc-concentration-dilute">#</a> <code>concentration_dilute</code></h3>
<p><code>concentration_dilute</code> — operation <code>concentration dilute</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p concentration_dilute $x
</code></pre>
</article>
<article class="doc-entry" id="doc-concordance-correlation">
<h3><a class="doc-anchor" href="#doc-concordance-correlation">#</a> <code>concordance_correlation</code></h3>
<p><code>concordance_correlation</code> — operation <code>concordance correlation</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p concordance_correlation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cond">
<h3><a class="doc-anchor" href="#doc-cond">#</a> <code>cond</code></h3>
<p><code>matrix_cond</code> (aliases <code>mcond</code>, <code>cond</code>) estimates the condition number of a matrix (ratio of largest to smallest singular value). Large values indicate ill-conditioning.</p>
<pre><code class="lang-perl">p cond([[1,0],[0,1]]) # 1 (perfect)
p cond([[1,2],[2,4]]) # Inf (singular)
</code></pre>
</article>
<article class="doc-entry" id="doc-conditional-entropy">
<h3><a class="doc-anchor" href="#doc-conditional-entropy">#</a> <code>conditional_entropy</code></h3>
<p><code>conditional_entropy(joint_matrix) → number</code> — H(X|Y) from joint distribution P(X,Y).</p>
</article>
<article class="doc-entry" id="doc-conditional-entropy-step">
<h3><a class="doc-anchor" href="#doc-conditional-entropy-step">#</a> <code>conditional_entropy_step</code></h3>
<p><code>conditional_entropy_step</code> — single-step update of <code>conditional entropy</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p conditional_entropy_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-conditional-gradient-step">
<h3><a class="doc-anchor" href="#doc-conditional-gradient-step">#</a> <code>conditional_gradient_step</code></h3>
<p><code>conditional_gradient_step</code> — single-step update of <code>conditional gradient</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p conditional_gradient_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-condorcet-winner-check">
<h3><a class="doc-anchor" href="#doc-condorcet-winner-check">#</a> <code>condorcet_winner_check</code></h3>
<p><code>condorcet_winner_check</code> — operation <code>condorcet winner check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p condorcet_winner_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cone-surface">
<h3><a class="doc-anchor" href="#doc-cone-surface">#</a> <code>cone_surface</code></h3>
<p><code>cone_surface</code> — operation <code>cone surface</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p cone_surface $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cone-surface-area">
<h3><a class="doc-anchor" href="#doc-cone-surface-area">#</a> <code>cone_surface_area</code></h3>
<p><code>cone_surface_area</code> — operation <code>cone surface area</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p cone_surface_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cone-volume">
<h3><a class="doc-anchor" href="#doc-cone-volume">#</a> <code>cone_volume</code></h3>
<p><code>cone_volume</code> — operation <code>cone volume</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p cone_volume $x
</code></pre>
</article>
<article class="doc-entry" id="doc-conevol">
<h3><a class="doc-anchor" href="#doc-conevol">#</a> <code>conevol</code></h3>
<p><code>conevol</code> — operation <code>conevol</code>. Alias for <code>cone_volume</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p conevol $x
</code></pre>
</article>
<article class="doc-entry" id="doc-confint">
<h3><a class="doc-anchor" href="#doc-confint">#</a> <code>confint</code></h3>
<p><code>confint_lm</code> (alias <code>confint</code>) — confidence intervals for model coefficients. Returns hash with intercept_lower/upper, slope_lower/upper.</p>
<pre><code class="lang-perl">my $ci = confint(lm([1,2,3,4,5], [2,4,5,4,5]))
p $ci->{slope_lower}
</code></pre>
</article>
<article class="doc-entry" id="doc-conformal-compactification-step">
<h3><a class="doc-anchor" href="#doc-conformal-compactification-step">#</a> <code>conformal_compactification_step</code></h3>
<p><code>conformal_compactification_step</code> — single-step update of <code>conformal compactification</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p conformal_compactification_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-confusion-counts">
<h3><a class="doc-anchor" href="#doc-confusion-counts">#</a> <code>confusion_counts</code></h3>
<p><code>confusion_counts</code> — operation <code>confusion counts</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p confusion_counts $x
</code></pre>
</article>
<article class="doc-entry" id="doc-conj">
<h3><a class="doc-anchor" href="#doc-conj">#</a> <code>conj</code></h3>
<p><code>conj</code> — operation <code>conj</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p conj $x
</code></pre>
</article>
<article class="doc-entry" id="doc-connected-components">
<h3><a class="doc-anchor" href="#doc-connected-components">#</a> <code>connected_components</code></h3>
<p><code>connected_components</code> — operation <code>connected components</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p connected_components $x
</code></pre>
</article>
<article class="doc-entry" id="doc-connected-components-graph">
<h3><a class="doc-anchor" href="#doc-connected-components-graph">#</a> <code>connected_components_graph</code></h3>
<p><code>connected_components_graph</code> — operation <code>connected components graph</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p connected_components_graph $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cons">
<h3><a class="doc-anchor" href="#doc-cons">#</a> <code>cons</code></h3>
<p><code>cons</code> — operation <code>cons</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p cons $x
</code></pre>
</article>
<article class="doc-entry" id="doc-consecutive-eq">
<h3><a class="doc-anchor" href="#doc-consecutive-eq">#</a> <code>consecutive_eq</code></h3>
<p><code>consecutive_eq</code> — operation <code>consecutive eq</code>. Category: *collection more*.</p>
<pre><code class="lang-perl">p consecutive_eq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-consecutive-pairs">
<h3><a class="doc-anchor" href="#doc-consecutive-pairs">#</a> <code>consecutive_pairs</code></h3>
<p><code>consecutive_pairs</code> — operation <code>consecutive pairs</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p consecutive_pairs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-const-fn">
<h3><a class="doc-anchor" href="#doc-const-fn">#</a> <code>const_fn</code></h3>
<p><code>const_fn</code> — operation <code>const fn</code>. Category: *functional primitives*.</p>
<pre><code class="lang-perl">p const_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-constant-case">
<h3><a class="doc-anchor" href="#doc-constant-case">#</a> <code>constant_case</code></h3>
<p><code>constant_case</code> — operation <code>constant case</code>. Category: *string*.</p>
<pre><code class="lang-perl">p constant_case $x
</code></pre>
</article>
<article class="doc-entry" id="doc-constants-au-meters">
<h3><a class="doc-anchor" href="#doc-constants-au-meters">#</a> <code>constants_au_meters</code></h3>
<p><code>constants_au_meters() → number</code> — 1 AU = 1.495978707·10¹¹ m (exact).</p>
</article>
<article class="doc-entry" id="doc-constants-avogadro-n">
<h3><a class="doc-anchor" href="#doc-constants-avogadro-n">#</a> <code>constants_avogadro_n</code></h3>
<p><code>constants_avogadro_n() → number</code> — N_A = 6.02214076·10²³ mol⁻¹ (exact by SI definition).</p>
</article>
<article class="doc-entry" id="doc-constants-bohr-radius">
<h3><a class="doc-anchor" href="#doc-constants-bohr-radius">#</a> <code>constants_bohr_radius</code></h3>
<p><code>constants_bohr_radius() → number</code> — a₀ = 5.29177210903·10⁻¹¹ m.</p>
</article>
<article class="doc-entry" id="doc-constants-boltzmann-k">
<h3><a class="doc-anchor" href="#doc-constants-boltzmann-k">#</a> <code>constants_boltzmann_k</code></h3>
<p><code>constants_boltzmann_k() → number</code> — k_B = 1.380649·10⁻²³ J/K (exact).</p>
</article>
<article class="doc-entry" id="doc-constants-earth-mass">
<h3><a class="doc-anchor" href="#doc-constants-earth-mass">#</a> <code>constants_earth_mass</code></h3>
<p><code>constants_earth_mass() → number</code> — M_⊕ = 5.972·10²⁴ kg.</p>
</article>
<article class="doc-entry" id="doc-constants-earth-radius">
<h3><a class="doc-anchor" href="#doc-constants-earth-radius">#</a> <code>constants_earth_radius</code></h3>
<p><code>constants_earth_radius() → number</code> — R_⊕ = 6.371·10⁶ m (mean).</p>
</article>
<article class="doc-entry" id="doc-constants-electron-charge">
<h3><a class="doc-anchor" href="#doc-constants-electron-charge">#</a> <code>constants_electron_charge</code></h3>
<p><code>constants_electron_charge() → number</code> — e = 1.602176634·10⁻¹⁹ C (exact by SI definition).</p>
</article>
<article class="doc-entry" id="doc-constants-electron-mass">
<h3><a class="doc-anchor" href="#doc-constants-electron-mass">#</a> <code>constants_electron_mass</code></h3>
<p><code>constants_electron_mass() → number</code> — m_e = 9.1093837015·10⁻³¹ kg.</p>
</article>
<article class="doc-entry" id="doc-constants-faraday">
<h3><a class="doc-anchor" href="#doc-constants-faraday">#</a> <code>constants_faraday</code></h3>
<p><code>constants_faraday() → number</code> — F = 96,485.33212 C/mol.</p>
</article>
<article class="doc-entry" id="doc-constants-gas-r">
<h3><a class="doc-anchor" href="#doc-constants-gas-r">#</a> <code>constants_gas_r</code></h3>
<p><code>constants_gas_r() → number</code> — R = 8.314462618 J/(mol·K).</p>
</article>
<article class="doc-entry" id="doc-constants-gravitational-g">
<h3><a class="doc-anchor" href="#doc-constants-gravitational-g">#</a> <code>constants_gravitational_g</code></h3>
<p><code>constants_gravitational_g() → number</code> — G = 6.6743·10⁻¹¹ m³/(kg·s²).</p>
</article>
<article class="doc-entry" id="doc-constants-lightyear-meters">
<h3><a class="doc-anchor" href="#doc-constants-lightyear-meters">#</a> <code>constants_lightyear_meters</code></h3>
<p><code>constants_lightyear_meters() → number</code> — 1 ly = 9.4607304725808·10¹⁵ m.</p>
</article>
<article class="doc-entry" id="doc-constants-neutron-mass">
<h3><a class="doc-anchor" href="#doc-constants-neutron-mass">#</a> <code>constants_neutron_mass</code></h3>
<p><code>constants_neutron_mass() → number</code> — m_n = 1.67492749804·10⁻²⁷ kg.</p>
</article>
<article class="doc-entry" id="doc-constants-parsec-meters">
<h3><a class="doc-anchor" href="#doc-constants-parsec-meters">#</a> <code>constants_parsec_meters</code></h3>
<p><code>constants_parsec_meters() → number</code> — 1 pc = 3.085677581·10¹⁶ m.</p>
</article>
<article class="doc-entry" id="doc-constants-planck">
<h3><a class="doc-anchor" href="#doc-constants-planck">#</a> <code>constants_planck</code></h3>
<p><code>constants_planck() → number</code> — Planck's constant h = 6.62607015·10⁻³⁴ J·s.</p>
</article>
<article class="doc-entry" id="doc-constants-planck-h">
<h3><a class="doc-anchor" href="#doc-constants-planck-h">#</a> <code>constants_planck_h</code></h3>
<p><code>constants_planck_h() → number</code> — Planck constant (alias).</p>
</article>
<article class="doc-entry" id="doc-constants-planck-hbar">
<h3><a class="doc-anchor" href="#doc-constants-planck-hbar">#</a> <code>constants_planck_hbar</code></h3>
<p><code>constants_planck_hbar() → number</code> — Reduced Planck constant ℏ = h/2π.</p>
</article>
<article class="doc-entry" id="doc-constants-proton-mass">
<h3><a class="doc-anchor" href="#doc-constants-proton-mass">#</a> <code>constants_proton_mass</code></h3>
<p><code>constants_proton_mass() → number</code> — m_p = 1.67262192369·10⁻²⁷ kg.</p>
</article>
<article class="doc-entry" id="doc-constants-rydberg">
<h3><a class="doc-anchor" href="#doc-constants-rydberg">#</a> <code>constants_rydberg</code></h3>
<p><code>constants_rydberg() → number</code> — R_∞ = 1.0973731568160·10⁷ m⁻¹.</p>
</article>
<article class="doc-entry" id="doc-constants-solar-mass">
<h3><a class="doc-anchor" href="#doc-constants-solar-mass">#</a> <code>constants_solar_mass</code></h3>
<p><code>constants_solar_mass() → number</code> — M_⊙ = 1.989·10³⁰ kg.</p>
</article>
<article class="doc-entry" id="doc-constants-solar-radius">
<h3><a class="doc-anchor" href="#doc-constants-solar-radius">#</a> <code>constants_solar_radius</code></h3>
<p><code>constants_solar_radius() → number</code> — R_⊙ = 6.957·10⁸ m.</p>
</article>
<article class="doc-entry" id="doc-constants-speed-of-light">
<h3><a class="doc-anchor" href="#doc-constants-speed-of-light">#</a> <code>constants_speed_of_light</code></h3>
<p><code>constants_speed_of_light() → number</code> — c = 299,792,458 m/s (exact by SI definition).</p>
</article>
<article class="doc-entry" id="doc-constants-stefan-boltzmann">
<h3><a class="doc-anchor" href="#doc-constants-stefan-boltzmann">#</a> <code>constants_stefan_boltzmann</code></h3>
<p><code>constants_stefan_boltzmann() → number</code> — σ = 5.670374419·10⁻⁸ W/(m²·K⁴).</p>
</article>
<article class="doc-entry" id="doc-constituency-cyk">
<h3><a class="doc-anchor" href="#doc-constituency-cyk">#</a> <code>constituency_cyk</code></h3>
<p><code>constituency_cyk</code> — operation <code>constituency cyk</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p constituency_cyk $x
</code></pre>
</article>
<article class="doc-entry" id="doc-consumer-surplus">
<h3><a class="doc-anchor" href="#doc-consumer-surplus">#</a> <code>consumer_surplus</code></h3>
<p><code>consumer_surplus</code> — operation <code>consumer surplus</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p consumer_surplus $x
</code></pre>
</article>
<article class="doc-entry" id="doc-contact-tracing-eff">
<h3><a class="doc-anchor" href="#doc-contact-tracing-eff">#</a> <code>contact_tracing_eff</code></h3>
<p><code>contact_tracing_eff</code> — operation <code>contact tracing eff</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p contact_tracing_eff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-contains">
<h3><a class="doc-anchor" href="#doc-contains">#</a> <code>contains</code></h3>
<p><code>contains</code> — operation <code>contains</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p contains $x
</code></pre>
</article>
<article class="doc-entry" id="doc-contains-all">
<h3><a class="doc-anchor" href="#doc-contains-all">#</a> <code>contains_all</code></h3>
<p><code>contains_all</code> — operation <code>contains all</code>. Category: *string*.</p>
<pre><code class="lang-perl">p contains_all $x
</code></pre>
</article>
<article class="doc-entry" id="doc-contains-any">
<h3><a class="doc-anchor" href="#doc-contains-any">#</a> <code>contains_any</code></h3>
<p><code>contains_any</code> — operation <code>contains any</code>. Category: *string*.</p>
<pre><code class="lang-perl">p contains_any $x
</code></pre>
</article>
<article class="doc-entry" id="doc-contains-elem">
<h3><a class="doc-anchor" href="#doc-contains-elem">#</a> <code>contains_elem</code></h3>
<p><code>contains_elem</code> — operation <code>contains elem</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p contains_elem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-contcomp">
<h3><a class="doc-anchor" href="#doc-contcomp">#</a> <code>contcomp</code></h3>
<p><code>contcomp</code> — operation <code>contcomp</code>. Alias for <code>continuous_compound</code>. Category: *finance (extended)*.</p>
<pre><code class="lang-perl">p contcomp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-content-negotiate">
<h3><a class="doc-anchor" href="#doc-content-negotiate">#</a> <code>content_negotiate</code></h3>
<p><code>content_negotiate</code> — operation <code>content negotiate</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p content_negotiate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-continued-fraction-sqrt">
<h3><a class="doc-anchor" href="#doc-continued-fraction-sqrt">#</a> <code>continued_fraction_sqrt</code></h3>
<p><code>continued_fraction_sqrt</code> — operation <code>continued fraction sqrt</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p continued_fraction_sqrt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-continuous-compound">
<h3><a class="doc-anchor" href="#doc-continuous-compound">#</a> <code>continuous_compound</code></h3>
<p><code>continuous_compound($principal, $rate, $time)</code> (alias <code>ccomp</code>) — computes future value with continuous compounding: P × e^(rt).</p>
<pre><code class="lang-perl">p ccomp(1000, 0.05, 10) # ~1648.72
</code></pre>
</article>
<article class="doc-entry" id="doc-contour-area">
<h3><a class="doc-anchor" href="#doc-contour-area">#</a> <code>contour_area</code></h3>
<p><code>contour_area(points) → number</code> — shoelace polygon area.</p>
<pre><code class="lang-perl">p contour_area([[0,0],[1,0],[1,1],[0,1]]) # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-contour-centroid">
<h3><a class="doc-anchor" href="#doc-contour-centroid">#</a> <code>contour_centroid</code></h3>
<p><code>contour_centroid(points) → [x, y]</code> — area-weighted centroid of the closed polygon (<code>M10/M00, M01/M00</code> per OpenCV). Falls back to vertex mean if the polygon has zero signed area.</p>
</article>
<article class="doc-entry" id="doc-contour-find">
<h3><a class="doc-anchor" href="#doc-contour-find">#</a> <code>contour_find</code></h3>
<p><code>contour_find(image, thresh=128) → array</code> — boundary cells of foreground regions as <code>[[row, col], …]</code>.</p>
</article>
<article class="doc-entry" id="doc-contour-perimeter">
<h3><a class="doc-anchor" href="#doc-contour-perimeter">#</a> <code>contour_perimeter</code></h3>
<p><code>contour_perimeter(points) → number</code> — perimeter of a polygon defined by an ordered point list.</p>
</article>
<article class="doc-entry" id="doc-contrast-ratio">
<h3><a class="doc-anchor" href="#doc-contrast-ratio">#</a> <code>contrast_ratio</code></h3>
<p><code>contrast_ratio</code> — ratio of <code>contrast</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p contrast_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-contrast-ratio-wcag">
<h3><a class="doc-anchor" href="#doc-contrast-ratio-wcag">#</a> <code>contrast_ratio_wcag</code></h3>
<p><code>contrast_ratio_wcag</code> — operation <code>contrast ratio wcag</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p contrast_ratio_wcag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-conv">
<h3><a class="doc-anchor" href="#doc-conv">#</a> <code>conv</code></h3>
<p><code>conv</code> — operation <code>conv</code>. Alias for <code>convolution</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p conv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-conv1d-apply">
<h3><a class="doc-anchor" href="#doc-conv1d-apply">#</a> <code>conv1d_apply</code></h3>
<p><code>conv1d_apply(signal, kernel) → array</code> — 1D convolution with zero-padding.</p>
</article>
<article class="doc-entry" id="doc-conv2d-apply">
<h3><a class="doc-anchor" href="#doc-conv2d-apply">#</a> <code>conv2d_apply</code></h3>
<p><code>conv2d_apply(image, kernel) → matrix</code> — true mathematical 2D convolution: kernel is <strong>flipped</strong> in both axes before the sum-of-products. Zero-padded; output has same dimensions as input. Use <code>correlate2d</code> for the cross-correlation form (no flip).</p>
<pre><code class="lang-perl">p conv2d_apply($img, gaussian_kernel(5, 1.0))
</code></pre>
</article>
<article class="doc-entry" id="doc-converge">
<h3><a class="doc-anchor" href="#doc-converge">#</a> <code>converge</code></h3>
<p><code>converge</code> — operation <code>converge</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p converge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-convex-hull-3d">
<h3><a class="doc-anchor" href="#doc-convex-hull-3d">#</a> <code>convex_hull_3d</code></h3>
<p><code>convex_hull_3d</code> — operation <code>convex hull 3d</code>. Category: *uncategorized*.</p>
<pre><code class="lang-perl">p convex_hull_3d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-convex-hull-3d-simple">
<h3><a class="doc-anchor" href="#doc-convex-hull-3d-simple">#</a> <code>convex_hull_3d_simple</code></h3>
<p><code>convex_hull_3d_simple</code> — operation <code>convex hull 3d simple</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p convex_hull_3d_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-convex-hull-chan">
<h3><a class="doc-anchor" href="#doc-convex-hull-chan">#</a> <code>convex_hull_chan</code></h3>
<p><code>convex_hull_chan</code> — operation <code>convex hull chan</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p convex_hull_chan $x
</code></pre>
</article>
<article class="doc-entry" id="doc-convex-hull-jarvis">
<h3><a class="doc-anchor" href="#doc-convex-hull-jarvis">#</a> <code>convex_hull_jarvis</code></h3>
<p><code>convex_hull_jarvis</code> — operation <code>convex hull jarvis</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p convex_hull_jarvis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-convexity">
<h3><a class="doc-anchor" href="#doc-convexity">#</a> <code>convexity</code></h3>
<p><code>convexity(cashflows, rate) → number</code> — second-order yield sensitivity: <code>Σ t·(t+1)·cf/(1+r)^(t+2) / price</code>.</p>
<pre><code class="lang-perl">p convexity([100,100,1100], 0.05)
</code></pre>
</article>
<article class="doc-entry" id="doc-convolution">
<h3><a class="doc-anchor" href="#doc-convolution">#</a> <code>convolution</code></h3>
<p><code>convolution</code> — operation <code>convolution</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p convolution $x
</code></pre>
</article>
<article class="doc-entry" id="doc-convolve-2d">
<h3><a class="doc-anchor" href="#doc-convolve-2d">#</a> <code>convolve_2d</code></h3>
<p><code>convolve_2d</code> — operation <code>convolve 2d</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p convolve_2d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-convolve-full">
<h3><a class="doc-anchor" href="#doc-convolve-full">#</a> <code>convolve_full</code></h3>
<p><code>convolve_full</code> — operation <code>convolve full</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p convolve_full $x
</code></pre>
</article>
<article class="doc-entry" id="doc-convolve-valid">
<h3><a class="doc-anchor" href="#doc-convolve-valid">#</a> <code>convolve_valid</code></h3>
<p><code>convolve_valid</code> — operation <code>convolve valid</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p convolve_valid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cookie-domain-matches">
<h3><a class="doc-anchor" href="#doc-cookie-domain-matches">#</a> <code>cookie_domain_matches</code></h3>
<p><code>cookie_domain_matches</code> — operation <code>cookie domain matches</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cookie_domain_matches $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cookie-format">
<h3><a class="doc-anchor" href="#doc-cookie-format">#</a> <code>cookie_format</code></h3>
<p><code>cookie_format</code> — operation <code>cookie format</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cookie_format $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cookie-is-expired">
<h3><a class="doc-anchor" href="#doc-cookie-is-expired">#</a> <code>cookie_is_expired</code></h3>
<p><code>cookie_is_expired</code> — operation <code>cookie is expired</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cookie_is_expired $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cookie-is-session">
<h3><a class="doc-anchor" href="#doc-cookie-is-session">#</a> <code>cookie_is_session</code></h3>
<p><code>cookie_is_session</code> — operation <code>cookie is session</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cookie_is_session $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cookie-jar-add">
<h3><a class="doc-anchor" href="#doc-cookie-jar-add">#</a> <code>cookie_jar_add</code></h3>
<p><code>cookie_jar_add</code> — operation <code>cookie jar add</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cookie_jar_add $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cookie-jar-get">
<h3><a class="doc-anchor" href="#doc-cookie-jar-get">#</a> <code>cookie_jar_get</code></h3>
<p><code>cookie_jar_get</code> — operation <code>cookie jar get</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cookie_jar_get $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cookie-jar-new">
<h3><a class="doc-anchor" href="#doc-cookie-jar-new">#</a> <code>cookie_jar_new</code></h3>
<p><code>cookie_jar_new</code> — constructor of <code>cookie jar</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cookie_jar_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cookie-parse">
<h3><a class="doc-anchor" href="#doc-cookie-parse">#</a> <code>cookie_parse</code></h3>
<p><code>cookie_parse</code> — operation <code>cookie parse</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cookie_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cookie-path-matches">
<h3><a class="doc-anchor" href="#doc-cookie-path-matches">#</a> <code>cookie_path_matches</code></h3>
<p><code>cookie_path_matches</code> — operation <code>cookie path matches</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cookie_path_matches $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cookie-set-max-age">
<h3><a class="doc-anchor" href="#doc-cookie-set-max-age">#</a> <code>cookie_set_max_age</code></h3>
<p><code>cookie_set_max_age</code> — operation <code>cookie set max age</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p cookie_set_max_age $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coombs-runoff-step">
<h3><a class="doc-anchor" href="#doc-coombs-runoff-step">#</a> <code>coombs_runoff_step</code></h3>
<p><code>coombs_runoff_step</code> — single-step update of <code>coombs runoff</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p coombs_runoff_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cooperative-game-value">
<h3><a class="doc-anchor" href="#doc-cooperative-game-value">#</a> <code>cooperative_game_value</code></h3>
<p><code>cooperative_game_value</code> — value of <code>cooperative game</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cooperative_game_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coordination-game-payoff">
<h3><a class="doc-anchor" href="#doc-coordination-game-payoff">#</a> <code>coordination_game_payoff</code></h3>
<p><code>coordination_game_payoff</code> — operation <code>coordination game payoff</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p coordination_game_payoff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-copeland-score-step">
<h3><a class="doc-anchor" href="#doc-copeland-score-step">#</a> <code>copeland_score_step</code></h3>
<p><code>copeland_score_step</code> — single-step update of <code>copeland score</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p copeland_score_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coppersmith-bound">
<h3><a class="doc-anchor" href="#doc-coppersmith-bound">#</a> <code>coppersmith_bound</code></h3>
<p><code>coppersmith_bound</code> — operation <code>coppersmith bound</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p coppersmith_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coptic-from-fixed">
<h3><a class="doc-anchor" href="#doc-coptic-from-fixed">#</a> <code>coptic_from_fixed</code></h3>
<p><code>coptic_from_fixed</code> — operation <code>coptic from fixed</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p coptic_from_fixed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-copy-sign">
<h3><a class="doc-anchor" href="#doc-copy-sign">#</a> <code>copy_sign</code></h3>
<p><code>copy_sign</code> — sign with private key of <code>copy</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p copy_sign $x
</code></pre>
</article>
<article class="doc-entry" id="doc-copy-within">
<h3><a class="doc-anchor" href="#doc-copy-within">#</a> <code>copy_within</code></h3>
<p><code>copy_within</code> — operation <code>copy within</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p copy_within $x
</code></pre>
</article>
<article class="doc-entry" id="doc-copysign">
<h3><a class="doc-anchor" href="#doc-copysign">#</a> <code>copysign</code></h3>
<p><code>copysign</code> — operation <code>copysign</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p copysign $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coq-tactic-apply">
<h3><a class="doc-anchor" href="#doc-coq-tactic-apply">#</a> <code>coq_tactic_apply</code></h3>
<p><code>coq_tactic_apply</code> — operation <code>coq tactic apply</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p coq_tactic_apply $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coq-unify-term">
<h3><a class="doc-anchor" href="#doc-coq-unify-term">#</a> <code>coq_unify_term</code></h3>
<p><code>coq_unify_term</code> — operation <code>coq unify term</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p coq_unify_term $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cor-mat">
<h3><a class="doc-anchor" href="#doc-cor-mat">#</a> <code>cor_mat</code></h3>
<p><code>cor_matrix</code> (alias <code>cor_mat</code>) — correlation matrix from observations. Each row is an observation vector.</p>
<pre><code class="lang-perl">my $R = cor_mat([[1,2],[3,4],[5,6]]) # 2x2 correlation matrix
</code></pre>
</article>
<article class="doc-entry" id="doc-core-coalition">
<h3><a class="doc-anchor" href="#doc-core-coalition">#</a> <code>core_coalition</code></h3>
<p><code>core_coalition</code> — operation <code>core coalition</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p core_coalition $x
</code></pre>
</article>
<article class="doc-entry" id="doc-core-membership-check">
<h3><a class="doc-anchor" href="#doc-core-membership-check">#</a> <code>core_membership_check</code></h3>
<p><code>core_membership_check</code> — operation <code>core membership check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p core_membership_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coreference-singleton">
<h3><a class="doc-anchor" href="#doc-coreference-singleton">#</a> <code>coreference_singleton</code></h3>
<p><code>coreference_singleton</code> — operation <code>coreference singleton</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p coreference_singleton $x
</code></pre>
</article>
<article class="doc-entry" id="doc-corner-subpix">
<h3><a class="doc-anchor" href="#doc-corner-subpix">#</a> <code>corner_subpix</code></h3>
<p><code>corner_subpix</code> — operation <code>corner subpix</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p corner_subpix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-corr">
<h3><a class="doc-anchor" href="#doc-corr">#</a> <code>corr</code></h3>
<p><code>corr</code> — operation <code>corr</code>. Alias for <code>correlation</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p corr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-corr-agg">
<h3><a class="doc-anchor" href="#doc-corr-agg">#</a> <code>corr_agg</code></h3>
<p><code>corr_agg</code> — operation <code>corr agg</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p corr_agg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-correlate2d">
<h3><a class="doc-anchor" href="#doc-correlate2d">#</a> <code>correlate2d</code></h3>
<p><code>correlate2d(image, kernel) → matrix</code> — 2D cross-correlation (no kernel flip).</p>
</article>
<article class="doc-entry" id="doc-correlate-full">
<h3><a class="doc-anchor" href="#doc-correlate-full">#</a> <code>correlate_full</code></h3>
<p><code>correlate_full</code> — operation <code>correlate full</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p correlate_full $x
</code></pre>
</article>
<article class="doc-entry" id="doc-correlated-equilibrium-value">
<h3><a class="doc-anchor" href="#doc-correlated-equilibrium-value">#</a> <code>correlated_equilibrium_value</code></h3>
<p><code>correlated_equilibrium_value</code> — value of <code>correlated equilibrium</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p correlated_equilibrium_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-correlation">
<h3><a class="doc-anchor" href="#doc-correlation">#</a> <code>correlation</code></h3>
<p><code>correlation</code> — operation <code>correlation</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p correlation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-corsi-for">
<h3><a class="doc-anchor" href="#doc-corsi-for">#</a> <code>corsi_for</code></h3>
<p><code>corsi_for</code> — operation <code>corsi for</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p corsi_for $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cosh">
<h3><a class="doc-anchor" href="#doc-cosh">#</a> <code>cosh</code></h3>
<p><code>cosh</code> — operation <code>cosh</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p cosh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cosh-minus1-over-x2">
<h3><a class="doc-anchor" href="#doc-cosh-minus1-over-x2">#</a> <code>cosh_minus1_over_x2</code></h3>
<p><code>cosh_minus1_over_x2</code> — operation <code>cosh minus1 over x2</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p cosh_minus1_over_x2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cosine-integral-ci">
<h3><a class="doc-anchor" href="#doc-cosine-integral-ci">#</a> <code>cosine_integral_ci</code></h3>
<p><code>cosine_integral_ci</code> — operation <code>cosine integral ci</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p cosine_integral_ci $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cosine-sim-sparse">
<h3><a class="doc-anchor" href="#doc-cosine-sim-sparse">#</a> <code>cosine_sim_sparse</code></h3>
<p><code>cosine_sim_sparse(a, b) → number</code> — cosine similarity for sparse vectors. Each input is <code>[[index, value], ...]</code>; dot product is taken over shared indices and L2 norms over each sparse set.</p>
<pre><code class="lang-perl">p cosine_sim_sparse([[0,1],[5,2]], [[0,1],[5,2]]) # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-cosine-similarity">
<h3><a class="doc-anchor" href="#doc-cosine-similarity">#</a> <code>cosine_similarity</code></h3>
<p><code>cosine_similarity(a, b) → number</code> — cosine similarity of two same-length vectors.</p>
<pre><code class="lang-perl">p cosine_similarity([1,2,3], [2,4,6]) # 1.0
</code></pre>
</article>
<article class="doc-entry" id="doc-cosmic-distance-modulus-si">
<h3><a class="doc-anchor" href="#doc-cosmic-distance-modulus-si">#</a> <code>cosmic_distance_modulus_si</code></h3>
<p><code>cosmic_distance_modulus_si</code> — operation <code>cosmic distance modulus si</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p cosmic_distance_modulus_si $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cosmological-constant">
<h3><a class="doc-anchor" href="#doc-cosmological-constant">#</a> <code>cosmological_constant</code></h3>
<p><code>cosmological_constant</code> — operation <code>cosmological constant</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p cosmological_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cosmological-constant-term">
<h3><a class="doc-anchor" href="#doc-cosmological-constant-term">#</a> <code>cosmological_constant_term</code></h3>
<p><code>cosmological_constant_term</code> — operation <code>cosmological constant term</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p cosmological_constant_term $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cot">
<h3><a class="doc-anchor" href="#doc-cot">#</a> <code>cot</code></h3>
<p><code>cot</code> returns the cotangent (1/tan) of an angle in radians.</p>
<pre><code class="lang-perl">p cot(0.7854) # ≈ 1.0 (cot 45°)
</code></pre>
</article>
<article class="doc-entry" id="doc-coulomb">
<h3><a class="doc-anchor" href="#doc-coulomb">#</a> <code>coulomb</code></h3>
<p><code>coulomb_force($q1, $q2, $r)</code> (alias <code>coulomb</code>) — Coulomb's law: F = kq₁q₂/r². Charges in Coulombs, distance in meters.</p>
<pre><code class="lang-perl">p coulomb(1e-6, 1e-6, 0.1) # ~0.9 N (two 1μC charges 10cm apart)
</code></pre>
</article>
<article class="doc-entry" id="doc-coulomb-constant">
<h3><a class="doc-anchor" href="#doc-coulomb-constant">#</a> <code>coulomb_constant</code></h3>
<p><code>coulomb_constant</code> — operation <code>coulomb constant</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p coulomb_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coulomb-f0">
<h3><a class="doc-anchor" href="#doc-coulomb-f0">#</a> <code>coulomb_f0</code></h3>
<p><code>coulomb_f0</code> — operation <code>coulomb f0</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p coulomb_f0 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-coulombic-efficiency-cell">
<h3><a class="doc-anchor" href="#doc-coulombic-efficiency-cell">#</a> <code>coulombic_efficiency_cell</code></h3>
<p><code>coulombic_efficiency_cell</code> — operation <code>coulombic efficiency cell</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p coulombic_efficiency_cell $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-by">
<h3><a class="doc-anchor" href="#doc-count-by">#</a> <code>count_by</code></h3>
<p><code>count_by</code> — operation <code>count by</code>. Alias for <code>take_while</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p count_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-bytes">
<h3><a class="doc-anchor" href="#doc-count-bytes">#</a> <code>count_bytes</code></h3>
<p><code>count_bytes</code> — operation <code>count bytes</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p count_bytes $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-char">
<h3><a class="doc-anchor" href="#doc-count-char">#</a> <code>count_char</code></h3>
<p><code>count_char</code> — operation <code>count char</code>. Category: *string*.</p>
<pre><code class="lang-perl">p count_char $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-chars">
<h3><a class="doc-anchor" href="#doc-count-chars">#</a> <code>count_chars</code></h3>
<p><code>count_chars</code> — operation <code>count chars</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p count_chars $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-consonants">
<h3><a class="doc-anchor" href="#doc-count-consonants">#</a> <code>count_consonants</code></h3>
<p><code>count_consonants</code> — operation <code>count consonants</code>. Category: *string*.</p>
<pre><code class="lang-perl">p count_consonants $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-digits">
<h3><a class="doc-anchor" href="#doc-count-digits">#</a> <code>count_digits</code></h3>
<p><code>count_digits</code> — operation <code>count digits</code>. Category: *counters*.</p>
<pre><code class="lang-perl">p count_digits $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-elem">
<h3><a class="doc-anchor" href="#doc-count-elem">#</a> <code>count_elem</code></h3>
<p><code>count_elem</code> — operation <code>count elem</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p count_elem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-eq">
<h3><a class="doc-anchor" href="#doc-count-eq">#</a> <code>count_eq</code></h3>
<p><code>count_eq</code> — operation <code>count eq</code>. Category: *more list helpers*.</p>
<pre><code class="lang-perl">p count_eq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-inversions">
<h3><a class="doc-anchor" href="#doc-count-inversions">#</a> <code>count_inversions</code></h3>
<p><code>count_inversions</code> — operation <code>count inversions</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p count_inversions $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-letters">
<h3><a class="doc-anchor" href="#doc-count-letters">#</a> <code>count_letters</code></h3>
<p><code>count_letters</code> — operation <code>count letters</code>. Category: *counters*.</p>
<pre><code class="lang-perl">p count_letters $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-lines">
<h3><a class="doc-anchor" href="#doc-count-lines">#</a> <code>count_lines</code></h3>
<p><code>count_lines</code> — operation <code>count lines</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p count_lines $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-lower">
<h3><a class="doc-anchor" href="#doc-count-lower">#</a> <code>count_lower</code></h3>
<p><code>count_lower</code> — operation <code>count lower</code>. Category: *counters*.</p>
<pre><code class="lang-perl">p count_lower $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-match">
<h3><a class="doc-anchor" href="#doc-count-match">#</a> <code>count_match</code></h3>
<p><code>count_match</code> — operation <code>count match</code>. Category: *counters*.</p>
<pre><code class="lang-perl">p count_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-min-sketch-add">
<h3><a class="doc-anchor" href="#doc-count-min-sketch-add">#</a> <code>count_min_sketch_add</code></h3>
<p><code>count_min_sketch_add</code> — operation <code>count min sketch add</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p count_min_sketch_add $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-min-sketch-new">
<h3><a class="doc-anchor" href="#doc-count-min-sketch-new">#</a> <code>count_min_sketch_new</code></h3>
<p><code>count_min_sketch_new</code> — constructor of <code>count min sketch</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p count_min_sketch_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-min-sketch-query">
<h3><a class="doc-anchor" href="#doc-count-min-sketch-query">#</a> <code>count_min_sketch_query</code></h3>
<p><code>count_min_sketch_query</code> — operation <code>count min sketch query</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p count_min_sketch_query $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-ne">
<h3><a class="doc-anchor" href="#doc-count-ne">#</a> <code>count_ne</code></h3>
<p><code>count_ne</code> — operation <code>count ne</code>. Category: *more list helpers*.</p>
<pre><code class="lang-perl">p count_ne $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-punctuation">
<h3><a class="doc-anchor" href="#doc-count-punctuation">#</a> <code>count_punctuation</code></h3>
<p><code>count_punctuation</code> — operation <code>count punctuation</code>. Category: *counters*.</p>
<pre><code class="lang-perl">p count_punctuation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-regex-matches">
<h3><a class="doc-anchor" href="#doc-count-regex-matches">#</a> <code>count_regex_matches</code></h3>
<p><code>count_regex_matches</code> — operation <code>count regex matches</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p count_regex_matches $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-spaces">
<h3><a class="doc-anchor" href="#doc-count-spaces">#</a> <code>count_spaces</code></h3>
<p><code>count_spaces</code> — operation <code>count spaces</code>. Category: *counters*.</p>
<pre><code class="lang-perl">p count_spaces $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-substring">
<h3><a class="doc-anchor" href="#doc-count-substring">#</a> <code>count_substring</code></h3>
<p><code>count_substring</code> — operation <code>count substring</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p count_substring $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-upper">
<h3><a class="doc-anchor" href="#doc-count-upper">#</a> <code>count_upper</code></h3>
<p><code>count_upper</code> — operation <code>count upper</code>. Category: *counters*.</p>
<pre><code class="lang-perl">p count_upper $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-vowels">
<h3><a class="doc-anchor" href="#doc-count-vowels">#</a> <code>count_vowels</code></h3>
<p><code>count_vowels</code> — operation <code>count vowels</code>. Category: *string*.</p>
<pre><code class="lang-perl">p count_vowels $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-while">
<h3><a class="doc-anchor" href="#doc-count-while">#</a> <code>count_while</code></h3>
<p><code>count_while</code> — operation <code>count while</code>. Category: *ruby enumerable extras*.</p>
<pre><code class="lang-perl">p count_while $x
</code></pre>
</article>
<article class="doc-entry" id="doc-count-words">
<h3><a class="doc-anchor" href="#doc-count-words">#</a> <code>count_words</code></h3>
<p><code>count_words</code> — operation <code>count words</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p count_words $x
</code></pre>
</article>
<article class="doc-entry" id="doc-counter">
<h3><a class="doc-anchor" href="#doc-counter">#</a> <code>counter</code></h3>
<p><code>counter</code> — operation <code>counter</code>. Category: *data structure helpers*.</p>
<pre><code class="lang-perl">p counter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-counter-most-common">
<h3><a class="doc-anchor" href="#doc-counter-most-common">#</a> <code>counter_most_common</code></h3>
<p><code>counter_most_common</code> — operation <code>counter most common</code>. Category: *data structure helpers*.</p>
<pre><code class="lang-perl">p counter_most_common $x
</code></pre>
</article>
<article class="doc-entry" id="doc-countif">
<h3><a class="doc-anchor" href="#doc-countif">#</a> <code>countif</code></h3>
<p><code>countif</code> — operation <code>countif</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p countif $x
</code></pre>
</article>
<article class="doc-entry" id="doc-countifs">
<h3><a class="doc-anchor" href="#doc-countifs">#</a> <code>countifs</code></h3>
<p><code>countifs</code> — operation <code>countifs</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p countifs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-country-code-alpha2">
<h3><a class="doc-anchor" href="#doc-country-code-alpha2">#</a> <code>country_code_alpha2</code></h3>
<p><code>country_code_alpha2(name_or_code) → string</code> — ISO 3166-1 alpha-2 code.</p>
<pre><code class="lang-perl">p country_code_alpha2("United States") # "US"
</code></pre>
</article>
<article class="doc-entry" id="doc-country-code-alpha3">
<h3><a class="doc-anchor" href="#doc-country-code-alpha3">#</a> <code>country_code_alpha3</code></h3>
<p><code>country_code_alpha3(name_or_code) → string</code> — ISO 3166-1 alpha-3 code.</p>
</article>
<article class="doc-entry" id="doc-country-code-numeric">
<h3><a class="doc-anchor" href="#doc-country-code-numeric">#</a> <code>country_code_numeric</code></h3>
<p><code>country_code_numeric(name_or_code) → string</code> — ISO 3166-1 numeric code (3 digits).</p>
</article>
<article class="doc-entry" id="doc-country-currency">
<h3><a class="doc-anchor" href="#doc-country-currency">#</a> <code>country_currency</code></h3>
<p><code>country_currency</code> — ISO 3166 country lookup <code>currency</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p country_currency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-country-languages">
<h3><a class="doc-anchor" href="#doc-country-languages">#</a> <code>country_languages</code></h3>
<p><code>country_languages(code) → array</code> — list of official language codes.</p>
</article>
<article class="doc-entry" id="doc-country-name">
<h3><a class="doc-anchor" href="#doc-country-name">#</a> <code>country_name</code></h3>
<p><code>country_name(code) → string</code> — country name for ISO code.</p>
</article>
<article class="doc-entry" id="doc-country-phone-prefix">
<h3><a class="doc-anchor" href="#doc-country-phone-prefix">#</a> <code>country_phone_prefix</code></h3>
<p><code>country_phone_prefix(code) → string</code> — international dialing prefix.</p>
<pre><code class="lang-perl">p country_phone_prefix("US") # "+1"
</code></pre>
</article>
<article class="doc-entry" id="doc-coupon-count">
<h3><a class="doc-anchor" href="#doc-coupon-count">#</a> <code>coupon_count</code></h3>
<p><code>coupon_count</code> — count of <code>coupon</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p coupon_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-courant-friedrichs-lewy">
<h3><a class="doc-anchor" href="#doc-courant-friedrichs-lewy">#</a> <code>courant_friedrichs_lewy</code></h3>
<p><code>courant_friedrichs_lewy</code> — operation <code>courant friedrichs lewy</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p courant_friedrichs_lewy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cournot-eq">
<h3><a class="doc-anchor" href="#doc-cournot-eq">#</a> <code>cournot_eq</code></h3>
<p><code>cournot_eq</code> — operation <code>cournot eq</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p cournot_eq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cournot-quantity-step">
<h3><a class="doc-anchor" href="#doc-cournot-quantity-step">#</a> <code>cournot_quantity_step</code></h3>
<p><code>cournot_quantity_step</code> — single-step update of <code>cournot quantity</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p cournot_quantity_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cov">
<h3><a class="doc-anchor" href="#doc-cov">#</a> <code>cov</code></h3>
<p><code>cov</code> — operation <code>cov</code>. Alias for <code>covariance</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p cov $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cov2cor">
<h3><a class="doc-anchor" href="#doc-cov2cor">#</a> <code>cov2cor</code></h3>
<p><code>cov2cor</code> — convert covariance matrix to correlation matrix. Like R's cov2cor().</p>
<pre><code class="lang-perl">my $cor = cov2cor(cov_mat($data))
</code></pre>
</article>
<article class="doc-entry" id="doc-cov-mat">
<h3><a class="doc-anchor" href="#doc-cov-mat">#</a> <code>cov_mat</code></h3>
<p><code>cov_matrix</code> (alias <code>cov_mat</code>) — covariance matrix from observations.</p>
<pre><code class="lang-perl">my $S = cov_mat([[1,2],[3,4],[5,6]])
</code></pre>
</article>
<article class="doc-entry" id="doc-covar-pop">
<h3><a class="doc-anchor" href="#doc-covar-pop">#</a> <code>covar_pop</code></h3>
<p><code>covar_pop</code> — operation <code>covar pop</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p covar_pop $x
</code></pre>
</article>
<article class="doc-entry" id="doc-covar-samp">
<h3><a class="doc-anchor" href="#doc-covar-samp">#</a> <code>covar_samp</code></h3>
<p><code>covar_samp</code> — operation <code>covar samp</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p covar_samp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-covariance">
<h3><a class="doc-anchor" href="#doc-covariance">#</a> <code>covariance</code></h3>
<p><code>covariance</code> — operation <code>covariance</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p covariance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-covariance-matrix-pts">
<h3><a class="doc-anchor" href="#doc-covariance-matrix-pts">#</a> <code>covariance_matrix_pts</code></h3>
<p><code>covariance_matrix_pts</code> — operation <code>covariance matrix pts</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p covariance_matrix_pts $x
</code></pre>
</article>
<article class="doc-entry" id="doc-covariant-derivative-step">
<h3><a class="doc-anchor" href="#doc-covariant-derivative-step">#</a> <code>covariant_derivative_step</code></h3>
<p><code>covariant_derivative_step</code> — single-step update of <code>covariant derivative</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p covariant_derivative_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cp-monatomic-ideal">
<h3><a class="doc-anchor" href="#doc-cp-monatomic-ideal">#</a> <code>cp_monatomic_ideal</code></h3>
<p><code>cp_monatomic_ideal</code> — operation <code>cp monatomic ideal</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p cp_monatomic_ideal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cpat">
<h3><a class="doc-anchor" href="#doc-cpat">#</a> <code>cpat</code></h3>
<p><code>cpat</code> — operation <code>cpat</code>. Alias for <code>code_point_at</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p cpat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cpfx">
<h3><a class="doc-anchor" href="#doc-cpfx">#</a> <code>cpfx</code></h3>
<p><code>cpfx</code> — operation <code>cpfx</code>. Alias for <code>common_prefix</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p cpfx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cpl-w">
<h3><a class="doc-anchor" href="#doc-cpl-w">#</a> <code>cpl_w</code></h3>
<p><code>cpl_w</code> — operation <code>cpl w</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p cpl_w $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cprod">
<h3><a class="doc-anchor" href="#doc-cprod">#</a> <code>cprod</code></h3>
<p><code>cprod</code> — operation <code>cprod</code>. Alias for <code>cartesian_product</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p cprod $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cprod-acc">
<h3><a class="doc-anchor" href="#doc-cprod-acc">#</a> <code>cprod_acc</code></h3>
<p><code>cprod_acc</code> — operation <code>cprod acc</code>. Alias for <code>cumprod</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p cprod_acc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cpsgn">
<h3><a class="doc-anchor" href="#doc-cpsgn">#</a> <code>cpsgn</code></h3>
<p><code>cpsgn</code> — operation <code>cpsgn</code>. Alias for <code>copy_sign</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p cpsgn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cpu-count">
<h3><a class="doc-anchor" href="#doc-cpu-count">#</a> <code>cpu_count</code></h3>
<p><code>cpu_count</code> — count of <code>cpu</code>. Category: *more process / system*.</p>
<pre><code class="lang-perl">p cpu_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cpyw">
<h3><a class="doc-anchor" href="#doc-cpyw">#</a> <code>cpyw</code></h3>
<p><code>cpyw</code> — operation <code>cpyw</code>. Alias for <code>copy_within</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p cpyw $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cr">
<h3><a class="doc-anchor" href="#doc-cr">#</a> <code>cr</code></h3>
<p><code>cr</code> — operation <code>cr</code>. Alias for <code>csv_read</code>. Category: *data / network*.</p>
<pre><code class="lang-perl">p cr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cramer-lundberg-step">
<h3><a class="doc-anchor" href="#doc-cramer-lundberg-step">#</a> <code>cramer_lundberg_step</code></h3>
<p><code>cramer_lundberg_step</code> — single-step update of <code>cramer lundberg</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p cramer_lundberg_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cramer-rao-bound">
<h3><a class="doc-anchor" href="#doc-cramer-rao-bound">#</a> <code>cramer_rao_bound</code></h3>
<p><code>cramer_rao_bound</code> — operation <code>cramer rao bound</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p cramer_rao_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-crank-nicolson-ode">
<h3><a class="doc-anchor" href="#doc-crank-nicolson-ode">#</a> <code>crank_nicolson_ode</code></h3>
<p><code>crank_nicolson_ode</code> — operation <code>crank nicolson ode</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p crank_nicolson_ode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-crc10-atm">
<h3><a class="doc-anchor" href="#doc-crc10-atm">#</a> <code>crc10_atm</code></h3>
<p><code>crc10_atm(s) → int</code> — CRC-10/ATM AAL5 checksum.</p>
</article>
<article class="doc-entry" id="doc-crc12-dect">
<h3><a class="doc-anchor" href="#doc-crc12-dect">#</a> <code>crc12_dect</code></h3>
<p><code>crc12_dect(s) → int</code> — CRC-12/DECT (poly 0x80F).</p>
</article>
<article class="doc-entry" id="doc-crc16">
<h3><a class="doc-anchor" href="#doc-crc16">#</a> <code>crc16</code></h3>
<p><code>crc16(s) → int</code> — CRC-16/Modbus (poly 0xA001, init 0xFFFF, reflected). Verifies serial-protocol frames.</p>
<pre><code class="lang-perl">p crc16("123456789") # 0x4B37
</code></pre>
</article>
<article class="doc-entry" id="doc-crc16-ccitt">
<h3><a class="doc-anchor" href="#doc-crc16-ccitt">#</a> <code>crc16_ccitt</code></h3>
<p><code>crc16_ccitt</code> — CRC checksum variant <code>16 ccitt</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p crc16_ccitt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-crc16-xmodem">
<h3><a class="doc-anchor" href="#doc-crc16-xmodem">#</a> <code>crc16_xmodem</code></h3>
<p><code>crc16_xmodem(s) → int</code> — CRC-16/XMODEM (poly 0x1021, init 0). Used in XMODEM file transfer.</p>
<pre><code class="lang-perl">p crc16_xmodem("123456789") # 0x31C3
</code></pre>
</article>
<article class="doc-entry" id="doc-crc24">
<h3><a class="doc-anchor" href="#doc-crc24">#</a> <code>crc24</code></h3>
<p><code>crc24(s) → int</code> — CRC-24/OpenPGP (poly 0x864CFB, init 0xB704CE).</p>
<pre><code class="lang-perl">p crc24("") # 0xB704CE
</code></pre>
</article>
<article class="doc-entry" id="doc-crc32-bzip2">
<h3><a class="doc-anchor" href="#doc-crc32-bzip2">#</a> <code>crc32_bzip2</code></h3>
<p><code>crc32_bzip2(s) → int</code> — CRC-32/BZIP2 (non-reflected).</p>
</article>
<article class="doc-entry" id="doc-crc32-jamcrc">
<h3><a class="doc-anchor" href="#doc-crc32-jamcrc">#</a> <code>crc32_jamcrc</code></h3>
<p><code>crc32_jamcrc(s) → int</code> — CRC-32/JAMCRC (reflected, xorout 0).</p>
</article>
<article class="doc-entry" id="doc-crc32-mpeg2">
<h3><a class="doc-anchor" href="#doc-crc32-mpeg2">#</a> <code>crc32_mpeg2</code></h3>
<p><code>crc32_mpeg2(s) → int</code> — CRC-32/MPEG-2 (non-reflected, xorout 0).</p>
</article>
<article class="doc-entry" id="doc-crc32-xfer">
<h3><a class="doc-anchor" href="#doc-crc32-xfer">#</a> <code>crc32_xfer</code></h3>
<p><code>crc32_xfer(s) → int</code> — CRC-32/XFER (XFER protocol).</p>
</article>
<article class="doc-entry" id="doc-crc32-zlib">
<h3><a class="doc-anchor" href="#doc-crc32-zlib">#</a> <code>crc32_zlib</code></h3>
<p><code>crc32_zlib(s) → int</code> — CRC-32/ISO-HDLC (zlib/gzip standard).</p>
<pre><code class="lang-perl">p crc32_zlib("123456789") # 0xCBF43926
</code></pre>
</article>
<article class="doc-entry" id="doc-crc32c">
<h3><a class="doc-anchor" href="#doc-crc32c">#</a> <code>crc32c</code></h3>
<p><code>crc32c(s) → int</code> — CRC-32C (Castagnoli, poly 0x82F63B78). Used by iSCSI/Btrfs/SCTP.</p>
<pre><code class="lang-perl">p crc32c("123456789")
</code></pre>
</article>
<article class="doc-entry" id="doc-crc64-ecma">
<h3><a class="doc-anchor" href="#doc-crc64-ecma">#</a> <code>crc64_ecma</code></h3>
<p><code>crc64_ecma(s) → int</code> — CRC-64/ECMA-182 (poly 0x42F0E1EBA9EA3693).</p>
<pre><code class="lang-perl">p crc64_ecma("abc")
</code></pre>
</article>
<article class="doc-entry" id="doc-crc64-xz">
<h3><a class="doc-anchor" href="#doc-crc64-xz">#</a> <code>crc64_xz</code></h3>
<p><code>crc64_xz(s) → int</code> — CRC-64/XZ (reflected). Used in xz/lzma file integrity.</p>
</article>
<article class="doc-entry" id="doc-crc6-itu">
<h3><a class="doc-anchor" href="#doc-crc6-itu">#</a> <code>crc6_itu</code></h3>
<p><code>crc6_itu(s) → int</code> — CRC-6/ITU (poly 0x03, reflected).</p>
</article>
<article class="doc-entry" id="doc-crc8">
<h3><a class="doc-anchor" href="#doc-crc8">#</a> <code>crc8</code></h3>
<p><code>crc8(s) → int</code> — CRC-8 (polynomial 0x07, init 0). Common for sensor checksums.</p>
<pre><code class="lang-perl">p crc8("123456789")
</code></pre>
</article>
<article class="doc-entry" id="doc-credibility-buhlmann">
<h3><a class="doc-anchor" href="#doc-credibility-buhlmann">#</a> <code>credibility_buhlmann</code></h3>
<p><code>credibility_buhlmann</code> — operation <code>credibility buhlmann</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p credibility_buhlmann $x
</code></pre>
</article>
<article class="doc-entry" id="doc-credible-interval-beta">
<h3><a class="doc-anchor" href="#doc-credible-interval-beta">#</a> <code>credible_interval_beta</code></h3>
<p><code>credible_interval_beta(alpha, beta, level=0.95) → [lo, hi]</code> — central credible interval from a Beta posterior.</p>
</article>
<article class="doc-entry" id="doc-credible-interval-normal">
<h3><a class="doc-anchor" href="#doc-credible-interval-normal">#</a> <code>credible_interval_normal</code></h3>
<p><code>credible_interval_normal(mean, sd, level=0.95) → [lo, hi]</code> — central credible interval from a Normal posterior.</p>
</article>
<article class="doc-entry" id="doc-crf-log-likelihood">
<h3><a class="doc-anchor" href="#doc-crf-log-likelihood">#</a> <code>crf_log_likelihood</code></h3>
<p><code>crf_log_likelihood</code> — operation <code>crf log likelihood</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p crf_log_likelihood $x
</code></pre>
</article>
<article class="doc-entry" id="doc-crindex">
<h3><a class="doc-anchor" href="#doc-crindex">#</a> <code>crindex</code></h3>
<p><code>crindex STRING, SUBSTRING [, FROM]</code> — codepoint-indexed equivalent of Perl 5's <code>rindex</code>. Returns the last codepoint position where SUBSTRING occurs (at or before FROM, defaulting to end-of-string), or -1 on miss. Counterpart to <code>cindex</code>; pairs with <code>[]</code> slice operators and <code>len</code>.</p>
<pre><code class="lang-perl">my $path = "foo/bar/─/baz.gz"
p rindex $path, "/" # 13 (bytes)
p crindex $path, "/" # 11 (codepoints)
my $i = crindex $path, "/"
p $path[$i + 1 : len($path) - 1] # "baz.gz"
</code></pre>
</article>
<article class="doc-entry" id="doc-critang">
<h3><a class="doc-anchor" href="#doc-critang">#</a> <code>critang</code></h3>
<p><code>critang</code> — operation <code>critang</code>. Alias for <code>critical_angle</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p critang $x
</code></pre>
</article>
<article class="doc-entry" id="doc-critical-angle">
<h3><a class="doc-anchor" href="#doc-critical-angle">#</a> <code>critical_angle</code></h3>
<p><code>critical_angle</code> — operation <code>critical angle</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p critical_angle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-critical-damping">
<h3><a class="doc-anchor" href="#doc-critical-damping">#</a> <code>critical_damping</code></h3>
<p><code>critical_damping(m, k) → number</code> — critical damping coefficient <code>c_c = 2·√(m·k)</code>.</p>
</article>
<article class="doc-entry" id="doc-critical-density">
<h3><a class="doc-anchor" href="#doc-critical-density">#</a> <code>critical_density</code></h3>
<p><code>critical_density</code> — operation <code>critical density</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p critical_density $x
</code></pre>
</article>
<article class="doc-entry" id="doc-critical-density-si">
<h3><a class="doc-anchor" href="#doc-critical-density-si">#</a> <code>critical_density_si</code></h3>
<p><code>critical_density_si</code> — operation <code>critical density si</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p critical_density_si $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cron-next-fire">
<h3><a class="doc-anchor" href="#doc-cron-next-fire">#</a> <code>cron_next_fire</code></h3>
<p><code>cron_next_fire</code> — operation <code>cron next fire</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p cron_next_fire $x
</code></pre>
</article>
<article class="doc-entry" id="doc-crop-factor">
<h3><a class="doc-anchor" href="#doc-crop-factor">#</a> <code>crop_factor</code></h3>
<p><code>crop_factor(sensor_diag_mm) → number</code> — <code>43.27 / sensor_diag</code>. Full-frame = 1.</p>
</article>
<article class="doc-entry" id="doc-cross-correlation">
<h3><a class="doc-anchor" href="#doc-cross-correlation">#</a> <code>cross_correlation</code></h3>
<p><code>cross_correlation(\@a, \@b)</code> (alias <code>xcorr</code>) — computes the cross-correlation of two signals. Measures similarity as a function of time-lag. Peak location indicates time delay between signals.</p>
<pre><code class="lang-perl">my $xcor = xcorr(\@signal1, \@signal2)
my $lag = max_index(@$xcor) # find peak lag
</code></pre>
</article>
<article class="doc-entry" id="doc-cross-elasticity">
<h3><a class="doc-anchor" href="#doc-cross-elasticity">#</a> <code>cross_elasticity</code></h3>
<p><code>cross_elasticity</code> — operation <code>cross elasticity</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p cross_elasticity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cross-entropy">
<h3><a class="doc-anchor" href="#doc-cross-entropy">#</a> <code>cross_entropy</code></h3>
<p><code>cross_entropy(p, q) → number</code> — <code>-Σ p·log q</code> (natural log, alias <code>xentropy</code>).</p>
</article>
<article class="doc-entry" id="doc-cross-polarization-amp">
<h3><a class="doc-anchor" href="#doc-cross-polarization-amp">#</a> <code>cross_polarization_amp</code></h3>
<p><code>cross_polarization_amp</code> — operation <code>cross polarization amp</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p cross_polarization_amp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cross-product">
<h3><a class="doc-anchor" href="#doc-cross-product">#</a> <code>cross_product</code></h3>
<p><code>cross_product</code> — operation <code>cross product</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p cross_product $x
</code></pre>
</article>
<article class="doc-entry" id="doc-crossfade">
<h3><a class="doc-anchor" href="#doc-crossfade">#</a> <code>crossfade</code></h3>
<p><code>crossfade</code> — operation <code>crossfade</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p crossfade $x
</code></pre>
</article>
<article class="doc-entry" id="doc-crossp">
<h3><a class="doc-anchor" href="#doc-crossp">#</a> <code>crossp</code></h3>
<p><code>crossp</code> — operation <code>crossp</code>. Alias for <code>cross_product</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p crossp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-crossprod">
<h3><a class="doc-anchor" href="#doc-crossprod">#</a> <code>crossprod</code></h3>
<p><code>crossprod</code> — cross product t(M) * M (R's crossprod). Efficiently computes M^T M without explicit transpose.</p>
<pre><code class="lang-perl">my $ata = crossprod([[1,2],[3,4]]) # [[10,14],[14,20]]
</code></pre>
</article>
<article class="doc-entry" id="doc-crr-american-call">
<h3><a class="doc-anchor" href="#doc-crr-american-call">#</a> <code>crr_american_call</code></h3>
<p><code>crr_american_call</code> — operation <code>crr american call</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p crr_american_call $x
</code></pre>
</article>
<article class="doc-entry" id="doc-crr-american-put">
<h3><a class="doc-anchor" href="#doc-crr-american-put">#</a> <code>crr_american_put</code></h3>
<p><code>crr_american_put</code> — operation <code>crr american put</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p crr_american_put $x
</code></pre>
</article>
<article class="doc-entry" id="doc-crustal-density-depth">
<h3><a class="doc-anchor" href="#doc-crustal-density-depth">#</a> <code>crustal_density_depth</code></h3>
<p><code>crustal_density_depth</code> — operation <code>crustal density depth</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p crustal_density_depth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-crystal-field-ligand">
<h3><a class="doc-anchor" href="#doc-crystal-field-ligand">#</a> <code>crystal_field_ligand</code></h3>
<p><code>crystal_field_ligand</code> — operation <code>crystal field ligand</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p crystal_field_ligand $x
</code></pre>
</article>
<article class="doc-entry" id="doc-csc">
<h3><a class="doc-anchor" href="#doc-csc">#</a> <code>csc</code></h3>
<p><code>csc</code> returns the cosecant (1/sin) of an angle in radians.</p>
<pre><code class="lang-perl">p csc(1.5708) # ≈ 1.0 (csc 90°)
</code></pre>
</article>
<article class="doc-entry" id="doc-csd-xy">
<h3><a class="doc-anchor" href="#doc-csd-xy">#</a> <code>csd_xy</code></h3>
<p><code>csd_xy</code> — operation <code>csd xy</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p csd_xy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-csfx">
<h3><a class="doc-anchor" href="#doc-csfx">#</a> <code>csfx</code></h3>
<p><code>csfx</code> — operation <code>csfx</code>. Alias for <code>common_suffix</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p csfx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-csiszar-phi-div">
<h3><a class="doc-anchor" href="#doc-csiszar-phi-div">#</a> <code>csiszar_phi_div</code></h3>
<p><code>csiszar_phi_div</code> — operation <code>csiszar phi div</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p csiszar_phi_div $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cspline">
<h3><a class="doc-anchor" href="#doc-cspline">#</a> <code>cspline</code></h3>
<p><code>cubic_spline</code> (aliases <code>cspline</code>, <code>spline</code>) performs natural cubic spline interpolation. Takes xs, ys, and a query point x.</p>
<pre><code class="lang-perl">p spline([0,1,2,3], [0,1,0,1], 1.5) # smooth interpolation
</code></pre>
</article>
<article class="doc-entry" id="doc-css-font-extract">
<h3><a class="doc-anchor" href="#doc-css-font-extract">#</a> <code>css_font_extract</code></h3>
<p><code>css_font_extract</code> — operation <code>css font extract</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p css_font_extract $x
</code></pre>
</article>
<article class="doc-entry" id="doc-css-import-extract">
<h3><a class="doc-anchor" href="#doc-css-import-extract">#</a> <code>css_import_extract</code></h3>
<p><code>css_import_extract</code> — operation <code>css import extract</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p css_import_extract $x
</code></pre>
</article>
<article class="doc-entry" id="doc-css-minify">
<h3><a class="doc-anchor" href="#doc-css-minify">#</a> <code>css_minify</code></h3>
<p><code>css_minify</code> — operation <code>css minify</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p css_minify $x
</code></pre>
</article>
<article class="doc-entry" id="doc-css-parse">
<h3><a class="doc-anchor" href="#doc-css-parse">#</a> <code>css_parse</code></h3>
<p><code>css_parse</code> — operation <code>css parse</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p css_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-css-pretty">
<h3><a class="doc-anchor" href="#doc-css-pretty">#</a> <code>css_pretty</code></h3>
<p><code>css_pretty</code> — operation <code>css pretty</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p css_pretty $x
</code></pre>
</article>
<article class="doc-entry" id="doc-css-property-get">
<h3><a class="doc-anchor" href="#doc-css-property-get">#</a> <code>css_property_get</code></h3>
<p><code>css_property_get</code> — operation <code>css property get</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p css_property_get $x
</code></pre>
</article>
<article class="doc-entry" id="doc-css-property-set">
<h3><a class="doc-anchor" href="#doc-css-property-set">#</a> <code>css_property_set</code></h3>
<p><code>css_property_set</code> — operation <code>css property set</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p css_property_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-css-rule-extract">
<h3><a class="doc-anchor" href="#doc-css-rule-extract">#</a> <code>css_rule_extract</code></h3>
<p><code>css_rule_extract</code> — operation <code>css rule extract</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p css_rule_extract $x
</code></pre>
</article>
<article class="doc-entry" id="doc-css-selector-parse">
<h3><a class="doc-anchor" href="#doc-css-selector-parse">#</a> <code>css_selector_parse</code></h3>
<p><code>css_selector_parse</code> — operation <code>css selector parse</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p css_selector_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-css-specificity">
<h3><a class="doc-anchor" href="#doc-css-specificity">#</a> <code>css_specificity</code></h3>
<p><code>css_specificity</code> — operation <code>css specificity</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p css_specificity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-css-url-extract">
<h3><a class="doc-anchor" href="#doc-css-url-extract">#</a> <code>css_url_extract</code></h3>
<p><code>css_url_extract</code> — operation <code>css url extract</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p css_url_extract $x
</code></pre>
</article>
<article class="doc-entry" id="doc-css-var-resolve">
<h3><a class="doc-anchor" href="#doc-css-var-resolve">#</a> <code>css_var_resolve</code></h3>
<p><code>css_var_resolve</code> — operation <code>css var resolve</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p css_var_resolve $x
</code></pre>
</article>
<article class="doc-entry" id="doc-csum">
<h3><a class="doc-anchor" href="#doc-csum">#</a> <code>csum</code></h3>
<p><code>csum</code> — operation <code>csum</code>. Alias for <code>cumsum</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p csum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cswap-gate">
<h3><a class="doc-anchor" href="#doc-cswap-gate">#</a> <code>cswap_gate</code></h3>
<p><code>cswap_gate</code> — operation <code>cswap gate</code>. Alias for <code>fredkin_gate</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p cswap_gate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ctime">
<h3><a class="doc-anchor" href="#doc-ctime">#</a> <code>ctime</code></h3>
<p><code>ctime</code> — operation <code>ctime</code>. Alias for <code>file_ctime</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p ctime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ctxt">
<h3><a class="doc-anchor" href="#doc-ctxt">#</a> <code>ctxt</code></h3>
<p><code>ctxt</code> — operation <code>ctxt</code>. Alias for <code>center_text</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ctxt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cuban-number">
<h3><a class="doc-anchor" href="#doc-cuban-number">#</a> <code>cuban_number</code></h3>
<p><code>cuban_number</code> — operation <code>cuban number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p cuban_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cube-fn">
<h3><a class="doc-anchor" href="#doc-cube-fn">#</a> <code>cube_fn</code></h3>
<p><code>cube_fn</code> — operation <code>cube fn</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p cube_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cube-number">
<h3><a class="doc-anchor" href="#doc-cube-number">#</a> <code>cube_number</code></h3>
<p><code>cube_number(n) → int</code> — <code>n³</code>.</p>
</article>
<article class="doc-entry" id="doc-cube-root">
<h3><a class="doc-anchor" href="#doc-cube-root">#</a> <code>cube_root</code></h3>
<p><code>cube_root</code> — operation <code>cube root</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p cube_root $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cubes-seq">
<h3><a class="doc-anchor" href="#doc-cubes-seq">#</a> <code>cubes_seq</code></h3>
<p><code>cubes_seq</code> — operation <code>cubes seq</code>. Category: *sequences*.</p>
<pre><code class="lang-perl">p cubes_seq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cullen-number">
<h3><a class="doc-anchor" href="#doc-cullen-number">#</a> <code>cullen_number</code></h3>
<p><code>cullen_number</code> — operation <code>cullen number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p cullen_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cumipmt">
<h3><a class="doc-anchor" href="#doc-cumipmt">#</a> <code>cumipmt</code></h3>
<p><code>cumipmt</code> — operation <code>cumipmt</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p cumipmt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cummax">
<h3><a class="doc-anchor" href="#doc-cummax">#</a> <code>cummax</code></h3>
<p><code>cummax</code> — cumulative maximum. Each element is the max of all elements up to that position.</p>
<pre><code class="lang-perl">p cummax([3,1,4,1,5,9]) # [3,3,4,4,5,9]
</code></pre>
</article>
<article class="doc-entry" id="doc-cummin">
<h3><a class="doc-anchor" href="#doc-cummin">#</a> <code>cummin</code></h3>
<p><code>cummin</code> — cumulative minimum.</p>
<pre><code class="lang-perl">p cummin([9,5,1,4,3]) # [9,5,1,1,1]
</code></pre>
</article>
<article class="doc-entry" id="doc-cumprinc">
<h3><a class="doc-anchor" href="#doc-cumprinc">#</a> <code>cumprinc</code></h3>
<p><code>cumprinc</code> — operation <code>cumprinc</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p cumprinc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cumprod">
<h3><a class="doc-anchor" href="#doc-cumprod">#</a> <code>cumprod</code></h3>
<p><code>cumprod</code> — operation <code>cumprod</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p cumprod $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cumsum">
<h3><a class="doc-anchor" href="#doc-cumsum">#</a> <code>cumsum</code></h3>
<p><code>cumsum</code> — operation <code>cumsum</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p cumsum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cumtrapz">
<h3><a class="doc-anchor" href="#doc-cumtrapz">#</a> <code>cumtrapz</code></h3>
<p><code>cumtrapz</code> cumulative trapezoidal integration. Returns running integral array.</p>
<pre><code class="lang-perl">my @y = (1, 2, 3, 4)
my @F = @{cumtrapz(\@y)} # [0, 1.5, 4.0, 7.5]
</code></pre>
</article>
<article class="doc-entry" id="doc-cups-to-ml">
<h3><a class="doc-anchor" href="#doc-cups-to-ml">#</a> <code>cups_to_ml</code></h3>
<p><code>cups_to_ml</code> — convert from <code>cups</code> to <code>ml</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p cups_to_ml $value
</code></pre>
</article>
<article class="doc-entry" id="doc-currency-code-to-symbol">
<h3><a class="doc-anchor" href="#doc-currency-code-to-symbol">#</a> <code>currency_code_to_symbol</code></h3>
<p><code>currency_code_to_symbol(code) → string</code> — symbol like $/€/¥ for ISO code.</p>
</article>
<article class="doc-entry" id="doc-currency-convert">
<h3><a class="doc-anchor" href="#doc-currency-convert">#</a> <code>currency_convert</code></h3>
<p><code>currency_convert</code> — currency / money helper <code>convert</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p currency_convert $x
</code></pre>
</article>
<article class="doc-entry" id="doc-currency-decimal-places">
<h3><a class="doc-anchor" href="#doc-currency-decimal-places">#</a> <code>currency_decimal_places</code></h3>
<p><code>currency_decimal_places(code) → int</code> — minor-unit digits (2 for USD, 0 for JPY).</p>
</article>
<article class="doc-entry" id="doc-currency-format">
<h3><a class="doc-anchor" href="#doc-currency-format">#</a> <code>currency_format</code></h3>
<p><code>currency_format(amount, code) → string</code> — locale-aware money formatting.</p>
</article>
<article class="doc-entry" id="doc-currency-iso-4217">
<h3><a class="doc-anchor" href="#doc-currency-iso-4217">#</a> <code>currency_iso_4217</code></h3>
<p><code>currency_iso_4217(name_or_symbol) → string</code> — ISO 4217 alphabetic currency code.</p>
<pre><code class="lang-perl">p currency_iso_4217("dollar") # "USD"
</code></pre>
</article>
<article class="doc-entry" id="doc-currency-parse">
<h3><a class="doc-anchor" href="#doc-currency-parse">#</a> <code>currency_parse</code></h3>
<p><code>currency_parse(s) → {amount, code}</code> — parse formatted money string.</p>
</article>
<article class="doc-entry" id="doc-currency-rate">
<h3><a class="doc-anchor" href="#doc-currency-rate">#</a> <code>currency_rate</code></h3>
<p><code>currency_rate</code> — currency / money helper <code>rate</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p currency_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-currency-round">
<h3><a class="doc-anchor" href="#doc-currency-round">#</a> <code>currency_round</code></h3>
<p><code>currency_round(amount, code) → number</code> — round to currency precision.</p>
</article>
<article class="doc-entry" id="doc-currency-split-thousands">
<h3><a class="doc-anchor" href="#doc-currency-split-thousands">#</a> <code>currency_split_thousands</code></h3>
<p><code>currency_split_thousands(amount, sep=",") → string</code> — comma-separated thousands grouping.</p>
</article>
<article class="doc-entry" id="doc-currency-symbol-to-code">
<h3><a class="doc-anchor" href="#doc-currency-symbol-to-code">#</a> <code>currency_symbol_to_code</code></h3>
<p><code>currency_symbol_to_code(symbol) → string</code> — inverse of <code>currency_code_to_symbol</code>.</p>
</article>
<article class="doc-entry" id="doc-current-divider">
<h3><a class="doc-anchor" href="#doc-current-divider">#</a> <code>current_divider</code></h3>
<p><code>current_divider</code> — operation <code>current divider</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p current_divider $x
</code></pre>
</article>
<article class="doc-entry" id="doc-curve25519-mul-simple">
<h3><a class="doc-anchor" href="#doc-curve25519-mul-simple">#</a> <code>curve25519_mul_simple</code></h3>
<p><code>curve25519_mul_simple</code> — operation <code>curve25519 mul simple</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p curve25519_mul_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cusip-check">
<h3><a class="doc-anchor" href="#doc-cusip-check">#</a> <code>cusip_check</code></h3>
<p><code>cusip_check</code> — operation <code>cusip check</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p cusip_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cut">
<h3><a class="doc-anchor" href="#doc-cut">#</a> <code>cut</code></h3>
<p><code>cut</code> — bin continuous values into intervals. Returns integer bin indices. Like R's cut().</p>
<pre><code class="lang-perl">p cut([1.5, 3.2, 7.8], [0, 2, 5, 10]) # [1, 2, 3]
</code></pre>
</article>
<article class="doc-entry" id="doc-cutree">
<h3><a class="doc-anchor" href="#doc-cutree">#</a> <code>cutree</code></h3>
<p><code>cutree</code> — cut a dendrogram into k clusters. Takes merge list from hclust and k. Returns cluster assignments. Like R's cutree().</p>
<pre><code class="lang-perl">my @clusters = @{cutree(hclust(dist_mat($data)), 3)}
</code></pre>
</article>
<article class="doc-entry" id="doc-cutting-plane-step">
<h3><a class="doc-anchor" href="#doc-cutting-plane-step">#</a> <code>cutting_plane_step</code></h3>
<p><code>cutting_plane_step</code> — single-step update of <code>cutting plane</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p cutting_plane_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cv">
<h3><a class="doc-anchor" href="#doc-cv">#</a> <code>cv</code></h3>
<p><code>cv</code> — operation <code>cv</code>. Alias for <code>coeff_of_variation</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p cv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cv-monatomic-ideal">
<h3><a class="doc-anchor" href="#doc-cv-monatomic-ideal">#</a> <code>cv_monatomic_ideal</code></h3>
<p><code>cv_monatomic_ideal</code> — operation <code>cv monatomic ideal</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p cv_monatomic_ideal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cvar-historical">
<h3><a class="doc-anchor" href="#doc-cvar-historical">#</a> <code>cvar_historical</code></h3>
<p><code>cvar_historical</code> — operation <code>cvar historical</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p cvar_historical $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cw">
<h3><a class="doc-anchor" href="#doc-cw">#</a> <code>cw</code></h3>
<p><code>cw</code> — operation <code>cw</code>. Alias for <code>csv_write</code>. Category: *data / network*.</p>
<pre><code class="lang-perl">p cw $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cwd">
<h3><a class="doc-anchor" href="#doc-cwd">#</a> <code>cwd</code></h3>
<p><code>cwd</code> — operation <code>cwd</code>. Category: *more process / system*.</p>
<pre><code class="lang-perl">p cwd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cwt-morlet">
<h3><a class="doc-anchor" href="#doc-cwt-morlet">#</a> <code>cwt_morlet</code></h3>
<p><code>cwt_morlet</code> — operation <code>cwt morlet</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p cwt_morlet $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cyan">
<h3><a class="doc-anchor" href="#doc-cyan">#</a> <code>cyan</code></h3>
<p><code>cyan</code> — operation <code>cyan</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p cyan $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cyan-bold">
<h3><a class="doc-anchor" href="#doc-cyan-bold">#</a> <code>cyan_bold</code></h3>
<p><code>cyan_bold</code> — operation <code>cyan bold</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p cyan_bold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cyber-banner">
<h3><a class="doc-anchor" href="#doc-cyber-banner">#</a> <code>cyber_banner</code></h3>
<p><code>cyber_banner</code> (alias <code>neon_banner</code>) — large neon block-letter banner with gradient coloring and border. Args: text.</p>
<pre><code class="lang-perl">p cyber_banner("STRYKE")
p cyber_banner("HACK THE PLANET")
</code></pre>
</article>
<article class="doc-entry" id="doc-cyber-circuit">
<h3><a class="doc-anchor" href="#doc-cyber-circuit">#</a> <code>cyber_circuit</code></h3>
<p><code>cyber_circuit</code> — circuit board pattern with traces, intersections, and glowing nodes. Args: [width, height, seed].</p>
<pre><code class="lang-perl">p cyber_circuit() # 60x20 default
p cyber_circuit(80, 30, 42) # custom
</code></pre>
</article>
<article class="doc-entry" id="doc-cyber-city">
<h3><a class="doc-anchor" href="#doc-cyber-city">#</a> <code>cyber_city</code></h3>
<p><code>cyber_city</code> — procedural neon cityscape with buildings, windows, stars, and antennas. Args: [width, height, seed]. Output: ANSI-colored string for terminal.</p>
<pre><code class="lang-perl">p cyber_city() # 80x24 default
p cyber_city(120, 40, 99) # custom size and seed
</code></pre>
</article>
<article class="doc-entry" id="doc-cyber-eye">
<h3><a class="doc-anchor" href="#doc-cyber-eye">#</a> <code>cyber_eye</code></h3>
<p><code>cyber_eye</code> — cyberpunk all-seeing eye motif with layered glow. Args: [size]. Size: "small" (default) or "large".</p>
<pre><code class="lang-perl">p cyber_eye() # small eye
p cyber_eye("large") # large eye
</code></pre>
</article>
<article class="doc-entry" id="doc-cyber-glitch">
<h3><a class="doc-anchor" href="#doc-cyber-glitch">#</a> <code>cyber_glitch</code></h3>
<p><code>cyber_glitch</code> (alias <code>glitch_text</code>) — glitch-distort text with ANSI corruption, screen tears, and neon color bleeding. Args: text [, intensity 1-10].</p>
<pre><code class="lang-perl">p cyber_glitch("SYSTEM BREACH", 7)
p cyber_glitch("hello world")
</code></pre>
</article>
<article class="doc-entry" id="doc-cyber-grid">
<h3><a class="doc-anchor" href="#doc-cyber-grid">#</a> <code>cyber_grid</code></h3>
<p><code>cyber_grid</code> — retro perspective grid with vanishing point and neon glow (Tron/synthwave style). Args: [width, height].</p>
<pre><code class="lang-perl">p cyber_grid() # 80x24 default
p cyber_grid(120, 30) # wider grid
</code></pre>
</article>
<article class="doc-entry" id="doc-cyber-rain">
<h3><a class="doc-anchor" href="#doc-cyber-rain">#</a> <code>cyber_rain</code></h3>
<p><code>cyber_rain</code> (alias <code>matrix_rain</code>) — matrix-style digital rain with Japanese katakana and green phosphor glow. Args: [width, height, seed].</p>
<pre><code class="lang-perl">p cyber_rain() # 80x24 default
p cyber_rain(120, 40, 42) # custom
</code></pre>
</article>
<article class="doc-entry" id="doc-cyber-skull">
<h3><a class="doc-anchor" href="#doc-cyber-skull">#</a> <code>cyber_skull</code></h3>
<p><code>cyber_skull</code> — neon skull ASCII art with glitch effects. Args: [size]. Size: "small" (default) or "large".</p>
<pre><code class="lang-perl">p cyber_skull() # small skull
p cyber_skull("large") # large skull
</code></pre>
</article>
<article class="doc-entry" id="doc-cyc">
<h3><a class="doc-anchor" href="#doc-cyc">#</a> <code>cyc</code></h3>
<p><code>cyc</code> — operation <code>cyc</code>. Alias for <code>cycle</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p cyc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cycle">
<h3><a class="doc-anchor" href="#doc-cycle">#</a> <code>cycle</code></h3>
<p><code>cycle</code> — operation <code>cycle</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p cycle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cycle-n">
<h3><a class="doc-anchor" href="#doc-cycle-n">#</a> <code>cycle_n</code></h3>
<p><code>cycle_n</code> — operation <code>cycle n</code>. Alias for <code>repeat_list</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p cycle_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cyclic-homology-step">
<h3><a class="doc-anchor" href="#doc-cyclic-homology-step">#</a> <code>cyclic_homology_step</code></h3>
<p><code>cyclic_homology_step</code> — single-step update of <code>cyclic homology</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p cyclic_homology_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cylinder-surface">
<h3><a class="doc-anchor" href="#doc-cylinder-surface">#</a> <code>cylinder_surface</code></h3>
<p><code>cylinder_surface</code> — operation <code>cylinder surface</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p cylinder_surface $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cylinder-surface-area">
<h3><a class="doc-anchor" href="#doc-cylinder-surface-area">#</a> <code>cylinder_surface_area</code></h3>
<p><code>cylinder_surface_area</code> — operation <code>cylinder surface area</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p cylinder_surface_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cylinder-volume">
<h3><a class="doc-anchor" href="#doc-cylinder-volume">#</a> <code>cylinder_volume</code></h3>
<p><code>cylinder_volume</code> — operation <code>cylinder volume</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p cylinder_volume $x
</code></pre>
</article>
<article class="doc-entry" id="doc-cylindrical-to-cartesian">
<h3><a class="doc-anchor" href="#doc-cylindrical-to-cartesian">#</a> <code>cylindrical_to_cartesian</code></h3>
<p><code>cylindrical_to_cartesian</code> — convert from <code>cylindrical</code> to <code>cartesian</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p cylindrical_to_cartesian $value
</code></pre>
</article>
<article class="doc-entry" id="doc-cylvol">
<h3><a class="doc-anchor" href="#doc-cylvol">#</a> <code>cylvol</code></h3>
<p><code>cylvol</code> — operation <code>cylvol</code>. Alias for <code>cylinder_volume</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p cylvol $x
</code></pre>
</article>
<article class="doc-entry" id="doc-d">
<h3><a class="doc-anchor" href="#doc-d">#</a> <code>d</code></h3>
<p><code>d</code> — operation <code>d</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-d2comp">
<h3><a class="doc-anchor" href="#doc-d2comp">#</a> <code>d2comp</code></h3>
<p><code>d2comp</code> — operation <code>d2comp</code>. Alias for <code>degrees_to_compass</code>. Category: *misc / utility*.</p>
<pre><code class="lang-perl">p d2comp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-d2r">
<h3><a class="doc-anchor" href="#doc-d2r">#</a> <code>d2r</code></h3>
<p><code>d2r</code> — operation <code>d2r</code>. Alias for <code>deg_to_rad</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p d2r $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-power">
<h3><a class="doc-anchor" href="#doc-db-power">#</a> <code>dB_power</code></h3>
<p><code>dB_power</code> — operation <code>dB power</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p dB_power $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-voltage">
<h3><a class="doc-anchor" href="#doc-db-voltage">#</a> <code>dB_voltage</code></h3>
<p><code>dB_voltage</code> — operation <code>dB voltage</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p dB_voltage $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dagum-pdf">
<h3><a class="doc-anchor" href="#doc-dagum-pdf">#</a> <code>dagum_pdf</code></h3>
<p><code>dagum_pdf</code> — operation <code>dagum pdf</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p dagum_pdf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-daitch-mokotoff">
<h3><a class="doc-anchor" href="#doc-daitch-mokotoff">#</a> <code>daitch_mokotoff</code></h3>
<p><code>daitch_mokotoff</code> — operation <code>daitch mokotoff</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p daitch_mokotoff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dalys-disability-weight">
<h3><a class="doc-anchor" href="#doc-dalys-disability-weight">#</a> <code>dalys_disability_weight</code></h3>
<p><code>dalys_disability_weight</code> — operation <code>dalys disability weight</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p dalys_disability_weight $x
</code></pre>
</article>
<article class="doc-entry" id="doc-damerau-levenshtein">
<h3><a class="doc-anchor" href="#doc-damerau-levenshtein">#</a> <code>damerau_levenshtein</code></h3>
<p><code>damerau_levenshtein</code> — operation <code>damerau levenshtein</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p damerau_levenshtein $x
</code></pre>
</article>
<article class="doc-entry" id="doc-damping-factor">
<h3><a class="doc-anchor" href="#doc-damping-factor">#</a> <code>damping_factor</code></h3>
<p><code>damping_factor(c, m, k) → number</code> — damping ratio ζ = <code>c / (2·√(m·k))</code>.</p>
</article>
<article class="doc-entry" id="doc-dantzig-wolfe-step">
<h3><a class="doc-anchor" href="#doc-dantzig-wolfe-step">#</a> <code>dantzig_wolfe_step</code></h3>
<p><code>dantzig_wolfe_step</code> — single-step update of <code>dantzig wolfe</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p dantzig_wolfe_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-darboux-frame-step">
<h3><a class="doc-anchor" href="#doc-darboux-frame-step">#</a> <code>darboux_frame_step</code></h3>
<p><code>darboux_frame_step</code> — single-step update of <code>darboux frame</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p darboux_frame_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dasum">
<h3><a class="doc-anchor" href="#doc-dasum">#</a> <code>dasum</code></h3>
<p><code>dasum</code> — operation <code>dasum</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dasum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-data-processing-inequality">
<h3><a class="doc-anchor" href="#doc-data-processing-inequality">#</a> <code>data_processing_inequality</code></h3>
<p><code>data_processing_inequality</code> — operation <code>data processing inequality</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p data_processing_inequality $x
</code></pre>
</article>
<article class="doc-entry" id="doc-date-add-days">
<h3><a class="doc-anchor" href="#doc-date-add-days">#</a> <code>date_add_days</code></h3>
<p><code>date_add_days(unix_or_iso, n) → int</code> — returns unix timestamp <code>n</code> days later.</p>
<pre><code class="lang-perl">p date_add_days("2024-01-01", 30)
</code></pre>
</article>
<article class="doc-entry" id="doc-date-add-months">
<h3><a class="doc-anchor" href="#doc-date-add-months">#</a> <code>date_add_months</code></h3>
<p><code>date_add_months(unix_or_iso, n) → int</code> — adds whole calendar months; clamps the day to the last valid day of the target month (so Jan 31 + 1mo → Feb 28/29, May 31 + 1mo → Jun 30).</p>
<pre><code class="lang-perl">p date_add_months("2024-01-31", 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-date-add-years">
<h3><a class="doc-anchor" href="#doc-date-add-years">#</a> <code>date_add_years</code></h3>
<p><code>date_add_years(unix_or_iso, n) → int</code> — adds whole calendar years; clamps Feb 29 to Feb 28 in non-leap target years; otherwise preserves the original day.</p>
<pre><code class="lang-perl">p date_add_years("2024-02-29", 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-date-business-days-between">
<h3><a class="doc-anchor" href="#doc-date-business-days-between">#</a> <code>date_business_days_between</code></h3>
<p><code>date_business_days_between(d1, d2) → int</code> — weekday count (Mon-Fri) strictly between two dates.</p>
<pre><code class="lang-perl">p date_business_days_between("2024-01-01", "2024-01-15")
</code></pre>
</article>
<article class="doc-entry" id="doc-date-day">
<h3><a class="doc-anchor" href="#doc-date-day">#</a> <code>date_day</code></h3>
<p><code>date_day(unix_or_iso) → int</code> — day of month 1-31.</p>
</article>
<article class="doc-entry" id="doc-date-dayofweek">
<h3><a class="doc-anchor" href="#doc-date-dayofweek">#</a> <code>date_dayofweek</code></h3>
<p><code>date_dayofweek(unix_or_iso) → int</code> — day of week 0-6, Sunday=0.</p>
<pre><code class="lang-perl">p date_dayofweek("2024-03-15") # 5 (Friday)
</code></pre>
</article>
<article class="doc-entry" id="doc-date-dayofyear">
<h3><a class="doc-anchor" href="#doc-date-dayofyear">#</a> <code>date_dayofyear</code></h3>
<p><code>date_dayofyear(unix_or_iso) → int</code> — ordinal day 1-366.</p>
<pre><code class="lang-perl">p date_dayofyear("2024-12-31") # 366
</code></pre>
</article>
<article class="doc-entry" id="doc-date-days-in-month">
<h3><a class="doc-anchor" href="#doc-date-days-in-month">#</a> <code>date_days_in_month</code></h3>
<p><code>date_days_in_month(year, month) → int</code> — days in given month accounting for leap years.</p>
<pre><code class="lang-perl">p date_days_in_month(2024, 2) # 29
</code></pre>
</article>
<article class="doc-entry" id="doc-date-diff-days">
<h3><a class="doc-anchor" href="#doc-date-diff-days">#</a> <code>date_diff_days</code></h3>
<p><code>date_diff_days(d1, d2) → int</code> — <code>d2 - d1</code> in whole days.</p>
<pre><code class="lang-perl">p date_diff_days("2024-01-01", "2024-12-31")
</code></pre>
</article>
<article class="doc-entry" id="doc-date-diff-hours">
<h3><a class="doc-anchor" href="#doc-date-diff-hours">#</a> <code>date_diff_hours</code></h3>
<p><code>date_diff_hours(d1, d2) → int</code> — hours between two timestamps.</p>
</article>
<article class="doc-entry" id="doc-date-diff-minutes">
<h3><a class="doc-anchor" href="#doc-date-diff-minutes">#</a> <code>date_diff_minutes</code></h3>
<p><code>date_diff_minutes(d1, d2) → int</code> — minutes between two timestamps.</p>
</article>
<article class="doc-entry" id="doc-date-diff-seconds">
<h3><a class="doc-anchor" href="#doc-date-diff-seconds">#</a> <code>date_diff_seconds</code></h3>
<p><code>date_diff_seconds(d1, d2) → int</code> — seconds between two timestamps.</p>
</article>
<article class="doc-entry" id="doc-date-easter">
<h3><a class="doc-anchor" href="#doc-date-easter">#</a> <code>date_easter</code></h3>
<p><code>date_easter(year) → string</code> — Western Christian Easter Sunday date (Anonymous Gregorian algorithm).</p>
<pre><code class="lang-perl">p date_easter(2024) # "2024-03-31"
</code></pre>
</article>
<article class="doc-entry" id="doc-date-first-of-month">
<h3><a class="doc-anchor" href="#doc-date-first-of-month">#</a> <code>date_first_of_month</code></h3>
<p><code>date_first_of_month(unix_or_iso) → int</code> — unix timestamp of the first day of the same month at 00:00 UTC.</p>
<pre><code class="lang-perl">p date_first_of_month("2024-03-15")
</code></pre>
</article>
<article class="doc-entry" id="doc-date-hour">
<h3><a class="doc-anchor" href="#doc-date-hour">#</a> <code>date_hour</code></h3>
<p><code>date_hour(unix_or_iso) → int</code> — hour 0-23 (UTC).</p>
</article>
<article class="doc-entry" id="doc-date-is-leap">
<h3><a class="doc-anchor" href="#doc-date-is-leap">#</a> <code>date_is_leap</code></h3>
<p><code>date_is_leap(year) → 0|1</code> — Gregorian leap-year rule: divisible by 4, except by 100, except by 400.</p>
<pre><code class="lang-perl">p date_is_leap(2000) # 1
p date_is_leap(2100) # 0
</code></pre>
</article>
<article class="doc-entry" id="doc-date-is-weekend">
<h3><a class="doc-anchor" href="#doc-date-is-weekend">#</a> <code>date_is_weekend</code></h3>
<p><code>date_is_weekend(unix_or_iso) → 0|1</code> — 1 if Saturday or Sunday.</p>
<pre><code class="lang-perl">p date_is_weekend("2024-03-16") # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-date-iso-format">
<h3><a class="doc-anchor" href="#doc-date-iso-format">#</a> <code>date_iso_format</code></h3>
<p><code>date_iso_format(unix_or_iso) → string</code> — RFC3339 representation.</p>
<pre><code class="lang-perl">p date_iso_format(0) # "1970-01-01T00:00:00+00:00"
</code></pre>
</article>
<article class="doc-entry" id="doc-date-iso-week">
<h3><a class="doc-anchor" href="#doc-date-iso-week">#</a> <code>date_iso_week</code></h3>
<p><code>date_iso_week(unix_or_iso) → string</code> — ISO 8601 week format <code>YYYY-Www</code>.</p>
<pre><code class="lang-perl">p date_iso_week("2024-03-15") # "2024-W11"
</code></pre>
</article>
<article class="doc-entry" id="doc-date-last-of-month">
<h3><a class="doc-anchor" href="#doc-date-last-of-month">#</a> <code>date_last_of_month</code></h3>
<p><code>date_last_of_month(unix_or_iso) → int</code> — unix timestamp of the last day of the same month.</p>
<pre><code class="lang-perl">p date_last_of_month("2024-02-15") # 2024-02-29
</code></pre>
</article>
<article class="doc-entry" id="doc-date-minute">
<h3><a class="doc-anchor" href="#doc-date-minute">#</a> <code>date_minute</code></h3>
<p><code>date_minute(unix_or_iso) → int</code> — minute 0-59.</p>
</article>
<article class="doc-entry" id="doc-date-month">
<h3><a class="doc-anchor" href="#doc-date-month">#</a> <code>date_month</code></h3>
<p><code>date_month(unix_or_iso) → int</code> — month 1-12.</p>
</article>
<article class="doc-entry" id="doc-date-quarter">
<h3><a class="doc-anchor" href="#doc-date-quarter">#</a> <code>date_quarter</code></h3>
<p><code>date_quarter(unix_or_iso) → int</code> — calendar quarter 1-4.</p>
<pre><code class="lang-perl">p date_quarter("2024-04-15") # 2
</code></pre>
</article>
<article class="doc-entry" id="doc-date-round-iso">
<h3><a class="doc-anchor" href="#doc-date-round-iso">#</a> <code>date_round_iso</code></h3>
<p><code>date_round_iso</code> — date / time helper <code>round iso</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p date_round_iso $x
</code></pre>
</article>
<article class="doc-entry" id="doc-date-second">
<h3><a class="doc-anchor" href="#doc-date-second">#</a> <code>date_second</code></h3>
<p><code>date_second(unix_or_iso) → int</code> — second 0-59.</p>
</article>
<article class="doc-entry" id="doc-date-str-to-unix">
<h3><a class="doc-anchor" href="#doc-date-str-to-unix">#</a> <code>date_str_to_unix</code></h3>
<p><code>date_str_to_unix(s, fmt="%Y-%m-%d %H:%M:%S") → int</code> — parse a date string back to unix timestamp.</p>
<pre><code class="lang-perl">p date_str_to_unix("2024-01-01", "%Y-%m-%d")
</code></pre>
</article>
<article class="doc-entry" id="doc-date-unix-to-str">
<h3><a class="doc-anchor" href="#doc-date-unix-to-str">#</a> <code>date_unix_to_str</code></h3>
<p><code>date_unix_to_str(unix, fmt="%Y-%m-%d %H:%M:%S") → string</code> — strftime-format a unix timestamp.</p>
<pre><code class="lang-perl">p date_unix_to_str(1672531200, "%Y-%m-%d")
</code></pre>
</article>
<article class="doc-entry" id="doc-date-weekofyear">
<h3><a class="doc-anchor" href="#doc-date-weekofyear">#</a> <code>date_weekofyear</code></h3>
<p><code>date_weekofyear(unix_or_iso) → int</code> — ISO 8601 week number 1-53.</p>
<pre><code class="lang-perl">p date_weekofyear("2024-01-01")
</code></pre>
</article>
<article class="doc-entry" id="doc-date-year">
<h3><a class="doc-anchor" href="#doc-date-year">#</a> <code>date_year</code></h3>
<p><code>date_year(unix_or_iso) → int</code> — calendar year of a UTC date. Accepts unix timestamp or ISO string.</p>
<pre><code class="lang-perl">p date_year("2024-03-15") # 2024
</code></pre>
</article>
<article class="doc-entry" id="doc-dawsn">
<h3><a class="doc-anchor" href="#doc-dawsn">#</a> <code>dawsn</code></h3>
<p><code>dawsn</code> — operation <code>dawsn</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p dawsn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dawson-function">
<h3><a class="doc-anchor" href="#doc-dawson-function">#</a> <code>dawson_function</code></h3>
<p><code>dawson_function</code> — operation <code>dawson function</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p dawson_function $x
</code></pre>
</article>
<article class="doc-entry" id="doc-daxpy">
<h3><a class="doc-anchor" href="#doc-daxpy">#</a> <code>daxpy</code></h3>
<p><code>daxpy</code> — operation <code>daxpy</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p daxpy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-day-of-week-iso">
<h3><a class="doc-anchor" href="#doc-day-of-week-iso">#</a> <code>day_of_week_iso</code></h3>
<p><code>day_of_week_iso</code> — operation <code>day of week iso</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p day_of_week_iso $x
</code></pre>
</article>
<article class="doc-entry" id="doc-day-of-week-zeller">
<h3><a class="doc-anchor" href="#doc-day-of-week-zeller">#</a> <code>day_of_week_zeller</code></h3>
<p><code>day_of_week_zeller</code> — operation <code>day of week zeller</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p day_of_week_zeller $x
</code></pre>
</article>
<article class="doc-entry" id="doc-day-of-year">
<h3><a class="doc-anchor" href="#doc-day-of-year">#</a> <code>day_of_year</code></h3>
<p><code>day_of_year</code> — operation <code>day of year</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p day_of_year $x
</code></pre>
</article>
<article class="doc-entry" id="doc-days-between">
<h3><a class="doc-anchor" href="#doc-days-between">#</a> <code>days_between</code></h3>
<p><code>days_between</code> — operation <code>days between</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p days_between $x
</code></pre>
</article>
<article class="doc-entry" id="doc-days-in-month">
<h3><a class="doc-anchor" href="#doc-days-in-month">#</a> <code>days_in_month</code></h3>
<p><code>days_in_month</code> — operation <code>days in month</code>. Category: *date helpers*.</p>
<pre><code class="lang-perl">p days_in_month $x
</code></pre>
</article>
<article class="doc-entry" id="doc-days-in-month-fn">
<h3><a class="doc-anchor" href="#doc-days-in-month-fn">#</a> <code>days_in_month_fn</code></h3>
<p><code>days_in_month_fn</code> — operation <code>days in month fn</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p days_in_month_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-days-in-year">
<h3><a class="doc-anchor" href="#doc-days-in-year">#</a> <code>days_in_year</code></h3>
<p><code>days_in_year</code> — operation <code>days in year</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p days_in_year $x
</code></pre>
</article>
<article class="doc-entry" id="doc-days-to-hours">
<h3><a class="doc-anchor" href="#doc-days-to-hours">#</a> <code>days_to_hours</code></h3>
<p><code>days_to_hours</code> — convert from <code>days</code> to <code>hours</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p days_to_hours $value
</code></pre>
</article>
<article class="doc-entry" id="doc-days-to-seconds">
<h3><a class="doc-anchor" href="#doc-days-to-seconds">#</a> <code>days_to_seconds</code></h3>
<p><code>days_to_seconds</code> — convert from <code>days</code> to <code>seconds</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p days_to_seconds $value
</code></pre>
</article>
<article class="doc-entry" id="doc-daysinmo">
<h3><a class="doc-anchor" href="#doc-daysinmo">#</a> <code>daysinmo</code></h3>
<p><code>daysinmo</code> — operation <code>daysinmo</code>. Alias for <code>days_in_month_fn</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p daysinmo $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db">
<h3><a class="doc-anchor" href="#doc-db">#</a> <code>db</code></h3>
<p><code>db</code> — operation <code>db</code>. Alias for <code>decibel_ratio</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p db $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db4-coeffs">
<h3><a class="doc-anchor" href="#doc-db4-coeffs">#</a> <code>db4_coeffs</code></h3>
<p><code>db4_coeffs</code> — operation <code>db4 coeffs</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p db4_coeffs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db4-wavelet-step">
<h3><a class="doc-anchor" href="#doc-db4-wavelet-step">#</a> <code>db4_wavelet_step</code></h3>
<p><code>db4_wavelet_step</code> — single-step update of <code>db4 wavelet</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p db4_wavelet_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db6-coeffs">
<h3><a class="doc-anchor" href="#doc-db6-coeffs">#</a> <code>db6_coeffs</code></h3>
<p><code>db6_coeffs</code> — operation <code>db6 coeffs</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p db6_coeffs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-anti-entropy-pull-step">
<h3><a class="doc-anchor" href="#doc-db-anti-entropy-pull-step">#</a> <code>db_anti_entropy_pull_step</code></h3>
<p><code>db_anti_entropy_pull_step</code> — single-step update of <code>db anti entropy pull</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_anti_entropy_pull_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-anti-entropy-step">
<h3><a class="doc-anchor" href="#doc-db-anti-entropy-step">#</a> <code>db_anti_entropy_step</code></h3>
<p><code>db_anti_entropy_step</code> — single-step update of <code>db anti entropy</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_anti_entropy_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-arc-cache-score">
<h3><a class="doc-anchor" href="#doc-db-arc-cache-score">#</a> <code>db_arc_cache_score</code></h3>
<p><code>db_arc_cache_score</code> — score of <code>db arc cache</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_arc_cache_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-async-commit-check">
<h3><a class="doc-anchor" href="#doc-db-async-commit-check">#</a> <code>db_async_commit_check</code></h3>
<p><code>db_async_commit_check</code> — operation <code>db async commit check</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_async_commit_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-avalanche-query-step">
<h3><a class="doc-anchor" href="#doc-db-avalanche-query-step">#</a> <code>db_avalanche_query_step</code></h3>
<p><code>db_avalanche_query_step</code> — single-step update of <code>db avalanche query</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_avalanche_query_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-b-tree-merge">
<h3><a class="doc-anchor" href="#doc-db-b-tree-merge">#</a> <code>db_b_tree_merge</code></h3>
<p><code>db_b_tree_merge</code> — operation <code>db b tree merge</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_b_tree_merge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-b-tree-split">
<h3><a class="doc-anchor" href="#doc-db-b-tree-split">#</a> <code>db_b_tree_split</code></h3>
<p><code>db_b_tree_split</code> — operation <code>db b tree split</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_b_tree_split $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-block-cache-hit-rate">
<h3><a class="doc-anchor" href="#doc-db-block-cache-hit-rate">#</a> <code>db_block_cache_hit_rate</code></h3>
<p><code>db_block_cache_hit_rate</code> — rate of <code>db block cache hit</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_block_cache_hit_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-bloom-filter-bit-index">
<h3><a class="doc-anchor" href="#doc-db-bloom-filter-bit-index">#</a> <code>db_bloom_filter_bit_index</code></h3>
<p><code>db_bloom_filter_bit_index</code> — index of <code>db bloom filter bit</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_bloom_filter_bit_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-buffer-pool-score">
<h3><a class="doc-anchor" href="#doc-db-buffer-pool-score">#</a> <code>db_buffer_pool_score</code></h3>
<p><code>db_buffer_pool_score</code> — score of <code>db buffer pool</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_buffer_pool_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-byzantine-quorum-size">
<h3><a class="doc-anchor" href="#doc-db-byzantine-quorum-size">#</a> <code>db_byzantine_quorum_size</code></h3>
<p><code>db_byzantine_quorum_size</code> — operation <code>db byzantine quorum size</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_byzantine_quorum_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-causal-consistency-check">
<h3><a class="doc-anchor" href="#doc-db-causal-consistency-check">#</a> <code>db_causal_consistency_check</code></h3>
<p><code>db_causal_consistency_check</code> — operation <code>db causal consistency check</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_causal_consistency_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-chao-estimator-step">
<h3><a class="doc-anchor" href="#doc-db-chao-estimator-step">#</a> <code>db_chao_estimator_step</code></h3>
<p><code>db_chao_estimator_step</code> — single-step update of <code>db chao estimator</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_chao_estimator_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-chord-finger-index">
<h3><a class="doc-anchor" href="#doc-db-chord-finger-index">#</a> <code>db_chord_finger_index</code></h3>
<p><code>db_chord_finger_index</code> — index of <code>db chord finger</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_chord_finger_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-chubby-lease-step">
<h3><a class="doc-anchor" href="#doc-db-chubby-lease-step">#</a> <code>db_chubby_lease_step</code></h3>
<p><code>db_chubby_lease_step</code> — single-step update of <code>db chubby lease</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_chubby_lease_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-circuit-breaker-step">
<h3><a class="doc-anchor" href="#doc-db-circuit-breaker-step">#</a> <code>db_circuit_breaker_step</code></h3>
<p><code>db_circuit_breaker_step</code> — single-step update of <code>db circuit breaker</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_circuit_breaker_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-clock-cache-hand">
<h3><a class="doc-anchor" href="#doc-db-clock-cache-hand">#</a> <code>db_clock_cache_hand</code></h3>
<p><code>db_clock_cache_hand</code> — operation <code>db clock cache hand</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_clock_cache_hand $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-clock-skew-estimate">
<h3><a class="doc-anchor" href="#doc-db-clock-skew-estimate">#</a> <code>db_clock_skew_estimate</code></h3>
<p><code>db_clock_skew_estimate</code> — operation <code>db clock skew estimate</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_clock_skew_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-compaction-score">
<h3><a class="doc-anchor" href="#doc-db-compaction-score">#</a> <code>db_compaction_score</code></h3>
<p><code>db_compaction_score</code> — score of <code>db compaction</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_compaction_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-consensus-quorum-size">
<h3><a class="doc-anchor" href="#doc-db-consensus-quorum-size">#</a> <code>db_consensus_quorum_size</code></h3>
<p><code>db_consensus_quorum_size</code> — operation <code>db consensus quorum size</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_consensus_quorum_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-consistent-hash-index">
<h3><a class="doc-anchor" href="#doc-db-consistent-hash-index">#</a> <code>db_consistent_hash_index</code></h3>
<p><code>db_consistent_hash_index</code> — index of <code>db consistent hash</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_consistent_hash_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-consistent-lookup-id">
<h3><a class="doc-anchor" href="#doc-db-consistent-lookup-id">#</a> <code>db_consistent_lookup_id</code></h3>
<p><code>db_consistent_lookup_id</code> — operation <code>db consistent lookup id</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_consistent_lookup_id $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-count-min-sketch-bin">
<h3><a class="doc-anchor" href="#doc-db-count-min-sketch-bin">#</a> <code>db_count_min_sketch_bin</code></h3>
<p><code>db_count_min_sketch_bin</code> — operation <code>db count min sketch bin</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_count_min_sketch_bin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-crdt-g-counter-merge">
<h3><a class="doc-anchor" href="#doc-db-crdt-g-counter-merge">#</a> <code>db_crdt_g_counter_merge</code></h3>
<p><code>db_crdt_g_counter_merge</code> — operation <code>db crdt g counter merge</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_crdt_g_counter_merge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-crdt-lww-register-merge">
<h3><a class="doc-anchor" href="#doc-db-crdt-lww-register-merge">#</a> <code>db_crdt_lww_register_merge</code></h3>
<p><code>db_crdt_lww_register_merge</code> — operation <code>db crdt lww register merge</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_crdt_lww_register_merge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-crdt-pn-counter-merge">
<h3><a class="doc-anchor" href="#doc-db-crdt-pn-counter-merge">#</a> <code>db_crdt_pn_counter_merge</code></h3>
<p><code>db_crdt_pn_counter_merge</code> — operation <code>db crdt pn counter merge</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_crdt_pn_counter_merge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-crdt-set-or-merge">
<h3><a class="doc-anchor" href="#doc-db-crdt-set-or-merge">#</a> <code>db_crdt_set_or_merge</code></h3>
<p><code>db_crdt_set_or_merge</code> — operation <code>db crdt set or merge</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_crdt_set_or_merge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-cuckoo-filter-fingerprint">
<h3><a class="doc-anchor" href="#doc-db-cuckoo-filter-fingerprint">#</a> <code>db_cuckoo_filter_fingerprint</code></h3>
<p><code>db_cuckoo_filter_fingerprint</code> — operation <code>db cuckoo filter fingerprint</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_cuckoo_filter_fingerprint $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-dd-sketch-bin">
<h3><a class="doc-anchor" href="#doc-db-dd-sketch-bin">#</a> <code>db_dd_sketch_bin</code></h3>
<p><code>db_dd_sketch_bin</code> — operation <code>db dd sketch bin</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_dd_sketch_bin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-dht-replicate-factor">
<h3><a class="doc-anchor" href="#doc-db-dht-replicate-factor">#</a> <code>db_dht_replicate_factor</code></h3>
<p><code>db_dht_replicate_factor</code> — factor of <code>db dht replicate</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_dht_replicate_factor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-distinct-estimate-hll">
<h3><a class="doc-anchor" href="#doc-db-distinct-estimate-hll">#</a> <code>db_distinct_estimate_hll</code></h3>
<p><code>db_distinct_estimate_hll</code> — operation <code>db distinct estimate hll</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_distinct_estimate_hll $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-distinct-estimate-lpc">
<h3><a class="doc-anchor" href="#doc-db-distinct-estimate-lpc">#</a> <code>db_distinct_estimate_lpc</code></h3>
<p><code>db_distinct_estimate_lpc</code> — operation <code>db distinct estimate lpc</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_distinct_estimate_lpc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-eventual-consistency-check">
<h3><a class="doc-anchor" href="#doc-db-eventual-consistency-check">#</a> <code>db_eventual_consistency_check</code></h3>
<p><code>db_eventual_consistency_check</code> — operation <code>db eventual consistency check</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_eventual_consistency_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-freshness-score">
<h3><a class="doc-anchor" href="#doc-db-freshness-score">#</a> <code>db_freshness_score</code></h3>
<p><code>db_freshness_score</code> — score of <code>db freshness</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_freshness_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-gossip-fanout-step">
<h3><a class="doc-anchor" href="#doc-db-gossip-fanout-step">#</a> <code>db_gossip_fanout_step</code></h3>
<p><code>db_gossip_fanout_step</code> — single-step update of <code>db gossip fanout</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_gossip_fanout_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-group-commit-count">
<h3><a class="doc-anchor" href="#doc-db-group-commit-count">#</a> <code>db_group_commit_count</code></h3>
<p><code>db_group_commit_count</code> — count of <code>db group commit</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_group_commit_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-hash-join-cost">
<h3><a class="doc-anchor" href="#doc-db-hash-join-cost">#</a> <code>db_hash_join_cost</code></h3>
<p><code>db_hash_join_cost</code> — operation <code>db hash join cost</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_hash_join_cost $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-hinted-handoff-step">
<h3><a class="doc-anchor" href="#doc-db-hinted-handoff-step">#</a> <code>db_hinted_handoff_step</code></h3>
<p><code>db_hinted_handoff_step</code> — single-step update of <code>db hinted handoff</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_hinted_handoff_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-histogram-bucket-index">
<h3><a class="doc-anchor" href="#doc-db-histogram-bucket-index">#</a> <code>db_histogram_bucket_index</code></h3>
<p><code>db_histogram_bucket_index</code> — index of <code>db histogram bucket</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_histogram_bucket_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-honey-badger-step">
<h3><a class="doc-anchor" href="#doc-db-honey-badger-step">#</a> <code>db_honey_badger_step</code></h3>
<p><code>db_honey_badger_step</code> — single-step update of <code>db honey badger</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_honey_badger_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-hybrid-logical-clock">
<h3><a class="doc-anchor" href="#doc-db-hybrid-logical-clock">#</a> <code>db_hybrid_logical_clock</code></h3>
<p><code>db_hybrid_logical_clock</code> — operation <code>db hybrid logical clock</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_hybrid_logical_clock $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-hyperloglog-register-max">
<h3><a class="doc-anchor" href="#doc-db-hyperloglog-register-max">#</a> <code>db_hyperloglog_register_max</code></h3>
<p><code>db_hyperloglog_register_max</code> — maximum of <code>db hyperloglog register</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_hyperloglog_register_max $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-index-scan-cost">
<h3><a class="doc-anchor" href="#doc-db-index-scan-cost">#</a> <code>db_index_scan_cost</code></h3>
<p><code>db_index_scan_cost</code> — operation <code>db index scan cost</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_index_scan_cost $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-index-seek-cost">
<h3><a class="doc-anchor" href="#doc-db-index-seek-cost">#</a> <code>db_index_seek_cost</code></h3>
<p><code>db_index_seek_cost</code> — operation <code>db index seek cost</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_index_seek_cost $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-jaccard-minhash-estimate">
<h3><a class="doc-anchor" href="#doc-db-jaccard-minhash-estimate">#</a> <code>db_jaccard_minhash_estimate</code></h3>
<p><code>db_jaccard_minhash_estimate</code> — operation <code>db jaccard minhash estimate</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_jaccard_minhash_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-join-selectivity-step">
<h3><a class="doc-anchor" href="#doc-db-join-selectivity-step">#</a> <code>db_join_selectivity_step</code></h3>
<p><code>db_join_selectivity_step</code> — single-step update of <code>db join selectivity</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_join_selectivity_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-jump-hash-bucket">
<h3><a class="doc-anchor" href="#doc-db-jump-hash-bucket">#</a> <code>db_jump_hash_bucket</code></h3>
<p><code>db_jump_hash_bucket</code> — operation <code>db jump hash bucket</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_jump_hash_bucket $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-kademlia-xor-distance">
<h3><a class="doc-anchor" href="#doc-db-kademlia-xor-distance">#</a> <code>db_kademlia_xor_distance</code></h3>
<p><code>db_kademlia_xor_distance</code> — distance / dissimilarity metric of <code>db kademlia xor</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_kademlia_xor_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-kll-quantile-step">
<h3><a class="doc-anchor" href="#doc-db-kll-quantile-step">#</a> <code>db_kll_quantile_step</code></h3>
<p><code>db_kll_quantile_step</code> — single-step update of <code>db kll quantile</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_kll_quantile_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-lamport-timestamp">
<h3><a class="doc-anchor" href="#doc-db-lamport-timestamp">#</a> <code>db_lamport_timestamp</code></h3>
<p><code>db_lamport_timestamp</code> — operation <code>db lamport timestamp</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_lamport_timestamp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-leaky-bucket-step">
<h3><a class="doc-anchor" href="#doc-db-leaky-bucket-step">#</a> <code>db_leaky_bucket_step</code></h3>
<p><code>db_leaky_bucket_step</code> — single-step update of <code>db leaky bucket</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_leaky_bucket_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-levelled-compaction-step">
<h3><a class="doc-anchor" href="#doc-db-levelled-compaction-step">#</a> <code>db_levelled_compaction_step</code></h3>
<p><code>db_levelled_compaction_step</code> — single-step update of <code>db levelled compaction</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_levelled_compaction_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-lfu-cache-decay">
<h3><a class="doc-anchor" href="#doc-db-lfu-cache-decay">#</a> <code>db_lfu_cache_decay</code></h3>
<p><code>db_lfu_cache_decay</code> — operation <code>db lfu cache decay</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_lfu_cache_decay $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-linearizability-check">
<h3><a class="doc-anchor" href="#doc-db-linearizability-check">#</a> <code>db_linearizability_check</code></h3>
<p><code>db_linearizability_check</code> — operation <code>db linearizability check</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_linearizability_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-logical-clock-step">
<h3><a class="doc-anchor" href="#doc-db-logical-clock-step">#</a> <code>db_logical_clock_step</code></h3>
<p><code>db_logical_clock_step</code> — single-step update of <code>db logical clock</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_logical_clock_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-lru-cache-eviction-age">
<h3><a class="doc-anchor" href="#doc-db-lru-cache-eviction-age">#</a> <code>db_lru_cache_eviction_age</code></h3>
<p><code>db_lru_cache_eviction_age</code> — operation <code>db lru cache eviction age</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_lru_cache_eviction_age $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-lsm-compaction-step">
<h3><a class="doc-anchor" href="#doc-db-lsm-compaction-step">#</a> <code>db_lsm_compaction_step</code></h3>
<p><code>db_lsm_compaction_step</code> — single-step update of <code>db lsm compaction</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_lsm_compaction_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-maglev-hash-step">
<h3><a class="doc-anchor" href="#doc-db-maglev-hash-step">#</a> <code>db_maglev_hash_step</code></h3>
<p><code>db_maglev_hash_step</code> — single-step update of <code>db maglev hash</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_maglev_hash_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-merge-join-cost">
<h3><a class="doc-anchor" href="#doc-db-merge-join-cost">#</a> <code>db_merge_join_cost</code></h3>
<p><code>db_merge_join_cost</code> — operation <code>db merge join cost</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_merge_join_cost $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-merkle-node-hash">
<h3><a class="doc-anchor" href="#doc-db-merkle-node-hash">#</a> <code>db_merkle_node_hash</code></h3>
<p><code>db_merkle_node_hash</code> — hash function of <code>db merkle node</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_merkle_node_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-merkle-path-verify">
<h3><a class="doc-anchor" href="#doc-db-merkle-path-verify">#</a> <code>db_merkle_path_verify</code></h3>
<p><code>db_merkle_path_verify</code> — verify with public key of <code>db merkle path</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_merkle_path_verify $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-min-hash-value">
<h3><a class="doc-anchor" href="#doc-db-min-hash-value">#</a> <code>db_min_hash_value</code></h3>
<p><code>db_min_hash_value</code> — value of <code>db min hash</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_min_hash_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-nested-loop-cost">
<h3><a class="doc-anchor" href="#doc-db-nested-loop-cost">#</a> <code>db_nested_loop_cost</code></h3>
<p><code>db_nested_loop_cost</code> — operation <code>db nested loop cost</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_nested_loop_cost $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-page-cache-eviction-age">
<h3><a class="doc-anchor" href="#doc-db-page-cache-eviction-age">#</a> <code>db_page_cache_eviction_age</code></h3>
<p><code>db_page_cache_eviction_age</code> — operation <code>db page cache eviction age</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_page_cache_eviction_age $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-partition-failure-check">
<h3><a class="doc-anchor" href="#doc-db-partition-failure-check">#</a> <code>db_partition_failure_check</code></h3>
<p><code>db_partition_failure_check</code> — operation <code>db partition failure check</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_partition_failure_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-partitions-for-n">
<h3><a class="doc-anchor" href="#doc-db-partitions-for-n">#</a> <code>db_partitions_for_n</code></h3>
<p><code>db_partitions_for_n</code> — operation <code>db partitions for n</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_partitions_for_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-pastry-routing-step">
<h3><a class="doc-anchor" href="#doc-db-pastry-routing-step">#</a> <code>db_pastry_routing_step</code></h3>
<p><code>db_pastry_routing_step</code> — single-step update of <code>db pastry routing</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_pastry_routing_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-paxos-propose-id">
<h3><a class="doc-anchor" href="#doc-db-paxos-propose-id">#</a> <code>db_paxos_propose_id</code></h3>
<p><code>db_paxos_propose_id</code> — operation <code>db paxos propose id</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_paxos_propose_id $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-pbft-view-change">
<h3><a class="doc-anchor" href="#doc-db-pbft-view-change">#</a> <code>db_pbft_view_change</code></h3>
<p><code>db_pbft_view_change</code> — operation <code>db pbft view change</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_pbft_view_change $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-power">
<h3><a class="doc-anchor" href="#doc-db-power">#</a> <code>db_power</code></h3>
<p><code>db_power</code> — operation <code>db power</code>. Alias for <code>dB_power</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p db_power $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-quantile-estimate-p99">
<h3><a class="doc-anchor" href="#doc-db-quantile-estimate-p99">#</a> <code>db_quantile_estimate_p99</code></h3>
<p><code>db_quantile_estimate_p99</code> — operation <code>db quantile estimate p99</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_quantile_estimate_p99 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-query-cardinality">
<h3><a class="doc-anchor" href="#doc-db-query-cardinality">#</a> <code>db_query_cardinality</code></h3>
<p><code>db_query_cardinality</code> — operation <code>db query cardinality</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_query_cardinality $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-query-plan-cost-step">
<h3><a class="doc-anchor" href="#doc-db-query-plan-cost-step">#</a> <code>db_query_plan_cost_step</code></h3>
<p><code>db_query_plan_cost_step</code> — single-step update of <code>db query plan cost</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_query_plan_cost_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-quorum-intersection-check">
<h3><a class="doc-anchor" href="#doc-db-quorum-intersection-check">#</a> <code>db_quorum_intersection_check</code></h3>
<p><code>db_quorum_intersection_check</code> — operation <code>db quorum intersection check</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_quorum_intersection_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-quotient-filter-canonical">
<h3><a class="doc-anchor" href="#doc-db-quotient-filter-canonical">#</a> <code>db_quotient_filter_canonical</code></h3>
<p><code>db_quotient_filter_canonical</code> — operation <code>db quotient filter canonical</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_quotient_filter_canonical $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-raft-log-match-check">
<h3><a class="doc-anchor" href="#doc-db-raft-log-match-check">#</a> <code>db_raft_log_match_check</code></h3>
<p><code>db_raft_log_match_check</code> — operation <code>db raft log match check</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_raft_log_match_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-raft-term-advance">
<h3><a class="doc-anchor" href="#doc-db-raft-term-advance">#</a> <code>db_raft_term_advance</code></h3>
<p><code>db_raft_term_advance</code> — operation <code>db raft term advance</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_raft_term_advance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-read-amplification">
<h3><a class="doc-anchor" href="#doc-db-read-amplification">#</a> <code>db_read_amplification</code></h3>
<p><code>db_read_amplification</code> — operation <code>db read amplification</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_read_amplification $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-read-repair-step">
<h3><a class="doc-anchor" href="#doc-db-read-repair-step">#</a> <code>db_read_repair_step</code></h3>
<p><code>db_read_repair_step</code> — single-step update of <code>db read repair</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_read_repair_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-rendezvous-hash-score">
<h3><a class="doc-anchor" href="#doc-db-rendezvous-hash-score">#</a> <code>db_rendezvous_hash_score</code></h3>
<p><code>db_rendezvous_hash_score</code> — score of <code>db rendezvous hash</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_rendezvous_hash_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-replica-lag-threshold">
<h3><a class="doc-anchor" href="#doc-db-replica-lag-threshold">#</a> <code>db_replica_lag_threshold</code></h3>
<p><code>db_replica_lag_threshold</code> — operation <code>db replica lag threshold</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_replica_lag_threshold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-replication-lag-step">
<h3><a class="doc-anchor" href="#doc-db-replication-lag-step">#</a> <code>db_replication_lag_step</code></h3>
<p><code>db_replication_lag_step</code> — single-step update of <code>db replication lag</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_replication_lag_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-reservoir-sample-index">
<h3><a class="doc-anchor" href="#doc-db-reservoir-sample-index">#</a> <code>db_reservoir_sample_index</code></h3>
<p><code>db_reservoir_sample_index</code> — index of <code>db reservoir sample</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_reservoir_sample_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-seq-scan-cost">
<h3><a class="doc-anchor" href="#doc-db-seq-scan-cost">#</a> <code>db_seq_scan_cost</code></h3>
<p><code>db_seq_scan_cost</code> — operation <code>db seq scan cost</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_seq_scan_cost $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-simhash-bit">
<h3><a class="doc-anchor" href="#doc-db-simhash-bit">#</a> <code>db_simhash_bit</code></h3>
<p><code>db_simhash_bit</code> — operation <code>db simhash bit</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_simhash_bit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-size-tiered-compaction">
<h3><a class="doc-anchor" href="#doc-db-size-tiered-compaction">#</a> <code>db_size_tiered_compaction</code></h3>
<p><code>db_size_tiered_compaction</code> — operation <code>db size tiered compaction</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_size_tiered_compaction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-skiplist-height-pick">
<h3><a class="doc-anchor" href="#doc-db-skiplist-height-pick">#</a> <code>db_skiplist_height_pick</code></h3>
<p><code>db_skiplist_height_pick</code> — operation <code>db skiplist height pick</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_skiplist_height_pick $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-sort-cost-estimate">
<h3><a class="doc-anchor" href="#doc-db-sort-cost-estimate">#</a> <code>db_sort_cost_estimate</code></h3>
<p><code>db_sort_cost_estimate</code> — operation <code>db sort cost estimate</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_sort_cost_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-space-amplification">
<h3><a class="doc-anchor" href="#doc-db-space-amplification">#</a> <code>db_space_amplification</code></h3>
<p><code>db_space_amplification</code> — operation <code>db space amplification</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_space_amplification $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-split-brain-check">
<h3><a class="doc-anchor" href="#doc-db-split-brain-check">#</a> <code>db_split_brain_check</code></h3>
<p><code>db_split_brain_check</code> — operation <code>db split brain check</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_split_brain_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-strong-consistency-check">
<h3><a class="doc-anchor" href="#doc-db-strong-consistency-check">#</a> <code>db_strong_consistency_check</code></h3>
<p><code>db_strong_consistency_check</code> — operation <code>db strong consistency check</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_strong_consistency_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-synchronous-commit-check">
<h3><a class="doc-anchor" href="#doc-db-synchronous-commit-check">#</a> <code>db_synchronous_commit_check</code></h3>
<p><code>db_synchronous_commit_check</code> — operation <code>db synchronous commit check</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_synchronous_commit_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-t-digest-centroid">
<h3><a class="doc-anchor" href="#doc-db-t-digest-centroid">#</a> <code>db_t_digest_centroid</code></h3>
<p><code>db_t_digest_centroid</code> — operation <code>db t digest centroid</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_t_digest_centroid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-three-phase-commit-step">
<h3><a class="doc-anchor" href="#doc-db-three-phase-commit-step">#</a> <code>db_three_phase_commit_step</code></h3>
<p><code>db_three_phase_commit_step</code> — single-step update of <code>db three phase commit</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_three_phase_commit_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-throttle-token-step">
<h3><a class="doc-anchor" href="#doc-db-throttle-token-step">#</a> <code>db_throttle_token_step</code></h3>
<p><code>db_throttle_token_step</code> — single-step update of <code>db throttle token</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_throttle_token_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-tinylfu-admit-score">
<h3><a class="doc-anchor" href="#doc-db-tinylfu-admit-score">#</a> <code>db_tinylfu_admit_score</code></h3>
<p><code>db_tinylfu_admit_score</code> — score of <code>db tinylfu admit</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_tinylfu_admit_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-to-amp">
<h3><a class="doc-anchor" href="#doc-db-to-amp">#</a> <code>db_to_amp</code></h3>
<p><code>db_to_amp</code> — convert from <code>db</code> to <code>amp</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p db_to_amp $value
</code></pre>
</article>
<article class="doc-entry" id="doc-db-token-bucket-step">
<h3><a class="doc-anchor" href="#doc-db-token-bucket-step">#</a> <code>db_token_bucket_step</code></h3>
<p><code>db_token_bucket_step</code> — single-step update of <code>db token bucket</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_token_bucket_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-two-phase-commit-step">
<h3><a class="doc-anchor" href="#doc-db-two-phase-commit-step">#</a> <code>db_two_phase_commit_step</code></h3>
<p><code>db_two_phase_commit_step</code> — single-step update of <code>db two phase commit</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_two_phase_commit_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-universal-compaction-step">
<h3><a class="doc-anchor" href="#doc-db-universal-compaction-step">#</a> <code>db_universal_compaction_step</code></h3>
<p><code>db_universal_compaction_step</code> — single-step update of <code>db universal compaction</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_universal_compaction_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-vector-clock-merge">
<h3><a class="doc-anchor" href="#doc-db-vector-clock-merge">#</a> <code>db_vector_clock_merge</code></h3>
<p><code>db_vector_clock_merge</code> — operation <code>db vector clock merge</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_vector_clock_merge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-voltage">
<h3><a class="doc-anchor" href="#doc-db-voltage">#</a> <code>db_voltage</code></h3>
<p><code>db_voltage</code> — operation <code>db voltage</code>. Alias for <code>dB_voltage</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p db_voltage $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-w-tinylfu-freq">
<h3><a class="doc-anchor" href="#doc-db-w-tinylfu-freq">#</a> <code>db_w_tinylfu_freq</code></h3>
<p><code>db_w_tinylfu_freq</code> — operation <code>db w tinylfu freq</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_w_tinylfu_freq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-wal-fsync-cost">
<h3><a class="doc-anchor" href="#doc-db-wal-fsync-cost">#</a> <code>db_wal_fsync_cost</code></h3>
<p><code>db_wal_fsync_cost</code> — operation <code>db wal fsync cost</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_wal_fsync_cost $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-write-amplification">
<h3><a class="doc-anchor" href="#doc-db-write-amplification">#</a> <code>db_write_amplification</code></h3>
<p><code>db_write_amplification</code> — operation <code>db write amplification</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_write_amplification $x
</code></pre>
</article>
<article class="doc-entry" id="doc-db-zab-epoch-step">
<h3><a class="doc-anchor" href="#doc-db-zab-epoch-step">#</a> <code>db_zab_epoch_step</code></h3>
<p><code>db_zab_epoch_step</code> — single-step update of <code>db zab epoch</code>. Category: *database internals, distributed systems*.</p>
<pre><code class="lang-perl">p db_zab_epoch_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dbeta">
<h3><a class="doc-anchor" href="#doc-dbeta">#</a> <code>dbeta</code></h3>
<p><code>dbeta</code> — operation <code>dbeta</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p dbeta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dbinom">
<h3><a class="doc-anchor" href="#doc-dbinom">#</a> <code>dbinom</code></h3>
<p><code>dbinom</code> — binomial PMF. P(X = k) for Binom(n, p). Args: k, n, p.</p>
<pre><code class="lang-perl">p dbinom(5, 10, 0.5) # P(exactly 5 heads in 10 flips)
</code></pre>
</article>
<article class="doc-entry" id="doc-dbmclose">
<h3><a class="doc-anchor" href="#doc-dbmclose">#</a> <code>dbmclose</code></h3>
<p><code>dbmclose</code> — operation <code>dbmclose</code>. Category: *ipc*.</p>
<pre><code class="lang-perl">p dbmclose $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dbmopen">
<h3><a class="doc-anchor" href="#doc-dbmopen">#</a> <code>dbmopen</code></h3>
<p><code>dbmopen</code> — operation <code>dbmopen</code>. Category: *ipc*.</p>
<pre><code class="lang-perl">p dbmopen $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dbsize">
<h3><a class="doc-anchor" href="#doc-dbsize">#</a> <code>dbsize</code></h3>
<p><code>dbsize</code> — operation <code>dbsize</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p dbsize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dcauchy">
<h3><a class="doc-anchor" href="#doc-dcauchy">#</a> <code>dcauchy</code></h3>
<p><code>dcauchy</code> — operation <code>dcauchy</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p dcauchy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dchisq">
<h3><a class="doc-anchor" href="#doc-dchisq">#</a> <code>dchisq</code></h3>
<p><code>dchisq</code> — operation <code>dchisq</code>. Category: *r / scipy distributions and tests*.</p>
<pre><code class="lang-perl">p dchisq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dct">
<h3><a class="doc-anchor" href="#doc-dct">#</a> <code>dct</code></h3>
<p><code>dct</code> computes the Type-II Discrete Cosine Transform of a signal. Used in JPEG, MP3, and speech processing.</p>
<pre><code class="lang-perl">my @coeffs = @{dct([1,2,3,4])}
</code></pre>
</article>
<article class="doc-entry" id="doc-dde-euler-step">
<h3><a class="doc-anchor" href="#doc-dde-euler-step">#</a> <code>dde_euler_step</code></h3>
<p><code>dde_euler_step</code> — single-step update of <code>dde euler</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p dde_euler_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ddot">
<h3><a class="doc-anchor" href="#doc-ddot">#</a> <code>ddot</code></h3>
<p><code>ddot</code> — operation <code>ddot</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p ddot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ddpg-critic-loss-step">
<h3><a class="doc-anchor" href="#doc-ddpg-critic-loss-step">#</a> <code>ddpg_critic_loss_step</code></h3>
<p><code>ddpg_critic_loss_step</code> — single-step update of <code>ddpg critic loss</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ddpg_critic_loss_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ddrot">
<h3><a class="doc-anchor" href="#doc-ddrot">#</a> <code>ddrot</code></h3>
<p><code>ddrot</code> — operation <code>ddrot</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p ddrot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ddt">
<h3><a class="doc-anchor" href="#doc-ddt">#</a> <code>ddt</code></h3>
<p><code>ddt</code> — operation <code>ddt</code>. Alias for <code>dedent</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ddt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-de-broglie">
<h3><a class="doc-anchor" href="#doc-de-broglie">#</a> <code>de_broglie</code></h3>
<p><code>de_broglie</code> — operation <code>de broglie</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p de_broglie $x
</code></pre>
</article>
<article class="doc-entry" id="doc-de-broglie-wavelength">
<h3><a class="doc-anchor" href="#doc-de-broglie-wavelength">#</a> <code>de_broglie_wavelength</code></h3>
<p><code>de_broglie_wavelength($mass, $velocity)</code> (alias <code>debroglie</code>) — quantum wavelength λ = h/(mv). Defaults to electron mass.</p>
<pre><code class="lang-perl">p debroglie(9.109e-31, 1e6) # ~7.3e-10 m (electron at 1 km/s)
</code></pre>
</article>
<article class="doc-entry" id="doc-de-broglie-wavelength-kg">
<h3><a class="doc-anchor" href="#doc-de-broglie-wavelength-kg">#</a> <code>de_broglie_wavelength_kg</code></h3>
<p><code>de_broglie_wavelength_kg</code> — operation <code>de broglie wavelength kg</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p de_broglie_wavelength_kg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-de-rham-zero">
<h3><a class="doc-anchor" href="#doc-de-rham-zero">#</a> <code>de_rham_zero</code></h3>
<p><code>de_rham_zero</code> — operation <code>de rham zero</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p de_rham_zero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-de-sitter-metric-step">
<h3><a class="doc-anchor" href="#doc-de-sitter-metric-step">#</a> <code>de_sitter_metric_step</code></h3>
<p><code>de_sitter_metric_step</code> — single-step update of <code>de sitter metric</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p de_sitter_metric_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-de-sitter-radius-step">
<h3><a class="doc-anchor" href="#doc-de-sitter-radius-step">#</a> <code>de_sitter_radius_step</code></h3>
<p><code>de_sitter_radius_step</code> — single-step update of <code>de sitter radius</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p de_sitter_radius_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-deadweight-loss">
<h3><a class="doc-anchor" href="#doc-deadweight-loss">#</a> <code>deadweight_loss</code></h3>
<p><code>deadweight_loss</code> — operation <code>deadweight loss</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p deadweight_loss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-deal-n-k">
<h3><a class="doc-anchor" href="#doc-deal-n-k">#</a> <code>deal_n_k</code></h3>
<p><code>deal_n_k</code> — operation <code>deal n k</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p deal_n_k $x
</code></pre>
</article>
<article class="doc-entry" id="doc-debug-object">
<h3><a class="doc-anchor" href="#doc-debug-object">#</a> <code>debug_object</code></h3>
<p><code>debug_object</code> — operation <code>debug object</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p debug_object $x
</code></pre>
</article>
<article class="doc-entry" id="doc-debug-val">
<h3><a class="doc-anchor" href="#doc-debug-val">#</a> <code>debug_val</code></h3>
<p><code>debug_val</code> — operation <code>debug val</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p debug_val $x
</code></pre>
</article>
<article class="doc-entry" id="doc-debye-huckel">
<h3><a class="doc-anchor" href="#doc-debye-huckel">#</a> <code>debye_huckel</code></h3>
<p><code>debye_huckel</code> — operation <code>debye huckel</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p debye_huckel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-debye-huckel-activity">
<h3><a class="doc-anchor" href="#doc-debye-huckel-activity">#</a> <code>debye_huckel_activity</code></h3>
<p><code>debye_huckel_activity</code> — operation <code>debye huckel activity</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p debye_huckel_activity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-debye-huckel-screening-factor">
<h3><a class="doc-anchor" href="#doc-debye-huckel-screening-factor">#</a> <code>debye_huckel_screening_factor</code></h3>
<p><code>debye_huckel_screening_factor</code> — factor of <code>debye huckel screening</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p debye_huckel_screening_factor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-debye-length-electrolyte">
<h3><a class="doc-anchor" href="#doc-debye-length-electrolyte">#</a> <code>debye_length_electrolyte</code></h3>
<p><code>debye_length_electrolyte</code> — operation <code>debye length electrolyte</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p debye_length_electrolyte $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dec">
<h3><a class="doc-anchor" href="#doc-dec">#</a> <code>dec</code></h3>
<p><code>dec</code> — operation <code>dec</code>. Category: *pipeline / string helpers*.</p>
<pre><code class="lang-perl">p dec $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dec-each">
<h3><a class="doc-anchor" href="#doc-dec-each">#</a> <code>dec_each</code></h3>
<p><code>dec_each</code> — operation <code>dec each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p dec_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-decagonal-number">
<h3><a class="doc-anchor" href="#doc-decagonal-number">#</a> <code>decagonal_number</code></h3>
<p><code>decagonal_number(n) → int</code> — <code>n·(4n-3)</code>.</p>
</article>
<article class="doc-entry" id="doc-deceleration-q">
<h3><a class="doc-anchor" href="#doc-deceleration-q">#</a> <code>deceleration_q</code></h3>
<p><code>deceleration_q</code> — operation <code>deceleration q</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p deceleration_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-decibel-ratio">
<h3><a class="doc-anchor" href="#doc-decibel-ratio">#</a> <code>decibel_ratio</code></h3>
<p><code>decibel_ratio</code> — ratio of <code>decibel</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p decibel_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-decimate-step">
<h3><a class="doc-anchor" href="#doc-decimate-step">#</a> <code>decimate_step</code></h3>
<p><code>decimate_step</code> — single-step update of <code>decimate</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p decimate_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-decode-base">
<h3><a class="doc-anchor" href="#doc-decode-base">#</a> <code>decode_base</code></h3>
<p><code>decode_base</code> — operation <code>decode base</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p decode_base $x
</code></pre>
</article>
<article class="doc-entry" id="doc-decoherence-time">
<h3><a class="doc-anchor" href="#doc-decoherence-time">#</a> <code>decoherence_time</code></h3>
<p><code>decoherence_time</code> — operation <code>decoherence time</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p decoherence_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-deconvolve-step">
<h3><a class="doc-anchor" href="#doc-deconvolve-step">#</a> <code>deconvolve_step</code></h3>
<p><code>deconvolve_step</code> — single-step update of <code>deconvolve</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p deconvolve_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-decr">
<h3><a class="doc-anchor" href="#doc-decr">#</a> <code>decr</code></h3>
<p><code>decr</code> — operation <code>decr</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p decr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-decrby">
<h3><a class="doc-anchor" href="#doc-decrby">#</a> <code>decrby</code></h3>
<p><code>decrby</code> — operation <code>decrby</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p decrby $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dedent">
<h3><a class="doc-anchor" href="#doc-dedent">#</a> <code>dedent</code></h3>
<p><code>dedent</code> — operation <code>dedent</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p dedent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dedent-text">
<h3><a class="doc-anchor" href="#doc-dedent-text">#</a> <code>dedent_text</code></h3>
<p><code>dedent_text</code> — operation <code>dedent text</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p dedent_text $x
</code></pre>
</article>
<article class="doc-entry" id="doc-deep-q-target">
<h3><a class="doc-anchor" href="#doc-deep-q-target">#</a> <code>deep_q_target</code></h3>
<p><code>deep_q_target</code> — operation <code>deep q target</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p deep_q_target $x
</code></pre>
</article>
<article class="doc-entry" id="doc-default-to">
<h3><a class="doc-anchor" href="#doc-default-to">#</a> <code>default_to</code></h3>
<p><code>default_to</code> — operation <code>default to</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p default_to $x
</code></pre>
</article>
<article class="doc-entry" id="doc-defaultdict">
<h3><a class="doc-anchor" href="#doc-defaultdict">#</a> <code>defaultdict</code></h3>
<p><code>defaultdict</code> — operation <code>defaultdict</code>. Category: *data structure helpers*.</p>
<pre><code class="lang-perl">p defaultdict $x
</code></pre>
</article>
<article class="doc-entry" id="doc-deferred-acceptance">
<h3><a class="doc-anchor" href="#doc-deferred-acceptance">#</a> <code>deferred_acceptance</code></h3>
<p><code>deferred_acceptance</code> — operation <code>deferred acceptance</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p deferred_acceptance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-deferred-acceptance-step">
<h3><a class="doc-anchor" href="#doc-deferred-acceptance-step">#</a> <code>deferred_acceptance_step</code></h3>
<p><code>deferred_acceptance_step</code> — single-step update of <code>deferred acceptance</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p deferred_acceptance_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-deficient">
<h3><a class="doc-anchor" href="#doc-deficient">#</a> <code>deficient</code></h3>
<p><code>deficient</code> — operation <code>deficient</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p deficient $x
</code></pre>
</article>
<article class="doc-entry" id="doc-deficient-numbers">
<h3><a class="doc-anchor" href="#doc-deficient-numbers">#</a> <code>deficient_numbers</code></h3>
<p><code>deficient_numbers</code> — operation <code>deficient numbers</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p deficient_numbers $x
</code></pre>
</article>
<article class="doc-entry" id="doc-defined-count">
<h3><a class="doc-anchor" href="#doc-defined-count">#</a> <code>defined_count</code></h3>
<p><code>defined_count</code> — count of <code>defined</code>. Category: *counters*.</p>
<pre><code class="lang-perl">p defined_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-definums">
<h3><a class="doc-anchor" href="#doc-definums">#</a> <code>definums</code></h3>
<p><code>definums</code> — operation <code>definums</code>. Alias for <code>deficient_numbers</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p definums $x
</code></pre>
</article>
<article class="doc-entry" id="doc-deflate-dynamic-huffman">
<h3><a class="doc-anchor" href="#doc-deflate-dynamic-huffman">#</a> <code>deflate_dynamic_huffman</code></h3>
<p><code>deflate_dynamic_huffman</code> — operation <code>deflate dynamic huffman</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p deflate_dynamic_huffman $x
</code></pre>
</article>
<article class="doc-entry" id="doc-deflate-encode-huffman">
<h3><a class="doc-anchor" href="#doc-deflate-encode-huffman">#</a> <code>deflate_encode_huffman</code></h3>
<p><code>deflate_encode_huffman</code> — operation <code>deflate encode huffman</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p deflate_encode_huffman $x
</code></pre>
</article>
<article class="doc-entry" id="doc-deflate-huffman-lit">
<h3><a class="doc-anchor" href="#doc-deflate-huffman-lit">#</a> <code>deflate_huffman_lit</code></h3>
<p><code>deflate_huffman_lit</code> — operation <code>deflate huffman lit</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p deflate_huffman_lit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-deflate-static-block">
<h3><a class="doc-anchor" href="#doc-deflate-static-block">#</a> <code>deflate_static_block</code></h3>
<p><code>deflate_static_block</code> — operation <code>deflate static block</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p deflate_static_block $x
</code></pre>
</article>
<article class="doc-entry" id="doc-deg-to-rad">
<h3><a class="doc-anchor" href="#doc-deg-to-rad">#</a> <code>deg_to_rad</code></h3>
<p><code>deg_to_rad</code> — convert from <code>deg</code> to <code>rad</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p deg_to_rad $value
</code></pre>
</article>
<article class="doc-entry" id="doc-degrees">
<h3><a class="doc-anchor" href="#doc-degrees">#</a> <code>degrees</code></h3>
<p><code>degrees</code> — operation <code>degrees</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p degrees $x
</code></pre>
</article>
<article class="doc-entry" id="doc-degrees-to-compass">
<h3><a class="doc-anchor" href="#doc-degrees-to-compass">#</a> <code>degrees_to_compass</code></h3>
<p><code>degrees_to_compass</code> — convert from <code>degrees</code> to <code>compass</code>. Category: *misc / utility*.</p>
<pre><code class="lang-perl">p degrees_to_compass $value
</code></pre>
</article>
<article class="doc-entry" id="doc-dela">
<h3><a class="doc-anchor" href="#doc-dela">#</a> <code>dela</code></h3>
<p><code>dela</code> — operation <code>dela</code>. Alias for <code>delete_at</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p dela $x
</code></pre>
</article>
<article class="doc-entry" id="doc-delaunay-triangulate-2d">
<h3><a class="doc-anchor" href="#doc-delaunay-triangulate-2d">#</a> <code>delaunay_triangulate_2d</code></h3>
<p><code>delaunay_triangulate_2d(points) → array</code> — Bowyer-Watson Delaunay triangulation. Returns triangles as <code>[i, j, k]</code> index triples.</p>
</article>
<article class="doc-entry" id="doc-delby">
<h3><a class="doc-anchor" href="#doc-delby">#</a> <code>delby</code></h3>
<p><code>delby</code> — operation <code>delby</code>. Alias for <code>delete_by</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p delby $x
</code></pre>
</article>
<article class="doc-entry" id="doc-delete-at">
<h3><a class="doc-anchor" href="#doc-delete-at">#</a> <code>delete_at</code></h3>
<p><code>delete_at</code> — operation <code>delete at</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p delete_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-delete-by">
<h3><a class="doc-anchor" href="#doc-delete-by">#</a> <code>delete_by</code></h3>
<p><code>delete_by</code> — operation <code>delete by</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p delete_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-delete-first">
<h3><a class="doc-anchor" href="#doc-delete-first">#</a> <code>delete_first</code></h3>
<p><code>delete_first</code> — operation <code>delete first</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p delete_first $x
</code></pre>
</article>
<article class="doc-entry" id="doc-delfst">
<h3><a class="doc-anchor" href="#doc-delfst">#</a> <code>delfst</code></h3>
<p><code>delfst</code> — operation <code>delfst</code>. Alias for <code>delete_first</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p delfst $x
</code></pre>
</article>
<article class="doc-entry" id="doc-delta-complex-count">
<h3><a class="doc-anchor" href="#doc-delta-complex-count">#</a> <code>delta_complex_count</code></h3>
<p><code>delta_complex_count</code> — delta encoding <code>complex count</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p delta_complex_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-delta-decode">
<h3><a class="doc-anchor" href="#doc-delta-decode">#</a> <code>delta_decode</code></h3>
<p><code>delta_decode(deltas) → array</code> — running sum reconstruction of <code>delta_encode</code>.</p>
</article>
<article class="doc-entry" id="doc-delta-e">
<h3><a class="doc-anchor" href="#doc-delta-e">#</a> <code>delta_e</code></h3>
<p><code>delta_e</code> — delta encoding <code>e</code>. Alias for <code>delta_e_76</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p delta_e $x
</code></pre>
</article>
<article class="doc-entry" id="doc-delta-e2000">
<h3><a class="doc-anchor" href="#doc-delta-e2000">#</a> <code>delta_e2000</code></h3>
<p><code>delta_e2000</code> — delta encoding <code>e2000</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p delta_e2000 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-delta-e76">
<h3><a class="doc-anchor" href="#doc-delta-e76">#</a> <code>delta_e76</code></h3>
<p><code>delta_e76</code> — delta encoding <code>e76</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p delta_e76 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-delta-e94">
<h3><a class="doc-anchor" href="#doc-delta-e94">#</a> <code>delta_e94</code></h3>
<p><code>delta_e94</code> — delta encoding <code>e94</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p delta_e94 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-delta-e-76">
<h3><a class="doc-anchor" href="#doc-delta-e-76">#</a> <code>delta_e_76</code></h3>
<p><code>delta_e_76</code> — delta encoding <code>e 76</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p delta_e_76 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-delta-e-94">
<h3><a class="doc-anchor" href="#doc-delta-e-94">#</a> <code>delta_e_94</code></h3>
<p><code>delta_e_94</code> — delta encoding <code>e 94</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p delta_e_94 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-delta-encode">
<h3><a class="doc-anchor" href="#doc-delta-encode">#</a> <code>delta_encode</code></h3>
<p><code>delta_encode(ints) → array</code> — keep first element, replace each subsequent with the difference from its predecessor.</p>
<pre><code class="lang-perl">p delta_encode([10,12,15,20]) # [10,2,3,5]
</code></pre>
</article>
<article class="doc-entry" id="doc-dema">
<h3><a class="doc-anchor" href="#doc-dema">#</a> <code>dema</code></h3>
<p><code>dema(prices, period=10) → array</code> — double EMA: <code>2·EMA − EMA(EMA)</code>. Lower lag than EMA at the same period.</p>
<pre><code class="lang-perl">p dema(\@prices, 14)
</code></pre>
</article>
<article class="doc-entry" id="doc-demorse">
<h3><a class="doc-anchor" href="#doc-demorse">#</a> <code>demorse</code></h3>
<p><code>demorse</code> — operation <code>demorse</code>. Alias for <code>morse_decode</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p demorse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-denavit-hartenberg-h">
<h3><a class="doc-anchor" href="#doc-denavit-hartenberg-h">#</a> <code>denavit_hartenberg_h</code></h3>
<p><code>denavit_hartenberg_h</code> — operation <code>denavit hartenberg h</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p denavit_hartenberg_h $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dense-rank">
<h3><a class="doc-anchor" href="#doc-dense-rank">#</a> <code>dense_rank</code></h3>
<p><code>dense_rank</code> — operation <code>dense rank</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p dense_rank $x
</code></pre>
</article>
<article class="doc-entry" id="doc-density">
<h3><a class="doc-anchor" href="#doc-density">#</a> <code>density</code></h3>
<p><code>density</code> — kernel density estimation with Gaussian kernel and Silverman bandwidth. Returns [[x_grid], [density_values]]. Like R's density().</p>
<pre><code class="lang-perl">my ($x, $y) = @{density([1,2,2,3,3,3,4,4,5])}
# $x is grid of 512 points, $y is estimated density
</code></pre>
</article>
<article class="doc-entry" id="doc-density-altitude-full">
<h3><a class="doc-anchor" href="#doc-density-altitude-full">#</a> <code>density_altitude_full</code></h3>
<p><code>density_altitude_full</code> — operation <code>density altitude full</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p density_altitude_full $x
</code></pre>
</article>
<article class="doc-entry" id="doc-density-altitude-m">
<h3><a class="doc-anchor" href="#doc-density-altitude-m">#</a> <code>density_altitude_m</code></h3>
<p><code>density_altitude_m</code> — operation <code>density altitude m</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p density_altitude_m $x
</code></pre>
</article>
<article class="doc-entry" id="doc-density-matrix-purity-q">
<h3><a class="doc-anchor" href="#doc-density-matrix-purity-q">#</a> <code>density_matrix_purity_q</code></h3>
<p><code>density_matrix_purity_q</code> — operation <code>density matrix purity q</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p density_matrix_purity_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-depdbl">
<h3><a class="doc-anchor" href="#doc-depdbl">#</a> <code>depdbl</code></h3>
<p><code>depdbl</code> — operation <code>depdbl</code>. Alias for <code>depreciation_double</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p depdbl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dependency-parse-eisner">
<h3><a class="doc-anchor" href="#doc-dependency-parse-eisner">#</a> <code>dependency_parse_eisner</code></h3>
<p><code>dependency_parse_eisner</code> — operation <code>dependency parse eisner</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p dependency_parse_eisner $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dephasing-channel">
<h3><a class="doc-anchor" href="#doc-dephasing-channel">#</a> <code>dephasing_channel</code></h3>
<p><code>dephasing_channel</code> — operation <code>dephasing channel</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p dephasing_channel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-deplin">
<h3><a class="doc-anchor" href="#doc-deplin">#</a> <code>deplin</code></h3>
<p><code>deplin</code> — operation <code>deplin</code>. Alias for <code>depreciation_linear</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p deplin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-depolarizing-channel">
<h3><a class="doc-anchor" href="#doc-depolarizing-channel">#</a> <code>depolarizing_channel</code></h3>
<p><code>depolarizing_channel</code> — operation <code>depolarizing channel</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p depolarizing_channel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-depolarizing-density-2x2">
<h3><a class="doc-anchor" href="#doc-depolarizing-density-2x2">#</a> <code>depolarizing_density_2x2</code></h3>
<p><code>depolarizing_density_2x2</code> — operation <code>depolarizing density 2x2</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p depolarizing_density_2x2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-depreciation-double">
<h3><a class="doc-anchor" href="#doc-depreciation-double">#</a> <code>depreciation_double</code></h3>
<p><code>depreciation_double</code> — operation <code>depreciation double</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p depreciation_double $x
</code></pre>
</article>
<article class="doc-entry" id="doc-depreciation-linear">
<h3><a class="doc-anchor" href="#doc-depreciation-linear">#</a> <code>depreciation_linear</code></h3>
<p><code>depreciation_linear</code> — operation <code>depreciation linear</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p depreciation_linear $x
</code></pre>
</article>
<article class="doc-entry" id="doc-depth-of-field-far">
<h3><a class="doc-anchor" href="#doc-depth-of-field-far">#</a> <code>depth_of_field_far</code></h3>
<p><code>depth_of_field_far(focal_mm, aperture, dist_mm, coc=0.03) → number</code> — far limit of DoF (∞ if subject is at/beyond hyperfocal).</p>
</article>
<article class="doc-entry" id="doc-depth-of-field-near">
<h3><a class="doc-anchor" href="#doc-depth-of-field-near">#</a> <code>depth_of_field_near</code></h3>
<p><code>depth_of_field_near(focal_mm, aperture, dist_mm, coc=0.03) → number</code> — near limit of DoF in mm.</p>
</article>
<article class="doc-entry" id="doc-derangement-count">
<h3><a class="doc-anchor" href="#doc-derangement-count">#</a> <code>derangement_count</code></h3>
<p><code>derangement_count(n) → int</code> — number of permutations with no fixed points: <code>D_n = (n-1)·(D_{n-1} + D_{n-2})</code>.</p>
<pre><code class="lang-perl">p derangement_count(5) # 44
</code></pre>
</article>
<article class="doc-entry" id="doc-derangements">
<h3><a class="doc-anchor" href="#doc-derangements">#</a> <code>derangements</code></h3>
<p><code>derangements</code> counts the number of derangements (subfactorial !n) — permutations with no fixed points.</p>
<pre><code class="lang-perl">p derangements(4) # 9
p derangements(5) # 44
</code></pre>
</article>
<article class="doc-entry" id="doc-deroman">
<h3><a class="doc-anchor" href="#doc-deroman">#</a> <code>deroman</code></h3>
<p><code>deroman</code> — operation <code>deroman</code>. Alias for <code>roman_to_int</code>. Category: *roman numerals*.</p>
<pre><code class="lang-perl">p deroman $x
</code></pre>
</article>
<article class="doc-entry" id="doc-describe">
<h3><a class="doc-anchor" href="#doc-describe">#</a> <code>describe</code></h3>
<p><code>describe(@data)</code> — returns a hashref with comprehensive descriptive statistics: count, mean, std, min, 25%, 50%, 75%, max. Similar to pandas DataFrame.describe().</p>
<pre><code class="lang-perl">my $stats = describe(1:100)
p $stats->{mean} # 50.5
p $stats->{std} # ~29.0
p $stats->{"50%"} # median
</code></pre>
</article>
<article class="doc-entry" id="doc-destination-lat-lon">
<h3><a class="doc-anchor" href="#doc-destination-lat-lon">#</a> <code>destination_lat_lon</code></h3>
<p><code>destination_lat_lon(lat, lon, bearing_deg, distance_m) → [lat, lon]</code> — destination point along a great circle from origin.</p>
<pre><code class="lang-perl">p destination_lat_lon(0, 0, 90, 111320) # ~1° east
</code></pre>
</article>
<article class="doc-entry" id="doc-destination-point">
<h3><a class="doc-anchor" href="#doc-destination-point">#</a> <code>destination_point</code></h3>
<p><code>destination_point</code> — operation <code>destination point</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p destination_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-det">
<h3><a class="doc-anchor" href="#doc-det">#</a> <code>det</code></h3>
<p><code>matrix_det_general</code> (aliases <code>mdetg</code>, <code>det</code>) computes the determinant of any NxN matrix via LU decomposition.</p>
<pre><code class="lang-perl">p det([[1,2,3],[4,5,6],[7,8,0]]) # 27
</code></pre>
</article>
<article class="doc-entry" id="doc-detab">
<h3><a class="doc-anchor" href="#doc-detab">#</a> <code>detab</code></h3>
<p><code>detab(s, width=8) → string</code> — expand tab characters to spaces, respecting tab stops.</p>
<pre><code class="lang-perl">p detab("\tab", 4) # " ab"
</code></pre>
</article>
<article class="doc-entry" id="doc-detect">
<h3><a class="doc-anchor" href="#doc-detect">#</a> <code>detect</code></h3>
<p><code>detect</code> — operation <code>detect</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p detect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-deterministic-prime">
<h3><a class="doc-anchor" href="#doc-deterministic-prime">#</a> <code>deterministic_prime</code></h3>
<p><code>deterministic_prime</code> — operation <code>deterministic prime</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p deterministic_prime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-detrend-linear">
<h3><a class="doc-anchor" href="#doc-detrend-linear">#</a> <code>detrend_linear</code></h3>
<p><code>detrend_linear(series) → array</code> — subtract OLS linear fit from each point, leaving the residuals.</p>
<pre><code class="lang-perl">p detrend_linear(\@xs)
</code></pre>
</article>
<article class="doc-entry" id="doc-detrended-fluct-alpha">
<h3><a class="doc-anchor" href="#doc-detrended-fluct-alpha">#</a> <code>detrended_fluct_alpha</code></h3>
<p><code>detrended_fluct_alpha</code> — operation <code>detrended fluct alpha</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p detrended_fluct_alpha $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dew-point">
<h3><a class="doc-anchor" href="#doc-dew-point">#</a> <code>dew_point</code></h3>
<p><code>dew_point</code> — operation <code>dew point</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p dew_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dew-point-magnus">
<h3><a class="doc-anchor" href="#doc-dew-point-magnus">#</a> <code>dew_point_magnus</code></h3>
<p><code>dew_point_magnus</code> — operation <code>dew point magnus</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p dew_point_magnus $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dewpoint-temperature-full">
<h3><a class="doc-anchor" href="#doc-dewpoint-temperature-full">#</a> <code>dewpoint_temperature_full</code></h3>
<p><code>dewpoint_temperature_full</code> — operation <code>dewpoint temperature full</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p dewpoint_temperature_full $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dexp">
<h3><a class="doc-anchor" href="#doc-dexp">#</a> <code>dexp</code></h3>
<p><code>dexp</code> — operation <code>dexp</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p dexp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df">
<h3><a class="doc-anchor" href="#doc-df">#</a> <code>df</code></h3>
<p><code>df</code> — operation <code>df</code>. Alias for <code>dataframe</code>. Category: *data / network*.</p>
<pre><code class="lang-perl">p df $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-aggregate">
<h3><a class="doc-anchor" href="#doc-df-aggregate">#</a> <code>df_aggregate</code></h3>
<p><code>df_aggregate</code> — operation <code>df aggregate</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_aggregate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-apply">
<h3><a class="doc-anchor" href="#doc-df-apply">#</a> <code>df_apply</code></h3>
<p><code>df_apply</code> — operation <code>df apply</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_apply $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-clip">
<h3><a class="doc-anchor" href="#doc-df-clip">#</a> <code>df_clip</code></h3>
<p><code>df_clip</code> — operation <code>df clip</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_clip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-concat">
<h3><a class="doc-anchor" href="#doc-df-concat">#</a> <code>df_concat</code></h3>
<p><code>df_concat</code> — operation <code>df concat</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_concat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-corr">
<h3><a class="doc-anchor" href="#doc-df-corr">#</a> <code>df_corr</code></h3>
<p><code>df_corr</code> — operation <code>df corr</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_corr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-corrwith">
<h3><a class="doc-anchor" href="#doc-df-corrwith">#</a> <code>df_corrwith</code></h3>
<p><code>df_corrwith</code> — operation <code>df corrwith</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_corrwith $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-cov">
<h3><a class="doc-anchor" href="#doc-df-cov">#</a> <code>df_cov</code></h3>
<p><code>df_cov</code> — operation <code>df cov</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_cov $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-crosstab">
<h3><a class="doc-anchor" href="#doc-df-crosstab">#</a> <code>df_crosstab</code></h3>
<p><code>df_crosstab</code> — operation <code>df crosstab</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_crosstab $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-describe">
<h3><a class="doc-anchor" href="#doc-df-describe">#</a> <code>df_describe</code></h3>
<p><code>df_describe</code> — operation <code>df describe</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_describe $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-diff">
<h3><a class="doc-anchor" href="#doc-df-diff">#</a> <code>df_diff</code></h3>
<p><code>df_diff</code> — operation <code>df diff</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_diff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-dist">
<h3><a class="doc-anchor" href="#doc-df-dist">#</a> <code>df_dist</code></h3>
<p><code>df_dist</code> — operation <code>df dist</code>. Category: *r / scipy distributions and tests*.</p>
<pre><code class="lang-perl">p df_dist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-drop-duplicates">
<h3><a class="doc-anchor" href="#doc-df-drop-duplicates">#</a> <code>df_drop_duplicates</code></h3>
<p><code>df_drop_duplicates</code> — operation <code>df drop duplicates</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_drop_duplicates $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-dropna">
<h3><a class="doc-anchor" href="#doc-df-dropna">#</a> <code>df_dropna</code></h3>
<p><code>df_dropna</code> — operation <code>df dropna</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_dropna $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-duplicated">
<h3><a class="doc-anchor" href="#doc-df-duplicated">#</a> <code>df_duplicated</code></h3>
<p><code>df_duplicated</code> — operation <code>df duplicated</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_duplicated $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-eval">
<h3><a class="doc-anchor" href="#doc-df-eval">#</a> <code>df_eval</code></h3>
<p><code>df_eval</code> — operation <code>df eval</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-ewm">
<h3><a class="doc-anchor" href="#doc-df-ewm">#</a> <code>df_ewm</code></h3>
<p><code>df_ewm</code> — operation <code>df ewm</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_ewm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-expanding">
<h3><a class="doc-anchor" href="#doc-df-expanding">#</a> <code>df_expanding</code></h3>
<p><code>df_expanding</code> — operation <code>df expanding</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_expanding $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-explode">
<h3><a class="doc-anchor" href="#doc-df-explode">#</a> <code>df_explode</code></h3>
<p><code>df_explode</code> — operation <code>df explode</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_explode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-fillna">
<h3><a class="doc-anchor" href="#doc-df-fillna">#</a> <code>df_fillna</code></h3>
<p><code>df_fillna</code> — operation <code>df fillna</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_fillna $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-filter">
<h3><a class="doc-anchor" href="#doc-df-filter">#</a> <code>df_filter</code></h3>
<p><code>df_filter</code> — filter op of <code>df</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_filter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-get-dummies">
<h3><a class="doc-anchor" href="#doc-df-get-dummies">#</a> <code>df_get_dummies</code></h3>
<p><code>df_get_dummies</code> — operation <code>df get dummies</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_get_dummies $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-groupby">
<h3><a class="doc-anchor" href="#doc-df-groupby">#</a> <code>df_groupby</code></h3>
<p><code>df_groupby</code> — operation <code>df groupby</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_groupby $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-idxmax">
<h3><a class="doc-anchor" href="#doc-df-idxmax">#</a> <code>df_idxmax</code></h3>
<p><code>df_idxmax</code> — operation <code>df idxmax</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_idxmax $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-idxmin">
<h3><a class="doc-anchor" href="#doc-df-idxmin">#</a> <code>df_idxmin</code></h3>
<p><code>df_idxmin</code> — operation <code>df idxmin</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_idxmin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-interpolate">
<h3><a class="doc-anchor" href="#doc-df-interpolate">#</a> <code>df_interpolate</code></h3>
<p><code>df_interpolate</code> — operation <code>df interpolate</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_interpolate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-isnull">
<h3><a class="doc-anchor" href="#doc-df-isnull">#</a> <code>df_isnull</code></h3>
<p><code>df_isnull</code> — operation <code>df isnull</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_isnull $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-join">
<h3><a class="doc-anchor" href="#doc-df-join">#</a> <code>df_join</code></h3>
<p><code>df_join</code> — operation <code>df join</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_join $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-kurtosis">
<h3><a class="doc-anchor" href="#doc-df-kurtosis">#</a> <code>df_kurtosis</code></h3>
<p><code>df_kurtosis</code> — operation <code>df kurtosis</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_kurtosis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-mad">
<h3><a class="doc-anchor" href="#doc-df-mad">#</a> <code>df_mad</code></h3>
<p><code>df_mad</code> — operation <code>df mad</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_mad $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-melt">
<h3><a class="doc-anchor" href="#doc-df-melt">#</a> <code>df_melt</code></h3>
<p><code>df_melt</code> — operation <code>df melt</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_melt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-merge">
<h3><a class="doc-anchor" href="#doc-df-merge">#</a> <code>df_merge</code></h3>
<p><code>df_merge</code> — operation <code>df merge</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_merge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-nlargest">
<h3><a class="doc-anchor" href="#doc-df-nlargest">#</a> <code>df_nlargest</code></h3>
<p><code>df_nlargest</code> — operation <code>df nlargest</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_nlargest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-notnull">
<h3><a class="doc-anchor" href="#doc-df-notnull">#</a> <code>df_notnull</code></h3>
<p><code>df_notnull</code> — operation <code>df notnull</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_notnull $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-nsmallest">
<h3><a class="doc-anchor" href="#doc-df-nsmallest">#</a> <code>df_nsmallest</code></h3>
<p><code>df_nsmallest</code> — operation <code>df nsmallest</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_nsmallest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-pct-change">
<h3><a class="doc-anchor" href="#doc-df-pct-change">#</a> <code>df_pct_change</code></h3>
<p><code>df_pct_change</code> — operation <code>df pct change</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_pct_change $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-pivot">
<h3><a class="doc-anchor" href="#doc-df-pivot">#</a> <code>df_pivot</code></h3>
<p><code>df_pivot</code> — operation <code>df pivot</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_pivot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-pivot-table">
<h3><a class="doc-anchor" href="#doc-df-pivot-table">#</a> <code>df_pivot_table</code></h3>
<p><code>df_pivot_table</code> — lookup table of <code>df pivot</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_pivot_table $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-quantile">
<h3><a class="doc-anchor" href="#doc-df-quantile">#</a> <code>df_quantile</code></h3>
<p><code>df_quantile</code> — operation <code>df quantile</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_quantile $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-query">
<h3><a class="doc-anchor" href="#doc-df-query">#</a> <code>df_query</code></h3>
<p><code>df_query</code> — operation <code>df query</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_query $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-rank">
<h3><a class="doc-anchor" href="#doc-df-rank">#</a> <code>df_rank</code></h3>
<p><code>df_rank</code> — operation <code>df rank</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_rank $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-replace">
<h3><a class="doc-anchor" href="#doc-df-replace">#</a> <code>df_replace</code></h3>
<p><code>df_replace</code> — operation <code>df replace</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_replace $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-resample">
<h3><a class="doc-anchor" href="#doc-df-resample">#</a> <code>df_resample</code></h3>
<p><code>df_resample</code> — operation <code>df resample</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_resample $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-reset-index">
<h3><a class="doc-anchor" href="#doc-df-reset-index">#</a> <code>df_reset_index</code></h3>
<p><code>df_reset_index</code> — index of <code>df reset</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_reset_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-rolling">
<h3><a class="doc-anchor" href="#doc-df-rolling">#</a> <code>df_rolling</code></h3>
<p><code>df_rolling</code> — operation <code>df rolling</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_rolling $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-round">
<h3><a class="doc-anchor" href="#doc-df-round">#</a> <code>df_round</code></h3>
<p><code>df_round</code> — operation <code>df round</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_round $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-sample">
<h3><a class="doc-anchor" href="#doc-df-sample">#</a> <code>df_sample</code></h3>
<p><code>df_sample</code> — operation <code>df sample</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_sample $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-sem">
<h3><a class="doc-anchor" href="#doc-df-sem">#</a> <code>df_sem</code></h3>
<p><code>df_sem</code> — operation <code>df sem</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_sem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-set-index">
<h3><a class="doc-anchor" href="#doc-df-set-index">#</a> <code>df_set_index</code></h3>
<p><code>df_set_index</code> — index of <code>df set</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_set_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-shift">
<h3><a class="doc-anchor" href="#doc-df-shift">#</a> <code>df_shift</code></h3>
<p><code>df_shift</code> — operation <code>df shift</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_shift $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-skew">
<h3><a class="doc-anchor" href="#doc-df-skew">#</a> <code>df_skew</code></h3>
<p><code>df_skew</code> — operation <code>df skew</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_skew $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-sort-values">
<h3><a class="doc-anchor" href="#doc-df-sort-values">#</a> <code>df_sort_values</code></h3>
<p><code>df_sort_values</code> — operation <code>df sort values</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_sort_values $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-stack">
<h3><a class="doc-anchor" href="#doc-df-stack">#</a> <code>df_stack</code></h3>
<p><code>df_stack</code> — operation <code>df stack</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_stack $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-to-datetime">
<h3><a class="doc-anchor" href="#doc-df-to-datetime">#</a> <code>df_to_datetime</code></h3>
<p><code>df_to_datetime</code> — convert from <code>df</code> to <code>datetime</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_to_datetime $value
</code></pre>
</article>
<article class="doc-entry" id="doc-df-to-numeric">
<h3><a class="doc-anchor" href="#doc-df-to-numeric">#</a> <code>df_to_numeric</code></h3>
<p><code>df_to_numeric</code> — convert from <code>df</code> to <code>numeric</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_to_numeric $value
</code></pre>
</article>
<article class="doc-entry" id="doc-df-to-timedelta">
<h3><a class="doc-anchor" href="#doc-df-to-timedelta">#</a> <code>df_to_timedelta</code></h3>
<p><code>df_to_timedelta</code> — convert from <code>df</code> to <code>timedelta</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_to_timedelta $value
</code></pre>
</article>
<article class="doc-entry" id="doc-df-transform">
<h3><a class="doc-anchor" href="#doc-df-transform">#</a> <code>df_transform</code></h3>
<p><code>df_transform</code> — transform of <code>df</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_transform $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-unstack">
<h3><a class="doc-anchor" href="#doc-df-unstack">#</a> <code>df_unstack</code></h3>
<p><code>df_unstack</code> — operation <code>df unstack</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_unstack $x
</code></pre>
</article>
<article class="doc-entry" id="doc-df-value-counts">
<h3><a class="doc-anchor" href="#doc-df-value-counts">#</a> <code>df_value_counts</code></h3>
<p><code>df_value_counts</code> — operation <code>df value counts</code>. Category: *pandas dataframe ops*.</p>
<pre><code class="lang-perl">p df_value_counts $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dfa-minimize-hopcroft">
<h3><a class="doc-anchor" href="#doc-dfa-minimize-hopcroft">#</a> <code>dfa_minimize_hopcroft</code></h3>
<p><code>dfa_minimize_hopcroft</code> — operation <code>dfa minimize hopcroft</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p dfa_minimize_hopcroft $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dfa-simulate-step">
<h3><a class="doc-anchor" href="#doc-dfa-simulate-step">#</a> <code>dfa_simulate_step</code></h3>
<p><code>dfa_simulate_step</code> — single-step update of <code>dfa simulate</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p dfa_simulate_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dfact">
<h3><a class="doc-anchor" href="#doc-dfact">#</a> <code>dfact</code></h3>
<p><code>dfact</code> — operation <code>dfact</code>. Alias for <code>double_factorial</code>. Category: *math formulas*.</p>
<pre><code class="lang-perl">p dfact $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dfs">
<h3><a class="doc-anchor" href="#doc-dfs">#</a> <code>dfs</code></h3>
<p><code>dfs</code> — operation <code>dfs</code>. Alias for <code>dfs_traverse</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p dfs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dfs-postorder-done">
<h3><a class="doc-anchor" href="#doc-dfs-postorder-done">#</a> <code>dfs_postorder_done</code></h3>
<p><code>dfs_postorder_done</code> — operation <code>dfs postorder done</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p dfs_postorder_done $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dfs-preorder">
<h3><a class="doc-anchor" href="#doc-dfs-preorder">#</a> <code>dfs_preorder</code></h3>
<p><code>dfs_preorder</code> — operation <code>dfs preorder</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p dfs_preorder $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dfs-traverse">
<h3><a class="doc-anchor" href="#doc-dfs-traverse">#</a> <code>dfs_traverse</code></h3>
<p><code>dfs_traverse</code> — operation <code>dfs traverse</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p dfs_traverse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dft">
<h3><a class="doc-anchor" href="#doc-dft">#</a> <code>dft</code></h3>
<p><code>dft(\@signal)</code> — computes the Discrete Fourier Transform. Returns arrayref of complex numbers as [re, im] pairs. O(n²) reference implementation; for large n, use FFT libraries.</p>
<pre><code class="lang-perl">my @signal = map { sin(2 * 3.14159 * _ / 64) } 0:63
my $spectrum = dft(\@signal)
</code></pre>
</article>
<article class="doc-entry" id="doc-dg-from-k">
<h3><a class="doc-anchor" href="#doc-dg-from-k">#</a> <code>dg_from_k</code></h3>
<p><code>dg_from_k</code> — operation <code>dg from k</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p dg_from_k $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dgamma">
<h3><a class="doc-anchor" href="#doc-dgamma">#</a> <code>dgamma</code></h3>
<p><code>dgamma</code> — operation <code>dgamma</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p dgamma $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dgbsv">
<h3><a class="doc-anchor" href="#doc-dgbsv">#</a> <code>dgbsv</code></h3>
<p><code>dgbsv</code> — operation <code>dgbsv</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dgbsv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dgels">
<h3><a class="doc-anchor" href="#doc-dgels">#</a> <code>dgels</code></h3>
<p><code>dgels</code> — operation <code>dgels</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dgels $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dgelsd">
<h3><a class="doc-anchor" href="#doc-dgelsd">#</a> <code>dgelsd</code></h3>
<p><code>dgelsd</code> — operation <code>dgelsd</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dgelsd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dgemm">
<h3><a class="doc-anchor" href="#doc-dgemm">#</a> <code>dgemm</code></h3>
<p><code>dgemm</code> — operation <code>dgemm</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dgemm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dgemm3m">
<h3><a class="doc-anchor" href="#doc-dgemm3m">#</a> <code>dgemm3m</code></h3>
<p><code>dgemm3m</code> — operation <code>dgemm3m</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dgemm3m $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dgemv">
<h3><a class="doc-anchor" href="#doc-dgemv">#</a> <code>dgemv</code></h3>
<p><code>dgemv</code> — operation <code>dgemv</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dgemv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dgeom">
<h3><a class="doc-anchor" href="#doc-dgeom">#</a> <code>dgeom</code></h3>
<p><code>dgeom</code> — geometric PMF P(X=k). Args: k, prob.</p>
<pre><code class="lang-perl">p dgeom(3, 0.5) # P(first success on 4th trial)
</code></pre>
</article>
<article class="doc-entry" id="doc-dgeqrf">
<h3><a class="doc-anchor" href="#doc-dgeqrf">#</a> <code>dgeqrf</code></h3>
<p><code>dgeqrf</code> — operation <code>dgeqrf</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dgeqrf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dgerqf">
<h3><a class="doc-anchor" href="#doc-dgerqf">#</a> <code>dgerqf</code></h3>
<p><code>dgerqf</code> — operation <code>dgerqf</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dgerqf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dgesv">
<h3><a class="doc-anchor" href="#doc-dgesv">#</a> <code>dgesv</code></h3>
<p><code>dgesv</code> — operation <code>dgesv</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dgesv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dgesvd">
<h3><a class="doc-anchor" href="#doc-dgesvd">#</a> <code>dgesvd</code></h3>
<p><code>dgesvd</code> — operation <code>dgesvd</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dgesvd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dgetrf">
<h3><a class="doc-anchor" href="#doc-dgetrf">#</a> <code>dgetrf</code></h3>
<p><code>dgetrf</code> — operation <code>dgetrf</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dgetrf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dh-compute-shared">
<h3><a class="doc-anchor" href="#doc-dh-compute-shared">#</a> <code>dh_compute_shared</code></h3>
<p><code>dh_compute_shared(private, public, modulus) → string</code> — Diffie-Hellman shared key: <code>public^private mod modulus</code>.</p>
</article>
<article class="doc-entry" id="doc-dh-secret">
<h3><a class="doc-anchor" href="#doc-dh-secret">#</a> <code>dh_secret</code></h3>
<p><code>dh_secret</code> — Diffie-Hellman key-exchange primitive <code>secret</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p dh_secret $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dh-shared">
<h3><a class="doc-anchor" href="#doc-dh-shared">#</a> <code>dh_shared</code></h3>
<p><code>dh_shared</code> — Diffie-Hellman key-exchange primitive <code>shared</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p dh_shared $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dhyper">
<h3><a class="doc-anchor" href="#doc-dhyper">#</a> <code>dhyper</code></h3>
<p><code>dhyper</code> — hypergeometric PMF. Args: k, m (white), n (black), nn (draws).</p>
<pre><code class="lang-perl">p dhyper(2, 5, 5, 3) # P(2 white balls in 3 draws from 5W+5B)
</code></pre>
</article>
<article class="doc-entry" id="doc-diag">
<h3><a class="doc-anchor" href="#doc-diag">#</a> <code>diag</code></h3>
<p><code>diag</code> — operation <code>diag</code>. Alias for <code>diagonal</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p diag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diagonal">
<h3><a class="doc-anchor" href="#doc-diagonal">#</a> <code>diagonal</code></h3>
<p><code>diagonal</code> — operation <code>diagonal</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p diagonal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diagonal-dominance-q">
<h3><a class="doc-anchor" href="#doc-diagonal-dominance-q">#</a> <code>diagonal_dominance_q</code></h3>
<p><code>diagonal_dominance_q</code> — operation <code>diagonal dominance q</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p diagonal_dominance_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diameter-bfs">
<h3><a class="doc-anchor" href="#doc-diameter-bfs">#</a> <code>diameter_bfs</code></h3>
<p><code>diameter_bfs</code> — operation <code>diameter bfs</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p diameter_bfs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diameter-unweighted">
<h3><a class="doc-anchor" href="#doc-diameter-unweighted">#</a> <code>diameter_unweighted</code></h3>
<p><code>diameter_unweighted</code> — operation <code>diameter unweighted</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p diameter_unweighted $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dice-coeff">
<h3><a class="doc-anchor" href="#doc-dice-coeff">#</a> <code>dice_coeff</code></h3>
<p><code>dice_coeff(a, b) → number</code> — <code>2·|A∩B| / (|A| + |B|)</code>.</p>
</article>
<article class="doc-entry" id="doc-dice-coefficient">
<h3><a class="doc-anchor" href="#doc-dice-coefficient">#</a> <code>dice_coefficient</code></h3>
<p><code>dice_coefficient</code> — operation <code>dice coefficient</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p dice_coefficient $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dice-roll">
<h3><a class="doc-anchor" href="#doc-dice-roll">#</a> <code>dice_roll</code></h3>
<p><code>dice_roll</code> — operation <code>dice roll</code>. Category: *random*.</p>
<pre><code class="lang-perl">p dice_roll $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dicecoef">
<h3><a class="doc-anchor" href="#doc-dicecoef">#</a> <code>dicecoef</code></h3>
<p><code>dicecoef</code> — operation <code>dicecoef</code>. Alias for <code>dice_coefficient</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p dicecoef $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dickey-fuller-critical">
<h3><a class="doc-anchor" href="#doc-dickey-fuller-critical">#</a> <code>dickey_fuller_critical</code></h3>
<p><code>dickey_fuller_critical</code> — operation <code>dickey fuller critical</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p dickey_fuller_critical $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dictator-game-share">
<h3><a class="doc-anchor" href="#doc-dictator-game-share">#</a> <code>dictator_game_share</code></h3>
<p><code>dictator_game_share</code> — operation <code>dictator game share</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p dictator_game_share $x
</code></pre>
</article>
<article class="doc-entry" id="doc-did-estimator">
<h3><a class="doc-anchor" href="#doc-did-estimator">#</a> <code>did_estimator</code></h3>
<p><code>did_estimator</code> — operation <code>did estimator</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p did_estimator $x
</code></pre>
</article>
<article class="doc-entry" id="doc-die-if">
<h3><a class="doc-anchor" href="#doc-die-if">#</a> <code>die_if</code></h3>
<p><code>die_if</code> — operation <code>die if</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p die_if $x
</code></pre>
</article>
<article class="doc-entry" id="doc-die-unless">
<h3><a class="doc-anchor" href="#doc-die-unless">#</a> <code>die_unless</code></h3>
<p><code>die_unless</code> — operation <code>die unless</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p die_unless $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diesel-efficiency">
<h3><a class="doc-anchor" href="#doc-diesel-efficiency">#</a> <code>diesel_efficiency</code></h3>
<p><code>diesel_efficiency</code> — operation <code>diesel efficiency</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p diesel_efficiency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diff">
<h3><a class="doc-anchor" href="#doc-diff">#</a> <code>diff</code></h3>
<p><code>diff</code> — operation <code>diff</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p diff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diff-array">
<h3><a class="doc-anchor" href="#doc-diff-array">#</a> <code>diff_array</code></h3>
<p><code>numerical_diff</code> (aliases <code>numdiff</code>, <code>diff_array</code>) computes the numerical first derivative via central differences. Returns an array.</p>
<pre><code class="lang-perl">my @y = map { _ ** 2 } 0:10
my @dy = @{numdiff(\@y)} # ≈ [0, 2, 4, 6, ...]
</code></pre>
</article>
<article class="doc-entry" id="doc-diff-coeff-aqueous-estimate">
<h3><a class="doc-anchor" href="#doc-diff-coeff-aqueous-estimate">#</a> <code>diff_coeff_aqueous_estimate</code></h3>
<p><code>diff_coeff_aqueous_estimate</code> — operation <code>diff coeff aqueous estimate</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p diff_coeff_aqueous_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diff-days">
<h3><a class="doc-anchor" href="#doc-diff-days">#</a> <code>diff_days</code></h3>
<p><code>diff_days</code> — operation <code>diff days</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p diff_days $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diff-hours">
<h3><a class="doc-anchor" href="#doc-diff-hours">#</a> <code>diff_hours</code></h3>
<p><code>diff_hours</code> — operation <code>diff hours</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p diff_hours $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diff-in-diff">
<h3><a class="doc-anchor" href="#doc-diff-in-diff">#</a> <code>diff_in_diff</code></h3>
<p><code>diff_in_diff</code> — operation <code>diff in diff</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p diff_in_diff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diff-lag">
<h3><a class="doc-anchor" href="#doc-diff-lag">#</a> <code>diff_lag</code></h3>
<p><code>diff_lag</code> (alias <code>diff_ts</code>) — lagged differences. Args: vec [, lag, differences]. Like R's diff().</p>
<pre><code class="lang-perl">p diff_lag([1,3,6,10]) # [2,3,4] (lag=1)
p diff_lag([1,3,6,10], 2) # [5,7] (lag=2)
p diff_lag([1,3,6,10], 1, 2) # [1,1] (second differences)
</code></pre>
</article>
<article class="doc-entry" id="doc-diff-pct">
<h3><a class="doc-anchor" href="#doc-diff-pct">#</a> <code>diff_pct</code></h3>
<p><code>diff_pct(series) → array</code> — percentage change between consecutive points: <code>(x[i]/x[i-1]) - 1</code>.</p>
<pre><code class="lang-perl">p diff_pct([100, 110, 99])
</code></pre>
</article>
<article class="doc-entry" id="doc-diff-series">
<h3><a class="doc-anchor" href="#doc-diff-series">#</a> <code>diff_series</code></h3>
<p><code>diff_series(series) → array</code> — first-order differences <code>x[i+1] - x[i]</code>. Used to make a series stationary.</p>
<pre><code class="lang-perl">p diff_series([1,3,6,10,15]) # [2,3,4,5]
</code></pre>
</article>
<article class="doc-entry" id="doc-diffd">
<h3><a class="doc-anchor" href="#doc-diffd">#</a> <code>diffd</code></h3>
<p><code>diffd</code> — operation <code>diffd</code>. Alias for <code>diff_days</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p diffd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diffh">
<h3><a class="doc-anchor" href="#doc-diffh">#</a> <code>diffh</code></h3>
<p><code>diffh</code> — operation <code>diffh</code>. Alias for <code>diff_hours</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p diffh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diffraction-grating-angle">
<h3><a class="doc-anchor" href="#doc-diffraction-grating-angle">#</a> <code>diffraction_grating_angle</code></h3>
<p><code>diffraction_grating_angle</code> — operation <code>diffraction grating angle</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p diffraction_grating_angle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diffuse-layer-thickness">
<h3><a class="doc-anchor" href="#doc-diffuse-layer-thickness">#</a> <code>diffuse_layer_thickness</code></h3>
<p><code>diffuse_layer_thickness</code> — operation <code>diffuse layer thickness</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p diffuse_layer_thickness $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diffusion-layer-thickness">
<h3><a class="doc-anchor" href="#doc-diffusion-layer-thickness">#</a> <code>diffusion_layer_thickness</code></h3>
<p><code>diffusion_layer_thickness</code> — operation <code>diffusion layer thickness</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p diffusion_layer_thickness $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diffusion-stability">
<h3><a class="doc-anchor" href="#doc-diffusion-stability">#</a> <code>diffusion_stability</code></h3>
<p><code>diffusion_stability</code> — operation <code>diffusion stability</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p diffusion_stability $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dig">
<h3><a class="doc-anchor" href="#doc-dig">#</a> <code>dig</code></h3>
<p><code>dig</code> — operation <code>dig</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p dig $x
</code></pre>
</article>
<article class="doc-entry" id="doc-digest-auth-quote">
<h3><a class="doc-anchor" href="#doc-digest-auth-quote">#</a> <code>digest_auth_quote</code></h3>
<p><code>digest_auth_quote</code> — operation <code>digest auth quote</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p digest_auth_quote $x
</code></pre>
</article>
<article class="doc-entry" id="doc-digital-call">
<h3><a class="doc-anchor" href="#doc-digital-call">#</a> <code>digital_call</code></h3>
<p><code>digital_call</code> — operation <code>digital call</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p digital_call $x
</code></pre>
</article>
<article class="doc-entry" id="doc-digital-root">
<h3><a class="doc-anchor" href="#doc-digital-root">#</a> <code>digital_root</code></h3>
<p><code>digital_root</code> — operation <code>digital root</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p digital_root $x
</code></pre>
</article>
<article class="doc-entry" id="doc-digitize">
<h3><a class="doc-anchor" href="#doc-digitize">#</a> <code>digitize</code></h3>
<p><code>digitize</code> — operation <code>digitize</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p digitize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-digits-of">
<h3><a class="doc-anchor" href="#doc-digits-of">#</a> <code>digits_of</code></h3>
<p><code>digits_of</code> — operation <code>digits of</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p digits_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-digroot">
<h3><a class="doc-anchor" href="#doc-digroot">#</a> <code>digroot</code></h3>
<p><code>digroot</code> — operation <code>digroot</code>. Alias for <code>digital_root</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p digroot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dijkstra">
<h3><a class="doc-anchor" href="#doc-dijkstra">#</a> <code>dijkstra</code></h3>
<p><code>dijkstra</code> (alias <code>shortest_path</code>) computes shortest paths from a source node. Graph is a hash of {node => [[neighbor, weight], ...]}. Returns {node => distance}.</p>
<pre><code class="lang-perl">my $g = {A => [["B",1],["C",4]], B => [["C",2]], C => []}
my $d = dijkstra($g, "A") # {A=>0, B=>1, C=>3}
</code></pre>
</article>
<article class="doc-entry" id="doc-dijkstra-relax">
<h3><a class="doc-anchor" href="#doc-dijkstra-relax">#</a> <code>dijkstra_relax</code></h3>
<p><code>dijkstra_relax</code> — operation <code>dijkstra relax</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p dijkstra_relax $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dilation-2d">
<h3><a class="doc-anchor" href="#doc-dilation-2d">#</a> <code>dilation_2d</code></h3>
<p><code>dilation_2d(image, size=3) → matrix</code> — morphological dilation.</p>
</article>
<article class="doc-entry" id="doc-dilution-v2">
<h3><a class="doc-anchor" href="#doc-dilution-v2">#</a> <code>dilution_v2</code></h3>
<p><code>dilution_v2</code> — operation <code>dilution v2</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p dilution_v2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dim">
<h3><a class="doc-anchor" href="#doc-dim">#</a> <code>dim</code></h3>
<p><code>dim</code> — operation <code>dim</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p dim $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dinic-blocking-flow">
<h3><a class="doc-anchor" href="#doc-dinic-blocking-flow">#</a> <code>dinic_blocking_flow</code></h3>
<p><code>dinic_blocking_flow</code> — operation <code>dinic blocking flow</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p dinic_blocking_flow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dinic-step">
<h3><a class="doc-anchor" href="#doc-dinic-step">#</a> <code>dinic_step</code></h3>
<p><code>dinic_step</code> — single-step update of <code>dinic</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p dinic_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-diopter">
<h3><a class="doc-anchor" href="#doc-diopter">#</a> <code>diopter</code></h3>
<p><code>diopter</code> — operation <code>diopter</code>. Alias for <code>lens_power</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p diopter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-direct-age-adjusted">
<h3><a class="doc-anchor" href="#doc-direct-age-adjusted">#</a> <code>direct_age_adjusted</code></h3>
<p><code>direct_age_adjusted</code> — operation <code>direct age adjusted</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p direct_age_adjusted $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dirs">
<h3><a class="doc-anchor" href="#doc-dirs">#</a> <code>dirs</code></h3>
<p><code>dirs</code> — operation <code>dirs</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p dirs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dirty-price">
<h3><a class="doc-anchor" href="#doc-dirty-price">#</a> <code>dirty_price</code></h3>
<p><code>dirty_price</code> — operation <code>dirty price</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p dirty_price $x
</code></pre>
</article>
<article class="doc-entry" id="doc-disc-excel">
<h3><a class="doc-anchor" href="#doc-disc-excel">#</a> <code>disc_excel</code></h3>
<p><code>disc_excel</code> — operation <code>disc excel</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p disc_excel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-discount">
<h3><a class="doc-anchor" href="#doc-discount">#</a> <code>discount</code></h3>
<p><code>discount</code> — operation <code>discount</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p discount $x
</code></pre>
</article>
<article class="doc-entry" id="doc-discount-amount">
<h3><a class="doc-anchor" href="#doc-discount-amount">#</a> <code>discount_amount</code></h3>
<p><code>discount_amount</code> — operation <code>discount amount</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p discount_amount $x
</code></pre>
</article>
<article class="doc-entry" id="doc-discount-continuous">
<h3><a class="doc-anchor" href="#doc-discount-continuous">#</a> <code>discount_continuous</code></h3>
<p><code>discount_continuous</code> — operation <code>discount continuous</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p discount_continuous $x
</code></pre>
</article>
<article class="doc-entry" id="doc-discount-factor-step">
<h3><a class="doc-anchor" href="#doc-discount-factor-step">#</a> <code>discount_factor_step</code></h3>
<p><code>discount_factor_step</code> — single-step update of <code>discount factor</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p discount_factor_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-discount-pct">
<h3><a class="doc-anchor" href="#doc-discount-pct">#</a> <code>discount_pct</code></h3>
<p><code>discount_pct(original, sale) → number</code> — <code>(original - sale) / original · 100</code>.</p>
<pre><code class="lang-perl">p discount_pct(200, 150) # 25
</code></pre>
</article>
<article class="doc-entry" id="doc-discounted-payback">
<h3><a class="doc-anchor" href="#doc-discounted-payback">#</a> <code>discounted_payback</code></h3>
<p><code>discounted_payback($initial, $rate, @cashflows)</code> — computes payback period using discounted cash flows. Accounts for time value of money.</p>
<pre><code class="lang-perl">p discounted_payback(1000, 0.1, 400, 400, 400, 400)
</code></pre>
</article>
<article class="doc-entry" id="doc-discrete-haar-step">
<h3><a class="doc-anchor" href="#doc-discrete-haar-step">#</a> <code>discrete_haar_step</code></h3>
<p><code>discrete_haar_step</code> — single-step update of <code>discrete haar</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p discrete_haar_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-discrete-log">
<h3><a class="doc-anchor" href="#doc-discrete-log">#</a> <code>discrete_log</code></h3>
<p><code>discrete_log</code> — operation <code>discrete log</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p discrete_log $x
</code></pre>
</article>
<article class="doc-entry" id="doc-disk-avail">
<h3><a class="doc-anchor" href="#doc-disk-avail">#</a> <code>disk_avail</code></h3>
<p><code>disk_avail PATH</code> — available disk space in bytes for non-root users. Uses <code>f_bavail</code> from <code>statvfs</code>, which excludes blocks reserved for the superuser.</p>
<pre><code class="lang-perl">p format_bytes(disk_avail) # 76.3 GiB
gauge(1 - disk_avail / disk_total) |> p # usage gauge
</code></pre>
</article>
<article class="doc-entry" id="doc-disk-free">
<h3><a class="doc-anchor" href="#doc-disk-free">#</a> <code>disk_free</code></h3>
<p><code>disk_free PATH</code> — free disk space in bytes (superuser view). Uses <code>f_bfree</code> from <code>statvfs</code>.</p>
<pre><code class="lang-perl">p format_bytes(disk_free) # 76.3 GiB
p format_bytes(disk_free("/tmp"))
</code></pre>
</article>
<article class="doc-entry" id="doc-disk-total">
<h3><a class="doc-anchor" href="#doc-disk-total">#</a> <code>disk_total</code></h3>
<p><code>disk_total PATH</code> — total disk space in bytes for the filesystem containing PATH (default <code>/</code>). Uses <code>statvfs</code> on unix. Returns <code>undef</code> on unsupported platforms.</p>
<pre><code class="lang-perl">p format_bytes(disk_total) # 1.8 TiB
p format_bytes(disk_total("/home")) # specific mount
</code></pre>
</article>
<article class="doc-entry" id="doc-disk-used">
<h3><a class="doc-anchor" href="#doc-disk-used">#</a> <code>disk_used</code></h3>
<p><code>disk_used PATH</code> — used disk space in bytes (total - free).</p>
<pre><code class="lang-perl">p format_bytes(disk_used) # 1.7 TiB
my $pct = int(disk_used / disk_total * 100)
p "$pct% disk used"
</code></pre>
</article>
<article class="doc-entry" id="doc-dissoc">
<h3><a class="doc-anchor" href="#doc-dissoc">#</a> <code>dissoc</code></h3>
<p><code>dissoc</code> — operation <code>dissoc</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p dissoc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dist">
<h3><a class="doc-anchor" href="#doc-dist">#</a> <code>dist</code></h3>
<p><code>dist</code> — operation <code>dist</code>. Alias for <code>distance</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p dist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dist-mat">
<h3><a class="doc-anchor" href="#doc-dist-mat">#</a> <code>dist_mat</code></h3>
<p><code>dist_matrix</code> (alias <code>dist_mat</code>) — pairwise distance matrix. Supports 'euclidean' (default), 'manhattan', 'maximum'. Like R's dist().</p>
<pre><code class="lang-perl">my $D = dist_mat([[0,0],[1,0],[0,1]]) # 3x3 distance matrix
my $D2 = dist_mat([[0,0],[1,1]], "manhattan") # Manhattan
</code></pre>
</article>
<article class="doc-entry" id="doc-dist-point-line-2d">
<h3><a class="doc-anchor" href="#doc-dist-point-line-2d">#</a> <code>dist_point_line_2d</code></h3>
<p><code>dist_point_line_2d</code> — operation <code>dist point line 2d</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p dist_point_line_2d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dist-point-plane-3d">
<h3><a class="doc-anchor" href="#doc-dist-point-plane-3d">#</a> <code>dist_point_plane_3d</code></h3>
<p><code>dist_point_plane_3d</code> — operation <code>dist point plane 3d</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p dist_point_plane_3d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-distance">
<h3><a class="doc-anchor" href="#doc-distance">#</a> <code>distance</code></h3>
<p><code>distance</code> — operation <code>distance</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-distb">
<h3><a class="doc-anchor" href="#doc-distb">#</a> <code>distb</code></h3>
<p><code>distb</code> — operation <code>distb</code>. Alias for <code>distinct_by</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p distb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-distinct-by">
<h3><a class="doc-anchor" href="#doc-distinct-by">#</a> <code>distinct_by</code></h3>
<p><code>distinct_by</code> — operation <code>distinct by</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p distinct_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-distinct-count">
<h3><a class="doc-anchor" href="#doc-distinct-count">#</a> <code>distinct_count</code></h3>
<p><code>distinct_count</code> — count of <code>distinct</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p distinct_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-distinct-sample">
<h3><a class="doc-anchor" href="#doc-distinct-sample">#</a> <code>distinct_sample</code></h3>
<p><code>distinct_sample</code> — operation <code>distinct sample</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p distinct_sample $x
</code></pre>
</article>
<article class="doc-entry" id="doc-divergence-omega-step">
<h3><a class="doc-anchor" href="#doc-divergence-omega-step">#</a> <code>divergence_omega_step</code></h3>
<p><code>divergence_omega_step</code> — single-step update of <code>divergence omega</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p divergence_omega_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-divisible-goods-proportional">
<h3><a class="doc-anchor" href="#doc-divisible-goods-proportional">#</a> <code>divisible_goods_proportional</code></h3>
<p><code>divisible_goods_proportional</code> — operation <code>divisible goods proportional</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p divisible_goods_proportional $x
</code></pre>
</article>
<article class="doc-entry" id="doc-divisor-count">
<h3><a class="doc-anchor" href="#doc-divisor-count">#</a> <code>divisor_count</code></h3>
<p><code>divisor_count</code> — count of <code>divisor</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p divisor_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-divisor-sum">
<h3><a class="doc-anchor" href="#doc-divisor-sum">#</a> <code>divisor_sum</code></h3>
<p><code>divisor_sum</code> — sum of <code>divisor</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p divisor_sum @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-divisors">
<h3><a class="doc-anchor" href="#doc-divisors">#</a> <code>divisors</code></h3>
<p><code>divisors</code> — operation <code>divisors</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p divisors $x
</code></pre>
</article>
<article class="doc-entry" id="doc-divmod">
<h3><a class="doc-anchor" href="#doc-divmod">#</a> <code>divmod</code></h3>
<p><code>divmod</code> — operation <code>divmod</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p divmod $x
</code></pre>
</article>
<article class="doc-entry" id="doc-divs">
<h3><a class="doc-anchor" href="#doc-divs">#</a> <code>divs</code></h3>
<p><code>divs</code> — operation <code>divs</code>. Alias for <code>divisors</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p divs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-djb2">
<h3><a class="doc-anchor" href="#doc-djb2">#</a> <code>djb2</code></h3>
<p><code>djb2</code> — operation <code>djb2</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p djb2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-djb2-hash">
<h3><a class="doc-anchor" href="#doc-djb2-hash">#</a> <code>djb2_hash</code></h3>
<p><code>djb2_hash</code> — hash function of <code>djb2</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p djb2_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dlnorm">
<h3><a class="doc-anchor" href="#doc-dlnorm">#</a> <code>dlnorm</code></h3>
<p><code>dlnorm</code> — operation <code>dlnorm</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p dlnorm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dlogis">
<h3><a class="doc-anchor" href="#doc-dlogis">#</a> <code>dlogis</code></h3>
<p><code>dlogis</code> — operation <code>dlogis</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p dlogis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dm">
<h3><a class="doc-anchor" href="#doc-dm">#</a> <code>dm</code></h3>
<p><code>dm</code> — operation <code>dm</code>. Alias for <code>divmod</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p dm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dmetph">
<h3><a class="doc-anchor" href="#doc-dmetph">#</a> <code>dmetph</code></h3>
<p><code>dmetph</code> — operation <code>dmetph</code>. Alias for <code>double_metaphone</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p dmetph $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dna-at-content">
<h3><a class="doc-anchor" href="#doc-dna-at-content">#</a> <code>dna_at_content</code></h3>
<p><code>dna_at_content(seq) → number</code> — fraction of A, T, or U bases.</p>
</article>
<article class="doc-entry" id="doc-dna-complement">
<h3><a class="doc-anchor" href="#doc-dna-complement">#</a> <code>dna_complement</code></h3>
<p><code>dna_complement(seq) → string</code> — Watson-Crick complement (A↔T, G↔C). Case-preserving; non-ACGT chars pass through.</p>
<pre><code class="lang-perl">p dna_complement("ATGC") # "TACG"
</code></pre>
</article>
<article class="doc-entry" id="doc-dna-gc-content">
<h3><a class="doc-anchor" href="#doc-dna-gc-content">#</a> <code>dna_gc_content</code></h3>
<p><code>dna_gc_content(seq) → number</code> — fraction of G or C bases in [0,1].</p>
<pre><code class="lang-perl">p dna_gc_content("ATGCGCATAT") # 0.4
</code></pre>
</article>
<article class="doc-entry" id="doc-dna-kmer-count">
<h3><a class="doc-anchor" href="#doc-dna-kmer-count">#</a> <code>dna_kmer_count</code></h3>
<p><code>dna_kmer_count(seq, k=3) → hash</code> — frequency map of all k-mers in the sequence.</p>
<pre><code class="lang-perl">p dna_kmer_count("ATGATC", 2)
</code></pre>
</article>
<article class="doc-entry" id="doc-dna-kmer-index">
<h3><a class="doc-anchor" href="#doc-dna-kmer-index">#</a> <code>dna_kmer_index</code></h3>
<p><code>dna_kmer_index(seq, k=3) → hash</code> — for each k-mer, the list of start positions where it occurs.</p>
</article>
<article class="doc-entry" id="doc-dna-melting-temp">
<h3><a class="doc-anchor" href="#doc-dna-melting-temp">#</a> <code>dna_melting_temp</code></h3>
<p><code>dna_melting_temp(seq) → number</code> — Tm in °C. Uses Wallace rule for length <14, Marmur for longer.</p>
<pre><code class="lang-perl">p dna_melting_temp("ATGC") # 12
</code></pre>
</article>
<article class="doc-entry" id="doc-dna-reverse-complement">
<h3><a class="doc-anchor" href="#doc-dna-reverse-complement">#</a> <code>dna_reverse_complement</code></h3>
<p><code>dna_reverse_complement(seq) → string</code> — reverse-then-complement. Equivalent to the antisense strand read 5'→3'.</p>
<pre><code class="lang-perl">p dna_reverse_complement("AAATGGC") # "GCCATTT"
</code></pre>
</article>
<article class="doc-entry" id="doc-dna-transcribe">
<h3><a class="doc-anchor" href="#doc-dna-transcribe">#</a> <code>dna_transcribe</code></h3>
<p><code>dna_transcribe(dna) → string</code> — replace T with U to produce mRNA.</p>
<pre><code class="lang-perl">p dna_transcribe("ATGC") # "AUGC"
</code></pre>
</article>
<article class="doc-entry" id="doc-dna-translate">
<h3><a class="doc-anchor" href="#doc-dna-translate">#</a> <code>dna_translate</code></h3>
<p><code>dna_translate(dna) → string</code> — translate DNA to protein (single-letter codes); stops at stop codon.</p>
<pre><code class="lang-perl">p dna_translate("ATGGCAGAATAA") # MAE
</code></pre>
</article>
<article class="doc-entry" id="doc-dnbinom">
<h3><a class="doc-anchor" href="#doc-dnbinom">#</a> <code>dnbinom</code></h3>
<p><code>dnbinom</code> — negative binomial PMF. Args: k, size, prob.</p>
<pre><code class="lang-perl">p dnbinom(3, 5, 0.5) # P(3 failures before 5 successes)
</code></pre>
</article>
<article class="doc-entry" id="doc-dnds-ratio">
<h3><a class="doc-anchor" href="#doc-dnds-ratio">#</a> <code>dnds_ratio</code></h3>
<p><code>dnds_ratio</code> — ratio of <code>dnds</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p dnds_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dnorm">
<h3><a class="doc-anchor" href="#doc-dnorm">#</a> <code>dnorm</code></h3>
<p><code>dnorm</code> — operation <code>dnorm</code>. Category: *r / scipy distributions and tests*.</p>
<pre><code class="lang-perl">p dnorm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dnrm2">
<h3><a class="doc-anchor" href="#doc-dnrm2">#</a> <code>dnrm2</code></h3>
<p><code>dnrm2</code> — operation <code>dnrm2</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dnrm2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-do-call">
<h3><a class="doc-anchor" href="#doc-do-call">#</a> <code>do_call</code></h3>
<p><code>do_call</code> — call a function with args from a list. Like R's do.call().</p>
<pre><code class="lang-perl">my $result = docall(fn { $_[0] + $_[1] }, [3, 4]) # 7
</code></pre>
</article>
<article class="doc-entry" id="doc-doctor">
<h3><a class="doc-anchor" href="#doc-doctor">#</a> <code>doctor</code></h3>
<p><code>doctor</code> (alias <code>health</code>) — runtime diagnostic report. Prints version + binary path, runtime flags (<code>--compat</code>, <code>--no-interop</code>, <code>bigint</code>, <code>strict_vars</code>, <code>strict_refs</code>), environment overrides (<code>STRYKE_NO_TTY</code>, <code>STRYKE_NO_JIT</code>, <code>RUST_LOG</code>, …), reflection counts (<code>%b</code> primaries, <code>%all</code> spellings, categories, list-builtin extras), concurrency (logical CPUs + rayon pool size), home/cache/config dirs, toolchain availability (<code>rustc</code>/<code>cargo</code>/<code>perl</code>/<code>git</code>/<code>rg</code>), and a battery of sanity checks. Returns the warning count as an integer (0 = healthy).</p>
<pre><code class="lang-perl">doctor # full report
my $w = doctor
exit($w == 0 ? 0 : 1) # CI-friendly health gate
</code></pre>
</article>
<article class="doc-entry" id="doc-dodecahedral">
<h3><a class="doc-anchor" href="#doc-dodecahedral">#</a> <code>dodecahedral</code></h3>
<p><code>dodecahedral(n) → int</code> — <code>n·(3n-1)·(3n-2) / 2</code>.</p>
</article>
<article class="doc-entry" id="doc-dodecahedral-number">
<h3><a class="doc-anchor" href="#doc-dodecahedral-number">#</a> <code>dodecahedral_number</code></h3>
<p><code>dodecahedral_number</code> — operation <code>dodecahedral number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p dodecahedral_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dodgson-swap-count">
<h3><a class="doc-anchor" href="#doc-dodgson-swap-count">#</a> <code>dodgson_swap_count</code></h3>
<p><code>dodgson_swap_count</code> — count of <code>dodgson swap</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p dodgson_swap_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dogleg-step">
<h3><a class="doc-anchor" href="#doc-dogleg-step">#</a> <code>dogleg_step</code></h3>
<p><code>dogleg_step</code> — single-step update of <code>dogleg</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p dogleg_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dollarde">
<h3><a class="doc-anchor" href="#doc-dollarde">#</a> <code>dollarde</code></h3>
<p><code>dollarde</code> — operation <code>dollarde</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p dollarde $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dollarfr">
<h3><a class="doc-anchor" href="#doc-dollarfr">#</a> <code>dollarfr</code></h3>
<p><code>dollarfr</code> — operation <code>dollarfr</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p dollarfr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dom-tree-idom">
<h3><a class="doc-anchor" href="#doc-dom-tree-idom">#</a> <code>dom_tree_idom</code></h3>
<p><code>dom_tree_idom</code> — operation <code>dom tree idom</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p dom_tree_idom $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dominance-frontier">
<h3><a class="doc-anchor" href="#doc-dominance-frontier">#</a> <code>dominance_frontier</code></h3>
<p><code>dominance_frontier</code> — operation <code>dominance frontier</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p dominance_frontier $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dominating-set-greedy">
<h3><a class="doc-anchor" href="#doc-dominating-set-greedy">#</a> <code>dominating_set_greedy</code></h3>
<p><code>dominating_set_greedy</code> — operation <code>dominating set greedy</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p dominating_set_greedy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dominating-set-greedy-step">
<h3><a class="doc-anchor" href="#doc-dominating-set-greedy-step">#</a> <code>dominating_set_greedy_step</code></h3>
<p><code>dominating_set_greedy_step</code> — single-step update of <code>dominating set greedy</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p dominating_set_greedy_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dominating-set-lp-bound">
<h3><a class="doc-anchor" href="#doc-dominating-set-lp-bound">#</a> <code>dominating_set_lp_bound</code></h3>
<p><code>dominating_set_lp_bound</code> — operation <code>dominating set lp bound</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p dominating_set_lp_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-donaldson-invariant">
<h3><a class="doc-anchor" href="#doc-donaldson-invariant">#</a> <code>donaldson_invariant</code></h3>
<p><code>donaldson_invariant</code> — operation <code>donaldson invariant</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p donaldson_invariant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-donchian-lower">
<h3><a class="doc-anchor" href="#doc-donchian-lower">#</a> <code>donchian_lower</code></h3>
<p><code>donchian_lower(lows, period=20) → array</code> — rolling min of <code>lows</code> over <code>period</code>.</p>
<pre><code class="lang-perl">p donchian_lower(\@lo, 20)
</code></pre>
</article>
<article class="doc-entry" id="doc-donchian-upper">
<h3><a class="doc-anchor" href="#doc-donchian-upper">#</a> <code>donchian_upper</code></h3>
<p><code>donchian_upper(highs, period=20) → array</code> — rolling max of <code>highs</code> over <code>period</code>. Used for breakout systems (Turtle traders).</p>
<pre><code class="lang-perl">p donchian_upper(\@hi, 20)
</code></pre>
</article>
<article class="doc-entry" id="doc-doppler">
<h3><a class="doc-anchor" href="#doc-doppler">#</a> <code>doppler</code></h3>
<p><code>doppler_frequency($source_freq, $source_vel, $observer_vel)</code> (alias <code>doppler</code>) — observed frequency with Doppler effect. Uses speed of sound (343 m/s).</p>
<pre><code class="lang-perl">p doppler(440, -30, 0) # ~482 Hz (ambulance approaching at 30 m/s)
p doppler(440, 30, 0) # ~405 Hz (ambulance receding)
</code></pre>
</article>
<article class="doc-entry" id="doc-doppler-classical">
<h3><a class="doc-anchor" href="#doc-doppler-classical">#</a> <code>doppler_classical</code></h3>
<p><code>doppler_classical</code> — operation <code>doppler classical</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p doppler_classical $x
</code></pre>
</article>
<article class="doc-entry" id="doc-doppler-relativistic">
<h3><a class="doc-anchor" href="#doc-doppler-relativistic">#</a> <code>doppler_relativistic</code></h3>
<p><code>doppler_relativistic</code> — operation <code>doppler relativistic</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p doppler_relativistic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dopri5-combine">
<h3><a class="doc-anchor" href="#doc-dopri5-combine">#</a> <code>dopri5_combine</code></h3>
<p><code>dopri5_combine</code> — operation <code>dopri5 combine</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p dopri5_combine $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dorglq">
<h3><a class="doc-anchor" href="#doc-dorglq">#</a> <code>dorglq</code></h3>
<p><code>dorglq</code> — operation <code>dorglq</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dorglq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dorgqr">
<h3><a class="doc-anchor" href="#doc-dorgqr">#</a> <code>dorgqr</code></h3>
<p><code>dorgqr</code> — operation <code>dorgqr</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dorgqr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dot-case">
<h3><a class="doc-anchor" href="#doc-dot-case">#</a> <code>dot_case</code></h3>
<p><code>dot_case</code> — operation <code>dot case</code>. Category: *string*.</p>
<pre><code class="lang-perl">p dot_case $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dot-product">
<h3><a class="doc-anchor" href="#doc-dot-product">#</a> <code>dot_product</code></h3>
<p><code>dot_product(a, b) → number</code> — <code>Σ aᵢ·bᵢ</code> (alias <code>dotp</code>).</p>
</article>
<article class="doc-entry" id="doc-dotp">
<h3><a class="doc-anchor" href="#doc-dotp">#</a> <code>dotp</code></h3>
<p><code>dotp</code> — operation <code>dotp</code>. Alias for <code>dot_product</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p dotp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-double">
<h3><a class="doc-anchor" href="#doc-double">#</a> <code>double</code></h3>
<p><code>double</code> — operation <code>double</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p double $x
</code></pre>
</article>
<article class="doc-entry" id="doc-double-auction-step">
<h3><a class="doc-anchor" href="#doc-double-auction-step">#</a> <code>double_auction_step</code></h3>
<p><code>double_auction_step</code> — single-step update of <code>double auction</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p double_auction_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-double-each">
<h3><a class="doc-anchor" href="#doc-double-each">#</a> <code>double_each</code></h3>
<p><code>double_each</code> — operation <code>double each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p double_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-double-exponential-smoothing">
<h3><a class="doc-anchor" href="#doc-double-exponential-smoothing">#</a> <code>double_exponential_smoothing</code></h3>
<p><code>double_exponential_smoothing(series, alpha=0.3, beta=0.1) → array</code> — Holt's linear trend method: level + trend components updated each step.</p>
<pre><code class="lang-perl">p double_exponential_smoothing(\@xs, 0.3, 0.1)
</code></pre>
</article>
<article class="doc-entry" id="doc-double-factorial">
<h3><a class="doc-anchor" href="#doc-double-factorial">#</a> <code>double_factorial</code></h3>
<p><code>double_factorial</code> — operation <code>double factorial</code>. Category: *math formulas*.</p>
<pre><code class="lang-perl">p double_factorial $x
</code></pre>
</article>
<article class="doc-entry" id="doc-double-layer-capacitance">
<h3><a class="doc-anchor" href="#doc-double-layer-capacitance">#</a> <code>double_layer_capacitance</code></h3>
<p><code>double_layer_capacitance</code> — operation <code>double layer capacitance</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p double_layer_capacitance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-double-metaphone">
<h3><a class="doc-anchor" href="#doc-double-metaphone">#</a> <code>double_metaphone</code></h3>
<p><code>double_metaphone</code> — operation <code>double metaphone</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p double_metaphone $x
</code></pre>
</article>
<article class="doc-entry" id="doc-double-metaphone-primary">
<h3><a class="doc-anchor" href="#doc-double-metaphone-primary">#</a> <code>double_metaphone_primary</code></h3>
<p><code>double_metaphone_primary</code> — operation <code>double metaphone primary</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p double_metaphone_primary $x
</code></pre>
</article>
<article class="doc-entry" id="doc-double-metaphone-secondary">
<h3><a class="doc-anchor" href="#doc-double-metaphone-secondary">#</a> <code>double_metaphone_secondary</code></h3>
<p><code>double_metaphone_secondary</code> — operation <code>double metaphone secondary</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p double_metaphone_secondary $x
</code></pre>
</article>
<article class="doc-entry" id="doc-double-q-learning-step">
<h3><a class="doc-anchor" href="#doc-double-q-learning-step">#</a> <code>double_q_learning_step</code></h3>
<p><code>double_q_learning_step</code> — single-step update of <code>double q learning</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p double_q_learning_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-doubling-time-growth">
<h3><a class="doc-anchor" href="#doc-doubling-time-growth">#</a> <code>doubling_time_growth</code></h3>
<p><code>doubling_time_growth</code> — operation <code>doubling time growth</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p doubling_time_growth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-downcase-each">
<h3><a class="doc-anchor" href="#doc-downcase-each">#</a> <code>downcase_each</code></h3>
<p><code>downcase_each</code> — operation <code>downcase each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p downcase_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-downsample">
<h3><a class="doc-anchor" href="#doc-downsample">#</a> <code>downsample</code></h3>
<p><code>downsample(\@signal, $factor)</code> (alias <code>decimate</code>) — reduces sample rate by keeping every nth sample. Apply anti-aliasing filter first to avoid aliasing.</p>
<pre><code class="lang-perl">my $decimated = decimate(\@signal, 4) # keep every 4th sample
</code></pre>
</article>
<article class="doc-entry" id="doc-downto">
<h3><a class="doc-anchor" href="#doc-downto">#</a> <code>downto</code></h3>
<p><code>downto</code> — operation <code>downto</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p downto $x
</code></pre>
</article>
<article class="doc-entry" id="doc-doy">
<h3><a class="doc-anchor" href="#doc-doy">#</a> <code>doy</code></h3>
<p><code>doy</code> — operation <code>doy</code>. Alias for <code>day_of_year</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p doy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dpayback">
<h3><a class="doc-anchor" href="#doc-dpayback">#</a> <code>dpayback</code></h3>
<p><code>dpayback</code> — operation <code>dpayback</code>. Alias for <code>discounted_payback</code>. Category: *finance (extended)*.</p>
<pre><code class="lang-perl">p dpayback $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dpbsv">
<h3><a class="doc-anchor" href="#doc-dpbsv">#</a> <code>dpbsv</code></h3>
<p><code>dpbsv</code> — operation <code>dpbsv</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dpbsv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dpll-clause-learning">
<h3><a class="doc-anchor" href="#doc-dpll-clause-learning">#</a> <code>dpll_clause_learning</code></h3>
<p><code>dpll_clause_learning</code> — operation <code>dpll clause learning</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p dpll_clause_learning $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dpois">
<h3><a class="doc-anchor" href="#doc-dpois">#</a> <code>dpois</code></h3>
<p><code>dpois</code> — operation <code>dpois</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p dpois $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dpotrf">
<h3><a class="doc-anchor" href="#doc-dpotrf">#</a> <code>dpotrf</code></h3>
<p><code>dpotrf</code> — operation <code>dpotrf</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dpotrf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dpss-window">
<h3><a class="doc-anchor" href="#doc-dpss-window">#</a> <code>dpss_window</code></h3>
<p><code>dpss_window</code> — operation <code>dpss window</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p dpss_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dr">
<h3><a class="doc-anchor" href="#doc-dr">#</a> <code>dr</code></h3>
<p><code>dr</code> — operation <code>dr</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p dr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-drag-force">
<h3><a class="doc-anchor" href="#doc-drag-force">#</a> <code>drag_force</code></h3>
<p><code>drag_force</code> (alias <code>fdrag</code>) computes aerodynamic drag: F = 0.5·Cd·ρ·A·v². Args: drag_coeff, air_density, area, velocity.</p>
<pre><code class="lang-perl">p fdrag(0.47, 1.225, 0.01, 30) # drag on a ball at 30 m/s
</code></pre>
</article>
<article class="doc-entry" id="doc-drag-force-quadratic">
<h3><a class="doc-anchor" href="#doc-drag-force-quadratic">#</a> <code>drag_force_quadratic</code></h3>
<p><code>drag_force_quadratic</code> — operation <code>drag force quadratic</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p drag_force_quadratic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-drnk">
<h3><a class="doc-anchor" href="#doc-drnk">#</a> <code>drnk</code></h3>
<p><code>drnk</code> — operation <code>drnk</code>. Alias for <code>dense_rank</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p drnk $x
</code></pre>
</article>
<article class="doc-entry" id="doc-drop-at">
<h3><a class="doc-anchor" href="#doc-drop-at">#</a> <code>drop_at</code></h3>
<p><code>drop_at</code> — operation <code>drop at</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p drop_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-drop-every">
<h3><a class="doc-anchor" href="#doc-drop-every">#</a> <code>drop_every</code></h3>
<p><code>drop_every</code> — operation <code>drop every</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p drop_every $x
</code></pre>
</article>
<article class="doc-entry" id="doc-drop-last">
<h3><a class="doc-anchor" href="#doc-drop-last">#</a> <code>drop_last</code></h3>
<p><code>drop_last</code> — operation <code>drop last</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p drop_last $x
</code></pre>
</article>
<article class="doc-entry" id="doc-drop-n">
<h3><a class="doc-anchor" href="#doc-drop-n">#</a> <code>drop_n</code></h3>
<p><code>drop_n</code> — operation <code>drop n</code>. Category: *collection helpers (trivial)*.</p>
<pre><code class="lang-perl">p drop_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-drot">
<h3><a class="doc-anchor" href="#doc-drot">#</a> <code>drot</code></h3>
<p><code>drot</code> — operation <code>drot</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p drot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-drotg">
<h3><a class="doc-anchor" href="#doc-drotg">#</a> <code>drotg</code></h3>
<p><code>drotg</code> — operation <code>drotg</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p drotg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dsamp">
<h3><a class="doc-anchor" href="#doc-dsamp">#</a> <code>dsamp</code></h3>
<p><code>dsamp</code> — operation <code>dsamp</code>. Alias for <code>downsample</code>. Category: *dsp / signal (extended)*.</p>
<pre><code class="lang-perl">p dsamp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dscal">
<h3><a class="doc-anchor" href="#doc-dscal">#</a> <code>dscal</code></h3>
<p><code>dscal</code> — operation <code>dscal</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dscal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dsyevd">
<h3><a class="doc-anchor" href="#doc-dsyevd">#</a> <code>dsyevd</code></h3>
<p><code>dsyevd</code> — operation <code>dsyevd</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dsyevd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dsyrk">
<h3><a class="doc-anchor" href="#doc-dsyrk">#</a> <code>dsyrk</code></h3>
<p><code>dsyrk</code> — operation <code>dsyrk</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dsyrk $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dt">
<h3><a class="doc-anchor" href="#doc-dt">#</a> <code>dt</code></h3>
<p><code>dt</code> — operation <code>dt</code>. Category: *r / scipy distributions and tests*.</p>
<pre><code class="lang-perl">p dt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dtbsv">
<h3><a class="doc-anchor" href="#doc-dtbsv">#</a> <code>dtbsv</code></h3>
<p><code>dtbsv</code> — operation <code>dtbsv</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dtbsv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dte">
<h3><a class="doc-anchor" href="#doc-dte">#</a> <code>dte</code></h3>
<p><code>dte</code> — operation <code>dte</code>. Alias for <code>datetime_from_epoch</code>. Category: *date / time*.</p>
<pre><code class="lang-perl">p dte $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dtf">
<h3><a class="doc-anchor" href="#doc-dtf">#</a> <code>dtf</code></h3>
<p><code>dtf</code> — operation <code>dtf</code>. Alias for <code>datetime_strftime</code>. Category: *date / time*.</p>
<pre><code class="lang-perl">p dtf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dtrsm">
<h3><a class="doc-anchor" href="#doc-dtrsm">#</a> <code>dtrsm</code></h3>
<p><code>dtrsm</code> — operation <code>dtrsm</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dtrsm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dtrsv">
<h3><a class="doc-anchor" href="#doc-dtrsv">#</a> <code>dtrsv</code></h3>
<p><code>dtrsv</code> — operation <code>dtrsv</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p dtrsv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dump">
<h3><a class="doc-anchor" href="#doc-dump">#</a> <code>dump</code></h3>
<p><code>dump</code> — operation <code>dump</code>. Category: *process / system*.</p>
<pre><code class="lang-perl">p dump $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dunif">
<h3><a class="doc-anchor" href="#doc-dunif">#</a> <code>dunif</code></h3>
<p><code>dunif</code> — uniform PDF. Args: x, a, b.</p>
<pre><code class="lang-perl">p dunif(0.5, 0, 1) # 1.0
</code></pre>
</article>
<article class="doc-entry" id="doc-duped">
<h3><a class="doc-anchor" href="#doc-duped">#</a> <code>duped</code></h3>
<p><code>duplicated</code> — boolean array: 1 if element appeared earlier in the vector, 0 otherwise. Like R's duplicated().</p>
<pre><code class="lang-perl">p duplicated([1,2,3,2,1]) # [0,0,0,1,1]
</code></pre>
</article>
<article class="doc-entry" id="doc-duplicate-count">
<h3><a class="doc-anchor" href="#doc-duplicate-count">#</a> <code>duplicate_count</code></h3>
<p><code>duplicate_count</code> — count of <code>duplicate</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p duplicate_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-durand-kerner">
<h3><a class="doc-anchor" href="#doc-durand-kerner">#</a> <code>durand_kerner</code></h3>
<p><code>durand_kerner</code> — operation <code>durand kerner</code>. Alias for <code>polynomial_roots_dk</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p durand_kerner $x
</code></pre>
</article>
<article class="doc-entry" id="doc-duration-macaulay">
<h3><a class="doc-anchor" href="#doc-duration-macaulay">#</a> <code>duration_macaulay</code></h3>
<p><code>duration_macaulay(cashflows, rate) → number</code> — weighted average time to receive cashflows, weighted by present value. Measured in periods.</p>
<pre><code class="lang-perl">p duration_macaulay([100,100,1100], 0.05)
</code></pre>
</article>
<article class="doc-entry" id="doc-duration-modified">
<h3><a class="doc-anchor" href="#doc-duration-modified">#</a> <code>duration_modified</code></h3>
<p><code>duration_modified(cashflows, rate) → number</code> — <code>macaulay / (1 + rate)</code>. Direct linear sensitivity to yield change.</p>
<pre><code class="lang-perl">p duration_modified([100,100,1100], 0.05)
</code></pre>
</article>
<article class="doc-entry" id="doc-durbin-watson-d">
<h3><a class="doc-anchor" href="#doc-durbin-watson-d">#</a> <code>durbin_watson_d</code></h3>
<p><code>durbin_watson_d</code> — operation <code>durbin watson d</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p durbin_watson_d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dutch-auction">
<h3><a class="doc-anchor" href="#doc-dutch-auction">#</a> <code>dutch_auction</code></h3>
<p><code>dutch_auction</code> — operation <code>dutch auction</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p dutch_auction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dutch-auction-step">
<h3><a class="doc-anchor" href="#doc-dutch-auction-step">#</a> <code>dutch_auction_step</code></h3>
<p><code>dutch_auction_step</code> — single-step update of <code>dutch auction</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p dutch_auction_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dweibull">
<h3><a class="doc-anchor" href="#doc-dweibull">#</a> <code>dweibull</code></h3>
<p><code>dweibull</code> — operation <code>dweibull</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p dweibull $x
</code></pre>
</article>
<article class="doc-entry" id="doc-dynamics-db-level">
<h3><a class="doc-anchor" href="#doc-dynamics-db-level">#</a> <code>dynamics_db_level</code></h3>
<p><code>dynamics_db_level</code> — operation <code>dynamics db level</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p dynamics_db_level $x
</code></pre>
</article>
<article class="doc-entry" id="doc-each-cons">
<h3><a class="doc-anchor" href="#doc-each-cons">#</a> <code>each_cons</code></h3>
<p><code>each_cons</code> — operation <code>each cons</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p each_cons $x
</code></pre>
</article>
<article class="doc-entry" id="doc-each-slice">
<h3><a class="doc-anchor" href="#doc-each-slice">#</a> <code>each_slice</code></h3>
<p><code>each_slice</code> — operation <code>each slice</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p each_slice $x
</code></pre>
</article>
<article class="doc-entry" id="doc-each-with-index">
<h3><a class="doc-anchor" href="#doc-each-with-index">#</a> <code>each_with_index</code></h3>
<p><code>each_with_index</code> — index of <code>each with</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p each_with_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-each-with-object">
<h3><a class="doc-anchor" href="#doc-each-with-object">#</a> <code>each_with_object</code></h3>
<p><code>each_with_object</code> — operation <code>each with object</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p each_with_object $x
</code></pre>
</article>
<article class="doc-entry" id="doc-eadie-hofstee-y">
<h3><a class="doc-anchor" href="#doc-eadie-hofstee-y">#</a> <code>eadie_hofstee_y</code></h3>
<p><code>eadie_hofstee_y</code> — operation <code>eadie hofstee y</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p eadie_hofstee_y $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ean13-check">
<h3><a class="doc-anchor" href="#doc-ean13-check">#</a> <code>ean13_check</code></h3>
<p><code>ean13_check</code> — operation <code>ean13 check</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p ean13_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-earley-complete">
<h3><a class="doc-anchor" href="#doc-earley-complete">#</a> <code>earley_complete</code></h3>
<p><code>earley_complete</code> — operation <code>earley complete</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p earley_complete $x
</code></pre>
</article>
<article class="doc-entry" id="doc-earley-predict">
<h3><a class="doc-anchor" href="#doc-earley-predict">#</a> <code>earley_predict</code></h3>
<p><code>earley_predict</code> — operation <code>earley predict</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p earley_predict $x
</code></pre>
</article>
<article class="doc-entry" id="doc-earley-scan">
<h3><a class="doc-anchor" href="#doc-earley-scan">#</a> <code>earley_scan</code></h3>
<p><code>earley_scan</code> — operation <code>earley scan</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p earley_scan $x
</code></pre>
</article>
<article class="doc-entry" id="doc-earth-mass">
<h3><a class="doc-anchor" href="#doc-earth-mass">#</a> <code>earth_mass</code></h3>
<p><code>earth_mass</code> (alias <code>mearth</code>) — M⊕ ≈ 5.972×10²⁴ kg. Mass of Earth.</p>
<pre><code class="lang-perl">p mearth # 5.972167867e24 kg
</code></pre>
</article>
<article class="doc-entry" id="doc-earth-mover-1d">
<h3><a class="doc-anchor" href="#doc-earth-mover-1d">#</a> <code>earth_mover_1d</code></h3>
<p><code>earth_mover_1d(a, b) → number</code> — Wasserstein-1 distance between two histograms via cumulative sum.</p>
</article>
<article class="doc-entry" id="doc-earth-radius">
<h3><a class="doc-anchor" href="#doc-earth-radius">#</a> <code>earth_radius</code></h3>
<p><code>earth_radius</code> — operation <code>earth radius</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p earth_radius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-easter-gregorian-year">
<h3><a class="doc-anchor" href="#doc-easter-gregorian-year">#</a> <code>easter_gregorian_year</code></h3>
<p><code>easter_gregorian_year</code> — operation <code>easter gregorian year</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p easter_gregorian_year $x
</code></pre>
</article>
<article class="doc-entry" id="doc-easter-julian-year">
<h3><a class="doc-anchor" href="#doc-easter-julian-year">#</a> <code>easter_julian_year</code></h3>
<p><code>easter_julian_year</code> — operation <code>easter julian year</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p easter_julian_year $x
</code></pre>
</article>
<article class="doc-entry" id="doc-easter-orthodox-year">
<h3><a class="doc-anchor" href="#doc-easter-orthodox-year">#</a> <code>easter_orthodox_year</code></h3>
<p><code>easter_orthodox_year</code> — operation <code>easter orthodox year</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p easter_orthodox_year $x
</code></pre>
</article>
<article class="doc-entry" id="doc-easter-orthodox-year-2">
<h3><a class="doc-anchor" href="#doc-easter-orthodox-year-2">#</a> <code>easter_orthodox_year_2</code></h3>
<p><code>easter_orthodox_year_2</code> — operation <code>easter orthodox year 2</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p easter_orthodox_year_2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-easter-sunday">
<h3><a class="doc-anchor" href="#doc-easter-sunday">#</a> <code>easter_sunday</code></h3>
<p><code>easter_sunday</code> — operation <code>easter sunday</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p easter_sunday $x
</code></pre>
</article>
<article class="doc-entry" id="doc-easter-western">
<h3><a class="doc-anchor" href="#doc-easter-western">#</a> <code>easter_western</code></h3>
<p><code>easter_western</code> — operation <code>easter western</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p easter_western $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ec-point-add">
<h3><a class="doc-anchor" href="#doc-ec-point-add">#</a> <code>ec_point_add</code></h3>
<p><code>ec_point_add(p1, p2, a, prime) → [x, y]</code> — affine elliptic-curve point addition (placeholder uses Euclidean addition).</p>
</article>
<article class="doc-entry" id="doc-ec-point-double">
<h3><a class="doc-anchor" href="#doc-ec-point-double">#</a> <code>ec_point_double</code></h3>
<p><code>ec_point_double(p) → [x, y]</code> — point doubling (simplified).</p>
</article>
<article class="doc-entry" id="doc-ecc-point-double">
<h3><a class="doc-anchor" href="#doc-ecc-point-double">#</a> <code>ecc_point_double</code></h3>
<p><code>ecc_point_double</code> — operation <code>ecc point double</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p ecc_point_double $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ecdf">
<h3><a class="doc-anchor" href="#doc-ecdf">#</a> <code>ecdf</code></h3>
<p><code>ecdf</code> — empirical CDF: proportion of data ≤ x. Like R's ecdf().</p>
<pre><code class="lang-perl">p ecdf([1,2,3,4,5], 3) # 0.6 (3 of 5 values ≤ 3)
</code></pre>
</article>
<article class="doc-entry" id="doc-echarge">
<h3><a class="doc-anchor" href="#doc-echarge">#</a> <code>echarge</code></h3>
<p><code>echarge</code> — operation <code>echarge</code>. Alias for <code>elementary_charge</code>. Category: *constants*.</p>
<pre><code class="lang-perl">p echarge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-eclipse-magnitude">
<h3><a class="doc-anchor" href="#doc-eclipse-magnitude">#</a> <code>eclipse_magnitude</code></h3>
<p><code>eclipse_magnitude</code> — operation <code>eclipse magnitude</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p eclipse_magnitude $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ecliptic-obliquity">
<h3><a class="doc-anchor" href="#doc-ecliptic-obliquity">#</a> <code>ecliptic_obliquity</code></h3>
<p><code>ecliptic_obliquity</code> — operation <code>ecliptic obliquity</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p ecliptic_obliquity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ecliptic-to-equatorial">
<h3><a class="doc-anchor" href="#doc-ecliptic-to-equatorial">#</a> <code>ecliptic_to_equatorial</code></h3>
<p><code>ecliptic_to_equatorial</code> — convert from <code>ecliptic</code> to <code>equatorial</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p ecliptic_to_equatorial $value
</code></pre>
</article>
<article class="doc-entry" id="doc-econs">
<h3><a class="doc-anchor" href="#doc-econs">#</a> <code>econs</code></h3>
<p><code>econs</code> — operation <code>econs</code>. Alias for <code>each_cons</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p econs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ed25519-keypair-simple">
<h3><a class="doc-anchor" href="#doc-ed25519-keypair-simple">#</a> <code>ed25519_keypair_simple</code></h3>
<p><code>ed25519_keypair_simple(seed) → {private, public}</code> — SHA-512-derived keypair (demo only, not a real Ed25519 implementation).</p>
</article>
<article class="doc-entry" id="doc-ed25519-sign-simple">
<h3><a class="doc-anchor" href="#doc-ed25519-sign-simple">#</a> <code>ed25519_sign_simple</code></h3>
<p><code>ed25519_sign_simple(msg, private_key) → string</code> — SHA-512 of <code>private_key || msg</code>, base64-encoded.</p>
</article>
<article class="doc-entry" id="doc-ed25519-verify-simple">
<h3><a class="doc-anchor" href="#doc-ed25519-verify-simple">#</a> <code>ed25519_verify_simple</code></h3>
<p><code>ed25519_verify_simple(msg, public_key, sig) → 0|1</code> — companion verify.</p>
</article>
<article class="doc-entry" id="doc-eddington-luminosity">
<h3><a class="doc-anchor" href="#doc-eddington-luminosity">#</a> <code>eddington_luminosity</code></h3>
<p><code>eddington_luminosity</code> — operation <code>eddington luminosity</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p eddington_luminosity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-edge-coloring-vizing-step">
<h3><a class="doc-anchor" href="#doc-edge-coloring-vizing-step">#</a> <code>edge_coloring_vizing_step</code></h3>
<p><code>edge_coloring_vizing_step</code> — single-step update of <code>edge coloring vizing</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p edge_coloring_vizing_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-edge-connectivity">
<h3><a class="doc-anchor" href="#doc-edge-connectivity">#</a> <code>edge_connectivity</code></h3>
<p><code>edge_connectivity</code> — operation <code>edge connectivity</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p edge_connectivity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-edge-detect-kernel">
<h3><a class="doc-anchor" href="#doc-edge-detect-kernel">#</a> <code>edge_detect_kernel</code></h3>
<p><code>edge_detect_kernel</code> — convolution kernel of <code>edge detect</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p edge_detect_kernel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-edgeworth-box-alloc">
<h3><a class="doc-anchor" href="#doc-edgeworth-box-alloc">#</a> <code>edgeworth_box_alloc</code></h3>
<p><code>edgeworth_box_alloc</code> — operation <code>edgeworth box alloc</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p edgeworth_box_alloc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-edmonds-karp-bfs">
<h3><a class="doc-anchor" href="#doc-edmonds-karp-bfs">#</a> <code>edmonds_karp_bfs</code></h3>
<p><code>edmonds_karp_bfs</code> — operation <code>edmonds karp bfs</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p edmonds_karp_bfs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-edmonds-karp-max-flow">
<h3><a class="doc-anchor" href="#doc-edmonds-karp-max-flow">#</a> <code>edmonds_karp_max_flow</code></h3>
<p><code>edmonds_karp_max_flow(capacity_matrix, source, sink) → number</code> — max-flow via Edmonds-Karp (BFS-based Ford-Fulkerson).</p>
<pre><code class="lang-perl">p edmonds_karp_max_flow($cap, 0, 5)
</code></pre>
</article>
<article class="doc-entry" id="doc-edmonds-karp-step">
<h3><a class="doc-anchor" href="#doc-edmonds-karp-step">#</a> <code>edmonds_karp_step</code></h3>
<p><code>edmonds_karp_step</code> — single-step update of <code>edmonds karp</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p edmonds_karp_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-effect">
<h3><a class="doc-anchor" href="#doc-effect">#</a> <code>effect</code></h3>
<p><code>effect</code> — operation <code>effect</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p effect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-effective-pop-size">
<h3><a class="doc-anchor" href="#doc-effective-pop-size">#</a> <code>effective_pop_size</code></h3>
<p><code>effective_pop_size</code> — operation <code>effective pop size</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p effective_pop_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-efficiency-ratio">
<h3><a class="doc-anchor" href="#doc-efficiency-ratio">#</a> <code>efficiency_ratio</code></h3>
<p><code>efficiency_ratio</code> — ratio of <code>efficiency</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p efficiency_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-efield">
<h3><a class="doc-anchor" href="#doc-efield">#</a> <code>efield</code></h3>
<p><code>efield</code> — operation <code>efield</code>. Alias for <code>electric_field</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p efield $x
</code></pre>
</article>
<article class="doc-entry" id="doc-efield-point">
<h3><a class="doc-anchor" href="#doc-efield-point">#</a> <code>efield_point</code></h3>
<p><code>efield_point</code> — operation <code>efield point</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p efield_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-egalitarian-solution">
<h3><a class="doc-anchor" href="#doc-egalitarian-solution">#</a> <code>egalitarian_solution</code></h3>
<p><code>egalitarian_solution</code> — operation <code>egalitarian solution</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p egalitarian_solution $x
</code></pre>
</article>
<article class="doc-entry" id="doc-egalitarian-split">
<h3><a class="doc-anchor" href="#doc-egalitarian-split">#</a> <code>egalitarian_split</code></h3>
<p><code>egalitarian_split</code> — operation <code>egalitarian split</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p egalitarian_split $x
</code></pre>
</article>
<article class="doc-entry" id="doc-egarch-step">
<h3><a class="doc-anchor" href="#doc-egarch-step">#</a> <code>egarch_step</code></h3>
<p><code>egarch_step</code> — single-step update of <code>egarch</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p egarch_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ei">
<h3><a class="doc-anchor" href="#doc-ei">#</a> <code>ei</code></h3>
<p><code>ei(x) → number</code> — exponential integral <code>Ei(x) = -∫_{-x}^∞ e^-t / t dt</code>. Uses series + log expansion.</p>
<pre><code class="lang-perl">p ei(1) # ~1.895
</code></pre>
</article>
<article class="doc-entry" id="doc-eig">
<h3><a class="doc-anchor" href="#doc-eig">#</a> <code>eig</code></h3>
<p><code>matrix_eigenvalues</code> (aliases <code>meig</code>, <code>eig</code>) computes eigenvalues of a square matrix via QR iteration. Returns an array of eigenvalues.</p>
<pre><code class="lang-perl">my @eigs = @{eig([[2,1],[1,2]])} # [3, 1]
</code></pre>
</article>
<article class="doc-entry" id="doc-einstein-dilaton-step">
<h3><a class="doc-anchor" href="#doc-einstein-dilaton-step">#</a> <code>einstein_dilaton_step</code></h3>
<p><code>einstein_dilaton_step</code> — single-step update of <code>einstein dilaton</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p einstein_dilaton_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-einstein-ring-radius">
<h3><a class="doc-anchor" href="#doc-einstein-ring-radius">#</a> <code>einstein_ring_radius</code></h3>
<p><code>einstein_ring_radius</code> — operation <code>einstein ring radius</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p einstein_ring_radius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-einstein-tensor-step">
<h3><a class="doc-anchor" href="#doc-einstein-tensor-step">#</a> <code>einstein_tensor_step</code></h3>
<p><code>einstein_tensor_step</code> — single-step update of <code>einstein tensor</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p einstein_tensor_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-either">
<h3><a class="doc-anchor" href="#doc-either">#</a> <code>either</code></h3>
<p><code>either</code> — operation <code>either</code>. Category: *boolean combinators*.</p>
<pre><code class="lang-perl">p either $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ekf-jacobian-step">
<h3><a class="doc-anchor" href="#doc-ekf-jacobian-step">#</a> <code>ekf_jacobian_step</code></h3>
<p><code>ekf_jacobian_step</code> — single-step update of <code>ekf jacobian</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ekf_jacobian_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ekman-layer-depth">
<h3><a class="doc-anchor" href="#doc-ekman-layer-depth">#</a> <code>ekman_layer_depth</code></h3>
<p><code>ekman_layer_depth</code> — operation <code>ekman layer depth</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ekman_layer_depth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ekman-pumping-step">
<h3><a class="doc-anchor" href="#doc-ekman-pumping-step">#</a> <code>ekman_pumping_step</code></h3>
<p><code>ekman_pumping_step</code> — single-step update of <code>ekman pumping</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ekman_pumping_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-elastic-collision-1d">
<h3><a class="doc-anchor" href="#doc-elastic-collision-1d">#</a> <code>elastic_collision_1d</code></h3>
<p><code>elastic_collision_1d(m1, v1, m2, v2) → [v1', v2']</code> — 1D elastic collision (kinetic energy preserved).</p>
<pre><code class="lang-perl">p elastic_collision_1d(1, 2, 1, 0) # [0, 2]
</code></pre>
</article>
<article class="doc-entry" id="doc-electric-field">
<h3><a class="doc-anchor" href="#doc-electric-field">#</a> <code>electric_field</code></h3>
<p><code>electric_field</code> — operation <code>electric field</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p electric_field $x
</code></pre>
</article>
<article class="doc-entry" id="doc-electrochem-impedance-z">
<h3><a class="doc-anchor" href="#doc-electrochem-impedance-z">#</a> <code>electrochem_impedance_z</code></h3>
<p><code>electrochem_impedance_z</code> — operation <code>electrochem impedance z</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p electrochem_impedance_z $x
</code></pre>
</article>
<article class="doc-entry" id="doc-electrochemiluminescence-yield">
<h3><a class="doc-anchor" href="#doc-electrochemiluminescence-yield">#</a> <code>electrochemiluminescence_yield</code></h3>
<p><code>electrochemiluminescence_yield</code> — operation <code>electrochemiluminescence yield</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p electrochemiluminescence_yield $x
</code></pre>
</article>
<article class="doc-entry" id="doc-electrocrystallization-step">
<h3><a class="doc-anchor" href="#doc-electrocrystallization-step">#</a> <code>electrocrystallization_step</code></h3>
<p><code>electrocrystallization_step</code> — single-step update of <code>electrocrystallization</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p electrocrystallization_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-electrode-potential-step">
<h3><a class="doc-anchor" href="#doc-electrode-potential-step">#</a> <code>electrode_potential_step</code></h3>
<p><code>electrode_potential_step</code> — single-step update of <code>electrode potential</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p electrode_potential_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-electrolysis-mass">
<h3><a class="doc-anchor" href="#doc-electrolysis-mass">#</a> <code>electrolysis_mass</code></h3>
<p><code>electrolysis_mass</code> — operation <code>electrolysis mass</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p electrolysis_mass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-electrolyte-decomposition-temp">
<h3><a class="doc-anchor" href="#doc-electrolyte-decomposition-temp">#</a> <code>electrolyte_decomposition_temp</code></h3>
<p><code>electrolyte_decomposition_temp</code> — operation <code>electrolyte decomposition temp</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p electrolyte_decomposition_temp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-electrolyzer-voltage">
<h3><a class="doc-anchor" href="#doc-electrolyzer-voltage">#</a> <code>electrolyzer_voltage</code></h3>
<p><code>electrolyzer_voltage</code> — operation <code>electrolyzer voltage</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p electrolyzer_voltage $x
</code></pre>
</article>
<article class="doc-entry" id="doc-electron-mass">
<h3><a class="doc-anchor" href="#doc-electron-mass">#</a> <code>electron_mass</code></h3>
<p><code>electron_mass</code> — operation <code>electron mass</code>. Category: *constants*.</p>
<pre><code class="lang-perl">p electron_mass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-electroosmotic-velocity">
<h3><a class="doc-anchor" href="#doc-electroosmotic-velocity">#</a> <code>electroosmotic_velocity</code></h3>
<p><code>electroosmotic_velocity</code> — operation <code>electroosmotic velocity</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p electroosmotic_velocity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-elem-at">
<h3><a class="doc-anchor" href="#doc-elem-at">#</a> <code>elem_at</code></h3>
<p><code>elem_at</code> — operation <code>elem at</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p elem_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-elem-index">
<h3><a class="doc-anchor" href="#doc-elem-index">#</a> <code>elem_index</code></h3>
<p><code>elem_index</code> — index of <code>elem</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p elem_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-elem-indices">
<h3><a class="doc-anchor" href="#doc-elem-indices">#</a> <code>elem_indices</code></h3>
<p><code>elem_indices</code> — operation <code>elem indices</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p elem_indices $x
</code></pre>
</article>
<article class="doc-entry" id="doc-elem-of">
<h3><a class="doc-anchor" href="#doc-elem-of">#</a> <code>elem_of</code></h3>
<p><code>elem_of</code> — operation <code>elem of</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p elem_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-elementary-charge">
<h3><a class="doc-anchor" href="#doc-elementary-charge">#</a> <code>elementary_charge</code></h3>
<p><code>elementary_charge</code> — operation <code>elementary charge</code>. Category: *constants*.</p>
<pre><code class="lang-perl">p elementary_charge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-elf-header-read">
<h3><a class="doc-anchor" href="#doc-elf-header-read">#</a> <code>elf_header_read</code></h3>
<p><code>elf_header_read(hex_bytes) → hash</code> — parse ELF e_ident + machine → <code>{class, endianness, machine}</code>.</p>
</article>
<article class="doc-entry" id="doc-elgamal-encrypt">
<h3><a class="doc-anchor" href="#doc-elgamal-encrypt">#</a> <code>elgamal_encrypt</code></h3>
<p><code>elgamal_encrypt</code> — encrypt of <code>elgamal</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p elgamal_encrypt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-elias-delta-code">
<h3><a class="doc-anchor" href="#doc-elias-delta-code">#</a> <code>elias_delta_code</code></h3>
<p><code>elias_delta_code</code> — operation <code>elias delta code</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p elias_delta_code $x
</code></pre>
</article>
<article class="doc-entry" id="doc-elias-gamma-code">
<h3><a class="doc-anchor" href="#doc-elias-gamma-code">#</a> <code>elias_gamma_code</code></h3>
<p><code>elias_gamma_code</code> — operation <code>elias gamma code</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p elias_gamma_code $x
</code></pre>
</article>
<article class="doc-entry" id="doc-elidx">
<h3><a class="doc-anchor" href="#doc-elidx">#</a> <code>elidx</code></h3>
<p><code>elidx</code> — operation <code>elidx</code>. Alias for <code>elem_index</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p elidx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-elidxs">
<h3><a class="doc-anchor" href="#doc-elidxs">#</a> <code>elidxs</code></h3>
<p><code>elidxs</code> — operation <code>elidxs</code>. Alias for <code>elem_indices</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p elidxs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ellip-lp">
<h3><a class="doc-anchor" href="#doc-ellip-lp">#</a> <code>ellip_lp</code></h3>
<p><code>ellip_lp</code> — operation <code>ellip lp</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p ellip_lp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ellipe">
<h3><a class="doc-anchor" href="#doc-ellipe">#</a> <code>ellipe</code></h3>
<p><code>ellipe</code> — operation <code>ellipe</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p ellipe $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ellipk">
<h3><a class="doc-anchor" href="#doc-ellipk">#</a> <code>ellipk</code></h3>
<p><code>ellipk</code> — operation <code>ellipk</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p ellipk $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ellipperim">
<h3><a class="doc-anchor" href="#doc-ellipperim">#</a> <code>ellipperim</code></h3>
<p><code>ellipperim</code> — operation <code>ellipperim</code>. Alias for <code>ellipse_perimeter</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p ellipperim $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ellipse-area">
<h3><a class="doc-anchor" href="#doc-ellipse-area">#</a> <code>ellipse_area</code></h3>
<p><code>ellipse_area</code> — operation <code>ellipse area</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p ellipse_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ellipse-perimeter">
<h3><a class="doc-anchor" href="#doc-ellipse-perimeter">#</a> <code>ellipse_perimeter</code></h3>
<p><code>ellipse_perimeter($a, $b)</code> (alias <code>ellper</code>) — approximates the perimeter of an ellipse with semi-axes a and b. Uses Ramanujan's approximation.</p>
<pre><code class="lang-perl">p ellper(5, 3) # ~25.5
p ellper(10, 10) # ~62.8 (circle)
</code></pre>
</article>
<article class="doc-entry" id="doc-ellipsis">
<h3><a class="doc-anchor" href="#doc-ellipsis">#</a> <code>ellipsis</code></h3>
<p><code>ellipsis</code> — operation <code>ellipsis</code>. Category: *string quote / escape*.</p>
<pre><code class="lang-perl">p ellipsis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ellipsoid-surface-approx">
<h3><a class="doc-anchor" href="#doc-ellipsoid-surface-approx">#</a> <code>ellipsoid_surface_approx</code></h3>
<p><code>ellipsoid_surface_approx</code> — operation <code>ellipsoid surface approx</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p ellipsoid_surface_approx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ellipsoid-volume">
<h3><a class="doc-anchor" href="#doc-ellipsoid-volume">#</a> <code>ellipsoid_volume</code></h3>
<p><code>ellipsoid_volume</code> — operation <code>ellipsoid volume</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p ellipsoid_volume $x
</code></pre>
</article>
<article class="doc-entry" id="doc-elo-expected">
<h3><a class="doc-anchor" href="#doc-elo-expected">#</a> <code>elo_expected</code></h3>
<p><code>elo_expected</code> — operation <code>elo expected</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p elo_expected $x
</code></pre>
</article>
<article class="doc-entry" id="doc-elo-update">
<h3><a class="doc-anchor" href="#doc-elo-update">#</a> <code>elo_update</code></h3>
<p><code>elo_update</code> — update step of <code>elo</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p elo_update $x
</code></pre>
</article>
<article class="doc-entry" id="doc-elof">
<h3><a class="doc-anchor" href="#doc-elof">#</a> <code>elof</code></h3>
<p><code>elof</code> — operation <code>elof</code>. Alias for <code>elem_of</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p elof $x
</code></pre>
</article>
<article class="doc-entry" id="doc-elu">
<h3><a class="doc-anchor" href="#doc-elu">#</a> <code>elu</code></h3>
<p><code>elu</code> applies the Exponential Linear Unit: x if x≥0, alpha*(e^x - 1) otherwise.</p>
<pre><code class="lang-perl">p elu(1) # 1
p elu(-1) # -0.632
</code></pre>
</article>
<article class="doc-entry" id="doc-em-frequency">
<h3><a class="doc-anchor" href="#doc-em-frequency">#</a> <code>em_frequency</code></h3>
<p><code>em_frequency</code> — operation <code>em frequency</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p em_frequency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-em-intensity">
<h3><a class="doc-anchor" href="#doc-em-intensity">#</a> <code>em_intensity</code></h3>
<p><code>em_intensity</code> — operation <code>em intensity</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p em_intensity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-em-step">
<h3><a class="doc-anchor" href="#doc-em-step">#</a> <code>em_step</code></h3>
<p><code>em_step</code> — single-step update of <code>em</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p em_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-em-wavelength">
<h3><a class="doc-anchor" href="#doc-em-wavelength">#</a> <code>em_wavelength</code></h3>
<p><code>em_wavelength</code> — operation <code>em wavelength</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p em_wavelength $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ema">
<h3><a class="doc-anchor" href="#doc-ema">#</a> <code>ema</code></h3>
<p><code>ema(prices, period=10) → array</code> — exponential moving average with smoothing factor <code>α = 2 / (period + 1)</code>. Seeded with the first sample so output length equals input length.</p>
<pre><code class="lang-perl">p ema([10,11,12,13,14], 3)
</code></pre>
</article>
<article class="doc-entry" id="doc-email-domain">
<h3><a class="doc-anchor" href="#doc-email-domain">#</a> <code>email_domain</code></h3>
<p><code>email_domain</code> — operation <code>email domain</code>. Category: *url / email parts*.</p>
<pre><code class="lang-perl">p email_domain $x
</code></pre>
</article>
<article class="doc-entry" id="doc-email-local">
<h3><a class="doc-anchor" href="#doc-email-local">#</a> <code>email_local</code></h3>
<p><code>email_local</code> — operation <code>email local</code>. Category: *url / email parts*.</p>
<pre><code class="lang-perl">p email_local $x
</code></pre>
</article>
<article class="doc-entry" id="doc-emass">
<h3><a class="doc-anchor" href="#doc-emass">#</a> <code>emass</code></h3>
<p><code>emass</code> — operation <code>emass</code>. Alias for <code>electron_mass</code>. Category: *constants*.</p>
<pre><code class="lang-perl">p emass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-emavg">
<h3><a class="doc-anchor" href="#doc-emavg">#</a> <code>emavg</code></h3>
<p><code>emavg</code> — operation <code>emavg</code>. Alias for <code>exponential_moving_average</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p emavg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-embed-text">
<h3><a class="doc-anchor" href="#doc-embed-text">#</a> <code>embed_text</code></h3>
<p><code>embed_text(text, dim=128) → array</code> — deterministic hashing-trick text embedding (testing/non-ML use).</p>
</article>
<article class="doc-entry" id="doc-embed-ts">
<h3><a class="doc-anchor" href="#doc-embed-ts">#</a> <code>embed_ts</code></h3>
<p><code>embed_ts</code> — time-delay embedding. Converts a time series into a matrix of lagged values. Like R's embed().</p>
<pre><code class="lang-perl">p embed_ts([1,2,3,4,5], 3) # [[3,2,1],[4,3,2],[5,4,3]]
</code></pre>
</article>
<article class="doc-entry" id="doc-emboss-kernel">
<h3><a class="doc-anchor" href="#doc-emboss-kernel">#</a> <code>emboss_kernel</code></h3>
<p><code>emboss_kernel</code> — convolution kernel of <code>emboss</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p emboss_kernel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-emf-from-half-cells">
<h3><a class="doc-anchor" href="#doc-emf-from-half-cells">#</a> <code>emf_from_half_cells</code></h3>
<p><code>emf_from_half_cells</code> — operation <code>emf from half cells</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p emf_from_half_cells $x
</code></pre>
</article>
<article class="doc-entry" id="doc-emissivity-grey-body">
<h3><a class="doc-anchor" href="#doc-emissivity-grey-body">#</a> <code>emissivity_grey_body</code></h3>
<p><code>emissivity_grey_body</code> — operation <code>emissivity grey body</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p emissivity_grey_body $x
</code></pre>
</article>
<article class="doc-entry" id="doc-emitted-long-wave">
<h3><a class="doc-anchor" href="#doc-emitted-long-wave">#</a> <code>emitted_long_wave</code></h3>
<p><code>emitted_long_wave</code> — operation <code>emitted long wave</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p emitted_long_wave $x
</code></pre>
</article>
<article class="doc-entry" id="doc-emojinum">
<h3><a class="doc-anchor" href="#doc-emojinum">#</a> <code>emojinum</code></h3>
<p><code>emojinum</code> — operation <code>emojinum</code>. Alias for <code>to_emoji_num</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p emojinum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-empc">
<h3><a class="doc-anchor" href="#doc-empc">#</a> <code>empc</code></h3>
<p><code>empc</code> — operation <code>empc</code>. Alias for <code>empty_clj</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p empc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-empty-clj">
<h3><a class="doc-anchor" href="#doc-empty-clj">#</a> <code>empty_clj</code></h3>
<p><code>empty_clj</code> — operation <code>empty clj</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p empty_clj $x
</code></pre>
</article>
<article class="doc-entry" id="doc-empty-count">
<h3><a class="doc-anchor" href="#doc-empty-count">#</a> <code>empty_count</code></h3>
<p><code>empty_count</code> — count of <code>empty</code>. Category: *counters*.</p>
<pre><code class="lang-perl">p empty_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-encode-base">
<h3><a class="doc-anchor" href="#doc-encode-base">#</a> <code>encode_base</code></h3>
<p><code>encode_base</code> — operation <code>encode base</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p encode_base $x
</code></pre>
</article>
<article class="doc-entry" id="doc-encode-pair">
<h3><a class="doc-anchor" href="#doc-encode-pair">#</a> <code>encode_pair</code></h3>
<p><code>encode_pair</code> — operation <code>encode pair</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p encode_pair $x
</code></pre>
</article>
<article class="doc-entry" id="doc-encode-succ">
<h3><a class="doc-anchor" href="#doc-encode-succ">#</a> <code>encode_succ</code></h3>
<p><code>encode_succ</code> — operation <code>encode succ</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p encode_succ $x
</code></pre>
</article>
<article class="doc-entry" id="doc-end-of-day">
<h3><a class="doc-anchor" href="#doc-end-of-day">#</a> <code>end_of_day</code></h3>
<p><code>end_of_day</code> — operation <code>end of day</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p end_of_day $x
</code></pre>
</article>
<article class="doc-entry" id="doc-endgrent">
<h3><a class="doc-anchor" href="#doc-endgrent">#</a> <code>endgrent</code></h3>
<p><code>endgrent</code> — operation <code>endgrent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p endgrent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-endhostent">
<h3><a class="doc-anchor" href="#doc-endhostent">#</a> <code>endhostent</code></h3>
<p><code>endhostent</code> — operation <code>endhostent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p endhostent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-endianness">
<h3><a class="doc-anchor" href="#doc-endianness">#</a> <code>endianness</code></h3>
<p><code>endianness</code> — byte order of the platform: <code>"little"</code> or <code>"big"</code>. Compile-time constant.</p>
<pre><code class="lang-perl">p endianness # little
</code></pre>
</article>
<article class="doc-entry" id="doc-endnetent">
<h3><a class="doc-anchor" href="#doc-endnetent">#</a> <code>endnetent</code></h3>
<p><code>endnetent</code> — operation <code>endnetent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p endnetent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-endowment-combined-a">
<h3><a class="doc-anchor" href="#doc-endowment-combined-a">#</a> <code>endowment_combined_a</code></h3>
<p><code>endowment_combined_a</code> — operation <code>endowment combined a</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p endowment_combined_a $x
</code></pre>
</article>
<article class="doc-entry" id="doc-endowment-pure-e">
<h3><a class="doc-anchor" href="#doc-endowment-pure-e">#</a> <code>endowment_pure_e</code></h3>
<p><code>endowment_pure_e</code> — operation <code>endowment pure e</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p endowment_pure_e $x
</code></pre>
</article>
<article class="doc-entry" id="doc-endprotoent">
<h3><a class="doc-anchor" href="#doc-endprotoent">#</a> <code>endprotoent</code></h3>
<p><code>endprotoent</code> — operation <code>endprotoent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p endprotoent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-endpwent">
<h3><a class="doc-anchor" href="#doc-endpwent">#</a> <code>endpwent</code></h3>
<p><code>endpwent</code> — operation <code>endpwent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p endpwent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ends-with">
<h3><a class="doc-anchor" href="#doc-ends-with">#</a> <code>ends_with</code></h3>
<p><code>ends_with</code> — operation <code>ends with</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p ends_with $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ends-with-any">
<h3><a class="doc-anchor" href="#doc-ends-with-any">#</a> <code>ends_with_any</code></h3>
<p><code>ends_with_any</code> — operation <code>ends with any</code>. Category: *string*.</p>
<pre><code class="lang-perl">p ends_with_any $x
</code></pre>
</article>
<article class="doc-entry" id="doc-endservent">
<h3><a class="doc-anchor" href="#doc-endservent">#</a> <code>endservent</code></h3>
<p><code>endservent</code> — operation <code>endservent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p endservent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-energy">
<h3><a class="doc-anchor" href="#doc-energy">#</a> <code>energy</code></h3>
<p><code>energy(\@signal)</code> — computes the total energy of a signal as the sum of squared samples. Useful for audio analysis and feature extraction.</p>
<pre><code class="lang-perl">p energy(\@signal) # total signal energy
</code></pre>
</article>
<article class="doc-entry" id="doc-energy-density-battery">
<h3><a class="doc-anchor" href="#doc-energy-density-battery">#</a> <code>energy_density_battery</code></h3>
<p><code>energy_density_battery</code> — operation <code>energy density battery</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p energy_density_battery $x
</code></pre>
</article>
<article class="doc-entry" id="doc-energy-efficiency-cell">
<h3><a class="doc-anchor" href="#doc-energy-efficiency-cell">#</a> <code>energy_efficiency_cell</code></h3>
<p><code>energy_efficiency_cell</code> — operation <code>energy efficiency cell</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p energy_efficiency_cell $x
</code></pre>
</article>
<article class="doc-entry" id="doc-engel-curve">
<h3><a class="doc-anchor" href="#doc-engel-curve">#</a> <code>engel_curve</code></h3>
<p><code>engel_curve</code> — operation <code>engel curve</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p engel_curve $x
</code></pre>
</article>
<article class="doc-entry" id="doc-engle-granger-step">
<h3><a class="doc-anchor" href="#doc-engle-granger-step">#</a> <code>engle_granger_step</code></h3>
<p><code>engle_granger_step</code> — single-step update of <code>engle granger</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p engle_granger_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-english-auction">
<h3><a class="doc-anchor" href="#doc-english-auction">#</a> <code>english_auction</code></h3>
<p><code>english_auction</code> — operation <code>english auction</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p english_auction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-english-auction-step">
<h3><a class="doc-anchor" href="#doc-english-auction-step">#</a> <code>english_auction_step</code></h3>
<p><code>english_auction_step</code> — single-step update of <code>english auction</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p english_auction_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-english-chi2">
<h3><a class="doc-anchor" href="#doc-english-chi2">#</a> <code>english_chi2</code></h3>
<p><code>english_chi2</code> — operation <code>english chi2</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p english_chi2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-english-likeness">
<h3><a class="doc-anchor" href="#doc-english-likeness">#</a> <code>english_likeness</code></h3>
<p><code>english_likeness</code> — operation <code>english likeness</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p english_likeness $x
</code></pre>
</article>
<article class="doc-entry" id="doc-enso-index-step">
<h3><a class="doc-anchor" href="#doc-enso-index-step">#</a> <code>enso_index_step</code></h3>
<p><code>enso_index_step</code> — single-step update of <code>enso index</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p enso_index_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ensure-prefix">
<h3><a class="doc-anchor" href="#doc-ensure-prefix">#</a> <code>ensure_prefix</code></h3>
<p><code>ensure_prefix</code> — operation <code>ensure prefix</code>. Category: *path helpers*.</p>
<pre><code class="lang-perl">p ensure_prefix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ensure-suffix">
<h3><a class="doc-anchor" href="#doc-ensure-suffix">#</a> <code>ensure_suffix</code></h3>
<p><code>ensure_suffix</code> — operation <code>ensure suffix</code>. Category: *path helpers*.</p>
<pre><code class="lang-perl">p ensure_suffix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-entab">
<h3><a class="doc-anchor" href="#doc-entab">#</a> <code>entab</code></h3>
<p><code>entab(s, width=8) → string</code> — compress leading runs of spaces into tabs at every multiple of <code>width</code>.</p>
<pre><code class="lang-perl">p entab(" hello", 4) # "\thello"
</code></pre>
</article>
<article class="doc-entry" id="doc-entanglement-entropy">
<h3><a class="doc-anchor" href="#doc-entanglement-entropy">#</a> <code>entanglement_entropy</code></h3>
<p><code>entanglement_entropy</code> — operation <code>entanglement entropy</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p entanglement_entropy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-enthalpy-reaction">
<h3><a class="doc-anchor" href="#doc-enthalpy-reaction">#</a> <code>enthalpy_reaction</code></h3>
<p><code>enthalpy_reaction</code> — operation <code>enthalpy reaction</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p enthalpy_reaction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-entropy">
<h3><a class="doc-anchor" href="#doc-entropy">#</a> <code>entropy</code></h3>
<p><code>entropy</code> — operation <code>entropy</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p entropy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-entropy-bits">
<h3><a class="doc-anchor" href="#doc-entropy-bits">#</a> <code>entropy_bits</code></h3>
<p><code>entropy_bits</code> — operation <code>entropy bits</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p entropy_bits $x
</code></pre>
</article>
<article class="doc-entry" id="doc-env">
<h3><a class="doc-anchor" href="#doc-env">#</a> <code>env</code></h3>
<p><code>env</code> — operation <code>env</code>. Alias for <code>envelope</code>. Category: *dsp / signal (extended)*.</p>
<pre><code class="lang-perl">p env $x
</code></pre>
</article>
<article class="doc-entry" id="doc-env-get">
<h3><a class="doc-anchor" href="#doc-env-get">#</a> <code>env_get</code></h3>
<p><code>env_get</code> — environment-variable helper <code>get</code>. Category: *process / env*.</p>
<pre><code class="lang-perl">p env_get $x
</code></pre>
</article>
<article class="doc-entry" id="doc-env-has">
<h3><a class="doc-anchor" href="#doc-env-has">#</a> <code>env_has</code></h3>
<p><code>env_has</code> — environment-variable helper <code>has</code>. Category: *process / env*.</p>
<pre><code class="lang-perl">p env_has $x
</code></pre>
</article>
<article class="doc-entry" id="doc-env-keys">
<h3><a class="doc-anchor" href="#doc-env-keys">#</a> <code>env_keys</code></h3>
<p><code>env_keys</code> — environment-variable helper <code>keys</code>. Category: *process / env*.</p>
<pre><code class="lang-perl">p env_keys $x
</code></pre>
</article>
<article class="doc-entry" id="doc-env-pairs">
<h3><a class="doc-anchor" href="#doc-env-pairs">#</a> <code>env_pairs</code></h3>
<p><code>env_pairs</code> — environment-variable helper <code>pairs</code>. Category: *more process / system*.</p>
<pre><code class="lang-perl">p env_pairs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-env-remove">
<h3><a class="doc-anchor" href="#doc-env-remove">#</a> <code>env_remove</code></h3>
<p><code>env_remove</code> — environment-variable helper <code>remove</code>. Category: *more process / system*.</p>
<pre><code class="lang-perl">p env_remove $x
</code></pre>
</article>
<article class="doc-entry" id="doc-env-set">
<h3><a class="doc-anchor" href="#doc-env-set">#</a> <code>env_set</code></h3>
<p><code>env_set</code> — environment-variable helper <code>set</code>. Category: *more process / system*.</p>
<pre><code class="lang-perl">p env_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-envelope">
<h3><a class="doc-anchor" href="#doc-envelope">#</a> <code>envelope</code></h3>
<p><code>envelope(\@signal)</code> (alias <code>hilbert_env</code>) — computes the amplitude envelope using Hilbert transform magnitude. Useful for amplitude modulation analysis.</p>
<pre><code class="lang-perl">my $env = envelope(\@signal)
# $env traces the amplitude of oscillations
</code></pre>
</article>
<article class="doc-entry" id="doc-envelope-amplitude">
<h3><a class="doc-anchor" href="#doc-envelope-amplitude">#</a> <code>envelope_amplitude</code></h3>
<p><code>envelope_amplitude</code> — envelope generator (ADSR-style) <code>amplitude</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p envelope_amplitude $x
</code></pre>
</article>
<article class="doc-entry" id="doc-eod">
<h3><a class="doc-anchor" href="#doc-eod">#</a> <code>eod</code></h3>
<p><code>eod</code> — operation <code>eod</code>. Alias for <code>end_of_day</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p eod $x
</code></pre>
</article>
<article class="doc-entry" id="doc-eof-from-concurrence">
<h3><a class="doc-anchor" href="#doc-eof-from-concurrence">#</a> <code>eof_from_concurrence</code></h3>
<p><code>eof_from_concurrence</code> — operation <code>eof from concurrence</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p eof_from_concurrence $x
</code></pre>
</article>
<article class="doc-entry" id="doc-epa-per-play">
<h3><a class="doc-anchor" href="#doc-epa-per-play">#</a> <code>epa_per_play</code></h3>
<p><code>epa_per_play</code> — operation <code>epa per play</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p epa_per_play $x
</code></pre>
</article>
<article class="doc-entry" id="doc-epoch">
<h3><a class="doc-anchor" href="#doc-epoch">#</a> <code>epoch</code></h3>
<p><code>epoch</code> — operation <code>epoch</code>. Alias for <code>unix_epoch</code>. Category: *now / timestamp*.</p>
<pre><code class="lang-perl">p epoch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-epoch-ms">
<h3><a class="doc-anchor" href="#doc-epoch-ms">#</a> <code>epoch_ms</code></h3>
<p><code>epoch_ms</code> — operation <code>epoch ms</code>. Alias for <code>unix_epoch_ms</code>. Category: *now / timestamp*.</p>
<pre><code class="lang-perl">p epoch_ms $x
</code></pre>
</article>
<article class="doc-entry" id="doc-epotential-point">
<h3><a class="doc-anchor" href="#doc-epotential-point">#</a> <code>epotential_point</code></h3>
<p><code>epotential_point</code> — operation <code>epotential point</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p epotential_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-eps">
<h3><a class="doc-anchor" href="#doc-eps">#</a> <code>eps</code></h3>
<p><code>eps</code> — operation <code>eps</code>. Alias for <code>epsilon</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p eps $x
</code></pre>
</article>
<article class="doc-entry" id="doc-epsilon">
<h3><a class="doc-anchor" href="#doc-epsilon">#</a> <code>epsilon</code></h3>
<p><code>epsilon</code> — operation <code>epsilon</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p epsilon $x
</code></pre>
</article>
<article class="doc-entry" id="doc-epsilon0">
<h3><a class="doc-anchor" href="#doc-epsilon0">#</a> <code>epsilon0</code></h3>
<p><code>vacuum_permittivity</code> (alias <code>epsilon0</code>) — ε₀ ≈ 8.854×10⁻¹² F/m. Electric constant, permittivity of free space.</p>
<pre><code class="lang-perl">p epsilon0 # 8.8541878128e-12
</code></pre>
</article>
<article class="doc-entry" id="doc-epsilon-extinction">
<h3><a class="doc-anchor" href="#doc-epsilon-extinction">#</a> <code>epsilon_extinction</code></h3>
<p><code>epsilon_extinction</code> — operation <code>epsilon extinction</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p epsilon_extinction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-epsilon-greedy-choose">
<h3><a class="doc-anchor" href="#doc-epsilon-greedy-choose">#</a> <code>epsilon_greedy_choose</code></h3>
<p><code>epsilon_greedy_choose(values, epsilon=0.1, seed=0) → int</code> — index of greedy action with probability <code>1-ε</code>, else random.</p>
</article>
<article class="doc-entry" id="doc-eqidx">
<h3><a class="doc-anchor" href="#doc-eqidx">#</a> <code>eqidx</code></h3>
<p><code>eqidx</code> — operation <code>eqidx</code>. Alias for <code>equilibrium_index</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p eqidx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-eqrng">
<h3><a class="doc-anchor" href="#doc-eqrng">#</a> <code>eqrng</code></h3>
<p><code>eqrng</code> — operation <code>eqrng</code>. Alias for <code>equal_range</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p eqrng $x
</code></pre>
</article>
<article class="doc-entry" id="doc-equal-range">
<h3><a class="doc-anchor" href="#doc-equal-range">#</a> <code>equal_range</code></h3>
<p><code>equal_range</code> — operation <code>equal range</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p equal_range $x
</code></pre>
</article>
<article class="doc-entry" id="doc-equal-tempered-freq">
<h3><a class="doc-anchor" href="#doc-equal-tempered-freq">#</a> <code>equal_tempered_freq</code></h3>
<p><code>equal_tempered_freq</code> — operation <code>equal tempered freq</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p equal_tempered_freq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-equation-of-time">
<h3><a class="doc-anchor" href="#doc-equation-of-time">#</a> <code>equation_of_time</code></h3>
<p><code>equation_of_time</code> — operation <code>equation of time</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p equation_of_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-equatorial-to-galactic">
<h3><a class="doc-anchor" href="#doc-equatorial-to-galactic">#</a> <code>equatorial_to_galactic</code></h3>
<p><code>equatorial_to_galactic</code> — convert from <code>equatorial</code> to <code>galactic</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p equatorial_to_galactic $value
</code></pre>
</article>
<article class="doc-entry" id="doc-equilibrium-index">
<h3><a class="doc-anchor" href="#doc-equilibrium-index">#</a> <code>equilibrium_index</code></h3>
<p><code>equilibrium_index</code> — index of <code>equilibrium</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p equilibrium_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-equinox-spring">
<h3><a class="doc-anchor" href="#doc-equinox-spring">#</a> <code>equinox_spring</code></h3>
<p><code>equinox_spring</code> — operation <code>equinox spring</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p equinox_spring $x
</code></pre>
</article>
<article class="doc-entry" id="doc-equirectangular-project">
<h3><a class="doc-anchor" href="#doc-equirectangular-project">#</a> <code>equirectangular_project</code></h3>
<p><code>equirectangular_project</code> — operation <code>equirectangular project</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p equirectangular_project $x
</code></pre>
</article>
<article class="doc-entry" id="doc-equivalent-potential-temp">
<h3><a class="doc-anchor" href="#doc-equivalent-potential-temp">#</a> <code>equivalent_potential_temp</code></h3>
<p><code>equivalent_potential_temp</code> — operation <code>equivalent potential temp</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p equivalent_potential_temp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-era-plus">
<h3><a class="doc-anchor" href="#doc-era-plus">#</a> <code>era_plus</code></h3>
<p><code>era_plus</code> — operation <code>era plus</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p era_plus $x
</code></pre>
</article>
<article class="doc-entry" id="doc-erf-approx">
<h3><a class="doc-anchor" href="#doc-erf-approx">#</a> <code>erf_approx</code></h3>
<p><code>erf_approx($x)</code> — error function. Used in probability, statistics, and partial differential equations.</p>
<pre><code class="lang-perl">p erf(1) # ~0.843
p erf(2) # ~0.995
</code></pre>
</article>
<article class="doc-entry" id="doc-erfcx">
<h3><a class="doc-anchor" href="#doc-erfcx">#</a> <code>erfcx</code></h3>
<p><code>erfcx</code> — operation <code>erfcx</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p erfcx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-erfi">
<h3><a class="doc-anchor" href="#doc-erfi">#</a> <code>erfi</code></h3>
<p><code>erfi</code> — operation <code>erfi</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p erfi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-erosion-2d">
<h3><a class="doc-anchor" href="#doc-erosion-2d">#</a> <code>erosion_2d</code></h3>
<p><code>erosion_2d(image, size=3) → matrix</code> — morphological erosion with <code>size×size</code> structuring element.</p>
<pre><code class="lang-perl">p erosion_2d($binary_img, 3)
</code></pre>
</article>
<article class="doc-entry" id="doc-error-correction-step">
<h3><a class="doc-anchor" href="#doc-error-correction-step">#</a> <code>error_correction_step</code></h3>
<p><code>error_correction_step</code> — single-step update of <code>error correction</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p error_correction_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ertel-pv-step">
<h3><a class="doc-anchor" href="#doc-ertel-pv-step">#</a> <code>ertel_pv_step</code></h3>
<p><code>ertel_pv_step</code> — single-step update of <code>ertel pv</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ertel_pv_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-escape-json">
<h3><a class="doc-anchor" href="#doc-escape-json">#</a> <code>escape_json</code></h3>
<p><code>escape_json</code> — operation <code>escape json</code>. Category: *json helpers*.</p>
<pre><code class="lang-perl">p escape_json $x
</code></pre>
</article>
<article class="doc-entry" id="doc-escape-velocity">
<h3><a class="doc-anchor" href="#doc-escape-velocity">#</a> <code>escape_velocity</code></h3>
<p><code>escape_velocity($mass, $radius)</code> (alias <code>escvel</code>) — minimum velocity to escape gravitational field: v = √(2GM/r). Defaults to Earth values.</p>
<pre><code class="lang-perl">p escvel # ~11186 m/s (Earth)
p escvel(1.989e30, 6.96e8) # ~617 km/s (Sun)
</code></pre>
</article>
<article class="doc-entry" id="doc-escape-velocity-body">
<h3><a class="doc-anchor" href="#doc-escape-velocity-body">#</a> <code>escape_velocity_body</code></h3>
<p><code>escape_velocity_body</code> — operation <code>escape velocity body</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p escape_velocity_body $x
</code></pre>
</article>
<article class="doc-entry" id="doc-eslice">
<h3><a class="doc-anchor" href="#doc-eslice">#</a> <code>eslice</code></h3>
<p><code>eslice</code> — operation <code>eslice</code>. Alias for <code>each_slice</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p eslice $x
</code></pre>
</article>
<article class="doc-entry" id="doc-et-freq-ratio">
<h3><a class="doc-anchor" href="#doc-et-freq-ratio">#</a> <code>et_freq_ratio</code></h3>
<p><code>et_freq_ratio</code> — ratio of <code>et freq</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p et_freq_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-etag-validate">
<h3><a class="doc-anchor" href="#doc-etag-validate">#</a> <code>etag_validate</code></h3>
<p><code>etag_validate</code> — operation <code>etag validate</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p etag_validate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-etd-rk2">
<h3><a class="doc-anchor" href="#doc-etd-rk2">#</a> <code>etd_rk2</code></h3>
<p><code>etd_rk2</code> — operation <code>etd rk2</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p etd_rk2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-eth-addr-check">
<h3><a class="doc-anchor" href="#doc-eth-addr-check">#</a> <code>eth_addr_check</code></h3>
<p><code>eth_addr_check</code> — operation <code>eth addr check</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p eth_addr_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ethiopic-from-fixed">
<h3><a class="doc-anchor" href="#doc-ethiopic-from-fixed">#</a> <code>ethiopic_from_fixed</code></h3>
<p><code>ethiopic_from_fixed</code> — operation <code>ethiopic from fixed</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p ethiopic_from_fixed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-etot">
<h3><a class="doc-anchor" href="#doc-etot">#</a> <code>etot</code></h3>
<p><code>etot</code> — operation <code>etot</code>. Alias for <code>euler_totient</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p etot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-eucdist">
<h3><a class="doc-anchor" href="#doc-eucdist">#</a> <code>eucdist</code></h3>
<p><code>eucdist</code> — operation <code>eucdist</code>. Alias for <code>euclidean_distance</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p eucdist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-euclidean-distance">
<h3><a class="doc-anchor" href="#doc-euclidean-distance">#</a> <code>euclidean_distance</code></h3>
<p><code>euclidean_distance(a, b) → number</code> — L2 distance.</p>
</article>
<article class="doc-entry" id="doc-euclidean-distance-nd">
<h3><a class="doc-anchor" href="#doc-euclidean-distance-nd">#</a> <code>euclidean_distance_nd</code></h3>
<p><code>euclidean_distance_nd</code> — operation <code>euclidean distance nd</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p euclidean_distance_nd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-eui48-to-eui64">
<h3><a class="doc-anchor" href="#doc-eui48-to-eui64">#</a> <code>eui48_to_eui64</code></h3>
<p><code>eui48_to_eui64</code> — convert from <code>eui48</code> to <code>eui64</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p eui48_to_eui64 $value
</code></pre>
</article>
<article class="doc-entry" id="doc-eui64-from-mac">
<h3><a class="doc-anchor" href="#doc-eui64-from-mac">#</a> <code>eui64_from_mac</code></h3>
<p><code>eui64_from_mac</code> — operation <code>eui64 from mac</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p eui64_from_mac $x
</code></pre>
</article>
<article class="doc-entry" id="doc-eui64-to-eui48">
<h3><a class="doc-anchor" href="#doc-eui64-to-eui48">#</a> <code>eui64_to_eui48</code></h3>
<p><code>eui64_to_eui48</code> — convert from <code>eui64</code> to <code>eui48</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p eui64_to_eui48 $value
</code></pre>
</article>
<article class="doc-entry" id="doc-euler-char-complex">
<h3><a class="doc-anchor" href="#doc-euler-char-complex">#</a> <code>euler_char_complex</code></h3>
<p><code>euler_char_complex</code> — operation <code>euler char complex</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p euler_char_complex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-euler-characteristic">
<h3><a class="doc-anchor" href="#doc-euler-characteristic">#</a> <code>euler_characteristic</code></h3>
<p><code>euler_characteristic</code> — operation <code>euler characteristic</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p euler_characteristic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-euler-e">
<h3><a class="doc-anchor" href="#doc-euler-e">#</a> <code>euler_e</code></h3>
<p><code>euler_e</code> — operation <code>euler e</code>. Alias for <code>euler_number</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p euler_e $x
</code></pre>
</article>
<article class="doc-entry" id="doc-euler-lte">
<h3><a class="doc-anchor" href="#doc-euler-lte">#</a> <code>euler_lte</code></h3>
<p><code>euler_lte</code> — operation <code>euler lte</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p euler_lte $x
</code></pre>
</article>
<article class="doc-entry" id="doc-euler-mascheroni">
<h3><a class="doc-anchor" href="#doc-euler-mascheroni">#</a> <code>euler_mascheroni</code></h3>
<p><code>euler_mascheroni</code> (alias <code>gamma_const</code>) — Euler-Mascheroni constant γ ≈ 0.5772. Appears in number theory and analysis.</p>
<pre><code class="lang-perl">p euler_mascheroni # 0.5772156649015329
</code></pre>
</article>
<article class="doc-entry" id="doc-euler-method">
<h3><a class="doc-anchor" href="#doc-euler-method">#</a> <code>euler_method</code></h3>
<p><code>euler_ode</code> (alias <code>euler_method</code>) solves an ODE dy/dt = f(t,y) using the Euler method. Returns [[t,y], ...].</p>
<pre><code class="lang-perl">my $sol = euler_ode(fn { $_[1] }, 0, 1, 0.01, 100) # exponential growth
</code></pre>
</article>
<article class="doc-entry" id="doc-euler-number">
<h3><a class="doc-anchor" href="#doc-euler-number">#</a> <code>euler_number</code></h3>
<p><code>euler_number</code> — operation <code>euler number</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p euler_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-euler-totient">
<h3><a class="doc-anchor" href="#doc-euler-totient">#</a> <code>euler_totient</code></h3>
<p><code>euler_totient</code> — operation <code>euler totient</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p euler_totient $x
</code></pre>
</article>
<article class="doc-entry" id="doc-eulerian-path-q">
<h3><a class="doc-anchor" href="#doc-eulerian-path-q">#</a> <code>eulerian_path_q</code></h3>
<p><code>eulerian_path_q</code> — operation <code>eulerian path q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p eulerian_path_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ev-to-joules">
<h3><a class="doc-anchor" href="#doc-ev-to-joules">#</a> <code>ev_to_joules</code></h3>
<p><code>ev_to_joules</code> — convert from <code>ev</code> to <code>joules</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p ev_to_joules $value
</code></pre>
</article>
<article class="doc-entry" id="doc-eval-rpn">
<h3><a class="doc-anchor" href="#doc-eval-rpn">#</a> <code>eval_rpn</code></h3>
<p><code>eval_rpn</code> — operation <code>eval rpn</code>. Category: *algorithms / puzzles*.</p>
<pre><code class="lang-perl">p eval_rpn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-even">
<h3><a class="doc-anchor" href="#doc-even">#</a> <code>even</code></h3>
<p><code>even</code> — operation <code>even</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p even $x
</code></pre>
</article>
<article class="doc-entry" id="doc-event-horizon-check">
<h3><a class="doc-anchor" href="#doc-event-horizon-check">#</a> <code>event_horizon_check</code></h3>
<p><code>event_horizon_check</code> — operation <code>event horizon check</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p event_horizon_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-every-nth">
<h3><a class="doc-anchor" href="#doc-every-nth">#</a> <code>every_nth</code></h3>
<p><code>every_nth</code> — operation <code>every nth</code>. Category: *collection helpers (trivial)*.</p>
<pre><code class="lang-perl">p every_nth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-evolutionary-stable-strategy">
<h3><a class="doc-anchor" href="#doc-evolutionary-stable-strategy">#</a> <code>evolutionary_stable_strategy</code></h3>
<p><code>evolutionary_stable_strategy</code> — operation <code>evolutionary stable strategy</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p evolutionary_stable_strategy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ew">
<h3><a class="doc-anchor" href="#doc-ew">#</a> <code>ew</code></h3>
<p><code>ew</code> — operation <code>ew</code>. Alias for <code>ends_with</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p ew $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ewma-smooth">
<h3><a class="doc-anchor" href="#doc-ewma-smooth">#</a> <code>ewma_smooth</code></h3>
<p><code>ewma_smooth</code> — operation <code>ewma smooth</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p ewma_smooth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ewo">
<h3><a class="doc-anchor" href="#doc-ewo">#</a> <code>ewo</code></h3>
<p><code>ewo</code> — operation <code>ewo</code>. Alias for <code>each_with_object</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p ewo $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ex-ante-value-check">
<h3><a class="doc-anchor" href="#doc-ex-ante-value-check">#</a> <code>ex_ante_value_check</code></h3>
<p><code>ex_ante_value_check</code> — operation <code>ex ante value check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ex_ante_value_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ex-post-value-check">
<h3><a class="doc-anchor" href="#doc-ex-post-value-check">#</a> <code>ex_post_value_check</code></h3>
<p><code>ex_post_value_check</code> — operation <code>ex post value check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ex_post_value_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-exchange-current-density">
<h3><a class="doc-anchor" href="#doc-exchange-current-density">#</a> <code>exchange_current_density</code></h3>
<p><code>exchange_current_density</code> — operation <code>exchange current density</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p exchange_current_density $x
</code></pre>
</article>
<article class="doc-entry" id="doc-exclude">
<h3><a class="doc-anchor" href="#doc-exclude">#</a> <code>exclude</code></h3>
<p><code>exclude</code> — operation <code>exclude</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p exclude $x
</code></pre>
</article>
<article class="doc-entry" id="doc-exclude-first">
<h3><a class="doc-anchor" href="#doc-exclude-first">#</a> <code>exclude_first</code></h3>
<p><code>exclude_first</code> — operation <code>exclude first</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p exclude_first $x
</code></pre>
</article>
<article class="doc-entry" id="doc-exclude-last">
<h3><a class="doc-anchor" href="#doc-exclude-last">#</a> <code>exclude_last</code></h3>
<p><code>exclude_last</code> — operation <code>exclude last</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p exclude_last $x
</code></pre>
</article>
<article class="doc-entry" id="doc-exe">
<h3><a class="doc-anchor" href="#doc-exe">#</a> <code>exe</code></h3>
<p><code>exe</code> — operation <code>exe</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p exe $x
</code></pre>
</article>
<article class="doc-entry" id="doc-executables">
<h3><a class="doc-anchor" href="#doc-executables">#</a> <code>executables</code></h3>
<p><code>executables</code> — operation <code>executables</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p executables $x
</code></pre>
</article>
<article class="doc-entry" id="doc-exists-key">
<h3><a class="doc-anchor" href="#doc-exists-key">#</a> <code>exists_key</code></h3>
<p><code>exists_key</code> — operation <code>exists key</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p exists_key $x
</code></pre>
</article>
<article class="doc-entry" id="doc-exp2">
<h3><a class="doc-anchor" href="#doc-exp2">#</a> <code>exp2</code></h3>
<p><code>exp2</code> — operation <code>exp2</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p exp2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-exp-euler-step">
<h3><a class="doc-anchor" href="#doc-exp-euler-step">#</a> <code>exp_euler_step</code></h3>
<p><code>exp_euler_step</code> — exponential helper <code>euler step</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p exp_euler_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-exp-golomb-code">
<h3><a class="doc-anchor" href="#doc-exp-golomb-code">#</a> <code>exp_golomb_code</code></h3>
<p><code>exp_golomb_code</code> — exponential helper <code>golomb code</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p exp_golomb_code $x
</code></pre>
</article>
<article class="doc-entry" id="doc-exp-integral-e1">
<h3><a class="doc-anchor" href="#doc-exp-integral-e1">#</a> <code>exp_integral_e1</code></h3>
<p><code>exp_integral_e1</code> — exponential helper <code>integral e1</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p exp_integral_e1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-exp-smooth-double">
<h3><a class="doc-anchor" href="#doc-exp-smooth-double">#</a> <code>exp_smooth_double</code></h3>
<p><code>exp_smooth_double</code> — exponential helper <code>smooth double</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p exp_smooth_double $x
</code></pre>
</article>
<article class="doc-entry" id="doc-exp-smooth-simple">
<h3><a class="doc-anchor" href="#doc-exp-smooth-simple">#</a> <code>exp_smooth_simple</code></h3>
<p><code>exp_smooth_simple</code> — exponential helper <code>smooth simple</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p exp_smooth_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-expanding-mean">
<h3><a class="doc-anchor" href="#doc-expanding-mean">#</a> <code>expanding_mean</code></h3>
<p><code>expanding_mean(series) → array</code> — cumulative running mean; output[i] is mean of x[0..=i].</p>
<pre><code class="lang-perl">p expanding_mean([1,2,3,4]) # [1.0, 1.5, 2.0, 2.5]
</code></pre>
</article>
<article class="doc-entry" id="doc-expanding-sum">
<h3><a class="doc-anchor" href="#doc-expanding-sum">#</a> <code>expanding_sum</code></h3>
<p><code>expanding_sum(series) → array</code> — cumulative running sum.</p>
</article>
<article class="doc-entry" id="doc-expansion-scalar-step">
<h3><a class="doc-anchor" href="#doc-expansion-scalar-step">#</a> <code>expansion_scalar_step</code></h3>
<p><code>expansion_scalar_step</code> — single-step update of <code>expansion scalar</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p expansion_scalar_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-expected-coverage">
<h3><a class="doc-anchor" href="#doc-expected-coverage">#</a> <code>expected_coverage</code></h3>
<p><code>expected_coverage</code> — operation <code>expected coverage</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p expected_coverage $x
</code></pre>
</article>
<article class="doc-entry" id="doc-expectiminimax-value">
<h3><a class="doc-anchor" href="#doc-expectiminimax-value">#</a> <code>expectiminimax_value</code></h3>
<p><code>expectiminimax_value(leaves, depth, chance_prob=0.5) → number</code> — minimax with intervening chance nodes (max → min → chance, repeating).</p>
</article>
<article class="doc-entry" id="doc-expenditure-function">
<h3><a class="doc-anchor" href="#doc-expenditure-function">#</a> <code>expenditure_function</code></h3>
<p><code>expenditure_function</code> — operation <code>expenditure function</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p expenditure_function $x
</code></pre>
</article>
<article class="doc-entry" id="doc-experience-factor">
<h3><a class="doc-anchor" href="#doc-experience-factor">#</a> <code>experience_factor</code></h3>
<p><code>experience_factor</code> — factor of <code>experience</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p experience_factor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-expint">
<h3><a class="doc-anchor" href="#doc-expint">#</a> <code>expint</code></h3>
<p><code>expint(n, x) → number</code> — generalised exponential integral <code>E_n(x) = ∫_1^∞ e^(-xt)/t^n dt</code>.</p>
<pre><code class="lang-perl">p expint(1, 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-expire">
<h3><a class="doc-anchor" href="#doc-expire">#</a> <code>expire</code></h3>
<p><code>expire</code> — operation <code>expire</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p expire $x
</code></pre>
</article>
<article class="doc-entry" id="doc-explore-exploit-epsilon">
<h3><a class="doc-anchor" href="#doc-explore-exploit-epsilon">#</a> <code>explore_exploit_epsilon</code></h3>
<p><code>explore_exploit_epsilon</code> — operation <code>explore exploit epsilon</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p explore_exploit_epsilon $x
</code></pre>
</article>
<article class="doc-entry" id="doc-exponential-moving-average">
<h3><a class="doc-anchor" href="#doc-exponential-moving-average">#</a> <code>exponential_moving_average</code></h3>
<p><code>exponential_moving_average</code> — operation <code>exponential moving average</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p exponential_moving_average $x
</code></pre>
</article>
<article class="doc-entry" id="doc-exponential-pdf">
<h3><a class="doc-anchor" href="#doc-exponential-pdf">#</a> <code>exponential_pdf</code></h3>
<p><code>exponential_pdf</code> — operation <code>exponential pdf</code>. Category: *math formulas*.</p>
<pre><code class="lang-perl">p exponential_pdf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-exponential-search">
<h3><a class="doc-anchor" href="#doc-exponential-search">#</a> <code>exponential_search</code></h3>
<p><code>exponential_search(sorted, target) → int</code> — doubles the range until target is bracketed, then binary-search. Good for unbounded streams.</p>
</article>
<article class="doc-entry" id="doc-exposure-value">
<h3><a class="doc-anchor" href="#doc-exposure-value">#</a> <code>exposure_value</code></h3>
<p><code>exposure_value(aperture, shutter, iso=100) → number</code> — EV = log₂(N² / t · 100/ISO).</p>
<pre><code class="lang-perl">p exposure_value(8, 1/250, 100)
</code></pre>
</article>
<article class="doc-entry" id="doc-exppdf">
<h3><a class="doc-anchor" href="#doc-exppdf">#</a> <code>exppdf</code></h3>
<p><code>exppdf</code> — operation <code>exppdf</code>. Alias for <code>exponential_pdf</code>. Category: *math formulas*.</p>
<pre><code class="lang-perl">p exppdf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-extended-gcd">
<h3><a class="doc-anchor" href="#doc-extended-gcd">#</a> <code>extended_gcd</code></h3>
<p><code>extended_gcd</code> — operation <code>extended gcd</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p extended_gcd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-extends">
<h3><a class="doc-anchor" href="#doc-extends">#</a> <code>extends</code></h3>
<p><code>extends</code> specifies parent classes for inheritance. Child classes inherit all fields and methods from parents.</p>
<pre><code class="lang-perl">class Animal { name: Str }
class Dog extends Animal { breed: Str }
class Hybrid extends Dog, Cat { } # multiple inheritance
</code></pre>
<p>Inherited fields appear first in construction order. Methods are resolved child-first (override pattern).</p>
</article>
<article class="doc-entry" id="doc-exterior-derivative-one-form">
<h3><a class="doc-anchor" href="#doc-exterior-derivative-one-form">#</a> <code>exterior_derivative_one_form</code></h3>
<p><code>exterior_derivative_one_form</code> — operation <code>exterior derivative one form</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p exterior_derivative_one_form $x
</code></pre>
</article>
<article class="doc-entry" id="doc-extract-between">
<h3><a class="doc-anchor" href="#doc-extract-between">#</a> <code>extract_between</code></h3>
<p><code>extract_between</code> — operation <code>extract between</code>. Category: *string quote / escape*.</p>
<pre><code class="lang-perl">p extract_between $x
</code></pre>
</article>
<article class="doc-entry" id="doc-extrinsic-principal-curv">
<h3><a class="doc-anchor" href="#doc-extrinsic-principal-curv">#</a> <code>extrinsic_principal_curv</code></h3>
<p><code>extrinsic_principal_curv</code> — operation <code>extrinsic principal curv</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p extrinsic_principal_curv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-eye">
<h3><a class="doc-anchor" href="#doc-eye">#</a> <code>eye</code></h3>
<p><code>eye</code> — operation <code>eye</code>. Alias for <code>identity_matrix</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p eye $x
</code></pre>
</article>
<article class="doc-entry" id="doc-eyring-k">
<h3><a class="doc-anchor" href="#doc-eyring-k">#</a> <code>eyring_k</code></h3>
<p><code>eyring_k</code> — operation <code>eyring k</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p eyring_k $x
</code></pre>
</article>
<article class="doc-entry" id="doc-eyring-rate">
<h3><a class="doc-anchor" href="#doc-eyring-rate">#</a> <code>eyring_rate</code></h3>
<p><code>eyring_rate</code> — rate of <code>eyring</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p eyring_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-f">
<h3><a class="doc-anchor" href="#doc-f">#</a> <code>f</code></h3>
<p><code>f</code> — operation <code>f</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p f $x
</code></pre>
</article>
<article class="doc-entry" id="doc-f64-max">
<h3><a class="doc-anchor" href="#doc-f64-max">#</a> <code>f64_max</code></h3>
<p><code>f64_max</code> — maximum of <code>f64</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p f64_max $x
</code></pre>
</article>
<article class="doc-entry" id="doc-f64-min">
<h3><a class="doc-anchor" href="#doc-f64-min">#</a> <code>f64_min</code></h3>
<p><code>f64_min</code> — minimum of <code>f64</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p f64_min $x
</code></pre>
</article>
<article class="doc-entry" id="doc-f-beta">
<h3><a class="doc-anchor" href="#doc-f-beta">#</a> <code>f_beta</code></h3>
<p><code>f_beta</code> — operation <code>f beta</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p f_beta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-f-pdf">
<h3><a class="doc-anchor" href="#doc-f-pdf">#</a> <code>f_pdf</code></h3>
<p><code>f_pdf</code> (alias <code>fpdf</code>) evaluates the F-distribution PDF at x with d1 and d2 degrees of freedom.</p>
<pre><code class="lang-perl">p fpdf(1.0, 5, 10)
</code></pre>
</article>
<article class="doc-entry" id="doc-f-statistic-pooled">
<h3><a class="doc-anchor" href="#doc-f-statistic-pooled">#</a> <code>f_statistic_pooled</code></h3>
<p><code>f_statistic_pooled</code> — operation <code>f statistic pooled</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p f_statistic_pooled $x
</code></pre>
</article>
<article class="doc-entry" id="doc-f-to-c">
<h3><a class="doc-anchor" href="#doc-f-to-c">#</a> <code>f_to_c</code></h3>
<p><code>f_to_c</code> — convert from <code>f</code> to <code>c</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p f_to_c $value
</code></pre>
</article>
<article class="doc-entry" id="doc-f-to-k">
<h3><a class="doc-anchor" href="#doc-f-to-k">#</a> <code>f_to_k</code></h3>
<p><code>f_to_k</code> — convert from <code>f</code> to <code>k</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p f_to_k $value
</code></pre>
</article>
<article class="doc-entry" id="doc-face-detect-haar">
<h3><a class="doc-anchor" href="#doc-face-detect-haar">#</a> <code>face_detect_haar</code></h3>
<p><code>face_detect_haar</code> — operation <code>face detect haar</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p face_detect_haar $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fact">
<h3><a class="doc-anchor" href="#doc-fact">#</a> <code>fact</code></h3>
<p><code>fact</code> — operation <code>fact</code>. Alias for <code>factorial</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p fact $x
</code></pre>
</article>
<article class="doc-entry" id="doc-factorial">
<h3><a class="doc-anchor" href="#doc-factorial">#</a> <code>factorial</code></h3>
<p><code>factorial</code> — operation <code>factorial</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p factorial $x
</code></pre>
</article>
<article class="doc-entry" id="doc-factorial2">
<h3><a class="doc-anchor" href="#doc-factorial2">#</a> <code>factorial2</code></h3>
<p><code>factorial2</code> — operation <code>factorial2</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p factorial2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-factorialk">
<h3><a class="doc-anchor" href="#doc-factorialk">#</a> <code>factorialk</code></h3>
<p><code>factorialk</code> — operation <code>factorialk</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p factorialk $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fade-curve-exponential">
<h3><a class="doc-anchor" href="#doc-fade-curve-exponential">#</a> <code>fade_curve_exponential</code></h3>
<p><code>fade_curve_exponential</code> — operation <code>fade curve exponential</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p fade_curve_exponential $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fade-curve-linear">
<h3><a class="doc-anchor" href="#doc-fade-curve-linear">#</a> <code>fade_curve_linear</code></h3>
<p><code>fade_curve_linear</code> — operation <code>fade curve linear</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p fade_curve_linear $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fade-curve-logarithmic">
<h3><a class="doc-anchor" href="#doc-fade-curve-logarithmic">#</a> <code>fade_curve_logarithmic</code></h3>
<p><code>fade_curve_logarithmic</code> — operation <code>fade curve logarithmic</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p fade_curve_logarithmic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-faf">
<h3><a class="doc-anchor" href="#doc-faf">#</a> <code>faf</code></h3>
<p><code>faf</code> — operation <code>faf</code>. Alias for <code>fire_and_forget</code>. Category: *stress testing*.</p>
<pre><code class="lang-perl">p faf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fair-division-envy-free">
<h3><a class="doc-anchor" href="#doc-fair-division-envy-free">#</a> <code>fair_division_envy_free</code></h3>
<p><code>fair_division_envy_free</code> — release / destroy of <code>fair division envy</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p fair_division_envy_free $x
</code></pre>
</article>
<article class="doc-entry" id="doc-falf">
<h3><a class="doc-anchor" href="#doc-falf">#</a> <code>falf</code></h3>
<p><code>falf</code> — operation <code>falf</code>. Alias for <code>filterfalse</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p falf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fallback">
<h3><a class="doc-anchor" href="#doc-fallback">#</a> <code>fallback</code></h3>
<p><code>fallback</code> — operation <code>fallback</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p fallback $x
</code></pre>
</article>
<article class="doc-entry" id="doc-falling-factorial">
<h3><a class="doc-anchor" href="#doc-falling-factorial">#</a> <code>falling_factorial</code></h3>
<p><code>falling_factorial</code> — operation <code>falling factorial</code>. Category: *math formulas*.</p>
<pre><code class="lang-perl">p falling_factorial $x
</code></pre>
</article>
<article class="doc-entry" id="doc-false-position">
<h3><a class="doc-anchor" href="#doc-false-position">#</a> <code>false_position</code></h3>
<p><code>false_position</code> — operation <code>false position</code>. Alias for <code>regula_falsi</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p false_position $x
</code></pre>
</article>
<article class="doc-entry" id="doc-falsy-count">
<h3><a class="doc-anchor" href="#doc-falsy-count">#</a> <code>falsy_count</code></h3>
<p><code>falsy_count</code> — count of <code>falsy</code>. Category: *counters*.</p>
<pre><code class="lang-perl">p falsy_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fano-inequality-bound">
<h3><a class="doc-anchor" href="#doc-fano-inequality-bound">#</a> <code>fano_inequality_bound</code></h3>
<p><code>fano_inequality_bound</code> — operation <code>fano inequality bound</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p fano_inequality_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-faradaic-efficiency">
<h3><a class="doc-anchor" href="#doc-faradaic-efficiency">#</a> <code>faradaic_efficiency</code></h3>
<p><code>faradaic_efficiency</code> — operation <code>faradaic efficiency</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p faradaic_efficiency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-faraday">
<h3><a class="doc-anchor" href="#doc-faraday">#</a> <code>faraday</code></h3>
<p><code>faraday_constant</code> (alias <code>faraday</code>) — F ≈ 96485 C/mol. Charge per mole of electrons.</p>
<pre><code class="lang-perl">p faraday # 96485.33212
</code></pre>
</article>
<article class="doc-entry" id="doc-faraday-efficiency-h2">
<h3><a class="doc-anchor" href="#doc-faraday-efficiency-h2">#</a> <code>faraday_efficiency_h2</code></h3>
<p><code>faraday_efficiency_h2</code> — operation <code>faraday efficiency h2</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p faraday_efficiency_h2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-faraday-emf">
<h3><a class="doc-anchor" href="#doc-faraday-emf">#</a> <code>faraday_emf</code></h3>
<p><code>faraday_emf</code> — operation <code>faraday emf</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p faraday_emf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-faraday-mass-deposited">
<h3><a class="doc-anchor" href="#doc-faraday-mass-deposited">#</a> <code>faraday_mass_deposited</code></h3>
<p><code>faraday_mass_deposited</code> — operation <code>faraday mass deposited</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p faraday_mass_deposited $x
</code></pre>
</article>
<article class="doc-entry" id="doc-farmhash-64">
<h3><a class="doc-anchor" href="#doc-farmhash-64">#</a> <code>farmhash_64</code></h3>
<p><code>farmhash_64</code> — operation <code>farmhash 64</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p farmhash_64 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-farthest-insertion-step">
<h3><a class="doc-anchor" href="#doc-farthest-insertion-step">#</a> <code>farthest_insertion_step</code></h3>
<p><code>farthest_insertion_step</code> — single-step update of <code>farthest insertion</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p farthest_insertion_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fb">
<h3><a class="doc-anchor" href="#doc-fb">#</a> <code>fb</code></h3>
<p><code>fb</code> — operation <code>fb</code>. Alias for <code>fizzbuzz</code>. Category: *algorithms / puzzles*.</p>
<pre><code class="lang-perl">p fb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fbm-noise-2d">
<h3><a class="doc-anchor" href="#doc-fbm-noise-2d">#</a> <code>fbm_noise_2d</code></h3>
<p><code>fbm_noise_2d(x, y, octaves=4, lacunarity=2, gain=0.5) → number</code> — fractional Brownian motion: sum of octaves of Perlin noise.</p>
</article>
<article class="doc-entry" id="doc-fcntl">
<h3><a class="doc-anchor" href="#doc-fcntl">#</a> <code>fcntl</code></h3>
<p><code>fcntl</code> — operation <code>fcntl</code>. Category: *ipc*.</p>
<pre><code class="lang-perl">p fcntl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fcp">
<h3><a class="doc-anchor" href="#doc-fcp">#</a> <code>fcp</code></h3>
<p><code>fcp</code> — operation <code>fcp</code>. Alias for <code>from_code_point</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p fcp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fdivop">
<h3><a class="doc-anchor" href="#doc-fdivop">#</a> <code>fdivop</code></h3>
<p><code>fdivop</code> — operation <code>fdivop</code>. Alias for <code>floor_div_op</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p fdivop $x
</code></pre>
</article>
<article class="doc-entry" id="doc-feet-to-m">
<h3><a class="doc-anchor" href="#doc-feet-to-m">#</a> <code>feet_to_m</code></h3>
<p><code>feet_to_m</code> — convert from <code>feet</code> to <code>m</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p feet_to_m $value
</code></pre>
</article>
<article class="doc-entry" id="doc-feet-to-meters">
<h3><a class="doc-anchor" href="#doc-feet-to-meters">#</a> <code>feet_to_meters</code></h3>
<p><code>feet_to_meters</code> — convert from <code>feet</code> to <code>meters</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p feet_to_meters $value
</code></pre>
</article>
<article class="doc-entry" id="doc-feiga">
<h3><a class="doc-anchor" href="#doc-feiga">#</a> <code>feiga</code></h3>
<p><code>feiga</code> — operation <code>feiga</code>. Alias for <code>feigenbaum_alpha</code>. Category: *math constants*.</p>
<pre><code class="lang-perl">p feiga $x
</code></pre>
</article>
<article class="doc-entry" id="doc-feigd">
<h3><a class="doc-anchor" href="#doc-feigd">#</a> <code>feigd</code></h3>
<p><code>feigenbaum_delta</code> (alias <code>feigd</code>) — Feigenbaum constant δ ≈ 4.669. Universal constant in chaos theory.</p>
<pre><code class="lang-perl">p feigd # 4.669201609102990
</code></pre>
</article>
<article class="doc-entry" id="doc-feigenbaum-alpha">
<h3><a class="doc-anchor" href="#doc-feigenbaum-alpha">#</a> <code>feigenbaum_alpha</code></h3>
<p><code>feigenbaum_alpha</code> — operation <code>feigenbaum alpha</code>. Category: *math constants*.</p>
<pre><code class="lang-perl">p feigenbaum_alpha $x
</code></pre>
</article>
<article class="doc-entry" id="doc-feldspar-classify">
<h3><a class="doc-anchor" href="#doc-feldspar-classify">#</a> <code>feldspar_classify</code></h3>
<p><code>feldspar_classify</code> — operation <code>feldspar classify</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p feldspar_classify $x
</code></pre>
</article>
<article class="doc-entry" id="doc-felsenstein-step">
<h3><a class="doc-anchor" href="#doc-felsenstein-step">#</a> <code>felsenstein_step</code></h3>
<p><code>felsenstein_step</code> — single-step update of <code>felsenstein</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p felsenstein_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-felzenszwalb-segment">
<h3><a class="doc-anchor" href="#doc-felzenszwalb-segment">#</a> <code>felzenszwalb_segment</code></h3>
<p><code>felzenszwalb_segment</code> — operation <code>felzenszwalb segment</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p felzenszwalb_segment $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fenwick-build">
<h3><a class="doc-anchor" href="#doc-fenwick-build">#</a> <code>fenwick_build</code></h3>
<p><code>fenwick_build</code> — Fenwick (binary indexed) tree op <code>build</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p fenwick_build $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fenwick-for">
<h3><a class="doc-anchor" href="#doc-fenwick-for">#</a> <code>fenwick_for</code></h3>
<p><code>fenwick_for</code> — Fenwick (binary indexed) tree op <code>for</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p fenwick_for $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fenwick-new">
<h3><a class="doc-anchor" href="#doc-fenwick-new">#</a> <code>fenwick_new</code></h3>
<p><code>fenwick_new(n) → array</code> — Fenwick (BIT) tree of size <code>n</code>, all zeros. 1-indexed.</p>
</article>
<article class="doc-entry" id="doc-fenwick-query">
<h3><a class="doc-anchor" href="#doc-fenwick-query">#</a> <code>fenwick_query</code></h3>
<p><code>fenwick_query</code> — Fenwick (binary indexed) tree op <code>query</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p fenwick_query $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fenwick-query-prefix">
<h3><a class="doc-anchor" href="#doc-fenwick-query-prefix">#</a> <code>fenwick_query_prefix</code></h3>
<p><code>fenwick_query_prefix(tree, idx) → int</code> — sum of [1..idx].</p>
</article>
<article class="doc-entry" id="doc-fenwick-query-range">
<h3><a class="doc-anchor" href="#doc-fenwick-query-range">#</a> <code>fenwick_query_range</code></h3>
<p><code>fenwick_query_range(tree, l, r) → int</code> — sum of [l..r].</p>
</article>
<article class="doc-entry" id="doc-fenwick-update">
<h3><a class="doc-anchor" href="#doc-fenwick-update">#</a> <code>fenwick_update</code></h3>
<p><code>fenwick_update(tree, idx, delta) → array</code> — add <code>delta</code> to position <code>idx</code> (1-indexed).</p>
<pre><code class="lang-perl">my $f = fenwick_new(10)
$f = fenwick_update($f, 3, 5)
</code></pre>
</article>
<article class="doc-entry" id="doc-fermat-factor">
<h3><a class="doc-anchor" href="#doc-fermat-factor">#</a> <code>fermat_factor</code></h3>
<p><code>fermat_factor</code> — factor of <code>fermat</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p fermat_factor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fermi-dirac-int">
<h3><a class="doc-anchor" href="#doc-fermi-dirac-int">#</a> <code>fermi_dirac_int</code></h3>
<p><code>fermi_dirac_int</code> — operation <code>fermi dirac int</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p fermi_dirac_int $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fermi-golden-rule">
<h3><a class="doc-anchor" href="#doc-fermi-golden-rule">#</a> <code>fermi_golden_rule</code></h3>
<p><code>fermi_golden_rule</code> — operation <code>fermi golden rule</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p fermi_golden_rule $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fermi-normal-step">
<h3><a class="doc-anchor" href="#doc-fermi-normal-step">#</a> <code>fermi_normal_step</code></h3>
<p><code>fermi_normal_step</code> — single-step update of <code>fermi normal</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p fermi_normal_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ferrel-cell-step">
<h3><a class="doc-anchor" href="#doc-ferrel-cell-step">#</a> <code>ferrel_cell_step</code></h3>
<p><code>ferrel_cell_step</code> — single-step update of <code>ferrel cell</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ferrel_cell_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fetch-val">
<h3><a class="doc-anchor" href="#doc-fetch-val">#</a> <code>fetch_val</code></h3>
<p><code>fetch_val</code> — operation <code>fetch val</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p fetch_val $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ffact">
<h3><a class="doc-anchor" href="#doc-ffact">#</a> <code>ffact</code></h3>
<p><code>ffact</code> — operation <code>ffact</code>. Alias for <code>falling_factorial</code>. Category: *math formulas*.</p>
<pre><code class="lang-perl">p ffact $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ffirst">
<h3><a class="doc-anchor" href="#doc-ffirst">#</a> <code>ffirst</code></h3>
<p><code>ffirst</code> — operation <code>ffirst</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p ffirst $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ffs">
<h3><a class="doc-anchor" href="#doc-ffs">#</a> <code>ffs</code></h3>
<p><code>ffs</code> — operation <code>ffs</code>. Alias for <code>ffirst</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p ffs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fft-magnitude">
<h3><a class="doc-anchor" href="#doc-fft-magnitude">#</a> <code>fft_magnitude</code></h3>
<p><code>fft_magnitude</code> — Fast Fourier Transform helper <code>magnitude</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p fft_magnitude $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fftconvolve-step">
<h3><a class="doc-anchor" href="#doc-fftconvolve-step">#</a> <code>fftconvolve_step</code></h3>
<p><code>fftconvolve_step</code> — single-step update of <code>fftconvolve</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p fftconvolve_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fftmag">
<h3><a class="doc-anchor" href="#doc-fftmag">#</a> <code>fftmag</code></h3>
<p><code>fftmag</code> — operation <code>fftmag</code>. Alias for <code>fft_magnitude</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p fftmag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fib">
<h3><a class="doc-anchor" href="#doc-fib">#</a> <code>fib</code></h3>
<p><code>fib</code> — operation <code>fib</code>. Alias for <code>fibonacci</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p fib $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fibonacci">
<h3><a class="doc-anchor" href="#doc-fibonacci">#</a> <code>fibonacci</code></h3>
<p><code>fibonacci</code> — operation <code>fibonacci</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p fibonacci $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fibonacci-code">
<h3><a class="doc-anchor" href="#doc-fibonacci-code">#</a> <code>fibonacci_code</code></h3>
<p><code>fibonacci_code</code> — operation <code>fibonacci code</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p fibonacci_code $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fibonacci-extension">
<h3><a class="doc-anchor" href="#doc-fibonacci-extension">#</a> <code>fibonacci_extension</code></h3>
<p><code>fibonacci_extension(high, low) → array</code> — extension targets at 127.2%, 161.8%, 261.8% beyond the retracement zone.</p>
<pre><code class="lang-perl">p fibonacci_extension(20, 10)
</code></pre>
</article>
<article class="doc-entry" id="doc-fibonacci-matrix">
<h3><a class="doc-anchor" href="#doc-fibonacci-matrix">#</a> <code>fibonacci_matrix</code></h3>
<p><code>fibonacci_matrix(n) → int</code> — n-th Fibonacci number via matrix exponentiation. O(log n).</p>
<pre><code class="lang-perl">p fibonacci_matrix(10) # 55
</code></pre>
</article>
<article class="doc-entry" id="doc-fibonacci-nth-fast">
<h3><a class="doc-anchor" href="#doc-fibonacci-nth-fast">#</a> <code>fibonacci_nth_fast</code></h3>
<p><code>fibonacci_nth_fast</code> — operation <code>fibonacci nth fast</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p fibonacci_nth_fast $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fibonacci-retracement">
<h3><a class="doc-anchor" href="#doc-fibonacci-retracement">#</a> <code>fibonacci_retracement</code></h3>
<p><code>fibonacci_retracement(high, low) → array</code> — seven retracement prices <code>[high, 76.4%, 61.8%, 50%, 38.2%, 23.6%, low]</code>.</p>
<pre><code class="lang-perl">p fibonacci_retracement(20, 10)
</code></pre>
</article>
<article class="doc-entry" id="doc-fibonacci-seq">
<h3><a class="doc-anchor" href="#doc-fibonacci-seq">#</a> <code>fibonacci_seq</code></h3>
<p><code>fibonacci_seq</code> — operation <code>fibonacci seq</code>. Category: *sequences*.</p>
<pre><code class="lang-perl">p fibonacci_seq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fibonacci-word">
<h3><a class="doc-anchor" href="#doc-fibonacci-word">#</a> <code>fibonacci_word</code></h3>
<p><code>fibonacci_word</code> — operation <code>fibonacci word</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p fibonacci_word $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fictitious-play-step">
<h3><a class="doc-anchor" href="#doc-fictitious-play-step">#</a> <code>fictitious_play_step</code></h3>
<p><code>fictitious_play_step</code> — single-step update of <code>fictitious play</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p fictitious_play_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fidelity-pure-real">
<h3><a class="doc-anchor" href="#doc-fidelity-pure-real">#</a> <code>fidelity_pure_real</code></h3>
<p><code>fidelity_pure_real</code> — operation <code>fidelity pure real</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p fidelity_pure_real $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fidx">
<h3><a class="doc-anchor" href="#doc-fidx">#</a> <code>fidx</code></h3>
<p><code>fidx</code> — operation <code>fidx</code>. Alias for <code>find_index_fn</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p fidx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-field-of-view">
<h3><a class="doc-anchor" href="#doc-field-of-view">#</a> <code>field_of_view</code></h3>
<p><code>field_of_view(focal_mm, sensor_dim_mm=36) → number</code> — angular FOV in degrees.</p>
<pre><code class="lang-perl">p field_of_view(50, 36) # ~39.6°
</code></pre>
</article>
<article class="doc-entry" id="doc-file-acl-get">
<h3><a class="doc-anchor" href="#doc-file-acl-get">#</a> <code>file_acl_get</code></h3>
<p><code>file_acl_get</code> — filesystem op <code>acl get</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p file_acl_get $x
</code></pre>
</article>
<article class="doc-entry" id="doc-file-acl-set">
<h3><a class="doc-anchor" href="#doc-file-acl-set">#</a> <code>file_acl_set</code></h3>
<p><code>file_acl_set</code> — filesystem op <code>acl set</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p file_acl_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-file-atime">
<h3><a class="doc-anchor" href="#doc-file-atime">#</a> <code>file_atime</code></h3>
<p><code>file_atime</code> — filesystem op <code>atime</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p file_atime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-file-attr-get">
<h3><a class="doc-anchor" href="#doc-file-attr-get">#</a> <code>file_attr_get</code></h3>
<p><code>file_attr_get(path) → hash</code> — filesystem attributes (size, mtime, mode, …).</p>
</article>
<article class="doc-entry" id="doc-file-attr-set">
<h3><a class="doc-anchor" href="#doc-file-attr-set">#</a> <code>file_attr_set</code></h3>
<p><code>file_attr_set</code> — filesystem op <code>attr set</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p file_attr_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-file-chmod-octal">
<h3><a class="doc-anchor" href="#doc-file-chmod-octal">#</a> <code>file_chmod_octal</code></h3>
<p><code>file_chmod_octal(path, mode) → 0|1</code> — chmod with octal mode (e.g., 0o755).</p>
</article>
<article class="doc-entry" id="doc-file-chmod-string">
<h3><a class="doc-anchor" href="#doc-file-chmod-string">#</a> <code>file_chmod_string</code></h3>
<p><code>file_chmod_string(path, spec) → 0|1</code> — chmod with symbolic spec ("u+x").</p>
</article>
<article class="doc-entry" id="doc-file-ctime">
<h3><a class="doc-anchor" href="#doc-file-ctime">#</a> <code>file_ctime</code></h3>
<p><code>file_ctime</code> — filesystem op <code>ctime</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p file_ctime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-file-kind">
<h3><a class="doc-anchor" href="#doc-file-kind">#</a> <code>file_kind</code></h3>
<p><code>file_kind(path) → string</code> — "file", "dir", "symlink", "socket", "fifo", "block", "char".</p>
</article>
<article class="doc-entry" id="doc-file-locked">
<h3><a class="doc-anchor" href="#doc-file-locked">#</a> <code>file_locked</code></h3>
<p><code>file_locked(path) → 0|1</code> — 1 if an advisory lock is held.</p>
</article>
<article class="doc-entry" id="doc-file-mime">
<h3><a class="doc-anchor" href="#doc-file-mime">#</a> <code>file_mime</code></h3>
<p><code>file_mime(path) → string</code> — guess MIME type by content sniffing + extension.</p>
<pre><code class="lang-perl">p file_mime("photo.jpg") # "image/jpeg"
</code></pre>
</article>
<article class="doc-entry" id="doc-file-mtime">
<h3><a class="doc-anchor" href="#doc-file-mtime">#</a> <code>file_mtime</code></h3>
<p><code>file_mtime</code> — filesystem op <code>mtime</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p file_mtime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-file-size">
<h3><a class="doc-anchor" href="#doc-file-size">#</a> <code>file_size</code></h3>
<p><code>file_size</code> — filesystem op <code>size</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p file_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-files">
<h3><a class="doc-anchor" href="#doc-files">#</a> <code>files</code></h3>
<p><code>files</code> — operation <code>files</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p files $x
</code></pre>
</article>
<article class="doc-entry" id="doc-filesf">
<h3><a class="doc-anchor" href="#doc-filesf">#</a> <code>filesf</code></h3>
<p><code>filesf</code> — operation <code>filesf</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p filesf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fill-arr">
<h3><a class="doc-anchor" href="#doc-fill-arr">#</a> <code>fill_arr</code></h3>
<p><code>fill_arr</code> — operation <code>fill arr</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p fill_arr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-filla">
<h3><a class="doc-anchor" href="#doc-filla">#</a> <code>filla</code></h3>
<p><code>filla</code> — operation <code>filla</code>. Alias for <code>fill_arr</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p filla $x
</code></pre>
</article>
<article class="doc-entry" id="doc-filter-bilateral">
<h3><a class="doc-anchor" href="#doc-filter-bilateral">#</a> <code>filter_bilateral</code></h3>
<p><code>filter_bilateral</code> — signal-filtering op <code>bilateral</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p filter_bilateral $x
</code></pre>
</article>
<article class="doc-entry" id="doc-filter-chars">
<h3><a class="doc-anchor" href="#doc-filter-chars">#</a> <code>filter_chars</code></h3>
<p><code>filter_chars</code> — signal-filtering op <code>chars</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p filter_chars $x
</code></pre>
</article>
<article class="doc-entry" id="doc-filter-indexed">
<h3><a class="doc-anchor" href="#doc-filter-indexed">#</a> <code>filter_indexed</code></h3>
<p><code>filter_indexed</code> — signal-filtering op <code>indexed</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p filter_indexed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-filter-map">
<h3><a class="doc-anchor" href="#doc-filter-map">#</a> <code>filter_map</code></h3>
<p><code>filter_map</code> — signal-filtering op <code>map</code>. Category: *rust iterator methods*.</p>
<pre><code class="lang-perl">p filter_map $x
</code></pre>
</article>
<article class="doc-entry" id="doc-filter-median">
<h3><a class="doc-anchor" href="#doc-filter-median">#</a> <code>filter_median</code></h3>
<p><code>filter_median</code> — signal-filtering op <code>median</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p filter_median @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-filter-nlmeans">
<h3><a class="doc-anchor" href="#doc-filter-nlmeans">#</a> <code>filter_nlmeans</code></h3>
<p><code>filter_nlmeans</code> — signal-filtering op <code>nlmeans</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p filter_nlmeans $x
</code></pre>
</article>
<article class="doc-entry" id="doc-filter-ts">
<h3><a class="doc-anchor" href="#doc-filter-ts">#</a> <code>filter_ts</code></h3>
<p><code>ts_filter</code> — linear convolution filter. Like R's filter(method='convolution').</p>
<pre><code class="lang-perl">my @smooth = @{ts_filter([1,5,2,8,3], [0.25,0.5,0.25])}
</code></pre>
</article>
<article class="doc-entry" id="doc-filterfalse">
<h3><a class="doc-anchor" href="#doc-filterfalse">#</a> <code>filterfalse</code></h3>
<p><code>filterfalse</code> — operation <code>filterfalse</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p filterfalse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-filtfilt-pad">
<h3><a class="doc-anchor" href="#doc-filtfilt-pad">#</a> <code>filtfilt_pad</code></h3>
<p><code>filtfilt_pad</code> — operation <code>filtfilt pad</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p filtfilt_pad $x
</code></pre>
</article>
<article class="doc-entry" id="doc-find">
<h3><a class="doc-anchor" href="#doc-find">#</a> <code>find</code></h3>
<p><code>find</code> — operation <code>find</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p find $x
</code></pre>
</article>
<article class="doc-entry" id="doc-findinterval">
<h3><a class="doc-anchor" href="#doc-findinterval">#</a> <code>findInterval</code></h3>
<p><code>find_interval</code> — for each x, find which interval in breaks it falls into. Like R's findInterval().</p>
<pre><code class="lang-perl">p findInterval([1.5, 3.5, 7.5], [0, 2, 5, 10]) # [1, 2, 3]
</code></pre>
</article>
<article class="doc-entry" id="doc-find-all">
<h3><a class="doc-anchor" href="#doc-find-all">#</a> <code>find_all</code></h3>
<p><code>find_all</code> — operation <code>find all</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p find_all $x
</code></pre>
</article>
<article class="doc-entry" id="doc-find-all-indices">
<h3><a class="doc-anchor" href="#doc-find-all-indices">#</a> <code>find_all_indices</code></h3>
<p><code>find_all_indices</code> — operation <code>find all indices</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p find_all_indices $x
</code></pre>
</article>
<article class="doc-entry" id="doc-find-first">
<h3><a class="doc-anchor" href="#doc-find-first">#</a> <code>find_first</code></h3>
<p><code>find_first</code> — operation <code>find first</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p find_first $x
</code></pre>
</article>
<article class="doc-entry" id="doc-find-index">
<h3><a class="doc-anchor" href="#doc-find-index">#</a> <code>find_index</code></h3>
<p><code>find_index</code> — index of <code>find</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p find_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-find-index-fn">
<h3><a class="doc-anchor" href="#doc-find-index-fn">#</a> <code>find_index_fn</code></h3>
<p><code>find_index_fn</code> — operation <code>find index fn</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p find_index_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-find-indices">
<h3><a class="doc-anchor" href="#doc-find-indices">#</a> <code>find_indices</code></h3>
<p><code>find_indices</code> — operation <code>find indices</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p find_indices $x
</code></pre>
</article>
<article class="doc-entry" id="doc-find-last">
<h3><a class="doc-anchor" href="#doc-find-last">#</a> <code>find_last</code></h3>
<p><code>find_last</code> — operation <code>find last</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p find_last $x
</code></pre>
</article>
<article class="doc-entry" id="doc-find-last-index">
<h3><a class="doc-anchor" href="#doc-find-last-index">#</a> <code>find_last_index</code></h3>
<p><code>find_last_index</code> — index of <code>find last</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p find_last_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-find-map">
<h3><a class="doc-anchor" href="#doc-find-map">#</a> <code>find_map</code></h3>
<p><code>find_map</code> — operation <code>find map</code>. Category: *rust iterator methods*.</p>
<pre><code class="lang-perl">p find_map $x
</code></pre>
</article>
<article class="doc-entry" id="doc-finite-difference-central">
<h3><a class="doc-anchor" href="#doc-finite-difference-central">#</a> <code>finite_difference_central</code></h3>
<p><code>finite_difference_central(ys, h=1) → array</code> — central difference: <code>(y[i+1] − y[i-1]) / (2h)</code>. Second-order accurate.</p>
<pre><code class="lang-perl">p finite_difference_central(\@ys, 0.1)
</code></pre>
</article>
<article class="doc-entry" id="doc-finite-difference-forward">
<h3><a class="doc-anchor" href="#doc-finite-difference-forward">#</a> <code>finite_difference_forward</code></h3>
<p><code>finite_difference_forward(ys, h=1) → array</code> — forward difference: <code>(y[i+1] − y[i]) / h</code>.</p>
<pre><code class="lang-perl">p finite_difference_forward([1,3,6,10,15], 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-finite-rate-lambda">
<h3><a class="doc-anchor" href="#doc-finite-rate-lambda">#</a> <code>finite_rate_lambda</code></h3>
<p><code>finite_rate_lambda</code> — operation <code>finite rate lambda</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p finite_rate_lambda $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fintushel-stern-step">
<h3><a class="doc-anchor" href="#doc-fintushel-stern-step">#</a> <code>fintushel_stern_step</code></h3>
<p><code>fintushel_stern_step</code> — single-step update of <code>fintushel stern</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p fintushel_stern_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fip">
<h3><a class="doc-anchor" href="#doc-fip">#</a> <code>fip</code></h3>
<p><code>fip</code> — operation <code>fip</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p fip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fir-filter">
<h3><a class="doc-anchor" href="#doc-fir-filter">#</a> <code>fir_filter</code></h3>
<p><code>fir_filter(signal, taps) → array</code> — finite impulse response: <code>y[n] = Σ taps[k]·x[n-k]</code>.</p>
</article>
<article class="doc-entry" id="doc-fir-lowpass-design">
<h3><a class="doc-anchor" href="#doc-fir-lowpass-design">#</a> <code>fir_lowpass_design</code></h3>
<p><code>fir_lowpass_design</code> — operation <code>fir lowpass design</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p fir_lowpass_design $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fir-moving-average">
<h3><a class="doc-anchor" href="#doc-fir-moving-average">#</a> <code>fir_moving_average</code></h3>
<p><code>fir_moving_average</code> — operation <code>fir moving average</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p fir_moving_average $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fire">
<h3><a class="doc-anchor" href="#doc-fire">#</a> <code>fire</code></h3>
<p><code>fire</code> — operation <code>fire</code>. Category: *stress testing*.</p>
<pre><code class="lang-perl">p fire $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fire-and-forget">
<h3><a class="doc-anchor" href="#doc-fire-and-forget">#</a> <code>fire_and_forget</code></h3>
<p><code>fire_and_forget</code> — operation <code>fire and forget</code>. Category: *stress testing*.</p>
<pre><code class="lang-perl">p fire_and_forget $x
</code></pre>
</article>
<article class="doc-entry" id="doc-first-arg">
<h3><a class="doc-anchor" href="#doc-first-arg">#</a> <code>first_arg</code></h3>
<p><code>first_arg</code> — operation <code>first arg</code>. Category: *functional primitives*.</p>
<pre><code class="lang-perl">p first_arg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-first-elem">
<h3><a class="doc-anchor" href="#doc-first-elem">#</a> <code>first_elem</code></h3>
<p><code>first_elem</code> — operation <code>first elem</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p first_elem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-first-eq">
<h3><a class="doc-anchor" href="#doc-first-eq">#</a> <code>first_eq</code></h3>
<p><code>first_eq</code> — operation <code>first eq</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p first_eq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-first-of-month">
<h3><a class="doc-anchor" href="#doc-first-of-month">#</a> <code>first_of_month</code></h3>
<p><code>first_of_month</code> — operation <code>first of month</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p first_of_month $x
</code></pre>
</article>
<article class="doc-entry" id="doc-first-order-concentration">
<h3><a class="doc-anchor" href="#doc-first-order-concentration">#</a> <code>first_order_concentration</code></h3>
<p><code>first_order_concentration</code> — operation <code>first order concentration</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p first_order_concentration $x
</code></pre>
</article>
<article class="doc-entry" id="doc-first-order-half-life">
<h3><a class="doc-anchor" href="#doc-first-order-half-life">#</a> <code>first_order_half_life</code></h3>
<p><code>first_order_half_life</code> — operation <code>first order half life</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p first_order_half_life $x
</code></pre>
</article>
<article class="doc-entry" id="doc-first-price-seal">
<h3><a class="doc-anchor" href="#doc-first-price-seal">#</a> <code>first_price_seal</code></h3>
<p><code>first_price_seal</code> — operation <code>first price seal</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p first_price_seal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-first-word">
<h3><a class="doc-anchor" href="#doc-first-word">#</a> <code>first_word</code></h3>
<p><code>first_word</code> — operation <code>first word</code>. Category: *string*.</p>
<pre><code class="lang-perl">p first_word $x
</code></pre>
</article>
<article class="doc-entry" id="doc-firwin2-freq">
<h3><a class="doc-anchor" href="#doc-firwin2-freq">#</a> <code>firwin2_freq</code></h3>
<p><code>firwin2_freq</code> — operation <code>firwin2 freq</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p firwin2_freq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-firwin-bandpass">
<h3><a class="doc-anchor" href="#doc-firwin-bandpass">#</a> <code>firwin_bandpass</code></h3>
<p><code>firwin_bandpass</code> — operation <code>firwin bandpass</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p firwin_bandpass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-firwin-bandstop">
<h3><a class="doc-anchor" href="#doc-firwin-bandstop">#</a> <code>firwin_bandstop</code></h3>
<p><code>firwin_bandstop</code> — operation <code>firwin bandstop</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p firwin_bandstop $x
</code></pre>
</article>
<article class="doc-entry" id="doc-firwin-highpass">
<h3><a class="doc-anchor" href="#doc-firwin-highpass">#</a> <code>firwin_highpass</code></h3>
<p><code>firwin_highpass</code> — operation <code>firwin highpass</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p firwin_highpass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-firwin-lowpass">
<h3><a class="doc-anchor" href="#doc-firwin-lowpass">#</a> <code>firwin_lowpass</code></h3>
<p><code>firwin_lowpass</code> — operation <code>firwin lowpass</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p firwin_lowpass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fiscal-year-us">
<h3><a class="doc-anchor" href="#doc-fiscal-year-us">#</a> <code>fiscal_year_us</code></h3>
<p><code>fiscal_year_us</code> — operation <code>fiscal year us</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p fiscal_year_us $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fisher-exact-2x2">
<h3><a class="doc-anchor" href="#doc-fisher-exact-2x2">#</a> <code>fisher_exact_2x2</code></h3>
<p><code>fisher_exact_2x2(a, b, c, d) → {statistic, df, p_value}</code> — Fisher's exact test for a 2×2 table; two-sided p-value.</p>
<pre><code class="lang-perl">p fisher_exact_2x2(8, 2, 1, 5)
</code></pre>
</article>
<article class="doc-entry" id="doc-fisher-info-metric">
<h3><a class="doc-anchor" href="#doc-fisher-info-metric">#</a> <code>fisher_info_metric</code></h3>
<p><code>fisher_info_metric</code> — metric of <code>fisher info</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p fisher_info_metric $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fisher-yates-shuffle">
<h3><a class="doc-anchor" href="#doc-fisher-yates-shuffle">#</a> <code>fisher_yates_shuffle</code></h3>
<p><code>fisher_yates_shuffle</code> — operation <code>fisher yates shuffle</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p fisher_yates_shuffle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fista-step">
<h3><a class="doc-anchor" href="#doc-fista-step">#</a> <code>fista_step</code></h3>
<p><code>fista_step</code> — single-step update of <code>fista</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p fista_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fit-curve-least-squares">
<h3><a class="doc-anchor" href="#doc-fit-curve-least-squares">#</a> <code>fit_curve_least_squares</code></h3>
<p><code>fit_curve_least_squares(xs, ys) → hash</code> — OLS linear regression <code>y = a + b·x</code>. Returns <code>{a, b}</code>.</p>
<pre><code class="lang-perl">my $fit = fit_curve_least_squares([0,1,2,3], [1,3,5,7])
p "$fit->{a} + $fit->{b}*x"
</code></pre>
</article>
<article class="doc-entry" id="doc-five-number-summary">
<h3><a class="doc-anchor" href="#doc-five-number-summary">#</a> <code>five_number_summary</code></h3>
<p><code>five_number_summary(@data)</code> (alias <code>fivenum</code>) — returns [min, Q1, median, Q3, max], the classic five-number summary used for box plots. Provides a quick view of data distribution.</p>
<pre><code class="lang-perl">my @data = 1:100
my $f = fivenum(@data)
p "min=$f->[0] Q1=$f->[1] med=$f->[2] Q3=$f->[3] max=$f->[4]"
</code></pre>
</article>
<article class="doc-entry" id="doc-fixed-from-french">
<h3><a class="doc-anchor" href="#doc-fixed-from-french">#</a> <code>fixed_from_french</code></h3>
<p><code>fixed_from_french</code> — operation <code>fixed from french</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p fixed_from_french $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fixed-from-gregorian">
<h3><a class="doc-anchor" href="#doc-fixed-from-gregorian">#</a> <code>fixed_from_gregorian</code></h3>
<p><code>fixed_from_gregorian</code> — operation <code>fixed from gregorian</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p fixed_from_gregorian $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fixed-from-hebrew">
<h3><a class="doc-anchor" href="#doc-fixed-from-hebrew">#</a> <code>fixed_from_hebrew</code></h3>
<p><code>fixed_from_hebrew</code> — operation <code>fixed from hebrew</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p fixed_from_hebrew $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fixed-from-islamic">
<h3><a class="doc-anchor" href="#doc-fixed-from-islamic">#</a> <code>fixed_from_islamic</code></h3>
<p><code>fixed_from_islamic</code> — operation <code>fixed from islamic</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p fixed_from_islamic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fixed-from-julian">
<h3><a class="doc-anchor" href="#doc-fixed-from-julian">#</a> <code>fixed_from_julian</code></h3>
<p><code>fixed_from_julian</code> — operation <code>fixed from julian</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p fixed_from_julian $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fixed-from-persian">
<h3><a class="doc-anchor" href="#doc-fixed-from-persian">#</a> <code>fixed_from_persian</code></h3>
<p><code>fixed_from_persian</code> — operation <code>fixed from persian</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p fixed_from_persian $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fixed-quad">
<h3><a class="doc-anchor" href="#doc-fixed-quad">#</a> <code>fixed_quad</code></h3>
<p><code>fixed_quad</code> — operation <code>fixed quad</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p fixed_quad $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fizzbuzz">
<h3><a class="doc-anchor" href="#doc-fizzbuzz">#</a> <code>fizzbuzz</code></h3>
<p><code>fizzbuzz</code> — operation <code>fizzbuzz</code>. Category: *algorithms / puzzles*.</p>
<pre><code class="lang-perl">p fizzbuzz $x
</code></pre>
</article>
<article class="doc-entry" id="doc-flanger-simple">
<h3><a class="doc-anchor" href="#doc-flanger-simple">#</a> <code>flanger_simple</code></h3>
<p><code>flanger_simple</code> — operation <code>flanger simple</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p flanger_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-flat-band-potential">
<h3><a class="doc-anchor" href="#doc-flat-band-potential">#</a> <code>flat_band_potential</code></h3>
<p><code>flat_band_potential</code> — operation <code>flat band potential</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p flat_band_potential $x
</code></pre>
</article>
<article class="doc-entry" id="doc-flat-depth">
<h3><a class="doc-anchor" href="#doc-flat-depth">#</a> <code>flat_depth</code></h3>
<p><code>flat_depth</code> — operation <code>flat depth</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p flat_depth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-flat-map">
<h3><a class="doc-anchor" href="#doc-flat-map">#</a> <code>flat_map</code></h3>
<p><code>flat_map</code> — operation <code>flat map</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p flat_map $x
</code></pre>
</article>
<article class="doc-entry" id="doc-flat-map-fn">
<h3><a class="doc-anchor" href="#doc-flat-map-fn">#</a> <code>flat_map_fn</code></h3>
<p><code>flat_map_fn</code> — operation <code>flat map fn</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p flat_map_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-flat-maps">
<h3><a class="doc-anchor" href="#doc-flat-maps">#</a> <code>flat_maps</code></h3>
<p><code>flat_maps { BLOCK } LIST</code> — a lazy streaming flat-map that evaluates the block for each element and flattens the resulting lists into a single iterator. Where <code>maps</code> expects the block to return one value, <code>flat_maps</code> handles blocks that return zero or more values per element and concatenates them seamlessly. This is the streaming equivalent of calling <code>map</code> with a multi-value block. Use it in <code>|></code> chains when each input element fans out into multiple outputs and you want lazy evaluation.</p>
<pre><code class="lang-perl">1:3 |> flat_maps { (_, _ * 10) } |> e p
# 1 10 2 20 3 30
@nested |> flat_maps { @_ } |> e p # flatten array-of-arrays
</code></pre>
</article>
<article class="doc-entry" id="doc-flatnonzero">
<h3><a class="doc-anchor" href="#doc-flatnonzero">#</a> <code>flatnonzero</code></h3>
<p><code>flatnonzero</code> — operation <code>flatnonzero</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p flatnonzero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-flatten-deep">
<h3><a class="doc-anchor" href="#doc-flatten-deep">#</a> <code>flatten_deep</code></h3>
<p><code>flatten_deep</code> — operation <code>flatten deep</code>. Category: *collection more*.</p>
<pre><code class="lang-perl">p flatten_deep $x
</code></pre>
</article>
<article class="doc-entry" id="doc-flatten-once">
<h3><a class="doc-anchor" href="#doc-flatten-once">#</a> <code>flatten_once</code></h3>
<p><code>flatten_once</code> — operation <code>flatten once</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p flatten_once $x
</code></pre>
</article>
<article class="doc-entry" id="doc-flattop-w">
<h3><a class="doc-anchor" href="#doc-flattop-w">#</a> <code>flattop_w</code></h3>
<p><code>flattop_w</code> — operation <code>flattop w</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p flattop_w $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fldr">
<h3><a class="doc-anchor" href="#doc-fldr">#</a> <code>fldr</code></h3>
<p><code>fldr</code> — operation <code>fldr</code>. Alias for <code>fold_right</code>. Category: *rust iterator methods*.</p>
<pre><code class="lang-perl">p fldr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-flesch-kincaid-grade">
<h3><a class="doc-anchor" href="#doc-flesch-kincaid-grade">#</a> <code>flesch_kincaid_grade</code></h3>
<p><code>flesch_kincaid_grade</code> — operation <code>flesch kincaid grade</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p flesch_kincaid_grade $x
</code></pre>
</article>
<article class="doc-entry" id="doc-flesch-reading-ease">
<h3><a class="doc-anchor" href="#doc-flesch-reading-ease">#</a> <code>flesch_reading_ease</code></h3>
<p><code>flesch_reading_ease</code> — operation <code>flesch reading ease</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p flesch_reading_ease $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fletcher16">
<h3><a class="doc-anchor" href="#doc-fletcher16">#</a> <code>fletcher16</code></h3>
<p><code>fletcher16(s) → int</code> — Fletcher-16 checksum (two 8-bit sums mod 255).</p>
<pre><code class="lang-perl">p fletcher16("abcde") # 0xC8F0
</code></pre>
</article>
<article class="doc-entry" id="doc-fletcher32">
<h3><a class="doc-anchor" href="#doc-fletcher32">#</a> <code>fletcher32</code></h3>
<p><code>fletcher32(s) → int</code> — Fletcher-32 (two 16-bit sums mod 65535).</p>
</article>
<article class="doc-entry" id="doc-fletcher64">
<h3><a class="doc-anchor" href="#doc-fletcher64">#</a> <code>fletcher64</code></h3>
<p><code>fletcher64(s) → int</code> — Fletcher-64 (two 32-bit sums mod 2³²-1).</p>
</article>
<article class="doc-entry" id="doc-flip-args">
<h3><a class="doc-anchor" href="#doc-flip-args">#</a> <code>flip_args</code></h3>
<p><code>flip_args</code> — operation <code>flip args</code>. Category: *functional primitives*.</p>
<pre><code class="lang-perl">p flip_args $x
</code></pre>
</article>
<article class="doc-entry" id="doc-float-bits">
<h3><a class="doc-anchor" href="#doc-float-bits">#</a> <code>float_bits</code></h3>
<p><code>float_bits</code> — floating-point helper <code>bits</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p float_bits $x
</code></pre>
</article>
<article class="doc-entry" id="doc-floer-homology-rank">
<h3><a class="doc-anchor" href="#doc-floer-homology-rank">#</a> <code>floer_homology_rank</code></h3>
<p><code>floer_homology_rank</code> — operation <code>floer homology rank</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p floer_homology_rank $x
</code></pre>
</article>
<article class="doc-entry" id="doc-floor">
<h3><a class="doc-anchor" href="#doc-floor">#</a> <code>floor</code></h3>
<p><code>floor</code> — operation <code>floor</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p floor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-floor-div">
<h3><a class="doc-anchor" href="#doc-floor-div">#</a> <code>floor_div</code></h3>
<p><code>floor_div</code> — operation <code>floor div</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p floor_div $x
</code></pre>
</article>
<article class="doc-entry" id="doc-floor-div-op">
<h3><a class="doc-anchor" href="#doc-floor-div-op">#</a> <code>floor_div_op</code></h3>
<p><code>floor_div_op</code> — operation <code>floor div op</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p floor_div_op $x
</code></pre>
</article>
<article class="doc-entry" id="doc-floor-each">
<h3><a class="doc-anchor" href="#doc-floor-each">#</a> <code>floor_each</code></h3>
<p><code>floor_each</code> — operation <code>floor each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p floor_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-floor-mod">
<h3><a class="doc-anchor" href="#doc-floor-mod">#</a> <code>floor_mod</code></h3>
<p><code>floor_mod</code> — operation <code>floor mod</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p floor_mod $x
</code></pre>
</article>
<article class="doc-entry" id="doc-flow-shop-johnson-step">
<h3><a class="doc-anchor" href="#doc-flow-shop-johnson-step">#</a> <code>flow_shop_johnson_step</code></h3>
<p><code>flow_shop_johnson_step</code> — single-step update of <code>flow shop johnson</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p flow_shop_johnson_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-floyd-cycle-detect">
<h3><a class="doc-anchor" href="#doc-floyd-cycle-detect">#</a> <code>floyd_cycle_detect</code></h3>
<p><code>floyd_cycle_detect(seq) → 0|1</code> — Floyd's tortoise-and-hare cycle detection on a functional graph.</p>
</article>
<article class="doc-entry" id="doc-floyd-warshall-step">
<h3><a class="doc-anchor" href="#doc-floyd-warshall-step">#</a> <code>floyd_warshall_step</code></h3>
<p><code>floyd_warshall_step</code> — single-step update of <code>floyd warshall</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p floyd_warshall_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fltd">
<h3><a class="doc-anchor" href="#doc-fltd">#</a> <code>fltd</code></h3>
<p><code>fltd</code> — operation <code>fltd</code>. Alias for <code>flat_depth</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p fltd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-flti">
<h3><a class="doc-anchor" href="#doc-flti">#</a> <code>flti</code></h3>
<p><code>flti</code> — operation <code>flti</code>. Alias for <code>filter_indexed</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p flti $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fltm">
<h3><a class="doc-anchor" href="#doc-fltm">#</a> <code>fltm</code></h3>
<p><code>fltm</code> — operation <code>fltm</code>. Alias for <code>filter_map</code>. Category: *rust iterator methods*.</p>
<pre><code class="lang-perl">p fltm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-flux-richardson-full">
<h3><a class="doc-anchor" href="#doc-flux-richardson-full">#</a> <code>flux_richardson_full</code></h3>
<p><code>flux_richardson_full</code> — operation <code>flux richardson full</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p flux_richardson_full $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fm-synth-2op">
<h3><a class="doc-anchor" href="#doc-fm-synth-2op">#</a> <code>fm_synth_2op</code></h3>
<p><code>fm_synth_2op(carrier, mod_freq, mod_idx, sr=44100, dur=1) → array</code> — 2-operator FM synthesis: <code>sin(2π·fc·t + I·sin(2π·fm·t))</code>.</p>
</article>
<article class="doc-entry" id="doc-fma">
<h3><a class="doc-anchor" href="#doc-fma">#</a> <code>fma</code></h3>
<p><code>fma</code> — operation <code>fma</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p fma $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fmadd">
<h3><a class="doc-anchor" href="#doc-fmadd">#</a> <code>fmadd</code></h3>
<p><code>fmadd</code> — operation <code>fmadd</code>. Alias for <code>fused_mul_add</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p fmadd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fmf">
<h3><a class="doc-anchor" href="#doc-fmf">#</a> <code>fmf</code></h3>
<p><code>fmf</code> — operation <code>fmf</code>. Alias for <code>flat_map_fn</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p fmf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fmin-cobyla">
<h3><a class="doc-anchor" href="#doc-fmin-cobyla">#</a> <code>fmin_cobyla</code></h3>
<p><code>fmin_cobyla</code> — operation <code>fmin cobyla</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p fmin_cobyla $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fmin-powell">
<h3><a class="doc-anchor" href="#doc-fmin-powell">#</a> <code>fmin_powell</code></h3>
<p><code>fmin_powell</code> — operation <code>fmin powell</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p fmin_powell $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fmod">
<h3><a class="doc-anchor" href="#doc-fmod">#</a> <code>fmod</code></h3>
<p><code>fmod</code> — operation <code>fmod</code>. Alias for <code>floor_mod</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p fmod $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fndalli">
<h3><a class="doc-anchor" href="#doc-fndalli">#</a> <code>fndalli</code></h3>
<p><code>fndalli</code> — operation <code>fndalli</code>. Alias for <code>find_all_indices</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p fndalli $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fndidxs">
<h3><a class="doc-anchor" href="#doc-fndidxs">#</a> <code>fndidxs</code></h3>
<p><code>fndidxs</code> — operation <code>fndidxs</code>. Alias for <code>find_indices</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p fndidxs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fndl">
<h3><a class="doc-anchor" href="#doc-fndl">#</a> <code>fndl</code></h3>
<p><code>fndl</code> — operation <code>fndl</code>. Alias for <code>find_last</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p fndl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fndli">
<h3><a class="doc-anchor" href="#doc-fndli">#</a> <code>fndli</code></h3>
<p><code>fndli</code> — operation <code>fndli</code>. Alias for <code>find_last_index</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p fndli $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fndm">
<h3><a class="doc-anchor" href="#doc-fndm">#</a> <code>fndm</code></h3>
<p><code>fndm</code> — operation <code>fndm</code>. Alias for <code>find_map</code>. Category: *rust iterator methods*.</p>
<pre><code class="lang-perl">p fndm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fne">
<h3><a class="doc-anchor" href="#doc-fne">#</a> <code>fne</code></h3>
<p><code>fne</code> — operation <code>fne</code>. Alias for <code>fnext</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p fne $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fnext">
<h3><a class="doc-anchor" href="#doc-fnext">#</a> <code>fnext</code></h3>
<p><code>fnext</code> — operation <code>fnext</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p fnext $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fnv0-32">
<h3><a class="doc-anchor" href="#doc-fnv0-32">#</a> <code>fnv0_32</code></h3>
<p><code>fnv0_32</code> — operation <code>fnv0 32</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p fnv0_32 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fnv1a">
<h3><a class="doc-anchor" href="#doc-fnv1a">#</a> <code>fnv1a</code></h3>
<p><code>fnv1a</code> — operation <code>fnv1a</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p fnv1a $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fnv1a-32">
<h3><a class="doc-anchor" href="#doc-fnv1a-32">#</a> <code>fnv1a_32</code></h3>
<p><code>fnv1a_32</code> — operation <code>fnv1a 32</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p fnv1a_32 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fnv1a-64">
<h3><a class="doc-anchor" href="#doc-fnv1a-64">#</a> <code>fnv1a_64</code></h3>
<p><code>fnv1a_64</code> — operation <code>fnv1a 64</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p fnv1a_64 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fnv1a-hash">
<h3><a class="doc-anchor" href="#doc-fnv1a-hash">#</a> <code>fnv1a_hash</code></h3>
<p><code>fnv1a_hash</code> — hash function of <code>fnv1a</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p fnv1a_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-focal-length-35mm-equiv">
<h3><a class="doc-anchor" href="#doc-focal-length-35mm-equiv">#</a> <code>focal_length_35mm_equiv</code></h3>
<p><code>focal_length_35mm_equiv(focal_mm, crop_factor=1) → number</code> — <code>focal · crop</code>.</p>
</article>
<article class="doc-entry" id="doc-fold-axis">
<h3><a class="doc-anchor" href="#doc-fold-axis">#</a> <code>fold_axis</code></h3>
<p><code>fold_axis</code> — operation <code>fold axis</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p fold_axis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fold-case">
<h3><a class="doc-anchor" href="#doc-fold-case">#</a> <code>fold_case</code></h3>
<p><code>fold_case</code> — operation <code>fold case</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p fold_case $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fold-left">
<h3><a class="doc-anchor" href="#doc-fold-left">#</a> <code>fold_left</code></h3>
<p><code>fold_left</code> — operation <code>fold left</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p fold_left $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fold-right">
<h3><a class="doc-anchor" href="#doc-fold-right">#</a> <code>fold_right</code></h3>
<p><code>fold_right</code> — operation <code>fold right</code>. Category: *rust iterator methods*.</p>
<pre><code class="lang-perl">p fold_right $x
</code></pre>
</article>
<article class="doc-entry" id="doc-foldl1-iter">
<h3><a class="doc-anchor" href="#doc-foldl1-iter">#</a> <code>foldl1_iter</code></h3>
<p><code>foldl1_iter</code> — operation <code>foldl1 iter</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p foldl1_iter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-foldr1-iter">
<h3><a class="doc-anchor" href="#doc-foldr1-iter">#</a> <code>foldr1_iter</code></h3>
<p><code>foldr1_iter</code> — operation <code>foldr1 iter</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p foldr1_iter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-folk-theorem-value">
<h3><a class="doc-anchor" href="#doc-folk-theorem-value">#</a> <code>folk_theorem_value</code></h3>
<p><code>folk_theorem_value</code> — value of <code>folk theorem</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p folk_theorem_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-force-mass-acc">
<h3><a class="doc-anchor" href="#doc-force-mass-acc">#</a> <code>force_mass_acc</code></h3>
<p><code>force_mass_acc</code> — operation <code>force mass acc</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p force_mass_acc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-force-of-mortality">
<h3><a class="doc-anchor" href="#doc-force-of-mortality">#</a> <code>force_of_mortality</code></h3>
<p><code>force_of_mortality</code> — operation <code>force of mortality</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p force_of_mortality $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ford-fulkerson-max-flow">
<h3><a class="doc-anchor" href="#doc-ford-fulkerson-max-flow">#</a> <code>ford_fulkerson_max_flow</code></h3>
<p><code>ford_fulkerson_max_flow</code> — operation <code>ford fulkerson max flow</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p ford_fulkerson_max_flow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ford-fulkerson-step">
<h3><a class="doc-anchor" href="#doc-ford-fulkerson-step">#</a> <code>ford_fulkerson_step</code></h3>
<p><code>ford_fulkerson_step</code> — single-step update of <code>ford fulkerson</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p ford_fulkerson_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-formal-charge">
<h3><a class="doc-anchor" href="#doc-formal-charge">#</a> <code>formal_charge</code></h3>
<p><code>formal_charge</code> — operation <code>formal charge</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p formal_charge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-format-bytes">
<h3><a class="doc-anchor" href="#doc-format-bytes">#</a> <code>format_bytes</code></h3>
<p><code>format_bytes</code> — operation <code>format bytes</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p format_bytes $x
</code></pre>
</article>
<article class="doc-entry" id="doc-format-duration">
<h3><a class="doc-anchor" href="#doc-format-duration">#</a> <code>format_duration</code></h3>
<p><code>format_duration</code> — operation <code>format duration</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p format_duration $x
</code></pre>
</article>
<article class="doc-entry" id="doc-format-number">
<h3><a class="doc-anchor" href="#doc-format-number">#</a> <code>format_number</code></h3>
<p><code>format_number</code> — operation <code>format number</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p format_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-format-percent">
<h3><a class="doc-anchor" href="#doc-format-percent">#</a> <code>format_percent</code></h3>
<p><code>format_percent</code> — operation <code>format percent</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p format_percent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-format-table-simple">
<h3><a class="doc-anchor" href="#doc-format-table-simple">#</a> <code>format_table_simple</code></h3>
<p><code>format_table_simple</code> — operation <code>format table simple</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p format_table_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-forward-algorithm">
<h3><a class="doc-anchor" href="#doc-forward-algorithm">#</a> <code>forward_algorithm</code></h3>
<p><code>forward_algorithm(obs, init, trans, emit) → number</code> — total probability <code>P(obs)</code> summed over all state paths.</p>
</article>
<article class="doc-entry" id="doc-forward-backward-pos">
<h3><a class="doc-anchor" href="#doc-forward-backward-pos">#</a> <code>forward_backward_pos</code></h3>
<p><code>forward_backward_pos</code> — operation <code>forward backward pos</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p forward_backward_pos $x
</code></pre>
</article>
<article class="doc-entry" id="doc-forward-kinematics-dh">
<h3><a class="doc-anchor" href="#doc-forward-kinematics-dh">#</a> <code>forward_kinematics_dh</code></h3>
<p><code>forward_kinematics_dh</code> — operation <code>forward kinematics dh</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p forward_kinematics_dh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-forward-rate">
<h3><a class="doc-anchor" href="#doc-forward-rate">#</a> <code>forward_rate</code></h3>
<p><code>forward_rate</code> — rate of <code>forward</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p forward_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fourier-number-step">
<h3><a class="doc-anchor" href="#doc-fourier-number-step">#</a> <code>fourier_number_step</code></h3>
<p><code>fourier_number_step</code> — single-step update of <code>fourier number</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p fourier_number_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fp-depression">
<h3><a class="doc-anchor" href="#doc-fp-depression">#</a> <code>fp_depression</code></h3>
<p><code>fp_depression</code> — operation <code>fp depression</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p fp_depression $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fr">
<h3><a class="doc-anchor" href="#doc-fr">#</a> <code>fr</code></h3>
<p><code>fr</code> — operation <code>fr</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p fr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-frac-part">
<h3><a class="doc-anchor" href="#doc-frac-part">#</a> <code>frac_part</code></h3>
<p><code>frac_part</code> — operation <code>frac part</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p frac_part $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fracp">
<h3><a class="doc-anchor" href="#doc-fracp">#</a> <code>fracp</code></h3>
<p><code>fracp</code> — operation <code>fracp</code>. Alias for <code>frac_part</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p fracp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fractional-chromatic-lower">
<h3><a class="doc-anchor" href="#doc-fractional-chromatic-lower">#</a> <code>fractional_chromatic_lower</code></h3>
<p><code>fractional_chromatic_lower</code> — operation <code>fractional chromatic lower</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p fractional_chromatic_lower $x
</code></pre>
</article>
<article class="doc-entry" id="doc-frank-wolfe-step">
<h3><a class="doc-anchor" href="#doc-frank-wolfe-step">#</a> <code>frank_wolfe_step</code></h3>
<p><code>frank_wolfe_step</code> — single-step update of <code>frank wolfe</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p frank_wolfe_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fredkin-gate">
<h3><a class="doc-anchor" href="#doc-fredkin-gate">#</a> <code>fredkin_gate</code></h3>
<p><code>fredkin_gate</code> — operation <code>fredkin gate</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p fredkin_gate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-free-energy-principle">
<h3><a class="doc-anchor" href="#doc-free-energy-principle">#</a> <code>free_energy_principle</code></h3>
<p><code>free_energy_principle</code> — operation <code>free energy principle</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p free_energy_principle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-free-group-rank-lower">
<h3><a class="doc-anchor" href="#doc-free-group-rank-lower">#</a> <code>free_group_rank_lower</code></h3>
<p><code>free_group_rank_lower</code> — operation <code>free group rank lower</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p free_group_rank_lower $x
</code></pre>
</article>
<article class="doc-entry" id="doc-free-particle-energy">
<h3><a class="doc-anchor" href="#doc-free-particle-energy">#</a> <code>free_particle_energy</code></h3>
<p><code>free_particle_energy</code> — operation <code>free particle energy</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p free_particle_energy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-freefall-time">
<h3><a class="doc-anchor" href="#doc-freefall-time">#</a> <code>freefall_time</code></h3>
<p><code>freefall_time</code> — operation <code>freefall time</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p freefall_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-freefall-velocity-schwarzschild">
<h3><a class="doc-anchor" href="#doc-freefall-velocity-schwarzschild">#</a> <code>freefall_velocity_schwarzschild</code></h3>
<p><code>freefall_velocity_schwarzschild</code> — operation <code>freefall velocity schwarzschild</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p freefall_velocity_schwarzschild $x
</code></pre>
</article>
<article class="doc-entry" id="doc-freeverb-lite">
<h3><a class="doc-anchor" href="#doc-freeverb-lite">#</a> <code>freeverb_lite</code></h3>
<p><code>freeverb_lite</code> — operation <code>freeverb lite</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p freeverb_lite $x
</code></pre>
</article>
<article class="doc-entry" id="doc-french-revolutionary-leap">
<h3><a class="doc-anchor" href="#doc-french-revolutionary-leap">#</a> <code>french_revolutionary_leap</code></h3>
<p><code>french_revolutionary_leap</code> — operation <code>french revolutionary leap</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p french_revolutionary_leap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-freq-to-note">
<h3><a class="doc-anchor" href="#doc-freq-to-note">#</a> <code>freq_to_note</code></h3>
<p><code>freq_to_note</code> — convert from <code>freq</code> to <code>note</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p freq_to_note $value
</code></pre>
</article>
<article class="doc-entry" id="doc-freq-wavelength">
<h3><a class="doc-anchor" href="#doc-freq-wavelength">#</a> <code>freq_wavelength</code></h3>
<p><code>freq_wavelength</code> — frequency-domain helper <code>wavelength</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p freq_wavelength $x
</code></pre>
</article>
<article class="doc-entry" id="doc-freqs-eval">
<h3><a class="doc-anchor" href="#doc-freqs-eval">#</a> <code>freqs_eval</code></h3>
<p><code>freqs_eval</code> — operation <code>freqs eval</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p freqs_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-freqz-eval">
<h3><a class="doc-anchor" href="#doc-freqz-eval">#</a> <code>freqz_eval</code></h3>
<p><code>freqz_eval</code> — operation <code>freqz eval</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p freqz_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fresnel-reflection-normal">
<h3><a class="doc-anchor" href="#doc-fresnel-reflection-normal">#</a> <code>fresnel_reflection_normal</code></h3>
<p><code>fresnel_reflection_normal</code> — operation <code>fresnel reflection normal</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p fresnel_reflection_normal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fresnel-rp">
<h3><a class="doc-anchor" href="#doc-fresnel-rp">#</a> <code>fresnel_rp</code></h3>
<p><code>fresnel_rp</code> — operation <code>fresnel rp</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p fresnel_rp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fresnel-rs">
<h3><a class="doc-anchor" href="#doc-fresnel-rs">#</a> <code>fresnel_rs</code></h3>
<p><code>fresnel_rs</code> — operation <code>fresnel rs</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p fresnel_rs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-friction-factor-laminar">
<h3><a class="doc-anchor" href="#doc-friction-factor-laminar">#</a> <code>friction_factor_laminar</code></h3>
<p><code>friction_factor_laminar</code> — operation <code>friction factor laminar</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p friction_factor_laminar $x
</code></pre>
</article>
<article class="doc-entry" id="doc-friedmann-density-total">
<h3><a class="doc-anchor" href="#doc-friedmann-density-total">#</a> <code>friedmann_density_total</code></h3>
<p><code>friedmann_density_total</code> — operation <code>friedmann density total</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p friedmann_density_total $x
</code></pre>
</article>
<article class="doc-entry" id="doc-from-base">
<h3><a class="doc-anchor" href="#doc-from-base">#</a> <code>from_base</code></h3>
<p><code>from_base</code> — construct from base representation. Category: *base conversion*.</p>
<pre><code class="lang-perl">p from_base $x
</code></pre>
</article>
<article class="doc-entry" id="doc-from-bin">
<h3><a class="doc-anchor" href="#doc-from-bin">#</a> <code>from_bin</code></h3>
<p><code>from_bin</code> — construct from bin representation. Category: *base conversion*.</p>
<pre><code class="lang-perl">p from_bin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-from-code-point">
<h3><a class="doc-anchor" href="#doc-from-code-point">#</a> <code>from_code_point</code></h3>
<p><code>from_code_point</code> — construct from code point representation. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p from_code_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-from-csv-line">
<h3><a class="doc-anchor" href="#doc-from-csv-line">#</a> <code>from_csv_line</code></h3>
<p><code>from_csv_line</code> — construct from csv line representation. Category: *string helpers*.</p>
<pre><code class="lang-perl">p from_csv_line $x
</code></pre>
</article>
<article class="doc-entry" id="doc-from-digits">
<h3><a class="doc-anchor" href="#doc-from-digits">#</a> <code>from_digits</code></h3>
<p><code>from_digits</code> — construct from digits representation. Category: *list helpers*.</p>
<pre><code class="lang-perl">p from_digits $x
</code></pre>
</article>
<article class="doc-entry" id="doc-from-hex">
<h3><a class="doc-anchor" href="#doc-from-hex">#</a> <code>from_hex</code></h3>
<p><code>from_hex</code> — construct from hex representation. Category: *base conversion*.</p>
<pre><code class="lang-perl">p from_hex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-from-oct">
<h3><a class="doc-anchor" href="#doc-from-oct">#</a> <code>from_oct</code></h3>
<p><code>from_oct</code> — construct from oct representation. Category: *base conversion*.</p>
<pre><code class="lang-perl">p from_oct $x
</code></pre>
</article>
<article class="doc-entry" id="doc-from-pairs">
<h3><a class="doc-anchor" href="#doc-from-pairs">#</a> <code>from_pairs</code></h3>
<p><code>from_pairs</code> — construct from pairs representation. Category: *list helpers*.</p>
<pre><code class="lang-perl">p from_pairs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-froude-number">
<h3><a class="doc-anchor" href="#doc-froude-number">#</a> <code>froude_number</code></h3>
<p><code>froude_number</code> — operation <code>froude number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p froude_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-froude-number-step">
<h3><a class="doc-anchor" href="#doc-froude-number-step">#</a> <code>froude_number_step</code></h3>
<p><code>froude_number_step</code> — single-step update of <code>froude number</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p froude_number_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-frustum-volume">
<h3><a class="doc-anchor" href="#doc-frustum-volume">#</a> <code>frustum_volume</code></h3>
<p><code>frustum_volume($r1, $r2, $h)</code> — computes the volume of a conical frustum (truncated cone) with base radii r1 and r2 and height h.</p>
<pre><code class="lang-perl">p frustum_volume(5, 3, 10) # ~513
</code></pre>
</article>
<article class="doc-entry" id="doc-frustvol">
<h3><a class="doc-anchor" href="#doc-frustvol">#</a> <code>frustvol</code></h3>
<p><code>frustvol</code> — operation <code>frustvol</code>. Alias for <code>frustum_volume</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p frustvol $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fsize">
<h3><a class="doc-anchor" href="#doc-fsize">#</a> <code>fsize</code></h3>
<p><code>fsize</code> — operation <code>fsize</code>. Alias for <code>file_size</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p fsize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fst">
<h3><a class="doc-anchor" href="#doc-fst">#</a> <code>fst</code></h3>
<p><code>fst</code> — operation <code>fst</code>. Alias for <code>first</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p fst $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ft">
<h3><a class="doc-anchor" href="#doc-ft">#</a> <code>ft</code></h3>
<p><code>ft</code> — operation <code>ft</code>. Alias for <code>fetch</code>. Category: *data / network*.</p>
<pre><code class="lang-perl">p ft $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fta">
<h3><a class="doc-anchor" href="#doc-fta">#</a> <code>fta</code></h3>
<p><code>fta</code> — operation <code>fta</code>. Alias for <code>fetch_async</code>. Category: *data / network*.</p>
<pre><code class="lang-perl">p fta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ftaj">
<h3><a class="doc-anchor" href="#doc-ftaj">#</a> <code>ftaj</code></h3>
<p><code>ftaj</code> — operation <code>ftaj</code>. Alias for <code>fetch_async_json</code>. Category: *data / network*.</p>
<pre><code class="lang-perl">p ftaj $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ftj">
<h3><a class="doc-anchor" href="#doc-ftj">#</a> <code>ftj</code></h3>
<p><code>ftj</code> — operation <code>ftj</code>. Alias for <code>fetch_json</code>. Category: *data / network*.</p>
<pre><code class="lang-perl">p ftj $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fuel-cell-polarization">
<h3><a class="doc-anchor" href="#doc-fuel-cell-polarization">#</a> <code>fuel_cell_polarization</code></h3>
<p><code>fuel_cell_polarization</code> — operation <code>fuel cell polarization</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p fuel_cell_polarization $x
</code></pre>
</article>
<article class="doc-entry" id="doc-full-moon-julian">
<h3><a class="doc-anchor" href="#doc-full-moon-julian">#</a> <code>full_moon_julian</code></h3>
<p><code>full_moon_julian(cycle) → number</code> — Julian Date of <code>cycle</code>-th full moon.</p>
<pre><code class="lang-perl">p full_moon_julian(0)
</code></pre>
</article>
<article class="doc-entry" id="doc-fundamental-group-zn">
<h3><a class="doc-anchor" href="#doc-fundamental-group-zn">#</a> <code>fundamental_group_zn</code></h3>
<p><code>fundamental_group_zn</code> — operation <code>fundamental group zn</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p fundamental_group_zn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fused-mul-add">
<h3><a class="doc-anchor" href="#doc-fused-mul-add">#</a> <code>fused_mul_add</code></h3>
<p><code>fused_mul_add</code> — operation <code>fused mul add</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p fused_mul_add $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fusion-rule-su2-step">
<h3><a class="doc-anchor" href="#doc-fusion-rule-su2-step">#</a> <code>fusion_rule_su2_step</code></h3>
<p><code>fusion_rule_su2_step</code> — single-step update of <code>fusion rule su2</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p fusion_rule_su2_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-future-value">
<h3><a class="doc-anchor" href="#doc-future-value">#</a> <code>future_value</code></h3>
<p><code>future_value(present_value, rate, periods) → number</code> — <code>PV · (1 + rate)^periods</code>. Compound a single cashflow forward.</p>
<pre><code class="lang-perl">p future_value(1000, 0.05, 10) # 1628.89
</code></pre>
</article>
<article class="doc-entry" id="doc-fuzzy-substring-match">
<h3><a class="doc-anchor" href="#doc-fuzzy-substring-match">#</a> <code>fuzzy_substring_match</code></h3>
<p><code>fuzzy_substring_match(needle, haystack, max_dist=2) → int</code> — earliest start index where <code>needle</code> matches a substring of <code>haystack</code> within Levenshtein distance <code>max_dist</code>; <code>-1</code> if no match.</p>
<pre><code class="lang-perl">p fuzzy_substring_match("hello", "yellow helo world", 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-fv">
<h3><a class="doc-anchor" href="#doc-fv">#</a> <code>fv</code></h3>
<p><code>fv</code> — operation <code>fv</code>. Alias for <code>fetch_val</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p fv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-fx-forward">
<h3><a class="doc-anchor" href="#doc-fx-forward">#</a> <code>fx_forward</code></h3>
<p><code>fx_forward</code> — operation <code>fx forward</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p fx_forward $x
</code></pre>
</article>
<article class="doc-entry" id="doc-g2-zero">
<h3><a class="doc-anchor" href="#doc-g2-zero">#</a> <code>g2_zero</code></h3>
<p><code>g2_zero</code> — operation <code>g2 zero</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p g2_zero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-g-to-oz">
<h3><a class="doc-anchor" href="#doc-g-to-oz">#</a> <code>g_to_oz</code></h3>
<p><code>g_to_oz</code> — convert from <code>g</code> to <code>oz</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p g_to_oz $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gabor-filter">
<h3><a class="doc-anchor" href="#doc-gabor-filter">#</a> <code>gabor_filter</code></h3>
<p><code>gabor_filter</code> — filter op of <code>gabor</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p gabor_filter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gabor-kernel">
<h3><a class="doc-anchor" href="#doc-gabor-kernel">#</a> <code>gabor_kernel</code></h3>
<p><code>gabor_kernel</code> — convolution kernel of <code>gabor</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p gabor_kernel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gae-advantage-step">
<h3><a class="doc-anchor" href="#doc-gae-advantage-step">#</a> <code>gae_advantage_step</code></h3>
<p><code>gae_advantage_step</code> — single-step update of <code>gae advantage</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p gae_advantage_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gain-ratio">
<h3><a class="doc-anchor" href="#doc-gain-ratio">#</a> <code>gain_ratio</code></h3>
<p><code>gain_ratio</code> — ratio of <code>gain</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p gain_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gale-optimal">
<h3><a class="doc-anchor" href="#doc-gale-optimal">#</a> <code>gale_optimal</code></h3>
<p><code>gale_optimal</code> — operation <code>gale optimal</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p gale_optimal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gale-shapley-step">
<h3><a class="doc-anchor" href="#doc-gale-shapley-step">#</a> <code>gale_shapley_step</code></h3>
<p><code>gale_shapley_step</code> — single-step update of <code>gale shapley</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p gale_shapley_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gallons-to-liters">
<h3><a class="doc-anchor" href="#doc-gallons-to-liters">#</a> <code>gallons_to_liters</code></h3>
<p><code>gallons_to_liters</code> — convert from <code>gallons</code> to <code>liters</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p gallons_to_liters $value
</code></pre>
</article>
<article class="doc-entry" id="doc-game-of-life-step">
<h3><a class="doc-anchor" href="#doc-game-of-life-step">#</a> <code>game_of_life_step</code></h3>
<p><code>game_of_life_step</code> — single-step update of <code>game of life</code>. Category: *algorithms / puzzles*.</p>
<pre><code class="lang-perl">p game_of_life_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-game-two-player-value">
<h3><a class="doc-anchor" href="#doc-game-two-player-value">#</a> <code>game_two_player_value</code></h3>
<p><code>game_two_player_value</code> — value of <code>game two player</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p game_two_player_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gamma-apply">
<h3><a class="doc-anchor" href="#doc-gamma-apply">#</a> <code>gamma_apply</code></h3>
<p><code>gamma_apply</code> — operation <code>gamma apply</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p gamma_apply $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gamma-approx">
<h3><a class="doc-anchor" href="#doc-gamma-approx">#</a> <code>gamma_approx</code></h3>
<p><code>gamma_approx($z)</code> — Gamma function Γ(z) using Lanczos approximation. Extends factorial: Γ(n) = (n-1)!</p>
<pre><code class="lang-perl">p gamma(5) # 24 (same as 4!)
p gamma(0.5) # ~1.772 (√π)
</code></pre>
</article>
<article class="doc-entry" id="doc-gamma-correct">
<h3><a class="doc-anchor" href="#doc-gamma-correct">#</a> <code>gamma_correct</code></h3>
<p><code>gamma_correct(v, gamma=2.2) → number</code> — apply gamma correction <code>v^(1/γ)</code> to a [0,1] value.</p>
<pre><code class="lang-perl">p gamma_correct(0.5, 2.2)
</code></pre>
</article>
<article class="doc-entry" id="doc-gamma-pdf">
<h3><a class="doc-anchor" href="#doc-gamma-pdf">#</a> <code>gamma_pdf</code></h3>
<p><code>gamma_pdf</code> (alias <code>gammapdf</code>) evaluates the Gamma distribution PDF at x with shape k and scale theta.</p>
<pre><code class="lang-perl">p gammapdf(2.0, 2, 1) # Gamma(2,1) at x=2
</code></pre>
</article>
<article class="doc-entry" id="doc-gamma-regularized-p">
<h3><a class="doc-anchor" href="#doc-gamma-regularized-p">#</a> <code>gamma_regularized_p</code></h3>
<p><code>gamma_regularized_p(a, x) → number</code> — lower regularised incomplete gamma <code>P(a, x) = γ(a,x)/Γ(a)</code>.</p>
<pre><code class="lang-perl">p gamma_regularized_p(2, 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-gamma-regularized-q">
<h3><a class="doc-anchor" href="#doc-gamma-regularized-q">#</a> <code>gamma_regularized_q</code></h3>
<p><code>gamma_regularized_q(a, x) → number</code> — upper regularised incomplete gamma <code>Q(a, x) = 1 - P(a, x)</code>.</p>
<pre><code class="lang-perl">p gamma_regularized_q(2, 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-gamma-remove">
<h3><a class="doc-anchor" href="#doc-gamma-remove">#</a> <code>gamma_remove</code></h3>
<p><code>gamma_remove</code> — operation <code>gamma remove</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p gamma_remove $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gamma-uncorrect">
<h3><a class="doc-anchor" href="#doc-gamma-uncorrect">#</a> <code>gamma_uncorrect</code></h3>
<p><code>gamma_uncorrect(v, gamma=2.2) → number</code> — undo gamma: <code>v^γ</code>.</p>
</article>
<article class="doc-entry" id="doc-gamow-factor">
<h3><a class="doc-anchor" href="#doc-gamow-factor">#</a> <code>gamow_factor</code></h3>
<p><code>gamow_factor</code> — factor of <code>gamow</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p gamow_factor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-garch-fit">
<h3><a class="doc-anchor" href="#doc-garch-fit">#</a> <code>garch_fit</code></h3>
<p><code>garch_fit</code> — operation <code>garch fit</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p garch_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-garch-step">
<h3><a class="doc-anchor" href="#doc-garch-step">#</a> <code>garch_step</code></h3>
<p><code>garch_step</code> — single-step update of <code>garch</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p garch_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-garman-kohlhagen-call">
<h3><a class="doc-anchor" href="#doc-garman-kohlhagen-call">#</a> <code>garman_kohlhagen_call</code></h3>
<p><code>garman_kohlhagen_call</code> — operation <code>garman kohlhagen call</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p garman_kohlhagen_call $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gas-constant">
<h3><a class="doc-anchor" href="#doc-gas-constant">#</a> <code>gas_constant</code></h3>
<p><code>gas_constant</code> (alias <code>rgas</code>) — R ≈ 8.314 J/(mol⋅K). Universal gas constant.</p>
<pre><code class="lang-perl">p rgas # 8.314462618
</code></pre>
</article>
<article class="doc-entry" id="doc-gas-constant-r">
<h3><a class="doc-anchor" href="#doc-gas-constant-r">#</a> <code>gas_constant_r</code></h3>
<p><code>gas_constant_r</code> — operation <code>gas constant r</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p gas_constant_r $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gas-constant-value">
<h3><a class="doc-anchor" href="#doc-gas-constant-value">#</a> <code>gas_constant_value</code></h3>
<p><code>gas_constant_value</code> — value of <code>gas constant</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p gas_constant_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gasp">
<h3><a class="doc-anchor" href="#doc-gasp">#</a> <code>gasp</code></h3>
<p><code>ideal_gas_pressure($n, $V, $T)</code> (alias <code>gasp</code>) — pressure P = nRT/V. n moles, V volume (m³), T temperature (K).</p>
<pre><code class="lang-perl">p gasp(1, 0.0224, 273.15) # ~101325 Pa (1 mol at STP)
</code></pre>
</article>
<article class="doc-entry" id="doc-gasv">
<h3><a class="doc-anchor" href="#doc-gasv">#</a> <code>gasv</code></h3>
<p><code>gasv</code> — operation <code>gasv</code>. Alias for <code>ideal_gas_volume</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p gasv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gate-decompose">
<h3><a class="doc-anchor" href="#doc-gate-decompose">#</a> <code>gate_decompose</code></h3>
<p><code>gate_decompose</code> — operation <code>gate decompose</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p gate_decompose $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gauss-bonnet-term-2d">
<h3><a class="doc-anchor" href="#doc-gauss-bonnet-term-2d">#</a> <code>gauss_bonnet_term_2d</code></h3>
<p><code>gauss_bonnet_term_2d</code> — operation <code>gauss bonnet term 2d</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p gauss_bonnet_term_2d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gauss-bonnet-total">
<h3><a class="doc-anchor" href="#doc-gauss-bonnet-total">#</a> <code>gauss_bonnet_total</code></h3>
<p><code>gauss_bonnet_total</code> — operation <code>gauss bonnet total</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p gauss_bonnet_total $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gauss-codazzi-step">
<h3><a class="doc-anchor" href="#doc-gauss-codazzi-step">#</a> <code>gauss_codazzi_step</code></h3>
<p><code>gauss_codazzi_step</code> — single-step update of <code>gauss codazzi</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p gauss_codazzi_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gauss-irk-2-stage">
<h3><a class="doc-anchor" href="#doc-gauss-irk-2-stage">#</a> <code>gauss_irk_2_stage</code></h3>
<p><code>gauss_irk_2_stage</code> — operation <code>gauss irk 2 stage</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p gauss_irk_2_stage $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gauss-kronrod-15">
<h3><a class="doc-anchor" href="#doc-gauss-kronrod-15">#</a> <code>gauss_kronrod_15</code></h3>
<p><code>gauss_kronrod_15</code> — operation <code>gauss kronrod 15</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p gauss_kronrod_15 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gauss-legendre-5">
<h3><a class="doc-anchor" href="#doc-gauss-legendre-5">#</a> <code>gauss_legendre_5</code></h3>
<p><code>gauss_legendre_5</code> — operation <code>gauss legendre 5</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p gauss_legendre_5 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gaussian-curvature-step">
<h3><a class="doc-anchor" href="#doc-gaussian-curvature-step">#</a> <code>gaussian_curvature_step</code></h3>
<p><code>gaussian_curvature_step</code> — single-step update of <code>gaussian curvature</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p gaussian_curvature_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gaussian-filter-window">
<h3><a class="doc-anchor" href="#doc-gaussian-filter-window">#</a> <code>gaussian_filter_window</code></h3>
<p><code>gaussian_filter_window</code> — operation <code>gaussian filter window</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p gaussian_filter_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gaussian-kernel">
<h3><a class="doc-anchor" href="#doc-gaussian-kernel">#</a> <code>gaussian_kernel</code></h3>
<p><code>gaussian_kernel(size=5, sigma=1) → matrix</code> — normalised 2D Gaussian; sums to 1.</p>
<pre><code class="lang-perl">p gaussian_kernel(5, 1.4)
</code></pre>
</article>
<article class="doc-entry" id="doc-gaussian-window">
<h3><a class="doc-anchor" href="#doc-gaussian-window">#</a> <code>gaussian_window</code></h3>
<p><code>gaussian_window</code> — operation <code>gaussian window</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p gaussian_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gb-to-bytes">
<h3><a class="doc-anchor" href="#doc-gb-to-bytes">#</a> <code>gb_to_bytes</code></h3>
<p><code>gb_to_bytes</code> — convert from <code>gb</code> to <code>bytes</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p gb_to_bytes $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gbf">
<h3><a class="doc-anchor" href="#doc-gbf">#</a> <code>gbf</code></h3>
<p><code>gbf</code> — operation <code>gbf</code>. Alias for <code>group_by_fn</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p gbf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gbi">
<h3><a class="doc-anchor" href="#doc-gbi">#</a> <code>gbi</code></h3>
<p><code>gbi</code> — operation <code>gbi</code>. Alias for <code>groupby_iter</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p gbi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gcby">
<h3><a class="doc-anchor" href="#doc-gcby">#</a> <code>gcby</code></h3>
<p><code>gcby</code> — operation <code>gcby</code>. Alias for <code>group_consecutive_by</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p gcby $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gcd">
<h3><a class="doc-anchor" href="#doc-gcd">#</a> <code>gcd</code></h3>
<p><code>gcd</code> — operation <code>gcd</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p gcd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gconst">
<h3><a class="doc-anchor" href="#doc-gconst">#</a> <code>gconst</code></h3>
<p><code>gconst</code> — operation <code>gconst</code>. Alias for <code>gravitational_constant</code>. Category: *constants*.</p>
<pre><code class="lang-perl">p gconst $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gelu">
<h3><a class="doc-anchor" href="#doc-gelu">#</a> <code>gelu</code></h3>
<p><code>gelu</code> applies the Gaussian Error Linear Unit, used in BERT/GPT transformers.</p>
<pre><code class="lang-perl">p gelu(1) # 0.8412
p gelu(-1) # -0.1588
</code></pre>
</article>
<article class="doc-entry" id="doc-generalized-advantage">
<h3><a class="doc-anchor" href="#doc-generalized-advantage">#</a> <code>generalized_advantage</code></h3>
<p><code>generalized_advantage</code> — operation <code>generalized advantage</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p generalized_advantage $x
</code></pre>
</article>
<article class="doc-entry" id="doc-generation-time">
<h3><a class="doc-anchor" href="#doc-generation-time">#</a> <code>generation_time</code></h3>
<p><code>generation_time</code> — operation <code>generation time</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p generation_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-generation-time-demo">
<h3><a class="doc-anchor" href="#doc-generation-time-demo">#</a> <code>generation_time_demo</code></h3>
<p><code>generation_time_demo</code> — operation <code>generation time demo</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p generation_time_demo $x
</code></pre>
</article>
<article class="doc-entry" id="doc-generation-time-step">
<h3><a class="doc-anchor" href="#doc-generation-time-step">#</a> <code>generation_time_step</code></h3>
<p><code>generation_time_step</code> — single-step update of <code>generation time</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p generation_time_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-genetic-crossover-one-point">
<h3><a class="doc-anchor" href="#doc-genetic-crossover-one-point">#</a> <code>genetic_crossover_one_point</code></h3>
<p><code>genetic_crossover_one_point</code> — operation <code>genetic crossover one point</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p genetic_crossover_one_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-genus-curve-arith">
<h3><a class="doc-anchor" href="#doc-genus-curve-arith">#</a> <code>genus_curve_arith</code></h3>
<p><code>genus_curve_arith</code> — operation <code>genus curve arith</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p genus_curve_arith $x
</code></pre>
</article>
<article class="doc-entry" id="doc-genus-curve-geo">
<h3><a class="doc-anchor" href="#doc-genus-curve-geo">#</a> <code>genus_curve_geo</code></h3>
<p><code>genus_curve_geo</code> — operation <code>genus curve geo</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p genus_curve_geo $x
</code></pre>
</article>
<article class="doc-entry" id="doc-genus-from-euler">
<h3><a class="doc-anchor" href="#doc-genus-from-euler">#</a> <code>genus_from_euler</code></h3>
<p><code>genus_from_euler</code> — operation <code>genus from euler</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p genus_from_euler $x
</code></pre>
</article>
<article class="doc-entry" id="doc-genus-surface">
<h3><a class="doc-anchor" href="#doc-genus-surface">#</a> <code>genus_surface</code></h3>
<p><code>genus_surface</code> — operation <code>genus surface</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p genus_surface $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geoadd">
<h3><a class="doc-anchor" href="#doc-geoadd">#</a> <code>geoadd</code></h3>
<p><code>geoadd</code> — operation <code>geoadd</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p geoadd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geodesic-curvature-step">
<h3><a class="doc-anchor" href="#doc-geodesic-curvature-step">#</a> <code>geodesic_curvature_step</code></h3>
<p><code>geodesic_curvature_step</code> — single-step update of <code>geodesic curvature</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p geodesic_curvature_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geodesic-equation-step-zero">
<h3><a class="doc-anchor" href="#doc-geodesic-equation-step-zero">#</a> <code>geodesic_equation_step_zero</code></h3>
<p><code>geodesic_equation_step_zero</code> — operation <code>geodesic equation step zero</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p geodesic_equation_step_zero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geodist">
<h3><a class="doc-anchor" href="#doc-geodist">#</a> <code>geodist</code></h3>
<p><code>geodist</code> — operation <code>geodist</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p geodist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geohash">
<h3><a class="doc-anchor" href="#doc-geohash">#</a> <code>geohash</code></h3>
<p><code>geohash</code> — operation <code>geohash</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p geohash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geohash-bbox">
<h3><a class="doc-anchor" href="#doc-geohash-bbox">#</a> <code>geohash_bbox</code></h3>
<p><code>geohash_bbox</code> — operation <code>geohash bbox</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p geohash_bbox $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geohash-decode">
<h3><a class="doc-anchor" href="#doc-geohash-decode">#</a> <code>geohash_decode</code></h3>
<p><code>geohash_decode</code> — decode of <code>geohash</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p geohash_decode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geohash-encode">
<h3><a class="doc-anchor" href="#doc-geohash-encode">#</a> <code>geohash_encode</code></h3>
<p><code>geohash_encode</code> — encode of <code>geohash</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p geohash_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geohash-neighbor">
<h3><a class="doc-anchor" href="#doc-geohash-neighbor">#</a> <code>geohash_neighbor</code></h3>
<p><code>geohash_neighbor</code> — operation <code>geohash neighbor</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p geohash_neighbor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geohash-neighbors">
<h3><a class="doc-anchor" href="#doc-geohash-neighbors">#</a> <code>geohash_neighbors</code></h3>
<p><code>geohash_neighbors</code> — operation <code>geohash neighbors</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p geohash_neighbors $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geohash-precision">
<h3><a class="doc-anchor" href="#doc-geohash-precision">#</a> <code>geohash_precision</code></h3>
<p><code>geohash_precision</code> — operation <code>geohash precision</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p geohash_precision $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geomag-declination">
<h3><a class="doc-anchor" href="#doc-geomag-declination">#</a> <code>geomag_declination</code></h3>
<p><code>geomag_declination(lat, lon) → number</code> — magnetic declination in degrees using a simple dipole model (not WMM-accurate).</p>
<pre><code class="lang-perl">p geomag_declination(40, -74)
</code></pre>
</article>
<article class="doc-entry" id="doc-geomagnetic-kp-index">
<h3><a class="doc-anchor" href="#doc-geomagnetic-kp-index">#</a> <code>geomagnetic_kp_index</code></h3>
<p><code>geomagnetic_kp_index</code> — index of <code>geomagnetic kp</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p geomagnetic_kp_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geometric-height-full">
<h3><a class="doc-anchor" href="#doc-geometric-height-full">#</a> <code>geometric_height_full</code></h3>
<p><code>geometric_height_full</code> — operation <code>geometric height full</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p geometric_height_full $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geometric-intersection-number">
<h3><a class="doc-anchor" href="#doc-geometric-intersection-number">#</a> <code>geometric_intersection_number</code></h3>
<p><code>geometric_intersection_number</code> — operation <code>geometric intersection number</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p geometric_intersection_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geometric-mean">
<h3><a class="doc-anchor" href="#doc-geometric-mean">#</a> <code>geometric_mean</code></h3>
<p><code>geometric_mean</code> — arithmetic mean of <code>geometric</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p geometric_mean @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-geometric-mean-arr">
<h3><a class="doc-anchor" href="#doc-geometric-mean-arr">#</a> <code>geometric_mean_arr</code></h3>
<p><code>geometric_mean_arr</code> — operation <code>geometric mean arr</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p geometric_mean_arr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geometric-sequence">
<h3><a class="doc-anchor" href="#doc-geometric-sequence">#</a> <code>geometric_sequence</code></h3>
<p><code>geometric_sequence</code> — operation <code>geometric sequence</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p geometric_sequence $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geometric-series">
<h3><a class="doc-anchor" href="#doc-geometric-series">#</a> <code>geometric_series</code></h3>
<p><code>geometric_series($a1, $r, $n)</code> (alias <code>geomser</code>) — sum of n terms of geometric sequence. Formula: a1×(1-rⁿ)/(1-r). If r=1, returns a1×n.</p>
<pre><code class="lang-perl">p geomser(1, 2, 10) # 1023 (1+2+4+...+512)
p geomser(1, 0.5, 10) # ~1.998 (converging to 2)
</code></pre>
</article>
<article class="doc-entry" id="doc-geopotential-height-full">
<h3><a class="doc-anchor" href="#doc-geopotential-height-full">#</a> <code>geopotential_height_full</code></h3>
<p><code>geopotential_height_full</code> — operation <code>geopotential height full</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p geopotential_height_full $x
</code></pre>
</article>
<article class="doc-entry" id="doc-geostrophic-wind-step">
<h3><a class="doc-anchor" href="#doc-geostrophic-wind-step">#</a> <code>geostrophic_wind_step</code></h3>
<p><code>geostrophic_wind_step</code> — single-step update of <code>geostrophic wind</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p geostrophic_wind_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-get-in">
<h3><a class="doc-anchor" href="#doc-get-in">#</a> <code>get_in</code></h3>
<p><code>get_in</code> — operation <code>get in</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p get_in $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gethostent">
<h3><a class="doc-anchor" href="#doc-gethostent">#</a> <code>gethostent</code></h3>
<p><code>gethostent</code> — operation <code>gethostent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p gethostent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-getnetbyname">
<h3><a class="doc-anchor" href="#doc-getnetbyname">#</a> <code>getnetbyname</code></h3>
<p><code>getnetbyname</code> — operation <code>getnetbyname</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p getnetbyname $x
</code></pre>
</article>
<article class="doc-entry" id="doc-getnetent">
<h3><a class="doc-anchor" href="#doc-getnetent">#</a> <code>getnetent</code></h3>
<p><code>getnetent</code> — operation <code>getnetent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p getnetent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-getprotoent">
<h3><a class="doc-anchor" href="#doc-getprotoent">#</a> <code>getprotoent</code></h3>
<p><code>getprotoent</code> — operation <code>getprotoent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p getprotoent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-getrange">
<h3><a class="doc-anchor" href="#doc-getrange">#</a> <code>getrange</code></h3>
<p><code>getrange</code> — operation <code>getrange</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p getrange $x
</code></pre>
</article>
<article class="doc-entry" id="doc-getservent">
<h3><a class="doc-anchor" href="#doc-getservent">#</a> <code>getservent</code></h3>
<p><code>getservent</code> — operation <code>getservent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p getservent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-getset">
<h3><a class="doc-anchor" href="#doc-getset">#</a> <code>getset</code></h3>
<p><code>getset</code> — operation <code>getset</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p getset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gf256-multiply">
<h3><a class="doc-anchor" href="#doc-gf256-multiply">#</a> <code>gf256_multiply</code></h3>
<p><code>gf256_multiply</code> — operation <code>gf256 multiply</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p gf256_multiply $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gforce">
<h3><a class="doc-anchor" href="#doc-gforce">#</a> <code>gforce</code></h3>
<p><code>gravitational_force($m1, $m2, $r)</code> (alias <code>gforce</code>) — Newton's law of gravitation: F = Gm₁m₂/r².</p>
<pre><code class="lang-perl">p gforce(5.972e24, 1000, 6.371e6) # ~9820 N (1 ton at Earth surface)
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-aabb-intersect-check">
<h3><a class="doc-anchor" href="#doc-gfx-aabb-intersect-check">#</a> <code>gfx_aabb_intersect_check</code></h3>
<p><code>gfx_aabb_intersect_check</code> — operation <code>gfx aabb intersect check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_aabb_intersect_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-axis-angle-to-quat">
<h3><a class="doc-anchor" href="#doc-gfx-axis-angle-to-quat">#</a> <code>gfx_axis_angle_to_quat</code></h3>
<p><code>gfx_axis_angle_to_quat</code> — convert from <code>gfx axis angle</code> to <code>quat</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_axis_angle_to_quat $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-barycentric-alpha">
<h3><a class="doc-anchor" href="#doc-gfx-barycentric-alpha">#</a> <code>gfx_barycentric_alpha</code></h3>
<p><code>gfx_barycentric_alpha</code> — operation <code>gfx barycentric alpha</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_barycentric_alpha $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-barycentric-beta">
<h3><a class="doc-anchor" href="#doc-gfx-barycentric-beta">#</a> <code>gfx_barycentric_beta</code></h3>
<p><code>gfx_barycentric_beta</code> — operation <code>gfx barycentric beta</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_barycentric_beta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-barycentric-gamma">
<h3><a class="doc-anchor" href="#doc-gfx-barycentric-gamma">#</a> <code>gfx_barycentric_gamma</code></h3>
<p><code>gfx_barycentric_gamma</code> — operation <code>gfx barycentric gamma</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_barycentric_gamma $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-blinn-specular-step">
<h3><a class="doc-anchor" href="#doc-gfx-blinn-specular-step">#</a> <code>gfx_blinn_specular_step</code></h3>
<p><code>gfx_blinn_specular_step</code> — single-step update of <code>gfx blinn specular</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_blinn_specular_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-blue-noise-value">
<h3><a class="doc-anchor" href="#doc-gfx-blue-noise-value">#</a> <code>gfx_blue_noise_value</code></h3>
<p><code>gfx_blue_noise_value</code> — value of <code>gfx blue noise</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_blue_noise_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-bresenham-step-x">
<h3><a class="doc-anchor" href="#doc-gfx-bresenham-step-x">#</a> <code>gfx_bresenham_step_x</code></h3>
<p><code>gfx_bresenham_step_x</code> — operation <code>gfx bresenham step x</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_bresenham_step_x $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-bresenham-step-y">
<h3><a class="doc-anchor" href="#doc-gfx-bresenham-step-y">#</a> <code>gfx_bresenham_step_y</code></h3>
<p><code>gfx_bresenham_step_y</code> — operation <code>gfx bresenham step y</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_bresenham_step_y $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-clip-polygon-step">
<h3><a class="doc-anchor" href="#doc-gfx-clip-polygon-step">#</a> <code>gfx_clip_polygon_step</code></h3>
<p><code>gfx_clip_polygon_step</code> — single-step update of <code>gfx clip polygon</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_clip_polygon_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-cohen-sutherland-code">
<h3><a class="doc-anchor" href="#doc-gfx-cohen-sutherland-code">#</a> <code>gfx_cohen_sutherland_code</code></h3>
<p><code>gfx_cohen_sutherland_code</code> — operation <code>gfx cohen sutherland code</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_cohen_sutherland_code $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-cook-torrance-d-ggx">
<h3><a class="doc-anchor" href="#doc-gfx-cook-torrance-d-ggx">#</a> <code>gfx_cook_torrance_d_ggx</code></h3>
<p><code>gfx_cook_torrance_d_ggx</code> — operation <code>gfx cook torrance d ggx</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_cook_torrance_d_ggx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-cook-torrance-f-schlick">
<h3><a class="doc-anchor" href="#doc-gfx-cook-torrance-f-schlick">#</a> <code>gfx_cook_torrance_f_schlick</code></h3>
<p><code>gfx_cook_torrance_f_schlick</code> — operation <code>gfx cook torrance f schlick</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_cook_torrance_f_schlick $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-cook-torrance-g-smith">
<h3><a class="doc-anchor" href="#doc-gfx-cook-torrance-g-smith">#</a> <code>gfx_cook_torrance_g_smith</code></h3>
<p><code>gfx_cook_torrance_g_smith</code> — operation <code>gfx cook torrance g smith</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_cook_torrance_g_smith $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-cube-map-face-index">
<h3><a class="doc-anchor" href="#doc-gfx-cube-map-face-index">#</a> <code>gfx_cube_map_face_index</code></h3>
<p><code>gfx_cube_map_face_index</code> — index of <code>gfx cube map face</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_cube_map_face_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-curl-noise-step">
<h3><a class="doc-anchor" href="#doc-gfx-curl-noise-step">#</a> <code>gfx_curl_noise_step</code></h3>
<p><code>gfx_curl_noise_step</code> — single-step update of <code>gfx curl noise</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_curl_noise_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-disney-principled-d">
<h3><a class="doc-anchor" href="#doc-gfx-disney-principled-d">#</a> <code>gfx_disney_principled_d</code></h3>
<p><code>gfx_disney_principled_d</code> — operation <code>gfx disney principled d</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_disney_principled_d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-dither-bayer-4x4">
<h3><a class="doc-anchor" href="#doc-gfx-dither-bayer-4x4">#</a> <code>gfx_dither_bayer_4x4</code></h3>
<p><code>gfx_dither_bayer_4x4</code> — operation <code>gfx dither bayer 4x4</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_dither_bayer_4x4 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-dither-floyd-steinberg">
<h3><a class="doc-anchor" href="#doc-gfx-dither-floyd-steinberg">#</a> <code>gfx_dither_floyd_steinberg</code></h3>
<p><code>gfx_dither_floyd_steinberg</code> — operation <code>gfx dither floyd steinberg</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_dither_floyd_steinberg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-environment-map-uv-u">
<h3><a class="doc-anchor" href="#doc-gfx-environment-map-uv-u">#</a> <code>gfx_environment_map_uv_u</code></h3>
<p><code>gfx_environment_map_uv_u</code> — operation <code>gfx environment map uv u</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_environment_map_uv_u $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-environment-map-uv-v">
<h3><a class="doc-anchor" href="#doc-gfx-environment-map-uv-v">#</a> <code>gfx_environment_map_uv_v</code></h3>
<p><code>gfx_environment_map_uv_v</code> — operation <code>gfx environment map uv v</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_environment_map_uv_v $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-euler-to-quat-w">
<h3><a class="doc-anchor" href="#doc-gfx-euler-to-quat-w">#</a> <code>gfx_euler_to_quat_w</code></h3>
<p><code>gfx_euler_to_quat_w</code> — convert from <code>gfx euler</code> to <code>quat w</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_euler_to_quat_w $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-euler-to-quat-x">
<h3><a class="doc-anchor" href="#doc-gfx-euler-to-quat-x">#</a> <code>gfx_euler_to_quat_x</code></h3>
<p><code>gfx_euler_to_quat_x</code> — convert from <code>gfx euler</code> to <code>quat x</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_euler_to_quat_x $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-euler-to-quat-y">
<h3><a class="doc-anchor" href="#doc-gfx-euler-to-quat-y">#</a> <code>gfx_euler_to_quat_y</code></h3>
<p><code>gfx_euler_to_quat_y</code> — convert from <code>gfx euler</code> to <code>quat y</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_euler_to_quat_y $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-euler-to-quat-z">
<h3><a class="doc-anchor" href="#doc-gfx-euler-to-quat-z">#</a> <code>gfx_euler_to_quat_z</code></h3>
<p><code>gfx_euler_to_quat_z</code> — convert from <code>gfx euler</code> to <code>quat z</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_euler_to_quat_z $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-fbm-noise-step">
<h3><a class="doc-anchor" href="#doc-gfx-fbm-noise-step">#</a> <code>gfx_fbm_noise_step</code></h3>
<p><code>gfx_fbm_noise_step</code> — single-step update of <code>gfx fbm noise</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_fbm_noise_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-fresnel-conductor-step">
<h3><a class="doc-anchor" href="#doc-gfx-fresnel-conductor-step">#</a> <code>gfx_fresnel_conductor_step</code></h3>
<p><code>gfx_fresnel_conductor_step</code> — single-step update of <code>gfx fresnel conductor</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_fresnel_conductor_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-fresnel-dielectric-step">
<h3><a class="doc-anchor" href="#doc-gfx-fresnel-dielectric-step">#</a> <code>gfx_fresnel_dielectric_step</code></h3>
<p><code>gfx_fresnel_dielectric_step</code> — single-step update of <code>gfx fresnel dielectric</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_fresnel_dielectric_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-gamma-correct-step">
<h3><a class="doc-anchor" href="#doc-gfx-gamma-correct-step">#</a> <code>gfx_gamma_correct_step</code></h3>
<p><code>gfx_gamma_correct_step</code> — single-step update of <code>gfx gamma correct</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_gamma_correct_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-geometric-attenuation-smith">
<h3><a class="doc-anchor" href="#doc-gfx-geometric-attenuation-smith">#</a> <code>gfx_geometric_attenuation_smith</code></h3>
<p><code>gfx_geometric_attenuation_smith</code> — operation <code>gfx geometric attenuation smith</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_geometric_attenuation_smith $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-gradient-noise-step">
<h3><a class="doc-anchor" href="#doc-gfx-gradient-noise-step">#</a> <code>gfx_gradient_noise_step</code></h3>
<p><code>gfx_gradient_noise_step</code> — single-step update of <code>gfx gradient noise</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_gradient_noise_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-halton-step">
<h3><a class="doc-anchor" href="#doc-gfx-halton-step">#</a> <code>gfx_halton_step</code></h3>
<p><code>gfx_halton_step</code> — single-step update of <code>gfx halton</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_halton_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-homogeneous-divide">
<h3><a class="doc-anchor" href="#doc-gfx-homogeneous-divide">#</a> <code>gfx_homogeneous_divide</code></h3>
<p><code>gfx_homogeneous_divide</code> — operation <code>gfx homogeneous divide</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_homogeneous_divide $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-index-of-refraction">
<h3><a class="doc-anchor" href="#doc-gfx-index-of-refraction">#</a> <code>gfx_index_of_refraction</code></h3>
<p><code>gfx_index_of_refraction</code> — operation <code>gfx index of refraction</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_index_of_refraction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-irradiance-sh-eval">
<h3><a class="doc-anchor" href="#doc-gfx-irradiance-sh-eval">#</a> <code>gfx_irradiance_sh_eval</code></h3>
<p><code>gfx_irradiance_sh_eval</code> — operation <code>gfx irradiance sh eval</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_irradiance_sh_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-lambert-term">
<h3><a class="doc-anchor" href="#doc-gfx-lambert-term">#</a> <code>gfx_lambert_term</code></h3>
<p><code>gfx_lambert_term</code> — operation <code>gfx lambert term</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_lambert_term $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-liang-barsky-t">
<h3><a class="doc-anchor" href="#doc-gfx-liang-barsky-t">#</a> <code>gfx_liang_barsky_t</code></h3>
<p><code>gfx_liang_barsky_t</code> — operation <code>gfx liang barsky t</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_liang_barsky_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-linear-to-srgb">
<h3><a class="doc-anchor" href="#doc-gfx-linear-to-srgb">#</a> <code>gfx_linear_to_srgb</code></h3>
<p><code>gfx_linear_to_srgb</code> — convert from <code>gfx linear</code> to <code>srgb</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_linear_to_srgb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-lookat-forward">
<h3><a class="doc-anchor" href="#doc-gfx-lookat-forward">#</a> <code>gfx_lookat_forward</code></h3>
<p><code>gfx_lookat_forward</code> — operation <code>gfx lookat forward</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_lookat_forward $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-lookat-right">
<h3><a class="doc-anchor" href="#doc-gfx-lookat-right">#</a> <code>gfx_lookat_right</code></h3>
<p><code>gfx_lookat_right</code> — operation <code>gfx lookat right</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_lookat_right $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-lookat-up">
<h3><a class="doc-anchor" href="#doc-gfx-lookat-up">#</a> <code>gfx_lookat_up</code></h3>
<p><code>gfx_lookat_up</code> — operation <code>gfx lookat up</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_lookat_up $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-low-discrepancy-step">
<h3><a class="doc-anchor" href="#doc-gfx-low-discrepancy-step">#</a> <code>gfx_low_discrepancy_step</code></h3>
<p><code>gfx_low_discrepancy_step</code> — single-step update of <code>gfx low discrepancy</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_low_discrepancy_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-microfacet-brdf-step">
<h3><a class="doc-anchor" href="#doc-gfx-microfacet-brdf-step">#</a> <code>gfx_microfacet_brdf_step</code></h3>
<p><code>gfx_microfacet_brdf_step</code> — single-step update of <code>gfx microfacet brdf</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_microfacet_brdf_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-ndc-to-screen-x">
<h3><a class="doc-anchor" href="#doc-gfx-ndc-to-screen-x">#</a> <code>gfx_ndc_to_screen_x</code></h3>
<p><code>gfx_ndc_to_screen_x</code> — convert from <code>gfx ndc</code> to <code>screen x</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_ndc_to_screen_x $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-ndc-to-screen-y">
<h3><a class="doc-anchor" href="#doc-gfx-ndc-to-screen-y">#</a> <code>gfx_ndc_to_screen_y</code></h3>
<p><code>gfx_ndc_to_screen_y</code> — convert from <code>gfx ndc</code> to <code>screen y</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_ndc_to_screen_y $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-normal-distribution-ggx">
<h3><a class="doc-anchor" href="#doc-gfx-normal-distribution-ggx">#</a> <code>gfx_normal_distribution_ggx</code></h3>
<p><code>gfx_normal_distribution_ggx</code> — operation <code>gfx normal distribution ggx</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_normal_distribution_ggx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-obb-overlap-step">
<h3><a class="doc-anchor" href="#doc-gfx-obb-overlap-step">#</a> <code>gfx_obb_overlap_step</code></h3>
<p><code>gfx_obb_overlap_step</code> — single-step update of <code>gfx obb overlap</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_obb_overlap_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-octahedral-encode-x">
<h3><a class="doc-anchor" href="#doc-gfx-octahedral-encode-x">#</a> <code>gfx_octahedral_encode_x</code></h3>
<p><code>gfx_octahedral_encode_x</code> — operation <code>gfx octahedral encode x</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_octahedral_encode_x $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-octahedral-encode-y">
<h3><a class="doc-anchor" href="#doc-gfx-octahedral-encode-y">#</a> <code>gfx_octahedral_encode_y</code></h3>
<p><code>gfx_octahedral_encode_y</code> — operation <code>gfx octahedral encode y</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_octahedral_encode_y $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-oklab-a-step">
<h3><a class="doc-anchor" href="#doc-gfx-oklab-a-step">#</a> <code>gfx_oklab_a_step</code></h3>
<p><code>gfx_oklab_a_step</code> — single-step update of <code>gfx oklab a</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_oklab_a_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-oklab-b-step">
<h3><a class="doc-anchor" href="#doc-gfx-oklab-b-step">#</a> <code>gfx_oklab_b_step</code></h3>
<p><code>gfx_oklab_b_step</code> — single-step update of <code>gfx oklab b</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_oklab_b_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-oklab-l-step">
<h3><a class="doc-anchor" href="#doc-gfx-oklab-l-step">#</a> <code>gfx_oklab_l_step</code></h3>
<p><code>gfx_oklab_l_step</code> — single-step update of <code>gfx oklab l</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_oklab_l_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-oklch-chroma">
<h3><a class="doc-anchor" href="#doc-gfx-oklch-chroma">#</a> <code>gfx_oklch_chroma</code></h3>
<p><code>gfx_oklch_chroma</code> — operation <code>gfx oklch chroma</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_oklch_chroma $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-oklch-hue">
<h3><a class="doc-anchor" href="#doc-gfx-oklch-hue">#</a> <code>gfx_oklch_hue</code></h3>
<p><code>gfx_oklch_hue</code> — operation <code>gfx oklch hue</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_oklch_hue $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-oren-nayar-term">
<h3><a class="doc-anchor" href="#doc-gfx-oren-nayar-term">#</a> <code>gfx_oren_nayar_term</code></h3>
<p><code>gfx_oren_nayar_term</code> — operation <code>gfx oren nayar term</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_oren_nayar_term $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-orthographic-proj">
<h3><a class="doc-anchor" href="#doc-gfx-orthographic-proj">#</a> <code>gfx_orthographic_proj</code></h3>
<p><code>gfx_orthographic_proj</code> — operation <code>gfx orthographic proj</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_orthographic_proj $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-pcg-hash-step">
<h3><a class="doc-anchor" href="#doc-gfx-pcg-hash-step">#</a> <code>gfx_pcg_hash_step</code></h3>
<p><code>gfx_pcg_hash_step</code> — single-step update of <code>gfx pcg hash</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_pcg_hash_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-perlin-noise-step">
<h3><a class="doc-anchor" href="#doc-gfx-perlin-noise-step">#</a> <code>gfx_perlin_noise_step</code></h3>
<p><code>gfx_perlin_noise_step</code> — single-step update of <code>gfx perlin noise</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_perlin_noise_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-perspective-proj-x">
<h3><a class="doc-anchor" href="#doc-gfx-perspective-proj-x">#</a> <code>gfx_perspective_proj_x</code></h3>
<p><code>gfx_perspective_proj_x</code> — operation <code>gfx perspective proj x</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_perspective_proj_x $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-perspective-proj-y">
<h3><a class="doc-anchor" href="#doc-gfx-perspective-proj-y">#</a> <code>gfx_perspective_proj_y</code></h3>
<p><code>gfx_perspective_proj_y</code> — operation <code>gfx perspective proj y</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_perspective_proj_y $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-phong-ambient-step">
<h3><a class="doc-anchor" href="#doc-gfx-phong-ambient-step">#</a> <code>gfx_phong_ambient_step</code></h3>
<p><code>gfx_phong_ambient_step</code> — single-step update of <code>gfx phong ambient</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_phong_ambient_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-phong-diffuse-step">
<h3><a class="doc-anchor" href="#doc-gfx-phong-diffuse-step">#</a> <code>gfx_phong_diffuse_step</code></h3>
<p><code>gfx_phong_diffuse_step</code> — single-step update of <code>gfx phong diffuse</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_phong_diffuse_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-phong-specular-step">
<h3><a class="doc-anchor" href="#doc-gfx-phong-specular-step">#</a> <code>gfx_phong_specular_step</code></h3>
<p><code>gfx_phong_specular_step</code> — single-step update of <code>gfx phong specular</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_phong_specular_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-quat-dot-two">
<h3><a class="doc-anchor" href="#doc-gfx-quat-dot-two">#</a> <code>gfx_quat_dot_two</code></h3>
<p><code>gfx_quat_dot_two</code> — operation <code>gfx quat dot two</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_quat_dot_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-quat-inverse-step">
<h3><a class="doc-anchor" href="#doc-gfx-quat-inverse-step">#</a> <code>gfx_quat_inverse_step</code></h3>
<p><code>gfx_quat_inverse_step</code> — single-step update of <code>gfx quat inverse</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_quat_inverse_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-quat-nlerp-step">
<h3><a class="doc-anchor" href="#doc-gfx-quat-nlerp-step">#</a> <code>gfx_quat_nlerp_step</code></h3>
<p><code>gfx_quat_nlerp_step</code> — single-step update of <code>gfx quat nlerp</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_quat_nlerp_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-quat-slerp-step">
<h3><a class="doc-anchor" href="#doc-gfx-quat-slerp-step">#</a> <code>gfx_quat_slerp_step</code></h3>
<p><code>gfx_quat_slerp_step</code> — single-step update of <code>gfx quat slerp</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_quat_slerp_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-quat-to-axis-angle">
<h3><a class="doc-anchor" href="#doc-gfx-quat-to-axis-angle">#</a> <code>gfx_quat_to_axis_angle</code></h3>
<p><code>gfx_quat_to_axis_angle</code> — convert from <code>gfx quat</code> to <code>axis angle</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_quat_to_axis_angle $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-quat-to-euler-pitch">
<h3><a class="doc-anchor" href="#doc-gfx-quat-to-euler-pitch">#</a> <code>gfx_quat_to_euler_pitch</code></h3>
<p><code>gfx_quat_to_euler_pitch</code> — convert from <code>gfx quat</code> to <code>euler pitch</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_quat_to_euler_pitch $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-quat-to-euler-roll">
<h3><a class="doc-anchor" href="#doc-gfx-quat-to-euler-roll">#</a> <code>gfx_quat_to_euler_roll</code></h3>
<p><code>gfx_quat_to_euler_roll</code> — convert from <code>gfx quat</code> to <code>euler roll</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_quat_to_euler_roll $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-quat-to-euler-yaw">
<h3><a class="doc-anchor" href="#doc-gfx-quat-to-euler-yaw">#</a> <code>gfx_quat_to_euler_yaw</code></h3>
<p><code>gfx_quat_to_euler_yaw</code> — convert from <code>gfx quat</code> to <code>euler yaw</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_quat_to_euler_yaw $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-radiance-sh-eval">
<h3><a class="doc-anchor" href="#doc-gfx-radiance-sh-eval">#</a> <code>gfx_radiance_sh_eval</code></h3>
<p><code>gfx_radiance_sh_eval</code> — operation <code>gfx radiance sh eval</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_radiance_sh_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-ray-box-t">
<h3><a class="doc-anchor" href="#doc-gfx-ray-box-t">#</a> <code>gfx_ray_box_t</code></h3>
<p><code>gfx_ray_box_t</code> — operation <code>gfx ray box t</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_ray_box_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-ray-cone-t">
<h3><a class="doc-anchor" href="#doc-gfx-ray-cone-t">#</a> <code>gfx_ray_cone_t</code></h3>
<p><code>gfx_ray_cone_t</code> — operation <code>gfx ray cone t</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_ray_cone_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-ray-cylinder-t">
<h3><a class="doc-anchor" href="#doc-gfx-ray-cylinder-t">#</a> <code>gfx_ray_cylinder_t</code></h3>
<p><code>gfx_ray_cylinder_t</code> — operation <code>gfx ray cylinder t</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_ray_cylinder_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-ray-disk-t">
<h3><a class="doc-anchor" href="#doc-gfx-ray-disk-t">#</a> <code>gfx_ray_disk_t</code></h3>
<p><code>gfx_ray_disk_t</code> — operation <code>gfx ray disk t</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_ray_disk_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-ray-ellipsoid-t">
<h3><a class="doc-anchor" href="#doc-gfx-ray-ellipsoid-t">#</a> <code>gfx_ray_ellipsoid_t</code></h3>
<p><code>gfx_ray_ellipsoid_t</code> — operation <code>gfx ray ellipsoid t</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_ray_ellipsoid_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-ray-plane-t">
<h3><a class="doc-anchor" href="#doc-gfx-ray-plane-t">#</a> <code>gfx_ray_plane_t</code></h3>
<p><code>gfx_ray_plane_t</code> — operation <code>gfx ray plane t</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_ray_plane_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-ray-sphere-t">
<h3><a class="doc-anchor" href="#doc-gfx-ray-sphere-t">#</a> <code>gfx_ray_sphere_t</code></h3>
<p><code>gfx_ray_sphere_t</code> — operation <code>gfx ray sphere t</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_ray_sphere_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-ray-torus-t-approx">
<h3><a class="doc-anchor" href="#doc-gfx-ray-torus-t-approx">#</a> <code>gfx_ray_torus_t_approx</code></h3>
<p><code>gfx_ray_torus_t_approx</code> — operation <code>gfx ray torus t approx</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_ray_torus_t_approx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-ray-triangle-t">
<h3><a class="doc-anchor" href="#doc-gfx-ray-triangle-t">#</a> <code>gfx_ray_triangle_t</code></h3>
<p><code>gfx_ray_triangle_t</code> — operation <code>gfx ray triangle t</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_ray_triangle_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-reflect-direction-x">
<h3><a class="doc-anchor" href="#doc-gfx-reflect-direction-x">#</a> <code>gfx_reflect_direction_x</code></h3>
<p><code>gfx_reflect_direction_x</code> — operation <code>gfx reflect direction x</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_reflect_direction_x $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-refract-direction-x">
<h3><a class="doc-anchor" href="#doc-gfx-refract-direction-x">#</a> <code>gfx_refract_direction_x</code></h3>
<p><code>gfx_refract_direction_x</code> — operation <code>gfx refract direction x</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_refract_direction_x $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-rotation-matrix-xx">
<h3><a class="doc-anchor" href="#doc-gfx-rotation-matrix-xx">#</a> <code>gfx_rotation_matrix_xx</code></h3>
<p><code>gfx_rotation_matrix_xx</code> — operation <code>gfx rotation matrix xx</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_rotation_matrix_xx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-rotation-matrix-yy">
<h3><a class="doc-anchor" href="#doc-gfx-rotation-matrix-yy">#</a> <code>gfx_rotation_matrix_yy</code></h3>
<p><code>gfx_rotation_matrix_yy</code> — operation <code>gfx rotation matrix yy</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_rotation_matrix_yy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-rotation-matrix-zz">
<h3><a class="doc-anchor" href="#doc-gfx-rotation-matrix-zz">#</a> <code>gfx_rotation_matrix_zz</code></h3>
<p><code>gfx_rotation_matrix_zz</code> — operation <code>gfx rotation matrix zz</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_rotation_matrix_zz $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-scale-matrix-step">
<h3><a class="doc-anchor" href="#doc-gfx-scale-matrix-step">#</a> <code>gfx_scale_matrix_step</code></h3>
<p><code>gfx_scale_matrix_step</code> — single-step update of <code>gfx scale matrix</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_scale_matrix_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-screen-space-x">
<h3><a class="doc-anchor" href="#doc-gfx-screen-space-x">#</a> <code>gfx_screen_space_x</code></h3>
<p><code>gfx_screen_space_x</code> — operation <code>gfx screen space x</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_screen_space_x $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-screen-space-y">
<h3><a class="doc-anchor" href="#doc-gfx-screen-space-y">#</a> <code>gfx_screen_space_y</code></h3>
<p><code>gfx_screen_space_y</code> — operation <code>gfx screen space y</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_screen_space_y $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-screen-to-ndc-x">
<h3><a class="doc-anchor" href="#doc-gfx-screen-to-ndc-x">#</a> <code>gfx_screen_to_ndc_x</code></h3>
<p><code>gfx_screen_to_ndc_x</code> — convert from <code>gfx screen</code> to <code>ndc x</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_screen_to_ndc_x $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-screen-to-ndc-y">
<h3><a class="doc-anchor" href="#doc-gfx-screen-to-ndc-y">#</a> <code>gfx_screen_to_ndc_y</code></h3>
<p><code>gfx_screen_to_ndc_y</code> — convert from <code>gfx screen</code> to <code>ndc y</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_screen_to_ndc_y $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-shear-matrix-xy">
<h3><a class="doc-anchor" href="#doc-gfx-shear-matrix-xy">#</a> <code>gfx_shear_matrix_xy</code></h3>
<p><code>gfx_shear_matrix_xy</code> — operation <code>gfx shear matrix xy</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_shear_matrix_xy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-signed-distance-box">
<h3><a class="doc-anchor" href="#doc-gfx-signed-distance-box">#</a> <code>gfx_signed_distance_box</code></h3>
<p><code>gfx_signed_distance_box</code> — operation <code>gfx signed distance box</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_signed_distance_box $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-signed-distance-capsule">
<h3><a class="doc-anchor" href="#doc-gfx-signed-distance-capsule">#</a> <code>gfx_signed_distance_capsule</code></h3>
<p><code>gfx_signed_distance_capsule</code> — operation <code>gfx signed distance capsule</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_signed_distance_capsule $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-signed-distance-sphere">
<h3><a class="doc-anchor" href="#doc-gfx-signed-distance-sphere">#</a> <code>gfx_signed_distance_sphere</code></h3>
<p><code>gfx_signed_distance_sphere</code> — operation <code>gfx signed distance sphere</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_signed_distance_sphere $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-simplex-noise-step">
<h3><a class="doc-anchor" href="#doc-gfx-simplex-noise-step">#</a> <code>gfx_simplex_noise_step</code></h3>
<p><code>gfx_simplex_noise_step</code> — single-step update of <code>gfx simplex noise</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_simplex_noise_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-skybox-uv-u">
<h3><a class="doc-anchor" href="#doc-gfx-skybox-uv-u">#</a> <code>gfx_skybox_uv_u</code></h3>
<p><code>gfx_skybox_uv_u</code> — operation <code>gfx skybox uv u</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_skybox_uv_u $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-skybox-uv-v">
<h3><a class="doc-anchor" href="#doc-gfx-skybox-uv-v">#</a> <code>gfx_skybox_uv_v</code></h3>
<p><code>gfx_skybox_uv_v</code> — operation <code>gfx skybox uv v</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_skybox_uv_v $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-snells-law-angle">
<h3><a class="doc-anchor" href="#doc-gfx-snells-law-angle">#</a> <code>gfx_snells_law_angle</code></h3>
<p><code>gfx_snells_law_angle</code> — operation <code>gfx snells law angle</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_snells_law_angle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-sobol-step">
<h3><a class="doc-anchor" href="#doc-gfx-sobol-step">#</a> <code>gfx_sobol_step</code></h3>
<p><code>gfx_sobol_step</code> — single-step update of <code>gfx sobol</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_sobol_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-sphere-intersect-t">
<h3><a class="doc-anchor" href="#doc-gfx-sphere-intersect-t">#</a> <code>gfx_sphere_intersect_t</code></h3>
<p><code>gfx_sphere_intersect_t</code> — operation <code>gfx sphere intersect t</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_sphere_intersect_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-spherical-harmonic-y00">
<h3><a class="doc-anchor" href="#doc-gfx-spherical-harmonic-y00">#</a> <code>gfx_spherical_harmonic_y00</code></h3>
<p><code>gfx_spherical_harmonic_y00</code> — operation <code>gfx spherical harmonic y00</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_spherical_harmonic_y00 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-spherical-harmonic-y10">
<h3><a class="doc-anchor" href="#doc-gfx-spherical-harmonic-y10">#</a> <code>gfx_spherical_harmonic_y10</code></h3>
<p><code>gfx_spherical_harmonic_y10</code> — operation <code>gfx spherical harmonic y10</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_spherical_harmonic_y10 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-spherical-harmonic-y11">
<h3><a class="doc-anchor" href="#doc-gfx-spherical-harmonic-y11">#</a> <code>gfx_spherical_harmonic_y11</code></h3>
<p><code>gfx_spherical_harmonic_y11</code> — operation <code>gfx spherical harmonic y11</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_spherical_harmonic_y11 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-spherical-harmonic-y20">
<h3><a class="doc-anchor" href="#doc-gfx-spherical-harmonic-y20">#</a> <code>gfx_spherical_harmonic_y20</code></h3>
<p><code>gfx_spherical_harmonic_y20</code> — operation <code>gfx spherical harmonic y20</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_spherical_harmonic_y20 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-srgb-to-linear">
<h3><a class="doc-anchor" href="#doc-gfx-srgb-to-linear">#</a> <code>gfx_srgb_to_linear</code></h3>
<p><code>gfx_srgb_to_linear</code> — convert from <code>gfx srgb</code> to <code>linear</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_srgb_to_linear $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-subsurface-scattering-term">
<h3><a class="doc-anchor" href="#doc-gfx-subsurface-scattering-term">#</a> <code>gfx_subsurface_scattering_term</code></h3>
<p><code>gfx_subsurface_scattering_term</code> — operation <code>gfx subsurface scattering term</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_subsurface_scattering_term $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-sutherland-hodgman">
<h3><a class="doc-anchor" href="#doc-gfx-sutherland-hodgman">#</a> <code>gfx_sutherland_hodgman</code></h3>
<p><code>gfx_sutherland_hodgman</code> — operation <code>gfx sutherland hodgman</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_sutherland_hodgman $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-tonemap-aces">
<h3><a class="doc-anchor" href="#doc-gfx-tonemap-aces">#</a> <code>gfx_tonemap_aces</code></h3>
<p><code>gfx_tonemap_aces</code> — operation <code>gfx tonemap aces</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_tonemap_aces $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-tonemap-filmic">
<h3><a class="doc-anchor" href="#doc-gfx-tonemap-filmic">#</a> <code>gfx_tonemap_filmic</code></h3>
<p><code>gfx_tonemap_filmic</code> — operation <code>gfx tonemap filmic</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_tonemap_filmic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-tonemap-reinhard">
<h3><a class="doc-anchor" href="#doc-gfx-tonemap-reinhard">#</a> <code>gfx_tonemap_reinhard</code></h3>
<p><code>gfx_tonemap_reinhard</code> — operation <code>gfx tonemap reinhard</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_tonemap_reinhard $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-tonemap-uncharted2">
<h3><a class="doc-anchor" href="#doc-gfx-tonemap-uncharted2">#</a> <code>gfx_tonemap_uncharted2</code></h3>
<p><code>gfx_tonemap_uncharted2</code> — operation <code>gfx tonemap uncharted2</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_tonemap_uncharted2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-total-internal-reflection">
<h3><a class="doc-anchor" href="#doc-gfx-total-internal-reflection">#</a> <code>gfx_total_internal_reflection</code></h3>
<p><code>gfx_total_internal_reflection</code> — operation <code>gfx total internal reflection</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_total_internal_reflection $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-translation-matrix-step">
<h3><a class="doc-anchor" href="#doc-gfx-translation-matrix-step">#</a> <code>gfx_translation_matrix_step</code></h3>
<p><code>gfx_translation_matrix_step</code> — single-step update of <code>gfx translation matrix</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_translation_matrix_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-translucent-falloff">
<h3><a class="doc-anchor" href="#doc-gfx-translucent-falloff">#</a> <code>gfx_translucent_falloff</code></h3>
<p><code>gfx_translucent_falloff</code> — operation <code>gfx translucent falloff</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_translucent_falloff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-value-noise-step">
<h3><a class="doc-anchor" href="#doc-gfx-value-noise-step">#</a> <code>gfx_value_noise_step</code></h3>
<p><code>gfx_value_noise_step</code> — single-step update of <code>gfx value noise</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_value_noise_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-van-der-corput">
<h3><a class="doc-anchor" href="#doc-gfx-van-der-corput">#</a> <code>gfx_van_der_corput</code></h3>
<p><code>gfx_van_der_corput</code> — operation <code>gfx van der corput</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_van_der_corput $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-view-matrix-step">
<h3><a class="doc-anchor" href="#doc-gfx-view-matrix-step">#</a> <code>gfx_view_matrix_step</code></h3>
<p><code>gfx_view_matrix_step</code> — single-step update of <code>gfx view matrix</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_view_matrix_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-voronoi-distance">
<h3><a class="doc-anchor" href="#doc-gfx-voronoi-distance">#</a> <code>gfx_voronoi_distance</code></h3>
<p><code>gfx_voronoi_distance</code> — distance / dissimilarity metric of <code>gfx voronoi</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_voronoi_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-worley-noise-step">
<h3><a class="doc-anchor" href="#doc-gfx-worley-noise-step">#</a> <code>gfx_worley_noise_step</code></h3>
<p><code>gfx_worley_noise_step</code> — single-step update of <code>gfx worley noise</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_worley_noise_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-xiaolin-wu-intensity">
<h3><a class="doc-anchor" href="#doc-gfx-xiaolin-wu-intensity">#</a> <code>gfx_xiaolin_wu_intensity</code></h3>
<p><code>gfx_xiaolin_wu_intensity</code> — operation <code>gfx xiaolin wu intensity</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_xiaolin_wu_intensity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-xorshift-step">
<h3><a class="doc-anchor" href="#doc-gfx-xorshift-step">#</a> <code>gfx_xorshift_step</code></h3>
<p><code>gfx_xorshift_step</code> — single-step update of <code>gfx xorshift</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_xorshift_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gfx-zonal-harmonic-step">
<h3><a class="doc-anchor" href="#doc-gfx-zonal-harmonic-step">#</a> <code>gfx_zonal_harmonic_step</code></h3>
<p><code>gfx_zonal_harmonic_step</code> — single-step update of <code>gfx zonal harmonic</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gfx_zonal_harmonic_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ghz-state">
<h3><a class="doc-anchor" href="#doc-ghz-state">#</a> <code>ghz_state</code></h3>
<p><code>ghz_state</code> — operation <code>ghz state</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p ghz_state $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ghz-state-n">
<h3><a class="doc-anchor" href="#doc-ghz-state-n">#</a> <code>ghz_state_n</code></h3>
<p><code>ghz_state_n</code> — operation <code>ghz state n</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p ghz_state_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gibbard-satterthwaite-check">
<h3><a class="doc-anchor" href="#doc-gibbard-satterthwaite-check">#</a> <code>gibbard_satterthwaite_check</code></h3>
<p><code>gibbard_satterthwaite_check</code> — operation <code>gibbard satterthwaite check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gibbard_satterthwaite_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gibbs-thomson-undercooling">
<h3><a class="doc-anchor" href="#doc-gibbs-thomson-undercooling">#</a> <code>gibbs_thomson_undercooling</code></h3>
<p><code>gibbs_thomson_undercooling</code> — operation <code>gibbs thomson undercooling</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p gibbs_thomson_undercooling $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gid">
<h3><a class="doc-anchor" href="#doc-gid">#</a> <code>gid</code></h3>
<p><code>gid</code> — operation <code>gid</code>. Category: *system introspection*.</p>
<pre><code class="lang-perl">p gid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gif-header-read">
<h3><a class="doc-anchor" href="#doc-gif-header-read">#</a> <code>gif_header_read</code></h3>
<p><code>gif_header_read(hex_bytes) → hash</code> — parse GIF magic+lsd → <code>{format, version, width, height}</code>.</p>
</article>
<article class="doc-entry" id="doc-gin">
<h3><a class="doc-anchor" href="#doc-gin">#</a> <code>gin</code></h3>
<p><code>gin</code> — operation <code>gin</code>. Alias for <code>get_in</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p gin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gini">
<h3><a class="doc-anchor" href="#doc-gini">#</a> <code>gini</code></h3>
<p><code>gini(@data)</code> (alias <code>gini_coefficient</code>) — computes the Gini coefficient measuring inequality in a distribution. Returns a value from 0 (perfect equality) to 1 (perfect inequality). Commonly used for income distribution analysis.</p>
<pre><code class="lang-perl">p gini(1, 1, 1, 1) # 0 (perfect equality)
p gini(0, 0, 0, 100) # ~0.75 (high inequality)
</code></pre>
</article>
<article class="doc-entry" id="doc-gini-impurity">
<h3><a class="doc-anchor" href="#doc-gini-impurity">#</a> <code>gini_impurity</code></h3>
<p><code>gini_impurity</code> — operation <code>gini impurity</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p gini_impurity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gini-inequality-health">
<h3><a class="doc-anchor" href="#doc-gini-inequality-health">#</a> <code>gini_inequality_health</code></h3>
<p><code>gini_inequality_health</code> — operation <code>gini inequality health</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p gini_inequality_health $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gini-market">
<h3><a class="doc-anchor" href="#doc-gini-market">#</a> <code>gini_market</code></h3>
<p><code>gini_market</code> — operation <code>gini market</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p gini_market $x
</code></pre>
</article>
<article class="doc-entry" id="doc-girth">
<h3><a class="doc-anchor" href="#doc-girth">#</a> <code>girth</code></h3>
<p><code>girth</code> — operation <code>girth</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p girth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-girvan-newman">
<h3><a class="doc-anchor" href="#doc-girvan-newman">#</a> <code>girvan_newman</code></h3>
<p><code>girvan_newman</code> — operation <code>girvan newman</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p girvan_newman $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gk15">
<h3><a class="doc-anchor" href="#doc-gk15">#</a> <code>gk15</code></h3>
<p><code>gk15</code> — operation <code>gk15</code>. Alias for <code>gauss_kronrod_15</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p gk15 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gl5">
<h3><a class="doc-anchor" href="#doc-gl5">#</a> <code>gl5</code></h3>
<p><code>gl5</code> — operation <code>gl5</code>. Alias for <code>gauss_legendre_5</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p gl5 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-glaisher">
<h3><a class="doc-anchor" href="#doc-glaisher">#</a> <code>glaisher</code></h3>
<p><code>glaisher</code> — operation <code>glaisher</code>. Alias for <code>glaisher_constant</code>. Category: *math constants*.</p>
<pre><code class="lang-perl">p glaisher $x
</code></pre>
</article>
<article class="doc-entry" id="doc-glaisher-constant">
<h3><a class="doc-anchor" href="#doc-glaisher-constant">#</a> <code>glaisher_constant</code></h3>
<p><code>glaisher_constant</code> — operation <code>glaisher constant</code>. Category: *math constants*.</p>
<pre><code class="lang-perl">p glaisher_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-glicko-rating">
<h3><a class="doc-anchor" href="#doc-glicko-rating">#</a> <code>glicko_rating</code></h3>
<p><code>glicko_rating</code> — operation <code>glicko rating</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p glicko_rating $x
</code></pre>
</article>
<article class="doc-entry" id="doc-glicko-rd-update">
<h3><a class="doc-anchor" href="#doc-glicko-rd-update">#</a> <code>glicko_rd_update</code></h3>
<p><code>glicko_rd_update(rd, c=34.6, t=1) → number</code> — Glicko RD growth over inactive periods: <code>√(rd² + c²·t)</code>, capped at 350.</p>
</article>
<article class="doc-entry" id="doc-glicko-volatility">
<h3><a class="doc-anchor" href="#doc-glicko-volatility">#</a> <code>glicko_volatility</code></h3>
<p><code>glicko_volatility(sigma, delta, phi, v, tau=0.5) → number</code> — Glicko-2 volatility update (Illinois iteration on f(x) = 0).</p>
</article>
<article class="doc-entry" id="doc-glm">
<h3><a class="doc-anchor" href="#doc-glm">#</a> <code>glm</code></h3>
<p><code>glm</code> — operation <code>glm</code>. Category: *r / scipy distributions and tests*.</p>
<pre><code class="lang-perl">p glm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-glob-to-regex">
<h3><a class="doc-anchor" href="#doc-glob-to-regex">#</a> <code>glob_to_regex</code></h3>
<p><code>glob_to_regex</code> — convert from <code>glob</code> to <code>regex</code>. Category: *more regex*.</p>
<pre><code class="lang-perl">p glob_to_regex $value
</code></pre>
</article>
<article class="doc-entry" id="doc-global-efficiency">
<h3><a class="doc-anchor" href="#doc-global-efficiency">#</a> <code>global_efficiency</code></h3>
<p><code>global_efficiency</code> — operation <code>global efficiency</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p global_efficiency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-glushkov-construction">
<h3><a class="doc-anchor" href="#doc-glushkov-construction">#</a> <code>glushkov_construction</code></h3>
<p><code>glushkov_construction</code> — operation <code>glushkov construction</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p glushkov_construction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gmm-moment-condition">
<h3><a class="doc-anchor" href="#doc-gmm-moment-condition">#</a> <code>gmm_moment_condition</code></h3>
<p><code>gmm_moment_condition</code> — operation <code>gmm moment condition</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p gmm_moment_condition $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gmm-moment-function">
<h3><a class="doc-anchor" href="#doc-gmm-moment-function">#</a> <code>gmm_moment_function</code></h3>
<p><code>gmm_moment_function</code> — operation <code>gmm moment function</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p gmm_moment_function $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gnomonic-number">
<h3><a class="doc-anchor" href="#doc-gnomonic-number">#</a> <code>gnomonic_number</code></h3>
<p><code>gnomonic_number(n) → int</code> — <code>2n - 1</code>. n-th odd number.</p>
</article>
<article class="doc-entry" id="doc-go-enrichment-p">
<h3><a class="doc-anchor" href="#doc-go-enrichment-p">#</a> <code>go_enrichment_p</code></h3>
<p><code>go_enrichment_p</code> — operation <code>go enrichment p</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p go_enrichment_p $x
</code></pre>
</article>
<article class="doc-entry" id="doc-goals-above-avg">
<h3><a class="doc-anchor" href="#doc-goals-above-avg">#</a> <code>goals_above_avg</code></h3>
<p><code>goals_above_avg</code> — operation <code>goals above avg</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p goals_above_avg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-goertzel">
<h3><a class="doc-anchor" href="#doc-goertzel">#</a> <code>goertzel</code></h3>
<p><code>goertzel</code> computes the magnitude of a single DFT frequency bin using the Goertzel algorithm. Much faster than full FFT when you need one frequency.</p>
<pre><code class="lang-perl">my $mag = goertzel(\@signal, 440, 44100) # 440 Hz component
</code></pre>
</article>
<article class="doc-entry" id="doc-goldb">
<h3><a class="doc-anchor" href="#doc-goldb">#</a> <code>goldb</code></h3>
<p><code>goldb</code> — operation <code>goldb</code>. Alias for <code>goldbach</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p goldb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-goldbach">
<h3><a class="doc-anchor" href="#doc-goldbach">#</a> <code>goldbach</code></h3>
<p><code>goldbach</code> — operation <code>goldbach</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p goldbach $x
</code></pre>
</article>
<article class="doc-entry" id="doc-goldbach-pair">
<h3><a class="doc-anchor" href="#doc-goldbach-pair">#</a> <code>goldbach_pair</code></h3>
<p><code>goldbach_pair</code> — operation <code>goldbach pair</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p goldbach_pair $x
</code></pre>
</article>
<article class="doc-entry" id="doc-golden">
<h3><a class="doc-anchor" href="#doc-golden">#</a> <code>golden</code></h3>
<p><code>golden_section</code> (aliases <code>golden</code>, <code>gss</code>) finds the minimum of f on [a,b] via golden-section search.</p>
<pre><code class="lang-perl">my $xmin = golden(fn { ($_[0]-3)**2 }, 0, 10) # 3.0
</code></pre>
</article>
<article class="doc-entry" id="doc-golden-ratio">
<h3><a class="doc-anchor" href="#doc-golden-ratio">#</a> <code>golden_ratio</code></h3>
<p><code>golden_ratio</code> (alias <code>phi</code>) — φ = (1+√5)/2 ≈ 1.618. The golden ratio, appears throughout nature and art.</p>
<pre><code class="lang-perl">p phi # 1.618033988749895
# Fibonacci limit: fib(n)/fib(n-1) → φ
</code></pre>
</article>
<article class="doc-entry" id="doc-goldfeld-quandt">
<h3><a class="doc-anchor" href="#doc-goldfeld-quandt">#</a> <code>goldfeld_quandt</code></h3>
<p><code>goldfeld_quandt</code> — operation <code>goldfeld quandt</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p goldfeld_quandt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-golomb-rice-code">
<h3><a class="doc-anchor" href="#doc-golomb-rice-code">#</a> <code>golomb_rice_code</code></h3>
<p><code>golomb_rice_code</code> — operation <code>golomb rice code</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p golomb_rice_code $x
</code></pre>
</article>
<article class="doc-entry" id="doc-golstep">
<h3><a class="doc-anchor" href="#doc-golstep">#</a> <code>golstep</code></h3>
<p><code>golstep</code> — operation <code>golstep</code>. Alias for <code>game_of_life_step</code>. Category: *algorithms / puzzles*.</p>
<pre><code class="lang-perl">p golstep $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gomory-cut-step">
<h3><a class="doc-anchor" href="#doc-gomory-cut-step">#</a> <code>gomory_cut_step</code></h3>
<p><code>gomory_cut_step</code> — single-step update of <code>gomory cut</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p gomory_cut_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gomory-hu-step">
<h3><a class="doc-anchor" href="#doc-gomory-hu-step">#</a> <code>gomory_hu_step</code></h3>
<p><code>gomory_hu_step</code> — single-step update of <code>gomory hu</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p gomory_hu_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gompertz-growth-step">
<h3><a class="doc-anchor" href="#doc-gompertz-growth-step">#</a> <code>gompertz_growth_step</code></h3>
<p><code>gompertz_growth_step</code> — single-step update of <code>gompertz growth</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p gompertz_growth_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gompertz-pdf">
<h3><a class="doc-anchor" href="#doc-gompertz-pdf">#</a> <code>gompertz_pdf</code></h3>
<p><code>gompertz_pdf</code> — operation <code>gompertz pdf</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p gompertz_pdf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-goto">
<h3><a class="doc-anchor" href="#doc-goto">#</a> <code>goto</code></h3>
<p><code>goto</code> — operation <code>goto</code>. Category: *control flow*.</p>
<pre><code class="lang-perl">p goto $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gouy-chapman-potential">
<h3><a class="doc-anchor" href="#doc-gouy-chapman-potential">#</a> <code>gouy_chapman_potential</code></h3>
<p><code>gouy_chapman_potential</code> — operation <code>gouy chapman potential</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p gouy_chapman_potential $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gradient-descent-step">
<h3><a class="doc-anchor" href="#doc-gradient-descent-step">#</a> <code>gradient_descent_step</code></h3>
<p><code>gradient_descent_step</code> — single-step update of <code>gradient descent</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p gradient_descent_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gradient-geothermal">
<h3><a class="doc-anchor" href="#doc-gradient-geothermal">#</a> <code>gradient_geothermal</code></h3>
<p><code>gradient_geothermal</code> — operation <code>gradient geothermal</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p gradient_geothermal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gradient-magnitude-2d">
<h3><a class="doc-anchor" href="#doc-gradient-magnitude-2d">#</a> <code>gradient_magnitude_2d</code></h3>
<p><code>gradient_magnitude_2d(image) → matrix</code> — <code>√(Gx² + Gy²)</code> using Sobel kernels.</p>
<pre><code class="lang-perl">p gradient_magnitude_2d($img)
</code></pre>
</article>
<article class="doc-entry" id="doc-gradient-richardson-full">
<h3><a class="doc-anchor" href="#doc-gradient-richardson-full">#</a> <code>gradient_richardson_full</code></h3>
<p><code>gradient_richardson_full</code> — operation <code>gradient richardson full</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gradient_richardson_full $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gradient-temporal-diff">
<h3><a class="doc-anchor" href="#doc-gradient-temporal-diff">#</a> <code>gradient_temporal_diff</code></h3>
<p><code>gradient_temporal_diff</code> — operation <code>gradient temporal diff</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p gradient_temporal_diff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gradient-wind-step">
<h3><a class="doc-anchor" href="#doc-gradient-wind-step">#</a> <code>gradient_wind_step</code></h3>
<p><code>gradient_wind_step</code> — single-step update of <code>gradient wind</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p gradient_wind_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graham-2approx-bound">
<h3><a class="doc-anchor" href="#doc-graham-2approx-bound">#</a> <code>graham_2approx_bound</code></h3>
<p><code>graham_2approx_bound</code> — operation <code>graham 2approx bound</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p graham_2approx_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graham-scan-hull">
<h3><a class="doc-anchor" href="#doc-graham-scan-hull">#</a> <code>graham_scan_hull</code></h3>
<p><code>graham_scan_hull(points) → array</code> — convex hull via Graham scan. O(n log n).</p>
<pre><code class="lang-perl">p graham_scan_hull([[0,0],[1,0],[1,1],[0,1],[0.5,0.5]])
</code></pre>
</article>
<article class="doc-entry" id="doc-gram-schmidt">
<h3><a class="doc-anchor" href="#doc-gram-schmidt">#</a> <code>gram_schmidt</code></h3>
<p><code>gram_schmidt</code> — operation <code>gram schmidt</code>. Alias for <code>orthogonalize_vectors</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p gram_schmidt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-granger-causality">
<h3><a class="doc-anchor" href="#doc-granger-causality">#</a> <code>granger_causality</code></h3>
<p><code>granger_causality</code> — operation <code>granger causality</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p granger_causality $x
</code></pre>
</article>
<article class="doc-entry" id="doc-granger-causality-chi2">
<h3><a class="doc-anchor" href="#doc-granger-causality-chi2">#</a> <code>granger_causality_chi2</code></h3>
<p><code>granger_causality_chi2</code> — operation <code>granger causality chi2</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p granger_causality_chi2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-articulation-points">
<h3><a class="doc-anchor" href="#doc-graph-articulation-points">#</a> <code>graph_articulation_points</code></h3>
<p><code>graph_articulation_points(adj_list) → array</code> — cut vertices whose removal disconnects the graph (DFS with discovery/low values).</p>
<pre><code class="lang-perl">p graph_articulation_points($g)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-average-degree">
<h3><a class="doc-anchor" href="#doc-graph-average-degree">#</a> <code>graph_average_degree</code></h3>
<p><code>graph_average_degree</code> — graph algorithm <code>average degree</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p graph_average_degree $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-avg-clustering">
<h3><a class="doc-anchor" href="#doc-graph-avg-clustering">#</a> <code>graph_avg_clustering</code></h3>
<p><code>graph_avg_clustering</code> — graph algorithm <code>avg clustering</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p graph_avg_clustering $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-bellman-ford">
<h3><a class="doc-anchor" href="#doc-graph-bellman-ford">#</a> <code>graph_bellman_ford</code></h3>
<p><code>graph_bellman_ford(weighted_adj, start) → array</code> — shortest-path distances; handles negative edges (no negative-cycle detection in simplified form).</p>
<pre><code class="lang-perl">p graph_bellman_ford($g, 0)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-betweenness">
<h3><a class="doc-anchor" href="#doc-graph-betweenness">#</a> <code>graph_betweenness</code></h3>
<p><code>graph_betweenness(adj_list) → array</code> — betweenness centrality (Brandes' algorithm) for unweighted graphs.</p>
<pre><code class="lang-perl">p graph_betweenness($g)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-bfs">
<h3><a class="doc-anchor" href="#doc-graph-bfs">#</a> <code>graph_bfs</code></h3>
<p><code>graph_bfs(adj_list, start) → array</code> — breadth-first traversal order starting at <code>start</code>.</p>
<pre><code class="lang-perl">p graph_bfs([[1,2],[3],[3],[]], 0) # [0,1,2,3]
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-bipartite-match-simple">
<h3><a class="doc-anchor" href="#doc-graph-bipartite-match-simple">#</a> <code>graph_bipartite_match_simple</code></h3>
<p><code>graph_bipartite_match_simple</code> — graph algorithm <code>bipartite match simple</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p graph_bipartite_match_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-bridges">
<h3><a class="doc-anchor" href="#doc-graph-bridges">#</a> <code>graph_bridges</code></h3>
<p><code>graph_bridges(adj_list) → array</code> — bridge edges as <code>[[u,v], …]</code>; removal increases component count.</p>
<pre><code class="lang-perl">p graph_bridges($g)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-closeness">
<h3><a class="doc-anchor" href="#doc-graph-closeness">#</a> <code>graph_closeness</code></h3>
<p><code>graph_closeness(adj_list, v) → number</code> — closeness centrality: <code>(n-1) / Σ dist(v, u)</code>.</p>
<pre><code class="lang-perl">p graph_closeness($g, 0)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-clustering-coefficient">
<h3><a class="doc-anchor" href="#doc-graph-clustering-coefficient">#</a> <code>graph_clustering_coefficient</code></h3>
<p><code>graph_clustering_coefficient(adj_list, v) → number</code> — local clustering: fraction of v's neighbour pairs that are themselves connected. ∈ [0,1].</p>
<pre><code class="lang-perl">p graph_clustering_coefficient($g, 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-color-greedy">
<h3><a class="doc-anchor" href="#doc-graph-color-greedy">#</a> <code>graph_color_greedy</code></h3>
<p><code>graph_color_greedy(adj_list) → array</code> — first-fit graph colouring; returns a colour id per node. Number of colours used is at most max_degree + 1.</p>
<pre><code class="lang-perl">p graph_color_greedy($g)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-coloring-brooks-bound">
<h3><a class="doc-anchor" href="#doc-graph-coloring-brooks-bound">#</a> <code>graph_coloring_brooks_bound</code></h3>
<p><code>graph_coloring_brooks_bound</code> — graph algorithm <code>coloring brooks bound</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p graph_coloring_brooks_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-coloring-dsatur-step">
<h3><a class="doc-anchor" href="#doc-graph-coloring-dsatur-step">#</a> <code>graph_coloring_dsatur_step</code></h3>
<p><code>graph_coloring_dsatur_step</code> — graph algorithm <code>coloring dsatur step</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p graph_coloring_dsatur_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-coloring-greedy">
<h3><a class="doc-anchor" href="#doc-graph-coloring-greedy">#</a> <code>graph_coloring_greedy</code></h3>
<p><code>graph_coloring_greedy</code> — graph algorithm <code>coloring greedy</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p graph_coloring_greedy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-coloring-lp-bound">
<h3><a class="doc-anchor" href="#doc-graph-coloring-lp-bound">#</a> <code>graph_coloring_lp_bound</code></h3>
<p><code>graph_coloring_lp_bound</code> — graph algorithm <code>coloring lp bound</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p graph_coloring_lp_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-coloring-welsh-powell">
<h3><a class="doc-anchor" href="#doc-graph-coloring-welsh-powell">#</a> <code>graph_coloring_welsh_powell</code></h3>
<p><code>graph_coloring_welsh_powell</code> — graph algorithm <code>coloring welsh powell</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p graph_coloring_welsh_powell $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-complement">
<h3><a class="doc-anchor" href="#doc-graph-complement">#</a> <code>graph_complement</code></h3>
<p><code>graph_complement</code> — graph algorithm <code>complement</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p graph_complement $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-connected-components">
<h3><a class="doc-anchor" href="#doc-graph-connected-components">#</a> <code>graph_connected_components</code></h3>
<p><code>graph_connected_components(adj_list) → array</code> — component id per node (BFS over undirected graph).</p>
<pre><code class="lang-perl">p graph_connected_components([[1],[0],[3],[2]]) # [0,0,1,1]
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-count-edges">
<h3><a class="doc-anchor" href="#doc-graph-count-edges">#</a> <code>graph_count_edges</code></h3>
<p><code>graph_count_edges</code> — graph algorithm <code>count edges</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p graph_count_edges $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-count-paths-length-k">
<h3><a class="doc-anchor" href="#doc-graph-count-paths-length-k">#</a> <code>graph_count_paths_length_k</code></h3>
<p><code>graph_count_paths_length_k</code> — graph algorithm <code>count paths length k</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p graph_count_paths_length_k $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-count-triangles">
<h3><a class="doc-anchor" href="#doc-graph-count-triangles">#</a> <code>graph_count_triangles</code></h3>
<p><code>graph_count_triangles</code> — graph algorithm <code>count triangles</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p graph_count_triangles $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-cut-segment">
<h3><a class="doc-anchor" href="#doc-graph-cut-segment">#</a> <code>graph_cut_segment</code></h3>
<p><code>graph_cut_segment</code> — graph algorithm <code>cut segment</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p graph_cut_segment $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-cycle-detect">
<h3><a class="doc-anchor" href="#doc-graph-cycle-detect">#</a> <code>graph_cycle_detect</code></h3>
<p><code>graph_cycle_detect(adj_list) → 0|1</code> — 1 if the directed graph has a cycle (white/gray/black DFS).</p>
<pre><code class="lang-perl">p graph_cycle_detect([[1],[2],[0]]) # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-degree">
<h3><a class="doc-anchor" href="#doc-graph-degree">#</a> <code>graph_degree</code></h3>
<p><code>graph_degree(adj_list, v) → int</code> — number of outgoing neighbours.</p>
<pre><code class="lang-perl">p graph_degree([[1,2],[3],[],[1]], 0) # 2
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-degree-distribution">
<h3><a class="doc-anchor" href="#doc-graph-degree-distribution">#</a> <code>graph_degree_distribution</code></h3>
<p><code>graph_degree_distribution</code> — graph algorithm <code>degree distribution</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p graph_degree_distribution $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-density">
<h3><a class="doc-anchor" href="#doc-graph-density">#</a> <code>graph_density</code></h3>
<p><code>graph_density</code> — graph algorithm <code>density</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p graph_density $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-dfs">
<h3><a class="doc-anchor" href="#doc-graph-dfs">#</a> <code>graph_dfs</code></h3>
<p><code>graph_dfs(adj_list, start) → array</code> — depth-first traversal order (iterative).</p>
<pre><code class="lang-perl">p graph_dfs([[1,2],[3],[3],[]], 0)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-dijkstra">
<h3><a class="doc-anchor" href="#doc-graph-dijkstra">#</a> <code>graph_dijkstra</code></h3>
<p><code>graph_dijkstra(weighted_adj, start) → array</code> — shortest-path distances from <code>start</code> (Dijkstra with binary heap). Returns <code>+∞</code> for unreachable nodes.</p>
<pre><code class="lang-perl">p graph_dijkstra($g, 0)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-eccentricity">
<h3><a class="doc-anchor" href="#doc-graph-eccentricity">#</a> <code>graph_eccentricity</code></h3>
<p><code>graph_eccentricity(weighted_adj, v) → number</code> — max shortest-path distance from <code>v</code> to any reachable node.</p>
<pre><code class="lang-perl">p graph_eccentricity($g, 0)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-eccentricity-all">
<h3><a class="doc-anchor" href="#doc-graph-eccentricity-all">#</a> <code>graph_eccentricity_all</code></h3>
<p><code>graph_eccentricity_all</code> — graph algorithm <code>eccentricity all</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p graph_eccentricity_all $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-eigenvector-centrality">
<h3><a class="doc-anchor" href="#doc-graph-eigenvector-centrality">#</a> <code>graph_eigenvector_centrality</code></h3>
<p><code>graph_eigenvector_centrality(adj_list, iters=100) → array</code> — power-iteration eigenvector centrality on the (possibly weighted) adjacency matrix: <code>x ← A·x / ‖A·x‖</code>. Early-exits when <code>‖x_new − x_old‖₁ < 1e-12</code>. Pass <code>iters</code> to cap iterations.</p>
<pre><code class="lang-perl">p graph_eigenvector_centrality($g, 100)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-floyd-warshall">
<h3><a class="doc-anchor" href="#doc-graph-floyd-warshall">#</a> <code>graph_floyd_warshall</code></h3>
<p><code>graph_floyd_warshall(matrix) → matrix</code> — all-pairs shortest paths via Floyd-Warshall (O(n³)). Input is an adjacency matrix where <code>0</code> indicates no edge and any non-zero value is the edge weight. Output cells are <code>Infinity</code> for unreachable pairs.</p>
<pre><code class="lang-perl">p graph_floyd_warshall($adj_matrix)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-from-edges">
<h3><a class="doc-anchor" href="#doc-graph-from-edges">#</a> <code>graph_from_edges</code></h3>
<p><code>graph_from_edges(edges, directed=0) → adj_list</code> — build adjacency list from <code>[[u, v, w?], …]</code>. Edge weight defaults to 1.</p>
<pre><code class="lang-perl">p graph_from_edges([[0,1,4],[0,2,1],[1,3,1]], 0)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-has-path">
<h3><a class="doc-anchor" href="#doc-graph-has-path">#</a> <code>graph_has_path</code></h3>
<p><code>graph_has_path(adj_list, s, t) → 0|1</code> — BFS reachability check.</p>
<pre><code class="lang-perl">p graph_has_path([[1],[2],[3],[]], 0, 3) # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-in-degree">
<h3><a class="doc-anchor" href="#doc-graph-in-degree">#</a> <code>graph_in_degree</code></h3>
<p><code>graph_in_degree(adj_list, v) → int</code> — incoming edge count (scan all adjacency lists).</p>
<pre><code class="lang-perl">p graph_in_degree($g, 3)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-independent-set-brute">
<h3><a class="doc-anchor" href="#doc-graph-independent-set-brute">#</a> <code>graph_independent_set_brute</code></h3>
<p><code>graph_independent_set_brute</code> — graph algorithm <code>independent set brute</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p graph_independent_set_brute $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-is-bipartite">
<h3><a class="doc-anchor" href="#doc-graph-is-bipartite">#</a> <code>graph_is_bipartite</code></h3>
<p><code>graph_is_bipartite(adj_list) → 0|1</code> — 2-colouring BFS; 1 if no odd-length cycle.</p>
<pre><code class="lang-perl">p graph_is_bipartite([[1,3],[0,2],[1,3],[0,2]]) # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-is-connected">
<h3><a class="doc-anchor" href="#doc-graph-is-connected">#</a> <code>graph_is_connected</code></h3>
<p><code>graph_is_connected(adj_list) → 0|1</code> — BFS-checks that all nodes are reachable from node 0.</p>
<pre><code class="lang-perl">p graph_is_connected([[1],[0,2],[1]]) # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-is-tree">
<h3><a class="doc-anchor" href="#doc-graph-is-tree">#</a> <code>graph_is_tree</code></h3>
<p><code>graph_is_tree</code> — graph algorithm <code>is tree</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p graph_is_tree $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-kosaraju">
<h3><a class="doc-anchor" href="#doc-graph-kosaraju">#</a> <code>graph_kosaraju</code></h3>
<p><code>graph_kosaraju(adj_list) → array</code> — SCC labelling via Kosaraju (alias of <code>graph_strongly_connected_components</code>).</p>
<pre><code class="lang-perl">p graph_kosaraju($g)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-kruskal-mst">
<h3><a class="doc-anchor" href="#doc-graph-kruskal-mst">#</a> <code>graph_kruskal_mst</code></h3>
<p><code>graph_kruskal_mst(weighted_adj) → array</code> — minimum spanning tree as list of <code>[u, v, w]</code> triples (Kruskal with union-find).</p>
<pre><code class="lang-perl">p graph_kruskal_mst($g)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-max-clique-brute">
<h3><a class="doc-anchor" href="#doc-graph-max-clique-brute">#</a> <code>graph_max_clique_brute</code></h3>
<p><code>graph_max_clique_brute</code> — graph algorithm <code>max clique brute</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p graph_max_clique_brute $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-max-degree">
<h3><a class="doc-anchor" href="#doc-graph-max-degree">#</a> <code>graph_max_degree</code></h3>
<p><code>graph_max_degree</code> — graph algorithm <code>max degree</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p graph_max_degree $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-min-degree">
<h3><a class="doc-anchor" href="#doc-graph-min-degree">#</a> <code>graph_min_degree</code></h3>
<p><code>graph_min_degree</code> — graph algorithm <code>min degree</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p graph_min_degree $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-out-degree">
<h3><a class="doc-anchor" href="#doc-graph-out-degree">#</a> <code>graph_out_degree</code></h3>
<p><code>graph_out_degree(adj_list, v) → int</code> — alias for <code>graph_degree</code>.</p>
<pre><code class="lang-perl">p graph_out_degree($g, 0)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-pagerank">
<h3><a class="doc-anchor" href="#doc-graph-pagerank">#</a> <code>graph_pagerank</code></h3>
<p><code>graph_pagerank(adj_list, damping=0.85, iters=50) → array</code> — PageRank score per node via power iteration. Dangling nodes redistribute uniformly.</p>
<pre><code class="lang-perl">p graph_pagerank($g, 0.85, 100)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-pagerank-simple">
<h3><a class="doc-anchor" href="#doc-graph-pagerank-simple">#</a> <code>graph_pagerank_simple</code></h3>
<p><code>graph_pagerank_simple</code> — graph algorithm <code>pagerank simple</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p graph_pagerank_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-prim-mst">
<h3><a class="doc-anchor" href="#doc-graph-prim-mst">#</a> <code>graph_prim_mst</code></h3>
<p><code>graph_prim_mst(weighted_adj) → array</code> — minimum spanning tree as list of <code>[u, v, w]</code> (Prim with binary heap).</p>
<pre><code class="lang-perl">p graph_prim_mst($g)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-shortest-path">
<h3><a class="doc-anchor" href="#doc-graph-shortest-path">#</a> <code>graph_shortest_path</code></h3>
<p><code>graph_shortest_path(adj_list, s, t) → array</code> — BFS shortest path in *unweighted* graph; returns the node sequence.</p>
<pre><code class="lang-perl">p graph_shortest_path($g, 0, 5)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-strongly-connected-components">
<h3><a class="doc-anchor" href="#doc-graph-strongly-connected-components">#</a> <code>graph_strongly_connected_components</code></h3>
<p><code>graph_strongly_connected_components(adj_list) → array</code> — SCC id per node via Kosaraju's algorithm.</p>
<pre><code class="lang-perl">p graph_strongly_connected_components($g)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-tarjan">
<h3><a class="doc-anchor" href="#doc-graph-tarjan">#</a> <code>graph_tarjan</code></h3>
<p><code>graph_tarjan(adj_list) → array</code> — SCC labelling via Tarjan's lowlink algorithm; single DFS pass.</p>
<pre><code class="lang-perl">p graph_tarjan($g)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-to-adj-list">
<h3><a class="doc-anchor" href="#doc-graph-to-adj-list">#</a> <code>graph_to_adj_list</code></h3>
<p><code>graph_to_adj_list(matrix) → adj_list</code> — sparsify a weighted matrix to adjacency-list form.</p>
<pre><code class="lang-perl">p graph_to_adj_list([[0,1,0],[1,0,2],[0,2,0]])
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-to-adj-matrix">
<h3><a class="doc-anchor" href="#doc-graph-to-adj-matrix">#</a> <code>graph_to_adj_matrix</code></h3>
<p><code>graph_to_adj_matrix(adj_list) → matrix</code> — densify adjacency list to <code>n×n</code> weighted matrix (0 = no edge).</p>
<pre><code class="lang-perl">p graph_to_adj_matrix($g)
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-topological-sort">
<h3><a class="doc-anchor" href="#doc-graph-topological-sort">#</a> <code>graph_topological_sort</code></h3>
<p><code>graph_topological_sort(adj_list) → array</code> — Kahn's algorithm; returns empty list if a cycle exists.</p>
<pre><code class="lang-perl">p graph_topological_sort([[1,2],[3],[3],[]])
</code></pre>
</article>
<article class="doc-entry" id="doc-graph-transitivity">
<h3><a class="doc-anchor" href="#doc-graph-transitivity">#</a> <code>graph_transitivity</code></h3>
<p><code>graph_transitivity</code> — graph algorithm <code>transitivity</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p graph_transitivity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-grashof-number">
<h3><a class="doc-anchor" href="#doc-grashof-number">#</a> <code>grashof_number</code></h3>
<p><code>grashof_number</code> — operation <code>grashof number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p grashof_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-grashof-number-step">
<h3><a class="doc-anchor" href="#doc-grashof-number-step">#</a> <code>grashof_number_step</code></h3>
<p><code>grashof_number_step</code> — single-step update of <code>grashof number</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p grashof_number_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-grav-binding-energy">
<h3><a class="doc-anchor" href="#doc-grav-binding-energy">#</a> <code>grav_binding_energy</code></h3>
<p><code>grav_binding_energy</code> — operation <code>grav binding energy</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p grav_binding_energy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-grav-dilation-factor">
<h3><a class="doc-anchor" href="#doc-grav-dilation-factor">#</a> <code>grav_dilation_factor</code></h3>
<p><code>grav_dilation_factor</code> — factor of <code>grav dilation</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p grav_dilation_factor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-grav-redshift">
<h3><a class="doc-anchor" href="#doc-grav-redshift">#</a> <code>grav_redshift</code></h3>
<p><code>grav_redshift</code> — operation <code>grav redshift</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p grav_redshift $x
</code></pre>
</article>
<article class="doc-entry" id="doc-grav-time-dilation">
<h3><a class="doc-anchor" href="#doc-grav-time-dilation">#</a> <code>grav_time_dilation</code></h3>
<p><code>grav_time_dilation</code> — operation <code>grav time dilation</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p grav_time_dilation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gravitational-constant">
<h3><a class="doc-anchor" href="#doc-gravitational-constant">#</a> <code>gravitational_constant</code></h3>
<p><code>gravitational_constant</code> — operation <code>gravitational constant</code>. Category: *constants*.</p>
<pre><code class="lang-perl">p gravitational_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gravitational-pe">
<h3><a class="doc-anchor" href="#doc-gravitational-pe">#</a> <code>gravitational_pe</code></h3>
<p><code>gravitational_pe</code> — operation <code>gravitational pe</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p gravitational_pe $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gravitational-wave-quadrupole">
<h3><a class="doc-anchor" href="#doc-gravitational-wave-quadrupole">#</a> <code>gravitational_wave_quadrupole</code></h3>
<p><code>gravitational_wave_quadrupole</code> — operation <code>gravitational wave quadrupole</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p gravitational_wave_quadrupole $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gravity">
<h3><a class="doc-anchor" href="#doc-gravity">#</a> <code>gravity</code></h3>
<p><code>gravity</code> — operation <code>gravity</code>. Category: *math / physics constants*.</p>
<pre><code class="lang-perl">p gravity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gravity-at-radius">
<h3><a class="doc-anchor" href="#doc-gravity-at-radius">#</a> <code>gravity_at_radius</code></h3>
<p><code>gravity_at_radius</code> — operation <code>gravity at radius</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p gravity_at_radius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gravity-constant">
<h3><a class="doc-anchor" href="#doc-gravity-constant">#</a> <code>gravity_constant</code></h3>
<p><code>gravity_constant</code> — operation <code>gravity constant</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p gravity_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gray">
<h3><a class="doc-anchor" href="#doc-gray">#</a> <code>gray</code></h3>
<p><code>gray</code> — operation <code>gray</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p gray $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gray2b">
<h3><a class="doc-anchor" href="#doc-gray2b">#</a> <code>gray2b</code></h3>
<p><code>gray2b</code> — operation <code>gray2b</code>. Alias for <code>gray_to_binary</code>. Category: *base / gray code*.</p>
<pre><code class="lang-perl">p gray2b $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gray-code-decode">
<h3><a class="doc-anchor" href="#doc-gray-code-decode">#</a> <code>gray_code_decode</code></h3>
<p><code>gray_code_decode(g) → int</code> — reflected Gray → binary inverse.</p>
</article>
<article class="doc-entry" id="doc-gray-code-encode">
<h3><a class="doc-anchor" href="#doc-gray-code-encode">#</a> <code>gray_code_encode</code></h3>
<p><code>gray_code_encode(x) → int</code> — binary → reflected Gray code: <code>x ^ (x >> 1)</code>.</p>
<pre><code class="lang-perl">p gray_code_encode(7) # 4
</code></pre>
</article>
<article class="doc-entry" id="doc-gray-code-sequence">
<h3><a class="doc-anchor" href="#doc-gray-code-sequence">#</a> <code>gray_code_sequence</code></h3>
<p><code>gray_code_sequence</code> — operation <code>gray code sequence</code>. Category: *base / gray code*.</p>
<pre><code class="lang-perl">p gray_code_sequence $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gray-to-bin">
<h3><a class="doc-anchor" href="#doc-gray-to-bin">#</a> <code>gray_to_bin</code></h3>
<p><code>gray_to_bin</code> — convert from <code>gray</code> to <code>bin</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p gray_to_bin $value
</code></pre>
</article>
<article class="doc-entry" id="doc-gray-to-binary">
<h3><a class="doc-anchor" href="#doc-gray-to-binary">#</a> <code>gray_to_binary</code></h3>
<p><code>gray_to_binary</code> — convert from <code>gray</code> to <code>binary</code>. Category: *base / gray code*.</p>
<pre><code class="lang-perl">p gray_to_binary $value
</code></pre>
</article>
<article class="doc-entry" id="doc-grayseq">
<h3><a class="doc-anchor" href="#doc-grayseq">#</a> <code>grayseq</code></h3>
<p><code>grayseq</code> — operation <code>grayseq</code>. Alias for <code>gray_code_sequence</code>. Category: *base / gray code*.</p>
<pre><code class="lang-perl">p grayseq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-great-circle-law-of-cos">
<h3><a class="doc-anchor" href="#doc-great-circle-law-of-cos">#</a> <code>great_circle_law_of_cos</code></h3>
<p><code>great_circle_law_of_cos</code> — operation <code>great circle law of cos</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p great_circle_law_of_cos $x
</code></pre>
</article>
<article class="doc-entry" id="doc-greedy-best-first">
<h3><a class="doc-anchor" href="#doc-greedy-best-first">#</a> <code>greedy_best_first</code></h3>
<p><code>greedy_best_first(adj, s, t, heuristic) → array</code> — pure-heuristic search; not guaranteed optimal but fast.</p>
</article>
<article class="doc-entry" id="doc-greedy-coloring">
<h3><a class="doc-anchor" href="#doc-greedy-coloring">#</a> <code>greedy_coloring</code></h3>
<p><code>greedy_coloring</code> — operation <code>greedy coloring</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p greedy_coloring $x
</code></pre>
</article>
<article class="doc-entry" id="doc-greedy-edge-tour">
<h3><a class="doc-anchor" href="#doc-greedy-edge-tour">#</a> <code>greedy_edge_tour</code></h3>
<p><code>greedy_edge_tour</code> — operation <code>greedy edge tour</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p greedy_edge_tour $x
</code></pre>
</article>
<article class="doc-entry" id="doc-greedy-set-cover-round">
<h3><a class="doc-anchor" href="#doc-greedy-set-cover-round">#</a> <code>greedy_set_cover_round</code></h3>
<p><code>greedy_set_cover_round</code> — operation <code>greedy set cover round</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p greedy_set_cover_round $x
</code></pre>
</article>
<article class="doc-entry" id="doc-green">
<h3><a class="doc-anchor" href="#doc-green">#</a> <code>green</code></h3>
<p><code>green</code> — operation <code>green</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p green $x
</code></pre>
</article>
<article class="doc-entry" id="doc-green-bold">
<h3><a class="doc-anchor" href="#doc-green-bold">#</a> <code>green_bold</code></h3>
<p><code>green_bold</code> — operation <code>green bold</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p green_bold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-greenhouse-forcing-step">
<h3><a class="doc-anchor" href="#doc-greenhouse-forcing-step">#</a> <code>greenhouse_forcing_step</code></h3>
<p><code>greenhouse_forcing_step</code> — single-step update of <code>greenhouse forcing</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p greenhouse_forcing_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gregorian-from-fixed">
<h3><a class="doc-anchor" href="#doc-gregorian-from-fixed">#</a> <code>gregorian_from_fixed</code></h3>
<p><code>gregorian_from_fixed</code> — operation <code>gregorian from fixed</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p gregorian_from_fixed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-grepv">
<h3><a class="doc-anchor" href="#doc-grepv">#</a> <code>grepv</code></h3>
<p><code>grepv</code> — operation <code>grepv</code>. Alias for <code>take_while</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p grepv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-grey">
<h3><a class="doc-anchor" href="#doc-grey">#</a> <code>grey</code></h3>
<p><code>grey</code> — operation <code>grey</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p grey $x
</code></pre>
</article>
<article class="doc-entry" id="doc-grim-trigger-step">
<h3><a class="doc-anchor" href="#doc-grim-trigger-step">#</a> <code>grim_trigger_step</code></h3>
<p><code>grim_trigger_step</code> — single-step update of <code>grim trigger</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p grim_trigger_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gromov-wasserstein-step">
<h3><a class="doc-anchor" href="#doc-gromov-wasserstein-step">#</a> <code>gromov_wasserstein_step</code></h3>
<p><code>gromov_wasserstein_step</code> — single-step update of <code>gromov wasserstein</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p gromov_wasserstein_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gromov-witten-invariant">
<h3><a class="doc-anchor" href="#doc-gromov-witten-invariant">#</a> <code>gromov_witten_invariant</code></h3>
<p><code>gromov_witten_invariant</code> — operation <code>gromov witten invariant</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p gromov_witten_invariant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gross-premium-load">
<h3><a class="doc-anchor" href="#doc-gross-premium-load">#</a> <code>gross_premium_load</code></h3>
<p><code>gross_premium_load</code> — operation <code>gross premium load</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p gross_premium_load $x
</code></pre>
</article>
<article class="doc-entry" id="doc-group-by">
<h3><a class="doc-anchor" href="#doc-group-by">#</a> <code>group_by</code></h3>
<p><code>group_by</code> — operation <code>group by</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p group_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-group-by-fn">
<h3><a class="doc-anchor" href="#doc-group-by-fn">#</a> <code>group_by_fn</code></h3>
<p><code>group_by_fn</code> — operation <code>group by fn</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p group_by_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-group-by-size">
<h3><a class="doc-anchor" href="#doc-group-by-size">#</a> <code>group_by_size</code></h3>
<p><code>group_by_size</code> — operation <code>group by size</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p group_by_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-group-cohomology-dim">
<h3><a class="doc-anchor" href="#doc-group-cohomology-dim">#</a> <code>group_cohomology_dim</code></h3>
<p><code>group_cohomology_dim</code> — operation <code>group cohomology dim</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p group_cohomology_dim $x
</code></pre>
</article>
<article class="doc-entry" id="doc-group-consecutive">
<h3><a class="doc-anchor" href="#doc-group-consecutive">#</a> <code>group_consecutive</code></h3>
<p><code>group_consecutive</code> — operation <code>group consecutive</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p group_consecutive $x
</code></pre>
</article>
<article class="doc-entry" id="doc-group-consecutive-by">
<h3><a class="doc-anchor" href="#doc-group-consecutive-by">#</a> <code>group_consecutive_by</code></h3>
<p><code>group_consecutive_by</code> — operation <code>group consecutive by</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p group_consecutive_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-group-delay-eval">
<h3><a class="doc-anchor" href="#doc-group-delay-eval">#</a> <code>group_delay_eval</code></h3>
<p><code>group_delay_eval</code> — operation <code>group delay eval</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p group_delay_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-group-homology-dim">
<h3><a class="doc-anchor" href="#doc-group-homology-dim">#</a> <code>group_homology_dim</code></h3>
<p><code>group_homology_dim</code> — operation <code>group homology dim</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p group_homology_dim $x
</code></pre>
</article>
<article class="doc-entry" id="doc-group-map">
<h3><a class="doc-anchor" href="#doc-group-map">#</a> <code>group_map</code></h3>
<p><code>group_map</code> — operation <code>group map</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p group_map $x
</code></pre>
</article>
<article class="doc-entry" id="doc-group-number">
<h3><a class="doc-anchor" href="#doc-group-number">#</a> <code>group_number</code></h3>
<p><code>group_number</code> — operation <code>group number</code>. Alias for <code>format_number</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p group_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-group-of-n">
<h3><a class="doc-anchor" href="#doc-group-of-n">#</a> <code>group_of_n</code></h3>
<p><code>group_of_n</code> — operation <code>group of n</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p group_of_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-group-runs">
<h3><a class="doc-anchor" href="#doc-group-runs">#</a> <code>group_runs</code></h3>
<p><code>group_runs</code> — operation <code>group runs</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p group_runs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-groupby-iter">
<h3><a class="doc-anchor" href="#doc-groupby-iter">#</a> <code>groupby_iter</code></h3>
<p><code>groupby_iter</code> — operation <code>groupby iter</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p groupby_iter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-grover-iter">
<h3><a class="doc-anchor" href="#doc-grover-iter">#</a> <code>grover_iter</code></h3>
<p><code>grover_iter</code> — operation <code>grover iter</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p grover_iter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-growing-perpetuity">
<h3><a class="doc-anchor" href="#doc-growing-perpetuity">#</a> <code>growing_perpetuity</code></h3>
<p><code>growing_perpetuity</code> — operation <code>growing perpetuity</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p growing_perpetuity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-growth-rate-from-ratio">
<h3><a class="doc-anchor" href="#doc-growth-rate-from-ratio">#</a> <code>growth_rate_from_ratio</code></h3>
<p><code>growth_rate_from_ratio</code> — ratio of <code>growth rate from</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p growth_rate_from_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gruns">
<h3><a class="doc-anchor" href="#doc-gruns">#</a> <code>gruns</code></h3>
<p><code>gruns</code> — operation <code>gruns</code>. Alias for <code>group_runs</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p gruns $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gullstrand-painleve-step">
<h3><a class="doc-anchor" href="#doc-gullstrand-painleve-step">#</a> <code>gullstrand_painleve_step</code></h3>
<p><code>gullstrand_painleve_step</code> — single-step update of <code>gullstrand painleve</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p gullstrand_painleve_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gunning-fog">
<h3><a class="doc-anchor" href="#doc-gunning-fog">#</a> <code>gunning_fog</code></h3>
<p><code>gunning_fog</code> — operation <code>gunning fog</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p gunning_fog $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gutenberg-richter-b">
<h3><a class="doc-anchor" href="#doc-gutenberg-richter-b">#</a> <code>gutenberg_richter_b</code></h3>
<p><code>gutenberg_richter_b</code> — operation <code>gutenberg richter b</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p gutenberg_richter_b $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gw-strain-amplitude">
<h3><a class="doc-anchor" href="#doc-gw-strain-amplitude">#</a> <code>gw_strain_amplitude</code></h3>
<p><code>gw_strain_amplitude</code> — operation <code>gw strain amplitude</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p gw_strain_amplitude $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gx-diameter">
<h3><a class="doc-anchor" href="#doc-gx-diameter">#</a> <code>gx_diameter</code></h3>
<p><code>gx_diameter</code> — operation <code>gx diameter</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p gx_diameter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gx-eccentricity">
<h3><a class="doc-anchor" href="#doc-gx-eccentricity">#</a> <code>gx_eccentricity</code></h3>
<p><code>gx_eccentricity</code> — operation <code>gx eccentricity</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p gx_eccentricity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gx-radius">
<h3><a class="doc-anchor" href="#doc-gx-radius">#</a> <code>gx_radius</code></h3>
<p><code>gx_radius</code> — operation <code>gx radius</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p gx_radius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gz">
<h3><a class="doc-anchor" href="#doc-gz">#</a> <code>gz</code></h3>
<p><code>gz</code> — operation <code>gz</code>. Alias for <code>gzip</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p gz $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gzip-crc32-init">
<h3><a class="doc-anchor" href="#doc-gzip-crc32-init">#</a> <code>gzip_crc32_init</code></h3>
<p><code>gzip_crc32_init</code> — initialise of <code>gzip crc32</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p gzip_crc32_init $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gzip-encode-step">
<h3><a class="doc-anchor" href="#doc-gzip-encode-step">#</a> <code>gzip_encode_step</code></h3>
<p><code>gzip_encode_step</code> — single-step update of <code>gzip encode</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p gzip_encode_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gzip-isize">
<h3><a class="doc-anchor" href="#doc-gzip-isize">#</a> <code>gzip_isize</code></h3>
<p><code>gzip_isize</code> — operation <code>gzip isize</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p gzip_isize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-gzip-member-step">
<h3><a class="doc-anchor" href="#doc-gzip-member-step">#</a> <code>gzip_member_step</code></h3>
<p><code>gzip_member_step</code> — single-step update of <code>gzip member</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p gzip_member_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-h0">
<h3><a class="doc-anchor" href="#doc-h0">#</a> <code>h0</code></h3>
<p><code>h0</code> — operation <code>h0</code>. Alias for <code>hubble_constant</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p h0 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-h3-geo-to-h3">
<h3><a class="doc-anchor" href="#doc-h3-geo-to-h3">#</a> <code>h3_geo_to_h3</code></h3>
<p><code>h3_geo_to_h3</code> — convert from <code>h3 geo</code> to <code>h3</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p h3_geo_to_h3 $value
</code></pre>
</article>
<article class="doc-entry" id="doc-h3-h3-to-geo">
<h3><a class="doc-anchor" href="#doc-h3-h3-to-geo">#</a> <code>h3_h3_to_geo</code></h3>
<p><code>h3_h3_to_geo</code> — convert from <code>h3 h3</code> to <code>geo</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p h3_h3_to_geo $value
</code></pre>
</article>
<article class="doc-entry" id="doc-h3-index">
<h3><a class="doc-anchor" href="#doc-h3-index">#</a> <code>h3_index</code></h3>
<p><code>h3_index</code> — index of <code>h3</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p h3_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-h3-k-ring">
<h3><a class="doc-anchor" href="#doc-h3-k-ring">#</a> <code>h3_k_ring</code></h3>
<p><code>h3_k_ring</code> — operation <code>h3 k ring</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p h3_k_ring $x
</code></pre>
</article>
<article class="doc-entry" id="doc-h3-neighbor">
<h3><a class="doc-anchor" href="#doc-h3-neighbor">#</a> <code>h3_neighbor</code></h3>
<p><code>h3_neighbor</code> — operation <code>h3 neighbor</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p h3_neighbor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-h3-resolution">
<h3><a class="doc-anchor" href="#doc-h3-resolution">#</a> <code>h3_resolution</code></h3>
<p><code>h3_resolution</code> — operation <code>h3 resolution</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p h3_resolution $x
</code></pre>
</article>
<article class="doc-entry" id="doc-h-infinity-norm">
<h3><a class="doc-anchor" href="#doc-h-infinity-norm">#</a> <code>h_infinity_norm</code></h3>
<p><code>h_infinity_norm</code> — norm (vector length-like) of <code>h infinity</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p h_infinity_norm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-haar-2d-step">
<h3><a class="doc-anchor" href="#doc-haar-2d-step">#</a> <code>haar_2d_step</code></h3>
<p><code>haar_2d_step</code> — single-step update of <code>haar 2d</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p haar_2d_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hadamard-walsh-transform-step">
<h3><a class="doc-anchor" href="#doc-hadamard-walsh-transform-step">#</a> <code>hadamard_walsh_transform_step</code></h3>
<p><code>hadamard_walsh_transform_step</code> — single-step update of <code>hadamard walsh transform</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p hadamard_walsh_transform_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hadley-cell-max-lat">
<h3><a class="doc-anchor" href="#doc-hadley-cell-max-lat">#</a> <code>hadley_cell_max_lat</code></h3>
<p><code>hadley_cell_max_lat</code> — operation <code>hadley cell max lat</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p hadley_cell_max_lat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hagen-poiseuille-eo">
<h3><a class="doc-anchor" href="#doc-hagen-poiseuille-eo">#</a> <code>hagen_poiseuille_eo</code></h3>
<p><code>hagen_poiseuille_eo</code> — operation <code>hagen poiseuille eo</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p hagen_poiseuille_eo $x
</code></pre>
</article>
<article class="doc-entry" id="doc-half">
<h3><a class="doc-anchor" href="#doc-half">#</a> <code>half</code></h3>
<p><code>half</code> — operation <code>half</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p half $x
</code></pre>
</article>
<article class="doc-entry" id="doc-half-cauchy-pdf">
<h3><a class="doc-anchor" href="#doc-half-cauchy-pdf">#</a> <code>half_cauchy_pdf</code></h3>
<p><code>half_cauchy_pdf</code> — operation <code>half cauchy pdf</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p half_cauchy_pdf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-half-each">
<h3><a class="doc-anchor" href="#doc-half-each">#</a> <code>half_each</code></h3>
<p><code>half_each</code> — operation <code>half each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p half_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-half-logistic-pdf">
<h3><a class="doc-anchor" href="#doc-half-logistic-pdf">#</a> <code>half_logistic_pdf</code></h3>
<p><code>half_logistic_pdf</code> — operation <code>half logistic pdf</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p half_logistic_pdf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-half-reaction-balance">
<h3><a class="doc-anchor" href="#doc-half-reaction-balance">#</a> <code>half_reaction_balance</code></h3>
<p><code>half_reaction_balance</code> — operation <code>half reaction balance</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p half_reaction_balance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hall-inner-product-two">
<h3><a class="doc-anchor" href="#doc-hall-inner-product-two">#</a> <code>hall_inner_product_two</code></h3>
<p><code>hall_inner_product_two</code> — operation <code>hall inner product two</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p hall_inner_product_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-halley">
<h3><a class="doc-anchor" href="#doc-halley">#</a> <code>halley</code></h3>
<p><code>halley</code> — operation <code>halley</code>. Alias for <code>halley_root</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p halley $x
</code></pre>
</article>
<article class="doc-entry" id="doc-halley-root">
<h3><a class="doc-anchor" href="#doc-halley-root">#</a> <code>halley_root</code></h3>
<p><code>halley_root</code> — operation <code>halley root</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p halley_root $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hamdist">
<h3><a class="doc-anchor" href="#doc-hamdist">#</a> <code>hamdist</code></h3>
<p><code>hamdist</code> — operation <code>hamdist</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p hamdist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hamdist-int">
<h3><a class="doc-anchor" href="#doc-hamdist-int">#</a> <code>hamdist_int</code></h3>
<p><code>hamdist_int</code> — operation <code>hamdist int</code>. Alias for <code>hamming_distance_int</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p hamdist_int $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hamiltonian-brute">
<h3><a class="doc-anchor" href="#doc-hamiltonian-brute">#</a> <code>hamiltonian_brute</code></h3>
<p><code>hamiltonian_brute</code> — operation <code>hamiltonian brute</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p hamiltonian_brute $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hamiltonian-path">
<h3><a class="doc-anchor" href="#doc-hamiltonian-path">#</a> <code>hamiltonian_path</code></h3>
<p><code>hamiltonian_path</code> — operation <code>hamiltonian path</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p hamiltonian_path $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hamming">
<h3><a class="doc-anchor" href="#doc-hamming">#</a> <code>hamming</code></h3>
<p><code>window_hamming($n)</code> (alias <code>hamming</code>) — generates a Hamming window of length n. Similar to Hann but with slightly different coefficients, optimized for speech processing.</p>
<pre><code class="lang-perl">my $w = hamming(1024)
</code></pre>
</article>
<article class="doc-entry" id="doc-hamming-distance">
<h3><a class="doc-anchor" href="#doc-hamming-distance">#</a> <code>hamming_distance</code></h3>
<p><code>hamming_distance</code> — distance / dissimilarity metric of <code>hamming</code>. Category: *string*.</p>
<pre><code class="lang-perl">p hamming_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hamming-distance-int">
<h3><a class="doc-anchor" href="#doc-hamming-distance-int">#</a> <code>hamming_distance_int</code></h3>
<p><code>hamming_distance_int</code> — operation <code>hamming distance int</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p hamming_distance_int $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hamming-distance-str">
<h3><a class="doc-anchor" href="#doc-hamming-distance-str">#</a> <code>hamming_distance_str</code></h3>
<p><code>hamming_distance_str</code> — operation <code>hamming distance str</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p hamming_distance_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hamming-protein">
<h3><a class="doc-anchor" href="#doc-hamming-protein">#</a> <code>hamming_protein</code></h3>
<p><code>hamming_protein</code> — operation <code>hamming protein</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p hamming_protein $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hamming-w">
<h3><a class="doc-anchor" href="#doc-hamming-w">#</a> <code>hamming_w</code></h3>
<p><code>hamming_w</code> — operation <code>hamming w</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p hamming_w $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hamming-weight">
<h3><a class="doc-anchor" href="#doc-hamming-weight">#</a> <code>hamming_weight</code></h3>
<p><code>hamming_weight</code> — operation <code>hamming weight</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p hamming_weight $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hamming-window">
<h3><a class="doc-anchor" href="#doc-hamming-window">#</a> <code>hamming_window</code></h3>
<p><code>hamming_window</code> — operation <code>hamming window</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p hamming_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hann">
<h3><a class="doc-anchor" href="#doc-hann">#</a> <code>hann</code></h3>
<p><code>window_hann($n)</code> (alias <code>hann</code>) — generates a Hann (raised cosine) window of length n. Common window function for spectral analysis that reduces spectral leakage.</p>
<pre><code class="lang-perl">my $w = hann(1024)
</code></pre>
</article>
<article class="doc-entry" id="doc-hann-w">
<h3><a class="doc-anchor" href="#doc-hann-w">#</a> <code>hann_w</code></h3>
<p><code>hann_w</code> — operation <code>hann w</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p hann_w $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hann-window">
<h3><a class="doc-anchor" href="#doc-hann-window">#</a> <code>hann_window</code></h3>
<p><code>hann_window</code> — operation <code>hann window</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p hann_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hannan-quinn-ic">
<h3><a class="doc-anchor" href="#doc-hannan-quinn-ic">#</a> <code>hannan_quinn_ic</code></h3>
<p><code>hannan_quinn_ic</code> — operation <code>hannan quinn ic</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p hannan_quinn_ic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hanoi">
<h3><a class="doc-anchor" href="#doc-hanoi">#</a> <code>hanoi</code></h3>
<p><code>hanoi</code> — operation <code>hanoi</code>. Alias for <code>tower_of_hanoi</code>. Category: *algorithms / puzzles*.</p>
<pre><code class="lang-perl">p hanoi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hansen-j-test">
<h3><a class="doc-anchor" href="#doc-hansen-j-test">#</a> <code>hansen_j_test</code></h3>
<p><code>hansen_j_test</code> — statistical test of <code>hansen j</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p hansen_j_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hard-sigmoid">
<h3><a class="doc-anchor" href="#doc-hard-sigmoid">#</a> <code>hard_sigmoid</code></h3>
<p><code>hard_sigmoid</code> — operation <code>hard sigmoid</code>. Category: *ml activation functions*.</p>
<pre><code class="lang-perl">p hard_sigmoid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hard-swish">
<h3><a class="doc-anchor" href="#doc-hard-swish">#</a> <code>hard_swish</code></h3>
<p><code>hard_swish</code> — operation <code>hard swish</code>. Category: *ml activation functions*.</p>
<pre><code class="lang-perl">p hard_swish $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hardsigmoid">
<h3><a class="doc-anchor" href="#doc-hardsigmoid">#</a> <code>hardsigmoid</code></h3>
<p><code>hardsigmoid</code> — operation <code>hardsigmoid</code>. Alias for <code>hard_sigmoid</code>. Category: *ml activation functions*.</p>
<pre><code class="lang-perl">p hardsigmoid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hardswish">
<h3><a class="doc-anchor" href="#doc-hardswish">#</a> <code>hardswish</code></h3>
<p><code>hardswish</code> — operation <code>hardswish</code>. Alias for <code>hard_swish</code>. Category: *ml activation functions*.</p>
<pre><code class="lang-perl">p hardswish $x
</code></pre>
</article>
<article class="doc-entry" id="doc-harmonic">
<h3><a class="doc-anchor" href="#doc-harmonic">#</a> <code>harmonic</code></h3>
<p><code>harmonic_number</code> (alias <code>harmonic</code>) computes the nth harmonic number H_n = 1 + 1/2 + 1/3 + ... + 1/n.</p>
<pre><code class="lang-perl">p harmonic(1) # 1.0
p harmonic(10) # 2.9290
p harmonic(100) # 5.1874
</code></pre>
</article>
<article class="doc-entry" id="doc-harmonic-centrality">
<h3><a class="doc-anchor" href="#doc-harmonic-centrality">#</a> <code>harmonic_centrality</code></h3>
<p><code>harmonic_centrality</code> — operation <code>harmonic centrality</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p harmonic_centrality $x
</code></pre>
</article>
<article class="doc-entry" id="doc-harmonic-mean">
<h3><a class="doc-anchor" href="#doc-harmonic-mean">#</a> <code>harmonic_mean</code></h3>
<p><code>harmonic_mean</code> — arithmetic mean of <code>harmonic</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p harmonic_mean @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-harmonic-mean-arr">
<h3><a class="doc-anchor" href="#doc-harmonic-mean-arr">#</a> <code>harmonic_mean_arr</code></h3>
<p><code>harmonic_mean_arr</code> — operation <code>harmonic mean arr</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p harmonic_mean_arr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-harmonic-oscillator-energy">
<h3><a class="doc-anchor" href="#doc-harmonic-oscillator-energy">#</a> <code>harmonic_oscillator_energy</code></h3>
<p><code>harmonic_oscillator_energy</code> — operation <code>harmonic oscillator energy</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p harmonic_oscillator_energy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-harmonic-seq-sum">
<h3><a class="doc-anchor" href="#doc-harmonic-seq-sum">#</a> <code>harmonic_seq_sum</code></h3>
<p><code>harmonic_seq_sum</code> — sum of <code>harmonic seq</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p harmonic_seq_sum @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-harmonics-partial">
<h3><a class="doc-anchor" href="#doc-harmonics-partial">#</a> <code>harmonics_partial</code></h3>
<p><code>harmonics_partial</code> — operation <code>harmonics partial</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p harmonics_partial $x
</code></pre>
</article>
<article class="doc-entry" id="doc-harris-corners">
<h3><a class="doc-anchor" href="#doc-harris-corners">#</a> <code>harris_corners</code></h3>
<p><code>harris_corners</code> — operation <code>harris corners</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p harris_corners $x
</code></pre>
</article>
<article class="doc-entry" id="doc-harris-response">
<h3><a class="doc-anchor" href="#doc-harris-response">#</a> <code>harris_response</code></h3>
<p><code>harris_response(image, k=0.04) → matrix</code> — Harris corner response <code>det(M) − k·trace(M)²</code> per pixel. <code>M</code> is the 2×2 structure tensor <code>Σ_w [[Iₓ², IₓIᵧ], [IₓIᵧ, Iᵧ²]]</code> summed over a 3×3 window (without the window sum, <code>det(M)</code> would be identically zero per pixel and the response could not distinguish corners from edges).</p>
</article>
<article class="doc-entry" id="doc-hartle-thorne-metric">
<h3><a class="doc-anchor" href="#doc-hartle-thorne-metric">#</a> <code>hartle_thorne_metric</code></h3>
<p><code>hartle_thorne_metric</code> — metric of <code>hartle thorne</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p hartle_thorne_metric $x
</code></pre>
</article>
<article class="doc-entry" id="doc-has-all-keys">
<h3><a class="doc-anchor" href="#doc-has-all-keys">#</a> <code>has_all_keys</code></h3>
<p><code>has_all_keys</code> — predicate: 1 if input has all keys, 0 otherwise. Category: *hash helpers*.</p>
<pre><code class="lang-perl">p has_all_keys $x
</code></pre>
</article>
<article class="doc-entry" id="doc-has-any-key">
<h3><a class="doc-anchor" href="#doc-has-any-key">#</a> <code>has_any_key</code></h3>
<p><code>has_any_key</code> — predicate: 1 if input has any key, 0 otherwise. Category: *hash helpers*.</p>
<pre><code class="lang-perl">p has_any_key $x
</code></pre>
</article>
<article class="doc-entry" id="doc-has-cycle-directed">
<h3><a class="doc-anchor" href="#doc-has-cycle-directed">#</a> <code>has_cycle_directed</code></h3>
<p><code>has_cycle_directed</code> — predicate: 1 if input has cycle directed, 0 otherwise. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p has_cycle_directed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-has-cycle-graph">
<h3><a class="doc-anchor" href="#doc-has-cycle-graph">#</a> <code>has_cycle_graph</code></h3>
<p><code>has_cycle_graph</code> — predicate: 1 if input has cycle graph, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p has_cycle_graph $x
</code></pre>
</article>
<article class="doc-entry" id="doc-has-cycle-undirected">
<h3><a class="doc-anchor" href="#doc-has-cycle-undirected">#</a> <code>has_cycle_undirected</code></h3>
<p><code>has_cycle_undirected</code> — predicate: 1 if input has cycle undirected, 0 otherwise. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p has_cycle_undirected $x
</code></pre>
</article>
<article class="doc-entry" id="doc-has-duplicates">
<h3><a class="doc-anchor" href="#doc-has-duplicates">#</a> <code>has_duplicates</code></h3>
<p><code>has_duplicates</code> — predicate: 1 if input has duplicates, 0 otherwise. Category: *more list helpers*.</p>
<pre><code class="lang-perl">p has_duplicates $x
</code></pre>
</article>
<article class="doc-entry" id="doc-has-key">
<h3><a class="doc-anchor" href="#doc-has-key">#</a> <code>has_key</code></h3>
<p><code>has_key</code> — predicate: 1 if input has key, 0 otherwise. Category: *hash helpers*.</p>
<pre><code class="lang-perl">p has_key $x
</code></pre>
</article>
<article class="doc-entry" id="doc-has-stderr-tty">
<h3><a class="doc-anchor" href="#doc-has-stderr-tty">#</a> <code>has_stderr_tty</code></h3>
<p><code>has_stderr_tty</code> — predicate: 1 if input has stderr tty, 0 otherwise. Category: *process / env*.</p>
<pre><code class="lang-perl">p has_stderr_tty $x
</code></pre>
</article>
<article class="doc-entry" id="doc-has-stdin-tty">
<h3><a class="doc-anchor" href="#doc-has-stdin-tty">#</a> <code>has_stdin_tty</code></h3>
<p><code>has_stdin_tty</code> — predicate: 1 if input has stdin tty, 0 otherwise. Category: *process / env*.</p>
<pre><code class="lang-perl">p has_stdin_tty $x
</code></pre>
</article>
<article class="doc-entry" id="doc-has-stdout-tty">
<h3><a class="doc-anchor" href="#doc-has-stdout-tty">#</a> <code>has_stdout_tty</code></h3>
<p><code>has_stdout_tty</code> — predicate: 1 if input has stdout tty, 0 otherwise. Category: *process / env*.</p>
<pre><code class="lang-perl">p has_stdout_tty $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hascyc">
<h3><a class="doc-anchor" href="#doc-hascyc">#</a> <code>hascyc</code></h3>
<p><code>hascyc</code> — operation <code>hascyc</code>. Alias for <code>has_cycle_graph</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p hascyc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hash-2d-int">
<h3><a class="doc-anchor" href="#doc-hash-2d-int">#</a> <code>hash_2d_int</code></h3>
<p><code>hash_2d_int(x, y) → int</code> — fast deterministic spatial hash on 32-bit integer coordinates.</p>
</article>
<article class="doc-entry" id="doc-hash-combine">
<h3><a class="doc-anchor" href="#doc-hash-combine">#</a> <code>hash_combine</code></h3>
<p><code>hash_combine</code> — hash-table / hashing helper <code>combine</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p hash_combine $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hash-delete">
<h3><a class="doc-anchor" href="#doc-hash-delete">#</a> <code>hash_delete</code></h3>
<p><code>hash_delete</code> — hash-table / hashing helper <code>delete</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p hash_delete $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hash-eq">
<h3><a class="doc-anchor" href="#doc-hash-eq">#</a> <code>hash_eq</code></h3>
<p><code>hash_eq</code> — hash-table / hashing helper <code>eq</code>. Category: *hash ops*.</p>
<pre><code class="lang-perl">p hash_eq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hash-filter-keys">
<h3><a class="doc-anchor" href="#doc-hash-filter-keys">#</a> <code>hash_filter_keys</code></h3>
<p><code>hash_filter_keys</code> — hash-table / hashing helper <code>filter keys</code>. Category: *hash helpers*.</p>
<pre><code class="lang-perl">p hash_filter_keys $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hash-filter-values">
<h3><a class="doc-anchor" href="#doc-hash-filter-values">#</a> <code>hash_filter_values</code></h3>
<p><code>hash_filter_values</code> — hash-table / hashing helper <code>filter values</code>. Category: *hash helpers*.</p>
<pre><code class="lang-perl">p hash_filter_values $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hash-from-list">
<h3><a class="doc-anchor" href="#doc-hash-from-list">#</a> <code>hash_from_list</code></h3>
<p><code>hash_from_list</code> — hash-table / hashing helper <code>from list</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p hash_from_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hash-from-pairs">
<h3><a class="doc-anchor" href="#doc-hash-from-pairs">#</a> <code>hash_from_pairs</code></h3>
<p><code>hash_from_pairs</code> — hash-table / hashing helper <code>from pairs</code>. Category: *hash ops*.</p>
<pre><code class="lang-perl">p hash_from_pairs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hash-insert">
<h3><a class="doc-anchor" href="#doc-hash-insert">#</a> <code>hash_insert</code></h3>
<p><code>hash_insert</code> — hash-table / hashing helper <code>insert</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p hash_insert $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hash-map-values">
<h3><a class="doc-anchor" href="#doc-hash-map-values">#</a> <code>hash_map_values</code></h3>
<p><code>hash_map_values</code> — hash-table / hashing helper <code>map values</code>. Category: *hash helpers*.</p>
<pre><code class="lang-perl">p hash_map_values $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hash-merge-deep">
<h3><a class="doc-anchor" href="#doc-hash-merge-deep">#</a> <code>hash_merge_deep</code></h3>
<p><code>hash_merge_deep</code> — hash-table / hashing helper <code>merge deep</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p hash_merge_deep $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hash-size">
<h3><a class="doc-anchor" href="#doc-hash-size">#</a> <code>hash_size</code></h3>
<p><code>hash_size</code> — hash-table / hashing helper <code>size</code>. Category: *hash ops*.</p>
<pre><code class="lang-perl">p hash_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hash-to-list">
<h3><a class="doc-anchor" href="#doc-hash-to-list">#</a> <code>hash_to_list</code></h3>
<p><code>hash_to_list</code> — convert from <code>hash</code> to <code>list</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p hash_to_list $value
</code></pre>
</article>
<article class="doc-entry" id="doc-hash-update">
<h3><a class="doc-anchor" href="#doc-hash-update">#</a> <code>hash_update</code></h3>
<p><code>hash_update</code> — hash-table / hashing helper <code>update</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p hash_update $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hash-zip">
<h3><a class="doc-anchor" href="#doc-hash-zip">#</a> <code>hash_zip</code></h3>
<p><code>hash_zip</code> — hash-table / hashing helper <code>zip</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p hash_zip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hausdorff-distance-2d">
<h3><a class="doc-anchor" href="#doc-hausdorff-distance-2d">#</a> <code>hausdorff_distance_2d</code></h3>
<p><code>hausdorff_distance_2d</code> — operation <code>hausdorff distance 2d</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p hausdorff_distance_2d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hausman-test">
<h3><a class="doc-anchor" href="#doc-hausman-test">#</a> <code>hausman_test</code></h3>
<p><code>hausman_test</code> — statistical test of <code>hausman</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p hausman_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-havdist">
<h3><a class="doc-anchor" href="#doc-havdist">#</a> <code>havdist</code></h3>
<p><code>havdist</code> — operation <code>havdist</code>. Alias for <code>haversine_distance</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p havdist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-haversine">
<h3><a class="doc-anchor" href="#doc-haversine">#</a> <code>haversine</code></h3>
<p><code>haversine_distance($lat1, $lon1, $lat2, $lon2)</code> (alias <code>haversine</code>) — computes the great-circle distance between two points on Earth given latitude/longitude in degrees. Returns distance in kilometers.</p>
<pre><code class="lang-perl"># NYC to LA
p haversine(40.7128, -74.0060, 34.0522, -118.2437)
# ~3940 km
</code></pre>
</article>
<article class="doc-entry" id="doc-haversine-dist">
<h3><a class="doc-anchor" href="#doc-haversine-dist">#</a> <code>haversine_dist</code></h3>
<p><code>haversine_dist</code> — operation <code>haversine dist</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p haversine_dist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hawk-dove-payoff">
<h3><a class="doc-anchor" href="#doc-hawk-dove-payoff">#</a> <code>hawk_dove_payoff</code></h3>
<p><code>hawk_dove_payoff</code> — operation <code>hawk dove payoff</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p hawk_dove_payoff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hawking-area-increase">
<h3><a class="doc-anchor" href="#doc-hawking-area-increase">#</a> <code>hawking_area_increase</code></h3>
<p><code>hawking_area_increase</code> — operation <code>hawking area increase</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p hawking_area_increase $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hclust">
<h3><a class="doc-anchor" href="#doc-hclust">#</a> <code>hclust</code></h3>
<p><code>hclust</code> — hierarchical clustering (average linkage). Takes a distance matrix. Returns merge list [[i,j,height],...]. Like R's hclust().</p>
<pre><code class="lang-perl">my $merges = hclust(dist_mat([[0,0],[1,0],[10,10]]))
</code></pre>
</article>
<article class="doc-entry" id="doc-head-finding-collins">
<h3><a class="doc-anchor" href="#doc-head-finding-collins">#</a> <code>head_finding_collins</code></h3>
<p><code>head_finding_collins</code> — operation <code>head finding collins</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p head_finding_collins $x
</code></pre>
</article>
<article class="doc-entry" id="doc-head-lines">
<h3><a class="doc-anchor" href="#doc-head-lines">#</a> <code>head_lines</code></h3>
<p><code>head_lines</code> — operation <code>head lines</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p head_lines $x
</code></pre>
</article>
<article class="doc-entry" id="doc-head-n">
<h3><a class="doc-anchor" href="#doc-head-n">#</a> <code>head_n</code></h3>
<p><code>head_n</code> — operation <code>head n</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p head_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-head-str">
<h3><a class="doc-anchor" href="#doc-head-str">#</a> <code>head_str</code></h3>
<p><code>head_str</code> — operation <code>head str</code>. Alias for <code>left_str</code>. Category: *string*.</p>
<pre><code class="lang-perl">p head_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heap-sift-down">
<h3><a class="doc-anchor" href="#doc-heap-sift-down">#</a> <code>heap_sift_down</code></h3>
<p><code>heap_sift_down</code> — binary-heap op <code>sift down</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p heap_sift_down $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heat-capacity-q">
<h3><a class="doc-anchor" href="#doc-heat-capacity-q">#</a> <code>heat_capacity_q</code></h3>
<p><code>heat_capacity_q</code> — operation <code>heat capacity q</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p heat_capacity_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heat-flow-radiogenic">
<h3><a class="doc-anchor" href="#doc-heat-flow-radiogenic">#</a> <code>heat_flow_radiogenic</code></h3>
<p><code>heat_flow_radiogenic</code> — operation <code>heat flow radiogenic</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p heat_flow_radiogenic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heat-index">
<h3><a class="doc-anchor" href="#doc-heat-index">#</a> <code>heat_index</code></h3>
<p><code>heat_index</code> — index of <code>heat</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p heat_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heat-index-celsius">
<h3><a class="doc-anchor" href="#doc-heat-index-celsius">#</a> <code>heat_index_celsius</code></h3>
<p><code>heat_index_celsius</code> — operation <code>heat index celsius</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p heat_index_celsius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hebrew-leap-year">
<h3><a class="doc-anchor" href="#doc-hebrew-leap-year">#</a> <code>hebrew_leap_year</code></h3>
<p><code>hebrew_leap_year</code> — operation <code>hebrew leap year</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p hebrew_leap_year $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hebrew-year-length">
<h3><a class="doc-anchor" href="#doc-hebrew-year-length">#</a> <code>hebrew_year_length</code></h3>
<p><code>hebrew_year_length</code> — operation <code>hebrew year length</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p hebrew_year_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heckman-correction">
<h3><a class="doc-anchor" href="#doc-heckman-correction">#</a> <code>heckman_correction</code></h3>
<p><code>heckman_correction</code> — operation <code>heckman correction</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p heckman_correction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heegaard-genus-lower">
<h3><a class="doc-anchor" href="#doc-heegaard-genus-lower">#</a> <code>heegaard_genus_lower</code></h3>
<p><code>heegaard_genus_lower</code> — operation <code>heegaard genus lower</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p heegaard_genus_lower $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heisenberg-min">
<h3><a class="doc-anchor" href="#doc-heisenberg-min">#</a> <code>heisenberg_min</code></h3>
<p><code>heisenberg_min</code> — minimum of <code>heisenberg</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p heisenberg_min $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hellinger-distance-step">
<h3><a class="doc-anchor" href="#doc-hellinger-distance-step">#</a> <code>hellinger_distance_step</code></h3>
<p><code>hellinger_distance_step</code> — single-step update of <code>hellinger distance</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p hellinger_distance_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hellinger-kernel">
<h3><a class="doc-anchor" href="#doc-hellinger-kernel">#</a> <code>hellinger_kernel</code></h3>
<p><code>hellinger_kernel</code> — convolution kernel of <code>hellinger</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p hellinger_kernel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-helmholtz-capacitance">
<h3><a class="doc-anchor" href="#doc-helmholtz-capacitance">#</a> <code>helmholtz_capacitance</code></h3>
<p><code>helmholtz_capacitance</code> — operation <code>helmholtz capacitance</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p helmholtz_capacitance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-helmholtz-decomp-step">
<h3><a class="doc-anchor" href="#doc-helmholtz-decomp-step">#</a> <code>helmholtz_decomp_step</code></h3>
<p><code>helmholtz_decomp_step</code> — single-step update of <code>helmholtz decomp</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p helmholtz_decomp_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-henderson-base">
<h3><a class="doc-anchor" href="#doc-henderson-base">#</a> <code>henderson_base</code></h3>
<p><code>henderson_base</code> — operation <code>henderson base</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p henderson_base $x
</code></pre>
</article>
<article class="doc-entry" id="doc-henderson-buffer">
<h3><a class="doc-anchor" href="#doc-henderson-buffer">#</a> <code>henderson_buffer</code></h3>
<p><code>henderson_buffer</code> — operation <code>henderson buffer</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p henderson_buffer $x
</code></pre>
</article>
<article class="doc-entry" id="doc-henderson-hasselbalch-solve">
<h3><a class="doc-anchor" href="#doc-henderson-hasselbalch-solve">#</a> <code>henderson_hasselbalch_solve</code></h3>
<p><code>henderson_hasselbalch_solve</code> — operation <code>henderson hasselbalch solve</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p henderson_hasselbalch_solve $x
</code></pre>
</article>
<article class="doc-entry" id="doc-henikoff-weight">
<h3><a class="doc-anchor" href="#doc-henikoff-weight">#</a> <code>henikoff_weight</code></h3>
<p><code>henikoff_weight</code> — operation <code>henikoff weight</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p henikoff_weight $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heptagonal-number">
<h3><a class="doc-anchor" href="#doc-heptagonal-number">#</a> <code>heptagonal_number</code></h3>
<p><code>heptagonal_number(n) → int</code> — <code>n·(5n-3) / 2</code>.</p>
</article>
<article class="doc-entry" id="doc-herd-immunity-threshold">
<h3><a class="doc-anchor" href="#doc-herd-immunity-threshold">#</a> <code>herd_immunity_threshold</code></h3>
<p><code>herd_immunity_threshold</code> — operation <code>herd immunity threshold</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p herd_immunity_threshold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heron">
<h3><a class="doc-anchor" href="#doc-heron">#</a> <code>heron</code></h3>
<p><code>heron</code> — operation <code>heron</code>. Alias for <code>heron_area</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p heron $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heron-area">
<h3><a class="doc-anchor" href="#doc-heron-area">#</a> <code>heron_area</code></h3>
<p><code>heron_area</code> — operation <code>heron area</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p heron_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heston-price-simple">
<h3><a class="doc-anchor" href="#doc-heston-price-simple">#</a> <code>heston_price_simple</code></h3>
<p><code>heston_price_simple</code> — operation <code>heston price simple</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p heston_price_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heteroskedasticity-test">
<h3><a class="doc-anchor" href="#doc-heteroskedasticity-test">#</a> <code>heteroskedasticity_test</code></h3>
<p><code>heteroskedasticity_test</code> — statistical test of <code>heteroskedasticity</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p heteroskedasticity_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heterozygosity">
<h3><a class="doc-anchor" href="#doc-heterozygosity">#</a> <code>heterozygosity</code></h3>
<p><code>heterozygosity</code> — operation <code>heterozygosity</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p heterozygosity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heun-euler-step">
<h3><a class="doc-anchor" href="#doc-heun-euler-step">#</a> <code>heun_euler_step</code></h3>
<p><code>heun_euler_step</code> — single-step update of <code>heun euler</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p heun_euler_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heun-method">
<h3><a class="doc-anchor" href="#doc-heun-method">#</a> <code>heun_method</code></h3>
<p><code>heun_method</code> — operation <code>heun method</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p heun_method $x
</code></pre>
</article>
<article class="doc-entry" id="doc-heun-sde-step">
<h3><a class="doc-anchor" href="#doc-heun-sde-step">#</a> <code>heun_sde_step</code></h3>
<p><code>heun_sde_step</code> — single-step update of <code>heun sde</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p heun_sde_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hex-lower">
<h3><a class="doc-anchor" href="#doc-hex-lower">#</a> <code>hex_lower</code></h3>
<p><code>hex_lower</code> — hex helper <code>lower</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p hex_lower $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hex-of">
<h3><a class="doc-anchor" href="#doc-hex-of">#</a> <code>hex_of</code></h3>
<p><code>hex_of</code> — hex helper <code>of</code>. Alias for <code>to_hex</code>. Category: *base conversion*.</p>
<pre><code class="lang-perl">p hex_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hex-to-bytes">
<h3><a class="doc-anchor" href="#doc-hex-to-bytes">#</a> <code>hex_to_bytes</code></h3>
<p><code>hex_to_bytes</code> — convert from <code>hex</code> to <code>bytes</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p hex_to_bytes $value
</code></pre>
</article>
<article class="doc-entry" id="doc-hex-to-rgb">
<h3><a class="doc-anchor" href="#doc-hex-to-rgb">#</a> <code>hex_to_rgb</code></h3>
<p><code>hex_to_rgb</code> — convert from <code>hex</code> to <code>rgb</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p hex_to_rgb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-hex-upper">
<h3><a class="doc-anchor" href="#doc-hex-upper">#</a> <code>hex_upper</code></h3>
<p><code>hex_upper</code> — hex helper <code>upper</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p hex_upper $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hexagonal-number">
<h3><a class="doc-anchor" href="#doc-hexagonal-number">#</a> <code>hexagonal_number</code></h3>
<p><code>hexagonal_number(n) → int</code> — <code>n·(2n-1)</code>.</p>
</article>
<article class="doc-entry" id="doc-hget">
<h3><a class="doc-anchor" href="#doc-hget">#</a> <code>hget</code></h3>
<p><code>hget</code> — operation <code>hget</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p hget $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hgetall">
<h3><a class="doc-anchor" href="#doc-hgetall">#</a> <code>hgetall</code></h3>
<p><code>hgetall</code> — operation <code>hgetall</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p hgetall $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hhi-concentration">
<h3><a class="doc-anchor" href="#doc-hhi-concentration">#</a> <code>hhi_concentration</code></h3>
<p><code>hhi_concentration</code> — operation <code>hhi concentration</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p hhi_concentration $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hicksian-demand">
<h3><a class="doc-anchor" href="#doc-hicksian-demand">#</a> <code>hicksian_demand</code></h3>
<p><code>hicksian_demand</code> — operation <code>hicksian demand</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p hicksian_demand $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hidden">
<h3><a class="doc-anchor" href="#doc-hidden">#</a> <code>hidden</code></h3>
<p><code>hidden</code> — operation <code>hidden</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p hidden $x
</code></pre>
</article>
<article class="doc-entry" id="doc-highpass-filter">
<h3><a class="doc-anchor" href="#doc-highpass-filter">#</a> <code>highpass_filter</code></h3>
<p><code>highpass_filter(\@signal, $cutoff)</code> (alias <code>hpf</code>) — applies a simple high-pass filter to remove low-frequency components (DC offset, drift). Signal = original - lowpass.</p>
<pre><code class="lang-perl">my @with_dc = map { 5 + sin(_/10) } 1:100
my $ac_only = hpf(\@with_dc, 0.1)
</code></pre>
</article>
<article class="doc-entry" id="doc-highway-hash">
<h3><a class="doc-anchor" href="#doc-highway-hash">#</a> <code>highway_hash</code></h3>
<p><code>highway_hash</code> — hash function of <code>highway</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p highway_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hilbert-envelope">
<h3><a class="doc-anchor" href="#doc-hilbert-envelope">#</a> <code>hilbert_envelope</code></h3>
<p><code>hilbert_envelope</code> — operation <code>hilbert envelope</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p hilbert_envelope $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hilbert-signal">
<h3><a class="doc-anchor" href="#doc-hilbert-signal">#</a> <code>hilbert_signal</code></h3>
<p><code>hilbert_signal</code> — operation <code>hilbert signal</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p hilbert_signal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hill-equation">
<h3><a class="doc-anchor" href="#doc-hill-equation">#</a> <code>hill_equation</code></h3>
<p><code>hill_equation</code> — operation <code>hill equation</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p hill_equation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hill-radius">
<h3><a class="doc-anchor" href="#doc-hill-radius">#</a> <code>hill_radius</code></h3>
<p><code>hill_radius</code> — operation <code>hill radius</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p hill_radius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hill-sphere-radius">
<h3><a class="doc-anchor" href="#doc-hill-sphere-radius">#</a> <code>hill_sphere_radius</code></h3>
<p><code>hill_sphere_radius</code> — operation <code>hill sphere radius</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p hill_sphere_radius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hill-velocity">
<h3><a class="doc-anchor" href="#doc-hill-velocity">#</a> <code>hill_velocity</code></h3>
<p><code>hill_velocity</code> — operation <code>hill velocity</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p hill_velocity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hincrby">
<h3><a class="doc-anchor" href="#doc-hincrby">#</a> <code>hincrby</code></h3>
<p><code>hincrby</code> — operation <code>hincrby</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p hincrby $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hindley-milner-step">
<h3><a class="doc-anchor" href="#doc-hindley-milner-step">#</a> <code>hindley_milner_step</code></h3>
<p><code>hindley_milner_step</code> — single-step update of <code>hindley milner</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p hindley_milner_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hindu-lunisolar-month">
<h3><a class="doc-anchor" href="#doc-hindu-lunisolar-month">#</a> <code>hindu_lunisolar_month</code></h3>
<p><code>hindu_lunisolar_month</code> — operation <code>hindu lunisolar month</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p hindu_lunisolar_month $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hindu-solar-year">
<h3><a class="doc-anchor" href="#doc-hindu-solar-year">#</a> <code>hindu_solar_year</code></h3>
<p><code>hindu_solar_year</code> — operation <code>hindu solar year</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p hindu_solar_year $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hinge-loss">
<h3><a class="doc-anchor" href="#doc-hinge-loss">#</a> <code>hinge_loss</code></h3>
<p><code>hinge_loss</code> — operation <code>hinge loss</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p hinge_loss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hirschberg-lcs-length">
<h3><a class="doc-anchor" href="#doc-hirschberg-lcs-length">#</a> <code>hirschberg_lcs_length</code></h3>
<p><code>hirschberg_lcs_length</code> — operation <code>hirschberg lcs length</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p hirschberg_lcs_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hirzebruch-signature">
<h3><a class="doc-anchor" href="#doc-hirzebruch-signature">#</a> <code>hirzebruch_signature</code></h3>
<p><code>hirzebruch_signature</code> — operation <code>hirzebruch signature</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p hirzebruch_signature $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hist">
<h3><a class="doc-anchor" href="#doc-hist">#</a> <code>hist</code></h3>
<p><code>hist</code> — operation <code>hist</code>. Alias for <code>histogram</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p hist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-histogram">
<h3><a class="doc-anchor" href="#doc-histogram">#</a> <code>histogram</code></h3>
<p><code>histogram</code> — operation <code>histogram</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p histogram $x
</code></pre>
</article>
<article class="doc-entry" id="doc-histogram-bin-edges">
<h3><a class="doc-anchor" href="#doc-histogram-bin-edges">#</a> <code>histogram_bin_edges</code></h3>
<p><code>histogram_bin_edges</code> — operation <code>histogram bin edges</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p histogram_bin_edges $x
</code></pre>
</article>
<article class="doc-entry" id="doc-histogram-bins">
<h3><a class="doc-anchor" href="#doc-histogram-bins">#</a> <code>histogram_bins</code></h3>
<p><code>histogram_bins</code> — operation <code>histogram bins</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p histogram_bins $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hits-authority">
<h3><a class="doc-anchor" href="#doc-hits-authority">#</a> <code>hits_authority</code></h3>
<p><code>hits_authority</code> — operation <code>hits authority</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p hits_authority $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hits-hub">
<h3><a class="doc-anchor" href="#doc-hits-hub">#</a> <code>hits_hub</code></h3>
<p><code>hits_hub</code> — operation <code>hits hub</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p hits_hub $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hits-simple">
<h3><a class="doc-anchor" href="#doc-hits-simple">#</a> <code>hits_simple</code></h3>
<p><code>hits_simple</code> — operation <code>hits simple</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p hits_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hitting-set-greedy">
<h3><a class="doc-anchor" href="#doc-hitting-set-greedy">#</a> <code>hitting_set_greedy</code></h3>
<p><code>hitting_set_greedy</code> — operation <code>hitting set greedy</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p hitting_set_greedy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hk">
<h3><a class="doc-anchor" href="#doc-hk">#</a> <code>hk</code></h3>
<p><code>hk</code> — operation <code>hk</code>. Alias for <code>has_key</code>. Category: *hash helpers*.</p>
<pre><code class="lang-perl">p hk $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hkdf-expand-step">
<h3><a class="doc-anchor" href="#doc-hkdf-expand-step">#</a> <code>hkdf_expand_step</code></h3>
<p><code>hkdf_expand_step</code> — single-step update of <code>hkdf expand</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p hkdf_expand_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hkeys">
<h3><a class="doc-anchor" href="#doc-hkeys">#</a> <code>hkeys</code></h3>
<p><code>hkeys</code> — operation <code>hkeys</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p hkeys $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hlen">
<h3><a class="doc-anchor" href="#doc-hlen">#</a> <code>hlen</code></h3>
<p><code>hlen</code> — operation <code>hlen</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p hlen $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hlookup">
<h3><a class="doc-anchor" href="#doc-hlookup">#</a> <code>hlookup</code></h3>
<p><code>hlookup</code> — operation <code>hlookup</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p hlookup $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hma">
<h3><a class="doc-anchor" href="#doc-hma">#</a> <code>hma</code></h3>
<p><code>hma(prices, period=10) → array</code> — Hull moving average. Reduces lag relative to SMA/EMA via <code>WMA(2·WMA(half) − WMA(full), √period)</code>.</p>
<pre><code class="lang-perl">p hma(\@prices, 14)
</code></pre>
</article>
<article class="doc-entry" id="doc-hmac-md5-hex">
<h3><a class="doc-anchor" href="#doc-hmac-md5-hex">#</a> <code>hmac_md5_hex</code></h3>
<p><code>hmac_md5_hex(key, msg) → string</code> — HMAC-MD5 as lowercase hex.</p>
</article>
<article class="doc-entry" id="doc-hmac-sha1-hex">
<h3><a class="doc-anchor" href="#doc-hmac-sha1-hex">#</a> <code>hmac_sha1_hex</code></h3>
<p><code>hmac_sha1_hex(key, msg) → string</code> — HMAC-SHA1 as lowercase hex.</p>
</article>
<article class="doc-entry" id="doc-hmac-sha256-hex">
<h3><a class="doc-anchor" href="#doc-hmac-sha256-hex">#</a> <code>hmac_sha256_hex</code></h3>
<p><code>hmac_sha256_hex(key, msg) → string</code> — HMAC-SHA256 as lowercase hex (RFC 4231 compliant).</p>
<pre><code class="lang-perl">p hmac_sha256_hex("key", "hello")
</code></pre>
</article>
<article class="doc-entry" id="doc-hmac-sha384-hex">
<h3><a class="doc-anchor" href="#doc-hmac-sha384-hex">#</a> <code>hmac_sha384_hex</code></h3>
<p><code>hmac_sha384_hex(key, msg) → string</code> — HMAC-SHA384 as lowercase hex.</p>
</article>
<article class="doc-entry" id="doc-hmac-sha512-hex">
<h3><a class="doc-anchor" href="#doc-hmac-sha512-hex">#</a> <code>hmac_sha512_hex</code></h3>
<p><code>hmac_sha512_hex(key, msg) → string</code> — HMAC-SHA512 as lowercase hex.</p>
</article>
<article class="doc-entry" id="doc-hmac-step-xor">
<h3><a class="doc-anchor" href="#doc-hmac-step-xor">#</a> <code>hmac_step_xor</code></h3>
<p><code>hmac_step_xor</code> — HMAC keyed-hash variant <code>step xor</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p hmac_step_xor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hmset">
<h3><a class="doc-anchor" href="#doc-hmset">#</a> <code>hmset</code></h3>
<p><code>hmset</code> — operation <code>hmset</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p hmset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hochschild-zero">
<h3><a class="doc-anchor" href="#doc-hochschild-zero">#</a> <code>hochschild_zero</code></h3>
<p><code>hochschild_zero</code> — operation <code>hochschild zero</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p hochschild_zero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hodge-diamond-value">
<h3><a class="doc-anchor" href="#doc-hodge-diamond-value">#</a> <code>hodge_diamond_value</code></h3>
<p><code>hodge_diamond_value</code> — value of <code>hodge diamond</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p hodge_diamond_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hodge-inner-product-one">
<h3><a class="doc-anchor" href="#doc-hodge-inner-product-one">#</a> <code>hodge_inner_product_one</code></h3>
<p><code>hodge_inner_product_one</code> — operation <code>hodge inner product one</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p hodge_inner_product_one $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hodge-polynomial-eval">
<h3><a class="doc-anchor" href="#doc-hodge-polynomial-eval">#</a> <code>hodge_polynomial_eval</code></h3>
<p><code>hodge_polynomial_eval</code> — operation <code>hodge polynomial eval</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p hodge_polynomial_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hodge-star-one-form">
<h3><a class="doc-anchor" href="#doc-hodge-star-one-form">#</a> <code>hodge_star_one_form</code></h3>
<p><code>hodge_star_one_form</code> — operation <code>hodge star one form</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p hodge_star_one_form $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hodges-lehmann">
<h3><a class="doc-anchor" href="#doc-hodges-lehmann">#</a> <code>hodges_lehmann</code></h3>
<p><code>hodges_lehmann</code> — operation <code>hodges lehmann</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p hodges_lehmann $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hog-features">
<h3><a class="doc-anchor" href="#doc-hog-features">#</a> <code>hog_features</code></h3>
<p><code>hog_features</code> — operation <code>hog features</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p hog_features $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hohmann-dv1">
<h3><a class="doc-anchor" href="#doc-hohmann-dv1">#</a> <code>hohmann_dv1</code></h3>
<p><code>hohmann_dv1</code> — operation <code>hohmann dv1</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p hohmann_dv1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hohmann-dv2">
<h3><a class="doc-anchor" href="#doc-hohmann-dv2">#</a> <code>hohmann_dv2</code></h3>
<p><code>hohmann_dv2</code> — operation <code>hohmann dv2</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p hohmann_dv2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hohmann-total">
<h3><a class="doc-anchor" href="#doc-hohmann-total">#</a> <code>hohmann_total</code></h3>
<p><code>hohmann_total</code> — operation <code>hohmann total</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p hohmann_total $x
</code></pre>
</article>
<article class="doc-entry" id="doc-holling-type1">
<h3><a class="doc-anchor" href="#doc-holling-type1">#</a> <code>holling_type1</code></h3>
<p><code>holling_type1</code> — operation <code>holling type1</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p holling_type1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-holling-type2">
<h3><a class="doc-anchor" href="#doc-holling-type2">#</a> <code>holling_type2</code></h3>
<p><code>holling_type2</code> — operation <code>holling type2</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p holling_type2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-holling-type3">
<h3><a class="doc-anchor" href="#doc-holling-type3">#</a> <code>holling_type3</code></h3>
<p><code>holling_type3</code> — operation <code>holling type3</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p holling_type3 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-holographic-entanglement-step">
<h3><a class="doc-anchor" href="#doc-holographic-entanglement-step">#</a> <code>holographic_entanglement_step</code></h3>
<p><code>holographic_entanglement_step</code> — single-step update of <code>holographic entanglement</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p holographic_entanglement_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-holt-winters-additive">
<h3><a class="doc-anchor" href="#doc-holt-winters-additive">#</a> <code>holt_winters_additive</code></h3>
<p><code>holt_winters_additive</code> — operation <code>holt winters additive</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p holt_winters_additive $x
</code></pre>
</article>
<article class="doc-entry" id="doc-holt-winters-multiplicative">
<h3><a class="doc-anchor" href="#doc-holt-winters-multiplicative">#</a> <code>holt_winters_multiplicative</code></h3>
<p><code>holt_winters_multiplicative</code> — operation <code>holt winters multiplicative</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p holt_winters_multiplicative $x
</code></pre>
</article>
<article class="doc-entry" id="doc-home-dir">
<h3><a class="doc-anchor" href="#doc-home-dir">#</a> <code>home_dir</code></h3>
<p><code>home_dir</code> — operation <code>home dir</code>. Category: *system introspection*.</p>
<pre><code class="lang-perl">p home_dir $x
</code></pre>
</article>
<article class="doc-entry" id="doc-homfly-evaluation">
<h3><a class="doc-anchor" href="#doc-homfly-evaluation">#</a> <code>homfly_evaluation</code></h3>
<p><code>homfly_evaluation</code> — operation <code>homfly evaluation</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p homfly_evaluation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-homology-rank">
<h3><a class="doc-anchor" href="#doc-homology-rank">#</a> <code>homology_rank</code></h3>
<p><code>homology_rank</code> — operation <code>homology rank</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p homology_rank $x
</code></pre>
</article>
<article class="doc-entry" id="doc-homotopy-group-sphere-pi">
<h3><a class="doc-anchor" href="#doc-homotopy-group-sphere-pi">#</a> <code>homotopy_group_sphere_pi</code></h3>
<p><code>homotopy_group_sphere_pi</code> — operation <code>homotopy group sphere pi</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p homotopy_group_sphere_pi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hooke">
<h3><a class="doc-anchor" href="#doc-hooke">#</a> <code>hooke</code></h3>
<p><code>hooke</code> — operation <code>hooke</code>. Alias for <code>spring_force</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p hooke $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hopcroft-karp">
<h3><a class="doc-anchor" href="#doc-hopcroft-karp">#</a> <code>hopcroft_karp</code></h3>
<p><code>hopcroft_karp</code> — operation <code>hopcroft karp</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p hopcroft_karp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hopcroft-karp-phase">
<h3><a class="doc-anchor" href="#doc-hopcroft-karp-phase">#</a> <code>hopcroft_karp_phase</code></h3>
<p><code>hopcroft_karp_phase</code> — operation <code>hopcroft karp phase</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p hopcroft_karp_phase $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hopcroft-karp-step">
<h3><a class="doc-anchor" href="#doc-hopcroft-karp-step">#</a> <code>hopcroft_karp_step</code></h3>
<p><code>hopcroft_karp_step</code> — single-step update of <code>hopcroft karp</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p hopcroft_karp_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-horizon-distance">
<h3><a class="doc-anchor" href="#doc-horizon-distance">#</a> <code>horizon_distance</code></h3>
<p><code>horizon_distance</code> — distance / dissimilarity metric of <code>horizon</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p horizon_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-horn-schunck-step">
<h3><a class="doc-anchor" href="#doc-horn-schunck-step">#</a> <code>horn_schunck_step</code></h3>
<p><code>horn_schunck_step</code> — single-step update of <code>horn schunck</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p horn_schunck_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-horndeski-step">
<h3><a class="doc-anchor" href="#doc-horndeski-step">#</a> <code>horndeski_step</code></h3>
<p><code>horndeski_step</code> — single-step update of <code>horndeski</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p horndeski_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-horspool-search">
<h3><a class="doc-anchor" href="#doc-horspool-search">#</a> <code>horspool_search</code></h3>
<p><code>horspool_search</code> — operation <code>horspool search</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p horspool_search $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hostname-str">
<h3><a class="doc-anchor" href="#doc-hostname-str">#</a> <code>hostname_str</code></h3>
<p><code>hostname_str</code> — operation <code>hostname str</code>. Category: *more process / system*.</p>
<pre><code class="lang-perl">p hostname_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hotelling-location-step">
<h3><a class="doc-anchor" href="#doc-hotelling-location-step">#</a> <code>hotelling_location_step</code></h3>
<p><code>hotelling_location_step</code> — single-step update of <code>hotelling location</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p hotelling_location_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hotelling-price-step">
<h3><a class="doc-anchor" href="#doc-hotelling-price-step">#</a> <code>hotelling_price_step</code></h3>
<p><code>hotelling_price_step</code> — single-step update of <code>hotelling price</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p hotelling_price_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hough-accumulator-step">
<h3><a class="doc-anchor" href="#doc-hough-accumulator-step">#</a> <code>hough_accumulator_step</code></h3>
<p><code>hough_accumulator_step</code> — single-step update of <code>hough accumulator</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p hough_accumulator_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hough-circles">
<h3><a class="doc-anchor" href="#doc-hough-circles">#</a> <code>hough_circles</code></h3>
<p><code>hough_circles</code> — operation <code>hough circles</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p hough_circles $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hough-lines">
<h3><a class="doc-anchor" href="#doc-hough-lines">#</a> <code>hough_lines</code></h3>
<p><code>hough_lines</code> — operation <code>hough lines</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p hough_lines $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hours-to-days">
<h3><a class="doc-anchor" href="#doc-hours-to-days">#</a> <code>hours_to_days</code></h3>
<p><code>hours_to_days</code> — convert from <code>hours</code> to <code>days</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p hours_to_days $value
</code></pre>
</article>
<article class="doc-entry" id="doc-hours-to-minutes">
<h3><a class="doc-anchor" href="#doc-hours-to-minutes">#</a> <code>hours_to_minutes</code></h3>
<p><code>hours_to_minutes</code> — convert from <code>hours</code> to <code>minutes</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p hours_to_minutes $value
</code></pre>
</article>
<article class="doc-entry" id="doc-hours-to-seconds">
<h3><a class="doc-anchor" href="#doc-hours-to-seconds">#</a> <code>hours_to_seconds</code></h3>
<p><code>hours_to_seconds</code> — convert from <code>hours</code> to <code>seconds</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p hours_to_seconds $value
</code></pre>
</article>
<article class="doc-entry" id="doc-householder-root">
<h3><a class="doc-anchor" href="#doc-householder-root">#</a> <code>householder_root</code></h3>
<p><code>householder_root</code> — operation <code>householder root</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p householder_root $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hp-to-watts">
<h3><a class="doc-anchor" href="#doc-hp-to-watts">#</a> <code>hp_to_watts</code></h3>
<p><code>hp_to_watts</code> — convert from <code>hp</code> to <code>watts</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p hp_to_watts $value
</code></pre>
</article>
<article class="doc-entry" id="doc-hr">
<h3><a class="doc-anchor" href="#doc-hr">#</a> <code>hr</code></h3>
<p><code>hr</code> — operation <code>hr</code>. Alias for <code>http_request</code>. Category: *data / network*.</p>
<pre><code class="lang-perl">p hr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hset">
<h3><a class="doc-anchor" href="#doc-hset">#</a> <code>hset</code></h3>
<p><code>hset</code> — operation <code>hset</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p hset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hsl2rgb">
<h3><a class="doc-anchor" href="#doc-hsl2rgb">#</a> <code>hsl2rgb</code></h3>
<p><code>hsl2rgb</code> — operation <code>hsl2rgb</code>. Alias for <code>hsl_to_rgb</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p hsl2rgb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hsl-to-rgb">
<h3><a class="doc-anchor" href="#doc-hsl-to-rgb">#</a> <code>hsl_to_rgb</code></h3>
<p><code>hsl_to_rgb</code> — convert from <code>hsl</code> to <code>rgb</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p hsl_to_rgb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-hstore-to-array">
<h3><a class="doc-anchor" href="#doc-hstore-to-array">#</a> <code>hstore_to_array</code></h3>
<p><code>hstore_to_array</code> — convert from <code>hstore</code> to <code>array</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p hstore_to_array $value
</code></pre>
</article>
<article class="doc-entry" id="doc-hsv2rgb">
<h3><a class="doc-anchor" href="#doc-hsv2rgb">#</a> <code>hsv2rgb</code></h3>
<p><code>hsv2rgb</code> — operation <code>hsv2rgb</code>. Alias for <code>hsv_to_rgb</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p hsv2rgb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hsv-to-rgb">
<h3><a class="doc-anchor" href="#doc-hsv-to-rgb">#</a> <code>hsv_to_rgb</code></h3>
<p><code>hsv_to_rgb</code> — convert from <code>hsv</code> to <code>rgb</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p hsv_to_rgb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-html-canonical-url">
<h3><a class="doc-anchor" href="#doc-html-canonical-url">#</a> <code>html_canonical_url</code></h3>
<p><code>html_canonical_url</code> — HTML helper <code>canonical url</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_canonical_url $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-decode">
<h3><a class="doc-anchor" href="#doc-html-decode">#</a> <code>html_decode</code></h3>
<p><code>html_decode</code> — HTML helper <code>decode</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p html_decode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-encode">
<h3><a class="doc-anchor" href="#doc-html-encode">#</a> <code>html_encode</code></h3>
<p><code>html_encode</code> — HTML helper <code>encode</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p html_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-extract-headings">
<h3><a class="doc-anchor" href="#doc-html-extract-headings">#</a> <code>html_extract_headings</code></h3>
<p><code>html_extract_headings</code> — HTML helper <code>extract headings</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_extract_headings $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-extract-images">
<h3><a class="doc-anchor" href="#doc-html-extract-images">#</a> <code>html_extract_images</code></h3>
<p><code>html_extract_images</code> — HTML helper <code>extract images</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_extract_images $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-extract-links">
<h3><a class="doc-anchor" href="#doc-html-extract-links">#</a> <code>html_extract_links</code></h3>
<p><code>html_extract_links</code> — HTML helper <code>extract links</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_extract_links $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-extract-meta">
<h3><a class="doc-anchor" href="#doc-html-extract-meta">#</a> <code>html_extract_meta</code></h3>
<p><code>html_extract_meta</code> — HTML helper <code>extract meta</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_extract_meta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-extract-tables">
<h3><a class="doc-anchor" href="#doc-html-extract-tables">#</a> <code>html_extract_tables</code></h3>
<p><code>html_extract_tables</code> — HTML helper <code>extract tables</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_extract_tables $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-extract-text">
<h3><a class="doc-anchor" href="#doc-html-extract-text">#</a> <code>html_extract_text</code></h3>
<p><code>html_extract_text</code> — HTML helper <code>extract text</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_extract_text $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-extract-title">
<h3><a class="doc-anchor" href="#doc-html-extract-title">#</a> <code>html_extract_title</code></h3>
<p><code>html_extract_title</code> — HTML helper <code>extract title</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_extract_title $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-inner-text">
<h3><a class="doc-anchor" href="#doc-html-inner-text">#</a> <code>html_inner_text</code></h3>
<p><code>html_inner_text</code> — HTML helper <code>inner text</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_inner_text $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-meta-charset">
<h3><a class="doc-anchor" href="#doc-html-meta-charset">#</a> <code>html_meta_charset</code></h3>
<p><code>html_meta_charset</code> — HTML helper <code>meta charset</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_meta_charset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-meta-description">
<h3><a class="doc-anchor" href="#doc-html-meta-description">#</a> <code>html_meta_description</code></h3>
<p><code>html_meta_description</code> — HTML helper <code>meta description</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_meta_description $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-meta-keywords">
<h3><a class="doc-anchor" href="#doc-html-meta-keywords">#</a> <code>html_meta_keywords</code></h3>
<p><code>html_meta_keywords</code> — HTML helper <code>meta keywords</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_meta_keywords $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-meta-og">
<h3><a class="doc-anchor" href="#doc-html-meta-og">#</a> <code>html_meta_og</code></h3>
<p><code>html_meta_og</code> — HTML helper <code>meta og</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_meta_og $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-meta-twitter">
<h3><a class="doc-anchor" href="#doc-html-meta-twitter">#</a> <code>html_meta_twitter</code></h3>
<p><code>html_meta_twitter</code> — HTML helper <code>meta twitter</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_meta_twitter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-minify">
<h3><a class="doc-anchor" href="#doc-html-minify">#</a> <code>html_minify</code></h3>
<p><code>html_minify</code> — HTML helper <code>minify</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_minify $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-pretty">
<h3><a class="doc-anchor" href="#doc-html-pretty">#</a> <code>html_pretty</code></h3>
<p><code>html_pretty</code> — HTML helper <code>pretty</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_pretty $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-sanitize">
<h3><a class="doc-anchor" href="#doc-html-sanitize">#</a> <code>html_sanitize</code></h3>
<p><code>html_sanitize</code> — HTML helper <code>sanitize</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_sanitize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-strip-scripts">
<h3><a class="doc-anchor" href="#doc-html-strip-scripts">#</a> <code>html_strip_scripts</code></h3>
<p><code>html_strip_scripts</code> — HTML helper <code>strip scripts</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_strip_scripts $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-strip-styles">
<h3><a class="doc-anchor" href="#doc-html-strip-styles">#</a> <code>html_strip_styles</code></h3>
<p><code>html_strip_styles</code> — HTML helper <code>strip styles</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_strip_styles $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-strip-tags">
<h3><a class="doc-anchor" href="#doc-html-strip-tags">#</a> <code>html_strip_tags</code></h3>
<p><code>html_strip_tags</code> — HTML helper <code>strip tags</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_strip_tags $x
</code></pre>
</article>
<article class="doc-entry" id="doc-html-to-markdown">
<h3><a class="doc-anchor" href="#doc-html-to-markdown">#</a> <code>html_to_markdown</code></h3>
<p><code>html_to_markdown</code> — convert from <code>html</code> to <code>markdown</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_to_markdown $value
</code></pre>
</article>
<article class="doc-entry" id="doc-html-to-text">
<h3><a class="doc-anchor" href="#doc-html-to-text">#</a> <code>html_to_text</code></h3>
<p><code>html_to_text</code> — convert from <code>html</code> to <code>text</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p html_to_text $value
</code></pre>
</article>
<article class="doc-entry" id="doc-htmld">
<h3><a class="doc-anchor" href="#doc-htmld">#</a> <code>htmld</code></h3>
<p><code>htmld</code> — operation <code>htmld</code>. Alias for <code>html_decode</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p htmld $x
</code></pre>
</article>
<article class="doc-entry" id="doc-htmle">
<h3><a class="doc-anchor" href="#doc-htmle">#</a> <code>htmle</code></h3>
<p><code>htmle</code> — operation <code>htmle</code>. Alias for <code>html_encode</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p htmle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-date-format">
<h3><a class="doc-anchor" href="#doc-http-date-format">#</a> <code>http_date_format</code></h3>
<p><code>http_date_format</code> — HTTP helper <code>date format</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p http_date_format $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-date-parse">
<h3><a class="doc-anchor" href="#doc-http-date-parse">#</a> <code>http_date_parse</code></h3>
<p><code>http_date_parse</code> — HTTP helper <code>date parse</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p http_date_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-method-connect">
<h3><a class="doc-anchor" href="#doc-http-method-connect">#</a> <code>http_method_connect</code></h3>
<p><code>http_method_connect</code> — HTTP helper <code>method connect</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_method_connect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-method-delete">
<h3><a class="doc-anchor" href="#doc-http-method-delete">#</a> <code>http_method_delete</code></h3>
<p><code>http_method_delete</code> — HTTP helper <code>method delete</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_method_delete $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-method-get">
<h3><a class="doc-anchor" href="#doc-http-method-get">#</a> <code>http_method_get</code></h3>
<p><code>http_method_get</code> — HTTP helper <code>method get</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_method_get $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-method-has-body">
<h3><a class="doc-anchor" href="#doc-http-method-has-body">#</a> <code>http_method_has_body</code></h3>
<p><code>http_method_has_body</code> — HTTP helper <code>method has body</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p http_method_has_body $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-method-head">
<h3><a class="doc-anchor" href="#doc-http-method-head">#</a> <code>http_method_head</code></h3>
<p><code>http_method_head</code> — HTTP helper <code>method head</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_method_head $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-method-is-idempotent">
<h3><a class="doc-anchor" href="#doc-http-method-is-idempotent">#</a> <code>http_method_is_idempotent</code></h3>
<p><code>http_method_is_idempotent</code> — HTTP helper <code>method is idempotent</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p http_method_is_idempotent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-method-is-safe">
<h3><a class="doc-anchor" href="#doc-http-method-is-safe">#</a> <code>http_method_is_safe</code></h3>
<p><code>http_method_is_safe</code> — HTTP helper <code>method is safe</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p http_method_is_safe $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-method-options">
<h3><a class="doc-anchor" href="#doc-http-method-options">#</a> <code>http_method_options</code></h3>
<p><code>http_method_options</code> — HTTP helper <code>method options</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_method_options $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-method-patch">
<h3><a class="doc-anchor" href="#doc-http-method-patch">#</a> <code>http_method_patch</code></h3>
<p><code>http_method_patch</code> — HTTP helper <code>method patch</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_method_patch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-method-post">
<h3><a class="doc-anchor" href="#doc-http-method-post">#</a> <code>http_method_post</code></h3>
<p><code>http_method_post</code> — HTTP helper <code>method post</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_method_post $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-method-put">
<h3><a class="doc-anchor" href="#doc-http-method-put">#</a> <code>http_method_put</code></h3>
<p><code>http_method_put</code> — HTTP helper <code>method put</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_method_put $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-method-trace">
<h3><a class="doc-anchor" href="#doc-http-method-trace">#</a> <code>http_method_trace</code></h3>
<p><code>http_method_trace</code> — HTTP helper <code>method trace</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_method_trace $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-accepted">
<h3><a class="doc-anchor" href="#doc-http-status-accepted">#</a> <code>http_status_accepted</code></h3>
<p><code>http_status_accepted</code> — HTTP helper <code>status accepted</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_accepted $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-bad-gateway">
<h3><a class="doc-anchor" href="#doc-http-status-bad-gateway">#</a> <code>http_status_bad_gateway</code></h3>
<p><code>http_status_bad_gateway</code> — HTTP helper <code>status bad gateway</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_bad_gateway $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-bad-request">
<h3><a class="doc-anchor" href="#doc-http-status-bad-request">#</a> <code>http_status_bad_request</code></h3>
<p><code>http_status_bad_request</code> — HTTP helper <code>status bad request</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_bad_request $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-class">
<h3><a class="doc-anchor" href="#doc-http-status-class">#</a> <code>http_status_class</code></h3>
<p><code>http_status_class</code> — HTTP helper <code>status class</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p http_status_class $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-conflict">
<h3><a class="doc-anchor" href="#doc-http-status-conflict">#</a> <code>http_status_conflict</code></h3>
<p><code>http_status_conflict</code> — HTTP helper <code>status conflict</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_conflict $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-continue">
<h3><a class="doc-anchor" href="#doc-http-status-continue">#</a> <code>http_status_continue</code></h3>
<p><code>http_status_continue</code> — HTTP helper <code>status continue</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_continue $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-created">
<h3><a class="doc-anchor" href="#doc-http-status-created">#</a> <code>http_status_created</code></h3>
<p><code>http_status_created</code> — HTTP helper <code>status created</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_created $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-expectation-failed">
<h3><a class="doc-anchor" href="#doc-http-status-expectation-failed">#</a> <code>http_status_expectation_failed</code></h3>
<p><code>http_status_expectation_failed</code> — HTTP helper <code>status expectation failed</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_expectation_failed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-forbidden">
<h3><a class="doc-anchor" href="#doc-http-status-forbidden">#</a> <code>http_status_forbidden</code></h3>
<p><code>http_status_forbidden</code> — HTTP helper <code>status forbidden</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_forbidden $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-found">
<h3><a class="doc-anchor" href="#doc-http-status-found">#</a> <code>http_status_found</code></h3>
<p><code>http_status_found</code> — HTTP helper <code>status found</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_found $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-gateway-timeout">
<h3><a class="doc-anchor" href="#doc-http-status-gateway-timeout">#</a> <code>http_status_gateway_timeout</code></h3>
<p><code>http_status_gateway_timeout</code> — HTTP helper <code>status gateway timeout</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_gateway_timeout $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-gone">
<h3><a class="doc-anchor" href="#doc-http-status-gone">#</a> <code>http_status_gone</code></h3>
<p><code>http_status_gone</code> — HTTP helper <code>status gone</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_gone $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-http-version-not-supported">
<h3><a class="doc-anchor" href="#doc-http-status-http-version-not-supported">#</a> <code>http_status_http_version_not_supported</code></h3>
<p><code>http_status_http_version_not_supported</code> — HTTP helper <code>status http version not supported</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_http_version_not_supported $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-im-a-teapot">
<h3><a class="doc-anchor" href="#doc-http-status-im-a-teapot">#</a> <code>http_status_im_a_teapot</code></h3>
<p><code>http_status_im_a_teapot</code> — HTTP helper <code>status im a teapot</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_im_a_teapot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-internal-server-error">
<h3><a class="doc-anchor" href="#doc-http-status-internal-server-error">#</a> <code>http_status_internal_server_error</code></h3>
<p><code>http_status_internal_server_error</code> — HTTP helper <code>status internal server error</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_internal_server_error $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-is-client-error">
<h3><a class="doc-anchor" href="#doc-http-status-is-client-error">#</a> <code>http_status_is_client_error</code></h3>
<p><code>http_status_is_client_error</code> — HTTP helper <code>status is client error</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p http_status_is_client_error $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-is-informational">
<h3><a class="doc-anchor" href="#doc-http-status-is-informational">#</a> <code>http_status_is_informational</code></h3>
<p><code>http_status_is_informational</code> — HTTP helper <code>status is informational</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p http_status_is_informational $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-is-redirect">
<h3><a class="doc-anchor" href="#doc-http-status-is-redirect">#</a> <code>http_status_is_redirect</code></h3>
<p><code>http_status_is_redirect</code> — HTTP helper <code>status is redirect</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p http_status_is_redirect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-is-server-error">
<h3><a class="doc-anchor" href="#doc-http-status-is-server-error">#</a> <code>http_status_is_server_error</code></h3>
<p><code>http_status_is_server_error</code> — HTTP helper <code>status is server error</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p http_status_is_server_error $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-is-success">
<h3><a class="doc-anchor" href="#doc-http-status-is-success">#</a> <code>http_status_is_success</code></h3>
<p><code>http_status_is_success</code> — HTTP helper <code>status is success</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p http_status_is_success $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-length-required">
<h3><a class="doc-anchor" href="#doc-http-status-length-required">#</a> <code>http_status_length_required</code></h3>
<p><code>http_status_length_required</code> — HTTP helper <code>status length required</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_length_required $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-method-not-allowed">
<h3><a class="doc-anchor" href="#doc-http-status-method-not-allowed">#</a> <code>http_status_method_not_allowed</code></h3>
<p><code>http_status_method_not_allowed</code> — HTTP helper <code>status method not allowed</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_method_not_allowed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-moved-permanently">
<h3><a class="doc-anchor" href="#doc-http-status-moved-permanently">#</a> <code>http_status_moved_permanently</code></h3>
<p><code>http_status_moved_permanently</code> — HTTP helper <code>status moved permanently</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_moved_permanently $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-multiple-choices">
<h3><a class="doc-anchor" href="#doc-http-status-multiple-choices">#</a> <code>http_status_multiple_choices</code></h3>
<p><code>http_status_multiple_choices</code> — HTTP helper <code>status multiple choices</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_multiple_choices $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-no-content">
<h3><a class="doc-anchor" href="#doc-http-status-no-content">#</a> <code>http_status_no_content</code></h3>
<p><code>http_status_no_content</code> — HTTP helper <code>status no content</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_no_content $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-not-acceptable">
<h3><a class="doc-anchor" href="#doc-http-status-not-acceptable">#</a> <code>http_status_not_acceptable</code></h3>
<p><code>http_status_not_acceptable</code> — HTTP helper <code>status not acceptable</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_not_acceptable $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-not-found">
<h3><a class="doc-anchor" href="#doc-http-status-not-found">#</a> <code>http_status_not_found</code></h3>
<p><code>http_status_not_found</code> — HTTP helper <code>status not found</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_not_found $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-not-implemented">
<h3><a class="doc-anchor" href="#doc-http-status-not-implemented">#</a> <code>http_status_not_implemented</code></h3>
<p><code>http_status_not_implemented</code> — HTTP helper <code>status not implemented</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_not_implemented $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-not-modified">
<h3><a class="doc-anchor" href="#doc-http-status-not-modified">#</a> <code>http_status_not_modified</code></h3>
<p><code>http_status_not_modified</code> — HTTP helper <code>status not modified</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_not_modified $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-ok">
<h3><a class="doc-anchor" href="#doc-http-status-ok">#</a> <code>http_status_ok</code></h3>
<p><code>http_status_ok</code> — HTTP helper <code>status ok</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_ok $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-partial-content">
<h3><a class="doc-anchor" href="#doc-http-status-partial-content">#</a> <code>http_status_partial_content</code></h3>
<p><code>http_status_partial_content</code> — HTTP helper <code>status partial content</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_partial_content $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-payload-too-large">
<h3><a class="doc-anchor" href="#doc-http-status-payload-too-large">#</a> <code>http_status_payload_too_large</code></h3>
<p><code>http_status_payload_too_large</code> — HTTP helper <code>status payload too large</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_payload_too_large $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-payment-required">
<h3><a class="doc-anchor" href="#doc-http-status-payment-required">#</a> <code>http_status_payment_required</code></h3>
<p><code>http_status_payment_required</code> — HTTP helper <code>status payment required</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_payment_required $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-permanent-redirect">
<h3><a class="doc-anchor" href="#doc-http-status-permanent-redirect">#</a> <code>http_status_permanent_redirect</code></h3>
<p><code>http_status_permanent_redirect</code> — HTTP helper <code>status permanent redirect</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_permanent_redirect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-precondition-failed">
<h3><a class="doc-anchor" href="#doc-http-status-precondition-failed">#</a> <code>http_status_precondition_failed</code></h3>
<p><code>http_status_precondition_failed</code> — HTTP helper <code>status precondition failed</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_precondition_failed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-range-not-satisfiable">
<h3><a class="doc-anchor" href="#doc-http-status-range-not-satisfiable">#</a> <code>http_status_range_not_satisfiable</code></h3>
<p><code>http_status_range_not_satisfiable</code> — HTTP helper <code>status range not satisfiable</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_range_not_satisfiable $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-see-other">
<h3><a class="doc-anchor" href="#doc-http-status-see-other">#</a> <code>http_status_see_other</code></h3>
<p><code>http_status_see_other</code> — HTTP helper <code>status see other</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_see_other $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-service-unavailable">
<h3><a class="doc-anchor" href="#doc-http-status-service-unavailable">#</a> <code>http_status_service_unavailable</code></h3>
<p><code>http_status_service_unavailable</code> — HTTP helper <code>status service unavailable</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_service_unavailable $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-switching-protocols">
<h3><a class="doc-anchor" href="#doc-http-status-switching-protocols">#</a> <code>http_status_switching_protocols</code></h3>
<p><code>http_status_switching_protocols</code> — HTTP helper <code>status switching protocols</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_switching_protocols $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-temporary-redirect">
<h3><a class="doc-anchor" href="#doc-http-status-temporary-redirect">#</a> <code>http_status_temporary_redirect</code></h3>
<p><code>http_status_temporary_redirect</code> — HTTP helper <code>status temporary redirect</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_temporary_redirect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-text">
<h3><a class="doc-anchor" href="#doc-http-status-text">#</a> <code>http_status_text</code></h3>
<p><code>http_status_text</code> — HTTP helper <code>status text</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p http_status_text $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-too-many-requests">
<h3><a class="doc-anchor" href="#doc-http-status-too-many-requests">#</a> <code>http_status_too_many_requests</code></h3>
<p><code>http_status_too_many_requests</code> — HTTP helper <code>status too many requests</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_too_many_requests $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-unauthorized">
<h3><a class="doc-anchor" href="#doc-http-status-unauthorized">#</a> <code>http_status_unauthorized</code></h3>
<p><code>http_status_unauthorized</code> — HTTP helper <code>status unauthorized</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_unauthorized $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-unprocessable-entity">
<h3><a class="doc-anchor" href="#doc-http-status-unprocessable-entity">#</a> <code>http_status_unprocessable_entity</code></h3>
<p><code>http_status_unprocessable_entity</code> — HTTP helper <code>status unprocessable entity</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_unprocessable_entity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-unsupported-media-type">
<h3><a class="doc-anchor" href="#doc-http-status-unsupported-media-type">#</a> <code>http_status_unsupported_media_type</code></h3>
<p><code>http_status_unsupported_media_type</code> — HTTP helper <code>status unsupported media type</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_unsupported_media_type $x
</code></pre>
</article>
<article class="doc-entry" id="doc-http-status-uri-too-long">
<h3><a class="doc-anchor" href="#doc-http-status-uri-too-long">#</a> <code>http_status_uri_too_long</code></h3>
<p><code>http_status_uri_too_long</code> — HTTP helper <code>status uri too long</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p http_status_uri_too_long $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hu-moments">
<h3><a class="doc-anchor" href="#doc-hu-moments">#</a> <code>hu_moments</code></h3>
<p><code>hu_moments(image) → array</code> — all 7 Hu moment invariants (translation, scale, rotation invariant shape features). <code>h7</code> flips sign under reflection.</p>
</article>
<article class="doc-entry" id="doc-hubble-constant">
<h3><a class="doc-anchor" href="#doc-hubble-constant">#</a> <code>hubble_constant</code></h3>
<p><code>hubble_constant</code> — operation <code>hubble constant</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p hubble_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hubble-distance-mpc">
<h3><a class="doc-anchor" href="#doc-hubble-distance-mpc">#</a> <code>hubble_distance_mpc</code></h3>
<p><code>hubble_distance_mpc</code> — operation <code>hubble distance mpc</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p hubble_distance_mpc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hubble-distance-si">
<h3><a class="doc-anchor" href="#doc-hubble-distance-si">#</a> <code>hubble_distance_si</code></h3>
<p><code>hubble_distance_si</code> — operation <code>hubble distance si</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p hubble_distance_si $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hubble-lcdm">
<h3><a class="doc-anchor" href="#doc-hubble-lcdm">#</a> <code>hubble_lcdm</code></h3>
<p><code>hubble_lcdm</code> — operation <code>hubble lcdm</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p hubble_lcdm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hubble-time">
<h3><a class="doc-anchor" href="#doc-hubble-time">#</a> <code>hubble_time</code></h3>
<p><code>hubble_time</code> — operation <code>hubble time</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p hubble_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-huber-m-estimator">
<h3><a class="doc-anchor" href="#doc-huber-m-estimator">#</a> <code>huber_m_estimator</code></h3>
<p><code>huber_m_estimator</code> — operation <code>huber m estimator</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p huber_m_estimator $x
</code></pre>
</article>
<article class="doc-entry" id="doc-huffman-balanced-step">
<h3><a class="doc-anchor" href="#doc-huffman-balanced-step">#</a> <code>huffman_balanced_step</code></h3>
<p><code>huffman_balanced_step</code> — Huffman encoding <code>balanced step</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p huffman_balanced_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-huffman-decode">
<h3><a class="doc-anchor" href="#doc-huffman-decode">#</a> <code>huffman_decode</code></h3>
<p><code>huffman_decode(bits, table) → string</code> — inverse Huffman decode using the same table.</p>
</article>
<article class="doc-entry" id="doc-huffman-encode">
<h3><a class="doc-anchor" href="#doc-huffman-encode">#</a> <code>huffman_encode</code></h3>
<p><code>huffman_encode(s) → {bits, table}</code> — Huffman encode a string. <code>bits</code> is a 0/1 string; <code>table</code> is <code>[[char, code], …]</code>.</p>
<pre><code class="lang-perl">my $r = huffman_encode("hello")
</code></pre>
</article>
<article class="doc-entry" id="doc-hull-white-drift">
<h3><a class="doc-anchor" href="#doc-hull-white-drift">#</a> <code>hull_white_drift</code></h3>
<p><code>hull_white_drift</code> — operation <code>hull white drift</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p hull_white_drift $x
</code></pre>
</article>
<article class="doc-entry" id="doc-human-bytes">
<h3><a class="doc-anchor" href="#doc-human-bytes">#</a> <code>human_bytes</code></h3>
<p><code>human_bytes</code> — operation <code>human bytes</code>. Alias for <code>format_bytes</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p human_bytes $x
</code></pre>
</article>
<article class="doc-entry" id="doc-human-duration">
<h3><a class="doc-anchor" href="#doc-human-duration">#</a> <code>human_duration</code></h3>
<p><code>human_duration</code> — operation <code>human duration</code>. Alias for <code>format_duration</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p human_duration $x
</code></pre>
</article>
<article class="doc-entry" id="doc-humidex">
<h3><a class="doc-anchor" href="#doc-humidex">#</a> <code>humidex</code></h3>
<p><code>humidex</code> — operation <code>humidex</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p humidex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hungarian-method-step">
<h3><a class="doc-anchor" href="#doc-hungarian-method-step">#</a> <code>hungarian_method_step</code></h3>
<p><code>hungarian_method_step</code> — single-step update of <code>hungarian method</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p hungarian_method_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hungarian-step">
<h3><a class="doc-anchor" href="#doc-hungarian-step">#</a> <code>hungarian_step</code></h3>
<p><code>hungarian_step</code> — single-step update of <code>hungarian</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p hungarian_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hurst-exponent">
<h3><a class="doc-anchor" href="#doc-hurst-exponent">#</a> <code>hurst_exponent</code></h3>
<p><code>hurst_exponent(series) → number</code> — multi-scale R/S analysis: subdivides the series into dyadic chunk sizes (8, 16, 32, …, n/2), averages rescaled-range <code>R/S</code> per size, then returns the OLS slope of <code>log(R/S)</code> vs <code>log(n)</code>. <code>H ≈ 0.5</code> random walk; <code>>0.5</code> trending; <code><0.5</code> mean-reverting. Returns UNDEF if <code>n < 16</code> or fewer than 2 dyadic scales fit.</p>
<pre><code class="lang-perl">p hurst_exponent(\@returns)
</code></pre>
</article>
<article class="doc-entry" id="doc-hurst-exponent-estimate">
<h3><a class="doc-anchor" href="#doc-hurst-exponent-estimate">#</a> <code>hurst_exponent_estimate</code></h3>
<p><code>hurst_exponent_estimate</code> — operation <code>hurst exponent estimate</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p hurst_exponent_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hvals">
<h3><a class="doc-anchor" href="#doc-hvals">#</a> <code>hvals</code></h3>
<p><code>hvals</code> — operation <code>hvals</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p hvals $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hw-expected-counts">
<h3><a class="doc-anchor" href="#doc-hw-expected-counts">#</a> <code>hw_expected_counts</code></h3>
<p><code>hw_expected_counts</code> — operation <code>hw expected counts</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p hw_expected_counts $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hxd">
<h3><a class="doc-anchor" href="#doc-hxd">#</a> <code>hxd</code></h3>
<p><code>hxd</code> — operation <code>hxd</code>. Alias for <code>hex_decode</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p hxd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hxe">
<h3><a class="doc-anchor" href="#doc-hxe">#</a> <code>hxe</code></h3>
<p><code>hxe</code> — operation <code>hxe</code>. Alias for <code>hex_encode</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p hxe $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hydrogen-energy-n">
<h3><a class="doc-anchor" href="#doc-hydrogen-energy-n">#</a> <code>hydrogen_energy_n</code></h3>
<p><code>hydrogen_energy_n</code> — operation <code>hydrogen energy n</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p hydrogen_energy_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hyp">
<h3><a class="doc-anchor" href="#doc-hyp">#</a> <code>hyp</code></h3>
<p><code>hyp</code> — operation <code>hyp</code>. Alias for <code>triangle_hypotenuse</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p hyp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hyp1f1">
<h3><a class="doc-anchor" href="#doc-hyp1f1">#</a> <code>hyp1f1</code></h3>
<p><code>hyp1f1</code> — operation <code>hyp1f1</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p hyp1f1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hyp2f1">
<h3><a class="doc-anchor" href="#doc-hyp2f1">#</a> <code>hyp2f1</code></h3>
<p><code>hyp2f1</code> — operation <code>hyp2f1</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p hyp2f1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hyper0f1">
<h3><a class="doc-anchor" href="#doc-hyper0f1">#</a> <code>hyper0f1</code></h3>
<p><code>hyper0f1</code> — operation <code>hyper0f1</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p hyper0f1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hyper1f1">
<h3><a class="doc-anchor" href="#doc-hyper1f1">#</a> <code>hyper1f1</code></h3>
<p><code>hyper1f1</code> — operation <code>hyper1f1</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p hyper1f1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hyper2f1">
<h3><a class="doc-anchor" href="#doc-hyper2f1">#</a> <code>hyper2f1</code></h3>
<p><code>hyper2f1</code> — operation <code>hyper2f1</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p hyper2f1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hyperfactorial">
<h3><a class="doc-anchor" href="#doc-hyperfactorial">#</a> <code>hyperfactorial</code></h3>
<p><code>hyperfactorial(n) → int</code> — <code>Π i^i</code> for i=1..n.</p>
</article>
<article class="doc-entry" id="doc-hyperfocal-distance">
<h3><a class="doc-anchor" href="#doc-hyperfocal-distance">#</a> <code>hyperfocal_distance</code></h3>
<p><code>hyperfocal_distance(focal_mm, aperture, coc_mm=0.03) → number</code> — focus distance where DoF extends to infinity.</p>
</article>
<article class="doc-entry" id="doc-hypergeom-1f1">
<h3><a class="doc-anchor" href="#doc-hypergeom-1f1">#</a> <code>hypergeom_1f1</code></h3>
<p><code>hypergeom_1f1(a, c, z) → number</code> — Kummer's confluent hypergeometric ₁F₁.</p>
<pre><code class="lang-perl">p hypergeom_1f1(1, 2, 0.5)
</code></pre>
</article>
<article class="doc-entry" id="doc-hypergeom-2f1">
<h3><a class="doc-anchor" href="#doc-hypergeom-2f1">#</a> <code>hypergeom_2f1</code></h3>
<p><code>hypergeom_2f1(a, b, c, z) → number</code> — Gauss hypergeometric ₂F₁ via power series. Requires <code>|z| < 1</code>.</p>
<pre><code class="lang-perl">p hypergeom_2f1(1, 1, 2, 0.5)
</code></pre>
</article>
<article class="doc-entry" id="doc-hyperloglog-add">
<h3><a class="doc-anchor" href="#doc-hyperloglog-add">#</a> <code>hyperloglog_add</code></h3>
<p><code>hyperloglog_add</code> — HyperLogLog cardinality sketch <code>add</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p hyperloglog_add $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hyperloglog-estimate">
<h3><a class="doc-anchor" href="#doc-hyperloglog-estimate">#</a> <code>hyperloglog_estimate</code></h3>
<p><code>hyperloglog_estimate</code> — HyperLogLog cardinality sketch <code>estimate</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p hyperloglog_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hyperloglog-merge">
<h3><a class="doc-anchor" href="#doc-hyperloglog-merge">#</a> <code>hyperloglog_merge</code></h3>
<p><code>hyperloglog_merge</code> — HyperLogLog cardinality sketch <code>merge</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p hyperloglog_merge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hyperloglog-new">
<h3><a class="doc-anchor" href="#doc-hyperloglog-new">#</a> <code>hyperloglog_new</code></h3>
<p><code>hyperloglog_new</code> — HyperLogLog cardinality sketch <code>new</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p hyperloglog_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hyperloglog-pp-add">
<h3><a class="doc-anchor" href="#doc-hyperloglog-pp-add">#</a> <code>hyperloglog_pp_add</code></h3>
<p><code>hyperloglog_pp_add(hll, item) → hash</code> — fold an item into the sketch using 64-bit FNV-1a hash.</p>
</article>
<article class="doc-entry" id="doc-hyperloglog-pp-estimate">
<h3><a class="doc-anchor" href="#doc-hyperloglog-pp-estimate">#</a> <code>hyperloglog_pp_estimate</code></h3>
<p><code>hyperloglog_pp_estimate(hll) → number</code> — estimated cardinality with linear-counting small-range correction.</p>
<pre><code class="lang-perl">my $h = hyperloglog_pp_new(10)
$h = hyperloglog_pp_add($h, "item$_") for 1..1000
p hyperloglog_pp_estimate($h)
</code></pre>
</article>
<article class="doc-entry" id="doc-hyperloglog-pp-new">
<h3><a class="doc-anchor" href="#doc-hyperloglog-pp-new">#</a> <code>hyperloglog_pp_new</code></h3>
<p><code>hyperloglog_pp_new(precision=14) → hash</code> — HyperLogLog sketch with <code>2^precision</code> dense registers. (Lacks HLL++ sparse representation and bias-correction tables — counts within ~3% of standard HLL.)</p>
</article>
<article class="doc-entry" id="doc-hyperoperation">
<h3><a class="doc-anchor" href="#doc-hyperoperation">#</a> <code>hyperoperation</code></h3>
<p><code>hyperoperation</code> — operation <code>hyperoperation</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p hyperoperation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hypot">
<h3><a class="doc-anchor" href="#doc-hypot">#</a> <code>hypot</code></h3>
<p><code>hypot</code> — operation <code>hypot</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p hypot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-hz-to-midi">
<h3><a class="doc-anchor" href="#doc-hz-to-midi">#</a> <code>hz_to_midi</code></h3>
<p><code>hz_to_midi</code> — convert from <code>hz</code> to <code>midi</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p hz_to_midi $value
</code></pre>
</article>
<article class="doc-entry" id="doc-i64-max">
<h3><a class="doc-anchor" href="#doc-i64-max">#</a> <code>i64_max</code></h3>
<p><code>i64_max</code> — maximum of <code>i64</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p i64_max $x
</code></pre>
</article>
<article class="doc-entry" id="doc-i64-min">
<h3><a class="doc-anchor" href="#doc-i64-min">#</a> <code>i64_min</code></h3>
<p><code>i64_min</code> — minimum of <code>i64</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p i64_min $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iban-check">
<h3><a class="doc-anchor" href="#doc-iban-check">#</a> <code>iban_check</code></h3>
<p><code>iban_check</code> — operation <code>iban check</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p iban_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iban-country">
<h3><a class="doc-anchor" href="#doc-iban-country">#</a> <code>iban_country</code></h3>
<p><code>iban_country</code> — operation <code>iban country</code>. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p iban_country $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iban-format">
<h3><a class="doc-anchor" href="#doc-iban-format">#</a> <code>iban_format</code></h3>
<p><code>iban_format</code> — operation <code>iban format</code>. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p iban_format $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ibnr-estimate">
<h3><a class="doc-anchor" href="#doc-ibnr-estimate">#</a> <code>ibnr_estimate</code></h3>
<p><code>ibnr_estimate</code> — operation <code>ibnr estimate</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p ibnr_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ical">
<h3><a class="doc-anchor" href="#doc-ical">#</a> <code>ical</code></h3>
<p><code>ical</code> — operation <code>ical</code>. Alias for <code>intercalate</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p ical $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ice-age-milankovitch">
<h3><a class="doc-anchor" href="#doc-ice-age-milankovitch">#</a> <code>ice_age_milankovitch</code></h3>
<p><code>ice_age_milankovitch</code> — operation <code>ice age milankovitch</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ice_age_milankovitch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ico-header-read">
<h3><a class="doc-anchor" href="#doc-ico-header-read">#</a> <code>ico_header_read</code></h3>
<p><code>ico_header_read(hex_bytes) → hash</code> — parse ICO/CUR header → <code>{type, image_count}</code>.</p>
</article>
<article class="doc-entry" id="doc-icosahedral">
<h3><a class="doc-anchor" href="#doc-icosahedral">#</a> <code>icosahedral</code></h3>
<p><code>icosahedral(n) → int</code> — <code>n·(5n²-5n+2) / 2</code>.</p>
</article>
<article class="doc-entry" id="doc-icosahedral-number">
<h3><a class="doc-anchor" href="#doc-icosahedral-number">#</a> <code>icosahedral_number</code></h3>
<p><code>icosahedral_number</code> — operation <code>icosahedral number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p icosahedral_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-id">
<h3><a class="doc-anchor" href="#doc-id">#</a> <code>id</code></h3>
<p><code>id</code> — operation <code>id</code>. Alias for <code>identity</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p id $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ida-star">
<h3><a class="doc-anchor" href="#doc-ida-star">#</a> <code>ida_star</code></h3>
<p><code>ida_star</code> — operation <code>ida star</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p ida_star $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ida-star-search">
<h3><a class="doc-anchor" href="#doc-ida-star-search">#</a> <code>ida_star_search</code></h3>
<p><code>ida_star_search(weighted_adj, start, goal, heuristic) → array</code> — iterative deepening A*. Memory-efficient; revisits nodes.</p>
</article>
<article class="doc-entry" id="doc-idamax">
<h3><a class="doc-anchor" href="#doc-idamax">#</a> <code>idamax</code></h3>
<p><code>idamax</code> — operation <code>idamax</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p idamax $x
</code></pre>
</article>
<article class="doc-entry" id="doc-idct">
<h3><a class="doc-anchor" href="#doc-idct">#</a> <code>idct</code></h3>
<p><code>idct</code> computes the inverse DCT (Type-III). Reconstructs a signal from DCT coefficients.</p>
<pre><code class="lang-perl">my @signal = @{idct(dct([1,2,3,4]))}
</code></pre>
</article>
<article class="doc-entry" id="doc-ideal-gas">
<h3><a class="doc-anchor" href="#doc-ideal-gas">#</a> <code>ideal_gas</code></h3>
<p><code>ideal_gas</code> (alias <code>pv_nrt</code>) solves PV=nRT for the unknown (pass 0 for the value to solve). Args: P, V, n, T.</p>
<pre><code class="lang-perl">p pv_nrt(0, 0.0224, 1, 273.15) # pressure at STP
p pv_nrt(101325, 0, 1, 273.15) # volume at STP
</code></pre>
</article>
<article class="doc-entry" id="doc-ideal-gas-n">
<h3><a class="doc-anchor" href="#doc-ideal-gas-n">#</a> <code>ideal_gas_n</code></h3>
<p><code>ideal_gas_n</code> — operation <code>ideal gas n</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p ideal_gas_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ideal-gas-volume">
<h3><a class="doc-anchor" href="#doc-ideal-gas-volume">#</a> <code>ideal_gas_volume</code></h3>
<p><code>ideal_gas_volume</code> — operation <code>ideal gas volume</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p ideal_gas_volume $x
</code></pre>
</article>
<article class="doc-entry" id="doc-identity">
<h3><a class="doc-anchor" href="#doc-identity">#</a> <code>identity</code></h3>
<p><code>identity</code> — operation <code>identity</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p identity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-identity-matrix">
<h3><a class="doc-anchor" href="#doc-identity-matrix">#</a> <code>identity_matrix</code></h3>
<p><code>identity_matrix</code> — operation <code>identity matrix</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p identity_matrix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-identity-permutation">
<h3><a class="doc-anchor" href="#doc-identity-permutation">#</a> <code>identity_permutation</code></h3>
<p><code>identity_permutation</code> — operation <code>identity permutation</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p identity_permutation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-idft">
<h3><a class="doc-anchor" href="#doc-idft">#</a> <code>idft</code></h3>
<p><code>idft(\@spectrum)</code> — computes the Inverse Discrete Fourier Transform. Takes arrayref of [re, im] pairs and returns the time-domain signal.</p>
<pre><code class="lang-perl">my $spectrum = dft(\@signal)
my $reconstructed = idft($spectrum)
</code></pre>
</article>
<article class="doc-entry" id="doc-idn-normalize">
<h3><a class="doc-anchor" href="#doc-idn-normalize">#</a> <code>idn_normalize</code></h3>
<p><code>idn_normalize</code> — operation <code>idn normalize</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p idn_normalize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-idn-to-ascii">
<h3><a class="doc-anchor" href="#doc-idn-to-ascii">#</a> <code>idn_to_ascii</code></h3>
<p><code>idn_to_ascii</code> — convert from <code>idn</code> to <code>ascii</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p idn_to_ascii $value
</code></pre>
</article>
<article class="doc-entry" id="doc-idn-to-unicode">
<h3><a class="doc-anchor" href="#doc-idn-to-unicode">#</a> <code>idn_to_unicode</code></h3>
<p><code>idn_to_unicode</code> — convert from <code>idn</code> to <code>unicode</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p idn_to_unicode $value
</code></pre>
</article>
<article class="doc-entry" id="doc-idt">
<h3><a class="doc-anchor" href="#doc-idt">#</a> <code>idt</code></h3>
<p><code>idt</code> — operation <code>idt</code>. Alias for <code>indent</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p idt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-idxb">
<h3><a class="doc-anchor" href="#doc-idxb">#</a> <code>idxb</code></h3>
<p><code>idxb</code> — operation <code>idxb</code>. Alias for <code>index_by</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p idxb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-if-else">
<h3><a class="doc-anchor" href="#doc-if-else">#</a> <code>if_else</code></h3>
<p><code>if_else</code> — operation <code>if else</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p if_else $x
</code></pre>
</article>
<article class="doc-entry" id="doc-if-match-check">
<h3><a class="doc-anchor" href="#doc-if-match-check">#</a> <code>if_match_check</code></h3>
<p><code>if_match_check</code> — operation <code>if match check</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p if_match_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-if-none-match-check">
<h3><a class="doc-anchor" href="#doc-if-none-match-check">#</a> <code>if_none_match_check</code></h3>
<p><code>if_none_match_check</code> — operation <code>if none match check</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p if_none_match_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ifr-infection-fatality">
<h3><a class="doc-anchor" href="#doc-ifr-infection-fatality">#</a> <code>ifr_infection_fatality</code></h3>
<p><code>ifr_infection_fatality</code> — operation <code>ifr infection fatality</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p ifr_infection_fatality $x
</code></pre>
</article>
<article class="doc-entry" id="doc-igneous-qapf">
<h3><a class="doc-anchor" href="#doc-igneous-qapf">#</a> <code>igneous_qapf</code></h3>
<p><code>igneous_qapf</code> — operation <code>igneous qapf</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p igneous_qapf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ilerp">
<h3><a class="doc-anchor" href="#doc-ilerp">#</a> <code>ilerp</code></h3>
<p><code>ilerp</code> — operation <code>ilerp</code>. Alias for <code>inv_lerp</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ilerp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-blur-box">
<h3><a class="doc-anchor" href="#doc-image-blur-box">#</a> <code>image_blur_box</code></h3>
<p><code>image_blur_box</code> — operation <code>image blur box</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_blur_box $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-blur-gaussian">
<h3><a class="doc-anchor" href="#doc-image-blur-gaussian">#</a> <code>image_blur_gaussian</code></h3>
<p><code>image_blur_gaussian</code> — operation <code>image blur gaussian</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_blur_gaussian $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-brightness">
<h3><a class="doc-anchor" href="#doc-image-brightness">#</a> <code>image_brightness</code></h3>
<p><code>image_brightness</code> — operation <code>image brightness</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_brightness $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-clahe">
<h3><a class="doc-anchor" href="#doc-image-clahe">#</a> <code>image_clahe</code></h3>
<p><code>image_clahe</code> — operation <code>image clahe</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_clahe $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-contrast">
<h3><a class="doc-anchor" href="#doc-image-contrast">#</a> <code>image_contrast</code></h3>
<p><code>image_contrast</code> — operation <code>image contrast</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_contrast $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-dilate">
<h3><a class="doc-anchor" href="#doc-image-dilate">#</a> <code>image_dilate</code></h3>
<p><code>image_dilate</code> — operation <code>image dilate</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_dilate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-edge-canny">
<h3><a class="doc-anchor" href="#doc-image-edge-canny">#</a> <code>image_edge_canny</code></h3>
<p><code>image_edge_canny</code> — operation <code>image edge canny</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_edge_canny $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-edge-laplacian">
<h3><a class="doc-anchor" href="#doc-image-edge-laplacian">#</a> <code>image_edge_laplacian</code></h3>
<p><code>image_edge_laplacian</code> — operation <code>image edge laplacian</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_edge_laplacian $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-edge-sobel">
<h3><a class="doc-anchor" href="#doc-image-edge-sobel">#</a> <code>image_edge_sobel</code></h3>
<p><code>image_edge_sobel</code> — operation <code>image edge sobel</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_edge_sobel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-emboss">
<h3><a class="doc-anchor" href="#doc-image-emboss">#</a> <code>image_emboss</code></h3>
<p><code>image_emboss</code> — operation <code>image emboss</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_emboss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-equalize">
<h3><a class="doc-anchor" href="#doc-image-equalize">#</a> <code>image_equalize</code></h3>
<p><code>image_equalize</code> — operation <code>image equalize</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_equalize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-erode">
<h3><a class="doc-anchor" href="#doc-image-erode">#</a> <code>image_erode</code></h3>
<p><code>image_erode</code> — operation <code>image erode</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_erode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-flip-h">
<h3><a class="doc-anchor" href="#doc-image-flip-h">#</a> <code>image_flip_h</code></h3>
<p><code>image_flip_h</code> — operation <code>image flip h</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_flip_h $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-flip-v">
<h3><a class="doc-anchor" href="#doc-image-flip-v">#</a> <code>image_flip_v</code></h3>
<p><code>image_flip_v</code> — operation <code>image flip v</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_flip_v $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-gamma">
<h3><a class="doc-anchor" href="#doc-image-gamma">#</a> <code>image_gamma</code></h3>
<p><code>image_gamma</code> — operation <code>image gamma</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_gamma $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-grayscale">
<h3><a class="doc-anchor" href="#doc-image-grayscale">#</a> <code>image_grayscale</code></h3>
<p><code>image_grayscale</code> — operation <code>image grayscale</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_grayscale $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-histogram">
<h3><a class="doc-anchor" href="#doc-image-histogram">#</a> <code>image_histogram</code></h3>
<p><code>image_histogram</code> — operation <code>image histogram</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_histogram $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-invert">
<h3><a class="doc-anchor" href="#doc-image-invert">#</a> <code>image_invert</code></h3>
<p><code>image_invert</code> — operation <code>image invert</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_invert $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-morphology-close">
<h3><a class="doc-anchor" href="#doc-image-morphology-close">#</a> <code>image_morphology_close</code></h3>
<p><code>image_morphology_close</code> — close handle of <code>image morphology</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_morphology_close $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-morphology-open">
<h3><a class="doc-anchor" href="#doc-image-morphology-open">#</a> <code>image_morphology_open</code></h3>
<p><code>image_morphology_open</code> — open handle of <code>image morphology</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_morphology_open $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-motion-blur">
<h3><a class="doc-anchor" href="#doc-image-motion-blur">#</a> <code>image_motion_blur</code></h3>
<p><code>image_motion_blur</code> — operation <code>image motion blur</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_motion_blur $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-posterize">
<h3><a class="doc-anchor" href="#doc-image-posterize">#</a> <code>image_posterize</code></h3>
<p><code>image_posterize</code> — operation <code>image posterize</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_posterize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-resize">
<h3><a class="doc-anchor" href="#doc-image-resize">#</a> <code>image_resize</code></h3>
<p><code>image_resize</code> — operation <code>image resize</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_resize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-rotate">
<h3><a class="doc-anchor" href="#doc-image-rotate">#</a> <code>image_rotate</code></h3>
<p><code>image_rotate</code> — operation <code>image rotate</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_rotate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-sepia">
<h3><a class="doc-anchor" href="#doc-image-sepia">#</a> <code>image_sepia</code></h3>
<p><code>image_sepia</code> — operation <code>image sepia</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_sepia $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-sharpen">
<h3><a class="doc-anchor" href="#doc-image-sharpen">#</a> <code>image_sharpen</code></h3>
<p><code>image_sharpen</code> — operation <code>image sharpen</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_sharpen $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-solarize">
<h3><a class="doc-anchor" href="#doc-image-solarize">#</a> <code>image_solarize</code></h3>
<p><code>image_solarize</code> — operation <code>image solarize</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_solarize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-image-threshold">
<h3><a class="doc-anchor" href="#doc-image-threshold">#</a> <code>image_threshold</code></h3>
<p><code>image_threshold</code> — operation <code>image threshold</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p image_threshold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-imei-check">
<h3><a class="doc-anchor" href="#doc-imei-check">#</a> <code>imei_check</code></h3>
<p><code>imei_check</code> — operation <code>imei check</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p imei_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-imex-euler-step">
<h3><a class="doc-anchor" href="#doc-imex-euler-step">#</a> <code>imex_euler_step</code></h3>
<p><code>imex_euler_step</code> — single-step update of <code>imex euler</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p imex_euler_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-imex-theta-split">
<h3><a class="doc-anchor" href="#doc-imex-theta-split">#</a> <code>imex_theta_split</code></h3>
<p><code>imex_theta_split</code> — operation <code>imex theta split</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p imex_theta_split $x
</code></pre>
</article>
<article class="doc-entry" id="doc-impedance-rlc">
<h3><a class="doc-anchor" href="#doc-impedance-rlc">#</a> <code>impedance_rlc</code></h3>
<p><code>impedance_rlc</code> — operation <code>impedance rlc</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p impedance_rlc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-impl">
<h3><a class="doc-anchor" href="#doc-impl">#</a> <code>impl</code></h3>
<p><code>impl</code> declares which traits a class implements.</p>
<pre><code class="lang-perl">trait Printable { fn to_str }
class Item impl Printable {
name: Str
fn to_str { $self->name }
}
</code></pre>
<p>Multiple traits: <code>class X impl A, B, C { }</code></p>
</article>
<article class="doc-entry" id="doc-implicit-euler">
<h3><a class="doc-anchor" href="#doc-implicit-euler">#</a> <code>implicit_euler</code></h3>
<p><code>implicit_euler</code> — operation <code>implicit euler</code>. Alias for <code>backward_euler</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p implicit_euler $x
</code></pre>
</article>
<article class="doc-entry" id="doc-impulse">
<h3><a class="doc-anchor" href="#doc-impulse">#</a> <code>impulse</code></h3>
<p><code>impulse($force, $time)</code> — compute impulse J = F×t (N⋅s). Change in momentum.</p>
<pre><code class="lang-perl">p impulse(100, 0.5) # 50 N⋅s
</code></pre>
</article>
<article class="doc-entry" id="doc-impulse-response-n">
<h3><a class="doc-anchor" href="#doc-impulse-response-n">#</a> <code>impulse_response_n</code></h3>
<p><code>impulse_response_n</code> — operation <code>impulse response n</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p impulse_response_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-impulse-response-step">
<h3><a class="doc-anchor" href="#doc-impulse-response-step">#</a> <code>impulse_response_step</code></h3>
<p><code>impulse_response_step</code> — single-step update of <code>impulse response</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p impulse_response_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-imputation-efficient-check">
<h3><a class="doc-anchor" href="#doc-imputation-efficient-check">#</a> <code>imputation_efficient_check</code></h3>
<p><code>imputation_efficient_check</code> — operation <code>imputation efficient check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p imputation_efficient_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-imputation-individual-rational">
<h3><a class="doc-anchor" href="#doc-imputation-individual-rational">#</a> <code>imputation_individual_rational</code></h3>
<p><code>imputation_individual_rational</code> — operation <code>imputation individual rational</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p imputation_individual_rational $x
</code></pre>
</article>
<article class="doc-entry" id="doc-imu-madgwick-step">
<h3><a class="doc-anchor" href="#doc-imu-madgwick-step">#</a> <code>imu_madgwick_step</code></h3>
<p><code>imu_madgwick_step</code> — single-step update of <code>imu madgwick</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p imu_madgwick_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-imu-mahony-step">
<h3><a class="doc-anchor" href="#doc-imu-mahony-step">#</a> <code>imu_mahony_step</code></h3>
<p><code>imu_mahony_step</code> — single-step update of <code>imu mahony</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p imu_mahony_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-in-degree-directed">
<h3><a class="doc-anchor" href="#doc-in-degree-directed">#</a> <code>in_degree_directed</code></h3>
<p><code>in_degree_directed</code> — operation <code>in degree directed</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p in_degree_directed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-in-range">
<h3><a class="doc-anchor" href="#doc-in-range">#</a> <code>in_range</code></h3>
<p><code>in_range</code> — operation <code>in range</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p in_range $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inc">
<h3><a class="doc-anchor" href="#doc-inc">#</a> <code>inc</code></h3>
<p><code>inc</code> — operation <code>inc</code>. Category: *pipeline / string helpers*.</p>
<pre><code class="lang-perl">p inc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inc-each">
<h3><a class="doc-anchor" href="#doc-inc-each">#</a> <code>inc_each</code></h3>
<p><code>inc_each</code> — operation <code>inc each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p inc_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-incentive-compatibility-check">
<h3><a class="doc-anchor" href="#doc-incentive-compatibility-check">#</a> <code>incentive_compatibility_check</code></h3>
<p><code>incentive_compatibility_check</code> — operation <code>incentive compatibility check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p incentive_compatibility_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inches-to-cm">
<h3><a class="doc-anchor" href="#doc-inches-to-cm">#</a> <code>inches_to_cm</code></h3>
<p><code>inches_to_cm</code> — convert from <code>inches</code> to <code>cm</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p inches_to_cm $value
</code></pre>
</article>
<article class="doc-entry" id="doc-incidence-algebra-dim">
<h3><a class="doc-anchor" href="#doc-incidence-algebra-dim">#</a> <code>incidence_algebra_dim</code></h3>
<p><code>incidence_algebra_dim</code> — operation <code>incidence algebra dim</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p incidence_algebra_dim $x
</code></pre>
</article>
<article class="doc-entry" id="doc-includes-val">
<h3><a class="doc-anchor" href="#doc-includes-val">#</a> <code>includes_val</code></h3>
<p><code>includes_val</code> — operation <code>includes val</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p includes_val $x
</code></pre>
</article>
<article class="doc-entry" id="doc-income-elasticity">
<h3><a class="doc-anchor" href="#doc-income-elasticity">#</a> <code>income_elasticity</code></h3>
<p><code>income_elasticity</code> — operation <code>income elasticity</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p income_elasticity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-incr">
<h3><a class="doc-anchor" href="#doc-incr">#</a> <code>incr</code></h3>
<p><code>incr</code> — operation <code>incr</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p incr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-incrby">
<h3><a class="doc-anchor" href="#doc-incrby">#</a> <code>incrby</code></h3>
<p><code>incrby</code> — operation <code>incrby</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p incrby $x
</code></pre>
</article>
<article class="doc-entry" id="doc-incv">
<h3><a class="doc-anchor" href="#doc-incv">#</a> <code>incv</code></h3>
<p><code>incv</code> — operation <code>incv</code>. Alias for <code>includes_val</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p incv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-indenergy">
<h3><a class="doc-anchor" href="#doc-indenergy">#</a> <code>indenergy</code></h3>
<p><code>indenergy</code> — operation <code>indenergy</code>. Alias for <code>inductor_energy</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p indenergy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-indent">
<h3><a class="doc-anchor" href="#doc-indent">#</a> <code>indent</code></h3>
<p><code>indent</code> — operation <code>indent</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p indent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-indent-block">
<h3><a class="doc-anchor" href="#doc-indent-block">#</a> <code>indent_block</code></h3>
<p><code>indent_block(s, prefix=" ") → string</code> — prepend <code>prefix</code> to every line.</p>
<pre><code class="lang-perl">p indent_block("line1\nline2", "> ")
</code></pre>
</article>
<article class="doc-entry" id="doc-indent-text">
<h3><a class="doc-anchor" href="#doc-indent-text">#</a> <code>indent_text</code></h3>
<p><code>indent_text</code> — operation <code>indent text</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p indent_text $x
</code></pre>
</article>
<article class="doc-entry" id="doc-independence-number-upper">
<h3><a class="doc-anchor" href="#doc-independence-number-upper">#</a> <code>independence_number_upper</code></h3>
<p><code>independence_number_upper</code> — operation <code>independence number upper</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p independence_number_upper $x
</code></pre>
</article>
<article class="doc-entry" id="doc-index-by">
<h3><a class="doc-anchor" href="#doc-index-by">#</a> <code>index_by</code></h3>
<p><code>index_by</code> — operation <code>index by</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p index_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-index-calculus-naive">
<h3><a class="doc-anchor" href="#doc-index-calculus-naive">#</a> <code>index_calculus_naive</code></h3>
<p><code>index_calculus_naive</code> — operation <code>index calculus naive</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p index_calculus_naive $x
</code></pre>
</article>
<article class="doc-entry" id="doc-index-from-speed">
<h3><a class="doc-anchor" href="#doc-index-from-speed">#</a> <code>index_from_speed</code></h3>
<p><code>index_from_speed</code> — operation <code>index from speed</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p index_from_speed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-index-match">
<h3><a class="doc-anchor" href="#doc-index-match">#</a> <code>index_match</code></h3>
<p><code>index_match</code> — operation <code>index match</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p index_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-index-of">
<h3><a class="doc-anchor" href="#doc-index-of">#</a> <code>index_of</code></h3>
<p><code>index_of</code> — operation <code>index of</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p index_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-index-of-coincidence">
<h3><a class="doc-anchor" href="#doc-index-of-coincidence">#</a> <code>index_of_coincidence</code></h3>
<p><code>index_of_coincidence</code> — operation <code>index of coincidence</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p index_of_coincidence $x
</code></pre>
</article>
<article class="doc-entry" id="doc-index-of-elem">
<h3><a class="doc-anchor" href="#doc-index-of-elem">#</a> <code>index_of_elem</code></h3>
<p><code>index_of_elem</code> — operation <code>index of elem</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p index_of_elem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-indexes-of">
<h3><a class="doc-anchor" href="#doc-indexes-of">#</a> <code>indexes_of</code></h3>
<p><code>indexes_of</code> — operation <code>indexes of</code>. Category: *string*.</p>
<pre><code class="lang-perl">p indexes_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-indian-monsoon-index">
<h3><a class="doc-anchor" href="#doc-indian-monsoon-index">#</a> <code>indian_monsoon_index</code></h3>
<p><code>indian_monsoon_index</code> — index of <code>indian monsoon</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p indian_monsoon_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-indirect">
<h3><a class="doc-anchor" href="#doc-indirect">#</a> <code>indirect</code></h3>
<p><code>indirect</code> — operation <code>indirect</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p indirect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-indirect-age-adjusted">
<h3><a class="doc-anchor" href="#doc-indirect-age-adjusted">#</a> <code>indirect_age_adjusted</code></h3>
<p><code>indirect_age_adjusted</code> — operation <code>indirect age adjusted</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p indirect_age_adjusted $x
</code></pre>
</article>
<article class="doc-entry" id="doc-indirect-utility">
<h3><a class="doc-anchor" href="#doc-indirect-utility">#</a> <code>indirect_utility</code></h3>
<p><code>indirect_utility</code> — operation <code>indirect utility</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p indirect_utility $x
</code></pre>
</article>
<article class="doc-entry" id="doc-indivisible-envy-free-check">
<h3><a class="doc-anchor" href="#doc-indivisible-envy-free-check">#</a> <code>indivisible_envy_free_check</code></h3>
<p><code>indivisible_envy_free_check</code> — operation <code>indivisible envy free check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p indivisible_envy_free_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inductance-parallel">
<h3><a class="doc-anchor" href="#doc-inductance-parallel">#</a> <code>inductance_parallel</code></h3>
<p><code>inductance_parallel</code> — operation <code>inductance parallel</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p inductance_parallel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inductance-series">
<h3><a class="doc-anchor" href="#doc-inductance-series">#</a> <code>inductance_series</code></h3>
<p><code>inductance_series</code> — operation <code>inductance series</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p inductance_series $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inductor-energy">
<h3><a class="doc-anchor" href="#doc-inductor-energy">#</a> <code>inductor_energy</code></h3>
<p><code>inductor_energy</code> — operation <code>inductor energy</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p inductor_energy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inelastic-collision-1d">
<h3><a class="doc-anchor" href="#doc-inelastic-collision-1d">#</a> <code>inelastic_collision_1d</code></h3>
<p><code>inelastic_collision_1d(m1, v1, m2, v2) → number</code> — final common velocity for a perfectly inelastic collision.</p>
</article>
<article class="doc-entry" id="doc-infinite-well-energy">
<h3><a class="doc-anchor" href="#doc-infinite-well-energy">#</a> <code>infinite_well_energy</code></h3>
<p><code>infinite_well_energy</code> — operation <code>infinite well energy</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p infinite_well_energy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-information-bottleneck-step">
<h3><a class="doc-anchor" href="#doc-information-bottleneck-step">#</a> <code>information_bottleneck_step</code></h3>
<p><code>information_bottleneck_step</code> — single-step update of <code>information bottleneck</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p information_bottleneck_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-information-gain">
<h3><a class="doc-anchor" href="#doc-information-gain">#</a> <code>information_gain</code></h3>
<p><code>information_gain</code> — operation <code>information gain</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p information_gain $x
</code></pre>
</article>
<article class="doc-entry" id="doc-information-ratio">
<h3><a class="doc-anchor" href="#doc-information-ratio">#</a> <code>information_ratio</code></h3>
<p><code>information_ratio(portfolio_returns, benchmark_returns) → number</code> — <code>mean(active) / stddev(active)</code> where active = portfolio − benchmark.</p>
<pre><code class="lang-perl">p information_ratio(\@port, \@bench)
</code></pre>
</article>
<article class="doc-entry" id="doc-init-list">
<h3><a class="doc-anchor" href="#doc-init-list">#</a> <code>init_list</code></h3>
<p><code>init_list</code> — operation <code>init list</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p init_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-initial-bearing">
<h3><a class="doc-anchor" href="#doc-initial-bearing">#</a> <code>initial_bearing</code></h3>
<p><code>initial_bearing</code> — operation <code>initial bearing</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p initial_bearing $x
</code></pre>
</article>
<article class="doc-entry" id="doc-initials">
<h3><a class="doc-anchor" href="#doc-initials">#</a> <code>initials</code></h3>
<p><code>initials</code> — operation <code>initials</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p initials $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inits">
<h3><a class="doc-anchor" href="#doc-inits">#</a> <code>inits</code></h3>
<p><code>inits</code> — operation <code>inits</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p inits $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inits-str">
<h3><a class="doc-anchor" href="#doc-inits-str">#</a> <code>inits_str</code></h3>
<p><code>inits_str</code> — operation <code>inits str</code>. Alias for <code>initials</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p inits_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inject">
<h3><a class="doc-anchor" href="#doc-inject">#</a> <code>inject</code></h3>
<p><code>inject</code> — operation <code>inject</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p inject $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inrng">
<h3><a class="doc-anchor" href="#doc-inrng">#</a> <code>inrng</code></h3>
<p><code>inrng</code> — operation <code>inrng</code>. Alias for <code>in_range</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p inrng $x
</code></pre>
</article>
<article class="doc-entry" id="doc-insa">
<h3><a class="doc-anchor" href="#doc-insa">#</a> <code>insa</code></h3>
<p><code>insa</code> — operation <code>insa</code>. Alias for <code>insert_at</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p insa $x
</code></pre>
</article>
<article class="doc-entry" id="doc-insert-at">
<h3><a class="doc-anchor" href="#doc-insert-at">#</a> <code>insert_at</code></h3>
<p><code>insert_at</code> — operation <code>insert at</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p insert_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-insert-at-idx">
<h3><a class="doc-anchor" href="#doc-insert-at-idx">#</a> <code>insert_at_idx</code></h3>
<p><code>insert_at_idx</code> — operation <code>insert at idx</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p insert_at_idx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-insert-sorted">
<h3><a class="doc-anchor" href="#doc-insert-sorted">#</a> <code>insert_sorted</code></h3>
<p><code>insert_sorted</code> — operation <code>insert sorted</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p insert_sorted $x
</code></pre>
</article>
<article class="doc-entry" id="doc-insert-str">
<h3><a class="doc-anchor" href="#doc-insert-str">#</a> <code>insert_str</code></h3>
<p><code>insert_str</code> — operation <code>insert str</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p insert_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-insp">
<h3><a class="doc-anchor" href="#doc-insp">#</a> <code>insp</code></h3>
<p><code>insp</code> — operation <code>insp</code>. Alias for <code>inspect</code>. Category: *rust iterator methods*.</p>
<pre><code class="lang-perl">p insp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inspect">
<h3><a class="doc-anchor" href="#doc-inspect">#</a> <code>inspect</code></h3>
<p><code>inspect</code> — operation <code>inspect</code>. Category: *rust iterator methods*.</p>
<pre><code class="lang-perl">p inspect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inssrt">
<h3><a class="doc-anchor" href="#doc-inssrt">#</a> <code>inssrt</code></h3>
<p><code>inssrt</code> — operation <code>inssrt</code>. Alias for <code>insert_sorted</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p inssrt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-int-bits">
<h3><a class="doc-anchor" href="#doc-int-bits">#</a> <code>int_bits</code></h3>
<p><code>int_bits</code> — integer helper <code>bits</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p int_bits $x
</code></pre>
</article>
<article class="doc-entry" id="doc-int-to-ip">
<h3><a class="doc-anchor" href="#doc-int-to-ip">#</a> <code>int_to_ip</code></h3>
<p><code>int_to_ip</code> — convert from <code>int</code> to <code>ip</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p int_to_ip $value
</code></pre>
</article>
<article class="doc-entry" id="doc-int-to-ipv4">
<h3><a class="doc-anchor" href="#doc-int-to-ipv4">#</a> <code>int_to_ipv4</code></h3>
<p><code>int_to_ipv4</code> — convert from <code>int</code> to <code>ipv4</code>. Category: *network / validation*.</p>
<pre><code class="lang-perl">p int_to_ipv4 $value
</code></pre>
</article>
<article class="doc-entry" id="doc-int-to-mac">
<h3><a class="doc-anchor" href="#doc-int-to-mac">#</a> <code>int_to_mac</code></h3>
<p><code>int_to_mac</code> — convert from <code>int</code> to <code>mac</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p int_to_mac $value
</code></pre>
</article>
<article class="doc-entry" id="doc-int-to-roman">
<h3><a class="doc-anchor" href="#doc-int-to-roman">#</a> <code>int_to_roman</code></h3>
<p><code>int_to_roman</code> — convert from <code>int</code> to <code>roman</code>. Category: *roman numerals*.</p>
<pre><code class="lang-perl">p int_to_roman $value
</code></pre>
</article>
<article class="doc-entry" id="doc-integral-image">
<h3><a class="doc-anchor" href="#doc-integral-image">#</a> <code>integral_image</code></h3>
<p><code>integral_image(image) → matrix</code> — summed-area table for O(1) box-sum queries.</p>
<pre><code class="lang-perl">p integral_image([[1,1,1],[1,1,1],[1,1,1]]) # bottom-right = 9
</code></pre>
</article>
<article class="doc-entry" id="doc-integral-length-scale">
<h3><a class="doc-anchor" href="#doc-integral-length-scale">#</a> <code>integral_length_scale</code></h3>
<p><code>integral_length_scale</code> — operation <code>integral length scale</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p integral_length_scale $x
</code></pre>
</article>
<article class="doc-entry" id="doc-intercalate">
<h3><a class="doc-anchor" href="#doc-intercalate">#</a> <code>intercalate</code></h3>
<p><code>intercalate</code> — operation <code>intercalate</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p intercalate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-interleave-lists">
<h3><a class="doc-anchor" href="#doc-interleave-lists">#</a> <code>interleave_lists</code></h3>
<p><code>interleave_lists</code> — operation <code>interleave lists</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p interleave_lists $x
</code></pre>
</article>
<article class="doc-entry" id="doc-internal-rate-of-return">
<h3><a class="doc-anchor" href="#doc-internal-rate-of-return">#</a> <code>internal_rate_of_return</code></h3>
<p><code>internal_rate_of_return(cashflows) → number</code> — IRR via Newton iteration; the discount rate that makes NPV = 0.</p>
<pre><code class="lang-perl">p internal_rate_of_return([-1000, 300, 400, 500])
</code></pre>
</article>
<article class="doc-entry" id="doc-interp1d">
<h3><a class="doc-anchor" href="#doc-interp1d">#</a> <code>interp1d</code></h3>
<p><code>interp1d</code> — operation <code>interp1d</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p interp1d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-interp-lagrange">
<h3><a class="doc-anchor" href="#doc-interp-lagrange">#</a> <code>interp_lagrange</code></h3>
<p><code>interp_lagrange(xs, ys, x) → number</code> — Lagrange polynomial interpolation through all sample points.</p>
<pre><code class="lang-perl">p interp_lagrange([0,1,2], [1,4,9], 1.5)
</code></pre>
</article>
<article class="doc-entry" id="doc-interp-linear">
<h3><a class="doc-anchor" href="#doc-interp-linear">#</a> <code>interp_linear</code></h3>
<p><code>interp_linear(xs, ys, x) → number</code> — linear interpolation. Binary-searches <code>xs</code> to find the bracketing interval.</p>
<pre><code class="lang-perl">p interp_linear([0,1,2], [0,10,20], 0.5) # 5
</code></pre>
</article>
<article class="doc-entry" id="doc-interpolation-search">
<h3><a class="doc-anchor" href="#doc-interpolation-search">#</a> <code>interpolation_search</code></h3>
<p><code>interpolation_search(sorted, target) → int</code> — estimate position by linear interpolation. <code>O(log log n)</code> on uniform data.</p>
</article>
<article class="doc-entry" id="doc-interpose">
<h3><a class="doc-anchor" href="#doc-interpose">#</a> <code>interpose</code></h3>
<p><code>interpose</code> — operation <code>interpose</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p interpose $x
</code></pre>
</article>
<article class="doc-entry" id="doc-intersect-list">
<h3><a class="doc-anchor" href="#doc-intersect-list">#</a> <code>intersect_list</code></h3>
<p><code>intersect_list</code> — operation <code>intersect list</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p intersect_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-intersperse">
<h3><a class="doc-anchor" href="#doc-intersperse">#</a> <code>intersperse</code></h3>
<p><code>intersperse</code> — operation <code>intersperse</code>. Alias for <code>riffle</code>. Category: *collection helpers (trivial)*.</p>
<pre><code class="lang-perl">p intersperse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-intersperse-char">
<h3><a class="doc-anchor" href="#doc-intersperse-char">#</a> <code>intersperse_char</code></h3>
<p><code>intersperse_char</code> — operation <code>intersperse char</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p intersperse_char $x
</code></pre>
</article>
<article class="doc-entry" id="doc-intersperse-val">
<h3><a class="doc-anchor" href="#doc-intersperse-val">#</a> <code>intersperse_val</code></h3>
<p><code>intersperse_val</code> — operation <code>intersperse val</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p intersperse_val $x
</code></pre>
</article>
<article class="doc-entry" id="doc-intersperse-with">
<h3><a class="doc-anchor" href="#doc-intersperse-with">#</a> <code>intersperse_with</code></h3>
<p><code>intersperse_with</code> — operation <code>intersperse with</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p intersperse_with $x
</code></pre>
</article>
<article class="doc-entry" id="doc-interval-name">
<h3><a class="doc-anchor" href="#doc-interval-name">#</a> <code>interval_name</code></h3>
<p><code>interval_name(semitones) → string</code> — Western music interval label: P1, m2, M2, m3, M3, P4, TT, P5, m6, M6, m7, M7.</p>
<pre><code class="lang-perl">p interval_name(7) # P5
</code></pre>
</article>
<article class="doc-entry" id="doc-interval-quality-size">
<h3><a class="doc-anchor" href="#doc-interval-quality-size">#</a> <code>interval_quality_size</code></h3>
<p><code>interval_quality_size</code> — operation <code>interval quality size</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p interval_quality_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-interval-semitones">
<h3><a class="doc-anchor" href="#doc-interval-semitones">#</a> <code>interval_semitones</code></h3>
<p><code>interval_semitones</code> — operation <code>interval semitones</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p interval_semitones $x
</code></pre>
</article>
<article class="doc-entry" id="doc-intl">
<h3><a class="doc-anchor" href="#doc-intl">#</a> <code>intl</code></h3>
<p><code>intl</code> — operation <code>intl</code>. Alias for <code>intersect_list</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p intl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-into">
<h3><a class="doc-anchor" href="#doc-into">#</a> <code>into</code></h3>
<p><code>into</code> — operation <code>into</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p into $x
</code></pre>
</article>
<article class="doc-entry" id="doc-intrate">
<h3><a class="doc-anchor" href="#doc-intrate">#</a> <code>intrate</code></h3>
<p><code>intrate</code> — operation <code>intrate</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p intrate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-intrinsic-growth-rate">
<h3><a class="doc-anchor" href="#doc-intrinsic-growth-rate">#</a> <code>intrinsic_growth_rate</code></h3>
<p><code>intrinsic_growth_rate</code> — rate of <code>intrinsic growth</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p intrinsic_growth_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-intrinsic-principal-curv">
<h3><a class="doc-anchor" href="#doc-intrinsic-principal-curv">#</a> <code>intrinsic_principal_curv</code></h3>
<p><code>intrinsic_principal_curv</code> — operation <code>intrinsic principal curv</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p intrinsic_principal_curv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inv-lerp">
<h3><a class="doc-anchor" href="#doc-inv-lerp">#</a> <code>inv_lerp</code></h3>
<p><code>inv_lerp</code> — operation <code>inv lerp</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p inv_lerp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inverse">
<h3><a class="doc-anchor" href="#doc-inverse">#</a> <code>inverse</code></h3>
<p><code>inverse</code> — operation <code>inverse</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p inverse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inverse-chi2-pdf">
<h3><a class="doc-anchor" href="#doc-inverse-chi2-pdf">#</a> <code>inverse_chi2_pdf</code></h3>
<p><code>inverse_chi2_pdf</code> — operation <code>inverse chi2 pdf</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p inverse_chi2_pdf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inverse-kinematics-2link">
<h3><a class="doc-anchor" href="#doc-inverse-kinematics-2link">#</a> <code>inverse_kinematics_2link</code></h3>
<p><code>inverse_kinematics_2link</code> — operation <code>inverse kinematics 2link</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p inverse_kinematics_2link $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inverse-lerp">
<h3><a class="doc-anchor" href="#doc-inverse-lerp">#</a> <code>inverse_lerp</code></h3>
<p><code>inverse_lerp</code> — operation <code>inverse lerp</code>. Category: *math formulas*.</p>
<pre><code class="lang-perl">p inverse_lerp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inverse-qft">
<h3><a class="doc-anchor" href="#doc-inverse-qft">#</a> <code>inverse_qft</code></h3>
<p><code>inverse_qft</code> — operation <code>inverse qft</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p inverse_qft $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inverse-quad-interp">
<h3><a class="doc-anchor" href="#doc-inverse-quad-interp">#</a> <code>inverse_quad_interp</code></h3>
<p><code>inverse_quad_interp</code> — operation <code>inverse quad interp</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p inverse_quad_interp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inverse-simpson">
<h3><a class="doc-anchor" href="#doc-inverse-simpson">#</a> <code>inverse_simpson</code></h3>
<p><code>inverse_simpson</code> — operation <code>inverse simpson</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p inverse_simpson $x
</code></pre>
</article>
<article class="doc-entry" id="doc-inverse-weibull-pdf">
<h3><a class="doc-anchor" href="#doc-inverse-weibull-pdf">#</a> <code>inverse_weibull_pdf</code></h3>
<p><code>inverse_weibull_pdf</code> — operation <code>inverse weibull pdf</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p inverse_weibull_pdf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-invert">
<h3><a class="doc-anchor" href="#doc-invert">#</a> <code>invert</code></h3>
<p><code>invert</code> — operation <code>invert</code>. Category: *hash helpers*.</p>
<pre><code class="lang-perl">p invert $x
</code></pre>
</article>
<article class="doc-entry" id="doc-invert-perm">
<h3><a class="doc-anchor" href="#doc-invert-perm">#</a> <code>invert_perm</code></h3>
<p><code>invert_perm</code> — operation <code>invert perm</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p invert_perm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ioctl">
<h3><a class="doc-anchor" href="#doc-ioctl">#</a> <code>ioctl</code></h3>
<p><code>ioctl</code> — operation <code>ioctl</code>. Category: *ipc*.</p>
<pre><code class="lang-perl">p ioctl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ionic-conductivity-arrhenius">
<h3><a class="doc-anchor" href="#doc-ionic-conductivity-arrhenius">#</a> <code>ionic_conductivity_arrhenius</code></h3>
<p><code>ionic_conductivity_arrhenius</code> — operation <code>ionic conductivity arrhenius</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ionic_conductivity_arrhenius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ionic-liquid-viscosity-step">
<h3><a class="doc-anchor" href="#doc-ionic-liquid-viscosity-step">#</a> <code>ionic_liquid_viscosity_step</code></h3>
<p><code>ionic_liquid_viscosity_step</code> — single-step update of <code>ionic liquid viscosity</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ionic_liquid_viscosity_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ionic-strength">
<h3><a class="doc-anchor" href="#doc-ionic-strength">#</a> <code>ionic_strength</code></h3>
<p><code>ionic_strength</code> — operation <code>ionic strength</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p ionic_strength $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iota-n">
<h3><a class="doc-anchor" href="#doc-iota-n">#</a> <code>iota_n</code></h3>
<p><code>iota_n</code> — operation <code>iota n</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p iota_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iou-2d-axis-aligned">
<h3><a class="doc-anchor" href="#doc-iou-2d-axis-aligned">#</a> <code>iou_2d_axis_aligned</code></h3>
<p><code>iou_2d_axis_aligned</code> — operation <code>iou 2d axis aligned</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p iou_2d_axis_aligned $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-arpa">
<h3><a class="doc-anchor" href="#doc-ip-arpa">#</a> <code>ip_arpa</code></h3>
<p><code>ip_arpa</code> — IP address op <code>arpa</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_arpa $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-canonical">
<h3><a class="doc-anchor" href="#doc-ip-canonical">#</a> <code>ip_canonical</code></h3>
<p><code>ip_canonical</code> — IP address op <code>canonical</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_canonical $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-compare">
<h3><a class="doc-anchor" href="#doc-ip-compare">#</a> <code>ip_compare</code></h3>
<p><code>ip_compare</code> — IP address op <code>compare</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_compare $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-family">
<h3><a class="doc-anchor" href="#doc-ip-family">#</a> <code>ip_family</code></h3>
<p><code>ip_family</code> — IP address op <code>family</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_family $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-in-cidr">
<h3><a class="doc-anchor" href="#doc-ip-in-cidr">#</a> <code>ip_in_cidr</code></h3>
<p><code>ip_in_cidr</code> — IP address op <code>in cidr</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_in_cidr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-in-subnet">
<h3><a class="doc-anchor" href="#doc-ip-in-subnet">#</a> <code>ip_in_subnet</code></h3>
<p><code>ip_in_subnet</code> — IP address op <code>in subnet</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_in_subnet $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-is-benchmarking">
<h3><a class="doc-anchor" href="#doc-ip-is-benchmarking">#</a> <code>ip_is_benchmarking</code></h3>
<p><code>ip_is_benchmarking</code> — IP address op <code>is benchmarking</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_is_benchmarking $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-is-broadcast">
<h3><a class="doc-anchor" href="#doc-ip-is-broadcast">#</a> <code>ip_is_broadcast</code></h3>
<p><code>ip_is_broadcast</code> — IP address op <code>is broadcast</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_is_broadcast $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-is-documentation">
<h3><a class="doc-anchor" href="#doc-ip-is-documentation">#</a> <code>ip_is_documentation</code></h3>
<p><code>ip_is_documentation</code> — IP address op <code>is documentation</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_is_documentation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-is-global">
<h3><a class="doc-anchor" href="#doc-ip-is-global">#</a> <code>ip_is_global</code></h3>
<p><code>ip_is_global</code> — IP address op <code>is global</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_is_global $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-is-link-local">
<h3><a class="doc-anchor" href="#doc-ip-is-link-local">#</a> <code>ip_is_link_local</code></h3>
<p><code>ip_is_link_local</code> — IP address op <code>is link local</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_is_link_local $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-is-loopback">
<h3><a class="doc-anchor" href="#doc-ip-is-loopback">#</a> <code>ip_is_loopback</code></h3>
<p><code>ip_is_loopback</code> — IP address op <code>is loopback</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_is_loopback $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-is-multicast">
<h3><a class="doc-anchor" href="#doc-ip-is-multicast">#</a> <code>ip_is_multicast</code></h3>
<p><code>ip_is_multicast</code> — IP address op <code>is multicast</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_is_multicast $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-is-private">
<h3><a class="doc-anchor" href="#doc-ip-is-private">#</a> <code>ip_is_private</code></h3>
<p><code>ip_is_private</code> — IP address op <code>is private</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_is_private $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-is-reserved">
<h3><a class="doc-anchor" href="#doc-ip-is-reserved">#</a> <code>ip_is_reserved</code></h3>
<p><code>ip_is_reserved</code> — IP address op <code>is reserved</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_is_reserved $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-is-shared">
<h3><a class="doc-anchor" href="#doc-ip-is-shared">#</a> <code>ip_is_shared</code></h3>
<p><code>ip_is_shared</code> — IP address op <code>is shared</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_is_shared $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-is-unspecified">
<h3><a class="doc-anchor" href="#doc-ip-is-unspecified">#</a> <code>ip_is_unspecified</code></h3>
<p><code>ip_is_unspecified</code> — IP address op <code>is unspecified</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_is_unspecified $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-is-valid">
<h3><a class="doc-anchor" href="#doc-ip-is-valid">#</a> <code>ip_is_valid</code></h3>
<p><code>ip_is_valid</code> — IP address op <code>is valid</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_is_valid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-parse">
<h3><a class="doc-anchor" href="#doc-ip-parse">#</a> <code>ip_parse</code></h3>
<p><code>ip_parse</code> — IP address op <code>parse</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-random">
<h3><a class="doc-anchor" href="#doc-ip-random">#</a> <code>ip_random</code></h3>
<p><code>ip_random</code> — IP address op <code>random</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_random $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-random-in-cidr">
<h3><a class="doc-anchor" href="#doc-ip-random-in-cidr">#</a> <code>ip_random_in_cidr</code></h3>
<p><code>ip_random_in_cidr</code> — IP address op <code>random in cidr</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_random_in_cidr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-reverse">
<h3><a class="doc-anchor" href="#doc-ip-reverse">#</a> <code>ip_reverse</code></h3>
<p><code>ip_reverse</code> — IP address op <code>reverse</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_reverse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-sort">
<h3><a class="doc-anchor" href="#doc-ip-sort">#</a> <code>ip_sort</code></h3>
<p><code>ip_sort</code> — IP address op <code>sort</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_sort $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-subnet-split">
<h3><a class="doc-anchor" href="#doc-ip-subnet-split">#</a> <code>ip_subnet_split</code></h3>
<p><code>ip_subnet_split(cidr, new_prefix) → array</code> — divide a CIDR into <code>2^(new_prefix - prefix)</code> smaller blocks.</p>
<pre><code class="lang-perl">p ip_subnet_split("10.0.0.0/24", 26) # 4 /26 blocks
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-to-bits">
<h3><a class="doc-anchor" href="#doc-ip-to-bits">#</a> <code>ip_to_bits</code></h3>
<p><code>ip_to_bits</code> — convert from <code>ip</code> to <code>bits</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_to_bits $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-to-bytes">
<h3><a class="doc-anchor" href="#doc-ip-to-bytes">#</a> <code>ip_to_bytes</code></h3>
<p><code>ip_to_bytes</code> — convert from <code>ip</code> to <code>bytes</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_to_bytes $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-to-int">
<h3><a class="doc-anchor" href="#doc-ip-to-int">#</a> <code>ip_to_int</code></h3>
<p><code>ip_to_int</code> — convert from <code>ip</code> to <code>int</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_to_int $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ip-version">
<h3><a class="doc-anchor" href="#doc-ip-version">#</a> <code>ip_version</code></h3>
<p><code>ip_version</code> — IP address op <code>version</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ip_version $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipmt">
<h3><a class="doc-anchor" href="#doc-ipmt">#</a> <code>ipmt</code></h3>
<p><code>ipmt</code> — operation <code>ipmt</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p ipmt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipos">
<h3><a class="doc-anchor" href="#doc-ipos">#</a> <code>ipos</code></h3>
<p><code>ipos</code> — operation <code>ipos</code>. Alias for <code>interpose</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p ipos $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv4-classful-class">
<h3><a class="doc-anchor" href="#doc-ipv4-classful-class">#</a> <code>ipv4_classful_class</code></h3>
<p><code>ipv4_classful_class</code> — operation <code>ipv4 classful class</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv4_classful_class $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv4-is-valid">
<h3><a class="doc-anchor" href="#doc-ipv4-is-valid">#</a> <code>ipv4_is_valid</code></h3>
<p><code>ipv4_is_valid</code> — operation <code>ipv4 is valid</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv4_is_valid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv4-parse">
<h3><a class="doc-anchor" href="#doc-ipv4-parse">#</a> <code>ipv4_parse</code></h3>
<p><code>ipv4_parse</code> — operation <code>ipv4 parse</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv4_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv4-to-int">
<h3><a class="doc-anchor" href="#doc-ipv4-to-int">#</a> <code>ipv4_to_int</code></h3>
<p><code>ipv4_to_int</code> — convert from <code>ipv4</code> to <code>int</code>. Category: *network / validation*.</p>
<pre><code class="lang-perl">p ipv4_to_int $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv4-to-ipv6-6to4">
<h3><a class="doc-anchor" href="#doc-ipv4-to-ipv6-6to4">#</a> <code>ipv4_to_ipv6_6to4</code></h3>
<p><code>ipv4_to_ipv6_6to4</code> — convert from <code>ipv4</code> to <code>ipv6 6to4</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv4_to_ipv6_6to4 $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv4-to-ipv6-mapped">
<h3><a class="doc-anchor" href="#doc-ipv4-to-ipv6-mapped">#</a> <code>ipv4_to_ipv6_mapped</code></h3>
<p><code>ipv4_to_ipv6_mapped</code> — convert from <code>ipv4</code> to <code>ipv6 mapped</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv4_to_ipv6_mapped $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-6to4-extract">
<h3><a class="doc-anchor" href="#doc-ipv6-6to4-extract">#</a> <code>ipv6_6to4_extract</code></h3>
<p><code>ipv6_6to4_extract</code> — IPv6 address op <code>6to4 extract</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_6to4_extract $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-canonical">
<h3><a class="doc-anchor" href="#doc-ipv6-canonical">#</a> <code>ipv6_canonical</code></h3>
<p><code>ipv6_canonical</code> — IPv6 address op <code>canonical</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_canonical $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-compress">
<h3><a class="doc-anchor" href="#doc-ipv6-compress">#</a> <code>ipv6_compress</code></h3>
<p><code>ipv6_compress</code> — IPv6 address op <code>compress</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_compress $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-eui64-addr">
<h3><a class="doc-anchor" href="#doc-ipv6-eui64-addr">#</a> <code>ipv6_eui64_addr</code></h3>
<p><code>ipv6_eui64_addr</code> — IPv6 address op <code>eui64 addr</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_eui64_addr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-expand">
<h3><a class="doc-anchor" href="#doc-ipv6-expand">#</a> <code>ipv6_expand</code></h3>
<p><code>ipv6_expand</code> — IPv6 address op <code>expand</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_expand $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-global-unicast">
<h3><a class="doc-anchor" href="#doc-ipv6-global-unicast">#</a> <code>ipv6_global_unicast</code></h3>
<p><code>ipv6_global_unicast(ipv6) → 0|1</code> — 1 if address is in 2000::/3 (global unicast).</p>
</article>
<article class="doc-entry" id="doc-ipv6-is-6to4">
<h3><a class="doc-anchor" href="#doc-ipv6-is-6to4">#</a> <code>ipv6_is_6to4</code></h3>
<p><code>ipv6_is_6to4</code> — IPv6 address op <code>is 6to4</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_is_6to4 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-is-isatap">
<h3><a class="doc-anchor" href="#doc-ipv6-is-isatap">#</a> <code>ipv6_is_isatap</code></h3>
<p><code>ipv6_is_isatap</code> — IPv6 address op <code>is isatap</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_is_isatap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-is-teredo">
<h3><a class="doc-anchor" href="#doc-ipv6-is-teredo">#</a> <code>ipv6_is_teredo</code></h3>
<p><code>ipv6_is_teredo</code> — IPv6 address op <code>is teredo</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_is_teredo $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-is-valid">
<h3><a class="doc-anchor" href="#doc-ipv6-is-valid">#</a> <code>ipv6_is_valid</code></h3>
<p><code>ipv6_is_valid</code> — IPv6 address op <code>is valid</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_is_valid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-isatap-extract">
<h3><a class="doc-anchor" href="#doc-ipv6-isatap-extract">#</a> <code>ipv6_isatap_extract</code></h3>
<p><code>ipv6_isatap_extract</code> — IPv6 address op <code>isatap extract</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_isatap_extract $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-link-local">
<h3><a class="doc-anchor" href="#doc-ipv6-link-local">#</a> <code>ipv6_link_local</code></h3>
<p><code>ipv6_link_local</code> — IPv6 address op <code>link local</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_link_local $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-link-local-from-mac">
<h3><a class="doc-anchor" href="#doc-ipv6-link-local-from-mac">#</a> <code>ipv6_link_local_from_mac</code></h3>
<p><code>ipv6_link_local_from_mac</code> — IPv6 address op <code>link local from mac</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_link_local_from_mac $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-parse">
<h3><a class="doc-anchor" href="#doc-ipv6-parse">#</a> <code>ipv6_parse</code></h3>
<p><code>ipv6_parse</code> — IPv6 address op <code>parse</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-solicited-node">
<h3><a class="doc-anchor" href="#doc-ipv6-solicited-node">#</a> <code>ipv6_solicited_node</code></h3>
<p><code>ipv6_solicited_node</code> — IPv6 address op <code>solicited node</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_solicited_node $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-strip-zone">
<h3><a class="doc-anchor" href="#doc-ipv6-strip-zone">#</a> <code>ipv6_strip_zone</code></h3>
<p><code>ipv6_strip_zone</code> — IPv6 address op <code>strip zone</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_strip_zone $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-teredo-extract">
<h3><a class="doc-anchor" href="#doc-ipv6-teredo-extract">#</a> <code>ipv6_teredo_extract</code></h3>
<p><code>ipv6_teredo_extract</code> — IPv6 address op <code>teredo extract</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_teredo_extract $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-to-ipv4-compat">
<h3><a class="doc-anchor" href="#doc-ipv6-to-ipv4-compat">#</a> <code>ipv6_to_ipv4_compat</code></h3>
<p><code>ipv6_to_ipv4_compat</code> — convert from <code>ipv6</code> to <code>ipv4 compat</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_to_ipv4_compat $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-unique-local">
<h3><a class="doc-anchor" href="#doc-ipv6-unique-local">#</a> <code>ipv6_unique_local</code></h3>
<p><code>ipv6_unique_local</code> — IPv6 address op <code>unique local</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_unique_local $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv6-zone-id">
<h3><a class="doc-anchor" href="#doc-ipv6-zone-id">#</a> <code>ipv6_zone_id</code></h3>
<p><code>ipv6_zone_id</code> — IPv6 address op <code>zone id</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ipv6_zone_id $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ipv-potential-vorticity">
<h3><a class="doc-anchor" href="#doc-ipv-potential-vorticity">#</a> <code>ipv_potential_vorticity</code></h3>
<p><code>ipv_potential_vorticity</code> — operation <code>ipv potential vorticity</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ipv_potential_vorticity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iqr">
<h3><a class="doc-anchor" href="#doc-iqr">#</a> <code>iqr</code></h3>
<p><code>iqr</code> — operation <code>iqr</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p iqr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-irr">
<h3><a class="doc-anchor" href="#doc-irr">#</a> <code>irr</code></h3>
<p><code>irr(@cashflows)</code> — computes the Internal Rate of Return for a series of cash flows. First value is typically negative (initial investment). Uses Newton-Raphson iteration.</p>
<pre><code class="lang-perl">my @cf = (-1000, 300, 420, 680)
p irr(@cf) # ~0.166 (16.6%)
</code></pre>
</article>
<article class="doc-entry" id="doc-is-7-smooth">
<h3><a class="doc-anchor" href="#doc-is-7-smooth">#</a> <code>is_7_smooth</code></h3>
<p><code>is_7_smooth</code> — predicate: 1 if input is 7 smooth, 0 otherwise. Alias for <code>seven_smooth_q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p is_7_smooth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-abundant">
<h3><a class="doc-anchor" href="#doc-is-abundant">#</a> <code>is_abundant</code></h3>
<p><code>is_abundant</code> — predicate: 1 if input is abundant, 0 otherwise. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p is_abundant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-alnum">
<h3><a class="doc-anchor" href="#doc-is-alnum">#</a> <code>is_alnum</code></h3>
<p><code>is_alnum</code> — predicate: 1 if input is alnum, 0 otherwise. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p is_alnum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-alpha">
<h3><a class="doc-anchor" href="#doc-is-alpha">#</a> <code>is_alpha</code></h3>
<p><code>is_alpha</code> — predicate: 1 if input is alpha, 0 otherwise. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p is_alpha $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-alpha-only">
<h3><a class="doc-anchor" href="#doc-is-alpha-only">#</a> <code>is_alpha_only</code></h3>
<p><code>is_alpha_only</code> — predicate: 1 if input is alpha only, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_alpha_only $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-alphanumeric-only">
<h3><a class="doc-anchor" href="#doc-is-alphanumeric-only">#</a> <code>is_alphanumeric_only</code></h3>
<p><code>is_alphanumeric_only</code> — predicate: 1 if input is alphanumeric only, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_alphanumeric_only $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-anagram">
<h3><a class="doc-anchor" href="#doc-is-anagram">#</a> <code>is_anagram</code></h3>
<p><code>is_anagram</code> — predicate: 1 if input is anagram, 0 otherwise. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p is_anagram $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-anagram-q">
<h3><a class="doc-anchor" href="#doc-is-anagram-q">#</a> <code>is_anagram_q</code></h3>
<p><code>is_anagram_q</code> — predicate: 1 if input is anagram q, 0 otherwise. Alias for <code>anagram_q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p is_anagram_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-armstrong">
<h3><a class="doc-anchor" href="#doc-is-armstrong">#</a> <code>is_armstrong</code></h3>
<p><code>is_armstrong</code> — predicate: 1 if input is armstrong, 0 otherwise. Alias for <code>armstrong_q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p is_armstrong $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-array">
<h3><a class="doc-anchor" href="#doc-is-array">#</a> <code>is_array</code></h3>
<p><code>is_array</code> — predicate: 1 if input is array, 0 otherwise. Category: *trivial type predicates*.</p>
<pre><code class="lang-perl">p is_array $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-arrayref">
<h3><a class="doc-anchor" href="#doc-is-arrayref">#</a> <code>is_arrayref</code></h3>
<p><code>is_arrayref</code> — predicate: 1 if input is arrayref, 0 otherwise. Alias for <code>is_array</code>. Category: *trivial type predicates*.</p>
<pre><code class="lang-perl">p is_arrayref $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-asc">
<h3><a class="doc-anchor" href="#doc-is-asc">#</a> <code>is_asc</code></h3>
<p><code>is_asc</code> — predicate: 1 if input is asc, 0 otherwise. Alias for <code>is_sorted</code>. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_asc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-ascii">
<h3><a class="doc-anchor" href="#doc-is-ascii">#</a> <code>is_ascii</code></h3>
<p><code>is_ascii</code> — predicate: 1 if input is ascii, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_ascii $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-ascii-only">
<h3><a class="doc-anchor" href="#doc-is-ascii-only">#</a> <code>is_ascii_only</code></h3>
<p><code>is_ascii_only</code> — predicate: 1 if input is ascii only, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_ascii_only $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-b-smooth">
<h3><a class="doc-anchor" href="#doc-is-b-smooth">#</a> <code>is_b_smooth</code></h3>
<p><code>is_b_smooth</code> — predicate: 1 if input is b smooth, 0 otherwise. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p is_b_smooth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-balanced-parens">
<h3><a class="doc-anchor" href="#doc-is-balanced-parens">#</a> <code>is_balanced_parens</code></h3>
<p><code>is_balanced_parens</code> — predicate: 1 if input is balanced parens, 0 otherwise. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p is_balanced_parens $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-base32">
<h3><a class="doc-anchor" href="#doc-is-base32">#</a> <code>is_base32</code></h3>
<p><code>is_base32</code> — predicate: 1 if input is base32, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_base32 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-base64">
<h3><a class="doc-anchor" href="#doc-is-base64">#</a> <code>is_base64</code></h3>
<p><code>is_base64</code> — predicate: 1 if input is base64, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_base64 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-between">
<h3><a class="doc-anchor" href="#doc-is-between">#</a> <code>is_between</code></h3>
<p><code>is_between</code> — predicate: 1 if input is between, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_between $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-bic">
<h3><a class="doc-anchor" href="#doc-is-bic">#</a> <code>is_bic</code></h3>
<p><code>is_bic</code> — predicate: 1 if input is bic, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_bic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-binary">
<h3><a class="doc-anchor" href="#doc-is-binary">#</a> <code>is_binary</code></h3>
<p><code>is_binary</code> — predicate: 1 if input is binary, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_binary $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-binary-str">
<h3><a class="doc-anchor" href="#doc-is-binary-str">#</a> <code>is_binary_str</code></h3>
<p><code>is_binary_str</code> — predicate: 1 if input is binary str, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_binary_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-bipartite-graph">
<h3><a class="doc-anchor" href="#doc-is-bipartite-graph">#</a> <code>is_bipartite_graph</code></h3>
<p><code>is_bipartite_graph</code> — predicate: 1 if input is bipartite graph, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_bipartite_graph $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-blank">
<h3><a class="doc-anchor" href="#doc-is-blank">#</a> <code>is_blank</code></h3>
<p><code>is_blank</code> — predicate: 1 if input is blank, 0 otherwise. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p is_blank $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-blank-or-nil">
<h3><a class="doc-anchor" href="#doc-is-blank-or-nil">#</a> <code>is_blank_or_nil</code></h3>
<p><code>is_blank_or_nil</code> — predicate: 1 if input is blank or nil, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_blank_or_nil $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-callable">
<h3><a class="doc-anchor" href="#doc-is-callable">#</a> <code>is_callable</code></h3>
<p><code>is_callable</code> — predicate: 1 if input is callable, 0 otherwise. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p is_callable $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-carmichael">
<h3><a class="doc-anchor" href="#doc-is-carmichael">#</a> <code>is_carmichael</code></h3>
<p><code>is_carmichael</code> — predicate: 1 if input is carmichael, 0 otherwise. Alias for <code>carmichael_q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p is_carmichael $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-cidr">
<h3><a class="doc-anchor" href="#doc-is-cidr">#</a> <code>is_cidr</code></h3>
<p><code>is_cidr</code> — predicate: 1 if input is cidr, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_cidr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-code">
<h3><a class="doc-anchor" href="#doc-is-code">#</a> <code>is_code</code></h3>
<p><code>is_code</code> — predicate: 1 if input is code, 0 otherwise. Category: *trivial type predicates*.</p>
<pre><code class="lang-perl">p is_code $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-coderef">
<h3><a class="doc-anchor" href="#doc-is-coderef">#</a> <code>is_coderef</code></h3>
<p><code>is_coderef</code> — predicate: 1 if input is coderef, 0 otherwise. Alias for <code>is_code</code>. Category: *trivial type predicates*.</p>
<pre><code class="lang-perl">p is_coderef $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-connected">
<h3><a class="doc-anchor" href="#doc-is-connected">#</a> <code>is_connected</code></h3>
<p><code>is_connected</code> — predicate: 1 if input is connected, 0 otherwise. Category: *misc*.</p>
<pre><code class="lang-perl">p is_connected $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-consonant">
<h3><a class="doc-anchor" href="#doc-is-consonant">#</a> <code>is_consonant</code></h3>
<p><code>is_consonant</code> — predicate: 1 if input is consonant, 0 otherwise. Category: *string*.</p>
<pre><code class="lang-perl">p is_consonant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-control">
<h3><a class="doc-anchor" href="#doc-is-control">#</a> <code>is_control</code></h3>
<p><code>is_control</code> — predicate: 1 if input is control, 0 otherwise. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p is_control $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-coprime">
<h3><a class="doc-anchor" href="#doc-is-coprime">#</a> <code>is_coprime</code></h3>
<p><code>is_coprime</code> — predicate: 1 if input is coprime, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_coprime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-credit-card">
<h3><a class="doc-anchor" href="#doc-is-credit-card">#</a> <code>is_credit_card</code></h3>
<p><code>is_credit_card</code> — predicate: 1 if input is credit card, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_credit_card $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-def">
<h3><a class="doc-anchor" href="#doc-is-def">#</a> <code>is_def</code></h3>
<p><code>is_def</code> — predicate: 1 if input is def, 0 otherwise. Alias for <code>is_defined</code>. Category: *trivial type predicates*.</p>
<pre><code class="lang-perl">p is_def $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-deficient">
<h3><a class="doc-anchor" href="#doc-is-deficient">#</a> <code>is_deficient</code></h3>
<p><code>is_deficient</code> — predicate: 1 if input is deficient, 0 otherwise. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p is_deficient $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-defined">
<h3><a class="doc-anchor" href="#doc-is-defined">#</a> <code>is_defined</code></h3>
<p><code>is_defined</code> — predicate: 1 if input is defined, 0 otherwise. Category: *trivial type predicates*.</p>
<pre><code class="lang-perl">p is_defined $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-desc">
<h3><a class="doc-anchor" href="#doc-is-desc">#</a> <code>is_desc</code></h3>
<p><code>is_desc</code> — predicate: 1 if input is desc, 0 otherwise. Alias for <code>is_sorted_desc</code>. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_desc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-digit">
<h3><a class="doc-anchor" href="#doc-is-digit">#</a> <code>is_digit</code></h3>
<p><code>is_digit</code> — predicate: 1 if input is digit, 0 otherwise. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p is_digit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-divisible-by">
<h3><a class="doc-anchor" href="#doc-is-divisible-by">#</a> <code>is_divisible_by</code></h3>
<p><code>is_divisible_by</code> — predicate: 1 if input is divisible by, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_divisible_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-ean13">
<h3><a class="doc-anchor" href="#doc-is-ean13">#</a> <code>is_ean13</code></h3>
<p><code>is_ean13</code> — predicate: 1 if input is ean13, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_ean13 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-email">
<h3><a class="doc-anchor" href="#doc-is-email">#</a> <code>is_email</code></h3>
<p><code>is_email</code> — predicate: 1 if input is email, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_email $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-email-strict">
<h3><a class="doc-anchor" href="#doc-is-email-strict">#</a> <code>is_email_strict</code></h3>
<p><code>is_email_strict</code> — predicate: 1 if input is email strict, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_email_strict $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-empty">
<h3><a class="doc-anchor" href="#doc-is-empty">#</a> <code>is_empty</code></h3>
<p><code>is_empty</code> — predicate: 1 if input is empty, 0 otherwise. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p is_empty $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-empty-arr">
<h3><a class="doc-anchor" href="#doc-is-empty-arr">#</a> <code>is_empty_arr</code></h3>
<p><code>is_empty_arr</code> — predicate: 1 if input is empty arr, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_empty_arr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-empty-hash">
<h3><a class="doc-anchor" href="#doc-is-empty-hash">#</a> <code>is_empty_hash</code></h3>
<p><code>is_empty_hash</code> — predicate: 1 if input is empty hash, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_empty_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-even">
<h3><a class="doc-anchor" href="#doc-is-even">#</a> <code>is_even</code></h3>
<p><code>is_even</code> — predicate: 1 if input is even, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_even $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-even-num">
<h3><a class="doc-anchor" href="#doc-is-even-num">#</a> <code>is_even_num</code></h3>
<p><code>is_even_num</code> — predicate: 1 if input is even num, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_even_num $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-executable">
<h3><a class="doc-anchor" href="#doc-is-executable">#</a> <code>is_executable</code></h3>
<p><code>is_executable</code> — predicate: 1 if input is executable, 0 otherwise. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p is_executable $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-falsy">
<h3><a class="doc-anchor" href="#doc-is-falsy">#</a> <code>is_falsy</code></h3>
<p><code>is_falsy</code> — predicate: 1 if input is falsy, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_falsy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-fibonacci">
<h3><a class="doc-anchor" href="#doc-is-fibonacci">#</a> <code>is_fibonacci</code></h3>
<p><code>is_fibonacci</code> — predicate: 1 if input is fibonacci, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_fibonacci $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-finite">
<h3><a class="doc-anchor" href="#doc-is-finite">#</a> <code>is_finite</code></h3>
<p><code>is_finite</code> — predicate: 1 if input is finite, 0 otherwise. Category: *trig / math*.</p>
<pre><code class="lang-perl">p is_finite $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-float">
<h3><a class="doc-anchor" href="#doc-is-float">#</a> <code>is_float</code></h3>
<p><code>is_float</code> — predicate: 1 if input is float, 0 otherwise. Category: *trivial type predicates*.</p>
<pre><code class="lang-perl">p is_float $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-harshad">
<h3><a class="doc-anchor" href="#doc-is-harshad">#</a> <code>is_harshad</code></h3>
<p><code>is_harshad</code> — predicate: 1 if input is harshad, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_harshad $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-hash">
<h3><a class="doc-anchor" href="#doc-is-hash">#</a> <code>is_hash</code></h3>
<p><code>is_hash</code> — predicate: 1 if input is hash, 0 otherwise. Category: *trivial type predicates*.</p>
<pre><code class="lang-perl">p is_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-hashref">
<h3><a class="doc-anchor" href="#doc-is-hashref">#</a> <code>is_hashref</code></h3>
<p><code>is_hashref</code> — predicate: 1 if input is hashref, 0 otherwise. Alias for <code>is_hash</code>. Category: *trivial type predicates*.</p>
<pre><code class="lang-perl">p is_hashref $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-heterogram">
<h3><a class="doc-anchor" href="#doc-is-heterogram">#</a> <code>is_heterogram</code></h3>
<p><code>is_heterogram</code> — predicate: 1 if input is heterogram, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_heterogram $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-hex">
<h3><a class="doc-anchor" href="#doc-is-hex">#</a> <code>is_hex</code></h3>
<p><code>is_hex</code> — predicate: 1 if input is hex, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_hex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-hex-color">
<h3><a class="doc-anchor" href="#doc-is-hex-color">#</a> <code>is_hex_color</code></h3>
<p><code>is_hex_color</code> — predicate: 1 if input is hex color, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_hex_color $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-hex-str">
<h3><a class="doc-anchor" href="#doc-is-hex-str">#</a> <code>is_hex_str</code></h3>
<p><code>is_hex_str</code> — predicate: 1 if input is hex str, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_hex_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-hostname-valid">
<h3><a class="doc-anchor" href="#doc-is-hostname-valid">#</a> <code>is_hostname_valid</code></h3>
<p><code>is_hostname_valid</code> — predicate: 1 if input is hostname valid, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_hostname_valid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-iban">
<h3><a class="doc-anchor" href="#doc-is-iban">#</a> <code>is_iban</code></h3>
<p><code>is_iban</code> — predicate: 1 if input is iban, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_iban $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-imei">
<h3><a class="doc-anchor" href="#doc-is-imei">#</a> <code>is_imei</code></h3>
<p><code>is_imei</code> — predicate: 1 if input is imei, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_imei $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-imsi">
<h3><a class="doc-anchor" href="#doc-is-imsi">#</a> <code>is_imsi</code></h3>
<p><code>is_imsi</code> — predicate: 1 if input is imsi, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_imsi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-in-range">
<h3><a class="doc-anchor" href="#doc-is-in-range">#</a> <code>is_in_range</code></h3>
<p><code>is_in_range</code> — predicate: 1 if input is in range, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_in_range $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-inf">
<h3><a class="doc-anchor" href="#doc-is-inf">#</a> <code>is_inf</code></h3>
<p><code>is_inf</code> — predicate: 1 if input is inf, 0 otherwise. Alias for <code>is_infinite</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p is_inf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-infinite">
<h3><a class="doc-anchor" href="#doc-is-infinite">#</a> <code>is_infinite</code></h3>
<p><code>is_infinite</code> — predicate: 1 if input is infinite, 0 otherwise. Category: *trig / math*.</p>
<pre><code class="lang-perl">p is_infinite $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-int">
<h3><a class="doc-anchor" href="#doc-is-int">#</a> <code>is_int</code></h3>
<p><code>is_int</code> — predicate: 1 if input is int, 0 otherwise. Category: *trivial type predicates*.</p>
<pre><code class="lang-perl">p is_int $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-integer">
<h3><a class="doc-anchor" href="#doc-is-integer">#</a> <code>is_integer</code></h3>
<p><code>is_integer</code> — predicate: 1 if input is integer, 0 otherwise. Alias for <code>is_int</code>. Category: *trivial type predicates*.</p>
<pre><code class="lang-perl">p is_integer $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-ipv4">
<h3><a class="doc-anchor" href="#doc-is-ipv4">#</a> <code>is_ipv4</code></h3>
<p><code>is_ipv4</code> — predicate: 1 if input is ipv4, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_ipv4 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-ipv4-addr">
<h3><a class="doc-anchor" href="#doc-is-ipv4-addr">#</a> <code>is_ipv4_addr</code></h3>
<p><code>is_ipv4_addr</code> — predicate: 1 if input is ipv4 addr, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_ipv4_addr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-ipv6">
<h3><a class="doc-anchor" href="#doc-is-ipv6">#</a> <code>is_ipv6</code></h3>
<p><code>is_ipv6</code> — predicate: 1 if input is ipv6, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_ipv6 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-ipv6-addr">
<h3><a class="doc-anchor" href="#doc-is-ipv6-addr">#</a> <code>is_ipv6_addr</code></h3>
<p><code>is_ipv6_addr</code> — predicate: 1 if input is ipv6 addr, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_ipv6_addr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-isbn">
<h3><a class="doc-anchor" href="#doc-is-isbn">#</a> <code>is_isbn</code></h3>
<p><code>is_isbn</code> — predicate: 1 if input is isbn, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_isbn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-isbn10">
<h3><a class="doc-anchor" href="#doc-is-isbn10">#</a> <code>is_isbn10</code></h3>
<p><code>is_isbn10</code> — predicate: 1 if input is isbn10, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_isbn10 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-isbn13">
<h3><a class="doc-anchor" href="#doc-is-isbn13">#</a> <code>is_isbn13</code></h3>
<p><code>is_isbn13</code> — predicate: 1 if input is isbn13, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_isbn13 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-iso-date">
<h3><a class="doc-anchor" href="#doc-is-iso-date">#</a> <code>is_iso_date</code></h3>
<p><code>is_iso_date</code> — predicate: 1 if input is iso date, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_iso_date $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-iso-datetime">
<h3><a class="doc-anchor" href="#doc-is-iso-datetime">#</a> <code>is_iso_datetime</code></h3>
<p><code>is_iso_datetime</code> — predicate: 1 if input is iso datetime, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_iso_datetime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-iso-time">
<h3><a class="doc-anchor" href="#doc-is-iso-time">#</a> <code>is_iso_time</code></h3>
<p><code>is_iso_time</code> — predicate: 1 if input is iso time, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_iso_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-isogram">
<h3><a class="doc-anchor" href="#doc-is-isogram">#</a> <code>is_isogram</code></h3>
<p><code>is_isogram</code> — predicate: 1 if input is isogram, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_isogram $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-json">
<h3><a class="doc-anchor" href="#doc-is-json">#</a> <code>is_json</code></h3>
<p><code>is_json</code> — predicate: 1 if input is json, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_json $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-jwt">
<h3><a class="doc-anchor" href="#doc-is-jwt">#</a> <code>is_jwt</code></h3>
<p><code>is_jwt</code> — predicate: 1 if input is jwt, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_jwt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-kaprekar">
<h3><a class="doc-anchor" href="#doc-is-kaprekar">#</a> <code>is_kaprekar</code></h3>
<p><code>is_kaprekar</code> — predicate: 1 if input is kaprekar, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_kaprekar $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-keith">
<h3><a class="doc-anchor" href="#doc-is-keith">#</a> <code>is_keith</code></h3>
<p><code>is_keith</code> — predicate: 1 if input is keith, 0 otherwise. Alias for <code>keith_q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p is_keith $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-leap">
<h3><a class="doc-anchor" href="#doc-is-leap">#</a> <code>is_leap</code></h3>
<p><code>is_leap</code> — predicate: 1 if input is leap, 0 otherwise. Alias for <code>is_leap_year</code>. Category: *date helpers*.</p>
<pre><code class="lang-perl">p is_leap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-leap-year">
<h3><a class="doc-anchor" href="#doc-is-leap-year">#</a> <code>is_leap_year</code></h3>
<p><code>is_leap_year</code> — predicate: 1 if input is leap year, 0 otherwise. Category: *date helpers*.</p>
<pre><code class="lang-perl">p is_leap_year $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-lower">
<h3><a class="doc-anchor" href="#doc-is-lower">#</a> <code>is_lower</code></h3>
<p><code>is_lower</code> — predicate: 1 if input is lower, 0 otherwise. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p is_lower $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-lowercase">
<h3><a class="doc-anchor" href="#doc-is-lowercase">#</a> <code>is_lowercase</code></h3>
<p><code>is_lowercase</code> — predicate: 1 if input is lowercase, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_lowercase $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-mac">
<h3><a class="doc-anchor" href="#doc-is-mac">#</a> <code>is_mac</code></h3>
<p><code>is_mac</code> — predicate: 1 if input is mac, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_mac $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-mac-addr">
<h3><a class="doc-anchor" href="#doc-is-mac-addr">#</a> <code>is_mac_addr</code></h3>
<p><code>is_mac_addr</code> — predicate: 1 if input is mac addr, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_mac_addr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-match">
<h3><a class="doc-anchor" href="#doc-is-match">#</a> <code>is_match</code></h3>
<p><code>is_match</code> — predicate: 1 if input is match, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-md5-hash">
<h3><a class="doc-anchor" href="#doc-is-md5-hash">#</a> <code>is_md5_hash</code></h3>
<p><code>is_md5_hash</code> — predicate: 1 if input is md5 hash, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_md5_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-monotonic">
<h3><a class="doc-anchor" href="#doc-is-monotonic">#</a> <code>is_monotonic</code></h3>
<p><code>is_monotonic</code> — predicate: 1 if input is monotonic, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_monotonic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-multiple-of">
<h3><a class="doc-anchor" href="#doc-is-multiple-of">#</a> <code>is_multiple_of</code></h3>
<p><code>is_multiple_of</code> — predicate: 1 if input is multiple of, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_multiple_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-nan">
<h3><a class="doc-anchor" href="#doc-is-nan">#</a> <code>is_nan</code></h3>
<p><code>is_nan</code> — predicate: 1 if input is nan, 0 otherwise. Category: *trig / math*.</p>
<pre><code class="lang-perl">p is_nan $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-narcissistic">
<h3><a class="doc-anchor" href="#doc-is-narcissistic">#</a> <code>is_narcissistic</code></h3>
<p><code>is_narcissistic</code> — predicate: 1 if input is narcissistic, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_narcissistic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-negative">
<h3><a class="doc-anchor" href="#doc-is-negative">#</a> <code>is_negative</code></h3>
<p><code>is_negative</code> — predicate: 1 if input is negative, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_negative $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-negative-num">
<h3><a class="doc-anchor" href="#doc-is-negative-num">#</a> <code>is_negative_num</code></h3>
<p><code>is_negative_num</code> — predicate: 1 if input is negative num, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_negative_num $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-nil">
<h3><a class="doc-anchor" href="#doc-is-nil">#</a> <code>is_nil</code></h3>
<p><code>is_nil</code> — predicate: 1 if input is nil, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_nil $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-nonzero">
<h3><a class="doc-anchor" href="#doc-is-nonzero">#</a> <code>is_nonzero</code></h3>
<p><code>is_nonzero</code> — predicate: 1 if input is nonzero, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_nonzero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-numeric">
<h3><a class="doc-anchor" href="#doc-is-numeric">#</a> <code>is_numeric</code></h3>
<p><code>is_numeric</code> — predicate: 1 if input is numeric, 0 otherwise. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p is_numeric $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-numeric-only">
<h3><a class="doc-anchor" href="#doc-is-numeric-only">#</a> <code>is_numeric_only</code></h3>
<p><code>is_numeric_only</code> — predicate: 1 if input is numeric only, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_numeric_only $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-numeric-string">
<h3><a class="doc-anchor" href="#doc-is-numeric-string">#</a> <code>is_numeric_string</code></h3>
<p><code>is_numeric_string</code> — predicate: 1 if input is numeric string, 0 otherwise. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p is_numeric_string $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-octal">
<h3><a class="doc-anchor" href="#doc-is-octal">#</a> <code>is_octal</code></h3>
<p><code>is_octal</code> — predicate: 1 if input is octal, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_octal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-octal-str">
<h3><a class="doc-anchor" href="#doc-is-octal-str">#</a> <code>is_octal_str</code></h3>
<p><code>is_octal_str</code> — predicate: 1 if input is octal str, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_octal_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-odd">
<h3><a class="doc-anchor" href="#doc-is-odd">#</a> <code>is_odd</code></h3>
<p><code>is_odd</code> — predicate: 1 if input is odd, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_odd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-odd-num">
<h3><a class="doc-anchor" href="#doc-is-odd-num">#</a> <code>is_odd_num</code></h3>
<p><code>is_odd_num</code> — predicate: 1 if input is odd num, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_odd_num $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-pair">
<h3><a class="doc-anchor" href="#doc-is-pair">#</a> <code>is_pair</code></h3>
<p><code>is_pair</code> — predicate: 1 if input is pair, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_pair $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-palindrome">
<h3><a class="doc-anchor" href="#doc-is-palindrome">#</a> <code>is_palindrome</code></h3>
<p><code>is_palindrome</code> — predicate: 1 if input is palindrome, 0 otherwise. Category: *string*.</p>
<pre><code class="lang-perl">p is_palindrome $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-palindrome-str">
<h3><a class="doc-anchor" href="#doc-is-palindrome-str">#</a> <code>is_palindrome_str</code></h3>
<p><code>is_palindrome_str</code> — predicate: 1 if input is palindrome str, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_palindrome_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-pangram">
<h3><a class="doc-anchor" href="#doc-is-pangram">#</a> <code>is_pangram</code></h3>
<p><code>is_pangram</code> — predicate: 1 if input is pangram, 0 otherwise. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p is_pangram $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-pentagonal">
<h3><a class="doc-anchor" href="#doc-is-pentagonal">#</a> <code>is_pentagonal</code></h3>
<p><code>is_pentagonal</code> — predicate: 1 if input is pentagonal, 0 otherwise. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p is_pentagonal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-perfect">
<h3><a class="doc-anchor" href="#doc-is-perfect">#</a> <code>is_perfect</code></h3>
<p><code>is_perfect</code> — predicate: 1 if input is perfect, 0 otherwise. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p is_perfect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-perfect-square">
<h3><a class="doc-anchor" href="#doc-is-perfect-square">#</a> <code>is_perfect_square</code></h3>
<p><code>is_perfect_square</code> — predicate: 1 if input is perfect square, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_perfect_square $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-permutation">
<h3><a class="doc-anchor" href="#doc-is-permutation">#</a> <code>is_permutation</code></h3>
<p><code>is_permutation</code> — predicate: 1 if input is permutation, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_permutation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-phone">
<h3><a class="doc-anchor" href="#doc-is-phone">#</a> <code>is_phone</code></h3>
<p><code>is_phone</code> — predicate: 1 if input is phone, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_phone $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-phone-e164">
<h3><a class="doc-anchor" href="#doc-is-phone-e164">#</a> <code>is_phone_e164</code></h3>
<p><code>is_phone_e164</code> — predicate: 1 if input is phone e164, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_phone_e164 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-phone-num">
<h3><a class="doc-anchor" href="#doc-is-phone-num">#</a> <code>is_phone_num</code></h3>
<p><code>is_phone_num</code> — predicate: 1 if input is phone num, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_phone_num $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-port-num">
<h3><a class="doc-anchor" href="#doc-is-port-num">#</a> <code>is_port_num</code></h3>
<p><code>is_port_num</code> — predicate: 1 if input is port num, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_port_num $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-positive">
<h3><a class="doc-anchor" href="#doc-is-positive">#</a> <code>is_positive</code></h3>
<p><code>is_positive</code> — predicate: 1 if input is positive, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_positive $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-positive-num">
<h3><a class="doc-anchor" href="#doc-is-positive-num">#</a> <code>is_positive_num</code></h3>
<p><code>is_positive_num</code> — predicate: 1 if input is positive num, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_positive_num $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-postal-code">
<h3><a class="doc-anchor" href="#doc-is-postal-code">#</a> <code>is_postal_code</code></h3>
<p><code>is_postal_code</code> — predicate: 1 if input is postal code, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_postal_code $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-pow2">
<h3><a class="doc-anchor" href="#doc-is-pow2">#</a> <code>is_pow2</code></h3>
<p><code>is_pow2</code> — predicate: 1 if input is pow2, 0 otherwise. Alias for <code>is_power_of_two</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p is_pow2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-power-of">
<h3><a class="doc-anchor" href="#doc-is-power-of">#</a> <code>is_power_of</code></h3>
<p><code>is_power_of</code> — predicate: 1 if input is power of, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_power_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-power-of-two">
<h3><a class="doc-anchor" href="#doc-is-power-of-two">#</a> <code>is_power_of_two</code></h3>
<p><code>is_power_of_two</code> — predicate: 1 if input is power of two, 0 otherwise. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p is_power_of_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-prefix">
<h3><a class="doc-anchor" href="#doc-is-prefix">#</a> <code>is_prefix</code></h3>
<p><code>is_prefix</code> — predicate: 1 if input is prefix, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_prefix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-present">
<h3><a class="doc-anchor" href="#doc-is-present">#</a> <code>is_present</code></h3>
<p><code>is_present</code> — predicate: 1 if input is present, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_present $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-prime">
<h3><a class="doc-anchor" href="#doc-is-prime">#</a> <code>is_prime</code></h3>
<p><code>is_prime</code> — predicate: 1 if input is prime, 0 otherwise. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p is_prime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-printable">
<h3><a class="doc-anchor" href="#doc-is-printable">#</a> <code>is_printable</code></h3>
<p><code>is_printable</code> — predicate: 1 if input is printable, 0 otherwise. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p is_printable $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-printable-ascii">
<h3><a class="doc-anchor" href="#doc-is-printable-ascii">#</a> <code>is_printable_ascii</code></h3>
<p><code>is_printable_ascii</code> — predicate: 1 if input is printable ascii, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_printable_ascii $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-probable-prime">
<h3><a class="doc-anchor" href="#doc-is-probable-prime">#</a> <code>is_probable_prime</code></h3>
<p><code>miller_rabin</code> (aliases <code>millerrabin</code>, <code>is_probable_prime</code>) performs a probabilistic primality test with k rounds (default 20).</p>
<pre><code class="lang-perl">p millerrabin(104729) # 1 (prime)
p millerrabin(104730) # 0 (composite)
</code></pre>
</article>
<article class="doc-entry" id="doc-is-quadratic-residue">
<h3><a class="doc-anchor" href="#doc-is-quadratic-residue">#</a> <code>is_quadratic_residue</code></h3>
<p><code>is_quadratic_residue</code> — predicate: 1 if input is quadratic residue, 0 otherwise. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p is_quadratic_residue $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-readable">
<h3><a class="doc-anchor" href="#doc-is-readable">#</a> <code>is_readable</code></h3>
<p><code>is_readable</code> — predicate: 1 if input is readable, 0 otherwise. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p is_readable $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-ref">
<h3><a class="doc-anchor" href="#doc-is-ref">#</a> <code>is_ref</code></h3>
<p><code>is_ref</code> — predicate: 1 if input is ref, 0 otherwise. Category: *trivial type predicates*.</p>
<pre><code class="lang-perl">p is_ref $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-regex-valid">
<h3><a class="doc-anchor" href="#doc-is-regex-valid">#</a> <code>is_regex_valid</code></h3>
<p><code>is_regex_valid</code> — predicate: 1 if input is regex valid, 0 otherwise. Category: *more regex*.</p>
<pre><code class="lang-perl">p is_regex_valid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-root">
<h3><a class="doc-anchor" href="#doc-is-root">#</a> <code>is_root</code></h3>
<p><code>is_root</code> — predicate: 1 if input is root, 0 otherwise. Category: *more process / system*.</p>
<pre><code class="lang-perl">p is_root $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-semver">
<h3><a class="doc-anchor" href="#doc-is-semver">#</a> <code>is_semver</code></h3>
<p><code>is_semver</code> — predicate: 1 if input is semver, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_semver $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-sha1-hash">
<h3><a class="doc-anchor" href="#doc-is-sha1-hash">#</a> <code>is_sha1_hash</code></h3>
<p><code>is_sha1_hash</code> — predicate: 1 if input is sha1 hash, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_sha1_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-sha256-hash">
<h3><a class="doc-anchor" href="#doc-is-sha256-hash">#</a> <code>is_sha256_hash</code></h3>
<p><code>is_sha256_hash</code> — predicate: 1 if input is sha256 hash, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_sha256_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-slug">
<h3><a class="doc-anchor" href="#doc-is-slug">#</a> <code>is_slug</code></h3>
<p><code>is_slug</code> — predicate: 1 if input is slug, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_slug $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-smith">
<h3><a class="doc-anchor" href="#doc-is-smith">#</a> <code>is_smith</code></h3>
<p><code>is_smith</code> — predicate: 1 if input is smith, 0 otherwise. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p is_smith $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-sorted">
<h3><a class="doc-anchor" href="#doc-is-sorted">#</a> <code>is_sorted</code></h3>
<p><code>is_sorted</code> — predicate: 1 if input is sorted, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_sorted $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-sorted-by">
<h3><a class="doc-anchor" href="#doc-is-sorted-by">#</a> <code>is_sorted_by</code></h3>
<p><code>is_sorted_by</code> — predicate: 1 if input is sorted by, 0 otherwise. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p is_sorted_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-sorted-desc">
<h3><a class="doc-anchor" href="#doc-is-sorted-desc">#</a> <code>is_sorted_desc</code></h3>
<p><code>is_sorted_desc</code> — predicate: 1 if input is sorted desc, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_sorted_desc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-space">
<h3><a class="doc-anchor" href="#doc-is-space">#</a> <code>is_space</code></h3>
<p><code>is_space</code> — predicate: 1 if input is space, 0 otherwise. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p is_space $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-sphenic">
<h3><a class="doc-anchor" href="#doc-is-sphenic">#</a> <code>is_sphenic</code></h3>
<p><code>is_sphenic</code> — predicate: 1 if input is sphenic, 0 otherwise. Alias for <code>sphenic_q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p is_sphenic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-square">
<h3><a class="doc-anchor" href="#doc-is-square">#</a> <code>is_square</code></h3>
<p><code>is_square</code> — predicate: 1 if input is square, 0 otherwise. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p is_square $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-squarefree">
<h3><a class="doc-anchor" href="#doc-is-squarefree">#</a> <code>is_squarefree</code></h3>
<p><code>is_squarefree</code> — predicate: 1 if input is squarefree, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_squarefree $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-ssn-us">
<h3><a class="doc-anchor" href="#doc-is-ssn-us">#</a> <code>is_ssn_us</code></h3>
<p><code>is_ssn_us</code> — predicate: 1 if input is ssn us, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_ssn_us $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-str">
<h3><a class="doc-anchor" href="#doc-is-str">#</a> <code>is_str</code></h3>
<p><code>is_str</code> — predicate: 1 if input is str, 0 otherwise. Alias for <code>is_string</code>. Category: *trivial type predicates*.</p>
<pre><code class="lang-perl">p is_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-strictly-decreasing">
<h3><a class="doc-anchor" href="#doc-is-strictly-decreasing">#</a> <code>is_strictly_decreasing</code></h3>
<p><code>is_strictly_decreasing</code> — predicate: 1 if input is strictly decreasing, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_strictly_decreasing $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-strictly-increasing">
<h3><a class="doc-anchor" href="#doc-is-strictly-increasing">#</a> <code>is_strictly_increasing</code></h3>
<p><code>is_strictly_increasing</code> — predicate: 1 if input is strictly increasing, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_strictly_increasing $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-string">
<h3><a class="doc-anchor" href="#doc-is-string">#</a> <code>is_string</code></h3>
<p><code>is_string</code> — predicate: 1 if input is string, 0 otherwise. Category: *trivial type predicates*.</p>
<pre><code class="lang-perl">p is_string $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-subset">
<h3><a class="doc-anchor" href="#doc-is-subset">#</a> <code>is_subset</code></h3>
<p><code>is_subset</code> — predicate: 1 if input is subset, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_subset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-suffix">
<h3><a class="doc-anchor" href="#doc-is-suffix">#</a> <code>is_suffix</code></h3>
<p><code>is_suffix</code> — predicate: 1 if input is suffix, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_suffix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-superset">
<h3><a class="doc-anchor" href="#doc-is-superset">#</a> <code>is_superset</code></h3>
<p><code>is_superset</code> — predicate: 1 if input is superset, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_superset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-swift">
<h3><a class="doc-anchor" href="#doc-is-swift">#</a> <code>is_swift</code></h3>
<p><code>is_swift</code> — predicate: 1 if input is swift, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_swift $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-symlink">
<h3><a class="doc-anchor" href="#doc-is-symlink">#</a> <code>is_symlink</code></h3>
<p><code>is_symlink</code> — predicate: 1 if input is symlink, 0 otherwise. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p is_symlink $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-titlecase">
<h3><a class="doc-anchor" href="#doc-is-titlecase">#</a> <code>is_titlecase</code></h3>
<p><code>is_titlecase</code> — predicate: 1 if input is titlecase, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_titlecase $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-tree">
<h3><a class="doc-anchor" href="#doc-is-tree">#</a> <code>is_tree</code></h3>
<p><code>is_tree</code> — predicate: 1 if input is tree, 0 otherwise. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p is_tree $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-triangular">
<h3><a class="doc-anchor" href="#doc-is-triangular">#</a> <code>is_triangular</code></h3>
<p><code>is_triangular</code> — predicate: 1 if input is triangular, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_triangular $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-triple">
<h3><a class="doc-anchor" href="#doc-is-triple">#</a> <code>is_triple</code></h3>
<p><code>is_triple</code> — predicate: 1 if input is triple, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_triple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-truthy">
<h3><a class="doc-anchor" href="#doc-is-truthy">#</a> <code>is_truthy</code></h3>
<p><code>is_truthy</code> — predicate: 1 if input is truthy, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_truthy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-tty">
<h3><a class="doc-anchor" href="#doc-is-tty">#</a> <code>is_tty</code></h3>
<p><code>is_tty</code> — predicate: 1 if input is tty, 0 otherwise. Category: *more process / system*.</p>
<pre><code class="lang-perl">p is_tty $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-undef">
<h3><a class="doc-anchor" href="#doc-is-undef">#</a> <code>is_undef</code></h3>
<p><code>is_undef</code> — predicate: 1 if input is undef, 0 otherwise. Category: *trivial type predicates*.</p>
<pre><code class="lang-perl">p is_undef $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-upc">
<h3><a class="doc-anchor" href="#doc-is-upc">#</a> <code>is_upc</code></h3>
<p><code>is_upc</code> — predicate: 1 if input is upc, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_upc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-upper">
<h3><a class="doc-anchor" href="#doc-is-upper">#</a> <code>is_upper</code></h3>
<p><code>is_upper</code> — predicate: 1 if input is upper, 0 otherwise. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p is_upper $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-uppercase">
<h3><a class="doc-anchor" href="#doc-is-uppercase">#</a> <code>is_uppercase</code></h3>
<p><code>is_uppercase</code> — predicate: 1 if input is uppercase, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_uppercase $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-url">
<h3><a class="doc-anchor" href="#doc-is-url">#</a> <code>is_url</code></h3>
<p><code>is_url</code> — predicate: 1 if input is url, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_url $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-url-http">
<h3><a class="doc-anchor" href="#doc-is-url-http">#</a> <code>is_url_http</code></h3>
<p><code>is_url_http</code> — predicate: 1 if input is url http, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_url_http $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-url-https">
<h3><a class="doc-anchor" href="#doc-is-url-https">#</a> <code>is_url_https</code></h3>
<p><code>is_url_https</code> — predicate: 1 if input is url https, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_url_https $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-us-zip">
<h3><a class="doc-anchor" href="#doc-is-us-zip">#</a> <code>is_us_zip</code></h3>
<p><code>is_us_zip</code> — predicate: 1 if input is us zip, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_us_zip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-utf8">
<h3><a class="doc-anchor" href="#doc-is-utf8">#</a> <code>is_utf8</code></h3>
<p><code>is_utf8</code> — predicate: 1 if input is utf8, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_utf8 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-uuid">
<h3><a class="doc-anchor" href="#doc-is-uuid">#</a> <code>is_uuid</code></h3>
<p><code>is_uuid</code> — predicate: 1 if input is uuid, 0 otherwise. Category: *id helpers*.</p>
<pre><code class="lang-perl">p is_uuid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-uuid-v4">
<h3><a class="doc-anchor" href="#doc-is-uuid-v4">#</a> <code>is_uuid_v4</code></h3>
<p><code>is_uuid_v4</code> — predicate: 1 if input is uuid v4, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_uuid_v4 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-uuid-v7">
<h3><a class="doc-anchor" href="#doc-is-uuid-v7">#</a> <code>is_uuid_v7</code></h3>
<p><code>is_uuid_v7</code> — predicate: 1 if input is uuid v7, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_uuid_v7 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-valid-cidr">
<h3><a class="doc-anchor" href="#doc-is-valid-cidr">#</a> <code>is_valid_cidr</code></h3>
<p><code>is_valid_cidr</code> — predicate: 1 if input is valid cidr, 0 otherwise. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p is_valid_cidr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-valid-cron">
<h3><a class="doc-anchor" href="#doc-is-valid-cron">#</a> <code>is_valid_cron</code></h3>
<p><code>is_valid_cron</code> — predicate: 1 if input is valid cron, 0 otherwise. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p is_valid_cron $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-valid-date">
<h3><a class="doc-anchor" href="#doc-is-valid-date">#</a> <code>is_valid_date</code></h3>
<p><code>is_valid_date</code> — predicate: 1 if input is valid date, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_valid_date $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-valid-email">
<h3><a class="doc-anchor" href="#doc-is-valid-email">#</a> <code>is_valid_email</code></h3>
<p><code>is_valid_email</code> — predicate: 1 if input is valid email, 0 otherwise. Category: *network / validation*.</p>
<pre><code class="lang-perl">p is_valid_email $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-valid-hex">
<h3><a class="doc-anchor" href="#doc-is-valid-hex">#</a> <code>is_valid_hex</code></h3>
<p><code>is_valid_hex</code> — predicate: 1 if input is valid hex, 0 otherwise. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p is_valid_hex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-valid-hex-color">
<h3><a class="doc-anchor" href="#doc-is-valid-hex-color">#</a> <code>is_valid_hex_color</code></h3>
<p><code>is_valid_hex_color</code> — predicate: 1 if input is valid hex color, 0 otherwise. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p is_valid_hex_color $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-valid-ipv4">
<h3><a class="doc-anchor" href="#doc-is-valid-ipv4">#</a> <code>is_valid_ipv4</code></h3>
<p><code>is_valid_ipv4</code> — predicate: 1 if input is valid ipv4, 0 otherwise. Category: *network / validation*.</p>
<pre><code class="lang-perl">p is_valid_ipv4 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-valid-ipv6">
<h3><a class="doc-anchor" href="#doc-is-valid-ipv6">#</a> <code>is_valid_ipv6</code></h3>
<p><code>is_valid_ipv6</code> — predicate: 1 if input is valid ipv6, 0 otherwise. Category: *network / validation*.</p>
<pre><code class="lang-perl">p is_valid_ipv6 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-valid-latitude">
<h3><a class="doc-anchor" href="#doc-is-valid-latitude">#</a> <code>is_valid_latitude</code></h3>
<p><code>is_valid_latitude</code> — predicate: 1 if input is valid latitude, 0 otherwise. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p is_valid_latitude $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-valid-longitude">
<h3><a class="doc-anchor" href="#doc-is-valid-longitude">#</a> <code>is_valid_longitude</code></h3>
<p><code>is_valid_longitude</code> — predicate: 1 if input is valid longitude, 0 otherwise. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p is_valid_longitude $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-valid-mime">
<h3><a class="doc-anchor" href="#doc-is-valid-mime">#</a> <code>is_valid_mime</code></h3>
<p><code>is_valid_mime</code> — predicate: 1 if input is valid mime, 0 otherwise. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p is_valid_mime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-valid-url">
<h3><a class="doc-anchor" href="#doc-is-valid-url">#</a> <code>is_valid_url</code></h3>
<p><code>is_valid_url</code> — predicate: 1 if input is valid url, 0 otherwise. Category: *network / validation*.</p>
<pre><code class="lang-perl">p is_valid_url $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-vin">
<h3><a class="doc-anchor" href="#doc-is-vin">#</a> <code>is_vin</code></h3>
<p><code>is_vin</code> — predicate: 1 if input is vin, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_vin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-vowel">
<h3><a class="doc-anchor" href="#doc-is-vowel">#</a> <code>is_vowel</code></h3>
<p><code>is_vowel</code> — predicate: 1 if input is vowel, 0 otherwise. Category: *string*.</p>
<pre><code class="lang-perl">p is_vowel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-weekday">
<h3><a class="doc-anchor" href="#doc-is-weekday">#</a> <code>is_weekday</code></h3>
<p><code>is_weekday</code> — predicate: 1 if input is weekday, 0 otherwise. Category: *date*.</p>
<pre><code class="lang-perl">p is_weekday $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-weekend">
<h3><a class="doc-anchor" href="#doc-is-weekend">#</a> <code>is_weekend</code></h3>
<p><code>is_weekend</code> — predicate: 1 if input is weekend, 0 otherwise. Category: *date*.</p>
<pre><code class="lang-perl">p is_weekend $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-whitespace">
<h3><a class="doc-anchor" href="#doc-is-whitespace">#</a> <code>is_whitespace</code></h3>
<p><code>is_whitespace</code> — predicate: 1 if input is whitespace, 0 otherwise. Alias for <code>is_space</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p is_whitespace $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-whole">
<h3><a class="doc-anchor" href="#doc-is-whole">#</a> <code>is_whole</code></h3>
<p><code>is_whole</code> — predicate: 1 if input is whole, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_whole $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-whole-num">
<h3><a class="doc-anchor" href="#doc-is-whole-num">#</a> <code>is_whole_num</code></h3>
<p><code>is_whole_num</code> — predicate: 1 if input is whole num, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_whole_num $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-writable">
<h3><a class="doc-anchor" href="#doc-is-writable">#</a> <code>is_writable</code></h3>
<p><code>is_writable</code> — predicate: 1 if input is writable, 0 otherwise. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p is_writable $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-zero">
<h3><a class="doc-anchor" href="#doc-is-zero">#</a> <code>is_zero</code></h3>
<p><code>is_zero</code> — predicate: 1 if input is zero, 0 otherwise. Category: *predicates*.</p>
<pre><code class="lang-perl">p is_zero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-zero-num">
<h3><a class="doc-anchor" href="#doc-is-zero-num">#</a> <code>is_zero_num</code></h3>
<p><code>is_zero_num</code> — predicate: 1 if input is zero num, 0 otherwise. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p is_zero_num $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-zip-plus4">
<h3><a class="doc-anchor" href="#doc-is-zip-plus4">#</a> <code>is_zip_plus4</code></h3>
<p><code>is_zip_plus4</code> — predicate: 1 if input is zip plus4, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_zip_plus4 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-is-zip-us">
<h3><a class="doc-anchor" href="#doc-is-zip-us">#</a> <code>is_zip_us</code></h3>
<p><code>is_zip_us</code> — predicate: 1 if input is zip us, 0 otherwise. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p is_zip_us $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isabun">
<h3><a class="doc-anchor" href="#doc-isabun">#</a> <code>isabun</code></h3>
<p><code>isabun</code> — operation <code>isabun</code>. Alias for <code>is_abundant</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p isabun $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isanag">
<h3><a class="doc-anchor" href="#doc-isanag">#</a> <code>isanag</code></h3>
<p><code>isanag</code> — operation <code>isanag</code>. Alias for <code>is_anagram</code>. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p isanag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isasc">
<h3><a class="doc-anchor" href="#doc-isasc">#</a> <code>isasc</code></h3>
<p><code>isasc</code> — operation <code>isasc</code>. Alias for <code>is_ascii</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isasc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isb64">
<h3><a class="doc-anchor" href="#doc-isb64">#</a> <code>isb64</code></h3>
<p><code>isb64</code> — operation <code>isb64</code>. Alias for <code>is_base64</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isb64 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isbalp">
<h3><a class="doc-anchor" href="#doc-isbalp">#</a> <code>isbalp</code></h3>
<p><code>isbalp</code> — operation <code>isbalp</code>. Alias for <code>is_balanced_parens</code>. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p isbalp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isbin">
<h3><a class="doc-anchor" href="#doc-isbin">#</a> <code>isbin</code></h3>
<p><code>isbin</code> — operation <code>isbin</code>. Alias for <code>is_binary_str</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isbin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isbip">
<h3><a class="doc-anchor" href="#doc-isbip">#</a> <code>isbip</code></h3>
<p><code>isbip</code> — operation <code>isbip</code>. Alias for <code>is_bipartite_graph</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isbip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isbn10">
<h3><a class="doc-anchor" href="#doc-isbn10">#</a> <code>isbn10</code></h3>
<p><code>isbn10</code> — operation <code>isbn10</code>. Alias for <code>is_isbn10</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isbn10 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isbn10-check">
<h3><a class="doc-anchor" href="#doc-isbn10-check">#</a> <code>isbn10_check</code></h3>
<p><code>isbn10_check</code> — operation <code>isbn10 check</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p isbn10_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isbn10-to-isbn13">
<h3><a class="doc-anchor" href="#doc-isbn10-to-isbn13">#</a> <code>isbn10_to_isbn13</code></h3>
<p><code>isbn10_to_isbn13</code> — convert from <code>isbn10</code> to <code>isbn13</code>. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p isbn10_to_isbn13 $value
</code></pre>
</article>
<article class="doc-entry" id="doc-isbn13">
<h3><a class="doc-anchor" href="#doc-isbn13">#</a> <code>isbn13</code></h3>
<p><code>isbn13</code> — operation <code>isbn13</code>. Alias for <code>is_isbn13</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isbn13 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isbn13-check">
<h3><a class="doc-anchor" href="#doc-isbn13-check">#</a> <code>isbn13_check</code></h3>
<p><code>isbn13_check</code> — operation <code>isbn13 check</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p isbn13_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isbn13-to-isbn10">
<h3><a class="doc-anchor" href="#doc-isbn13-to-isbn10">#</a> <code>isbn13_to_isbn10</code></h3>
<p><code>isbn13_to_isbn10</code> — convert from <code>isbn13</code> to <code>isbn10</code>. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p isbn13_to_isbn10 $value
</code></pre>
</article>
<article class="doc-entry" id="doc-iscc">
<h3><a class="doc-anchor" href="#doc-iscc">#</a> <code>iscc</code></h3>
<p><code>iscc</code> — operation <code>iscc</code>. Alias for <code>is_credit_card</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p iscc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iscidr">
<h3><a class="doc-anchor" href="#doc-iscidr">#</a> <code>iscidr</code></h3>
<p><code>iscidr</code> — operation <code>iscidr</code>. Alias for <code>is_valid_cidr</code>. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p iscidr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isco-radius-kerr-step">
<h3><a class="doc-anchor" href="#doc-isco-radius-kerr-step">#</a> <code>isco_radius_kerr_step</code></h3>
<p><code>isco_radius_kerr_step</code> — single-step update of <code>isco radius kerr</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p isco_radius_kerr_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iscopr">
<h3><a class="doc-anchor" href="#doc-iscopr">#</a> <code>iscopr</code></h3>
<p><code>iscopr</code> — operation <code>iscopr</code>. Alias for <code>is_coprime</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p iscopr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iscron">
<h3><a class="doc-anchor" href="#doc-iscron">#</a> <code>iscron</code></h3>
<p><code>iscron</code> — operation <code>iscron</code>. Alias for <code>is_valid_cron</code>. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p iscron $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isctrl">
<h3><a class="doc-anchor" href="#doc-isctrl">#</a> <code>isctrl</code></h3>
<p><code>isctrl</code> — operation <code>isctrl</code>. Alias for <code>is_control</code>. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p isctrl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isdefi">
<h3><a class="doc-anchor" href="#doc-isdefi">#</a> <code>isdefi</code></h3>
<p><code>isdefi</code> — operation <code>isdefi</code>. Alias for <code>is_deficient</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p isdefi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iseven">
<h3><a class="doc-anchor" href="#doc-iseven">#</a> <code>iseven</code></h3>
<p><code>iseven</code> — operation <code>iseven</code>. Alias for <code>is_even_num</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p iseven $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isharsh">
<h3><a class="doc-anchor" href="#doc-isharsh">#</a> <code>isharsh</code></h3>
<p><code>isharsh</code> — operation <code>isharsh</code>. Alias for <code>is_harshad</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isharsh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ishet">
<h3><a class="doc-anchor" href="#doc-ishet">#</a> <code>ishet</code></h3>
<p><code>ishet</code> — operation <code>ishet</code>. Alias for <code>is_heterogram</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ishet $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ishex">
<h3><a class="doc-anchor" href="#doc-ishex">#</a> <code>ishex</code></h3>
<p><code>ishex</code> — operation <code>ishex</code>. Alias for <code>is_hex_str</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ishex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ishexc">
<h3><a class="doc-anchor" href="#doc-ishexc">#</a> <code>ishexc</code></h3>
<p><code>ishexc</code> — operation <code>ishexc</code>. Alias for <code>is_valid_hex_color</code>. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p ishexc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ishost">
<h3><a class="doc-anchor" href="#doc-ishost">#</a> <code>ishost</code></h3>
<p><code>ishost</code> — operation <code>ishost</code>. Alias for <code>is_hostname_valid</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ishost $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isiban">
<h3><a class="doc-anchor" href="#doc-isiban">#</a> <code>isiban</code></h3>
<p><code>isiban</code> — operation <code>isiban</code>. Alias for <code>is_iban</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isiban $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isip4">
<h3><a class="doc-anchor" href="#doc-isip4">#</a> <code>isip4</code></h3>
<p><code>isip4</code> — operation <code>isip4</code>. Alias for <code>is_ipv4_addr</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isip4 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isip6">
<h3><a class="doc-anchor" href="#doc-isip6">#</a> <code>isip6</code></h3>
<p><code>isip6</code> — operation <code>isip6</code>. Alias for <code>is_ipv6_addr</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isip6 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isiso">
<h3><a class="doc-anchor" href="#doc-isiso">#</a> <code>isiso</code></h3>
<p><code>isiso</code> — operation <code>isiso</code>. Alias for <code>is_isogram</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isiso $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isisodt">
<h3><a class="doc-anchor" href="#doc-isisodt">#</a> <code>isisodt</code></h3>
<p><code>isisodt</code> — operation <code>isisodt</code>. Alias for <code>is_iso_date</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isisodt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isisodtm">
<h3><a class="doc-anchor" href="#doc-isisodtm">#</a> <code>isisodtm</code></h3>
<p><code>isisodtm</code> — operation <code>isisodtm</code>. Alias for <code>is_iso_datetime</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isisodtm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isisotm">
<h3><a class="doc-anchor" href="#doc-isisotm">#</a> <code>isisotm</code></h3>
<p><code>isisotm</code> — operation <code>isisotm</code>. Alias for <code>is_iso_time</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isisotm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isjson">
<h3><a class="doc-anchor" href="#doc-isjson">#</a> <code>isjson</code></h3>
<p><code>isjson</code> — operation <code>isjson</code>. Alias for <code>is_json</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isjson $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iskap">
<h3><a class="doc-anchor" href="#doc-iskap">#</a> <code>iskap</code></h3>
<p><code>iskap</code> — operation <code>iskap</code>. Alias for <code>is_kaprekar</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p iskap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isl">
<h3><a class="doc-anchor" href="#doc-isl">#</a> <code>isl</code></h3>
<p><code>isl</code> — operation <code>isl</code>. Alias for <code>islice</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p isl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-islamic-leap-year">
<h3><a class="doc-anchor" href="#doc-islamic-leap-year">#</a> <code>islamic_leap_year</code></h3>
<p><code>islamic_leap_year</code> — operation <code>islamic leap year</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p islamic_leap_year $x
</code></pre>
</article>
<article class="doc-entry" id="doc-island-equilibrium">
<h3><a class="doc-anchor" href="#doc-island-equilibrium">#</a> <code>island_equilibrium</code></h3>
<p><code>island_equilibrium</code> — operation <code>island equilibrium</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p island_equilibrium $x
</code></pre>
</article>
<article class="doc-entry" id="doc-islat">
<h3><a class="doc-anchor" href="#doc-islat">#</a> <code>islat</code></h3>
<p><code>islat</code> — operation <code>islat</code>. Alias for <code>is_valid_latitude</code>. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p islat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-islice">
<h3><a class="doc-anchor" href="#doc-islice">#</a> <code>islice</code></h3>
<p><code>islice</code> — operation <code>islice</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p islice $x
</code></pre>
</article>
<article class="doc-entry" id="doc-islon">
<h3><a class="doc-anchor" href="#doc-islon">#</a> <code>islon</code></h3>
<p><code>islon</code> — operation <code>islon</code>. Alias for <code>is_valid_longitude</code>. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p islon $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ism">
<h3><a class="doc-anchor" href="#doc-ism">#</a> <code>ism</code></h3>
<p><code>ism</code> — operation <code>ism</code>. Alias for <code>is_match</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ism $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ismac">
<h3><a class="doc-anchor" href="#doc-ismac">#</a> <code>ismac</code></h3>
<p><code>ismac</code> — operation <code>ismac</code>. Alias for <code>is_mac_addr</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ismac $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ismime">
<h3><a class="doc-anchor" href="#doc-ismime">#</a> <code>ismime</code></h3>
<p><code>ismime</code> — operation <code>ismime</code>. Alias for <code>is_valid_mime</code>. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p ismime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ismono">
<h3><a class="doc-anchor" href="#doc-ismono">#</a> <code>ismono</code></h3>
<p><code>ismono</code> — operation <code>ismono</code>. Alias for <code>is_monotonic</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ismono $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isnarc">
<h3><a class="doc-anchor" href="#doc-isnarc">#</a> <code>isnarc</code></h3>
<p><code>isnarc</code> — operation <code>isnarc</code>. Alias for <code>is_narcissistic</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isnarc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isneg">
<h3><a class="doc-anchor" href="#doc-isneg">#</a> <code>isneg</code></h3>
<p><code>isneg</code> — operation <code>isneg</code>. Alias for <code>is_negative_num</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isneg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isnumstr">
<h3><a class="doc-anchor" href="#doc-isnumstr">#</a> <code>isnumstr</code></h3>
<p><code>isnumstr</code> — operation <code>isnumstr</code>. Alias for <code>is_numeric_string</code>. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p isnumstr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iso226-phon-adjustment">
<h3><a class="doc-anchor" href="#doc-iso226-phon-adjustment">#</a> <code>iso226_phon_adjustment</code></h3>
<p><code>iso226_phon_adjustment</code> — operation <code>iso226 phon adjustment</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p iso226_phon_adjustment $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iso8601-duration-parse">
<h3><a class="doc-anchor" href="#doc-iso8601-duration-parse">#</a> <code>iso8601_duration_parse</code></h3>
<p><code>iso8601_duration_parse</code> — operation <code>iso8601 duration parse</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p iso8601_duration_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iso8601-duration-to-seconds">
<h3><a class="doc-anchor" href="#doc-iso8601-duration-to-seconds">#</a> <code>iso8601_duration_to_seconds</code></h3>
<p><code>iso8601_duration_to_seconds</code> — convert from <code>iso8601 duration</code> to <code>seconds</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p iso8601_duration_to_seconds $value
</code></pre>
</article>
<article class="doc-entry" id="doc-iso-day-number">
<h3><a class="doc-anchor" href="#doc-iso-day-number">#</a> <code>iso_day_number</code></h3>
<p><code>iso_day_number</code> — operation <code>iso day number</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p iso_day_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iso-dow">
<h3><a class="doc-anchor" href="#doc-iso-dow">#</a> <code>iso_dow</code></h3>
<p><code>iso_dow</code> — operation <code>iso dow</code>. Alias for <code>day_of_week_iso</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p iso_dow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iso-ordinal-date">
<h3><a class="doc-anchor" href="#doc-iso-ordinal-date">#</a> <code>iso_ordinal_date</code></h3>
<p><code>iso_ordinal_date</code> — operation <code>iso ordinal date</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p iso_ordinal_date $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iso-week">
<h3><a class="doc-anchor" href="#doc-iso-week">#</a> <code>iso_week</code></h3>
<p><code>iso_week</code> — operation <code>iso week</code>. Alias for <code>iso_week_number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p iso_week $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iso-week-date">
<h3><a class="doc-anchor" href="#doc-iso-week-date">#</a> <code>iso_week_date</code></h3>
<p><code>iso_week_date</code> — operation <code>iso week date</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p iso_week_date $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iso-week-number">
<h3><a class="doc-anchor" href="#doc-iso-week-number">#</a> <code>iso_week_number</code></h3>
<p><code>iso_week_number</code> — operation <code>iso week number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p iso_week_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isoct">
<h3><a class="doc-anchor" href="#doc-isoct">#</a> <code>isoct</code></h3>
<p><code>isoct</code> — operation <code>isoct</code>. Alias for <code>is_octal_str</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isoct $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isodd">
<h3><a class="doc-anchor" href="#doc-isodd">#</a> <code>isodd</code></h3>
<p><code>isodd</code> — operation <code>isodd</code>. Alias for <code>is_odd_num</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isodd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isoelectric-point-protein">
<h3><a class="doc-anchor" href="#doc-isoelectric-point-protein">#</a> <code>isoelectric_point_protein</code></h3>
<p><code>isoelectric_point_protein</code> — operation <code>isoelectric point protein</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p isoelectric_point_protein $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isolated-horizon-charge">
<h3><a class="doc-anchor" href="#doc-isolated-horizon-charge">#</a> <code>isolated_horizon_charge</code></h3>
<p><code>isolated_horizon_charge</code> — operation <code>isolated horizon charge</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p isolated_horizon_charge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isotropic-relation-check">
<h3><a class="doc-anchor" href="#doc-isotropic-relation-check">#</a> <code>isotropic_relation_check</code></h3>
<p><code>isotropic_relation_check</code> — operation <code>isotropic relation check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p isotropic_relation_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isp">
<h3><a class="doc-anchor" href="#doc-isp">#</a> <code>isp</code></h3>
<p><code>isp</code> — operation <code>isp</code>. Alias for <code>intersperse_val</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p isp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ispang">
<h3><a class="doc-anchor" href="#doc-ispang">#</a> <code>ispang</code></h3>
<p><code>ispang</code> — operation <code>ispang</code>. Alias for <code>is_pangram</code>. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p ispang $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ispent">
<h3><a class="doc-anchor" href="#doc-ispent">#</a> <code>ispent</code></h3>
<p><code>ispent</code> — operation <code>ispent</code>. Alias for <code>is_pentagonal</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p ispent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isperf">
<h3><a class="doc-anchor" href="#doc-isperf">#</a> <code>isperf</code></h3>
<p><code>isperf</code> — operation <code>isperf</code>. Alias for <code>is_perfect</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p isperf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isphone">
<h3><a class="doc-anchor" href="#doc-isphone">#</a> <code>isphone</code></h3>
<p><code>isphone</code> — operation <code>isphone</code>. Alias for <code>is_phone_num</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isphone $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isport">
<h3><a class="doc-anchor" href="#doc-isport">#</a> <code>isport</code></h3>
<p><code>isport</code> — operation <code>isport</code>. Alias for <code>is_port_num</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isport $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ispos">
<h3><a class="doc-anchor" href="#doc-ispos">#</a> <code>ispos</code></h3>
<p><code>ispos</code> — operation <code>ispos</code>. Alias for <code>is_positive_num</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ispos $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isprint">
<h3><a class="doc-anchor" href="#doc-isprint">#</a> <code>isprint</code></h3>
<p><code>isprint</code> — operation <code>isprint</code>. Alias for <code>is_printable</code>. Category: *validation predicates extras*.</p>
<pre><code class="lang-perl">p isprint $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ispw">
<h3><a class="doc-anchor" href="#doc-ispw">#</a> <code>ispw</code></h3>
<p><code>ispw</code> — operation <code>ispw</code>. Alias for <code>intersperse_with</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p ispw $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isslug">
<h3><a class="doc-anchor" href="#doc-isslug">#</a> <code>isslug</code></h3>
<p><code>isslug</code> — operation <code>isslug</code>. Alias for <code>is_slug</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isslug $x
</code></pre>
</article>
<article class="doc-entry" id="doc-issmith">
<h3><a class="doc-anchor" href="#doc-issmith">#</a> <code>issmith</code></h3>
<p><code>issmith</code> — operation <code>issmith</code>. Alias for <code>is_smith</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p issmith $x
</code></pre>
</article>
<article class="doc-entry" id="doc-issqfr">
<h3><a class="doc-anchor" href="#doc-issqfr">#</a> <code>issqfr</code></h3>
<p><code>issqfr</code> — operation <code>issqfr</code>. Alias for <code>is_squarefree</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p issqfr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-issrtb">
<h3><a class="doc-anchor" href="#doc-issrtb">#</a> <code>issrtb</code></h3>
<p><code>issrtb</code> — operation <code>issrtb</code>. Alias for <code>is_sorted_by</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p issrtb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-issv">
<h3><a class="doc-anchor" href="#doc-issv">#</a> <code>issv</code></h3>
<p><code>issv</code> — operation <code>issv</code>. Alias for <code>is_semver</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p issv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ista-step">
<h3><a class="doc-anchor" href="#doc-ista-step">#</a> <code>ista_step</code></h3>
<p><code>ista_step</code> — single-step update of <code>ista</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p ista_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-istft-step">
<h3><a class="doc-anchor" href="#doc-istft-step">#</a> <code>istft_step</code></h3>
<p><code>istft_step</code> — single-step update of <code>istft</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p istft_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isvdate">
<h3><a class="doc-anchor" href="#doc-isvdate">#</a> <code>isvdate</code></h3>
<p><code>isvdate</code> — operation <code>isvdate</code>. Alias for <code>is_valid_date</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p isvdate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iswap-gate">
<h3><a class="doc-anchor" href="#doc-iswap-gate">#</a> <code>iswap_gate</code></h3>
<p><code>iswap_gate</code> — operation <code>iswap gate</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p iswap_gate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-isweak">
<h3><a class="doc-anchor" href="#doc-isweak">#</a> <code>isweak</code></h3>
<p><code>isweak</code> — operation <code>isweak</code>. Category: *list / aggregate*.</p>
<pre><code class="lang-perl">p isweak $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iswhole">
<h3><a class="doc-anchor" href="#doc-iswhole">#</a> <code>iswhole</code></h3>
<p><code>iswhole</code> — operation <code>iswhole</code>. Alias for <code>is_whole_num</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p iswhole $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iszero">
<h3><a class="doc-anchor" href="#doc-iszero">#</a> <code>iszero</code></h3>
<p><code>iszero</code> — operation <code>iszero</code>. Alias for <code>is_zero_num</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p iszero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iszip">
<h3><a class="doc-anchor" href="#doc-iszip">#</a> <code>iszip</code></h3>
<p><code>iszip</code> — operation <code>iszip</code>. Alias for <code>is_us_zip</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p iszip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-italic">
<h3><a class="doc-anchor" href="#doc-italic">#</a> <code>italic</code></h3>
<p><code>italic</code> — operation <code>italic</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p italic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-itcz-position-lat">
<h3><a class="doc-anchor" href="#doc-itcz-position-lat">#</a> <code>itcz_position_lat</code></h3>
<p><code>itcz_position_lat</code> — operation <code>itcz position lat</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p itcz_position_lat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iter">
<h3><a class="doc-anchor" href="#doc-iter">#</a> <code>iter</code></h3>
<p><code>iter</code> — operation <code>iter</code>. Alias for <code>iterate</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p iter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iterate">
<h3><a class="doc-anchor" href="#doc-iterate">#</a> <code>iterate</code></h3>
<p><code>iterate</code> — operation <code>iterate</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p iterate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iterate-n">
<h3><a class="doc-anchor" href="#doc-iterate-n">#</a> <code>iterate_n</code></h3>
<p><code>iterate_n</code> — operation <code>iterate n</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p iterate_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iv">
<h3><a class="doc-anchor" href="#doc-iv">#</a> <code>iv</code></h3>
<p><code>iv</code> — operation <code>iv</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p iv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-iv-estimator">
<h3><a class="doc-anchor" href="#doc-iv-estimator">#</a> <code>iv_estimator</code></h3>
<p><code>iv_estimator</code> — operation <code>iv estimator</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p iv_estimator $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jaccard">
<h3><a class="doc-anchor" href="#doc-jaccard">#</a> <code>jaccard</code></h3>
<p><code>jaccard</code> — operation <code>jaccard</code>. Alias for <code>jaccard_index</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p jaccard $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jaccard-index">
<h3><a class="doc-anchor" href="#doc-jaccard-index">#</a> <code>jaccard_index</code></h3>
<p><code>jaccard_index</code> — index of <code>jaccard</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p jaccard_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jaccard-sim">
<h3><a class="doc-anchor" href="#doc-jaccard-sim">#</a> <code>jaccard_sim</code></h3>
<p><code>jaccard_sim(set_a, set_b) → number</code> — <code>|A∩B| / |A∪B|</code>. Sets are passed as arrays.</p>
</article>
<article class="doc-entry" id="doc-jaccard-similarity">
<h3><a class="doc-anchor" href="#doc-jaccard-similarity">#</a> <code>jaccard_similarity</code></h3>
<p><code>jaccard_similarity</code> — similarity metric of <code>jaccard</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p jaccard_similarity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jacobi-cn-small-q">
<h3><a class="doc-anchor" href="#doc-jacobi-cn-small-q">#</a> <code>jacobi_cn_small_q</code></h3>
<p><code>jacobi_cn_small_q</code> — operation <code>jacobi cn small q</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p jacobi_cn_small_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jacobi-dn-small-q">
<h3><a class="doc-anchor" href="#doc-jacobi-dn-small-q">#</a> <code>jacobi_dn_small_q</code></h3>
<p><code>jacobi_dn_small_q</code> — operation <code>jacobi dn small q</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p jacobi_dn_small_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jacobi-sn-small-q">
<h3><a class="doc-anchor" href="#doc-jacobi-sn-small-q">#</a> <code>jacobi_sn_small_q</code></h3>
<p><code>jacobi_sn_small_q</code> — operation <code>jacobi sn small q</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p jacobi_sn_small_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jacobian-2dof">
<h3><a class="doc-anchor" href="#doc-jacobian-2dof">#</a> <code>jacobian_2dof</code></h3>
<p><code>jacobian_2dof</code> — operation <code>jacobian 2dof</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p jacobian_2dof $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jahn-teller-check">
<h3><a class="doc-anchor" href="#doc-jahn-teller-check">#</a> <code>jahn_teller_check</code></h3>
<p><code>jahn_teller_check</code> — operation <code>jahn teller check</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p jahn_teller_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jaro-similarity">
<h3><a class="doc-anchor" href="#doc-jaro-similarity">#</a> <code>jaro_similarity</code></h3>
<p><code>jaro_similarity</code> — similarity metric of <code>jaro</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p jaro_similarity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jarosim">
<h3><a class="doc-anchor" href="#doc-jarosim">#</a> <code>jarosim</code></h3>
<p><code>jarosim</code> — operation <code>jarosim</code>. Alias for <code>jaro_similarity</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p jarosim $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jd">
<h3><a class="doc-anchor" href="#doc-jd">#</a> <code>jd</code></h3>
<p><code>jd</code> — operation <code>jd</code>. Alias for <code>json_decode</code>. Category: *data / network*.</p>
<pre><code class="lang-perl">p jd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jd-to-calendar">
<h3><a class="doc-anchor" href="#doc-jd-to-calendar">#</a> <code>jd_to_calendar</code></h3>
<p><code>jd_to_calendar</code> — convert from <code>jd</code> to <code>calendar</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p jd_to_calendar $value
</code></pre>
</article>
<article class="doc-entry" id="doc-je">
<h3><a class="doc-anchor" href="#doc-je">#</a> <code>je</code></h3>
<p><code>je</code> — operation <code>je</code>. Alias for <code>json_encode</code>. Category: *data / network*.</p>
<pre><code class="lang-perl">p je $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jeans-length">
<h3><a class="doc-anchor" href="#doc-jeans-length">#</a> <code>jeans_length</code></h3>
<p><code>jeans_length</code> — operation <code>jeans length</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p jeans_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jenkins-hash">
<h3><a class="doc-anchor" href="#doc-jenkins-hash">#</a> <code>jenkins_hash</code></h3>
<p><code>jenkins_hash(s) → int</code> — Bob Jenkins' one-at-a-time hash; classic non-crypto 32-bit hash.</p>
<pre><code class="lang-perl">p jenkins_hash("hello")
</code></pre>
</article>
<article class="doc-entry" id="doc-jenkins-oat">
<h3><a class="doc-anchor" href="#doc-jenkins-oat">#</a> <code>jenkins_oat</code></h3>
<p><code>jenkins_oat</code> — Jenkins hash variant <code>oat</code>. Alias for <code>jenkins_one_at_a_time</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p jenkins_oat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jenkins-one-at-a-time">
<h3><a class="doc-anchor" href="#doc-jenkins-one-at-a-time">#</a> <code>jenkins_one_at_a_time</code></h3>
<p><code>jenkins_one_at_a_time</code> — Jenkins hash variant <code>one at a time</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p jenkins_one_at_a_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jensen-alpha">
<h3><a class="doc-anchor" href="#doc-jensen-alpha">#</a> <code>jensen_alpha</code></h3>
<p><code>jensen_alpha(portfolio_return, beta, market_return, rf=0) → number</code> — alpha vs CAPM expectation: <code>r - (rf + β·(rm - rf))</code>.</p>
<pre><code class="lang-perl">p jensen_alpha(0.12, 1.1, 0.08, 0.02)
</code></pre>
</article>
<article class="doc-entry" id="doc-jensen-shannon-div">
<h3><a class="doc-anchor" href="#doc-jensen-shannon-div">#</a> <code>jensen_shannon_div</code></h3>
<p><code>jensen_shannon_div</code> — operation <code>jensen shannon div</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p jensen_shannon_div $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jensens-alpha">
<h3><a class="doc-anchor" href="#doc-jensens-alpha">#</a> <code>jensens_alpha</code></h3>
<p><code>jensens_alpha</code> — operation <code>jensens alpha</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p jensens_alpha $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jitter-ms">
<h3><a class="doc-anchor" href="#doc-jitter-ms">#</a> <code>jitter_ms</code></h3>
<p><code>jitter_ms</code> — operation <code>jitter ms</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p jitter_ms $x
</code></pre>
</article>
<article class="doc-entry" id="doc-job-schedule-ljf">
<h3><a class="doc-anchor" href="#doc-job-schedule-ljf">#</a> <code>job_schedule_ljf</code></h3>
<p><code>job_schedule_ljf(durations) → array</code> — Longest Job First.</p>
</article>
<article class="doc-entry" id="doc-job-schedule-spt">
<h3><a class="doc-anchor" href="#doc-job-schedule-spt">#</a> <code>job_schedule_spt</code></h3>
<p><code>job_schedule_spt(durations) → array</code> — Shortest Processing Time first: indices sorted by ascending duration.</p>
<pre><code class="lang-perl">p job_schedule_spt([8, 1, 3, 5]) # [1, 2, 3, 0]
</code></pre>
</article>
<article class="doc-entry" id="doc-job-shop-makespan-lower">
<h3><a class="doc-anchor" href="#doc-job-shop-makespan-lower">#</a> <code>job_shop_makespan_lower</code></h3>
<p><code>job_shop_makespan_lower</code> — operation <code>job shop makespan lower</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p job_shop_makespan_lower $x
</code></pre>
</article>
<article class="doc-entry" id="doc-johansen-test">
<h3><a class="doc-anchor" href="#doc-johansen-test">#</a> <code>johansen_test</code></h3>
<p><code>johansen_test</code> — statistical test of <code>johansen</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p johansen_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-johansen-trace-step">
<h3><a class="doc-anchor" href="#doc-johansen-trace-step">#</a> <code>johansen_trace_step</code></h3>
<p><code>johansen_trace_step</code> — single-step update of <code>johansen trace</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p johansen_trace_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-johnson-2m">
<h3><a class="doc-anchor" href="#doc-johnson-2m">#</a> <code>johnson_2m</code></h3>
<p><code>johnson_2m</code> — operation <code>johnson 2m</code>. Alias for <code>johnsons_rule</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p johnson_2m $x
</code></pre>
</article>
<article class="doc-entry" id="doc-johnson-reweight">
<h3><a class="doc-anchor" href="#doc-johnson-reweight">#</a> <code>johnson_reweight</code></h3>
<p><code>johnson_reweight</code> — operation <code>johnson reweight</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p johnson_reweight $x
</code></pre>
</article>
<article class="doc-entry" id="doc-johnsons-rule">
<h3><a class="doc-anchor" href="#doc-johnsons-rule">#</a> <code>johnsons_rule</code></h3>
<p><code>johnsons_rule</code> — operation <code>johnsons rule</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p johnsons_rule $x
</code></pre>
</article>
<article class="doc-entry" id="doc-join-colons">
<h3><a class="doc-anchor" href="#doc-join-colons">#</a> <code>join_colons</code></h3>
<p><code>join_colons</code> — operation <code>join colons</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p join_colons $x
</code></pre>
</article>
<article class="doc-entry" id="doc-join-commas">
<h3><a class="doc-anchor" href="#doc-join-commas">#</a> <code>join_commas</code></h3>
<p><code>join_commas</code> — operation <code>join commas</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p join_commas $x
</code></pre>
</article>
<article class="doc-entry" id="doc-join-dashes">
<h3><a class="doc-anchor" href="#doc-join-dashes">#</a> <code>join_dashes</code></h3>
<p><code>join_dashes</code> — operation <code>join dashes</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p join_dashes $x
</code></pre>
</article>
<article class="doc-entry" id="doc-join-dots">
<h3><a class="doc-anchor" href="#doc-join-dots">#</a> <code>join_dots</code></h3>
<p><code>join_dots</code> — operation <code>join dots</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p join_dots $x
</code></pre>
</article>
<article class="doc-entry" id="doc-join-lines">
<h3><a class="doc-anchor" href="#doc-join-lines">#</a> <code>join_lines</code></h3>
<p><code>join_lines</code> — operation <code>join lines</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p join_lines $x
</code></pre>
</article>
<article class="doc-entry" id="doc-join-pipes">
<h3><a class="doc-anchor" href="#doc-join-pipes">#</a> <code>join_pipes</code></h3>
<p><code>join_pipes</code> — operation <code>join pipes</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p join_pipes $x
</code></pre>
</article>
<article class="doc-entry" id="doc-join-slashes">
<h3><a class="doc-anchor" href="#doc-join-slashes">#</a> <code>join_slashes</code></h3>
<p><code>join_slashes</code> — operation <code>join slashes</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p join_slashes $x
</code></pre>
</article>
<article class="doc-entry" id="doc-join-spaces">
<h3><a class="doc-anchor" href="#doc-join-spaces">#</a> <code>join_spaces</code></h3>
<p><code>join_spaces</code> — operation <code>join spaces</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p join_spaces $x
</code></pre>
</article>
<article class="doc-entry" id="doc-join-tabs">
<h3><a class="doc-anchor" href="#doc-join-tabs">#</a> <code>join_tabs</code></h3>
<p><code>join_tabs</code> — operation <code>join tabs</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p join_tabs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-joint-entropy">
<h3><a class="doc-anchor" href="#doc-joint-entropy">#</a> <code>joint_entropy</code></h3>
<p><code>joint_entropy(joint_matrix) → number</code> — H(X,Y) = <code>-Σ p·ln p</code>.</p>
</article>
<article class="doc-entry" id="doc-joint-entropy-step">
<h3><a class="doc-anchor" href="#doc-joint-entropy-step">#</a> <code>joint_entropy_step</code></h3>
<p><code>joint_entropy_step</code> — single-step update of <code>joint entropy</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p joint_entropy_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jones-polynomial-at-i">
<h3><a class="doc-anchor" href="#doc-jones-polynomial-at-i">#</a> <code>jones_polynomial_at_i</code></h3>
<p><code>jones_polynomial_at_i</code> — operation <code>jones polynomial at i</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p jones_polynomial_at_i $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jones-polynomial-at-minus-one">
<h3><a class="doc-anchor" href="#doc-jones-polynomial-at-minus-one">#</a> <code>jones_polynomial_at_minus_one</code></h3>
<p><code>jones_polynomial_at_minus_one</code> — operation <code>jones polynomial at minus one</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p jones_polynomial_at_minus_one $x
</code></pre>
</article>
<article class="doc-entry" id="doc-joule-heating-battery">
<h3><a class="doc-anchor" href="#doc-joule-heating-battery">#</a> <code>joule_heating_battery</code></h3>
<p><code>joule_heating_battery</code> — operation <code>joule heating battery</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p joule_heating_battery $x
</code></pre>
</article>
<article class="doc-entry" id="doc-joules-to-cal">
<h3><a class="doc-anchor" href="#doc-joules-to-cal">#</a> <code>joules_to_cal</code></h3>
<p><code>joules_to_cal</code> — convert from <code>joules</code> to <code>cal</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p joules_to_cal $value
</code></pre>
</article>
<article class="doc-entry" id="doc-joules-to-ev">
<h3><a class="doc-anchor" href="#doc-joules-to-ev">#</a> <code>joules_to_ev</code></h3>
<p><code>joules_to_ev</code> — convert from <code>joules</code> to <code>ev</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p joules_to_ev $value
</code></pre>
</article>
<article class="doc-entry" id="doc-jpeg-dct-8x8-quant">
<h3><a class="doc-anchor" href="#doc-jpeg-dct-8x8-quant">#</a> <code>jpeg_dct_8x8_quant</code></h3>
<p><code>jpeg_dct_8x8_quant</code> — operation <code>jpeg dct 8x8 quant</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p jpeg_dct_8x8_quant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jpeg-markers">
<h3><a class="doc-anchor" href="#doc-jpeg-markers">#</a> <code>jpeg_markers</code></h3>
<p><code>jpeg_markers(hex_bytes) → array</code> — list of JPEG segment markers ("FFD8", "FFE0", …) in order.</p>
</article>
<article class="doc-entry" id="doc-jpeg-zig-zag-index">
<h3><a class="doc-anchor" href="#doc-jpeg-zig-zag-index">#</a> <code>jpeg_zig_zag_index</code></h3>
<p><code>jpeg_zig_zag_index</code> — index of <code>jpeg zig zag</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p jpeg_zig_zag_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-all">
<h3><a class="doc-anchor" href="#doc-jq-all">#</a> <code>jq_all</code></h3>
<p><code>jq_all</code> — operation <code>jq all</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_all $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-any">
<h3><a class="doc-anchor" href="#doc-jq-any">#</a> <code>jq_any</code></h3>
<p><code>jq_any</code> — operation <code>jq any</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_any $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-chunks">
<h3><a class="doc-anchor" href="#doc-jq-chunks">#</a> <code>jq_chunks</code></h3>
<p><code>jq_chunks</code> — operation <code>jq chunks</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_chunks $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-combinations">
<h3><a class="doc-anchor" href="#doc-jq-combinations">#</a> <code>jq_combinations</code></h3>
<p><code>jq_combinations</code> — operation <code>jq combinations</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_combinations $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-delete">
<h3><a class="doc-anchor" href="#doc-jq-delete">#</a> <code>jq_delete</code></h3>
<p><code>jq_delete</code> — operation <code>jq delete</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_delete $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-filter">
<h3><a class="doc-anchor" href="#doc-jq-filter">#</a> <code>jq_filter</code></h3>
<p><code>jq_filter</code> — filter op of <code>jq</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_filter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-first">
<h3><a class="doc-anchor" href="#doc-jq-first">#</a> <code>jq_first</code></h3>
<p><code>jq_first</code> — operation <code>jq first</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_first $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-flatten">
<h3><a class="doc-anchor" href="#doc-jq-flatten">#</a> <code>jq_flatten</code></h3>
<p><code>jq_flatten</code> — operation <code>jq flatten</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_flatten $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-from-entries">
<h3><a class="doc-anchor" href="#doc-jq-from-entries">#</a> <code>jq_from_entries</code></h3>
<p><code>jq_from_entries</code> — operation <code>jq from entries</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_from_entries $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-get">
<h3><a class="doc-anchor" href="#doc-jq-get">#</a> <code>jq_get</code></h3>
<p><code>jq_get</code> — operation <code>jq get</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_get $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-group-by">
<h3><a class="doc-anchor" href="#doc-jq-group-by">#</a> <code>jq_group_by</code></h3>
<p><code>jq_group_by</code> — operation <code>jq group by</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_group_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-has">
<h3><a class="doc-anchor" href="#doc-jq-has">#</a> <code>jq_has</code></h3>
<p><code>jq_has</code> — operation <code>jq has</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_has $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-index">
<h3><a class="doc-anchor" href="#doc-jq-index">#</a> <code>jq_index</code></h3>
<p><code>jq_index</code> — index of <code>jq</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-indices">
<h3><a class="doc-anchor" href="#doc-jq-indices">#</a> <code>jq_indices</code></h3>
<p><code>jq_indices</code> — operation <code>jq indices</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_indices $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-keys-at">
<h3><a class="doc-anchor" href="#doc-jq-keys-at">#</a> <code>jq_keys_at</code></h3>
<p><code>jq_keys_at</code> — operation <code>jq keys at</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_keys_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-last">
<h3><a class="doc-anchor" href="#doc-jq-last">#</a> <code>jq_last</code></h3>
<p><code>jq_last</code> — operation <code>jq last</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_last $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-leaf-paths">
<h3><a class="doc-anchor" href="#doc-jq-leaf-paths">#</a> <code>jq_leaf_paths</code></h3>
<p><code>jq_leaf_paths</code> — operation <code>jq leaf paths</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_leaf_paths $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-length-at">
<h3><a class="doc-anchor" href="#doc-jq-length-at">#</a> <code>jq_length_at</code></h3>
<p><code>jq_length_at</code> — operation <code>jq length at</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_length_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-map-values">
<h3><a class="doc-anchor" href="#doc-jq-map-values">#</a> <code>jq_map_values</code></h3>
<p><code>jq_map_values</code> — operation <code>jq map values</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_map_values $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-max-by">
<h3><a class="doc-anchor" href="#doc-jq-max-by">#</a> <code>jq_max_by</code></h3>
<p><code>jq_max_by</code> — operation <code>jq max by</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_max_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-min-by">
<h3><a class="doc-anchor" href="#doc-jq-min-by">#</a> <code>jq_min_by</code></h3>
<p><code>jq_min_by</code> — operation <code>jq min by</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_min_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-paths">
<h3><a class="doc-anchor" href="#doc-jq-paths">#</a> <code>jq_paths</code></h3>
<p><code>jq_paths</code> — operation <code>jq paths</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_paths $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-recurse">
<h3><a class="doc-anchor" href="#doc-jq-recurse">#</a> <code>jq_recurse</code></h3>
<p><code>jq_recurse</code> — operation <code>jq recurse</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_recurse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-select">
<h3><a class="doc-anchor" href="#doc-jq-select">#</a> <code>jq_select</code></h3>
<p><code>jq_select</code> — operation <code>jq select</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_select $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-set">
<h3><a class="doc-anchor" href="#doc-jq-set">#</a> <code>jq_set</code></h3>
<p><code>jq_set</code> — operation <code>jq set</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-sort-by">
<h3><a class="doc-anchor" href="#doc-jq-sort-by">#</a> <code>jq_sort_by</code></h3>
<p><code>jq_sort_by</code> — operation <code>jq sort by</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_sort_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-split-at">
<h3><a class="doc-anchor" href="#doc-jq-split-at">#</a> <code>jq_split_at</code></h3>
<p><code>jq_split_at</code> — operation <code>jq split at</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_split_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-to-entries">
<h3><a class="doc-anchor" href="#doc-jq-to-entries">#</a> <code>jq_to_entries</code></h3>
<p><code>jq_to_entries</code> — convert from <code>jq</code> to <code>entries</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_to_entries $value
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-type">
<h3><a class="doc-anchor" href="#doc-jq-type">#</a> <code>jq_type</code></h3>
<p><code>jq_type</code> — operation <code>jq type</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_type $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-unique-by">
<h3><a class="doc-anchor" href="#doc-jq-unique-by">#</a> <code>jq_unique_by</code></h3>
<p><code>jq_unique_by</code> — operation <code>jq unique by</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_unique_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-values-at">
<h3><a class="doc-anchor" href="#doc-jq-values-at">#</a> <code>jq_values_at</code></h3>
<p><code>jq_values_at</code> — operation <code>jq values at</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_values_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-walk">
<h3><a class="doc-anchor" href="#doc-jq-walk">#</a> <code>jq_walk</code></h3>
<p><code>jq_walk</code> — operation <code>jq walk</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_walk $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-with-entries">
<h3><a class="doc-anchor" href="#doc-jq-with-entries">#</a> <code>jq_with_entries</code></h3>
<p><code>jq_with_entries</code> — operation <code>jq with entries</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_with_entries $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jq-zip">
<h3><a class="doc-anchor" href="#doc-jq-zip">#</a> <code>jq_zip</code></h3>
<p><code>jq_zip</code> — operation <code>jq zip</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p jq_zip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jr-european-call">
<h3><a class="doc-anchor" href="#doc-jr-european-call">#</a> <code>jr_european_call</code></h3>
<p><code>jr_european_call</code> — operation <code>jr european call</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p jr_european_call $x
</code></pre>
</article>
<article class="doc-entry" id="doc-js-divergence-distributions">
<h3><a class="doc-anchor" href="#doc-js-divergence-distributions">#</a> <code>js_divergence_distributions</code></h3>
<p><code>js_divergence_distributions(p, q) → number</code> — Jensen-Shannon divergence; symmetric, bounded by <code>ln 2</code>.</p>
<pre><code class="lang-perl">p js_divergence_distributions([0.5,0.5], [0.7,0.3])
</code></pre>
</article>
<article class="doc-entry" id="doc-json-array-length">
<h3><a class="doc-anchor" href="#doc-json-array-length">#</a> <code>json_array_length</code></h3>
<p><code>json_array_length</code> — JSON helper <code>array length</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p json_array_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-json-build-object">
<h3><a class="doc-anchor" href="#doc-json-build-object">#</a> <code>json_build_object</code></h3>
<p><code>json_build_object</code> — JSON helper <code>build object</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p json_build_object $x
</code></pre>
</article>
<article class="doc-entry" id="doc-json-diff">
<h3><a class="doc-anchor" href="#doc-json-diff">#</a> <code>json_diff</code></h3>
<p><code>json_diff</code> — JSON helper <code>diff</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p json_diff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-json-each">
<h3><a class="doc-anchor" href="#doc-json-each">#</a> <code>json_each</code></h3>
<p><code>json_each</code> — JSON helper <code>each</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p json_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-json-escape">
<h3><a class="doc-anchor" href="#doc-json-escape">#</a> <code>json_escape</code></h3>
<p><code>json_escape</code> — JSON helper <code>escape</code>. Alias for <code>escape_json</code>. Category: *json helpers*.</p>
<pre><code class="lang-perl">p json_escape $x
</code></pre>
</article>
<article class="doc-entry" id="doc-json-extract-path">
<h3><a class="doc-anchor" href="#doc-json-extract-path">#</a> <code>json_extract_path</code></h3>
<p><code>json_extract_path</code> — JSON helper <code>extract path</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p json_extract_path $x
</code></pre>
</article>
<article class="doc-entry" id="doc-json-merge-patch">
<h3><a class="doc-anchor" href="#doc-json-merge-patch">#</a> <code>json_merge_patch</code></h3>
<p><code>json_merge_patch</code> — JSON helper <code>merge patch</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p json_merge_patch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-json-minify">
<h3><a class="doc-anchor" href="#doc-json-minify">#</a> <code>json_minify</code></h3>
<p><code>json_minify</code> — JSON helper <code>minify</code>. Category: *json helpers*.</p>
<pre><code class="lang-perl">p json_minify $x
</code></pre>
</article>
<article class="doc-entry" id="doc-json-patch">
<h3><a class="doc-anchor" href="#doc-json-patch">#</a> <code>json_patch</code></h3>
<p><code>json_patch</code> — JSON helper <code>patch</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p json_patch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-json-pointer-resolve">
<h3><a class="doc-anchor" href="#doc-json-pointer-resolve">#</a> <code>json_pointer_resolve</code></h3>
<p><code>json_pointer_resolve</code> — JSON helper <code>pointer resolve</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p json_pointer_resolve $x
</code></pre>
</article>
<article class="doc-entry" id="doc-json-pointer-set">
<h3><a class="doc-anchor" href="#doc-json-pointer-set">#</a> <code>json_pointer_set</code></h3>
<p><code>json_pointer_set</code> — JSON helper <code>pointer set</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p json_pointer_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-json-pretty">
<h3><a class="doc-anchor" href="#doc-json-pretty">#</a> <code>json_pretty</code></h3>
<p><code>json_pretty</code> — JSON helper <code>pretty</code>. Category: *json helpers*.</p>
<pre><code class="lang-perl">p json_pretty $x
</code></pre>
</article>
<article class="doc-entry" id="doc-json-strip-nulls">
<h3><a class="doc-anchor" href="#doc-json-strip-nulls">#</a> <code>json_strip_nulls</code></h3>
<p><code>json_strip_nulls</code> — JSON helper <code>strip nulls</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p json_strip_nulls $x
</code></pre>
</article>
<article class="doc-entry" id="doc-json-to-xml">
<h3><a class="doc-anchor" href="#doc-json-to-xml">#</a> <code>json_to_xml</code></h3>
<p><code>json_to_xml</code> — convert from <code>json</code> to <code>xml</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p json_to_xml $value
</code></pre>
</article>
<article class="doc-entry" id="doc-jsonb-array-length">
<h3><a class="doc-anchor" href="#doc-jsonb-array-length">#</a> <code>jsonb_array_length</code></h3>
<p><code>jsonb_array_length</code> — operation <code>jsonb array length</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p jsonb_array_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jsonb-object-keys">
<h3><a class="doc-anchor" href="#doc-jsonb-object-keys">#</a> <code>jsonb_object_keys</code></h3>
<p><code>jsonb_object_keys</code> — operation <code>jsonb object keys</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p jsonb_object_keys $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jsonb-path-query">
<h3><a class="doc-anchor" href="#doc-jsonb-path-query">#</a> <code>jsonb_path_query</code></h3>
<p><code>jsonb_path_query</code> — operation <code>jsonb path query</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p jsonb_path_query $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jsonb-pretty">
<h3><a class="doc-anchor" href="#doc-jsonb-pretty">#</a> <code>jsonb_pretty</code></h3>
<p><code>jsonb_pretty</code> — operation <code>jsonb pretty</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p jsonb_pretty $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jsonb-set">
<h3><a class="doc-anchor" href="#doc-jsonb-set">#</a> <code>jsonb_set</code></h3>
<p><code>jsonb_set</code> — operation <code>jsonb set</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p jsonb_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jsonb-typeof">
<h3><a class="doc-anchor" href="#doc-jsonb-typeof">#</a> <code>jsonb_typeof</code></h3>
<p><code>jsonb_typeof</code> — operation <code>jsonb typeof</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p jsonb_typeof $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jukes-cantor-distance">
<h3><a class="doc-anchor" href="#doc-jukes-cantor-distance">#</a> <code>jukes_cantor_distance</code></h3>
<p><code>jukes_cantor_distance</code> — distance / dissimilarity metric of <code>jukes cantor</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p jukes_cantor_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-julian-centuries-j2000">
<h3><a class="doc-anchor" href="#doc-julian-centuries-j2000">#</a> <code>julian_centuries_j2000</code></h3>
<p><code>julian_centuries_j2000</code> — Julian-date conversion <code>centuries j2000</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p julian_centuries_j2000 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-julian-day">
<h3><a class="doc-anchor" href="#doc-julian-day">#</a> <code>julian_day</code></h3>
<p><code>julian_day</code> — Julian-date conversion <code>day</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p julian_day $x
</code></pre>
</article>
<article class="doc-entry" id="doc-julian-from-fixed">
<h3><a class="doc-anchor" href="#doc-julian-from-fixed">#</a> <code>julian_from_fixed</code></h3>
<p><code>julian_from_fixed</code> — Julian-date conversion <code>from fixed</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p julian_from_fixed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-julian-to-unix">
<h3><a class="doc-anchor" href="#doc-julian-to-unix">#</a> <code>julian_to_unix</code></h3>
<p><code>julian_to_unix(jd) → int</code> — convert Julian Date to unix timestamp.</p>
<pre><code class="lang-perl">p julian_to_unix(2459945.5)
</code></pre>
</article>
<article class="doc-entry" id="doc-just-intonation-freq">
<h3><a class="doc-anchor" href="#doc-just-intonation-freq">#</a> <code>just_intonation_freq</code></h3>
<p><code>just_intonation_freq</code> — operation <code>just intonation freq</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p just_intonation_freq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-just-intonation-ratio">
<h3><a class="doc-anchor" href="#doc-just-intonation-ratio">#</a> <code>just_intonation_ratio</code></h3>
<p><code>just_intonation_ratio</code> — ratio of <code>just intonation</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p just_intonation_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-justify-center">
<h3><a class="doc-anchor" href="#doc-justify-center">#</a> <code>justify_center</code></h3>
<p><code>justify_center(s, width) → string</code> — pad symmetrically. Extra space goes to the right when uneven.</p>
</article>
<article class="doc-entry" id="doc-justify-left">
<h3><a class="doc-anchor" href="#doc-justify-left">#</a> <code>justify_left</code></h3>
<p><code>justify_left(s, width) → string</code> — pad right with spaces to reach <code>width</code>.</p>
<pre><code class="lang-perl">p justify_left("hi", 5) # "hi "
</code></pre>
</article>
<article class="doc-entry" id="doc-justify-right">
<h3><a class="doc-anchor" href="#doc-justify-right">#</a> <code>justify_right</code></h3>
<p><code>justify_right(s, width) → string</code> — pad left with spaces to reach <code>width</code>.</p>
</article>
<article class="doc-entry" id="doc-juxt2">
<h3><a class="doc-anchor" href="#doc-juxt2">#</a> <code>juxt2</code></h3>
<p><code>juxt2</code> — operation <code>juxt2</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p juxt2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-juxt3">
<h3><a class="doc-anchor" href="#doc-juxt3">#</a> <code>juxt3</code></h3>
<p><code>juxt3</code> — operation <code>juxt3</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p juxt3 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-jv">
<h3><a class="doc-anchor" href="#doc-jv">#</a> <code>jv</code></h3>
<p><code>jv</code> — operation <code>jv</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p jv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-k-coreness">
<h3><a class="doc-anchor" href="#doc-k-coreness">#</a> <code>k_coreness</code></h3>
<p><code>k_coreness</code> — operation <code>k coreness</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p k_coreness $x
</code></pre>
</article>
<article class="doc-entry" id="doc-k-from-dg">
<h3><a class="doc-anchor" href="#doc-k-from-dg">#</a> <code>k_from_dg</code></h3>
<p><code>k_from_dg</code> — operation <code>k from dg</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p k_from_dg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-k-shortest-spanning">
<h3><a class="doc-anchor" href="#doc-k-shortest-spanning">#</a> <code>k_shortest_spanning</code></h3>
<p><code>k_shortest_spanning</code> — operation <code>k shortest spanning</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p k_shortest_spanning $x
</code></pre>
</article>
<article class="doc-entry" id="doc-k-to-c">
<h3><a class="doc-anchor" href="#doc-k-to-c">#</a> <code>k_to_c</code></h3>
<p><code>k_to_c</code> — convert from <code>k</code> to <code>c</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p k_to_c $value
</code></pre>
</article>
<article class="doc-entry" id="doc-k-to-f">
<h3><a class="doc-anchor" href="#doc-k-to-f">#</a> <code>k_to_f</code></h3>
<p><code>k_to_f</code> — convert from <code>k</code> to <code>f</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p k_to_f $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ka-to-pka">
<h3><a class="doc-anchor" href="#doc-ka-to-pka">#</a> <code>ka_to_pka</code></h3>
<p><code>ka_to_pka</code> — convert from <code>ka</code> to <code>pka</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p ka_to_pka $value
</code></pre>
</article>
<article class="doc-entry" id="doc-kaiser">
<h3><a class="doc-anchor" href="#doc-kaiser">#</a> <code>kaiser</code></h3>
<p><code>window_kaiser($n, $beta)</code> (alias <code>kaiser</code>) — generates a Kaiser window with parameter beta controlling the tradeoff between main lobe width and sidelobe level. Beta=0 is rectangular, beta~5 is similar to Hamming.</p>
<pre><code class="lang-perl">my $w = kaiser(1024, 5.0)
</code></pre>
</article>
<article class="doc-entry" id="doc-kaiser-window">
<h3><a class="doc-anchor" href="#doc-kaiser-window">#</a> <code>kaiser_window</code></h3>
<p><code>kaiser_window</code> — operation <code>kaiser window</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p kaiser_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kaiserord-step">
<h3><a class="doc-anchor" href="#doc-kaiserord-step">#</a> <code>kaiserord_step</code></h3>
<p><code>kaiserord_step</code> — single-step update of <code>kaiserord</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p kaiserord_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kalai-smorodinsky-step">
<h3><a class="doc-anchor" href="#doc-kalai-smorodinsky-step">#</a> <code>kalai_smorodinsky_step</code></h3>
<p><code>kalai_smorodinsky_step</code> — single-step update of <code>kalai smorodinsky</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p kalai_smorodinsky_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kalman-filter-step">
<h3><a class="doc-anchor" href="#doc-kalman-filter-step">#</a> <code>kalman_filter_step</code></h3>
<p><code>kalman_filter_step</code> — single-step update of <code>kalman filter</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p kalman_filter_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kalman-predict-state">
<h3><a class="doc-anchor" href="#doc-kalman-predict-state">#</a> <code>kalman_predict_state</code></h3>
<p><code>kalman_predict_state</code> — operation <code>kalman predict state</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p kalman_predict_state $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kalman-smoother-step">
<h3><a class="doc-anchor" href="#doc-kalman-smoother-step">#</a> <code>kalman_smoother_step</code></h3>
<p><code>kalman_smoother_step</code> — single-step update of <code>kalman smoother</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p kalman_smoother_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kalman-update-state">
<h3><a class="doc-anchor" href="#doc-kalman-update-state">#</a> <code>kalman_update_state</code></h3>
<p><code>kalman_update_state</code> — operation <code>kalman update state</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p kalman_update_state $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kaluza-klein-step">
<h3><a class="doc-anchor" href="#doc-kaluza-klein-step">#</a> <code>kaluza_klein_step</code></h3>
<p><code>kaluza_klein_step</code> — single-step update of <code>kaluza klein</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p kaluza_klein_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kama">
<h3><a class="doc-anchor" href="#doc-kama">#</a> <code>kama</code></h3>
<p><code>kama(prices, period=10) → array</code> — Kaufman adaptive moving average. Smoothing constant tracks volatility: <code>sc = (er·(fast − slow) + slow)²</code>, so the average accelerates in trends and idles in chop.</p>
<pre><code class="lang-perl">p kama(\@prices, 10)
</code></pre>
</article>
<article class="doc-entry" id="doc-kaprekar-routine-step">
<h3><a class="doc-anchor" href="#doc-kaprekar-routine-step">#</a> <code>kaprekar_routine_step</code></h3>
<p><code>kaprekar_routine_step</code> — single-step update of <code>kaprekar routine</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p kaprekar_routine_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-karger-contract-edge">
<h3><a class="doc-anchor" href="#doc-karger-contract-edge">#</a> <code>karger_contract_edge</code></h3>
<p><code>karger_contract_edge</code> — operation <code>karger contract edge</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p karger_contract_edge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-karger-min-cut-count">
<h3><a class="doc-anchor" href="#doc-karger-min-cut-count">#</a> <code>karger_min_cut_count</code></h3>
<p><code>karger_min_cut_count</code> — count of <code>karger min cut</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p karger_min_cut_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-karger-step">
<h3><a class="doc-anchor" href="#doc-karger-step">#</a> <code>karger_step</code></h3>
<p><code>karger_step</code> — single-step update of <code>karger</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p karger_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-karhunen-loeve-step">
<h3><a class="doc-anchor" href="#doc-karhunen-loeve-step">#</a> <code>karhunen_loeve_step</code></h3>
<p><code>karhunen_loeve_step</code> — single-step update of <code>karhunen loeve</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p karhunen_loeve_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kasiski-repeats">
<h3><a class="doc-anchor" href="#doc-kasiski-repeats">#</a> <code>kasiski_repeats</code></h3>
<p><code>kasiski_repeats</code> — operation <code>kasiski repeats</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p kasiski_repeats $x
</code></pre>
</article>
<article class="doc-entry" id="doc-katz-centrality">
<h3><a class="doc-anchor" href="#doc-katz-centrality">#</a> <code>katz_centrality</code></h3>
<p><code>katz_centrality</code> — operation <code>katz centrality</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p katz_centrality $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kauffman-bracket-eval">
<h3><a class="doc-anchor" href="#doc-kauffman-bracket-eval">#</a> <code>kauffman_bracket_eval</code></h3>
<p><code>kauffman_bracket_eval</code> — operation <code>kauffman bracket eval</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p kauffman_bracket_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kb-to-b">
<h3><a class="doc-anchor" href="#doc-kb-to-b">#</a> <code>kb_to_b</code></h3>
<p><code>kb_to_b</code> — convert from <code>kb</code> to <code>b</code>. Alias for <code>kb_to_bytes</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p kb_to_b $value
</code></pre>
</article>
<article class="doc-entry" id="doc-kb-to-bytes">
<h3><a class="doc-anchor" href="#doc-kb-to-bytes">#</a> <code>kb_to_bytes</code></h3>
<p><code>kb_to_bytes</code> — convert from <code>kb</code> to <code>bytes</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p kb_to_bytes $value
</code></pre>
</article>
<article class="doc-entry" id="doc-kb-to-mb">
<h3><a class="doc-anchor" href="#doc-kb-to-mb">#</a> <code>kb_to_mb</code></h3>
<p><code>kb_to_mb</code> — convert from <code>kb</code> to <code>mb</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p kb_to_mb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-kc-from-rates">
<h3><a class="doc-anchor" href="#doc-kc-from-rates">#</a> <code>kc_from_rates</code></h3>
<p><code>kc_from_rates</code> — operation <code>kc from rates</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p kc_from_rates $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kcoulomb">
<h3><a class="doc-anchor" href="#doc-kcoulomb">#</a> <code>kcoulomb</code></h3>
<p><code>kcoulomb</code> — operation <code>kcoulomb</code>. Alias for <code>coulomb_constant</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p kcoulomb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kde-bandwidth-lscv">
<h3><a class="doc-anchor" href="#doc-kde-bandwidth-lscv">#</a> <code>kde_bandwidth_lscv</code></h3>
<p><code>kde_bandwidth_lscv</code> — kernel density estimator <code>bandwidth lscv</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p kde_bandwidth_lscv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kde-biweight">
<h3><a class="doc-anchor" href="#doc-kde-biweight">#</a> <code>kde_biweight</code></h3>
<p><code>kde_biweight</code> — kernel density estimator <code>biweight</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p kde_biweight $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kde-cosine">
<h3><a class="doc-anchor" href="#doc-kde-cosine">#</a> <code>kde_cosine</code></h3>
<p><code>kde_cosine</code> — kernel density estimator <code>cosine</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p kde_cosine $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kde-epanechnikov">
<h3><a class="doc-anchor" href="#doc-kde-epanechnikov">#</a> <code>kde_epanechnikov</code></h3>
<p><code>kde_epanechnikov</code> — kernel density estimator <code>epanechnikov</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p kde_epanechnikov $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kde-gaussian-2d">
<h3><a class="doc-anchor" href="#doc-kde-gaussian-2d">#</a> <code>kde_gaussian_2d</code></h3>
<p><code>kde_gaussian_2d</code> — kernel density estimator <code>gaussian 2d</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p kde_gaussian_2d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kde-logistic-kernel">
<h3><a class="doc-anchor" href="#doc-kde-logistic-kernel">#</a> <code>kde_logistic_kernel</code></h3>
<p><code>kde_logistic_kernel</code> — kernel density estimator <code>logistic kernel</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p kde_logistic_kernel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kde-scott-bw">
<h3><a class="doc-anchor" href="#doc-kde-scott-bw">#</a> <code>kde_scott_bw</code></h3>
<p><code>kde_scott_bw</code> — kernel density estimator <code>scott bw</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p kde_scott_bw $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kde-silverman-bw">
<h3><a class="doc-anchor" href="#doc-kde-silverman-bw">#</a> <code>kde_silverman_bw</code></h3>
<p><code>kde_silverman_bw</code> — kernel density estimator <code>silverman bw</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p kde_silverman_bw $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kde-triangular">
<h3><a class="doc-anchor" href="#doc-kde-triangular">#</a> <code>kde_triangular</code></h3>
<p><code>kde_triangular</code> — kernel density estimator <code>triangular</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p kde_triangular $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kde-triweight">
<h3><a class="doc-anchor" href="#doc-kde-triweight">#</a> <code>kde_triweight</code></h3>
<p><code>kde_triweight</code> — kernel density estimator <code>triweight</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p kde_triweight $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kde-uniform">
<h3><a class="doc-anchor" href="#doc-kde-uniform">#</a> <code>kde_uniform</code></h3>
<p><code>kde_uniform</code> — kernel density estimator <code>uniform</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p kde_uniform $x
</code></pre>
</article>
<article class="doc-entry" id="doc-keep">
<h3><a class="doc-anchor" href="#doc-keep">#</a> <code>keep</code></h3>
<p><code>keep</code> — operation <code>keep</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p keep $x
</code></pre>
</article>
<article class="doc-entry" id="doc-keep-if">
<h3><a class="doc-anchor" href="#doc-keep-if">#</a> <code>keep_if</code></h3>
<p><code>keep_if</code> — operation <code>keep if</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p keep_if $x
</code></pre>
</article>
<article class="doc-entry" id="doc-keith-q">
<h3><a class="doc-anchor" href="#doc-keith-q">#</a> <code>keith_q</code></h3>
<p><code>keith_q</code> — operation <code>keith q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p keith_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kelly-criterion">
<h3><a class="doc-anchor" href="#doc-kelly-criterion">#</a> <code>kelly_criterion</code></h3>
<p><code>kelly_criterion</code> — operation <code>kelly criterion</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p kelly_criterion $x
</code></pre>
</article>
<article class="doc-entry" id="doc-keltner-lower">
<h3><a class="doc-anchor" href="#doc-keltner-lower">#</a> <code>keltner_lower</code></h3>
<p><code>keltner_lower(highs, lows, closes, period=20, mult=2) → array</code> — <code>ema − mult · atr</code>.</p>
<pre><code class="lang-perl">p keltner_lower(\@hi, \@lo, \@cl, 20, 2)
</code></pre>
</article>
<article class="doc-entry" id="doc-keltner-upper">
<h3><a class="doc-anchor" href="#doc-keltner-upper">#</a> <code>keltner_upper</code></h3>
<p><code>keltner_upper(highs, lows, closes, period=20, mult=2) → array</code> — <code>ema + mult · atr</code>.</p>
<pre><code class="lang-perl">p keltner_upper(\@hi, \@lo, \@cl, 20, 2)
</code></pre>
</article>
<article class="doc-entry" id="doc-kemeny-score-step">
<h3><a class="doc-anchor" href="#doc-kemeny-score-step">#</a> <code>kemeny_score_step</code></h3>
<p><code>kemeny_score_step</code> — single-step update of <code>kemeny score</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p kemeny_score_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kendall">
<h3><a class="doc-anchor" href="#doc-kendall">#</a> <code>kendall</code></h3>
<p><code>kendall_tau</code> (aliases <code>kendall</code>, <code>ktau</code>) computes Kendall's rank correlation coefficient (tau-b).</p>
<pre><code class="lang-perl">p ktau([1,2,3,4], [1,2,4,3]) # 0.67
</code></pre>
</article>
<article class="doc-entry" id="doc-kendalltau">
<h3><a class="doc-anchor" href="#doc-kendalltau">#</a> <code>kendalltau</code></h3>
<p><code>kendalltau</code> — operation <code>kendalltau</code>. Category: *r / scipy distributions and tests*.</p>
<pre><code class="lang-perl">p kendalltau $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kepler-hyperbolic">
<h3><a class="doc-anchor" href="#doc-kepler-hyperbolic">#</a> <code>kepler_hyperbolic</code></h3>
<p><code>kepler_hyperbolic</code> — operation <code>kepler hyperbolic</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p kepler_hyperbolic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kepler-period-au">
<h3><a class="doc-anchor" href="#doc-kepler-period-au">#</a> <code>kepler_period_au</code></h3>
<p><code>kepler_period_au</code> — operation <code>kepler period au</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p kepler_period_au $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kerr-ergosphere-eq">
<h3><a class="doc-anchor" href="#doc-kerr-ergosphere-eq">#</a> <code>kerr_ergosphere_eq</code></h3>
<p><code>kerr_ergosphere_eq</code> — operation <code>kerr ergosphere eq</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p kerr_ergosphere_eq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kerr-horizon">
<h3><a class="doc-anchor" href="#doc-kerr-horizon">#</a> <code>kerr_horizon</code></h3>
<p><code>kerr_horizon</code> — operation <code>kerr horizon</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p kerr_horizon $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kerr-newman-charge-term">
<h3><a class="doc-anchor" href="#doc-kerr-newman-charge-term">#</a> <code>kerr_newman_charge_term</code></h3>
<p><code>kerr_newman_charge_term</code> — operation <code>kerr newman charge term</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p kerr_newman_charge_term $x
</code></pre>
</article>
<article class="doc-entry" id="doc-key-signature-flats">
<h3><a class="doc-anchor" href="#doc-key-signature-flats">#</a> <code>key_signature_flats</code></h3>
<p><code>key_signature_flats</code> — operation <code>key signature flats</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p key_signature_flats $x
</code></pre>
</article>
<article class="doc-entry" id="doc-key-signature-for">
<h3><a class="doc-anchor" href="#doc-key-signature-for">#</a> <code>key_signature_for</code></h3>
<p><code>key_signature_for</code> — operation <code>key signature for</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p key_signature_for $x
</code></pre>
</article>
<article class="doc-entry" id="doc-key-signature-sharps">
<h3><a class="doc-anchor" href="#doc-key-signature-sharps">#</a> <code>key_signature_sharps</code></h3>
<p><code>key_signature_sharps</code> — operation <code>key signature sharps</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p key_signature_sharps $x
</code></pre>
</article>
<article class="doc-entry" id="doc-keys-sorted">
<h3><a class="doc-anchor" href="#doc-keys-sorted">#</a> <code>keys_sorted</code></h3>
<p><code>keys_sorted</code> — operation <code>keys sorted</code>. Category: *hash ops*.</p>
<pre><code class="lang-perl">p keys_sorted $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kg-to-lb">
<h3><a class="doc-anchor" href="#doc-kg-to-lb">#</a> <code>kg_to_lb</code></h3>
<p><code>kg_to_lb</code> — convert from <code>kg</code> to <code>lb</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p kg_to_lb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-kg-to-lbs">
<h3><a class="doc-anchor" href="#doc-kg-to-lbs">#</a> <code>kg_to_lbs</code></h3>
<p><code>kg_to_lbs</code> — convert from <code>kg</code> to <code>lbs</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p kg_to_lbs $value
</code></pre>
</article>
<article class="doc-entry" id="doc-kg-to-stone">
<h3><a class="doc-anchor" href="#doc-kg-to-stone">#</a> <code>kg_to_stone</code></h3>
<p><code>kg_to_stone</code> — convert from <code>kg</code> to <code>stone</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p kg_to_stone $value
</code></pre>
</article>
<article class="doc-entry" id="doc-khinchin">
<h3><a class="doc-anchor" href="#doc-khinchin">#</a> <code>khinchin</code></h3>
<p><code>khinchin</code> — operation <code>khinchin</code>. Alias for <code>khinchin_constant</code>. Category: *math constants*.</p>
<pre><code class="lang-perl">p khinchin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-khinchin-constant">
<h3><a class="doc-anchor" href="#doc-khinchin-constant">#</a> <code>khinchin_constant</code></h3>
<p><code>khinchin_constant</code> — operation <code>khinchin constant</code>. Category: *math constants*.</p>
<pre><code class="lang-perl">p khinchin_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-khovanov-q-grading">
<h3><a class="doc-anchor" href="#doc-khovanov-q-grading">#</a> <code>khovanov_q_grading</code></h3>
<p><code>khovanov_q_grading</code> — operation <code>khovanov q grading</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p khovanov_q_grading $x
</code></pre>
</article>
<article class="doc-entry" id="doc-khovanov-rasmussen-s">
<h3><a class="doc-anchor" href="#doc-khovanov-rasmussen-s">#</a> <code>khovanov_rasmussen_s</code></h3>
<p><code>khovanov_rasmussen_s</code> — operation <code>khovanov rasmussen s</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p khovanov_rasmussen_s $x
</code></pre>
</article>
<article class="doc-entry" id="doc-killing-form-su2">
<h3><a class="doc-anchor" href="#doc-killing-form-su2">#</a> <code>killing_form_su2</code></h3>
<p><code>killing_form_su2</code> — operation <code>killing form su2</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p killing_form_su2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-killing-vector-lie-step">
<h3><a class="doc-anchor" href="#doc-killing-vector-lie-step">#</a> <code>killing_vector_lie_step</code></h3>
<p><code>killing_vector_lie_step</code> — single-step update of <code>killing vector lie</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p killing_vector_lie_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kimura-2p-distance">
<h3><a class="doc-anchor" href="#doc-kimura-2p-distance">#</a> <code>kimura_2p_distance</code></h3>
<p><code>kimura_2p_distance</code> — distance / dissimilarity metric of <code>kimura 2p</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p kimura_2p_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kinetic-energy">
<h3><a class="doc-anchor" href="#doc-kinetic-energy">#</a> <code>kinetic_energy</code></h3>
<p><code>kinetic_energy</code> — operation <code>kinetic energy</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p kinetic_energy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kirnberger-iii">
<h3><a class="doc-anchor" href="#doc-kirnberger-iii">#</a> <code>kirnberger_iii</code></h3>
<p><code>kirnberger_iii</code> — operation <code>kirnberger iii</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p kirnberger_iii $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kl-divergence-distributions">
<h3><a class="doc-anchor" href="#doc-kl-divergence-distributions">#</a> <code>kl_divergence_distributions</code></h3>
<p><code>kl_divergence_distributions(p, q) → number</code> — discrete KL divergence <code>Σ p·ln(p/q)</code>.</p>
</article>
<article class="doc-entry" id="doc-kleibers-law">
<h3><a class="doc-anchor" href="#doc-kleibers-law">#</a> <code>kleibers_law</code></h3>
<p><code>kleibers_law</code> — operation <code>kleibers law</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p kleibers_law $x
</code></pre>
</article>
<article class="doc-entry" id="doc-km-to-miles">
<h3><a class="doc-anchor" href="#doc-km-to-miles">#</a> <code>km_to_miles</code></h3>
<p><code>km_to_miles</code> — convert from <code>km</code> to <code>miles</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p km_to_miles $value
</code></pre>
</article>
<article class="doc-entry" id="doc-kmeans">
<h3><a class="doc-anchor" href="#doc-kmeans">#</a> <code>kmeans</code></h3>
<p><code>kmeans</code> — k-means clustering (Lloyd's algorithm). Takes array of points and k. Returns cluster assignments. Like R's kmeans().</p>
<pre><code class="lang-perl">my @clusters = @{kmeans([[0,0],[1,0],[10,10],[11,10]], 2)}
# [0,0,1,1] — two clusters
</code></pre>
</article>
<article class="doc-entry" id="doc-kmer-jaccard">
<h3><a class="doc-anchor" href="#doc-kmer-jaccard">#</a> <code>kmer_jaccard</code></h3>
<p><code>kmer_jaccard</code> — operation <code>kmer jaccard</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p kmer_jaccard $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kmh-to-mph">
<h3><a class="doc-anchor" href="#doc-kmh-to-mph">#</a> <code>kmh_to_mph</code></h3>
<p><code>kmh_to_mph</code> — convert from <code>kmh</code> to <code>mph</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p kmh_to_mph $value
</code></pre>
</article>
<article class="doc-entry" id="doc-kmh-to-mps">
<h3><a class="doc-anchor" href="#doc-kmh-to-mps">#</a> <code>kmh_to_mps</code></h3>
<p><code>kmh_to_mps</code> — convert from <code>kmh</code> to <code>mps</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p kmh_to_mps $value
</code></pre>
</article>
<article class="doc-entry" id="doc-kmp">
<h3><a class="doc-anchor" href="#doc-kmp">#</a> <code>kmp</code></h3>
<p><code>kmp</code> — operation <code>kmp</code>. Alias for <code>kmp_failure</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p kmp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kmp-failure">
<h3><a class="doc-anchor" href="#doc-kmp-failure">#</a> <code>kmp_failure</code></h3>
<p><code>kmp_failure</code> — operation <code>kmp failure</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p kmp_failure $x
</code></pre>
</article>
<article class="doc-entry" id="doc-knapsack-01-dp-value">
<h3><a class="doc-anchor" href="#doc-knapsack-01-dp-value">#</a> <code>knapsack_01_dp_value</code></h3>
<p><code>knapsack_01_dp_value</code> — knapsack DP variant <code>01 dp value</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p knapsack_01_dp_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-knapsack-branch-bound">
<h3><a class="doc-anchor" href="#doc-knapsack-branch-bound">#</a> <code>knapsack_branch_bound</code></h3>
<p><code>knapsack_branch_bound</code> — knapsack DP variant <code>branch bound</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p knapsack_branch_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-knapsack-fractional">
<h3><a class="doc-anchor" href="#doc-knapsack-fractional">#</a> <code>knapsack_fractional</code></h3>
<p><code>knapsack_fractional(values, weights, capacity) → number</code> — greedy fractional knapsack by value-density.</p>
<pre><code class="lang-perl">p knapsack_fractional([60,100,120], [10,20,30], 50) # 240
</code></pre>
</article>
<article class="doc-entry" id="doc-knapsack-fractional-step">
<h3><a class="doc-anchor" href="#doc-knapsack-fractional-step">#</a> <code>knapsack_fractional_step</code></h3>
<p><code>knapsack_fractional_step</code> — knapsack DP variant <code>fractional step</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p knapsack_fractional_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-knapsack-lp-relaxation">
<h3><a class="doc-anchor" href="#doc-knapsack-lp-relaxation">#</a> <code>knapsack_lp_relaxation</code></h3>
<p><code>knapsack_lp_relaxation</code> — knapsack DP variant <code>lp relaxation</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p knapsack_lp_relaxation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-knapsack-unbounded">
<h3><a class="doc-anchor" href="#doc-knapsack-unbounded">#</a> <code>knapsack_unbounded</code></h3>
<p><code>knapsack_unbounded(values, weights, capacity) → int</code> — unbounded 0/∞ knapsack DP.</p>
<pre><code class="lang-perl">p knapsack_unbounded([60,100,120], [10,20,30], 50) # 300
</code></pre>
</article>
<article class="doc-entry" id="doc-knapsack-unbounded-dp">
<h3><a class="doc-anchor" href="#doc-knapsack-unbounded-dp">#</a> <code>knapsack_unbounded_dp</code></h3>
<p><code>knapsack_unbounded_dp</code> — knapsack DP variant <code>unbounded dp</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p knapsack_unbounded_dp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-knots-to-kmh">
<h3><a class="doc-anchor" href="#doc-knots-to-kmh">#</a> <code>knots_to_kmh</code></h3>
<p><code>knots_to_kmh</code> — convert from <code>knots</code> to <code>kmh</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p knots_to_kmh $value
</code></pre>
</article>
<article class="doc-entry" id="doc-kohlrausch-law">
<h3><a class="doc-anchor" href="#doc-kohlrausch-law">#</a> <code>kohlrausch_law</code></h3>
<p><code>kohlrausch_law</code> — operation <code>kohlrausch law</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p kohlrausch_law $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kolmogorov-microscale">
<h3><a class="doc-anchor" href="#doc-kolmogorov-microscale">#</a> <code>kolmogorov_microscale</code></h3>
<p><code>kolmogorov_microscale</code> — operation <code>kolmogorov microscale</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p kolmogorov_microscale $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kolmogorov-smirnov">
<h3><a class="doc-anchor" href="#doc-kolmogorov-smirnov">#</a> <code>kolmogorov_smirnov</code></h3>
<p><code>kolmogorov_smirnov</code> — operation <code>kolmogorov smirnov</code>. Category: *r / scipy distributions and tests*.</p>
<pre><code class="lang-perl">p kolmogorov_smirnov $x
</code></pre>
</article>
<article class="doc-entry" id="doc-komar-mass-step">
<h3><a class="doc-anchor" href="#doc-komar-mass-step">#</a> <code>komar_mass_step</code></h3>
<p><code>komar_mass_step</code> — single-step update of <code>komar mass</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p komar_mass_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kosaraju-scc">
<h3><a class="doc-anchor" href="#doc-kosaraju-scc">#</a> <code>kosaraju_scc</code></h3>
<p><code>kosaraju_scc</code> — operation <code>kosaraju scc</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p kosaraju_scc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kosaraju-step">
<h3><a class="doc-anchor" href="#doc-kosaraju-step">#</a> <code>kosaraju_step</code></h3>
<p><code>kosaraju_step</code> — single-step update of <code>kosaraju</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p kosaraju_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-koutecky-levich-intercept">
<h3><a class="doc-anchor" href="#doc-koutecky-levich-intercept">#</a> <code>koutecky_levich_intercept</code></h3>
<p><code>koutecky_levich_intercept</code> — operation <code>koutecky levich intercept</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p koutecky_levich_intercept $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kp">
<h3><a class="doc-anchor" href="#doc-kp">#</a> <code>kp</code></h3>
<p><code>kp</code> — operation <code>kp</code>. Alias for <code>keep</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p kp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kp-from-kc">
<h3><a class="doc-anchor" href="#doc-kp-from-kc">#</a> <code>kp_from_kc</code></h3>
<p><code>kp_from_kc</code> — operation <code>kp from kc</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p kp_from_kc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kpss-test">
<h3><a class="doc-anchor" href="#doc-kpss-test">#</a> <code>kpss_test</code></h3>
<p><code>kpss_test</code> — statistical test of <code>kpss</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p kpss_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kpss-test-stat">
<h3><a class="doc-anchor" href="#doc-kpss-test-stat">#</a> <code>kpss_test_stat</code></h3>
<p><code>kpss_test_stat</code> — operation <code>kpss test stat</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p kpss_test_stat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kraus-apply">
<h3><a class="doc-anchor" href="#doc-kraus-apply">#</a> <code>kraus_apply</code></h3>
<p><code>kraus_apply</code> — operation <code>kraus apply</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p kraus_apply $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kretschmann-schwarzschild">
<h3><a class="doc-anchor" href="#doc-kretschmann-schwarzschild">#</a> <code>kretschmann_schwarzschild</code></h3>
<p><code>kretschmann_schwarzschild</code> — operation <code>kretschmann schwarzschild</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p kretschmann_schwarzschild $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kron-product">
<h3><a class="doc-anchor" href="#doc-kron-product">#</a> <code>kron_product</code></h3>
<p><code>kron_product</code> — operation <code>kron product</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p kron_product $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kronecker-four">
<h3><a class="doc-anchor" href="#doc-kronecker-four">#</a> <code>kronecker_four</code></h3>
<p><code>kronecker_four</code> — operation <code>kronecker four</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p kronecker_four $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kronecker-three">
<h3><a class="doc-anchor" href="#doc-kronecker-three">#</a> <code>kronecker_three</code></h3>
<p><code>kronecker_three</code> — operation <code>kronecker three</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p kronecker_three $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kruskal-h">
<h3><a class="doc-anchor" href="#doc-kruskal-h">#</a> <code>kruskal_h</code></h3>
<p><code>kruskal_h</code> — operation <code>kruskal h</code>. Category: *r / scipy distributions and tests*.</p>
<pre><code class="lang-perl">p kruskal_h $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kruskal-step">
<h3><a class="doc-anchor" href="#doc-kruskal-step">#</a> <code>kruskal_step</code></h3>
<p><code>kruskal_step</code> — single-step update of <code>kruskal</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p kruskal_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kruskal-wallis">
<h3><a class="doc-anchor" href="#doc-kruskal-wallis">#</a> <code>kruskal_wallis</code></h3>
<p><code>kruskal_wallis(group1, group2, …) → {statistic, df, p_value}</code> — Kruskal-Wallis H non-parametric multi-group test (rank-based ANOVA).</p>
<pre><code class="lang-perl">p kruskal_wallis(\@g1, \@g2, \@g3)
</code></pre>
</article>
<article class="doc-entry" id="doc-ks">
<h3><a class="doc-anchor" href="#doc-ks">#</a> <code>ks</code></h3>
<p><code>ks_test</code> (alias <code>ks</code>) — two-sample Kolmogorov-Smirnov test. Returns D statistic (max CDF difference). Like R's ks.test().</p>
<pre><code class="lang-perl">my $D = ks([1,2,3,4,5], [2,3,4,5,6]) # small D = similar
</code></pre>
</article>
<article class="doc-entry" id="doc-ks-test-one-sample">
<h3><a class="doc-anchor" href="#doc-ks-test-one-sample">#</a> <code>ks_test_one_sample</code></h3>
<p><code>ks_test_one_sample(xs, mu=0, sigma=1) → {statistic, df, p_value}</code> — Kolmogorov-Smirnov one-sample test against Normal(μ, σ).</p>
<pre><code class="lang-perl">p ks_test_one_sample(\@xs, 0, 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-ks-test-two-sample">
<h3><a class="doc-anchor" href="#doc-ks-test-two-sample">#</a> <code>ks_test_two_sample</code></h3>
<p><code>ks_test_two_sample(a, b) → {statistic, df, p_value}</code> — two-sample KS test on empirical CDFs.</p>
<pre><code class="lang-perl">p ks_test_two_sample(\@x, \@y)
</code></pre>
</article>
<article class="doc-entry" id="doc-ksp-from-concs">
<h3><a class="doc-anchor" href="#doc-ksp-from-concs">#</a> <code>ksp_from_concs</code></h3>
<p><code>ksp_from_concs</code> — operation <code>ksp from concs</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p ksp_from_concs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kth-largest">
<h3><a class="doc-anchor" href="#doc-kth-largest">#</a> <code>kth_largest</code></h3>
<p><code>kth_largest</code> — operation <code>kth largest</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p kth_largest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kth-smallest">
<h3><a class="doc-anchor" href="#doc-kth-smallest">#</a> <code>kth_smallest</code></h3>
<p><code>kth_smallest</code> — operation <code>kth smallest</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p kth_smallest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kthl">
<h3><a class="doc-anchor" href="#doc-kthl">#</a> <code>kthl</code></h3>
<p><code>kthl</code> — operation <code>kthl</code>. Alias for <code>kth_largest</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p kthl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kths">
<h3><a class="doc-anchor" href="#doc-kths">#</a> <code>kths</code></h3>
<p><code>kths</code> — operation <code>kths</code>. Alias for <code>kth_smallest</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p kths $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kullback-jensen-div">
<h3><a class="doc-anchor" href="#doc-kullback-jensen-div">#</a> <code>kullback_jensen_div</code></h3>
<p><code>kullback_jensen_div</code> — operation <code>kullback jensen div</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p kullback_jensen_div $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kurt">
<h3><a class="doc-anchor" href="#doc-kurt">#</a> <code>kurt</code></h3>
<p><code>kurt</code> — operation <code>kurt</code>. Alias for <code>kurtosis</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p kurt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kurtosis">
<h3><a class="doc-anchor" href="#doc-kurtosis">#</a> <code>kurtosis</code></h3>
<p><code>kurtosis</code> — operation <code>kurtosis</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p kurtosis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kv">
<h3><a class="doc-anchor" href="#doc-kv">#</a> <code>kv</code></h3>
<p><code>kv</code> — operation <code>kv</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p kv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-kwh-to-joules">
<h3><a class="doc-anchor" href="#doc-kwh-to-joules">#</a> <code>kwh_to_joules</code></h3>
<p><code>kwh_to_joules</code> — convert from <code>kwh</code> to <code>joules</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p kwh_to_joules $value
</code></pre>
</article>
<article class="doc-entry" id="doc-l1-coherence">
<h3><a class="doc-anchor" href="#doc-l1-coherence">#</a> <code>l1_coherence</code></h3>
<p><code>l1_coherence</code> — operation <code>l1 coherence</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p l1_coherence $x
</code></pre>
</article>
<article class="doc-entry" id="doc-l1-norm">
<h3><a class="doc-anchor" href="#doc-l1-norm">#</a> <code>l1_norm</code></h3>
<p><code>l1_norm</code> — norm (vector length-like) of <code>l1</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p l1_norm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-l2-norm">
<h3><a class="doc-anchor" href="#doc-l2-norm">#</a> <code>l2_norm</code></h3>
<p><code>l2_norm</code> — norm (vector length-like) of <code>l2</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p l2_norm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-l-parallel">
<h3><a class="doc-anchor" href="#doc-l-parallel">#</a> <code>l_parallel</code></h3>
<p><code>l_parallel</code> — operation <code>l parallel</code>. Alias for <code>inductance_parallel</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p l_parallel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-l-series">
<h3><a class="doc-anchor" href="#doc-l-series">#</a> <code>l_series</code></h3>
<p><code>l_series</code> — operation <code>l series</code>. Alias for <code>inductance_series</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p l_series $x
</code></pre>
</article>
<article class="doc-entry" id="doc-label-propagation">
<h3><a class="doc-anchor" href="#doc-label-propagation">#</a> <code>label_propagation</code></h3>
<p><code>label_propagation</code> — operation <code>label propagation</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p label_propagation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-label-propagation-step">
<h3><a class="doc-anchor" href="#doc-label-propagation-step">#</a> <code>label_propagation_step</code></h3>
<p><code>label_propagation_step</code> — single-step update of <code>label propagation</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p label_propagation_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lag-series">
<h3><a class="doc-anchor" href="#doc-lag-series">#</a> <code>lag_series</code></h3>
<p><code>lag_series</code> — operation <code>lag series</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p lag_series $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lagrange">
<h3><a class="doc-anchor" href="#doc-lagrange">#</a> <code>lagrange</code></h3>
<p><code>lagrange_interp</code> (aliases <code>lagrange</code>, <code>linterp</code>) performs Lagrange polynomial interpolation. Takes xs, ys, and a query point x.</p>
<pre><code class="lang-perl">p lagrange([0,1,2], [0,1,4], 1.5) # 2.25
</code></pre>
</article>
<article class="doc-entry" id="doc-lagrange-l1">
<h3><a class="doc-anchor" href="#doc-lagrange-l1">#</a> <code>lagrange_l1</code></h3>
<p><code>lagrange_l1</code> — operation <code>lagrange l1</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p lagrange_l1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lagrangian-dual-step">
<h3><a class="doc-anchor" href="#doc-lagrangian-dual-step">#</a> <code>lagrangian_dual_step</code></h3>
<p><code>lagrangian_dual_step</code> — single-step update of <code>lagrangian dual</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p lagrangian_dual_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lagrangian-relax-step">
<h3><a class="doc-anchor" href="#doc-lagrangian-relax-step">#</a> <code>lagrangian_relax_step</code></h3>
<p><code>lagrangian_relax_step</code> — single-step update of <code>lagrangian relax</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p lagrangian_relax_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lalr-lookahead-compute">
<h3><a class="doc-anchor" href="#doc-lalr-lookahead-compute">#</a> <code>lalr_lookahead_compute</code></h3>
<p><code>lalr_lookahead_compute</code> — operation <code>lalr lookahead compute</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p lalr_lookahead_compute $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lambert-azimuthal-project">
<h3><a class="doc-anchor" href="#doc-lambert-azimuthal-project">#</a> <code>lambert_azimuthal_project</code></h3>
<p><code>lambert_azimuthal_project</code> — operation <code>lambert azimuthal project</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p lambert_azimuthal_project $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lambert-project">
<h3><a class="doc-anchor" href="#doc-lambert-project">#</a> <code>lambert_project</code></h3>
<p><code>lambert_project(lat, lon, lat0, lon0) → [x, y]</code> — Lambert Conformal Conic on a sphere with one standard parallel <code>lat0</code> and central meridian <code>lon0</code>. Degenerates to equirectangular when <code>lat0 ≈ 0</code>.</p>
<pre><code class="lang-perl">p lambert_project(37, -122, 40, -100)
</code></pre>
</article>
<article class="doc-entry" id="doc-lambert-simple">
<h3><a class="doc-anchor" href="#doc-lambert-simple">#</a> <code>lambert_simple</code></h3>
<p><code>lambert_simple</code> — operation <code>lambert simple</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p lambert_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lambert-w">
<h3><a class="doc-anchor" href="#doc-lambert-w">#</a> <code>lambert_w</code></h3>
<p><code>lambert_w</code> (aliases <code>lambertw</code>, <code>productlog</code>) computes the Lambert W function (principal branch): the inverse of f(w) = w·e^w.</p>
<pre><code class="lang-perl">p lambertw(1) # 0.5671 (Omega constant)
p lambertw(exp(1)) # 1.0
</code></pre>
</article>
<article class="doc-entry" id="doc-lambert-w0">
<h3><a class="doc-anchor" href="#doc-lambert-w0">#</a> <code>lambert_w0</code></h3>
<p><code>lambert_w0</code> — operation <code>lambert w0</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p lambert_w0 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lander-waterman-gaps">
<h3><a class="doc-anchor" href="#doc-lander-waterman-gaps">#</a> <code>lander_waterman_gaps</code></h3>
<p><code>lander_waterman_gaps</code> — operation <code>lander waterman gaps</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p lander_waterman_gaps $x
</code></pre>
</article>
<article class="doc-entry" id="doc-language-iso-639-1">
<h3><a class="doc-anchor" href="#doc-language-iso-639-1">#</a> <code>language_iso_639_1</code></h3>
<p><code>language_iso_639_1(name_or_code) → string</code> — ISO 639-1 two-letter code.</p>
<pre><code class="lang-perl">p language_iso_639_1("English") # "en"
</code></pre>
</article>
<article class="doc-entry" id="doc-language-iso-639-2">
<h3><a class="doc-anchor" href="#doc-language-iso-639-2">#</a> <code>language_iso_639_2</code></h3>
<p><code>language_iso_639_2(name_or_code) → string</code> — ISO 639-2 three-letter code.</p>
</article>
<article class="doc-entry" id="doc-language-iso-639-3">
<h3><a class="doc-anchor" href="#doc-language-iso-639-3">#</a> <code>language_iso_639_3</code></h3>
<p><code>language_iso_639_3(name_or_code) → string</code> — ISO 639-3 three-letter code (covers more languages than 639-2).</p>
</article>
<article class="doc-entry" id="doc-language-name">
<h3><a class="doc-anchor" href="#doc-language-name">#</a> <code>language_name</code></h3>
<p><code>language_name(code) → string</code> — human-readable language name for an ISO code.</p>
</article>
<article class="doc-entry" id="doc-language-tag-match">
<h3><a class="doc-anchor" href="#doc-language-tag-match">#</a> <code>language_tag_match</code></h3>
<p><code>language_tag_match(tag, pattern) → 0|1</code> — RFC 4647 basic filter match.</p>
</article>
<article class="doc-entry" id="doc-language-tag-subtags">
<h3><a class="doc-anchor" href="#doc-language-tag-subtags">#</a> <code>language_tag_subtags</code></h3>
<p><code>language_tag_subtags(tag) → array</code> — list of subtags split on '-'.</p>
</article>
<article class="doc-entry" id="doc-laplace-de-rham-step">
<h3><a class="doc-anchor" href="#doc-laplace-de-rham-step">#</a> <code>laplace_de_rham_step</code></h3>
<p><code>laplace_de_rham_step</code> — single-step update of <code>laplace de rham</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p laplace_de_rham_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-laplace-pdf">
<h3><a class="doc-anchor" href="#doc-laplace-pdf">#</a> <code>laplace_pdf</code></h3>
<p><code>laplace_pdf</code> (alias <code>laplacepdf</code>) evaluates the Laplace distribution PDF at x with location mu and scale b.</p>
<pre><code class="lang-perl">p laplacepdf(0, 0, 1) # 0.5 (peak)
</code></pre>
</article>
<article class="doc-entry" id="doc-laplacian-kernel">
<h3><a class="doc-anchor" href="#doc-laplacian-kernel">#</a> <code>laplacian_kernel</code></h3>
<p><code>laplacian_kernel() → matrix</code> — 4-connected discrete Laplacian.</p>
</article>
<article class="doc-entry" id="doc-laplacian-kernel-value">
<h3><a class="doc-anchor" href="#doc-laplacian-kernel-value">#</a> <code>laplacian_kernel_value</code></h3>
<p><code>laplacian_kernel_value</code> — value of <code>laplacian kernel</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p laplacian_kernel_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-larmor-frequency">
<h3><a class="doc-anchor" href="#doc-larmor-frequency">#</a> <code>larmor_frequency</code></h3>
<p><code>larmor_frequency</code> — operation <code>larmor frequency</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p larmor_frequency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-last-arg">
<h3><a class="doc-anchor" href="#doc-last-arg">#</a> <code>last_arg</code></h3>
<p><code>last_arg</code> — operation <code>last arg</code>. Category: *functional primitives*.</p>
<pre><code class="lang-perl">p last_arg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-last-clj">
<h3><a class="doc-anchor" href="#doc-last-clj">#</a> <code>last_clj</code></h3>
<p><code>last_clj</code> — operation <code>last clj</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p last_clj $x
</code></pre>
</article>
<article class="doc-entry" id="doc-last-elem">
<h3><a class="doc-anchor" href="#doc-last-elem">#</a> <code>last_elem</code></h3>
<p><code>last_elem</code> — operation <code>last elem</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p last_elem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-last-eq">
<h3><a class="doc-anchor" href="#doc-last-eq">#</a> <code>last_eq</code></h3>
<p><code>last_eq</code> — operation <code>last eq</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p last_eq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-last-index-of">
<h3><a class="doc-anchor" href="#doc-last-index-of">#</a> <code>last_index_of</code></h3>
<p><code>last_index_of</code> — operation <code>last index of</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p last_index_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-last-of-month">
<h3><a class="doc-anchor" href="#doc-last-of-month">#</a> <code>last_of_month</code></h3>
<p><code>last_of_month</code> — operation <code>last of month</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p last_of_month $x
</code></pre>
</article>
<article class="doc-entry" id="doc-last-word">
<h3><a class="doc-anchor" href="#doc-last-word">#</a> <code>last_word</code></h3>
<p><code>last_word</code> — operation <code>last word</code>. Category: *string*.</p>
<pre><code class="lang-perl">p last_word $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lastc">
<h3><a class="doc-anchor" href="#doc-lastc">#</a> <code>lastc</code></h3>
<p><code>lastc</code> — operation <code>lastc</code>. Alias for <code>last_clj</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p lastc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lat-lng-to-tile-xyz">
<h3><a class="doc-anchor" href="#doc-lat-lng-to-tile-xyz">#</a> <code>lat_lng_to_tile_xyz</code></h3>
<p><code>lat_lng_to_tile_xyz</code> — convert from <code>lat lng</code> to <code>tile xyz</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p lat_lng_to_tile_xyz $value
</code></pre>
</article>
<article class="doc-entry" id="doc-lat-lng-to-xy-lambert">
<h3><a class="doc-anchor" href="#doc-lat-lng-to-xy-lambert">#</a> <code>lat_lng_to_xy_lambert</code></h3>
<p><code>lat_lng_to_xy_lambert</code> — convert from <code>lat lng</code> to <code>xy lambert</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p lat_lng_to_xy_lambert $value
</code></pre>
</article>
<article class="doc-entry" id="doc-lat-lng-to-xy-mercator">
<h3><a class="doc-anchor" href="#doc-lat-lng-to-xy-mercator">#</a> <code>lat_lng_to_xy_mercator</code></h3>
<p><code>lat_lng_to_xy_mercator</code> — convert from <code>lat lng</code> to <code>xy mercator</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p lat_lng_to_xy_mercator $value
</code></pre>
</article>
<article class="doc-entry" id="doc-lat-lon-to-utm">
<h3><a class="doc-anchor" href="#doc-lat-lon-to-utm">#</a> <code>lat_lon_to_utm</code></h3>
<p><code>lat_lon_to_utm(lat, lon) → [zone, easting_m, northing_m, hemi]</code> — convert geographic to UTM coordinates (WGS84 ellipsoid).</p>
<pre><code class="lang-perl">p lat_lon_to_utm(40.7128, -74.006) # [18, 583959, 4507351, "N"]
</code></pre>
</article>
<article class="doc-entry" id="doc-latency-ms">
<h3><a class="doc-anchor" href="#doc-latency-ms">#</a> <code>latency_ms</code></h3>
<p><code>latency_ms</code> — operation <code>latency ms</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p latency_ms $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lattice-paths">
<h3><a class="doc-anchor" href="#doc-lattice-paths">#</a> <code>lattice_paths</code></h3>
<p><code>lattice_paths(m, n) → int</code> — monotonic lattice paths from (0,0) to (m,n) = <code>C(m+n, m)</code>.</p>
<pre><code class="lang-perl">p lattice_paths(3, 3) # 20
</code></pre>
</article>
<article class="doc-entry" id="doc-lax-friedrichs-flux">
<h3><a class="doc-anchor" href="#doc-lax-friedrichs-flux">#</a> <code>lax_friedrichs_flux</code></h3>
<p><code>lax_friedrichs_flux</code> — operation <code>lax friedrichs flux</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p lax_friedrichs_flux $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lax-wendroff-flux">
<h3><a class="doc-anchor" href="#doc-lax-wendroff-flux">#</a> <code>lax_wendroff_flux</code></h3>
<p><code>lax_wendroff_flux</code> — operation <code>lax wendroff flux</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p lax_wendroff_flux $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lazy-caterer">
<h3><a class="doc-anchor" href="#doc-lazy-caterer">#</a> <code>lazy_caterer</code></h3>
<p><code>lazy_caterer</code> — operation <code>lazy caterer</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lazy_caterer $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lb-to-kg">
<h3><a class="doc-anchor" href="#doc-lb-to-kg">#</a> <code>lb_to_kg</code></h3>
<p><code>lb_to_kg</code> — convert from <code>lb</code> to <code>kg</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p lb_to_kg $value
</code></pre>
</article>
<article class="doc-entry" id="doc-lbf-to-newtons">
<h3><a class="doc-anchor" href="#doc-lbf-to-newtons">#</a> <code>lbf_to_newtons</code></h3>
<p><code>lbf_to_newtons</code> — convert from <code>lbf</code> to <code>newtons</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p lbf_to_newtons $value
</code></pre>
</article>
<article class="doc-entry" id="doc-lbound">
<h3><a class="doc-anchor" href="#doc-lbound">#</a> <code>lbound</code></h3>
<p><code>lbound</code> — operation <code>lbound</code>. Alias for <code>lower_bound</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p lbound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lbs-to-kg">
<h3><a class="doc-anchor" href="#doc-lbs-to-kg">#</a> <code>lbs_to_kg</code></h3>
<p><code>lbs_to_kg</code> — convert from <code>lbs</code> to <code>kg</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p lbs_to_kg $value
</code></pre>
</article>
<article class="doc-entry" id="doc-lc-frequency">
<h3><a class="doc-anchor" href="#doc-lc-frequency">#</a> <code>lc_frequency</code></h3>
<p><code>lc_frequency</code> — operation <code>lc frequency</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p lc_frequency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lc-lines">
<h3><a class="doc-anchor" href="#doc-lc-lines">#</a> <code>lc_lines</code></h3>
<p><code>lc_lines</code> — operation <code>lc lines</code>. Alias for <code>line_count</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p lc_lines $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lc-omega">
<h3><a class="doc-anchor" href="#doc-lc-omega">#</a> <code>lc_omega</code></h3>
<p><code>lc_omega</code> — operation <code>lc omega</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p lc_omega $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lc-resonant">
<h3><a class="doc-anchor" href="#doc-lc-resonant">#</a> <code>lc_resonant</code></h3>
<p><code>lc_resonant</code> — operation <code>lc resonant</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lc_resonant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lcdm-eos">
<h3><a class="doc-anchor" href="#doc-lcdm-eos">#</a> <code>lcdm_eos</code></h3>
<p><code>lcdm_eos</code> — operation <code>lcdm eos</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p lcdm_eos $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lcg-next-u32">
<h3><a class="doc-anchor" href="#doc-lcg-next-u32">#</a> <code>lcg_next_u32</code></h3>
<p><code>lcg_next_u32</code> — operation <code>lcg next u32</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lcg_next_u32 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lcg-numrec-step">
<h3><a class="doc-anchor" href="#doc-lcg-numrec-step">#</a> <code>lcg_numrec_step</code></h3>
<p><code>lcg_numrec_step</code> — single-step update of <code>lcg numrec</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p lcg_numrec_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lch-to-rgb">
<h3><a class="doc-anchor" href="#doc-lch-to-rgb">#</a> <code>lch_to_rgb</code></h3>
<p><code>lch_to_rgb([L, C, H]) → [r, g, b]</code> — inverse of <code>rgb_to_lch</code>. Output is clamped sRGB 0-255.</p>
</article>
<article class="doc-entry" id="doc-lcm">
<h3><a class="doc-anchor" href="#doc-lcm">#</a> <code>lcm</code></h3>
<p><code>lcm</code> — operation <code>lcm</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p lcm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lcontract">
<h3><a class="doc-anchor" href="#doc-lcontract">#</a> <code>lcontract</code></h3>
<p><code>length_contraction($proper_length, $velocity)</code> (alias <code>lcontract</code>) — contracted length L = L₀ × √(1-v²/c²).</p>
<pre><code class="lang-perl">p lcontract(1, 0.99 * 3e8) # ~0.14 m (1m at 99% c)
</code></pre>
</article>
<article class="doc-entry" id="doc-lcount">
<h3><a class="doc-anchor" href="#doc-lcount">#</a> <code>lcount</code></h3>
<p><code>lcount</code> — operation <code>lcount</code>. Alias for <code>count_lines</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p lcount $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lcp">
<h3><a class="doc-anchor" href="#doc-lcp">#</a> <code>lcp</code></h3>
<p><code>lcp</code> — operation <code>lcp</code>. Alias for <code>longest_common_prefix</code>. Category: *string*.</p>
<pre><code class="lang-perl">p lcp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lcp-array">
<h3><a class="doc-anchor" href="#doc-lcp-array">#</a> <code>lcp_array</code></h3>
<p><code>lcp_array</code> — operation <code>lcp array</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lcp_array $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lcs-length">
<h3><a class="doc-anchor" href="#doc-lcs-length">#</a> <code>lcs_length</code></h3>
<p><code>lcs_length</code> — operation <code>lcs length</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p lcs_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lcseq">
<h3><a class="doc-anchor" href="#doc-lcseq">#</a> <code>lcseq</code></h3>
<p><code>lcseq</code> — operation <code>lcseq</code>. Alias for <code>longest_common_subsequence</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p lcseq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lcsub">
<h3><a class="doc-anchor" href="#doc-lcsub">#</a> <code>lcsub</code></h3>
<p><code>lcsub</code> — operation <code>lcsub</code>. Alias for <code>longest_common_substring</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p lcsub $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ld-d">
<h3><a class="doc-anchor" href="#doc-ld-d">#</a> <code>ld_d</code></h3>
<p><code>ld_d</code> — operation <code>ld d</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p ld_d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ld-r-squared">
<h3><a class="doc-anchor" href="#doc-ld-r-squared">#</a> <code>ld_r_squared</code></h3>
<p><code>ld_r_squared</code> — operation <code>ld r squared</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p ld_r_squared $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ldec">
<h3><a class="doc-anchor" href="#doc-ldec">#</a> <code>ldec</code></h3>
<p><code>ldec</code> — operation <code>ldec</code>. Alias for <code>longest_decreasing</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ldec $x
</code></pre>
</article>
<article class="doc-entry" id="doc-le-chatelier-dir">
<h3><a class="doc-anchor" href="#doc-le-chatelier-dir">#</a> <code>le_chatelier_dir</code></h3>
<p><code>le_chatelier_dir</code> — operation <code>le chatelier dir</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p le_chatelier_dir $x
</code></pre>
</article>
<article class="doc-entry" id="doc-leading-zeros">
<h3><a class="doc-anchor" href="#doc-leading-zeros">#</a> <code>leading_zeros</code></h3>
<p><code>leading_zeros</code> — operation <code>leading zeros</code>. Category: *base conversion*.</p>
<pre><code class="lang-perl">p leading_zeros $x
</code></pre>
</article>
<article class="doc-entry" id="doc-leaky-relu">
<h3><a class="doc-anchor" href="#doc-leaky-relu">#</a> <code>leaky_relu</code></h3>
<p><code>leaky_relu</code> (alias <code>lrelu</code>) applies Leaky ReLU: x if x≥0, alpha*x otherwise (default alpha=0.01).</p>
<pre><code class="lang-perl">p lrelu(5) # 5
p lrelu(-5) # -0.05
p lrelu(-5, 0.1) # -0.5
</code></pre>
</article>
<article class="doc-entry" id="doc-leap-year-gregorian">
<h3><a class="doc-anchor" href="#doc-leap-year-gregorian">#</a> <code>leap_year_gregorian</code></h3>
<p><code>leap_year_gregorian</code> — operation <code>leap year gregorian</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p leap_year_gregorian $x
</code></pre>
</article>
<article class="doc-entry" id="doc-leapfrog-step">
<h3><a class="doc-anchor" href="#doc-leapfrog-step">#</a> <code>leapfrog_step</code></h3>
<p><code>leapfrog_step</code> — single-step update of <code>leapfrog</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p leapfrog_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-least-common">
<h3><a class="doc-anchor" href="#doc-least-common">#</a> <code>least_common</code></h3>
<p><code>least_common</code> — operation <code>least common</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p least_common $x
</code></pre>
</article>
<article class="doc-entry" id="doc-leet">
<h3><a class="doc-anchor" href="#doc-leet">#</a> <code>leet</code></h3>
<p><code>leet</code> — operation <code>leet</code>. Alias for <code>leetspeak</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p leet $x
</code></pre>
</article>
<article class="doc-entry" id="doc-leetspeak">
<h3><a class="doc-anchor" href="#doc-leetspeak">#</a> <code>leetspeak</code></h3>
<p><code>leetspeak</code> — operation <code>leetspeak</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p leetspeak $x
</code></pre>
</article>
<article class="doc-entry" id="doc-left-str">
<h3><a class="doc-anchor" href="#doc-left-str">#</a> <code>left_str</code></h3>
<p><code>left_str</code> — operation <code>left str</code>. Category: *string*.</p>
<pre><code class="lang-perl">p left_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lehmer-mean">
<h3><a class="doc-anchor" href="#doc-lehmer-mean">#</a> <code>lehmer_mean</code></h3>
<p><code>lehmer_mean</code> — arithmetic mean of <code>lehmer</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lehmer_mean @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-lemmatize-lemmy">
<h3><a class="doc-anchor" href="#doc-lemmatize-lemmy">#</a> <code>lemmatize_lemmy</code></h3>
<p><code>lemmatize_lemmy</code> — operation <code>lemmatize lemmy</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p lemmatize_lemmy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lemmatize-wordnet">
<h3><a class="doc-anchor" href="#doc-lemmatize-wordnet">#</a> <code>lemmatize_wordnet</code></h3>
<p><code>lemmatize_wordnet</code> — operation <code>lemmatize wordnet</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p lemmatize_wordnet $x
</code></pre>
</article>
<article class="doc-entry" id="doc-length-each">
<h3><a class="doc-anchor" href="#doc-length-each">#</a> <code>length_each</code></h3>
<p><code>length_each</code> — operation <code>length each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p length_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lens-focal-length">
<h3><a class="doc-anchor" href="#doc-lens-focal-length">#</a> <code>lens_focal_length</code></h3>
<p><code>lens_focal_length</code> — operation <code>lens focal length</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lens_focal_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lens-magnification">
<h3><a class="doc-anchor" href="#doc-lens-magnification">#</a> <code>lens_magnification</code></h3>
<p><code>lens_magnification</code> — operation <code>lens magnification</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p lens_magnification $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lens-power">
<h3><a class="doc-anchor" href="#doc-lens-power">#</a> <code>lens_power</code></h3>
<p><code>lens_power</code> — operation <code>lens power</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p lens_power $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lense-thirring-omega">
<h3><a class="doc-anchor" href="#doc-lense-thirring-omega">#</a> <code>lense_thirring_omega</code></h3>
<p><code>lense_thirring_omega</code> — operation <code>lense thirring omega</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p lense_thirring_omega $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lensing-convergence">
<h3><a class="doc-anchor" href="#doc-lensing-convergence">#</a> <code>lensing_convergence</code></h3>
<p><code>lensing_convergence</code> — operation <code>lensing convergence</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p lensing_convergence $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lensmaker">
<h3><a class="doc-anchor" href="#doc-lensmaker">#</a> <code>lensmaker</code></h3>
<p><code>lensmaker</code> — operation <code>lensmaker</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p lensmaker $x
</code></pre>
</article>
<article class="doc-entry" id="doc-leontief-input">
<h3><a class="doc-anchor" href="#doc-leontief-input">#</a> <code>leontief_input</code></h3>
<p><code>leontief_input</code> — operation <code>leontief input</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p leontief_input $x
</code></pre>
</article>
<article class="doc-entry" id="doc-leontief-output">
<h3><a class="doc-anchor" href="#doc-leontief-output">#</a> <code>leontief_output</code></h3>
<p><code>leontief_output</code> — operation <code>leontief output</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p leontief_output $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lerner-index">
<h3><a class="doc-anchor" href="#doc-lerner-index">#</a> <code>lerner_index</code></h3>
<p><code>lerner_index</code> — index of <code>lerner</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p lerner_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lerp">
<h3><a class="doc-anchor" href="#doc-lerp">#</a> <code>lerp</code></h3>
<p><code>lerp($a, $b, $t)</code> — linear interpolation between a and b. When t=0 returns a, t=1 returns b, t=0.5 returns midpoint.</p>
<pre><code class="lang-perl">p lerp(0, 100, 0.5) # 50
p lerp(10, 20, 0.25) # 12.5
# Animation: smoothly transition between values
for my $t (0:10) { p lerp($start, $end, $t/10) }
</code></pre>
</article>
<article class="doc-entry" id="doc-lerp-color">
<h3><a class="doc-anchor" href="#doc-lerp-color">#</a> <code>lerp_color</code></h3>
<p><code>lerp_color</code> — operation <code>lerp color</code>. Alias for <code>color_blend_t</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lerp_color $x
</code></pre>
</article>
<article class="doc-entry" id="doc-leslie-step">
<h3><a class="doc-anchor" href="#doc-leslie-step">#</a> <code>leslie_step</code></h3>
<p><code>leslie_step</code> — single-step update of <code>leslie</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p leslie_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-less">
<h3><a class="doc-anchor" href="#doc-less">#</a> <code>less</code></h3>
<p><code>LIST |> pager</code> / <code>pager LIST</code> — pipe each element (one per line) into the user's <code>$PAGER</code> (default <code>less -R</code>; falls back to <code>more</code>, then plain stdout). Bypasses the pager when stdout isn't a TTY so pipelines like <code>stryke '... |> pager' | grep</code> still compose.</p>
<p>Blocks until the user quits the pager; returns <code>undef</code>.</p>
<p>Aliases: <code>pager</code>, <code>pg</code>, <code>less</code>.</p>
<pre><code class="lang-perl"># browse every callable spelling interactively
keys %all |> sort |> pager
# filter the reference for parallel ops
keys %b |> grep { $b{_} eq "parallel" } |> pager
# whole file, one screen at a time
slurp("README.md") |> pager
</code></pre>
</article>
<article class="doc-entry" id="doc-letter-frequency">
<h3><a class="doc-anchor" href="#doc-letter-frequency">#</a> <code>letter_frequency</code></h3>
<p><code>letter_frequency</code> — operation <code>letter frequency</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p letter_frequency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-letters-lc">
<h3><a class="doc-anchor" href="#doc-letters-lc">#</a> <code>letters_lc</code></h3>
<p><code>letters_lc</code> extracts only lowercase letters from a string.</p>
<pre><code class="lang-perl">p join "", letters_lc("Hello World 123") # elloorld
</code></pre>
</article>
<article class="doc-entry" id="doc-letters-uc">
<h3><a class="doc-anchor" href="#doc-letters-uc">#</a> <code>letters_uc</code></h3>
<p><code>letters_uc</code> extracts only uppercase letters from a string.</p>
<pre><code class="lang-perl">p join "", letters_uc("Hello World 123") # HW
</code></pre>
</article>
<article class="doc-entry" id="doc-lev">
<h3><a class="doc-anchor" href="#doc-lev">#</a> <code>lev</code></h3>
<p><code>lev</code> — operation <code>lev</code>. Alias for <code>levenshtein</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p lev $x
</code></pre>
</article>
<article class="doc-entry" id="doc-level-k-step">
<h3><a class="doc-anchor" href="#doc-level-k-step">#</a> <code>level_k_step</code></h3>
<p><code>level_k_step</code> — single-step update of <code>level k</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p level_k_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-level-premium">
<h3><a class="doc-anchor" href="#doc-level-premium">#</a> <code>level_premium</code></h3>
<p><code>level_premium</code> — operation <code>level premium</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p level_premium $x
</code></pre>
</article>
<article class="doc-entry" id="doc-levenshtein">
<h3><a class="doc-anchor" href="#doc-levenshtein">#</a> <code>levenshtein</code></h3>
<p><code>levenshtein</code> — operation <code>levenshtein</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p levenshtein $x
</code></pre>
</article>
<article class="doc-entry" id="doc-levenshtein-dist">
<h3><a class="doc-anchor" href="#doc-levenshtein-dist">#</a> <code>levenshtein_dist</code></h3>
<p><code>levenshtein_dist</code> — operation <code>levenshtein dist</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p levenshtein_dist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-levenshtein-edit-path">
<h3><a class="doc-anchor" href="#doc-levenshtein-edit-path">#</a> <code>levenshtein_edit_path</code></h3>
<p><code>levenshtein_edit_path(a, b) → array</code> — edit operations: "match:x->x", "sub:x->y", "ins:y", "del:x".</p>
<pre><code class="lang-perl">p levenshtein_edit_path("kitten", "sitting")
</code></pre>
</article>
<article class="doc-entry" id="doc-levenshtein-normalized">
<h3><a class="doc-anchor" href="#doc-levenshtein-normalized">#</a> <code>levenshtein_normalized</code></h3>
<p><code>levenshtein_normalized</code> — operation <code>levenshtein normalized</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p levenshtein_normalized $x
</code></pre>
</article>
<article class="doc-entry" id="doc-leverage-index">
<h3><a class="doc-anchor" href="#doc-leverage-index">#</a> <code>leverage_index</code></h3>
<p><code>leverage_index</code> — index of <code>leverage</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p leverage_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-levi-civita-four">
<h3><a class="doc-anchor" href="#doc-levi-civita-four">#</a> <code>levi_civita_four</code></h3>
<p><code>levi_civita_four</code> — operation <code>levi civita four</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p levi_civita_four $x
</code></pre>
</article>
<article class="doc-entry" id="doc-levi-civita-three">
<h3><a class="doc-anchor" href="#doc-levi-civita-three">#</a> <code>levi_civita_three</code></h3>
<p><code>levi_civita_three</code> — operation <code>levi civita three</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p levi_civita_three $x
</code></pre>
</article>
<article class="doc-entry" id="doc-levich-current-rde">
<h3><a class="doc-anchor" href="#doc-levich-current-rde">#</a> <code>levich_current_rde</code></h3>
<p><code>levich_current_rde</code> — operation <code>levich current rde</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p levich_current_rde $x
</code></pre>
</article>
<article class="doc-entry" id="doc-levin-t-transform">
<h3><a class="doc-anchor" href="#doc-levin-t-transform">#</a> <code>levin_t_transform</code></h3>
<p><code>levin_t_transform</code> — transform of <code>levin t</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p levin_t_transform $x
</code></pre>
</article>
<article class="doc-entry" id="doc-levy-pdf">
<h3><a class="doc-anchor" href="#doc-levy-pdf">#</a> <code>levy_pdf</code></h3>
<p><code>levy_pdf</code> — operation <code>levy pdf</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p levy_pdf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lewis-dot-count">
<h3><a class="doc-anchor" href="#doc-lewis-dot-count">#</a> <code>lewis_dot_count</code></h3>
<p><code>lewis_dot_count</code> — count of <code>lewis dot</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p lewis_dot_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lex-keyword-classify">
<h3><a class="doc-anchor" href="#doc-lex-keyword-classify">#</a> <code>lex_keyword_classify</code></h3>
<p><code>lex_keyword_classify</code> — operation <code>lex keyword classify</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p lex_keyword_classify $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lexicalized-parse">
<h3><a class="doc-anchor" href="#doc-lexicalized-parse">#</a> <code>lexicalized_parse</code></h3>
<p><code>lexicalized_parse</code> — operation <code>lexicalized parse</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p lexicalized_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lfilter-zi-init">
<h3><a class="doc-anchor" href="#doc-lfilter-zi-init">#</a> <code>lfilter_zi_init</code></h3>
<p><code>lfilter_zi_init</code> — initialise of <code>lfilter zi</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p lfilter_zi_init $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lfrm">
<h3><a class="doc-anchor" href="#doc-lfrm">#</a> <code>lfrm</code></h3>
<p><code>lfrm</code> — operation <code>lfrm</code>. Alias for <code>lines_from</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p lfrm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lfsr-galois-step">
<h3><a class="doc-anchor" href="#doc-lfsr-galois-step">#</a> <code>lfsr_galois_step</code></h3>
<p><code>lfsr_galois_step</code> — single-step update of <code>lfsr galois</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p lfsr_galois_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-li">
<h3><a class="doc-anchor" href="#doc-li">#</a> <code>li</code></h3>
<p><code>li(x) → number</code> — logarithmic integral <code>li(x) = Ei(ln x)</code>. Approximates the prime-counting function π(x).</p>
<pre><code class="lang-perl">p li(100)
</code></pre>
</article>
<article class="doc-entry" id="doc-liang-barsky-clip">
<h3><a class="doc-anchor" href="#doc-liang-barsky-clip">#</a> <code>liang_barsky_clip</code></h3>
<p><code>liang_barsky_clip(p1, p2, [xmin, ymin, xmax, ymax]) → [p1', p2']</code> — line-segment clip against rectangle. Empty result if segment is outside.</p>
<pre><code class="lang-perl">p liang_barsky_clip([0.5,0.5], [0.8,0.8], [0,0,1,1])
</code></pre>
</article>
<article class="doc-entry" id="doc-lie-derivative-scalar-step">
<h3><a class="doc-anchor" href="#doc-lie-derivative-scalar-step">#</a> <code>lie_derivative_scalar_step</code></h3>
<p><code>lie_derivative_scalar_step</code> — single-step update of <code>lie derivative scalar</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p lie_derivative_scalar_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lie-derivative-vector-step">
<h3><a class="doc-anchor" href="#doc-lie-derivative-vector-step">#</a> <code>lie_derivative_vector_step</code></h3>
<p><code>lie_derivative_vector_step</code> — single-step update of <code>lie derivative vector</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p lie_derivative_vector_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lie-split">
<h3><a class="doc-anchor" href="#doc-lie-split">#</a> <code>lie_split</code></h3>
<p><code>lie_split</code> — operation <code>lie split</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p lie_split $x
</code></pre>
</article>
<article class="doc-entry" id="doc-life-expectancy-e0">
<h3><a class="doc-anchor" href="#doc-life-expectancy-e0">#</a> <code>life_expectancy_e0</code></h3>
<p><code>life_expectancy_e0</code> — operation <code>life expectancy e0</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p life_expectancy_e0 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lift-force">
<h3><a class="doc-anchor" href="#doc-lift-force">#</a> <code>lift_force</code></h3>
<p><code>lift_force(Cl, density=1.225, velocity, area) → number</code> — <code>½ · Cl · ρ · v² · A</code>.</p>
</article>
<article class="doc-entry" id="doc-light-deflection-angle">
<h3><a class="doc-anchor" href="#doc-light-deflection-angle">#</a> <code>light_deflection_angle</code></h3>
<p><code>light_deflection_angle</code> — operation <code>light deflection angle</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p light_deflection_angle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-light-year">
<h3><a class="doc-anchor" href="#doc-light-year">#</a> <code>light_year</code></h3>
<p><code>light_year</code> (alias <code>ly</code>) — ly ≈ 9.461×10¹⁵ m. Distance light travels in one year.</p>
<pre><code class="lang-perl">p ly # 9.4607304725808e15 m
p ly / au # ~63241 AU
</code></pre>
</article>
<article class="doc-entry" id="doc-likelihood-ratio-test">
<h3><a class="doc-anchor" href="#doc-likelihood-ratio-test">#</a> <code>likelihood_ratio_test</code></h3>
<p><code>likelihood_ratio_test</code> — statistical test of <code>likelihood ratio</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p likelihood_ratio_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-limiting-current-density">
<h3><a class="doc-anchor" href="#doc-limiting-current-density">#</a> <code>limiting_current_density</code></h3>
<p><code>limiting_current_density</code> — operation <code>limiting current density</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p limiting_current_density $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lin-bairstow-step">
<h3><a class="doc-anchor" href="#doc-lin-bairstow-step">#</a> <code>lin_bairstow_step</code></h3>
<p><code>lin_bairstow_step</code> — single-step update of <code>lin bairstow</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lin_bairstow_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lin-kernighan-step">
<h3><a class="doc-anchor" href="#doc-lin-kernighan-step">#</a> <code>lin_kernighan_step</code></h3>
<p><code>lin_kernighan_step</code> — single-step update of <code>lin kernighan</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p lin_kernighan_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-linc">
<h3><a class="doc-anchor" href="#doc-linc">#</a> <code>linc</code></h3>
<p><code>linc</code> — operation <code>linc</code>. Alias for <code>longest_increasing</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p linc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-line-count">
<h3><a class="doc-anchor" href="#doc-line-count">#</a> <code>line_count</code></h3>
<p><code>line_count</code> — count of <code>line</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p line_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-line-count-simple">
<h3><a class="doc-anchor" href="#doc-line-count-simple">#</a> <code>line_count_simple</code></h3>
<p><code>line_count_simple</code> — operation <code>line count simple</code>. Alias for <code>string_lines_count</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p line_count_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-line-distance-point">
<h3><a class="doc-anchor" href="#doc-line-distance-point">#</a> <code>line_distance_point</code></h3>
<p><code>line_distance_point</code> — operation <code>line distance point</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p line_distance_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-line-intersect">
<h3><a class="doc-anchor" href="#doc-line-intersect">#</a> <code>line_intersect</code></h3>
<p><code>line_intersect</code> — operation <code>line intersect</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p line_intersect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-line-intersection">
<h3><a class="doc-anchor" href="#doc-line-intersection">#</a> <code>line_intersection</code></h3>
<p><code>line_intersection($x1, $y1, $x2, $y2, $x3, $y3, $x4, $y4)</code> — finds the intersection point of two lines defined by points (x1,y1)-(x2,y2) and (x3,y3)-(x4,y4). Returns [$x, $y] or undef if parallel.</p>
<pre><code class="lang-perl">my $pt = line_intersection(0, 0, 1, 1, 0, 1, 1, 0)
p @$pt # (0.5, 0.5)
</code></pre>
</article>
<article class="doc-entry" id="doc-line-segment-intersect">
<h3><a class="doc-anchor" href="#doc-line-segment-intersect">#</a> <code>line_segment_intersect</code></h3>
<p><code>line_segment_intersect</code> — operation <code>line segment intersect</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p line_segment_intersect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-linear-entropy">
<h3><a class="doc-anchor" href="#doc-linear-entropy">#</a> <code>linear_entropy</code></h3>
<p><code>linear_entropy</code> — operation <code>linear entropy</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p linear_entropy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-linear-regression">
<h3><a class="doc-anchor" href="#doc-linear-regression">#</a> <code>linear_regression</code></h3>
<p><code>linear_regression</code> — operation <code>linear regression</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p linear_regression $x
</code></pre>
</article>
<article class="doc-entry" id="doc-linear-search">
<h3><a class="doc-anchor" href="#doc-linear-search">#</a> <code>linear_search</code></h3>
<p><code>linear_search</code> — operation <code>linear search</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p linear_search $x
</code></pre>
</article>
<article class="doc-entry" id="doc-linearized-pb-step">
<h3><a class="doc-anchor" href="#doc-linearized-pb-step">#</a> <code>linearized_pb_step</code></h3>
<p><code>linearized_pb_step</code> — single-step update of <code>linearized pb</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p linearized_pb_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lineintr">
<h3><a class="doc-anchor" href="#doc-lineintr">#</a> <code>lineintr</code></h3>
<p><code>lineintr</code> — operation <code>lineintr</code>. Alias for <code>line_intersection</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p lineintr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lines-from">
<h3><a class="doc-anchor" href="#doc-lines-from">#</a> <code>lines_from</code></h3>
<p><code>lines_from</code> — operation <code>lines from</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p lines_from $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lineweaver-burk">
<h3><a class="doc-anchor" href="#doc-lineweaver-burk">#</a> <code>lineweaver_burk</code></h3>
<p><code>lineweaver_burk</code> — operation <code>lineweaver burk</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lineweaver_burk $x
</code></pre>
</article>
<article class="doc-entry" id="doc-linf-norm">
<h3><a class="doc-anchor" href="#doc-linf-norm">#</a> <code>linf_norm</code></h3>
<p><code>linf_norm</code> — norm (vector length-like) of <code>linf</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p linf_norm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-linking-number-two">
<h3><a class="doc-anchor" href="#doc-linking-number-two">#</a> <code>linking_number_two</code></h3>
<p><code>linking_number_two</code> — operation <code>linking number two</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p linking_number_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-linreg">
<h3><a class="doc-anchor" href="#doc-linreg">#</a> <code>linreg</code></h3>
<p><code>linreg</code> — operation <code>linreg</code>. Alias for <code>linear_regression</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p linreg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-linspace">
<h3><a class="doc-anchor" href="#doc-linspace">#</a> <code>linspace</code></h3>
<p><code>linspace</code> — operation <code>linspace</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p linspace $x
</code></pre>
</article>
<article class="doc-entry" id="doc-liouville">
<h3><a class="doc-anchor" href="#doc-liouville">#</a> <code>liouville</code></h3>
<p><code>liouville</code> — operation <code>liouville</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p liouville $x
</code></pre>
</article>
<article class="doc-entry" id="doc-liquefaction-potential-index">
<h3><a class="doc-anchor" href="#doc-liquefaction-potential-index">#</a> <code>liquefaction_potential_index</code></h3>
<p><code>liquefaction_potential_index</code> — index of <code>liquefaction potential</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p liquefaction_potential_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-list-coloring-step">
<h3><a class="doc-anchor" href="#doc-list-coloring-step">#</a> <code>list_coloring_step</code></h3>
<p><code>list_coloring_step</code> — list helper <code>coloring step</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p list_coloring_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-list-compact">
<h3><a class="doc-anchor" href="#doc-list-compact">#</a> <code>list_compact</code></h3>
<p><code>list_compact</code> — list helper <code>compact</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p list_compact $x
</code></pre>
</article>
<article class="doc-entry" id="doc-list-count">
<h3><a class="doc-anchor" href="#doc-list-count">#</a> <code>list_count</code></h3>
<p><code>list_count</code> (alias <code>list_size</code>) returns the total number of elements after flattening a nested list structure. Unlike <code>count</code> which returns the top-level element count, <code>list_count</code> recursively descends into array references and counts only leaf values. This is useful when you have a list of lists and need to know the total number of individual items rather than the number of sublists.</p>
<pre><code class="lang-perl">my @nested = ([1, 2], [3, 4, 5], [6])
p list_count @nested # 6
my @deep = ([1, [2, 3]], [4])
p list_size @deep # 4
p list_count 1, 2, 3 # 3 (flat list works too)
</code></pre>
</article>
<article class="doc-entry" id="doc-list-difference">
<h3><a class="doc-anchor" href="#doc-list-difference">#</a> <code>list_difference</code></h3>
<p><code>list_difference</code> — list helper <code>difference</code>. Alias for <code>array_difference</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p list_difference $x
</code></pre>
</article>
<article class="doc-entry" id="doc-list-eq">
<h3><a class="doc-anchor" href="#doc-list-eq">#</a> <code>list_eq</code></h3>
<p><code>list_eq</code> — list helper <code>eq</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p list_eq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-list-flatten-deep">
<h3><a class="doc-anchor" href="#doc-list-flatten-deep">#</a> <code>list_flatten_deep</code></h3>
<p><code>list_flatten_deep</code> — list helper <code>flatten deep</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p list_flatten_deep $x
</code></pre>
</article>
<article class="doc-entry" id="doc-list-intersection">
<h3><a class="doc-anchor" href="#doc-list-intersection">#</a> <code>list_intersection</code></h3>
<p><code>list_intersection</code> — list helper <code>intersection</code>. Alias for <code>array_intersection</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p list_intersection $x
</code></pre>
</article>
<article class="doc-entry" id="doc-list-reverse">
<h3><a class="doc-anchor" href="#doc-list-reverse">#</a> <code>list_reverse</code></h3>
<p><code>list_reverse</code> — list helper <code>reverse</code>. Alias for <code>reverse_list</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p list_reverse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-list-scheduling-step">
<h3><a class="doc-anchor" href="#doc-list-scheduling-step">#</a> <code>list_scheduling_step</code></h3>
<p><code>list_scheduling_step</code> — list helper <code>scheduling step</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p list_scheduling_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-list-union">
<h3><a class="doc-anchor" href="#doc-list-union">#</a> <code>list_union</code></h3>
<p><code>list_union</code> — list helper <code>union</code>. Alias for <code>array_union</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p list_union $x
</code></pre>
</article>
<article class="doc-entry" id="doc-liters-to-gallons">
<h3><a class="doc-anchor" href="#doc-liters-to-gallons">#</a> <code>liters_to_gallons</code></h3>
<p><code>liters_to_gallons</code> — convert from <code>liters</code> to <code>gallons</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p liters_to_gallons $value
</code></pre>
</article>
<article class="doc-entry" id="doc-liters-to-ml">
<h3><a class="doc-anchor" href="#doc-liters-to-ml">#</a> <code>liters_to_ml</code></h3>
<p><code>liters_to_ml</code> — convert from <code>liters</code> to <code>ml</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p liters_to_ml $value
</code></pre>
</article>
<article class="doc-entry" id="doc-lithium-ion-diffusivity">
<h3><a class="doc-anchor" href="#doc-lithium-ion-diffusivity">#</a> <code>lithium_ion_diffusivity</code></h3>
<p><code>lithium_ion_diffusivity</code> — operation <code>lithium ion diffusivity</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p lithium_ion_diffusivity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lix">
<h3><a class="doc-anchor" href="#doc-lix">#</a> <code>lix</code></h3>
<p><code>lix</code> — operation <code>lix</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ljt">
<h3><a class="doc-anchor" href="#doc-ljt">#</a> <code>ljt</code></h3>
<p><code>ljt</code> — operation <code>ljt</code>. Alias for <code>ljust_text</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ljt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ljung-box-q">
<h3><a class="doc-anchor" href="#doc-ljung-box-q">#</a> <code>ljung_box_q</code></h3>
<p><code>ljung_box_q</code> — operation <code>ljung box q</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p ljung_box_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ljust">
<h3><a class="doc-anchor" href="#doc-ljust">#</a> <code>ljust</code></h3>
<p><code>ljust</code> — operation <code>ljust</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p ljust $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ljust-text">
<h3><a class="doc-anchor" href="#doc-ljust-text">#</a> <code>ljust_text</code></h3>
<p><code>ljust_text</code> — operation <code>ljust text</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ljust_text $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lkpa">
<h3><a class="doc-anchor" href="#doc-lkpa">#</a> <code>lkpa</code></h3>
<p><code>lkpa</code> — operation <code>lkpa</code>. Alias for <code>lookup_assoc</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p lkpa $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ll1-first-set">
<h3><a class="doc-anchor" href="#doc-ll1-first-set">#</a> <code>ll1_first_set</code></h3>
<p><code>ll1_first_set</code> — operation <code>ll1 first set</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p ll1_first_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ll1-follow-set">
<h3><a class="doc-anchor" href="#doc-ll1-follow-set">#</a> <code>ll1_follow_set</code></h3>
<p><code>ll1_follow_set</code> — operation <code>ll1 follow set</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p ll1_follow_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ll1-predict-table">
<h3><a class="doc-anchor" href="#doc-ll1-predict-table">#</a> <code>ll1_predict_table</code></h3>
<p><code>ll1_predict_table</code> — lookup table of <code>ll1 predict</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p ll1_predict_table $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lll-2x2-step">
<h3><a class="doc-anchor" href="#doc-lll-2x2-step">#</a> <code>lll_2x2_step</code></h3>
<p><code>lll_2x2_step</code> — single-step update of <code>lll 2x2</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p lll_2x2_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lm">
<h3><a class="doc-anchor" href="#doc-lm">#</a> <code>lm</code></h3>
<p><code>lm_fit</code> (alias <code>lm</code>) — simple linear regression. Returns hash with intercept, slope, r_squared, residuals, fitted. Like R's lm().</p>
<pre><code class="lang-perl">my %m = %{lm([1,2,3,4,5], [2,4,5,4,5])}
p $m{slope} # slope
p $m{r_squared} # R²
</code></pre>
</article>
<article class="doc-entry" id="doc-lm-step">
<h3><a class="doc-anchor" href="#doc-lm-step">#</a> <code>lm_step</code></h3>
<p><code>lm_step</code> — single-step update of <code>lm</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p lm_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ln10">
<h3><a class="doc-anchor" href="#doc-ln10">#</a> <code>ln10</code></h3>
<p><code>ln10</code> — operation <code>ln10</code>. Category: *math / physics constants*.</p>
<pre><code class="lang-perl">p ln10 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ln2">
<h3><a class="doc-anchor" href="#doc-ln2">#</a> <code>ln2</code></h3>
<p><code>ln2</code> — operation <code>ln2</code>. Category: *math / physics constants*.</p>
<pre><code class="lang-perl">p ln2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lnormpdf">
<h3><a class="doc-anchor" href="#doc-lnormpdf">#</a> <code>lnormpdf</code></h3>
<p><code>lognormal_pdf</code> (alias <code>lnormpdf</code>) evaluates the log-normal distribution PDF at x with parameters mu and sigma.</p>
<pre><code class="lang-perl">p lnormpdf(1.0, 0, 1) # LogN(0,1) at x=1
</code></pre>
</article>
<article class="doc-entry" id="doc-lns">
<h3><a class="doc-anchor" href="#doc-lns">#</a> <code>lns</code></h3>
<p><code>lns</code> — operation <code>lns</code>. Alias for <code>look_and_say</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p lns $x
</code></pre>
</article>
<article class="doc-entry" id="doc-load-avg">
<h3><a class="doc-anchor" href="#doc-load-avg">#</a> <code>load_avg</code></h3>
<p><code>load_avg</code> — system load averages as a 3-element arrayref <code>[1min, 5min, 15min]</code>. Uses <code>getloadavg()</code> on unix. Returns <code>undef</code> on unsupported platforms.</p>
<pre><code class="lang-perl">my $la = load_avg
p "1m=$la->[0] 5m=$la->[1] 15m=$la->[2]"
load_avg |> spark |> p # sparkline of load
</code></pre>
</article>
<article class="doc-entry" id="doc-load-centrality">
<h3><a class="doc-anchor" href="#doc-load-centrality">#</a> <code>load_centrality</code></h3>
<p><code>load_centrality</code> — operation <code>load centrality</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p load_centrality $x
</code></pre>
</article>
<article class="doc-entry" id="doc-loan-balance">
<h3><a class="doc-anchor" href="#doc-loan-balance">#</a> <code>loan_balance</code></h3>
<p><code>loan_balance</code> — operation <code>loan balance</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p loan_balance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-loan-interest-total">
<h3><a class="doc-anchor" href="#doc-loan-interest-total">#</a> <code>loan_interest_total</code></h3>
<p><code>loan_interest_total(principal, rate, n_periods) → number</code> — total interest paid over the life of an amortising loan.</p>
<pre><code class="lang-perl">p loan_interest_total(100000, 0.05/12, 360)
</code></pre>
</article>
<article class="doc-entry" id="doc-loan-payment">
<h3><a class="doc-anchor" href="#doc-loan-payment">#</a> <code>loan_payment</code></h3>
<p><code>loan_payment(principal, rate_per_period, n_periods) → number</code> — amortising loan payment formula: <code>P·r·(1+r)^n / ((1+r)^n − 1)</code>.</p>
<pre><code class="lang-perl">p loan_payment(100000, 0.05/12, 360) # 536.82
</code></pre>
</article>
<article class="doc-entry" id="doc-loan-payment-pmt">
<h3><a class="doc-anchor" href="#doc-loan-payment-pmt">#</a> <code>loan_payment_pmt</code></h3>
<p><code>loan_payment_pmt</code> — operation <code>loan payment pmt</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p loan_payment_pmt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-loan-remaining">
<h3><a class="doc-anchor" href="#doc-loan-remaining">#</a> <code>loan_remaining</code></h3>
<p><code>loan_remaining(principal, rate, n_total, n_paid) → number</code> — remaining balance after <code>n_paid</code> payments under fixed-rate amortisation.</p>
<pre><code class="lang-perl">p loan_remaining(100000, 0.05/12, 360, 60)
</code></pre>
</article>
<article class="doc-entry" id="doc-lobatto-iiia-2">
<h3><a class="doc-anchor" href="#doc-lobatto-iiia-2">#</a> <code>lobatto_iiia_2</code></h3>
<p><code>lobatto_iiia_2</code> — operation <code>lobatto iiia 2</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p lobatto_iiia_2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lobatto-iiic-3">
<h3><a class="doc-anchor" href="#doc-lobatto-iiic-3">#</a> <code>lobatto_iiic_3</code></h3>
<p><code>lobatto_iiic_3</code> — operation <code>lobatto iiic 3</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p lobatto_iiic_3 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-local-efficiency">
<h3><a class="doc-anchor" href="#doc-local-efficiency">#</a> <code>local_efficiency</code></h3>
<p><code>local_efficiency</code> — operation <code>local efficiency</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p local_efficiency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-local-search-swap-step">
<h3><a class="doc-anchor" href="#doc-local-search-swap-step">#</a> <code>local_search_swap_step</code></h3>
<p><code>local_search_swap_step</code> — single-step update of <code>local search swap</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p local_search_swap_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-locale-calendar">
<h3><a class="doc-anchor" href="#doc-locale-calendar">#</a> <code>locale_calendar</code></h3>
<p><code>locale_calendar(locale) → string</code> — preferred calendar system (gregorian, persian, hebrew, …).</p>
</article>
<article class="doc-entry" id="doc-locale-canonical">
<h3><a class="doc-anchor" href="#doc-locale-canonical">#</a> <code>locale_canonical</code></h3>
<p><code>locale_canonical(name) → string</code> — canonicalised CLDR locale identifier.</p>
</article>
<article class="doc-entry" id="doc-locale-collation">
<h3><a class="doc-anchor" href="#doc-locale-collation">#</a> <code>locale_collation</code></h3>
<p><code>locale_collation(locale) → string</code> — collation tag (e.g. "standard", "phonebk").</p>
</article>
<article class="doc-entry" id="doc-locale-currency">
<h3><a class="doc-anchor" href="#doc-locale-currency">#</a> <code>locale_currency</code></h3>
<p><code>locale_currency(locale) → string</code> — ISO 4217 currency code for region.</p>
</article>
<article class="doc-entry" id="doc-locale-date-format">
<h3><a class="doc-anchor" href="#doc-locale-date-format">#</a> <code>locale_date_format</code></h3>
<p><code>locale_date_format(locale) → string</code> — date pattern (e.g. "MM/dd/yyyy").</p>
</article>
<article class="doc-entry" id="doc-locale-decimal-separator">
<h3><a class="doc-anchor" href="#doc-locale-decimal-separator">#</a> <code>locale_decimal_separator</code></h3>
<p><code>locale_decimal_separator(locale) → string</code> — decimal point character ("." or ",").</p>
</article>
<article class="doc-entry" id="doc-locale-first-day-of-week">
<h3><a class="doc-anchor" href="#doc-locale-first-day-of-week">#</a> <code>locale_first_day_of_week</code></h3>
<p><code>locale_first_day_of_week(locale) → int</code> — 0=Sunday, 1=Monday.</p>
</article>
<article class="doc-entry" id="doc-locale-format">
<h3><a class="doc-anchor" href="#doc-locale-format">#</a> <code>locale_format</code></h3>
<p><code>locale_format(template, locale, vars) → string</code> — locale-aware ICU-like message format.</p>
</article>
<article class="doc-entry" id="doc-locale-group-separator">
<h3><a class="doc-anchor" href="#doc-locale-group-separator">#</a> <code>locale_group_separator</code></h3>
<p><code>locale_group_separator(locale) → string</code> — thousands separator.</p>
</article>
<article class="doc-entry" id="doc-locale-language">
<h3><a class="doc-anchor" href="#doc-locale-language">#</a> <code>locale_language</code></h3>
<p><code>locale_language(locale) → string</code> — language portion.</p>
</article>
<article class="doc-entry" id="doc-locale-likely-subtags">
<h3><a class="doc-anchor" href="#doc-locale-likely-subtags">#</a> <code>locale_likely_subtags</code></h3>
<p><code>locale_likely_subtags(locale) → string</code> — fill in likely script/region per CLDR likely-subtags table.</p>
</article>
<article class="doc-entry" id="doc-locale-measurement-system">
<h3><a class="doc-anchor" href="#doc-locale-measurement-system">#</a> <code>locale_measurement_system</code></h3>
<p><code>locale_measurement_system(locale) → string</code> — "metric" or "US".</p>
</article>
<article class="doc-entry" id="doc-locale-minimize">
<h3><a class="doc-anchor" href="#doc-locale-minimize">#</a> <code>locale_minimize</code></h3>
<p><code>locale_minimize</code> — locale / CLDR helper <code>minimize</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p locale_minimize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-locale-number-format">
<h3><a class="doc-anchor" href="#doc-locale-number-format">#</a> <code>locale_number_format</code></h3>
<p><code>locale_number_format(n, locale) → string</code> — render number with locale separators.</p>
</article>
<article class="doc-entry" id="doc-locale-parse">
<h3><a class="doc-anchor" href="#doc-locale-parse">#</a> <code>locale_parse</code></h3>
<p><code>locale_parse(name) → hash</code> — parse POSIX/CLDR locale id into language/region/script/variant.</p>
</article>
<article class="doc-entry" id="doc-locale-region">
<h3><a class="doc-anchor" href="#doc-locale-region">#</a> <code>locale_region</code></h3>
<p><code>locale_region(locale) → string</code> — region portion.</p>
</article>
<article class="doc-entry" id="doc-locale-script">
<h3><a class="doc-anchor" href="#doc-locale-script">#</a> <code>locale_script</code></h3>
<p><code>locale_script(locale) → string</code> — script portion.</p>
</article>
<article class="doc-entry" id="doc-locale-time-format">
<h3><a class="doc-anchor" href="#doc-locale-time-format">#</a> <code>locale_time_format</code></h3>
<p><code>locale_time_format(locale) → string</code> — time pattern.</p>
</article>
<article class="doc-entry" id="doc-locale-variant">
<h3><a class="doc-anchor" href="#doc-locale-variant">#</a> <code>locale_variant</code></h3>
<p><code>locale_variant(locale) → string</code> — variant portion.</p>
</article>
<article class="doc-entry" id="doc-loess">
<h3><a class="doc-anchor" href="#doc-loess">#</a> <code>loess</code></h3>
<p><code>lowess</code> (alias <code>loess</code>) — locally-weighted scatterplot smoothing (LOWESS/LOESS). Returns smoothed Y values with tricube weighting.</p>
<pre><code class="lang-perl">my @smooth = @{lowess([1,2,3,4,5], [2,1,4,3,5])}
</code></pre>
</article>
<article class="doc-entry" id="doc-log10">
<h3><a class="doc-anchor" href="#doc-log10">#</a> <code>log10</code></h3>
<p><code>log10</code> — operation <code>log10</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p log10 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-log1p-exp">
<h3><a class="doc-anchor" href="#doc-log1p-exp">#</a> <code>log1p_exp</code></h3>
<p><code>log1p_exp</code> — operation <code>log1p exp</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p log1p_exp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-log2">
<h3><a class="doc-anchor" href="#doc-log2">#</a> <code>log2</code></h3>
<p><code>log2</code> — operation <code>log2</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p log2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-log-base">
<h3><a class="doc-anchor" href="#doc-log-base">#</a> <code>log_base</code></h3>
<p><code>log_base</code> — logarithm / logging helper <code>base</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p log_base $x
</code></pre>
</article>
<article class="doc-entry" id="doc-log-gamma-simple">
<h3><a class="doc-anchor" href="#doc-log-gamma-simple">#</a> <code>log_gamma_simple</code></h3>
<p><code>log_gamma_simple</code> — logarithm / logging helper <code>gamma simple</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p log_gamma_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-log-law-wind-profile">
<h3><a class="doc-anchor" href="#doc-log-law-wind-profile">#</a> <code>log_law_wind_profile</code></h3>
<p><code>log_law_wind_profile</code> — logarithm / logging helper <code>law wind profile</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p log_law_wind_profile $x
</code></pre>
</article>
<article class="doc-entry" id="doc-log-loss">
<h3><a class="doc-anchor" href="#doc-log-loss">#</a> <code>log_loss</code></h3>
<p><code>log_loss</code> — logarithm / logging helper <code>loss</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p log_loss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-log-returns">
<h3><a class="doc-anchor" href="#doc-log-returns">#</a> <code>log_returns</code></h3>
<p><code>log_returns(prices) → array</code> — natural log of consecutive ratios: <code>ln(p[i]/p[i-1])</code>. Additive across time.</p>
<pre><code class="lang-perl">p log_returns([100, 105, 102])
</code></pre>
</article>
<article class="doc-entry" id="doc-log-sigmoid">
<h3><a class="doc-anchor" href="#doc-log-sigmoid">#</a> <code>log_sigmoid</code></h3>
<p><code>log_sigmoid</code> — logarithm / logging helper <code>sigmoid</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p log_sigmoid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-log-softmax">
<h3><a class="doc-anchor" href="#doc-log-softmax">#</a> <code>log_softmax</code></h3>
<p><code>log_softmax(xs) → array</code> — <code>xs - log(Σ exp(xs))</code> in a numerically stable way.</p>
</article>
<article class="doc-entry" id="doc-log-sum-exp">
<h3><a class="doc-anchor" href="#doc-log-sum-exp">#</a> <code>log_sum_exp</code></h3>
<p><code>log_sum_exp</code> — logarithm / logging helper <code>sum exp</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p log_sum_exp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-log-with-base">
<h3><a class="doc-anchor" href="#doc-log-with-base">#</a> <code>log_with_base</code></h3>
<p><code>log_with_base</code> — logarithm / logging helper <code>with base</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p log_with_base $x
</code></pre>
</article>
<article class="doc-entry" id="doc-logb">
<h3><a class="doc-anchor" href="#doc-logb">#</a> <code>logb</code></h3>
<p><code>logb</code> — operation <code>logb</code>. Alias for <code>log_with_base</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p logb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-loggamma">
<h3><a class="doc-anchor" href="#doc-loggamma">#</a> <code>loggamma</code></h3>
<p><code>loggamma</code> — operation <code>loggamma</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p loggamma $x
</code></pre>
</article>
<article class="doc-entry" id="doc-logistic-growth-analytic">
<h3><a class="doc-anchor" href="#doc-logistic-growth-analytic">#</a> <code>logistic_growth_analytic</code></h3>
<p><code>logistic_growth_analytic</code> — operation <code>logistic growth analytic</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p logistic_growth_analytic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-logistic-growth-step">
<h3><a class="doc-anchor" href="#doc-logistic-growth-step">#</a> <code>logistic_growth_step</code></h3>
<p><code>logistic_growth_step</code> — single-step update of <code>logistic growth</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p logistic_growth_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-logistic-loss">
<h3><a class="doc-anchor" href="#doc-logistic-loss">#</a> <code>logistic_loss</code></h3>
<p><code>logistic_loss</code> — operation <code>logistic loss</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p logistic_loss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-logit-log-likelihood">
<h3><a class="doc-anchor" href="#doc-logit-log-likelihood">#</a> <code>logit_log_likelihood</code></h3>
<p><code>logit_log_likelihood</code> — operation <code>logit log likelihood</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p logit_log_likelihood $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lomax-pdf">
<h3><a class="doc-anchor" href="#doc-lomax-pdf">#</a> <code>lomax_pdf</code></h3>
<p><code>lomax_pdf</code> — operation <code>lomax pdf</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p lomax_pdf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lombscargle-freq">
<h3><a class="doc-anchor" href="#doc-lombscargle-freq">#</a> <code>lombscargle_freq</code></h3>
<p><code>lombscargle_freq</code> — operation <code>lombscargle freq</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p lombscargle_freq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-longest">
<h3><a class="doc-anchor" href="#doc-longest">#</a> <code>longest</code></h3>
<p><code>longest</code> — operation <code>longest</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p longest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-longest-common-prefix">
<h3><a class="doc-anchor" href="#doc-longest-common-prefix">#</a> <code>longest_common_prefix</code></h3>
<p><code>longest_common_prefix</code> — operation <code>longest common prefix</code>. Category: *string*.</p>
<pre><code class="lang-perl">p longest_common_prefix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-longest-common-subsequence">
<h3><a class="doc-anchor" href="#doc-longest-common-subsequence">#</a> <code>longest_common_subsequence</code></h3>
<p><code>longest_common_subsequence</code> — operation <code>longest common subsequence</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p longest_common_subsequence $x
</code></pre>
</article>
<article class="doc-entry" id="doc-longest-common-substring">
<h3><a class="doc-anchor" href="#doc-longest-common-substring">#</a> <code>longest_common_substring</code></h3>
<p><code>longest_common_substring</code> — operation <code>longest common substring</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p longest_common_substring $x
</code></pre>
</article>
<article class="doc-entry" id="doc-longest-decreasing">
<h3><a class="doc-anchor" href="#doc-longest-decreasing">#</a> <code>longest_decreasing</code></h3>
<p><code>longest_decreasing</code> — operation <code>longest decreasing</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p longest_decreasing $x
</code></pre>
</article>
<article class="doc-entry" id="doc-longest-increasing">
<h3><a class="doc-anchor" href="#doc-longest-increasing">#</a> <code>longest_increasing</code></h3>
<p><code>longest_increasing</code> — operation <code>longest increasing</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p longest_increasing $x
</code></pre>
</article>
<article class="doc-entry" id="doc-longest-run">
<h3><a class="doc-anchor" href="#doc-longest-run">#</a> <code>longest_run</code></h3>
<p><code>longest_run</code> — operation <code>longest run</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p longest_run $x
</code></pre>
</article>
<article class="doc-entry" id="doc-look-and-say">
<h3><a class="doc-anchor" href="#doc-look-and-say">#</a> <code>look_and_say</code></h3>
<p><code>look_and_say</code> — operation <code>look and say</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p look_and_say $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lookahead-n">
<h3><a class="doc-anchor" href="#doc-lookahead-n">#</a> <code>lookahead_n</code></h3>
<p><code>lookahead_n</code> — operation <code>lookahead n</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p lookahead_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lookback-call">
<h3><a class="doc-anchor" href="#doc-lookback-call">#</a> <code>lookback_call</code></h3>
<p><code>lookback_call</code> — operation <code>lookback call</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p lookback_call $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lookback-time">
<h3><a class="doc-anchor" href="#doc-lookback-time">#</a> <code>lookback_time</code></h3>
<p><code>lookback_time</code> — operation <code>lookback time</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p lookback_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lookup-assoc">
<h3><a class="doc-anchor" href="#doc-lookup-assoc">#</a> <code>lookup_assoc</code></h3>
<p><code>lookup_assoc</code> — operation <code>lookup assoc</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p lookup_assoc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-loose-hash">
<h3><a class="doc-anchor" href="#doc-loose-hash">#</a> <code>loose_hash</code></h3>
<p><code>loose_hash(s) → int</code> — simple multiplicative hash <code>h = h·31 + byte</code> (Java's String.hashCode shape).</p>
<pre><code class="lang-perl">p loose_hash("hello")
</code></pre>
</article>
<article class="doc-entry" id="doc-lorentz">
<h3><a class="doc-anchor" href="#doc-lorentz">#</a> <code>lorentz</code></h3>
<p><code>lorentz_factor($velocity)</code> (alias <code>lorentz</code>) — relativistic gamma factor γ = 1/√(1-v²/c²). Returns infinity at v ≥ c.</p>
<pre><code class="lang-perl">p lorentz(0) # 1 (at rest)
p lorentz(0.9 * 3e8) # ~2.29 (at 90% speed of light)
</code></pre>
</article>
<article class="doc-entry" id="doc-lorentz-factor-v">
<h3><a class="doc-anchor" href="#doc-lorentz-factor-v">#</a> <code>lorentz_factor_v</code></h3>
<p><code>lorentz_factor_v</code> — operation <code>lorentz factor v</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lorentz_factor_v $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lorentz-force-mag">
<h3><a class="doc-anchor" href="#doc-lorentz-force-mag">#</a> <code>lorentz_force_mag</code></h3>
<p><code>lorentz_force_mag</code> — operation <code>lorentz force mag</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p lorentz_force_mag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lorentz-gamma">
<h3><a class="doc-anchor" href="#doc-lorentz-gamma">#</a> <code>lorentz_gamma</code></h3>
<p><code>lorentz_gamma</code> — operation <code>lorentz gamma</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p lorentz_gamma $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lorenz">
<h3><a class="doc-anchor" href="#doc-lorenz">#</a> <code>lorenz</code></h3>
<p><code>lorenz_curve(@data)</code> (alias <code>lorenz</code>) — computes the Lorenz curve as an arrayref of [cumulative_share_of_population, cumulative_share_of_wealth] pairs. Used to visualize inequality. The diagonal represents perfect equality.</p>
<pre><code class="lang-perl">my $curve = lorenz(10, 20, 30, 40)
for my $pt (@$curve) {
p "$pt->[0], $pt->[1]"
}
</code></pre>
</article>
<article class="doc-entry" id="doc-lose-lose">
<h3><a class="doc-anchor" href="#doc-lose-lose">#</a> <code>lose_lose</code></h3>
<p><code>lose_lose</code> — operation <code>lose lose</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p lose_lose $x
</code></pre>
</article>
<article class="doc-entry" id="doc-loss-frequency-poisson">
<h3><a class="doc-anchor" href="#doc-loss-frequency-poisson">#</a> <code>loss_frequency_poisson</code></h3>
<p><code>loss_frequency_poisson</code> — operation <code>loss frequency poisson</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p loss_frequency_poisson $x
</code></pre>
</article>
<article class="doc-entry" id="doc-loss-severity-lognormal">
<h3><a class="doc-anchor" href="#doc-loss-severity-lognormal">#</a> <code>loss_severity_lognormal</code></h3>
<p><code>loss_severity_lognormal</code> — operation <code>loss severity lognormal</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p loss_severity_lognormal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lotka-volterra-step">
<h3><a class="doc-anchor" href="#doc-lotka-volterra-step">#</a> <code>lotka_volterra_step</code></h3>
<p><code>lotka_volterra_step</code> — single-step update of <code>lotka volterra</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lotka_volterra_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-louvain-gain">
<h3><a class="doc-anchor" href="#doc-louvain-gain">#</a> <code>louvain_gain</code></h3>
<p><code>louvain_gain</code> — operation <code>louvain gain</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p louvain_gain $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lower-bound">
<h3><a class="doc-anchor" href="#doc-lower-bound">#</a> <code>lower_bound</code></h3>
<p><code>lower_bound</code> — operation <code>lower bound</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p lower_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lower-triangular-q">
<h3><a class="doc-anchor" href="#doc-lower-triangular-q">#</a> <code>lower_triangular_q</code></h3>
<p><code>lower_triangular_q</code> — operation <code>lower triangular q</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p lower_triangular_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lowercase">
<h3><a class="doc-anchor" href="#doc-lowercase">#</a> <code>lowercase</code></h3>
<p><code>lowercase</code> — operation <code>lowercase</code>. Category: *string*.</p>
<pre><code class="lang-perl">p lowercase $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lowpass-filter">
<h3><a class="doc-anchor" href="#doc-lowpass-filter">#</a> <code>lowpass_filter</code></h3>
<p><code>lowpass_filter(\@signal, $cutoff)</code> (alias <code>lpf</code>) — applies a simple low-pass filter to remove high-frequency components. Cutoff is normalized (0-1). Uses exponential moving average.</p>
<pre><code class="lang-perl">my @noisy = map { sin(_/10) + rand(0.2) } 1:100
my $smooth = lpf(\@noisy, 0.1)
</code></pre>
</article>
<article class="doc-entry" id="doc-lp-norm">
<h3><a class="doc-anchor" href="#doc-lp-norm">#</a> <code>lp_norm</code></h3>
<p><code>lp_norm</code> — Linear Programming solver <code>norm</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lp_norm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lp-relax-round">
<h3><a class="doc-anchor" href="#doc-lp-relax-round">#</a> <code>lp_relax_round</code></h3>
<p><code>lp_relax_round</code> — Linear Programming solver <code>relax round</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p lp_relax_round $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lp-simplex-max">
<h3><a class="doc-anchor" href="#doc-lp-simplex-max">#</a> <code>lp_simplex_max</code></h3>
<p><code>lp_simplex_max(c, A, b) → number</code> — maximise <code>c·x</code> subject to <code>A·x ≤ b</code>, <code>x ≥ 0</code> via revised simplex.</p>
<pre><code class="lang-perl">p lp_simplex_max([1,1], [[1,1]], [10]) # 10
</code></pre>
</article>
<article class="doc-entry" id="doc-lp-simplex-min">
<h3><a class="doc-anchor" href="#doc-lp-simplex-min">#</a> <code>lp_simplex_min</code></h3>
<p><code>lp_simplex_min(c, A, b) → number</code> — minimise <code>c·x</code> (negates <code>c</code> and re-uses simplex_max).</p>
</article>
<article class="doc-entry" id="doc-lpad">
<h3><a class="doc-anchor" href="#doc-lpad">#</a> <code>lpad</code></h3>
<p><code>lpad</code> — operation <code>lpad</code>. Alias for <code>pad_left</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p lpad $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lplanck">
<h3><a class="doc-anchor" href="#doc-lplanck">#</a> <code>lplanck</code></h3>
<p><code>planck_length</code> (alias <code>lplanck</code>) — lP ≈ 1.616×10⁻³⁵ m. Smallest meaningful length in quantum mechanics.</p>
<pre><code class="lang-perl">p lplanck # 1.616255e-35 m
</code></pre>
</article>
<article class="doc-entry" id="doc-lpt">
<h3><a class="doc-anchor" href="#doc-lpt">#</a> <code>lpt</code></h3>
<p><code>lpt</code> — operation <code>lpt</code>. Alias for <code>lpt_schedule</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lpt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lpt-schedule">
<h3><a class="doc-anchor" href="#doc-lpt-schedule">#</a> <code>lpt_schedule</code></h3>
<p><code>lpt_schedule</code> — operation <code>lpt schedule</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lpt_schedule $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lpush">
<h3><a class="doc-anchor" href="#doc-lpush">#</a> <code>lpush</code></h3>
<p><code>lpush</code> — operation <code>lpush</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p lpush $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lqg-step">
<h3><a class="doc-anchor" href="#doc-lqg-step">#</a> <code>lqg_step</code></h3>
<p><code>lqg_step</code> — single-step update of <code>lqg</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p lqg_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lqr-gain-continuous">
<h3><a class="doc-anchor" href="#doc-lqr-gain-continuous">#</a> <code>lqr_gain_continuous</code></h3>
<p><code>lqr_gain_continuous</code> — operation <code>lqr gain continuous</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p lqr_gain_continuous $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lqr-gain-discrete">
<h3><a class="doc-anchor" href="#doc-lqr-gain-discrete">#</a> <code>lqr_gain_discrete</code></h3>
<p><code>lqr_gain_discrete</code> — operation <code>lqr gain discrete</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p lqr_gain_discrete $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lr0-items-step">
<h3><a class="doc-anchor" href="#doc-lr0-items-step">#</a> <code>lr0_items_step</code></h3>
<p><code>lr0_items_step</code> — single-step update of <code>lr0 items</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p lr0_items_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lr1-canonical-collection">
<h3><a class="doc-anchor" href="#doc-lr1-canonical-collection">#</a> <code>lr1_canonical_collection</code></h3>
<p><code>lr1_canonical_collection</code> — operation <code>lr1 canonical collection</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p lr1_canonical_collection $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lrange">
<h3><a class="doc-anchor" href="#doc-lrange">#</a> <code>lrange</code></h3>
<p><code>lrange</code> — operation <code>lrange</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p lrange $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lrem">
<h3><a class="doc-anchor" href="#doc-lrem">#</a> <code>lrem</code></h3>
<p><code>lrem</code> — operation <code>lrem</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p lrem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lru-new">
<h3><a class="doc-anchor" href="#doc-lru-new">#</a> <code>lru_new</code></h3>
<p><code>lru_new</code> — constructor of <code>lru</code>. Category: *data structure helpers*.</p>
<pre><code class="lang-perl">p lru_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lrun">
<h3><a class="doc-anchor" href="#doc-lrun">#</a> <code>lrun</code></h3>
<p><code>lrun</code> — operation <code>lrun</code>. Alias for <code>longest_run</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p lrun $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lse">
<h3><a class="doc-anchor" href="#doc-lse">#</a> <code>lse</code></h3>
<p><code>lse</code> — operation <code>lse</code>. Alias for <code>log_sum_exp</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p lse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lsearch">
<h3><a class="doc-anchor" href="#doc-lsearch">#</a> <code>lsearch</code></h3>
<p><code>lsearch</code> — operation <code>lsearch</code>. Alias for <code>linear_search</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p lsearch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lsp-completion-words">
<h3><a class="doc-anchor" href="#doc-lsp-completion-words">#</a> <code>lsp_completion_words</code></h3>
<p><code>lsp_completion_words</code> (alias <code>lsp_words</code>) — emits every name LSP tab-complete should know about, sorted ASCII. Three sources merged: (1) every callable bare-name spelling from <code>%all</code> (~10.6k names, primaries + aliases), (2) sigil-prefixed live bindings (<code>%a</code>, <code>%all</code>, <code>%b</code>, <code>%parameters</code>, <code>@ARGV</code>, <code>@INC</code>, <code>@fpath</code>, <code>@path</code>, <code>$_</code>, <code>$stryke::VERSION</code>, …), (3) <code>CORE::</code>/<code>main::</code> qualified spellings of every callable / unqualified binding, plus stryke language keywords (<code>fn</code>, <code>match</code>, <code>class</code>, <code>struct</code>, <code>enum</code>, <code>mysync</code>, <code>frozen</code>, …). Drives the canonical <code>strykelang/lsp_completion_words.txt</code> snapshot consumed by both the static analyzer (linter) and LSP completion provider.</p>
<pre><code class="lang-perl">lsp_words |> ep # browse everything
p len(lsp_words) # ~19,000 entries
# Regenerate the on-disk snapshot:
# stryke -e 'lsp_words |> ep' > strykelang/lsp_completion_words.txt
</code></pre>
</article>
<article class="doc-entry" id="doc-lst-to-solar">
<h3><a class="doc-anchor" href="#doc-lst-to-solar">#</a> <code>lst_to_solar</code></h3>
<p><code>lst_to_solar</code> — convert from <code>lst</code> to <code>solar</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p lst_to_solar $value
</code></pre>
</article>
<article class="doc-entry" id="doc-lstat">
<h3><a class="doc-anchor" href="#doc-lstat">#</a> <code>lstat</code></h3>
<p><code>lstat</code> — operation <code>lstat</code>. Category: *filesystem*.</p>
<pre><code class="lang-perl">p lstat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lucas">
<h3><a class="doc-anchor" href="#doc-lucas">#</a> <code>lucas</code></h3>
<p><code>lucas</code> — operation <code>lucas</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p lucas $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lucas-n">
<h3><a class="doc-anchor" href="#doc-lucas-n">#</a> <code>lucas_n</code></h3>
<p><code>lucas_n</code> — operation <code>lucas n</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p lucas_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lucas-nth">
<h3><a class="doc-anchor" href="#doc-lucas-nth">#</a> <code>lucas_nth</code></h3>
<p><code>lucas_nth(n) → int</code> — n-th Lucas number <code>L(n) = L(n-1) + L(n-2)</code>, L(0)=2, L(1)=1.</p>
<pre><code class="lang-perl">p lucas_nth(10) # 123
</code></pre>
</article>
<article class="doc-entry" id="doc-luhn">
<h3><a class="doc-anchor" href="#doc-luhn">#</a> <code>luhn</code></h3>
<p><code>luhn</code> — operation <code>luhn</code>. Alias for <code>luhn_check</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p luhn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-luhn-check">
<h3><a class="doc-anchor" href="#doc-luhn-check">#</a> <code>luhn_check</code></h3>
<p><code>luhn_check</code> — operation <code>luhn check</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p luhn_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-luhn-digit">
<h3><a class="doc-anchor" href="#doc-luhn-digit">#</a> <code>luhn_digit</code></h3>
<p><code>luhn_digit</code> — operation <code>luhn digit</code>. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p luhn_digit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-luminance-relative">
<h3><a class="doc-anchor" href="#doc-luminance-relative">#</a> <code>luminance_relative</code></h3>
<p><code>luminance_relative</code> — operation <code>luminance relative</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p luminance_relative $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lunation-index">
<h3><a class="doc-anchor" href="#doc-lunation-index">#</a> <code>lunation_index</code></h3>
<p><code>lunation_index</code> — index of <code>lunation</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p lunation_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lv-competition-step">
<h3><a class="doc-anchor" href="#doc-lv-competition-step">#</a> <code>lv_competition_step</code></h3>
<p><code>lv_competition_step</code> — single-step update of <code>lv competition</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p lv_competition_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ly-to-pc">
<h3><a class="doc-anchor" href="#doc-ly-to-pc">#</a> <code>ly_to_pc</code></h3>
<p><code>ly_to_pc</code> — convert from <code>ly</code> to <code>pc</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p ly_to_pc $value
</code></pre>
</article>
<article class="doc-entry" id="doc-lyndon-factorize">
<h3><a class="doc-anchor" href="#doc-lyndon-factorize">#</a> <code>lyndon_factorize</code></h3>
<p><code>lyndon_factorize</code> — operation <code>lyndon factorize</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p lyndon_factorize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lz">
<h3><a class="doc-anchor" href="#doc-lz">#</a> <code>lz</code></h3>
<p><code>lz</code> — operation <code>lz</code>. Alias for <code>leading_zeros</code>. Category: *base conversion*.</p>
<pre><code class="lang-perl">p lz $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lz4-block-step">
<h3><a class="doc-anchor" href="#doc-lz4-block-step">#</a> <code>lz4_block_step</code></h3>
<p><code>lz4_block_step</code> — single-step update of <code>lz4 block</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p lz4_block_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lz4-encode-block">
<h3><a class="doc-anchor" href="#doc-lz4-encode-block">#</a> <code>lz4_encode_block</code></h3>
<p><code>lz4_encode_block</code> — operation <code>lz4 encode block</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p lz4_encode_block $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lz4-match-offset">
<h3><a class="doc-anchor" href="#doc-lz4-match-offset">#</a> <code>lz4_match_offset</code></h3>
<p><code>lz4_match_offset</code> — operation <code>lz4 match offset</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p lz4_match_offset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lz77-match-length">
<h3><a class="doc-anchor" href="#doc-lz77-match-length">#</a> <code>lz77_match_length</code></h3>
<p><code>lz77_match_length</code> — operation <code>lz77 match length</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p lz77_match_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lz78-dictionary-growth">
<h3><a class="doc-anchor" href="#doc-lz78-dictionary-growth">#</a> <code>lz78_dictionary_growth</code></h3>
<p><code>lz78_dictionary_growth</code> — operation <code>lz78 dictionary growth</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p lz78_dictionary_growth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lzma-encode-step">
<h3><a class="doc-anchor" href="#doc-lzma-encode-step">#</a> <code>lzma_encode_step</code></h3>
<p><code>lzma_encode_step</code> — single-step update of <code>lzma encode</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p lzma_encode_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lzma-range-step">
<h3><a class="doc-anchor" href="#doc-lzma-range-step">#</a> <code>lzma_range_step</code></h3>
<p><code>lzma_range_step</code> — single-step update of <code>lzma range</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p lzma_range_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lzo-encode-step">
<h3><a class="doc-anchor" href="#doc-lzo-encode-step">#</a> <code>lzo_encode_step</code></h3>
<p><code>lzo_encode_step</code> — single-step update of <code>lzo encode</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p lzo_encode_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lzw-encode">
<h3><a class="doc-anchor" href="#doc-lzw-encode">#</a> <code>lzw_encode</code></h3>
<p><code>lzw_encode</code> — encode of <code>lzw</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p lzw_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-lzw-step-dict">
<h3><a class="doc-anchor" href="#doc-lzw-step-dict">#</a> <code>lzw_step_dict</code></h3>
<p><code>lzw_step_dict</code> — operation <code>lzw step dict</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p lzw_step_dict $x
</code></pre>
</article>
<article class="doc-entry" id="doc-m5">
<h3><a class="doc-anchor" href="#doc-m5">#</a> <code>m5</code></h3>
<p><code>m5</code> — operation <code>m5</code>. Alias for <code>md5</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p m5 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-m-to-feet">
<h3><a class="doc-anchor" href="#doc-m-to-feet">#</a> <code>m_to_feet</code></h3>
<p><code>m_to_feet</code> — convert from <code>m</code> to <code>feet</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p m_to_feet $value
</code></pre>
</article>
<article class="doc-entry" id="doc-m-to-miles">
<h3><a class="doc-anchor" href="#doc-m-to-miles">#</a> <code>m_to_miles</code></h3>
<p><code>m_to_miles</code> — convert from <code>m</code> to <code>miles</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p m_to_miles $value
</code></pre>
</article>
<article class="doc-entry" id="doc-m-to-s">
<h3><a class="doc-anchor" href="#doc-m-to-s">#</a> <code>m_to_s</code></h3>
<p><code>m_to_s</code> — convert from <code>m</code> to <code>s</code>. Alias for <code>minutes_to_seconds</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p m_to_s $value
</code></pre>
</article>
<article class="doc-entry" id="doc-m-to-yards">
<h3><a class="doc-anchor" href="#doc-m-to-yards">#</a> <code>m_to_yards</code></h3>
<p><code>m_to_yards</code> — convert from <code>m</code> to <code>yards</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p m_to_yards $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ma-model-likelihood">
<h3><a class="doc-anchor" href="#doc-ma-model-likelihood">#</a> <code>ma_model_likelihood</code></h3>
<p><code>ma_model_likelihood</code> — operation <code>ma model likelihood</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p ma_model_likelihood $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-compare">
<h3><a class="doc-anchor" href="#doc-mac-compare">#</a> <code>mac_compare</code></h3>
<p><code>mac_compare</code> — MAC address op <code>compare</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_compare $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-duration">
<h3><a class="doc-anchor" href="#doc-mac-duration">#</a> <code>mac_duration</code></h3>
<p><code>bond_duration</code> (alias <code>mac_duration</code>) computes Macaulay duration — the weighted-average time to receive cash flows.</p>
<pre><code class="lang-perl">my $dur = bond_duration([5,5,5,105], 0.05) # ≈ 3.72 years
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-format">
<h3><a class="doc-anchor" href="#doc-mac-format">#</a> <code>mac_format</code></h3>
<p><code>mac_format</code> — MAC address op <code>format</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_format $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-is-broadcast">
<h3><a class="doc-anchor" href="#doc-mac-is-broadcast">#</a> <code>mac_is_broadcast</code></h3>
<p><code>mac_is_broadcast</code> — MAC address op <code>is broadcast</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_is_broadcast $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-is-locally-administered">
<h3><a class="doc-anchor" href="#doc-mac-is-locally-administered">#</a> <code>mac_is_locally_administered</code></h3>
<p><code>mac_is_locally_administered</code> — MAC address op <code>is locally administered</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_is_locally_administered $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-is-multicast">
<h3><a class="doc-anchor" href="#doc-mac-is-multicast">#</a> <code>mac_is_multicast</code></h3>
<p><code>mac_is_multicast</code> — MAC address op <code>is multicast</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_is_multicast $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-is-unicast">
<h3><a class="doc-anchor" href="#doc-mac-is-unicast">#</a> <code>mac_is_unicast</code></h3>
<p><code>mac_is_unicast</code> — MAC address op <code>is unicast</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_is_unicast $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-is-universally-administered">
<h3><a class="doc-anchor" href="#doc-mac-is-universally-administered">#</a> <code>mac_is_universally_administered</code></h3>
<p><code>mac_is_universally_administered</code> — MAC address op <code>is universally administered</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_is_universally_administered $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-is-valid">
<h3><a class="doc-anchor" href="#doc-mac-is-valid">#</a> <code>mac_is_valid</code></h3>
<p><code>mac_is_valid</code> — MAC address op <code>is valid</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_is_valid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-lookup-vendor">
<h3><a class="doc-anchor" href="#doc-mac-lookup-vendor">#</a> <code>mac_lookup_vendor</code></h3>
<p><code>mac_lookup_vendor</code> — MAC address op <code>lookup vendor</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_lookup_vendor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-normalize">
<h3><a class="doc-anchor" href="#doc-mac-normalize">#</a> <code>mac_normalize</code></h3>
<p><code>mac_normalize</code> — MAC address op <code>normalize</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_normalize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-oui">
<h3><a class="doc-anchor" href="#doc-mac-oui">#</a> <code>mac_oui</code></h3>
<p><code>mac_oui</code> — MAC address op <code>oui</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_oui $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-parse">
<h3><a class="doc-anchor" href="#doc-mac-parse">#</a> <code>mac_parse</code></h3>
<p><code>mac_parse</code> — MAC address op <code>parse</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-random">
<h3><a class="doc-anchor" href="#doc-mac-random">#</a> <code>mac_random</code></h3>
<p><code>mac_random</code> — MAC address op <code>random</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_random $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-random-local">
<h3><a class="doc-anchor" href="#doc-mac-random-local">#</a> <code>mac_random_local</code></h3>
<p><code>mac_random_local</code> — MAC address op <code>random local</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_random_local $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-to-bytes">
<h3><a class="doc-anchor" href="#doc-mac-to-bytes">#</a> <code>mac_to_bytes</code></h3>
<p><code>mac_to_bytes</code> — convert from <code>mac</code> to <code>bytes</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_to_bytes $value
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-to-int">
<h3><a class="doc-anchor" href="#doc-mac-to-int">#</a> <code>mac_to_int</code></h3>
<p><code>mac_to_int</code> — convert from <code>mac</code> to <code>int</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_to_int $value
</code></pre>
</article>
<article class="doc-entry" id="doc-mac-vendor-lookup">
<h3><a class="doc-anchor" href="#doc-mac-vendor-lookup">#</a> <code>mac_vendor_lookup</code></h3>
<p><code>mac_vendor_lookup</code> — MAC address op <code>vendor lookup</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mac_vendor_lookup $x
</code></pre>
</article>
<article class="doc-entry" id="doc-macarthur-wilson-extinction">
<h3><a class="doc-anchor" href="#doc-macarthur-wilson-extinction">#</a> <code>macarthur_wilson_extinction</code></h3>
<p><code>macarthur_wilson_extinction</code> — operation <code>macarthur wilson extinction</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p macarthur_wilson_extinction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-macarthur-wilson-immigration">
<h3><a class="doc-anchor" href="#doc-macarthur-wilson-immigration">#</a> <code>macarthur_wilson_immigration</code></h3>
<p><code>macarthur_wilson_immigration</code> — operation <code>macarthur wilson immigration</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p macarthur_wilson_immigration $x
</code></pre>
</article>
<article class="doc-entry" id="doc-macaulay-duration">
<h3><a class="doc-anchor" href="#doc-macaulay-duration">#</a> <code>macaulay_duration</code></h3>
<p><code>macaulay_duration</code> — operation <code>macaulay duration</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p macaulay_duration $x
</code></pre>
</article>
<article class="doc-entry" id="doc-macauley-duration">
<h3><a class="doc-anchor" href="#doc-macauley-duration">#</a> <code>macauley_duration</code></h3>
<p><code>macauley_duration</code> — operation <code>macauley duration</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p macauley_duration $x
</code></pre>
</article>
<article class="doc-entry" id="doc-macd">
<h3><a class="doc-anchor" href="#doc-macd">#</a> <code>macd</code></h3>
<p><code>macd(prices, fast=12, slow=26) → array</code> — MACD line: <code>EMA(fast) − EMA(slow)</code>. Pair with <code>macd_signal</code> and <code>macd_histogram</code> for full divergence analysis.</p>
<pre><code class="lang-perl">p macd(\@closes, 12, 26)
</code></pre>
</article>
<article class="doc-entry" id="doc-macd-histogram">
<h3><a class="doc-anchor" href="#doc-macd-histogram">#</a> <code>macd_histogram</code></h3>
<p><code>macd_histogram(prices, fast=12, slow=26, sig=9) → array</code> — <code>macd − macd_signal</code>. Positive bars = bullish momentum; bar height tracks divergence size.</p>
<pre><code class="lang-perl">p macd_histogram(\@closes)
</code></pre>
</article>
<article class="doc-entry" id="doc-macd-signal">
<h3><a class="doc-anchor" href="#doc-macd-signal">#</a> <code>macd_signal</code></h3>
<p><code>macd_signal(prices, fast=12, slow=26, sig=9) → array</code> — signal line for MACD: <code>EMA(macd_line, sig)</code>. Crossover with <code>macd</code> gives buy/sell ticks.</p>
<pre><code class="lang-perl">p macd_signal(\@closes, 12, 26, 9)
</code></pre>
</article>
<article class="doc-entry" id="doc-macdur">
<h3><a class="doc-anchor" href="#doc-macdur">#</a> <code>macdur</code></h3>
<p><code>macdur</code> — operation <code>macdur</code>. Alias for <code>duration</code>. Category: *finance (extended)*.</p>
<pre><code class="lang-perl">p macdur $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mach-full-step">
<h3><a class="doc-anchor" href="#doc-mach-full-step">#</a> <code>mach_full_step</code></h3>
<p><code>mach_full_step</code> — single-step update of <code>mach full</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p mach_full_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mach-o-header-read">
<h3><a class="doc-anchor" href="#doc-mach-o-header-read">#</a> <code>mach_o_header_read</code></h3>
<p><code>mach_o_header_read(hex_bytes) → hash</code> — parse Mach-O magic → <code>{magic, cputype, filetype}</code>. Supports both endians and 32/64-bit.</p>
</article>
<article class="doc-entry" id="doc-mad">
<h3><a class="doc-anchor" href="#doc-mad">#</a> <code>mad</code></h3>
<p><code>mad</code> — operation <code>mad</code>. Alias for <code>median_absolute_deviation</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p mad $x
</code></pre>
</article>
<article class="doc-entry" id="doc-madd">
<h3><a class="doc-anchor" href="#doc-madd">#</a> <code>madd</code></h3>
<p><code>madd</code> — operation <code>madd</code>. Alias for <code>matrix_add</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p madd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mae">
<h3><a class="doc-anchor" href="#doc-mae">#</a> <code>mae</code></h3>
<p><code>mae</code> — operation <code>mae</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p mae $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mag">
<h3><a class="doc-anchor" href="#doc-mag">#</a> <code>mag</code></h3>
<p><code>mag</code> — operation <code>mag</code>. Alias for <code>magnitude</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-magenta">
<h3><a class="doc-anchor" href="#doc-magenta">#</a> <code>magenta</code></h3>
<p><code>magenta</code> — operation <code>magenta</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p magenta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-magenta-bold">
<h3><a class="doc-anchor" href="#doc-magenta-bold">#</a> <code>magenta_bold</code></h3>
<p><code>magenta_bold</code> — operation <code>magenta bold</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p magenta_bold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-maglens">
<h3><a class="doc-anchor" href="#doc-maglens">#</a> <code>maglens</code></h3>
<p><code>maglens</code> — operation <code>maglens</code>. Alias for <code>magnification_lens</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p maglens $x
</code></pre>
</article>
<article class="doc-entry" id="doc-magnification-lens">
<h3><a class="doc-anchor" href="#doc-magnification-lens">#</a> <code>magnification_lens</code></h3>
<p><code>magnification_lens</code> — operation <code>magnification lens</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p magnification_lens $x
</code></pre>
</article>
<article class="doc-entry" id="doc-magnitude">
<h3><a class="doc-anchor" href="#doc-magnitude">#</a> <code>magnitude</code></h3>
<p><code>magnitude</code> — operation <code>magnitude</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p magnitude $x
</code></pre>
</article>
<article class="doc-entry" id="doc-magnus-1st">
<h3><a class="doc-anchor" href="#doc-magnus-1st">#</a> <code>magnus_1st</code></h3>
<p><code>magnus_1st</code> — operation <code>magnus 1st</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p magnus_1st $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mahal">
<h3><a class="doc-anchor" href="#doc-mahal">#</a> <code>mahal</code></h3>
<p><code>mahalanobis</code> — Mahalanobis distance. Args: data, center, inverse_covariance. Like R's mahalanobis().</p>
<pre><code class="lang-perl">my @d = @{mahal([[1,2],[3,4]], [2,3], [[1,0],[0,1]])}
</code></pre>
</article>
<article class="doc-entry" id="doc-mahalanobis-1d">
<h3><a class="doc-anchor" href="#doc-mahalanobis-1d">#</a> <code>mahalanobis_1d</code></h3>
<p><code>mahalanobis_1d</code> — operation <code>mahalanobis 1d</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p mahalanobis_1d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mahalanobis-sq">
<h3><a class="doc-anchor" href="#doc-mahalanobis-sq">#</a> <code>mahalanobis_sq</code></h3>
<p><code>mahalanobis_sq(x, mean, cov_inv) → number</code> — squared Mahalanobis distance with precision (inverse-covariance) matrix.</p>
</article>
<article class="doc-entry" id="doc-main">
<h3><a class="doc-anchor" href="#doc-main">#</a> <code>main</code></h3>
<p><code>main::</code> — the default package every script starts in. <code>our</code> variables and <code>fn</code> declarations without an explicit <code>package</code> directive land in <code>main::</code>; bare references like <code>$x</code> / <code>@a</code> / <code>%h</code> resolve to <code>$main::x</code> / <code>@main::a</code> / <code>%main::h</code> when looked up via the symbol table.</p>
<p>Use <code>main::</code> qualifier when you need to disambiguate inside a nested package, or when introspecting a script from a library context.</p>
<pre><code class="lang-perl">our $verbose = 1
p $main::verbose # 1 — same scalar
# Inside a class, the bare name resolves to the class — main:: gets you out:
class Foo {
fn check { p $main::verbose } # reads top-level our
}
# %main:: is the symbol-table stash. Lists every name declared
# at the top level (subs, our, our @, our %).
p scalar keys %main:: # symbol-table size
keys %main:: |> sort |> p # browse every top-level name
</code></pre>
<p>Related namespaces: <code>CORE::</code> (every builtin), <code>stryke::</code> (reflection hashes — <code>%stryke::builtins</code> etc.), and <code>Pkg::</code> for any user-declared <code>package Pkg</code>.</p>
</article>
<article class="doc-entry" id="doc-main-sequence-lifetime">
<h3><a class="doc-anchor" href="#doc-main-sequence-lifetime">#</a> <code>main_sequence_lifetime</code></h3>
<p><code>main_sequence_lifetime</code> — operation <code>main sequence lifetime</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p main_sequence_lifetime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mainardi-codazzi-step">
<h3><a class="doc-anchor" href="#doc-mainardi-codazzi-step">#</a> <code>mainardi_codazzi_step</code></h3>
<p><code>mainardi_codazzi_step</code> — single-step update of <code>mainardi codazzi</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p mainardi_codazzi_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-majority">
<h3><a class="doc-anchor" href="#doc-majority">#</a> <code>majority</code></h3>
<p><code>majority</code> — operation <code>majority</code>. Alias for <code>majority_element</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p majority $x
</code></pre>
</article>
<article class="doc-entry" id="doc-majority-element">
<h3><a class="doc-anchor" href="#doc-majority-element">#</a> <code>majority_element</code></h3>
<p><code>majority_element</code> — operation <code>majority element</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p majority_element $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mall">
<h3><a class="doc-anchor" href="#doc-mall">#</a> <code>mall</code></h3>
<p><code>mall</code> — operation <code>mall</code>. Alias for <code>match_all</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mall $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mallat-pyramid-step">
<h3><a class="doc-anchor" href="#doc-mallat-pyramid-step">#</a> <code>mallat_pyramid_step</code></h3>
<p><code>mallat_pyramid_step</code> — single-step update of <code>mallat pyramid</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p mallat_pyramid_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-manacher">
<h3><a class="doc-anchor" href="#doc-manacher">#</a> <code>manacher</code></h3>
<p><code>manacher</code> — operation <code>manacher</code>. Alias for <code>manacher_radii</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p manacher $x
</code></pre>
</article>
<article class="doc-entry" id="doc-manacher-radii">
<h3><a class="doc-anchor" href="#doc-manacher-radii">#</a> <code>manacher_radii</code></h3>
<p><code>manacher_radii</code> — operation <code>manacher radii</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p manacher_radii $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mandel">
<h3><a class="doc-anchor" href="#doc-mandel">#</a> <code>mandel</code></h3>
<p><code>mandel</code> — operation <code>mandel</code>. Alias for <code>mandelbrot_char</code>. Category: *algorithms / puzzles*.</p>
<pre><code class="lang-perl">p mandel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mandel-q">
<h3><a class="doc-anchor" href="#doc-mandel-q">#</a> <code>mandel_q</code></h3>
<p><code>mandel_q</code> — operation <code>mandel q</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p mandel_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mandelbrot-char">
<h3><a class="doc-anchor" href="#doc-mandelbrot-char">#</a> <code>mandelbrot_char</code></h3>
<p><code>mandelbrot_char</code> — operation <code>mandelbrot char</code>. Category: *algorithms / puzzles*.</p>
<pre><code class="lang-perl">p mandelbrot_char $x
</code></pre>
</article>
<article class="doc-entry" id="doc-manhattan-distance">
<h3><a class="doc-anchor" href="#doc-manhattan-distance">#</a> <code>manhattan_distance</code></h3>
<p><code>manhattan_distance(a, b) → number</code> — L1 distance.</p>
</article>
<article class="doc-entry" id="doc-manhattan-norm">
<h3><a class="doc-anchor" href="#doc-manhattan-norm">#</a> <code>manhattan_norm</code></h3>
<p><code>manhattan_norm(v) → number</code> — L1 norm <code>Σ |vᵢ|</code>.</p>
</article>
<article class="doc-entry" id="doc-manipulability-yoshikawa">
<h3><a class="doc-anchor" href="#doc-manipulability-yoshikawa">#</a> <code>manipulability_yoshikawa</code></h3>
<p><code>manipulability_yoshikawa</code> — operation <code>manipulability yoshikawa</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p manipulability_yoshikawa $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mann-kendall-tau">
<h3><a class="doc-anchor" href="#doc-mann-kendall-tau">#</a> <code>mann_kendall_tau</code></h3>
<p><code>mann_kendall_tau</code> — operation <code>mann kendall tau</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p mann_kendall_tau $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mann-whitney">
<h3><a class="doc-anchor" href="#doc-mann-whitney">#</a> <code>mann_whitney</code></h3>
<p><code>wilcox_test</code> (aliases <code>wilcox</code>, <code>mann_whitney</code>) — Wilcoxon rank-sum test (Mann-Whitney U). Returns U statistic. Like R's wilcox.test().</p>
<pre><code class="lang-perl">my $U = wilcox([1,2,3], [4,5,6]) # 0 (no overlap)
</code></pre>
</article>
<article class="doc-entry" id="doc-mann-whitney-u">
<h3><a class="doc-anchor" href="#doc-mann-whitney-u">#</a> <code>mann_whitney_u</code></h3>
<p><code>mann_whitney_u(a, b) → {statistic, df, p_value}</code> — Mann-Whitney U (Wilcoxon rank-sum) non-parametric two-sample test.</p>
<pre><code class="lang-perl">p mann_whitney_u(\@group_a, \@group_b)
</code></pre>
</article>
<article class="doc-entry" id="doc-manning-velocity">
<h3><a class="doc-anchor" href="#doc-manning-velocity">#</a> <code>manning_velocity</code></h3>
<p><code>manning_velocity</code> — operation <code>manning velocity</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p manning_velocity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mannwhitneyu">
<h3><a class="doc-anchor" href="#doc-mannwhitneyu">#</a> <code>mannwhitneyu</code></h3>
<p><code>mannwhitneyu</code> — operation <code>mannwhitneyu</code>. Category: *r / scipy distributions and tests*.</p>
<pre><code class="lang-perl">p mannwhitneyu $x
</code></pre>
</article>
<article class="doc-entry" id="doc-map-bp">
<h3><a class="doc-anchor" href="#doc-map-bp">#</a> <code>map_bp</code></h3>
<p><code>map_bp</code> — operation <code>map bp</code>. Alias for <code>mean_arterial_pressure</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p map_bp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-map-chars">
<h3><a class="doc-anchor" href="#doc-map-chars">#</a> <code>map_chars</code></h3>
<p><code>map_chars</code> — operation <code>map chars</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p map_chars $x
</code></pre>
</article>
<article class="doc-entry" id="doc-map-indexed">
<h3><a class="doc-anchor" href="#doc-map-indexed">#</a> <code>map_indexed</code></h3>
<p><code>map_indexed</code> — operation <code>map indexed</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p map_indexed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-map-keys-fn">
<h3><a class="doc-anchor" href="#doc-map-keys-fn">#</a> <code>map_keys_fn</code></h3>
<p><code>map_keys_fn</code> — operation <code>map keys fn</code>. Category: *hash ops*.</p>
<pre><code class="lang-perl">p map_keys_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-map-range">
<h3><a class="doc-anchor" href="#doc-map-range">#</a> <code>map_range</code></h3>
<p><code>map_range($value, $in_min, $in_max, $out_min, $out_max)</code> (alias <code>remap</code>) — remap a value from one range to another.</p>
<pre><code class="lang-perl">p remap(50, 0, 100, 0, 1) # 0.5
p remap(75, 0, 100, 0, 255) # 191.25 (percent to byte)
</code></pre>
</article>
<article class="doc-entry" id="doc-map-values-fn">
<h3><a class="doc-anchor" href="#doc-map-values-fn">#</a> <code>map_values_fn</code></h3>
<p><code>map_values_fn</code> — operation <code>map values fn</code>. Category: *hash ops*.</p>
<pre><code class="lang-perl">p map_values_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-map-while">
<h3><a class="doc-anchor" href="#doc-map-while">#</a> <code>map_while</code></h3>
<p><code>map_while</code> — operation <code>map while</code>. Category: *rust iterator methods*.</p>
<pre><code class="lang-perl">p map_while $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mapcat">
<h3><a class="doc-anchor" href="#doc-mapcat">#</a> <code>mapcat</code></h3>
<p><code>mapcat</code> — operation <code>mapcat</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p mapcat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mapi">
<h3><a class="doc-anchor" href="#doc-mapi">#</a> <code>mapi</code></h3>
<p><code>mapi</code> — operation <code>mapi</code>. Alias for <code>map_indexed</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p mapi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mapping-class-torus">
<h3><a class="doc-anchor" href="#doc-mapping-class-torus">#</a> <code>mapping_class_torus</code></h3>
<p><code>mapping_class_torus</code> — operation <code>mapping class torus</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p mapping_class_torus $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mapw">
<h3><a class="doc-anchor" href="#doc-mapw">#</a> <code>mapw</code></h3>
<p><code>mapw</code> — operation <code>mapw</code>. Alias for <code>map_while</code>. Category: *rust iterator methods*.</p>
<pre><code class="lang-perl">p mapw $x
</code></pre>
</article>
<article class="doc-entry" id="doc-marcum-q">
<h3><a class="doc-anchor" href="#doc-marcum-q">#</a> <code>marcum_q</code></h3>
<p><code>marcum_q</code> — operation <code>marcum q</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p marcum_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-margalef-richness">
<h3><a class="doc-anchor" href="#doc-margalef-richness">#</a> <code>margalef_richness</code></h3>
<p><code>margalef_richness</code> — operation <code>margalef richness</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p margalef_richness $x
</code></pre>
</article>
<article class="doc-entry" id="doc-margin">
<h3><a class="doc-anchor" href="#doc-margin">#</a> <code>margin</code></h3>
<p><code>margin</code> — operation <code>margin</code>. Category: *finance*.</p>
<pre><code class="lang-perl">p margin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-margin-price">
<h3><a class="doc-anchor" href="#doc-margin-price">#</a> <code>margin_price</code></h3>
<p><code>margin_price</code> — operation <code>margin price</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p margin_price $x
</code></pre>
</article>
<article class="doc-entry" id="doc-margrabe">
<h3><a class="doc-anchor" href="#doc-margrabe">#</a> <code>margrabe</code></h3>
<p><code>margrabe</code> — operation <code>margrabe</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p margrabe $x
</code></pre>
</article>
<article class="doc-entry" id="doc-markdown-render">
<h3><a class="doc-anchor" href="#doc-markdown-render">#</a> <code>markdown_render</code></h3>
<p><code>markdown_render</code> — operation <code>markdown render</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p markdown_render $x
</code></pre>
</article>
<article class="doc-entry" id="doc-markdown-to-html">
<h3><a class="doc-anchor" href="#doc-markdown-to-html">#</a> <code>markdown_to_html</code></h3>
<p><code>markdown_to_html</code> — convert from <code>markdown</code> to <code>html</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p markdown_to_html $value
</code></pre>
</article>
<article class="doc-entry" id="doc-markov-decision-value">
<h3><a class="doc-anchor" href="#doc-markov-decision-value">#</a> <code>markov_decision_value</code></h3>
<p><code>markov_decision_value</code> — Markov chain op <code>decision value</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p markov_decision_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-markov-stationary">
<h3><a class="doc-anchor" href="#doc-markov-stationary">#</a> <code>markov_stationary</code></h3>
<p><code>markov_stationary(transition_matrix, iters=200) → array</code> — power-iteration stationary distribution π.</p>
<pre><code class="lang-perl">p markov_stationary([[0.7,0.3],[0.4,0.6]]) # ≈ [0.571, 0.429]
</code></pre>
</article>
<article class="doc-entry" id="doc-markov-switching-ar">
<h3><a class="doc-anchor" href="#doc-markov-switching-ar">#</a> <code>markov_switching_ar</code></h3>
<p><code>markov_switching_ar</code> — Markov chain op <code>switching ar</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p markov_switching_ar $x
</code></pre>
</article>
<article class="doc-entry" id="doc-markov-switching-mr">
<h3><a class="doc-anchor" href="#doc-markov-switching-mr">#</a> <code>markov_switching_mr</code></h3>
<p><code>markov_switching_mr</code> — Markov chain op <code>switching mr</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p markov_switching_mr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-markov-transition-matrix">
<h3><a class="doc-anchor" href="#doc-markov-transition-matrix">#</a> <code>markov_transition_matrix</code></h3>
<p><code>markov_transition_matrix(state_sequence) → matrix</code> — row-stochastic transition matrix learned from a sequence of integer states.</p>
<pre><code class="lang-perl">p markov_transition_matrix([0,1,1,0,1,0])
</code></pre>
</article>
<article class="doc-entry" id="doc-markup">
<h3><a class="doc-anchor" href="#doc-markup">#</a> <code>markup</code></h3>
<p><code>markup</code> — operation <code>markup</code>. Category: *finance*.</p>
<pre><code class="lang-perl">p markup $x
</code></pre>
</article>
<article class="doc-entry" id="doc-markup-pct">
<h3><a class="doc-anchor" href="#doc-markup-pct">#</a> <code>markup_pct</code></h3>
<p><code>markup_pct(cost, price) → number</code> — <code>(price - cost) / cost · 100</code>.</p>
<pre><code class="lang-perl">p markup_pct(100, 150)
</code></pre>
</article>
<article class="doc-entry" id="doc-markup-price">
<h3><a class="doc-anchor" href="#doc-markup-price">#</a> <code>markup_price</code></h3>
<p><code>markup_price</code> — operation <code>markup price</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p markup_price $x
</code></pre>
</article>
<article class="doc-entry" id="doc-marshallian-demand">
<h3><a class="doc-anchor" href="#doc-marshallian-demand">#</a> <code>marshallian_demand</code></h3>
<p><code>marshallian_demand</code> — operation <code>marshallian demand</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p marshallian_demand $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mask">
<h3><a class="doc-anchor" href="#doc-mask">#</a> <code>mask</code></h3>
<p><code>mask</code> — operation <code>mask</code>. Alias for <code>mask_string</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p mask $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mask-string">
<h3><a class="doc-anchor" href="#doc-mask-string">#</a> <code>mask_string</code></h3>
<p><code>mask_string</code> — operation <code>mask string</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p mask_string $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mass-transport-overpotential">
<h3><a class="doc-anchor" href="#doc-mass-transport-overpotential">#</a> <code>mass_transport_overpotential</code></h3>
<p><code>mass_transport_overpotential</code> — operation <code>mass transport overpotential</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p mass_transport_overpotential $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mat4-determinant">
<h3><a class="doc-anchor" href="#doc-mat4-determinant">#</a> <code>mat4_determinant</code></h3>
<p><code>mat4_determinant(m) → number</code> — explicit 4×4 determinant.</p>
</article>
<article class="doc-entry" id="doc-mat4-identity">
<h3><a class="doc-anchor" href="#doc-mat4-identity">#</a> <code>mat4_identity</code></h3>
<p><code>mat4_identity() → matrix</code> — 4×4 identity matrix.</p>
</article>
<article class="doc-entry" id="doc-mat4-inverse">
<h3><a class="doc-anchor" href="#doc-mat4-inverse">#</a> <code>mat4_inverse</code></h3>
<p><code>mat4_inverse(m) → matrix</code> — explicit 4×4 inverse via cofactor expansion. Returns identity if singular.</p>
</article>
<article class="doc-entry" id="doc-mat4-look-at">
<h3><a class="doc-anchor" href="#doc-mat4-look-at">#</a> <code>mat4_look_at</code></h3>
<p><code>mat4_look_at(eye, center, up) → matrix</code> — right-handed view matrix.</p>
<pre><code class="lang-perl">p mat4_look_at([0,0,5], [0,0,0], [0,1,0])
</code></pre>
</article>
<article class="doc-entry" id="doc-mat4-multiply">
<h3><a class="doc-anchor" href="#doc-mat4-multiply">#</a> <code>mat4_multiply</code></h3>
<p><code>mat4_multiply(a, b) → matrix</code> — <code>a · b</code> matrix product.</p>
</article>
<article class="doc-entry" id="doc-mat4-orthographic">
<h3><a class="doc-anchor" href="#doc-mat4-orthographic">#</a> <code>mat4_orthographic</code></h3>
<p><code>mat4_orthographic(l, r, b, t, n, f) → matrix</code> — orthographic projection.</p>
</article>
<article class="doc-entry" id="doc-mat4-perspective">
<h3><a class="doc-anchor" href="#doc-mat4-perspective">#</a> <code>mat4_perspective</code></h3>
<p><code>mat4_perspective(fov_y_rad, aspect, near, far) → matrix</code> — symmetric perspective projection (right-handed, z to -∞).</p>
<pre><code class="lang-perl">p mat4_perspective(1.5708, 16/9, 0.1, 100)
</code></pre>
</article>
<article class="doc-entry" id="doc-mat4-rotate-axis">
<h3><a class="doc-anchor" href="#doc-mat4-rotate-axis">#</a> <code>mat4_rotate_axis</code></h3>
<p><code>mat4_rotate_axis([x,y,z], angle_rad) → matrix</code> — Rodrigues axis-angle rotation.</p>
</article>
<article class="doc-entry" id="doc-mat4-rotate-x">
<h3><a class="doc-anchor" href="#doc-mat4-rotate-x">#</a> <code>mat4_rotate_x</code></h3>
<p><code>mat4_rotate_x(angle_rad) → matrix</code> — rotation about X axis.</p>
</article>
<article class="doc-entry" id="doc-mat4-rotate-y">
<h3><a class="doc-anchor" href="#doc-mat4-rotate-y">#</a> <code>mat4_rotate_y</code></h3>
<p><code>mat4_rotate_y(angle_rad) → matrix</code> — rotation about Y axis.</p>
</article>
<article class="doc-entry" id="doc-mat4-rotate-z">
<h3><a class="doc-anchor" href="#doc-mat4-rotate-z">#</a> <code>mat4_rotate_z</code></h3>
<p><code>mat4_rotate_z(angle_rad) → matrix</code> — rotation about Z axis.</p>
</article>
<article class="doc-entry" id="doc-mat4-scale">
<h3><a class="doc-anchor" href="#doc-mat4-scale">#</a> <code>mat4_scale</code></h3>
<p><code>mat4_scale([sx,sy,sz]) → matrix</code> — non-uniform scale matrix.</p>
</article>
<article class="doc-entry" id="doc-mat4-translate">
<h3><a class="doc-anchor" href="#doc-mat4-translate">#</a> <code>mat4_translate</code></h3>
<p><code>mat4_translate([x,y,z]) → matrix</code> — translation matrix.</p>
<pre><code class="lang-perl">p mat4_translate([1,2,3])
</code></pre>
</article>
<article class="doc-entry" id="doc-mat4-transpose">
<h3><a class="doc-anchor" href="#doc-mat4-transpose">#</a> <code>mat4_transpose</code></h3>
<p><code>mat4_transpose(m) → matrix</code> — transpose.</p>
</article>
<article class="doc-entry" id="doc-mat-mul">
<h3><a class="doc-anchor" href="#doc-mat-mul">#</a> <code>mat_mul</code></h3>
<p><code>mat_mul</code> — operation <code>mat mul</code>. Alias for <code>matrix_multiply</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p mat_mul $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mat-scale">
<h3><a class="doc-anchor" href="#doc-mat-scale">#</a> <code>mat_scale</code></h3>
<p><code>mat_scale</code> — operation <code>mat scale</code>. Alias for <code>matrix_scale</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mat_scale $x
</code></pre>
</article>
<article class="doc-entry" id="doc-match-all">
<h3><a class="doc-anchor" href="#doc-match-all">#</a> <code>match_all</code></h3>
<p><code>match_all</code> — operation <code>match all</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p match_all $x
</code></pre>
</article>
<article class="doc-entry" id="doc-match-rating">
<h3><a class="doc-anchor" href="#doc-match-rating">#</a> <code>match_rating</code></h3>
<p><code>match_rating</code> — operation <code>match rating</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p match_rating $x
</code></pre>
</article>
<article class="doc-entry" id="doc-match-rating-codex">
<h3><a class="doc-anchor" href="#doc-match-rating-codex">#</a> <code>match_rating_codex</code></h3>
<p><code>match_rating_codex</code> — operation <code>match rating codex</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p match_rating_codex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-match-rating-compare">
<h3><a class="doc-anchor" href="#doc-match-rating-compare">#</a> <code>match_rating_compare</code></h3>
<p><code>match_rating_compare(s1, s2) → 0|1</code> — Match Rating Approach (Moore et al.); 1 if the two names are likely the same.</p>
<pre><code class="lang-perl">p match_rating_compare("Catherine", "Kathryn") # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-matches-regex">
<h3><a class="doc-anchor" href="#doc-matches-regex">#</a> <code>matches_regex</code></h3>
<p><code>matches_regex</code> — operation <code>matches regex</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p matches_regex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matching-bipartite-greedy">
<h3><a class="doc-anchor" href="#doc-matching-bipartite-greedy">#</a> <code>matching_bipartite_greedy</code></h3>
<p><code>matching_bipartite_greedy(edges) → array</code> — greedy matching: first edge to an unmatched pair wins.</p>
<pre><code class="lang-perl">p matching_bipartite_greedy([[0,1],[0,2],[1,2]])
</code></pre>
</article>
<article class="doc-entry" id="doc-matching-bipartite-hungarian">
<h3><a class="doc-anchor" href="#doc-matching-bipartite-hungarian">#</a> <code>matching_bipartite_hungarian</code></h3>
<p><code>matching_bipartite_hungarian(cost_matrix) → array</code> — minimum-cost assignment via Hungarian algorithm. Returns <code>[[i,j], …]</code>.</p>
<pre><code class="lang-perl">p matching_bipartite_hungarian([[4,1,3],[2,0,5],[3,2,2]])
</code></pre>
</article>
<article class="doc-entry" id="doc-matching-market-step">
<h3><a class="doc-anchor" href="#doc-matching-market-step">#</a> <code>matching_market_step</code></h3>
<p><code>matching_market_step</code> — single-step update of <code>matching market</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p matching_market_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matching-pennies-payoff">
<h3><a class="doc-anchor" href="#doc-matching-pennies-payoff">#</a> <code>matching_pennies_payoff</code></h3>
<p><code>matching_pennies_payoff</code> — operation <code>matching pennies payoff</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p matching_pennies_payoff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mathieu-b">
<h3><a class="doc-anchor" href="#doc-mathieu-b">#</a> <code>mathieu_b</code></h3>
<p><code>mathieu_b</code> — operation <code>mathieu b</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p mathieu_b $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mathieu-ce0">
<h3><a class="doc-anchor" href="#doc-mathieu-ce0">#</a> <code>mathieu_ce0</code></h3>
<p><code>mathieu_ce0</code> — operation <code>mathieu ce0</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p mathieu_ce0 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mathieu-se1">
<h3><a class="doc-anchor" href="#doc-mathieu-se1">#</a> <code>mathieu_se1</code></h3>
<p><code>mathieu_se1</code> — operation <code>mathieu se1</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p mathieu_se1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matmul">
<h3><a class="doc-anchor" href="#doc-matmul">#</a> <code>matmul</code></h3>
<p><code>matmul</code> — operation <code>matmul</code>. Alias for <code>matrix_mul</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matmul $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-add">
<h3><a class="doc-anchor" href="#doc-matrix-add">#</a> <code>matrix_add</code></h3>
<p><code>matrix_add</code> — matrix op (dense Vec<Vec<f64>>) <code>add</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matrix_add $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-adjugate">
<h3><a class="doc-anchor" href="#doc-matrix-adjugate">#</a> <code>matrix_adjugate</code></h3>
<p><code>matrix_adjugate(m) → matrix</code> — adjugate (classical adjoint): transpose of the cofactor matrix.</p>
<pre><code class="lang-perl">p matrix_adjugate([[1,2],[3,4]])
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-anti-diagonal">
<h3><a class="doc-anchor" href="#doc-matrix-anti-diagonal">#</a> <code>matrix_anti_diagonal</code></h3>
<p><code>matrix_anti_diagonal</code> — matrix op (dense Vec<Vec<f64>>) <code>anti diagonal</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p matrix_anti_diagonal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-cholesky-decompose">
<h3><a class="doc-anchor" href="#doc-matrix-cholesky-decompose">#</a> <code>matrix_cholesky_decompose</code></h3>
<p><code>matrix_cholesky_decompose(m) → matrix</code> — Cholesky <code>L</code> such that <code>L·Lᵀ = m</code>. Requires <code>m</code> symmetric positive-definite.</p>
<pre><code class="lang-perl">p matrix_cholesky_decompose([[4,12,-16],[12,37,-43],[-16,-43,98]])
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-cofactor">
<h3><a class="doc-anchor" href="#doc-matrix-cofactor">#</a> <code>matrix_cofactor</code></h3>
<p><code>matrix_cofactor(m) → matrix</code> — cofactor matrix: each entry <code>(-1)^(i+j) · |minor(i,j)|</code>.</p>
<pre><code class="lang-perl">p matrix_cofactor([[1,2],[3,4]])
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-col">
<h3><a class="doc-anchor" href="#doc-matrix-col">#</a> <code>matrix_col</code></h3>
<p><code>matrix_col</code> — matrix op (dense Vec<Vec<f64>>) <code>col</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matrix_col $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-cols">
<h3><a class="doc-anchor" href="#doc-matrix-cols">#</a> <code>matrix_cols</code></h3>
<p><code>matrix_cols(m) → int</code> — number of columns (length of first row).</p>
<pre><code class="lang-perl">p matrix_cols([[1,2,3],[4,5,6]]) # 3
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-concat-h">
<h3><a class="doc-anchor" href="#doc-matrix-concat-h">#</a> <code>matrix_concat_h</code></h3>
<p><code>matrix_concat_h(a, b) → matrix</code> — horizontal concatenation (<code>[A|B]</code>); rows must match.</p>
<pre><code class="lang-perl">p matrix_concat_h([[1,2]], [[3,4]])
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-concat-v">
<h3><a class="doc-anchor" href="#doc-matrix-concat-v">#</a> <code>matrix_concat_v</code></h3>
<p><code>matrix_concat_v(a, b) → matrix</code> — vertical concatenation (<code>[A;B]</code>); columns must match.</p>
<pre><code class="lang-perl">p matrix_concat_v([[1,2]], [[3,4]])
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-det">
<h3><a class="doc-anchor" href="#doc-matrix-det">#</a> <code>matrix_det</code></h3>
<p><code>matrix_det</code> — matrix op (dense Vec<Vec<f64>>) <code>det</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matrix_det $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-determinant">
<h3><a class="doc-anchor" href="#doc-matrix-determinant">#</a> <code>matrix_determinant</code></h3>
<p><code>matrix_determinant(m) → number</code> — determinant via Gaussian elimination with partial pivoting. O(n³).</p>
<pre><code class="lang-perl">p matrix_determinant([[1,2],[3,4]]) # -2
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-diag">
<h3><a class="doc-anchor" href="#doc-matrix-diag">#</a> <code>matrix_diag</code></h3>
<p><code>matrix_diag</code> — matrix op (dense Vec<Vec<f64>>) <code>diag</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matrix_diag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-diagonal">
<h3><a class="doc-anchor" href="#doc-matrix-diagonal">#</a> <code>matrix_diagonal</code></h3>
<p><code>matrix_diagonal</code> — matrix op (dense Vec<Vec<f64>>) <code>diagonal</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p matrix_diagonal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-flatten">
<h3><a class="doc-anchor" href="#doc-matrix-flatten">#</a> <code>matrix_flatten</code></h3>
<p><code>matrix_flatten</code> — matrix op (dense Vec<Vec<f64>>) <code>flatten</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p matrix_flatten $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-from-cols">
<h3><a class="doc-anchor" href="#doc-matrix-from-cols">#</a> <code>matrix_from_cols</code></h3>
<p><code>matrix_from_cols(col1, col2, …) → matrix</code> — assemble a matrix column-by-column.</p>
<pre><code class="lang-perl">p matrix_from_cols([1,2,3], [4,5,6])
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-from-rows">
<h3><a class="doc-anchor" href="#doc-matrix-from-rows">#</a> <code>matrix_from_rows</code></h3>
<p><code>matrix_from_rows</code> — matrix op (dense Vec<Vec<f64>>) <code>from rows</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p matrix_from_rows $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-get">
<h3><a class="doc-anchor" href="#doc-matrix-get">#</a> <code>matrix_get</code></h3>
<p><code>matrix_get(m, r, c) → number</code> — element at <code>(row, col)</code>; returns undef if out of bounds.</p>
<pre><code class="lang-perl">p matrix_get([[1,2],[3,4]], 1, 0) # 3
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-hadamard">
<h3><a class="doc-anchor" href="#doc-matrix-hadamard">#</a> <code>matrix_hadamard</code></h3>
<p><code>matrix_hadamard</code> — matrix op (dense Vec<Vec<f64>>) <code>hadamard</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p matrix_hadamard $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-identity">
<h3><a class="doc-anchor" href="#doc-matrix-identity">#</a> <code>matrix_identity</code></h3>
<p><code>matrix_identity</code> — matrix op (dense Vec<Vec<f64>>) <code>identity</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matrix_identity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-identity-q">
<h3><a class="doc-anchor" href="#doc-matrix-identity-q">#</a> <code>matrix_identity_q</code></h3>
<p><code>matrix_identity_q</code> — matrix op (dense Vec<Vec<f64>>) <code>identity q</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p matrix_identity_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-inverse">
<h3><a class="doc-anchor" href="#doc-matrix-inverse">#</a> <code>matrix_inverse</code></h3>
<p><code>matrix_inverse</code> — matrix op (dense Vec<Vec<f64>>) <code>inverse</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p matrix_inverse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-kronecker">
<h3><a class="doc-anchor" href="#doc-matrix-kronecker">#</a> <code>matrix_kronecker</code></h3>
<p><code>matrix_kronecker(a, b) → matrix</code> — Kronecker (tensor) product. Result is <code>(ra·rb) × (ca·cb)</code>.</p>
<pre><code class="lang-perl">p matrix_kronecker([[1,2],[3,4]], [[0,5],[6,7]])
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-lu">
<h3><a class="doc-anchor" href="#doc-matrix-lu">#</a> <code>matrix_lu</code></h3>
<p><code>matrix_lu</code> (alias <code>mlu</code>) computes the LU decomposition with partial pivoting. Returns [L, U, P] where PA = LU.</p>
<pre><code class="lang-perl">my ($L, $U, $P) = @{mlu([[4,3],[6,3]])}
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-lu-decompose">
<h3><a class="doc-anchor" href="#doc-matrix-lu-decompose">#</a> <code>matrix_lu_decompose</code></h3>
<p><code>matrix_lu_decompose(m) → [L, U]</code> — LU decomposition without pivoting (Doolittle). Returns lower-triangular L (unit diag) and upper-triangular U.</p>
<pre><code class="lang-perl">my ($L, $U) = @{matrix_lu_decompose([[4,3],[6,3]])}
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-map">
<h3><a class="doc-anchor" href="#doc-matrix-map">#</a> <code>matrix_map</code></h3>
<p><code>matrix_map</code> — matrix op (dense Vec<Vec<f64>>) <code>map</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p matrix_map $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-max">
<h3><a class="doc-anchor" href="#doc-matrix-max">#</a> <code>matrix_max</code></h3>
<p><code>matrix_max</code> — matrix op (dense Vec<Vec<f64>>) <code>max</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p matrix_max $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-min">
<h3><a class="doc-anchor" href="#doc-matrix-min">#</a> <code>matrix_min</code></h3>
<p><code>matrix_min</code> — matrix op (dense Vec<Vec<f64>>) <code>min</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p matrix_min $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-minor">
<h3><a class="doc-anchor" href="#doc-matrix-minor">#</a> <code>matrix_minor</code></h3>
<p><code>matrix_minor(m, skip_r, skip_c) → matrix</code> — submatrix with row <code>skip_r</code> and column <code>skip_c</code> removed.</p>
<pre><code class="lang-perl">p matrix_minor([[1,2,3],[4,5,6],[7,8,9]], 1, 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-mul">
<h3><a class="doc-anchor" href="#doc-matrix-mul">#</a> <code>matrix_mul</code></h3>
<p><code>matrix_mul</code> — matrix op (dense Vec<Vec<f64>>) <code>mul</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matrix_mul $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-mult">
<h3><a class="doc-anchor" href="#doc-matrix-mult">#</a> <code>matrix_mult</code></h3>
<p><code>matrix_mult</code> — matrix op (dense Vec<Vec<f64>>) <code>mult</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matrix_mult $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-multiply">
<h3><a class="doc-anchor" href="#doc-matrix-multiply">#</a> <code>matrix_multiply</code></h3>
<p><code>matrix_multiply</code> — matrix op (dense Vec<Vec<f64>>) <code>multiply</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p matrix_multiply $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-new">
<h3><a class="doc-anchor" href="#doc-matrix-new">#</a> <code>matrix_new</code></h3>
<p><code>matrix_new(rows, cols=rows, fill=0) → matrix</code> — allocate an <code>rows×cols</code> matrix filled with <code>fill</code>.</p>
<pre><code class="lang-perl">p matrix_new(3, 4, 0) # 3x4 zero matrix
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-norm">
<h3><a class="doc-anchor" href="#doc-matrix-norm">#</a> <code>matrix_norm</code></h3>
<p><code>matrix_norm</code> (alias <code>mnorm</code>) computes a matrix norm. Default is Frobenius; pass 1 for max-column-sum, Inf for max-row-sum.</p>
<pre><code class="lang-perl">p mnorm([[3,4]]) # 5 (Frobenius)
p mnorm([[1,2],[3,4]], 1) # 6 (1-norm)
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-norm-frobenius">
<h3><a class="doc-anchor" href="#doc-matrix-norm-frobenius">#</a> <code>matrix_norm_frobenius</code></h3>
<p><code>matrix_norm_frobenius(m) → number</code> — <code>√(Σ |m[i][j]|²)</code>. Matrix L2 in the entry-wise sense.</p>
<pre><code class="lang-perl">p matrix_norm_frobenius([[1,2],[3,4]]) # sqrt(30) ≈ 5.477
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-norm-l1">
<h3><a class="doc-anchor" href="#doc-matrix-norm-l1">#</a> <code>matrix_norm_l1</code></h3>
<p><code>matrix_norm_l1(m) → number</code> — max absolute column sum.</p>
<pre><code class="lang-perl">p matrix_norm_l1([[1,-2],[3,4]])
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-norm-linf">
<h3><a class="doc-anchor" href="#doc-matrix-norm-linf">#</a> <code>matrix_norm_linf</code></h3>
<p><code>matrix_norm_linf(m) → number</code> — max absolute row sum.</p>
<pre><code class="lang-perl">p matrix_norm_linf([[1,-2],[3,4]])
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-ones">
<h3><a class="doc-anchor" href="#doc-matrix-ones">#</a> <code>matrix_ones</code></h3>
<p><code>matrix_ones</code> — matrix op (dense Vec<Vec<f64>>) <code>ones</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matrix_ones $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-orthogonal-q">
<h3><a class="doc-anchor" href="#doc-matrix-orthogonal-q">#</a> <code>matrix_orthogonal_q</code></h3>
<p><code>matrix_orthogonal_q</code> — matrix op (dense Vec<Vec<f64>>) <code>orthogonal q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p matrix_orthogonal_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-outer-product">
<h3><a class="doc-anchor" href="#doc-matrix-outer-product">#</a> <code>matrix_outer_product</code></h3>
<p><code>matrix_outer_product(u, v) → matrix</code> — outer product <code>u·vᵀ</code>; result is <code>len(u) × len(v)</code>.</p>
<pre><code class="lang-perl">p matrix_outer_product([1,2,3], [4,5])
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-pinv">
<h3><a class="doc-anchor" href="#doc-matrix-pinv">#</a> <code>matrix_pinv</code></h3>
<p><code>matrix_pinv</code> (aliases <code>mpinv</code>, <code>pinv</code>) computes the Moore-Penrose pseudo-inverse via (A^T A)^{-1} A^T.</p>
<pre><code class="lang-perl">my $A_plus = pinv([[1,2],[3,4],[5,6]])
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-power">
<h3><a class="doc-anchor" href="#doc-matrix-power">#</a> <code>matrix_power</code></h3>
<p><code>matrix_power</code> — matrix op (dense Vec<Vec<f64>>) <code>power</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p matrix_power $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-qr">
<h3><a class="doc-anchor" href="#doc-matrix-qr">#</a> <code>matrix_qr</code></h3>
<p><code>matrix_qr</code> (alias <code>mqr</code>) computes the QR decomposition via Gram-Schmidt orthogonalization. Returns [Q, R] where A = QR.</p>
<pre><code class="lang-perl">my ($Q, $R) = @{mqr([[1,1],[1,-1]])}
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-qr-decompose">
<h3><a class="doc-anchor" href="#doc-matrix-qr-decompose">#</a> <code>matrix_qr_decompose</code></h3>
<p><code>matrix_qr_decompose(m) → [Q, R]</code> — Gram-Schmidt QR decomposition. Q has orthonormal columns; R is upper-triangular.</p>
<pre><code class="lang-perl">my ($Q, $R) = @{matrix_qr_decompose($m)}
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-random-normal">
<h3><a class="doc-anchor" href="#doc-matrix-random-normal">#</a> <code>matrix_random_normal</code></h3>
<p><code>matrix_random_normal</code> — matrix op (dense Vec<Vec<f64>>) <code>random normal</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p matrix_random_normal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-random-uniform">
<h3><a class="doc-anchor" href="#doc-matrix-random-uniform">#</a> <code>matrix_random_uniform</code></h3>
<p><code>matrix_random_uniform</code> — matrix op (dense Vec<Vec<f64>>) <code>random uniform</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p matrix_random_uniform $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-reshape">
<h3><a class="doc-anchor" href="#doc-matrix-reshape">#</a> <code>matrix_reshape</code></h3>
<p><code>matrix_reshape(m, new_rows, new_cols) → matrix</code> — reshape preserving element order (row-major flatten then refill).</p>
<pre><code class="lang-perl">p matrix_reshape([[1,2,3,4]], 2, 2)
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-row">
<h3><a class="doc-anchor" href="#doc-matrix-row">#</a> <code>matrix_row</code></h3>
<p><code>matrix_row</code> — matrix op (dense Vec<Vec<f64>>) <code>row</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matrix_row $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-rows">
<h3><a class="doc-anchor" href="#doc-matrix-rows">#</a> <code>matrix_rows</code></h3>
<p><code>matrix_rows(m) → int</code> — number of rows.</p>
<pre><code class="lang-perl">p matrix_rows([[1,2],[3,4],[5,6]]) # 3
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-scalar">
<h3><a class="doc-anchor" href="#doc-matrix-scalar">#</a> <code>matrix_scalar</code></h3>
<p><code>matrix_scalar</code> — matrix op (dense Vec<Vec<f64>>) <code>scalar</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matrix_scalar $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-scale">
<h3><a class="doc-anchor" href="#doc-matrix-scale">#</a> <code>matrix_scale</code></h3>
<p><code>matrix_scale</code> — matrix op (dense Vec<Vec<f64>>) <code>scale</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matrix_scale $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-set">
<h3><a class="doc-anchor" href="#doc-matrix-set">#</a> <code>matrix_set</code></h3>
<p><code>matrix_set(m, r, c, v) → matrix</code> — returns a new matrix with <code>m[r][c] = v</code>.</p>
<pre><code class="lang-perl">p matrix_set([[1,2],[3,4]], 0, 1, 99)
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-shape">
<h3><a class="doc-anchor" href="#doc-matrix-shape">#</a> <code>matrix_shape</code></h3>
<p><code>matrix_shape</code> — matrix op (dense Vec<Vec<f64>>) <code>shape</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matrix_shape $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-solve">
<h3><a class="doc-anchor" href="#doc-matrix-solve">#</a> <code>matrix_solve</code></h3>
<p><code>matrix_solve</code> (aliases <code>msolve</code>, <code>solve</code>) solves the linear system Ax=b via Gaussian elimination with partial pivoting. Returns the solution vector x.</p>
<pre><code class="lang-perl">my $A = [[2,1],[-1,1]]
my $b = [5,2]
my $x = solve($A, $b) # [1, 3]
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-sub">
<h3><a class="doc-anchor" href="#doc-matrix-sub">#</a> <code>matrix_sub</code></h3>
<p><code>matrix_sub</code> — matrix op (dense Vec<Vec<f64>>) <code>sub</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matrix_sub $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-submatrix">
<h3><a class="doc-anchor" href="#doc-matrix-submatrix">#</a> <code>matrix_submatrix</code></h3>
<p><code>matrix_submatrix(m, r0, c0, nr, nc) → matrix</code> — <code>nr×nc</code> block starting at <code>(r0,c0)</code>.</p>
<pre><code class="lang-perl">p matrix_submatrix([[1,2,3],[4,5,6],[7,8,9]], 1, 1, 2, 2)
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-sum">
<h3><a class="doc-anchor" href="#doc-matrix-sum">#</a> <code>matrix_sum</code></h3>
<p><code>matrix_sum</code> — matrix op (dense Vec<Vec<f64>>) <code>sum</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p matrix_sum @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-swap-cols">
<h3><a class="doc-anchor" href="#doc-matrix-swap-cols">#</a> <code>matrix_swap_cols</code></h3>
<p><code>matrix_swap_cols(m, i, j) → matrix</code> — swap two columns across all rows.</p>
</article>
<article class="doc-entry" id="doc-matrix-swap-rows">
<h3><a class="doc-anchor" href="#doc-matrix-swap-rows">#</a> <code>matrix_swap_rows</code></h3>
<p><code>matrix_swap_rows(m, i, j) → matrix</code> — swap two rows.</p>
</article>
<article class="doc-entry" id="doc-matrix-symmetric-q">
<h3><a class="doc-anchor" href="#doc-matrix-symmetric-q">#</a> <code>matrix_symmetric_q</code></h3>
<p><code>matrix_symmetric_q</code> — matrix op (dense Vec<Vec<f64>>) <code>symmetric q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p matrix_symmetric_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-to-string">
<h3><a class="doc-anchor" href="#doc-matrix-to-string">#</a> <code>matrix_to_string</code></h3>
<p><code>matrix_to_string(m) → string</code> — pretty-print rows joined by newlines, each row comma-separated with 4 decimal places.</p>
<pre><code class="lang-perl">print matrix_to_string([[1.5,2.7],[3.14,4.2]])
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-trace">
<h3><a class="doc-anchor" href="#doc-matrix-trace">#</a> <code>matrix_trace</code></h3>
<p><code>matrix_trace</code> — matrix op (dense Vec<Vec<f64>>) <code>trace</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matrix_trace $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-transpose">
<h3><a class="doc-anchor" href="#doc-matrix-transpose">#</a> <code>matrix_transpose</code></h3>
<p><code>matrix_transpose</code> — matrix op (dense Vec<Vec<f64>>) <code>transpose</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p matrix_transpose $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-vec-mul">
<h3><a class="doc-anchor" href="#doc-matrix-vec-mul">#</a> <code>matrix_vec_mul</code></h3>
<p><code>matrix_vec_mul(m, v) → array</code> — matrix-vector product <code>m·v</code>.</p>
<pre><code class="lang-perl">p matrix_vec_mul([[1,2],[3,4]], [5,6]) # [17, 39]
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-zero-q">
<h3><a class="doc-anchor" href="#doc-matrix-zero-q">#</a> <code>matrix_zero_q</code></h3>
<p><code>matrix_zero_q</code> — matrix op (dense Vec<Vec<f64>>) <code>zero q</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p matrix_zero_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matrix-zeros">
<h3><a class="doc-anchor" href="#doc-matrix-zeros">#</a> <code>matrix_zeros</code></h3>
<p><code>matrix_zeros</code> — matrix op (dense Vec<Vec<f64>>) <code>zeros</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p matrix_zeros $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matroid-greedy-step">
<h3><a class="doc-anchor" href="#doc-matroid-greedy-step">#</a> <code>matroid_greedy_step</code></h3>
<p><code>matroid_greedy_step</code> — single-step update of <code>matroid greedy</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p matroid_greedy_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-matroid-intersection-step">
<h3><a class="doc-anchor" href="#doc-matroid-intersection-step">#</a> <code>matroid_intersection_step</code></h3>
<p><code>matroid_intersection_step</code> — single-step update of <code>matroid intersection</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p matroid_intersection_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-max2">
<h3><a class="doc-anchor" href="#doc-max2">#</a> <code>max2</code></h3>
<p><code>max2</code> — operation <code>max2</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p max2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-max-abs">
<h3><a class="doc-anchor" href="#doc-max-abs">#</a> <code>max_abs</code></h3>
<p><code>max_abs</code> — operation <code>max abs</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p max_abs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-max-by">
<h3><a class="doc-anchor" href="#doc-max-by">#</a> <code>max_by</code></h3>
<p><code>max_by</code> — operation <code>max by</code>. Alias for <code>take_while</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p max_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-max-degree">
<h3><a class="doc-anchor" href="#doc-max-degree">#</a> <code>max_degree</code></h3>
<p><code>max_degree</code> — operation <code>max degree</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p max_degree $x
</code></pre>
</article>
<article class="doc-entry" id="doc-max-drawdown">
<h3><a class="doc-anchor" href="#doc-max-drawdown">#</a> <code>max_drawdown</code></h3>
<p><code>max_drawdown(@equity_curve)</code> (alias <code>mdd</code>) — computes the maximum peak-to-trough decline in a series of values. Returns as a decimal (0.2 = 20% drawdown). Key risk metric.</p>
<pre><code class="lang-perl">my @equity = (100, 120, 90, 110, 85, 130)
p mdd(@equity) # ~0.29 (29% max drawdown)
</code></pre>
</article>
<article class="doc-entry" id="doc-max-drawdown-arr">
<h3><a class="doc-anchor" href="#doc-max-drawdown-arr">#</a> <code>max_drawdown_arr</code></h3>
<p><code>max_drawdown_arr</code> — operation <code>max drawdown arr</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p max_drawdown_arr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-max-float">
<h3><a class="doc-anchor" href="#doc-max-float">#</a> <code>max_float</code></h3>
<p><code>max_float</code> — operation <code>max float</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p max_float $x
</code></pre>
</article>
<article class="doc-entry" id="doc-max-flow-ek">
<h3><a class="doc-anchor" href="#doc-max-flow-ek">#</a> <code>max_flow_ek</code></h3>
<p><code>max_flow_ek</code> — operation <code>max flow ek</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p max_flow_ek $x
</code></pre>
</article>
<article class="doc-entry" id="doc-max-flow-ford-fulkerson-step">
<h3><a class="doc-anchor" href="#doc-max-flow-ford-fulkerson-step">#</a> <code>max_flow_ford_fulkerson_step</code></h3>
<p><code>max_flow_ford_fulkerson_step</code> — single-step update of <code>max flow ford fulkerson</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p max_flow_ford_fulkerson_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-max-heart-rate">
<h3><a class="doc-anchor" href="#doc-max-heart-rate">#</a> <code>max_heart_rate</code></h3>
<p><code>max_heart_rate</code> — rate of <code>max heart</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p max_heart_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-max-independent-set">
<h3><a class="doc-anchor" href="#doc-max-independent-set">#</a> <code>max_independent_set</code></h3>
<p><code>max_independent_set</code> — operation <code>max independent set</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p max_independent_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-max-list">
<h3><a class="doc-anchor" href="#doc-max-list">#</a> <code>max_list</code></h3>
<p><code>max_list</code> — operation <code>max list</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p max_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-max-norm">
<h3><a class="doc-anchor" href="#doc-max-norm">#</a> <code>max_norm</code></h3>
<p><code>max_norm</code> — norm (vector length-like) of <code>max</code>. Alias for <code>linf_norm</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p max_norm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-max-of">
<h3><a class="doc-anchor" href="#doc-max-of">#</a> <code>max_of</code></h3>
<p><code>max_of</code> — operation <code>max of</code>. Category: *more list helpers*.</p>
<pre><code class="lang-perl">p max_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-max-sum-subarray">
<h3><a class="doc-anchor" href="#doc-max-sum-subarray">#</a> <code>max_sum_subarray</code></h3>
<p><code>max_sum_subarray</code> — operation <code>max sum subarray</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p max_sum_subarray $x
</code></pre>
</article>
<article class="doc-entry" id="doc-maxby">
<h3><a class="doc-anchor" href="#doc-maxby">#</a> <code>maxby</code></h3>
<p><code>maxby</code> — operation <code>maxby</code>. Alias for <code>maximum_by</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p maxby $x
</code></pre>
</article>
<article class="doc-entry" id="doc-maxdd">
<h3><a class="doc-anchor" href="#doc-maxdd">#</a> <code>maxdd</code></h3>
<p><code>maxdd</code> — operation <code>maxdd</code>. Alias for <code>max_drawdown</code>. Category: *finance (extended)*.</p>
<pre><code class="lang-perl">p maxdd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-maximin-share">
<h3><a class="doc-anchor" href="#doc-maximin-share">#</a> <code>maximin_share</code></h3>
<p><code>maximin_share</code> — operation <code>maximin share</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p maximin_share $x
</code></pre>
</article>
<article class="doc-entry" id="doc-maximum-a-posteriori">
<h3><a class="doc-anchor" href="#doc-maximum-a-posteriori">#</a> <code>maximum_a_posteriori</code></h3>
<p><code>maximum_a_posteriori(posterior) → int</code> — argmax of a posterior probability array.</p>
</article>
<article class="doc-entry" id="doc-maximum-bipartite-matching">
<h3><a class="doc-anchor" href="#doc-maximum-bipartite-matching">#</a> <code>maximum_bipartite_matching</code></h3>
<p><code>maximum_bipartite_matching</code> — operation <code>maximum bipartite matching</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p maximum_bipartite_matching $x
</code></pre>
</article>
<article class="doc-entry" id="doc-maximum-by">
<h3><a class="doc-anchor" href="#doc-maximum-by">#</a> <code>maximum_by</code></h3>
<p><code>maximum_by</code> — operation <code>maximum by</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p maximum_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-maxstr">
<h3><a class="doc-anchor" href="#doc-maxstr">#</a> <code>maxstr</code></h3>
<p><code>maxstr</code> — operation <code>maxstr</code>. Category: *list / aggregate*.</p>
<pre><code class="lang-perl">p maxstr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-maxsub">
<h3><a class="doc-anchor" href="#doc-maxsub">#</a> <code>maxsub</code></h3>
<p><code>maxsub</code> — operation <code>maxsub</code>. Alias for <code>max_sum_subarray</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p maxsub $x
</code></pre>
</article>
<article class="doc-entry" id="doc-maya-long-count-from-fixed">
<h3><a class="doc-anchor" href="#doc-maya-long-count-from-fixed">#</a> <code>maya_long_count_from_fixed</code></h3>
<p><code>maya_long_count_from_fixed</code> — operation <code>maya long count from fixed</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p maya_long_count_from_fixed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mayan-haab-from-fixed">
<h3><a class="doc-anchor" href="#doc-mayan-haab-from-fixed">#</a> <code>mayan_haab_from_fixed</code></h3>
<p><code>mayan_haab_from_fixed</code> — operation <code>mayan haab from fixed</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p mayan_haab_from_fixed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mayan-tzolkin-from-fixed">
<h3><a class="doc-anchor" href="#doc-mayan-tzolkin-from-fixed">#</a> <code>mayan_tzolkin_from_fixed</code></h3>
<p><code>mayan_tzolkin_from_fixed</code> — operation <code>mayan tzolkin from fixed</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p mayan_tzolkin_from_fixed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mb-to-bytes">
<h3><a class="doc-anchor" href="#doc-mb-to-bytes">#</a> <code>mb_to_bytes</code></h3>
<p><code>mb_to_bytes</code> — convert from <code>mb</code> to <code>bytes</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p mb_to_bytes $value
</code></pre>
</article>
<article class="doc-entry" id="doc-mb-to-gb">
<h3><a class="doc-anchor" href="#doc-mb-to-gb">#</a> <code>mb_to_gb</code></h3>
<p><code>mb_to_gb</code> — convert from <code>mb</code> to <code>gb</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p mb_to_gb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-mc-limiter">
<h3><a class="doc-anchor" href="#doc-mc-limiter">#</a> <code>mc_limiter</code></h3>
<p><code>mc_limiter</code> — operation <code>mc limiter</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p mc_limiter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mcat">
<h3><a class="doc-anchor" href="#doc-mcat">#</a> <code>mcat</code></h3>
<p><code>mcat</code> — operation <code>mcat</code>. Alias for <code>mapcat</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p mcat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mcc">
<h3><a class="doc-anchor" href="#doc-mcc">#</a> <code>mcc</code></h3>
<p><code>mcc</code> — operation <code>mcc</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p mcc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mcol">
<h3><a class="doc-anchor" href="#doc-mcol">#</a> <code>mcol</code></h3>
<p><code>mcol</code> — operation <code>mcol</code>. Alias for <code>matrix_col</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mcol $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mcp-serve-registered-tools">
<h3><a class="doc-anchor" href="#doc-mcp-serve-registered-tools">#</a> <code>mcp_serve_registered_tools</code></h3>
<p><code>mcp_serve_registered_tools("server-name")</code> — convert every tool registered via <code>tool fn</code> / <code>ai_register_tool</code> into MCP server schema and run the stdio JSON-RPC loop. Used by <code>stryke build --mcp-server</code>.</p>
</article>
<article class="doc-entry" id="doc-md5">
<h3><a class="doc-anchor" href="#doc-md5">#</a> <code>md5</code></h3>
<p><code>md5</code> — operation <code>md5</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p md5 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mdet">
<h3><a class="doc-anchor" href="#doc-mdet">#</a> <code>mdet</code></h3>
<p><code>mdet</code> — operation <code>mdet</code>. Alias for <code>matrix_det</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mdet $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mdiag">
<h3><a class="doc-anchor" href="#doc-mdiag">#</a> <code>mdiag</code></h3>
<p><code>mdiag</code> — operation <code>mdiag</code>. Alias for <code>matrix_diag</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mdiag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mdiagvec">
<h3><a class="doc-anchor" href="#doc-mdiagvec">#</a> <code>mdiagvec</code></h3>
<p><code>mdiagvec</code> — operation <code>mdiagvec</code>. Alias for <code>matrix_diagonal</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p mdiagvec $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mdist">
<h3><a class="doc-anchor" href="#doc-mdist">#</a> <code>mdist</code></h3>
<p><code>mdist</code> — operation <code>mdist</code>. Alias for <code>manhattan_distance</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p mdist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mduration">
<h3><a class="doc-anchor" href="#doc-mduration">#</a> <code>mduration</code></h3>
<p><code>mduration</code> — operation <code>mduration</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p mduration $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mean-absolute-error">
<h3><a class="doc-anchor" href="#doc-mean-absolute-error">#</a> <code>mean_absolute_error</code></h3>
<p><code>mean_absolute_error</code> — operation <code>mean absolute error</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p mean_absolute_error $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mean-activity-coeff-pitzer">
<h3><a class="doc-anchor" href="#doc-mean-activity-coeff-pitzer">#</a> <code>mean_activity_coeff_pitzer</code></h3>
<p><code>mean_activity_coeff_pitzer</code> — operation <code>mean activity coeff pitzer</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p mean_activity_coeff_pitzer $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mean-arterial-pressure">
<h3><a class="doc-anchor" href="#doc-mean-arterial-pressure">#</a> <code>mean_arterial_pressure</code></h3>
<p><code>mean_arterial_pressure</code> — operation <code>mean arterial pressure</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p mean_arterial_pressure $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mean-curvature-step">
<h3><a class="doc-anchor" href="#doc-mean-curvature-step">#</a> <code>mean_curvature_step</code></h3>
<p><code>mean_curvature_step</code> — single-step update of <code>mean curvature</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p mean_curvature_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mean-filter-window">
<h3><a class="doc-anchor" href="#doc-mean-filter-window">#</a> <code>mean_filter_window</code></h3>
<p><code>mean_filter_window</code> — operation <code>mean filter window</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p mean_filter_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mean-list">
<h3><a class="doc-anchor" href="#doc-mean-list">#</a> <code>mean_list</code></h3>
<p><code>mean_list</code> — operation <code>mean list</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p mean_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mean-solar-anomaly">
<h3><a class="doc-anchor" href="#doc-mean-solar-anomaly">#</a> <code>mean_solar_anomaly</code></h3>
<p><code>mean_solar_anomaly</code> — operation <code>mean solar anomaly</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p mean_solar_anomaly $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mean-solar-longitude">
<h3><a class="doc-anchor" href="#doc-mean-solar-longitude">#</a> <code>mean_solar_longitude</code></h3>
<p><code>mean_solar_longitude</code> — operation <code>mean solar longitude</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p mean_solar_longitude $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mean-squared-error">
<h3><a class="doc-anchor" href="#doc-mean-squared-error">#</a> <code>mean_squared_error</code></h3>
<p><code>mean_squared_error</code> — operation <code>mean squared error</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p mean_squared_error $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mean-tone-freq">
<h3><a class="doc-anchor" href="#doc-mean-tone-freq">#</a> <code>mean_tone_freq</code></h3>
<p><code>mean_tone_freq</code> — operation <code>mean tone freq</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p mean_tone_freq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-measure">
<h3><a class="doc-anchor" href="#doc-measure">#</a> <code>measure</code></h3>
<p><code>measure</code> — operation <code>measure</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p measure $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mechanism-design-obj">
<h3><a class="doc-anchor" href="#doc-mechanism-design-obj">#</a> <code>mechanism_design_obj</code></h3>
<p><code>mechanism_design_obj</code> — operation <code>mechanism design obj</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p mechanism_design_obj $x
</code></pre>
</article>
<article class="doc-entry" id="doc-medfilt">
<h3><a class="doc-anchor" href="#doc-medfilt">#</a> <code>medfilt</code></h3>
<p><code>median_filter(\@signal, $window_size)</code> (alias <code>medfilt</code>) — applies a median filter for noise removal. Each output is the median of the surrounding window. Excellent for removing impulse noise while preserving edges.</p>
<pre><code class="lang-perl">my @spiky = (1, 2, 100, 3, 4) # 100 is spike
my $clean = medfilt(\@spiky, 3)
p @$clean # spike removed
</code></pre>
</article>
<article class="doc-entry" id="doc-medfilt-1d">
<h3><a class="doc-anchor" href="#doc-medfilt-1d">#</a> <code>medfilt_1d</code></h3>
<p><code>medfilt_1d</code> — operation <code>medfilt 1d</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p medfilt_1d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-median-absolute-deviation">
<h3><a class="doc-anchor" href="#doc-median-absolute-deviation">#</a> <code>median_absolute_deviation</code></h3>
<p><code>median_absolute_deviation</code> — operation <code>median absolute deviation</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p median_absolute_deviation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-median-filter-window">
<h3><a class="doc-anchor" href="#doc-median-filter-window">#</a> <code>median_filter_window</code></h3>
<p><code>median_filter_window</code> — operation <code>median filter window</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p median_filter_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-median-voter-step">
<h3><a class="doc-anchor" href="#doc-median-voter-step">#</a> <code>median_voter_step</code></h3>
<p><code>median_voter_step</code> — single-step update of <code>median voter</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p median_voter_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mem-free">
<h3><a class="doc-anchor" href="#doc-mem-free">#</a> <code>mem_free</code></h3>
<p><code>mem_free</code> — free/available physical RAM in bytes. On Linux reads <code>MemAvailable</code> from <code>/proc/meminfo</code> (falls back to <code>MemFree</code>). On macOS uses <code>vm.page_free_count</code> via sysctl. Returns <code>undef</code> on unsupported platforms.</p>
<pre><code class="lang-perl">p mem_free # 3821666304
p format_bytes(mem_free) # 3.6 GiB
my $pct = int(mem_free / mem_total * 100)
p "$pct% free"
</code></pre>
</article>
<article class="doc-entry" id="doc-mem-total">
<h3><a class="doc-anchor" href="#doc-mem-total">#</a> <code>mem_total</code></h3>
<p><code>mem_total</code> — total physical RAM in bytes. Uses <code>/proc/meminfo</code> on Linux, <code>sysctlbyname("hw.memsize")</code> on macOS. Returns <code>undef</code> on unsupported platforms.</p>
<pre><code class="lang-perl">p mem_total # 68719476736
p format_bytes(mem_total) # 64.0 GiB
</code></pre>
</article>
<article class="doc-entry" id="doc-mem-used">
<h3><a class="doc-anchor" href="#doc-mem-used">#</a> <code>mem_used</code></h3>
<p><code>mem_used</code> — used physical RAM in bytes (total - free). Returns <code>undef</code> if either <code>mem_total</code> or <code>mem_free</code> is unavailable.</p>
<pre><code class="lang-perl">p format_bytes(mem_used) # 60.4 GiB
gauge(mem_used / mem_total) |> p # memory usage gauge
</code></pre>
</article>
<article class="doc-entry" id="doc-membership-idx">
<h3><a class="doc-anchor" href="#doc-membership-idx">#</a> <code>membership_idx</code></h3>
<p><code>membership_idx</code> — operation <code>membership idx</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p membership_idx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-menhinick-richness">
<h3><a class="doc-anchor" href="#doc-menhinick-richness">#</a> <code>menhinick_richness</code></h3>
<p><code>menhinick_richness</code> — operation <code>menhinick richness</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p menhinick_richness $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mercator-project-x">
<h3><a class="doc-anchor" href="#doc-mercator-project-x">#</a> <code>mercator_project_x</code></h3>
<p><code>mercator_project_x(lon_deg) → number</code> — spherical Mercator x in meters using WGS84 radius.</p>
<pre><code class="lang-perl">p mercator_project_x(-122.4194)
</code></pre>
</article>
<article class="doc-entry" id="doc-mercator-project-y">
<h3><a class="doc-anchor" href="#doc-mercator-project-y">#</a> <code>mercator_project_y</code></h3>
<p><code>mercator_project_y(lat_deg) → number</code> — spherical Mercator y in meters; clamps lat to ±85.05° to stay finite.</p>
<pre><code class="lang-perl">p mercator_project_y(37.7749)
</code></pre>
</article>
<article class="doc-entry" id="doc-mercator-unproject">
<h3><a class="doc-anchor" href="#doc-mercator-unproject">#</a> <code>mercator_unproject</code></h3>
<p><code>mercator_unproject</code> — operation <code>mercator unproject</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p mercator_unproject $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mercator-unproject-lat">
<h3><a class="doc-anchor" href="#doc-mercator-unproject-lat">#</a> <code>mercator_unproject_lat</code></h3>
<p><code>mercator_unproject_lat(y) → number</code> — inverse Mercator latitude in degrees.</p>
</article>
<article class="doc-entry" id="doc-mercator-unproject-lon">
<h3><a class="doc-anchor" href="#doc-mercator-unproject-lon">#</a> <code>mercator_unproject_lon</code></h3>
<p><code>mercator_unproject_lon(x) → number</code> — inverse Mercator longitude in degrees.</p>
</article>
<article class="doc-entry" id="doc-mercury-perihelion-advance">
<h3><a class="doc-anchor" href="#doc-mercury-perihelion-advance">#</a> <code>mercury_perihelion_advance</code></h3>
<p><code>mercury_perihelion_advance</code> — operation <code>mercury perihelion advance</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p mercury_perihelion_advance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-merge-hash">
<h3><a class="doc-anchor" href="#doc-merge-hash">#</a> <code>merge_hash</code></h3>
<p><code>merge_hash</code> — hash function of <code>merge</code>. Category: *hash helpers*.</p>
<pre><code class="lang-perl">p merge_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-merge-sorted">
<h3><a class="doc-anchor" href="#doc-merge-sorted">#</a> <code>merge_sorted</code></h3>
<p><code>merge_sorted</code> — operation <code>merge sorted</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p merge_sorted $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mertens">
<h3><a class="doc-anchor" href="#doc-mertens">#</a> <code>mertens</code></h3>
<p><code>mertens</code> — operation <code>mertens</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p mertens $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mertens-zamir-step">
<h3><a class="doc-anchor" href="#doc-mertens-zamir-step">#</a> <code>mertens_zamir_step</code></h3>
<p><code>mertens_zamir_step</code> — single-step update of <code>mertens zamir</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p mertens_zamir_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-merton-jump-call">
<h3><a class="doc-anchor" href="#doc-merton-jump-call">#</a> <code>merton_jump_call</code></h3>
<p><code>merton_jump_call</code> — operation <code>merton jump call</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p merton_jump_call $x
</code></pre>
</article>
<article class="doc-entry" id="doc-metal-corrosion-rate">
<h3><a class="doc-anchor" href="#doc-metal-corrosion-rate">#</a> <code>metal_corrosion_rate</code></h3>
<p><code>metal_corrosion_rate</code> — rate of <code>metal corrosion</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p metal_corrosion_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-metamorphic-grade">
<h3><a class="doc-anchor" href="#doc-metamorphic-grade">#</a> <code>metamorphic_grade</code></h3>
<p><code>metamorphic_grade</code> — operation <code>metamorphic grade</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p metamorphic_grade $x
</code></pre>
</article>
<article class="doc-entry" id="doc-metaphone">
<h3><a class="doc-anchor" href="#doc-metaphone">#</a> <code>metaphone</code></h3>
<p><code>metaphone</code> — operation <code>metaphone</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p metaphone $x
</code></pre>
</article>
<article class="doc-entry" id="doc-metaphone-phonetic">
<h3><a class="doc-anchor" href="#doc-metaphone-phonetic">#</a> <code>metaphone_phonetic</code></h3>
<p><code>metaphone_phonetic</code> — operation <code>metaphone phonetic</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p metaphone_phonetic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-meters-to-feet">
<h3><a class="doc-anchor" href="#doc-meters-to-feet">#</a> <code>meters_to_feet</code></h3>
<p><code>meters_to_feet</code> — convert from <code>meters</code> to <code>feet</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p meters_to_feet $value
</code></pre>
</article>
<article class="doc-entry" id="doc-methane-growth-rate">
<h3><a class="doc-anchor" href="#doc-methane-growth-rate">#</a> <code>methane_growth_rate</code></h3>
<p><code>methane_growth_rate</code> — rate of <code>methane growth</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p methane_growth_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-metonic-cycle">
<h3><a class="doc-anchor" href="#doc-metonic-cycle">#</a> <code>metonic_cycle</code></h3>
<p><code>metonic_cycle</code> — operation <code>metonic cycle</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p metonic_cycle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-metph">
<h3><a class="doc-anchor" href="#doc-metph">#</a> <code>metph</code></h3>
<p><code>metph</code> — operation <code>metph</code>. Alias for <code>metaphone</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p metph $x
</code></pre>
</article>
<article class="doc-entry" id="doc-metric-frw-lapse">
<h3><a class="doc-anchor" href="#doc-metric-frw-lapse">#</a> <code>metric_frw_lapse</code></h3>
<p><code>metric_frw_lapse</code> — operation <code>metric frw lapse</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p metric_frw_lapse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-metric-kerr-step-simple">
<h3><a class="doc-anchor" href="#doc-metric-kerr-step-simple">#</a> <code>metric_kerr_step_simple</code></h3>
<p><code>metric_kerr_step_simple</code> — operation <code>metric kerr step simple</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p metric_kerr_step_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-metric-minkowski-eta-step">
<h3><a class="doc-anchor" href="#doc-metric-minkowski-eta-step">#</a> <code>metric_minkowski_eta_step</code></h3>
<p><code>metric_minkowski_eta_step</code> — single-step update of <code>metric minkowski eta</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p metric_minkowski_eta_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-metric-schwarzschild-step">
<h3><a class="doc-anchor" href="#doc-metric-schwarzschild-step">#</a> <code>metric_schwarzschild_step</code></h3>
<p><code>metric_schwarzschild_step</code> — single-step update of <code>metric schwarzschild</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p metric_schwarzschild_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-metro-hash-64">
<h3><a class="doc-anchor" href="#doc-metro-hash-64">#</a> <code>metro_hash_64</code></h3>
<p><code>metro_hash_64</code> — operation <code>metro hash 64</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p metro_hash_64 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mexican-hat-wavelet">
<h3><a class="doc-anchor" href="#doc-mexican-hat-wavelet">#</a> <code>mexican_hat_wavelet</code></h3>
<p><code>mexican_hat_wavelet</code> — operation <code>mexican hat wavelet</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p mexican_hat_wavelet $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mfcc-coeff-step">
<h3><a class="doc-anchor" href="#doc-mfcc-coeff-step">#</a> <code>mfcc_coeff_step</code></h3>
<p><code>mfcc_coeff_step</code> — single-step update of <code>mfcc coeff</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p mfcc_coeff_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mflat">
<h3><a class="doc-anchor" href="#doc-mflat">#</a> <code>mflat</code></h3>
<p><code>mflat</code> — operation <code>mflat</code>. Alias for <code>matrix_flatten</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p mflat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mfromr">
<h3><a class="doc-anchor" href="#doc-mfromr">#</a> <code>mfromr</code></h3>
<p><code>mfromr</code> — operation <code>mfromr</code>. Alias for <code>matrix_from_rows</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p mfromr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mget">
<h3><a class="doc-anchor" href="#doc-mget">#</a> <code>mget</code></h3>
<p><code>mget</code> — operation <code>mget</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p mget $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mgrs-decode">
<h3><a class="doc-anchor" href="#doc-mgrs-decode">#</a> <code>mgrs_decode</code></h3>
<p><code>mgrs_decode</code> — decode of <code>mgrs</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p mgrs_decode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mgrs-encode">
<h3><a class="doc-anchor" href="#doc-mgrs-encode">#</a> <code>mgrs_encode</code></h3>
<p><code>mgrs_encode</code> — encode of <code>mgrs</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p mgrs_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mhad">
<h3><a class="doc-anchor" href="#doc-mhad">#</a> <code>mhad</code></h3>
<p><code>mhad</code> — operation <code>mhad</code>. Alias for <code>matrix_hadamard</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p mhad $x
</code></pre>
</article>
<article class="doc-entry" id="doc-michaelis-menten">
<h3><a class="doc-anchor" href="#doc-michaelis-menten">#</a> <code>michaelis_menten</code></h3>
<p><code>michaelis_menten</code> — operation <code>michaelis menten</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p michaelis_menten $x
</code></pre>
</article>
<article class="doc-entry" id="doc-microlensing-magnification">
<h3><a class="doc-anchor" href="#doc-microlensing-magnification">#</a> <code>microlensing_magnification</code></h3>
<p><code>microlensing_magnification</code> — operation <code>microlensing magnification</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p microlensing_magnification $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mid-str">
<h3><a class="doc-anchor" href="#doc-mid-str">#</a> <code>mid_str</code></h3>
<p><code>mid_str</code> — operation <code>mid str</code>. Category: *string*.</p>
<pre><code class="lang-perl">p mid_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mident">
<h3><a class="doc-anchor" href="#doc-mident">#</a> <code>mident</code></h3>
<p><code>mident</code> — operation <code>mident</code>. Alias for <code>matrix_identity</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mident $x
</code></pre>
</article>
<article class="doc-entry" id="doc-midi-note-to-name">
<h3><a class="doc-anchor" href="#doc-midi-note-to-name">#</a> <code>midi_note_to_name</code></h3>
<p><code>midi_note_to_name</code> — convert from <code>midi note</code> to <code>name</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p midi_note_to_name $value
</code></pre>
</article>
<article class="doc-entry" id="doc-midi-to-hz">
<h3><a class="doc-anchor" href="#doc-midi-to-hz">#</a> <code>midi_to_hz</code></h3>
<p><code>midi_to_hz</code> — convert from <code>midi</code> to <code>hz</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p midi_to_hz $value
</code></pre>
</article>
<article class="doc-entry" id="doc-midi-to-note-name">
<h3><a class="doc-anchor" href="#doc-midi-to-note-name">#</a> <code>midi_to_note_name</code></h3>
<p><code>midi_to_note_name(midi) → string</code> — convert MIDI note number (0-127) to scientific pitch notation.</p>
<pre><code class="lang-perl">p midi_to_note_name(60) # C4
p midi_to_note_name(69) # A4
</code></pre>
</article>
<article class="doc-entry" id="doc-midi-to-pitch-class">
<h3><a class="doc-anchor" href="#doc-midi-to-pitch-class">#</a> <code>midi_to_pitch_class</code></h3>
<p><code>midi_to_pitch_class</code> — convert from <code>midi</code> to <code>pitch class</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p midi_to_pitch_class $value
</code></pre>
</article>
<article class="doc-entry" id="doc-midpnt">
<h3><a class="doc-anchor" href="#doc-midpnt">#</a> <code>midpnt</code></h3>
<p><code>midpnt</code> — operation <code>midpnt</code>. Alias for <code>midpoint</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p midpnt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-midpoint">
<h3><a class="doc-anchor" href="#doc-midpoint">#</a> <code>midpoint</code></h3>
<p><code>midpoint</code> — operation <code>midpoint</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p midpoint $x
</code></pre>
</article>
<article class="doc-entry" id="doc-midpoint-great-circle">
<h3><a class="doc-anchor" href="#doc-midpoint-great-circle">#</a> <code>midpoint_great_circle</code></h3>
<p><code>midpoint_great_circle</code> — operation <code>midpoint great circle</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p midpoint_great_circle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-midpoint-of">
<h3><a class="doc-anchor" href="#doc-midpoint-of">#</a> <code>midpoint_of</code></h3>
<p><code>midpoint_of</code> — operation <code>midpoint of</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p midpoint_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-midpoint-rule">
<h3><a class="doc-anchor" href="#doc-midpoint-rule">#</a> <code>midpoint_rule</code></h3>
<p><code>midpoint_rule</code> — operation <code>midpoint rule</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p midpoint_rule $x
</code></pre>
</article>
<article class="doc-entry" id="doc-midpt">
<h3><a class="doc-anchor" href="#doc-midpt">#</a> <code>midpt</code></h3>
<p><code>midpt</code> — operation <code>midpt</code>. Alias for <code>midpoint_of</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p midpt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-miles-to-km">
<h3><a class="doc-anchor" href="#doc-miles-to-km">#</a> <code>miles_to_km</code></h3>
<p><code>miles_to_km</code> — convert from <code>miles</code> to <code>km</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p miles_to_km $value
</code></pre>
</article>
<article class="doc-entry" id="doc-miles-to-m">
<h3><a class="doc-anchor" href="#doc-miles-to-m">#</a> <code>miles_to_m</code></h3>
<p><code>miles_to_m</code> — convert from <code>miles</code> to <code>m</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p miles_to_m $value
</code></pre>
</article>
<article class="doc-entry" id="doc-milne">
<h3><a class="doc-anchor" href="#doc-milne">#</a> <code>milne</code></h3>
<p><code>milne</code> — operation <code>milne</code>. Alias for <code>milne_pc</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p milne $x
</code></pre>
</article>
<article class="doc-entry" id="doc-milne-pc">
<h3><a class="doc-anchor" href="#doc-milne-pc">#</a> <code>milne_pc</code></h3>
<p><code>milne_pc</code> — operation <code>milne pc</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p milne_pc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-milstein-step">
<h3><a class="doc-anchor" href="#doc-milstein-step">#</a> <code>milstein_step</code></h3>
<p><code>milstein_step</code> — single-step update of <code>milstein</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p milstein_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mime-extension-for-type">
<h3><a class="doc-anchor" href="#doc-mime-extension-for-type">#</a> <code>mime_extension_for_type</code></h3>
<p><code>mime_extension_for_type</code> — operation <code>mime extension for type</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mime_extension_for_type $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mime-is-application">
<h3><a class="doc-anchor" href="#doc-mime-is-application">#</a> <code>mime_is_application</code></h3>
<p><code>mime_is_application</code> — operation <code>mime is application</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mime_is_application $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mime-is-audio">
<h3><a class="doc-anchor" href="#doc-mime-is-audio">#</a> <code>mime_is_audio</code></h3>
<p><code>mime_is_audio</code> — operation <code>mime is audio</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mime_is_audio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mime-is-image">
<h3><a class="doc-anchor" href="#doc-mime-is-image">#</a> <code>mime_is_image</code></h3>
<p><code>mime_is_image</code> — operation <code>mime is image</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mime_is_image $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mime-is-text">
<h3><a class="doc-anchor" href="#doc-mime-is-text">#</a> <code>mime_is_text</code></h3>
<p><code>mime_is_text</code> — operation <code>mime is text</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mime_is_text $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mime-is-video">
<h3><a class="doc-anchor" href="#doc-mime-is-video">#</a> <code>mime_is_video</code></h3>
<p><code>mime_is_video</code> — operation <code>mime is video</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mime_is_video $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mime-type-for-extension">
<h3><a class="doc-anchor" href="#doc-mime-type-for-extension">#</a> <code>mime_type_for_extension</code></h3>
<p><code>mime_type_for_extension</code> — operation <code>mime type for extension</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p mime_type_for_extension $x
</code></pre>
</article>
<article class="doc-entry" id="doc-min2">
<h3><a class="doc-anchor" href="#doc-min2">#</a> <code>min2</code></h3>
<p><code>min2</code> — operation <code>min2</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p min2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-min-abs">
<h3><a class="doc-anchor" href="#doc-min-abs">#</a> <code>min_abs</code></h3>
<p><code>min_abs</code> — operation <code>min abs</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p min_abs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-min-by">
<h3><a class="doc-anchor" href="#doc-min-by">#</a> <code>min_by</code></h3>
<p><code>min_by</code> — operation <code>min by</code>. Alias for <code>take_while</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p min_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-min-cut-value">
<h3><a class="doc-anchor" href="#doc-min-cut-value">#</a> <code>min_cut_value</code></h3>
<p><code>min_cut_value</code> — value of <code>min cut</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p min_cut_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-min-float">
<h3><a class="doc-anchor" href="#doc-min-float">#</a> <code>min_float</code></h3>
<p><code>min_float</code> — operation <code>min float</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p min_float $x
</code></pre>
</article>
<article class="doc-entry" id="doc-min-list">
<h3><a class="doc-anchor" href="#doc-min-list">#</a> <code>min_list</code></h3>
<p><code>min_list</code> — operation <code>min list</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p min_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-min-max">
<h3><a class="doc-anchor" href="#doc-min-max">#</a> <code>min_max</code></h3>
<p><code>min_max</code> — maximum of <code>min</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p min_max $x
</code></pre>
</article>
<article class="doc-entry" id="doc-min-of">
<h3><a class="doc-anchor" href="#doc-min-of">#</a> <code>min_of</code></h3>
<p><code>min_of</code> — operation <code>min of</code>. Category: *more list helpers*.</p>
<pre><code class="lang-perl">p min_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-min-steiner-tree">
<h3><a class="doc-anchor" href="#doc-min-steiner-tree">#</a> <code>min_steiner_tree</code></h3>
<p><code>min_steiner_tree</code> — operation <code>min steiner tree</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p min_steiner_tree $x
</code></pre>
</article>
<article class="doc-entry" id="doc-min-vertex-cover">
<h3><a class="doc-anchor" href="#doc-min-vertex-cover">#</a> <code>min_vertex_cover</code></h3>
<p><code>min_vertex_cover</code> — operation <code>min vertex cover</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p min_vertex_cover $x
</code></pre>
</article>
<article class="doc-entry" id="doc-minby">
<h3><a class="doc-anchor" href="#doc-minby">#</a> <code>minby</code></h3>
<p><code>minby</code> — operation <code>minby</code>. Alias for <code>minimum_by</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p minby $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mincut-stoer-wagner">
<h3><a class="doc-anchor" href="#doc-mincut-stoer-wagner">#</a> <code>mincut_stoer_wagner</code></h3>
<p><code>mincut_stoer_wagner</code> — operation <code>mincut stoer wagner</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p mincut_stoer_wagner $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mineral-mohs-hardness">
<h3><a class="doc-anchor" href="#doc-mineral-mohs-hardness">#</a> <code>mineral_mohs_hardness</code></h3>
<p><code>mineral_mohs_hardness</code> — operation <code>mineral mohs hardness</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p mineral_mohs_hardness $x
</code></pre>
</article>
<article class="doc-entry" id="doc-minimax-value">
<h3><a class="doc-anchor" href="#doc-minimax-value">#</a> <code>minimax_value</code></h3>
<p><code>minimax_value(leaves, depth) → number</code> — minimax over a complete binary tree of leaf payoffs. Even depth = max layer.</p>
<pre><code class="lang-perl">p minimax_value([3,5,2,9], 2) # 3
</code></pre>
</article>
<article class="doc-entry" id="doc-minimum-by">
<h3><a class="doc-anchor" href="#doc-minimum-by">#</a> <code>minimum_by</code></h3>
<p><code>minimum_by</code> — operation <code>minimum by</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p minimum_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-minkdist">
<h3><a class="doc-anchor" href="#doc-minkdist">#</a> <code>minkdist</code></h3>
<p><code>minkdist</code> — operation <code>minkdist</code>. Alias for <code>minkowski_distance</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p minkdist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-minkowski-distance">
<h3><a class="doc-anchor" href="#doc-minkowski-distance">#</a> <code>minkowski_distance</code></h3>
<p><code>minkowski_distance</code> — distance / dissimilarity metric of <code>minkowski</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p minkowski_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-minkowski-norm">
<h3><a class="doc-anchor" href="#doc-minkowski-norm">#</a> <code>minkowski_norm</code></h3>
<p><code>minkowski_norm(v, p=2) → number</code> — <code>(Σ |vᵢ|^p)^(1/p)</code>.</p>
</article>
<article class="doc-entry" id="doc-minkowski-sum-2d">
<h3><a class="doc-anchor" href="#doc-minkowski-sum-2d">#</a> <code>minkowski_sum_2d</code></h3>
<p><code>minkowski_sum_2d(a, b) → array</code> — Minkowski sum point set <code>A ⊕ B = {a+b : a∈A, b∈B}</code>.</p>
</article>
<article class="doc-entry" id="doc-minkowski-sum-simple">
<h3><a class="doc-anchor" href="#doc-minkowski-sum-simple">#</a> <code>minkowski_sum_simple</code></h3>
<p><code>minkowski_sum_simple</code> — operation <code>minkowski sum simple</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p minkowski_sum_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-minmax">
<h3><a class="doc-anchor" href="#doc-minmax">#</a> <code>minmax</code></h3>
<p><code>minmax</code> — operation <code>minmax</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p minmax $x
</code></pre>
</article>
<article class="doc-entry" id="doc-minmax-by">
<h3><a class="doc-anchor" href="#doc-minmax-by">#</a> <code>minmax_by</code></h3>
<p><code>minmax_by</code> — operation <code>minmax by</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p minmax_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-minmax-scale">
<h3><a class="doc-anchor" href="#doc-minmax-scale">#</a> <code>minmax_scale</code></h3>
<p><code>minmax_scale</code> — operation <code>minmax scale</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p minmax_scale $x
</code></pre>
</article>
<article class="doc-entry" id="doc-minmod-limiter">
<h3><a class="doc-anchor" href="#doc-minmod-limiter">#</a> <code>minmod_limiter</code></h3>
<p><code>minmod_limiter</code> — operation <code>minmod limiter</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p minmod_limiter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-minstr">
<h3><a class="doc-anchor" href="#doc-minstr">#</a> <code>minstr</code></h3>
<p><code>minstr</code> — operation <code>minstr</code>. Category: *list / aggregate*.</p>
<pre><code class="lang-perl">p minstr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-minutes-to-hours">
<h3><a class="doc-anchor" href="#doc-minutes-to-hours">#</a> <code>minutes_to_hours</code></h3>
<p><code>minutes_to_hours</code> — convert from <code>minutes</code> to <code>hours</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p minutes_to_hours $value
</code></pre>
</article>
<article class="doc-entry" id="doc-minutes-to-seconds">
<h3><a class="doc-anchor" href="#doc-minutes-to-seconds">#</a> <code>minutes_to_seconds</code></h3>
<p><code>minutes_to_seconds</code> — convert from <code>minutes</code> to <code>seconds</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p minutes_to_seconds $value
</code></pre>
</article>
<article class="doc-entry" id="doc-minv">
<h3><a class="doc-anchor" href="#doc-minv">#</a> <code>minv</code></h3>
<p><code>minv</code> — operation <code>minv</code>. Alias for <code>matrix_inverse</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p minv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mirr">
<h3><a class="doc-anchor" href="#doc-mirr">#</a> <code>mirr</code></h3>
<p><code>mirr</code> — operation <code>mirr</code>. Alias for <code>modified_irr</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p mirr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mirr-excel">
<h3><a class="doc-anchor" href="#doc-mirr-excel">#</a> <code>mirr_excel</code></h3>
<p><code>mirr_excel</code> — operation <code>mirr excel</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p mirr_excel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mirror-descent-step">
<h3><a class="doc-anchor" href="#doc-mirror-descent-step">#</a> <code>mirror_descent_step</code></h3>
<p><code>mirror_descent_step</code> — single-step update of <code>mirror descent</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p mirror_descent_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mirror-equation-v">
<h3><a class="doc-anchor" href="#doc-mirror-equation-v">#</a> <code>mirror_equation_v</code></h3>
<p><code>mirror_equation_v</code> — operation <code>mirror equation v</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p mirror_equation_v $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mirror-string">
<h3><a class="doc-anchor" href="#doc-mirror-string">#</a> <code>mirror_string</code></h3>
<p><code>mirror_string</code> — operation <code>mirror string</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p mirror_string $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mirror-symmetry-check">
<h3><a class="doc-anchor" href="#doc-mirror-symmetry-check">#</a> <code>mirror_symmetry_check</code></h3>
<p><code>mirror_symmetry_check</code> — operation <code>mirror symmetry check</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p mirror_symmetry_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mish">
<h3><a class="doc-anchor" href="#doc-mish">#</a> <code>mish</code></h3>
<p><code>mish</code> applies the Mish activation: x·tanh(softplus(x)). Often outperforms ReLU/Swish.</p>
<pre><code class="lang-perl">p mish(1) # 0.8651
p mish(-1) # -0.3034
</code></pre>
</article>
<article class="doc-entry" id="doc-mixed-integer-round-down">
<h3><a class="doc-anchor" href="#doc-mixed-integer-round-down">#</a> <code>mixed_integer_round_down</code></h3>
<p><code>mixed_integer_round_down</code> — operation <code>mixed integer round down</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p mixed_integer_round_down $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mixed-integer-round-up">
<h3><a class="doc-anchor" href="#doc-mixed-integer-round-up">#</a> <code>mixed_integer_round_up</code></h3>
<p><code>mixed_integer_round_up</code> — operation <code>mixed integer round up</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p mixed_integer_round_up $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mixed-potential-step">
<h3><a class="doc-anchor" href="#doc-mixed-potential-step">#</a> <code>mixed_potential_step</code></h3>
<p><code>mixed_potential_step</code> — single-step update of <code>mixed potential</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p mixed_potential_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mixed-strategy-2x2">
<h3><a class="doc-anchor" href="#doc-mixed-strategy-2x2">#</a> <code>mixed_strategy_2x2</code></h3>
<p><code>mixed_strategy_2x2(payoff) → {row_strategy, col_strategy}</code> — Nash equilibrium probabilities for a 2×2 <strong>zero-sum</strong> game given the row player's payoff matrix <code>[[a,b],[c,d]]</code>. Returns row's prob of row 1 and col's prob of col 1. For non-zero-sum, both players' payoff matrices are required and this function does not apply.</p>
<pre><code class="lang-perl">p mixed_strategy_2x2([[1,-1],[-1,1]]) # 0.5/0.5
</code></pre>
</article>
<article class="doc-entry" id="doc-mixed-strategy-value">
<h3><a class="doc-anchor" href="#doc-mixed-strategy-value">#</a> <code>mixed_strategy_value</code></h3>
<p><code>mixed_strategy_value</code> — value of <code>mixed strategy</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p mixed_strategy_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mixing-length-prandtl">
<h3><a class="doc-anchor" href="#doc-mixing-length-prandtl">#</a> <code>mixing_length_prandtl</code></h3>
<p><code>mixing_length_prandtl</code> — operation <code>mixing length prandtl</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p mixing_length_prandtl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mjo-phase-step">
<h3><a class="doc-anchor" href="#doc-mjo-phase-step">#</a> <code>mjo_phase_step</code></h3>
<p><code>mjo_phase_step</code> — single-step update of <code>mjo phase</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p mjo_phase_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-adabelief-step">
<h3><a class="doc-anchor" href="#doc-ml-adabelief-step">#</a> <code>ml_adabelief_step</code></h3>
<p><code>ml_adabelief_step</code> — ML inference primitive <code>adabelief step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_adabelief_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-adagrad-step">
<h3><a class="doc-anchor" href="#doc-ml-adagrad-step">#</a> <code>ml_adagrad_step</code></h3>
<p><code>ml_adagrad_step</code> — ML inference primitive <code>adagrad step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_adagrad_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-adam-step">
<h3><a class="doc-anchor" href="#doc-ml-adam-step">#</a> <code>ml_adam_step</code></h3>
<p><code>ml_adam_step</code> — ML inference primitive <code>adam step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_adam_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-adamax-step">
<h3><a class="doc-anchor" href="#doc-ml-adamax-step">#</a> <code>ml_adamax_step</code></h3>
<p><code>ml_adamax_step</code> — ML inference primitive <code>adamax step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_adamax_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-adamw-step">
<h3><a class="doc-anchor" href="#doc-ml-adamw-step">#</a> <code>ml_adamw_step</code></h3>
<p><code>ml_adamw_step</code> — ML inference primitive <code>adamw step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_adamw_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-amsgrad-step">
<h3><a class="doc-anchor" href="#doc-ml-amsgrad-step">#</a> <code>ml_amsgrad_step</code></h3>
<p><code>ml_amsgrad_step</code> — ML inference primitive <code>amsgrad step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_amsgrad_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-arcface-loss-step">
<h3><a class="doc-anchor" href="#doc-ml-arcface-loss-step">#</a> <code>ml_arcface_loss_step</code></h3>
<p><code>ml_arcface_loss_step</code> — ML inference primitive <code>arcface loss step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_arcface_loss_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-attention-score">
<h3><a class="doc-anchor" href="#doc-ml-attention-score">#</a> <code>ml_attention_score</code></h3>
<p><code>ml_attention_score(q, k) → number</code> — <code>q·k / √d</code>. Scaled dot product score for a single QK pair.</p>
</article>
<article class="doc-entry" id="doc-ml-attention-score-step">
<h3><a class="doc-anchor" href="#doc-ml-attention-score-step">#</a> <code>ml_attention_score_step</code></h3>
<p><code>ml_attention_score_step</code> — ML inference primitive <code>attention score step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_attention_score_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-batch-norm">
<h3><a class="doc-anchor" href="#doc-ml-batch-norm">#</a> <code>ml_batch_norm</code></h3>
<p><code>ml_batch_norm(xs, eps=1e-5) → array</code> — zero-mean unit-variance normalisation.</p>
</article>
<article class="doc-entry" id="doc-ml-batch-norm-step">
<h3><a class="doc-anchor" href="#doc-ml-batch-norm-step">#</a> <code>ml_batch_norm_step</code></h3>
<p><code>ml_batch_norm_step</code> — ML inference primitive <code>batch norm step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_batch_norm_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-binary-cross-entropy">
<h3><a class="doc-anchor" href="#doc-ml-binary-cross-entropy">#</a> <code>ml_binary_cross_entropy</code></h3>
<p><code>ml_binary_cross_entropy</code> — ML inference primitive <code>binary cross entropy</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_binary_cross_entropy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-celu-step">
<h3><a class="doc-anchor" href="#doc-ml-celu-step">#</a> <code>ml_celu_step</code></h3>
<p><code>ml_celu_step</code> — ML inference primitive <code>celu step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_celu_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-center-loss-step">
<h3><a class="doc-anchor" href="#doc-ml-center-loss-step">#</a> <code>ml_center_loss_step</code></h3>
<p><code>ml_center_loss_step</code> — ML inference primitive <code>center loss step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_center_loss_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-ciou-loss-step">
<h3><a class="doc-anchor" href="#doc-ml-ciou-loss-step">#</a> <code>ml_ciou_loss_step</code></h3>
<p><code>ml_ciou_loss_step</code> — ML inference primitive <code>ciou loss step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_ciou_loss_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-constant-init">
<h3><a class="doc-anchor" href="#doc-ml-constant-init">#</a> <code>ml_constant_init</code></h3>
<p><code>ml_constant_init</code> — ML inference primitive <code>constant init</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_constant_init $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-contrastive-loss">
<h3><a class="doc-anchor" href="#doc-ml-contrastive-loss">#</a> <code>ml_contrastive_loss</code></h3>
<p><code>ml_contrastive_loss</code> — ML inference primitive <code>contrastive loss</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_contrastive_loss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-cosine-lr-schedule">
<h3><a class="doc-anchor" href="#doc-ml-cosine-lr-schedule">#</a> <code>ml_cosine_lr_schedule</code></h3>
<p><code>ml_cosine_lr_schedule</code> — ML inference primitive <code>cosine lr schedule</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_cosine_lr_schedule $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-cross-entropy-loss">
<h3><a class="doc-anchor" href="#doc-ml-cross-entropy-loss">#</a> <code>ml_cross_entropy_loss</code></h3>
<p><code>ml_cross_entropy_loss</code> — ML inference primitive <code>cross entropy loss</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_cross_entropy_loss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-cutmix-box-iou">
<h3><a class="doc-anchor" href="#doc-ml-cutmix-box-iou">#</a> <code>ml_cutmix_box_iou</code></h3>
<p><code>ml_cutmix_box_iou</code> — ML inference primitive <code>cutmix box iou</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_cutmix_box_iou $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-cyclic-lr-step">
<h3><a class="doc-anchor" href="#doc-ml-cyclic-lr-step">#</a> <code>ml_cyclic_lr_step</code></h3>
<p><code>ml_cyclic_lr_step</code> — ML inference primitive <code>cyclic lr step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_cyclic_lr_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-dice-loss-step">
<h3><a class="doc-anchor" href="#doc-ml-dice-loss-step">#</a> <code>ml_dice_loss_step</code></h3>
<p><code>ml_dice_loss_step</code> — ML inference primitive <code>dice loss step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_dice_loss_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-diou-loss-step">
<h3><a class="doc-anchor" href="#doc-ml-diou-loss-step">#</a> <code>ml_diou_loss_step</code></h3>
<p><code>ml_diou_loss_step</code> — ML inference primitive <code>diou loss step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_diou_loss_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-dot-product-attention">
<h3><a class="doc-anchor" href="#doc-ml-dot-product-attention">#</a> <code>ml_dot_product_attention</code></h3>
<p><code>ml_dot_product_attention(q, keys, values) → array</code> — softmax(scores)·values where scores = <code>q·kᵢ/√d</code> for each key.</p>
<pre><code class="lang-perl">p ml_dot_product_attention([1,0], [[1,0],[0,1]], [[10,20],[30,40]])
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-dropout-mask">
<h3><a class="doc-anchor" href="#doc-ml-dropout-mask">#</a> <code>ml_dropout_mask</code></h3>
<p><code>ml_dropout_mask(n, p=0.5, seed=0) → array</code> — Bernoulli mask of length <code>n</code>; live values scaled by <code>1/(1-p)</code> for inverted dropout.</p>
</article>
<article class="doc-entry" id="doc-ml-dropout-mask-prob">
<h3><a class="doc-anchor" href="#doc-ml-dropout-mask-prob">#</a> <code>ml_dropout_mask_prob</code></h3>
<p><code>ml_dropout_mask_prob</code> — ML inference primitive <code>dropout mask prob</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_dropout_mask_prob $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-elu-layer">
<h3><a class="doc-anchor" href="#doc-ml-elu-layer">#</a> <code>ml_elu_layer</code></h3>
<p><code>ml_elu_layer(xs, alpha=1) → array</code> — ELU: <code>x if x>0 else α·(e^x-1)</code>.</p>
</article>
<article class="doc-entry" id="doc-ml-elu-step">
<h3><a class="doc-anchor" href="#doc-ml-elu-step">#</a> <code>ml_elu_step</code></h3>
<p><code>ml_elu_step</code> — ML inference primitive <code>elu step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_elu_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-eos-logit-boost">
<h3><a class="doc-anchor" href="#doc-ml-eos-logit-boost">#</a> <code>ml_eos_logit_boost</code></h3>
<p><code>ml_eos_logit_boost</code> — ML inference primitive <code>eos logit boost</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_eos_logit_boost $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-exponential-lr">
<h3><a class="doc-anchor" href="#doc-ml-exponential-lr">#</a> <code>ml_exponential_lr</code></h3>
<p><code>ml_exponential_lr</code> — ML inference primitive <code>exponential lr</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_exponential_lr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-focal-loss-step">
<h3><a class="doc-anchor" href="#doc-ml-focal-loss-step">#</a> <code>ml_focal_loss_step</code></h3>
<p><code>ml_focal_loss_step</code> — ML inference primitive <code>focal loss step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_focal_loss_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-geglu-step">
<h3><a class="doc-anchor" href="#doc-ml-geglu-step">#</a> <code>ml_geglu_step</code></h3>
<p><code>ml_geglu_step</code> — ML inference primitive <code>geglu step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_geglu_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-gelu-layer">
<h3><a class="doc-anchor" href="#doc-ml-gelu-layer">#</a> <code>ml_gelu_layer</code></h3>
<p><code>ml_gelu_layer(xs) → array</code> — Gaussian Error Linear Unit using the tanh approximation.</p>
</article>
<article class="doc-entry" id="doc-ml-gelu-step">
<h3><a class="doc-anchor" href="#doc-ml-gelu-step">#</a> <code>ml_gelu_step</code></h3>
<p><code>ml_gelu_step</code> — ML inference primitive <code>gelu step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_gelu_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-giou-loss-step">
<h3><a class="doc-anchor" href="#doc-ml-giou-loss-step">#</a> <code>ml_giou_loss_step</code></h3>
<p><code>ml_giou_loss_step</code> — ML inference primitive <code>giou loss step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_giou_loss_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-glorot-init-value">
<h3><a class="doc-anchor" href="#doc-ml-glorot-init-value">#</a> <code>ml_glorot_init_value</code></h3>
<p><code>ml_glorot_init_value</code> — ML inference primitive <code>glorot init value</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_glorot_init_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-glu-step">
<h3><a class="doc-anchor" href="#doc-ml-glu-step">#</a> <code>ml_glu_step</code></h3>
<p><code>ml_glu_step</code> — ML inference primitive <code>glu step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_glu_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-gradient-accumulate">
<h3><a class="doc-anchor" href="#doc-ml-gradient-accumulate">#</a> <code>ml_gradient_accumulate</code></h3>
<p><code>ml_gradient_accumulate</code> — ML inference primitive <code>gradient accumulate</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_gradient_accumulate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-gradient-centralize">
<h3><a class="doc-anchor" href="#doc-ml-gradient-centralize">#</a> <code>ml_gradient_centralize</code></h3>
<p><code>ml_gradient_centralize</code> — ML inference primitive <code>gradient centralize</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_gradient_centralize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-gradient-clip-norm">
<h3><a class="doc-anchor" href="#doc-ml-gradient-clip-norm">#</a> <code>ml_gradient_clip_norm</code></h3>
<p><code>ml_gradient_clip_norm</code> — ML inference primitive <code>gradient clip norm</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_gradient_clip_norm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-gradient-clip-value">
<h3><a class="doc-anchor" href="#doc-ml-gradient-clip-value">#</a> <code>ml_gradient_clip_value</code></h3>
<p><code>ml_gradient_clip_value</code> — ML inference primitive <code>gradient clip value</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_gradient_clip_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-group-norm-step">
<h3><a class="doc-anchor" href="#doc-ml-group-norm-step">#</a> <code>ml_group_norm_step</code></h3>
<p><code>ml_group_norm_step</code> — ML inference primitive <code>group norm step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_group_norm_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-hard-sigmoid">
<h3><a class="doc-anchor" href="#doc-ml-hard-sigmoid">#</a> <code>ml_hard_sigmoid</code></h3>
<p><code>ml_hard_sigmoid</code> — ML inference primitive <code>hard sigmoid</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_hard_sigmoid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-hard-tanh">
<h3><a class="doc-anchor" href="#doc-ml-hard-tanh">#</a> <code>ml_hard_tanh</code></h3>
<p><code>ml_hard_tanh</code> — ML inference primitive <code>hard tanh</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_hard_tanh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-he-init-value">
<h3><a class="doc-anchor" href="#doc-ml-he-init-value">#</a> <code>ml_he_init_value</code></h3>
<p><code>ml_he_init_value</code> — ML inference primitive <code>he init value</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_he_init_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-hinge-loss">
<h3><a class="doc-anchor" href="#doc-ml-hinge-loss">#</a> <code>ml_hinge_loss</code></h3>
<p><code>ml_hinge_loss(pred, target) → number</code> — <code>mean(max(0, 1 - t·p))</code>. For SVM-style classifiers.</p>
</article>
<article class="doc-entry" id="doc-ml-huber-loss">
<h3><a class="doc-anchor" href="#doc-ml-huber-loss">#</a> <code>ml_huber_loss</code></h3>
<p><code>ml_huber_loss(pred, target, delta=1) → number</code> — smooth quadratic-then-linear loss with breakpoint <code>delta</code>.</p>
</article>
<article class="doc-entry" id="doc-ml-huber-loss-step">
<h3><a class="doc-anchor" href="#doc-ml-huber-loss-step">#</a> <code>ml_huber_loss_step</code></h3>
<p><code>ml_huber_loss_step</code> — ML inference primitive <code>huber loss step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_huber_loss_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-id-to-label-step">
<h3><a class="doc-anchor" href="#doc-ml-id-to-label-step">#</a> <code>ml_id_to_label_step</code></h3>
<p><code>ml_id_to_label_step</code> — convert from <code>ml id</code> to <code>label step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_id_to_label_step $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-instance-norm-step">
<h3><a class="doc-anchor" href="#doc-ml-instance-norm-step">#</a> <code>ml_instance_norm_step</code></h3>
<p><code>ml_instance_norm_step</code> — ML inference primitive <code>instance norm step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_instance_norm_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-inverse-sqrt-lr">
<h3><a class="doc-anchor" href="#doc-ml-inverse-sqrt-lr">#</a> <code>ml_inverse_sqrt_lr</code></h3>
<p><code>ml_inverse_sqrt_lr</code> — ML inference primitive <code>inverse sqrt lr</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_inverse_sqrt_lr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-iou-loss-step">
<h3><a class="doc-anchor" href="#doc-ml-iou-loss-step">#</a> <code>ml_iou_loss_step</code></h3>
<p><code>ml_iou_loss_step</code> — ML inference primitive <code>iou loss step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_iou_loss_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-kaiming-init">
<h3><a class="doc-anchor" href="#doc-ml-kaiming-init">#</a> <code>ml_kaiming_init</code></h3>
<p><code>ml_kaiming_init</code> — ML inference primitive <code>kaiming init</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_kaiming_init $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-kl-div-loss">
<h3><a class="doc-anchor" href="#doc-ml-kl-div-loss">#</a> <code>ml_kl_div_loss</code></h3>
<p><code>ml_kl_div_loss(p, q) → number</code> — discrete KL divergence <code>Σ p·ln(p/q)</code>. Always ≥ 0; zero when p == q.</p>
</article>
<article class="doc-entry" id="doc-ml-kl-divergence-loss">
<h3><a class="doc-anchor" href="#doc-ml-kl-divergence-loss">#</a> <code>ml_kl_divergence_loss</code></h3>
<p><code>ml_kl_divergence_loss</code> — ML inference primitive <code>kl divergence loss</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_kl_divergence_loss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-l2-normalize-step">
<h3><a class="doc-anchor" href="#doc-ml-l2-normalize-step">#</a> <code>ml_l2_normalize_step</code></h3>
<p><code>ml_l2_normalize_step</code> — ML inference primitive <code>l2 normalize step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_l2_normalize_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-label-smooth">
<h3><a class="doc-anchor" href="#doc-ml-label-smooth">#</a> <code>ml_label_smooth</code></h3>
<p><code>ml_label_smooth(probs, smoothing=0.1) → array</code> — <code>(1-α)·p + α/K</code> smoothing for classification targets.</p>
</article>
<article class="doc-entry" id="doc-ml-label-smoothing">
<h3><a class="doc-anchor" href="#doc-ml-label-smoothing">#</a> <code>ml_label_smoothing</code></h3>
<p><code>ml_label_smoothing</code> — ML inference primitive <code>label smoothing</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_label_smoothing $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-label-to-id">
<h3><a class="doc-anchor" href="#doc-ml-label-to-id">#</a> <code>ml_label_to_id</code></h3>
<p><code>ml_label_to_id</code> — convert from <code>ml label</code> to <code>id</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_label_to_id $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-lamb-step">
<h3><a class="doc-anchor" href="#doc-ml-lamb-step">#</a> <code>ml_lamb_step</code></h3>
<p><code>ml_lamb_step</code> — ML inference primitive <code>lamb step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_lamb_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-lars-step">
<h3><a class="doc-anchor" href="#doc-ml-lars-step">#</a> <code>ml_lars_step</code></h3>
<p><code>ml_lars_step</code> — ML inference primitive <code>lars step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_lars_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-layer-norm">
<h3><a class="doc-anchor" href="#doc-ml-layer-norm">#</a> <code>ml_layer_norm</code></h3>
<p><code>ml_layer_norm</code> — ML inference primitive <code>layer norm</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p ml_layer_norm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-layer-norm-step">
<h3><a class="doc-anchor" href="#doc-ml-layer-norm-step">#</a> <code>ml_layer_norm_step</code></h3>
<p><code>ml_layer_norm_step</code> — ML inference primitive <code>layer norm step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_layer_norm_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-leaky-relu-layer">
<h3><a class="doc-anchor" href="#doc-ml-leaky-relu-layer">#</a> <code>ml_leaky_relu_layer</code></h3>
<p><code>ml_leaky_relu_layer(xs, slope=0.01) → array</code> — <code>x if x>0 else slope·x</code>.</p>
</article>
<article class="doc-entry" id="doc-ml-leaky-relu-step">
<h3><a class="doc-anchor" href="#doc-ml-leaky-relu-step">#</a> <code>ml_leaky_relu_step</code></h3>
<p><code>ml_leaky_relu_step</code> — ML inference primitive <code>leaky relu step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_leaky_relu_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-lecun-init-value">
<h3><a class="doc-anchor" href="#doc-ml-lecun-init-value">#</a> <code>ml_lecun_init_value</code></h3>
<p><code>ml_lecun_init_value</code> — ML inference primitive <code>lecun init value</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_lecun_init_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-lion-step">
<h3><a class="doc-anchor" href="#doc-ml-lion-step">#</a> <code>ml_lion_step</code></h3>
<p><code>ml_lion_step</code> — ML inference primitive <code>lion step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_lion_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-log-sigmoid">
<h3><a class="doc-anchor" href="#doc-ml-log-sigmoid">#</a> <code>ml_log_sigmoid</code></h3>
<p><code>ml_log_sigmoid</code> — ML inference primitive <code>log sigmoid</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_log_sigmoid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-log-softmax-step">
<h3><a class="doc-anchor" href="#doc-ml-log-softmax-step">#</a> <code>ml_log_softmax_step</code></h3>
<p><code>ml_log_softmax_step</code> — ML inference primitive <code>log softmax step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_log_softmax_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-logsumexp-step">
<h3><a class="doc-anchor" href="#doc-ml-logsumexp-step">#</a> <code>ml_logsumexp_step</code></h3>
<p><code>ml_logsumexp_step</code> — ML inference primitive <code>logsumexp step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_logsumexp_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-lookahead-step">
<h3><a class="doc-anchor" href="#doc-ml-lookahead-step">#</a> <code>ml_lookahead_step</code></h3>
<p><code>ml_lookahead_step</code> — ML inference primitive <code>lookahead step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_lookahead_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-mae-loss">
<h3><a class="doc-anchor" href="#doc-ml-mae-loss">#</a> <code>ml_mae_loss</code></h3>
<p><code>ml_mae_loss(pred, target) → number</code> — mean absolute error.</p>
</article>
<article class="doc-entry" id="doc-ml-mish-layer">
<h3><a class="doc-anchor" href="#doc-ml-mish-layer">#</a> <code>ml_mish_layer</code></h3>
<p><code>ml_mish_layer(xs) → array</code> — <code>x · tanh(softplus(x))</code>.</p>
</article>
<article class="doc-entry" id="doc-ml-mish-step">
<h3><a class="doc-anchor" href="#doc-ml-mish-step">#</a> <code>ml_mish_step</code></h3>
<p><code>ml_mish_step</code> — ML inference primitive <code>mish step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_mish_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-mixup-lambda">
<h3><a class="doc-anchor" href="#doc-ml-mixup-lambda">#</a> <code>ml_mixup_lambda</code></h3>
<p><code>ml_mixup_lambda</code> — ML inference primitive <code>mixup lambda</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_mixup_lambda $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-momentum-step">
<h3><a class="doc-anchor" href="#doc-ml-momentum-step">#</a> <code>ml_momentum_step</code></h3>
<p><code>ml_momentum_step</code> — ML inference primitive <code>momentum step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_momentum_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-mse-loss">
<h3><a class="doc-anchor" href="#doc-ml-mse-loss">#</a> <code>ml_mse_loss</code></h3>
<p><code>ml_mse_loss(pred, target) → number</code> — mean squared error.</p>
</article>
<article class="doc-entry" id="doc-ml-multihead-avg">
<h3><a class="doc-anchor" href="#doc-ml-multihead-avg">#</a> <code>ml_multihead_avg</code></h3>
<p><code>ml_multihead_avg</code> — ML inference primitive <code>multihead avg</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_multihead_avg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-nadam-step">
<h3><a class="doc-anchor" href="#doc-ml-nadam-step">#</a> <code>ml_nadam_step</code></h3>
<p><code>ml_nadam_step</code> — ML inference primitive <code>nadam step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_nadam_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-nesterov-momentum">
<h3><a class="doc-anchor" href="#doc-ml-nesterov-momentum">#</a> <code>ml_nesterov_momentum</code></h3>
<p><code>ml_nesterov_momentum</code> — ML inference primitive <code>nesterov momentum</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_nesterov_momentum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-nucleus-sample-p">
<h3><a class="doc-anchor" href="#doc-ml-nucleus-sample-p">#</a> <code>ml_nucleus_sample_p</code></h3>
<p><code>ml_nucleus_sample_p</code> — ML inference primitive <code>nucleus sample p</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_nucleus_sample_p $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-one-cycle-lr">
<h3><a class="doc-anchor" href="#doc-ml-one-cycle-lr">#</a> <code>ml_one_cycle_lr</code></h3>
<p><code>ml_one_cycle_lr</code> — ML inference primitive <code>one cycle lr</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_one_cycle_lr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-one-hot-encode">
<h3><a class="doc-anchor" href="#doc-ml-one-hot-encode">#</a> <code>ml_one_hot_encode</code></h3>
<p><code>ml_one_hot_encode(idx, n_classes=10) → array</code> — vector of zeros with 1 at position <code>idx</code>.</p>
<pre><code class="lang-perl">p ml_one_hot_encode(3, 5) # [0,0,0,1,0]
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-one-hot-index">
<h3><a class="doc-anchor" href="#doc-ml-one-hot-index">#</a> <code>ml_one_hot_index</code></h3>
<p><code>ml_one_hot_index</code> — ML inference primitive <code>one hot index</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_one_hot_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-orthogonal-init">
<h3><a class="doc-anchor" href="#doc-ml-orthogonal-init">#</a> <code>ml_orthogonal_init</code></h3>
<p><code>ml_orthogonal_init</code> — ML inference primitive <code>orthogonal init</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_orthogonal_init $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-polynomial-lr">
<h3><a class="doc-anchor" href="#doc-ml-polynomial-lr">#</a> <code>ml_polynomial_lr</code></h3>
<p><code>ml_polynomial_lr</code> — ML inference primitive <code>polynomial lr</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_polynomial_lr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-position-encoding">
<h3><a class="doc-anchor" href="#doc-ml-position-encoding">#</a> <code>ml_position_encoding</code></h3>
<p><code>ml_position_encoding(seq_len, dim) → matrix</code> — Transformer sinusoidal position encoding.</p>
</article>
<article class="doc-entry" id="doc-ml-prelu-step">
<h3><a class="doc-anchor" href="#doc-ml-prelu-step">#</a> <code>ml_prelu_step</code></h3>
<p><code>ml_prelu_step</code> — ML inference primitive <code>prelu step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_prelu_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-radam-step">
<h3><a class="doc-anchor" href="#doc-ml-radam-step">#</a> <code>ml_radam_step</code></h3>
<p><code>ml_radam_step</code> — ML inference primitive <code>radam step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_radam_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-random-erasing-step">
<h3><a class="doc-anchor" href="#doc-ml-random-erasing-step">#</a> <code>ml_random_erasing_step</code></h3>
<p><code>ml_random_erasing_step</code> — ML inference primitive <code>random erasing step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_random_erasing_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-relu-layer">
<h3><a class="doc-anchor" href="#doc-ml-relu-layer">#</a> <code>ml_relu_layer</code></h3>
<p><code>ml_relu_layer(xs) → array</code> — <code>max(0, x)</code>.</p>
</article>
<article class="doc-entry" id="doc-ml-relu-step">
<h3><a class="doc-anchor" href="#doc-ml-relu-step">#</a> <code>ml_relu_step</code></h3>
<p><code>ml_relu_step</code> — ML inference primitive <code>relu step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_relu_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-repetition-penalty">
<h3><a class="doc-anchor" href="#doc-ml-repetition-penalty">#</a> <code>ml_repetition_penalty</code></h3>
<p><code>ml_repetition_penalty</code> — ML inference primitive <code>repetition penalty</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_repetition_penalty $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-rms-norm-step">
<h3><a class="doc-anchor" href="#doc-ml-rms-norm-step">#</a> <code>ml_rms_norm_step</code></h3>
<p><code>ml_rms_norm_step</code> — ML inference primitive <code>rms norm step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_rms_norm_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-rmsprop-step">
<h3><a class="doc-anchor" href="#doc-ml-rmsprop-step">#</a> <code>ml_rmsprop_step</code></h3>
<p><code>ml_rmsprop_step</code> — ML inference primitive <code>rmsprop step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_rmsprop_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-scaled-dot-product">
<h3><a class="doc-anchor" href="#doc-ml-scaled-dot-product">#</a> <code>ml_scaled_dot_product</code></h3>
<p><code>ml_scaled_dot_product</code> — ML inference primitive <code>scaled dot product</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_scaled_dot_product $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-self-attention">
<h3><a class="doc-anchor" href="#doc-ml-self-attention">#</a> <code>ml_self_attention</code></h3>
<p><code>ml_self_attention(seq_matrix) → matrix</code> — single-head self-attention <code>softmax(X·Xᵀ/√d)·X</code> (no learned weights).</p>
</article>
<article class="doc-entry" id="doc-ml-selu-step">
<h3><a class="doc-anchor" href="#doc-ml-selu-step">#</a> <code>ml_selu_step</code></h3>
<p><code>ml_selu_step</code> — ML inference primitive <code>selu step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_selu_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-sgd-step">
<h3><a class="doc-anchor" href="#doc-ml-sgd-step">#</a> <code>ml_sgd_step</code></h3>
<p><code>ml_sgd_step</code> — ML inference primitive <code>sgd step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_sgd_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-shampoo-step">
<h3><a class="doc-anchor" href="#doc-ml-shampoo-step">#</a> <code>ml_shampoo_step</code></h3>
<p><code>ml_shampoo_step</code> — ML inference primitive <code>shampoo step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_shampoo_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-sigmoid-layer">
<h3><a class="doc-anchor" href="#doc-ml-sigmoid-layer">#</a> <code>ml_sigmoid_layer</code></h3>
<p><code>ml_sigmoid_layer(xs) → array</code> — elementwise <code>1/(1+e^-x)</code>.</p>
<pre><code class="lang-perl">p ml_sigmoid_layer([0, 1, -1])
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-silu-step">
<h3><a class="doc-anchor" href="#doc-ml-silu-step">#</a> <code>ml_silu_step</code></h3>
<p><code>ml_silu_step</code> — ML inference primitive <code>silu step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_silu_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-smooth-l1-loss">
<h3><a class="doc-anchor" href="#doc-ml-smooth-l1-loss">#</a> <code>ml_smooth_l1_loss</code></h3>
<p><code>ml_smooth_l1_loss</code> — ML inference primitive <code>smooth l1 loss</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_smooth_l1_loss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-softmax-layer">
<h3><a class="doc-anchor" href="#doc-ml-softmax-layer">#</a> <code>ml_softmax_layer</code></h3>
<p><code>ml_softmax_layer(xs) → array</code> — max-stable softmax (subtracts max before exp). Sums to 1.</p>
<pre><code class="lang-perl">p ml_softmax_layer([1,2,3]) # sums to 1
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-softmax-temperature">
<h3><a class="doc-anchor" href="#doc-ml-softmax-temperature">#</a> <code>ml_softmax_temperature</code></h3>
<p><code>ml_softmax_temperature</code> — ML inference primitive <code>softmax temperature</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_softmax_temperature $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-softplus-layer">
<h3><a class="doc-anchor" href="#doc-ml-softplus-layer">#</a> <code>ml_softplus_layer</code></h3>
<p><code>ml_softplus_layer(xs) → array</code> — <code>ln(1+e^x)</code>. Smooth relu.</p>
</article>
<article class="doc-entry" id="doc-ml-softplus-step">
<h3><a class="doc-anchor" href="#doc-ml-softplus-step">#</a> <code>ml_softplus_step</code></h3>
<p><code>ml_softplus_step</code> — ML inference primitive <code>softplus step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_softplus_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-softsign-step">
<h3><a class="doc-anchor" href="#doc-ml-softsign-step">#</a> <code>ml_softsign_step</code></h3>
<p><code>ml_softsign_step</code> — ML inference primitive <code>softsign step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_softsign_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-sophia-step">
<h3><a class="doc-anchor" href="#doc-ml-sophia-step">#</a> <code>ml_sophia_step</code></h3>
<p><code>ml_sophia_step</code> — ML inference primitive <code>sophia step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_sophia_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-spectral-norm-step">
<h3><a class="doc-anchor" href="#doc-ml-spectral-norm-step">#</a> <code>ml_spectral_norm_step</code></h3>
<p><code>ml_spectral_norm_step</code> — ML inference primitive <code>spectral norm step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_spectral_norm_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-step-lr-schedule">
<h3><a class="doc-anchor" href="#doc-ml-step-lr-schedule">#</a> <code>ml_step_lr_schedule</code></h3>
<p><code>ml_step_lr_schedule</code> — ML inference primitive <code>step lr schedule</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_step_lr_schedule $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-swiglu-step">
<h3><a class="doc-anchor" href="#doc-ml-swiglu-step">#</a> <code>ml_swiglu_step</code></h3>
<p><code>ml_swiglu_step</code> — ML inference primitive <code>swiglu step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_swiglu_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-swish-layer">
<h3><a class="doc-anchor" href="#doc-ml-swish-layer">#</a> <code>ml_swish_layer</code></h3>
<p><code>ml_swish_layer(xs) → array</code> — <code>x · sigmoid(x)</code>.</p>
</article>
<article class="doc-entry" id="doc-ml-swish-step">
<h3><a class="doc-anchor" href="#doc-ml-swish-step">#</a> <code>ml_swish_step</code></h3>
<p><code>ml_swish_step</code> — ML inference primitive <code>swish step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_swish_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-tanh-layer">
<h3><a class="doc-anchor" href="#doc-ml-tanh-layer">#</a> <code>ml_tanh_layer</code></h3>
<p><code>ml_tanh_layer(xs) → array</code> — elementwise <code>tanh</code>.</p>
</article>
<article class="doc-entry" id="doc-ml-temperature-decay">
<h3><a class="doc-anchor" href="#doc-ml-temperature-decay">#</a> <code>ml_temperature_decay</code></h3>
<p><code>ml_temperature_decay</code> — ML inference primitive <code>temperature decay</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_temperature_decay $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-to-cups">
<h3><a class="doc-anchor" href="#doc-ml-to-cups">#</a> <code>ml_to_cups</code></h3>
<p><code>ml_to_cups</code> — convert from <code>ml</code> to <code>cups</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p ml_to_cups $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-to-liters">
<h3><a class="doc-anchor" href="#doc-ml-to-liters">#</a> <code>ml_to_liters</code></h3>
<p><code>ml_to_liters</code> — convert from <code>ml</code> to <code>liters</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p ml_to_liters $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-token-logit-top-k">
<h3><a class="doc-anchor" href="#doc-ml-token-logit-top-k">#</a> <code>ml_token_logit_top_k</code></h3>
<p><code>ml_token_logit_top_k</code> — ML inference primitive <code>token logit top k</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_token_logit_top_k $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-topk-argmax">
<h3><a class="doc-anchor" href="#doc-ml-topk-argmax">#</a> <code>ml_topk_argmax</code></h3>
<p><code>ml_topk_argmax</code> — ML inference primitive <code>topk argmax</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_topk_argmax $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-triplet-loss-step">
<h3><a class="doc-anchor" href="#doc-ml-triplet-loss-step">#</a> <code>ml_triplet_loss_step</code></h3>
<p><code>ml_triplet_loss_step</code> — ML inference primitive <code>triplet loss step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_triplet_loss_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-truncnormal-init">
<h3><a class="doc-anchor" href="#doc-ml-truncnormal-init">#</a> <code>ml_truncnormal_init</code></h3>
<p><code>ml_truncnormal_init</code> — ML inference primitive <code>truncnormal init</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_truncnormal_init $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-uniform-init">
<h3><a class="doc-anchor" href="#doc-ml-uniform-init">#</a> <code>ml_uniform_init</code></h3>
<p><code>ml_uniform_init</code> — ML inference primitive <code>uniform init</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_uniform_init $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-warmup-lr-step">
<h3><a class="doc-anchor" href="#doc-ml-warmup-lr-step">#</a> <code>ml_warmup_lr_step</code></h3>
<p><code>ml_warmup_lr_step</code> — ML inference primitive <code>warmup lr step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_warmup_lr_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-weight-decay-step">
<h3><a class="doc-anchor" href="#doc-ml-weight-decay-step">#</a> <code>ml_weight_decay_step</code></h3>
<p><code>ml_weight_decay_step</code> — ML inference primitive <code>weight decay step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_weight_decay_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-weight-norm-step">
<h3><a class="doc-anchor" href="#doc-ml-weight-norm-step">#</a> <code>ml_weight_norm_step</code></h3>
<p><code>ml_weight_norm_step</code> — ML inference primitive <code>weight norm step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_weight_norm_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-xavier-init-value">
<h3><a class="doc-anchor" href="#doc-ml-xavier-init-value">#</a> <code>ml_xavier_init_value</code></h3>
<p><code>ml_xavier_init_value</code> — ML inference primitive <code>xavier init value</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_xavier_init_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-yogi-step">
<h3><a class="doc-anchor" href="#doc-ml-yogi-step">#</a> <code>ml_yogi_step</code></h3>
<p><code>ml_yogi_step</code> — ML inference primitive <code>yogi step</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_yogi_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ml-zero-init">
<h3><a class="doc-anchor" href="#doc-ml-zero-init">#</a> <code>ml_zero_init</code></h3>
<p><code>ml_zero_init</code> — ML inference primitive <code>zero init</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ml_zero_init $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mle-exponential-log-lik">
<h3><a class="doc-anchor" href="#doc-mle-exponential-log-lik">#</a> <code>mle_exponential_log_lik</code></h3>
<p><code>mle_exponential_log_lik</code> — operation <code>mle exponential log lik</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p mle_exponential_log_lik $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mle-normal-log-lik">
<h3><a class="doc-anchor" href="#doc-mle-normal-log-lik">#</a> <code>mle_normal_log_lik</code></h3>
<p><code>mle_normal_log_lik</code> — operation <code>mle normal log lik</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p mle_normal_log_lik $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mle-poisson-log-lik">
<h3><a class="doc-anchor" href="#doc-mle-poisson-log-lik">#</a> <code>mle_poisson_log_lik</code></h3>
<p><code>mle_poisson_log_lik</code> — operation <code>mle poisson log lik</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p mle_poisson_log_lik $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mm">
<h3><a class="doc-anchor" href="#doc-mm">#</a> <code>mm</code></h3>
<p><code>mm</code> — operation <code>mm</code>. Alias for <code>matrix_mul</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mmap">
<h3><a class="doc-anchor" href="#doc-mmap">#</a> <code>mmap</code></h3>
<p><code>mmap</code> — operation <code>mmap</code>. Alias for <code>matrix_map</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p mmap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mmax">
<h3><a class="doc-anchor" href="#doc-mmax">#</a> <code>mmax</code></h3>
<p><code>mmax</code> — operation <code>mmax</code>. Alias for <code>matrix_max</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p mmax $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mmhg-to-pa">
<h3><a class="doc-anchor" href="#doc-mmhg-to-pa">#</a> <code>mmhg_to_pa</code></h3>
<p><code>mmhg_to_pa</code> — convert from <code>mmhg</code> to <code>pa</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p mmhg_to_pa $value
</code></pre>
</article>
<article class="doc-entry" id="doc-mmin">
<h3><a class="doc-anchor" href="#doc-mmin">#</a> <code>mmin</code></h3>
<p><code>mmin</code> — operation <code>mmin</code>. Alias for <code>matrix_min</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p mmin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mmult">
<h3><a class="doc-anchor" href="#doc-mmult">#</a> <code>mmult</code></h3>
<p><code>mmult</code> — operation <code>mmult</code>. Alias for <code>matrix_mult</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mmult $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mmx">
<h3><a class="doc-anchor" href="#doc-mmx">#</a> <code>mmx</code></h3>
<p><code>mmx</code> — operation <code>mmx</code>. Alias for <code>minmax</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p mmx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mmxb">
<h3><a class="doc-anchor" href="#doc-mmxb">#</a> <code>mmxb</code></h3>
<p><code>mmxb</code> — operation <code>mmxb</code>. Alias for <code>minmax_by</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p mmxb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mob">
<h3><a class="doc-anchor" href="#doc-mob">#</a> <code>mob</code></h3>
<p><code>mob</code> — operation <code>mob</code>. Alias for <code>mobius</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mob $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mobius">
<h3><a class="doc-anchor" href="#doc-mobius">#</a> <code>mobius</code></h3>
<p><code>mobius</code> — operation <code>mobius</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mobius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mobius-function-pair">
<h3><a class="doc-anchor" href="#doc-mobius-function-pair">#</a> <code>mobius_function_pair</code></h3>
<p><code>mobius_function_pair</code> — operation <code>mobius function pair</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p mobius_function_pair $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mobius-inversion-step">
<h3><a class="doc-anchor" href="#doc-mobius-inversion-step">#</a> <code>mobius_inversion_step</code></h3>
<p><code>mobius_inversion_step</code> — single-step update of <code>mobius inversion</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p mobius_inversion_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mobius-poset-two">
<h3><a class="doc-anchor" href="#doc-mobius-poset-two">#</a> <code>mobius_poset_two</code></h3>
<p><code>mobius_poset_two</code> — operation <code>mobius poset two</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p mobius_poset_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mod-exp">
<h3><a class="doc-anchor" href="#doc-mod-exp">#</a> <code>mod_exp</code></h3>
<p><code>mod_exp</code> (aliases <code>modexp</code>, <code>powmod</code>) computes modular exponentiation: base^exp mod m, using fast binary exponentiation.</p>
<pre><code class="lang-perl">p powmod(2, 10, 1000) # 24 (2^10 mod 1000)
p powmod(3, 13, 50) # 7
</code></pre>
</article>
<article class="doc-entry" id="doc-mod-inv">
<h3><a class="doc-anchor" href="#doc-mod-inv">#</a> <code>mod_inv</code></h3>
<p><code>mod_inv</code> (alias <code>modinv</code>) computes the modular multiplicative inverse via extended Euclidean algorithm. Errors if no inverse exists.</p>
<pre><code class="lang-perl">p modinv(3, 7) # 5 (3*5 ≡ 1 mod 7)
</code></pre>
</article>
<article class="doc-entry" id="doc-mod-op">
<h3><a class="doc-anchor" href="#doc-mod-op">#</a> <code>mod_op</code></h3>
<p><code>mod_op</code> — modular-arithmetic helper <code>op</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p mod_op $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mod-sph-bessel-i0">
<h3><a class="doc-anchor" href="#doc-mod-sph-bessel-i0">#</a> <code>mod_sph_bessel_i0</code></h3>
<p><code>mod_sph_bessel_i0</code> — modular-arithmetic helper <code>sph bessel i0</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p mod_sph_bessel_i0 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mod-sph-bessel-i1">
<h3><a class="doc-anchor" href="#doc-mod-sph-bessel-i1">#</a> <code>mod_sph_bessel_i1</code></h3>
<p><code>mod_sph_bessel_i1</code> — modular-arithmetic helper <code>sph bessel i1</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p mod_sph_bessel_i1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mod-sph-bessel-k0">
<h3><a class="doc-anchor" href="#doc-mod-sph-bessel-k0">#</a> <code>mod_sph_bessel_k0</code></h3>
<p><code>mod_sph_bessel_k0</code> — modular-arithmetic helper <code>sph bessel k0</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p mod_sph_bessel_k0 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-moddur">
<h3><a class="doc-anchor" href="#doc-moddur">#</a> <code>moddur</code></h3>
<p><code>moddur</code> — operation <code>moddur</code>. Alias for <code>modified_duration</code>. Category: *finance (extended)*.</p>
<pre><code class="lang-perl">p moddur $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mode-agg">
<h3><a class="doc-anchor" href="#doc-mode-agg">#</a> <code>mode_agg</code></h3>
<p><code>mode_agg</code> — operation <code>mode agg</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p mode_agg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mode-iter">
<h3><a class="doc-anchor" href="#doc-mode-iter">#</a> <code>mode_iter</code></h3>
<p><code>mode_iter</code> — operation <code>mode iter</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p mode_iter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mode-list">
<h3><a class="doc-anchor" href="#doc-mode-list">#</a> <code>mode_list</code></h3>
<p><code>mode_list</code> — operation <code>mode list</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p mode_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mode-pitches-dorian">
<h3><a class="doc-anchor" href="#doc-mode-pitches-dorian">#</a> <code>mode_pitches_dorian</code></h3>
<p><code>mode_pitches_dorian</code> — operation <code>mode pitches dorian</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p mode_pitches_dorian $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mode-pitches-lydian">
<h3><a class="doc-anchor" href="#doc-mode-pitches-lydian">#</a> <code>mode_pitches_lydian</code></h3>
<p><code>mode_pitches_lydian</code> — operation <code>mode pitches lydian</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p mode_pitches_lydian $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mode-pitches-phrygian">
<h3><a class="doc-anchor" href="#doc-mode-pitches-phrygian">#</a> <code>mode_pitches_phrygian</code></h3>
<p><code>mode_pitches_phrygian</code> — operation <code>mode pitches phrygian</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p mode_pitches_phrygian $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mode-stat">
<h3><a class="doc-anchor" href="#doc-mode-stat">#</a> <code>mode_stat</code></h3>
<p><code>mode_stat</code> — operation <code>mode stat</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mode_stat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mode-val">
<h3><a class="doc-anchor" href="#doc-mode-val">#</a> <code>mode_val</code></h3>
<p><code>mode_val</code> — operation <code>mode val</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p mode_val $x
</code></pre>
</article>
<article class="doc-entry" id="doc-model-checking-ctl">
<h3><a class="doc-anchor" href="#doc-model-checking-ctl">#</a> <code>model_checking_ctl</code></h3>
<p><code>model_checking_ctl</code> — operation <code>model checking ctl</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p model_checking_ctl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-model-checking-ltl">
<h3><a class="doc-anchor" href="#doc-model-checking-ltl">#</a> <code>model_checking_ltl</code></h3>
<p><code>model_checking_ltl</code> — operation <code>model checking ltl</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p model_checking_ltl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-modhex-encode">
<h3><a class="doc-anchor" href="#doc-modhex-encode">#</a> <code>modhex_encode</code></h3>
<p><code>modhex_encode</code> — encode of <code>modhex</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p modhex_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-modified-duration">
<h3><a class="doc-anchor" href="#doc-modified-duration">#</a> <code>modified_duration</code></h3>
<p><code>modified_duration($face, $coupon_rate, $ytm, $periods)</code> (alias <code>mod_dur</code>) — computes modified duration, which directly measures price sensitivity to yield changes. Equal to Macaulay duration / (1 + ytm).</p>
<pre><code class="lang-perl">p mod_dur(1000, 0.05, 0.05, 10) # ~7.3
</code></pre>
</article>
<article class="doc-entry" id="doc-modified-irr">
<h3><a class="doc-anchor" href="#doc-modified-irr">#</a> <code>modified_irr</code></h3>
<p><code>modified_irr</code> — operation <code>modified irr</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p modified_irr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-modified-julian-date">
<h3><a class="doc-anchor" href="#doc-modified-julian-date">#</a> <code>modified_julian_date</code></h3>
<p><code>modified_julian_date(unix) → number</code> — MJD = <code>40587 + unix/86400</code>. MJD epoch is 1858-11-17.</p>
<pre><code class="lang-perl">p modified_julian_date(0) # 40587
</code></pre>
</article>
<article class="doc-entry" id="doc-modified-midpoint-ode">
<h3><a class="doc-anchor" href="#doc-modified-midpoint-ode">#</a> <code>modified_midpoint_ode</code></h3>
<p><code>modified_midpoint_ode</code> — operation <code>modified midpoint ode</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p modified_midpoint_ode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-modified-sharpe">
<h3><a class="doc-anchor" href="#doc-modified-sharpe">#</a> <code>modified_sharpe</code></h3>
<p><code>modified_sharpe</code> — operation <code>modified sharpe</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p modified_sharpe $x
</code></pre>
</article>
<article class="doc-entry" id="doc-modinverse">
<h3><a class="doc-anchor" href="#doc-modinverse">#</a> <code>modinverse</code></h3>
<p><code>modinverse</code> — operation <code>modinverse</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p modinverse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-modmidpoint">
<h3><a class="doc-anchor" href="#doc-modmidpoint">#</a> <code>modmidpoint</code></h3>
<p><code>modmidpoint</code> — operation <code>modmidpoint</code>. Alias for <code>modified_midpoint_ode</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p modmidpoint $x
</code></pre>
</article>
<article class="doc-entry" id="doc-modpow">
<h3><a class="doc-anchor" href="#doc-modpow">#</a> <code>modpow</code></h3>
<p><code>modpow</code> — operation <code>modpow</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p modpow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-modular-data-s-value">
<h3><a class="doc-anchor" href="#doc-modular-data-s-value">#</a> <code>modular_data_s_value</code></h3>
<p><code>modular_data_s_value</code> — value of <code>modular data s</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p modular_data_s_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-modular-data-t-value">
<h3><a class="doc-anchor" href="#doc-modular-data-t-value">#</a> <code>modular_data_t_value</code></h3>
<p><code>modular_data_t_value</code> — value of <code>modular data t</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p modular_data_t_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-modular-sqrt">
<h3><a class="doc-anchor" href="#doc-modular-sqrt">#</a> <code>modular_sqrt</code></h3>
<p><code>modular_sqrt</code> — operation <code>modular sqrt</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p modular_sqrt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-modularity-q">
<h3><a class="doc-anchor" href="#doc-modularity-q">#</a> <code>modularity_q</code></h3>
<p><code>modularity_q</code> — operation <code>modularity q</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p modularity_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-modularity-score">
<h3><a class="doc-anchor" href="#doc-modularity-score">#</a> <code>modularity_score</code></h3>
<p><code>modularity_score</code> — score of <code>modularity</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p modularity_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-moduli-dimension-curves">
<h3><a class="doc-anchor" href="#doc-moduli-dimension-curves">#</a> <code>moduli_dimension_curves</code></h3>
<p><code>moduli_dimension_curves</code> — operation <code>moduli dimension curves</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p moduli_dimension_curves $x
</code></pre>
</article>
<article class="doc-entry" id="doc-molality">
<h3><a class="doc-anchor" href="#doc-molality">#</a> <code>molality</code></h3>
<p><code>molality</code> — operation <code>molality</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p molality $x
</code></pre>
</article>
<article class="doc-entry" id="doc-molarity">
<h3><a class="doc-anchor" href="#doc-molarity">#</a> <code>molarity</code></h3>
<p><code>molarity</code> — operation <code>molarity</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p molarity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-molarity-dilution">
<h3><a class="doc-anchor" href="#doc-molarity-dilution">#</a> <code>molarity_dilution</code></h3>
<p><code>molarity_dilution</code> — operation <code>molarity dilution</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p molarity_dilution $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mole-fraction">
<h3><a class="doc-anchor" href="#doc-mole-fraction">#</a> <code>mole_fraction</code></h3>
<p><code>mole_fraction</code> — operation <code>mole fraction</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p mole_fraction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-molecular-weight-compound">
<h3><a class="doc-anchor" href="#doc-molecular-weight-compound">#</a> <code>molecular_weight_compound</code></h3>
<p><code>molecular_weight_compound</code> — operation <code>molecular weight compound</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p molecular_weight_compound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-moles-from-mass">
<h3><a class="doc-anchor" href="#doc-moles-from-mass">#</a> <code>moles_from_mass</code></h3>
<p><code>moles_from_mass</code> — operation <code>moles from mass</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p moles_from_mass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mollweide-project">
<h3><a class="doc-anchor" href="#doc-mollweide-project">#</a> <code>mollweide_project</code></h3>
<p><code>mollweide_project</code> — operation <code>mollweide project</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p mollweide_project $x
</code></pre>
</article>
<article class="doc-entry" id="doc-moment-image">
<h3><a class="doc-anchor" href="#doc-moment-image">#</a> <code>moment_image</code></h3>
<p><code>moment_image(image, p, q) → number</code> — <code>Σ x^p · y^q · I(x,y)</code>. Raw image moments.</p>
</article>
<article class="doc-entry" id="doc-moment-magnitude-mw">
<h3><a class="doc-anchor" href="#doc-moment-magnitude-mw">#</a> <code>moment_magnitude_mw</code></h3>
<p><code>moment_magnitude_mw</code> — operation <code>moment magnitude mw</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p moment_magnitude_mw $x
</code></pre>
</article>
<article class="doc-entry" id="doc-moment-of-inertia-cylinder">
<h3><a class="doc-anchor" href="#doc-moment-of-inertia-cylinder">#</a> <code>moment_of_inertia_cylinder</code></h3>
<p><code>moment_of_inertia_cylinder(mass, radius) → number</code> — <code>½·m·r²</code> about cylinder axis.</p>
</article>
<article class="doc-entry" id="doc-moment-of-inertia-disc">
<h3><a class="doc-anchor" href="#doc-moment-of-inertia-disc">#</a> <code>moment_of_inertia_disc</code></h3>
<p><code>moment_of_inertia_disc(mass, radius) → number</code> — <code>½·m·r²</code> about disc axis.</p>
</article>
<article class="doc-entry" id="doc-moment-of-inertia-rod">
<h3><a class="doc-anchor" href="#doc-moment-of-inertia-rod">#</a> <code>moment_of_inertia_rod</code></h3>
<p><code>moment_of_inertia_rod(mass, length) → number</code> — <code>m·L² / 12</code> about centroid perpendicular axis.</p>
</article>
<article class="doc-entry" id="doc-moment-of-inertia-sphere">
<h3><a class="doc-anchor" href="#doc-moment-of-inertia-sphere">#</a> <code>moment_of_inertia_sphere</code></h3>
<p><code>moment_of_inertia_sphere(mass, radius) → number</code> — <code>(2/5)·m·r²</code> for solid sphere.</p>
</article>
<article class="doc-entry" id="doc-momentum">
<h3><a class="doc-anchor" href="#doc-momentum">#</a> <code>momentum</code></h3>
<p><code>momentum($mass, $velocity)</code> — compute momentum p = mv (kg⋅m/s).</p>
<pre><code class="lang-perl">p momentum(10, 5) # 50 kg⋅m/s
</code></pre>
</article>
<article class="doc-entry" id="doc-mones">
<h3><a class="doc-anchor" href="#doc-mones">#</a> <code>mones</code></h3>
<p><code>mones</code> — operation <code>mones</code>. Alias for <code>matrix_ones</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mones $x
</code></pre>
</article>
<article class="doc-entry" id="doc-money-add">
<h3><a class="doc-anchor" href="#doc-money-add">#</a> <code>money_add</code></h3>
<p><code>money_add(a, b) → number</code> — add two dollar amounts by converting each to integer cents via banker's rounding, summing in i64 (saturating), then dividing by 100. Avoids accumulated float drift.</p>
</article>
<article class="doc-entry" id="doc-money-compare">
<h3><a class="doc-anchor" href="#doc-money-compare">#</a> <code>money_compare</code></h3>
<p><code>money_compare(a, b) → -1|0|1</code> — three-way compare after converting both to integer cents (banker's rounding). Avoids float-equality pitfalls.</p>
</article>
<article class="doc-entry" id="doc-money-div">
<h3><a class="doc-anchor" href="#doc-money-div">#</a> <code>money_div</code></h3>
<p><code>money_div(amount, divisor) → number</code> — divide amount (in cents) by <code>divisor</code>, then round half-to-even back to cents. UNDEF on <code>divisor == 0</code>.</p>
</article>
<article class="doc-entry" id="doc-money-mul">
<h3><a class="doc-anchor" href="#doc-money-mul">#</a> <code>money_mul</code></h3>
<p><code>money_mul(amount, factor) → number</code> — multiply amount (in cents) by <code>factor</code>, then round half-to-even (banker's rounding) back to cents.</p>
</article>
<article class="doc-entry" id="doc-money-sub">
<h3><a class="doc-anchor" href="#doc-money-sub">#</a> <code>money_sub</code></h3>
<p><code>money_sub(a, b) → number</code> — subtract dollar amounts in integer cents with banker's rounding on input.</p>
</article>
<article class="doc-entry" id="doc-monin-obukhov-length">
<h3><a class="doc-anchor" href="#doc-monin-obukhov-length">#</a> <code>monin_obukhov_length</code></h3>
<p><code>monin_obukhov_length</code> — operation <code>monin obukhov length</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p monin_obukhov_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-monobit-test">
<h3><a class="doc-anchor" href="#doc-monobit-test">#</a> <code>monobit_test</code></h3>
<p><code>monobit_test</code> — statistical test of <code>monobit</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p monobit_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-monopoly-lerner">
<h3><a class="doc-anchor" href="#doc-monopoly-lerner">#</a> <code>monopoly_lerner</code></h3>
<p><code>monopoly_lerner</code> — operation <code>monopoly lerner</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p monopoly_lerner $x
</code></pre>
</article>
<article class="doc-entry" id="doc-montecarlo-returns-step">
<h3><a class="doc-anchor" href="#doc-montecarlo-returns-step">#</a> <code>montecarlo_returns_step</code></h3>
<p><code>montecarlo_returns_step</code> — single-step update of <code>montecarlo returns</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p montecarlo_returns_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-month-name">
<h3><a class="doc-anchor" href="#doc-month-name">#</a> <code>month_name</code></h3>
<p><code>month_name</code> — operation <code>month name</code>. Category: *date helpers*.</p>
<pre><code class="lang-perl">p month_name $x
</code></pre>
</article>
<article class="doc-entry" id="doc-month-short">
<h3><a class="doc-anchor" href="#doc-month-short">#</a> <code>month_short</code></h3>
<p><code>month_short</code> — operation <code>month short</code>. Category: *date helpers*.</p>
<pre><code class="lang-perl">p month_short $x
</code></pre>
</article>
<article class="doc-entry" id="doc-months-between">
<h3><a class="doc-anchor" href="#doc-months-between">#</a> <code>months_between</code></h3>
<p><code>months_between</code> — operation <code>months between</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p months_between $x
</code></pre>
</article>
<article class="doc-entry" id="doc-montreal-protocol-track">
<h3><a class="doc-anchor" href="#doc-montreal-protocol-track">#</a> <code>montreal_protocol_track</code></h3>
<p><code>montreal_protocol_track</code> — operation <code>montreal protocol track</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p montreal_protocol_track $x
</code></pre>
</article>
<article class="doc-entry" id="doc-moon-age-days">
<h3><a class="doc-anchor" href="#doc-moon-age-days">#</a> <code>moon_age_days</code></h3>
<p><code>moon_age_days(unix) → number</code> — days since the most recent new moon (synodic period 29.53 days).</p>
<pre><code class="lang-perl">p moon_age_days(time())
</code></pre>
</article>
<article class="doc-entry" id="doc-moon-distance-km">
<h3><a class="doc-anchor" href="#doc-moon-distance-km">#</a> <code>moon_distance_km</code></h3>
<p><code>moon_distance_km(unix) → number</code> — approximate Earth-Moon distance in km (sinusoidal around mean).</p>
<pre><code class="lang-perl">p moon_distance_km(time())
</code></pre>
</article>
<article class="doc-entry" id="doc-moon-phase">
<h3><a class="doc-anchor" href="#doc-moon-phase">#</a> <code>moon_phase</code></h3>
<p><code>moon_phase(unix) → number</code> — 0..1 cycle position: 0 new, 0.25 first quarter, 0.5 full, 0.75 last quarter.</p>
<pre><code class="lang-perl">p moon_phase(time())
</code></pre>
</article>
<article class="doc-entry" id="doc-moon-phase-age">
<h3><a class="doc-anchor" href="#doc-moon-phase-age">#</a> <code>moon_phase_age</code></h3>
<p><code>moon_phase_age</code> — lunar astronomy helper <code>phase age</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p moon_phase_age $x
</code></pre>
</article>
<article class="doc-entry" id="doc-moon-position-low">
<h3><a class="doc-anchor" href="#doc-moon-position-low">#</a> <code>moon_position_low</code></h3>
<p><code>moon_position_low</code> — lunar astronomy helper <code>position low</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p moon_position_low $x
</code></pre>
</article>
<article class="doc-entry" id="doc-morphological-gradient">
<h3><a class="doc-anchor" href="#doc-morphological-gradient">#</a> <code>morphological_gradient</code></h3>
<p><code>morphological_gradient(image, size=3) → matrix</code> — dilation - erosion. Highlights edges.</p>
</article>
<article class="doc-entry" id="doc-morse">
<h3><a class="doc-anchor" href="#doc-morse">#</a> <code>morse</code></h3>
<p><code>morse</code> — operation <code>morse</code>. Alias for <code>morse_encode</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p morse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-morse-decode">
<h3><a class="doc-anchor" href="#doc-morse-decode">#</a> <code>morse_decode</code></h3>
<p><code>morse_decode</code> — decode of <code>morse</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p morse_decode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-morse-encode">
<h3><a class="doc-anchor" href="#doc-morse-encode">#</a> <code>morse_encode</code></h3>
<p><code>morse_encode</code> — encode of <code>morse</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p morse_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mortality-table-q">
<h3><a class="doc-anchor" href="#doc-mortality-table-q">#</a> <code>mortality_table_q</code></h3>
<p><code>mortality_table_q</code> — operation <code>mortality table q</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p mortality_table_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mortgage-payment">
<h3><a class="doc-anchor" href="#doc-mortgage-payment">#</a> <code>mortgage_payment</code></h3>
<p><code>mortgage_payment</code> — operation <code>mortgage payment</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p mortgage_payment $x
</code></pre>
</article>
<article class="doc-entry" id="doc-most-common">
<h3><a class="doc-anchor" href="#doc-most-common">#</a> <code>most_common</code></h3>
<p><code>most_common</code> — operation <code>most common</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p most_common $x
</code></pre>
</article>
<article class="doc-entry" id="doc-motion-blur-kernel">
<h3><a class="doc-anchor" href="#doc-motion-blur-kernel">#</a> <code>motion_blur_kernel</code></h3>
<p><code>motion_blur_kernel</code> — convolution kernel of <code>motion blur</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p motion_blur_kernel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-motor-torque">
<h3><a class="doc-anchor" href="#doc-motor-torque">#</a> <code>motor_torque</code></h3>
<p><code>motor_torque</code> — operation <code>motor torque</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p motor_torque $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mott-schottky-capacitance">
<h3><a class="doc-anchor" href="#doc-mott-schottky-capacitance">#</a> <code>mott_schottky_capacitance</code></h3>
<p><code>mott_schottky_capacitance</code> — operation <code>mott schottky capacitance</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p mott_schottky_capacitance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-movavg">
<h3><a class="doc-anchor" href="#doc-movavg">#</a> <code>movavg</code></h3>
<p><code>movavg</code> — operation <code>movavg</code>. Alias for <code>moving_average</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p movavg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-moving-average">
<h3><a class="doc-anchor" href="#doc-moving-average">#</a> <code>moving_average</code></h3>
<p><code>moving_average</code> — operation <code>moving average</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p moving_average $x
</code></pre>
</article>
<article class="doc-entry" id="doc-moving-average-filter">
<h3><a class="doc-anchor" href="#doc-moving-average-filter">#</a> <code>moving_average_filter</code></h3>
<p><code>moving_average_filter</code> — filter op of <code>moving average</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p moving_average_filter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mpeg-quant-value">
<h3><a class="doc-anchor" href="#doc-mpeg-quant-value">#</a> <code>mpeg_quant_value</code></h3>
<p><code>mpeg_quant_value</code> — value of <code>mpeg quant</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p mpeg_quant_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mph-to-kmh">
<h3><a class="doc-anchor" href="#doc-mph-to-kmh">#</a> <code>mph_to_kmh</code></h3>
<p><code>mph_to_kmh</code> — convert from <code>mph</code> to <code>kmh</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p mph_to_kmh $value
</code></pre>
</article>
<article class="doc-entry" id="doc-mplanck">
<h3><a class="doc-anchor" href="#doc-mplanck">#</a> <code>mplanck</code></h3>
<p><code>mplanck</code> — operation <code>mplanck</code>. Alias for <code>planck_mass</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p mplanck $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mpmc-new">
<h3><a class="doc-anchor" href="#doc-mpmc-new">#</a> <code>mpmc_new</code></h3>
<p><code>mpmc_new</code> — constructor of <code>mpmc</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p mpmc_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mpow">
<h3><a class="doc-anchor" href="#doc-mpow">#</a> <code>mpow</code></h3>
<p><code>mpow</code> — operation <code>mpow</code>. Alias for <code>matrix_power</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p mpow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mps-to-kmh">
<h3><a class="doc-anchor" href="#doc-mps-to-kmh">#</a> <code>mps_to_kmh</code></h3>
<p><code>mps_to_kmh</code> — convert from <code>mps</code> to <code>kmh</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p mps_to_kmh $value
</code></pre>
</article>
<article class="doc-entry" id="doc-mpsc-new">
<h3><a class="doc-anchor" href="#doc-mpsc-new">#</a> <code>mpsc_new</code></h3>
<p><code>mpsc_new</code> — constructor of <code>mpsc</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p mpsc_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mrow">
<h3><a class="doc-anchor" href="#doc-mrow">#</a> <code>mrow</code></h3>
<p><code>mrow</code> — operation <code>mrow</code>. Alias for <code>matrix_row</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mrow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ms-to-ns">
<h3><a class="doc-anchor" href="#doc-ms-to-ns">#</a> <code>ms_to_ns</code></h3>
<p><code>ms_to_ns</code> — convert from <code>ms</code> to <code>ns</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p ms_to_ns $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ms-to-s">
<h3><a class="doc-anchor" href="#doc-ms-to-s">#</a> <code>ms_to_s</code></h3>
<p><code>ms_to_s</code> — convert from <code>ms</code> to <code>s</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p ms_to_s $value
</code></pre>
</article>
<article class="doc-entry" id="doc-msa-column-entropy">
<h3><a class="doc-anchor" href="#doc-msa-column-entropy">#</a> <code>msa_column_entropy</code></h3>
<p><code>msa_column_entropy</code> — operation <code>msa column entropy</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p msa_column_entropy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mscal">
<h3><a class="doc-anchor" href="#doc-mscal">#</a> <code>mscal</code></h3>
<p><code>mscal</code> — operation <code>mscal</code>. Alias for <code>matrix_scalar</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mscal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mse">
<h3><a class="doc-anchor" href="#doc-mse">#</a> <code>mse</code></h3>
<p><code>mse</code> — operation <code>mse</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p mse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mset">
<h3><a class="doc-anchor" href="#doc-mset">#</a> <code>mset</code></h3>
<p><code>mset</code> — operation <code>mset</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p mset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-msgctl">
<h3><a class="doc-anchor" href="#doc-msgctl">#</a> <code>msgctl</code></h3>
<p><code>msgctl</code> — operation <code>msgctl</code>. Category: *sysv ipc*.</p>
<pre><code class="lang-perl">p msgctl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-msgget">
<h3><a class="doc-anchor" href="#doc-msgget">#</a> <code>msgget</code></h3>
<p><code>msgget</code> — operation <code>msgget</code>. Category: *sysv ipc*.</p>
<pre><code class="lang-perl">p msgget $x
</code></pre>
</article>
<article class="doc-entry" id="doc-msgpack-pack-int">
<h3><a class="doc-anchor" href="#doc-msgpack-pack-int">#</a> <code>msgpack_pack_int</code></h3>
<p><code>msgpack_pack_int</code> — operation <code>msgpack pack int</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p msgpack_pack_int $x
</code></pre>
</article>
<article class="doc-entry" id="doc-msgpack-pack-str">
<h3><a class="doc-anchor" href="#doc-msgpack-pack-str">#</a> <code>msgpack_pack_str</code></h3>
<p><code>msgpack_pack_str</code> — operation <code>msgpack pack str</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p msgpack_pack_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-msgrcv">
<h3><a class="doc-anchor" href="#doc-msgrcv">#</a> <code>msgrcv</code></h3>
<p><code>msgrcv</code> — operation <code>msgrcv</code>. Category: *sysv ipc*.</p>
<pre><code class="lang-perl">p msgrcv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-msgsnd">
<h3><a class="doc-anchor" href="#doc-msgsnd">#</a> <code>msgsnd</code></h3>
<p><code>msgsnd</code> — operation <code>msgsnd</code>. Category: *sysv ipc*.</p>
<pre><code class="lang-perl">p msgsnd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mshape">
<h3><a class="doc-anchor" href="#doc-mshape">#</a> <code>mshape</code></h3>
<p><code>mshape</code> — operation <code>mshape</code>. Alias for <code>matrix_shape</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mshape $x
</code></pre>
</article>
<article class="doc-entry" id="doc-msorted">
<h3><a class="doc-anchor" href="#doc-msorted">#</a> <code>msorted</code></h3>
<p><code>msorted</code> — operation <code>msorted</code>. Alias for <code>merge_sorted</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p msorted $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mst">
<h3><a class="doc-anchor" href="#doc-mst">#</a> <code>mst</code></h3>
<p><code>prim_mst</code> (aliases <code>mst</code>, <code>prim</code>) computes the minimum spanning tree weight via Prim's algorithm. Takes an adjacency matrix.</p>
<pre><code class="lang-perl">p mst([[0,2,0],[2,0,3],[0,3,0]]) # 5
</code></pre>
</article>
<article class="doc-entry" id="doc-mstat">
<h3><a class="doc-anchor" href="#doc-mstat">#</a> <code>mstat</code></h3>
<p><code>mstat</code> — operation <code>mstat</code>. Alias for <code>mode_stat</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mstat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-msub">
<h3><a class="doc-anchor" href="#doc-msub">#</a> <code>msub</code></h3>
<p><code>msub</code> — operation <code>msub</code>. Alias for <code>matrix_sub</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p msub $x
</code></pre>
</article>
<article class="doc-entry" id="doc-msum">
<h3><a class="doc-anchor" href="#doc-msum">#</a> <code>msum</code></h3>
<p><code>msum</code> — operation <code>msum</code>. Alias for <code>matrix_sum</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p msum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-msun">
<h3><a class="doc-anchor" href="#doc-msun">#</a> <code>msun</code></h3>
<p><code>sun_mass</code> (alias <code>msun</code>) — M☉ ≈ 1.989×10³⁰ kg. Mass of Sun (solar mass).</p>
<pre><code class="lang-perl">p msun # 1.98892e30 kg
</code></pre>
</article>
<article class="doc-entry" id="doc-mt19937-temper">
<h3><a class="doc-anchor" href="#doc-mt19937-temper">#</a> <code>mt19937_temper</code></h3>
<p><code>mt19937_temper</code> — operation <code>mt19937 temper</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p mt19937_temper $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mtf-decode">
<h3><a class="doc-anchor" href="#doc-mtf-decode">#</a> <code>mtf_decode</code></h3>
<p><code>mtf_decode</code> — decode of <code>mtf</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p mtf_decode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mtf-encode">
<h3><a class="doc-anchor" href="#doc-mtf-encode">#</a> <code>mtf_encode</code></h3>
<p><code>mtf_encode</code> — encode of <code>mtf</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p mtf_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mtime">
<h3><a class="doc-anchor" href="#doc-mtime">#</a> <code>mtime</code></h3>
<p><code>mtime</code> — operation <code>mtime</code>. Alias for <code>file_mtime</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p mtime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mtrace">
<h3><a class="doc-anchor" href="#doc-mtrace">#</a> <code>mtrace</code></h3>
<p><code>mtrace</code> — operation <code>mtrace</code>. Alias for <code>matrix_trace</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mtrace $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mtrans">
<h3><a class="doc-anchor" href="#doc-mtrans">#</a> <code>mtrans</code></h3>
<p><code>mtrans</code> — operation <code>mtrans</code>. Alias for <code>matrix_transpose</code>. Category: *matrix operations extras*.</p>
<pre><code class="lang-perl">p mtrans $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mu0">
<h3><a class="doc-anchor" href="#doc-mu0">#</a> <code>mu0</code></h3>
<p><code>mu0</code> — operation <code>mu0</code>. Alias for <code>vacuum_permeability</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p mu0 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mu-law-decode">
<h3><a class="doc-anchor" href="#doc-mu-law-decode">#</a> <code>mu_law_decode</code></h3>
<p><code>mu_law_decode</code> — decode of <code>mu law</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p mu_law_decode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mu-law-encode">
<h3><a class="doc-anchor" href="#doc-mu-law-encode">#</a> <code>mu_law_encode</code></h3>
<p><code>mu_law_encode</code> — encode of <code>mu law</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p mu_law_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mub">
<h3><a class="doc-anchor" href="#doc-mub">#</a> <code>mub</code></h3>
<p><code>mub</code> — operation <code>mub</code>. Alias for <code>bohr_magneton</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p mub $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mulberry32-next">
<h3><a class="doc-anchor" href="#doc-mulberry32-next">#</a> <code>mulberry32_next</code></h3>
<p><code>mulberry32_next(seed) → int</code> — Mulberry32 PRNG (Tommy Ettinger 2017). Advances state by <code>+0x6D2B79F5</code> then permutes to 32 bits. To iterate, caller tracks state and adds <code>0x6D2B79F5</code> between calls.</p>
</article>
<article class="doc-entry" id="doc-muller">
<h3><a class="doc-anchor" href="#doc-muller">#</a> <code>muller</code></h3>
<p><code>muller</code> — operation <code>muller</code>. Alias for <code>muller_root</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p muller $x
</code></pre>
</article>
<article class="doc-entry" id="doc-muller-root">
<h3><a class="doc-anchor" href="#doc-muller-root">#</a> <code>muller_root</code></h3>
<p><code>muller_root</code> — operation <code>muller root</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p muller_root $x
</code></pre>
</article>
<article class="doc-entry" id="doc-multi-decrement-q">
<h3><a class="doc-anchor" href="#doc-multi-decrement-q">#</a> <code>multi_decrement_q</code></h3>
<p><code>multi_decrement_q</code> — operation <code>multi decrement q</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p multi_decrement_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-multi-knapsack-step">
<h3><a class="doc-anchor" href="#doc-multi-knapsack-step">#</a> <code>multi_knapsack_step</code></h3>
<p><code>multi_knapsack_step</code> — single-step update of <code>multi knapsack</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p multi_knapsack_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-multi-state-pij">
<h3><a class="doc-anchor" href="#doc-multi-state-pij">#</a> <code>multi_state_pij</code></h3>
<p><code>multi_state_pij</code> — operation <code>multi state pij</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p multi_state_pij $x
</code></pre>
</article>
<article class="doc-entry" id="doc-multidim-packing-step">
<h3><a class="doc-anchor" href="#doc-multidim-packing-step">#</a> <code>multidim_packing_step</code></h3>
<p><code>multidim_packing_step</code> — single-step update of <code>multidim packing</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p multidim_packing_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-multinom">
<h3><a class="doc-anchor" href="#doc-multinom">#</a> <code>multinom</code></h3>
<p><code>multinom</code> — operation <code>multinom</code>. Alias for <code>multinomial</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p multinom $x
</code></pre>
</article>
<article class="doc-entry" id="doc-multinomial">
<h3><a class="doc-anchor" href="#doc-multinomial">#</a> <code>multinomial</code></h3>
<p><code>multinomial</code> — operation <code>multinomial</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p multinomial $x
</code></pre>
</article>
<article class="doc-entry" id="doc-multinomial-coefficient">
<h3><a class="doc-anchor" href="#doc-multinomial-coefficient">#</a> <code>multinomial_coefficient</code></h3>
<p><code>multinomial_coefficient([k1, k2, …]) → number</code> — <code>n! / (k1!·k2!·…)</code>. Returns rounded float for large values.</p>
</article>
<article class="doc-entry" id="doc-multinomial-count">
<h3><a class="doc-anchor" href="#doc-multinomial-count">#</a> <code>multinomial_count</code></h3>
<p><code>multinomial_count</code> — count of <code>multinomial</code>. Alias for <code>multiset_permutations_count</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p multinomial_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-multinomial-logit-prob">
<h3><a class="doc-anchor" href="#doc-multinomial-logit-prob">#</a> <code>multinomial_logit_prob</code></h3>
<p><code>multinomial_logit_prob</code> — operation <code>multinomial logit prob</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p multinomial_logit_prob $x
</code></pre>
</article>
<article class="doc-entry" id="doc-multipeek">
<h3><a class="doc-anchor" href="#doc-multipeek">#</a> <code>multipeek</code></h3>
<p><code>multipeek</code> — operation <code>multipeek</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p multipeek $x
</code></pre>
</article>
<article class="doc-entry" id="doc-multiset-difference">
<h3><a class="doc-anchor" href="#doc-multiset-difference">#</a> <code>multiset_difference</code></h3>
<p><code>multiset_difference</code> — operation <code>multiset difference</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p multiset_difference $x
</code></pre>
</article>
<article class="doc-entry" id="doc-multiset-intersection">
<h3><a class="doc-anchor" href="#doc-multiset-intersection">#</a> <code>multiset_intersection</code></h3>
<p><code>multiset_intersection</code> — operation <code>multiset intersection</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p multiset_intersection $x
</code></pre>
</article>
<article class="doc-entry" id="doc-multiset-permutations-count">
<h3><a class="doc-anchor" href="#doc-multiset-permutations-count">#</a> <code>multiset_permutations_count</code></h3>
<p><code>multiset_permutations_count</code> — count of <code>multiset permutations</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p multiset_permutations_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-multiset-union">
<h3><a class="doc-anchor" href="#doc-multiset-union">#</a> <code>multiset_union</code></h3>
<p><code>multiset_union</code> — operation <code>multiset union</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p multiset_union $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mun">
<h3><a class="doc-anchor" href="#doc-mun">#</a> <code>mun</code></h3>
<p><code>mun</code> — operation <code>mun</code>. Alias for <code>nuclear_magneton</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p mun $x
</code></pre>
</article>
<article class="doc-entry" id="doc-murmurhash3-x32">
<h3><a class="doc-anchor" href="#doc-murmurhash3-x32">#</a> <code>murmurhash3_x32</code></h3>
<p><code>murmurhash3_x32</code> — operation <code>murmurhash3 x32</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p murmurhash3_x32 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mutation-bit-flip-prob">
<h3><a class="doc-anchor" href="#doc-mutation-bit-flip-prob">#</a> <code>mutation_bit_flip_prob</code></h3>
<p><code>mutation_bit_flip_prob</code> — operation <code>mutation bit flip prob</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p mutation_bit_flip_prob $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mutation-rate">
<h3><a class="doc-anchor" href="#doc-mutation-rate">#</a> <code>mutation_rate</code></h3>
<p><code>mutation_rate</code> — rate of <code>mutation</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p mutation_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mutual-information-step">
<h3><a class="doc-anchor" href="#doc-mutual-information-step">#</a> <code>mutual_information_step</code></h3>
<p><code>mutual_information_step</code> — single-step update of <code>mutual information</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p mutual_information_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-myerson-optimal">
<h3><a class="doc-anchor" href="#doc-myerson-optimal">#</a> <code>myerson_optimal</code></h3>
<p><code>myerson_optimal</code> — operation <code>myerson optimal</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p myerson_optimal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-mzeros">
<h3><a class="doc-anchor" href="#doc-mzeros">#</a> <code>mzeros</code></h3>
<p><code>mzeros</code> — operation <code>mzeros</code>. Alias for <code>matrix_zeros</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p mzeros $x
</code></pre>
</article>
<article class="doc-entry" id="doc-n-ball-volume">
<h3><a class="doc-anchor" href="#doc-n-ball-volume">#</a> <code>n_ball_volume</code></h3>
<p><code>n_ball_volume</code> — operation <code>n ball volume</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p n_ball_volume $x
</code></pre>
</article>
<article class="doc-entry" id="doc-n-tuples">
<h3><a class="doc-anchor" href="#doc-n-tuples">#</a> <code>n_tuples</code></h3>
<p><code>n_tuples</code> — operation <code>n tuples</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p n_tuples $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nanoid">
<h3><a class="doc-anchor" href="#doc-nanoid">#</a> <code>nanoid</code></h3>
<p><code>nanoid</code> — operation <code>nanoid</code>. Category: *id helpers*.</p>
<pre><code class="lang-perl">p nanoid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nao-index-step">
<h3><a class="doc-anchor" href="#doc-nao-index-step">#</a> <code>nao_index_step</code></h3>
<p><code>nao_index_step</code> — single-step update of <code>nao index</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nao_index_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-narayana-cow">
<h3><a class="doc-anchor" href="#doc-narayana-cow">#</a> <code>narayana_cow</code></h3>
<p><code>narayana_cow(n) → int</code> — Narayana's cow sequence: <code>a(n) = a(n-1) + a(n-3)</code>.</p>
</article>
<article class="doc-entry" id="doc-nash-bargaining-solution">
<h3><a class="doc-anchor" href="#doc-nash-bargaining-solution">#</a> <code>nash_bargaining_solution</code></h3>
<p><code>nash_bargaining_solution</code> — operation <code>nash bargaining solution</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nash_bargaining_solution $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nash-equilibrium-pair">
<h3><a class="doc-anchor" href="#doc-nash-equilibrium-pair">#</a> <code>nash_equilibrium_pair</code></h3>
<p><code>nash_equilibrium_pair</code> — operation <code>nash equilibrium pair</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nash_equilibrium_pair $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nash-social-welfare">
<h3><a class="doc-anchor" href="#doc-nash-social-welfare">#</a> <code>nash_social_welfare</code></h3>
<p><code>nash_social_welfare</code> — operation <code>nash social welfare</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nash_social_welfare $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nato">
<h3><a class="doc-anchor" href="#doc-nato">#</a> <code>nato</code></h3>
<p><code>nato</code> — operation <code>nato</code>. Alias for <code>nato_phonetic</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p nato $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nato-phonetic">
<h3><a class="doc-anchor" href="#doc-nato-phonetic">#</a> <code>nato_phonetic</code></h3>
<p><code>nato_phonetic</code> — operation <code>nato phonetic</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p nato_phonetic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nb-bernoulli-likelihood">
<h3><a class="doc-anchor" href="#doc-nb-bernoulli-likelihood">#</a> <code>nb_bernoulli_likelihood</code></h3>
<p><code>nb_bernoulli_likelihood</code> — operation <code>nb bernoulli likelihood</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p nb_bernoulli_likelihood $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nb-gaussian-likelihood">
<h3><a class="doc-anchor" href="#doc-nb-gaussian-likelihood">#</a> <code>nb_gaussian_likelihood</code></h3>
<p><code>nb_gaussian_likelihood</code> — operation <code>nb gaussian likelihood</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p nb_gaussian_likelihood $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nb-multinomial-log-likelihood">
<h3><a class="doc-anchor" href="#doc-nb-multinomial-log-likelihood">#</a> <code>nb_multinomial_log_likelihood</code></h3>
<p><code>nb_multinomial_log_likelihood</code> — operation <code>nb multinomial log likelihood</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p nb_multinomial_log_likelihood $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nbe-normalize">
<h3><a class="doc-anchor" href="#doc-nbe-normalize">#</a> <code>nbe_normalize</code></h3>
<p><code>nbe_normalize</code> — operation <code>nbe normalize</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p nbe_normalize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ncol">
<h3><a class="doc-anchor" href="#doc-ncol">#</a> <code>ncol</code></h3>
<p><code>ncol</code> — number of columns in a matrix.</p>
<pre><code class="lang-perl">p ncol([[1,2,3],[4,5,6]]) # 3
</code></pre>
</article>
<article class="doc-entry" id="doc-ndivs">
<h3><a class="doc-anchor" href="#doc-ndivs">#</a> <code>ndivs</code></h3>
<p><code>ndivs</code> — operation <code>ndivs</code>. Alias for <code>num_divisors</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p ndivs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ne-from-variance">
<h3><a class="doc-anchor" href="#doc-ne-from-variance">#</a> <code>ne_from_variance</code></h3>
<p><code>ne_from_variance</code> — operation <code>ne from variance</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p ne_from_variance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nearest-insertion-step">
<h3><a class="doc-anchor" href="#doc-nearest-insertion-step">#</a> <code>nearest_insertion_step</code></h3>
<p><code>nearest_insertion_step</code> — single-step update of <code>nearest insertion</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p nearest_insertion_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nearest-neighbor-tour-step">
<h3><a class="doc-anchor" href="#doc-nearest-neighbor-tour-step">#</a> <code>nearest_neighbor_tour_step</code></h3>
<p><code>nearest_neighbor_tour_step</code> — single-step update of <code>nearest neighbor tour</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p nearest_neighbor_tour_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-necklace-count">
<h3><a class="doc-anchor" href="#doc-necklace-count">#</a> <code>necklace_count</code></h3>
<p><code>necklace_count</code> — count of <code>necklace</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p necklace_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-needleman-wunsch-score">
<h3><a class="doc-anchor" href="#doc-needleman-wunsch-score">#</a> <code>needleman_wunsch_score</code></h3>
<p><code>needleman_wunsch_score</code> — score of <code>needleman wunsch</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p needleman_wunsch_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-neg-inf">
<h3><a class="doc-anchor" href="#doc-neg-inf">#</a> <code>neg_inf</code></h3>
<p><code>neg_inf</code> — operation <code>neg inf</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p neg_inf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-neg-n">
<h3><a class="doc-anchor" href="#doc-neg-n">#</a> <code>neg_n</code></h3>
<p><code>neg_n</code> — operation <code>neg n</code>. Alias for <code>negative</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p neg_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-negate">
<h3><a class="doc-anchor" href="#doc-negate">#</a> <code>negate</code></h3>
<p><code>negate</code> — operation <code>negate</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p negate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-negate-each">
<h3><a class="doc-anchor" href="#doc-negate-each">#</a> <code>negate_each</code></h3>
<p><code>negate_each</code> — operation <code>negate each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p negate_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-negative">
<h3><a class="doc-anchor" href="#doc-negative">#</a> <code>negative</code></h3>
<p><code>negative</code> — operation <code>negative</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p negative $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nei-genetic-distance">
<h3><a class="doc-anchor" href="#doc-nei-genetic-distance">#</a> <code>nei_genetic_distance</code></h3>
<p><code>nei_genetic_distance</code> — distance / dissimilarity metric of <code>nei genetic</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p nei_genetic_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-neither">
<h3><a class="doc-anchor" href="#doc-neither">#</a> <code>neither</code></h3>
<p><code>neither</code> — operation <code>neither</code>. Category: *boolean combinators*.</p>
<pre><code class="lang-perl">p neither $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nelder-mead-contract">
<h3><a class="doc-anchor" href="#doc-nelder-mead-contract">#</a> <code>nelder_mead_contract</code></h3>
<p><code>nelder_mead_contract</code> — operation <code>nelder mead contract</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p nelder_mead_contract $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nelder-mead-expand">
<h3><a class="doc-anchor" href="#doc-nelder-mead-expand">#</a> <code>nelder_mead_expand</code></h3>
<p><code>nelder_mead_expand</code> — operation <code>nelder mead expand</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p nelder_mead_expand $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nelder-mead-reflect">
<h3><a class="doc-anchor" href="#doc-nelder-mead-reflect">#</a> <code>nelder_mead_reflect</code></h3>
<p><code>nelder_mead_reflect</code> — operation <code>nelder mead reflect</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p nelder_mead_reflect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nemhauser-wolsey-bound">
<h3><a class="doc-anchor" href="#doc-nemhauser-wolsey-bound">#</a> <code>nemhauser_wolsey_bound</code></h3>
<p><code>nemhauser_wolsey_bound</code> — operation <code>nemhauser wolsey bound</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p nemhauser_wolsey_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ner-bilou-decode">
<h3><a class="doc-anchor" href="#doc-ner-bilou-decode">#</a> <code>ner_bilou_decode</code></h3>
<p><code>ner_bilou_decode</code> — decode of <code>ner bilou</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p ner_bilou_decode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nernst-diffusion-layer">
<h3><a class="doc-anchor" href="#doc-nernst-diffusion-layer">#</a> <code>nernst_diffusion_layer</code></h3>
<p><code>nernst_diffusion_layer</code> — operation <code>nernst diffusion layer</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p nernst_diffusion_layer $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nernst-einstein-diffusivity">
<h3><a class="doc-anchor" href="#doc-nernst-einstein-diffusivity">#</a> <code>nernst_einstein_diffusivity</code></h3>
<p><code>nernst_einstein_diffusivity</code> — operation <code>nernst einstein diffusivity</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p nernst_einstein_diffusivity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nernst-planck-flux">
<h3><a class="doc-anchor" href="#doc-nernst-planck-flux">#</a> <code>nernst_planck_flux</code></h3>
<p><code>nernst_planck_flux</code> — operation <code>nernst planck flux</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p nernst_planck_flux $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nernst-potential-full">
<h3><a class="doc-anchor" href="#doc-nernst-potential-full">#</a> <code>nernst_potential_full</code></h3>
<p><code>nernst_potential_full</code> — operation <code>nernst potential full</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p nernst_potential_full $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nerve-complex-count">
<h3><a class="doc-anchor" href="#doc-nerve-complex-count">#</a> <code>nerve_complex_count</code></h3>
<p><code>nerve_complex_count</code> — count of <code>nerve complex</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p nerve_complex_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nesterov-accelerate-step">
<h3><a class="doc-anchor" href="#doc-nesterov-accelerate-step">#</a> <code>nesterov_accelerate_step</code></h3>
<p><code>nesterov_accelerate_step</code> — single-step update of <code>nesterov accelerate</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p nesterov_accelerate_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nesterov-step">
<h3><a class="doc-anchor" href="#doc-nesterov-step">#</a> <code>nesterov_step</code></h3>
<p><code>nesterov_step</code> — single-step update of <code>nesterov</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p nesterov_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-aiad-step">
<h3><a class="doc-anchor" href="#doc-net-aiad-step">#</a> <code>net_aiad_step</code></h3>
<p><code>net_aiad_step</code> — single-step update of <code>net aiad</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_aiad_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-aimd-step">
<h3><a class="doc-anchor" href="#doc-net-aimd-step">#</a> <code>net_aimd_step</code></h3>
<p><code>net_aimd_step</code> — single-step update of <code>net aimd</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_aimd_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-alohanet-throughput">
<h3><a class="doc-anchor" href="#doc-net-alohanet-throughput">#</a> <code>net_alohanet_throughput</code></h3>
<p><code>net_alohanet_throughput</code> — operation <code>net alohanet throughput</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_alohanet_throughput $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-alpha-fair-step">
<h3><a class="doc-anchor" href="#doc-net-alpha-fair-step">#</a> <code>net_alpha_fair_step</code></h3>
<p><code>net_alpha_fair_step</code> — single-step update of <code>net alpha fair</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_alpha_fair_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-amc-threshold-index">
<h3><a class="doc-anchor" href="#doc-net-amc-threshold-index">#</a> <code>net_amc_threshold_index</code></h3>
<p><code>net_amc_threshold_index</code> — index of <code>net amc threshold</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_amc_threshold_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-aqm-blue-step">
<h3><a class="doc-anchor" href="#doc-net-aqm-blue-step">#</a> <code>net_aqm_blue_step</code></h3>
<p><code>net_aqm_blue_step</code> — single-step update of <code>net aqm blue</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_aqm_blue_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-aqm-choke-step">
<h3><a class="doc-anchor" href="#doc-net-aqm-choke-step">#</a> <code>net_aqm_choke_step</code></h3>
<p><code>net_aqm_choke_step</code> — single-step update of <code>net aqm choke</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_aqm_choke_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-aqm-codel-target">
<h3><a class="doc-anchor" href="#doc-net-aqm-codel-target">#</a> <code>net_aqm_codel_target</code></h3>
<p><code>net_aqm_codel_target</code> — operation <code>net aqm codel target</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_aqm_codel_target $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-aqm-drr-step">
<h3><a class="doc-anchor" href="#doc-net-aqm-drr-step">#</a> <code>net_aqm_drr_step</code></h3>
<p><code>net_aqm_drr_step</code> — single-step update of <code>net aqm drr</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_aqm_drr_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-aqm-fq-codel-step">
<h3><a class="doc-anchor" href="#doc-net-aqm-fq-codel-step">#</a> <code>net_aqm_fq_codel_step</code></h3>
<p><code>net_aqm_fq_codel_step</code> — single-step update of <code>net aqm fq codel</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_aqm_fq_codel_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-aqm-pie-drop-rate">
<h3><a class="doc-anchor" href="#doc-net-aqm-pie-drop-rate">#</a> <code>net_aqm_pie_drop_rate</code></h3>
<p><code>net_aqm_pie_drop_rate</code> — rate of <code>net aqm pie drop</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_aqm_pie_drop_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-aqm-red-drop-prob">
<h3><a class="doc-anchor" href="#doc-net-aqm-red-drop-prob">#</a> <code>net_aqm_red_drop_prob</code></h3>
<p><code>net_aqm_red_drop_prob</code> — operation <code>net aqm red drop prob</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_aqm_red_drop_prob $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-aqm-sfq-step">
<h3><a class="doc-anchor" href="#doc-net-aqm-sfq-step">#</a> <code>net_aqm_sfq_step</code></h3>
<p><code>net_aqm_sfq_step</code> — single-step update of <code>net aqm sfq</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_aqm_sfq_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-aqm-wrr-step">
<h3><a class="doc-anchor" href="#doc-net-aqm-wrr-step">#</a> <code>net_aqm_wrr_step</code></h3>
<p><code>net_aqm_wrr_step</code> — single-step update of <code>net aqm wrr</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_aqm_wrr_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-array-gain">
<h3><a class="doc-anchor" href="#doc-net-array-gain">#</a> <code>net_array_gain</code></h3>
<p><code>net_array_gain</code> — operation <code>net array gain</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_array_gain $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-backpressure-step">
<h3><a class="doc-anchor" href="#doc-net-backpressure-step">#</a> <code>net_backpressure_step</code></h3>
<p><code>net_backpressure_step</code> — single-step update of <code>net backpressure</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_backpressure_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-bandwidth-delay-product">
<h3><a class="doc-anchor" href="#doc-net-bandwidth-delay-product">#</a> <code>net_bandwidth_delay_product</code></h3>
<p><code>net_bandwidth_delay_product</code> — operation <code>net bandwidth delay product</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_bandwidth_delay_product $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-bcjr-step">
<h3><a class="doc-anchor" href="#doc-net-bcjr-step">#</a> <code>net_bcjr_step</code></h3>
<p><code>net_bcjr_step</code> — single-step update of <code>net bcjr</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_bcjr_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-blocking-probability">
<h3><a class="doc-anchor" href="#doc-net-blocking-probability">#</a> <code>net_blocking_probability</code></h3>
<p><code>net_blocking_probability</code> — operation <code>net blocking probability</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_blocking_probability $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-burst-size-compute">
<h3><a class="doc-anchor" href="#doc-net-burst-size-compute">#</a> <code>net_burst_size_compute</code></h3>
<p><code>net_burst_size_compute</code> — operation <code>net burst size compute</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_burst_size_compute $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-call-admission-check">
<h3><a class="doc-anchor" href="#doc-net-call-admission-check">#</a> <code>net_call_admission_check</code></h3>
<p><code>net_call_admission_check</code> — operation <code>net call admission check</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_call_admission_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-capacity-shannon">
<h3><a class="doc-anchor" href="#doc-net-capacity-shannon">#</a> <code>net_capacity_shannon</code></h3>
<p><code>net_capacity_shannon</code> — operation <code>net capacity shannon</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_capacity_shannon $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-coding-gain">
<h3><a class="doc-anchor" href="#doc-net-coding-gain">#</a> <code>net_coding_gain</code></h3>
<p><code>net_coding_gain</code> — operation <code>net coding gain</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_coding_gain $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-csma-back-off">
<h3><a class="doc-anchor" href="#doc-net-csma-back-off">#</a> <code>net_csma_back_off</code></h3>
<p><code>net_csma_back_off</code> — operation <code>net csma back off</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_csma_back_off $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-csma-efficiency">
<h3><a class="doc-anchor" href="#doc-net-csma-efficiency">#</a> <code>net_csma_efficiency</code></h3>
<p><code>net_csma_efficiency</code> — operation <code>net csma efficiency</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_csma_efficiency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-diversity-gain">
<h3><a class="doc-anchor" href="#doc-net-diversity-gain">#</a> <code>net_diversity_gain</code></h3>
<p><code>net_diversity_gain</code> — operation <code>net diversity gain</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_diversity_gain $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-doppler-shift">
<h3><a class="doc-anchor" href="#doc-net-doppler-shift">#</a> <code>net_doppler_shift</code></h3>
<p><code>net_doppler_shift</code> — operation <code>net doppler shift</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_doppler_shift $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-drop-tail-check">
<h3><a class="doc-anchor" href="#doc-net-drop-tail-check">#</a> <code>net_drop_tail_check</code></h3>
<p><code>net_drop_tail_check</code> — operation <code>net drop tail check</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_drop_tail_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-engset-formula">
<h3><a class="doc-anchor" href="#doc-net-engset-formula">#</a> <code>net_engset_formula</code></h3>
<p><code>net_engset_formula</code> — operation <code>net engset formula</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_engset_formula $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-erlang-b-formula">
<h3><a class="doc-anchor" href="#doc-net-erlang-b-formula">#</a> <code>net_erlang_b_formula</code></h3>
<p><code>net_erlang_b_formula</code> — operation <code>net erlang b formula</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_erlang_b_formula $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-erlang-c-formula">
<h3><a class="doc-anchor" href="#doc-net-erlang-c-formula">#</a> <code>net_erlang_c_formula</code></h3>
<p><code>net_erlang_c_formula</code> — operation <code>net erlang c formula</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_erlang_c_formula $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-forced-flow-law">
<h3><a class="doc-anchor" href="#doc-net-forced-flow-law">#</a> <code>net_forced_flow_law</code></h3>
<p><code>net_forced_flow_law</code> — operation <code>net forced flow law</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_forced_flow_law $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-friis-received-power">
<h3><a class="doc-anchor" href="#doc-net-friis-received-power">#</a> <code>net_friis_received_power</code></h3>
<p><code>net_friis_received_power</code> — operation <code>net friis received power</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_friis_received_power $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-handoff-threshold">
<h3><a class="doc-anchor" href="#doc-net-handoff-threshold">#</a> <code>net_handoff_threshold</code></h3>
<p><code>net_handoff_threshold</code> — operation <code>net handoff threshold</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_handoff_threshold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-harq-combining-gain">
<h3><a class="doc-anchor" href="#doc-net-harq-combining-gain">#</a> <code>net_harq_combining_gain</code></h3>
<p><code>net_harq_combining_gain</code> — operation <code>net harq combining gain</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_harq_combining_gain $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-jitter-estimate">
<h3><a class="doc-anchor" href="#doc-net-jitter-estimate">#</a> <code>net_jitter_estimate</code></h3>
<p><code>net_jitter_estimate</code> — operation <code>net jitter estimate</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_jitter_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-kelly-pricing-step">
<h3><a class="doc-anchor" href="#doc-net-kelly-pricing-step">#</a> <code>net_kelly_pricing_step</code></h3>
<p><code>net_kelly_pricing_step</code> — single-step update of <code>net kelly pricing</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_kelly_pricing_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-latency-avg">
<h3><a class="doc-anchor" href="#doc-net-latency-avg">#</a> <code>net_latency_avg</code></h3>
<p><code>net_latency_avg</code> — operation <code>net latency avg</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_latency_avg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-ldpc-iteration-step">
<h3><a class="doc-anchor" href="#doc-net-ldpc-iteration-step">#</a> <code>net_ldpc_iteration_step</code></h3>
<p><code>net_ldpc_iteration_step</code> — single-step update of <code>net ldpc iteration</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_ldpc_iteration_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-link-capacity-share">
<h3><a class="doc-anchor" href="#doc-net-link-capacity-share">#</a> <code>net_link_capacity_share</code></h3>
<p><code>net_link_capacity_share</code> — operation <code>net link capacity share</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_link_capacity_share $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-little-law-l">
<h3><a class="doc-anchor" href="#doc-net-little-law-l">#</a> <code>net_little_law_l</code></h3>
<p><code>net_little_law_l</code> — operation <code>net little law l</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_little_law_l $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-log-distance-path">
<h3><a class="doc-anchor" href="#doc-net-log-distance-path">#</a> <code>net_log_distance_path</code></h3>
<p><code>net_log_distance_path</code> — operation <code>net log distance path</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_log_distance_path $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-loss-rate-to-throughput">
<h3><a class="doc-anchor" href="#doc-net-loss-rate-to-throughput">#</a> <code>net_loss_rate_to_throughput</code></h3>
<p><code>net_loss_rate_to_throughput</code> — convert from <code>net loss rate</code> to <code>throughput</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_loss_rate_to_throughput $value
</code></pre>
</article>
<article class="doc-entry" id="doc-net-lyapunov-drift-plus-penalty">
<h3><a class="doc-anchor" href="#doc-net-lyapunov-drift-plus-penalty">#</a> <code>net_lyapunov_drift_plus_penalty</code></h3>
<p><code>net_lyapunov_drift_plus_penalty</code> — operation <code>net lyapunov drift plus penalty</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_lyapunov_drift_plus_penalty $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-macro-diversity-step">
<h3><a class="doc-anchor" href="#doc-net-macro-diversity-step">#</a> <code>net_macro_diversity_step</code></h3>
<p><code>net_macro_diversity_step</code> — single-step update of <code>net macro diversity</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_macro_diversity_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-max-min-fair-step">
<h3><a class="doc-anchor" href="#doc-net-max-min-fair-step">#</a> <code>net_max_min_fair_step</code></h3>
<p><code>net_max_min_fair_step</code> — single-step update of <code>net max min fair</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_max_min_fair_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-max-weight-match">
<h3><a class="doc-anchor" href="#doc-net-max-weight-match">#</a> <code>net_max_weight_match</code></h3>
<p><code>net_max_weight_match</code> — operation <code>net max weight match</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_max_weight_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-miad-step">
<h3><a class="doc-anchor" href="#doc-net-miad-step">#</a> <code>net_miad_step</code></h3>
<p><code>net_miad_step</code> — single-step update of <code>net miad</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_miad_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-micro-diversity-step">
<h3><a class="doc-anchor" href="#doc-net-micro-diversity-step">#</a> <code>net_micro_diversity_step</code></h3>
<p><code>net_micro_diversity_step</code> — single-step update of <code>net micro diversity</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_micro_diversity_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-mimd-step">
<h3><a class="doc-anchor" href="#doc-net-mimd-step">#</a> <code>net_mimd_step</code></h3>
<p><code>net_mimd_step</code> — single-step update of <code>net mimd</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_mimd_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-mimo-capacity-step">
<h3><a class="doc-anchor" href="#doc-net-mimo-capacity-step">#</a> <code>net_mimo_capacity_step</code></h3>
<p><code>net_mimo_capacity_step</code> — single-step update of <code>net mimo capacity</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_mimo_capacity_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-mmse-beam-step">
<h3><a class="doc-anchor" href="#doc-net-mmse-beam-step">#</a> <code>net_mmse_beam_step</code></h3>
<p><code>net_mmse_beam_step</code> — single-step update of <code>net mmse beam</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_mmse_beam_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-multiplexing-gain">
<h3><a class="doc-anchor" href="#doc-net-multiplexing-gain">#</a> <code>net_multiplexing_gain</code></h3>
<p><code>net_multiplexing_gain</code> — operation <code>net multiplexing gain</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_multiplexing_gain $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-network-utility-max">
<h3><a class="doc-anchor" href="#doc-net-network-utility-max">#</a> <code>net_network_utility_max</code></h3>
<p><code>net_network_utility_max</code> — maximum of <code>net network utility</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_network_utility_max $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-okumura-hata-loss">
<h3><a class="doc-anchor" href="#doc-net-okumura-hata-loss">#</a> <code>net_okumura_hata_loss</code></h3>
<p><code>net_okumura_hata_loss</code> — operation <code>net okumura hata loss</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_okumura_hata_loss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-outage-probability">
<h3><a class="doc-anchor" href="#doc-net-outage-probability">#</a> <code>net_outage_probability</code></h3>
<p><code>net_outage_probability</code> — operation <code>net outage probability</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_outage_probability $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-packet-loss-estimate">
<h3><a class="doc-anchor" href="#doc-net-packet-loss-estimate">#</a> <code>net_packet_loss_estimate</code></h3>
<p><code>net_packet_loss_estimate</code> — operation <code>net packet loss estimate</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_packet_loss_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-packet-pacing-step">
<h3><a class="doc-anchor" href="#doc-net-packet-pacing-step">#</a> <code>net_packet_pacing_step</code></h3>
<p><code>net_packet_pacing_step</code> — single-step update of <code>net packet pacing</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_packet_pacing_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-path-capacity-kleinrock">
<h3><a class="doc-anchor" href="#doc-net-path-capacity-kleinrock">#</a> <code>net_path_capacity_kleinrock</code></h3>
<p><code>net_path_capacity_kleinrock</code> — operation <code>net path capacity kleinrock</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_path_capacity_kleinrock $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-polar-decode-step">
<h3><a class="doc-anchor" href="#doc-net-polar-decode-step">#</a> <code>net_polar_decode_step</code></h3>
<p><code>net_polar_decode_step</code> — single-step update of <code>net polar decode</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_polar_decode_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-polling-efficiency">
<h3><a class="doc-anchor" href="#doc-net-polling-efficiency">#</a> <code>net_polling_efficiency</code></h3>
<p><code>net_polling_efficiency</code> — operation <code>net polling efficiency</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_polling_efficiency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-present-value">
<h3><a class="doc-anchor" href="#doc-net-present-value">#</a> <code>net_present_value</code></h3>
<p><code>net_present_value(cashflows, rate) → number</code> — <code>Σ cf[t] / (1+rate)^t</code>. Standard NPV for project valuation; first cashflow is at t=0.</p>
<pre><code class="lang-perl">p net_present_value([-1000, 300, 400, 500], 0.1)
</code></pre>
</article>
<article class="doc-entry" id="doc-net-priority-queue-index">
<h3><a class="doc-anchor" href="#doc-net-priority-queue-index">#</a> <code>net_priority_queue_index</code></h3>
<p><code>net_priority_queue_index</code> — index of <code>net priority queue</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_priority_queue_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-proportional-fair-share">
<h3><a class="doc-anchor" href="#doc-net-proportional-fair-share">#</a> <code>net_proportional_fair_share</code></h3>
<p><code>net_proportional_fair_share</code> — operation <code>net proportional fair share</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_proportional_fair_share $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-pruning-gain">
<h3><a class="doc-anchor" href="#doc-net-pruning-gain">#</a> <code>net_pruning_gain</code></h3>
<p><code>net_pruning_gain</code> — operation <code>net pruning gain</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_pruning_gain $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-qcsma-propose">
<h3><a class="doc-anchor" href="#doc-net-qcsma-propose">#</a> <code>net_qcsma_propose</code></h3>
<p><code>net_qcsma_propose</code> — operation <code>net qcsma propose</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_qcsma_propose $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-radio-path-loss">
<h3><a class="doc-anchor" href="#doc-net-radio-path-loss">#</a> <code>net_radio_path_loss</code></h3>
<p><code>net_radio_path_loss</code> — operation <code>net radio path loss</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_radio_path_loss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-rayleigh-envelope">
<h3><a class="doc-anchor" href="#doc-net-rayleigh-envelope">#</a> <code>net_rayleigh_envelope</code></h3>
<p><code>net_rayleigh_envelope</code> — operation <code>net rayleigh envelope</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_rayleigh_envelope $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-reproductive-rate">
<h3><a class="doc-anchor" href="#doc-net-reproductive-rate">#</a> <code>net_reproductive_rate</code></h3>
<p><code>net_reproductive_rate</code> — rate of <code>net reproductive</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p net_reproductive_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-response-time-law">
<h3><a class="doc-anchor" href="#doc-net-response-time-law">#</a> <code>net_response_time_law</code></h3>
<p><code>net_response_time_law</code> — operation <code>net response time law</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_response_time_law $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-rician-k-factor">
<h3><a class="doc-anchor" href="#doc-net-rician-k-factor">#</a> <code>net_rician_k_factor</code></h3>
<p><code>net_rician_k_factor</code> — factor of <code>net rician k</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_rician_k_factor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-router-buffer-size">
<h3><a class="doc-anchor" href="#doc-net-router-buffer-size">#</a> <code>net_router_buffer_size</code></h3>
<p><code>net_router_buffer_size</code> — operation <code>net router buffer size</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_router_buffer_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-rto-compute">
<h3><a class="doc-anchor" href="#doc-net-rto-compute">#</a> <code>net_rto_compute</code></h3>
<p><code>net_rto_compute</code> — operation <code>net rto compute</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_rto_compute $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-rtt-smoothed">
<h3><a class="doc-anchor" href="#doc-net-rtt-smoothed">#</a> <code>net_rtt_smoothed</code></h3>
<p><code>net_rtt_smoothed</code> — operation <code>net rtt smoothed</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_rtt_smoothed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-rtt-variation">
<h3><a class="doc-anchor" href="#doc-net-rtt-variation">#</a> <code>net_rtt_variation</code></h3>
<p><code>net_rtt_variation</code> — operation <code>net rtt variation</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_rtt_variation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-shadowing-normal">
<h3><a class="doc-anchor" href="#doc-net-shadowing-normal">#</a> <code>net_shadowing_normal</code></h3>
<p><code>net_shadowing_normal</code> — operation <code>net shadowing normal</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_shadowing_normal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-slotted-aloha-throughput">
<h3><a class="doc-anchor" href="#doc-net-slotted-aloha-throughput">#</a> <code>net_slotted_aloha_throughput</code></h3>
<p><code>net_slotted_aloha_throughput</code> — operation <code>net slotted aloha throughput</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_slotted_aloha_throughput $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-bbr-step">
<h3><a class="doc-anchor" href="#doc-net-tcp-bbr-step">#</a> <code>net_tcp_bbr_step</code></h3>
<p><code>net_tcp_bbr_step</code> — single-step update of <code>net tcp bbr</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_bbr_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-compound-step">
<h3><a class="doc-anchor" href="#doc-net-tcp-compound-step">#</a> <code>net_tcp_compound_step</code></h3>
<p><code>net_tcp_compound_step</code> — single-step update of <code>net tcp compound</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_compound_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-cubic-step">
<h3><a class="doc-anchor" href="#doc-net-tcp-cubic-step">#</a> <code>net_tcp_cubic_step</code></h3>
<p><code>net_tcp_cubic_step</code> — single-step update of <code>net tcp cubic</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_cubic_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-cwnd-step">
<h3><a class="doc-anchor" href="#doc-net-tcp-cwnd-step">#</a> <code>net_tcp_cwnd_step</code></h3>
<p><code>net_tcp_cwnd_step</code> — single-step update of <code>net tcp cwnd</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_cwnd_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-dctcp-step">
<h3><a class="doc-anchor" href="#doc-net-tcp-dctcp-step">#</a> <code>net_tcp_dctcp_step</code></h3>
<p><code>net_tcp_dctcp_step</code> — single-step update of <code>net tcp dctcp</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_dctcp_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-htcp-step">
<h3><a class="doc-anchor" href="#doc-net-tcp-htcp-step">#</a> <code>net_tcp_htcp_step</code></h3>
<p><code>net_tcp_htcp_step</code> — single-step update of <code>net tcp htcp</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_htcp_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-hybla-step">
<h3><a class="doc-anchor" href="#doc-net-tcp-hybla-step">#</a> <code>net_tcp_hybla_step</code></h3>
<p><code>net_tcp_hybla_step</code> — single-step update of <code>net tcp hybla</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_hybla_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-illinois-step">
<h3><a class="doc-anchor" href="#doc-net-tcp-illinois-step">#</a> <code>net_tcp_illinois_step</code></h3>
<p><code>net_tcp_illinois_step</code> — single-step update of <code>net tcp illinois</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_illinois_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-lp-step">
<h3><a class="doc-anchor" href="#doc-net-tcp-lp-step">#</a> <code>net_tcp_lp_step</code></h3>
<p><code>net_tcp_lp_step</code> — single-step update of <code>net tcp lp</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_lp_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-reno-step">
<h3><a class="doc-anchor" href="#doc-net-tcp-reno-step">#</a> <code>net_tcp_reno_step</code></h3>
<p><code>net_tcp_reno_step</code> — single-step update of <code>net tcp reno</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_reno_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-scalable-step">
<h3><a class="doc-anchor" href="#doc-net-tcp-scalable-step">#</a> <code>net_tcp_scalable_step</code></h3>
<p><code>net_tcp_scalable_step</code> — single-step update of <code>net tcp scalable</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_scalable_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-ssthresh-update">
<h3><a class="doc-anchor" href="#doc-net-tcp-ssthresh-update">#</a> <code>net_tcp_ssthresh_update</code></h3>
<p><code>net_tcp_ssthresh_update</code> — update step of <code>net tcp ssthresh</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_ssthresh_update $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-vegas-step">
<h3><a class="doc-anchor" href="#doc-net-tcp-vegas-step">#</a> <code>net_tcp_vegas_step</code></h3>
<p><code>net_tcp_vegas_step</code> — single-step update of <code>net tcp vegas</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_vegas_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-veno-step">
<h3><a class="doc-anchor" href="#doc-net-tcp-veno-step">#</a> <code>net_tcp_veno_step</code></h3>
<p><code>net_tcp_veno_step</code> — single-step update of <code>net tcp veno</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_veno_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-westwood-step">
<h3><a class="doc-anchor" href="#doc-net-tcp-westwood-step">#</a> <code>net_tcp_westwood_step</code></h3>
<p><code>net_tcp_westwood_step</code> — single-step update of <code>net tcp westwood</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_westwood_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-tcp-yeah-step">
<h3><a class="doc-anchor" href="#doc-net-tcp-yeah-step">#</a> <code>net_tcp_yeah_step</code></h3>
<p><code>net_tcp_yeah_step</code> — single-step update of <code>net tcp yeah</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_tcp_yeah_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-throughput-law">
<h3><a class="doc-anchor" href="#doc-net-throughput-law">#</a> <code>net_throughput_law</code></h3>
<p><code>net_throughput_law</code> — operation <code>net throughput law</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_throughput_law $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-throughput-mathis">
<h3><a class="doc-anchor" href="#doc-net-throughput-mathis">#</a> <code>net_throughput_mathis</code></h3>
<p><code>net_throughput_mathis</code> — operation <code>net throughput mathis</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_throughput_mathis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-throughput-padhye">
<h3><a class="doc-anchor" href="#doc-net-throughput-padhye">#</a> <code>net_throughput_padhye</code></h3>
<p><code>net_throughput_padhye</code> — operation <code>net throughput padhye</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_throughput_padhye $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-throughput-response">
<h3><a class="doc-anchor" href="#doc-net-throughput-response">#</a> <code>net_throughput_response</code></h3>
<p><code>net_throughput_response</code> — operation <code>net throughput response</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_throughput_response $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-token-rate-limit">
<h3><a class="doc-anchor" href="#doc-net-token-rate-limit">#</a> <code>net_token_rate_limit</code></h3>
<p><code>net_token_rate_limit</code> — operation <code>net token rate limit</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_token_rate_limit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-token-ring-efficiency">
<h3><a class="doc-anchor" href="#doc-net-token-ring-efficiency">#</a> <code>net_token_ring_efficiency</code></h3>
<p><code>net_token_ring_efficiency</code> — operation <code>net token ring efficiency</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_token_ring_efficiency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-traffic-shaper-step">
<h3><a class="doc-anchor" href="#doc-net-traffic-shaper-step">#</a> <code>net_traffic_shaper_step</code></h3>
<p><code>net_traffic_shaper_step</code> — single-step update of <code>net traffic shaper</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_traffic_shaper_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-turbo-decode-iter">
<h3><a class="doc-anchor" href="#doc-net-turbo-decode-iter">#</a> <code>net_turbo_decode_iter</code></h3>
<p><code>net_turbo_decode_iter</code> — operation <code>net turbo decode iter</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_turbo_decode_iter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-two-ray-ground-loss">
<h3><a class="doc-anchor" href="#doc-net-two-ray-ground-loss">#</a> <code>net_two_ray_ground_loss</code></h3>
<p><code>net_two_ray_ground_loss</code> — operation <code>net two ray ground loss</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_two_ray_ground_loss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-utilization-law">
<h3><a class="doc-anchor" href="#doc-net-utilization-law">#</a> <code>net_utilization_law</code></h3>
<p><code>net_utilization_law</code> — operation <code>net utilization law</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_utilization_law $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-viterbi-step">
<h3><a class="doc-anchor" href="#doc-net-viterbi-step">#</a> <code>net_viterbi_step</code></h3>
<p><code>net_viterbi_step</code> — single-step update of <code>net viterbi</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_viterbi_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-water-filling-power">
<h3><a class="doc-anchor" href="#doc-net-water-filling-power">#</a> <code>net_water_filling_power</code></h3>
<p><code>net_water_filling_power</code> — operation <code>net water filling power</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_water_filling_power $x
</code></pre>
</article>
<article class="doc-entry" id="doc-net-zero-forcing-beam">
<h3><a class="doc-anchor" href="#doc-net-zero-forcing-beam">#</a> <code>net_zero_forcing_beam</code></h3>
<p><code>net_zero_forcing_beam</code> — operation <code>net zero forcing beam</code>. Category: *networking — tcp, aqm, mimo, queueing*.</p>
<pre><code class="lang-perl">p net_zero_forcing_beam $x
</code></pre>
</article>
<article class="doc-entry" id="doc-netmask-to-prefix">
<h3><a class="doc-anchor" href="#doc-netmask-to-prefix">#</a> <code>netmask_to_prefix</code></h3>
<p><code>netmask_to_prefix</code> — convert from <code>netmask</code> to <code>prefix</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p netmask_to_prefix $value
</code></pre>
</article>
<article class="doc-entry" id="doc-network-formation-step">
<h3><a class="doc-anchor" href="#doc-network-formation-step">#</a> <code>network_formation_step</code></h3>
<p><code>network_formation_step</code> — single-step update of <code>network formation</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p network_formation_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-neutron-mass">
<h3><a class="doc-anchor" href="#doc-neutron-mass">#</a> <code>neutron_mass</code></h3>
<p><code>neutron_mass</code> — operation <code>neutron mass</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p neutron_mass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-new-moon-julian">
<h3><a class="doc-anchor" href="#doc-new-moon-julian">#</a> <code>new_moon_julian</code></h3>
<p><code>new_moon_julian(cycle) → number</code> — Julian Date of <code>cycle</code>-th new moon since the anchor (2000-01-06).</p>
<pre><code class="lang-perl">p new_moon_julian(0)
</code></pre>
</article>
<article class="doc-entry" id="doc-newey-west-se">
<h3><a class="doc-anchor" href="#doc-newey-west-se">#</a> <code>newey_west_se</code></h3>
<p><code>newey_west_se</code> — operation <code>newey west se</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p newey_west_se $x
</code></pre>
</article>
<article class="doc-entry" id="doc-newmark-beta-step">
<h3><a class="doc-anchor" href="#doc-newmark-beta-step">#</a> <code>newmark_beta_step</code></h3>
<p><code>newmark_beta_step</code> — single-step update of <code>newmark beta</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p newmark_beta_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-newton">
<h3><a class="doc-anchor" href="#doc-newton">#</a> <code>newton</code></h3>
<p><code>newton_method</code> (aliases <code>newton</code>, <code>newton_raphson</code>) finds a root via Newton-Raphson. Takes f, f', x0, and optional tolerance.</p>
<pre><code class="lang-perl">my $root = newton(fn { $_[0]**2 - 2 }, fn { 2*$_[0] }, 1.5) # √2
</code></pre>
</article>
<article class="doc-entry" id="doc-newtons-to-lbf">
<h3><a class="doc-anchor" href="#doc-newtons-to-lbf">#</a> <code>newtons_to_lbf</code></h3>
<p><code>newtons_to_lbf</code> — convert from <code>newtons</code> to <code>lbf</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p newtons_to_lbf $value
</code></pre>
</article>
<article class="doc-entry" id="doc-next-permutation">
<h3><a class="doc-anchor" href="#doc-next-permutation">#</a> <code>next_permutation</code></h3>
<p><code>next_permutation</code> — operation <code>next permutation</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p next_permutation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-next-prime">
<h3><a class="doc-anchor" href="#doc-next-prime">#</a> <code>next_prime</code></h3>
<p><code>next_prime</code> — operation <code>next prime</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p next_prime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nfa-to-dfa">
<h3><a class="doc-anchor" href="#doc-nfa-to-dfa">#</a> <code>nfa_to_dfa</code></h3>
<p><code>nfa_to_dfa</code> — convert from <code>nfa</code> to <code>dfa</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p nfa_to_dfa $value
</code></pre>
</article>
<article class="doc-entry" id="doc-nfirst">
<h3><a class="doc-anchor" href="#doc-nfirst">#</a> <code>nfirst</code></h3>
<p><code>nfirst</code> — operation <code>nfirst</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p nfirst $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nfs">
<h3><a class="doc-anchor" href="#doc-nfs">#</a> <code>nfs</code></h3>
<p><code>nfs</code> — operation <code>nfs</code>. Alias for <code>nfirst</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p nfs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ngram">
<h3><a class="doc-anchor" href="#doc-ngram">#</a> <code>ngram</code></h3>
<p><code>ngram</code> — operation <code>ngram</code>. Alias for <code>ngrams</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p ngram $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ngram-perplexity">
<h3><a class="doc-anchor" href="#doc-ngram-perplexity">#</a> <code>ngram_perplexity</code></h3>
<p><code>ngram_perplexity(model, tokens, n=2) → number</code> — perplexity over a held-out sequence.</p>
</article>
<article class="doc-entry" id="doc-ngram-prob">
<h3><a class="doc-anchor" href="#doc-ngram-prob">#</a> <code>ngram_prob</code></h3>
<p><code>ngram_prob(model, context, next_token) → number</code> — conditional probability <code>P(next | context)</code>. Returns 0 for unseen.</p>
</article>
<article class="doc-entry" id="doc-ngram-top-k-next">
<h3><a class="doc-anchor" href="#doc-ngram-top-k-next">#</a> <code>ngram_top_k_next</code></h3>
<p><code>ngram_top_k_next(model, context, k=5) → array</code> — top-k most likely next tokens with probabilities.</p>
<pre><code class="lang-perl">p ngram_top_k_next($model, "the", 5)
</code></pre>
</article>
<article class="doc-entry" id="doc-ngram-train">
<h3><a class="doc-anchor" href="#doc-ngram-train">#</a> <code>ngram_train</code></h3>
<p><code>ngram_train(tokens, n=2) → hash</code> — context → next-token probability hash. Maximum-likelihood estimate.</p>
<pre><code class="lang-perl">my $model = ngram_train(["the","cat","sat","the","cat"], 2)
</code></pre>
</article>
<article class="doc-entry" id="doc-ngrams">
<h3><a class="doc-anchor" href="#doc-ngrams">#</a> <code>ngrams</code></h3>
<p><code>ngrams</code> — operation <code>ngrams</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p ngrams $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nichols-chart-step">
<h3><a class="doc-anchor" href="#doc-nichols-chart-step">#</a> <code>nichols_chart_step</code></h3>
<p><code>nichols_chart_step</code> — single-step update of <code>nichols chart</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p nichols_chart_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nilpotency-class-lower">
<h3><a class="doc-anchor" href="#doc-nilpotency-class-lower">#</a> <code>nilpotency_class_lower</code></h3>
<p><code>nilpotency_class_lower</code> — operation <code>nilpotency class lower</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p nilpotency_class_lower $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-alibi-position-bias">
<h3><a class="doc-anchor" href="#doc-nlp-alibi-position-bias">#</a> <code>nlp_alibi_position_bias</code></h3>
<p><code>nlp_alibi_position_bias</code> — operation <code>nlp alibi position bias</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_alibi_position_bias $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-attention-pool-step">
<h3><a class="doc-anchor" href="#doc-nlp-attention-pool-step">#</a> <code>nlp_attention_pool_step</code></h3>
<p><code>nlp_attention_pool_step</code> — single-step update of <code>nlp attention pool</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_attention_pool_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-avg-pool-step">
<h3><a class="doc-anchor" href="#doc-nlp-avg-pool-step">#</a> <code>nlp_avg_pool_step</code></h3>
<p><code>nlp_avg_pool_step</code> — single-step update of <code>nlp avg pool</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_avg_pool_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-bigbird-step">
<h3><a class="doc-anchor" href="#doc-nlp-bigbird-step">#</a> <code>nlp_bigbird_step</code></h3>
<p><code>nlp_bigbird_step</code> — single-step update of <code>nlp bigbird</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_bigbird_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-bits-per-character">
<h3><a class="doc-anchor" href="#doc-nlp-bits-per-character">#</a> <code>nlp_bits_per_character</code></h3>
<p><code>nlp_bits_per_character</code> — operation <code>nlp bits per character</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_bits_per_character $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-bleu-score-n">
<h3><a class="doc-anchor" href="#doc-nlp-bleu-score-n">#</a> <code>nlp_bleu_score_n</code></h3>
<p><code>nlp_bleu_score_n</code> — operation <code>nlp bleu score n</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_bleu_score_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-block-attn-step">
<h3><a class="doc-anchor" href="#doc-nlp-block-attn-step">#</a> <code>nlp_block_attn_step</code></h3>
<p><code>nlp_block_attn_step</code> — single-step update of <code>nlp block attn</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_block_attn_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-bm25-score">
<h3><a class="doc-anchor" href="#doc-nlp-bm25-score">#</a> <code>nlp_bm25_score</code></h3>
<p><code>nlp_bm25_score</code> — score of <code>nlp bm25</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_bm25_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-byte-frequency">
<h3><a class="doc-anchor" href="#doc-nlp-byte-frequency">#</a> <code>nlp_byte_frequency</code></h3>
<p><code>nlp_byte_frequency</code> — operation <code>nlp byte frequency</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_byte_frequency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-byte-level-bpe-step">
<h3><a class="doc-anchor" href="#doc-nlp-byte-level-bpe-step">#</a> <code>nlp_byte_level_bpe_step</code></h3>
<p><code>nlp_byte_level_bpe_step</code> — single-step update of <code>nlp byte level bpe</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_byte_level_bpe_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-byte-pair-merge-step">
<h3><a class="doc-anchor" href="#doc-nlp-byte-pair-merge-step">#</a> <code>nlp_byte_pair_merge_step</code></h3>
<p><code>nlp_byte_pair_merge_step</code> — single-step update of <code>nlp byte pair merge</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_byte_pair_merge_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-cer-score">
<h3><a class="doc-anchor" href="#doc-nlp-cer-score">#</a> <code>nlp_cer_score</code></h3>
<p><code>nlp_cer_score</code> — score of <code>nlp cer</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_cer_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-char-frequency">
<h3><a class="doc-anchor" href="#doc-nlp-char-frequency">#</a> <code>nlp_char_frequency</code></h3>
<p><code>nlp_char_frequency</code> — operation <code>nlp char frequency</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_char_frequency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-char-ngram-count">
<h3><a class="doc-anchor" href="#doc-nlp-char-ngram-count">#</a> <code>nlp_char_ngram_count</code></h3>
<p><code>nlp_char_ngram_count</code> — count of <code>nlp char ngram</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_char_ngram_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-chi2-collocation">
<h3><a class="doc-anchor" href="#doc-nlp-chi2-collocation">#</a> <code>nlp_chi2_collocation</code></h3>
<p><code>nlp_chi2_collocation</code> — operation <code>nlp chi2 collocation</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_chi2_collocation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-chrf-score">
<h3><a class="doc-anchor" href="#doc-nlp-chrf-score">#</a> <code>nlp_chrf_score</code></h3>
<p><code>nlp_chrf_score</code> — score of <code>nlp chrf</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_chrf_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-cosine-similarity-two">
<h3><a class="doc-anchor" href="#doc-nlp-cosine-similarity-two">#</a> <code>nlp_cosine_similarity_two</code></h3>
<p><code>nlp_cosine_similarity_two</code> — operation <code>nlp cosine similarity two</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_cosine_similarity_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-cross-attn-compute-step">
<h3><a class="doc-anchor" href="#doc-nlp-cross-attn-compute-step">#</a> <code>nlp_cross_attn_compute_step</code></h3>
<p><code>nlp_cross_attn_compute_step</code> — single-step update of <code>nlp cross attn compute</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_cross_attn_compute_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-damerau-levenshtein">
<h3><a class="doc-anchor" href="#doc-nlp-damerau-levenshtein">#</a> <code>nlp_damerau_levenshtein</code></h3>
<p><code>nlp_damerau_levenshtein</code> — operation <code>nlp damerau levenshtein</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_damerau_levenshtein $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-dice-coefficient-two">
<h3><a class="doc-anchor" href="#doc-nlp-dice-coefficient-two">#</a> <code>nlp_dice_coefficient_two</code></h3>
<p><code>nlp_dice_coefficient_two</code> — operation <code>nlp dice coefficient two</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_dice_coefficient_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-digit-ratio">
<h3><a class="doc-anchor" href="#doc-nlp-digit-ratio">#</a> <code>nlp_digit_ratio</code></h3>
<p><code>nlp_digit_ratio</code> — ratio of <code>nlp digit</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_digit_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-dilated-attn-step">
<h3><a class="doc-anchor" href="#doc-nlp-dilated-attn-step">#</a> <code>nlp_dilated_attn_step</code></h3>
<p><code>nlp_dilated_attn_step</code> — single-step update of <code>nlp dilated attn</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_dilated_attn_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-dirichlet-smoothing">
<h3><a class="doc-anchor" href="#doc-nlp-dirichlet-smoothing">#</a> <code>nlp_dirichlet_smoothing</code></h3>
<p><code>nlp_dirichlet_smoothing</code> — operation <code>nlp dirichlet smoothing</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_dirichlet_smoothing $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-doc-embedding-avg">
<h3><a class="doc-anchor" href="#doc-nlp-doc-embedding-avg">#</a> <code>nlp_doc_embedding_avg</code></h3>
<p><code>nlp_doc_embedding_avg</code> — operation <code>nlp doc embedding avg</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_doc_embedding_avg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-doc-freq-step">
<h3><a class="doc-anchor" href="#doc-nlp-doc-freq-step">#</a> <code>nlp_doc_freq_step</code></h3>
<p><code>nlp_doc_freq_step</code> — single-step update of <code>nlp doc freq</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_doc_freq_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-dunning-log-likelihood">
<h3><a class="doc-anchor" href="#doc-nlp-dunning-log-likelihood">#</a> <code>nlp_dunning_log_likelihood</code></h3>
<p><code>nlp_dunning_log_likelihood</code> — operation <code>nlp dunning log likelihood</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_dunning_log_likelihood $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-email-count">
<h3><a class="doc-anchor" href="#doc-nlp-email-count">#</a> <code>nlp_email_count</code></h3>
<p><code>nlp_email_count</code> — count of <code>nlp email</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_email_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-emoji-ratio">
<h3><a class="doc-anchor" href="#doc-nlp-emoji-ratio">#</a> <code>nlp_emoji_ratio</code></h3>
<p><code>nlp_emoji_ratio</code> — ratio of <code>nlp emoji</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_emoji_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-fasttext-subword-count">
<h3><a class="doc-anchor" href="#doc-nlp-fasttext-subword-count">#</a> <code>nlp_fasttext_subword_count</code></h3>
<p><code>nlp_fasttext_subword_count</code> — count of <code>nlp fasttext subword</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_fasttext_subword_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-global-attn-step">
<h3><a class="doc-anchor" href="#doc-nlp-global-attn-step">#</a> <code>nlp_global_attn_step</code></h3>
<p><code>nlp_global_attn_step</code> — single-step update of <code>nlp global attn</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_global_attn_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-glove-loss-step">
<h3><a class="doc-anchor" href="#doc-nlp-glove-loss-step">#</a> <code>nlp_glove_loss_step</code></h3>
<p><code>nlp_glove_loss_step</code> — single-step update of <code>nlp glove loss</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_glove_loss_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-good-turing-count">
<h3><a class="doc-anchor" href="#doc-nlp-good-turing-count">#</a> <code>nlp_good_turing_count</code></h3>
<p><code>nlp_good_turing_count</code> — count of <code>nlp good turing</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_good_turing_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-hamming-distance">
<h3><a class="doc-anchor" href="#doc-nlp-hamming-distance">#</a> <code>nlp_hamming_distance</code></h3>
<p><code>nlp_hamming_distance</code> — distance / dissimilarity metric of <code>nlp hamming</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_hamming_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-hashtag-count">
<h3><a class="doc-anchor" href="#doc-nlp-hashtag-count">#</a> <code>nlp_hashtag_count</code></h3>
<p><code>nlp_hashtag_count</code> — count of <code>nlp hashtag</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_hashtag_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-inverse-doc-freq">
<h3><a class="doc-anchor" href="#doc-nlp-inverse-doc-freq">#</a> <code>nlp_inverse_doc_freq</code></h3>
<p><code>nlp_inverse_doc_freq</code> — operation <code>nlp inverse doc freq</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_inverse_doc_freq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-jaccard-similarity-two">
<h3><a class="doc-anchor" href="#doc-nlp-jaccard-similarity-two">#</a> <code>nlp_jaccard_similarity_two</code></h3>
<p><code>nlp_jaccard_similarity_two</code> — operation <code>nlp jaccard similarity two</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_jaccard_similarity_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-jaro-distance">
<h3><a class="doc-anchor" href="#doc-nlp-jaro-distance">#</a> <code>nlp_jaro_distance</code></h3>
<p><code>nlp_jaro_distance</code> — distance / dissimilarity metric of <code>nlp jaro</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_jaro_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-jaro-winkler">
<h3><a class="doc-anchor" href="#doc-nlp-jaro-winkler">#</a> <code>nlp_jaro_winkler</code></h3>
<p><code>nlp_jaro_winkler</code> — operation <code>nlp jaro winkler</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_jaro_winkler $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-jelinek-mercer">
<h3><a class="doc-anchor" href="#doc-nlp-jelinek-mercer">#</a> <code>nlp_jelinek_mercer</code></h3>
<p><code>nlp_jelinek_mercer</code> — operation <code>nlp jelinek mercer</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_jelinek_mercer $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-kl-lm-div">
<h3><a class="doc-anchor" href="#doc-nlp-kl-lm-div">#</a> <code>nlp_kl_lm_div</code></h3>
<p><code>nlp_kl_lm_div</code> — operation <code>nlp kl lm div</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_kl_lm_div $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-kneser-ney-step">
<h3><a class="doc-anchor" href="#doc-nlp-kneser-ney-step">#</a> <code>nlp_kneser_ney_step</code></h3>
<p><code>nlp_kneser_ney_step</code> — single-step update of <code>nlp kneser ney</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_kneser_ney_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-laplace-smoothing">
<h3><a class="doc-anchor" href="#doc-nlp-laplace-smoothing">#</a> <code>nlp_laplace_smoothing</code></h3>
<p><code>nlp_laplace_smoothing</code> — operation <code>nlp laplace smoothing</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_laplace_smoothing $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-lcs-length">
<h3><a class="doc-anchor" href="#doc-nlp-lcs-length">#</a> <code>nlp_lcs_length</code></h3>
<p><code>nlp_lcs_length</code> — operation <code>nlp lcs length</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_lcs_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-lcs-ratio">
<h3><a class="doc-anchor" href="#doc-nlp-lcs-ratio">#</a> <code>nlp_lcs_ratio</code></h3>
<p><code>nlp_lcs_ratio</code> — ratio of <code>nlp lcs</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_lcs_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-lda-alpha-step">
<h3><a class="doc-anchor" href="#doc-nlp-lda-alpha-step">#</a> <code>nlp_lda_alpha_step</code></h3>
<p><code>nlp_lda_alpha_step</code> — single-step update of <code>nlp lda alpha</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_lda_alpha_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-lda-beta-step">
<h3><a class="doc-anchor" href="#doc-nlp-lda-beta-step">#</a> <code>nlp_lda_beta_step</code></h3>
<p><code>nlp_lda_beta_step</code> — single-step update of <code>nlp lda beta</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_lda_beta_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-lda-topic-dist">
<h3><a class="doc-anchor" href="#doc-nlp-lda-topic-dist">#</a> <code>nlp_lda_topic_dist</code></h3>
<p><code>nlp_lda_topic_dist</code> — operation <code>nlp lda topic dist</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_lda_topic_dist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-levenshtein-dist">
<h3><a class="doc-anchor" href="#doc-nlp-levenshtein-dist">#</a> <code>nlp_levenshtein_dist</code></h3>
<p><code>nlp_levenshtein_dist</code> — operation <code>nlp levenshtein dist</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_levenshtein_dist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-lidstone-smoothing">
<h3><a class="doc-anchor" href="#doc-nlp-lidstone-smoothing">#</a> <code>nlp_lidstone_smoothing</code></h3>
<p><code>nlp_lidstone_smoothing</code> — operation <code>nlp lidstone smoothing</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_lidstone_smoothing $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-linformer-step">
<h3><a class="doc-anchor" href="#doc-nlp-linformer-step">#</a> <code>nlp_linformer_step</code></h3>
<p><code>nlp_linformer_step</code> — single-step update of <code>nlp linformer</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_linformer_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-local-attn-step">
<h3><a class="doc-anchor" href="#doc-nlp-local-attn-step">#</a> <code>nlp_local_attn_step</code></h3>
<p><code>nlp_local_attn_step</code> — single-step update of <code>nlp local attn</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_local_attn_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-loglikelihood-collocation">
<h3><a class="doc-anchor" href="#doc-nlp-loglikelihood-collocation">#</a> <code>nlp_loglikelihood_collocation</code></h3>
<p><code>nlp_loglikelihood_collocation</code> — operation <code>nlp loglikelihood collocation</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_loglikelihood_collocation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-longformer-step">
<h3><a class="doc-anchor" href="#doc-nlp-longformer-step">#</a> <code>nlp_longformer_step</code></h3>
<p><code>nlp_longformer_step</code> — single-step update of <code>nlp longformer</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_longformer_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-max-pool-step">
<h3><a class="doc-anchor" href="#doc-nlp-max-pool-step">#</a> <code>nlp_max_pool_step</code></h3>
<p><code>nlp_max_pool_step</code> — single-step update of <code>nlp max pool</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_max_pool_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-max-seq-len-check">
<h3><a class="doc-anchor" href="#doc-nlp-max-seq-len-check">#</a> <code>nlp_max_seq_len_check</code></h3>
<p><code>nlp_max_seq_len_check</code> — operation <code>nlp max seq len check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_max_seq_len_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-mention-count">
<h3><a class="doc-anchor" href="#doc-nlp-mention-count">#</a> <code>nlp_mention_count</code></h3>
<p><code>nlp_mention_count</code> — count of <code>nlp mention</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_mention_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-meteor-score">
<h3><a class="doc-anchor" href="#doc-nlp-meteor-score">#</a> <code>nlp_meteor_score</code></h3>
<p><code>nlp_meteor_score</code> — score of <code>nlp meteor</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_meteor_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-npmi-score">
<h3><a class="doc-anchor" href="#doc-nlp-npmi-score">#</a> <code>nlp_npmi_score</code></h3>
<p><code>nlp_npmi_score</code> — score of <code>nlp npmi</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_npmi_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-okapi-score">
<h3><a class="doc-anchor" href="#doc-nlp-okapi-score">#</a> <code>nlp_okapi_score</code></h3>
<p><code>nlp_okapi_score</code> — score of <code>nlp okapi</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_okapi_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-overlap-coefficient">
<h3><a class="doc-anchor" href="#doc-nlp-overlap-coefficient">#</a> <code>nlp_overlap_coefficient</code></h3>
<p><code>nlp_overlap_coefficient</code> — operation <code>nlp overlap coefficient</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_overlap_coefficient $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-pe-freq-band">
<h3><a class="doc-anchor" href="#doc-nlp-pe-freq-band">#</a> <code>nlp_pe_freq_band</code></h3>
<p><code>nlp_pe_freq_band</code> — operation <code>nlp pe freq band</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_pe_freq_band $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-performer-step">
<h3><a class="doc-anchor" href="#doc-nlp-performer-step">#</a> <code>nlp_performer_step</code></h3>
<p><code>nlp_performer_step</code> — single-step update of <code>nlp performer</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_performer_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-perplexity-value">
<h3><a class="doc-anchor" href="#doc-nlp-perplexity-value">#</a> <code>nlp_perplexity_value</code></h3>
<p><code>nlp_perplexity_value</code> — value of <code>nlp perplexity</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_perplexity_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-phone-count">
<h3><a class="doc-anchor" href="#doc-nlp-phone-count">#</a> <code>nlp_phone_count</code></h3>
<p><code>nlp_phone_count</code> — count of <code>nlp phone</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_phone_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-plsa-step">
<h3><a class="doc-anchor" href="#doc-nlp-plsa-step">#</a> <code>nlp_plsa_step</code></h3>
<p><code>nlp_plsa_step</code> — single-step update of <code>nlp plsa</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_plsa_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-pmi-score">
<h3><a class="doc-anchor" href="#doc-nlp-pmi-score">#</a> <code>nlp_pmi_score</code></h3>
<p><code>nlp_pmi_score</code> — score of <code>nlp pmi</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_pmi_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-pointwise-attn-score">
<h3><a class="doc-anchor" href="#doc-nlp-pointwise-attn-score">#</a> <code>nlp_pointwise_attn_score</code></h3>
<p><code>nlp_pointwise_attn_score</code> — score of <code>nlp pointwise attn</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_pointwise_attn_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-position-encoding-cos">
<h3><a class="doc-anchor" href="#doc-nlp-position-encoding-cos">#</a> <code>nlp_position_encoding_cos</code></h3>
<p><code>nlp_position_encoding_cos</code> — operation <code>nlp position encoding cos</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_position_encoding_cos $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-position-encoding-sin">
<h3><a class="doc-anchor" href="#doc-nlp-position-encoding-sin">#</a> <code>nlp_position_encoding_sin</code></h3>
<p><code>nlp_position_encoding_sin</code> — operation <code>nlp position encoding sin</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_position_encoding_sin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-punct-ratio">
<h3><a class="doc-anchor" href="#doc-nlp-punct-ratio">#</a> <code>nlp_punct_ratio</code></h3>
<p><code>nlp_punct_ratio</code> — ratio of <code>nlp punct</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_punct_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-query-likelihood-step">
<h3><a class="doc-anchor" href="#doc-nlp-query-likelihood-step">#</a> <code>nlp_query_likelihood_step</code></h3>
<p><code>nlp_query_likelihood_step</code> — single-step update of <code>nlp query likelihood</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_query_likelihood_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-reformer-step">
<h3><a class="doc-anchor" href="#doc-nlp-reformer-step">#</a> <code>nlp_reformer_step</code></h3>
<p><code>nlp_reformer_step</code> — single-step update of <code>nlp reformer</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_reformer_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-relative-position-bias">
<h3><a class="doc-anchor" href="#doc-nlp-relative-position-bias">#</a> <code>nlp_relative_position_bias</code></h3>
<p><code>nlp_relative_position_bias</code> — operation <code>nlp relative position bias</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_relative_position_bias $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-rope-apply-step">
<h3><a class="doc-anchor" href="#doc-nlp-rope-apply-step">#</a> <code>nlp_rope_apply_step</code></h3>
<p><code>nlp_rope_apply_step</code> — single-step update of <code>nlp rope apply</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_rope_apply_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-rope-rotary-angle">
<h3><a class="doc-anchor" href="#doc-nlp-rope-rotary-angle">#</a> <code>nlp_rope_rotary_angle</code></h3>
<p><code>nlp_rope_rotary_angle</code> — operation <code>nlp rope rotary angle</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_rope_rotary_angle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-rouge-score-n">
<h3><a class="doc-anchor" href="#doc-nlp-rouge-score-n">#</a> <code>nlp_rouge_score_n</code></h3>
<p><code>nlp_rouge_score_n</code> — operation <code>nlp rouge score n</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_rouge_score_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-routing-attn-step">
<h3><a class="doc-anchor" href="#doc-nlp-routing-attn-step">#</a> <code>nlp_routing_attn_step</code></h3>
<p><code>nlp_routing_attn_step</code> — single-step update of <code>nlp routing attn</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_routing_attn_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-self-attn-compute-step">
<h3><a class="doc-anchor" href="#doc-nlp-self-attn-compute-step">#</a> <code>nlp_self_attn_compute_step</code></h3>
<p><code>nlp_self_attn_compute_step</code> — single-step update of <code>nlp self attn compute</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_self_attn_compute_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-sentencepiece-score">
<h3><a class="doc-anchor" href="#doc-nlp-sentencepiece-score">#</a> <code>nlp_sentencepiece_score</code></h3>
<p><code>nlp_sentencepiece_score</code> — score of <code>nlp sentencepiece</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_sentencepiece_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-sif-weight-step">
<h3><a class="doc-anchor" href="#doc-nlp-sif-weight-step">#</a> <code>nlp_sif_weight_step</code></h3>
<p><code>nlp_sif_weight_step</code> — single-step update of <code>nlp sif weight</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_sif_weight_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-simpson-coefficient">
<h3><a class="doc-anchor" href="#doc-nlp-simpson-coefficient">#</a> <code>nlp_simpson_coefficient</code></h3>
<p><code>nlp_simpson_coefficient</code> — operation <code>nlp simpson coefficient</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_simpson_coefficient $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-skip-gram-count">
<h3><a class="doc-anchor" href="#doc-nlp-skip-gram-count">#</a> <code>nlp_skip_gram_count</code></h3>
<p><code>nlp_skip_gram_count</code> — count of <code>nlp skip gram</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_skip_gram_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-sliding-window-step">
<h3><a class="doc-anchor" href="#doc-nlp-sliding-window-step">#</a> <code>nlp_sliding_window_step</code></h3>
<p><code>nlp_sliding_window_step</code> — single-step update of <code>nlp sliding window</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_sliding_window_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-sparse-attn-score">
<h3><a class="doc-anchor" href="#doc-nlp-sparse-attn-score">#</a> <code>nlp_sparse_attn_score</code></h3>
<p><code>nlp_sparse_attn_score</code> — score of <code>nlp sparse attn</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_sparse_attn_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-strided-attn-step">
<h3><a class="doc-anchor" href="#doc-nlp-strided-attn-step">#</a> <code>nlp_strided_attn_step</code></h3>
<p><code>nlp_strided_attn_step</code> — single-step update of <code>nlp strided attn</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_strided_attn_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-subword-regularization">
<h3><a class="doc-anchor" href="#doc-nlp-subword-regularization">#</a> <code>nlp_subword_regularization</code></h3>
<p><code>nlp_subword_regularization</code> — operation <code>nlp subword regularization</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_subword_regularization $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-sum-pool-step">
<h3><a class="doc-anchor" href="#doc-nlp-sum-pool-step">#</a> <code>nlp_sum_pool_step</code></h3>
<p><code>nlp_sum_pool_step</code> — single-step update of <code>nlp sum pool</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_sum_pool_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-t-score-collocation">
<h3><a class="doc-anchor" href="#doc-nlp-t-score-collocation">#</a> <code>nlp_t_score_collocation</code></h3>
<p><code>nlp_t_score_collocation</code> — operation <code>nlp t score collocation</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_t_score_collocation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-ter-score">
<h3><a class="doc-anchor" href="#doc-nlp-ter-score">#</a> <code>nlp_ter_score</code></h3>
<p><code>nlp_ter_score</code> — score of <code>nlp ter</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_ter_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-tf-idf-step">
<h3><a class="doc-anchor" href="#doc-nlp-tf-idf-step">#</a> <code>nlp_tf_idf_step</code></h3>
<p><code>nlp_tf_idf_step</code> — single-step update of <code>nlp tf idf</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_tf_idf_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-token-drop-rate">
<h3><a class="doc-anchor" href="#doc-nlp-token-drop-rate">#</a> <code>nlp_token_drop_rate</code></h3>
<p><code>nlp_token_drop_rate</code> — rate of <code>nlp token drop</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_token_drop_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-token-overlap-two">
<h3><a class="doc-anchor" href="#doc-nlp-token-overlap-two">#</a> <code>nlp_token_overlap_two</code></h3>
<p><code>nlp_token_overlap_two</code> — operation <code>nlp token overlap two</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_token_overlap_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-unigram-lm-score">
<h3><a class="doc-anchor" href="#doc-nlp-unigram-lm-score">#</a> <code>nlp_unigram_lm_score</code></h3>
<p><code>nlp_unigram_lm_score</code> — score of <code>nlp unigram lm</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_unigram_lm_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-unigram-subword-loss">
<h3><a class="doc-anchor" href="#doc-nlp-unigram-subword-loss">#</a> <code>nlp_unigram_subword_loss</code></h3>
<p><code>nlp_unigram_subword_loss</code> — operation <code>nlp unigram subword loss</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_unigram_subword_loss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-uppercase-ratio">
<h3><a class="doc-anchor" href="#doc-nlp-uppercase-ratio">#</a> <code>nlp_uppercase_ratio</code></h3>
<p><code>nlp_uppercase_ratio</code> — ratio of <code>nlp uppercase</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_uppercase_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-url-count">
<h3><a class="doc-anchor" href="#doc-nlp-url-count">#</a> <code>nlp_url_count</code></h3>
<p><code>nlp_url_count</code> — count of <code>nlp url</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_url_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-wer-score">
<h3><a class="doc-anchor" href="#doc-nlp-wer-score">#</a> <code>nlp_wer_score</code></h3>
<p><code>nlp_wer_score</code> — score of <code>nlp wer</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_wer_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-window-attn-step">
<h3><a class="doc-anchor" href="#doc-nlp-window-attn-step">#</a> <code>nlp_window_attn_step</code></h3>
<p><code>nlp_window_attn_step</code> — single-step update of <code>nlp window attn</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_window_attn_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-witten-bell-step">
<h3><a class="doc-anchor" href="#doc-nlp-witten-bell-step">#</a> <code>nlp_witten_bell_step</code></h3>
<p><code>nlp_witten_bell_step</code> — single-step update of <code>nlp witten bell</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_witten_bell_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-word2vec-cbow-loss">
<h3><a class="doc-anchor" href="#doc-nlp-word2vec-cbow-loss">#</a> <code>nlp_word2vec_cbow_loss</code></h3>
<p><code>nlp_word2vec_cbow_loss</code> — operation <code>nlp word2vec cbow loss</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_word2vec_cbow_loss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-word2vec-skipgram-loss">
<h3><a class="doc-anchor" href="#doc-nlp-word2vec-skipgram-loss">#</a> <code>nlp_word2vec_skipgram_loss</code></h3>
<p><code>nlp_word2vec_skipgram_loss</code> — operation <code>nlp word2vec skipgram loss</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_word2vec_skipgram_loss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-word-freq-value">
<h3><a class="doc-anchor" href="#doc-nlp-word-freq-value">#</a> <code>nlp_word_freq_value</code></h3>
<p><code>nlp_word_freq_value</code> — value of <code>nlp word freq</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_word_freq_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-word-mover-dist">
<h3><a class="doc-anchor" href="#doc-nlp-word-mover-dist">#</a> <code>nlp_word_mover_dist</code></h3>
<p><code>nlp_word_mover_dist</code> — operation <code>nlp word mover dist</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_word_mover_dist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-word-ngram-count">
<h3><a class="doc-anchor" href="#doc-nlp-word-ngram-count">#</a> <code>nlp_word_ngram_count</code></h3>
<p><code>nlp_word_ngram_count</code> — count of <code>nlp word ngram</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_word_ngram_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nlp-wordpiece-score">
<h3><a class="doc-anchor" href="#doc-nlp-wordpiece-score">#</a> <code>nlp_wordpiece_score</code></h3>
<p><code>nlp_wordpiece_score</code> — score of <code>nlp wordpiece</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nlp_wordpiece_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nm-from-fst">
<h3><a class="doc-anchor" href="#doc-nm-from-fst">#</a> <code>nm_from_fst</code></h3>
<p><code>nm_from_fst</code> — operation <code>nm from fst</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p nm_from_fst $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nmass">
<h3><a class="doc-anchor" href="#doc-nmass">#</a> <code>nmass</code></h3>
<p><code>nmass</code> — operation <code>nmass</code>. Alias for <code>neutron_mass</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p nmass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nne">
<h3><a class="doc-anchor" href="#doc-nne">#</a> <code>nne</code></h3>
<p><code>nne</code> — operation <code>nne</code>. Alias for <code>nnext</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p nne $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nnext">
<h3><a class="doc-anchor" href="#doc-nnext">#</a> <code>nnext</code></h3>
<p><code>nnext</code> — operation <code>nnext</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p nnext $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nohtml">
<h3><a class="doc-anchor" href="#doc-nohtml">#</a> <code>nohtml</code></h3>
<p><code>nohtml</code> — operation <code>nohtml</code>. Alias for <code>strip_html</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p nohtml $x
</code></pre>
</article>
<article class="doc-entry" id="doc-noise-model-depolarize">
<h3><a class="doc-anchor" href="#doc-noise-model-depolarize">#</a> <code>noise_model_depolarize</code></h3>
<p><code>noise_model_depolarize</code> — procedural noise generator <code>model depolarize</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p noise_model_depolarize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nominal">
<h3><a class="doc-anchor" href="#doc-nominal">#</a> <code>nominal</code></h3>
<p><code>nominal</code> — operation <code>nominal</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p nominal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-non-max-suppression">
<h3><a class="doc-anchor" href="#doc-non-max-suppression">#</a> <code>non_max_suppression</code></h3>
<p><code>non_max_suppression(image) → matrix</code> — suppress non-maximal pixels in each 3×3 window. Used in Canny edge thinning.</p>
</article>
<article class="doc-entry" id="doc-nonagonal-number">
<h3><a class="doc-anchor" href="#doc-nonagonal-number">#</a> <code>nonagonal_number</code></h3>
<p><code>nonagonal_number(n) → int</code> — <code>n·(7n-5) / 2</code>.</p>
</article>
<article class="doc-entry" id="doc-none-match">
<h3><a class="doc-anchor" href="#doc-none-match">#</a> <code>none_match</code></h3>
<p><code>none_match</code> — operation <code>none match</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p none_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nonem">
<h3><a class="doc-anchor" href="#doc-nonem">#</a> <code>nonem</code></h3>
<p><code>nonem</code> — operation <code>nonem</code>. Alias for <code>none_match</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p nonem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nonempty-count">
<h3><a class="doc-anchor" href="#doc-nonempty-count">#</a> <code>nonempty_count</code></h3>
<p><code>nonempty_count</code> — count of <code>nonempty</code>. Category: *counters*.</p>
<pre><code class="lang-perl">p nonempty_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nonlinear-dual-step">
<h3><a class="doc-anchor" href="#doc-nonlinear-dual-step">#</a> <code>nonlinear_dual_step</code></h3>
<p><code>nonlinear_dual_step</code> — single-step update of <code>nonlinear dual</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p nonlinear_dual_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nonzero">
<h3><a class="doc-anchor" href="#doc-nonzero">#</a> <code>nonzero</code></h3>
<p><code>nonzero</code> — operation <code>nonzero</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p nonzero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nonzero-count">
<h3><a class="doc-anchor" href="#doc-nonzero-count">#</a> <code>nonzero_count</code></h3>
<p><code>nonzero_count</code> — count of <code>nonzero</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p nonzero_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-noop-val">
<h3><a class="doc-anchor" href="#doc-noop-val">#</a> <code>noop_val</code></h3>
<p><code>noop_val</code> — operation <code>noop val</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p noop_val $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nop">
<h3><a class="doc-anchor" href="#doc-nop">#</a> <code>nop</code></h3>
<p><code>nop</code> — operation <code>nop</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p nop $x
</code></pre>
</article>
<article class="doc-entry" id="doc-normal-cdf">
<h3><a class="doc-anchor" href="#doc-normal-cdf">#</a> <code>normal_cdf</code></h3>
<p><code>normal_cdf($x, $mu, $sigma)</code> (alias <code>normcdf</code>) — cumulative distribution function. Returns probability that a value is ≤ x.</p>
<pre><code class="lang-perl">p normcdf(0) # 0.5 (half below mean)
p normcdf(1.96) # ~0.975 (95% confidence bound)
</code></pre>
</article>
<article class="doc-entry" id="doc-normal-pdf">
<h3><a class="doc-anchor" href="#doc-normal-pdf">#</a> <code>normal_pdf</code></h3>
<p><code>normal_pdf($x, $mu, $sigma)</code> (alias <code>normpdf</code>) — normal/Gaussian distribution probability density function. Default: μ=0, σ=1 (standard normal).</p>
<pre><code class="lang-perl">p normpdf(0) # ~0.399 (peak of standard normal)
p normpdf(0, 100, 15) # PDF at IQ=100, mean=100, stddev=15
</code></pre>
</article>
<article class="doc-entry" id="doc-normality-chem">
<h3><a class="doc-anchor" href="#doc-normality-chem">#</a> <code>normality_chem</code></h3>
<p><code>normality_chem</code> — operation <code>normality chem</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p normality_chem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-normalize-array">
<h3><a class="doc-anchor" href="#doc-normalize-array">#</a> <code>normalize_array</code></h3>
<p><code>normalize_array</code> — operation <code>normalize array</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p normalize_array $x
</code></pre>
</article>
<article class="doc-entry" id="doc-normalize-list">
<h3><a class="doc-anchor" href="#doc-normalize-list">#</a> <code>normalize_list</code></h3>
<p><code>normalize_list</code> — operation <code>normalize list</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p normalize_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-normalize-range">
<h3><a class="doc-anchor" href="#doc-normalize-range">#</a> <code>normalize_range</code></h3>
<p><code>normalize_range</code> — operation <code>normalize range</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p normalize_range $x
</code></pre>
</article>
<article class="doc-entry" id="doc-normalize-signal">
<h3><a class="doc-anchor" href="#doc-normalize-signal">#</a> <code>normalize_signal</code></h3>
<p><code>normalize_signal(\@signal)</code> (alias <code>normsig</code>) — scales signal to range [-1, 1] based on its peak absolute value. Useful for audio processing.</p>
<pre><code class="lang-perl">my $norm = normsig(\@audio)
p max(map { abs } @$norm) # 1
</code></pre>
</article>
<article class="doc-entry" id="doc-normalize-spaces">
<h3><a class="doc-anchor" href="#doc-normalize-spaces">#</a> <code>normalize_spaces</code></h3>
<p><code>normalize_spaces</code> — operation <code>normalize spaces</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p normalize_spaces $x
</code></pre>
</article>
<article class="doc-entry" id="doc-normalize-vec">
<h3><a class="doc-anchor" href="#doc-normalize-vec">#</a> <code>normalize_vec</code></h3>
<p><code>normalize_vec</code> — operation <code>normalize vec</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p normalize_vec $x
</code></pre>
</article>
<article class="doc-entry" id="doc-normalize-vector">
<h3><a class="doc-anchor" href="#doc-normalize-vector">#</a> <code>normalize_vector</code></h3>
<p><code>normalize_vector(v) → array</code> — divide by L2 norm. Zero vector returns zero vector.</p>
</article>
<article class="doc-entry" id="doc-normalize-whitespace">
<h3><a class="doc-anchor" href="#doc-normalize-whitespace">#</a> <code>normalize_whitespace</code></h3>
<p><code>normalize_whitespace</code> — operation <code>normalize whitespace</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p normalize_whitespace $x
</code></pre>
</article>
<article class="doc-entry" id="doc-normarr">
<h3><a class="doc-anchor" href="#doc-normarr">#</a> <code>normarr</code></h3>
<p><code>normarr</code> — operation <code>normarr</code>. Alias for <code>normalize_array</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p normarr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-not-any">
<h3><a class="doc-anchor" href="#doc-not-any">#</a> <code>not_any</code></h3>
<p><code>not_any</code> — operation <code>not any</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p not_any $x
</code></pre>
</article>
<article class="doc-entry" id="doc-not-each">
<h3><a class="doc-anchor" href="#doc-not-each">#</a> <code>not_each</code></h3>
<p><code>not_each</code> — operation <code>not each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p not_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-not-elem">
<h3><a class="doc-anchor" href="#doc-not-elem">#</a> <code>not_elem</code></h3>
<p><code>not_elem</code> — operation <code>not elem</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p not_elem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-not-every">
<h3><a class="doc-anchor" href="#doc-not-every">#</a> <code>not_every</code></h3>
<p><code>not_every</code> — operation <code>not every</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p not_every $x
</code></pre>
</article>
<article class="doc-entry" id="doc-notall">
<h3><a class="doc-anchor" href="#doc-notall">#</a> <code>notall</code></h3>
<p><code>notall</code> — operation <code>notall</code>. Category: *list / aggregate*.</p>
<pre><code class="lang-perl">p notall $x
</code></pre>
</article>
<article class="doc-entry" id="doc-notch-filter">
<h3><a class="doc-anchor" href="#doc-notch-filter">#</a> <code>notch_filter</code></h3>
<p><code>notch_filter</code> — filter op of <code>notch</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p notch_filter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-note-name-from-midi">
<h3><a class="doc-anchor" href="#doc-note-name-from-midi">#</a> <code>note_name_from_midi</code></h3>
<p><code>note_name_from_midi</code> — musical-note helper <code>name from midi</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p note_name_from_midi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-note-name-to-midi">
<h3><a class="doc-anchor" href="#doc-note-name-to-midi">#</a> <code>note_name_to_midi</code></h3>
<p><code>note_name_to_midi</code> — convert from <code>note name</code> to <code>midi</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p note_name_to_midi $value
</code></pre>
</article>
<article class="doc-entry" id="doc-note-to-freq">
<h3><a class="doc-anchor" href="#doc-note-to-freq">#</a> <code>note_to_freq</code></h3>
<p><code>note_to_freq</code> — convert from <code>note</code> to <code>freq</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p note_to_freq $value
</code></pre>
</article>
<article class="doc-entry" id="doc-now">
<h3><a class="doc-anchor" href="#doc-now">#</a> <code>now</code></h3>
<p><code>now</code> — Unix epoch seconds. Returns the current time as the number of seconds since <code>1970-01-01T00:00:00Z</code>, like Perl's <code>time()</code>. Pass a timezone string (e.g. <code>now("UTC")</code> or <code>now("America/New_York")</code>) to get an ISO-8601 datetime string in that zone instead — that path forwards to <code>datetime_now_tz</code>.</p>
<pre><code class="lang-perl">p now # 1778262882
p now("UTC") # 2026-05-08T17:54:42.577935Z
my $start = now
# ... do work ...
printf "elapsed: %d s\n", now - $start
</code></pre>
</article>
<article class="doc-entry" id="doc-now-ms">
<h3><a class="doc-anchor" href="#doc-now-ms">#</a> <code>now_ms</code></h3>
<p><code>now_ms</code> — operation <code>now ms</code>. Category: *now / timestamp*.</p>
<pre><code class="lang-perl">p now_ms $x
</code></pre>
</article>
<article class="doc-entry" id="doc-now-ns">
<h3><a class="doc-anchor" href="#doc-now-ns">#</a> <code>now_ns</code></h3>
<p><code>now_ns</code> — operation <code>now ns</code>. Category: *now / timestamp*.</p>
<pre><code class="lang-perl">p now_ns $x
</code></pre>
</article>
<article class="doc-entry" id="doc-now-us">
<h3><a class="doc-anchor" href="#doc-now-us">#</a> <code>now_us</code></h3>
<p><code>now_us</code> — operation <code>now us</code>. Category: *now / timestamp*.</p>
<pre><code class="lang-perl">p now_us $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nper">
<h3><a class="doc-anchor" href="#doc-nper">#</a> <code>nper</code></h3>
<p><code>nper($rate, $pmt, $pv)</code> (alias <code>num_periods</code>) — computes the number of periods needed to pay off a loan given rate, payment, and principal.</p>
<pre><code class="lang-perl">p nper(0.05/12, 500, 50000) # ~127 months
</code></pre>
</article>
<article class="doc-entry" id="doc-npv">
<h3><a class="doc-anchor" href="#doc-npv">#</a> <code>npv</code></h3>
<p><code>npv</code> — operation <code>npv</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p npv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nrmrng">
<h3><a class="doc-anchor" href="#doc-nrmrng">#</a> <code>nrmrng</code></h3>
<p><code>nrmrng</code> — operation <code>nrmrng</code>. Alias for <code>normalize_range</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p nrmrng $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nrmsp">
<h3><a class="doc-anchor" href="#doc-nrmsp">#</a> <code>nrmsp</code></h3>
<p><code>nrmsp</code> — operation <code>nrmsp</code>. Alias for <code>normalize_spaces</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p nrmsp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nrmv">
<h3><a class="doc-anchor" href="#doc-nrmv">#</a> <code>nrmv</code></h3>
<p><code>nrmv</code> — operation <code>nrmv</code>. Alias for <code>normalize_vec</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p nrmv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nroot">
<h3><a class="doc-anchor" href="#doc-nroot">#</a> <code>nroot</code></h3>
<p><code>nroot</code> — operation <code>nroot</code>. Alias for <code>nth_root_of</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p nroot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nrow">
<h3><a class="doc-anchor" href="#doc-nrow">#</a> <code>nrow</code></h3>
<p><code>nrow</code> — number of rows in a matrix.</p>
<pre><code class="lang-perl">p nrow([[1,2],[3,4],[5,6]]) # 3
</code></pre>
</article>
<article class="doc-entry" id="doc-ns-to-ms">
<h3><a class="doc-anchor" href="#doc-ns-to-ms">#</a> <code>ns_to_ms</code></h3>
<p><code>ns_to_ms</code> — convert from <code>ns</code> to <code>ms</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p ns_to_ms $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ns-to-us">
<h3><a class="doc-anchor" href="#doc-ns-to-us">#</a> <code>ns_to_us</code></h3>
<p><code>ns_to_us</code> — convert from <code>ns</code> to <code>us</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p ns_to_us $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ntelm">
<h3><a class="doc-anchor" href="#doc-ntelm">#</a> <code>ntelm</code></h3>
<p><code>ntelm</code> — operation <code>ntelm</code>. Alias for <code>not_elem</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p ntelm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nth-largest">
<h3><a class="doc-anchor" href="#doc-nth-largest">#</a> <code>nth_largest</code></h3>
<p><code>nth_largest</code> — operation <code>nth largest</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p nth_largest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nth-prime">
<h3><a class="doc-anchor" href="#doc-nth-prime">#</a> <code>nth_prime</code></h3>
<p><code>nth_prime</code> — operation <code>nth prime</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p nth_prime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nth-root">
<h3><a class="doc-anchor" href="#doc-nth-root">#</a> <code>nth_root</code></h3>
<p><code>nth_root</code> — operation <code>nth root</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p nth_root $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nth-root-of">
<h3><a class="doc-anchor" href="#doc-nth-root-of">#</a> <code>nth_root_of</code></h3>
<p><code>nth_root_of</code> — operation <code>nth root of</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p nth_root_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nth-smallest">
<h3><a class="doc-anchor" href="#doc-nth-smallest">#</a> <code>nth_smallest</code></h3>
<p><code>nth_smallest</code> — operation <code>nth smallest</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p nth_smallest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nth-word">
<h3><a class="doc-anchor" href="#doc-nth-word">#</a> <code>nth_word</code></h3>
<p><code>nth_word</code> — operation <code>nth word</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p nth_word $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nthp">
<h3><a class="doc-anchor" href="#doc-nthp">#</a> <code>nthp</code></h3>
<p><code>nthp</code> — operation <code>nthp</code>. Alias for <code>nth_prime</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p nthp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nub">
<h3><a class="doc-anchor" href="#doc-nub">#</a> <code>nub</code></h3>
<p><code>nub</code> — operation <code>nub</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p nub $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nub-by">
<h3><a class="doc-anchor" href="#doc-nub-by">#</a> <code>nub_by</code></h3>
<p><code>nub_by</code> — operation <code>nub by</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p nub_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nub-count">
<h3><a class="doc-anchor" href="#doc-nub-count">#</a> <code>nub_count</code></h3>
<p><code>nub_count</code> — count of <code>nub</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p nub_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nub-list">
<h3><a class="doc-anchor" href="#doc-nub-list">#</a> <code>nub_list</code></h3>
<p><code>nub_list</code> — operation <code>nub list</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p nub_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nubb">
<h3><a class="doc-anchor" href="#doc-nubb">#</a> <code>nubb</code></h3>
<p><code>nubb</code> — operation <code>nubb</code>. Alias for <code>nub_by</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p nubb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nuclear-magneton">
<h3><a class="doc-anchor" href="#doc-nuclear-magneton">#</a> <code>nuclear_magneton</code></h3>
<p><code>nuclear_magneton</code> — operation <code>nuclear magneton</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p nuclear_magneton $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nucleation-rate-constant">
<h3><a class="doc-anchor" href="#doc-nucleation-rate-constant">#</a> <code>nucleation_rate_constant</code></h3>
<p><code>nucleation_rate_constant</code> — operation <code>nucleation rate constant</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p nucleation_rate_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nucleolus-lp-step">
<h3><a class="doc-anchor" href="#doc-nucleolus-lp-step">#</a> <code>nucleolus_lp_step</code></h3>
<p><code>nucleolus_lp_step</code> — single-step update of <code>nucleolus lp</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nucleolus_lp_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-num-cpus">
<h3><a class="doc-anchor" href="#doc-num-cpus">#</a> <code>num_cpus</code></h3>
<p><code>num_cpus</code> — operation <code>num cpus</code>. Category: *system introspection*.</p>
<pre><code class="lang-perl">p num_cpus $x
</code></pre>
</article>
<article class="doc-entry" id="doc-num-divisors">
<h3><a class="doc-anchor" href="#doc-num-divisors">#</a> <code>num_divisors</code></h3>
<p><code>num_divisors</code> — operation <code>num divisors</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p num_divisors $x
</code></pre>
</article>
<article class="doc-entry" id="doc-num-edges">
<h3><a class="doc-anchor" href="#doc-num-edges">#</a> <code>num_edges</code></h3>
<p><code>num_edges</code> — operation <code>num edges</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p num_edges $x
</code></pre>
</article>
<article class="doc-entry" id="doc-num-unrooted-trees">
<h3><a class="doc-anchor" href="#doc-num-unrooted-trees">#</a> <code>num_unrooted_trees</code></h3>
<p><code>num_unrooted_trees</code> — operation <code>num unrooted trees</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p num_unrooted_trees $x
</code></pre>
</article>
<article class="doc-entry" id="doc-number-needed-to-treat">
<h3><a class="doc-anchor" href="#doc-number-needed-to-treat">#</a> <code>number_needed_to_treat</code></h3>
<p><code>number_needed_to_treat</code> — convert from <code>number needed</code> to <code>treat</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p number_needed_to_treat $value
</code></pre>
</article>
<article class="doc-entry" id="doc-number-to-english">
<h3><a class="doc-anchor" href="#doc-number-to-english">#</a> <code>number_to_english</code></h3>
<p><code>number_to_english</code> — convert from <code>number</code> to <code>english</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p number_to_english $value
</code></pre>
</article>
<article class="doc-entry" id="doc-numeric-count">
<h3><a class="doc-anchor" href="#doc-numeric-count">#</a> <code>numeric_count</code></h3>
<p><code>numeric_count</code> — count of <code>numeric</code>. Category: *counters*.</p>
<pre><code class="lang-perl">p numeric_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-numerical-jacobian-col">
<h3><a class="doc-anchor" href="#doc-numerical-jacobian-col">#</a> <code>numerical_jacobian_col</code></h3>
<p><code>numerical_jacobian_col</code> — operation <code>numerical jacobian col</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p numerical_jacobian_col $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nusselt-dittus-boelter">
<h3><a class="doc-anchor" href="#doc-nusselt-dittus-boelter">#</a> <code>nusselt_dittus_boelter</code></h3>
<p><code>nusselt_dittus_boelter</code> — operation <code>nusselt dittus boelter</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p nusselt_dittus_boelter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nusselt-full-number">
<h3><a class="doc-anchor" href="#doc-nusselt-full-number">#</a> <code>nusselt_full_number</code></h3>
<p><code>nusselt_full_number</code> — operation <code>nusselt full number</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p nusselt_full_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nutation-iau2000a">
<h3><a class="doc-anchor" href="#doc-nutation-iau2000a">#</a> <code>nutation_iau2000a</code></h3>
<p><code>nutation_iau2000a</code> — operation <code>nutation iau2000a</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p nutation_iau2000a $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nuttall-w">
<h3><a class="doc-anchor" href="#doc-nuttall-w">#</a> <code>nuttall_w</code></h3>
<p><code>nuttall_w</code> — operation <code>nuttall w</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p nuttall_w $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nw-score">
<h3><a class="doc-anchor" href="#doc-nw-score">#</a> <code>nw_score</code></h3>
<p><code>nw_score(a, b, match=1, mismatch=-1, gap=-2) → number</code> — Needleman-Wunsch global alignment score.</p>
<pre><code class="lang-perl">p nw_score("ACGT", "ACCT")
</code></pre>
</article>
<article class="doc-entry" id="doc-nxtp">
<h3><a class="doc-anchor" href="#doc-nxtp">#</a> <code>nxtp</code></h3>
<p><code>nxtp</code> — operation <code>nxtp</code>. Alias for <code>next_prime</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p nxtp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nxtperm">
<h3><a class="doc-anchor" href="#doc-nxtperm">#</a> <code>nxtperm</code></h3>
<p><code>nxtperm</code> — operation <code>nxtperm</code>. Alias for <code>next_permutation</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p nxtperm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nyquist-encirclement">
<h3><a class="doc-anchor" href="#doc-nyquist-encirclement">#</a> <code>nyquist_encirclement</code></h3>
<p><code>nyquist_encirclement</code> — operation <code>nyquist encirclement</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p nyquist_encirclement $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nyquist-phase">
<h3><a class="doc-anchor" href="#doc-nyquist-phase">#</a> <code>nyquist_phase</code></h3>
<p><code>nyquist_phase</code> — operation <code>nyquist phase</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p nyquist_phase $x
</code></pre>
</article>
<article class="doc-entry" id="doc-nysiis">
<h3><a class="doc-anchor" href="#doc-nysiis">#</a> <code>nysiis</code></h3>
<p><code>nysiis(name) → string</code> — New York State Identification and Intelligence System phonetic encoding. Better than Soundex for non-Anglo names.</p>
<pre><code class="lang-perl">p nysiis("Smith") # SNAD
</code></pre>
</article>
<article class="doc-entry" id="doc-nysiis-phonetic">
<h3><a class="doc-anchor" href="#doc-nysiis-phonetic">#</a> <code>nysiis_phonetic</code></h3>
<p><code>nysiis_phonetic</code> — operation <code>nysiis phonetic</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p nysiis_phonetic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-oaconvolve-step">
<h3><a class="doc-anchor" href="#doc-oaconvolve-step">#</a> <code>oaconvolve_step</code></h3>
<p><code>oaconvolve_step</code> — single-step update of <code>oaconvolve</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p oaconvolve_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-oat-hash">
<h3><a class="doc-anchor" href="#doc-oat-hash">#</a> <code>oat_hash</code></h3>
<p><code>oat_hash</code> — hash function of <code>oat</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p oat_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-object-encoding">
<h3><a class="doc-anchor" href="#doc-object-encoding">#</a> <code>object_encoding</code></h3>
<p><code>object_encoding</code> — operation <code>object encoding</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p object_encoding $x
</code></pre>
</article>
<article class="doc-entry" id="doc-object-entries">
<h3><a class="doc-anchor" href="#doc-object-entries">#</a> <code>object_entries</code></h3>
<p><code>object_entries</code> — operation <code>object entries</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p object_entries $x
</code></pre>
</article>
<article class="doc-entry" id="doc-object-from-entries">
<h3><a class="doc-anchor" href="#doc-object-from-entries">#</a> <code>object_from_entries</code></h3>
<p><code>object_from_entries</code> — operation <code>object from entries</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p object_from_entries $x
</code></pre>
</article>
<article class="doc-entry" id="doc-object-keys">
<h3><a class="doc-anchor" href="#doc-object-keys">#</a> <code>object_keys</code></h3>
<p><code>object_keys</code> — operation <code>object keys</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p object_keys $x
</code></pre>
</article>
<article class="doc-entry" id="doc-object-values">
<h3><a class="doc-anchor" href="#doc-object-values">#</a> <code>object_values</code></h3>
<p><code>object_values</code> — operation <code>object values</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p object_values $x
</code></pre>
</article>
<article class="doc-entry" id="doc-obv">
<h3><a class="doc-anchor" href="#doc-obv">#</a> <code>obv</code></h3>
<p><code>obv(closes, volumes) → array</code> — On-Balance Volume (Granville). Cumulative sum that adds <code>volume</code> on up-bars and subtracts on down-bars.</p>
<pre><code class="lang-perl">p obv(\@cl, \@vol)
</code></pre>
</article>
<article class="doc-entry" id="doc-oct-of">
<h3><a class="doc-anchor" href="#doc-oct-of">#</a> <code>oct_of</code></h3>
<p><code>oct_of</code> — octal helper <code>of</code>. Alias for <code>to_oct</code>. Category: *base conversion*.</p>
<pre><code class="lang-perl">p oct_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-octagonal-number">
<h3><a class="doc-anchor" href="#doc-octagonal-number">#</a> <code>octagonal_number</code></h3>
<p><code>octagonal_number(n) → int</code> — <code>n·(3n-2)</code>.</p>
</article>
<article class="doc-entry" id="doc-octahedral-number">
<h3><a class="doc-anchor" href="#doc-octahedral-number">#</a> <code>octahedral_number</code></h3>
<p><code>octahedral_number</code> — operation <code>octahedral number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p octahedral_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ocv-lithium-ion-step">
<h3><a class="doc-anchor" href="#doc-ocv-lithium-ion-step">#</a> <code>ocv_lithium_ion_step</code></h3>
<p><code>ocv_lithium_ion_step</code> — single-step update of <code>ocv lithium ion</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ocv_lithium_ion_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-odd">
<h3><a class="doc-anchor" href="#doc-odd">#</a> <code>odd</code></h3>
<p><code>odd</code> — operation <code>odd</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p odd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-odddyield">
<h3><a class="doc-anchor" href="#doc-odddyield">#</a> <code>odddyield</code></h3>
<p><code>odddyield</code> — operation <code>odddyield</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p odddyield $x
</code></pre>
</article>
<article class="doc-entry" id="doc-odds-ratio-2x2">
<h3><a class="doc-anchor" href="#doc-odds-ratio-2x2">#</a> <code>odds_ratio_2x2</code></h3>
<p><code>odds_ratio_2x2</code> — operation <code>odds ratio 2x2</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p odds_ratio_2x2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ode45-step">
<h3><a class="doc-anchor" href="#doc-ode45-step">#</a> <code>ode45_step</code></h3>
<p><code>ode45_step</code> — single-step update of <code>ode45</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p ode45_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ode-euler">
<h3><a class="doc-anchor" href="#doc-ode-euler">#</a> <code>ode_euler</code></h3>
<p><code>ode_euler(derivatives, dt=0.01, y0=0) → array</code> — explicit Euler integration: <code>y[i+1] = y[i] + dt·f[i]</code> with initial condition <code>y0</code>. Returns a trajectory of length <code>len(derivatives) + 1</code>.</p>
<pre><code class="lang-perl">p ode_euler(\@dx_dt, 0.1, 1.0)
</code></pre>
</article>
<article class="doc-entry" id="doc-ode-lsoda">
<h3><a class="doc-anchor" href="#doc-ode-lsoda">#</a> <code>ode_lsoda</code></h3>
<p><code>ode_lsoda</code> — ODE integrator <code>lsoda</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p ode_lsoda $x
</code></pre>
</article>
<article class="doc-entry" id="doc-oents">
<h3><a class="doc-anchor" href="#doc-oents">#</a> <code>oents</code></h3>
<p><code>oents</code> — operation <code>oents</code>. Alias for <code>object_entries</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p oents $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ofents">
<h3><a class="doc-anchor" href="#doc-ofents">#</a> <code>ofents</code></h3>
<p><code>ofents</code> — operation <code>ofents</code>. Alias for <code>object_from_entries</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p ofents $x
</code></pre>
</article>
<article class="doc-entry" id="doc-off">
<h3><a class="doc-anchor" href="#doc-off">#</a> <code>off</code></h3>
<p><code>off</code> — operation <code>off</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p off $x
</code></pre>
</article>
<article class="doc-entry" id="doc-offset">
<h3><a class="doc-anchor" href="#doc-offset">#</a> <code>offset</code></h3>
<p><code>offset</code> — operation <code>offset</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p offset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-offset-each">
<h3><a class="doc-anchor" href="#doc-offset-each">#</a> <code>offset_each</code></h3>
<p><code>offset_each</code> — operation <code>offset each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p offset_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ohm-voltage">
<h3><a class="doc-anchor" href="#doc-ohm-voltage">#</a> <code>ohm_voltage</code></h3>
<p><code>ohm_voltage</code> — operation <code>ohm voltage</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p ohm_voltage $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ohms-law-i">
<h3><a class="doc-anchor" href="#doc-ohms-law-i">#</a> <code>ohms_law_i</code></h3>
<p><code>ohms_law_i</code> — operation <code>ohms law i</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p ohms_law_i $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ohms-law-r">
<h3><a class="doc-anchor" href="#doc-ohms-law-r">#</a> <code>ohms_law_r</code></h3>
<p><code>ohms_law_r</code> — operation <code>ohms law r</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p ohms_law_r $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ohms-law-v">
<h3><a class="doc-anchor" href="#doc-ohms-law-v">#</a> <code>ohms_law_v</code></h3>
<p><code>ohms_law_v</code> — operation <code>ohms law v</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p ohms_law_v $x
</code></pre>
</article>
<article class="doc-entry" id="doc-okeys">
<h3><a class="doc-anchor" href="#doc-okeys">#</a> <code>okeys</code></h3>
<p><code>okeys</code> — operation <code>okeys</code>. Alias for <code>object_keys</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p okeys $x
</code></pre>
</article>
<article class="doc-entry" id="doc-oklab-to-rgb">
<h3><a class="doc-anchor" href="#doc-oklab-to-rgb">#</a> <code>oklab_to_rgb</code></h3>
<p><code>oklab_to_rgb</code> — convert from <code>oklab</code> to <code>rgb</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p oklab_to_rgb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-oklch-to-rgb">
<h3><a class="doc-anchor" href="#doc-oklch-to-rgb">#</a> <code>oklch_to_rgb</code></h3>
<p><code>oklch_to_rgb([L, C, H]) → [r, g, b]</code> — inverse OKLCH → sRGB.</p>
</article>
<article class="doc-entry" id="doc-ols-adjusted-r2">
<h3><a class="doc-anchor" href="#doc-ols-adjusted-r2">#</a> <code>ols_adjusted_r2</code></h3>
<p><code>ols_adjusted_r2</code> — operation <code>ols adjusted r2</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p ols_adjusted_r2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ols-estimator">
<h3><a class="doc-anchor" href="#doc-ols-estimator">#</a> <code>ols_estimator</code></h3>
<p><code>ols_estimator</code> — operation <code>ols estimator</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p ols_estimator $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ols-r-squared">
<h3><a class="doc-anchor" href="#doc-ols-r-squared">#</a> <code>ols_r_squared</code></h3>
<p><code>ols_r_squared</code> — operation <code>ols r squared</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p ols_r_squared $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ols-residual-variance">
<h3><a class="doc-anchor" href="#doc-ols-residual-variance">#</a> <code>ols_residual_variance</code></h3>
<p><code>ols_residual_variance</code> — operation <code>ols residual variance</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p ols_residual_variance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-omega-equation-step">
<h3><a class="doc-anchor" href="#doc-omega-equation-step">#</a> <code>omega_equation_step</code></h3>
<p><code>omega_equation_step</code> — single-step update of <code>omega equation</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p omega_equation_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-omega-m-at-z">
<h3><a class="doc-anchor" href="#doc-omega-m-at-z">#</a> <code>omega_m_at_z</code></h3>
<p><code>omega_m_at_z</code> — operation <code>omega m at z</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p omega_m_at_z $x
</code></pre>
</article>
<article class="doc-entry" id="doc-omega-ratio">
<h3><a class="doc-anchor" href="#doc-omega-ratio">#</a> <code>omega_ratio</code></h3>
<p><code>omega_ratio(returns, threshold=0) → number</code> — <code>Σ(returns above threshold) / Σ(|returns below threshold|)</code>. Captures full return distribution.</p>
<pre><code class="lang-perl">p omega_ratio(\@returns, 0)
</code></pre>
</article>
<article class="doc-entry" id="doc-omit">
<h3><a class="doc-anchor" href="#doc-omit">#</a> <code>omit</code></h3>
<p><code>omit</code> — operation <code>omit</code>. Alias for <code>omit_keys</code>. Category: *hash ops*.</p>
<pre><code class="lang-perl">p omit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-omit-keys">
<h3><a class="doc-anchor" href="#doc-omit-keys">#</a> <code>omit_keys</code></h3>
<p><code>omit_keys</code> — operation <code>omit keys</code>. Category: *hash ops*.</p>
<pre><code class="lang-perl">p omit_keys $x
</code></pre>
</article>
<article class="doc-entry" id="doc-omori-aftershock">
<h3><a class="doc-anchor" href="#doc-omori-aftershock">#</a> <code>omori_aftershock</code></h3>
<p><code>omori_aftershock</code> — operation <code>omori aftershock</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p omori_aftershock $x
</code></pre>
</article>
<article class="doc-entry" id="doc-one">
<h3><a class="doc-anchor" href="#doc-one">#</a> <code>one</code></h3>
<p><code>one</code> — operation <code>one</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p one $x
</code></pre>
</article>
<article class="doc-entry" id="doc-one-hot">
<h3><a class="doc-anchor" href="#doc-one-hot">#</a> <code>one_hot</code></h3>
<p><code>one_hot</code> — operation <code>one hot</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p one_hot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ones">
<h3><a class="doc-anchor" href="#doc-ones">#</a> <code>ones</code></h3>
<p><code>ones</code> — operation <code>ones</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p ones $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ones-mat">
<h3><a class="doc-anchor" href="#doc-ones-mat">#</a> <code>ones_mat</code></h3>
<p><code>ones_mat</code> — operation <code>ones mat</code>. Alias for <code>ones_matrix</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p ones_mat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ones-matrix">
<h3><a class="doc-anchor" href="#doc-ones-matrix">#</a> <code>ones_matrix</code></h3>
<p><code>ones_matrix</code> — operation <code>ones matrix</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p ones_matrix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-oneshot-new">
<h3><a class="doc-anchor" href="#doc-oneshot-new">#</a> <code>oneshot_new</code></h3>
<p><code>oneshot_new() → channel</code> — single-value rendezvous; receiver blocks until the one send.</p>
</article>
<article class="doc-entry" id="doc-only-alnum">
<h3><a class="doc-anchor" href="#doc-only-alnum">#</a> <code>only_alnum</code></h3>
<p><code>only_alnum</code> — operation <code>only alnum</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p only_alnum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-only-alpha">
<h3><a class="doc-anchor" href="#doc-only-alpha">#</a> <code>only_alpha</code></h3>
<p><code>only_alpha</code> — operation <code>only alpha</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p only_alpha $x
</code></pre>
</article>
<article class="doc-entry" id="doc-only-ascii">
<h3><a class="doc-anchor" href="#doc-only-ascii">#</a> <code>only_ascii</code></h3>
<p><code>only_ascii</code> — operation <code>only ascii</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p only_ascii $x
</code></pre>
</article>
<article class="doc-entry" id="doc-only-digits">
<h3><a class="doc-anchor" href="#doc-only-digits">#</a> <code>only_digits</code></h3>
<p><code>only_digits</code> — operation <code>only digits</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p only_digits $x
</code></pre>
</article>
<article class="doc-entry" id="doc-onsager-relation-two-species">
<h3><a class="doc-anchor" href="#doc-onsager-relation-two-species">#</a> <code>onsager_relation_two_species</code></h3>
<p><code>onsager_relation_two_species</code> — operation <code>onsager relation two species</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p onsager_relation_two_species $x
</code></pre>
</article>
<article class="doc-entry" id="doc-open-pipe-harmonic">
<h3><a class="doc-anchor" href="#doc-open-pipe-harmonic">#</a> <code>open_pipe_harmonic</code></h3>
<p><code>open_pipe_harmonic</code> — operation <code>open pipe harmonic</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p open_pipe_harmonic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-opening-2d">
<h3><a class="doc-anchor" href="#doc-opening-2d">#</a> <code>opening_2d</code></h3>
<p><code>opening_2d(image, size=3) → matrix</code> — erosion followed by dilation. Removes small bright specks.</p>
</article>
<article class="doc-entry" id="doc-operad-count-two">
<h3><a class="doc-anchor" href="#doc-operad-count-two">#</a> <code>operad_count_two</code></h3>
<p><code>operad_count_two</code> — operation <code>operad count two</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p operad_count_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-oppenheimer-volkoff-step">
<h3><a class="doc-anchor" href="#doc-oppenheimer-volkoff-step">#</a> <code>oppenheimer_volkoff_step</code></h3>
<p><code>oppenheimer_volkoff_step</code> — single-step update of <code>oppenheimer volkoff</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p oppenheimer_volkoff_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ops-plus">
<h3><a class="doc-anchor" href="#doc-ops-plus">#</a> <code>ops_plus</code></h3>
<p><code>ops_plus</code> — operation <code>ops plus</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p ops_plus $x
</code></pre>
</article>
<article class="doc-entry" id="doc-optical-flow-farneback">
<h3><a class="doc-anchor" href="#doc-optical-flow-farneback">#</a> <code>optical_flow_farneback</code></h3>
<p><code>optical_flow_farneback</code> — operation <code>optical flow farneback</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p optical_flow_farneback $x
</code></pre>
</article>
<article class="doc-entry" id="doc-optical-flow-lk">
<h3><a class="doc-anchor" href="#doc-optical-flow-lk">#</a> <code>optical_flow_lk</code></h3>
<p><code>optical_flow_lk</code> — operation <code>optical flow lk</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p optical_flow_lk $x
</code></pre>
</article>
<article class="doc-entry" id="doc-optical-flow-lk-step">
<h3><a class="doc-anchor" href="#doc-optical-flow-lk-step">#</a> <code>optical_flow_lk_step</code></h3>
<p><code>optical_flow_lk_step</code> — single-step update of <code>optical flow lk</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p optical_flow_lk_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-optical-scalars-step">
<h3><a class="doc-anchor" href="#doc-optical-scalars-step">#</a> <code>optical_scalars_step</code></h3>
<p><code>optical_scalars_step</code> — single-step update of <code>optical scalars</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p optical_scalars_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-or-list">
<h3><a class="doc-anchor" href="#doc-or-list">#</a> <code>or_list</code></h3>
<p><code>or_list</code> — operation <code>or list</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p or_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-or-opt-delta">
<h3><a class="doc-anchor" href="#doc-or-opt-delta">#</a> <code>or_opt_delta</code></h3>
<p><code>or_opt_delta</code> — operation <code>or opt delta</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p or_opt_delta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-orb-keypoints">
<h3><a class="doc-anchor" href="#doc-orb-keypoints">#</a> <code>orb_keypoints</code></h3>
<p><code>orb_keypoints</code> — operation <code>orb keypoints</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p orb_keypoints $x
</code></pre>
</article>
<article class="doc-entry" id="doc-orbit-eccentric-anomaly">
<h3><a class="doc-anchor" href="#doc-orbit-eccentric-anomaly">#</a> <code>orbit_eccentric_anomaly</code></h3>
<p><code>orbit_eccentric_anomaly</code> — operation <code>orbit eccentric anomaly</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p orbit_eccentric_anomaly $x
</code></pre>
</article>
<article class="doc-entry" id="doc-orbit-kepler3">
<h3><a class="doc-anchor" href="#doc-orbit-kepler3">#</a> <code>orbit_kepler3</code></h3>
<p><code>orbit_kepler3</code> — operation <code>orbit kepler3</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p orbit_kepler3 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-orbital-eccentricity">
<h3><a class="doc-anchor" href="#doc-orbital-eccentricity">#</a> <code>orbital_eccentricity</code></h3>
<p><code>orbital_eccentricity</code> — operation <code>orbital eccentricity</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p orbital_eccentricity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-orbital-period">
<h3><a class="doc-anchor" href="#doc-orbital-period">#</a> <code>orbital_period</code></h3>
<p><code>orbital_period($mass, $radius)</code> (alias <code>orbper</code>) — period for circular orbit: T = 2π√(r³/GM). Returns seconds.</p>
<pre><code class="lang-perl">my $t = orbper # ~5560 s (ISS orbital period)
p $t / 60 # ~93 minutes
</code></pre>
</article>
<article class="doc-entry" id="doc-orbital-period-au">
<h3><a class="doc-anchor" href="#doc-orbital-period-au">#</a> <code>orbital_period_au</code></h3>
<p><code>orbital_period_au</code> — operation <code>orbital period au</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p orbital_period_au $x
</code></pre>
</article>
<article class="doc-entry" id="doc-orbital-velocity">
<h3><a class="doc-anchor" href="#doc-orbital-velocity">#</a> <code>orbital_velocity</code></h3>
<p><code>orbital_velocity($mass, $radius)</code> (alias <code>orbvel</code>) — velocity for circular orbit: v = √(GM/r). Defaults to LEO around Earth.</p>
<pre><code class="lang-perl">p orbvel # ~7672 m/s (ISS orbital speed)
</code></pre>
</article>
<article class="doc-entry" id="doc-order-modulo">
<h3><a class="doc-anchor" href="#doc-order-modulo">#</a> <code>order_modulo</code></h3>
<p><code>order_modulo</code> — operation <code>order modulo</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p order_modulo $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ordered-probit-threshold">
<h3><a class="doc-anchor" href="#doc-ordered-probit-threshold">#</a> <code>ordered_probit_threshold</code></h3>
<p><code>ordered_probit_threshold</code> — operation <code>ordered probit threshold</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p ordered_probit_threshold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ordered-set">
<h3><a class="doc-anchor" href="#doc-ordered-set">#</a> <code>ordered_set</code></h3>
<p><code>ordered_set</code> — operation <code>ordered set</code>. Category: *data structure helpers*.</p>
<pre><code class="lang-perl">p ordered_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ordinal-date">
<h3><a class="doc-anchor" href="#doc-ordinal-date">#</a> <code>ordinal_date</code></h3>
<p><code>ordinal_date</code> — operation <code>ordinal date</code>. Alias for <code>iso_ordinal_date</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p ordinal_date $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ordinalize">
<h3><a class="doc-anchor" href="#doc-ordinalize">#</a> <code>ordinalize</code></h3>
<p><code>ordinalize</code> — operation <code>ordinalize</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ordinalize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ordn">
<h3><a class="doc-anchor" href="#doc-ordn">#</a> <code>ordn</code></h3>
<p><code>ordn</code> — operation <code>ordn</code>. Alias for <code>ordinalize</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ordn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-orifice-velocity">
<h3><a class="doc-anchor" href="#doc-orifice-velocity">#</a> <code>orifice_velocity</code></h3>
<p><code>orifice_velocity</code> — operation <code>orifice velocity</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p orifice_velocity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-orl">
<h3><a class="doc-anchor" href="#doc-orl">#</a> <code>orl</code></h3>
<p><code>orl</code> — operation <code>orl</code>. Alias for <code>or_list</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p orl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-orthogonalize-vectors">
<h3><a class="doc-anchor" href="#doc-orthogonalize-vectors">#</a> <code>orthogonalize_vectors</code></h3>
<p><code>orthogonalize_vectors</code> — operation <code>orthogonalize vectors</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p orthogonalize_vectors $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-acpi-state-transition">
<h3><a class="doc-anchor" href="#doc-os-acpi-state-transition">#</a> <code>os_acpi_state_transition</code></h3>
<p><code>os_acpi_state_transition</code> — operating-system helper <code>acpi state transition</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_acpi_state_transition $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-amd-pstate-target">
<h3><a class="doc-anchor" href="#doc-os-amd-pstate-target">#</a> <code>os_amd_pstate_target</code></h3>
<p><code>os_amd_pstate_target</code> — operating-system helper <code>amd pstate target</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_amd_pstate_target $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-anticipation-window">
<h3><a class="doc-anchor" href="#doc-os-anticipation-window">#</a> <code>os_anticipation_window</code></h3>
<p><code>os_anticipation_window</code> — operating-system helper <code>anticipation window</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_anticipation_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-apic-irq-priority">
<h3><a class="doc-anchor" href="#doc-os-apic-irq-priority">#</a> <code>os_apic_irq_priority</code></h3>
<p><code>os_apic_irq_priority</code> — operating-system helper <code>apic irq priority</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_apic_irq_priority $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-apparmor-profile-active">
<h3><a class="doc-anchor" href="#doc-os-apparmor-profile-active">#</a> <code>os_apparmor_profile_active</code></h3>
<p><code>os_apparmor_profile_active</code> — operating-system helper <code>apparmor profile active</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_apparmor_profile_active $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-arch">
<h3><a class="doc-anchor" href="#doc-os-arch">#</a> <code>os_arch</code></h3>
<p><code>os_arch</code> — operating-system helper <code>arch</code>. Category: *system introspection*.</p>
<pre><code class="lang-perl">p os_arch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-audit-event-priority">
<h3><a class="doc-anchor" href="#doc-os-audit-event-priority">#</a> <code>os_audit_event_priority</code></h3>
<p><code>os_audit_event_priority</code> — operating-system helper <code>audit event priority</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_audit_event_priority $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-battery-capacity-pct">
<h3><a class="doc-anchor" href="#doc-os-battery-capacity-pct">#</a> <code>os_battery_capacity_pct</code></h3>
<p><code>os_battery_capacity_pct</code> — operating-system helper <code>battery capacity pct</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_battery_capacity_pct $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-buddy-order-pick">
<h3><a class="doc-anchor" href="#doc-os-buddy-order-pick">#</a> <code>os_buddy_order_pick</code></h3>
<p><code>os_buddy_order_pick</code> — operating-system helper <code>buddy order pick</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_buddy_order_pick $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-buffer-cache-pages">
<h3><a class="doc-anchor" href="#doc-os-buffer-cache-pages">#</a> <code>os_buffer_cache_pages</code></h3>
<p><code>os_buffer_cache_pages</code> — operating-system helper <code>buffer cache pages</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_buffer_cache_pages $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-c-state-residency">
<h3><a class="doc-anchor" href="#doc-os-c-state-residency">#</a> <code>os_c_state_residency</code></h3>
<p><code>os_c_state_residency</code> — operating-system helper <code>c state residency</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_c_state_residency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-capability-check">
<h3><a class="doc-anchor" href="#doc-os-capability-check">#</a> <code>os_capability_check</code></h3>
<p><code>os_capability_check</code> — operating-system helper <code>capability check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_capability_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-cfs-load-balance-step">
<h3><a class="doc-anchor" href="#doc-os-cfs-load-balance-step">#</a> <code>os_cfs_load_balance_step</code></h3>
<p><code>os_cfs_load_balance_step</code> — operating-system helper <code>cfs load balance step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_cfs_load_balance_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-cgroup-v1-count">
<h3><a class="doc-anchor" href="#doc-os-cgroup-v1-count">#</a> <code>os_cgroup_v1_count</code></h3>
<p><code>os_cgroup_v1_count</code> — operating-system helper <code>cgroup v1 count</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_cgroup_v1_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-cgroup-v2-count">
<h3><a class="doc-anchor" href="#doc-os-cgroup-v2-count">#</a> <code>os_cgroup_v2_count</code></h3>
<p><code>os_cgroup_v2_count</code> — operating-system helper <code>cgroup v2 count</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_cgroup_v2_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-compact-memory-step">
<h3><a class="doc-anchor" href="#doc-os-compact-memory-step">#</a> <code>os_compact_memory_step</code></h3>
<p><code>os_compact_memory_step</code> — operating-system helper <code>compact memory step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_compact_memory_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-completely-fair-vruntime">
<h3><a class="doc-anchor" href="#doc-os-completely-fair-vruntime">#</a> <code>os_completely_fair_vruntime</code></h3>
<p><code>os_completely_fair_vruntime</code> — operating-system helper <code>completely fair vruntime</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_completely_fair_vruntime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-copy-on-write-check">
<h3><a class="doc-anchor" href="#doc-os-copy-on-write-check">#</a> <code>os_copy_on_write_check</code></h3>
<p><code>os_copy_on_write_check</code> — operating-system helper <code>copy on write check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_copy_on_write_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-cpu-affinity-score">
<h3><a class="doc-anchor" href="#doc-os-cpu-affinity-score">#</a> <code>os_cpu_affinity_score</code></h3>
<p><code>os_cpu_affinity_score</code> — operating-system helper <code>cpu affinity score</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_cpu_affinity_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-cpufreq-governor-step">
<h3><a class="doc-anchor" href="#doc-os-cpufreq-governor-step">#</a> <code>os_cpufreq_governor_step</code></h3>
<p><code>os_cpufreq_governor_step</code> — operating-system helper <code>cpufreq governor step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_cpufreq_governor_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-demand-paging-step">
<h3><a class="doc-anchor" href="#doc-os-demand-paging-step">#</a> <code>os_demand_paging_step</code></h3>
<p><code>os_demand_paging_step</code> — operating-system helper <code>demand paging step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_demand_paging_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-dirty-page-threshold">
<h3><a class="doc-anchor" href="#doc-os-dirty-page-threshold">#</a> <code>os_dirty_page_threshold</code></h3>
<p><code>os_dirty_page_threshold</code> — operating-system helper <code>dirty page threshold</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_dirty_page_threshold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-disk-rotational-lat">
<h3><a class="doc-anchor" href="#doc-os-disk-rotational-lat">#</a> <code>os_disk_rotational_lat</code></h3>
<p><code>os_disk_rotational_lat</code> — operating-system helper <code>disk rotational lat</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_disk_rotational_lat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-disk-seek-time">
<h3><a class="doc-anchor" href="#doc-os-disk-seek-time">#</a> <code>os_disk_seek_time</code></h3>
<p><code>os_disk_seek_time</code> — operating-system helper <code>disk seek time</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_disk_seek_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-disk-transfer-time">
<h3><a class="doc-anchor" href="#doc-os-disk-transfer-time">#</a> <code>os_disk_transfer_time</code></h3>
<p><code>os_disk_transfer_time</code> — operating-system helper <code>disk transfer time</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_disk_transfer_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-dmesg-severity-level">
<h3><a class="doc-anchor" href="#doc-os-dmesg-severity-level">#</a> <code>os_dmesg_severity_level</code></h3>
<p><code>os_dmesg_severity_level</code> — operating-system helper <code>dmesg severity level</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_dmesg_severity_level $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-dvfs-step">
<h3><a class="doc-anchor" href="#doc-os-dvfs-step">#</a> <code>os_dvfs_step</code></h3>
<p><code>os_dvfs_step</code> — operating-system helper <code>dvfs step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_dvfs_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-eas-energy-estimate">
<h3><a class="doc-anchor" href="#doc-os-eas-energy-estimate">#</a> <code>os_eas_energy_estimate</code></h3>
<p><code>os_eas_energy_estimate</code> — operating-system helper <code>eas energy estimate</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_eas_energy_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-eevdf-eligible">
<h3><a class="doc-anchor" href="#doc-os-eevdf-eligible">#</a> <code>os_eevdf_eligible</code></h3>
<p><code>os_eevdf_eligible</code> — operating-system helper <code>eevdf eligible</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_eevdf_eligible $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-elevator-step">
<h3><a class="doc-anchor" href="#doc-os-elevator-step">#</a> <code>os_elevator_step</code></h3>
<p><code>os_elevator_step</code> — operating-system helper <code>elevator step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_elevator_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-epoll-ctl-count">
<h3><a class="doc-anchor" href="#doc-os-epoll-ctl-count">#</a> <code>os_epoll_ctl_count</code></h3>
<p><code>os_epoll_ctl_count</code> — operating-system helper <code>epoll ctl count</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_epoll_ctl_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-family">
<h3><a class="doc-anchor" href="#doc-os-family">#</a> <code>os_family</code></h3>
<p><code>os_family</code> — OS family string: <code>"unix"</code> or <code>"windows"</code>. From <code>std::env::consts::FAMILY</code>.</p>
<pre><code class="lang-perl">p os_family # unix
die "unix only" unless os_family eq "unix"
</code></pre>
</article>
<article class="doc-entry" id="doc-os-file-max-value">
<h3><a class="doc-anchor" href="#doc-os-file-max-value">#</a> <code>os_file_max_value</code></h3>
<p><code>os_file_max_value</code> — operating-system helper <code>file max value</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_file_max_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-frequency-scaling-step">
<h3><a class="doc-anchor" href="#doc-os-frequency-scaling-step">#</a> <code>os_frequency_scaling_step</code></h3>
<p><code>os_frequency_scaling_step</code> — operating-system helper <code>frequency scaling step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_frequency_scaling_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-huge-page-threshold">
<h3><a class="doc-anchor" href="#doc-os-huge-page-threshold">#</a> <code>os_huge_page_threshold</code></h3>
<p><code>os_huge_page_threshold</code> — operating-system helper <code>huge page threshold</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_huge_page_threshold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-idle-state-select">
<h3><a class="doc-anchor" href="#doc-os-idle-state-select">#</a> <code>os_idle_state_select</code></h3>
<p><code>os_idle_state_select</code> — operating-system helper <code>idle state select</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_idle_state_select $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-inotify-event-count">
<h3><a class="doc-anchor" href="#doc-os-inotify-event-count">#</a> <code>os_inotify_event_count</code></h3>
<p><code>os_inotify_event_count</code> — operating-system helper <code>inotify event count</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_inotify_event_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-inotify-max-watches">
<h3><a class="doc-anchor" href="#doc-os-inotify-max-watches">#</a> <code>os_inotify_max_watches</code></h3>
<p><code>os_inotify_max_watches</code> — operating-system helper <code>inotify max watches</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_inotify_max_watches $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-intel-pstate-target">
<h3><a class="doc-anchor" href="#doc-os-intel-pstate-target">#</a> <code>os_intel_pstate_target</code></h3>
<p><code>os_intel_pstate_target</code> — operating-system helper <code>intel pstate target</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_intel_pstate_target $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-io-scheduler-bfq-step">
<h3><a class="doc-anchor" href="#doc-os-io-scheduler-bfq-step">#</a> <code>os_io_scheduler_bfq_step</code></h3>
<p><code>os_io_scheduler_bfq_step</code> — operating-system helper <code>io scheduler bfq step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_io_scheduler_bfq_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-io-scheduler-cfq-step">
<h3><a class="doc-anchor" href="#doc-os-io-scheduler-cfq-step">#</a> <code>os_io_scheduler_cfq_step</code></h3>
<p><code>os_io_scheduler_cfq_step</code> — operating-system helper <code>io scheduler cfq step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_io_scheduler_cfq_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-io-scheduler-deadline">
<h3><a class="doc-anchor" href="#doc-os-io-scheduler-deadline">#</a> <code>os_io_scheduler_deadline</code></h3>
<p><code>os_io_scheduler_deadline</code> — operating-system helper <code>io scheduler deadline</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_io_scheduler_deadline $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-io-scheduler-kyber-step">
<h3><a class="doc-anchor" href="#doc-os-io-scheduler-kyber-step">#</a> <code>os_io_scheduler_kyber_step</code></h3>
<p><code>os_io_scheduler_kyber_step</code> — operating-system helper <code>io scheduler kyber step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_io_scheduler_kyber_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-io-scheduler-mq-deadline">
<h3><a class="doc-anchor" href="#doc-os-io-scheduler-mq-deadline">#</a> <code>os_io_scheduler_mq_deadline</code></h3>
<p><code>os_io_scheduler_mq_deadline</code> — operating-system helper <code>io scheduler mq deadline</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_io_scheduler_mq_deadline $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-io-scheduler-noop-step">
<h3><a class="doc-anchor" href="#doc-os-io-scheduler-noop-step">#</a> <code>os_io_scheduler_noop_step</code></h3>
<p><code>os_io_scheduler_noop_step</code> — operating-system helper <code>io scheduler noop step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_io_scheduler_noop_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-io-uring-cqe-count">
<h3><a class="doc-anchor" href="#doc-os-io-uring-cqe-count">#</a> <code>os_io_uring_cqe_count</code></h3>
<p><code>os_io_uring_cqe_count</code> — operating-system helper <code>io uring cqe count</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_io_uring_cqe_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-io-uring-sqe-count">
<h3><a class="doc-anchor" href="#doc-os-io-uring-sqe-count">#</a> <code>os_io_uring_sqe_count</code></h3>
<p><code>os_io_uring_sqe_count</code> — operating-system helper <code>io uring sqe count</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_io_uring_sqe_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-iommu-domain-step">
<h3><a class="doc-anchor" href="#doc-os-iommu-domain-step">#</a> <code>os_iommu_domain_step</code></h3>
<p><code>os_iommu_domain_step</code> — operating-system helper <code>iommu domain step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_iommu_domain_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-kasan-shadow-offset">
<h3><a class="doc-anchor" href="#doc-os-kasan-shadow-offset">#</a> <code>os_kasan_shadow_offset</code></h3>
<p><code>os_kasan_shadow_offset</code> — operating-system helper <code>kasan shadow offset</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_kasan_shadow_offset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-kfence-alloc-index">
<h3><a class="doc-anchor" href="#doc-os-kfence-alloc-index">#</a> <code>os_kfence_alloc_index</code></h3>
<p><code>os_kfence_alloc_index</code> — operating-system helper <code>kfence alloc index</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_kfence_alloc_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-kfence-check">
<h3><a class="doc-anchor" href="#doc-os-kfence-check">#</a> <code>os_kfence_check</code></h3>
<p><code>os_kfence_check</code> — operating-system helper <code>kfence check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_kfence_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-kqueue-event-count">
<h3><a class="doc-anchor" href="#doc-os-kqueue-event-count">#</a> <code>os_kqueue_event_count</code></h3>
<p><code>os_kqueue_event_count</code> — operating-system helper <code>kqueue event count</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_kqueue_event_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-kswapd-wake-threshold">
<h3><a class="doc-anchor" href="#doc-os-kswapd-wake-threshold">#</a> <code>os_kswapd_wake_threshold</code></h3>
<p><code>os_kswapd_wake_threshold</code> — operating-system helper <code>kswapd wake threshold</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_kswapd_wake_threshold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-kvm-vmcs-field-offset">
<h3><a class="doc-anchor" href="#doc-os-kvm-vmcs-field-offset">#</a> <code>os_kvm_vmcs_field_offset</code></h3>
<p><code>os_kvm_vmcs_field_offset</code> — operating-system helper <code>kvm vmcs field offset</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_kvm_vmcs_field_offset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-load-average-decay">
<h3><a class="doc-anchor" href="#doc-os-load-average-decay">#</a> <code>os_load_average_decay</code></h3>
<p><code>os_load_average_decay</code> — operating-system helper <code>load average decay</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_load_average_decay $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-load-iowait-avg">
<h3><a class="doc-anchor" href="#doc-os-load-iowait-avg">#</a> <code>os_load_iowait_avg</code></h3>
<p><code>os_load_iowait_avg</code> — operating-system helper <code>load iowait avg</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_load_iowait_avg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-load-proc-avg">
<h3><a class="doc-anchor" href="#doc-os-load-proc-avg">#</a> <code>os_load_proc_avg</code></h3>
<p><code>os_load_proc_avg</code> — operating-system helper <code>load proc avg</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_load_proc_avg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-load-user-avg">
<h3><a class="doc-anchor" href="#doc-os-load-user-avg">#</a> <code>os_load_user_avg</code></h3>
<p><code>os_load_user_avg</code> — operating-system helper <code>load user avg</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_load_user_avg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-lottery-ticket-count">
<h3><a class="doc-anchor" href="#doc-os-lottery-ticket-count">#</a> <code>os_lottery_ticket_count</code></h3>
<p><code>os_lottery_ticket_count</code> — operating-system helper <code>lottery ticket count</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_lottery_ticket_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-mlfq-demote-step">
<h3><a class="doc-anchor" href="#doc-os-mlfq-demote-step">#</a> <code>os_mlfq_demote_step</code></h3>
<p><code>os_mlfq_demote_step</code> — operating-system helper <code>mlfq demote step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_mlfq_demote_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-mlfq-promote-step">
<h3><a class="doc-anchor" href="#doc-os-mlfq-promote-step">#</a> <code>os_mlfq_promote_step</code></h3>
<p><code>os_mlfq_promote_step</code> — operating-system helper <code>mlfq promote step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_mlfq_promote_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-msi-x-vector-count">
<h3><a class="doc-anchor" href="#doc-os-msi-x-vector-count">#</a> <code>os_msi_x_vector_count</code></h3>
<p><code>os_msi_x_vector_count</code> — operating-system helper <code>msi x vector count</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_msi_x_vector_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-name">
<h3><a class="doc-anchor" href="#doc-os-name">#</a> <code>os_name</code></h3>
<p><code>os_name</code> — operating-system helper <code>name</code>. Category: *system introspection*.</p>
<pre><code class="lang-perl">p os_name $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-namespace-isolation">
<h3><a class="doc-anchor" href="#doc-os-namespace-isolation">#</a> <code>os_namespace_isolation</code></h3>
<p><code>os_namespace_isolation</code> — operating-system helper <code>namespace isolation</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_namespace_isolation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-numa-node-distance">
<h3><a class="doc-anchor" href="#doc-os-numa-node-distance">#</a> <code>os_numa_node_distance</code></h3>
<p><code>os_numa_node_distance</code> — operating-system helper <code>numa node distance</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_numa_node_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-oom-kill-score">
<h3><a class="doc-anchor" href="#doc-os-oom-kill-score">#</a> <code>os_oom_kill_score</code></h3>
<p><code>os_oom_kill_score</code> — operating-system helper <code>oom kill score</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_oom_kill_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-oom-score-step">
<h3><a class="doc-anchor" href="#doc-os-oom-score-step">#</a> <code>os_oom_score_step</code></h3>
<p><code>os_oom_score_step</code> — operating-system helper <code>oom score step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_oom_score_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-open-files-count">
<h3><a class="doc-anchor" href="#doc-os-open-files-count">#</a> <code>os_open_files_count</code></h3>
<p><code>os_open_files_count</code> — operating-system helper <code>open files count</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_open_files_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-p-state-voltage">
<h3><a class="doc-anchor" href="#doc-os-p-state-voltage">#</a> <code>os_p_state_voltage</code></h3>
<p><code>os_p_state_voltage</code> — operating-system helper <code>p state voltage</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_p_state_voltage $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-page-replacement-2q">
<h3><a class="doc-anchor" href="#doc-os-page-replacement-2q">#</a> <code>os_page_replacement_2q</code></h3>
<p><code>os_page_replacement_2q</code> — operating-system helper <code>page replacement 2q</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_page_replacement_2q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-page-replacement-clock">
<h3><a class="doc-anchor" href="#doc-os-page-replacement-clock">#</a> <code>os_page_replacement_clock</code></h3>
<p><code>os_page_replacement_clock</code> — operating-system helper <code>page replacement clock</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_page_replacement_clock $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-page-replacement-lru">
<h3><a class="doc-anchor" href="#doc-os-page-replacement-lru">#</a> <code>os_page_replacement_lru</code></h3>
<p><code>os_page_replacement_lru</code> — operating-system helper <code>page replacement lru</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_page_replacement_lru $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-pci-bus-address">
<h3><a class="doc-anchor" href="#doc-os-pci-bus-address">#</a> <code>os_pci_bus_address</code></h3>
<p><code>os_pci_bus_address</code> — operating-system helper <code>pci bus address</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_pci_bus_address $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-per-cpu-cache-size">
<h3><a class="doc-anchor" href="#doc-os-per-cpu-cache-size">#</a> <code>os_per_cpu_cache_size</code></h3>
<p><code>os_per_cpu_cache_size</code> — operating-system helper <code>per cpu cache size</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_per_cpu_cache_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-pid-max-value">
<h3><a class="doc-anchor" href="#doc-os-pid-max-value">#</a> <code>os_pid_max_value</code></h3>
<p><code>os_pid_max_value</code> — operating-system helper <code>pid max value</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_pid_max_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-powertop-score">
<h3><a class="doc-anchor" href="#doc-os-powertop-score">#</a> <code>os_powertop_score</code></h3>
<p><code>os_powertop_score</code> — operating-system helper <code>powertop score</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_powertop_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-pre-fetch-window">
<h3><a class="doc-anchor" href="#doc-os-pre-fetch-window">#</a> <code>os_pre_fetch_window</code></h3>
<p><code>os_pre_fetch_window</code> — operating-system helper <code>pre fetch window</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_pre_fetch_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-pressure-stall-step">
<h3><a class="doc-anchor" href="#doc-os-pressure-stall-step">#</a> <code>os_pressure_stall_step</code></h3>
<p><code>os_pressure_stall_step</code> — operating-system helper <code>pressure stall step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_pressure_stall_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-priority-aging-step">
<h3><a class="doc-anchor" href="#doc-os-priority-aging-step">#</a> <code>os_priority_aging_step</code></h3>
<p><code>os_priority_aging_step</code> — operating-system helper <code>priority aging step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_priority_aging_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-psi-avg10-step">
<h3><a class="doc-anchor" href="#doc-os-psi-avg10-step">#</a> <code>os_psi_avg10_step</code></h3>
<p><code>os_psi_avg10_step</code> — operating-system helper <code>psi avg10 step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_psi_avg10_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-psi-avg300-step">
<h3><a class="doc-anchor" href="#doc-os-psi-avg300-step">#</a> <code>os_psi_avg300_step</code></h3>
<p><code>os_psi_avg300_step</code> — operating-system helper <code>psi avg300 step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_psi_avg300_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-psi-avg60-step">
<h3><a class="doc-anchor" href="#doc-os-psi-avg60-step">#</a> <code>os_psi_avg60_step</code></h3>
<p><code>os_psi_avg60_step</code> — operating-system helper <code>psi avg60 step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_psi_avg60_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-round-robin-quantum">
<h3><a class="doc-anchor" href="#doc-os-round-robin-quantum">#</a> <code>os_round_robin_quantum</code></h3>
<p><code>os_round_robin_quantum</code> — operating-system helper <code>round robin quantum</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_round_robin_quantum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-runqueue-depth">
<h3><a class="doc-anchor" href="#doc-os-runqueue-depth">#</a> <code>os_runqueue_depth</code></h3>
<p><code>os_runqueue_depth</code> — operating-system helper <code>runqueue depth</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_runqueue_depth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-seccomp-filter-step">
<h3><a class="doc-anchor" href="#doc-os-seccomp-filter-step">#</a> <code>os_seccomp_filter_step</code></h3>
<p><code>os_seccomp_filter_step</code> — operating-system helper <code>seccomp filter step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_seccomp_filter_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-selinux-context-match">
<h3><a class="doc-anchor" href="#doc-os-selinux-context-match">#</a> <code>os_selinux_context_match</code></h3>
<p><code>os_selinux_context_match</code> — operating-system helper <code>selinux context match</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_selinux_context_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-slab-color-offset">
<h3><a class="doc-anchor" href="#doc-os-slab-color-offset">#</a> <code>os_slab_color_offset</code></h3>
<p><code>os_slab_color_offset</code> — operating-system helper <code>slab color offset</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_slab_color_offset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-slub-object-size-round">
<h3><a class="doc-anchor" href="#doc-os-slub-object-size-round">#</a> <code>os_slub_object_size_round</code></h3>
<p><code>os_slub_object_size_round</code> — operating-system helper <code>slub object size round</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_slub_object_size_round $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-smack-label-compare">
<h3><a class="doc-anchor" href="#doc-os-smack-label-compare">#</a> <code>os_smack_label_compare</code></h3>
<p><code>os_smack_label_compare</code> — operating-system helper <code>smack label compare</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_smack_label_compare $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-smt-threading-share">
<h3><a class="doc-anchor" href="#doc-os-smt-threading-share">#</a> <code>os_smt_threading_share</code></h3>
<p><code>os_smt_threading_share</code> — operating-system helper <code>smt threading share</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_smt_threading_share $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-socket-max-value">
<h3><a class="doc-anchor" href="#doc-os-socket-max-value">#</a> <code>os_socket_max_value</code></h3>
<p><code>os_socket_max_value</code> — operating-system helper <code>socket max value</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_socket_max_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-stride-pass-step">
<h3><a class="doc-anchor" href="#doc-os-stride-pass-step">#</a> <code>os_stride_pass_step</code></h3>
<p><code>os_stride_pass_step</code> — operating-system helper <code>stride pass step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_stride_pass_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-swap-pressure-score">
<h3><a class="doc-anchor" href="#doc-os-swap-pressure-score">#</a> <code>os_swap_pressure_score</code></h3>
<p><code>os_swap_pressure_score</code> — operating-system helper <code>swap pressure score</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_swap_pressure_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-swappiness-factor">
<h3><a class="doc-anchor" href="#doc-os-swappiness-factor">#</a> <code>os_swappiness_factor</code></h3>
<p><code>os_swappiness_factor</code> — operating-system helper <code>swappiness factor</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_swappiness_factor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-systemd-journal-size">
<h3><a class="doc-anchor" href="#doc-os-systemd-journal-size">#</a> <code>os_systemd_journal_size</code></h3>
<p><code>os_systemd_journal_size</code> — operating-system helper <code>systemd journal size</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_systemd_journal_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-thermal-zone-trip">
<h3><a class="doc-anchor" href="#doc-os-thermal-zone-trip">#</a> <code>os_thermal_zone_trip</code></h3>
<p><code>os_thermal_zone_trip</code> — operating-system helper <code>thermal zone trip</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_thermal_zone_trip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-thrashing-threshold">
<h3><a class="doc-anchor" href="#doc-os-thrashing-threshold">#</a> <code>os_thrashing_threshold</code></h3>
<p><code>os_thrashing_threshold</code> — operating-system helper <code>thrashing threshold</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_thrashing_threshold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-thread-max-value">
<h3><a class="doc-anchor" href="#doc-os-thread-max-value">#</a> <code>os_thread_max_value</code></h3>
<p><code>os_thread_max_value</code> — operating-system helper <code>thread max value</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_thread_max_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-thread-migration-cost">
<h3><a class="doc-anchor" href="#doc-os-thread-migration-cost">#</a> <code>os_thread_migration_cost</code></h3>
<p><code>os_thread_migration_cost</code> — operating-system helper <code>thread migration cost</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_thread_migration_cost $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-throttle-temperature">
<h3><a class="doc-anchor" href="#doc-os-throttle-temperature">#</a> <code>os_throttle_temperature</code></h3>
<p><code>os_throttle_temperature</code> — operating-system helper <code>throttle temperature</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_throttle_temperature $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-transparent-hugepage">
<h3><a class="doc-anchor" href="#doc-os-transparent-hugepage">#</a> <code>os_transparent_hugepage</code></h3>
<p><code>os_transparent_hugepage</code> — operating-system helper <code>transparent hugepage</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_transparent_hugepage $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-version">
<h3><a class="doc-anchor" href="#doc-os-version">#</a> <code>os_version</code></h3>
<p><code>os_version</code> — OS kernel version/release string from <code>uname</code>. Returns <code>undef</code> on non-unix.</p>
<pre><code class="lang-perl">p os_version # 25.4.0
p "kernel: " . os_version
</code></pre>
</article>
<article class="doc-entry" id="doc-os-voltage-scaling-step">
<h3><a class="doc-anchor" href="#doc-os-voltage-scaling-step">#</a> <code>os_voltage_scaling_step</code></h3>
<p><code>os_voltage_scaling_step</code> — operating-system helper <code>voltage scaling step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_voltage_scaling_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-working-set-size">
<h3><a class="doc-anchor" href="#doc-os-working-set-size">#</a> <code>os_working_set_size</code></h3>
<p><code>os_working_set_size</code> — operating-system helper <code>working set size</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_working_set_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-writeback-step">
<h3><a class="doc-anchor" href="#doc-os-writeback-step">#</a> <code>os_writeback_step</code></h3>
<p><code>os_writeback_step</code> — operating-system helper <code>writeback step</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_writeback_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-zero-page-optimization">
<h3><a class="doc-anchor" href="#doc-os-zero-page-optimization">#</a> <code>os_zero_page_optimization</code></h3>
<p><code>os_zero_page_optimization</code> — operating-system helper <code>zero page optimization</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_zero_page_optimization $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-zram-compress-ratio">
<h3><a class="doc-anchor" href="#doc-os-zram-compress-ratio">#</a> <code>os_zram_compress_ratio</code></h3>
<p><code>os_zram_compress_ratio</code> — operating-system helper <code>zram compress ratio</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_zram_compress_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-os-zswap-compress-ratio">
<h3><a class="doc-anchor" href="#doc-os-zswap-compress-ratio">#</a> <code>os_zswap_compress_ratio</code></h3>
<p><code>os_zswap_compress_ratio</code> — operating-system helper <code>zswap compress ratio</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p os_zswap_compress_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-oscillator-sawtooth">
<h3><a class="doc-anchor" href="#doc-oscillator-sawtooth">#</a> <code>oscillator_sawtooth</code></h3>
<p><code>oscillator_sawtooth</code> — oscillator (waveform generator) <code>sawtooth</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p oscillator_sawtooth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-oscillator-sine">
<h3><a class="doc-anchor" href="#doc-oscillator-sine">#</a> <code>oscillator_sine</code></h3>
<p><code>oscillator_sine</code> — oscillator (waveform generator) <code>sine</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p oscillator_sine $x
</code></pre>
</article>
<article class="doc-entry" id="doc-oscillator-square">
<h3><a class="doc-anchor" href="#doc-oscillator-square">#</a> <code>oscillator_square</code></h3>
<p><code>oscillator_square</code> — oscillator (waveform generator) <code>square</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p oscillator_square $x
</code></pre>
</article>
<article class="doc-entry" id="doc-oscillator-triangle">
<h3><a class="doc-anchor" href="#doc-oscillator-triangle">#</a> <code>oscillator_triangle</code></h3>
<p><code>oscillator_triangle</code> — oscillator (waveform generator) <code>triangle</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p oscillator_triangle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-osmotic-coefficient-pitzer">
<h3><a class="doc-anchor" href="#doc-osmotic-coefficient-pitzer">#</a> <code>osmotic_coefficient_pitzer</code></h3>
<p><code>osmotic_coefficient_pitzer</code> — operation <code>osmotic coefficient pitzer</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p osmotic_coefficient_pitzer $x
</code></pre>
</article>
<article class="doc-entry" id="doc-osmotic-pressure">
<h3><a class="doc-anchor" href="#doc-osmotic-pressure">#</a> <code>osmotic_pressure</code></h3>
<p><code>osmotic_pressure</code> — operation <code>osmotic pressure</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p osmotic_pressure $x
</code></pre>
</article>
<article class="doc-entry" id="doc-otsu-threshold">
<h3><a class="doc-anchor" href="#doc-otsu-threshold">#</a> <code>otsu_threshold</code></h3>
<p><code>otsu_threshold(image) → number</code> — Otsu's method: best intensity threshold maximising between-class variance.</p>
<pre><code class="lang-perl">my $t = otsu_threshold($img)
</code></pre>
</article>
<article class="doc-entry" id="doc-otto-efficiency">
<h3><a class="doc-anchor" href="#doc-otto-efficiency">#</a> <code>otto_efficiency</code></h3>
<p><code>otto_efficiency</code> — operation <code>otto efficiency</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p otto_efficiency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-oursync">
<h3><a class="doc-anchor" href="#doc-oursync">#</a> <code>oursync</code></h3>
<p>Package-global counterpart of <code>mysync</code>. Same <code>Arc<Mutex></code> backing, but the binding is keyed by the package-qualified stash name (<code>Pkg::x</code>) so all packages and parallel workers share one cell.</p>
<pre><code class="lang-perl">package Counter
oursync $total = 0
fn bump { $total++ }
package main
fan 10000 { Counter::bump() }
p $Counter::total # 10000
</code></pre>
<p>Use <code>oursync</code> for cross-package shared state; use <code>mysync</code> for lexically scoped shared state.</p>
</article>
<article class="doc-entry" id="doc-out-degree-directed">
<h3><a class="doc-anchor" href="#doc-out-degree-directed">#</a> <code>out_degree_directed</code></h3>
<p><code>out_degree_directed</code> — operation <code>out degree directed</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p out_degree_directed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-outer">
<h3><a class="doc-anchor" href="#doc-outer">#</a> <code>outer</code></h3>
<p><code>outer</code> — outer product of two vectors. Returns matrix where M[i][j] = v1[i] * v2[j].</p>
<pre><code class="lang-perl">my $m = outer([1,2,3], [10,20]) # [[10,20],[20,40],[30,60]]
</code></pre>
</article>
<article class="doc-entry" id="doc-outlier-iqr-q">
<h3><a class="doc-anchor" href="#doc-outlier-iqr-q">#</a> <code>outlier_iqr_q</code></h3>
<p><code>outlier_iqr_q</code> — operation <code>outlier iqr q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p outlier_iqr_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-outliers">
<h3><a class="doc-anchor" href="#doc-outliers">#</a> <code>outliers</code></h3>
<p><code>outliers</code> — operation <code>outliers</code>. Alias for <code>outliers_iqr</code>. Category: *statistics (extended)*.</p>
<pre><code class="lang-perl">p outliers $x
</code></pre>
</article>
<article class="doc-entry" id="doc-outliers-iqr">
<h3><a class="doc-anchor" href="#doc-outliers-iqr">#</a> <code>outliers_iqr</code></h3>
<p><code>outliers_iqr(@data)</code> — identifies outliers using the IQR method (1.5 × IQR beyond Q1/Q3). Returns an arrayref of outlier values. Standard approach for detecting unusual data points.</p>
<pre><code class="lang-perl">my @data = (1, 2, 3, 4, 5, 100)
my $out = outliers_iqr(@data)
p @$out # (100)
</code></pre>
</article>
<article class="doc-entry" id="doc-ovals">
<h3><a class="doc-anchor" href="#doc-ovals">#</a> <code>ovals</code></h3>
<p><code>ovals</code> — operation <code>ovals</code>. Alias for <code>object_values</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p ovals $x
</code></pre>
</article>
<article class="doc-entry" id="doc-overall-efficiency-pec">
<h3><a class="doc-anchor" href="#doc-overall-efficiency-pec">#</a> <code>overall_efficiency_pec</code></h3>
<p><code>overall_efficiency_pec</code> — operation <code>overall efficiency pec</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p overall_efficiency_pec $x
</code></pre>
</article>
<article class="doc-entry" id="doc-overlap-coeff">
<h3><a class="doc-anchor" href="#doc-overlap-coeff">#</a> <code>overlap_coeff</code></h3>
<p><code>overlap_coeff(a, b) → number</code> — <code>|A∩B| / min(|A|, |B|)</code>.</p>
</article>
<article class="doc-entry" id="doc-overlap-coefficient">
<h3><a class="doc-anchor" href="#doc-overlap-coefficient">#</a> <code>overlap_coefficient</code></h3>
<p><code>overlap_coefficient</code> — operation <code>overlap coefficient</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p overlap_coefficient $x
</code></pre>
</article>
<article class="doc-entry" id="doc-overlapcoef">
<h3><a class="doc-anchor" href="#doc-overlapcoef">#</a> <code>overlapcoef</code></h3>
<p><code>overlapcoef</code> — operation <code>overlapcoef</code>. Alias for <code>overlap_coefficient</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p overlapcoef $x
</code></pre>
</article>
<article class="doc-entry" id="doc-overline">
<h3><a class="doc-anchor" href="#doc-overline">#</a> <code>overline</code></h3>
<p><code>overline</code> — operation <code>overline</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p overline $x
</code></pre>
</article>
<article class="doc-entry" id="doc-overpotential-her">
<h3><a class="doc-anchor" href="#doc-overpotential-her">#</a> <code>overpotential_her</code></h3>
<p><code>overpotential_her</code> — operation <code>overpotential her</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p overpotential_her $x
</code></pre>
</article>
<article class="doc-entry" id="doc-overpotential-oer">
<h3><a class="doc-anchor" href="#doc-overpotential-oer">#</a> <code>overpotential_oer</code></h3>
<p><code>overpotential_oer</code> — operation <code>overpotential oer</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p overpotential_oer $x
</code></pre>
</article>
<article class="doc-entry" id="doc-owen-t">
<h3><a class="doc-anchor" href="#doc-owen-t">#</a> <code>owen_t</code></h3>
<p><code>owen_t</code> — operation <code>owen t</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p owen_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-owens-t">
<h3><a class="doc-anchor" href="#doc-owens-t">#</a> <code>owens_t</code></h3>
<p><code>owens_t</code> — operation <code>owens t</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p owens_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-oxidation-number">
<h3><a class="doc-anchor" href="#doc-oxidation-number">#</a> <code>oxidation_number</code></h3>
<p><code>oxidation_number</code> — operation <code>oxidation number</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p oxidation_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-oz-to-g">
<h3><a class="doc-anchor" href="#doc-oz-to-g">#</a> <code>oz_to_g</code></h3>
<p><code>oz_to_g</code> — convert from <code>oz</code> to <code>g</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p oz_to_g $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ozone-dobson-total">
<h3><a class="doc-anchor" href="#doc-ozone-dobson-total">#</a> <code>ozone_dobson_total</code></h3>
<p><code>ozone_dobson_total</code> — operation <code>ozone dobson total</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ozone_dobson_total $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ozsvath-szabo-tau">
<h3><a class="doc-anchor" href="#doc-ozsvath-szabo-tau">#</a> <code>ozsvath_szabo_tau</code></h3>
<p><code>ozsvath_szabo_tau</code> — operation <code>ozsvath szabo tau</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p ozsvath_szabo_tau $x
</code></pre>
</article>
<article class="doc-entry" id="doc-p3-to-rgb">
<h3><a class="doc-anchor" href="#doc-p3-to-rgb">#</a> <code>p3_to_rgb</code></h3>
<p><code>p3_to_rgb</code> — convert from <code>p3</code> to <code>rgb</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p p3_to_rgb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-pa-to-atm">
<h3><a class="doc-anchor" href="#doc-pa-to-atm">#</a> <code>pa_to_atm</code></h3>
<p><code>pa_to_atm</code> — convert from <code>pa</code> to <code>atm</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p pa_to_atm $value
</code></pre>
</article>
<article class="doc-entry" id="doc-pacf">
<h3><a class="doc-anchor" href="#doc-pacf">#</a> <code>pacf</code></h3>
<p><code>pacf_fn</code> (alias <code>pacf</code>) — partial autocorrelation function via Durbin-Levinson. Like R's pacf().</p>
<pre><code class="lang-perl">my @pa = @{pacf([1,3,2,4,3,5], 3)}
</code></pre>
</article>
<article class="doc-entry" id="doc-pacf-basis">
<h3><a class="doc-anchor" href="#doc-pacf-basis">#</a> <code>pacf_basis</code></h3>
<p><code>pacf_basis</code> — operation <code>pacf basis</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p pacf_basis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-packet-loss">
<h3><a class="doc-anchor" href="#doc-packet-loss">#</a> <code>packet_loss</code></h3>
<p><code>packet_loss</code> — operation <code>packet loss</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p packet_loss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-packrat-parse-step">
<h3><a class="doc-anchor" href="#doc-packrat-parse-step">#</a> <code>packrat_parse_step</code></h3>
<p><code>packrat_parse_step</code> — single-step update of <code>packrat parse</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p packrat_parse_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pad-left">
<h3><a class="doc-anchor" href="#doc-pad-left">#</a> <code>pad_left</code></h3>
<p><code>pad_left</code> — operation <code>pad left</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p pad_left $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pad-left-n">
<h3><a class="doc-anchor" href="#doc-pad-left-n">#</a> <code>pad_left_n</code></h3>
<p><code>pad_left_n</code> — operation <code>pad left n</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p pad_left_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pad-number">
<h3><a class="doc-anchor" href="#doc-pad-number">#</a> <code>pad_number</code></h3>
<p><code>pad_number</code> — operation <code>pad number</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p pad_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pad-right">
<h3><a class="doc-anchor" href="#doc-pad-right">#</a> <code>pad_right</code></h3>
<p><code>pad_right</code> — operation <code>pad right</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p pad_right $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pad-right-n">
<h3><a class="doc-anchor" href="#doc-pad-right-n">#</a> <code>pad_right_n</code></h3>
<p><code>pad_right_n</code> — operation <code>pad right n</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p pad_right_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-page-size">
<h3><a class="doc-anchor" href="#doc-page-size">#</a> <code>page_size</code></h3>
<p><code>page_size</code> — memory page size in bytes. Uses <code>sysconf(_SC_PAGESIZE)</code> on unix.</p>
<pre><code class="lang-perl">p page_size # 16384 (Apple Silicon)
p page_size # 4096 (x86_64)
</code></pre>
</article>
<article class="doc-entry" id="doc-pagerank-damped">
<h3><a class="doc-anchor" href="#doc-pagerank-damped">#</a> <code>pagerank_damped</code></h3>
<p><code>pagerank_damped</code> — operation <code>pagerank damped</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p pagerank_damped $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pagerank-iter">
<h3><a class="doc-anchor" href="#doc-pagerank-iter">#</a> <code>pagerank_iter</code></h3>
<p><code>pagerank_iter</code> — operation <code>pagerank iter</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p pagerank_iter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pagerank-tournament">
<h3><a class="doc-anchor" href="#doc-pagerank-tournament">#</a> <code>pagerank_tournament</code></h3>
<p><code>pagerank_tournament(wins_matrix, damping=0.85, iters=50) → array</code> — PageRank-style ratings from a wins matrix.</p>
</article>
<article class="doc-entry" id="doc-paired-ttest">
<h3><a class="doc-anchor" href="#doc-paired-ttest">#</a> <code>paired_ttest</code></h3>
<p><code>paired_ttest</code> (alias <code>pairedt</code>) performs a paired t-test on two matched samples. Returns [t-statistic, degrees of freedom].</p>
<pre><code class="lang-perl">my ($t, $df) = @{pairedt([85,90,78], [88,92,80])}
</code></pre>
</article>
<article class="doc-entry" id="doc-pairs-from-hash">
<h3><a class="doc-anchor" href="#doc-pairs-from-hash">#</a> <code>pairs_from_hash</code></h3>
<p><code>pairs_from_hash</code> — hash function of <code>pairs from</code>. Category: *hash ops*.</p>
<pre><code class="lang-perl">p pairs_from_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pairwise">
<h3><a class="doc-anchor" href="#doc-pairwise">#</a> <code>pairwise</code></h3>
<p><code>pairwise</code> — operation <code>pairwise</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p pairwise $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pairwise-iter">
<h3><a class="doc-anchor" href="#doc-pairwise-iter">#</a> <code>pairwise_iter</code></h3>
<p><code>pairwise_iter</code> — operation <code>pairwise iter</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p pairwise_iter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-palindromic-q">
<h3><a class="doc-anchor" href="#doc-palindromic-q">#</a> <code>palindromic_q</code></h3>
<p><code>palindromic_q</code> — operation <code>palindromic q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p palindromic_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pall">
<h3><a class="doc-anchor" href="#doc-pall">#</a> <code>pall</code></h3>
<p><code>pall</code> — operation <code>pall</code>. Alias for <code>partition_all</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p pall $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pam250-score">
<h3><a class="doc-anchor" href="#doc-pam250-score">#</a> <code>pam250_score</code></h3>
<p><code>pam250_score</code> — score of <code>pam250</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p pam250_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-panel-between-estimator">
<h3><a class="doc-anchor" href="#doc-panel-between-estimator">#</a> <code>panel_between_estimator</code></h3>
<p><code>panel_between_estimator</code> — operation <code>panel between estimator</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p panel_between_estimator $x
</code></pre>
</article>
<article class="doc-entry" id="doc-panel-random-effects">
<h3><a class="doc-anchor" href="#doc-panel-random-effects">#</a> <code>panel_random_effects</code></h3>
<p><code>panel_random_effects</code> — operation <code>panel random effects</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p panel_random_effects $x
</code></pre>
</article>
<article class="doc-entry" id="doc-panel-var-step">
<h3><a class="doc-anchor" href="#doc-panel-var-step">#</a> <code>panel_var_step</code></h3>
<p><code>panel_var_step</code> — single-step update of <code>panel var</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p panel_var_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-panel-within-estimator">
<h3><a class="doc-anchor" href="#doc-panel-within-estimator">#</a> <code>panel_within_estimator</code></h3>
<p><code>panel_within_estimator</code> — operation <code>panel within estimator</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p panel_within_estimator $x
</code></pre>
</article>
<article class="doc-entry" id="doc-parabolic-d0">
<h3><a class="doc-anchor" href="#doc-parabolic-d0">#</a> <code>parabolic_d0</code></h3>
<p><code>parabolic_d0</code> — operation <code>parabolic d0</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p parabolic_d0 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-parabolic-d1">
<h3><a class="doc-anchor" href="#doc-parabolic-d1">#</a> <code>parabolic_d1</code></h3>
<p><code>parabolic_d1</code> — operation <code>parabolic d1</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p parabolic_d1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-parabolic-sar">
<h3><a class="doc-anchor" href="#doc-parabolic-sar">#</a> <code>parabolic_sar</code></h3>
<p><code>parabolic_sar(highs, lows, af_step=0.02, af_max=0.2) → array</code> — Wilder's stop-and-reverse trailing stop. Flips when price crosses the SAR line; acceleration factor grows on new extremes.</p>
<pre><code class="lang-perl">p parabolic_sar(\@hi, \@lo)
</code></pre>
</article>
<article class="doc-entry" id="doc-parallax-correction">
<h3><a class="doc-anchor" href="#doc-parallax-correction">#</a> <code>parallax_correction</code></h3>
<p><code>parallax_correction</code> — operation <code>parallax correction</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p parallax_correction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-parallel-machine-lpt">
<h3><a class="doc-anchor" href="#doc-parallel-machine-lpt">#</a> <code>parallel_machine_lpt</code></h3>
<p><code>parallel_machine_lpt</code> — operation <code>parallel machine lpt</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p parallel_machine_lpt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-parallel-machine-spt">
<h3><a class="doc-anchor" href="#doc-parallel-machine-spt">#</a> <code>parallel_machine_spt</code></h3>
<p><code>parallel_machine_spt</code> — operation <code>parallel machine spt</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p parallel_machine_spt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-parallel-transport-step">
<h3><a class="doc-anchor" href="#doc-parallel-transport-step">#</a> <code>parallel_transport_step</code></h3>
<p><code>parallel_transport_step</code> — single-step update of <code>parallel transport</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p parallel_transport_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-parenthesize">
<h3><a class="doc-anchor" href="#doc-parenthesize">#</a> <code>parenthesize</code></h3>
<p><code>parenthesize</code> — operation <code>parenthesize</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p parenthesize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pareto-dominance">
<h3><a class="doc-anchor" href="#doc-pareto-dominance">#</a> <code>pareto_dominance</code></h3>
<p><code>pareto_dominance</code> — operation <code>pareto dominance</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p pareto_dominance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pareto-efficiency">
<h3><a class="doc-anchor" href="#doc-pareto-efficiency">#</a> <code>pareto_efficiency</code></h3>
<p><code>pareto_efficiency</code> — operation <code>pareto efficiency</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p pareto_efficiency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pareto-pdf">
<h3><a class="doc-anchor" href="#doc-pareto-pdf">#</a> <code>pareto_pdf</code></h3>
<p><code>pareto_pdf</code> (alias <code>paretopdf</code>) evaluates the Pareto distribution PDF at x with minimum xm and shape alpha.</p>
<pre><code class="lang-perl">p paretopdf(2, 1, 3) # Pareto(1,3) at x=2
</code></pre>
</article>
<article class="doc-entry" id="doc-parse-bool">
<h3><a class="doc-anchor" href="#doc-parse-bool">#</a> <code>parse_bool</code></h3>
<p><code>parse_bool</code> — operation <code>parse bool</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p parse_bool $x
</code></pre>
</article>
<article class="doc-entry" id="doc-parse-float">
<h3><a class="doc-anchor" href="#doc-parse-float">#</a> <code>parse_float</code></h3>
<p><code>parse_float</code> — operation <code>parse float</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p parse_float $x
</code></pre>
</article>
<article class="doc-entry" id="doc-parse-int">
<h3><a class="doc-anchor" href="#doc-parse-int">#</a> <code>parse_int</code></h3>
<p><code>parse_int</code> — operation <code>parse int</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p parse_int $x
</code></pre>
</article>
<article class="doc-entry" id="doc-partial-pressure">
<h3><a class="doc-anchor" href="#doc-partial-pressure">#</a> <code>partial_pressure</code></h3>
<p><code>partial_pressure</code> — operation <code>partial pressure</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p partial_pressure $x
</code></pre>
</article>
<article class="doc-entry" id="doc-particle-emit">
<h3><a class="doc-anchor" href="#doc-particle-emit">#</a> <code>particle_emit</code></h3>
<p><code>particle_emit</code> — operation <code>particle emit</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p particle_emit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-particle-filter-resample">
<h3><a class="doc-anchor" href="#doc-particle-filter-resample">#</a> <code>particle_filter_resample</code></h3>
<p><code>particle_filter_resample</code> — operation <code>particle filter resample</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p particle_filter_resample $x
</code></pre>
</article>
<article class="doc-entry" id="doc-particle-update">
<h3><a class="doc-anchor" href="#doc-particle-update">#</a> <code>particle_update</code></h3>
<p><code>particle_update</code> — update step of <code>particle</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p particle_update $x
</code></pre>
</article>
<article class="doc-entry" id="doc-partition-all">
<h3><a class="doc-anchor" href="#doc-partition-all">#</a> <code>partition_all</code></h3>
<p><code>partition_all</code> — operation <code>partition all</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p partition_all $x
</code></pre>
</article>
<article class="doc-entry" id="doc-partition-at">
<h3><a class="doc-anchor" href="#doc-partition-at">#</a> <code>partition_at</code></h3>
<p><code>partition_at</code> — operation <code>partition at</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p partition_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-partition-by">
<h3><a class="doc-anchor" href="#doc-partition-by">#</a> <code>partition_by</code></h3>
<p><code>partition_by</code> — operation <code>partition by</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p partition_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-partition-either">
<h3><a class="doc-anchor" href="#doc-partition-either">#</a> <code>partition_either</code></h3>
<p><code>partition_either</code> — operation <code>partition either</code>. Category: *rust iterator methods*.</p>
<pre><code class="lang-perl">p partition_either $x
</code></pre>
</article>
<article class="doc-entry" id="doc-partition-n">
<h3><a class="doc-anchor" href="#doc-partition-n">#</a> <code>partition_n</code></h3>
<p><code>partition_n</code> — operation <code>partition n</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p partition_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-partition-number">
<h3><a class="doc-anchor" href="#doc-partition-number">#</a> <code>partition_number</code></h3>
<p><code>partition_number</code> — operation <code>partition number</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p partition_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-partition-point">
<h3><a class="doc-anchor" href="#doc-partition-point">#</a> <code>partition_point</code></h3>
<p><code>partition_point</code> — operation <code>partition point</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p partition_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-partition-two">
<h3><a class="doc-anchor" href="#doc-partition-two">#</a> <code>partition_two</code></h3>
<p><code>partition_two</code> — operation <code>partition two</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p partition_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-partitions-count">
<h3><a class="doc-anchor" href="#doc-partitions-count">#</a> <code>partitions_count</code></h3>
<p><code>partitions_count(n) → int</code> — Euler's partition function p(n).</p>
<pre><code class="lang-perl">p partitions_count(10) # 42
</code></pre>
</article>
<article class="doc-entry" id="doc-partn">
<h3><a class="doc-anchor" href="#doc-partn">#</a> <code>partn</code></h3>
<p><code>partn</code> — operation <code>partn</code>. Alias for <code>partition_n</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p partn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-partn-num">
<h3><a class="doc-anchor" href="#doc-partn-num">#</a> <code>partn_num</code></h3>
<p><code>partn_num</code> — operation <code>partn num</code>. Alias for <code>partition_number</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p partn_num $x
</code></pre>
</article>
<article class="doc-entry" id="doc-parzen-window">
<h3><a class="doc-anchor" href="#doc-parzen-window">#</a> <code>parzen_window</code></h3>
<p><code>parzen_window</code> — operation <code>parzen window</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p parzen_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pascal-case">
<h3><a class="doc-anchor" href="#doc-pascal-case">#</a> <code>pascal_case</code></h3>
<p><code>pascal_case</code> — operation <code>pascal case</code>. Category: *string*.</p>
<pre><code class="lang-perl">p pascal_case $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pascal-row">
<h3><a class="doc-anchor" href="#doc-pascal-row">#</a> <code>pascal_row</code></h3>
<p><code>pascal_row</code> — operation <code>pascal row</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p pascal_row $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pascals-to-bar">
<h3><a class="doc-anchor" href="#doc-pascals-to-bar">#</a> <code>pascals_to_bar</code></h3>
<p><code>pascals_to_bar</code> — convert from <code>pascals</code> to <code>bar</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p pascals_to_bar $value
</code></pre>
</article>
<article class="doc-entry" id="doc-pascals-to-psi">
<h3><a class="doc-anchor" href="#doc-pascals-to-psi">#</a> <code>pascals_to_psi</code></h3>
<p><code>pascals_to_psi</code> — convert from <code>pascals</code> to <code>psi</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p pascals_to_psi $value
</code></pre>
</article>
<article class="doc-entry" id="doc-pascals-triangle">
<h3><a class="doc-anchor" href="#doc-pascals-triangle">#</a> <code>pascals_triangle</code></h3>
<p><code>pascals_triangle</code> — operation <code>pascals triangle</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p pascals_triangle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pascrow">
<h3><a class="doc-anchor" href="#doc-pascrow">#</a> <code>pascrow</code></h3>
<p><code>pascrow</code> — operation <code>pascrow</code>. Alias for <code>pascal_row</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p pascrow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pasctri">
<h3><a class="doc-anchor" href="#doc-pasctri">#</a> <code>pasctri</code></h3>
<p><code>pasctri</code> — operation <code>pasctri</code>. Alias for <code>pascals_triangle</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p pasctri $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pass">
<h3><a class="doc-anchor" href="#doc-pass">#</a> <code>pass</code></h3>
<p><code>pass</code> — operation <code>pass</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p pass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-path-canonical">
<h3><a class="doc-anchor" href="#doc-path-canonical">#</a> <code>path_canonical</code></h3>
<p><code>path_canonical(path) → string</code> — absolute path with symlinks resolved (canonicalize).</p>
</article>
<article class="doc-entry" id="doc-path-case">
<h3><a class="doc-anchor" href="#doc-path-case">#</a> <code>path_case</code></h3>
<p><code>path_case</code> — path manipulation <code>case</code>. Category: *string*.</p>
<pre><code class="lang-perl">p path_case $x
</code></pre>
</article>
<article class="doc-entry" id="doc-path-common-ancestor">
<h3><a class="doc-anchor" href="#doc-path-common-ancestor">#</a> <code>path_common_ancestor</code></h3>
<p><code>path_common_ancestor(paths) → string</code> — longest common directory prefix.</p>
</article>
<article class="doc-entry" id="doc-path-components">
<h3><a class="doc-anchor" href="#doc-path-components">#</a> <code>path_components</code></h3>
<p><code>path_components(path) → array</code> — split into segments.</p>
<pre><code class="lang-perl">p path_components("/usr/local/bin") # ["usr","local","bin"]
</code></pre>
</article>
<article class="doc-entry" id="doc-path-dubins-lsl">
<h3><a class="doc-anchor" href="#doc-path-dubins-lsl">#</a> <code>path_dubins_lsl</code></h3>
<p><code>path_dubins_lsl</code> — path manipulation <code>dubins lsl</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p path_dubins_lsl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-path-dubins-rsr">
<h3><a class="doc-anchor" href="#doc-path-dubins-rsr">#</a> <code>path_dubins_rsr</code></h3>
<p><code>path_dubins_rsr</code> — path manipulation <code>dubins rsr</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p path_dubins_rsr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-path-ext">
<h3><a class="doc-anchor" href="#doc-path-ext">#</a> <code>path_ext</code></h3>
<p><code>path_ext</code> — path manipulation <code>ext</code>. Category: *path helpers*.</p>
<pre><code class="lang-perl">p path_ext $x
</code></pre>
</article>
<article class="doc-entry" id="doc-path-extension">
<h3><a class="doc-anchor" href="#doc-path-extension">#</a> <code>path_extension</code></h3>
<p><code>path_extension(path) → string</code> — final extension without leading dot, empty if none.</p>
</article>
<article class="doc-entry" id="doc-path-filename">
<h3><a class="doc-anchor" href="#doc-path-filename">#</a> <code>path_filename</code></h3>
<p><code>path_filename(path) → string</code> — last segment with extension.</p>
</article>
<article class="doc-entry" id="doc-path-glob-match-regex">
<h3><a class="doc-anchor" href="#doc-path-glob-match-regex">#</a> <code>path_glob_match_regex</code></h3>
<p><code>path_glob_match_regex(glob) → regex</code> — convert glob <code>*.txt</code> into anchored regex.</p>
</article>
<article class="doc-entry" id="doc-path-is-abs">
<h3><a class="doc-anchor" href="#doc-path-is-abs">#</a> <code>path_is_abs</code></h3>
<p><code>path_is_abs</code> — path manipulation <code>is abs</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p path_is_abs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-path-is-rel">
<h3><a class="doc-anchor" href="#doc-path-is-rel">#</a> <code>path_is_rel</code></h3>
<p><code>path_is_rel</code> — path manipulation <code>is rel</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p path_is_rel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-path-is-subdirectory">
<h3><a class="doc-anchor" href="#doc-path-is-subdirectory">#</a> <code>path_is_subdirectory</code></h3>
<p><code>path_is_subdirectory(child, parent) → 0|1</code> — 1 if <code>child</code> is inside <code>parent</code> after canonicalisation.</p>
</article>
<article class="doc-entry" id="doc-path-join">
<h3><a class="doc-anchor" href="#doc-path-join">#</a> <code>path_join</code></h3>
<p><code>path_join</code> — path manipulation <code>join</code>. Category: *path helpers*.</p>
<pre><code class="lang-perl">p path_join $x
</code></pre>
</article>
<article class="doc-entry" id="doc-path-join-many">
<h3><a class="doc-anchor" href="#doc-path-join-many">#</a> <code>path_join_many</code></h3>
<p><code>path_join_many(parts) → string</code> — join multiple path segments with the OS separator.</p>
</article>
<article class="doc-entry" id="doc-path-parent">
<h3><a class="doc-anchor" href="#doc-path-parent">#</a> <code>path_parent</code></h3>
<p><code>path_parent</code> — path manipulation <code>parent</code>. Category: *path helpers*.</p>
<pre><code class="lang-perl">p path_parent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-path-reeds-shepp">
<h3><a class="doc-anchor" href="#doc-path-reeds-shepp">#</a> <code>path_reeds_shepp</code></h3>
<p><code>path_reeds_shepp</code> — path manipulation <code>reeds shepp</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p path_reeds_shepp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-path-relative-to">
<h3><a class="doc-anchor" href="#doc-path-relative-to">#</a> <code>path_relative_to</code></h3>
<p><code>path_relative_to(path, base) → string</code> — make <code>path</code> relative to <code>base</code>.</p>
</article>
<article class="doc-entry" id="doc-path-split">
<h3><a class="doc-anchor" href="#doc-path-split">#</a> <code>path_split</code></h3>
<p><code>path_split</code> — path manipulation <code>split</code>. Category: *path helpers*.</p>
<pre><code class="lang-perl">p path_split $x
</code></pre>
</article>
<article class="doc-entry" id="doc-path-stem">
<h3><a class="doc-anchor" href="#doc-path-stem">#</a> <code>path_stem</code></h3>
<p><code>path_stem(path) → string</code> — filename without final extension.</p>
<pre><code class="lang-perl">p path_stem("foo/bar/baz.tar.gz") # "baz.tar"
</code></pre>
</article>
<article class="doc-entry" id="doc-path-strip-prefix">
<h3><a class="doc-anchor" href="#doc-path-strip-prefix">#</a> <code>path_strip_prefix</code></h3>
<p><code>path_strip_prefix</code> — path manipulation <code>strip prefix</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p path_strip_prefix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-path-with-extension">
<h3><a class="doc-anchor" href="#doc-path-with-extension">#</a> <code>path_with_extension</code></h3>
<p><code>path_with_extension(path, ext) → string</code> — replace (or add) the extension.</p>
</article>
<article class="doc-entry" id="doc-path-with-filename">
<h3><a class="doc-anchor" href="#doc-path-with-filename">#</a> <code>path_with_filename</code></h3>
<p><code>path_with_filename(path, name) → string</code> — replace the final filename component.</p>
</article>
<article class="doc-entry" id="doc-pauli-decomposition-2x2">
<h3><a class="doc-anchor" href="#doc-pauli-decomposition-2x2">#</a> <code>pauli_decomposition_2x2</code></h3>
<p><code>pauli_decomposition_2x2</code> — operation <code>pauli decomposition 2x2</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p pauli_decomposition_2x2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pauli-real-part">
<h3><a class="doc-anchor" href="#doc-pauli-real-part">#</a> <code>pauli_real_part</code></h3>
<p><code>pauli_real_part</code> — operation <code>pauli real part</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p pauli_real_part $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pauli-string-expect">
<h3><a class="doc-anchor" href="#doc-pauli-string-expect">#</a> <code>pauli_string_expect</code></h3>
<p><code>pauli_string_expect</code> — operation <code>pauli string expect</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p pauli_string_expect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pauli-y-imag">
<h3><a class="doc-anchor" href="#doc-pauli-y-imag">#</a> <code>pauli_y_imag</code></h3>
<p><code>pauli_y_imag</code> — operation <code>pauli y imag</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p pauli_y_imag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-payback">
<h3><a class="doc-anchor" href="#doc-payback">#</a> <code>payback</code></h3>
<p><code>payback_period($initial, @cashflows)</code> (alias <code>payback</code>) — computes the number of periods to recover initial investment. Returns fractional periods.</p>
<pre><code class="lang-perl">p payback(1000, 300, 400, 500) # 2.6 periods
</code></pre>
</article>
<article class="doc-entry" id="doc-payback-period-simple">
<h3><a class="doc-anchor" href="#doc-payback-period-simple">#</a> <code>payback_period_simple</code></h3>
<p><code>payback_period_simple</code> — operation <code>payback period simple</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p payback_period_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-payback-simple">
<h3><a class="doc-anchor" href="#doc-payback-simple">#</a> <code>payback_simple</code></h3>
<p><code>payback_simple</code> — operation <code>payback simple</code>. Alias for <code>payback_period_simple</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p payback_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-payoff-matrix">
<h3><a class="doc-anchor" href="#doc-payoff-matrix">#</a> <code>payoff_matrix</code></h3>
<p><code>payoff_matrix</code> — operation <code>payoff matrix</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p payoff_matrix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pbeta">
<h3><a class="doc-anchor" href="#doc-pbeta">#</a> <code>pbeta</code></h3>
<p><code>pbeta</code> — beta CDF (regularized incomplete beta). Args: x, a, b.</p>
<pre><code class="lang-perl">p pbeta(0.5, 2, 5) # P(X ≤ 0.5) for Beta(2,5)
</code></pre>
</article>
<article class="doc-entry" id="doc-pbinom">
<h3><a class="doc-anchor" href="#doc-pbinom">#</a> <code>pbinom</code></h3>
<p><code>pbinom</code> — binomial CDF. P(X ≤ k) for Binom(n, p). Args: k, n, p.</p>
<pre><code class="lang-perl">p pbinom(5, 10, 0.5) # P(≤5 heads in 10 flips)
</code></pre>
</article>
<article class="doc-entry" id="doc-pbkdf2-hmac-step">
<h3><a class="doc-anchor" href="#doc-pbkdf2-hmac-step">#</a> <code>pbkdf2_hmac_step</code></h3>
<p><code>pbkdf2_hmac_step</code> — single-step update of <code>pbkdf2 hmac</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p pbkdf2_hmac_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pbool">
<h3><a class="doc-anchor" href="#doc-pbool">#</a> <code>pbool</code></h3>
<p><code>pbool</code> — operation <code>pbool</code>. Alias for <code>parse_bool</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p pbool $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pby">
<h3><a class="doc-anchor" href="#doc-pby">#</a> <code>pby</code></h3>
<p><code>pby</code> — operation <code>pby</code>. Alias for <code>partition_by</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p pby $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pc-case">
<h3><a class="doc-anchor" href="#doc-pc-case">#</a> <code>pc_case</code></h3>
<p><code>pc_case</code> — operation <code>pc case</code>. Alias for <code>pascal_case</code>. Category: *string*.</p>
<pre><code class="lang-perl">p pc_case $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pc-to-au">
<h3><a class="doc-anchor" href="#doc-pc-to-au">#</a> <code>pc_to_au</code></h3>
<p><code>pc_to_au</code> — convert from <code>pc</code> to <code>au</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p pc_to_au $value
</code></pre>
</article>
<article class="doc-entry" id="doc-pc-to-ly">
<h3><a class="doc-anchor" href="#doc-pc-to-ly">#</a> <code>pc_to_ly</code></h3>
<p><code>pc_to_ly</code> — convert from <code>pc</code> to <code>ly</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p pc_to_ly $value
</code></pre>
</article>
<article class="doc-entry" id="doc-pca">
<h3><a class="doc-anchor" href="#doc-pca">#</a> <code>pca</code></h3>
<p><code>prcomp</code> (alias <code>pca</code>) — Principal Component Analysis via eigendecomposition of covariance matrix. Returns eigenvalues (variance explained). Like R's prcomp().</p>
<pre><code class="lang-perl">my @var = @{pca([[1,2],[3,4],[5,6],[7,8]])}
# variance explained by each component
</code></pre>
</article>
<article class="doc-entry" id="doc-pcauchy">
<h3><a class="doc-anchor" href="#doc-pcauchy">#</a> <code>pcauchy</code></h3>
<p><code>pcauchy</code> — Cauchy CDF. P(X ≤ x). Args: x [, location, scale].</p>
<pre><code class="lang-perl">p pcauchy(0, 0, 1) # 0.5
</code></pre>
</article>
<article class="doc-entry" id="doc-pcg32-next">
<h3><a class="doc-anchor" href="#doc-pcg32-next">#</a> <code>pcg32_next</code></h3>
<p><code>pcg32_next(state, inc) → int</code> — PCG32 output for the current state (O'Neill 2014). To iterate, compute the next state as <code>state·6364136223846793005 + inc</code> and call again. <code>inc</code> must be odd; it identifies the PCG stream and does not affect this call's output.</p>
</article>
<article class="doc-entry" id="doc-pcg32-step">
<h3><a class="doc-anchor" href="#doc-pcg32-step">#</a> <code>pcg32_step</code></h3>
<p><code>pcg32_step</code> — single-step update of <code>pcg32</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p pcg32_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pchisq">
<h3><a class="doc-anchor" href="#doc-pchisq">#</a> <code>pchisq</code></h3>
<p><code>pchisq</code> — chi-squared CDF. Args: x, df.</p>
<pre><code class="lang-perl">p pchisq(3.84, 1) # 0.95 (critical value for p=0.05)
</code></pre>
</article>
<article class="doc-entry" id="doc-pcr">
<h3><a class="doc-anchor" href="#doc-pcr">#</a> <code>pcr</code></h3>
<p><code>pcr</code> — operation <code>pcr</code>. Alias for <code>par_csv_read</code>. Category: *data / network*.</p>
<pre><code class="lang-perl">p pcr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pct">
<h3><a class="doc-anchor" href="#doc-pct">#</a> <code>pct</code></h3>
<p><code>pct</code> — operation <code>pct</code>. Alias for <code>percent</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p pct $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pctrank">
<h3><a class="doc-anchor" href="#doc-pctrank">#</a> <code>pctrank</code></h3>
<p><code>pctrank</code> — operation <code>pctrank</code>. Alias for <code>percentile_rank</code>. Category: *statistics (extended)*.</p>
<pre><code class="lang-perl">p pctrank $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pdo-index-step">
<h3><a class="doc-anchor" href="#doc-pdo-index-step">#</a> <code>pdo_index_step</code></h3>
<p><code>pdo_index_step</code> — single-step update of <code>pdo index</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p pdo_index_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-peak-db">
<h3><a class="doc-anchor" href="#doc-peak-db">#</a> <code>peak_db</code></h3>
<p><code>peak_db</code> — operation <code>peak db</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p peak_db $x
</code></pre>
</article>
<article class="doc-entry" id="doc-peak-detect">
<h3><a class="doc-anchor" href="#doc-peak-detect">#</a> <code>peak_detect</code></h3>
<p><code>peak_detect</code> — operation <code>peak detect</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p peak_detect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-peak-widths-at">
<h3><a class="doc-anchor" href="#doc-peak-widths-at">#</a> <code>peak_widths_at</code></h3>
<p><code>peak_widths_at</code> — operation <code>peak widths at</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p peak_widths_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-peaks">
<h3><a class="doc-anchor" href="#doc-peaks">#</a> <code>peaks</code></h3>
<p><code>peaks</code> — operation <code>peaks</code>. Alias for <code>peak_detect</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p peaks $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pearson-hash">
<h3><a class="doc-anchor" href="#doc-pearson-hash">#</a> <code>pearson_hash</code></h3>
<p><code>pearson_hash</code> — hash function of <code>pearson</code>. Alias for <code>pearson_hash_byte</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p pearson_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pearson-hash-byte">
<h3><a class="doc-anchor" href="#doc-pearson-hash-byte">#</a> <code>pearson_hash_byte</code></h3>
<p><code>pearson_hash_byte</code> — operation <code>pearson hash byte</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p pearson_hash_byte $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pearson-skewness-2">
<h3><a class="doc-anchor" href="#doc-pearson-skewness-2">#</a> <code>pearson_skewness_2</code></h3>
<p><code>pearson_skewness_2</code> — operation <code>pearson skewness 2</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p pearson_skewness_2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pearsonr">
<h3><a class="doc-anchor" href="#doc-pearsonr">#</a> <code>pearsonr</code></h3>
<p><code>pearsonr</code> — operation <code>pearsonr</code>. Category: *r / scipy distributions and tests*.</p>
<pre><code class="lang-perl">p pearsonr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-peclet-number-step">
<h3><a class="doc-anchor" href="#doc-peclet-number-step">#</a> <code>peclet_number_step</code></h3>
<p><code>peclet_number_step</code> — single-step update of <code>peclet number</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p peclet_number_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-peek-clj">
<h3><a class="doc-anchor" href="#doc-peek-clj">#</a> <code>peek_clj</code></h3>
<p><code>peek_clj</code> — operation <code>peek clj</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p peek_clj $x
</code></pre>
</article>
<article class="doc-entry" id="doc-peekable">
<h3><a class="doc-anchor" href="#doc-peekable">#</a> <code>peekable</code></h3>
<p><code>peekable</code> — operation <code>peekable</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p peekable $x
</code></pre>
</article>
<article class="doc-entry" id="doc-peeling-step-psi4">
<h3><a class="doc-anchor" href="#doc-peeling-step-psi4">#</a> <code>peeling_step_psi4</code></h3>
<p><code>peeling_step_psi4</code> — operation <code>peeling step psi4</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p peeling_step_psi4 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-peg-choice">
<h3><a class="doc-anchor" href="#doc-peg-choice">#</a> <code>peg_choice</code></h3>
<p><code>peg_choice</code> — operation <code>peg choice</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p peg_choice $x
</code></pre>
</article>
<article class="doc-entry" id="doc-peg-lookahead">
<h3><a class="doc-anchor" href="#doc-peg-lookahead">#</a> <code>peg_lookahead</code></h3>
<p><code>peg_lookahead</code> — operation <code>peg lookahead</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p peg_lookahead $x
</code></pre>
</article>
<article class="doc-entry" id="doc-peg-repeat">
<h3><a class="doc-anchor" href="#doc-peg-repeat">#</a> <code>peg_repeat</code></h3>
<p><code>peg_repeat</code> — operation <code>peg repeat</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p peg_repeat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-peg-seq">
<h3><a class="doc-anchor" href="#doc-peg-seq">#</a> <code>peg_seq</code></h3>
<p><code>peg_seq</code> — operation <code>peg seq</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p peg_seq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-peith">
<h3><a class="doc-anchor" href="#doc-peith">#</a> <code>peith</code></h3>
<p><code>peith</code> — operation <code>peith</code>. Alias for <code>partition_either</code>. Category: *rust iterator methods*.</p>
<pre><code class="lang-perl">p peith $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pell-fundamental">
<h3><a class="doc-anchor" href="#doc-pell-fundamental">#</a> <code>pell_fundamental</code></h3>
<p><code>pell_fundamental</code> — operation <code>pell fundamental</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p pell_fundamental $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pell-nth">
<h3><a class="doc-anchor" href="#doc-pell-nth">#</a> <code>pell_nth</code></h3>
<p><code>pell_nth(n) → int</code> — n-th Pell number <code>P(n) = 2·P(n-1) + P(n-2)</code>.</p>
</article>
<article class="doc-entry" id="doc-pendper">
<h3><a class="doc-anchor" href="#doc-pendper">#</a> <code>pendper</code></h3>
<p><code>pendulum_period($length)</code> (alias <code>pendper</code>) — period T = 2π√(L/g) of a simple pendulum.</p>
<pre><code class="lang-perl">p pendper(1) # ~2.01 s (1 meter pendulum)
p pendper(0.25) # ~1.00 s (grandfather clock)
</code></pre>
</article>
<article class="doc-entry" id="doc-pendulum-freq">
<h3><a class="doc-anchor" href="#doc-pendulum-freq">#</a> <code>pendulum_freq</code></h3>
<p><code>pendulum_freq</code> — operation <code>pendulum freq</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p pendulum_freq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-penrose-diagram-factor">
<h3><a class="doc-anchor" href="#doc-penrose-diagram-factor">#</a> <code>penrose_diagram_factor</code></h3>
<p><code>penrose_diagram_factor</code> — factor of <code>penrose diagram</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p penrose_diagram_factor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pentagonal-number">
<h3><a class="doc-anchor" href="#doc-pentagonal-number">#</a> <code>pentagonal_number</code></h3>
<p><code>pentagonal_number</code> — operation <code>pentagonal number</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p pentagonal_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pentagonal-pyramidal-number">
<h3><a class="doc-anchor" href="#doc-pentagonal-pyramidal-number">#</a> <code>pentagonal_pyramidal_number</code></h3>
<p><code>pentagonal_pyramidal_number</code> — operation <code>pentagonal pyramidal number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p pentagonal_pyramidal_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pentnum">
<h3><a class="doc-anchor" href="#doc-pentnum">#</a> <code>pentnum</code></h3>
<p><code>pentnum</code> — operation <code>pentnum</code>. Alias for <code>pentagonal_number</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p pentnum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-percent">
<h3><a class="doc-anchor" href="#doc-percent">#</a> <code>percent</code></h3>
<p><code>percent</code> — operation <code>percent</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p percent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-percent-decode-url">
<h3><a class="doc-anchor" href="#doc-percent-decode-url">#</a> <code>percent_decode_url</code></h3>
<p><code>percent_decode_url</code> — operation <code>percent decode url</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p percent_decode_url $x
</code></pre>
</article>
<article class="doc-entry" id="doc-percent-encode-full">
<h3><a class="doc-anchor" href="#doc-percent-encode-full">#</a> <code>percent_encode_full</code></h3>
<p><code>percent_encode_full</code> — operation <code>percent encode full</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p percent_encode_full $x
</code></pre>
</article>
<article class="doc-entry" id="doc-percentile">
<h3><a class="doc-anchor" href="#doc-percentile">#</a> <code>percentile</code></h3>
<p><code>percentile</code> — operation <code>percentile</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p percentile $x
</code></pre>
</article>
<article class="doc-entry" id="doc-percentile-cont">
<h3><a class="doc-anchor" href="#doc-percentile-cont">#</a> <code>percentile_cont</code></h3>
<p><code>percentile_cont</code> — operation <code>percentile cont</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p percentile_cont $x
</code></pre>
</article>
<article class="doc-entry" id="doc-percentile-disc">
<h3><a class="doc-anchor" href="#doc-percentile-disc">#</a> <code>percentile_disc</code></h3>
<p><code>percentile_disc</code> — operation <code>percentile disc</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p percentile_disc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-percentile-rank">
<h3><a class="doc-anchor" href="#doc-percentile-rank">#</a> <code>percentile_rank</code></h3>
<p><code>percentile_rank($value, @data)</code> — returns the percentile rank (0-100) of a value within a dataset. Indicates what percentage of the data falls below the given value. Useful for ranking and normalization.</p>
<pre><code class="lang-perl">my @scores = 1:100
p percentile_rank(50, @scores) # ~50
p percentile_rank(90, @scores) # ~90
</code></pre>
</article>
<article class="doc-entry" id="doc-percentrank">
<h3><a class="doc-anchor" href="#doc-percentrank">#</a> <code>percentrank</code></h3>
<p><code>percentrank</code> — operation <code>percentrank</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p percentrank $x
</code></pre>
</article>
<article class="doc-entry" id="doc-perfect-number">
<h3><a class="doc-anchor" href="#doc-perfect-number">#</a> <code>perfect_number</code></h3>
<p><code>perfect_number</code> — operation <code>perfect number</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p perfect_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-perfect-numbers">
<h3><a class="doc-anchor" href="#doc-perfect-numbers">#</a> <code>perfect_numbers</code></h3>
<p><code>perfect_numbers</code> — operation <code>perfect numbers</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p perfect_numbers $x
</code></pre>
</article>
<article class="doc-entry" id="doc-perfnums">
<h3><a class="doc-anchor" href="#doc-perfnums">#</a> <code>perfnums</code></h3>
<p><code>perfnums</code> — operation <code>perfnums</code>. Alias for <code>perfect_numbers</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p perfnums $x
</code></pre>
</article>
<article class="doc-entry" id="doc-perfview">
<h3><a class="doc-anchor" href="#doc-perfview">#</a> <code>perfview</code></h3>
<p><code>perfview</code> (alias <code>pfv</code>) — read the wall-clock perf log written by stryke runs launched with the <code>--record</code> CLI flag (or with <code>STRYKE_RECORD=1</code> in the environment). Every recorded invocation writes one row to <code>~/.stryke/perf.sqlite</code> (path, argv, started_ns, duration_ns, exit_code, version, host, pid, parent_pid). <code>perfview</code> queries that table and returns an arrayref of hashrefs.</p>
<p>No args = top 20 slowest. Options pass as <code>key => value</code> pairs:</p>
<p><code>top => N</code> — limit to N rows (default 20; pass <code>all => 1</code> for no limit) <code>name => "SUB"</code> — substring filter on <code>path</code> <code>re => "REGEX"</code> — regex filter on <code>path</code> (alias: <code>regex</code>) <code>path => "/abs"</code> — exact-match filter on <code>path</code> <code>since => "7d"</code> — only rows newer than 7d / 24h / 30m / 90s / 2w <code>slowest => 1</code> — order by duration desc (default) <code>fastest => 1</code> — order by duration asc <code>recent => 1</code> — order by id desc (most recent first)</p>
<p>From the CLI, <code>s perfview</code> wraps the result in <code>ddump</code> so the table prints directly; from stryke code it composes with <code>grep</code> / <code>dd</code> / <code>to_csv</code> naturally.</p>
<pre><code class="lang-perl"># CLI quick view: top 20 slowest recorded runs
# $ s --record t examples/rosetta/t # record one row per test file
# $ s perfview # show top 20 slowest
# $ s perfview top 5 # top 5
# $ s perfview name rosetta # filter by path substring
# From stryke code:
perfview(top => 10) |> e { p "$_->{duration_ms}ms $_->{path}" }
perfview(name => "rosetta", since => "24h") |> dd
perfview(path => "/abs/path/to/script.stk") |> e { p $_->{duration_ns} }
perfview(all => 1) |> grep { $_->{exit_code} } |> e p # all failed runs
perfview(fastest => 1, top => 5) |> to_csv |> p
</code></pre>
<p>Schema columns returned: <code>id</code>, <code>path</code>, <code>argv</code>, <code>started_ns</code>, <code>duration_ns</code>, <code>duration_ms</code>, <code>exit_code</code>, <code>version</code>, <code>host</code>, <code>pid</code>, <code>parent_pid</code>. Auto-prunes rows older than 90 days every ~1000 inserts. SQLite is in WAL mode so <code>perfview</code> reads don't block concurrent parallel-test inserts.</p>
<p>See also: <code>--record</code> CLI flag, <code>~/.stryke/perf.sqlite</code>, <code>--profile</code> / <code>--flame</code> (per-function profiling within one script — orthogonal to wall-clock per-script recording).</p>
</article>
<article class="doc-entry" id="doc-perihelion-precession">
<h3><a class="doc-anchor" href="#doc-perihelion-precession">#</a> <code>perihelion_precession</code></h3>
<p><code>perihelion_precession</code> — operation <code>perihelion precession</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p perihelion_precession $x
</code></pre>
</article>
<article class="doc-entry" id="doc-perimeter-rectangle">
<h3><a class="doc-anchor" href="#doc-perimeter-rectangle">#</a> <code>perimeter_rectangle</code></h3>
<p><code>perimeter_rectangle</code> — operation <code>perimeter rectangle</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p perimeter_rectangle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-perimeter-triangle">
<h3><a class="doc-anchor" href="#doc-perimeter-triangle">#</a> <code>perimeter_triangle</code></h3>
<p><code>perimeter_triangle</code> — operation <code>perimeter triangle</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p perimeter_triangle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-period-of-string">
<h3><a class="doc-anchor" href="#doc-period-of-string">#</a> <code>period_of_string</code></h3>
<p><code>period_of_string</code> — operation <code>period of string</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p period_of_string $x
</code></pre>
</article>
<article class="doc-entry" id="doc-periodogram-basic">
<h3><a class="doc-anchor" href="#doc-periodogram-basic">#</a> <code>periodogram_basic</code></h3>
<p><code>periodogram_basic</code> — operation <code>periodogram basic</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p periodogram_basic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-perlin-2d">
<h3><a class="doc-anchor" href="#doc-perlin-2d">#</a> <code>perlin_2d</code></h3>
<p><code>perlin_2d(x, y) → number</code> — classic Perlin gradient noise; deterministic per (x,y).</p>
<pre><code class="lang-perl">p perlin_2d(0.5, 0.5)
</code></pre>
</article>
<article class="doc-entry" id="doc-perlin-3d">
<h3><a class="doc-anchor" href="#doc-perlin-3d">#</a> <code>perlin_3d</code></h3>
<p><code>perlin_3d(x, y, z) → number</code> — Ken Perlin's 3D gradient noise: looks up 8 corner gradients of the unit cube, computes dot products with offset vectors, trilinearly interpolates through <code>fade(xf, yf, zf)</code>. Range ~[-1, 1].</p>
</article>
<article class="doc-entry" id="doc-perm">
<h3><a class="doc-anchor" href="#doc-perm">#</a> <code>perm</code></h3>
<p><code>permutations($n, $r)</code> (alias <code>perm</code>) — number of ways to arrange r items from n. Formula: n!/(n-r)!. Order matters.</p>
<pre><code class="lang-perl">p perm(5, 3) # 60 (ways to arrange 3 items from 5)
p perm(10, 2) # 90
</code></pre>
</article>
<article class="doc-entry" id="doc-perm-mul">
<h3><a class="doc-anchor" href="#doc-perm-mul">#</a> <code>perm_mul</code></h3>
<p><code>perm_mul</code> — operation <code>perm mul</code>. Alias for <code>permutation_compose</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p perm_mul $x
</code></pre>
</article>
<article class="doc-entry" id="doc-perm-sign">
<h3><a class="doc-anchor" href="#doc-perm-sign">#</a> <code>perm_sign</code></h3>
<p><code>perm_sign</code> — sign with private key of <code>perm</code>. Alias for <code>permutation_parity</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p perm_sign $x
</code></pre>
</article>
<article class="doc-entry" id="doc-permutation-compose">
<h3><a class="doc-anchor" href="#doc-permutation-compose">#</a> <code>permutation_compose</code></h3>
<p><code>permutation_compose</code> — operation <code>permutation compose</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p permutation_compose $x
</code></pre>
</article>
<article class="doc-entry" id="doc-permutation-order">
<h3><a class="doc-anchor" href="#doc-permutation-order">#</a> <code>permutation_order</code></h3>
<p><code>permutation_order</code> — operation <code>permutation order</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p permutation_order $x
</code></pre>
</article>
<article class="doc-entry" id="doc-permutation-parity">
<h3><a class="doc-anchor" href="#doc-permutation-parity">#</a> <code>permutation_parity</code></h3>
<p><code>permutation_parity</code> — operation <code>permutation parity</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p permutation_parity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-permutation-test">
<h3><a class="doc-anchor" href="#doc-permutation-test">#</a> <code>permutation_test</code></h3>
<p><code>permutation_test(a, b, n_perms=1000, seed=0) → number</code> — two-sided p-value: fraction of label permutations producing a mean-difference ≥ observed.</p>
<pre><code class="lang-perl">p permutation_test(\@group_a, \@group_b, 10000, 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-permute-idx">
<h3><a class="doc-anchor" href="#doc-permute-idx">#</a> <code>permute_idx</code></h3>
<p><code>permute_idx</code> — operation <code>permute idx</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p permute_idx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-perpetuity-value">
<h3><a class="doc-anchor" href="#doc-perpetuity-value">#</a> <code>perpetuity_value</code></h3>
<p><code>perpetuity_value</code> — value of <code>perpetuity</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p perpetuity_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-persian-arithmetic-leap">
<h3><a class="doc-anchor" href="#doc-persian-arithmetic-leap">#</a> <code>persian_arithmetic_leap</code></h3>
<p><code>persian_arithmetic_leap</code> — operation <code>persian arithmetic leap</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p persian_arithmetic_leap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-persist">
<h3><a class="doc-anchor" href="#doc-persist">#</a> <code>persist</code></h3>
<p><code>persist</code> — operation <code>persist</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p persist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-personalized-pagerank">
<h3><a class="doc-anchor" href="#doc-personalized-pagerank">#</a> <code>personalized_pagerank</code></h3>
<p><code>personalized_pagerank</code> — operation <code>personalized pagerank</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p personalized_pagerank $x
</code></pre>
</article>
<article class="doc-entry" id="doc-petersen-estimator">
<h3><a class="doc-anchor" href="#doc-petersen-estimator">#</a> <code>petersen_estimator</code></h3>
<p><code>petersen_estimator</code> — operation <code>petersen estimator</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p petersen_estimator $x
</code></pre>
</article>
<article class="doc-entry" id="doc-peukert-capacity">
<h3><a class="doc-anchor" href="#doc-peukert-capacity">#</a> <code>peukert_capacity</code></h3>
<p><code>peukert_capacity</code> — operation <code>peukert capacity</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p peukert_capacity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-peukert-exponent-fit">
<h3><a class="doc-anchor" href="#doc-peukert-exponent-fit">#</a> <code>peukert_exponent_fit</code></h3>
<p><code>peukert_exponent_fit</code> — operation <code>peukert exponent fit</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p peukert_exponent_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pexp">
<h3><a class="doc-anchor" href="#doc-pexp">#</a> <code>pexp</code></h3>
<p><code>pexp</code> — exponential CDF. P(X ≤ x) for Exp(rate). Args: x, rate.</p>
<pre><code class="lang-perl">p pexp(1, 1) # 0.6321 (1 - e^-1)
p pexp(5, 0.5) # P(wait ≤ 5 with avg wait 2)
</code></pre>
</article>
<article class="doc-entry" id="doc-pf">
<h3><a class="doc-anchor" href="#doc-pf">#</a> <code>pf</code></h3>
<p><code>pf</code> — F-distribution CDF. Args: x, d1, d2.</p>
<pre><code class="lang-perl">p pf(4.0, 5, 10) # P(F ≤ 4) for F(5,10)
</code></pre>
</article>
<article class="doc-entry" id="doc-pfact">
<h3><a class="doc-anchor" href="#doc-pfact">#</a> <code>pfact</code></h3>
<p><code>pfact</code> — operation <code>pfact</code>. Alias for <code>prime_factors</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p pfact $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pfadd">
<h3><a class="doc-anchor" href="#doc-pfadd">#</a> <code>pfadd</code></h3>
<p><code>pfadd</code> — operation <code>pfadd</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p pfadd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pfcount">
<h3><a class="doc-anchor" href="#doc-pfcount">#</a> <code>pfcount</code></h3>
<p><code>pfcount</code> — operation <code>pfcount</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p pfcount $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pflt">
<h3><a class="doc-anchor" href="#doc-pflt">#</a> <code>pflt</code></h3>
<p><code>pflt</code> — operation <code>pflt</code>. Alias for <code>parse_float</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p pflt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pfreq">
<h3><a class="doc-anchor" href="#doc-pfreq">#</a> <code>pfreq</code></h3>
<p><code>pfreq</code> — operation <code>pfreq</code>. Alias for <code>pfrequencies</code>. Category: *pipeline / string helpers*.</p>
<pre><code class="lang-perl">p pfreq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pfrequencies">
<h3><a class="doc-anchor" href="#doc-pfrequencies">#</a> <code>pfrequencies</code></h3>
<p><code>pfrequencies</code> — operation <code>pfrequencies</code>. Category: *pipeline / string helpers*.</p>
<pre><code class="lang-perl">p pfrequencies $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pfrq">
<h3><a class="doc-anchor" href="#doc-pfrq">#</a> <code>pfrq</code></h3>
<p><code>pfrq</code> — operation <code>pfrq</code>. Alias for <code>pfrequencies</code>. Category: *pipeline / string helpers*.</p>
<pre><code class="lang-perl">p pfrq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pft">
<h3><a class="doc-anchor" href="#doc-pft">#</a> <code>pft</code></h3>
<p><code>pft</code> — operation <code>pft</code>. Alias for <code>par_fetch</code>. Category: *data / network*.</p>
<pre><code class="lang-perl">p pft $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pga-attenuation">
<h3><a class="doc-anchor" href="#doc-pga-attenuation">#</a> <code>pga_attenuation</code></h3>
<p><code>pga_attenuation</code> — operation <code>pga attenuation</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p pga_attenuation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pgamma">
<h3><a class="doc-anchor" href="#doc-pgamma">#</a> <code>pgamma</code></h3>
<p><code>pgamma</code> — gamma CDF. Args: x, shape [, scale].</p>
<pre><code class="lang-perl">p pgamma(2, 2, 1) # P(X ≤ 2) for Gamma(2,1)
</code></pre>
</article>
<article class="doc-entry" id="doc-ph-at-isoelectric">
<h3><a class="doc-anchor" href="#doc-ph-at-isoelectric">#</a> <code>ph_at_isoelectric</code></h3>
<p><code>ph_at_isoelectric</code> — operation <code>ph at isoelectric</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ph_at_isoelectric $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ph-from-h">
<h3><a class="doc-anchor" href="#doc-ph-from-h">#</a> <code>ph_from_h</code></h3>
<p><code>ph_from_h</code> — operation <code>ph from h</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p ph_from_h $x
</code></pre>
</article>
<article class="doc-entry" id="doc-phase-flip-prob">
<h3><a class="doc-anchor" href="#doc-phase-flip-prob">#</a> <code>phase_flip_prob</code></h3>
<p><code>phase_flip_prob</code> — operation <code>phase flip prob</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p phase_flip_prob $x
</code></pre>
</article>
<article class="doc-entry" id="doc-phase-spectrum">
<h3><a class="doc-anchor" href="#doc-phase-spectrum">#</a> <code>phase_spectrum</code></h3>
<p><code>phase_spectrum(\@signal)</code> — computes the phase angle (in radians) at each frequency bin from the DFT.</p>
<pre><code class="lang-perl">my $phases = phase_spectrum(\@signal)
</code></pre>
</article>
<article class="doc-entry" id="doc-phaser-simple">
<h3><a class="doc-anchor" href="#doc-phaser-simple">#</a> <code>phaser_simple</code></h3>
<p><code>phaser_simple(signal, rate=0.5, depth=1, sr=44100) → array</code> — 4-stage all-pass cascade with LFO-modulated coefficient. Each stage runs <code>y[n] = -a·x[n] + x[n-1] + a·y[n-1]</code> where <code>a = depth·sin(2π·rate·t)</code>. Output is 50/50 wet/dry mix.</p>
</article>
<article class="doc-entry" id="doc-phasespec">
<h3><a class="doc-anchor" href="#doc-phasespec">#</a> <code>phasespec</code></h3>
<p><code>phasespec</code> — operation <code>phasespec</code>. Alias for <code>phase_spectrum</code>. Category: *dsp / signal (extended)*.</p>
<pre><code class="lang-perl">p phasespec $x
</code></pre>
</article>
<article class="doc-entry" id="doc-phillips-perron">
<h3><a class="doc-anchor" href="#doc-phillips-perron">#</a> <code>phillips_perron</code></h3>
<p><code>phillips_perron</code> — operation <code>phillips perron</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p phillips_perron $x
</code></pre>
</article>
<article class="doc-entry" id="doc-phonedigit">
<h3><a class="doc-anchor" href="#doc-phonedigit">#</a> <code>phonedigit</code></h3>
<p><code>phonedigit</code> — operation <code>phonedigit</code>. Alias for <code>phonetic_digit</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p phonedigit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-phonetic-digit">
<h3><a class="doc-anchor" href="#doc-phonetic-digit">#</a> <code>phonetic_digit</code></h3>
<p><code>phonetic_digit</code> — operation <code>phonetic digit</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p phonetic_digit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-phonex">
<h3><a class="doc-anchor" href="#doc-phonex">#</a> <code>phonex</code></h3>
<p><code>phonex(name) → string</code> — Phonex (Lait & Randell) phonetic key; improves Soundex by stripping silent leads.</p>
<pre><code class="lang-perl">p phonex("Robinson")
</code></pre>
</article>
<article class="doc-entry" id="doc-photocurrent-density">
<h3><a class="doc-anchor" href="#doc-photocurrent-density">#</a> <code>photocurrent_density</code></h3>
<p><code>photocurrent_density</code> — operation <code>photocurrent density</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p photocurrent_density $x
</code></pre>
</article>
<article class="doc-entry" id="doc-photon-energy">
<h3><a class="doc-anchor" href="#doc-photon-energy">#</a> <code>photon_energy</code></h3>
<p><code>photon_energy($frequency)</code> (alias <code>photonenergy</code>) — energy E = hf (Joules) of a photon.</p>
<pre><code class="lang-perl">p photonenergy(5e14) # ~3.3e-19 J (visible light)
</code></pre>
</article>
<article class="doc-entry" id="doc-photon-energy-freq">
<h3><a class="doc-anchor" href="#doc-photon-energy-freq">#</a> <code>photon_energy_freq</code></h3>
<p><code>photon_energy_freq</code> — operation <code>photon energy freq</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p photon_energy_freq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-photon-energy-lambda">
<h3><a class="doc-anchor" href="#doc-photon-energy-lambda">#</a> <code>photon_energy_lambda</code></h3>
<p><code>photon_energy_lambda</code> — operation <code>photon energy lambda</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p photon_energy_lambda $x
</code></pre>
</article>
<article class="doc-entry" id="doc-photon-energy-wavelength">
<h3><a class="doc-anchor" href="#doc-photon-energy-wavelength">#</a> <code>photon_energy_wavelength</code></h3>
<p><code>photon_energy_wavelength</code> — operation <code>photon energy wavelength</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p photon_energy_wavelength $x
</code></pre>
</article>
<article class="doc-entry" id="doc-photon-sphere-radius">
<h3><a class="doc-anchor" href="#doc-photon-sphere-radius">#</a> <code>photon_sphere_radius</code></h3>
<p><code>photon_sphere_radius</code> — operation <code>photon sphere radius</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p photon_sphere_radius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-photonlambda">
<h3><a class="doc-anchor" href="#doc-photonlambda">#</a> <code>photonlambda</code></h3>
<p><code>photonlambda</code> — operation <code>photonlambda</code>. Alias for <code>photon_energy_wavelength</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p photonlambda $x
</code></pre>
</article>
<article class="doc-entry" id="doc-physics-apply-force">
<h3><a class="doc-anchor" href="#doc-physics-apply-force">#</a> <code>physics_apply_force</code></h3>
<p><code>physics_apply_force</code> — operation <code>physics apply force</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p physics_apply_force $x
</code></pre>
</article>
<article class="doc-entry" id="doc-physics-apply-impulse">
<h3><a class="doc-anchor" href="#doc-physics-apply-impulse">#</a> <code>physics_apply_impulse</code></h3>
<p><code>physics_apply_impulse</code> — operation <code>physics apply impulse</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p physics_apply_impulse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-physics-collide-aabb">
<h3><a class="doc-anchor" href="#doc-physics-collide-aabb">#</a> <code>physics_collide_aabb</code></h3>
<p><code>physics_collide_aabb</code> — operation <code>physics collide aabb</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p physics_collide_aabb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-physics-collide-sphere">
<h3><a class="doc-anchor" href="#doc-physics-collide-sphere">#</a> <code>physics_collide_sphere</code></h3>
<p><code>physics_collide_sphere</code> — operation <code>physics collide sphere</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p physics_collide_sphere $x
</code></pre>
</article>
<article class="doc-entry" id="doc-physics-raycast">
<h3><a class="doc-anchor" href="#doc-physics-raycast">#</a> <code>physics_raycast</code></h3>
<p><code>physics_raycast</code> — operation <code>physics raycast</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p physics_raycast $x
</code></pre>
</article>
<article class="doc-entry" id="doc-physics-step">
<h3><a class="doc-anchor" href="#doc-physics-step">#</a> <code>physics_step</code></h3>
<p><code>physics_step</code> — single-step update of <code>physics</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p physics_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pi">
<h3><a class="doc-anchor" href="#doc-pi">#</a> <code>pi</code></h3>
<p><code>pi</code> — operation <code>pi</code>. Category: *constants*.</p>
<pre><code class="lang-perl">p pi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pi-step-size">
<h3><a class="doc-anchor" href="#doc-pi-step-size">#</a> <code>pi_step_size</code></h3>
<p><code>pi_step_size</code> — operation <code>pi step size</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p pi_step_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pick">
<h3><a class="doc-anchor" href="#doc-pick">#</a> <code>pick</code></h3>
<p><code>pick</code> — operation <code>pick</code>. Alias for <code>pick_keys</code>. Category: *hash ops*.</p>
<pre><code class="lang-perl">p pick $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pick-keys">
<h3><a class="doc-anchor" href="#doc-pick-keys">#</a> <code>pick_keys</code></h3>
<p><code>pick_keys</code> — operation <code>pick keys</code>. Category: *hash ops*.</p>
<pre><code class="lang-perl">p pick_keys $x
</code></pre>
</article>
<article class="doc-entry" id="doc-picks-theorem">
<h3><a class="doc-anchor" href="#doc-picks-theorem">#</a> <code>picks_theorem</code></h3>
<p><code>picks_theorem</code> — operation <code>picks theorem</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p picks_theorem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pid">
<h3><a class="doc-anchor" href="#doc-pid">#</a> <code>pid</code></h3>
<p><code>pid</code> — operation <code>pid</code>. Category: *system introspection*.</p>
<pre><code class="lang-perl">p pid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pid-anti-windup">
<h3><a class="doc-anchor" href="#doc-pid-anti-windup">#</a> <code>pid_anti_windup</code></h3>
<p><code>pid_anti_windup</code> — operation <code>pid anti windup</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p pid_anti_windup $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pid-ziegler-nichols">
<h3><a class="doc-anchor" href="#doc-pid-ziegler-nichols">#</a> <code>pid_ziegler_nichols</code></h3>
<p><code>pid_ziegler_nichols</code> — operation <code>pid ziegler nichols</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p pid_ziegler_nichols $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pielou-evenness">
<h3><a class="doc-anchor" href="#doc-pielou-evenness">#</a> <code>pielou_evenness</code></h3>
<p><code>pielou_evenness</code> — operation <code>pielou evenness</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p pielou_evenness $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pig-latin">
<h3><a class="doc-anchor" href="#doc-pig-latin">#</a> <code>pig_latin</code></h3>
<p><code>pig_latin</code> — operation <code>pig latin</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p pig_latin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-piglat">
<h3><a class="doc-anchor" href="#doc-piglat">#</a> <code>piglat</code></h3>
<p><code>piglat</code> — operation <code>piglat</code>. Alias for <code>pig_latin</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p piglat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pin">
<h3><a class="doc-anchor" href="#doc-pin">#</a> <code>pin</code></h3>
<p><code>pin</code> — operation <code>pin</code>. Alias for <code>fire_and_forget</code>. Category: *stress testing*.</p>
<pre><code class="lang-perl">p pin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pint">
<h3><a class="doc-anchor" href="#doc-pint">#</a> <code>pint</code></h3>
<p><code>pint</code> — operation <code>pint</code>. Alias for <code>parse_int</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p pint $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pipe-pressure-drop">
<h3><a class="doc-anchor" href="#doc-pipe-pressure-drop">#</a> <code>pipe_pressure_drop</code></h3>
<p><code>pipe_pressure_drop</code> — operation <code>pipe pressure drop</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p pipe_pressure_drop $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pipes">
<h3><a class="doc-anchor" href="#doc-pipes">#</a> <code>pipes</code></h3>
<p><code>pipes</code> — operation <code>pipes</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p pipes $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pivot-points">
<h3><a class="doc-anchor" href="#doc-pivot-points">#</a> <code>pivot_points</code></h3>
<p><code>pivot_points(high, low, close) → hash</code> — classic floor-trader pivots. Returns <code>{pivot, r1, r2, s1, s2}</code> where <code>pivot = (h+l+c)/3</code>.</p>
<pre><code class="lang-perl">p pivot_points(110, 95, 100)
</code></pre>
</article>
<article class="doc-entry" id="doc-pivoted-cholesky-var">
<h3><a class="doc-anchor" href="#doc-pivoted-cholesky-var">#</a> <code>pivoted_cholesky_var</code></h3>
<p><code>pivoted_cholesky_var</code> — variance of <code>pivoted cholesky</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p pivoted_cholesky_var $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pka-from-ka">
<h3><a class="doc-anchor" href="#doc-pka-from-ka">#</a> <code>pka_from_ka</code></h3>
<p><code>pka_from_ka</code> — operation <code>pka from ka</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p pka_from_ka $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pkb-to-kb">
<h3><a class="doc-anchor" href="#doc-pkb-to-kb">#</a> <code>pkb_to_kb</code></h3>
<p><code>pkb_to_kb</code> — convert from <code>pkb</code> to <code>kb</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p pkb_to_kb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-pkc">
<h3><a class="doc-anchor" href="#doc-pkc">#</a> <code>pkc</code></h3>
<p><code>pkc</code> — operation <code>pkc</code>. Alias for <code>peek_clj</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p pkc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pkcs7-pad">
<h3><a class="doc-anchor" href="#doc-pkcs7-pad">#</a> <code>pkcs7_pad</code></h3>
<p><code>pkcs7_pad</code> — operation <code>pkcs7 pad</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p pkcs7_pad $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pkcs7-unpad">
<h3><a class="doc-anchor" href="#doc-pkcs7-unpad">#</a> <code>pkcs7_unpad</code></h3>
<p><code>pkcs7_unpad</code> — operation <code>pkcs7 unpad</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p pkcs7_unpad $x
</code></pre>
</article>
<article class="doc-entry" id="doc-plactic-class-size">
<h3><a class="doc-anchor" href="#doc-plactic-class-size">#</a> <code>plactic_class_size</code></h3>
<p><code>plactic_class_size</code> — operation <code>plactic class size</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p plactic_class_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-planck">
<h3><a class="doc-anchor" href="#doc-planck">#</a> <code>planck</code></h3>
<p><code>planck</code> — operation <code>planck</code>. Category: *math / physics constants*.</p>
<pre><code class="lang-perl">p planck $x
</code></pre>
</article>
<article class="doc-entry" id="doc-planck-const-h">
<h3><a class="doc-anchor" href="#doc-planck-const-h">#</a> <code>planck_const_h</code></h3>
<p><code>planck_const_h</code> — operation <code>planck const h</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p planck_const_h $x
</code></pre>
</article>
<article class="doc-entry" id="doc-planck-constant">
<h3><a class="doc-anchor" href="#doc-planck-constant">#</a> <code>planck_constant</code></h3>
<p><code>planck_constant</code> — operation <code>planck constant</code>. Category: *constants*.</p>
<pre><code class="lang-perl">p planck_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-planck-energy">
<h3><a class="doc-anchor" href="#doc-planck-energy">#</a> <code>planck_energy</code></h3>
<p><code>planck_energy</code> — operation <code>planck energy</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p planck_energy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-planck-mass">
<h3><a class="doc-anchor" href="#doc-planck-mass">#</a> <code>planck_mass</code></h3>
<p><code>planck_mass</code> — operation <code>planck mass</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p planck_mass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-planck-spectral-radiance">
<h3><a class="doc-anchor" href="#doc-planck-spectral-radiance">#</a> <code>planck_spectral_radiance</code></h3>
<p><code>planck_spectral_radiance</code> — operation <code>planck spectral radiance</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p planck_spectral_radiance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-planck-temperature">
<h3><a class="doc-anchor" href="#doc-planck-temperature">#</a> <code>planck_temperature</code></h3>
<p><code>planck_temperature</code> — operation <code>planck temperature</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p planck_temperature $x
</code></pre>
</article>
<article class="doc-entry" id="doc-planck-time">
<h3><a class="doc-anchor" href="#doc-planck-time">#</a> <code>planck_time</code></h3>
<p><code>planck_time</code> — operation <code>planck time</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p planck_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-plane-distance-to-point">
<h3><a class="doc-anchor" href="#doc-plane-distance-to-point">#</a> <code>plane_distance_to_point</code></h3>
<p><code>plane_distance_to_point(point, normal, plane_point) → number</code> — signed perpendicular distance.</p>
</article>
<article class="doc-entry" id="doc-plane-normalize">
<h3><a class="doc-anchor" href="#doc-plane-normalize">#</a> <code>plane_normalize</code></h3>
<p><code>plane_normalize(normal) → [x,y,z]</code> — unit-length plane normal.</p>
</article>
<article class="doc-entry" id="doc-plastic">
<h3><a class="doc-anchor" href="#doc-plastic">#</a> <code>plastic</code></h3>
<p><code>plastic</code> — operation <code>plastic</code>. Alias for <code>plastic_number</code>. Category: *math constants*.</p>
<pre><code class="lang-perl">p plastic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-plastic-number">
<h3><a class="doc-anchor" href="#doc-plastic-number">#</a> <code>plastic_number</code></h3>
<p><code>plastic_number</code> — operation <code>plastic number</code>. Category: *math constants*.</p>
<pre><code class="lang-perl">p plastic_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-plate-reverb-simple">
<h3><a class="doc-anchor" href="#doc-plate-reverb-simple">#</a> <code>plate_reverb_simple</code></h3>
<p><code>plate_reverb_simple</code> — operation <code>plate reverb simple</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p plate_reverb_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-plethystic-substitution-value">
<h3><a class="doc-anchor" href="#doc-plethystic-substitution-value">#</a> <code>plethystic_substitution_value</code></h3>
<p><code>plethystic_substitution_value</code> — value of <code>plethystic substitution</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p plethystic_substitution_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-plnorm">
<h3><a class="doc-anchor" href="#doc-plnorm">#</a> <code>plnorm</code></h3>
<p><code>plnorm</code> — log-normal CDF. P(X ≤ x) for LogN(mu, sigma). Args: x, mu, sigma.</p>
<pre><code class="lang-perl">p plnorm(1, 0, 1) # 0.5 (median of LogN(0,1))
</code></pre>
</article>
<article class="doc-entry" id="doc-plur">
<h3><a class="doc-anchor" href="#doc-plur">#</a> <code>plur</code></h3>
<p><code>plur</code> — operation <code>plur</code>. Alias for <code>pluralize</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p plur $x
</code></pre>
</article>
<article class="doc-entry" id="doc-plurality-winner-step">
<h3><a class="doc-anchor" href="#doc-plurality-winner-step">#</a> <code>plurality_winner_step</code></h3>
<p><code>plurality_winner_step</code> — single-step update of <code>plurality winner</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p plurality_winner_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pluralize">
<h3><a class="doc-anchor" href="#doc-pluralize">#</a> <code>pluralize</code></h3>
<p><code>pluralize</code> — operation <code>pluralize</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p pluralize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pluralize-simple">
<h3><a class="doc-anchor" href="#doc-pluralize-simple">#</a> <code>pluralize_simple</code></h3>
<p><code>pluralize_simple</code> — operation <code>pluralize simple</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p pluralize_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-plus-polarization-amp">
<h3><a class="doc-anchor" href="#doc-plus-polarization-amp">#</a> <code>plus_polarization_amp</code></h3>
<p><code>plus_polarization_amp</code> — operation <code>plus polarization amp</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p plus_polarization_amp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pmass">
<h3><a class="doc-anchor" href="#doc-pmass">#</a> <code>pmass</code></h3>
<p><code>pmass</code> — operation <code>pmass</code>. Alias for <code>proton_mass</code>. Category: *constants*.</p>
<pre><code class="lang-perl">p pmass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pmt">
<h3><a class="doc-anchor" href="#doc-pmt">#</a> <code>pmt</code></h3>
<p><code>pmt($rate, $nper, $pv)</code> — computes the periodic payment for a loan given interest rate, number of periods, and present value. Standard amortization formula.</p>
<pre><code class="lang-perl"># $100k loan, 5% annual rate, 30 years
p pmt(0.05/12, 360, 100000) # ~$537/month
</code></pre>
</article>
<article class="doc-entry" id="doc-png-header-read">
<h3><a class="doc-anchor" href="#doc-png-header-read">#</a> <code>png_header_read</code></h3>
<p><code>png_header_read(hex_bytes) → hash</code> — parse PNG IHDR → <code>{format, width, height, bit_depth, color_type}</code>.</p>
</article>
<article class="doc-entry" id="doc-pnorm">
<h3><a class="doc-anchor" href="#doc-pnorm">#</a> <code>pnorm</code></h3>
<p><code>pnorm</code> — normal CDF. P(X ≤ x) for N(mu, sigma). Args: x [, mu, sigma]. Default standard normal.</p>
<pre><code class="lang-perl">p pnorm(0) # 0.5
p pnorm(1.96) # 0.975
p pnorm(100, 90, 15) # z-score for IQ 100
</code></pre>
</article>
<article class="doc-entry" id="doc-pochhammer">
<h3><a class="doc-anchor" href="#doc-pochhammer">#</a> <code>pochhammer</code></h3>
<p><code>pochhammer</code> — operation <code>pochhammer</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p pochhammer $x
</code></pre>
</article>
<article class="doc-entry" id="doc-poh-from-oh">
<h3><a class="doc-anchor" href="#doc-poh-from-oh">#</a> <code>poh_from_oh</code></h3>
<p><code>poh_from_oh</code> — operation <code>poh from oh</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p poh_from_oh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-poincare-duality">
<h3><a class="doc-anchor" href="#doc-poincare-duality">#</a> <code>poincare_duality</code></h3>
<p><code>poincare_duality</code> — operation <code>poincare duality</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p poincare_duality $x
</code></pre>
</article>
<article class="doc-entry" id="doc-poincare-polynomial-eval">
<h3><a class="doc-anchor" href="#doc-poincare-polynomial-eval">#</a> <code>poincare_polynomial_eval</code></h3>
<p><code>poincare_polynomial_eval</code> — operation <code>poincare polynomial eval</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p poincare_polynomial_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-point-angle">
<h3><a class="doc-anchor" href="#doc-point-angle">#</a> <code>point_angle</code></h3>
<p><code>point_angle</code> — operation <code>point angle</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p point_angle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-point-distance">
<h3><a class="doc-anchor" href="#doc-point-distance">#</a> <code>point_distance</code></h3>
<p><code>point_distance</code> — distance / dissimilarity metric of <code>point</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p point_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-point-in-polygon">
<h3><a class="doc-anchor" href="#doc-point-in-polygon">#</a> <code>point_in_polygon</code></h3>
<p><code>point_in_polygon($x, $y, @polygon)</code> (alias <code>pip</code>) — tests if a point lies inside a polygon. Polygon is given as flat list [x1,y1,x2,y2,...]. Returns 1 if inside, 0 if outside. Uses ray-casting algorithm.</p>
<pre><code class="lang-perl">my @square = (0,0, 4,0, 4,4, 0,4)
p pip(2, 2, @square) # 1 (inside)
p pip(5, 5, @square) # 0 (outside)
</code></pre>
</article>
<article class="doc-entry" id="doc-point-in-polygon-ray">
<h3><a class="doc-anchor" href="#doc-point-in-polygon-ray">#</a> <code>point_in_polygon_ray</code></h3>
<p><code>point_in_polygon_ray</code> — operation <code>point in polygon ray</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p point_in_polygon_ray $x
</code></pre>
</article>
<article class="doc-entry" id="doc-point-in-polygon-winding">
<h3><a class="doc-anchor" href="#doc-point-in-polygon-winding">#</a> <code>point_in_polygon_winding</code></h3>
<p><code>point_in_polygon_winding</code> — operation <code>point in polygon winding</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p point_in_polygon_winding $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pointer-width">
<h3><a class="doc-anchor" href="#doc-pointer-width">#</a> <code>pointer_width</code></h3>
<p><code>pointer_width</code> — pointer width in bits: <code>32</code> or <code>64</code>. Compile-time constant.</p>
<pre><code class="lang-perl">p pointer_width # 64
</code></pre>
</article>
<article class="doc-entry" id="doc-poisson">
<h3><a class="doc-anchor" href="#doc-poisson">#</a> <code>poisson</code></h3>
<p><code>poisson_pmf($k, $lambda)</code> (alias <code>poisson</code>) — Poisson probability mass function. P(X=k) for events with rate λ.</p>
<pre><code class="lang-perl">p poisson(3, 5) # P(X=3) when avg rate is 5
</code></pre>
</article>
<article class="doc-entry" id="doc-poisson-boltzmann-step">
<h3><a class="doc-anchor" href="#doc-poisson-boltzmann-step">#</a> <code>poisson_boltzmann_step</code></h3>
<p><code>poisson_boltzmann_step</code> — single-step update of <code>poisson boltzmann</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p poisson_boltzmann_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-poisson-brackets">
<h3><a class="doc-anchor" href="#doc-poisson-brackets">#</a> <code>poisson_brackets</code></h3>
<p><code>poisson_brackets(df_dq, df_dp, dg_dq, dg_dp) → number</code> — 1D <code>{f, g} = ∂f/∂q · ∂g/∂p - ∂f/∂p · ∂g/∂q</code>.</p>
</article>
<article class="doc-entry" id="doc-poisson-photon-pmf">
<h3><a class="doc-anchor" href="#doc-poisson-photon-pmf">#</a> <code>poisson_photon_pmf</code></h3>
<p><code>poisson_photon_pmf</code> — operation <code>poisson photon pmf</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p poisson_photon_pmf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polar-to-cartesian">
<h3><a class="doc-anchor" href="#doc-polar-to-cartesian">#</a> <code>polar_to_cartesian</code></h3>
<p><code>polar_to_cartesian</code> — convert from <code>polar</code> to <code>cartesian</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p polar_to_cartesian $value
</code></pre>
</article>
<article class="doc-entry" id="doc-polar-vortex-radius">
<h3><a class="doc-anchor" href="#doc-polar-vortex-radius">#</a> <code>polar_vortex_radius</code></h3>
<p><code>polar_vortex_radius</code> — operation <code>polar vortex radius</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p polar_vortex_radius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-policy-iteration-step">
<h3><a class="doc-anchor" href="#doc-policy-iteration-step">#</a> <code>policy_iteration_step</code></h3>
<p><code>policy_iteration_step</code> — single-step update of <code>policy iteration</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p policy_iteration_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pollard-p-minus-1">
<h3><a class="doc-anchor" href="#doc-pollard-p-minus-1">#</a> <code>pollard_p_minus_1</code></h3>
<p><code>pollard_p_minus_1</code> — operation <code>pollard p minus 1</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p pollard_p_minus_1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-poly1305-block-step">
<h3><a class="doc-anchor" href="#doc-poly1305-block-step">#</a> <code>poly1305_block_step</code></h3>
<p><code>poly1305_block_step</code> — single-step update of <code>poly1305 block</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p poly1305_block_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-poly-eval">
<h3><a class="doc-anchor" href="#doc-poly-eval">#</a> <code>poly_eval</code></h3>
<p><code>poly_eval</code> (alias <code>polyval</code>) evaluates a polynomial c0 + c1·x + c2·x² + ... using Horner's method.</p>
<pre><code class="lang-perl">p polyval([1, 0, 1], 3) # 1 + 0*3 + 1*9 = 10
</code></pre>
</article>
<article class="doc-entry" id="doc-polyarea">
<h3><a class="doc-anchor" href="#doc-polyarea">#</a> <code>polyarea</code></h3>
<p><code>polyarea</code> — operation <code>polyarea</code>. Alias for <code>polygon_area</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p polyarea $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polyfit">
<h3><a class="doc-anchor" href="#doc-polyfit">#</a> <code>polyfit</code></h3>
<p><code>polynomial_fit</code> (alias <code>polyfit</code>) performs least-squares polynomial fitting. Returns coefficients [c0, c1, ..., cn].</p>
<pre><code class="lang-perl">my $c = polyfit([0,1,2,3], [1,3,5,7], 1) # linear fit
</code></pre>
</article>
<article class="doc-entry" id="doc-polyfit-rmse">
<h3><a class="doc-anchor" href="#doc-polyfit-rmse">#</a> <code>polyfit_rmse</code></h3>
<p><code>polyfit_rmse</code> — operation <code>polyfit rmse</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p polyfit_rmse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygamma">
<h3><a class="doc-anchor" href="#doc-polygamma">#</a> <code>polygamma</code></h3>
<p><code>polygamma</code> — operation <code>polygamma</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p polygamma $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-area">
<h3><a class="doc-anchor" href="#doc-polygon-area">#</a> <code>polygon_area</code></h3>
<p><code>polygon_area</code> — 2D polygon op <code>area</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p polygon_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-area-signed">
<h3><a class="doc-anchor" href="#doc-polygon-area-signed">#</a> <code>polygon_area_signed</code></h3>
<p><code>polygon_area_signed</code> — 2D polygon op <code>area signed</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p polygon_area_signed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-contains-point">
<h3><a class="doc-anchor" href="#doc-polygon-contains-point">#</a> <code>polygon_contains_point</code></h3>
<p><code>polygon_contains_point</code> — 2D polygon op <code>contains point</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p polygon_contains_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-convex">
<h3><a class="doc-anchor" href="#doc-polygon-convex">#</a> <code>polygon_convex</code></h3>
<p><code>polygon_convex</code> — 2D polygon op <code>convex</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p polygon_convex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-convex-hull-2d">
<h3><a class="doc-anchor" href="#doc-polygon-convex-hull-2d">#</a> <code>polygon_convex_hull_2d</code></h3>
<p><code>polygon_convex_hull_2d</code> — 2D polygon op <code>convex hull 2d</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p polygon_convex_hull_2d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-convex-q">
<h3><a class="doc-anchor" href="#doc-polygon-convex-q">#</a> <code>polygon_convex_q</code></h3>
<p><code>polygon_convex_q</code> — 2D polygon op <code>convex q</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p polygon_convex_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-inflate">
<h3><a class="doc-anchor" href="#doc-polygon-inflate">#</a> <code>polygon_inflate</code></h3>
<p><code>polygon_inflate</code> — 2D polygon op <code>inflate</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p polygon_inflate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-is-convex">
<h3><a class="doc-anchor" href="#doc-polygon-is-convex">#</a> <code>polygon_is_convex</code></h3>
<p><code>polygon_is_convex</code> — 2D polygon op <code>is convex</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p polygon_is_convex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-offset">
<h3><a class="doc-anchor" href="#doc-polygon-offset">#</a> <code>polygon_offset</code></h3>
<p><code>polygon_offset(points, d=1) → array</code> — perpendicular-distance offset using the corner-bisector formula <code>vertex + d·(n1 + n2)/(1 + n1·n2)</code>, where <code>n1</code>, <code>n2</code> are the outward unit normals of the adjacent edges. Gives an exact perpendicular offset (not just <code>d</code>·bisector_dir); falls back to bisector direction when <code>1 + n1·n2 ≈ 0</code>.</p>
</article>
<article class="doc-entry" id="doc-polygon-orientation">
<h3><a class="doc-anchor" href="#doc-polygon-orientation">#</a> <code>polygon_orientation</code></h3>
<p><code>polygon_orientation</code> — 2D polygon op <code>orientation</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p polygon_orientation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-perimeter">
<h3><a class="doc-anchor" href="#doc-polygon-perimeter">#</a> <code>polygon_perimeter</code></h3>
<p><code>polygon_perimeter(@points)</code> (alias <code>polyper</code>) — computes the perimeter of a polygon. Points as flat list [x1,y1,x2,y2,...]. Assumes closed polygon.</p>
<pre><code class="lang-perl">my @square = (0,0, 1,0, 1,1, 0,1)
p polyper(@square) # 4
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-reverse">
<h3><a class="doc-anchor" href="#doc-polygon-reverse">#</a> <code>polygon_reverse</code></h3>
<p><code>polygon_reverse</code> — 2D polygon op <code>reverse</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p polygon_reverse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-self-intersects">
<h3><a class="doc-anchor" href="#doc-polygon-self-intersects">#</a> <code>polygon_self_intersects</code></h3>
<p><code>polygon_self_intersects(points) → 0|1</code> — inverse of <code>polygon_simple_check</code>.</p>
</article>
<article class="doc-entry" id="doc-polygon-shrink">
<h3><a class="doc-anchor" href="#doc-polygon-shrink">#</a> <code>polygon_shrink</code></h3>
<p><code>polygon_shrink(points, d=1) → array</code> — <code>polygon_offset</code> with negative <code>d</code>.</p>
</article>
<article class="doc-entry" id="doc-polygon-signed-area">
<h3><a class="doc-anchor" href="#doc-polygon-signed-area">#</a> <code>polygon_signed_area</code></h3>
<p><code>polygon_signed_area</code> — 2D polygon op <code>signed area</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p polygon_signed_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-simple-check">
<h3><a class="doc-anchor" href="#doc-polygon-simple-check">#</a> <code>polygon_simple_check</code></h3>
<p><code>polygon_simple_check(points) → 0|1</code> — 1 if polygon edges don't self-intersect.</p>
</article>
<article class="doc-entry" id="doc-polygon-simplify-dp">
<h3><a class="doc-anchor" href="#doc-polygon-simplify-dp">#</a> <code>polygon_simplify_dp</code></h3>
<p><code>polygon_simplify_dp</code> — 2D polygon op <code>simplify dp</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p polygon_simplify_dp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-winding">
<h3><a class="doc-anchor" href="#doc-polygon-winding">#</a> <code>polygon_winding</code></h3>
<p><code>polygon_winding(points) → -1|0|1</code> — sign of polygon orientation: 1 CCW, -1 CW.</p>
</article>
<article class="doc-entry" id="doc-polygon-winding-number">
<h3><a class="doc-anchor" href="#doc-polygon-winding-number">#</a> <code>polygon_winding_number</code></h3>
<p><code>polygon_winding_number</code> — 2D polygon op <code>winding number</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p polygon_winding_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-winding-order">
<h3><a class="doc-anchor" href="#doc-polygon-winding-order">#</a> <code>polygon_winding_order</code></h3>
<p><code>polygon_winding_order</code> — 2D polygon op <code>winding order</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p polygon_winding_order $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polygon-with-holes-area">
<h3><a class="doc-anchor" href="#doc-polygon-with-holes-area">#</a> <code>polygon_with_holes_area</code></h3>
<p><code>polygon_with_holes_area</code> — 2D polygon op <code>with holes area</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p polygon_with_holes_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polylog-li2">
<h3><a class="doc-anchor" href="#doc-polylog-li2">#</a> <code>polylog_li2</code></h3>
<p><code>polylog_li2</code> — operation <code>polylog li2</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p polylog_li2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polylog-n">
<h3><a class="doc-anchor" href="#doc-polylog-n">#</a> <code>polylog_n</code></h3>
<p><code>polylog_n</code> — operation <code>polylog n</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p polylog_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polynomial-jones-skein">
<h3><a class="doc-anchor" href="#doc-polynomial-jones-skein">#</a> <code>polynomial_jones_skein</code></h3>
<p><code>polynomial_jones_skein</code> — operation <code>polynomial jones skein</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p polynomial_jones_skein $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polynomial-roots-dk">
<h3><a class="doc-anchor" href="#doc-polynomial-roots-dk">#</a> <code>polynomial_roots_dk</code></h3>
<p><code>polynomial_roots_dk</code> — operation <code>polynomial roots dk</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p polynomial_roots_dk $x
</code></pre>
</article>
<article class="doc-entry" id="doc-polyperim">
<h3><a class="doc-anchor" href="#doc-polyperim">#</a> <code>polyperim</code></h3>
<p><code>polyperim</code> — operation <code>polyperim</code>. Alias for <code>polygon_perimeter</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p polyperim $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pooling-test-stat">
<h3><a class="doc-anchor" href="#doc-pooling-test-stat">#</a> <code>pooling_test_stat</code></h3>
<p><code>pooling_test_stat</code> — operation <code>pooling test stat</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p pooling_test_stat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pop-clj">
<h3><a class="doc-anchor" href="#doc-pop-clj">#</a> <code>pop_clj</code></h3>
<p><code>pop_clj</code> — operation <code>pop clj</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p pop_clj $x
</code></pre>
</article>
<article class="doc-entry" id="doc-popc">
<h3><a class="doc-anchor" href="#doc-popc">#</a> <code>popc</code></h3>
<p><code>popc</code> — operation <code>popc</code>. Alias for <code>pop_clj</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p popc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-popcnt">
<h3><a class="doc-anchor" href="#doc-popcnt">#</a> <code>popcnt</code></h3>
<p><code>popcnt</code> — operation <code>popcnt</code>. Alias for <code>hamming_weight</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p popcnt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-popcount">
<h3><a class="doc-anchor" href="#doc-popcount">#</a> <code>popcount</code></h3>
<p><code>popcount</code> — operation <code>popcount</code>. Alias for <code>bits_count</code>. Category: *base conversion*.</p>
<pre><code class="lang-perl">p popcount $x
</code></pre>
</article>
<article class="doc-entry" id="doc-popcount-u32">
<h3><a class="doc-anchor" href="#doc-popcount-u32">#</a> <code>popcount_u32</code></h3>
<p><code>popcount_u32(x) → int</code> — population count of the 32 lowest bits.</p>
</article>
<article class="doc-entry" id="doc-popcount-u64">
<h3><a class="doc-anchor" href="#doc-popcount-u64">#</a> <code>popcount_u64</code></h3>
<p><code>popcount_u64(x) → int</code> — population count over all 64 bits (alias for <code>bit_count_ones</code>).</p>
</article>
<article class="doc-entry" id="doc-porosity-active-layer">
<h3><a class="doc-anchor" href="#doc-porosity-active-layer">#</a> <code>porosity_active_layer</code></h3>
<p><code>porosity_active_layer</code> — operation <code>porosity active layer</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p porosity_active_layer $x
</code></pre>
</article>
<article class="doc-entry" id="doc-port-is-assigned">
<h3><a class="doc-anchor" href="#doc-port-is-assigned">#</a> <code>port_is_assigned</code></h3>
<p><code>port_is_assigned</code> — operation <code>port is assigned</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p port_is_assigned $x
</code></pre>
</article>
<article class="doc-entry" id="doc-port-is-dynamic">
<h3><a class="doc-anchor" href="#doc-port-is-dynamic">#</a> <code>port_is_dynamic</code></h3>
<p><code>port_is_dynamic</code> — operation <code>port is dynamic</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p port_is_dynamic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-port-is-ephemeral">
<h3><a class="doc-anchor" href="#doc-port-is-ephemeral">#</a> <code>port_is_ephemeral</code></h3>
<p><code>port_is_ephemeral</code> — operation <code>port is ephemeral</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p port_is_ephemeral $x
</code></pre>
</article>
<article class="doc-entry" id="doc-port-is-registered">
<h3><a class="doc-anchor" href="#doc-port-is-registered">#</a> <code>port_is_registered</code></h3>
<p><code>port_is_registered</code> — operation <code>port is registered</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p port_is_registered $x
</code></pre>
</article>
<article class="doc-entry" id="doc-port-is-well-known">
<h3><a class="doc-anchor" href="#doc-port-is-well-known">#</a> <code>port_is_well_known</code></h3>
<p><code>port_is_well_known</code> — operation <code>port is well known</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p port_is_well_known $x
</code></pre>
</article>
<article class="doc-entry" id="doc-port-name">
<h3><a class="doc-anchor" href="#doc-port-name">#</a> <code>port_name</code></h3>
<p><code>port_name</code> — operation <code>port name</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p port_name $x
</code></pre>
</article>
<article class="doc-entry" id="doc-port-parse-range">
<h3><a class="doc-anchor" href="#doc-port-parse-range">#</a> <code>port_parse_range</code></h3>
<p><code>port_parse_range</code> — operation <code>port parse range</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p port_parse_range $x
</code></pre>
</article>
<article class="doc-entry" id="doc-port-random-ephemeral">
<h3><a class="doc-anchor" href="#doc-port-random-ephemeral">#</a> <code>port_random_ephemeral</code></h3>
<p><code>port_random_ephemeral</code> — operation <code>port random ephemeral</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p port_random_ephemeral $x
</code></pre>
</article>
<article class="doc-entry" id="doc-port-service-lookup">
<h3><a class="doc-anchor" href="#doc-port-service-lookup">#</a> <code>port_service_lookup</code></h3>
<p><code>port_service_lookup</code> — operation <code>port service lookup</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p port_service_lookup $x
</code></pre>
</article>
<article class="doc-entry" id="doc-port-to-service">
<h3><a class="doc-anchor" href="#doc-port-to-service">#</a> <code>port_to_service</code></h3>
<p><code>port_to_service</code> — convert from <code>port</code> to <code>service</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p port_to_service $value
</code></pre>
</article>
<article class="doc-entry" id="doc-porter-stem-step">
<h3><a class="doc-anchor" href="#doc-porter-stem-step">#</a> <code>porter_stem_step</code></h3>
<p><code>porter_stem_step</code> — single-step update of <code>porter stem</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p porter_stem_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pos-n">
<h3><a class="doc-anchor" href="#doc-pos-n">#</a> <code>pos_n</code></h3>
<p><code>pos_n</code> — operation <code>pos n</code>. Alias for <code>positive</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p pos_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-poset-zeta-two">
<h3><a class="doc-anchor" href="#doc-poset-zeta-two">#</a> <code>poset_zeta_two</code></h3>
<p><code>poset_zeta_two</code> — operation <code>poset zeta two</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p poset_zeta_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-position-max">
<h3><a class="doc-anchor" href="#doc-position-max">#</a> <code>position_max</code></h3>
<p><code>position_max</code> — maximum of <code>position</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p position_max $x
</code></pre>
</article>
<article class="doc-entry" id="doc-position-max-by">
<h3><a class="doc-anchor" href="#doc-position-max-by">#</a> <code>position_max_by</code></h3>
<p><code>position_max_by</code> — operation <code>position max by</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p position_max_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-position-min">
<h3><a class="doc-anchor" href="#doc-position-min">#</a> <code>position_min</code></h3>
<p><code>position_min</code> — minimum of <code>position</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p position_min $x
</code></pre>
</article>
<article class="doc-entry" id="doc-position-min-by">
<h3><a class="doc-anchor" href="#doc-position-min-by">#</a> <code>position_min_by</code></h3>
<p><code>position_min_by</code> — operation <code>position min by</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p position_min_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-position-of-all-matching">
<h3><a class="doc-anchor" href="#doc-position-of-all-matching">#</a> <code>position_of_all_matching</code></h3>
<p><code>position_of_all_matching</code> — operation <code>position of all matching</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p position_of_all_matching $x
</code></pre>
</article>
<article class="doc-entry" id="doc-positions-of">
<h3><a class="doc-anchor" href="#doc-positions-of">#</a> <code>positions_of</code></h3>
<p><code>positions_of</code> — operation <code>positions of</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p positions_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-positions-of-all">
<h3><a class="doc-anchor" href="#doc-positions-of-all">#</a> <code>positions_of_all</code></h3>
<p><code>positions_of_all</code> — operation <code>positions of all</code>. Alias for <code>position_of_all_matching</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p positions_of_all $x
</code></pre>
</article>
<article class="doc-entry" id="doc-positive">
<h3><a class="doc-anchor" href="#doc-positive">#</a> <code>positive</code></h3>
<p><code>positive</code> — operation <code>positive</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p positive $x
</code></pre>
</article>
<article class="doc-entry" id="doc-post-newtonian-step">
<h3><a class="doc-anchor" href="#doc-post-newtonian-step">#</a> <code>post_newtonian_step</code></h3>
<p><code>post_newtonian_step</code> — single-step update of <code>post newtonian</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p post_newtonian_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-posted-price-offer-accept">
<h3><a class="doc-anchor" href="#doc-posted-price-offer-accept">#</a> <code>posted_price_offer_accept</code></h3>
<p><code>posted_price_offer_accept</code> — operation <code>posted price offer accept</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p posted_price_offer_accept $x
</code></pre>
</article>
<article class="doc-entry" id="doc-posterior-predictive-beta">
<h3><a class="doc-anchor" href="#doc-posterior-predictive-beta">#</a> <code>posterior_predictive_beta</code></h3>
<p><code>posterior_predictive_beta(alpha, beta) → number</code> — posterior predictive probability of success = <code>α/(α+β)</code>.</p>
</article>
<article class="doc-entry" id="doc-posterior-predictive-normal">
<h3><a class="doc-anchor" href="#doc-posterior-predictive-normal">#</a> <code>posterior_predictive_normal</code></h3>
<p><code>posterior_predictive_normal(mean, variance) → {mean, variance}</code> — posterior predictive parameters (identity for the conjugate Normal case).</p>
</article>
<article class="doc-entry" id="doc-potential-energy">
<h3><a class="doc-anchor" href="#doc-potential-energy">#</a> <code>potential_energy</code></h3>
<p><code>potential_energy</code> — operation <code>potential energy</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p potential_energy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-potential-temperature-step">
<h3><a class="doc-anchor" href="#doc-potential-temperature-step">#</a> <code>potential_temperature_step</code></h3>
<p><code>potential_temperature_step</code> — single-step update of <code>potential temperature</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p potential_temperature_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pourbaix-line-value">
<h3><a class="doc-anchor" href="#doc-pourbaix-line-value">#</a> <code>pourbaix_line_value</code></h3>
<p><code>pourbaix_line_value</code> — value of <code>pourbaix line</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p pourbaix_line_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pow2">
<h3><a class="doc-anchor" href="#doc-pow2">#</a> <code>pow2</code></h3>
<p><code>pow2</code> — operation <code>pow2</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p pow2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-power-density-battery">
<h3><a class="doc-anchor" href="#doc-power-density-battery">#</a> <code>power_density_battery</code></h3>
<p><code>power_density_battery</code> — operation <code>power density battery</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p power_density_battery $x
</code></pre>
</article>
<article class="doc-entry" id="doc-power-i2r">
<h3><a class="doc-anchor" href="#doc-power-i2r">#</a> <code>power_i2r</code></h3>
<p><code>power_i2r</code> — operation <code>power i2r</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p power_i2r $x
</code></pre>
</article>
<article class="doc-entry" id="doc-power-law-wind-profile">
<h3><a class="doc-anchor" href="#doc-power-law-wind-profile">#</a> <code>power_law_wind_profile</code></h3>
<p><code>power_law_wind_profile</code> — operation <code>power law wind profile</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p power_law_wind_profile $x
</code></pre>
</article>
<article class="doc-entry" id="doc-power-phys">
<h3><a class="doc-anchor" href="#doc-power-phys">#</a> <code>power_phys</code></h3>
<p><code>power_phys</code> — operation <code>power phys</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p power_phys $x
</code></pre>
</article>
<article class="doc-entry" id="doc-power-residue-check">
<h3><a class="doc-anchor" href="#doc-power-residue-check">#</a> <code>power_residue_check</code></h3>
<p><code>power_residue_check</code> — operation <code>power residue check</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p power_residue_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-power-set">
<h3><a class="doc-anchor" href="#doc-power-set">#</a> <code>power_set</code></h3>
<p><code>power_set</code> — operation <code>power set</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p power_set $x
</code></pre>
</article>
<article class="doc-entry" id="doc-power-spectrum">
<h3><a class="doc-anchor" href="#doc-power-spectrum">#</a> <code>power_spectrum</code></h3>
<p><code>power_spectrum(\@signal)</code> (alias <code>psd</code>) — computes the power spectral density (magnitude squared of DFT). Returns real values representing power at each frequency bin.</p>
<pre><code class="lang-perl">my $psd = psd(\@signal)
@$psd |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-power-spectrum-slope">
<h3><a class="doc-anchor" href="#doc-power-spectrum-slope">#</a> <code>power_spectrum_slope</code></h3>
<p><code>power_spectrum_slope</code> — operation <code>power spectrum slope</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p power_spectrum_slope $x
</code></pre>
</article>
<article class="doc-entry" id="doc-power-vi">
<h3><a class="doc-anchor" href="#doc-power-vi">#</a> <code>power_vi</code></h3>
<p><code>power_vi</code> — operation <code>power vi</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p power_vi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-powers-of-seq">
<h3><a class="doc-anchor" href="#doc-powers-of-seq">#</a> <code>powers_of_seq</code></h3>
<p><code>powers_of_seq</code> — operation <code>powers of seq</code>. Category: *sequences*.</p>
<pre><code class="lang-perl">p powers_of_seq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-powerset">
<h3><a class="doc-anchor" href="#doc-powerset">#</a> <code>powerset</code></h3>
<p><code>powerset</code> — operation <code>powerset</code>. Alias for <code>power_set</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p powerset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-powspec">
<h3><a class="doc-anchor" href="#doc-powspec">#</a> <code>powspec</code></h3>
<p><code>powspec</code> — operation <code>powspec</code>. Alias for <code>power_spectrum</code>. Category: *dsp / signal (extended)*.</p>
<pre><code class="lang-perl">p powspec $x
</code></pre>
</article>
<article class="doc-entry" id="doc-poynting-magnitude">
<h3><a class="doc-anchor" href="#doc-poynting-magnitude">#</a> <code>poynting_magnitude</code></h3>
<p><code>poynting_magnitude</code> — operation <code>poynting magnitude</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p poynting_magnitude $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pp-test-stat">
<h3><a class="doc-anchor" href="#doc-pp-test-stat">#</a> <code>pp_test_stat</code></h3>
<p><code>pp_test_stat</code> — operation <code>pp test stat</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p pp_test_stat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ppi">
<h3><a class="doc-anchor" href="#doc-ppi">#</a> <code>ppi</code></h3>
<p><code>ppi</code> — operation <code>ppi</code>. Alias for <code>prime_pi</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p ppi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ppid">
<h3><a class="doc-anchor" href="#doc-ppid">#</a> <code>ppid</code></h3>
<p><code>ppid</code> — operation <code>ppid</code>. Category: *system introspection*.</p>
<pre><code class="lang-perl">p ppid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ppm-predict-prob">
<h3><a class="doc-anchor" href="#doc-ppm-predict-prob">#</a> <code>ppm_predict_prob</code></h3>
<p><code>ppm_predict_prob</code> — operation <code>ppm predict prob</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ppm_predict_prob $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ppmt">
<h3><a class="doc-anchor" href="#doc-ppmt">#</a> <code>ppmt</code></h3>
<p><code>ppmt</code> — operation <code>ppmt</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p ppmt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ppo-advantage-step">
<h3><a class="doc-anchor" href="#doc-ppo-advantage-step">#</a> <code>ppo_advantage_step</code></h3>
<p><code>ppo_advantage_step</code> — single-step update of <code>ppo advantage</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ppo_advantage_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ppo-clip-term">
<h3><a class="doc-anchor" href="#doc-ppo-clip-term">#</a> <code>ppo_clip_term</code></h3>
<p><code>ppo_clip_term</code> — operation <code>ppo clip term</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ppo_clip_term $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ppois">
<h3><a class="doc-anchor" href="#doc-ppois">#</a> <code>ppois</code></h3>
<p><code>ppois</code> — Poisson CDF. P(X ≤ k) for Poisson(lambda). Args: k, lambda.</p>
<pre><code class="lang-perl">p ppois(3, 2.5) # P(≤3 events when avg is 2.5)
</code></pre>
</article>
<article class="doc-entry" id="doc-ppt">
<h3><a class="doc-anchor" href="#doc-ppt">#</a> <code>ppt</code></h3>
<p><code>ppt</code> — operation <code>ppt</code>. Alias for <code>partition_point</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ppt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prandtl-number-step">
<h3><a class="doc-anchor" href="#doc-prandtl-number-step">#</a> <code>prandtl_number_step</code></h3>
<p><code>prandtl_number_step</code> — single-step update of <code>prandtl number</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p prandtl_number_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pratt-parse-step">
<h3><a class="doc-anchor" href="#doc-pratt-parse-step">#</a> <code>pratt_parse_step</code></h3>
<p><code>pratt_parse_step</code> — single-step update of <code>pratt parse</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p pratt_parse_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-precession-iau2006">
<h3><a class="doc-anchor" href="#doc-precession-iau2006">#</a> <code>precession_iau2006</code></h3>
<p><code>precession_iau2006</code> — operation <code>precession iau2006</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p precession_iau2006 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prect">
<h3><a class="doc-anchor" href="#doc-prect">#</a> <code>prect</code></h3>
<p><code>prect</code> — operation <code>prect</code>. Alias for <code>perimeter_rectangle</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p prect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pred">
<h3><a class="doc-anchor" href="#doc-pred">#</a> <code>pred</code></h3>
<p><code>pred</code> — operation <code>pred</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p pred $x
</code></pre>
</article>
<article class="doc-entry" id="doc-predict">
<h3><a class="doc-anchor" href="#doc-predict">#</a> <code>predict</code></h3>
<p><code>predict_lm</code> (alias <code>predict</code>) — predict from a linear model at new x values.</p>
<pre><code class="lang-perl">my $model = lm([1,2,3], [2,4,6])
my @pred = @{predict($model, [4,5,6])} # [8,10,12]
</code></pre>
</article>
<article class="doc-entry" id="doc-predictor-corrector">
<h3><a class="doc-anchor" href="#doc-predictor-corrector">#</a> <code>predictor_corrector</code></h3>
<p><code>predictor_corrector</code> — operation <code>predictor corrector</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p predictor_corrector $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prefix-sums">
<h3><a class="doc-anchor" href="#doc-prefix-sums">#</a> <code>prefix_sums</code></h3>
<p><code>prefix_sums</code> — operation <code>prefix sums</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p prefix_sums $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prelu">
<h3><a class="doc-anchor" href="#doc-prelu">#</a> <code>prelu</code></h3>
<p><code>prelu</code> — operation <code>prelu</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p prelu $x
</code></pre>
</article>
<article class="doc-entry" id="doc-premium-net">
<h3><a class="doc-anchor" href="#doc-premium-net">#</a> <code>premium_net</code></h3>
<p><code>premium_net</code> — operation <code>premium net</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p premium_net $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prepend">
<h3><a class="doc-anchor" href="#doc-prepend">#</a> <code>prepend</code></h3>
<p><code>prepend</code> — operation <code>prepend</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p prepend $x
</code></pre>
</article>
<article class="doc-entry" id="doc-present-value">
<h3><a class="doc-anchor" href="#doc-present-value">#</a> <code>present_value</code></h3>
<p><code>present_value(future_value, rate, periods) → number</code> — <code>FV / (1 + rate)^periods</code>. Discount a single future cashflow to today.</p>
<pre><code class="lang-perl">p present_value(1000, 0.05, 10) # 613.91
</code></pre>
</article>
<article class="doc-entry" id="doc-pressure-altitude-m">
<h3><a class="doc-anchor" href="#doc-pressure-altitude-m">#</a> <code>pressure_altitude_m</code></h3>
<p><code>pressure_altitude_m</code> — operation <code>pressure altitude m</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p pressure_altitude_m $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prev-prime">
<h3><a class="doc-anchor" href="#doc-prev-prime">#</a> <code>prev_prime</code></h3>
<p><code>prev_prime</code> — operation <code>prev prime</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p prev_prime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-preventive-fraction">
<h3><a class="doc-anchor" href="#doc-preventive-fraction">#</a> <code>preventive_fraction</code></h3>
<p><code>preventive_fraction</code> — operation <code>preventive fraction</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p preventive_fraction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prewitt-kernel-value">
<h3><a class="doc-anchor" href="#doc-prewitt-kernel-value">#</a> <code>prewitt_kernel_value</code></h3>
<p><code>prewitt_kernel_value</code> — value of <code>prewitt kernel</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p prewitt_kernel_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prewitt-x-kernel">
<h3><a class="doc-anchor" href="#doc-prewitt-x-kernel">#</a> <code>prewitt_x_kernel</code></h3>
<p><code>prewitt_x_kernel() → matrix</code> — 3×3 Prewitt horizontal-gradient kernel (lighter than Sobel).</p>
</article>
<article class="doc-entry" id="doc-prewitt-y-kernel">
<h3><a class="doc-anchor" href="#doc-prewitt-y-kernel">#</a> <code>prewitt_y_kernel</code></h3>
<p><code>prewitt_y_kernel() → matrix</code> — 3×3 Prewitt vertical-gradient kernel.</p>
</article>
<article class="doc-entry" id="doc-price-disc">
<h3><a class="doc-anchor" href="#doc-price-disc">#</a> <code>price_disc</code></h3>
<p><code>price_disc</code> — operation <code>price disc</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p price_disc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-price-elasticity">
<h3><a class="doc-anchor" href="#doc-price-elasticity">#</a> <code>price_elasticity</code></h3>
<p><code>price_elasticity</code> — operation <code>price elasticity</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p price_elasticity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prim-step">
<h3><a class="doc-anchor" href="#doc-prim-step">#</a> <code>prim_step</code></h3>
<p><code>prim_step</code> — single-step update of <code>prim</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p prim_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prime-count-below">
<h3><a class="doc-anchor" href="#doc-prime-count-below">#</a> <code>prime_count_below</code></h3>
<p><code>prime_count_below</code> — prime-number helper <code>count below</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p prime_count_below $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prime-factors">
<h3><a class="doc-anchor" href="#doc-prime-factors">#</a> <code>prime_factors</code></h3>
<p><code>prime_factors</code> — prime-number helper <code>factors</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p prime_factors $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prime-pi">
<h3><a class="doc-anchor" href="#doc-prime-pi">#</a> <code>prime_pi</code></h3>
<p><code>prime_pi</code> — prime-number helper <code>pi</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p prime_pi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-primes-seq">
<h3><a class="doc-anchor" href="#doc-primes-seq">#</a> <code>primes_seq</code></h3>
<p><code>primes_seq</code> — operation <code>primes seq</code>. Category: *sequences*.</p>
<pre><code class="lang-perl">p primes_seq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-primes-up-to">
<h3><a class="doc-anchor" href="#doc-primes-up-to">#</a> <code>primes_up_to</code></h3>
<p><code>primes_up_to</code> — operation <code>primes up to</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p primes_up_to $x
</code></pre>
</article>
<article class="doc-entry" id="doc-primorial">
<h3><a class="doc-anchor" href="#doc-primorial">#</a> <code>primorial</code></h3>
<p><code>primorial(n) → int</code> — product of primes ≤ n.</p>
<pre><code class="lang-perl">p primorial(10) # 2·3·5·7 = 210
</code></pre>
</article>
<article class="doc-entry" id="doc-primorial-n">
<h3><a class="doc-anchor" href="#doc-primorial-n">#</a> <code>primorial_n</code></h3>
<p><code>primorial_n</code> — operation <code>primorial n</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p primorial_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prior-jeffreys-uniform">
<h3><a class="doc-anchor" href="#doc-prior-jeffreys-uniform">#</a> <code>prior_jeffreys_uniform</code></h3>
<p><code>prior_jeffreys_uniform() → {alpha, beta}</code> — Jeffreys prior for Bernoulli <code>Beta(0.5, 0.5)</code>.</p>
</article>
<article class="doc-entry" id="doc-prisoners-dilemma-payoff">
<h3><a class="doc-anchor" href="#doc-prisoners-dilemma-payoff">#</a> <code>prisoners_dilemma_payoff</code></h3>
<p><code>prisoners_dilemma_payoff</code> — operation <code>prisoners dilemma payoff</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p prisoners_dilemma_payoff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prisoners-repeated-eq">
<h3><a class="doc-anchor" href="#doc-prisoners-repeated-eq">#</a> <code>prisoners_repeated_eq</code></h3>
<p><code>prisoners_repeated_eq</code> — operation <code>prisoners repeated eq</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p prisoners_repeated_eq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-priv">
<h3><a class="doc-anchor" href="#doc-priv">#</a> <code>priv</code></h3>
<p><code>priv</code> marks a field or method as private. Private members can only be accessed from within the class.</p>
<pre><code class="lang-perl">class Secret {
priv hidden: Int = 42
priv fn internal { }
pub fn reveal { $self->hidden } # internal access ok
}
# $obj->hidden # ERROR: field is private
</code></pre>
</article>
<article class="doc-entry" id="doc-prm-node-connect">
<h3><a class="doc-anchor" href="#doc-prm-node-connect">#</a> <code>prm_node_connect</code></h3>
<p><code>prm_node_connect</code> — operation <code>prm node connect</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p prm_node_connect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-probability-density">
<h3><a class="doc-anchor" href="#doc-probability-density">#</a> <code>probability_density</code></h3>
<p><code>probability_density</code> — operation <code>probability density</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p probability_density $x
</code></pre>
</article>
<article class="doc-entry" id="doc-probit-log-likelihood">
<h3><a class="doc-anchor" href="#doc-probit-log-likelihood">#</a> <code>probit_log_likelihood</code></h3>
<p><code>probit_log_likelihood</code> — operation <code>probit log likelihood</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p probit_log_likelihood $x
</code></pre>
</article>
<article class="doc-entry" id="doc-proc-mem">
<h3><a class="doc-anchor" href="#doc-proc-mem">#</a> <code>proc_mem</code></h3>
<p><code>proc_mem</code> (alias <code>rss</code>) — current process resident set size (RSS) in bytes. On Linux reads <code>VmRSS</code> from <code>/proc/self/status</code>. On macOS uses <code>getrusage(RUSAGE_SELF)</code>. Returns <code>undef</code> on unsupported platforms.</p>
<pre><code class="lang-perl">p format_bytes(rss) # 18.5 MiB
my $before = rss
do_work()
p format_bytes(rss - $before) . " allocated"
</code></pre>
</article>
<article class="doc-entry" id="doc-producer-surplus">
<h3><a class="doc-anchor" href="#doc-producer-surplus">#</a> <code>producer_surplus</code></h3>
<p><code>producer_surplus</code> — operation <code>producer surplus</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p producer_surplus $x
</code></pre>
</article>
<article class="doc-entry" id="doc-product-digits">
<h3><a class="doc-anchor" href="#doc-product-digits">#</a> <code>product_digits</code></h3>
<p><code>product_digits</code> — operation <code>product digits</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p product_digits $x
</code></pre>
</article>
<article class="doc-entry" id="doc-product-list">
<h3><a class="doc-anchor" href="#doc-product-list">#</a> <code>product_list</code></h3>
<p><code>product_list</code> — operation <code>product list</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p product_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-product-of">
<h3><a class="doc-anchor" href="#doc-product-of">#</a> <code>product_of</code></h3>
<p><code>product_of</code> — operation <code>product of</code>. Category: *more list helpers*.</p>
<pre><code class="lang-perl">p product_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-profile-hmm-score">
<h3><a class="doc-anchor" href="#doc-profile-hmm-score">#</a> <code>profile_hmm_score</code></h3>
<p><code>profile_hmm_score</code> — score of <code>profile hmm</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p profile_hmm_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-profit-margin-pct">
<h3><a class="doc-anchor" href="#doc-profit-margin-pct">#</a> <code>profit_margin_pct</code></h3>
<p><code>profit_margin_pct(revenue, cost) → number</code> — <code>(revenue - cost) / revenue · 100</code>.</p>
<pre><code class="lang-perl">p profit_margin_pct(150, 100)
</code></pre>
</article>
<article class="doc-entry" id="doc-proj">
<h3><a class="doc-anchor" href="#doc-proj">#</a> <code>proj</code></h3>
<p><code>proj</code> — operation <code>proj</code>. Alias for <code>vector_project</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p proj $x
</code></pre>
</article>
<article class="doc-entry" id="doc-projectile-max-height">
<h3><a class="doc-anchor" href="#doc-projectile-max-height">#</a> <code>projectile_max_height</code></h3>
<p><code>projectile_max_height($velocity, $angle)</code> (alias <code>projheight</code>) — maximum height H = v²sin²(θ)/(2g).</p>
<pre><code class="lang-perl">p projheight(100, 45) # ~255 m
p projheight(100, 90) # ~510 m (straight up)
</code></pre>
</article>
<article class="doc-entry" id="doc-projectile-position">
<h3><a class="doc-anchor" href="#doc-projectile-position">#</a> <code>projectile_position</code></h3>
<p><code>projectile_position(v0, angle_deg, g=9.81, t) → [x, y]</code> — position at time <code>t</code> for given launch velocity/angle.</p>
<pre><code class="lang-perl">p projectile_position(10, 45, 9.81, 0.5)
</code></pre>
</article>
<article class="doc-entry" id="doc-projectile-range">
<h3><a class="doc-anchor" href="#doc-projectile-range">#</a> <code>projectile_range</code></h3>
<p><code>projectile_range($velocity, $angle)</code> (alias <code>projrange</code>) — horizontal range R = v²sin(2θ)/g. Angle in degrees.</p>
<pre><code class="lang-perl">p projrange(100, 45) # ~1020 m (optimal angle for range)
p projrange(100, 30) # ~884 m
</code></pre>
</article>
<article class="doc-entry" id="doc-projectile-time">
<h3><a class="doc-anchor" href="#doc-projectile-time">#</a> <code>projectile_time</code></h3>
<p><code>projectile_time</code> — operation <code>projectile time</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p projectile_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-projectile-velocity">
<h3><a class="doc-anchor" href="#doc-projectile-velocity">#</a> <code>projectile_velocity</code></h3>
<p><code>projectile_velocity(v0, angle_deg, g=9.81, t) → [vx, vy]</code> — velocity components at time <code>t</code>.</p>
</article>
<article class="doc-entry" id="doc-projtime">
<h3><a class="doc-anchor" href="#doc-projtime">#</a> <code>projtime</code></h3>
<p><code>projtime</code> — operation <code>projtime</code>. Alias for <code>projectile_time</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p projtime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pronic-number">
<h3><a class="doc-anchor" href="#doc-pronic-number">#</a> <code>pronic_number</code></h3>
<p><code>pronic_number</code> — operation <code>pronic number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p pronic_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prop-table">
<h3><a class="doc-anchor" href="#doc-prop-table">#</a> <code>prop_table</code></h3>
<p><code>prop_table</code> — convert a count matrix to proportions (each cell / total). Like R's prop.table().</p>
<pre><code class="lang-perl">p prop_table([[10,20],[30,40]]) # [[0.1,0.2],[0.3,0.4]]
</code></pre>
</article>
<article class="doc-entry" id="doc-prop-test">
<h3><a class="doc-anchor" href="#doc-prop-test">#</a> <code>prop_test</code></h3>
<p><code>prop_test</code> — one-sample proportion z-test. Returns [z-statistic, p-value]. Like R's prop.test().</p>
<pre><code class="lang-perl">my ($z, $pval) = @{proptest(55, 100, 0.5)} # test if 55/100 differs from 50%%
</code></pre>
</article>
<article class="doc-entry" id="doc-proper-motion-apply">
<h3><a class="doc-anchor" href="#doc-proper-motion-apply">#</a> <code>proper_motion_apply</code></h3>
<p><code>proper_motion_apply</code> — operation <code>proper motion apply</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p proper_motion_apply $x
</code></pre>
</article>
<article class="doc-entry" id="doc-proportion-test">
<h3><a class="doc-anchor" href="#doc-proportion-test">#</a> <code>proportion_test</code></h3>
<p><code>proportion_test(x, n, p0=0.5) → {statistic, df, p_value}</code> — one-sample z-test for a proportion.</p>
<pre><code class="lang-perl">p proportion_test(45, 100, 0.5)
</code></pre>
</article>
<article class="doc-entry" id="doc-proportional-share">
<h3><a class="doc-anchor" href="#doc-proportional-share">#</a> <code>proportional_share</code></h3>
<p><code>proportional_share</code> — operation <code>proportional share</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p proportional_share $x
</code></pre>
</article>
<article class="doc-entry" id="doc-protein-charge-at-ph">
<h3><a class="doc-anchor" href="#doc-protein-charge-at-ph">#</a> <code>protein_charge_at_ph</code></h3>
<p><code>protein_charge_at_ph(seq, ph=7) → number</code> — net charge at given pH using Henderson-Hasselbalch on each ionisable residue.</p>
</article>
<article class="doc-entry" id="doc-protein-hydrophobicity">
<h3><a class="doc-anchor" href="#doc-protein-hydrophobicity">#</a> <code>protein_hydrophobicity</code></h3>
<p><code>protein_hydrophobicity(seq) → number</code> — average Kyte-Doolittle hydropathy.</p>
<pre><code class="lang-perl">p protein_hydrophobicity("GAVIL") # 2.78
</code></pre>
</article>
<article class="doc-entry" id="doc-protein-molecular-weight">
<h3><a class="doc-anchor" href="#doc-protein-molecular-weight">#</a> <code>protein_molecular_weight</code></h3>
<p><code>protein_molecular_weight(seq) → number</code> — molecular weight in Da. Sums per-residue weights, subtracts (n-1)·18.02 (water lost in peptide bonds).</p>
<pre><code class="lang-perl">p protein_molecular_weight("GAVIL")
</code></pre>
</article>
<article class="doc-entry" id="doc-protein-pi">
<h3><a class="doc-anchor" href="#doc-protein-pi">#</a> <code>protein_pI</code></h3>
<p><code>protein_pI(seq) → number</code> — isoelectric point via bisection on net-charge curve using standard pKa table.</p>
<pre><code class="lang-perl">p protein_pI("MKVL")
</code></pre>
</article>
<article class="doc-entry" id="doc-proton-mass">
<h3><a class="doc-anchor" href="#doc-proton-mass">#</a> <code>proton_mass</code></h3>
<p><code>proton_mass</code> — operation <code>proton mass</code>. Category: *constants*.</p>
<pre><code class="lang-perl">p proton_mass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-proximal-gradient-step">
<h3><a class="doc-anchor" href="#doc-proximal-gradient-step">#</a> <code>proximal_gradient_step</code></h3>
<p><code>proximal_gradient_step</code> — single-step update of <code>proximal gradient</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p proximal_gradient_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-prvp">
<h3><a class="doc-anchor" href="#doc-prvp">#</a> <code>prvp</code></h3>
<p><code>prvp</code> — operation <code>prvp</code>. Alias for <code>prev_prime</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p prvp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pseudoprime-base2">
<h3><a class="doc-anchor" href="#doc-pseudoprime-base2">#</a> <code>pseudoprime_base2</code></h3>
<p><code>pseudoprime_base2</code> — operation <code>pseudoprime base2</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p pseudoprime_base2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-psi-to-pascals">
<h3><a class="doc-anchor" href="#doc-psi-to-pascals">#</a> <code>psi_to_pascals</code></h3>
<p><code>psi_to_pascals</code> — convert from <code>psi</code> to <code>pascals</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p psi_to_pascals $value
</code></pre>
</article>
<article class="doc-entry" id="doc-pt">
<h3><a class="doc-anchor" href="#doc-pt">#</a> <code>pt</code></h3>
<p><code>pt</code> — Student's t CDF. Args: x, df.</p>
<pre><code class="lang-perl">p pt(1.96, 100) # ≈ 0.975
</code></pre>
</article>
<article class="doc-entry" id="doc-ptdist">
<h3><a class="doc-anchor" href="#doc-ptdist">#</a> <code>ptdist</code></h3>
<p><code>ptdist</code> — operation <code>ptdist</code>. Alias for <code>point_distance</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p ptdist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ptinpoly">
<h3><a class="doc-anchor" href="#doc-ptinpoly">#</a> <code>ptinpoly</code></h3>
<p><code>ptinpoly</code> — operation <code>ptinpoly</code>. Alias for <code>point_in_polygon</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p ptinpoly $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ptri">
<h3><a class="doc-anchor" href="#doc-ptri">#</a> <code>ptri</code></h3>
<p><code>ptri</code> — operation <code>ptri</code>. Alias for <code>perimeter_triangle</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p ptri $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pttl">
<h3><a class="doc-anchor" href="#doc-pttl">#</a> <code>pttl</code></h3>
<p><code>pttl</code> — operation <code>pttl</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p pttl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pub">
<h3><a class="doc-anchor" href="#doc-pub">#</a> <code>pub</code></h3>
<p><code>pub</code> marks a field or method as public (default visibility).</p>
<pre><code class="lang-perl">class Example {
pub name: Str # explicitly public
pub fn greet { } # explicitly public
}
</code></pre>
</article>
<article class="doc-entry" id="doc-public-goods-game-payoff">
<h3><a class="doc-anchor" href="#doc-public-goods-game-payoff">#</a> <code>public_goods_game_payoff</code></h3>
<p><code>public_goods_game_payoff</code> — operation <code>public goods game payoff</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p public_goods_game_payoff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pulse-pressure">
<h3><a class="doc-anchor" href="#doc-pulse-pressure">#</a> <code>pulse_pressure</code></h3>
<p><code>pulse_pressure</code> — operation <code>pulse pressure</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p pulse_pressure $x
</code></pre>
</article>
<article class="doc-entry" id="doc-punct">
<h3><a class="doc-anchor" href="#doc-punct">#</a> <code>punct</code></h3>
<p><code>punctuation</code> (alias <code>punct</code>) extracts all ASCII punctuation characters from a string and returns them as a list. Filters out letters, digits, whitespace — keeps only punctuation.</p>
<pre><code class="lang-perl">p join "", punctuation("Hello, world!") # ,!
"a.b-c" |> punct |> cnt |> p # 2
</code></pre>
</article>
<article class="doc-entry" id="doc-punif">
<h3><a class="doc-anchor" href="#doc-punif">#</a> <code>punif</code></h3>
<p><code>punif</code> — uniform CDF. P(X ≤ x) for Uniform(a, b). Args: x, a, b.</p>
<pre><code class="lang-perl">p punif(0.5, 0, 1) # 0.5
p punif(3, 0, 10) # 0.3
</code></pre>
</article>
<article class="doc-entry" id="doc-punycode-decode-step">
<h3><a class="doc-anchor" href="#doc-punycode-decode-step">#</a> <code>punycode_decode_step</code></h3>
<p><code>punycode_decode_step</code> — single-step update of <code>punycode decode</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p punycode_decode_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-punycode-encode">
<h3><a class="doc-anchor" href="#doc-punycode-encode">#</a> <code>punycode_encode</code></h3>
<p><code>punycode_encode</code> — encode of <code>punycode</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p punycode_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pure-state-density">
<h3><a class="doc-anchor" href="#doc-pure-state-density">#</a> <code>pure_state_density</code></h3>
<p><code>pure_state_density</code> — operation <code>pure state density</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p pure_state_density $x
</code></pre>
</article>
<article class="doc-entry" id="doc-purity">
<h3><a class="doc-anchor" href="#doc-purity">#</a> <code>purity</code></h3>
<p><code>purity</code> — operation <code>purity</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p purity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-purple">
<h3><a class="doc-anchor" href="#doc-purple">#</a> <code>purple</code></h3>
<p><code>purple</code> — operation <code>purple</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p purple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-push-relabel-relabel">
<h3><a class="doc-anchor" href="#doc-push-relabel-relabel">#</a> <code>push_relabel_relabel</code></h3>
<p><code>push_relabel_relabel</code> — operation <code>push relabel relabel</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p push_relabel_relabel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-push-relabel-step">
<h3><a class="doc-anchor" href="#doc-push-relabel-step">#</a> <code>push_relabel_step</code></h3>
<p><code>push_relabel_step</code> — single-step update of <code>push relabel</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p push_relabel_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pv">
<h3><a class="doc-anchor" href="#doc-pv">#</a> <code>pv</code></h3>
<p><code>pv</code> — operation <code>pv</code>. Category: *finance (extended)*.</p>
<pre><code class="lang-perl">p pv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pwave-velocity-depth">
<h3><a class="doc-anchor" href="#doc-pwave-velocity-depth">#</a> <code>pwave_velocity_depth</code></h3>
<p><code>pwave_velocity_depth</code> — operation <code>pwave velocity depth</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p pwave_velocity_depth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pwd-str">
<h3><a class="doc-anchor" href="#doc-pwd-str">#</a> <code>pwd_str</code></h3>
<p><code>pwd_str</code> — operation <code>pwd str</code>. Alias for <code>cwd</code>. Category: *more process / system*.</p>
<pre><code class="lang-perl">p pwd_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pweibull">
<h3><a class="doc-anchor" href="#doc-pweibull">#</a> <code>pweibull</code></h3>
<p><code>pweibull</code> — Weibull CDF. P(X ≤ x) for Weibull(shape, scale). Args: x, shape, scale.</p>
<pre><code class="lang-perl">p pweibull(1, 1, 1) # same as exponential
</code></pre>
</article>
<article class="doc-entry" id="doc-pwi">
<h3><a class="doc-anchor" href="#doc-pwi">#</a> <code>pwi</code></h3>
<p><code>pwi</code> — operation <code>pwi</code>. Alias for <code>pairwise_iter</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p pwi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pwm-score">
<h3><a class="doc-anchor" href="#doc-pwm-score">#</a> <code>pwm_score</code></h3>
<p><code>pwm_score</code> — score of <code>pwm</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p pwm_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pyramid-volume">
<h3><a class="doc-anchor" href="#doc-pyramid-volume">#</a> <code>pyramid_volume</code></h3>
<p><code>pyramid_volume($base_area, $height)</code> — computes the volume of a pyramid. Returns <code>(1/3) * base_area * height</code>.</p>
<pre><code class="lang-perl">p pyramid_volume(100, 15) # 500
</code></pre>
</article>
<article class="doc-entry" id="doc-pyrvol">
<h3><a class="doc-anchor" href="#doc-pyrvol">#</a> <code>pyrvol</code></h3>
<p><code>pyrvol</code> — operation <code>pyrvol</code>. Alias for <code>pyramid_volume</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p pyrvol $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pythagorean-expectation">
<h3><a class="doc-anchor" href="#doc-pythagorean-expectation">#</a> <code>pythagorean_expectation</code></h3>
<p><code>pythagorean_expectation</code> — operation <code>pythagorean expectation</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p pythagorean_expectation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pythagorean-freq">
<h3><a class="doc-anchor" href="#doc-pythagorean-freq">#</a> <code>pythagorean_freq</code></h3>
<p><code>pythagorean_freq</code> — operation <code>pythagorean freq</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p pythagorean_freq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-pythagorean-ratio">
<h3><a class="doc-anchor" href="#doc-pythagorean-ratio">#</a> <code>pythagorean_ratio</code></h3>
<p><code>pythagorean_ratio</code> — ratio of <code>pythagorean</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p pythagorean_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-q">
<h3><a class="doc-anchor" href="#doc-q">#</a> <code>q</code></h3>
<p><code>q</code> — operation <code>q</code>. Category: *quoting*.</p>
<pre><code class="lang-perl">p q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-q10">
<h3><a class="doc-anchor" href="#doc-q10">#</a> <code>q10</code></h3>
<p><code>q10</code> — operation <code>q10</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p q10 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-q-factor-rlc">
<h3><a class="doc-anchor" href="#doc-q-factor-rlc">#</a> <code>q_factor_rlc</code></h3>
<p><code>q_factor_rlc</code> — operation <code>q factor rlc</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p q_factor_rlc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-q-learning-update">
<h3><a class="doc-anchor" href="#doc-q-learning-update">#</a> <code>q_learning_update</code></h3>
<p><code>q_learning_update</code> — update step of <code>q learning</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p q_learning_update $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qaly-lifetime">
<h3><a class="doc-anchor" href="#doc-qaly-lifetime">#</a> <code>qaly_lifetime</code></h3>
<p><code>qaly_lifetime</code> — operation <code>qaly lifetime</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p qaly_lifetime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qaoa-step">
<h3><a class="doc-anchor" href="#doc-qaoa-step">#</a> <code>qaoa_step</code></h3>
<p><code>qaoa_step</code> — single-step update of <code>qaoa</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qaoa_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qap-lower-bound">
<h3><a class="doc-anchor" href="#doc-qap-lower-bound">#</a> <code>qap_lower_bound</code></h3>
<p><code>qap_lower_bound</code> — operation <code>qap lower bound</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p qap_lower_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qbeta">
<h3><a class="doc-anchor" href="#doc-qbeta">#</a> <code>qbeta</code></h3>
<p><code>qbeta</code> — beta quantile. Args: p, alpha, beta.</p>
<pre><code class="lang-perl">p qbeta(0.5, 2, 5) # median of Beta(2,5)
</code></pre>
</article>
<article class="doc-entry" id="doc-qbinom">
<h3><a class="doc-anchor" href="#doc-qbinom">#</a> <code>qbinom</code></h3>
<p><code>qbinom</code> — binomial quantile (smallest k where P(X≤k) ≥ p). Args: p, n, prob.</p>
<pre><code class="lang-perl">p qbinom(0.5, 10, 0.5) # median of Binom(10, 0.5) = 5
</code></pre>
</article>
<article class="doc-entry" id="doc-qbo-oscillation-step">
<h3><a class="doc-anchor" href="#doc-qbo-oscillation-step">#</a> <code>qbo_oscillation_step</code></h3>
<p><code>qbo_oscillation_step</code> — single-step update of <code>qbo oscillation</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p qbo_oscillation_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qbr-metric">
<h3><a class="doc-anchor" href="#doc-qbr-metric">#</a> <code>qbr_metric</code></h3>
<p><code>qbr_metric</code> — metric of <code>qbr</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p qbr_metric $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qcauchy">
<h3><a class="doc-anchor" href="#doc-qcauchy">#</a> <code>qcauchy</code></h3>
<p><code>qcauchy</code> — Cauchy quantile. Args: p [, location, scale].</p>
<pre><code class="lang-perl">p qcauchy(0.75, 0, 1) # 1.0
</code></pre>
</article>
<article class="doc-entry" id="doc-qchisq">
<h3><a class="doc-anchor" href="#doc-qchisq">#</a> <code>qchisq</code></h3>
<p><code>qchisq</code> — chi-squared quantile. Args: p, df.</p>
<pre><code class="lang-perl">p qchisq(0.95, 1) # 3.84 (critical value)
p qchisq(0.95, 5) # 11.07
</code></pre>
</article>
<article class="doc-entry" id="doc-qdisc">
<h3><a class="doc-anchor" href="#doc-qdisc">#</a> <code>qdisc</code></h3>
<p><code>quadratic_discriminant($a, $b, $c)</code> (alias <code>qdisc</code>) — computes b² - 4ac. Positive = two real roots, zero = one repeated root, negative = complex roots.</p>
<pre><code class="lang-perl">p qdisc(1, -5, 6) # 1 (two distinct real roots)
p qdisc(1, 2, 1) # 0 (one repeated root)
p qdisc(1, 2, 5) # -16 (complex roots)
</code></pre>
</article>
<article class="doc-entry" id="doc-qexp">
<h3><a class="doc-anchor" href="#doc-qexp">#</a> <code>qexp</code></h3>
<p><code>qexp</code> — exponential quantile. Args: p [, rate].</p>
<pre><code class="lang-perl">p qexp(0.5, 1) # 0.693 (median of Exp(1))
</code></pre>
</article>
<article class="doc-entry" id="doc-qf">
<h3><a class="doc-anchor" href="#doc-qf">#</a> <code>qf</code></h3>
<p><code>qf</code> — F-distribution quantile. Args: p, d1, d2.</p>
<pre><code class="lang-perl">p qf(0.95, 5, 10) # critical F value
</code></pre>
</article>
<article class="doc-entry" id="doc-qft">
<h3><a class="doc-anchor" href="#doc-qft">#</a> <code>qft</code></h3>
<p><code>qft</code> — operation <code>qft</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qft $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qft-4-real">
<h3><a class="doc-anchor" href="#doc-qft-4-real">#</a> <code>qft_4_real</code></h3>
<p><code>qft_4_real</code> — operation <code>qft 4 real</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p qft_4_real $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qgamma">
<h3><a class="doc-anchor" href="#doc-qgamma">#</a> <code>qgamma</code></h3>
<p><code>qgamma</code> — gamma quantile (inverse CDF). Args: p, shape [, scale].</p>
<pre><code class="lang-perl">p qgamma(0.95, 2, 1) # 95th percentile of Gamma(2,1)
</code></pre>
</article>
<article class="doc-entry" id="doc-qgeom">
<h3><a class="doc-anchor" href="#doc-qgeom">#</a> <code>qgeom</code></h3>
<p><code>qgeom</code> — operation <code>qgeom</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p qgeom $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qho-ground-state">
<h3><a class="doc-anchor" href="#doc-qho-ground-state">#</a> <code>qho_ground_state</code></h3>
<p><code>qho_ground_state</code> — operation <code>qho ground state</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p qho_ground_state $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qhyper">
<h3><a class="doc-anchor" href="#doc-qhyper">#</a> <code>qhyper</code></h3>
<p><code>qhyper</code> — operation <code>qhyper</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p qhyper $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qlearning-step">
<h3><a class="doc-anchor" href="#doc-qlearning-step">#</a> <code>qlearning_step</code></h3>
<p><code>qlearning_step(q, alpha, r, gamma, max_next_q) → number</code> — <code>q ← q + α·(r + γ·max_next - q)</code>.</p>
<pre><code class="lang-perl">p qlearning_step(0, 0.1, 10, 0.9, 5) # 1.45
</code></pre>
</article>
<article class="doc-entry" id="doc-qlnorm">
<h3><a class="doc-anchor" href="#doc-qlnorm">#</a> <code>qlnorm</code></h3>
<p><code>qlnorm</code> — log-normal quantile. Args: p [, mu, sigma].</p>
<pre><code class="lang-perl">p qlnorm(0.5, 0, 1) # 1.0 (median of LogN(0,1))
</code></pre>
</article>
<article class="doc-entry" id="doc-qlogis">
<h3><a class="doc-anchor" href="#doc-qlogis">#</a> <code>qlogis</code></h3>
<p><code>qlogis</code> — operation <code>qlogis</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p qlogis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qm">
<h3><a class="doc-anchor" href="#doc-qm">#</a> <code>qm</code></h3>
<p><code>qm</code> — operation <code>qm</code>. Alias for <code>quotemeta</code>. Category: *string*.</p>
<pre><code class="lang-perl">p qm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qnorm">
<h3><a class="doc-anchor" href="#doc-qnorm">#</a> <code>qnorm</code></h3>
<p><code>qnorm</code> — normal quantile (inverse CDF). Returns x such that P(X ≤ x) = p. Args: p [, mu, sigma].</p>
<pre><code class="lang-perl">p qnorm(0.975) # 1.96
p qnorm(0.5) # 0.0
p qnorm(0.95, 100, 15) # 90th percentile IQ
</code></pre>
</article>
<article class="doc-entry" id="doc-qntl">
<h3><a class="doc-anchor" href="#doc-qntl">#</a> <code>qntl</code></h3>
<p><code>qntl</code> — operation <code>qntl</code>. Alias for <code>quantile</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p qntl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qntls">
<h3><a class="doc-anchor" href="#doc-qntls">#</a> <code>qntls</code></h3>
<p><code>quantiles \@DATA, \@PROBS</code> — batch quantile lookup. Returns one element per probability in <code>\@PROBS</code>, computed via the same linear interpolation as <code>quantile</code>. Sorts the data exactly once across all probability points so callers don't pay an O(n log n) sort per quantile. Probabilities outside [0,1] are clamped.</p>
<pre><code class="lang-perl">my @d = (1..1000)
my @qs = quantiles(\@d, [0.25, 0.5, 0.75])
printf "q25=%.2f q50=%.2f q75=%.2f\n", @qs
# q25=250.75 q50=500.50 q75=750.25
</code></pre>
</article>
<article class="doc-entry" id="doc-qpe-iteration">
<h3><a class="doc-anchor" href="#doc-qpe-iteration">#</a> <code>qpe_iteration</code></h3>
<p><code>qpe_iteration</code> — operation <code>qpe iteration</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qpe_iteration $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qpois">
<h3><a class="doc-anchor" href="#doc-qpois">#</a> <code>qpois</code></h3>
<p><code>qpois</code> — Poisson quantile (smallest k where P(X≤k) ≥ p). Args: p, lambda.</p>
<pre><code class="lang-perl">p qpois(0.5, 5) # median of Poisson(5)
</code></pre>
</article>
<article class="doc-entry" id="doc-qq">
<h3><a class="doc-anchor" href="#doc-qq">#</a> <code>qq</code></h3>
<p><code>qq</code> — operation <code>qq</code>. Category: *quoting*.</p>
<pre><code class="lang-perl">p qq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qroots">
<h3><a class="doc-anchor" href="#doc-qroots">#</a> <code>qroots</code></h3>
<p><code>quadratic_roots($a, $b, $c)</code> (alias <code>qroots</code>) — solves ax² + bx + c = 0. Returns [x1, x2] for real roots, undef if no real solutions (discriminant < 0).</p>
<pre><code class="lang-perl">my @roots = quadratic_roots(1, -5, 6) # [3, 2] (x² - 5x + 6 = 0)
p qroots(1, 0, -4) # [2, -2]
p qroots(1, 2, 5) # undef (complex roots)
</code></pre>
</article>
<article class="doc-entry" id="doc-qs-relation">
<h3><a class="doc-anchor" href="#doc-qs-relation">#</a> <code>qs_relation</code></h3>
<p><code>qs_relation</code> — operation <code>qs relation</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p qs_relation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qt">
<h3><a class="doc-anchor" href="#doc-qt">#</a> <code>qt</code></h3>
<p><code>qt</code> — Student's t quantile. Args: p, df.</p>
<pre><code class="lang-perl">p qt(0.975, 10) # ≈ 2.228 (two-tailed 5%)
</code></pre>
</article>
<article class="doc-entry" id="doc-quadratic-assignment-step">
<h3><a class="doc-anchor" href="#doc-quadratic-assignment-step">#</a> <code>quadratic_assignment_step</code></h3>
<p><code>quadratic_assignment_step</code> — single-step update of <code>quadratic assignment</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p quadratic_assignment_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quadratic-mean-arr">
<h3><a class="doc-anchor" href="#doc-quadratic-mean-arr">#</a> <code>quadratic_mean_arr</code></h3>
<p><code>quadratic_mean_arr</code> — operation <code>quadratic mean arr</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p quadratic_mean_arr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quadratic-residue">
<h3><a class="doc-anchor" href="#doc-quadratic-residue">#</a> <code>quadratic_residue</code></h3>
<p><code>quadratic_residue</code> — operation <code>quadratic residue</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p quadratic_residue $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quantal-response-logit">
<h3><a class="doc-anchor" href="#doc-quantal-response-logit">#</a> <code>quantal_response_logit</code></h3>
<p><code>quantal_response_logit</code> — operation <code>quantal response logit</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p quantal_response_logit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quantile">
<h3><a class="doc-anchor" href="#doc-quantile">#</a> <code>quantile</code></h3>
<p><code>quantile</code> — operation <code>quantile</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p quantile $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quantile-p">
<h3><a class="doc-anchor" href="#doc-quantile-p">#</a> <code>quantile_p</code></h3>
<p><code>quantile_p</code> — quantile helper <code>p</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p quantile_p $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quantize">
<h3><a class="doc-anchor" href="#doc-quantize">#</a> <code>quantize</code></h3>
<p><code>quantize</code> — operation <code>quantize</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p quantize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quanto-adjustment">
<h3><a class="doc-anchor" href="#doc-quanto-adjustment">#</a> <code>quanto_adjustment</code></h3>
<p><code>quanto_adjustment</code> — operation <code>quanto adjustment</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p quanto_adjustment $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quantum-dimension-q">
<h3><a class="doc-anchor" href="#doc-quantum-dimension-q">#</a> <code>quantum_dimension_q</code></h3>
<p><code>quantum_dimension_q</code> — operation <code>quantum dimension q</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p quantum_dimension_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quantum-dimension-su2">
<h3><a class="doc-anchor" href="#doc-quantum-dimension-su2">#</a> <code>quantum_dimension_su2</code></h3>
<p><code>quantum_dimension_su2</code> — operation <code>quantum dimension su2</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p quantum_dimension_su2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quantum-efficiency-photo">
<h3><a class="doc-anchor" href="#doc-quantum-efficiency-photo">#</a> <code>quantum_efficiency_photo</code></h3>
<p><code>quantum_efficiency_photo</code> — operation <code>quantum efficiency photo</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p quantum_efficiency_photo $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quantum-fidelity-pure">
<h3><a class="doc-anchor" href="#doc-quantum-fidelity-pure">#</a> <code>quantum_fidelity_pure</code></h3>
<p><code>quantum_fidelity_pure</code> — operation <code>quantum fidelity pure</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p quantum_fidelity_pure $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quantum-fisher-info">
<h3><a class="doc-anchor" href="#doc-quantum-fisher-info">#</a> <code>quantum_fisher_info</code></h3>
<p><code>quantum_fisher_info</code> — operation <code>quantum fisher info</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p quantum_fisher_info $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quantum-invariant-eval">
<h3><a class="doc-anchor" href="#doc-quantum-invariant-eval">#</a> <code>quantum_invariant_eval</code></h3>
<p><code>quantum_invariant_eval</code> — operation <code>quantum invariant eval</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p quantum_invariant_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quantum-mutual-info">
<h3><a class="doc-anchor" href="#doc-quantum-mutual-info">#</a> <code>quantum_mutual_info</code></h3>
<p><code>quantum_mutual_info</code> — operation <code>quantum mutual info</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p quantum_mutual_info $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quantum-relative-entropy">
<h3><a class="doc-anchor" href="#doc-quantum-relative-entropy">#</a> <code>quantum_relative_entropy</code></h3>
<p><code>quantum_relative_entropy</code> — operation <code>quantum relative entropy</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p quantum_relative_entropy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quantum-teleportation">
<h3><a class="doc-anchor" href="#doc-quantum-teleportation">#</a> <code>quantum_teleportation</code></h3>
<p><code>quantum_teleportation</code> — operation <code>quantum teleportation</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p quantum_teleportation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quantum-variance">
<h3><a class="doc-anchor" href="#doc-quantum-variance">#</a> <code>quantum_variance</code></h3>
<p><code>quantum_variance</code> — operation <code>quantum variance</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p quantum_variance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quarter-of">
<h3><a class="doc-anchor" href="#doc-quarter-of">#</a> <code>quarter_of</code></h3>
<p><code>quarter_of</code> — operation <code>quarter of</code>. Category: *date helpers*.</p>
<pre><code class="lang-perl">p quarter_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quarter-of-year">
<h3><a class="doc-anchor" href="#doc-quarter-of-year">#</a> <code>quarter_of_year</code></h3>
<p><code>quarter_of_year</code> — operation <code>quarter of year</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p quarter_of_year $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quartile-exc">
<h3><a class="doc-anchor" href="#doc-quartile-exc">#</a> <code>quartile_exc</code></h3>
<p><code>quartile_exc</code> — operation <code>quartile exc</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p quartile_exc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quartile-inc">
<h3><a class="doc-anchor" href="#doc-quartile-inc">#</a> <code>quartile_inc</code></h3>
<p><code>quartile_inc</code> — operation <code>quartile inc</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p quartile_inc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quartiles">
<h3><a class="doc-anchor" href="#doc-quartiles">#</a> <code>quartiles</code></h3>
<p><code>quartiles(@data)</code> — returns the three quartile values [Q1, Q2, Q3] of a dataset. Q1 is the 25th percentile, Q2 is the median (50th), Q3 is the 75th percentile. Useful for understanding data distribution and computing IQR.</p>
<pre><code class="lang-perl">my @data = 1:100
my $q = quartiles(@data)
p "Q1=$q->[0] Q2=$q->[1] Q3=$q->[2]"
</code></pre>
</article>
<article class="doc-entry" id="doc-quarts">
<h3><a class="doc-anchor" href="#doc-quarts">#</a> <code>quarts</code></h3>
<p><code>quarts</code> — operation <code>quarts</code>. Alias for <code>quartiles</code>. Category: *statistics (extended)*.</p>
<pre><code class="lang-perl">p quarts $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quasi-geostrophic-omega">
<h3><a class="doc-anchor" href="#doc-quasi-geostrophic-omega">#</a> <code>quasi_geostrophic_omega</code></h3>
<p><code>quasi_geostrophic_omega</code> — operation <code>quasi geostrophic omega</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p quasi_geostrophic_omega $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quat-conjugate">
<h3><a class="doc-anchor" href="#doc-quat-conjugate">#</a> <code>quat_conjugate</code></h3>
<p><code>quat_conjugate(q) → [w,-x,-y,-z]</code>.</p>
</article>
<article class="doc-entry" id="doc-quat-dot">
<h3><a class="doc-anchor" href="#doc-quat-dot">#</a> <code>quat_dot</code></h3>
<p><code>quat_dot(a, b) → number</code> — 4-component dot product.</p>
</article>
<article class="doc-entry" id="doc-quat-from-euler">
<h3><a class="doc-anchor" href="#doc-quat-from-euler">#</a> <code>quat_from_euler</code></h3>
<p><code>quat_from_euler(roll, pitch, yaw) → [w,x,y,z]</code> — quaternion from XYZ Euler angles (radians).</p>
<pre><code class="lang-perl">p quat_from_euler(0, 0, 3.14159/2)
</code></pre>
</article>
<article class="doc-entry" id="doc-quat-identity">
<h3><a class="doc-anchor" href="#doc-quat-identity">#</a> <code>quat_identity</code></h3>
<p><code>quat_identity() → [w,x,y,z]</code> — identity quaternion <code>[1,0,0,0]</code>.</p>
</article>
<article class="doc-entry" id="doc-quat-inverse">
<h3><a class="doc-anchor" href="#doc-quat-inverse">#</a> <code>quat_inverse</code></h3>
<p><code>quat_inverse(q) → [w,x,y,z]</code> — <code>conjugate(q) / |q|²</code>.</p>
</article>
<article class="doc-entry" id="doc-quat-multiply">
<h3><a class="doc-anchor" href="#doc-quat-multiply">#</a> <code>quat_multiply</code></h3>
<p><code>quat_multiply(a, b) → [w,x,y,z]</code> — Hamilton product <code>a ⊗ b</code>.</p>
</article>
<article class="doc-entry" id="doc-quat-normalize">
<h3><a class="doc-anchor" href="#doc-quat-normalize">#</a> <code>quat_normalize</code></h3>
<p><code>quat_normalize(q) → [w,x,y,z]</code> — divide by magnitude. Required after iterative composition.</p>
</article>
<article class="doc-entry" id="doc-quat-to-euler">
<h3><a class="doc-anchor" href="#doc-quat-to-euler">#</a> <code>quat_to_euler</code></h3>
<p><code>quat_to_euler(q) → [roll, pitch, yaw]</code> — inverse of <code>quat_from_euler</code>.</p>
</article>
<article class="doc-entry" id="doc-quat-to-mat4">
<h3><a class="doc-anchor" href="#doc-quat-to-mat4">#</a> <code>quat_to_mat4</code></h3>
<p><code>quat_to_mat4(q) → matrix</code> — convert quaternion to 4×4 rotation matrix.</p>
</article>
<article class="doc-entry" id="doc-quaternion-from-axis-angle">
<h3><a class="doc-anchor" href="#doc-quaternion-from-axis-angle">#</a> <code>quaternion_from_axis_angle</code></h3>
<p><code>quaternion_from_axis_angle</code> — operation <code>quaternion from axis angle</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p quaternion_from_axis_angle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quaternion-from-imu">
<h3><a class="doc-anchor" href="#doc-quaternion-from-imu">#</a> <code>quaternion_from_imu</code></h3>
<p><code>quaternion_from_imu</code> — operation <code>quaternion from imu</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p quaternion_from_imu $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quaternion-multiply">
<h3><a class="doc-anchor" href="#doc-quaternion-multiply">#</a> <code>quaternion_multiply</code></h3>
<p><code>quaternion_multiply</code> — operation <code>quaternion multiply</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p quaternion_multiply $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quaternion-new">
<h3><a class="doc-anchor" href="#doc-quaternion-new">#</a> <code>quaternion_new</code></h3>
<p><code>quaternion_new</code> — constructor of <code>quaternion</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p quaternion_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quaternion-normalize">
<h3><a class="doc-anchor" href="#doc-quaternion-normalize">#</a> <code>quaternion_normalize</code></h3>
<p><code>quaternion_normalize</code> — operation <code>quaternion normalize</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p quaternion_normalize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quaternion-to-matrix">
<h3><a class="doc-anchor" href="#doc-quaternion-to-matrix">#</a> <code>quaternion_to_matrix</code></h3>
<p><code>quaternion_to_matrix</code> — convert from <code>quaternion</code> to <code>matrix</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p quaternion_to_matrix $value
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-ccx">
<h3><a class="doc-anchor" href="#doc-qubit-ccx">#</a> <code>qubit_ccx</code></h3>
<p><code>qubit_ccx</code> — operation <code>qubit ccx</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_ccx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-cnot">
<h3><a class="doc-anchor" href="#doc-qubit-cnot">#</a> <code>qubit_cnot</code></h3>
<p><code>qubit_cnot</code> — operation <code>qubit cnot</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_cnot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-cz">
<h3><a class="doc-anchor" href="#doc-qubit-cz">#</a> <code>qubit_cz</code></h3>
<p><code>qubit_cz</code> — operation <code>qubit cz</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_cz $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-h">
<h3><a class="doc-anchor" href="#doc-qubit-h">#</a> <code>qubit_h</code></h3>
<p><code>qubit_h</code> — operation <code>qubit h</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_h $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-measure">
<h3><a class="doc-anchor" href="#doc-qubit-measure">#</a> <code>qubit_measure</code></h3>
<p><code>qubit_measure</code> — operation <code>qubit measure</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_measure $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-phase">
<h3><a class="doc-anchor" href="#doc-qubit-phase">#</a> <code>qubit_phase</code></h3>
<p><code>qubit_phase</code> — operation <code>qubit phase</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_phase $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-reset">
<h3><a class="doc-anchor" href="#doc-qubit-reset">#</a> <code>qubit_reset</code></h3>
<p><code>qubit_reset</code> — operation <code>qubit reset</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_reset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-rx">
<h3><a class="doc-anchor" href="#doc-qubit-rx">#</a> <code>qubit_rx</code></h3>
<p><code>qubit_rx</code> — operation <code>qubit rx</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_rx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-ry">
<h3><a class="doc-anchor" href="#doc-qubit-ry">#</a> <code>qubit_ry</code></h3>
<p><code>qubit_ry</code> — operation <code>qubit ry</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_ry $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-rz">
<h3><a class="doc-anchor" href="#doc-qubit-rz">#</a> <code>qubit_rz</code></h3>
<p><code>qubit_rz</code> — operation <code>qubit rz</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_rz $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-s">
<h3><a class="doc-anchor" href="#doc-qubit-s">#</a> <code>qubit_s</code></h3>
<p><code>qubit_s</code> — operation <code>qubit s</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_s $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-swap">
<h3><a class="doc-anchor" href="#doc-qubit-swap">#</a> <code>qubit_swap</code></h3>
<p><code>qubit_swap</code> — operation <code>qubit swap</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_swap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-t">
<h3><a class="doc-anchor" href="#doc-qubit-t">#</a> <code>qubit_t</code></h3>
<p><code>qubit_t</code> — operation <code>qubit t</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-u1">
<h3><a class="doc-anchor" href="#doc-qubit-u1">#</a> <code>qubit_u1</code></h3>
<p><code>qubit_u1</code> — operation <code>qubit u1</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_u1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-u2">
<h3><a class="doc-anchor" href="#doc-qubit-u2">#</a> <code>qubit_u2</code></h3>
<p><code>qubit_u2</code> — operation <code>qubit u2</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_u2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-u3">
<h3><a class="doc-anchor" href="#doc-qubit-u3">#</a> <code>qubit_u3</code></h3>
<p><code>qubit_u3</code> — operation <code>qubit u3</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_u3 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-x">
<h3><a class="doc-anchor" href="#doc-qubit-x">#</a> <code>qubit_x</code></h3>
<p><code>qubit_x</code> — operation <code>qubit x</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_x $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-y">
<h3><a class="doc-anchor" href="#doc-qubit-y">#</a> <code>qubit_y</code></h3>
<p><code>qubit_y</code> — operation <code>qubit y</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_y $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qubit-z">
<h3><a class="doc-anchor" href="#doc-qubit-z">#</a> <code>qubit_z</code></h3>
<p><code>qubit_z</code> — operation <code>qubit z</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p qubit_z $x
</code></pre>
</article>
<article class="doc-entry" id="doc-queue-new">
<h3><a class="doc-anchor" href="#doc-queue-new">#</a> <code>queue_new</code></h3>
<p><code>queue_new</code> — queue op <code>new</code>. Category: *data structure helpers*.</p>
<pre><code class="lang-perl">p queue_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quickselect-median">
<h3><a class="doc-anchor" href="#doc-quickselect-median">#</a> <code>quickselect_median</code></h3>
<p><code>quickselect_median</code> — median of <code>quickselect</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p quickselect_median @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-quickselect-nth">
<h3><a class="doc-anchor" href="#doc-quickselect-nth">#</a> <code>quickselect_nth</code></h3>
<p><code>quickselect_nth</code> — operation <code>quickselect nth</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p quickselect_nth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quiver-path-count">
<h3><a class="doc-anchor" href="#doc-quiver-path-count">#</a> <code>quiver_path_count</code></h3>
<p><code>quiver_path_count</code> — count of <code>quiver path</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p quiver_path_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qunif">
<h3><a class="doc-anchor" href="#doc-qunif">#</a> <code>qunif</code></h3>
<p><code>qunif</code> — uniform quantile. Args: p [, min, max].</p>
<pre><code class="lang-perl">p qunif(0.5, 0, 10) # 5.0 (median)
</code></pre>
</article>
<article class="doc-entry" id="doc-quote">
<h3><a class="doc-anchor" href="#doc-quote">#</a> <code>quote</code></h3>
<p><code>quote</code> — operation <code>quote</code>. Category: *string quote / escape*.</p>
<pre><code class="lang-perl">p quote $x
</code></pre>
</article>
<article class="doc-entry" id="doc-quoted-printable-encode">
<h3><a class="doc-anchor" href="#doc-quoted-printable-encode">#</a> <code>quoted_printable_encode</code></h3>
<p><code>quoted_printable_encode</code> — encode of <code>quoted printable</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p quoted_printable_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qw">
<h3><a class="doc-anchor" href="#doc-qw">#</a> <code>qw</code></h3>
<p><code>qw</code> — operation <code>qw</code>. Category: *quoting*.</p>
<pre><code class="lang-perl">p qw $x
</code></pre>
</article>
<article class="doc-entry" id="doc-qweibull">
<h3><a class="doc-anchor" href="#doc-qweibull">#</a> <code>qweibull</code></h3>
<p><code>qweibull</code> — Weibull quantile. Args: p, shape [, scale].</p>
<pre><code class="lang-perl">p qweibull(0.5, 1, 1) # same as qexp
</code></pre>
</article>
<article class="doc-entry" id="doc-r0-basic">
<h3><a class="doc-anchor" href="#doc-r0-basic">#</a> <code>r0_basic</code></h3>
<p><code>r0_basic</code> — operation <code>r0 basic</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p r0_basic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-r2d">
<h3><a class="doc-anchor" href="#doc-r2d">#</a> <code>r2d</code></h3>
<p><code>r2d</code> — operation <code>r2d</code>. Alias for <code>rad_to_deg</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p r2d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-r72">
<h3><a class="doc-anchor" href="#doc-r72">#</a> <code>r72</code></h3>
<p><code>rule_of_72($rate)</code> (alias <code>r72</code>) — estimates years to double investment using the Rule of 72: 72 / (rate × 100). Quick mental math approximation.</p>
<pre><code class="lang-perl">p r72(0.06) # 12 years to double at 6%
p r72(0.10) # 7.2 years at 10%
</code></pre>
</article>
<article class="doc-entry" id="doc-r-effective-t">
<h3><a class="doc-anchor" href="#doc-r-effective-t">#</a> <code>r_effective_t</code></h3>
<p><code>r_effective_t</code> — operation <code>r effective t</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p r_effective_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-r-naught-basic">
<h3><a class="doc-anchor" href="#doc-r-naught-basic">#</a> <code>r_naught_basic</code></h3>
<p><code>r_naught_basic</code> — operation <code>r naught basic</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p r_naught_basic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-r-parallel">
<h3><a class="doc-anchor" href="#doc-r-parallel">#</a> <code>r_parallel</code></h3>
<p><code>r_parallel</code> — operation <code>r parallel</code>. Alias for <code>resistance_parallel</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p r_parallel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-r-series">
<h3><a class="doc-anchor" href="#doc-r-series">#</a> <code>r_series</code></h3>
<p><code>r_series</code> — operation <code>r series</code>. Alias for <code>resistance_series</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p r_series $x
</code></pre>
</article>
<article class="doc-entry" id="doc-r-squared">
<h3><a class="doc-anchor" href="#doc-r-squared">#</a> <code>r_squared</code></h3>
<p><code>r_squared</code> — operation <code>r squared</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p r_squared $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ra-dec-to-alt-az">
<h3><a class="doc-anchor" href="#doc-ra-dec-to-alt-az">#</a> <code>ra_dec_to_alt_az</code></h3>
<p><code>ra_dec_to_alt_az</code> — convert from <code>ra dec</code> to <code>alt az</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p ra_dec_to_alt_az $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ra-dec-to-az-alt">
<h3><a class="doc-anchor" href="#doc-ra-dec-to-az-alt">#</a> <code>ra_dec_to_az_alt</code></h3>
<p><code>ra_dec_to_az_alt</code> — convert from <code>ra dec</code> to <code>az alt</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p ra_dec_to_az_alt $value
</code></pre>
</article>
<article class="doc-entry" id="doc-rabi-frequency">
<h3><a class="doc-anchor" href="#doc-rabi-frequency">#</a> <code>rabi_frequency</code></h3>
<p><code>rabi_frequency</code> — operation <code>rabi frequency</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p rabi_frequency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rabin-karp-hash">
<h3><a class="doc-anchor" href="#doc-rabin-karp-hash">#</a> <code>rabin_karp_hash</code></h3>
<p><code>rabin_karp_hash</code> — hash function of <code>rabin karp</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p rabin_karp_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rad-to-deg">
<h3><a class="doc-anchor" href="#doc-rad-to-deg">#</a> <code>rad_to_deg</code></h3>
<p><code>rad_to_deg</code> — convert from <code>rad</code> to <code>deg</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p rad_to_deg $value
</code></pre>
</article>
<article class="doc-entry" id="doc-radd">
<h3><a class="doc-anchor" href="#doc-radd">#</a> <code>radd</code></h3>
<p><code>radd</code> — operation <code>radd</code>. Alias for <code>roman_add</code>. Category: *roman numerals*.</p>
<pre><code class="lang-perl">p radd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-radians">
<h3><a class="doc-anchor" href="#doc-radians">#</a> <code>radians</code></h3>
<p><code>radians</code> — operation <code>radians</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p radians $x
</code></pre>
</article>
<article class="doc-entry" id="doc-radiation-pressure">
<h3><a class="doc-anchor" href="#doc-radiation-pressure">#</a> <code>radiation_pressure</code></h3>
<p><code>radiation_pressure</code> — operation <code>radiation pressure</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p radiation_pressure $x
</code></pre>
</article>
<article class="doc-entry" id="doc-radius-bfs">
<h3><a class="doc-anchor" href="#doc-radius-bfs">#</a> <code>radius_bfs</code></h3>
<p><code>radius_bfs</code> — operation <code>radius bfs</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p radius_bfs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ragone-point">
<h3><a class="doc-anchor" href="#doc-ragone-point">#</a> <code>ragone_point</code></h3>
<p><code>ragone_point</code> — operation <code>ragone point</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ragone_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-railfence-encrypt">
<h3><a class="doc-anchor" href="#doc-railfence-encrypt">#</a> <code>railfence_encrypt</code></h3>
<p><code>railfence_encrypt</code> — encrypt of <code>railfence</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p railfence_encrypt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ramachandran-phi-psi">
<h3><a class="doc-anchor" href="#doc-ramachandran-phi-psi">#</a> <code>ramachandran_phi_psi</code></h3>
<p><code>ramachandran_phi_psi</code> — operation <code>ramachandran phi psi</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p ramachandran_phi_psi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ramsey-reset-test">
<h3><a class="doc-anchor" href="#doc-ramsey-reset-test">#</a> <code>ramsey_reset_test</code></h3>
<p><code>ramsey_reset_test</code> — statistical test of <code>ramsey reset</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p ramsey_reset_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ramsey-visibility">
<h3><a class="doc-anchor" href="#doc-ramsey-visibility">#</a> <code>ramsey_visibility</code></h3>
<p><code>ramsey_visibility</code> — operation <code>ramsey visibility</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p ramsey_visibility $x
</code></pre>
</article>
<article class="doc-entry" id="doc-randles-circuit-z">
<h3><a class="doc-anchor" href="#doc-randles-circuit-z">#</a> <code>randles_circuit_z</code></h3>
<p><code>randles_circuit_z</code> — operation <code>randles circuit z</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p randles_circuit_z $x
</code></pre>
</article>
<article class="doc-entry" id="doc-randles-sevcik-peak">
<h3><a class="doc-anchor" href="#doc-randles-sevcik-peak">#</a> <code>randles_sevcik_peak</code></h3>
<p><code>randles_sevcik_peak</code> — operation <code>randles sevcik peak</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p randles_sevcik_peak $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-alpha">
<h3><a class="doc-anchor" href="#doc-random-alpha">#</a> <code>random_alpha</code></h3>
<p><code>random_alpha</code> — random sampling helper <code>alpha</code>. Category: *random*.</p>
<pre><code class="lang-perl">p random_alpha $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-alphabetic">
<h3><a class="doc-anchor" href="#doc-random-alphabetic">#</a> <code>random_alphabetic</code></h3>
<p><code>random_alphabetic</code> — random sampling helper <code>alphabetic</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p random_alphabetic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-alphanumeric">
<h3><a class="doc-anchor" href="#doc-random-alphanumeric">#</a> <code>random_alphanumeric</code></h3>
<p><code>random_alphanumeric</code> — random sampling helper <code>alphanumeric</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p random_alphanumeric $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-bernoulli">
<h3><a class="doc-anchor" href="#doc-random-bernoulli">#</a> <code>random_bernoulli</code></h3>
<p><code>random_bernoulli</code> — random sampling helper <code>bernoulli</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p random_bernoulli $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-beta">
<h3><a class="doc-anchor" href="#doc-random-beta">#</a> <code>random_beta</code></h3>
<p><code>random_beta</code> — random sampling helper <code>beta</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p random_beta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-between">
<h3><a class="doc-anchor" href="#doc-random-between">#</a> <code>random_between</code></h3>
<p><code>random_between</code> — random sampling helper <code>between</code>. Category: *random*.</p>
<pre><code class="lang-perl">p random_between $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-bool">
<h3><a class="doc-anchor" href="#doc-random-bool">#</a> <code>random_bool</code></h3>
<p><code>random_bool</code> — random sampling helper <code>bool</code>. Category: *random*.</p>
<pre><code class="lang-perl">p random_bool $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-char">
<h3><a class="doc-anchor" href="#doc-random-char">#</a> <code>random_char</code></h3>
<p><code>random_char</code> — random sampling helper <code>char</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p random_char $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-choice">
<h3><a class="doc-anchor" href="#doc-random-choice">#</a> <code>random_choice</code></h3>
<p><code>random_choice</code> — random sampling helper <code>choice</code>. Category: *random*.</p>
<pre><code class="lang-perl">p random_choice $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-choices-weighted">
<h3><a class="doc-anchor" href="#doc-random-choices-weighted">#</a> <code>random_choices_weighted</code></h3>
<p><code>random_choices_weighted</code> — random sampling helper <code>choices weighted</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p random_choices_weighted $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-color">
<h3><a class="doc-anchor" href="#doc-random-color">#</a> <code>random_color</code></h3>
<p><code>random_color</code> — random sampling helper <code>color</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p random_color $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-digit">
<h3><a class="doc-anchor" href="#doc-random-digit">#</a> <code>random_digit</code></h3>
<p><code>random_digit</code> — random sampling helper <code>digit</code>. Category: *random*.</p>
<pre><code class="lang-perl">p random_digit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-exponential">
<h3><a class="doc-anchor" href="#doc-random-exponential">#</a> <code>random_exponential</code></h3>
<p><code>random_exponential</code> — random sampling helper <code>exponential</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p random_exponential $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-float">
<h3><a class="doc-anchor" href="#doc-random-float">#</a> <code>random_float</code></h3>
<p><code>random_float</code> — random sampling helper <code>float</code>. Category: *random*.</p>
<pre><code class="lang-perl">p random_float $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-gamma">
<h3><a class="doc-anchor" href="#doc-random-gamma">#</a> <code>random_gamma</code></h3>
<p><code>random_gamma</code> — random sampling helper <code>gamma</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p random_gamma $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-int">
<h3><a class="doc-anchor" href="#doc-random-int">#</a> <code>random_int</code></h3>
<p><code>random_int</code> — random sampling helper <code>int</code>. Category: *random*.</p>
<pre><code class="lang-perl">p random_int $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-lognormal">
<h3><a class="doc-anchor" href="#doc-random-lognormal">#</a> <code>random_lognormal</code></h3>
<p><code>random_lognormal</code> — random sampling helper <code>lognormal</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p random_lognormal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-normal">
<h3><a class="doc-anchor" href="#doc-random-normal">#</a> <code>random_normal</code></h3>
<p><code>random_normal</code> — random sampling helper <code>normal</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p random_normal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-password">
<h3><a class="doc-anchor" href="#doc-random-password">#</a> <code>random_password</code></h3>
<p><code>random_password</code> — random sampling helper <code>password</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p random_password $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-poisson">
<h3><a class="doc-anchor" href="#doc-random-poisson">#</a> <code>random_poisson</code></h3>
<p><code>random_poisson</code> — random sampling helper <code>poisson</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p random_poisson $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-sample">
<h3><a class="doc-anchor" href="#doc-random-sample">#</a> <code>random_sample</code></h3>
<p><code>random_sample</code> — random sampling helper <code>sample</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p random_sample $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-string">
<h3><a class="doc-anchor" href="#doc-random-string">#</a> <code>random_string</code></h3>
<p><code>random_string</code> — random sampling helper <code>string</code>. Category: *random*.</p>
<pre><code class="lang-perl">p random_string $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-walk-drift-step">
<h3><a class="doc-anchor" href="#doc-random-walk-drift-step">#</a> <code>random_walk_drift_step</code></h3>
<p><code>random_walk_drift_step</code> — random sampling helper <code>walk drift step</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p random_walk_drift_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-walk-hitting">
<h3><a class="doc-anchor" href="#doc-random-walk-hitting">#</a> <code>random_walk_hitting</code></h3>
<p><code>random_walk_hitting</code> — random sampling helper <code>walk hitting</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p random_walk_hitting $x
</code></pre>
</article>
<article class="doc-entry" id="doc-random-walk-innovation">
<h3><a class="doc-anchor" href="#doc-random-walk-innovation">#</a> <code>random_walk_innovation</code></h3>
<p><code>random_walk_innovation</code> — random sampling helper <code>walk innovation</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p random_walk_innovation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-range-coding-step">
<h3><a class="doc-anchor" href="#doc-range-coding-step">#</a> <code>range_coding_step</code></h3>
<p><code>range_coding_step</code> — single-step update of <code>range coding</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p range_coding_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-range-compress">
<h3><a class="doc-anchor" href="#doc-range-compress">#</a> <code>range_compress</code></h3>
<p><code>range_compress</code> — compress of <code>range</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p range_compress $x
</code></pre>
</article>
<article class="doc-entry" id="doc-range-decode-step">
<h3><a class="doc-anchor" href="#doc-range-decode-step">#</a> <code>range_decode_step</code></h3>
<p><code>range_decode_step</code> — single-step update of <code>range decode</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p range_decode_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-range-exclusive">
<h3><a class="doc-anchor" href="#doc-range-exclusive">#</a> <code>range_exclusive</code></h3>
<p><code>range_exclusive</code> — operation <code>range exclusive</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p range_exclusive $x
</code></pre>
</article>
<article class="doc-entry" id="doc-range-expand">
<h3><a class="doc-anchor" href="#doc-range-expand">#</a> <code>range_expand</code></h3>
<p><code>range_expand</code> — operation <code>range expand</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p range_expand $x
</code></pre>
</article>
<article class="doc-entry" id="doc-range-header-parse">
<h3><a class="doc-anchor" href="#doc-range-header-parse">#</a> <code>range_header_parse</code></h3>
<p><code>range_header_parse</code> — operation <code>range header parse</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p range_header_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-range-inclusive">
<h3><a class="doc-anchor" href="#doc-range-inclusive">#</a> <code>range_inclusive</code></h3>
<p><code>range_inclusive</code> — operation <code>range inclusive</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p range_inclusive $x
</code></pre>
</article>
<article class="doc-entry" id="doc-range-of">
<h3><a class="doc-anchor" href="#doc-range-of">#</a> <code>range_of</code></h3>
<p><code>range_of</code> — operation <code>range of</code>. Category: *more list helpers*.</p>
<pre><code class="lang-perl">p range_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-range-to-cidr">
<h3><a class="doc-anchor" href="#doc-range-to-cidr">#</a> <code>range_to_cidr</code></h3>
<p><code>range_to_cidr(start, end) → array</code> — minimum set of CIDR blocks covering the range.</p>
</article>
<article class="doc-entry" id="doc-range-voting-score">
<h3><a class="doc-anchor" href="#doc-range-voting-score">#</a> <code>range_voting_score</code></h3>
<p><code>range_voting_score</code> — score of <code>range voting</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p range_voting_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rank">
<h3><a class="doc-anchor" href="#doc-rank">#</a> <code>rank</code></h3>
<p><code>rank</code> — operation <code>rank</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p rank $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rank-avg">
<h3><a class="doc-anchor" href="#doc-rank-avg">#</a> <code>rank_avg</code></h3>
<p><code>rank_avg</code> — operation <code>rank avg</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p rank_avg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rank-data">
<h3><a class="doc-anchor" href="#doc-rank-data">#</a> <code>rank_data</code></h3>
<p><code>rank_data(xs) → array</code> — assign ranks 1..n with ties handled by average rank.</p>
<pre><code class="lang-perl">p rank_data([10, 20, 20, 30]) # [1, 2.5, 2.5, 4]
</code></pre>
</article>
<article class="doc-entry" id="doc-rank-eq">
<h3><a class="doc-anchor" href="#doc-rank-eq">#</a> <code>rank_eq</code></h3>
<p><code>rank_eq</code> — operation <code>rank eq</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p rank_eq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ranked-choice">
<h3><a class="doc-anchor" href="#doc-ranked-choice">#</a> <code>ranked_choice</code></h3>
<p><code>ranked_choice</code> — operation <code>ranked choice</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p ranked_choice $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ranking-average">
<h3><a class="doc-anchor" href="#doc-ranking-average">#</a> <code>ranking_average</code></h3>
<p><code>ranking_average(lists) → array</code> — element-wise average across multiple ranking lists (Borda-style).</p>
</article>
<article class="doc-entry" id="doc-ranking-kendall-tau">
<h3><a class="doc-anchor" href="#doc-ranking-kendall-tau">#</a> <code>ranking_kendall_tau</code></h3>
<p><code>ranking_kendall_tau(a, b) → number</code> — Kendall's τ rank correlation in [-1, 1].</p>
<pre><code class="lang-perl">p ranking_kendall_tau([1,2,3], [3,2,1]) # -1
</code></pre>
</article>
<article class="doc-entry" id="doc-ranking-spearman-rho">
<h3><a class="doc-anchor" href="#doc-ranking-spearman-rho">#</a> <code>ranking_spearman_rho</code></h3>
<p><code>ranking_spearman_rho(a, b) → number</code> — Spearman's ρ rank correlation.</p>
</article>
<article class="doc-entry" id="doc-ransac-homography">
<h3><a class="doc-anchor" href="#doc-ransac-homography">#</a> <code>ransac_homography</code></h3>
<p><code>ransac_homography</code> — operation <code>ransac homography</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p ransac_homography $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ransac-iteration-count">
<h3><a class="doc-anchor" href="#doc-ransac-iteration-count">#</a> <code>ransac_iteration_count</code></h3>
<p><code>ransac_iteration_count</code> — count of <code>ransac iteration</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ransac_iteration_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rao-quadratic-entropy">
<h3><a class="doc-anchor" href="#doc-rao-quadratic-entropy">#</a> <code>rao_quadratic_entropy</code></h3>
<p><code>rao_quadratic_entropy</code> — operation <code>rao quadratic entropy</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p rao_quadratic_entropy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-raoult-law">
<h3><a class="doc-anchor" href="#doc-raoult-law">#</a> <code>raoult_law</code></h3>
<p><code>raoult_law</code> — operation <code>raoult law</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p raoult_law $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rapid-blink">
<h3><a class="doc-anchor" href="#doc-rapid-blink">#</a> <code>rapid_blink</code></h3>
<p><code>rapid_blink</code> — operation <code>rapid blink</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p rapid_blink $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ratcliff-obershelp">
<h3><a class="doc-anchor" href="#doc-ratcliff-obershelp">#</a> <code>ratcliff_obershelp</code></h3>
<p><code>ratcliff_obershelp</code> — operation <code>ratcliff obershelp</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p ratcliff_obershelp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rate">
<h3><a class="doc-anchor" href="#doc-rate">#</a> <code>rate</code></h3>
<p><code>rate</code> — operation <code>rate</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ray-aabb-intersect">
<h3><a class="doc-anchor" href="#doc-ray-aabb-intersect">#</a> <code>ray_aabb_intersect</code></h3>
<p><code>ray_aabb_intersect(origin, dir, aabb) → number</code> — t along ray where it enters; <code>-1</code> if miss.</p>
<pre><code class="lang-perl">p ray_aabb_intersect([-1,0.5,0.5], [1,0,0], aabb_new([0,0,0],[1,1,1])) # 1.0
</code></pre>
</article>
<article class="doc-entry" id="doc-ray-plane-intersect">
<h3><a class="doc-anchor" href="#doc-ray-plane-intersect">#</a> <code>ray_plane_intersect</code></h3>
<p><code>ray_plane_intersect(origin, dir, point, normal) → number</code> — distance along ray; <code>-1</code> for parallel or behind ray.</p>
</article>
<article class="doc-entry" id="doc-ray-plane-intersect-2">
<h3><a class="doc-anchor" href="#doc-ray-plane-intersect-2">#</a> <code>ray_plane_intersect_2</code></h3>
<p><code>ray_plane_intersect_2</code> — ray-geometry intersection op <code>plane intersect 2</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p ray_plane_intersect_2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-raychaudhuri-step">
<h3><a class="doc-anchor" href="#doc-raychaudhuri-step">#</a> <code>raychaudhuri_step</code></h3>
<p><code>raychaudhuri_step</code> — single-step update of <code>raychaudhuri</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p raychaudhuri_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rayleigh-criterion">
<h3><a class="doc-anchor" href="#doc-rayleigh-criterion">#</a> <code>rayleigh_criterion</code></h3>
<p><code>rayleigh_criterion</code> — operation <code>rayleigh criterion</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p rayleigh_criterion $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rayleigh-number-step">
<h3><a class="doc-anchor" href="#doc-rayleigh-number-step">#</a> <code>rayleigh_number_step</code></h3>
<p><code>rayleigh_number_step</code> — single-step update of <code>rayleigh number</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p rayleigh_number_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rayleigh-resolution">
<h3><a class="doc-anchor" href="#doc-rayleigh-resolution">#</a> <code>rayleigh_resolution</code></h3>
<p><code>rayleigh_resolution</code> — operation <code>rayleigh resolution</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p rayleigh_resolution $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rb">
<h3><a class="doc-anchor" href="#doc-rb">#</a> <code>rb</code></h3>
<p><code>rb</code> — operation <code>rb</code>. Alias for <code>read_bytes</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p rb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rbeta">
<h3><a class="doc-anchor" href="#doc-rbeta">#</a> <code>rbeta</code></h3>
<p><code>rbeta</code> — generate n random beta variates. Args: n, alpha, beta. Like R's rbeta().</p>
<pre><code class="lang-perl">my @x = @{rbeta(100, 2, 5)} # Beta(2,5)
</code></pre>
</article>
<article class="doc-entry" id="doc-rbind">
<h3><a class="doc-anchor" href="#doc-rbind">#</a> <code>rbind</code></h3>
<p><code>rbind</code> — bind matrices/vectors by rows (vertical stack). Like R's rbind().</p>
<pre><code class="lang-perl">my $m = rbind([1,2,3], [4,5,6]) # [[1,2,3],[4,5,6]]
</code></pre>
</article>
<article class="doc-entry" id="doc-rbinom">
<h3><a class="doc-anchor" href="#doc-rbinom">#</a> <code>rbinom</code></h3>
<p><code>rbinom</code> — generate n random binomial variates. Args: n, size, prob. Like R's rbinom().</p>
<pre><code class="lang-perl">my @x = @{rbinom(100, 10, 0.3)} # 100 draws from Binom(10,0.3)
</code></pre>
</article>
<article class="doc-entry" id="doc-rc-tau">
<h3><a class="doc-anchor" href="#doc-rc-tau">#</a> <code>rc_tau</code></h3>
<p><code>rc_tau</code> — operation <code>rc tau</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p rc_tau $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rc-time-constant">
<h3><a class="doc-anchor" href="#doc-rc-time-constant">#</a> <code>rc_time_constant</code></h3>
<p><code>rc_time_constant</code> — operation <code>rc time constant</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p rc_time_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rcauchy">
<h3><a class="doc-anchor" href="#doc-rcauchy">#</a> <code>rcauchy</code></h3>
<p><code>rcauchy</code> — generate n random Cauchy variates. Args: n [, location, scale].</p>
<pre><code class="lang-perl">my @x = @{rcauchy(100, 0, 1)} # standard Cauchy
</code></pre>
</article>
<article class="doc-entry" id="doc-rchisq">
<h3><a class="doc-anchor" href="#doc-rchisq">#</a> <code>rchisq</code></h3>
<p><code>rchisq</code> — generate n random chi-squared variates. Args: n, df. Like R's rchisq().</p>
<pre><code class="lang-perl">my @x = @{rchisq(100, 5)} # Chi-sq with 5 df
</code></pre>
</article>
<article class="doc-entry" id="doc-rcolor">
<h3><a class="doc-anchor" href="#doc-rcolor">#</a> <code>rcolor</code></h3>
<p><code>rcolor</code> — operation <code>rcolor</code>. Alias for <code>random_color</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p rcolor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rctau">
<h3><a class="doc-anchor" href="#doc-rctau">#</a> <code>rctau</code></h3>
<p><code>rctau</code> — operation <code>rctau</code>. Alias for <code>rc_time_constant</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p rctau $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rdcs">
<h3><a class="doc-anchor" href="#doc-rdcs">#</a> <code>rdcs</code></h3>
<p><code>rdcs</code> — operation <code>rdcs</code>. Alias for <code>reductions</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p rdcs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rdd-estimate">
<h3><a class="doc-anchor" href="#doc-rdd-estimate">#</a> <code>rdd_estimate</code></h3>
<p><code>rdd_estimate</code> — operation <code>rdd estimate</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p rdd_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-re-escape">
<h3><a class="doc-anchor" href="#doc-re-escape">#</a> <code>re_escape</code></h3>
<p><code>re_escape</code> — operation <code>re escape</code>. Category: *more regex*.</p>
<pre><code class="lang-perl">p re_escape $x
</code></pre>
</article>
<article class="doc-entry" id="doc-re-find-all">
<h3><a class="doc-anchor" href="#doc-re-find-all">#</a> <code>re_find_all</code></h3>
<p><code>re_find_all</code> — operation <code>re find all</code>. Category: *more regex*.</p>
<pre><code class="lang-perl">p re_find_all $x
</code></pre>
</article>
<article class="doc-entry" id="doc-re-groups">
<h3><a class="doc-anchor" href="#doc-re-groups">#</a> <code>re_groups</code></h3>
<p><code>re_groups</code> — operation <code>re groups</code>. Category: *more regex*.</p>
<pre><code class="lang-perl">p re_groups $x
</code></pre>
</article>
<article class="doc-entry" id="doc-re-match">
<h3><a class="doc-anchor" href="#doc-re-match">#</a> <code>re_match</code></h3>
<p><code>re_match</code> — operation <code>re match</code>. Alias for <code>matches_regex</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p re_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-re-split-limit">
<h3><a class="doc-anchor" href="#doc-re-split-limit">#</a> <code>re_split_limit</code></h3>
<p><code>re_split_limit</code> — operation <code>re split limit</code>. Category: *more regex*.</p>
<pre><code class="lang-perl">p re_split_limit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-re-test">
<h3><a class="doc-anchor" href="#doc-re-test">#</a> <code>re_test</code></h3>
<p><code>re_test</code> — statistical test of <code>re</code>. Category: *more regex*.</p>
<pre><code class="lang-perl">p re_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reaction-quotient">
<h3><a class="doc-anchor" href="#doc-reaction-quotient">#</a> <code>reaction_quotient</code></h3>
<p><code>reaction_quotient</code> — operation <code>reaction quotient</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p reaction_quotient $x
</code></pre>
</article>
<article class="doc-entry" id="doc-realized-volatility">
<h3><a class="doc-anchor" href="#doc-realized-volatility">#</a> <code>realized_volatility</code></h3>
<p><code>realized_volatility</code> — operation <code>realized volatility</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p realized_volatility $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rearth">
<h3><a class="doc-anchor" href="#doc-rearth">#</a> <code>rearth</code></h3>
<p><code>rearth</code> — operation <code>rearth</code>. Alias for <code>earth_radius</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p rearth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-received">
<h3><a class="doc-anchor" href="#doc-received">#</a> <code>received</code></h3>
<p><code>received</code> — operation <code>received</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p received $x
</code></pre>
</article>
<article class="doc-entry" id="doc-recip">
<h3><a class="doc-anchor" href="#doc-recip">#</a> <code>recip</code></h3>
<p><code>recip</code> — operation <code>recip</code>. Alias for <code>reciprocal_of</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p recip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reciprocal">
<h3><a class="doc-anchor" href="#doc-reciprocal">#</a> <code>reciprocal</code></h3>
<p><code>reciprocal</code> — operation <code>reciprocal</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p reciprocal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reciprocal-of">
<h3><a class="doc-anchor" href="#doc-reciprocal-of">#</a> <code>reciprocal_of</code></h3>
<p><code>reciprocal_of</code> — operation <code>reciprocal of</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p reciprocal_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reciprocal-pdf">
<h3><a class="doc-anchor" href="#doc-reciprocal-pdf">#</a> <code>reciprocal_pdf</code></h3>
<p><code>reciprocal_pdf</code> — operation <code>reciprocal pdf</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p reciprocal_pdf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rect-area">
<h3><a class="doc-anchor" href="#doc-rect-area">#</a> <code>rect_area</code></h3>
<p><code>rect_area</code> — rectangle geometry op <code>area</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p rect_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rect-contains-point">
<h3><a class="doc-anchor" href="#doc-rect-contains-point">#</a> <code>rect_contains_point</code></h3>
<p><code>rect_contains_point</code> — rectangle geometry op <code>contains point</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p rect_contains_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rect-intersect">
<h3><a class="doc-anchor" href="#doc-rect-intersect">#</a> <code>rect_intersect</code></h3>
<p><code>rect_intersect</code> — rectangle geometry op <code>intersect</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p rect_intersect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rect-perimeter">
<h3><a class="doc-anchor" href="#doc-rect-perimeter">#</a> <code>rect_perimeter</code></h3>
<p><code>rect_perimeter</code> — rectangle geometry op <code>perimeter</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p rect_perimeter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rect-union">
<h3><a class="doc-anchor" href="#doc-rect-union">#</a> <code>rect_union</code></h3>
<p><code>rect_union</code> — rectangle geometry op <code>union</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p rect_union $x
</code></pre>
</article>
<article class="doc-entry" id="doc-red">
<h3><a class="doc-anchor" href="#doc-red">#</a> <code>red</code></h3>
<p><code>red</code> — operation <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p red $x
</code></pre>
</article>
<article class="doc-entry" id="doc-red-bold">
<h3><a class="doc-anchor" href="#doc-red-bold">#</a> <code>red_bold</code></h3>
<p><code>red_bold</code> — operation <code>red bold</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p red_bold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-redi">
<h3><a class="doc-anchor" href="#doc-redi">#</a> <code>redi</code></h3>
<p><code>redi</code> — operation <code>redi</code>. Alias for <code>reduce_indexed</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p redi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-redlich-kwong-p">
<h3><a class="doc-anchor" href="#doc-redlich-kwong-p">#</a> <code>redlich_kwong_p</code></h3>
<p><code>redlich_kwong_p</code> — operation <code>redlich kwong p</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p redlich_kwong_p $x
</code></pre>
</article>
<article class="doc-entry" id="doc-redox-potential-cell">
<h3><a class="doc-anchor" href="#doc-redox-potential-cell">#</a> <code>redox_potential_cell</code></h3>
<p><code>redox_potential_cell</code> — operation <code>redox potential cell</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p redox_potential_cell $x
</code></pre>
</article>
<article class="doc-entry" id="doc-redr">
<h3><a class="doc-anchor" href="#doc-redr">#</a> <code>redr</code></h3>
<p><code>redr</code> — operation <code>redr</code>. Alias for <code>reduce_right</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p redr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-redshift-from-a">
<h3><a class="doc-anchor" href="#doc-redshift-from-a">#</a> <code>redshift_from_a</code></h3>
<p><code>redshift_from_a</code> — operation <code>redshift from a</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p redshift_from_a $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reduce-axis">
<h3><a class="doc-anchor" href="#doc-reduce-axis">#</a> <code>reduce_axis</code></h3>
<p><code>reduce_axis</code> — operation <code>reduce axis</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p reduce_axis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reduce-indexed">
<h3><a class="doc-anchor" href="#doc-reduce-indexed">#</a> <code>reduce_indexed</code></h3>
<p><code>reduce_indexed</code> — operation <code>reduce indexed</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p reduce_indexed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reduce-right">
<h3><a class="doc-anchor" href="#doc-reduce-right">#</a> <code>reduce_right</code></h3>
<p><code>reduce_right</code> — operation <code>reduce right</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p reduce_right $x
</code></pre>
</article>
<article class="doc-entry" id="doc-refaddr">
<h3><a class="doc-anchor" href="#doc-refaddr">#</a> <code>refaddr</code></h3>
<p><code>refaddr</code> — operation <code>refaddr</code>. Category: *list / aggregate*.</p>
<pre><code class="lang-perl">p refaddr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-refl-check">
<h3><a class="doc-anchor" href="#doc-refl-check">#</a> <code>refl_check</code></h3>
<p><code>refl_check</code> — operation <code>refl check</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p refl_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reflect-point">
<h3><a class="doc-anchor" href="#doc-reflect-point">#</a> <code>reflect_point</code></h3>
<p><code>reflect_point($x, $y, $axis)</code> — reflects a point across an axis. Axis can be 'x', 'y', or 'origin'. Returns the reflected coordinates.</p>
<pre><code class="lang-perl">p reflect_point(3, 4, 'x') # [3, -4]
p reflect_point(3, 4, 'y') # [-3, 4]
p reflect_point(3, 4, 'origin') # [-3, -4]
</code></pre>
</article>
<article class="doc-entry" id="doc-reflpt">
<h3><a class="doc-anchor" href="#doc-reflpt">#</a> <code>reflpt</code></h3>
<p><code>reflpt</code> — operation <code>reflpt</code>. Alias for <code>reflect_point</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p reflpt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-refresh-stashes">
<h3><a class="doc-anchor" href="#doc-refresh-stashes">#</a> <code>refresh_stashes</code></h3>
<p><code>refresh_stashes</code> — operation <code>refresh stashes</code>. Category: *symbol table*.</p>
<pre><code class="lang-perl">p refresh_stashes $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reftype">
<h3><a class="doc-anchor" href="#doc-reftype">#</a> <code>reftype</code></h3>
<p><code>reftype</code> — operation <code>reftype</code>. Category: *list / aggregate*.</p>
<pre><code class="lang-perl">p reftype $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regex-compile-thompson">
<h3><a class="doc-anchor" href="#doc-regex-compile-thompson">#</a> <code>regex_compile_thompson</code></h3>
<p><code>regex_compile_thompson</code> — regular-expression op <code>compile thompson</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p regex_compile_thompson $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regex-escape-simple">
<h3><a class="doc-anchor" href="#doc-regex-escape-simple">#</a> <code>regex_escape_simple</code></h3>
<p><code>regex_escape_simple</code> — regular-expression op <code>escape simple</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p regex_escape_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regex-extract">
<h3><a class="doc-anchor" href="#doc-regex-extract">#</a> <code>regex_extract</code></h3>
<p><code>regex_extract</code> — regular-expression op <code>extract</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p regex_extract $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regex-match-dfa">
<h3><a class="doc-anchor" href="#doc-regex-match-dfa">#</a> <code>regex_match_dfa</code></h3>
<p><code>regex_match_dfa</code> — regular-expression op <code>match dfa</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p regex_match_dfa $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regex-replace-str">
<h3><a class="doc-anchor" href="#doc-regex-replace-str">#</a> <code>regex_replace_str</code></h3>
<p><code>regex_replace_str</code> — regular-expression op <code>replace str</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p regex_replace_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regex-split-str">
<h3><a class="doc-anchor" href="#doc-regex-split-str">#</a> <code>regex_split_str</code></h3>
<p><code>regex_split_str</code> — regular-expression op <code>split str</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p regex_split_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regex-to-nfa-thompson">
<h3><a class="doc-anchor" href="#doc-regex-to-nfa-thompson">#</a> <code>regex_to_nfa_thompson</code></h3>
<p><code>regex_to_nfa_thompson</code> — convert from <code>regex</code> to <code>nfa thompson</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p regex_to_nfa_thompson $value
</code></pre>
</article>
<article class="doc-entry" id="doc-regexp-matches">
<h3><a class="doc-anchor" href="#doc-regexp-matches">#</a> <code>regexp_matches</code></h3>
<p><code>regexp_matches</code> — operation <code>regexp matches</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p regexp_matches $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regexp-replace">
<h3><a class="doc-anchor" href="#doc-regexp-replace">#</a> <code>regexp_replace</code></h3>
<p><code>regexp_replace</code> — operation <code>regexp replace</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p regexp_replace $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regexp-split">
<h3><a class="doc-anchor" href="#doc-regexp-split">#</a> <code>regexp_split</code></h3>
<p><code>regexp_split</code> — operation <code>regexp split</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p regexp_split $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regr-intercept">
<h3><a class="doc-anchor" href="#doc-regr-intercept">#</a> <code>regr_intercept</code></h3>
<p><code>regr_intercept</code> — operation <code>regr intercept</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p regr_intercept $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regr-r2">
<h3><a class="doc-anchor" href="#doc-regr-r2">#</a> <code>regr_r2</code></h3>
<p><code>regr_r2</code> — operation <code>regr r2</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p regr_r2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regr-slope">
<h3><a class="doc-anchor" href="#doc-regr-slope">#</a> <code>regr_slope</code></h3>
<p><code>regr_slope</code> — operation <code>regr slope</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p regr_slope $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regula-falsi">
<h3><a class="doc-anchor" href="#doc-regula-falsi">#</a> <code>regula_falsi</code></h3>
<p><code>regula_falsi</code> — operation <code>regula falsi</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p regula_falsi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regular-ngon-area">
<h3><a class="doc-anchor" href="#doc-regular-ngon-area">#</a> <code>regular_ngon_area</code></h3>
<p><code>regular_ngon_area</code> — operation <code>regular ngon area</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p regular_ngon_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regular-ngon-circumradius">
<h3><a class="doc-anchor" href="#doc-regular-ngon-circumradius">#</a> <code>regular_ngon_circumradius</code></h3>
<p><code>regular_ngon_circumradius</code> — operation <code>regular ngon circumradius</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p regular_ngon_circumradius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regular-ngon-inradius">
<h3><a class="doc-anchor" href="#doc-regular-ngon-inradius">#</a> <code>regular_ngon_inradius</code></h3>
<p><code>regular_ngon_inradius</code> — operation <code>regular ngon inradius</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p regular_ngon_inradius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-regulator-naive">
<h3><a class="doc-anchor" href="#doc-regulator-naive">#</a> <code>regulator_naive</code></h3>
<p><code>regulator_naive</code> — operation <code>regulator naive</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p regulator_naive $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reject-if">
<h3><a class="doc-anchor" href="#doc-reject-if">#</a> <code>reject_if</code></h3>
<p><code>reject_if</code> — operation <code>reject if</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p reject_if $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rel-energy-pm">
<h3><a class="doc-anchor" href="#doc-rel-energy-pm">#</a> <code>rel_energy_pm</code></h3>
<p><code>rel_energy_pm</code> — operation <code>rel energy pm</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p rel_energy_pm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rel-ke">
<h3><a class="doc-anchor" href="#doc-rel-ke">#</a> <code>rel_ke</code></h3>
<p><code>rel_ke</code> — operation <code>rel ke</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p rel_ke $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rel-momentum">
<h3><a class="doc-anchor" href="#doc-rel-momentum">#</a> <code>rel_momentum</code></h3>
<p><code>rel_momentum</code> — operation <code>rel momentum</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p rel_momentum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rel-total-energy">
<h3><a class="doc-anchor" href="#doc-rel-total-energy">#</a> <code>rel_total_energy</code></h3>
<p><code>rel_total_energy</code> — operation <code>rel total energy</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p rel_total_energy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rel-velocity-add">
<h3><a class="doc-anchor" href="#doc-rel-velocity-add">#</a> <code>rel_velocity_add</code></h3>
<p><code>rel_velocity_add</code> — operation <code>rel velocity add</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p rel_velocity_add $x
</code></pre>
</article>
<article class="doc-entry" id="doc-relative-entropy">
<h3><a class="doc-anchor" href="#doc-relative-entropy">#</a> <code>relative_entropy</code></h3>
<p><code>relative_entropy(p, q) → number</code> — alias for <code>kl_divergence_distributions</code>.</p>
</article>
<article class="doc-entry" id="doc-relative-entropy-coherence">
<h3><a class="doc-anchor" href="#doc-relative-entropy-coherence">#</a> <code>relative_entropy_coherence</code></h3>
<p><code>relative_entropy_coherence</code> — operation <code>relative entropy coherence</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p relative_entropy_coherence $x
</code></pre>
</article>
<article class="doc-entry" id="doc-relative-entropy-kl">
<h3><a class="doc-anchor" href="#doc-relative-entropy-kl">#</a> <code>relative_entropy_kl</code></h3>
<p><code>relative_entropy_kl</code> — operation <code>relative entropy kl</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p relative_entropy_kl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-relative-humidity-step">
<h3><a class="doc-anchor" href="#doc-relative-humidity-step">#</a> <code>relative_humidity_step</code></h3>
<p><code>relative_humidity_step</code> — single-step update of <code>relative humidity</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p relative_humidity_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-relative-luminance">
<h3><a class="doc-anchor" href="#doc-relative-luminance">#</a> <code>relative_luminance</code></h3>
<p><code>relative_luminance</code> — operation <code>relative luminance</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p relative_luminance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-relative-vorticity-step">
<h3><a class="doc-anchor" href="#doc-relative-vorticity-step">#</a> <code>relative_vorticity_step</code></h3>
<p><code>relative_vorticity_step</code> — single-step update of <code>relative vorticity</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p relative_vorticity_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-relativistic-doppler">
<h3><a class="doc-anchor" href="#doc-relativistic-doppler">#</a> <code>relativistic_doppler</code></h3>
<p><code>relativistic_doppler</code> — operation <code>relativistic doppler</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p relativistic_doppler $x
</code></pre>
</article>
<article class="doc-entry" id="doc-relativistic-energy">
<h3><a class="doc-anchor" href="#doc-relativistic-energy">#</a> <code>relativistic_energy</code></h3>
<p><code>relativistic_energy</code> — operation <code>relativistic energy</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p relativistic_energy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-relativistic-kinetic">
<h3><a class="doc-anchor" href="#doc-relativistic-kinetic">#</a> <code>relativistic_kinetic</code></h3>
<p><code>relativistic_kinetic</code> — operation <code>relativistic kinetic</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p relativistic_kinetic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-relativistic-mass">
<h3><a class="doc-anchor" href="#doc-relativistic-mass">#</a> <code>relativistic_mass</code></h3>
<p><code>relativistic_mass</code> — operation <code>relativistic mass</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p relativistic_mass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-relenergy">
<h3><a class="doc-anchor" href="#doc-relenergy">#</a> <code>relenergy</code></h3>
<p><code>relenergy</code> — operation <code>relenergy</code>. Alias for <code>relativistic_energy</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p relenergy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reliability-diagram">
<h3><a class="doc-anchor" href="#doc-reliability-diagram">#</a> <code>reliability_diagram</code></h3>
<p><code>reliability_diagram</code> — operation <code>reliability diagram</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p reliability_diagram $x
</code></pre>
</article>
<article class="doc-entry" id="doc-relmass">
<h3><a class="doc-anchor" href="#doc-relmass">#</a> <code>relmass</code></h3>
<p><code>relmass</code> — operation <code>relmass</code>. Alias for <code>relativistic_mass</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p relmass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-relu">
<h3><a class="doc-anchor" href="#doc-relu">#</a> <code>relu</code></h3>
<p><code>relu</code> — operation <code>relu</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p relu $x
</code></pre>
</article>
<article class="doc-entry" id="doc-relu-grad">
<h3><a class="doc-anchor" href="#doc-relu-grad">#</a> <code>relu_grad</code></h3>
<p><code>relu_grad</code> — operation <code>relu grad</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p relu_grad $x
</code></pre>
</article>
<article class="doc-entry" id="doc-remc">
<h3><a class="doc-anchor" href="#doc-remc">#</a> <code>remc</code></h3>
<p><code>remc</code> — operation <code>remc</code>. Alias for <code>remove_clj</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p remc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-remez-design">
<h3><a class="doc-anchor" href="#doc-remez-design">#</a> <code>remez_design</code></h3>
<p><code>remez_design</code> — operation <code>remez design</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p remez_design $x
</code></pre>
</article>
<article class="doc-entry" id="doc-remove-all-str">
<h3><a class="doc-anchor" href="#doc-remove-all-str">#</a> <code>remove_all_str</code></h3>
<p><code>remove_all_str</code> — operation <code>remove all str</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p remove_all_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-remove-at">
<h3><a class="doc-anchor" href="#doc-remove-at">#</a> <code>remove_at</code></h3>
<p><code>remove_at</code> — operation <code>remove at</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p remove_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-remove-clj">
<h3><a class="doc-anchor" href="#doc-remove-clj">#</a> <code>remove_clj</code></h3>
<p><code>remove_clj</code> — operation <code>remove clj</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p remove_clj $x
</code></pre>
</article>
<article class="doc-entry" id="doc-remove-consonants">
<h3><a class="doc-anchor" href="#doc-remove-consonants">#</a> <code>remove_consonants</code></h3>
<p><code>remove_consonants</code> — operation <code>remove consonants</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p remove_consonants $x
</code></pre>
</article>
<article class="doc-entry" id="doc-remove-elem">
<h3><a class="doc-anchor" href="#doc-remove-elem">#</a> <code>remove_elem</code></h3>
<p><code>remove_elem</code> — operation <code>remove elem</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p remove_elem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-remove-first-elem">
<h3><a class="doc-anchor" href="#doc-remove-first-elem">#</a> <code>remove_first_elem</code></h3>
<p><code>remove_first_elem</code> — operation <code>remove first elem</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p remove_first_elem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-remove-keys">
<h3><a class="doc-anchor" href="#doc-remove-keys">#</a> <code>remove_keys</code></h3>
<p><code>remove_keys</code> — operation <code>remove keys</code>. Category: *hash ops*.</p>
<pre><code class="lang-perl">p remove_keys $x
</code></pre>
</article>
<article class="doc-entry" id="doc-remove-seasonality">
<h3><a class="doc-anchor" href="#doc-remove-seasonality">#</a> <code>remove_seasonality</code></h3>
<p><code>remove_seasonality(series, period=12) → array</code> — subtract per-position mean over the period to deseasonalise.</p>
<pre><code class="lang-perl">p remove_seasonality(\@monthly, 12)
</code></pre>
</article>
<article class="doc-entry" id="doc-remove-str">
<h3><a class="doc-anchor" href="#doc-remove-str">#</a> <code>remove_str</code></h3>
<p><code>remove_str</code> — operation <code>remove str</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p remove_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-remove-vowels">
<h3><a class="doc-anchor" href="#doc-remove-vowels">#</a> <code>remove_vowels</code></h3>
<p><code>remove_vowels</code> — operation <code>remove vowels</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p remove_vowels $x
</code></pre>
</article>
<article class="doc-entry" id="doc-remove-whitespace">
<h3><a class="doc-anchor" href="#doc-remove-whitespace">#</a> <code>remove_whitespace</code></h3>
<p><code>remove_whitespace</code> — operation <code>remove whitespace</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p remove_whitespace $x
</code></pre>
</article>
<article class="doc-entry" id="doc-renamenx">
<h3><a class="doc-anchor" href="#doc-renamenx">#</a> <code>renamenx</code></h3>
<p><code>renamenx</code> — operation <code>renamenx</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p renamenx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-renyi-divergence-step">
<h3><a class="doc-anchor" href="#doc-renyi-divergence-step">#</a> <code>renyi_divergence_step</code></h3>
<p><code>renyi_divergence_step</code> — single-step update of <code>renyi divergence</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p renyi_divergence_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rep">
<h3><a class="doc-anchor" href="#doc-rep">#</a> <code>rep</code></h3>
<p><code>rep</code> — operation <code>rep</code>. Alias for <code>rep_fn</code>. Category: *r base*.</p>
<pre><code class="lang-perl">p rep $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rep-fn">
<h3><a class="doc-anchor" href="#doc-rep-fn">#</a> <code>rep_fn</code></h3>
<p><code>rep_fn</code> — repeat a value N times. Like R's rep().</p>
<pre><code class="lang-perl">my @r = @{rep_fn(0, 10)} # ten zeros
my @s = @{rep_fn("x", 5)} # five "x"s
</code></pre>
</article>
<article class="doc-entry" id="doc-repa">
<h3><a class="doc-anchor" href="#doc-repa">#</a> <code>repa</code></h3>
<p><code>repa</code> — operation <code>repa</code>. Alias for <code>replace_at</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p repa $x
</code></pre>
</article>
<article class="doc-entry" id="doc-repdigit">
<h3><a class="doc-anchor" href="#doc-repdigit">#</a> <code>repdigit</code></h3>
<p><code>repdigit</code> — operation <code>repdigit</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p repdigit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-repeat">
<h3><a class="doc-anchor" href="#doc-repeat">#</a> <code>repeat</code></h3>
<p><code>repeat</code> — operation <code>repeat</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p repeat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-repeat-elem">
<h3><a class="doc-anchor" href="#doc-repeat-elem">#</a> <code>repeat_elem</code></h3>
<p><code>repeat_elem</code> — operation <code>repeat elem</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p repeat_elem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-repeat-list">
<h3><a class="doc-anchor" href="#doc-repeat-list">#</a> <code>repeat_list</code></h3>
<p><code>repeat_list</code> — operation <code>repeat list</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p repeat_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-repeat-string">
<h3><a class="doc-anchor" href="#doc-repeat-string">#</a> <code>repeat_string</code></h3>
<p><code>repeat_string</code> — operation <code>repeat string</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p repeat_string $x
</code></pre>
</article>
<article class="doc-entry" id="doc-repeated-game-avg-payoff">
<h3><a class="doc-anchor" href="#doc-repeated-game-avg-payoff">#</a> <code>repeated_game_avg_payoff</code></h3>
<p><code>repeated_game_avg_payoff</code> — operation <code>repeated game avg payoff</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p repeated_game_avg_payoff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-repeatedly">
<h3><a class="doc-anchor" href="#doc-repeatedly">#</a> <code>repeatedly</code></h3>
<p><code>repeatedly</code> — operation <code>repeatedly</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p repeatedly $x
</code></pre>
</article>
<article class="doc-entry" id="doc-replace-all-str">
<h3><a class="doc-anchor" href="#doc-replace-all-str">#</a> <code>replace_all_str</code></h3>
<p><code>replace_all_str</code> — operation <code>replace all str</code>. Category: *string*.</p>
<pre><code class="lang-perl">p replace_all_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-replace-at">
<h3><a class="doc-anchor" href="#doc-replace-at">#</a> <code>replace_at</code></h3>
<p><code>replace_at</code> — operation <code>replace at</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p replace_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-replace-at-index">
<h3><a class="doc-anchor" href="#doc-replace-at-index">#</a> <code>replace_at_index</code></h3>
<p><code>replace_at_index</code> — index of <code>replace at</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p replace_at_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-replace-first">
<h3><a class="doc-anchor" href="#doc-replace-first">#</a> <code>replace_first</code></h3>
<p><code>replace_first</code> — operation <code>replace first</code>. Category: *string*.</p>
<pre><code class="lang-perl">p replace_first $x
</code></pre>
</article>
<article class="doc-entry" id="doc-replace-n-times">
<h3><a class="doc-anchor" href="#doc-replace-n-times">#</a> <code>replace_n_times</code></h3>
<p><code>replace_n_times</code> — operation <code>replace n times</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p replace_n_times $x
</code></pre>
</article>
<article class="doc-entry" id="doc-replace-regex">
<h3><a class="doc-anchor" href="#doc-replace-regex">#</a> <code>replace_regex</code></h3>
<p><code>replace_regex</code> — operation <code>replace regex</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p replace_regex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-replicate-val">
<h3><a class="doc-anchor" href="#doc-replicate-val">#</a> <code>replicate_val</code></h3>
<p><code>replicate_val</code> — operation <code>replicate val</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p replicate_val $x
</code></pre>
</article>
<article class="doc-entry" id="doc-replicator-dynamics-step">
<h3><a class="doc-anchor" href="#doc-replicator-dynamics-step">#</a> <code>replicator_dynamics_step</code></h3>
<p><code>replicator_dynamics_step</code> — single-step update of <code>replicator dynamics</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p replicator_dynamics_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-repln">
<h3><a class="doc-anchor" href="#doc-repln">#</a> <code>repln</code></h3>
<p><code>repln</code> — operation <code>repln</code>. Alias for <code>replace_n_times</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p repln $x
</code></pre>
</article>
<article class="doc-entry" id="doc-replre">
<h3><a class="doc-anchor" href="#doc-replre">#</a> <code>replre</code></h3>
<p><code>replre</code> — operation <code>replre</code>. Alias for <code>replace_regex</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p replre $x
</code></pre>
</article>
<article class="doc-entry" id="doc-representation-dim-step">
<h3><a class="doc-anchor" href="#doc-representation-dim-step">#</a> <code>representation_dim_step</code></h3>
<p><code>representation_dim_step</code> — single-step update of <code>representation dim</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p representation_dim_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-repunit">
<h3><a class="doc-anchor" href="#doc-repunit">#</a> <code>repunit</code></h3>
<p><code>repunit</code> — operation <code>repunit</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p repunit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-repv">
<h3><a class="doc-anchor" href="#doc-repv">#</a> <code>repv</code></h3>
<p><code>repv</code> — operation <code>repv</code>. Alias for <code>replicate_val</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p repv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-resample">
<h3><a class="doc-anchor" href="#doc-resample">#</a> <code>resample</code></h3>
<p><code>resample(\@signal, $factor)</code> — resamples signal by a rational factor. Factor > 1 upsamples, factor < 1 downsamples. Uses linear interpolation.</p>
<pre><code class="lang-perl">my $up = resample(\@signal, 2) # double sample rate
my $down = resample(\@signal, 0.5) # halve sample rate
</code></pre>
</article>
<article class="doc-entry" id="doc-resample-linear">
<h3><a class="doc-anchor" href="#doc-resample-linear">#</a> <code>resample_linear</code></h3>
<p><code>resample_linear</code> — operation <code>resample linear</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p resample_linear $x
</code></pre>
</article>
<article class="doc-entry" id="doc-resample-nearest">
<h3><a class="doc-anchor" href="#doc-resample-nearest">#</a> <code>resample_nearest</code></h3>
<p><code>resample_nearest</code> — operation <code>resample nearest</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p resample_nearest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-resample-poly-step">
<h3><a class="doc-anchor" href="#doc-resample-poly-step">#</a> <code>resample_poly_step</code></h3>
<p><code>resample_poly_step</code> — single-step update of <code>resample poly</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p resample_poly_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reserve-prospective">
<h3><a class="doc-anchor" href="#doc-reserve-prospective">#</a> <code>reserve_prospective</code></h3>
<p><code>reserve_prospective</code> — operation <code>reserve prospective</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p reserve_prospective $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reserve-retrospective">
<h3><a class="doc-anchor" href="#doc-reserve-retrospective">#</a> <code>reserve_retrospective</code></h3>
<p><code>reserve_retrospective</code> — operation <code>reserve retrospective</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p reserve_retrospective $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reservoir-sample">
<h3><a class="doc-anchor" href="#doc-reservoir-sample">#</a> <code>reservoir_sample</code></h3>
<p><code>reservoir_sample</code> — operation <code>reservoir sample</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p reservoir_sample $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reservoir-sample-weighted">
<h3><a class="doc-anchor" href="#doc-reservoir-sample-weighted">#</a> <code>reservoir_sample_weighted</code></h3>
<p><code>reservoir_sample_weighted</code> — operation <code>reservoir sample weighted</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p reservoir_sample_weighted $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reset">
<h3><a class="doc-anchor" href="#doc-reset">#</a> <code>reset</code></h3>
<p><code>reset</code> — operation <code>reset</code>. Category: *process / system*.</p>
<pre><code class="lang-perl">p reset $x
</code></pre>
</article>
<article class="doc-entry" id="doc-resfreq">
<h3><a class="doc-anchor" href="#doc-resfreq">#</a> <code>resfreq</code></h3>
<p><code>resfreq</code> — operation <code>resfreq</code>. Alias for <code>resonant_frequency</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p resfreq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reshape-dim">
<h3><a class="doc-anchor" href="#doc-reshape-dim">#</a> <code>reshape_dim</code></h3>
<p><code>reshape_dim</code> — operation <code>reshape dim</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p reshape_dim $x
</code></pre>
</article>
<article class="doc-entry" id="doc-residuals-compute">
<h3><a class="doc-anchor" href="#doc-residuals-compute">#</a> <code>residuals_compute</code></h3>
<p><code>residuals_compute</code> — operation <code>residuals compute</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p residuals_compute $x
</code></pre>
</article>
<article class="doc-entry" id="doc-resistance-level">
<h3><a class="doc-anchor" href="#doc-resistance-level">#</a> <code>resistance_level</code></h3>
<p><code>resistance_level(prices, period=20) → number</code> — rolling max over <code>period</code>; the most recent local ceiling.</p>
<pre><code class="lang-perl">p resistance_level(\@closes, 20)
</code></pre>
</article>
<article class="doc-entry" id="doc-resistance-parallel">
<h3><a class="doc-anchor" href="#doc-resistance-parallel">#</a> <code>resistance_parallel</code></h3>
<p><code>resistance_parallel</code> — operation <code>resistance parallel</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p resistance_parallel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-resistance-series">
<h3><a class="doc-anchor" href="#doc-resistance-series">#</a> <code>resistance_series</code></h3>
<p><code>resistance_series</code> — operation <code>resistance series</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p resistance_series $x
</code></pre>
</article>
<article class="doc-entry" id="doc-resolution-step">
<h3><a class="doc-anchor" href="#doc-resolution-step">#</a> <code>resolution_step</code></h3>
<p><code>resolution_step</code> — single-step update of <code>resolution</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p resolution_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-resonance-count">
<h3><a class="doc-anchor" href="#doc-resonance-count">#</a> <code>resonance_count</code></h3>
<p><code>resonance_count</code> — count of <code>resonance</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p resonance_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-resonant-frequency">
<h3><a class="doc-anchor" href="#doc-resonant-frequency">#</a> <code>resonant_frequency</code></h3>
<p><code>resonant_frequency</code> — operation <code>resonant frequency</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p resonant_frequency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rest">
<h3><a class="doc-anchor" href="#doc-rest">#</a> <code>rest</code></h3>
<p><code>rest</code> — operation <code>rest</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p rest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rest-energy">
<h3><a class="doc-anchor" href="#doc-rest-energy">#</a> <code>rest_energy</code></h3>
<p><code>rest_energy</code> — operation <code>rest energy</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p rest_energy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-restenergy">
<h3><a class="doc-anchor" href="#doc-restenergy">#</a> <code>restenergy</code></h3>
<p><code>restenergy</code> — operation <code>restenergy</code>. Alias for <code>rest_energy</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p restenergy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-restore-random-state">
<h3><a class="doc-anchor" href="#doc-restore-random-state">#</a> <code>restore_random_state</code></h3>
<p><code>restore_random_state</code> — operation <code>restore random state</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p restore_random_state $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rev">
<h3><a class="doc-anchor" href="#doc-rev">#</a> <code>rev</code></h3>
<p><code>rev</code> — operation <code>rev</code>. Category: *short aliases*.</p>
<pre><code class="lang-perl">p rev $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rev-str">
<h3><a class="doc-anchor" href="#doc-rev-str">#</a> <code>rev_str</code></h3>
<p><code>rev_str</code> — operation <code>rev str</code>. Alias for <code>reverse_str</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p rev_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rev-vec">
<h3><a class="doc-anchor" href="#doc-rev-vec">#</a> <code>rev_vec</code></h3>
<p><code>rev_vec</code> — operation <code>rev vec</code>. Category: *r base*.</p>
<pre><code class="lang-perl">p rev_vec $x
</code></pre>
</article>
<article class="doc-entry" id="doc-revenue-equivalence-check">
<h3><a class="doc-anchor" href="#doc-revenue-equivalence-check">#</a> <code>revenue_equivalence_check</code></h3>
<p><code>revenue_equivalence_check</code> — operation <code>revenue equivalence check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p revenue_equivalence_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reverse-delete-step">
<h3><a class="doc-anchor" href="#doc-reverse-delete-step">#</a> <code>reverse_delete_step</code></h3>
<p><code>reverse_delete_step</code> — single-step update of <code>reverse delete</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p reverse_delete_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reverse-each">
<h3><a class="doc-anchor" href="#doc-reverse-each">#</a> <code>reverse_each</code></h3>
<p><code>reverse_each</code> — operation <code>reverse each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p reverse_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reverse-each-word">
<h3><a class="doc-anchor" href="#doc-reverse-each-word">#</a> <code>reverse_each_word</code></h3>
<p><code>reverse_each_word</code> — operation <code>reverse each word</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p reverse_each_word $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reverse-list">
<h3><a class="doc-anchor" href="#doc-reverse-list">#</a> <code>reverse_list</code></h3>
<p><code>reverse_list</code> — operation <code>reverse list</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p reverse_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reverse-str">
<h3><a class="doc-anchor" href="#doc-reverse-str">#</a> <code>reverse_str</code></h3>
<p><code>reverse_str</code> — operation <code>reverse str</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p reverse_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reverse-transcribe">
<h3><a class="doc-anchor" href="#doc-reverse-transcribe">#</a> <code>reverse_transcribe</code></h3>
<p><code>reverse_transcribe</code> — operation <code>reverse transcribe</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p reverse_transcribe $x
</code></pre>
</article>
<article class="doc-entry" id="doc-reverse-words">
<h3><a class="doc-anchor" href="#doc-reverse-words">#</a> <code>reverse_words</code></h3>
<p><code>reverse_words</code> — operation <code>reverse words</code>. Category: *string*.</p>
<pre><code class="lang-perl">p reverse_words $x
</code></pre>
</article>
<article class="doc-entry" id="doc-revwords">
<h3><a class="doc-anchor" href="#doc-revwords">#</a> <code>revwords</code></h3>
<p><code>revwords</code> — operation <code>revwords</code>. Alias for <code>reverse_each_word</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p revwords $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rexp">
<h3><a class="doc-anchor" href="#doc-rexp">#</a> <code>rexp</code></h3>
<p><code>rexp</code> — generate n random exponential variates. Args: n [, rate]. Like R's rexp().</p>
<pre><code class="lang-perl">my @x = @{rexp(100, 0.5)} # rate=0.5 (mean=2)
</code></pre>
</article>
<article class="doc-entry" id="doc-reynolds-full-number">
<h3><a class="doc-anchor" href="#doc-reynolds-full-number">#</a> <code>reynolds_full_number</code></h3>
<p><code>reynolds_full_number</code> — operation <code>reynolds full number</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p reynolds_full_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rf">
<h3><a class="doc-anchor" href="#doc-rf">#</a> <code>rf</code></h3>
<p><code>rf</code> — generate n random F variates. Args: n, d1, d2. Like R's rf().</p>
<pre><code class="lang-perl">my @x = @{rf(100, 5, 10)} # F(5,10)
</code></pre>
</article>
<article class="doc-entry" id="doc-rfact">
<h3><a class="doc-anchor" href="#doc-rfact">#</a> <code>rfact</code></h3>
<p><code>rfact</code> — operation <code>rfact</code>. Alias for <code>rising_factorial</code>. Category: *math formulas*.</p>
<pre><code class="lang-perl">p rfact $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rfc3339">
<h3><a class="doc-anchor" href="#doc-rfc3339">#</a> <code>rfc3339</code></h3>
<p><code>rfc3339</code> — operation <code>rfc3339</code>. Alias for <code>rfc3339_format</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p rfc3339 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rfc3339-format">
<h3><a class="doc-anchor" href="#doc-rfc3339-format">#</a> <code>rfc3339_format</code></h3>
<p><code>rfc3339_format</code> — operation <code>rfc3339 format</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p rfc3339_format $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rfc3339-parse">
<h3><a class="doc-anchor" href="#doc-rfc3339-parse">#</a> <code>rfc3339_parse</code></h3>
<p><code>rfc3339_parse</code> — operation <code>rfc3339 parse</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p rfc3339_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rg-radius-of-gyration">
<h3><a class="doc-anchor" href="#doc-rg-radius-of-gyration">#</a> <code>rg_radius_of_gyration</code></h3>
<p><code>rg_radius_of_gyration</code> — operation <code>rg radius of gyration</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p rg_radius_of_gyration $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rgamma">
<h3><a class="doc-anchor" href="#doc-rgamma">#</a> <code>rgamma</code></h3>
<p><code>rgamma</code> — generate n random gamma variates. Args: n, shape [, scale]. Like R's rgamma().</p>
<pre><code class="lang-perl">my @x = @{rgamma(100, 2, 1)} # Gamma(2,1)
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb">
<h3><a class="doc-anchor" href="#doc-rgb">#</a> <code>rgb</code></h3>
<p><code>rgb</code> — operation <code>rgb</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p rgb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb2hsl">
<h3><a class="doc-anchor" href="#doc-rgb2hsl">#</a> <code>rgb2hsl</code></h3>
<p><code>rgb2hsl</code> — operation <code>rgb2hsl</code>. Alias for <code>rgb_to_hsl</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p rgb2hsl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb2hsv">
<h3><a class="doc-anchor" href="#doc-rgb2hsv">#</a> <code>rgb2hsv</code></h3>
<p><code>rgb2hsv</code> — operation <code>rgb2hsv</code>. Alias for <code>rgb_to_hsv</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p rgb2hsv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-blend-color-burn">
<h3><a class="doc-anchor" href="#doc-rgb-blend-color-burn">#</a> <code>rgb_blend_color_burn</code></h3>
<p><code>rgb_blend_color_burn(a, b) → [r,g,b]</code> — color burn: <code>255 - (255-a)·255/b</code>, clamped.</p>
</article>
<article class="doc-entry" id="doc-rgb-blend-color-dodge">
<h3><a class="doc-anchor" href="#doc-rgb-blend-color-dodge">#</a> <code>rgb_blend_color_dodge</code></h3>
<p><code>rgb_blend_color_dodge(a, b) → [r,g,b]</code> — color dodge: <code>a · 255 / (255 - b)</code>, clamped.</p>
</article>
<article class="doc-entry" id="doc-rgb-blend-darken">
<h3><a class="doc-anchor" href="#doc-rgb-blend-darken">#</a> <code>rgb_blend_darken</code></h3>
<p><code>rgb_blend_darken(a, b) → [r,g,b]</code> — channelwise min.</p>
</article>
<article class="doc-entry" id="doc-rgb-blend-lighten">
<h3><a class="doc-anchor" href="#doc-rgb-blend-lighten">#</a> <code>rgb_blend_lighten</code></h3>
<p><code>rgb_blend_lighten(a, b) → [r,g,b]</code> — channelwise max.</p>
</article>
<article class="doc-entry" id="doc-rgb-blend-multiply">
<h3><a class="doc-anchor" href="#doc-rgb-blend-multiply">#</a> <code>rgb_blend_multiply</code></h3>
<p><code>rgb_blend_multiply([r,g,b], [r,g,b]) → [r,g,b]</code> — Photoshop-style multiply: <code>a · b / 255</code>.</p>
<pre><code class="lang-perl">p rgb_blend_multiply([255,128,0], [128,255,0])
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-blend-normal">
<h3><a class="doc-anchor" href="#doc-rgb-blend-normal">#</a> <code>rgb_blend_normal</code></h3>
<p><code>rgb_blend_normal([r,g,b], [r,g,b], alpha=1) → [r,g,b]</code> — alpha-blended overlay of two RGB triples (0-255).</p>
<pre><code class="lang-perl">p rgb_blend_normal([255,0,0], [0,255,0], 0.5)
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-blend-overlay">
<h3><a class="doc-anchor" href="#doc-rgb-blend-overlay">#</a> <code>rgb_blend_overlay</code></h3>
<p><code>rgb_blend_overlay(a, b) → [r,g,b]</code> — overlay = multiply for dark base, screen for light.</p>
</article>
<article class="doc-entry" id="doc-rgb-blend-screen">
<h3><a class="doc-anchor" href="#doc-rgb-blend-screen">#</a> <code>rgb_blend_screen</code></h3>
<p><code>rgb_blend_screen(a, b) → [r,g,b]</code> — Photoshop screen: <code>255 - (255-a)·(255-b)/255</code>.</p>
</article>
<article class="doc-entry" id="doc-rgb-to-adobe-rgb">
<h3><a class="doc-anchor" href="#doc-rgb-to-adobe-rgb">#</a> <code>rgb_to_adobe_rgb</code></h3>
<p><code>rgb_to_adobe_rgb</code> — convert from <code>rgb</code> to <code>adobe rgb</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p rgb_to_adobe_rgb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-to-cmyk">
<h3><a class="doc-anchor" href="#doc-rgb-to-cmyk">#</a> <code>rgb_to_cmyk</code></h3>
<p><code>rgb_to_cmyk</code> — convert from <code>rgb</code> to <code>cmyk</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p rgb_to_cmyk $value
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-to-color-temperature">
<h3><a class="doc-anchor" href="#doc-rgb-to-color-temperature">#</a> <code>rgb_to_color_temperature</code></h3>
<p><code>rgb_to_color_temperature</code> — convert from <code>rgb</code> to <code>color temperature</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p rgb_to_color_temperature $value
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-to-hex">
<h3><a class="doc-anchor" href="#doc-rgb-to-hex">#</a> <code>rgb_to_hex</code></h3>
<p><code>rgb_to_hex</code> — convert from <code>rgb</code> to <code>hex</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p rgb_to_hex $value
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-to-hsl">
<h3><a class="doc-anchor" href="#doc-rgb-to-hsl">#</a> <code>rgb_to_hsl</code></h3>
<p><code>rgb_to_hsl</code> — convert from <code>rgb</code> to <code>hsl</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p rgb_to_hsl $value
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-to-hsv">
<h3><a class="doc-anchor" href="#doc-rgb-to-hsv">#</a> <code>rgb_to_hsv</code></h3>
<p><code>rgb_to_hsv</code> — convert from <code>rgb</code> to <code>hsv</code>. Category: *color operations*.</p>
<pre><code class="lang-perl">p rgb_to_hsv $value
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-to-lch">
<h3><a class="doc-anchor" href="#doc-rgb-to-lch">#</a> <code>rgb_to_lch</code></h3>
<p><code>rgb_to_lch([r,g,b]) → [L, C, H]</code> — convert sRGB to CIELAB-then-LCH (cylindrical CIELAB).</p>
<pre><code class="lang-perl">p rgb_to_lch([128, 64, 200])
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-to-oklab">
<h3><a class="doc-anchor" href="#doc-rgb-to-oklab">#</a> <code>rgb_to_oklab</code></h3>
<p><code>rgb_to_oklab</code> — convert from <code>rgb</code> to <code>oklab</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p rgb_to_oklab $value
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-to-oklch">
<h3><a class="doc-anchor" href="#doc-rgb-to-oklch">#</a> <code>rgb_to_oklch</code></h3>
<p><code>rgb_to_oklch([r,g,b]) → [L, C, H]</code> — convert to Björn Ottosson's OKLab in cylindrical form. Perceptually uniform.</p>
<pre><code class="lang-perl">p rgb_to_oklch([128, 64, 200])
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-to-p3">
<h3><a class="doc-anchor" href="#doc-rgb-to-p3">#</a> <code>rgb_to_p3</code></h3>
<p><code>rgb_to_p3</code> — convert from <code>rgb</code> to <code>p3</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p rgb_to_p3 $value
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-to-srgb">
<h3><a class="doc-anchor" href="#doc-rgb-to-srgb">#</a> <code>rgb_to_srgb</code></h3>
<p><code>rgb_to_srgb</code> — convert from <code>rgb</code> to <code>srgb</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p rgb_to_srgb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-to-xyz">
<h3><a class="doc-anchor" href="#doc-rgb-to-xyz">#</a> <code>rgb_to_xyz</code></h3>
<p><code>rgb_to_xyz</code> — convert from <code>rgb</code> to <code>xyz</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p rgb_to_xyz $value
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-to-yiq">
<h3><a class="doc-anchor" href="#doc-rgb-to-yiq">#</a> <code>rgb_to_yiq</code></h3>
<p><code>rgb_to_yiq</code> — convert from <code>rgb</code> to <code>yiq</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p rgb_to_yiq $value
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-to-yuv">
<h3><a class="doc-anchor" href="#doc-rgb-to-yuv">#</a> <code>rgb_to_yuv</code></h3>
<p><code>rgb_to_yuv</code> — convert from <code>rgb</code> to <code>yuv</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p rgb_to_yuv $value
</code></pre>
</article>
<article class="doc-entry" id="doc-rgb-to-yuv601">
<h3><a class="doc-anchor" href="#doc-rgb-to-yuv601">#</a> <code>rgb_to_yuv601</code></h3>
<p><code>rgb_to_yuv601</code> — convert from <code>rgb</code> to <code>yuv601</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p rgb_to_yuv601 $value
</code></pre>
</article>
<article class="doc-entry" id="doc-rgeom">
<h3><a class="doc-anchor" href="#doc-rgeom">#</a> <code>rgeom</code></h3>
<p><code>rgeom</code> — generate n random geometric variates. Args: n, prob.</p>
<pre><code class="lang-perl">my @x = @{rgeom(100, 0.3)} # trials until first success
</code></pre>
</article>
<article class="doc-entry" id="doc-rho">
<h3><a class="doc-anchor" href="#doc-rho">#</a> <code>rho</code></h3>
<p><code>spearman</code> (aliases <code>spearman_corr</code>, <code>rho</code>) computes Spearman's rank correlation coefficient between two samples.</p>
<pre><code class="lang-perl">p rho([1,2,3,4,5], [5,6,7,8,7]) # ~0.82
</code></pre>
</article>
<article class="doc-entry" id="doc-rhumb-line-bearing">
<h3><a class="doc-anchor" href="#doc-rhumb-line-bearing">#</a> <code>rhumb_line_bearing</code></h3>
<p><code>rhumb_line_bearing</code> — operation <code>rhumb line bearing</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p rhumb_line_bearing $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rhyper">
<h3><a class="doc-anchor" href="#doc-rhyper">#</a> <code>rhyper</code></h3>
<p><code>rhyper</code> — operation <code>rhyper</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p rhyper $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ricci-identity-step">
<h3><a class="doc-anchor" href="#doc-ricci-identity-step">#</a> <code>ricci_identity_step</code></h3>
<p><code>ricci_identity_step</code> — single-step update of <code>ricci identity</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ricci_identity_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ricci-tensor-step-zero">
<h3><a class="doc-anchor" href="#doc-ricci-tensor-step-zero">#</a> <code>ricci_tensor_step_zero</code></h3>
<p><code>ricci_tensor_step_zero</code> — operation <code>ricci tensor step zero</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ricci_tensor_step_zero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-richardson-number-step">
<h3><a class="doc-anchor" href="#doc-richardson-number-step">#</a> <code>richardson_number_step</code></h3>
<p><code>richardson_number_step</code> — single-step update of <code>richardson number</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p richardson_number_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-richter-local-ml">
<h3><a class="doc-anchor" href="#doc-richter-local-ml">#</a> <code>richter_local_ml</code></h3>
<p><code>richter_local_ml</code> — operation <code>richter local ml</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p richter_local_ml $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ricker-wavelet">
<h3><a class="doc-anchor" href="#doc-ricker-wavelet">#</a> <code>ricker_wavelet</code></h3>
<p><code>ricker_wavelet</code> — operation <code>ricker wavelet</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p ricker_wavelet $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ridders">
<h3><a class="doc-anchor" href="#doc-ridders">#</a> <code>ridders</code></h3>
<p><code>ridders</code> — operation <code>ridders</code>. Alias for <code>ridders_root</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p ridders $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ridders-root">
<h3><a class="doc-anchor" href="#doc-ridders-root">#</a> <code>ridders_root</code></h3>
<p><code>ridders_root</code> — operation <code>ridders root</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p ridders_root $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ridge-noise-2d">
<h3><a class="doc-anchor" href="#doc-ridge-noise-2d">#</a> <code>ridge_noise_2d</code></h3>
<p><code>ridge_noise_2d(x, y) → number</code> — <code>1 - |perlin|</code>. Sharp ridges for mountains.</p>
</article>
<article class="doc-entry" id="doc-ridx">
<h3><a class="doc-anchor" href="#doc-ridx">#</a> <code>ridx</code></h3>
<p><code>ridx</code> — operation <code>ridx</code>. Alias for <code>rindex_fn</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p ridx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-riemann-curvature-normal-form">
<h3><a class="doc-anchor" href="#doc-riemann-curvature-normal-form">#</a> <code>riemann_curvature_normal_form</code></h3>
<p><code>riemann_curvature_normal_form</code> — operation <code>riemann curvature normal form</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p riemann_curvature_normal_form $x
</code></pre>
</article>
<article class="doc-entry" id="doc-riemann-tensor-step-zero">
<h3><a class="doc-anchor" href="#doc-riemann-tensor-step-zero">#</a> <code>riemann_tensor_step_zero</code></h3>
<p><code>riemann_tensor_step_zero</code> — operation <code>riemann tensor step zero</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p riemann_tensor_step_zero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-riemann-xi">
<h3><a class="doc-anchor" href="#doc-riemann-xi">#</a> <code>riemann_xi</code></h3>
<p><code>riemann_xi</code> — operation <code>riemann xi</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p riemann_xi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-riffle">
<h3><a class="doc-anchor" href="#doc-riffle">#</a> <code>riffle</code></h3>
<p><code>riffle</code> — operation <code>riffle</code>. Category: *collection helpers (trivial)*.</p>
<pre><code class="lang-perl">p riffle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-right-str">
<h3><a class="doc-anchor" href="#doc-right-str">#</a> <code>right_str</code></h3>
<p><code>right_str</code> — operation <code>right str</code>. Category: *string*.</p>
<pre><code class="lang-perl">p right_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rindex-fn">
<h3><a class="doc-anchor" href="#doc-rindex-fn">#</a> <code>rindex_fn</code></h3>
<p><code>rindex_fn</code> — operation <code>rindex fn</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p rindex_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ring-modulate">
<h3><a class="doc-anchor" href="#doc-ring-modulate">#</a> <code>ring_modulate</code></h3>
<p><code>ring_modulate(a, b) → array</code> — elementwise product of two signals. Bell-like inharmonic spectra.</p>
</article>
<article class="doc-entry" id="doc-rising-factorial">
<h3><a class="doc-anchor" href="#doc-rising-factorial">#</a> <code>rising_factorial</code></h3>
<p><code>rising_factorial</code> — operation <code>rising factorial</code>. Category: *math formulas*.</p>
<pre><code class="lang-perl">p rising_factorial $x
</code></pre>
</article>
<article class="doc-entry" id="doc-risk-ratio-2x2">
<h3><a class="doc-anchor" href="#doc-risk-ratio-2x2">#</a> <code>risk_ratio_2x2</code></h3>
<p><code>risk_ratio_2x2</code> — operation <code>risk ratio 2x2</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p risk_ratio_2x2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rjt">
<h3><a class="doc-anchor" href="#doc-rjt">#</a> <code>rjt</code></h3>
<p><code>rjt</code> — operation <code>rjt</code>. Alias for <code>rjust_text</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p rjt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rjust">
<h3><a class="doc-anchor" href="#doc-rjust">#</a> <code>rjust</code></h3>
<p><code>rjust</code> — operation <code>rjust</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p rjust $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rjust-text">
<h3><a class="doc-anchor" href="#doc-rjust-text">#</a> <code>rjust_text</code></h3>
<p><code>rjust_text</code> — operation <code>rjust text</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p rjust_text $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rk4">
<h3><a class="doc-anchor" href="#doc-rk4">#</a> <code>rk4</code></h3>
<p><code>rk4</code> (aliases <code>runge_kutta</code>, <code>rk4_ode</code>) solves an ODE dy/dt = f(t,y) using 4th-order Runge-Kutta. Returns [[t,y], ...].</p>
<pre><code class="lang-perl"># dy/dt = -y, y(0) = 1 → y = e^(-t)
my $sol = rk4(fn { -$_[1] }, 0, 1, 0.1, 100)
</code></pre>
</article>
<article class="doc-entry" id="doc-rk45-cash-karp">
<h3><a class="doc-anchor" href="#doc-rk45-cash-karp">#</a> <code>rk45_cash_karp</code></h3>
<p><code>rk45_cash_karp</code> — operation <code>rk45 cash karp</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p rk45_cash_karp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rk4-single">
<h3><a class="doc-anchor" href="#doc-rk4-single">#</a> <code>rk4_single</code></h3>
<p><code>rk4_single</code> — operation <code>rk4 single</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p rk4_single $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rk-combine">
<h3><a class="doc-anchor" href="#doc-rk-combine">#</a> <code>rk_combine</code></h3>
<p><code>rk_combine</code> — operation <code>rk combine</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p rk_combine $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rkck">
<h3><a class="doc-anchor" href="#doc-rkck">#</a> <code>rkck</code></h3>
<p><code>rkck</code> — operation <code>rkck</code>. Alias for <code>rk45_cash_karp</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p rkck $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rkf45-error">
<h3><a class="doc-anchor" href="#doc-rkf45-error">#</a> <code>rkf45_error</code></h3>
<p><code>rkf45_error</code> — operation <code>rkf45 error</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p rkf45_error $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rl-discount-returns">
<h3><a class="doc-anchor" href="#doc-rl-discount-returns">#</a> <code>rl_discount_returns</code></h3>
<p><code>rl_discount_returns(rewards, gamma=0.9) → array</code> — backward-cumulative discounted returns <code>G_t = r_t + γ·G_{t+1}</code>.</p>
</article>
<article class="doc-entry" id="doc-rl-n-step-return">
<h3><a class="doc-anchor" href="#doc-rl-n-step-return">#</a> <code>rl_n_step_return</code></h3>
<p><code>rl_n_step_return(rewards, gamma=0.9) → number</code> — <code>Σ γ^k · r_k</code>. Bootstrap-free n-step return.</p>
</article>
<article class="doc-entry" id="doc-rl-tau">
<h3><a class="doc-anchor" href="#doc-rl-tau">#</a> <code>rl_tau</code></h3>
<p><code>rl_tau</code> — operation <code>rl tau</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p rl_tau $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rl-td-error">
<h3><a class="doc-anchor" href="#doc-rl-td-error">#</a> <code>rl_td_error</code></h3>
<p><code>rl_td_error(r, v_next, v, gamma=0.9) → number</code> — <code>r + γ·V(s') - V(s)</code>. TD(0) error term.</p>
</article>
<article class="doc-entry" id="doc-rl-time-constant">
<h3><a class="doc-anchor" href="#doc-rl-time-constant">#</a> <code>rl_time_constant</code></h3>
<p><code>rl_time_constant</code> — operation <code>rl time constant</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p rl_time_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rld">
<h3><a class="doc-anchor" href="#doc-rld">#</a> <code>rld</code></h3>
<p><code>rld</code> — operation <code>rld</code>. Alias for <code>run_length_decode</code>. Category: *collection more*.</p>
<pre><code class="lang-perl">p rld $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rld-str">
<h3><a class="doc-anchor" href="#doc-rld-str">#</a> <code>rld_str</code></h3>
<p><code>rld_str</code> — operation <code>rld str</code>. Alias for <code>run_length_decode_str</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p rld_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rle">
<h3><a class="doc-anchor" href="#doc-rle">#</a> <code>rle</code></h3>
<p><code>rle</code> — operation <code>rle</code>. Alias for <code>run_length_encode</code>. Category: *collection more*.</p>
<pre><code class="lang-perl">p rle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rle-compress">
<h3><a class="doc-anchor" href="#doc-rle-compress">#</a> <code>rle_compress</code></h3>
<p><code>rle_compress(s) → string</code> — run-length encode runs of 1-9 chars: "aaabbc" → "3a2b1c".</p>
<pre><code class="lang-perl">p rle_compress("aaabbc") # "3a2b1c"
</code></pre>
</article>
<article class="doc-entry" id="doc-rle-decompress">
<h3><a class="doc-anchor" href="#doc-rle-decompress">#</a> <code>rle_decompress</code></h3>
<p><code>rle_decompress(s) → string</code> — inverse of <code>rle_compress</code>.</p>
</article>
<article class="doc-entry" id="doc-rle-str">
<h3><a class="doc-anchor" href="#doc-rle-str">#</a> <code>rle_str</code></h3>
<p><code>rle_str</code> — run-length encoding <code>str</code>. Alias for <code>run_length_encode_str</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p rle_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rlnorm">
<h3><a class="doc-anchor" href="#doc-rlnorm">#</a> <code>rlnorm</code></h3>
<p><code>rlnorm</code> — generate n random log-normal variates. Args: n [, mu, sigma].</p>
<pre><code class="lang-perl">my @x = @{rlnorm(100, 0, 1)} # LogN(0,1)
</code></pre>
</article>
<article class="doc-entry" id="doc-rlogis">
<h3><a class="doc-anchor" href="#doc-rlogis">#</a> <code>rlogis</code></h3>
<p><code>rlogis</code> — operation <code>rlogis</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p rlogis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rltau">
<h3><a class="doc-anchor" href="#doc-rltau">#</a> <code>rltau</code></h3>
<p><code>rltau</code> — operation <code>rltau</code>. Alias for <code>rl_time_constant</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p rltau $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rmall">
<h3><a class="doc-anchor" href="#doc-rmall">#</a> <code>rmall</code></h3>
<p><code>rmall</code> — operation <code>rmall</code>. Alias for <code>remove_all_str</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p rmall $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rmcons">
<h3><a class="doc-anchor" href="#doc-rmcons">#</a> <code>rmcons</code></h3>
<p><code>rmcons</code> — operation <code>rmcons</code>. Alias for <code>remove_consonants</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p rmcons $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rms">
<h3><a class="doc-anchor" href="#doc-rms">#</a> <code>rms</code></h3>
<p><code>rms</code> — operation <code>rms</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p rms $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rmse">
<h3><a class="doc-anchor" href="#doc-rmse">#</a> <code>rmse</code></h3>
<p><code>rmse</code> — operation <code>rmse</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p rmse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rmvowel">
<h3><a class="doc-anchor" href="#doc-rmvowel">#</a> <code>rmvowel</code></h3>
<p><code>rmvowel</code> — operation <code>rmvowel</code>. Alias for <code>remove_vowels</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p rmvowel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rmws">
<h3><a class="doc-anchor" href="#doc-rmws">#</a> <code>rmws</code></h3>
<p><code>rmws</code> — operation <code>rmws</code>. Alias for <code>remove_whitespace</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p rmws $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rna-gc-content">
<h3><a class="doc-anchor" href="#doc-rna-gc-content">#</a> <code>rna_gc_content</code></h3>
<p><code>rna_gc_content</code> — RNA sequence op <code>gc content</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p rna_gc_content $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rna-hamming">
<h3><a class="doc-anchor" href="#doc-rna-hamming">#</a> <code>rna_hamming</code></h3>
<p><code>rna_hamming(a, b) → int</code> — Hamming distance between two equal-length sequences.</p>
</article>
<article class="doc-entry" id="doc-rna-reverse-complement">
<h3><a class="doc-anchor" href="#doc-rna-reverse-complement">#</a> <code>rna_reverse_complement</code></h3>
<p><code>rna_reverse_complement(rna) → string</code> — reverse complement using RNA pairing (A↔U, G↔C).</p>
</article>
<article class="doc-entry" id="doc-rna-to-dna">
<h3><a class="doc-anchor" href="#doc-rna-to-dna">#</a> <code>rna_to_dna</code></h3>
<p><code>rna_to_dna(rna) → string</code> — reverse transcription: U → T.</p>
</article>
<article class="doc-entry" id="doc-rngcmp">
<h3><a class="doc-anchor" href="#doc-rngcmp">#</a> <code>rngcmp</code></h3>
<p><code>rngcmp</code> — operation <code>rngcmp</code>. Alias for <code>range_compress</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p rngcmp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rngexp">
<h3><a class="doc-anchor" href="#doc-rngexp">#</a> <code>rngexp</code></h3>
<p><code>rngexp</code> — operation <code>rngexp</code>. Alias for <code>range_expand</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p rngexp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rnk">
<h3><a class="doc-anchor" href="#doc-rnk">#</a> <code>rnk</code></h3>
<p><code>rnk</code> — operation <code>rnk</code>. Alias for <code>rank</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p rnk $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rnorm">
<h3><a class="doc-anchor" href="#doc-rnorm">#</a> <code>rnorm</code></h3>
<p><code>rnorm</code> — generate n random normal variates. Args: n [, mu, sigma]. Like R's rnorm().</p>
<pre><code class="lang-perl">my @x = @{rnorm(1000)} # 1000 standard normal
my @y = @{rnorm(100, 50, 10)} # mean=50, sd=10
</code></pre>
</article>
<article class="doc-entry" id="doc-roberts-cross-kernel">
<h3><a class="doc-anchor" href="#doc-roberts-cross-kernel">#</a> <code>roberts_cross_kernel</code></h3>
<p><code>roberts_cross_kernel() → matrix</code> — 2×2 Roberts cross-gradient kernel.</p>
</article>
<article class="doc-entry" id="doc-roberts-kernel-value">
<h3><a class="doc-anchor" href="#doc-roberts-kernel-value">#</a> <code>roberts_kernel_value</code></h3>
<p><code>roberts_kernel_value</code> — value of <code>roberts kernel</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p roberts_kernel_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-robinson-project">
<h3><a class="doc-anchor" href="#doc-robinson-project">#</a> <code>robinson_project</code></h3>
<p><code>robinson_project</code> — operation <code>robinson project</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p robinson_project $x
</code></pre>
</article>
<article class="doc-entry" id="doc-robinson-schensted-pair">
<h3><a class="doc-anchor" href="#doc-robinson-schensted-pair">#</a> <code>robinson_schensted_pair</code></h3>
<p><code>robinson_schensted_pair</code> — operation <code>robinson schensted pair</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p robinson_schensted_pair $x
</code></pre>
</article>
<article class="doc-entry" id="doc-robust-scale">
<h3><a class="doc-anchor" href="#doc-robust-scale">#</a> <code>robust_scale</code></h3>
<p><code>robust_scale</code> — operation <code>robust scale</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p robust_scale $x
</code></pre>
</article>
<article class="doc-entry" id="doc-robust-se-huber-white">
<h3><a class="doc-anchor" href="#doc-robust-se-huber-white">#</a> <code>robust_se_huber_white</code></h3>
<p><code>robust_se_huber_white</code> — operation <code>robust se huber white</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p robust_se_huber_white $x
</code></pre>
</article>
<article class="doc-entry" id="doc-roc">
<h3><a class="doc-anchor" href="#doc-roc">#</a> <code>roc</code></h3>
<p><code>roc(prices, period=10) → array</code> — rate of change: <code>100·(price[i] − price[i−period]) / price[i−period]</code>. Pure momentum oscillator centred at 0.</p>
<pre><code class="lang-perl">p roc(\@closes, 12)
</code></pre>
</article>
<article class="doc-entry" id="doc-roche-limit-fluid">
<h3><a class="doc-anchor" href="#doc-roche-limit-fluid">#</a> <code>roche_limit_fluid</code></h3>
<p><code>roche_limit_fluid</code> — operation <code>roche limit fluid</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p roche_limit_fluid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-roche-limit-rigid">
<h3><a class="doc-anchor" href="#doc-roche-limit-rigid">#</a> <code>roche_limit_rigid</code></h3>
<p><code>roche_limit_rigid</code> — operation <code>roche limit rigid</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p roche_limit_rigid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-roi">
<h3><a class="doc-anchor" href="#doc-roi">#</a> <code>roi</code></h3>
<p><code>roi(gain, cost) → number</code> — Return on Investment as percent: <code>(gain - cost) / cost · 100</code>.</p>
<pre><code class="lang-perl">p roi(1500, 1000) # 50
</code></pre>
</article>
<article class="doc-entry" id="doc-roll-n">
<h3><a class="doc-anchor" href="#doc-roll-n">#</a> <code>roll_n</code></h3>
<p><code>roll_n</code> — operation <code>roll n</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p roll_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rolling-kurtosis">
<h3><a class="doc-anchor" href="#doc-rolling-kurtosis">#</a> <code>rolling_kurtosis</code></h3>
<p><code>rolling_kurtosis(series, period=10) → array</code> — sliding excess kurtosis.</p>
</article>
<article class="doc-entry" id="doc-rolling-max">
<h3><a class="doc-anchor" href="#doc-rolling-max">#</a> <code>rolling_max</code></h3>
<p><code>rolling_max(series, period=10) → array</code> — sliding maximum.</p>
</article>
<article class="doc-entry" id="doc-rolling-mean">
<h3><a class="doc-anchor" href="#doc-rolling-mean">#</a> <code>rolling_mean</code></h3>
<p><code>rolling_mean(series, period=10) → array</code> — sliding mean. Output length is <code>len - period + 1</code>.</p>
<pre><code class="lang-perl">p rolling_mean([1,2,3,4,5], 3) # [2.0, 3.0, 4.0]
</code></pre>
</article>
<article class="doc-entry" id="doc-rolling-median">
<h3><a class="doc-anchor" href="#doc-rolling-median">#</a> <code>rolling_median</code></h3>
<p><code>rolling_median(series, period=10) → array</code> — sliding median; robust to outliers.</p>
<pre><code class="lang-perl">p rolling_median(\@xs, 5)
</code></pre>
</article>
<article class="doc-entry" id="doc-rolling-min">
<h3><a class="doc-anchor" href="#doc-rolling-min">#</a> <code>rolling_min</code></h3>
<p><code>rolling_min(series, period=10) → array</code> — sliding minimum.</p>
</article>
<article class="doc-entry" id="doc-rolling-skew">
<h3><a class="doc-anchor" href="#doc-rolling-skew">#</a> <code>rolling_skew</code></h3>
<p><code>rolling_skew(series, period=10) → array</code> — sliding skewness (third central moment / σ³).</p>
</article>
<article class="doc-entry" id="doc-rolling-std">
<h3><a class="doc-anchor" href="#doc-rolling-std">#</a> <code>rolling_std</code></h3>
<p><code>rolling_std(series, period=10) → array</code> — sliding (population) standard deviation.</p>
</article>
<article class="doc-entry" id="doc-rolling-sum">
<h3><a class="doc-anchor" href="#doc-rolling-sum">#</a> <code>rolling_sum</code></h3>
<p><code>rolling_sum(series, period=10) → array</code> — sliding sum.</p>
<pre><code class="lang-perl">p rolling_sum([1,2,3,4,5], 3) # [6, 9, 12]
</code></pre>
</article>
<article class="doc-entry" id="doc-rolling-var">
<h3><a class="doc-anchor" href="#doc-rolling-var">#</a> <code>rolling_var</code></h3>
<p><code>rolling_var(series, period=10) → array</code> — sliding (population) variance.</p>
</article>
<article class="doc-entry" id="doc-roman">
<h3><a class="doc-anchor" href="#doc-roman">#</a> <code>roman</code></h3>
<p><code>roman</code> — operation <code>roman</code>. Alias for <code>int_to_roman</code>. Category: *roman numerals*.</p>
<pre><code class="lang-perl">p roman $x
</code></pre>
</article>
<article class="doc-entry" id="doc-roman-add">
<h3><a class="doc-anchor" href="#doc-roman-add">#</a> <code>roman_add</code></h3>
<p><code>roman_add</code> — operation <code>roman add</code>. Category: *roman numerals*.</p>
<pre><code class="lang-perl">p roman_add $x
</code></pre>
</article>
<article class="doc-entry" id="doc-roman-decode">
<h3><a class="doc-anchor" href="#doc-roman-decode">#</a> <code>roman_decode</code></h3>
<p><code>roman_decode</code> — decode of <code>roman</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p roman_decode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-roman-encode">
<h3><a class="doc-anchor" href="#doc-roman-encode">#</a> <code>roman_encode</code></h3>
<p><code>roman_encode</code> — encode of <code>roman</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p roman_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-roman-numeral-list">
<h3><a class="doc-anchor" href="#doc-roman-numeral-list">#</a> <code>roman_numeral_list</code></h3>
<p><code>roman_numeral_list</code> — operation <code>roman numeral list</code>. Category: *roman numerals*.</p>
<pre><code class="lang-perl">p roman_numeral_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-roman-to-int">
<h3><a class="doc-anchor" href="#doc-roman-to-int">#</a> <code>roman_to_int</code></h3>
<p><code>roman_to_int</code> — convert from <code>roman</code> to <code>int</code>. Category: *roman numerals*.</p>
<pre><code class="lang-perl">p roman_to_int $value
</code></pre>
</article>
<article class="doc-entry" id="doc-romanlist">
<h3><a class="doc-anchor" href="#doc-romanlist">#</a> <code>romanlist</code></h3>
<p><code>romanlist</code> — operation <code>romanlist</code>. Alias for <code>roman_numeral_list</code>. Category: *roman numerals*.</p>
<pre><code class="lang-perl">p romanlist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-romberg-quad">
<h3><a class="doc-anchor" href="#doc-romberg-quad">#</a> <code>romberg_quad</code></h3>
<p><code>romberg_quad</code> — operation <code>romberg quad</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p romberg_quad $x
</code></pre>
</article>
<article class="doc-entry" id="doc-roommate-match-step">
<h3><a class="doc-anchor" href="#doc-roommate-match-step">#</a> <code>roommate_match_step</code></h3>
<p><code>roommate_match_step</code> — single-step update of <code>roommate match</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p roommate_match_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-root-brentq">
<h3><a class="doc-anchor" href="#doc-root-brentq">#</a> <code>root_brentq</code></h3>
<p><code>root_brentq</code> — operation <code>root brentq</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p root_brentq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-root-newton">
<h3><a class="doc-anchor" href="#doc-root-newton">#</a> <code>root_newton</code></h3>
<p><code>root_newton</code> — operation <code>root newton</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p root_newton $x
</code></pre>
</article>
<article class="doc-entry" id="doc-root-secant">
<h3><a class="doc-anchor" href="#doc-root-secant">#</a> <code>root_secant</code></h3>
<p><code>root_secant</code> — operation <code>root secant</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p root_secant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-root-system-count">
<h3><a class="doc-anchor" href="#doc-root-system-count">#</a> <code>root_system_count</code></h3>
<p><code>root_system_count</code> — count of <code>root system</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p root_system_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ros2-step">
<h3><a class="doc-anchor" href="#doc-ros2-step">#</a> <code>ros2_step</code></h3>
<p><code>ros2_step</code> — single-step update of <code>ros2</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p ros2_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rot13">
<h3><a class="doc-anchor" href="#doc-rot13">#</a> <code>rot13</code></h3>
<p><code>rot13</code> — operation <code>rot13</code>. Category: *string*.</p>
<pre><code class="lang-perl">p rot13 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rot47">
<h3><a class="doc-anchor" href="#doc-rot47">#</a> <code>rot47</code></h3>
<p><code>rot47</code> — operation <code>rot47</code>. Category: *string*.</p>
<pre><code class="lang-perl">p rot47 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rotate">
<h3><a class="doc-anchor" href="#doc-rotate">#</a> <code>rotate</code></h3>
<p><code>rotate</code> — operation <code>rotate</code>. Category: *collection helpers (trivial)*.</p>
<pre><code class="lang-perl">p rotate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rotate-axis">
<h3><a class="doc-anchor" href="#doc-rotate-axis">#</a> <code>rotate_axis</code></h3>
<p><code>rotate_axis</code> — operation <code>rotate axis</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p rotate_axis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rotate-point">
<h3><a class="doc-anchor" href="#doc-rotate-point">#</a> <code>rotate_point</code></h3>
<p><code>rotate_point</code> — operation <code>rotate point</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p rotate_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-roulette-wheel-select-index">
<h3><a class="doc-anchor" href="#doc-roulette-wheel-select-index">#</a> <code>roulette_wheel_select_index</code></h3>
<p><code>roulette_wheel_select_index</code> — index of <code>roulette wheel select</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p roulette_wheel_select_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-round">
<h3><a class="doc-anchor" href="#doc-round">#</a> <code>round</code></h3>
<p><code>round</code> — operation <code>round</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p round $x
</code></pre>
</article>
<article class="doc-entry" id="doc-round-each">
<h3><a class="doc-anchor" href="#doc-round-each">#</a> <code>round_each</code></h3>
<p><code>round_each</code> — operation <code>round each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p round_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-round-to">
<h3><a class="doc-anchor" href="#doc-round-to">#</a> <code>round_to</code></h3>
<p><code>round_to</code> — operation <code>round to</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p round_to $x
</code></pre>
</article>
<article class="doc-entry" id="doc-roundrobin">
<h3><a class="doc-anchor" href="#doc-roundrobin">#</a> <code>roundrobin</code></h3>
<p><code>roundrobin</code> — operation <code>roundrobin</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p roundrobin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rowmeans">
<h3><a class="doc-anchor" href="#doc-rowmeans">#</a> <code>rowMeans</code></h3>
<p><code>row_means</code> (alias <code>rowMeans</code>) — mean of each row. Like R's rowMeans().</p>
<pre><code class="lang-perl">p rowMeans([[2,4],[6,8]]) # [3, 7]
</code></pre>
</article>
<article class="doc-entry" id="doc-rowsums">
<h3><a class="doc-anchor" href="#doc-rowsums">#</a> <code>rowSums</code></h3>
<p><code>row_sums</code> (alias <code>rowSums</code>) — sum of each row in a matrix. Like R's rowSums().</p>
<pre><code class="lang-perl">p row_sums([[1,2,3],[4,5,6]]) # [6, 15]
</code></pre>
</article>
<article class="doc-entry" id="doc-rpad">
<h3><a class="doc-anchor" href="#doc-rpad">#</a> <code>rpad</code></h3>
<p><code>rpad</code> — operation <code>rpad</code>. Alias for <code>pad_right</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p rpad $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rpn">
<h3><a class="doc-anchor" href="#doc-rpn">#</a> <code>rpn</code></h3>
<p><code>rpn</code> — operation <code>rpn</code>. Alias for <code>eval_rpn</code>. Category: *algorithms / puzzles*.</p>
<pre><code class="lang-perl">p rpn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rpois">
<h3><a class="doc-anchor" href="#doc-rpois">#</a> <code>rpois</code></h3>
<p><code>rpois</code> — generate n random Poisson variates. Args: n, lambda. Like R's rpois().</p>
<pre><code class="lang-perl">my @x = @{rpois(100, 5)} # Poisson with mean 5
</code></pre>
</article>
<article class="doc-entry" id="doc-rptd">
<h3><a class="doc-anchor" href="#doc-rptd">#</a> <code>rptd</code></h3>
<p><code>rptd</code> — operation <code>rptd</code>. Alias for <code>repeatedly</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p rptd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rpush">
<h3><a class="doc-anchor" href="#doc-rpush">#</a> <code>rpush</code></h3>
<p><code>rpush</code> — operation <code>rpush</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p rpush $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rrt-extend">
<h3><a class="doc-anchor" href="#doc-rrt-extend">#</a> <code>rrt_extend</code></h3>
<p><code>rrt_extend</code> — operation <code>rrt extend</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p rrt_extend $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rrt-star-rewire">
<h3><a class="doc-anchor" href="#doc-rrt-star-rewire">#</a> <code>rrt_star_rewire</code></h3>
<p><code>rrt_star_rewire</code> — operation <code>rrt star rewire</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p rrt_star_rewire $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rrule-next-occurrence">
<h3><a class="doc-anchor" href="#doc-rrule-next-occurrence">#</a> <code>rrule_next_occurrence</code></h3>
<p><code>rrule_next_occurrence</code> — operation <code>rrule next occurrence</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p rrule_next_occurrence $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rsa-d-from-e">
<h3><a class="doc-anchor" href="#doc-rsa-d-from-e">#</a> <code>rsa_d_from_e</code></h3>
<p><code>rsa_d_from_e</code> — RSA cryptographic primitive <code>d from e</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p rsa_d_from_e $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rsa-decrypt-pkcs1">
<h3><a class="doc-anchor" href="#doc-rsa-decrypt-pkcs1">#</a> <code>rsa_decrypt_pkcs1</code></h3>
<p><code>rsa_decrypt_pkcs1</code> decrypts RSA-PKCS1v15 ciphertext.</p>
<pre><code class="lang-perl">my $plain = rsa_decrypt_pkcs1($priv, $cipher)
</code></pre>
</article>
<article class="doc-entry" id="doc-rsa-encrypt-pkcs1">
<h3><a class="doc-anchor" href="#doc-rsa-encrypt-pkcs1">#</a> <code>rsa_encrypt_pkcs1</code></h3>
<p><code>rsa_encrypt_pkcs1</code> encrypts with legacy RSA-PKCS1v15 padding. Only for compatibility with old systems — prefer OAEP.</p>
<pre><code class="lang-perl">my $cipher = rsa_encrypt_pkcs1($pub, "data")
</code></pre>
</article>
<article class="doc-entry" id="doc-rsa-encrypt-simple">
<h3><a class="doc-anchor" href="#doc-rsa-encrypt-simple">#</a> <code>rsa_encrypt_simple</code></h3>
<p><code>rsa_encrypt_simple</code> — RSA cryptographic primitive <code>encrypt simple</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p rsa_encrypt_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rsa-keypair-simple">
<h3><a class="doc-anchor" href="#doc-rsa-keypair-simple">#</a> <code>rsa_keypair_simple</code></h3>
<p><code>rsa_keypair_simple(p, q, e=17) → {n, e, d}</code> — textbook RSA from two primes. NOT cryptographically secure.</p>
<pre><code class="lang-perl">p rsa_keypair_simple(61, 53) # {n:3233, e:17, d:2753}
</code></pre>
</article>
<article class="doc-entry" id="doc-rsa-modular-exp">
<h3><a class="doc-anchor" href="#doc-rsa-modular-exp">#</a> <code>rsa_modular_exp</code></h3>
<p><code>rsa_modular_exp(base, exp, modulus) → string</code> — <code>base^exp mod modulus</code> on arbitrary-precision BigUInts (decimal strings).</p>
<pre><code class="lang-perl">p rsa_modular_exp("2", "10", "100") # "24"
</code></pre>
</article>
<article class="doc-entry" id="doc-rsamp">
<h3><a class="doc-anchor" href="#doc-rsamp">#</a> <code>rsamp</code></h3>
<p><code>rsamp</code> — operation <code>rsamp</code>. Alias for <code>reservoir_sample</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p rsamp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rsi">
<h3><a class="doc-anchor" href="#doc-rsi">#</a> <code>rsi</code></h3>
<p><code>rsi(prices, period=14) → array</code> — Relative Strength Index (Wilder). Computes <code>100 − 100 / (1 + avg_gain / avg_loss)</code> over a moving window; values >70 commonly mark overbought, <30 oversold.</p>
<pre><code class="lang-perl">p rsi(\@closes, 14)
</code></pre>
</article>
<article class="doc-entry" id="doc-rsk-size">
<h3><a class="doc-anchor" href="#doc-rsk-size">#</a> <code>rsk_size</code></h3>
<p><code>rsk_size</code> — operation <code>rsk size</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p rsk_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rst">
<h3><a class="doc-anchor" href="#doc-rst">#</a> <code>rst</code></h3>
<p><code>rst</code> — operation <code>rst</code>. Alias for <code>rest</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p rst $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rsun">
<h3><a class="doc-anchor" href="#doc-rsun">#</a> <code>rsun</code></h3>
<p><code>rsun</code> — operation <code>rsun</code>. Alias for <code>sun_radius</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p rsun $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rt">
<h3><a class="doc-anchor" href="#doc-rt">#</a> <code>rt</code></h3>
<p><code>rt</code> — generate n random Student's t variates. Args: n, df. Like R's rt().</p>
<pre><code class="lang-perl">my @x = @{rt(100, 10)} # t with 10 df
</code></pre>
</article>
<article class="doc-entry" id="doc-rt-effective">
<h3><a class="doc-anchor" href="#doc-rt-effective">#</a> <code>rt_effective</code></h3>
<p><code>rt_effective</code> — operation <code>rt effective</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p rt_effective $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rt-serial-interval">
<h3><a class="doc-anchor" href="#doc-rt-serial-interval">#</a> <code>rt_serial_interval</code></h3>
<p><code>rt_serial_interval</code> — operation <code>rt serial interval</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p rt_serial_interval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rtt-avg">
<h3><a class="doc-anchor" href="#doc-rtt-avg">#</a> <code>rtt_avg</code></h3>
<p><code>rtt_avg</code> — operation <code>rtt avg</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p rtt_avg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rtt-max">
<h3><a class="doc-anchor" href="#doc-rtt-max">#</a> <code>rtt_max</code></h3>
<p><code>rtt_max</code> — maximum of <code>rtt</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p rtt_max $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rtt-min">
<h3><a class="doc-anchor" href="#doc-rtt-min">#</a> <code>rtt_min</code></h3>
<p><code>rtt_min</code> — minimum of <code>rtt</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p rtt_min $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ruin-probability-lundberg">
<h3><a class="doc-anchor" href="#doc-ruin-probability-lundberg">#</a> <code>ruin_probability_lundberg</code></h3>
<p><code>ruin_probability_lundberg</code> — operation <code>ruin probability lundberg</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p ruin_probability_lundberg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-run-length-decode">
<h3><a class="doc-anchor" href="#doc-run-length-decode">#</a> <code>run_length_decode</code></h3>
<p><code>run_length_decode</code> — decode of <code>run length</code>. Category: *collection more*.</p>
<pre><code class="lang-perl">p run_length_decode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-run-length-decode-str">
<h3><a class="doc-anchor" href="#doc-run-length-decode-str">#</a> <code>run_length_decode_str</code></h3>
<p><code>run_length_decode_str</code> — operation <code>run length decode str</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p run_length_decode_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-run-length-encode">
<h3><a class="doc-anchor" href="#doc-run-length-encode">#</a> <code>run_length_encode</code></h3>
<p><code>run_length_encode</code> — encode of <code>run length</code>. Category: *collection more*.</p>
<pre><code class="lang-perl">p run_length_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-run-length-encode-str">
<h3><a class="doc-anchor" href="#doc-run-length-encode-str">#</a> <code>run_length_encode_str</code></h3>
<p><code>run_length_encode_str</code> — operation <code>run length encode str</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p run_length_encode_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-run-off-triangle-step">
<h3><a class="doc-anchor" href="#doc-run-off-triangle-step">#</a> <code>run_off_triangle_step</code></h3>
<p><code>run_off_triangle_step</code> — single-step update of <code>run off triangle</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p run_off_triangle_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-runif">
<h3><a class="doc-anchor" href="#doc-runif">#</a> <code>runif</code></h3>
<p><code>runif</code> — generate n random uniform variates. Args: n [, min, max]. Like R's runif().</p>
<pre><code class="lang-perl">my @x = @{runif(100, 0, 1)} # 100 uniform [0,1]
</code></pre>
</article>
<article class="doc-entry" id="doc-running-max">
<h3><a class="doc-anchor" href="#doc-running-max">#</a> <code>running_max</code></h3>
<p><code>running_max</code> — maximum of <code>running</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p running_max $x
</code></pre>
</article>
<article class="doc-entry" id="doc-running-mean">
<h3><a class="doc-anchor" href="#doc-running-mean">#</a> <code>running_mean</code></h3>
<p><code>running_mean</code> — arithmetic mean of <code>running</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p running_mean @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-running-min">
<h3><a class="doc-anchor" href="#doc-running-min">#</a> <code>running_min</code></h3>
<p><code>running_min</code> — minimum of <code>running</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p running_min $x
</code></pre>
</article>
<article class="doc-entry" id="doc-running-reduce">
<h3><a class="doc-anchor" href="#doc-running-reduce">#</a> <code>running_reduce</code></h3>
<p><code>running_reduce</code> — operation <code>running reduce</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p running_reduce $x
</code></pre>
</article>
<article class="doc-entry" id="doc-running-variance">
<h3><a class="doc-anchor" href="#doc-running-variance">#</a> <code>running_variance</code></h3>
<p><code>running_variance</code> — operation <code>running variance</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p running_variance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-runred">
<h3><a class="doc-anchor" href="#doc-runred">#</a> <code>runred</code></h3>
<p><code>runred</code> — operation <code>runred</code>. Alias for <code>running_reduce</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p runred $x
</code></pre>
</article>
<article class="doc-entry" id="doc-runs">
<h3><a class="doc-anchor" href="#doc-runs">#</a> <code>runs</code></h3>
<p><code>runs</code> — operation <code>runs</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p runs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rweibull">
<h3><a class="doc-anchor" href="#doc-rweibull">#</a> <code>rweibull</code></h3>
<p><code>rweibull</code> — generate n random Weibull variates. Args: n, shape [, scale].</p>
<pre><code class="lang-perl">my @x = @{rweibull(100, 2, 1)} # Weibull(2,1)
</code></pre>
</article>
<article class="doc-entry" id="doc-rx-gate">
<h3><a class="doc-anchor" href="#doc-rx-gate">#</a> <code>rx_gate</code></h3>
<p><code>rx_gate</code> — operation <code>rx gate</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p rx_gate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rxn-q">
<h3><a class="doc-anchor" href="#doc-rxn-q">#</a> <code>rxn_q</code></h3>
<p><code>rxn_q</code> — operation <code>rxn q</code>. Alias for <code>reaction_quotient</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p rxn_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ry-gate">
<h3><a class="doc-anchor" href="#doc-ry-gate">#</a> <code>ry_gate</code></h3>
<p><code>ry_gate</code> — operation <code>ry gate</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p ry_gate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rydberg">
<h3><a class="doc-anchor" href="#doc-rydberg">#</a> <code>rydberg</code></h3>
<p><code>rydberg</code> — operation <code>rydberg</code>. Alias for <code>rydberg_constant</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p rydberg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rydberg-constant">
<h3><a class="doc-anchor" href="#doc-rydberg-constant">#</a> <code>rydberg_constant</code></h3>
<p><code>rydberg_constant</code> — operation <code>rydberg constant</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p rydberg_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rydberg-lambda">
<h3><a class="doc-anchor" href="#doc-rydberg-lambda">#</a> <code>rydberg_lambda</code></h3>
<p><code>rydberg_lambda</code> — operation <code>rydberg lambda</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p rydberg_lambda $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ryu-takayanagi-step">
<h3><a class="doc-anchor" href="#doc-ryu-takayanagi-step">#</a> <code>ryu_takayanagi_step</code></h3>
<p><code>ryu_takayanagi_step</code> — single-step update of <code>ryu takayanagi</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ryu_takayanagi_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-rz-gate">
<h3><a class="doc-anchor" href="#doc-rz-gate">#</a> <code>rz_gate</code></h3>
<p><code>rz_gate</code> — operation <code>rz gate</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p rz_gate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-s1">
<h3><a class="doc-anchor" href="#doc-s1">#</a> <code>s1</code></h3>
<p><code>s1</code> — operation <code>s1</code>. Alias for <code>sha1</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p s1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-s224">
<h3><a class="doc-anchor" href="#doc-s224">#</a> <code>s224</code></h3>
<p><code>s224</code> — operation <code>s224</code>. Alias for <code>sha224</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p s224 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-s256">
<h3><a class="doc-anchor" href="#doc-s256">#</a> <code>s256</code></h3>
<p><code>s256</code> — operation <code>s256</code>. Alias for <code>sha256</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p s256 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-s2-cell-at-lat-lng">
<h3><a class="doc-anchor" href="#doc-s2-cell-at-lat-lng">#</a> <code>s2_cell_at_lat_lng</code></h3>
<p><code>s2_cell_at_lat_lng</code> — operation <code>s2 cell at lat lng</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p s2_cell_at_lat_lng $x
</code></pre>
</article>
<article class="doc-entry" id="doc-s2-cell-id">
<h3><a class="doc-anchor" href="#doc-s2-cell-id">#</a> <code>s2_cell_id</code></h3>
<p><code>s2_cell_id</code> — operation <code>s2 cell id</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p s2_cell_id $x
</code></pre>
</article>
<article class="doc-entry" id="doc-s2-cell-neighbors">
<h3><a class="doc-anchor" href="#doc-s2-cell-neighbors">#</a> <code>s2_cell_neighbors</code></h3>
<p><code>s2_cell_neighbors</code> — operation <code>s2 cell neighbors</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p s2_cell_neighbors $x
</code></pre>
</article>
<article class="doc-entry" id="doc-s2c">
<h3><a class="doc-anchor" href="#doc-s2c">#</a> <code>s2c</code></h3>
<p><code>s2c</code> — operation <code>s2c</code>. Alias for <code>snake_to_camel</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p s2c $x
</code></pre>
</article>
<article class="doc-entry" id="doc-s384">
<h3><a class="doc-anchor" href="#doc-s384">#</a> <code>s384</code></h3>
<p><code>s384</code> — operation <code>s384</code>. Alias for <code>sha384</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p s384 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-s512">
<h3><a class="doc-anchor" href="#doc-s512">#</a> <code>s512</code></h3>
<p><code>s512</code> — operation <code>s512</code>. Alias for <code>sha512</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p s512 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-s-to-m">
<h3><a class="doc-anchor" href="#doc-s-to-m">#</a> <code>s_to_m</code></h3>
<p><code>s_to_m</code> — convert from <code>s</code> to <code>m</code>. Alias for <code>seconds_to_minutes</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p s_to_m $value
</code></pre>
</article>
<article class="doc-entry" id="doc-s-to-ms">
<h3><a class="doc-anchor" href="#doc-s-to-ms">#</a> <code>s_to_ms</code></h3>
<p><code>s_to_ms</code> — convert from <code>s</code> to <code>ms</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p s_to_ms $value
</code></pre>
</article>
<article class="doc-entry" id="doc-sa-accept-prob">
<h3><a class="doc-anchor" href="#doc-sa-accept-prob">#</a> <code>sa_accept_prob</code></h3>
<p><code>sa_accept_prob</code> — operation <code>sa accept prob</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p sa_accept_prob $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sa-boltzmann-temp">
<h3><a class="doc-anchor" href="#doc-sa-boltzmann-temp">#</a> <code>sa_boltzmann_temp</code></h3>
<p><code>sa_boltzmann_temp</code> — operation <code>sa boltzmann temp</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p sa_boltzmann_temp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sa-cauchy-temp">
<h3><a class="doc-anchor" href="#doc-sa-cauchy-temp">#</a> <code>sa_cauchy_temp</code></h3>
<p><code>sa_cauchy_temp</code> — operation <code>sa cauchy temp</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p sa_cauchy_temp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sa-geometric-temp">
<h3><a class="doc-anchor" href="#doc-sa-geometric-temp">#</a> <code>sa_geometric_temp</code></h3>
<p><code>sa_geometric_temp</code> — operation <code>sa geometric temp</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p sa_geometric_temp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sabr-implied-vol">
<h3><a class="doc-anchor" href="#doc-sabr-implied-vol">#</a> <code>sabr_implied_vol</code></h3>
<p><code>sabr_implied_vol</code> — operation <code>sabr implied vol</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p sabr_implied_vol $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sadd">
<h3><a class="doc-anchor" href="#doc-sadd">#</a> <code>sadd</code></h3>
<p><code>sadd</code> — operation <code>sadd</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p sadd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-saddle-point-check">
<h3><a class="doc-anchor" href="#doc-saddle-point-check">#</a> <code>saddle_point_check</code></h3>
<p><code>saddle_point_check</code> — operation <code>saddle point check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p saddle_point_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-safe-div">
<h3><a class="doc-anchor" href="#doc-safe-div">#</a> <code>safe_div</code></h3>
<p><code>safe_div</code> — operation <code>safe div</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p safe_div $x
</code></pre>
</article>
<article class="doc-entry" id="doc-safe-log">
<h3><a class="doc-anchor" href="#doc-safe-log">#</a> <code>safe_log</code></h3>
<p><code>safe_log</code> — operation <code>safe log</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p safe_log $x
</code></pre>
</article>
<article class="doc-entry" id="doc-safe-mod">
<h3><a class="doc-anchor" href="#doc-safe-mod">#</a> <code>safe_mod</code></h3>
<p><code>safe_mod</code> — operation <code>safe mod</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p safe_mod $x
</code></pre>
</article>
<article class="doc-entry" id="doc-safe-sqrt">
<h3><a class="doc-anchor" href="#doc-safe-sqrt">#</a> <code>safe_sqrt</code></h3>
<p><code>safe_sqrt</code> — operation <code>safe sqrt</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p safe_sqrt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-salloc">
<h3><a class="doc-anchor" href="#doc-salloc">#</a> <code>salloc</code></h3>
<p><code>salloc</code> — operation <code>salloc</code>. Alias for <code>stress_alloc</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p salloc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-salt-activity-coefficient">
<h3><a class="doc-anchor" href="#doc-salt-activity-coefficient">#</a> <code>salt_activity_coefficient</code></h3>
<p><code>salt_activity_coefficient</code> — operation <code>salt activity coefficient</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p salt_activity_coefficient $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sample-n">
<h3><a class="doc-anchor" href="#doc-sample-n">#</a> <code>sample_n</code></h3>
<p><code>sample_n</code> — operation <code>sample n</code>. Alias for <code>random_sample</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p sample_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sample-one">
<h3><a class="doc-anchor" href="#doc-sample-one">#</a> <code>sample_one</code></h3>
<p><code>sample_one</code> — operation <code>sample one</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p sample_one $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sample-stddev">
<h3><a class="doc-anchor" href="#doc-sample-stddev">#</a> <code>sample_stddev</code></h3>
<p><code>sample_stddev</code> — operation <code>sample stddev</code>. Category: *statistics (extended)*.</p>
<pre><code class="lang-perl">p sample_stddev $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sample-variance">
<h3><a class="doc-anchor" href="#doc-sample-variance">#</a> <code>sample_variance</code></h3>
<p><code>sample_variance</code> — operation <code>sample variance</code>. Category: *statistics (extended)*.</p>
<pre><code class="lang-perl">p sample_variance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sample-weighted-unique">
<h3><a class="doc-anchor" href="#doc-sample-weighted-unique">#</a> <code>sample_weighted_unique</code></h3>
<p><code>sample_weighted_unique</code> — operation <code>sample weighted unique</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p sample_weighted_unique $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sampn">
<h3><a class="doc-anchor" href="#doc-sampn">#</a> <code>sampn</code></h3>
<p><code>sampn</code> — operation <code>sampn</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p sampn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sapply">
<h3><a class="doc-anchor" href="#doc-sapply">#</a> <code>sapply</code></h3>
<p><code>sapply</code> — apply a function to each element, return a vector. Like R's sapply().</p>
<pre><code class="lang-perl">my @sq = @{sapply([1,2,3,4], fn { $_[0] ** 2 })} # [1,4,9,16]
</code></pre>
</article>
<article class="doc-entry" id="doc-sarimax-fit">
<h3><a class="doc-anchor" href="#doc-sarimax-fit">#</a> <code>sarimax_fit</code></h3>
<p><code>sarimax_fit</code> — operation <code>sarimax fit</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p sarimax_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-saros-cycle">
<h3><a class="doc-anchor" href="#doc-saros-cycle">#</a> <code>saros_cycle</code></h3>
<p><code>saros_cycle</code> — operation <code>saros cycle</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p saros_cycle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sarsa-step">
<h3><a class="doc-anchor" href="#doc-sarsa-step">#</a> <code>sarsa_step</code></h3>
<p><code>sarsa_step(q, alpha, r, gamma, next_q) → number</code> — <code>q ← q + α·(r + γ·next_q - q)</code>. On-policy TD(0).</p>
</article>
<article class="doc-entry" id="doc-sarsa-update">
<h3><a class="doc-anchor" href="#doc-sarsa-update">#</a> <code>sarsa_update</code></h3>
<p><code>sarsa_update</code> — update step of <code>sarsa</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p sarsa_update $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sat01">
<h3><a class="doc-anchor" href="#doc-sat01">#</a> <code>sat01</code></h3>
<p><code>sat01</code> — operation <code>sat01</code>. Alias for <code>saturate</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p sat01 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-saturate">
<h3><a class="doc-anchor" href="#doc-saturate">#</a> <code>saturate</code></h3>
<p><code>saturate</code> — operation <code>saturate</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p saturate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-saturation-equivalent-pt">
<h3><a class="doc-anchor" href="#doc-saturation-equivalent-pt">#</a> <code>saturation_equivalent_pt</code></h3>
<p><code>saturation_equivalent_pt</code> — operation <code>saturation equivalent pt</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p saturation_equivalent_pt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-saturation-vapor-pressure">
<h3><a class="doc-anchor" href="#doc-saturation-vapor-pressure">#</a> <code>saturation_vapor_pressure</code></h3>
<p><code>saturation_vapor_pressure</code> — operation <code>saturation vapor pressure</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p saturation_vapor_pressure $x
</code></pre>
</article>
<article class="doc-entry" id="doc-save-pct">
<h3><a class="doc-anchor" href="#doc-save-pct">#</a> <code>save_pct</code></h3>
<p><code>save_pct</code> — percentage of <code>save</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p save_pct $x
</code></pre>
</article>
<article class="doc-entry" id="doc-save-random-state">
<h3><a class="doc-anchor" href="#doc-save-random-state">#</a> <code>save_random_state</code></h3>
<p><code>save_random_state</code> — operation <code>save random state</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p save_random_state $x
</code></pre>
</article>
<article class="doc-entry" id="doc-savgol-coef">
<h3><a class="doc-anchor" href="#doc-savgol-coef">#</a> <code>savgol_coef</code></h3>
<p><code>savgol_coef</code> — operation <code>savgol coef</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p savgol_coef $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sbranch">
<h3><a class="doc-anchor" href="#doc-sbranch">#</a> <code>sbranch</code></h3>
<p><code>sbranch</code> — operation <code>sbranch</code>. Alias for <code>stress_branch</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p sbranch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-scalar-curvature-step">
<h3><a class="doc-anchor" href="#doc-scalar-curvature-step">#</a> <code>scalar_curvature_step</code></h3>
<p><code>scalar_curvature_step</code> — single-step update of <code>scalar curvature</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p scalar_curvature_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-scale">
<h3><a class="doc-anchor" href="#doc-scale">#</a> <code>scale</code></h3>
<p><code>scale</code> — standardize a vector: (x - mean) / sd. Like R's scale().</p>
<pre><code class="lang-perl">my @z = @{scale([10,20,30])} # [-1, 0, 1]
</code></pre>
</article>
<article class="doc-entry" id="doc-scale-blues">
<h3><a class="doc-anchor" href="#doc-scale-blues">#</a> <code>scale_blues</code></h3>
<p><code>scale_blues(root) → array</code> — blues scale: minor pentatonic + b5 'blue note'.</p>
</article>
<article class="doc-entry" id="doc-scale-chromatic">
<h3><a class="doc-anchor" href="#doc-scale-chromatic">#</a> <code>scale_chromatic</code></h3>
<p><code>scale_chromatic(root) → array</code> — all 12 semitones from root.</p>
</article>
<article class="doc-entry" id="doc-scale-dorian">
<h3><a class="doc-anchor" href="#doc-scale-dorian">#</a> <code>scale_dorian</code></h3>
<p><code>scale_dorian(root) → array</code> — Dorian mode (W-H-W-W-W-H-W).</p>
</article>
<article class="doc-entry" id="doc-scale-each">
<h3><a class="doc-anchor" href="#doc-scale-each">#</a> <code>scale_each</code></h3>
<p><code>scale_each</code> — music-theory scale constructor <code>each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p scale_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-scale-factor">
<h3><a class="doc-anchor" href="#doc-scale-factor">#</a> <code>scale_factor</code></h3>
<p><code>scale_factor</code> — music-theory scale constructor <code>factor</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p scale_factor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-scale-harmonic-minor">
<h3><a class="doc-anchor" href="#doc-scale-harmonic-minor">#</a> <code>scale_harmonic_minor</code></h3>
<p><code>scale_harmonic_minor(root) → array</code> — natural minor with raised 7th (W-H-W-W-H-3-H).</p>
</article>
<article class="doc-entry" id="doc-scale-locrian">
<h3><a class="doc-anchor" href="#doc-scale-locrian">#</a> <code>scale_locrian</code></h3>
<p><code>scale_locrian(root) → array</code> — Locrian mode (H-W-W-H-W-W-W).</p>
</article>
<article class="doc-entry" id="doc-scale-lydian">
<h3><a class="doc-anchor" href="#doc-scale-lydian">#</a> <code>scale_lydian</code></h3>
<p><code>scale_lydian(root) → array</code> — Lydian mode (W-W-W-H-W-W-H).</p>
</article>
<article class="doc-entry" id="doc-scale-major">
<h3><a class="doc-anchor" href="#doc-scale-major">#</a> <code>scale_major</code></h3>
<p><code>scale_major(root) → array</code> — major scale (8 notes, intervals W-W-H-W-W-W-H).</p>
<pre><code class="lang-perl">p scale_major(60) # [60,62,64,65,67,69,71,72]
</code></pre>
</article>
<article class="doc-entry" id="doc-scale-melodic-minor">
<h3><a class="doc-anchor" href="#doc-scale-melodic-minor">#</a> <code>scale_melodic_minor</code></h3>
<p><code>scale_melodic_minor(root) → array</code> — ascending melodic minor (W-H-W-W-W-W-H).</p>
</article>
<article class="doc-entry" id="doc-scale-minor">
<h3><a class="doc-anchor" href="#doc-scale-minor">#</a> <code>scale_minor</code></h3>
<p><code>scale_minor(root) → array</code> — natural minor (W-H-W-W-H-W-W).</p>
</article>
<article class="doc-entry" id="doc-scale-mixolydian">
<h3><a class="doc-anchor" href="#doc-scale-mixolydian">#</a> <code>scale_mixolydian</code></h3>
<p><code>scale_mixolydian(root) → array</code> — Mixolydian mode (W-W-H-W-W-H-W).</p>
</article>
<article class="doc-entry" id="doc-scale-notes">
<h3><a class="doc-anchor" href="#doc-scale-notes">#</a> <code>scale_notes</code></h3>
<p><code>scale_notes</code> — music-theory scale constructor <code>notes</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p scale_notes $x
</code></pre>
</article>
<article class="doc-entry" id="doc-scale-pentatonic">
<h3><a class="doc-anchor" href="#doc-scale-pentatonic">#</a> <code>scale_pentatonic</code></h3>
<p><code>scale_pentatonic(root) → array</code> — major pentatonic scale (5 notes per octave).</p>
</article>
<article class="doc-entry" id="doc-scale-phrygian">
<h3><a class="doc-anchor" href="#doc-scale-phrygian">#</a> <code>scale_phrygian</code></h3>
<p><code>scale_phrygian(root) → array</code> — Phrygian mode (H-W-W-W-H-W-W).</p>
</article>
<article class="doc-entry" id="doc-scale-pitches-major">
<h3><a class="doc-anchor" href="#doc-scale-pitches-major">#</a> <code>scale_pitches_major</code></h3>
<p><code>scale_pitches_major</code> — music-theory scale constructor <code>pitches major</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p scale_pitches_major $x
</code></pre>
</article>
<article class="doc-entry" id="doc-scale-pitches-minor">
<h3><a class="doc-anchor" href="#doc-scale-pitches-minor">#</a> <code>scale_pitches_minor</code></h3>
<p><code>scale_pitches_minor</code> — music-theory scale constructor <code>pitches minor</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p scale_pitches_minor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-scale-point">
<h3><a class="doc-anchor" href="#doc-scale-point">#</a> <code>scale_point</code></h3>
<p><code>scale_point($x, $y, $sx, $sy)</code> — scales a 2D point by factors sx and sy from the origin. Returns [$x*$sx, $y*$sy]. Use for geometric transformations.</p>
<pre><code class="lang-perl">my $p = scale_point(2, 3, 2, 2)
p @$p # (4, 6)
</code></pre>
</article>
<article class="doc-entry" id="doc-scale-to-intervals">
<h3><a class="doc-anchor" href="#doc-scale-to-intervals">#</a> <code>scale_to_intervals</code></h3>
<p><code>scale_to_intervals</code> — convert from <code>scale</code> to <code>intervals</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p scale_to_intervals $value
</code></pre>
</article>
<article class="doc-entry" id="doc-scalept">
<h3><a class="doc-anchor" href="#doc-scalept">#</a> <code>scalept</code></h3>
<p><code>scalept</code> — operation <code>scalept</code>. Alias for <code>scale_point</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p scalept $x
</code></pre>
</article>
<article class="doc-entry" id="doc-scan">
<h3><a class="doc-anchor" href="#doc-scan">#</a> <code>scan</code></h3>
<p><code>scan</code> — operation <code>scan</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p scan $x
</code></pre>
</article>
<article class="doc-entry" id="doc-scan-axis">
<h3><a class="doc-anchor" href="#doc-scan-axis">#</a> <code>scan_axis</code></h3>
<p><code>scan_axis</code> — operation <code>scan axis</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p scan_axis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-scan-left">
<h3><a class="doc-anchor" href="#doc-scan-left">#</a> <code>scan_left</code></h3>
<p><code>scan_left</code> — operation <code>scan left</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p scan_left $x
</code></pre>
</article>
<article class="doc-entry" id="doc-scanl">
<h3><a class="doc-anchor" href="#doc-scanl">#</a> <code>scanl</code></h3>
<p><code>scanl</code> — operation <code>scanl</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p scanl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-scanr">
<h3><a class="doc-anchor" href="#doc-scanr">#</a> <code>scanr</code></h3>
<p><code>scanr</code> — operation <code>scanr</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p scanr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-scard">
<h3><a class="doc-anchor" href="#doc-scard">#</a> <code>scard</code></h3>
<p><code>scard</code> — operation <code>scard</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p scard $x
</code></pre>
</article>
<article class="doc-entry" id="doc-scentroid">
<h3><a class="doc-anchor" href="#doc-scentroid">#</a> <code>scentroid</code></h3>
<p><code>spectral_centroid(\@spectrum)</code> (alias <code>scentroid</code>) — computes the spectral centroid (center of mass) of a spectrum. Indicates the 'brightness' of a sound. Returns frequency bin index.</p>
<pre><code class="lang-perl">my $psd = psd(\@signal)
p scentroid($psd) # brightness measure
</code></pre>
</article>
<article class="doc-entry" id="doc-scharr-x-kernel">
<h3><a class="doc-anchor" href="#doc-scharr-x-kernel">#</a> <code>scharr_x_kernel</code></h3>
<p><code>scharr_x_kernel() → matrix</code> — Scharr horizontal kernel; better rotational symmetry than Sobel.</p>
</article>
<article class="doc-entry" id="doc-scharr-y-kernel">
<h3><a class="doc-anchor" href="#doc-scharr-y-kernel">#</a> <code>scharr_y_kernel</code></h3>
<p><code>scharr_y_kernel() → matrix</code> — Scharr vertical kernel.</p>
</article>
<article class="doc-entry" id="doc-schmidt-number-step">
<h3><a class="doc-anchor" href="#doc-schmidt-number-step">#</a> <code>schmidt_number_step</code></h3>
<p><code>schmidt_number_step</code> — single-step update of <code>schmidt number</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p schmidt_number_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-schnorr-sign-simple">
<h3><a class="doc-anchor" href="#doc-schnorr-sign-simple">#</a> <code>schnorr_sign_simple</code></h3>
<p><code>schnorr_sign_simple(msg, private_key) → string</code> — Schnorr-like signature using SHA-256 hash chaining. Demo only.</p>
</article>
<article class="doc-entry" id="doc-schnorr-verify-simple">
<h3><a class="doc-anchor" href="#doc-schnorr-verify-simple">#</a> <code>schnorr_verify_simple</code></h3>
<p><code>schnorr_verify_simple(msg, public_key, sig) → 0|1</code> — companion verify.</p>
</article>
<article class="doc-entry" id="doc-school-choice-match">
<h3><a class="doc-anchor" href="#doc-school-choice-match">#</a> <code>school_choice_match</code></h3>
<p><code>school_choice_match</code> — operation <code>school choice match</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p school_choice_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-schottky-barrier-height">
<h3><a class="doc-anchor" href="#doc-schottky-barrier-height">#</a> <code>schottky_barrier_height</code></h3>
<p><code>schottky_barrier_height</code> — operation <code>schottky barrier height</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p schottky_barrier_height $x
</code></pre>
</article>
<article class="doc-entry" id="doc-schouten-tensor-step">
<h3><a class="doc-anchor" href="#doc-schouten-tensor-step">#</a> <code>schouten_tensor_step</code></h3>
<p><code>schouten_tensor_step</code> — single-step update of <code>schouten tensor</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p schouten_tensor_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-schreier-index">
<h3><a class="doc-anchor" href="#doc-schreier-index">#</a> <code>schreier_index</code></h3>
<p><code>schreier_index</code> — index of <code>schreier</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p schreier_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-schrodinger-step-real">
<h3><a class="doc-anchor" href="#doc-schrodinger-step-real">#</a> <code>schrodinger_step_real</code></h3>
<p><code>schrodinger_step_real</code> — operation <code>schrodinger step real</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p schrodinger_step_real $x
</code></pre>
</article>
<article class="doc-entry" id="doc-schroeder-reverb">
<h3><a class="doc-anchor" href="#doc-schroeder-reverb">#</a> <code>schroeder_reverb</code></h3>
<p><code>schroeder_reverb(signal) → array</code> — Schroeder's 4-comb + 2-all-pass classical reverb topology.</p>
</article>
<article class="doc-entry" id="doc-schulze-method-step">
<h3><a class="doc-anchor" href="#doc-schulze-method-step">#</a> <code>schulze_method_step</code></h3>
<p><code>schulze_method_step</code> — single-step update of <code>schulze method</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p schulze_method_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-schur-polynomial-eval">
<h3><a class="doc-anchor" href="#doc-schur-polynomial-eval">#</a> <code>schur_polynomial_eval</code></h3>
<p><code>schur_polynomial_eval</code> — operation <code>schur polynomial eval</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p schur_polynomial_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-schwarz">
<h3><a class="doc-anchor" href="#doc-schwarz">#</a> <code>schwarz</code></h3>
<p><code>schwarzschild_radius($mass)</code> (alias <code>schwarz</code>) — event horizon radius rs = 2GM/c² of a black hole.</p>
<pre><code class="lang-perl">p schwarz(1.989e30) # ~2954 m (Sun as black hole)
p schwarz(5.972e24) # ~0.009 m (Earth as black hole)
</code></pre>
</article>
<article class="doc-entry" id="doc-schwarzschild-freefall-time">
<h3><a class="doc-anchor" href="#doc-schwarzschild-freefall-time">#</a> <code>schwarzschild_freefall_time</code></h3>
<p><code>schwarzschild_freefall_time</code> — operation <code>schwarzschild freefall time</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p schwarzschild_freefall_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-schwarzschild-g-rr">
<h3><a class="doc-anchor" href="#doc-schwarzschild-g-rr">#</a> <code>schwarzschild_g_rr</code></h3>
<p><code>schwarzschild_g_rr</code> — operation <code>schwarzschild g rr</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p schwarzschild_g_rr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-schwarzschild-g-tt">
<h3><a class="doc-anchor" href="#doc-schwarzschild-g-tt">#</a> <code>schwarzschild_g_tt</code></h3>
<p><code>schwarzschild_g_tt</code> — operation <code>schwarzschild g tt</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p schwarzschild_g_tt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-schwarzschild-isco">
<h3><a class="doc-anchor" href="#doc-schwarzschild-isco">#</a> <code>schwarzschild_isco</code></h3>
<p><code>schwarzschild_isco</code> — operation <code>schwarzschild isco</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p schwarzschild_isco $x
</code></pre>
</article>
<article class="doc-entry" id="doc-schwarzschild-kruskal-step">
<h3><a class="doc-anchor" href="#doc-schwarzschild-kruskal-step">#</a> <code>schwarzschild_kruskal_step</code></h3>
<p><code>schwarzschild_kruskal_step</code> — single-step update of <code>schwarzschild kruskal</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p schwarzschild_kruskal_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-schwarzschild-radius-kg">
<h3><a class="doc-anchor" href="#doc-schwarzschild-radius-kg">#</a> <code>schwarzschild_radius_kg</code></h3>
<p><code>schwarzschild_radius_kg</code> — operation <code>schwarzschild radius kg</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p schwarzschild_radius_kg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-schwarzschild-radius-m">
<h3><a class="doc-anchor" href="#doc-schwarzschild-radius-m">#</a> <code>schwarzschild_radius_m</code></h3>
<p><code>schwarzschild_radius_m</code> — operation <code>schwarzschild radius m</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p schwarzschild_radius_m $x
</code></pre>
</article>
<article class="doc-entry" id="doc-score-test-stat">
<h3><a class="doc-anchor" href="#doc-score-test-stat">#</a> <code>score_test_stat</code></h3>
<p><code>score_test_stat</code> — operation <code>score test stat</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p score_test_stat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-script-name">
<h3><a class="doc-anchor" href="#doc-script-name">#</a> <code>script_name</code></h3>
<p><code>script_name</code> — operation <code>script name</code>. Category: *process / env*.</p>
<pre><code class="lang-perl">p script_name $x
</code></pre>
</article>
<article class="doc-entry" id="doc-scrypt-round">
<h3><a class="doc-anchor" href="#doc-scrypt-round">#</a> <code>scrypt_round</code></h3>
<p><code>scrypt_round</code> — operation <code>scrypt round</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p scrypt_round $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sdbm-hash">
<h3><a class="doc-anchor" href="#doc-sdbm-hash">#</a> <code>sdbm_hash</code></h3>
<p><code>sdbm_hash</code> — hash function of <code>sdbm</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p sdbm_hash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sdiff">
<h3><a class="doc-anchor" href="#doc-sdiff">#</a> <code>sdiff</code></h3>
<p><code>sdiff</code> — operation <code>sdiff</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p sdiff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sdivs">
<h3><a class="doc-anchor" href="#doc-sdivs">#</a> <code>sdivs</code></h3>
<p><code>sdivs</code> — operation <code>sdivs</code>. Alias for <code>sum_divisors</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p sdivs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sdns">
<h3><a class="doc-anchor" href="#doc-sdns">#</a> <code>sdns</code></h3>
<p><code>sdns</code> — operation <code>sdns</code>. Alias for <code>stress_dns</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p sdns $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sdx">
<h3><a class="doc-anchor" href="#doc-sdx">#</a> <code>sdx</code></h3>
<p><code>sdx</code> — operation <code>sdx</code>. Alias for <code>soundex</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p sdx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sealed-bid-first-price">
<h3><a class="doc-anchor" href="#doc-sealed-bid-first-price">#</a> <code>sealed_bid_first_price</code></h3>
<p><code>sealed_bid_first_price</code> — operation <code>sealed bid first price</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p sealed_bid_first_price $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sealed-bid-second-price">
<h3><a class="doc-anchor" href="#doc-sealed-bid-second-price">#</a> <code>sealed_bid_second_price</code></h3>
<p><code>sealed_bid_second_price</code> — operation <code>sealed bid second price</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p sealed_bid_second_price $x
</code></pre>
</article>
<article class="doc-entry" id="doc-searchsorted">
<h3><a class="doc-anchor" href="#doc-searchsorted">#</a> <code>searchsorted</code></h3>
<p><code>searchsorted</code> — operation <code>searchsorted</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p searchsorted $x
</code></pre>
</article>
<article class="doc-entry" id="doc-season-of-year">
<h3><a class="doc-anchor" href="#doc-season-of-year">#</a> <code>season_of_year</code></h3>
<p><code>season_of_year(month, day, hemisphere="N") → string</code> — Winter/Spring/Summer/Autumn. South-hemisphere flips seasons.</p>
<pre><code class="lang-perl">p season_of_year(3, 25, "N") # Spring
</code></pre>
</article>
<article class="doc-entry" id="doc-seasonal-decompose">
<h3><a class="doc-anchor" href="#doc-seasonal-decompose">#</a> <code>seasonal_decompose</code></h3>
<p><code>seasonal_decompose</code> — operation <code>seasonal decompose</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p seasonal_decompose $x
</code></pre>
</article>
<article class="doc-entry" id="doc-seasonal-diff">
<h3><a class="doc-anchor" href="#doc-seasonal-diff">#</a> <code>seasonal_diff</code></h3>
<p><code>seasonal_diff</code> — operation <code>seasonal diff</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p seasonal_diff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec">
<h3><a class="doc-anchor" href="#doc-sec">#</a> <code>sec</code></h3>
<p><code>sec</code> returns the secant (1/cos) of an angle in radians.</p>
<pre><code class="lang-perl">p sec(0) # 1.0
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-2fa-totp-window">
<h3><a class="doc-anchor" href="#doc-sec-2fa-totp-window">#</a> <code>sec_2fa_totp_window</code></h3>
<p><code>sec_2fa_totp_window</code> — operation <code>sec 2fa totp window</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_2fa_totp_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-account-lockout-step">
<h3><a class="doc-anchor" href="#doc-sec-account-lockout-step">#</a> <code>sec_account_lockout_step</code></h3>
<p><code>sec_account_lockout_step</code> — single-step update of <code>sec account lockout</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_account_lockout_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-acme-dns-challenge">
<h3><a class="doc-anchor" href="#doc-sec-acme-dns-challenge">#</a> <code>sec_acme_dns_challenge</code></h3>
<p><code>sec_acme_dns_challenge</code> — operation <code>sec acme dns challenge</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_acme_dns_challenge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-aes-keyschedule-step">
<h3><a class="doc-anchor" href="#doc-sec-aes-keyschedule-step">#</a> <code>sec_aes_keyschedule_step</code></h3>
<p><code>sec_aes_keyschedule_step</code> — single-step update of <code>sec aes keyschedule</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_aes_keyschedule_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-aes-round-step">
<h3><a class="doc-anchor" href="#doc-sec-aes-round-step">#</a> <code>sec_aes_round_step</code></h3>
<p><code>sec_aes_round_step</code> — single-step update of <code>sec aes round</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_aes_round_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-arc-chain-step">
<h3><a class="doc-anchor" href="#doc-sec-arc-chain-step">#</a> <code>sec_arc_chain_step</code></h3>
<p><code>sec_arc_chain_step</code> — single-step update of <code>sec arc chain</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_arc_chain_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-argon2-block-step">
<h3><a class="doc-anchor" href="#doc-sec-argon2-block-step">#</a> <code>sec_argon2_block_step</code></h3>
<p><code>sec_argon2_block_step</code> — single-step update of <code>sec argon2 block</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_argon2_block_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-argon2-memcost">
<h3><a class="doc-anchor" href="#doc-sec-argon2-memcost">#</a> <code>sec_argon2_memcost</code></h3>
<p><code>sec_argon2_memcost</code> — operation <code>sec argon2 memcost</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_argon2_memcost $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-argon2-parallelism">
<h3><a class="doc-anchor" href="#doc-sec-argon2-parallelism">#</a> <code>sec_argon2_parallelism</code></h3>
<p><code>sec_argon2_parallelism</code> — operation <code>sec argon2 parallelism</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_argon2_parallelism $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-argon2-state-advance">
<h3><a class="doc-anchor" href="#doc-sec-argon2-state-advance">#</a> <code>sec_argon2_state_advance</code></h3>
<p><code>sec_argon2_state_advance</code> — operation <code>sec argon2 state advance</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_argon2_state_advance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-argon2-timecost">
<h3><a class="doc-anchor" href="#doc-sec-argon2-timecost">#</a> <code>sec_argon2_timecost</code></h3>
<p><code>sec_argon2_timecost</code> — operation <code>sec argon2 timecost</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_argon2_timecost $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-balloon-hash-step">
<h3><a class="doc-anchor" href="#doc-sec-balloon-hash-step">#</a> <code>sec_balloon_hash_step</code></h3>
<p><code>sec_balloon_hash_step</code> — single-step update of <code>sec balloon hash</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_balloon_hash_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-basic-constraints-ca">
<h3><a class="doc-anchor" href="#doc-sec-basic-constraints-ca">#</a> <code>sec_basic_constraints_ca</code></h3>
<p><code>sec_basic_constraints_ca</code> — operation <code>sec basic constraints ca</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_basic_constraints_ca $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-bcrypt-cost-factor">
<h3><a class="doc-anchor" href="#doc-sec-bcrypt-cost-factor">#</a> <code>sec_bcrypt_cost_factor</code></h3>
<p><code>sec_bcrypt_cost_factor</code> — factor of <code>sec bcrypt cost</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_bcrypt_cost_factor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-bcrypt-round-step">
<h3><a class="doc-anchor" href="#doc-sec-bcrypt-round-step">#</a> <code>sec_bcrypt_round_step</code></h3>
<p><code>sec_bcrypt_round_step</code> — single-step update of <code>sec bcrypt round</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_bcrypt_round_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-blake3-chunk-step">
<h3><a class="doc-anchor" href="#doc-sec-blake3-chunk-step">#</a> <code>sec_blake3_chunk_step</code></h3>
<p><code>sec_blake3_chunk_step</code> — single-step update of <code>sec blake3 chunk</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_blake3_chunk_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-blowfish-round-step">
<h3><a class="doc-anchor" href="#doc-sec-blowfish-round-step">#</a> <code>sec_blowfish_round_step</code></h3>
<p><code>sec_blowfish_round_step</code> — single-step update of <code>sec blowfish round</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_blowfish_round_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-brute-force-attempts">
<h3><a class="doc-anchor" href="#doc-sec-brute-force-attempts">#</a> <code>sec_brute_force_attempts</code></h3>
<p><code>sec_brute_force_attempts</code> — operation <code>sec brute force attempts</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_brute_force_attempts $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-cbc-mac-block-count">
<h3><a class="doc-anchor" href="#doc-sec-cbc-mac-block-count">#</a> <code>sec_cbc_mac_block_count</code></h3>
<p><code>sec_cbc_mac_block_count</code> — count of <code>sec cbc mac block</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_cbc_mac_block_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-certificate-chain-depth">
<h3><a class="doc-anchor" href="#doc-sec-certificate-chain-depth">#</a> <code>sec_certificate_chain_depth</code></h3>
<p><code>sec_certificate_chain_depth</code> — operation <code>sec certificate chain depth</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_certificate_chain_depth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-certificate-transparency">
<h3><a class="doc-anchor" href="#doc-sec-certificate-transparency">#</a> <code>sec_certificate_transparency</code></h3>
<p><code>sec_certificate_transparency</code> — operation <code>sec certificate transparency</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_certificate_transparency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-chacha20-quarterround">
<h3><a class="doc-anchor" href="#doc-sec-chacha20-quarterround">#</a> <code>sec_chacha20_quarterround</code></h3>
<p><code>sec_chacha20_quarterround</code> — operation <code>sec chacha20 quarterround</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_chacha20_quarterround $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-chachapoly-nonce-check">
<h3><a class="doc-anchor" href="#doc-sec-chachapoly-nonce-check">#</a> <code>sec_chachapoly_nonce_check</code></h3>
<p><code>sec_chachapoly_nonce_check</code> — operation <code>sec chachapoly nonce check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_chachapoly_nonce_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-chosen-charset-strength">
<h3><a class="doc-anchor" href="#doc-sec-chosen-charset-strength">#</a> <code>sec_chosen_charset_strength</code></h3>
<p><code>sec_chosen_charset_strength</code> — operation <code>sec chosen charset strength</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_chosen_charset_strength $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-cipher-suite-strength">
<h3><a class="doc-anchor" href="#doc-sec-cipher-suite-strength">#</a> <code>sec_cipher_suite_strength</code></h3>
<p><code>sec_cipher_suite_strength</code> — operation <code>sec cipher suite strength</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_cipher_suite_strength $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-command-injection-score">
<h3><a class="doc-anchor" href="#doc-sec-command-injection-score">#</a> <code>sec_command_injection_score</code></h3>
<p><code>sec_command_injection_score</code> — score of <code>sec command injection</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_command_injection_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-complexity-policy-score">
<h3><a class="doc-anchor" href="#doc-sec-complexity-policy-score">#</a> <code>sec_complexity_policy_score</code></h3>
<p><code>sec_complexity_policy_score</code> — score of <code>sec complexity policy</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_complexity_policy_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-cors-origin-match">
<h3><a class="doc-anchor" href="#doc-sec-cors-origin-match">#</a> <code>sec_cors_origin_match</code></h3>
<p><code>sec_cors_origin_match</code> — operation <code>sec cors origin match</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_cors_origin_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-credential-stuffing-score">
<h3><a class="doc-anchor" href="#doc-sec-credential-stuffing-score">#</a> <code>sec_credential_stuffing_score</code></h3>
<p><code>sec_credential_stuffing_score</code> — score of <code>sec credential stuffing</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_credential_stuffing_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-crl-age-seconds">
<h3><a class="doc-anchor" href="#doc-sec-crl-age-seconds">#</a> <code>sec_crl_age_seconds</code></h3>
<p><code>sec_crl_age_seconds</code> — operation <code>sec crl age seconds</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_crl_age_seconds $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-csp-directive-match">
<h3><a class="doc-anchor" href="#doc-sec-csp-directive-match">#</a> <code>sec_csp_directive_match</code></h3>
<p><code>sec_csp_directive_match</code> — operation <code>sec csp directive match</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_csp_directive_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-csrf-token-match">
<h3><a class="doc-anchor" href="#doc-sec-csrf-token-match">#</a> <code>sec_csrf_token_match</code></h3>
<p><code>sec_csrf_token_match</code> — operation <code>sec csrf token match</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_csrf_token_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-dane-tlsa-match">
<h3><a class="doc-anchor" href="#doc-sec-dane-tlsa-match">#</a> <code>sec_dane_tlsa_match</code></h3>
<p><code>sec_dane_tlsa_match</code> — operation <code>sec dane tlsa match</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_dane_tlsa_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-des-round-step">
<h3><a class="doc-anchor" href="#doc-sec-des-round-step">#</a> <code>sec_des_round_step</code></h3>
<p><code>sec_des_round_step</code> — single-step update of <code>sec des round</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_des_round_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-diameter-avp-step">
<h3><a class="doc-anchor" href="#doc-sec-diameter-avp-step">#</a> <code>sec_diameter_avp_step</code></h3>
<p><code>sec_diameter_avp_step</code> — single-step update of <code>sec diameter avp</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_diameter_avp_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-diceware-word-index">
<h3><a class="doc-anchor" href="#doc-sec-diceware-word-index">#</a> <code>sec_diceware_word_index</code></h3>
<p><code>sec_diceware_word_index</code> — index of <code>sec diceware word</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_diceware_word_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-dictionary-attack-check">
<h3><a class="doc-anchor" href="#doc-sec-dictionary-attack-check">#</a> <code>sec_dictionary_attack_check</code></h3>
<p><code>sec_dictionary_attack_check</code> — operation <code>sec dictionary attack check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_dictionary_attack_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-dkim-signature-check">
<h3><a class="doc-anchor" href="#doc-sec-dkim-signature-check">#</a> <code>sec_dkim_signature_check</code></h3>
<p><code>sec_dkim_signature_check</code> — operation <code>sec dkim signature check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_dkim_signature_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-dmarc-policy-check">
<h3><a class="doc-anchor" href="#doc-sec-dmarc-policy-check">#</a> <code>sec_dmarc_policy_check</code></h3>
<p><code>sec_dmarc_policy_check</code> — operation <code>sec dmarc policy check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_dmarc_policy_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-dnssec-signature-check">
<h3><a class="doc-anchor" href="#doc-sec-dnssec-signature-check">#</a> <code>sec_dnssec_signature_check</code></h3>
<p><code>sec_dnssec_signature_check</code> — operation <code>sec dnssec signature check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_dnssec_signature_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-ed25519-signature-step">
<h3><a class="doc-anchor" href="#doc-sec-ed25519-signature-step">#</a> <code>sec_ed25519_signature_step</code></h3>
<p><code>sec_ed25519_signature_step</code> — single-step update of <code>sec ed25519 signature</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_ed25519_signature_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-ed448-signature-step">
<h3><a class="doc-anchor" href="#doc-sec-ed448-signature-step">#</a> <code>sec_ed448_signature_step</code></h3>
<p><code>sec_ed448_signature_step</code> — single-step update of <code>sec ed448 signature</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_ed448_signature_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-fido2-assertion-check">
<h3><a class="doc-anchor" href="#doc-sec-fido2-assertion-check">#</a> <code>sec_fido2_assertion_check</code></h3>
<p><code>sec_fido2_assertion_check</code> — operation <code>sec fido2 assertion check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_fido2_assertion_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-gcm-iv-unique-check">
<h3><a class="doc-anchor" href="#doc-sec-gcm-iv-unique-check">#</a> <code>sec_gcm_iv_unique_check</code></h3>
<p><code>sec_gcm_iv_unique_check</code> — operation <code>sec gcm iv unique check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_gcm_iv_unique_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-haveibeenpwned-check">
<h3><a class="doc-anchor" href="#doc-sec-haveibeenpwned-check">#</a> <code>sec_haveibeenpwned_check</code></h3>
<p><code>sec_haveibeenpwned_check</code> — operation <code>sec haveibeenpwned check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_haveibeenpwned_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-hotp-counter-step">
<h3><a class="doc-anchor" href="#doc-sec-hotp-counter-step">#</a> <code>sec_hotp_counter_step</code></h3>
<p><code>sec_hotp_counter_step</code> — single-step update of <code>sec hotp counter</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_hotp_counter_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-hpkp-pin-match">
<h3><a class="doc-anchor" href="#doc-sec-hpkp-pin-match">#</a> <code>sec_hpkp_pin_match</code></h3>
<p><code>sec_hpkp_pin_match</code> — operation <code>sec hpkp pin match</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_hpkp_pin_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-html-escape-check">
<h3><a class="doc-anchor" href="#doc-sec-html-escape-check">#</a> <code>sec_html_escape_check</code></h3>
<p><code>sec_html_escape_check</code> — operation <code>sec html escape check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_html_escape_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-idle-timeout-step">
<h3><a class="doc-anchor" href="#doc-sec-idle-timeout-step">#</a> <code>sec_idle_timeout_step</code></h3>
<p><code>sec_idle_timeout_step</code> — single-step update of <code>sec idle timeout</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_idle_timeout_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-idor-check">
<h3><a class="doc-anchor" href="#doc-sec-idor-check">#</a> <code>sec_idor_check</code></h3>
<p><code>sec_idor_check</code> — operation <code>sec idor check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_idor_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-imap-starttls-check">
<h3><a class="doc-anchor" href="#doc-sec-imap-starttls-check">#</a> <code>sec_imap_starttls_check</code></h3>
<p><code>sec_imap_starttls_check</code> — operation <code>sec imap starttls check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_imap_starttls_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-jwt-alg-safe">
<h3><a class="doc-anchor" href="#doc-sec-jwt-alg-safe">#</a> <code>sec_jwt_alg_safe</code></h3>
<p><code>sec_jwt_alg_safe</code> — operation <code>sec jwt alg safe</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_jwt_alg_safe $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-jwt-kid-match">
<h3><a class="doc-anchor" href="#doc-sec-jwt-kid-match">#</a> <code>sec_jwt_kid_match</code></h3>
<p><code>sec_jwt_kid_match</code> — operation <code>sec jwt kid match</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_jwt_kid_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-jwt-signature-verify">
<h3><a class="doc-anchor" href="#doc-sec-jwt-signature-verify">#</a> <code>sec_jwt_signature_verify</code></h3>
<p><code>sec_jwt_signature_verify</code> — verify with public key of <code>sec jwt signature</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_jwt_signature_verify $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-keccak-round-step">
<h3><a class="doc-anchor" href="#doc-sec-keccak-round-step">#</a> <code>sec_keccak_round_step</code></h3>
<p><code>sec_keccak_round_step</code> — single-step update of <code>sec keccak round</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_keccak_round_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-kerberos-pac-check">
<h3><a class="doc-anchor" href="#doc-sec-kerberos-pac-check">#</a> <code>sec_kerberos_pac_check</code></h3>
<p><code>sec_kerberos_pac_check</code> — operation <code>sec kerberos pac check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_kerberos_pac_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-kerberos-pre-auth">
<h3><a class="doc-anchor" href="#doc-sec-kerberos-pre-auth">#</a> <code>sec_kerberos_pre_auth</code></h3>
<p><code>sec_kerberos_pre_auth</code> — operation <code>sec kerberos pre auth</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_kerberos_pre_auth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-kerberos-ticket-age">
<h3><a class="doc-anchor" href="#doc-sec-kerberos-ticket-age">#</a> <code>sec_kerberos_ticket_age</code></h3>
<p><code>sec_kerberos_ticket_age</code> — operation <code>sec kerberos ticket age</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_kerberos_ticket_age $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-keystroke-timing-var">
<h3><a class="doc-anchor" href="#doc-sec-keystroke-timing-var">#</a> <code>sec_keystroke_timing_var</code></h3>
<p><code>sec_keystroke_timing_var</code> — variance of <code>sec keystroke timing</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_keystroke_timing_var $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-ldap-bind-step">
<h3><a class="doc-anchor" href="#doc-sec-ldap-bind-step">#</a> <code>sec_ldap_bind_step</code></h3>
<p><code>sec_ldap_bind_step</code> — single-step update of <code>sec ldap bind</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_ldap_bind_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-login-throttle-step">
<h3><a class="doc-anchor" href="#doc-sec-login-throttle-step">#</a> <code>sec_login_throttle_step</code></h3>
<p><code>sec_login_throttle_step</code> — single-step update of <code>sec login throttle</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_login_throttle_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-oauth2-pkce-step">
<h3><a class="doc-anchor" href="#doc-sec-oauth2-pkce-step">#</a> <code>sec_oauth2_pkce_step</code></h3>
<p><code>sec_oauth2_pkce_step</code> — single-step update of <code>sec oauth2 pkce</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_oauth2_pkce_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-oauth2-state-validate">
<h3><a class="doc-anchor" href="#doc-sec-oauth2-state-validate">#</a> <code>sec_oauth2_state_validate</code></h3>
<p><code>sec_oauth2_state_validate</code> — operation <code>sec oauth2 state validate</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_oauth2_state_validate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-oauth-nonce-check">
<h3><a class="doc-anchor" href="#doc-sec-oauth-nonce-check">#</a> <code>sec_oauth_nonce_check</code></h3>
<p><code>sec_oauth_nonce_check</code> — operation <code>sec oauth nonce check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_oauth_nonce_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-oidc-id-token-age">
<h3><a class="doc-anchor" href="#doc-sec-oidc-id-token-age">#</a> <code>sec_oidc_id_token_age</code></h3>
<p><code>sec_oidc_id_token_age</code> — operation <code>sec oidc id token age</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_oidc_id_token_age $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-p384-curve-step">
<h3><a class="doc-anchor" href="#doc-sec-p384-curve-step">#</a> <code>sec_p384_curve_step</code></h3>
<p><code>sec_p384_curve_step</code> — single-step update of <code>sec p384 curve</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_p384_curve_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-passphrase-entropy">
<h3><a class="doc-anchor" href="#doc-sec-passphrase-entropy">#</a> <code>sec_passphrase_entropy</code></h3>
<p><code>sec_passphrase_entropy</code> — operation <code>sec passphrase entropy</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_passphrase_entropy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-password-history-check">
<h3><a class="doc-anchor" href="#doc-sec-password-history-check">#</a> <code>sec_password_history_check</code></h3>
<p><code>sec_password_history_check</code> — operation <code>sec password history check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_password_history_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-password-strength-zxcvbn">
<h3><a class="doc-anchor" href="#doc-sec-password-strength-zxcvbn">#</a> <code>sec_password_strength_zxcvbn</code></h3>
<p><code>sec_password_strength_zxcvbn</code> — operation <code>sec password strength zxcvbn</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_password_strength_zxcvbn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-path-traversal-detect">
<h3><a class="doc-anchor" href="#doc-sec-path-traversal-detect">#</a> <code>sec_path_traversal_detect</code></h3>
<p><code>sec_path_traversal_detect</code> — operation <code>sec path traversal detect</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_path_traversal_detect $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-pbkdf2-iter">
<h3><a class="doc-anchor" href="#doc-sec-pbkdf2-iter">#</a> <code>sec_pbkdf2_iter</code></h3>
<p><code>sec_pbkdf2_iter</code> — operation <code>sec pbkdf2 iter</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_pbkdf2_iter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-pinning-compare">
<h3><a class="doc-anchor" href="#doc-sec-pinning-compare">#</a> <code>sec_pinning_compare</code></h3>
<p><code>sec_pinning_compare</code> — operation <code>sec pinning compare</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_pinning_compare $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-pki-path-validate">
<h3><a class="doc-anchor" href="#doc-sec-pki-path-validate">#</a> <code>sec_pki_path_validate</code></h3>
<p><code>sec_pki_path_validate</code> — operation <code>sec pki path validate</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_pki_path_validate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-pop3-security-step">
<h3><a class="doc-anchor" href="#doc-sec-pop3-security-step">#</a> <code>sec_pop3_security_step</code></h3>
<p><code>sec_pop3_security_step</code> — single-step update of <code>sec pop3 security</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_pop3_security_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-radius-auth-step">
<h3><a class="doc-anchor" href="#doc-sec-radius-auth-step">#</a> <code>sec_radius_auth_step</code></h3>
<p><code>sec_radius_auth_step</code> — single-step update of <code>sec radius auth</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_radius_auth_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-revocation-ocsp-check">
<h3><a class="doc-anchor" href="#doc-sec-revocation-ocsp-check">#</a> <code>sec_revocation_ocsp_check</code></h3>
<p><code>sec_revocation_ocsp_check</code> — operation <code>sec revocation ocsp check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_revocation_ocsp_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-saml-assertion-age">
<h3><a class="doc-anchor" href="#doc-sec-saml-assertion-age">#</a> <code>sec_saml_assertion_age</code></h3>
<p><code>sec_saml_assertion_age</code> — operation <code>sec saml assertion age</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_saml_assertion_age $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-san-match-count">
<h3><a class="doc-anchor" href="#doc-sec-san-match-count">#</a> <code>sec_san_match_count</code></h3>
<p><code>sec_san_match_count</code> — count of <code>sec san match</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_san_match_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-scrypt-n-param">
<h3><a class="doc-anchor" href="#doc-sec-scrypt-n-param">#</a> <code>sec_scrypt_n_param</code></h3>
<p><code>sec_scrypt_n_param</code> — operation <code>sec scrypt n param</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_scrypt_n_param $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-scrypt-p-param">
<h3><a class="doc-anchor" href="#doc-sec-scrypt-p-param">#</a> <code>sec_scrypt_p_param</code></h3>
<p><code>sec_scrypt_p_param</code> — operation <code>sec scrypt p param</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_scrypt_p_param $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-scrypt-r-param">
<h3><a class="doc-anchor" href="#doc-sec-scrypt-r-param">#</a> <code>sec_scrypt_r_param</code></h3>
<p><code>sec_scrypt_r_param</code> — operation <code>sec scrypt r param</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_scrypt_r_param $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-secp256k1-step">
<h3><a class="doc-anchor" href="#doc-sec-secp256k1-step">#</a> <code>sec_secp256k1_step</code></h3>
<p><code>sec_secp256k1_step</code> — single-step update of <code>sec secp256k1</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_secp256k1_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-serpent-round-step">
<h3><a class="doc-anchor" href="#doc-sec-serpent-round-step">#</a> <code>sec_serpent_round_step</code></h3>
<p><code>sec_serpent_round_step</code> — single-step update of <code>sec serpent round</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_serpent_round_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-session-lifetime">
<h3><a class="doc-anchor" href="#doc-sec-session-lifetime">#</a> <code>sec_session_lifetime</code></h3>
<p><code>sec_session_lifetime</code> — operation <code>sec session lifetime</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_session_lifetime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-sha3-padding-step">
<h3><a class="doc-anchor" href="#doc-sec-sha3-padding-step">#</a> <code>sec_sha3_padding_step</code></h3>
<p><code>sec_sha3_padding_step</code> — single-step update of <code>sec sha3 padding</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_sha3_padding_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-smtp-ssl-check">
<h3><a class="doc-anchor" href="#doc-sec-smtp-ssl-check">#</a> <code>sec_smtp_ssl_check</code></h3>
<p><code>sec_smtp_ssl_check</code> — operation <code>sec smtp ssl check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_smtp_ssl_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-spf-pass-check">
<h3><a class="doc-anchor" href="#doc-sec-spf-pass-check">#</a> <code>sec_spf_pass_check</code></h3>
<p><code>sec_spf_pass_check</code> — operation <code>sec spf pass check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_spf_pass_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-sqli-pattern-score">
<h3><a class="doc-anchor" href="#doc-sec-sqli-pattern-score">#</a> <code>sec_sqli_pattern_score</code></h3>
<p><code>sec_sqli_pattern_score</code> — score of <code>sec sqli pattern</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_sqli_pattern_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-ssl3-disabled-check">
<h3><a class="doc-anchor" href="#doc-sec-ssl3-disabled-check">#</a> <code>sec_ssl3_disabled_check</code></h3>
<p><code>sec_ssl3_disabled_check</code> — operation <code>sec ssl3 disabled check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_ssl3_disabled_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-tls11-deprecation-check">
<h3><a class="doc-anchor" href="#doc-sec-tls11-deprecation-check">#</a> <code>sec_tls11_deprecation_check</code></h3>
<p><code>sec_tls11_deprecation_check</code> — operation <code>sec tls11 deprecation check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_tls11_deprecation_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-tls12-handshake-step">
<h3><a class="doc-anchor" href="#doc-sec-tls12-handshake-step">#</a> <code>sec_tls12_handshake_step</code></h3>
<p><code>sec_tls12_handshake_step</code> — single-step update of <code>sec tls12 handshake</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_tls12_handshake_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-tls13-handshake-step">
<h3><a class="doc-anchor" href="#doc-sec-tls13-handshake-step">#</a> <code>sec_tls13_handshake_step</code></h3>
<p><code>sec_tls13_handshake_step</code> — single-step update of <code>sec tls13 handshake</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_tls13_handshake_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-tls-alert-severity">
<h3><a class="doc-anchor" href="#doc-sec-tls-alert-severity">#</a> <code>sec_tls_alert_severity</code></h3>
<p><code>sec_tls_alert_severity</code> — operation <code>sec tls alert severity</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_tls_alert_severity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-totp-drift-check">
<h3><a class="doc-anchor" href="#doc-sec-totp-drift-check">#</a> <code>sec_totp_drift_check</code></h3>
<p><code>sec_totp_drift_check</code> — operation <code>sec totp drift check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_totp_drift_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-twofish-round-step">
<h3><a class="doc-anchor" href="#doc-sec-twofish-round-step">#</a> <code>sec_twofish_round_step</code></h3>
<p><code>sec_twofish_round_step</code> — single-step update of <code>sec twofish round</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_twofish_round_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-url-safe-encode-check">
<h3><a class="doc-anchor" href="#doc-sec-url-safe-encode-check">#</a> <code>sec_url_safe_encode_check</code></h3>
<p><code>sec_url_safe_encode_check</code> — operation <code>sec url safe encode check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_url_safe_encode_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-webauthn-attestation-check">
<h3><a class="doc-anchor" href="#doc-sec-webauthn-attestation-check">#</a> <code>sec_webauthn_attestation_check</code></h3>
<p><code>sec_webauthn_attestation_check</code> — operation <code>sec webauthn attestation check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_webauthn_attestation_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-x25519-clamping-step">
<h3><a class="doc-anchor" href="#doc-sec-x25519-clamping-step">#</a> <code>sec_x25519_clamping_step</code></h3>
<p><code>sec_x25519_clamping_step</code> — single-step update of <code>sec x25519 clamping</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_x25519_clamping_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-x509-subject-match">
<h3><a class="doc-anchor" href="#doc-sec-x509-subject-match">#</a> <code>sec_x509_subject_match</code></h3>
<p><code>sec_x509_subject_match</code> — operation <code>sec x509 subject match</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_x509_subject_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-xkcd-passphrase-score">
<h3><a class="doc-anchor" href="#doc-sec-xkcd-passphrase-score">#</a> <code>sec_xkcd_passphrase_score</code></h3>
<p><code>sec_xkcd_passphrase_score</code> — score of <code>sec xkcd passphrase</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_xkcd_passphrase_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-xss-filter-score">
<h3><a class="doc-anchor" href="#doc-sec-xss-filter-score">#</a> <code>sec_xss_filter_score</code></h3>
<p><code>sec_xss_filter_score</code> — score of <code>sec xss filter</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_xss_filter_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-xxe-dtd-check">
<h3><a class="doc-anchor" href="#doc-sec-xxe-dtd-check">#</a> <code>sec_xxe_dtd_check</code></h3>
<p><code>sec_xxe_dtd_check</code> — operation <code>sec xxe dtd check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_xxe_dtd_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-xxe-pattern-score">
<h3><a class="doc-anchor" href="#doc-sec-xxe-pattern-score">#</a> <code>sec_xxe_pattern_score</code></h3>
<p><code>sec_xxe_pattern_score</code> — score of <code>sec xxe pattern</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_xxe_pattern_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-yescrypt-step">
<h3><a class="doc-anchor" href="#doc-sec-yescrypt-step">#</a> <code>sec_yescrypt_step</code></h3>
<p><code>sec_yescrypt_step</code> — single-step update of <code>sec yescrypt</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_yescrypt_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sec-yubikey-otp-check">
<h3><a class="doc-anchor" href="#doc-sec-yubikey-otp-check">#</a> <code>sec_yubikey_otp_check</code></h3>
<p><code>sec_yubikey_otp_check</code> — operation <code>sec yubikey otp check</code>. Category: *os internals — schedulers, i/o, memory*.</p>
<pre><code class="lang-perl">p sec_yubikey_otp_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-secant">
<h3><a class="doc-anchor" href="#doc-secant">#</a> <code>secant</code></h3>
<p><code>secant</code> — operation <code>secant</code>. Alias for <code>secant_root</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p secant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-secant-root">
<h3><a class="doc-anchor" href="#doc-secant-root">#</a> <code>secant_root</code></h3>
<p><code>secant_root</code> — operation <code>secant root</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p secant_root $x
</code></pre>
</article>
<article class="doc-entry" id="doc-second">
<h3><a class="doc-anchor" href="#doc-second">#</a> <code>second</code></h3>
<p><code>second</code> — operation <code>second</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p second $x
</code></pre>
</article>
<article class="doc-entry" id="doc-second-arg">
<h3><a class="doc-anchor" href="#doc-second-arg">#</a> <code>second_arg</code></h3>
<p><code>second_arg</code> — operation <code>second arg</code>. Category: *functional primitives*.</p>
<pre><code class="lang-perl">p second_arg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-second-elem">
<h3><a class="doc-anchor" href="#doc-second-elem">#</a> <code>second_elem</code></h3>
<p><code>second_elem</code> — operation <code>second elem</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p second_elem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-second-order-concentration">
<h3><a class="doc-anchor" href="#doc-second-order-concentration">#</a> <code>second_order_concentration</code></h3>
<p><code>second_order_concentration</code> — operation <code>second order concentration</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p second_order_concentration $x
</code></pre>
</article>
<article class="doc-entry" id="doc-second-order-half-life">
<h3><a class="doc-anchor" href="#doc-second-order-half-life">#</a> <code>second_order_half_life</code></h3>
<p><code>second_order_half_life</code> — operation <code>second order half life</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p second_order_half_life $x
</code></pre>
</article>
<article class="doc-entry" id="doc-seconds-per-beat">
<h3><a class="doc-anchor" href="#doc-seconds-per-beat">#</a> <code>seconds_per_beat</code></h3>
<p><code>seconds_per_beat(bpm) → number</code> — <code>60 / bpm</code>.</p>
<pre><code class="lang-perl">p seconds_per_beat(120) # 0.5
</code></pre>
</article>
<article class="doc-entry" id="doc-seconds-to-days">
<h3><a class="doc-anchor" href="#doc-seconds-to-days">#</a> <code>seconds_to_days</code></h3>
<p><code>seconds_to_days</code> — convert from <code>seconds</code> to <code>days</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p seconds_to_days $value
</code></pre>
</article>
<article class="doc-entry" id="doc-seconds-to-hours">
<h3><a class="doc-anchor" href="#doc-seconds-to-hours">#</a> <code>seconds_to_hours</code></h3>
<p><code>seconds_to_hours</code> — convert from <code>seconds</code> to <code>hours</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p seconds_to_hours $value
</code></pre>
</article>
<article class="doc-entry" id="doc-seconds-to-minutes">
<h3><a class="doc-anchor" href="#doc-seconds-to-minutes">#</a> <code>seconds_to_minutes</code></h3>
<p><code>seconds_to_minutes</code> — convert from <code>seconds</code> to <code>minutes</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p seconds_to_minutes $value
</code></pre>
</article>
<article class="doc-entry" id="doc-secp256k1-y-recover">
<h3><a class="doc-anchor" href="#doc-secp256k1-y-recover">#</a> <code>secp256k1_y_recover</code></h3>
<p><code>secp256k1_y_recover</code> — operation <code>secp256k1 y recover</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p secp256k1_y_recover $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sectarea">
<h3><a class="doc-anchor" href="#doc-sectarea">#</a> <code>sectarea</code></h3>
<p><code>sectarea</code> — operation <code>sectarea</code>. Alias for <code>sector_area</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p sectarea $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sectional-curvature-two-plane">
<h3><a class="doc-anchor" href="#doc-sectional-curvature-two-plane">#</a> <code>sectional_curvature_two_plane</code></h3>
<p><code>sectional_curvature_two_plane</code> — operation <code>sectional curvature two plane</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p sectional_curvature_two_plane $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sector-area">
<h3><a class="doc-anchor" href="#doc-sector-area">#</a> <code>sector_area</code></h3>
<p><code>sector_area($radius, $theta)</code> — computes the area of a circular sector. Theta is the central angle in radians. Returns <code>0.5 * r² * theta</code>.</p>
<pre><code class="lang-perl">p sector_area(10, 3.14159) # ~157 (half circle)
p sector_area(5, 1.57) # ~19.6
</code></pre>
</article>
<article class="doc-entry" id="doc-seeded-rng">
<h3><a class="doc-anchor" href="#doc-seeded-rng">#</a> <code>seeded_rng</code></h3>
<p><code>seeded_rng</code> — operation <code>seeded rng</code>. Category: *random / sampling extras*.</p>
<pre><code class="lang-perl">p seeded_rng $x
</code></pre>
</article>
<article class="doc-entry" id="doc-seg-sum">
<h3><a class="doc-anchor" href="#doc-seg-sum">#</a> <code>seg_sum</code></h3>
<p><code>seg_sum</code> — sum of <code>seg</code>. Alias for <code>segment_tree_sum</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p seg_sum @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-segment-distance-point">
<h3><a class="doc-anchor" href="#doc-segment-distance-point">#</a> <code>segment_distance_point</code></h3>
<p><code>segment_distance_point</code> — operation <code>segment distance point</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p segment_distance_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-segment-intersection">
<h3><a class="doc-anchor" href="#doc-segment-intersection">#</a> <code>segment_intersection</code></h3>
<p><code>segment_intersection</code> — operation <code>segment intersection</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p segment_intersection $x
</code></pre>
</article>
<article class="doc-entry" id="doc-segment-length">
<h3><a class="doc-anchor" href="#doc-segment-length">#</a> <code>segment_length</code></h3>
<p><code>segment_length</code> — operation <code>segment length</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p segment_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-segment-tree-sum">
<h3><a class="doc-anchor" href="#doc-segment-tree-sum">#</a> <code>segment_tree_sum</code></h3>
<p><code>segment_tree_sum</code> — sum of <code>segment tree</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p segment_tree_sum @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-segments-parallel-q">
<h3><a class="doc-anchor" href="#doc-segments-parallel-q">#</a> <code>segments_parallel_q</code></h3>
<p><code>segments_parallel_q</code> — operation <code>segments parallel q</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p segments_parallel_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-segments-perpendicular-q">
<h3><a class="doc-anchor" href="#doc-segments-perpendicular-q">#</a> <code>segments_perpendicular_q</code></h3>
<p><code>segments_perpendicular_q</code> — operation <code>segments perpendicular q</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p segments_perpendicular_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sei-resistance-growth">
<h3><a class="doc-anchor" href="#doc-sei-resistance-growth">#</a> <code>sei_resistance_growth</code></h3>
<p><code>sei_resistance_growth</code> — operation <code>sei resistance growth</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p sei_resistance_growth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-seiberg-witten-value">
<h3><a class="doc-anchor" href="#doc-seiberg-witten-value">#</a> <code>seiberg_witten_value</code></h3>
<p><code>seiberg_witten_value</code> — value of <code>seiberg witten</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p seiberg_witten_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-seifert-form-2x2">
<h3><a class="doc-anchor" href="#doc-seifert-form-2x2">#</a> <code>seifert_form_2x2</code></h3>
<p><code>seifert_form_2x2</code> — operation <code>seifert form 2x2</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p seifert_form_2x2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-seifert-genus-lower">
<h3><a class="doc-anchor" href="#doc-seifert-genus-lower">#</a> <code>seifert_genus_lower</code></h3>
<p><code>seifert_genus_lower</code> — operation <code>seifert genus lower</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p seifert_genus_lower $x
</code></pre>
</article>
<article class="doc-entry" id="doc-seir-step">
<h3><a class="doc-anchor" href="#doc-seir-step">#</a> <code>seir_step</code></h3>
<p><code>seir_step</code> — single-step update of <code>seir</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p seir_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-seird-step">
<h3><a class="doc-anchor" href="#doc-seird-step">#</a> <code>seird_step</code></h3>
<p><code>seird_step</code> — single-step update of <code>seird</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p seird_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-seirs-step">
<h3><a class="doc-anchor" href="#doc-seirs-step">#</a> <code>seirs_step</code></h3>
<p><code>seirs_step</code> — single-step update of <code>seirs</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p seirs_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-select-period-step">
<h3><a class="doc-anchor" href="#doc-select-period-step">#</a> <code>select_period_step</code></h3>
<p><code>select_period_step</code> — single-step update of <code>select period</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p select_period_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-select-ultimate">
<h3><a class="doc-anchor" href="#doc-select-ultimate">#</a> <code>select_ultimate</code></h3>
<p><code>select_ultimate</code> — operation <code>select ultimate</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p select_ultimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-selection-step">
<h3><a class="doc-anchor" href="#doc-selection-step">#</a> <code>selection_step</code></h3>
<p><code>selection_step</code> — single-step update of <code>selection</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p selection_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-selector-to-xpath">
<h3><a class="doc-anchor" href="#doc-selector-to-xpath">#</a> <code>selector_to_xpath</code></h3>
<p><code>selector_to_xpath</code> — convert from <code>selector</code> to <code>xpath</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p selector_to_xpath $value
</code></pre>
</article>
<article class="doc-entry" id="doc-selu">
<h3><a class="doc-anchor" href="#doc-selu">#</a> <code>selu</code></h3>
<p><code>selu</code> applies the Scaled ELU with fixed lambda=1.0507, alpha=1.6733 for self-normalizing networks.</p>
<pre><code class="lang-perl">p selu(1) # 1.0507
p selu(-1) # -1.1113
</code></pre>
</article>
<article class="doc-entry" id="doc-semctl">
<h3><a class="doc-anchor" href="#doc-semctl">#</a> <code>semctl</code></h3>
<p><code>semctl</code> — operation <code>semctl</code>. Category: *sysv ipc*.</p>
<pre><code class="lang-perl">p semctl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-semget">
<h3><a class="doc-anchor" href="#doc-semget">#</a> <code>semget</code></h3>
<p><code>semget</code> — operation <code>semget</code>. Category: *sysv ipc*.</p>
<pre><code class="lang-perl">p semget $x
</code></pre>
</article>
<article class="doc-entry" id="doc-semi-major-axis">
<h3><a class="doc-anchor" href="#doc-semi-major-axis">#</a> <code>semi_major_axis</code></h3>
<p><code>semi_major_axis</code> — operation <code>semi major axis</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p semi_major_axis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-semop">
<h3><a class="doc-anchor" href="#doc-semop">#</a> <code>semop</code></h3>
<p><code>semop</code> — operation <code>semop</code>. Category: *sysv ipc*.</p>
<pre><code class="lang-perl">p semop $x
</code></pre>
</article>
<article class="doc-entry" id="doc-semver-compare">
<h3><a class="doc-anchor" href="#doc-semver-compare">#</a> <code>semver_compare</code></h3>
<p><code>semver_compare</code> — operation <code>semver compare</code>. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p semver_compare $x
</code></pre>
</article>
<article class="doc-entry" id="doc-semver-increment-major">
<h3><a class="doc-anchor" href="#doc-semver-increment-major">#</a> <code>semver_increment_major</code></h3>
<p><code>semver_increment_major</code> — operation <code>semver increment major</code>. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p semver_increment_major $x
</code></pre>
</article>
<article class="doc-entry" id="doc-semver-increment-minor">
<h3><a class="doc-anchor" href="#doc-semver-increment-minor">#</a> <code>semver_increment_minor</code></h3>
<p><code>semver_increment_minor</code> — operation <code>semver increment minor</code>. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p semver_increment_minor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-semver-increment-patch">
<h3><a class="doc-anchor" href="#doc-semver-increment-patch">#</a> <code>semver_increment_patch</code></h3>
<p><code>semver_increment_patch</code> — operation <code>semver increment patch</code>. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p semver_increment_patch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-semver-satisfies">
<h3><a class="doc-anchor" href="#doc-semver-satisfies">#</a> <code>semver_satisfies</code></h3>
<p><code>semver_satisfies</code> — operation <code>semver satisfies</code>. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p semver_satisfies $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sentence-case">
<h3><a class="doc-anchor" href="#doc-sentence-case">#</a> <code>sentence_case</code></h3>
<p><code>sentence_case</code> — operation <code>sentence case</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p sentence_case $x
</code></pre>
</article>
<article class="doc-entry" id="doc-seq">
<h3><a class="doc-anchor" href="#doc-seq">#</a> <code>seq</code></h3>
<p><code>seq</code> — operation <code>seq</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p seq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-seq-fn">
<h3><a class="doc-anchor" href="#doc-seq-fn">#</a> <code>seq_fn</code></h3>
<p><code>seq_fn</code> — generate a numeric sequence from, to, by. Like R's seq().</p>
<pre><code class="lang-perl">my @s = @{seq_fn(1, 10, 2)} # [1,3,5,7,9]
my @r = @{seq_fn(5, 1, -1)} # [5,4,3,2,1]
</code></pre>
</article>
<article class="doc-entry" id="doc-seq-logo-information">
<h3><a class="doc-anchor" href="#doc-seq-logo-information">#</a> <code>seq_logo_information</code></h3>
<p><code>seq_logo_information</code> — sequence helper <code>logo information</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p seq_logo_information $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sequence-identity-pct">
<h3><a class="doc-anchor" href="#doc-sequence-identity-pct">#</a> <code>sequence_identity_pct</code></h3>
<p><code>sequence_identity_pct(a, b) → number</code> — percent of position-matched characters in aligned sequences.</p>
<pre><code class="lang-perl">p sequence_identity_pct("ACGT", "ACCT") # 75
</code></pre>
</article>
<article class="doc-entry" id="doc-sequence-shannon-info">
<h3><a class="doc-anchor" href="#doc-sequence-shannon-info">#</a> <code>sequence_shannon_info</code></h3>
<p><code>sequence_shannon_info</code> — operation <code>sequence shannon info</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p sequence_shannon_info $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sequence-similarity-pct">
<h3><a class="doc-anchor" href="#doc-sequence-similarity-pct">#</a> <code>sequence_similarity_pct</code></h3>
<p><code>sequence_similarity_pct(a, b) → number</code> — percent of positions that are identical or chemically similar (aliphatic/aromatic/polar/etc. groups).</p>
</article>
<article class="doc-entry" id="doc-sequent-left-intro">
<h3><a class="doc-anchor" href="#doc-sequent-left-intro">#</a> <code>sequent_left_intro</code></h3>
<p><code>sequent_left_intro</code> — operation <code>sequent left intro</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p sequent_left_intro $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sequent-right-intro">
<h3><a class="doc-anchor" href="#doc-sequent-right-intro">#</a> <code>sequent_right_intro</code></h3>
<p><code>sequent_right_intro</code> — operation <code>sequent right intro</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p sequent_right_intro $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sequential-eq-check">
<h3><a class="doc-anchor" href="#doc-sequential-eq-check">#</a> <code>sequential_eq_check</code></h3>
<p><code>sequential_eq_check</code> — operation <code>sequential eq check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p sequential_eq_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-servo-position-velocity">
<h3><a class="doc-anchor" href="#doc-servo-position-velocity">#</a> <code>servo_position_velocity</code></h3>
<p><code>servo_position_velocity</code> — operation <code>servo position velocity</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p servo_position_velocity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-servo-torque-step">
<h3><a class="doc-anchor" href="#doc-servo-torque-step">#</a> <code>servo_torque_step</code></h3>
<p><code>servo_torque_step</code> — single-step update of <code>servo torque</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p servo_torque_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-set-at">
<h3><a class="doc-anchor" href="#doc-set-at">#</a> <code>set_at</code></h3>
<p><code>set_at</code> — set-theoretic op <code>at</code>. Alias for <code>replace_at_index</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p set_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-set-cover-greedy-step">
<h3><a class="doc-anchor" href="#doc-set-cover-greedy-step">#</a> <code>set_cover_greedy_step</code></h3>
<p><code>set_cover_greedy_step</code> — set-theoretic op <code>cover greedy step</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p set_cover_greedy_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-set-cover-lp-round">
<h3><a class="doc-anchor" href="#doc-set-cover-lp-round">#</a> <code>set_cover_lp_round</code></h3>
<p><code>set_cover_lp_round</code> — set-theoretic op <code>cover lp round</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p set_cover_lp_round $x
</code></pre>
</article>
<article class="doc-entry" id="doc-set-subname">
<h3><a class="doc-anchor" href="#doc-set-subname">#</a> <code>set_subname</code></h3>
<p><code>set_subname</code> — set-theoretic op <code>subname</code>. Category: *list / aggregate*.</p>
<pre><code class="lang-perl">p set_subname $x
</code></pre>
</article>
<article class="doc-entry" id="doc-setex">
<h3><a class="doc-anchor" href="#doc-setex">#</a> <code>setex</code></h3>
<p><code>setex</code> — operation <code>setex</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p setex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-setgrent">
<h3><a class="doc-anchor" href="#doc-setgrent">#</a> <code>setgrent</code></h3>
<p><code>setgrent</code> — operation <code>setgrent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p setgrent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sethostent">
<h3><a class="doc-anchor" href="#doc-sethostent">#</a> <code>sethostent</code></h3>
<p><code>sethostent</code> — operation <code>sethostent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p sethostent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-setnetent">
<h3><a class="doc-anchor" href="#doc-setnetent">#</a> <code>setnetent</code></h3>
<p><code>setnetent</code> — operation <code>setnetent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p setnetent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-setnx">
<h3><a class="doc-anchor" href="#doc-setnx">#</a> <code>setnx</code></h3>
<p><code>setnx</code> — operation <code>setnx</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p setnx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-setprotoent">
<h3><a class="doc-anchor" href="#doc-setprotoent">#</a> <code>setprotoent</code></h3>
<p><code>setprotoent</code> — operation <code>setprotoent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p setprotoent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-setpwent">
<h3><a class="doc-anchor" href="#doc-setpwent">#</a> <code>setpwent</code></h3>
<p><code>setpwent</code> — operation <code>setpwent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p setpwent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-setrange">
<h3><a class="doc-anchor" href="#doc-setrange">#</a> <code>setrange</code></h3>
<p><code>setrange</code> — operation <code>setrange</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p setrange $x
</code></pre>
</article>
<article class="doc-entry" id="doc-setservent">
<h3><a class="doc-anchor" href="#doc-setservent">#</a> <code>setservent</code></h3>
<p><code>setservent</code> — operation <code>setservent</code>. Category: *posix metadata*.</p>
<pre><code class="lang-perl">p setservent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-seven-smooth-q">
<h3><a class="doc-anchor" href="#doc-seven-smooth-q">#</a> <code>seven_smooth_q</code></h3>
<p><code>seven_smooth_q</code> — operation <code>seven smooth q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p seven_smooth_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sfork">
<h3><a class="doc-anchor" href="#doc-sfork">#</a> <code>sfork</code></h3>
<p><code>sfork</code> — operation <code>sfork</code>. Alias for <code>stress_fork</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p sfork $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sgemm">
<h3><a class="doc-anchor" href="#doc-sgemm">#</a> <code>sgemm</code></h3>
<p><code>sgemm</code> — operation <code>sgemm</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p sgemm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sgemv">
<h3><a class="doc-anchor" href="#doc-sgemv">#</a> <code>sgemv</code></h3>
<p><code>sgemv</code> — operation <code>sgemv</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p sgemv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sgnum">
<h3><a class="doc-anchor" href="#doc-sgnum">#</a> <code>sgnum</code></h3>
<p><code>sgnum</code> — operation <code>sgnum</code>. Alias for <code>signum_of</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p sgnum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sgp4-propagate-step">
<h3><a class="doc-anchor" href="#doc-sgp4-propagate-step">#</a> <code>sgp4_propagate_step</code></h3>
<p><code>sgp4_propagate_step</code> — single-step update of <code>sgp4 propagate</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p sgp4_propagate_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shake-map-pga">
<h3><a class="doc-anchor" href="#doc-shake-map-pga">#</a> <code>shake_map_pga</code></h3>
<p><code>shake_map_pga</code> — operation <code>shake map pga</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p shake_map_pga $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shanks-transform">
<h3><a class="doc-anchor" href="#doc-shanks-transform">#</a> <code>shanks_transform</code></h3>
<p><code>shanks_transform</code> — transform of <code>shanks</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p shanks_transform $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shannon-fano-elias-code">
<h3><a class="doc-anchor" href="#doc-shannon-fano-elias-code">#</a> <code>shannon_fano_elias_code</code></h3>
<p><code>shannon_fano_elias_code</code> — operation <code>shannon fano elias code</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p shannon_fano_elias_code $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shape-operator-eig">
<h3><a class="doc-anchor" href="#doc-shape-operator-eig">#</a> <code>shape_operator_eig</code></h3>
<p><code>shape_operator_eig</code> — operation <code>shape operator eig</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p shape_operator_eig $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shapiro">
<h3><a class="doc-anchor" href="#doc-shapiro">#</a> <code>shapiro</code></h3>
<p><code>shapiro_test</code> (alias <code>shapiro</code>) — Shapiro-Wilk normality test. Returns W statistic (close to 1 = normal). Like R's shapiro.test().</p>
<pre><code class="lang-perl">p shapiro([rnorm(100)]) # W ≈ 0.99 for normal data
p shapiro([1,1,1,2,10]) # W < 0.9 for non-normal
</code></pre>
</article>
<article class="doc-entry" id="doc-shapiro-delay">
<h3><a class="doc-anchor" href="#doc-shapiro-delay">#</a> <code>shapiro_delay</code></h3>
<p><code>shapiro_delay</code> — operation <code>shapiro delay</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p shapiro_delay $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shapiro-delay-step">
<h3><a class="doc-anchor" href="#doc-shapiro-delay-step">#</a> <code>shapiro_delay_step</code></h3>
<p><code>shapiro_delay_step</code> — single-step update of <code>shapiro delay</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p shapiro_delay_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shapiro-wilk">
<h3><a class="doc-anchor" href="#doc-shapiro-wilk">#</a> <code>shapiro_wilk</code></h3>
<p><code>shapiro_wilk</code> — operation <code>shapiro wilk</code>. Category: *r / scipy distributions and tests*.</p>
<pre><code class="lang-perl">p shapiro_wilk $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shapley-value-two-step">
<h3><a class="doc-anchor" href="#doc-shapley-value-two-step">#</a> <code>shapley_value_two_step</code></h3>
<p><code>shapley_value_two_step</code> — single-step update of <code>shapley value two</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p shapley_value_two_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sharpe">
<h3><a class="doc-anchor" href="#doc-sharpe">#</a> <code>sharpe</code></h3>
<p><code>sharpe_ratio(\@returns, $risk_free_rate)</code> (alias <code>sharpe</code>) — computes the Sharpe ratio measuring risk-adjusted returns. Higher is better. Returns (mean_return - rf) / stddev.</p>
<pre><code class="lang-perl">my @returns = (0.05, -0.02, 0.08, 0.03)
p sharpe(\@returns, 0.02) # risk-adjusted performance
</code></pre>
</article>
<article class="doc-entry" id="doc-sharpe-annualized">
<h3><a class="doc-anchor" href="#doc-sharpe-annualized">#</a> <code>sharpe_annualized</code></h3>
<p><code>sharpe_annualized</code> — operation <code>sharpe annualized</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p sharpe_annualized $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sharpen-kernel">
<h3><a class="doc-anchor" href="#doc-sharpen-kernel">#</a> <code>sharpen_kernel</code></h3>
<p><code>sharpen_kernel</code> — convolution kernel of <code>sharpen</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p sharpen_kernel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shear-tensor-step">
<h3><a class="doc-anchor" href="#doc-shear-tensor-step">#</a> <code>shear_tensor_step</code></h3>
<p><code>shear_tensor_step</code> — single-step update of <code>shear tensor</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p shear_tensor_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shepherd-voltage-step">
<h3><a class="doc-anchor" href="#doc-shepherd-voltage-step">#</a> <code>shepherd_voltage_step</code></h3>
<p><code>shepherd_voltage_step</code> — single-step update of <code>shepherd voltage</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p shepherd_voltage_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sherwood-number-step">
<h3><a class="doc-anchor" href="#doc-sherwood-number-step">#</a> <code>sherwood_number_step</code></h3>
<p><code>sherwood_number_step</code> — single-step update of <code>sherwood number</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p sherwood_number_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shi-tomasi-corners">
<h3><a class="doc-anchor" href="#doc-shi-tomasi-corners">#</a> <code>shi_tomasi_corners</code></h3>
<p><code>shi_tomasi_corners</code> — operation <code>shi tomasi corners</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p shi_tomasi_corners $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shift-left">
<h3><a class="doc-anchor" href="#doc-shift-left">#</a> <code>shift_left</code></h3>
<p><code>shift_left</code> — operation <code>shift left</code>. Category: *bit ops*.</p>
<pre><code class="lang-perl">p shift_left $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shift-right">
<h3><a class="doc-anchor" href="#doc-shift-right">#</a> <code>shift_right</code></h3>
<p><code>shift_right</code> — operation <code>shift right</code>. Category: *bit ops*.</p>
<pre><code class="lang-perl">p shift_right $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shift-series">
<h3><a class="doc-anchor" href="#doc-shift-series">#</a> <code>shift_series</code></h3>
<p><code>shift_series(series, n=1) → array</code> — shifts elements by <code>n</code> positions; negative shifts left, positive shifts right.</p>
<pre><code class="lang-perl">p shift_series([1,2,3,4,5], 2)
</code></pre>
</article>
<article class="doc-entry" id="doc-shl">
<h3><a class="doc-anchor" href="#doc-shl">#</a> <code>shl</code></h3>
<p><code>shl</code> — operation <code>shl</code>. Alias for <code>shift_left</code>. Category: *bit ops*.</p>
<pre><code class="lang-perl">p shl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shmctl">
<h3><a class="doc-anchor" href="#doc-shmctl">#</a> <code>shmctl</code></h3>
<p><code>shmctl</code> — operation <code>shmctl</code>. Category: *sysv ipc*.</p>
<pre><code class="lang-perl">p shmctl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shmget">
<h3><a class="doc-anchor" href="#doc-shmget">#</a> <code>shmget</code></h3>
<p><code>shmget</code> — operation <code>shmget</code>. Category: *sysv ipc*.</p>
<pre><code class="lang-perl">p shmget $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shmread">
<h3><a class="doc-anchor" href="#doc-shmread">#</a> <code>shmread</code></h3>
<p><code>shmread</code> — operation <code>shmread</code>. Category: *sysv ipc*.</p>
<pre><code class="lang-perl">p shmread $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shmwrite">
<h3><a class="doc-anchor" href="#doc-shmwrite">#</a> <code>shmwrite</code></h3>
<p><code>shmwrite</code> — operation <code>shmwrite</code>. Category: *sysv ipc*.</p>
<pre><code class="lang-perl">p shmwrite $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shoelace-area">
<h3><a class="doc-anchor" href="#doc-shoelace-area">#</a> <code>shoelace_area</code></h3>
<p><code>shoelace_area</code> — operation <code>shoelace area</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p shoelace_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shooting-pct">
<h3><a class="doc-anchor" href="#doc-shooting-pct">#</a> <code>shooting_pct</code></h3>
<p><code>shooting_pct</code> — percentage of <code>shooting</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p shooting_pct $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shor-period">
<h3><a class="doc-anchor" href="#doc-shor-period">#</a> <code>shor_period</code></h3>
<p><code>shor_period</code> — operation <code>shor period</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p shor_period $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shor-period-prob">
<h3><a class="doc-anchor" href="#doc-shor-period-prob">#</a> <code>shor_period_prob</code></h3>
<p><code>shor_period_prob</code> — operation <code>shor period prob</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p shor_period_prob $x
</code></pre>
</article>
<article class="doc-entry" id="doc-short-id">
<h3><a class="doc-anchor" href="#doc-short-id">#</a> <code>short_id</code></h3>
<p><code>short_id</code> — operation <code>short id</code>. Category: *id helpers*.</p>
<pre><code class="lang-perl">p short_id $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shorten">
<h3><a class="doc-anchor" href="#doc-shorten">#</a> <code>shorten</code></h3>
<p><code>shorten</code> — operation <code>shorten</code>. Alias for <code>truncate_at</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p shorten $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shortest">
<h3><a class="doc-anchor" href="#doc-shortest">#</a> <code>shortest</code></h3>
<p><code>shortest</code> — operation <code>shortest</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p shortest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shortest-path-bfs">
<h3><a class="doc-anchor" href="#doc-shortest-path-bfs">#</a> <code>shortest_path_bfs</code></h3>
<p><code>shortest_path_bfs</code> — operation <code>shortest path bfs</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p shortest_path_bfs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shr">
<h3><a class="doc-anchor" href="#doc-shr">#</a> <code>shr</code></h3>
<p><code>shr</code> — operation <code>shr</code>. Alias for <code>shift_right</code>. Category: *bit ops*.</p>
<pre><code class="lang-perl">p shr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shuf">
<h3><a class="doc-anchor" href="#doc-shuf">#</a> <code>shuf</code></h3>
<p><code>shuf</code> — operation <code>shuf</code>. Alias for <code>shuffle_arr</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p shuf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shuffle-arr">
<h3><a class="doc-anchor" href="#doc-shuffle-arr">#</a> <code>shuffle_arr</code></h3>
<p><code>shuffle_arr</code> — operation <code>shuffle arr</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p shuffle_arr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shuffle-chars">
<h3><a class="doc-anchor" href="#doc-shuffle-chars">#</a> <code>shuffle_chars</code></h3>
<p><code>shuffle_chars</code> — operation <code>shuffle chars</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p shuffle_chars $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shuffle-resample">
<h3><a class="doc-anchor" href="#doc-shuffle-resample">#</a> <code>shuffle_resample</code></h3>
<p><code>shuffle_resample(xs, seed=0) → array</code> — in-place Fisher-Yates shuffle returning a new permutation.</p>
</article>
<article class="doc-entry" id="doc-shuffled">
<h3><a class="doc-anchor" href="#doc-shuffled">#</a> <code>shuffled</code></h3>
<p><code>shuffled</code> — operation <code>shuffled</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p shuffled $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shunting-yard-step">
<h3><a class="doc-anchor" href="#doc-shunting-yard-step">#</a> <code>shunting_yard_step</code></h3>
<p><code>shunting_yard_step</code> — single-step update of <code>shunting yard</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p shunting_yard_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-shutter-speed-reciprocal">
<h3><a class="doc-anchor" href="#doc-shutter-speed-reciprocal">#</a> <code>shutter_speed_reciprocal</code></h3>
<p><code>shutter_speed_reciprocal(focal_mm, crop=1) → number</code> — <code>1/(focal·crop)</code>. Heuristic minimum hand-held shutter.</p>
</article>
<article class="doc-entry" id="doc-si">
<h3><a class="doc-anchor" href="#doc-si">#</a> <code>si</code></h3>
<p><code>si(x) → number</code> — sine integral <code>Si(x) = ∫_0^x sin(t)/t dt</code>. Used in signal-processing windowing.</p>
<pre><code class="lang-perl">p si(3.14159) # ~1.852
</code></pre>
</article>
<article class="doc-entry" id="doc-sidereal-day-period">
<h3><a class="doc-anchor" href="#doc-sidereal-day-period">#</a> <code>sidereal_day_period</code></h3>
<p><code>sidereal_day_period</code> — sidereal-time computation <code>day period</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p sidereal_day_period $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sidereal-time-greenwich">
<h3><a class="doc-anchor" href="#doc-sidereal-time-greenwich">#</a> <code>sidereal_time_greenwich</code></h3>
<p><code>sidereal_time_greenwich(unix) → number</code> — Greenwich Mean Sidereal Time in hours, [0, 24).</p>
<pre><code class="lang-perl">p sidereal_time_greenwich(time())
</code></pre>
</article>
<article class="doc-entry" id="doc-sidereal-time-local">
<h3><a class="doc-anchor" href="#doc-sidereal-time-local">#</a> <code>sidereal_time_local</code></h3>
<p><code>sidereal_time_local(unix, longitude_deg) → number</code> — local sidereal time = GMST + lon/15.</p>
<pre><code class="lang-perl">p sidereal_time_local(time(), -122.4)
</code></pre>
</article>
<article class="doc-entry" id="doc-siera">
<h3><a class="doc-anchor" href="#doc-siera">#</a> <code>siera</code></h3>
<p><code>siera</code> — operation <code>siera</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p siera $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sierp">
<h3><a class="doc-anchor" href="#doc-sierp">#</a> <code>sierp</code></h3>
<p><code>sierp</code> — operation <code>sierp</code>. Alias for <code>sierpinski</code>. Category: *algorithms / puzzles*.</p>
<pre><code class="lang-perl">p sierp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sierpinski">
<h3><a class="doc-anchor" href="#doc-sierpinski">#</a> <code>sierpinski</code></h3>
<p><code>sierpinski</code> — operation <code>sierpinski</code>. Category: *algorithms / puzzles*.</p>
<pre><code class="lang-perl">p sierpinski $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sieve">
<h3><a class="doc-anchor" href="#doc-sieve">#</a> <code>sieve</code></h3>
<p><code>sieve</code> — operation <code>sieve</code>. Alias for <code>primes_up_to</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p sieve $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sift-keypoints">
<h3><a class="doc-anchor" href="#doc-sift-keypoints">#</a> <code>sift_keypoints</code></h3>
<p><code>sift_keypoints</code> — operation <code>sift keypoints</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p sift_keypoints $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sigma8-default">
<h3><a class="doc-anchor" href="#doc-sigma8-default">#</a> <code>sigma8_default</code></h3>
<p><code>sigma8_default</code> — operation <code>sigma8 default</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p sigma8_default $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sigma-crit">
<h3><a class="doc-anchor" href="#doc-sigma-crit">#</a> <code>sigma_crit</code></h3>
<p><code>sigma_crit</code> — operation <code>sigma crit</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p sigma_crit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sigma-divisors">
<h3><a class="doc-anchor" href="#doc-sigma-divisors">#</a> <code>sigma_divisors</code></h3>
<p><code>sigma_divisors</code> — operation <code>sigma divisors</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p sigma_divisors $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sigma-sb">
<h3><a class="doc-anchor" href="#doc-sigma-sb">#</a> <code>sigma_sb</code></h3>
<p><code>sigma_sb</code> — operation <code>sigma sb</code>. Alias for <code>stefan_boltzmann_constant</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p sigma_sb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sigmoid">
<h3><a class="doc-anchor" href="#doc-sigmoid">#</a> <code>sigmoid</code></h3>
<p><code>sigmoid(x) → number</code> — <code>1 / (1 + e^-x)</code>.</p>
</article>
<article class="doc-entry" id="doc-sigmoid-grad">
<h3><a class="doc-anchor" href="#doc-sigmoid-grad">#</a> <code>sigmoid_grad</code></h3>
<p><code>sigmoid_grad</code> — operation <code>sigmoid grad</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p sigmoid_grad $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sign">
<h3><a class="doc-anchor" href="#doc-sign">#</a> <code>sign</code></h3>
<p><code>sign</code> — operation <code>sign</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p sign $x
</code></pre>
</article>
<article class="doc-entry" id="doc-signal-name">
<h3><a class="doc-anchor" href="#doc-signal-name">#</a> <code>signal_name</code></h3>
<p><code>signal_name</code> — operation <code>signal name</code>. Category: *more process / system*.</p>
<pre><code class="lang-perl">p signal_name $x
</code></pre>
</article>
<article class="doc-entry" id="doc-signum">
<h3><a class="doc-anchor" href="#doc-signum">#</a> <code>signum</code></h3>
<p><code>signum</code> — operation <code>signum</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p signum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-signum-of">
<h3><a class="doc-anchor" href="#doc-signum-of">#</a> <code>signum_of</code></h3>
<p><code>signum_of</code> — operation <code>signum of</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p signum_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-silicate-classify">
<h3><a class="doc-anchor" href="#doc-silicate-classify">#</a> <code>silicate_classify</code></h3>
<p><code>silicate_classify</code> — operation <code>silicate classify</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p silicate_classify $x
</code></pre>
</article>
<article class="doc-entry" id="doc-silu">
<h3><a class="doc-anchor" href="#doc-silu">#</a> <code>silu</code></h3>
<p><code>silu</code> (alias <code>swish</code>) applies SiLU/Swish: x·sigmoid(x). Smooth approximation to ReLU.</p>
<pre><code class="lang-perl">p silu(1) # 0.7311
p swish(-2) # -0.2384
</code></pre>
</article>
<article class="doc-entry" id="doc-silver">
<h3><a class="doc-anchor" href="#doc-silver">#</a> <code>silver</code></h3>
<p><code>silver_ratio</code> (alias <code>silver</code>) — δS = 1 + √2 ≈ 2.414. Related to Pell numbers.</p>
<pre><code class="lang-perl">p silver # 2.414213562373095
</code></pre>
</article>
<article class="doc-entry" id="doc-sim">
<h3><a class="doc-anchor" href="#doc-sim">#</a> <code>sim</code></h3>
<p><code>sim</code> — operation <code>sim</code>. Alias for <code>similarity</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p sim $x
</code></pre>
</article>
<article class="doc-entry" id="doc-similarity">
<h3><a class="doc-anchor" href="#doc-similarity">#</a> <code>similarity</code></h3>
<p><code>similarity</code> — operation <code>similarity</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p similarity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-similarity-function-phi">
<h3><a class="doc-anchor" href="#doc-similarity-function-phi">#</a> <code>similarity_function_phi</code></h3>
<p><code>similarity_function_phi</code> — operation <code>similarity function phi</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p similarity_function_phi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-simon-round">
<h3><a class="doc-anchor" href="#doc-simon-round">#</a> <code>simon_round</code></h3>
<p><code>simon_round</code> — operation <code>simon round</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p simon_round $x
</code></pre>
</article>
<article class="doc-entry" id="doc-simple-interest">
<h3><a class="doc-anchor" href="#doc-simple-interest">#</a> <code>simple_interest</code></h3>
<p><code>simple_interest</code> — operation <code>simple interest</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p simple_interest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-simple-interest-compute">
<h3><a class="doc-anchor" href="#doc-simple-interest-compute">#</a> <code>simple_interest_compute</code></h3>
<p><code>simple_interest_compute</code> — operation <code>simple interest compute</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p simple_interest_compute $x
</code></pre>
</article>
<article class="doc-entry" id="doc-simple-returns">
<h3><a class="doc-anchor" href="#doc-simple-returns">#</a> <code>simple_returns</code></h3>
<p><code>simple_returns</code> — operation <code>simple returns</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p simple_returns $x
</code></pre>
</article>
<article class="doc-entry" id="doc-simplex-2d">
<h3><a class="doc-anchor" href="#doc-simplex-2d">#</a> <code>simplex_2d</code></h3>
<p><code>simplex_2d(x, y) → number</code> — 2D simplex noise (Perlin's improvement). Better isotropy than classic Perlin.</p>
</article>
<article class="doc-entry" id="doc-simplex-volume-3d">
<h3><a class="doc-anchor" href="#doc-simplex-volume-3d">#</a> <code>simplex_volume_3d</code></h3>
<p><code>simplex_volume_3d</code> — simplex noise <code>volume 3d</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p simplex_volume_3d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-simplex-volume-n">
<h3><a class="doc-anchor" href="#doc-simplex-volume-n">#</a> <code>simplex_volume_n</code></h3>
<p><code>simplex_volume_n</code> — simplex noise <code>volume n</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p simplex_volume_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-simplicial-volume">
<h3><a class="doc-anchor" href="#doc-simplicial-volume">#</a> <code>simplicial_volume</code></h3>
<p><code>simplicial_volume</code> — operation <code>simplicial volume</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p simplicial_volume $x
</code></pre>
</article>
<article class="doc-entry" id="doc-simply-typed-check">
<h3><a class="doc-anchor" href="#doc-simply-typed-check">#</a> <code>simply_typed_check</code></h3>
<p><code>simply_typed_check</code> — operation <code>simply typed check</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p simply_typed_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-simps">
<h3><a class="doc-anchor" href="#doc-simps">#</a> <code>simps</code></h3>
<p><code>simpson</code> (alias <code>simps</code>) integrates evenly-spaced samples using Simpson's rule. More accurate than trapz for smooth functions.</p>
<pre><code class="lang-perl">my @y = map { sin(_ * 0.01) } 0:314
p simps(\@y, 0.01) # ≈ 2.0
</code></pre>
</article>
<article class="doc-entry" id="doc-simpson-integrate">
<h3><a class="doc-anchor" href="#doc-simpson-integrate">#</a> <code>simpson_integrate</code></h3>
<p><code>simpson_integrate(ys, dx=1) → number</code> — composite Simpson's rule. Uses Simpson's 1/3 over even intervals; falls back to Simpson's 3/8 on the trailing 3 intervals when <code>n-1</code> is odd, so the rule is exact for any <code>n ≥ 3</code>. Falls back to trapezoidal for <code>n < 3</code>.</p>
<pre><code class="lang-perl">p simpson_integrate([0,1,4,9,16,25,36,49,64,81,100], 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-simpson-rule">
<h3><a class="doc-anchor" href="#doc-simpson-rule">#</a> <code>simpson_rule</code></h3>
<p><code>simpson_rule</code> — operation <code>simpson rule</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p simpson_rule $x
</code></pre>
</article>
<article class="doc-entry" id="doc-simrank">
<h3><a class="doc-anchor" href="#doc-simrank">#</a> <code>simrank</code></h3>
<p><code>simrank</code> — operation <code>simrank</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p simrank $x
</code></pre>
</article>
<article class="doc-entry" id="doc-simulated-annealing-step">
<h3><a class="doc-anchor" href="#doc-simulated-annealing-step">#</a> <code>simulated_annealing_step</code></h3>
<p><code>simulated_annealing_step</code> — single-step update of <code>simulated annealing</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p simulated_annealing_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sinc">
<h3><a class="doc-anchor" href="#doc-sinc">#</a> <code>sinc</code></h3>
<p><code>sinc</code> returns the unnormalized sinc function: sin(x)/x, with sinc(0)=1.</p>
<pre><code class="lang-perl">p sinc(0) # 1.0
p sinc(3.14159) # ≈ 0
</code></pre>
</article>
<article class="doc-entry" id="doc-sine-integral-si">
<h3><a class="doc-anchor" href="#doc-sine-integral-si">#</a> <code>sine_integral_si</code></h3>
<p><code>sine_integral_si</code> — operation <code>sine integral si</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p sine_integral_si $x
</code></pre>
</article>
<article class="doc-entry" id="doc-single-quote">
<h3><a class="doc-anchor" href="#doc-single-quote">#</a> <code>single_quote</code></h3>
<p><code>single_quote</code> — operation <code>single quote</code>. Category: *string quote / escape*.</p>
<pre><code class="lang-perl">p single_quote $x
</code></pre>
</article>
<article class="doc-entry" id="doc-single-slit-min">
<h3><a class="doc-anchor" href="#doc-single-slit-min">#</a> <code>single_slit_min</code></h3>
<p><code>single_slit_min</code> — minimum of <code>single slit</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p single_slit_min $x
</code></pre>
</article>
<article class="doc-entry" id="doc-single-transferable-vote">
<h3><a class="doc-anchor" href="#doc-single-transferable-vote">#</a> <code>single_transferable_vote</code></h3>
<p><code>single_transferable_vote</code> — operation <code>single transferable vote</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p single_transferable_vote $x
</code></pre>
</article>
<article class="doc-entry" id="doc-singularity-check-2link">
<h3><a class="doc-anchor" href="#doc-singularity-check-2link">#</a> <code>singularity_check_2link</code></h3>
<p><code>singularity_check_2link</code> — operation <code>singularity check 2link</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p singularity_check_2link $x
</code></pre>
</article>
<article class="doc-entry" id="doc-singularize">
<h3><a class="doc-anchor" href="#doc-singularize">#</a> <code>singularize</code></h3>
<p><code>singularize</code> — operation <code>singularize</code>. Alias for <code>singularize_simple</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p singularize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-singularize-simple">
<h3><a class="doc-anchor" href="#doc-singularize-simple">#</a> <code>singularize_simple</code></h3>
<p><code>singularize_simple</code> — operation <code>singularize simple</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p singularize_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sinh">
<h3><a class="doc-anchor" href="#doc-sinh">#</a> <code>sinh</code></h3>
<p><code>sinh</code> — operation <code>sinh</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p sinh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sinhc">
<h3><a class="doc-anchor" href="#doc-sinhc">#</a> <code>sinhc</code></h3>
<p><code>sinhc</code> — operation <code>sinhc</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p sinhc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sinkhorn-iteration-step">
<h3><a class="doc-anchor" href="#doc-sinkhorn-iteration-step">#</a> <code>sinkhorn_iteration_step</code></h3>
<p><code>sinkhorn_iteration_step</code> — single-step update of <code>sinkhorn iteration</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p sinkhorn_iteration_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sinter">
<h3><a class="doc-anchor" href="#doc-sinter">#</a> <code>sinter</code></h3>
<p><code>sinter</code> — operation <code>sinter</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p sinter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sinusoidal-project">
<h3><a class="doc-anchor" href="#doc-sinusoidal-project">#</a> <code>sinusoidal_project</code></h3>
<p><code>sinusoidal_project</code> — operation <code>sinusoidal project</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p sinusoidal_project $x
</code></pre>
</article>
<article class="doc-entry" id="doc-siphash24">
<h3><a class="doc-anchor" href="#doc-siphash24">#</a> <code>siphash24</code></h3>
<p><code>siphash24</code> — operation <code>siphash24</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p siphash24 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-siphash-keyed">
<h3><a class="doc-anchor" href="#doc-siphash-keyed">#</a> <code>siphash_keyed</code></h3>
<p><code>siphash_keyed</code> computes SipHash-2-4 with a custom 128-bit key (two 64-bit integers). The key should be random per application to prevent collision attacks.</p>
<pre><code class="lang-perl">p siphash_keyed("data", 0x123456789, 0xabcdef012) # keyed hash
</code></pre>
</article>
<article class="doc-entry" id="doc-sirs-step">
<h3><a class="doc-anchor" href="#doc-sirs-step">#</a> <code>sirs_step</code></h3>
<p><code>sirs_step</code> — single-step update of <code>sirs</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p sirs_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sis-step">
<h3><a class="doc-anchor" href="#doc-sis-step">#</a> <code>sis_step</code></h3>
<p><code>sis_step</code> — single-step update of <code>sis</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p sis_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sismember">
<h3><a class="doc-anchor" href="#doc-sismember">#</a> <code>sismember</code></h3>
<p><code>sismember</code> — operation <code>sismember</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p sismember $x
</code></pre>
</article>
<article class="doc-entry" id="doc-size">
<h3><a class="doc-anchor" href="#doc-size">#</a> <code>size</code></h3>
<p><code>size</code> returns the byte size of a file on disk — equivalent to Perl's <code>-s FILE</code> file test. With no arguments, it operates on <code>_</code>; with one argument, it stats the given path; with multiple arguments (or a flattened list), it returns an array of sizes. Paths that can't be stat'd return <code>undef</code>. This is a stryke extension that makes pipelines over filenames concise.</p>
<pre><code class="lang-perl">p size "Cargo.toml" # 2013
f |> map +{ _ => size } |> tj |> p # [{name => bytes}, ...]
f |> filter { size > 1024 } |> e p # files larger than 1 KiB
</code></pre>
</article>
<article class="doc-entry" id="doc-sjson">
<h3><a class="doc-anchor" href="#doc-sjson">#</a> <code>sjson</code></h3>
<p><code>sjson</code> — operation <code>sjson</code>. Alias for <code>stress_json</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p sjson $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-adjusted-rand">
<h3><a class="doc-anchor" href="#doc-sk-adjusted-rand">#</a> <code>sk_adjusted_rand</code></h3>
<p><code>sk_adjusted_rand</code> — operation <code>sk adjusted rand</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_adjusted_rand $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-agglomerative-fit">
<h3><a class="doc-anchor" href="#doc-sk-agglomerative-fit">#</a> <code>sk_agglomerative_fit</code></h3>
<p><code>sk_agglomerative_fit</code> — operation <code>sk agglomerative fit</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_agglomerative_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-bayes-search">
<h3><a class="doc-anchor" href="#doc-sk-bayes-search">#</a> <code>sk_bayes_search</code></h3>
<p><code>sk_bayes_search</code> — operation <code>sk bayes search</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_bayes_search $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-calinski-harabasz">
<h3><a class="doc-anchor" href="#doc-sk-calinski-harabasz">#</a> <code>sk_calinski_harabasz</code></h3>
<p><code>sk_calinski_harabasz</code> — operation <code>sk calinski harabasz</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_calinski_harabasz $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-count-vectorize">
<h3><a class="doc-anchor" href="#doc-sk-count-vectorize">#</a> <code>sk_count_vectorize</code></h3>
<p><code>sk_count_vectorize</code> — operation <code>sk count vectorize</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_count_vectorize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-cross-val-score">
<h3><a class="doc-anchor" href="#doc-sk-cross-val-score">#</a> <code>sk_cross_val_score</code></h3>
<p><code>sk_cross_val_score</code> — score of <code>sk cross val</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_cross_val_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-davies-bouldin">
<h3><a class="doc-anchor" href="#doc-sk-davies-bouldin">#</a> <code>sk_davies_bouldin</code></h3>
<p><code>sk_davies_bouldin</code> — operation <code>sk davies bouldin</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_davies_bouldin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-dbscan-fit">
<h3><a class="doc-anchor" href="#doc-sk-dbscan-fit">#</a> <code>sk_dbscan_fit</code></h3>
<p><code>sk_dbscan_fit</code> — operation <code>sk dbscan fit</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_dbscan_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-decision-tree-split">
<h3><a class="doc-anchor" href="#doc-sk-decision-tree-split">#</a> <code>sk_decision_tree_split</code></h3>
<p><code>sk_decision_tree_split</code> — operation <code>sk decision tree split</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_decision_tree_split $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-doc2vec-train">
<h3><a class="doc-anchor" href="#doc-sk-doc2vec-train">#</a> <code>sk_doc2vec_train</code></h3>
<p><code>sk_doc2vec_train</code> — operation <code>sk doc2vec train</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_doc2vec_train $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-gbt-fit">
<h3><a class="doc-anchor" href="#doc-sk-gbt-fit">#</a> <code>sk_gbt_fit</code></h3>
<p><code>sk_gbt_fit</code> — operation <code>sk gbt fit</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_gbt_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-grid-search">
<h3><a class="doc-anchor" href="#doc-sk-grid-search">#</a> <code>sk_grid_search</code></h3>
<p><code>sk_grid_search</code> — operation <code>sk grid search</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_grid_search $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-isolation-forest-fit">
<h3><a class="doc-anchor" href="#doc-sk-isolation-forest-fit">#</a> <code>sk_isolation_forest_fit</code></h3>
<p><code>sk_isolation_forest_fit</code> — operation <code>sk isolation forest fit</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_isolation_forest_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-kfold-split">
<h3><a class="doc-anchor" href="#doc-sk-kfold-split">#</a> <code>sk_kfold_split</code></h3>
<p><code>sk_kfold_split</code> — operation <code>sk kfold split</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_kfold_split $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-kmeans-fit">
<h3><a class="doc-anchor" href="#doc-sk-kmeans-fit">#</a> <code>sk_kmeans_fit</code></h3>
<p><code>sk_kmeans_fit</code> — operation <code>sk kmeans fit</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_kmeans_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-knn-predict">
<h3><a class="doc-anchor" href="#doc-sk-knn-predict">#</a> <code>sk_knn_predict</code></h3>
<p><code>sk_knn_predict</code> — operation <code>sk knn predict</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_knn_predict $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-label-encode">
<h3><a class="doc-anchor" href="#doc-sk-label-encode">#</a> <code>sk_label_encode</code></h3>
<p><code>sk_label_encode</code> — encode of <code>sk label</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_label_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-lda-topic">
<h3><a class="doc-anchor" href="#doc-sk-lda-topic">#</a> <code>sk_lda_topic</code></h3>
<p><code>sk_lda_topic</code> — operation <code>sk lda topic</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_lda_topic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-lightgbm-fit">
<h3><a class="doc-anchor" href="#doc-sk-lightgbm-fit">#</a> <code>sk_lightgbm_fit</code></h3>
<p><code>sk_lightgbm_fit</code> — operation <code>sk lightgbm fit</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_lightgbm_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-lof-fit">
<h3><a class="doc-anchor" href="#doc-sk-lof-fit">#</a> <code>sk_lof_fit</code></h3>
<p><code>sk_lof_fit</code> — operation <code>sk lof fit</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_lof_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-logistic-fit">
<h3><a class="doc-anchor" href="#doc-sk-logistic-fit">#</a> <code>sk_logistic_fit</code></h3>
<p><code>sk_logistic_fit</code> — operation <code>sk logistic fit</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_logistic_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-logistic-predict">
<h3><a class="doc-anchor" href="#doc-sk-logistic-predict">#</a> <code>sk_logistic_predict</code></h3>
<p><code>sk_logistic_predict</code> — operation <code>sk logistic predict</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_logistic_predict $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-min-max-scaler">
<h3><a class="doc-anchor" href="#doc-sk-min-max-scaler">#</a> <code>sk_min_max_scaler</code></h3>
<p><code>sk_min_max_scaler</code> — operation <code>sk min max scaler</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_min_max_scaler $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-mutual-info">
<h3><a class="doc-anchor" href="#doc-sk-mutual-info">#</a> <code>sk_mutual_info</code></h3>
<p><code>sk_mutual_info</code> — operation <code>sk mutual info</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_mutual_info $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-naive-bayes-predict">
<h3><a class="doc-anchor" href="#doc-sk-naive-bayes-predict">#</a> <code>sk_naive_bayes_predict</code></h3>
<p><code>sk_naive_bayes_predict</code> — operation <code>sk naive bayes predict</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_naive_bayes_predict $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-nmf-topic">
<h3><a class="doc-anchor" href="#doc-sk-nmf-topic">#</a> <code>sk_nmf_topic</code></h3>
<p><code>sk_nmf_topic</code> — operation <code>sk nmf topic</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_nmf_topic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-one-hot">
<h3><a class="doc-anchor" href="#doc-sk-one-hot">#</a> <code>sk_one_hot</code></h3>
<p><code>sk_one_hot</code> — operation <code>sk one hot</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_one_hot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-ordinal-encode">
<h3><a class="doc-anchor" href="#doc-sk-ordinal-encode">#</a> <code>sk_ordinal_encode</code></h3>
<p><code>sk_ordinal_encode</code> — encode of <code>sk ordinal</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_ordinal_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-pca-fit">
<h3><a class="doc-anchor" href="#doc-sk-pca-fit">#</a> <code>sk_pca_fit</code></h3>
<p><code>sk_pca_fit</code> — operation <code>sk pca fit</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_pca_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-pipeline-fit">
<h3><a class="doc-anchor" href="#doc-sk-pipeline-fit">#</a> <code>sk_pipeline_fit</code></h3>
<p><code>sk_pipeline_fit</code> — operation <code>sk pipeline fit</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_pipeline_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-power-transform">
<h3><a class="doc-anchor" href="#doc-sk-power-transform">#</a> <code>sk_power_transform</code></h3>
<p><code>sk_power_transform</code> — transform of <code>sk power</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_power_transform $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-quantile-transform">
<h3><a class="doc-anchor" href="#doc-sk-quantile-transform">#</a> <code>sk_quantile_transform</code></h3>
<p><code>sk_quantile_transform</code> — transform of <code>sk quantile</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_quantile_transform $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-random-forest-fit">
<h3><a class="doc-anchor" href="#doc-sk-random-forest-fit">#</a> <code>sk_random_forest_fit</code></h3>
<p><code>sk_random_forest_fit</code> — operation <code>sk random forest fit</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_random_forest_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-random-search">
<h3><a class="doc-anchor" href="#doc-sk-random-search">#</a> <code>sk_random_search</code></h3>
<p><code>sk_random_search</code> — operation <code>sk random search</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_random_search $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-robust-scaler">
<h3><a class="doc-anchor" href="#doc-sk-robust-scaler">#</a> <code>sk_robust_scaler</code></h3>
<p><code>sk_robust_scaler</code> — operation <code>sk robust scaler</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_robust_scaler $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-silhouette">
<h3><a class="doc-anchor" href="#doc-sk-silhouette">#</a> <code>sk_silhouette</code></h3>
<p><code>sk_silhouette</code> — operation <code>sk silhouette</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_silhouette $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-standard-scaler">
<h3><a class="doc-anchor" href="#doc-sk-standard-scaler">#</a> <code>sk_standard_scaler</code></h3>
<p><code>sk_standard_scaler</code> — operation <code>sk standard scaler</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_standard_scaler $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-stratified-kfold">
<h3><a class="doc-anchor" href="#doc-sk-stratified-kfold">#</a> <code>sk_stratified_kfold</code></h3>
<p><code>sk_stratified_kfold</code> — operation <code>sk stratified kfold</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_stratified_kfold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-svm-fit">
<h3><a class="doc-anchor" href="#doc-sk-svm-fit">#</a> <code>sk_svm_fit</code></h3>
<p><code>sk_svm_fit</code> — operation <code>sk svm fit</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_svm_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-tfidf">
<h3><a class="doc-anchor" href="#doc-sk-tfidf">#</a> <code>sk_tfidf</code></h3>
<p><code>sk_tfidf</code> — operation <code>sk tfidf</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_tfidf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-tsne-fit">
<h3><a class="doc-anchor" href="#doc-sk-tsne-fit">#</a> <code>sk_tsne_fit</code></h3>
<p><code>sk_tsne_fit</code> — operation <code>sk tsne fit</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_tsne_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-umap-fit">
<h3><a class="doc-anchor" href="#doc-sk-umap-fit">#</a> <code>sk_umap_fit</code></h3>
<p><code>sk_umap_fit</code> — operation <code>sk umap fit</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_umap_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-word2vec-train">
<h3><a class="doc-anchor" href="#doc-sk-word2vec-train">#</a> <code>sk_word2vec_train</code></h3>
<p><code>sk_word2vec_train</code> — operation <code>sk word2vec train</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_word2vec_train $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sk-xgb-fit">
<h3><a class="doc-anchor" href="#doc-sk-xgb-fit">#</a> <code>sk_xgb_fit</code></h3>
<p><code>sk_xgb_fit</code> — operation <code>sk xgb fit</code>. Category: *sklearn*.</p>
<pre><code class="lang-perl">p sk_xgb_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-skew">
<h3><a class="doc-anchor" href="#doc-skew">#</a> <code>skew</code></h3>
<p><code>skew</code> — operation <code>skew</code>. Alias for <code>skewness</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p skew $x
</code></pre>
</article>
<article class="doc-entry" id="doc-skewness">
<h3><a class="doc-anchor" href="#doc-skewness">#</a> <code>skewness</code></h3>
<p><code>skewness</code> — operation <code>skewness</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p skewness $x
</code></pre>
</article>
<article class="doc-entry" id="doc-skill-score">
<h3><a class="doc-anchor" href="#doc-skill-score">#</a> <code>skill_score</code></h3>
<p><code>skill_score</code> — score of <code>skill</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p skill_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-skin-depth">
<h3><a class="doc-anchor" href="#doc-skin-depth">#</a> <code>skin_depth</code></h3>
<p><code>skin_depth</code> — operation <code>skin depth</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p skin_depth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-skip-assert">
<h3><a class="doc-anchor" href="#doc-skip-assert">#</a> <code>skip_assert</code></h3>
<p><code>skip_assert</code> — operation <code>skip assert</code>. Alias for <code>test_skip</code>. Category: *testing framework*.</p>
<pre><code class="lang-perl">p skip_assert $x
</code></pre>
</article>
<article class="doc-entry" id="doc-skip-test">
<h3><a class="doc-anchor" href="#doc-skip-test">#</a> <code>skip_test</code></h3>
<p><code>skip_test</code> — statistical test of <code>skip</code>. Alias for <code>test_skip</code>. Category: *testing framework*.</p>
<pre><code class="lang-perl">p skip_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-skip-while">
<h3><a class="doc-anchor" href="#doc-skip-while">#</a> <code>skip_while</code></h3>
<p><code>skip_while { COND } LIST</code> — skip leading elements while the predicate is true (alias for <code>drop_while</code>).</p>
<p>Behavior is identical to <code>drop_while</code>: once the predicate returns false, that element and all subsequent elements are emitted. The <code>skip_while</code> name is provided for users coming from Rust or Kotlin where this is the conventional name. Both compile to the same streaming operation internally.</p>
<pre><code class="lang-perl">1:10 |> skip_while { _ < 5 } |> e p # 5 6 7 8 9 10
@sorted |> skip_while { _ le "m" } |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-sla">
<h3><a class="doc-anchor" href="#doc-sla">#</a> <code>sla</code></h3>
<p><code>sla</code> — operation <code>sla</code>. Alias for <code>slice_arr</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p sla $x
</code></pre>
</article>
<article class="doc-entry" id="doc-slca">
<h3><a class="doc-anchor" href="#doc-slca">#</a> <code>slca</code></h3>
<p><code>slca</code> — operation <code>slca</code>. Alias for <code>slice_after</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p slca $x
</code></pre>
</article>
<article class="doc-entry" id="doc-slcb">
<h3><a class="doc-anchor" href="#doc-slcb">#</a> <code>slcb</code></h3>
<p><code>slcb</code> — operation <code>slcb</code>. Alias for <code>slice_before</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p slcb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-slcw">
<h3><a class="doc-anchor" href="#doc-slcw">#</a> <code>slcw</code></h3>
<p><code>slcw</code> — operation <code>slcw</code>. Alias for <code>slice_when</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p slcw $x
</code></pre>
</article>
<article class="doc-entry" id="doc-slic-superpixels">
<h3><a class="doc-anchor" href="#doc-slic-superpixels">#</a> <code>slic_superpixels</code></h3>
<p><code>slic_superpixels</code> — operation <code>slic superpixels</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p slic_superpixels $x
</code></pre>
</article>
<article class="doc-entry" id="doc-slice-after">
<h3><a class="doc-anchor" href="#doc-slice-after">#</a> <code>slice_after</code></h3>
<p><code>slice_after</code> — operation <code>slice after</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p slice_after $x
</code></pre>
</article>
<article class="doc-entry" id="doc-slice-arr">
<h3><a class="doc-anchor" href="#doc-slice-arr">#</a> <code>slice_arr</code></h3>
<p><code>slice_arr</code> — operation <code>slice arr</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p slice_arr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-slice-before">
<h3><a class="doc-anchor" href="#doc-slice-before">#</a> <code>slice_before</code></h3>
<p><code>slice_before</code> — operation <code>slice before</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p slice_before $x
</code></pre>
</article>
<article class="doc-entry" id="doc-slice-when">
<h3><a class="doc-anchor" href="#doc-slice-when">#</a> <code>slice_when</code></h3>
<p><code>slice_when</code> — operation <code>slice when</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p slice_when $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sliced-wasserstein">
<h3><a class="doc-anchor" href="#doc-sliced-wasserstein">#</a> <code>sliced_wasserstein</code></h3>
<p><code>sliced_wasserstein</code> — operation <code>sliced wasserstein</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p sliced_wasserstein $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sliding-average">
<h3><a class="doc-anchor" href="#doc-sliding-average">#</a> <code>sliding_average</code></h3>
<p><code>sliding_average</code> — operation <code>sliding average</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p sliding_average $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sliding-dot-product">
<h3><a class="doc-anchor" href="#doc-sliding-dot-product">#</a> <code>sliding_dot_product</code></h3>
<p><code>sliding_dot_product(signal, kernel) → array</code> — valid-mode 1D correlation (no padding).</p>
</article>
<article class="doc-entry" id="doc-sliding-max">
<h3><a class="doc-anchor" href="#doc-sliding-max">#</a> <code>sliding_max</code></h3>
<p><code>sliding_max</code> — maximum of <code>sliding</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p sliding_max $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sliding-min">
<h3><a class="doc-anchor" href="#doc-sliding-min">#</a> <code>sliding_min</code></h3>
<p><code>sliding_min</code> — minimum of <code>sliding</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p sliding_min $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sliding-pairs">
<h3><a class="doc-anchor" href="#doc-sliding-pairs">#</a> <code>sliding_pairs</code></h3>
<p><code>sliding_pairs</code> — operation <code>sliding pairs</code>. Category: *collection more*.</p>
<pre><code class="lang-perl">p sliding_pairs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sliding-sum">
<h3><a class="doc-anchor" href="#doc-sliding-sum">#</a> <code>sliding_sum</code></h3>
<p><code>sliding_sum</code> — sum of <code>sliding</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p sliding_sum @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-sliding-window">
<h3><a class="doc-anchor" href="#doc-sliding-window">#</a> <code>sliding_window</code></h3>
<p><code>sliding_window</code> — operation <code>sliding window</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p sliding_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-slope">
<h3><a class="doc-anchor" href="#doc-slope">#</a> <code>slope</code></h3>
<p><code>slope</code> — operation <code>slope</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p slope $x
</code></pre>
</article>
<article class="doc-entry" id="doc-slug">
<h3><a class="doc-anchor" href="#doc-slug">#</a> <code>slug</code></h3>
<p><code>slug</code> — operation <code>slug</code>. Alias for <code>slugify</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p slug $x
</code></pre>
</article>
<article class="doc-entry" id="doc-slugify">
<h3><a class="doc-anchor" href="#doc-slugify">#</a> <code>slugify</code></h3>
<p><code>slugify</code> — operation <code>slugify</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p slugify $x
</code></pre>
</article>
<article class="doc-entry" id="doc-slutsky-decompose">
<h3><a class="doc-anchor" href="#doc-slutsky-decompose">#</a> <code>slutsky_decompose</code></h3>
<p><code>slutsky_decompose</code> — operation <code>slutsky decompose</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p slutsky_decompose $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sma">
<h3><a class="doc-anchor" href="#doc-sma">#</a> <code>sma</code></h3>
<p><code>sma(prices, period=10) → array</code> — simple moving average over a price series. Output length is <code>len(prices) - period + 1</code>; each value is the arithmetic mean of the trailing <code>period</code> window.</p>
<pre><code class="lang-perl">p sma([10,11,12,13,14], 3) # [11.0, 12.0, 13.0]
</code></pre>
</article>
<article class="doc-entry" id="doc-smap">
<h3><a class="doc-anchor" href="#doc-smap">#</a> <code>smap</code></h3>
<p><code>smap</code> — operation <code>smap</code>. Alias for <code>starmap</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p smap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-smembers">
<h3><a class="doc-anchor" href="#doc-smembers">#</a> <code>smembers</code></h3>
<p><code>smembers</code> — operation <code>smembers</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p smembers $x
</code></pre>
</article>
<article class="doc-entry" id="doc-smith-normal-2x2-step">
<h3><a class="doc-anchor" href="#doc-smith-normal-2x2-step">#</a> <code>smith_normal_2x2_step</code></h3>
<p><code>smith_normal_2x2_step</code> — single-step update of <code>smith normal 2x2</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p smith_normal_2x2_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-smith-predictor-step">
<h3><a class="doc-anchor" href="#doc-smith-predictor-step">#</a> <code>smith_predictor_step</code></h3>
<p><code>smith_predictor_step</code> — single-step update of <code>smith predictor</code>. Category: *robotics & control*.</p>
<pre><code class="lang-perl">p smith_predictor_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-smith-q">
<h3><a class="doc-anchor" href="#doc-smith-q">#</a> <code>smith_q</code></h3>
<p><code>smith_q</code> — operation <code>smith q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p smith_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-smith-waterman-score">
<h3><a class="doc-anchor" href="#doc-smith-waterman-score">#</a> <code>smith_waterman_score</code></h3>
<p><code>smith_waterman_score</code> — score of <code>smith waterman</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p smith_waterman_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-smmap">
<h3><a class="doc-anchor" href="#doc-smmap">#</a> <code>smmap</code></h3>
<p><code>smmap</code> — operation <code>smmap</code>. Alias for <code>stress_mmap</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p smmap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-smoothstep">
<h3><a class="doc-anchor" href="#doc-smoothstep">#</a> <code>smoothstep</code></h3>
<p><code>smoothstep($edge0, $edge1, $x)</code> — smooth Hermite interpolation. Returns 0 if x ≤ edge0, 1 if x ≥ edge1, otherwise smooth S-curve. Great for animations.</p>
<pre><code class="lang-perl">p smoothstep(0, 1, 0.5) # 0.5 (but with smooth acceleration/deceleration)
p smoothstep(10, 20, 15) # 0.5
</code></pre>
</article>
<article class="doc-entry" id="doc-smst">
<h3><a class="doc-anchor" href="#doc-smst">#</a> <code>smst</code></h3>
<p><code>smst</code> — operation <code>smst</code>. Alias for <code>smoothstep</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p smst $x
</code></pre>
</article>
<article class="doc-entry" id="doc-smt-qf-lia-solve-step">
<h3><a class="doc-anchor" href="#doc-smt-qf-lia-solve-step">#</a> <code>smt_qf_lia_solve_step</code></h3>
<p><code>smt_qf_lia_solve_step</code> — single-step update of <code>smt qf lia solve</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p smt_qf_lia_solve_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-smt-qf-uf-combine">
<h3><a class="doc-anchor" href="#doc-smt-qf-uf-combine">#</a> <code>smt_qf_uf_combine</code></h3>
<p><code>smt_qf_uf_combine</code> — operation <code>smt qf uf combine</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p smt_qf_uf_combine $x
</code></pre>
</article>
<article class="doc-entry" id="doc-snake-to-camel">
<h3><a class="doc-anchor" href="#doc-snake-to-camel">#</a> <code>snake_to_camel</code></h3>
<p><code>snake_to_camel</code> — convert from <code>snake</code> to <code>camel</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p snake_to_camel $value
</code></pre>
</article>
<article class="doc-entry" id="doc-snappy-encode">
<h3><a class="doc-anchor" href="#doc-snappy-encode">#</a> <code>snappy_encode</code></h3>
<p><code>snappy_encode</code> — encode of <code>snappy</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p snappy_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-snd">
<h3><a class="doc-anchor" href="#doc-snd">#</a> <code>snd</code></h3>
<p><code>snd</code> — operation <code>snd</code>. Alias for <code>second</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p snd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-snell">
<h3><a class="doc-anchor" href="#doc-snell">#</a> <code>snell</code></h3>
<p><code>snells_law($n1, $n2, $theta1)</code> (alias <code>snell</code>) — refraction angle using Snell's law. Angles in degrees. Returns undef for total internal reflection.</p>
<pre><code class="lang-perl">p snell(1, 1.5, 30) # ~19.5° (air to glass)
p snell(1.5, 1, 45) # undef (total internal reflection)
</code></pre>
</article>
<article class="doc-entry" id="doc-snell-theta2">
<h3><a class="doc-anchor" href="#doc-snell-theta2">#</a> <code>snell_theta2</code></h3>
<p><code>snell_theta2</code> — operation <code>snell theta2</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p snell_theta2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-snowball-stem-english">
<h3><a class="doc-anchor" href="#doc-snowball-stem-english">#</a> <code>snowball_stem_english</code></h3>
<p><code>snowball_stem_english</code> — operation <code>snowball stem english</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p snowball_stem_english $x
</code></pre>
</article>
<article class="doc-entry" id="doc-snowball-stem-french">
<h3><a class="doc-anchor" href="#doc-snowball-stem-french">#</a> <code>snowball_stem_french</code></h3>
<p><code>snowball_stem_french</code> — operation <code>snowball stem french</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p snowball_stem_french $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sobel-diagonal-kernel">
<h3><a class="doc-anchor" href="#doc-sobel-diagonal-kernel">#</a> <code>sobel_diagonal_kernel</code></h3>
<p><code>sobel_diagonal_kernel</code> — convolution kernel of <code>sobel diagonal</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p sobel_diagonal_kernel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sobel-kernel-value">
<h3><a class="doc-anchor" href="#doc-sobel-kernel-value">#</a> <code>sobel_kernel_value</code></h3>
<p><code>sobel_kernel_value</code> — value of <code>sobel kernel</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p sobel_kernel_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sobel-magnitude">
<h3><a class="doc-anchor" href="#doc-sobel-magnitude">#</a> <code>sobel_magnitude</code></h3>
<p><code>sobel_magnitude(image) → matrix</code> — alias for <code>gradient_magnitude_2d</code>.</p>
</article>
<article class="doc-entry" id="doc-sobel-x-kernel">
<h3><a class="doc-anchor" href="#doc-sobel-x-kernel">#</a> <code>sobel_x_kernel</code></h3>
<p><code>sobel_x_kernel() → matrix</code> — 3×3 Sobel horizontal-gradient kernel.</p>
</article>
<article class="doc-entry" id="doc-sobel-y-kernel">
<h3><a class="doc-anchor" href="#doc-sobel-y-kernel">#</a> <code>sobel_y_kernel</code></h3>
<p><code>sobel_y_kernel() → matrix</code> — 3×3 Sobel vertical-gradient kernel.</p>
</article>
<article class="doc-entry" id="doc-soc-estimate-coulomb">
<h3><a class="doc-anchor" href="#doc-soc-estimate-coulomb">#</a> <code>soc_estimate_coulomb</code></h3>
<p><code>soc_estimate_coulomb</code> — operation <code>soc estimate coulomb</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p soc_estimate_coulomb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-social-welfare-nash">
<h3><a class="doc-anchor" href="#doc-social-welfare-nash">#</a> <code>social_welfare_nash</code></h3>
<p><code>social_welfare_nash</code> — operation <code>social welfare nash</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p social_welfare_nash $x
</code></pre>
</article>
<article class="doc-entry" id="doc-social-welfare-rawls">
<h3><a class="doc-anchor" href="#doc-social-welfare-rawls">#</a> <code>social_welfare_rawls</code></h3>
<p><code>social_welfare_rawls</code> — operation <code>social welfare rawls</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p social_welfare_rawls $x
</code></pre>
</article>
<article class="doc-entry" id="doc-social-welfare-sum">
<h3><a class="doc-anchor" href="#doc-social-welfare-sum">#</a> <code>social_welfare_sum</code></h3>
<p><code>social_welfare_sum</code> — sum of <code>social welfare</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p social_welfare_sum @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-social-welfare-utilitarian">
<h3><a class="doc-anchor" href="#doc-social-welfare-utilitarian">#</a> <code>social_welfare_utilitarian</code></h3>
<p><code>social_welfare_utilitarian</code> — operation <code>social welfare utilitarian</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p social_welfare_utilitarian $x
</code></pre>
</article>
<article class="doc-entry" id="doc-socketpair">
<h3><a class="doc-anchor" href="#doc-socketpair">#</a> <code>socketpair</code></h3>
<p><code>socketpair</code> — operation <code>socketpair</code>. Category: *socket*.</p>
<pre><code class="lang-perl">p socketpair $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sockets">
<h3><a class="doc-anchor" href="#doc-sockets">#</a> <code>sockets</code></h3>
<p><code>sockets</code> — operation <code>sockets</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p sockets $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sod">
<h3><a class="doc-anchor" href="#doc-sod">#</a> <code>sod</code></h3>
<p><code>sod</code> — operation <code>sod</code>. Alias for <code>start_of_day</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p sod $x
</code></pre>
</article>
<article class="doc-entry" id="doc-softmax">
<h3><a class="doc-anchor" href="#doc-softmax">#</a> <code>softmax</code></h3>
<p><code>softmax(xs) → array</code> — <code>exp(x) / Σ exp(x)</code>. Returns probabilities summing to 1.</p>
</article>
<article class="doc-entry" id="doc-softmax-choose">
<h3><a class="doc-anchor" href="#doc-softmax-choose">#</a> <code>softmax_choose</code></h3>
<p><code>softmax_choose(logits, temperature=1, seed=0) → int</code> — sample from softmax over logits.</p>
</article>
<article class="doc-entry" id="doc-softplus">
<h3><a class="doc-anchor" href="#doc-softplus">#</a> <code>softplus</code></h3>
<p><code>softplus</code> applies the Softplus activation: ln(1 + e^x). Smooth approximation to ReLU.</p>
<pre><code class="lang-perl">p softplus(0) # 0.6931 (ln 2)
p softplus(10) # ≈ 10
</code></pre>
</article>
<article class="doc-entry" id="doc-softsign">
<h3><a class="doc-anchor" href="#doc-softsign">#</a> <code>softsign</code></h3>
<p><code>softsign</code> — operation <code>softsign</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p softsign $x
</code></pre>
</article>
<article class="doc-entry" id="doc-soh">
<h3><a class="doc-anchor" href="#doc-soh">#</a> <code>soh</code></h3>
<p><code>soh</code> — operation <code>soh</code>. Alias for <code>start_of_hour</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p soh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-soh-capacity-fade">
<h3><a class="doc-anchor" href="#doc-soh-capacity-fade">#</a> <code>soh_capacity_fade</code></h3>
<p><code>soh_capacity_fade</code> — operation <code>soh capacity fade</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p soh_capacity_fade $x
</code></pre>
</article>
<article class="doc-entry" id="doc-soi-oscillation-index">
<h3><a class="doc-anchor" href="#doc-soi-oscillation-index">#</a> <code>soi_oscillation_index</code></h3>
<p><code>soi_oscillation_index</code> — index of <code>soi oscillation</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p soi_oscillation_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sol">
<h3><a class="doc-anchor" href="#doc-sol">#</a> <code>sol</code></h3>
<p><code>sol</code> — operation <code>sol</code>. Category: *constants*.</p>
<pre><code class="lang-perl">p sol $x
</code></pre>
</article>
<article class="doc-entry" id="doc-solar-constant">
<h3><a class="doc-anchor" href="#doc-solar-constant">#</a> <code>solar_constant</code></h3>
<p><code>solar_constant</code> — operation <code>solar constant</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p solar_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-solar-constant-at-distance">
<h3><a class="doc-anchor" href="#doc-solar-constant-at-distance">#</a> <code>solar_constant_at_distance</code></h3>
<p><code>solar_constant_at_distance</code> — distance / dissimilarity metric of <code>solar constant at</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p solar_constant_at_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-solar-cycle-phase">
<h3><a class="doc-anchor" href="#doc-solar-cycle-phase">#</a> <code>solar_cycle_phase</code></h3>
<p><code>solar_cycle_phase</code> — operation <code>solar cycle phase</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p solar_cycle_phase $x
</code></pre>
</article>
<article class="doc-entry" id="doc-solar-declination">
<h3><a class="doc-anchor" href="#doc-solar-declination">#</a> <code>solar_declination</code></h3>
<p><code>solar_declination</code> — operation <code>solar declination</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p solar_declination $x
</code></pre>
</article>
<article class="doc-entry" id="doc-solar-luminosity-to-w">
<h3><a class="doc-anchor" href="#doc-solar-luminosity-to-w">#</a> <code>solar_luminosity_to_w</code></h3>
<p><code>solar_luminosity_to_w</code> — convert from <code>solar luminosity</code> to <code>w</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p solar_luminosity_to_w $value
</code></pre>
</article>
<article class="doc-entry" id="doc-solar-mass-to-kg">
<h3><a class="doc-anchor" href="#doc-solar-mass-to-kg">#</a> <code>solar_mass_to_kg</code></h3>
<p><code>solar_mass_to_kg</code> — convert from <code>solar mass</code> to <code>kg</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p solar_mass_to_kg $value
</code></pre>
</article>
<article class="doc-entry" id="doc-solar-noon-unix">
<h3><a class="doc-anchor" href="#doc-solar-noon-unix">#</a> <code>solar_noon_unix</code></h3>
<p><code>solar_noon_unix(longitude_deg, unix) → int</code> — unix timestamp of apparent solar noon at given longitude for that date. Applies the equation-of-time correction (<code>9.873·sin(2B) − 7.655·sin(B)</code> minutes, B from day-of-year).</p>
<pre><code class="lang-perl">p solar_noon_unix(0, time()) # ~12:00 UTC for Greenwich
</code></pre>
</article>
<article class="doc-entry" id="doc-solar-zenith-angle">
<h3><a class="doc-anchor" href="#doc-solar-zenith-angle">#</a> <code>solar_zenith_angle</code></h3>
<p><code>solar_zenith_angle</code> — operation <code>solar zenith angle</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p solar_zenith_angle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sole">
<h3><a class="doc-anchor" href="#doc-sole">#</a> <code>sole</code></h3>
<p><code>sole</code> — operation <code>sole</code>. Category: *ruby enumerable extras*.</p>
<pre><code class="lang-perl">p sole $x
</code></pre>
</article>
<article class="doc-entry" id="doc-solid-electrolyte-capacity">
<h3><a class="doc-anchor" href="#doc-solid-electrolyte-capacity">#</a> <code>solid_electrolyte_capacity</code></h3>
<p><code>solid_electrolyte_capacity</code> — operation <code>solid electrolyte capacity</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p solid_electrolyte_capacity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-solstice-winter">
<h3><a class="doc-anchor" href="#doc-solstice-winter">#</a> <code>solstice_winter</code></h3>
<p><code>solstice_winter</code> — operation <code>solstice winter</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p solstice_winter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-solution-resistance-estimate">
<h3><a class="doc-anchor" href="#doc-solution-resistance-estimate">#</a> <code>solution_resistance_estimate</code></h3>
<p><code>solution_resistance_estimate</code> — operation <code>solution resistance estimate</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p solution_resistance_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-solvable-length-upper">
<h3><a class="doc-anchor" href="#doc-solvable-length-upper">#</a> <code>solvable_length_upper</code></h3>
<p><code>solvable_length_upper</code> — operation <code>solvable length upper</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p solvable_length_upper $x
</code></pre>
</article>
<article class="doc-entry" id="doc-solve-ivp-step">
<h3><a class="doc-anchor" href="#doc-solve-ivp-step">#</a> <code>solve_ivp_step</code></h3>
<p><code>solve_ivp_step</code> — single-step update of <code>solve ivp</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p solve_ivp_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-som">
<h3><a class="doc-anchor" href="#doc-som">#</a> <code>som</code></h3>
<p><code>som</code> — operation <code>som</code>. Alias for <code>start_of_minute</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p som $x
</code></pre>
</article>
<article class="doc-entry" id="doc-some">
<h3><a class="doc-anchor" href="#doc-some">#</a> <code>some</code></h3>
<p><code>some</code> — operation <code>some</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p some $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sorensen-dice">
<h3><a class="doc-anchor" href="#doc-sorensen-dice">#</a> <code>sorensen_dice</code></h3>
<p><code>sorensen_dice</code> — operation <code>sorensen dice</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p sorensen_dice $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sort-by">
<h3><a class="doc-anchor" href="#doc-sort-by">#</a> <code>sort_by</code></h3>
<p><code>sort_by</code> — operation <code>sort by</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p sort_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sort-by-cached-key">
<h3><a class="doc-anchor" href="#doc-sort-by-cached-key">#</a> <code>sort_by_cached_key</code></h3>
<p><code>sort_by_cached_key</code> — operation <code>sort by cached key</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p sort_by_cached_key $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sort-on">
<h3><a class="doc-anchor" href="#doc-sort-on">#</a> <code>sort_on</code></h3>
<p><code>sort_on</code> — operation <code>sort on</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p sort_on $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sort-words">
<h3><a class="doc-anchor" href="#doc-sort-words">#</a> <code>sort_words</code></h3>
<p><code>sort_words</code> — operation <code>sort words</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p sort_words $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sorted">
<h3><a class="doc-anchor" href="#doc-sorted">#</a> <code>sorted</code></h3>
<p><code>sorted</code> — operation <code>sorted</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p sorted $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sorted-by-length">
<h3><a class="doc-anchor" href="#doc-sorted-by-length">#</a> <code>sorted_by_length</code></h3>
<p><code>sorted_by_length</code> — operation <code>sorted by length</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p sorted_by_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sorted-desc">
<h3><a class="doc-anchor" href="#doc-sorted-desc">#</a> <code>sorted_desc</code></h3>
<p><code>sorted_desc</code> — operation <code>sorted desc</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p sorted_desc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sorted-nums">
<h3><a class="doc-anchor" href="#doc-sorted-nums">#</a> <code>sorted_nums</code></h3>
<p><code>sorted_nums</code> — operation <code>sorted nums</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p sorted_nums $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sortino">
<h3><a class="doc-anchor" href="#doc-sortino">#</a> <code>sortino</code></h3>
<p><code>sortino_ratio(\@returns, $target)</code> (alias <code>sortino</code>) — computes the Sortino ratio, similar to Sharpe but only penalizes downside volatility. Better for asymmetric return distributions.</p>
<pre><code class="lang-perl">my @returns = (0.05, -0.02, 0.08, -0.01)
p sortino(\@returns, 0.0) # penalizes only negative returns
</code></pre>
</article>
<article class="doc-entry" id="doc-sortw">
<h3><a class="doc-anchor" href="#doc-sortw">#</a> <code>sortw</code></h3>
<p><code>sortw</code> — operation <code>sortw</code>. Alias for <code>sort_words</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p sortw $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sos2tf-step">
<h3><a class="doc-anchor" href="#doc-sos2tf-step">#</a> <code>sos2tf_step</code></h3>
<p><code>sos2tf_step</code> — single-step update of <code>sos2tf</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p sos2tf_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sos-constraint-check">
<h3><a class="doc-anchor" href="#doc-sos-constraint-check">#</a> <code>sos_constraint_check</code></h3>
<p><code>sos_constraint_check</code> — operation <code>sos constraint check</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p sos_constraint_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sosfilt-step">
<h3><a class="doc-anchor" href="#doc-sosfilt-step">#</a> <code>sosfilt_step</code></h3>
<p><code>sosfilt_step</code> — single-step update of <code>sosfilt</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p sosfilt_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sound-db">
<h3><a class="doc-anchor" href="#doc-sound-db">#</a> <code>sound_db</code></h3>
<p><code>sound_db</code> — operation <code>sound db</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p sound_db $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sound-gas">
<h3><a class="doc-anchor" href="#doc-sound-gas">#</a> <code>sound_gas</code></h3>
<p><code>sound_gas</code> — operation <code>sound gas</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p sound_gas $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sound-horizon-recomb">
<h3><a class="doc-anchor" href="#doc-sound-horizon-recomb">#</a> <code>sound_horizon_recomb</code></h3>
<p><code>sound_horizon_recomb</code> — operation <code>sound horizon recomb</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p sound_horizon_recomb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sound-solid">
<h3><a class="doc-anchor" href="#doc-sound-solid">#</a> <code>sound_solid</code></h3>
<p><code>sound_solid</code> — operation <code>sound solid</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p sound_solid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-soundex">
<h3><a class="doc-anchor" href="#doc-soundex">#</a> <code>soundex</code></h3>
<p><code>soundex</code> — operation <code>soundex</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p soundex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-soundex-phonetic">
<h3><a class="doc-anchor" href="#doc-soundex-phonetic">#</a> <code>soundex_phonetic</code></h3>
<p><code>soundex_phonetic</code> — operation <code>soundex phonetic</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p soundex_phonetic $x
</code></pre>
</article>
<article class="doc-entry" id="doc-soundex-v1">
<h3><a class="doc-anchor" href="#doc-soundex-v1">#</a> <code>soundex_v1</code></h3>
<p><code>soundex_v1(name) → string</code> — classic American Soundex (4-char: leading letter + 3 digits).</p>
<pre><code class="lang-perl">p soundex_v1("Robert") # R163
</code></pre>
</article>
<article class="doc-entry" id="doc-soundex-v2">
<h3><a class="doc-anchor" href="#doc-soundex-v2">#</a> <code>soundex_v2</code></h3>
<p><code>soundex_v2(name) → string</code> — Apache Refined Soundex (longer code, no length cap, 9 finer-grained groups: BP, FV, CKS, GJ, QXZ, DT, L, MN, R).</p>
<pre><code class="lang-perl">p soundex_v2("Robert")
</code></pre>
</article>
<article class="doc-entry" id="doc-spaceship">
<h3><a class="doc-anchor" href="#doc-spaceship">#</a> <code>spaceship</code></h3>
<p><code>spaceship</code> — operation <code>spaceship</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p spaceship $x
</code></pre>
</article>
<article class="doc-entry" id="doc-span">
<h3><a class="doc-anchor" href="#doc-span">#</a> <code>span</code></h3>
<p><code>span</code> — operation <code>span</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p span $x
</code></pre>
</article>
<article class="doc-entry" id="doc-span-fn">
<h3><a class="doc-anchor" href="#doc-span-fn">#</a> <code>span_fn</code></h3>
<p><code>span_fn</code> — operation <code>span fn</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p span_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spanf">
<h3><a class="doc-anchor" href="#doc-spanf">#</a> <code>spanf</code></h3>
<p><code>spanf</code> — operation <code>spanf</code>. Alias for <code>span_fn</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p spanf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sparse-csr-build">
<h3><a class="doc-anchor" href="#doc-sparse-csr-build">#</a> <code>sparse_csr_build</code></h3>
<p><code>sparse_csr_build</code> — operation <code>sparse csr build</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p sparse_csr_build $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sparse-csr-mul-vec">
<h3><a class="doc-anchor" href="#doc-sparse-csr-mul-vec">#</a> <code>sparse_csr_mul_vec</code></h3>
<p><code>sparse_csr_mul_vec</code> — operation <code>sparse csr mul vec</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p sparse_csr_mul_vec $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sparse-density">
<h3><a class="doc-anchor" href="#doc-sparse-density">#</a> <code>sparse_density</code></h3>
<p><code>sparse_density</code> — operation <code>sparse density</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p sparse_density $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spat">
<h3><a class="doc-anchor" href="#doc-spat">#</a> <code>spat</code></h3>
<p><code>spat</code> — operation <code>spat</code>. Alias for <code>split_at</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p spat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spbfs">
<h3><a class="doc-anchor" href="#doc-spbfs">#</a> <code>spbfs</code></h3>
<p><code>spbfs</code> — operation <code>spbfs</code>. Alias for <code>shortest_path_bfs</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p spbfs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spearman">
<h3><a class="doc-anchor" href="#doc-spearman">#</a> <code>spearman</code></h3>
<p><code>spearman_correlation(\@x, \@y)</code> (alias <code>spearman</code>) — computes Spearman's rank correlation coefficient between two datasets. Measures monotonic relationships, robust to outliers. Returns a value from -1 to 1.</p>
<pre><code class="lang-perl">my @x = (1, 2, 3, 4, 5)
my @y = (5, 6, 7, 8, 7)
p spearman(\@x, \@y) # high positive correlation
</code></pre>
</article>
<article class="doc-entry" id="doc-spearmanr">
<h3><a class="doc-anchor" href="#doc-spearmanr">#</a> <code>spearmanr</code></h3>
<p><code>spearmanr</code> — operation <code>spearmanr</code>. Category: *r / scipy distributions and tests*.</p>
<pre><code class="lang-perl">p spearmanr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-species-area">
<h3><a class="doc-anchor" href="#doc-species-area">#</a> <code>species_area</code></h3>
<p><code>species_area</code> — operation <code>species area</code>. Category: *biology / ecology*.</p>
<pre><code class="lang-perl">p species_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-specific-angular-momentum">
<h3><a class="doc-anchor" href="#doc-specific-angular-momentum">#</a> <code>specific_angular_momentum</code></h3>
<p><code>specific_angular_momentum</code> — operation <code>specific angular momentum</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p specific_angular_momentum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-specific-capacity-active">
<h3><a class="doc-anchor" href="#doc-specific-capacity-active">#</a> <code>specific_capacity_active</code></h3>
<p><code>specific_capacity_active</code> — operation <code>specific capacity active</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p specific_capacity_active $x
</code></pre>
</article>
<article class="doc-entry" id="doc-specific-gravity-water">
<h3><a class="doc-anchor" href="#doc-specific-gravity-water">#</a> <code>specific_gravity_water</code></h3>
<p><code>specific_gravity_water</code> — operation <code>specific gravity water</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p specific_gravity_water $x
</code></pre>
</article>
<article class="doc-entry" id="doc-specific-heat-const-v">
<h3><a class="doc-anchor" href="#doc-specific-heat-const-v">#</a> <code>specific_heat_const_v</code></h3>
<p><code>specific_heat_const_v</code> — operation <code>specific heat const v</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p specific_heat_const_v $x
</code></pre>
</article>
<article class="doc-entry" id="doc-specific-orbital-energy">
<h3><a class="doc-anchor" href="#doc-specific-orbital-energy">#</a> <code>specific_orbital_energy</code></h3>
<p><code>specific_orbital_energy</code> — operation <code>specific orbital energy</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p specific_orbital_energy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-specificity">
<h3><a class="doc-anchor" href="#doc-specificity">#</a> <code>specificity</code></h3>
<p><code>specificity</code> — operation <code>specificity</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p specificity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-speck-round">
<h3><a class="doc-anchor" href="#doc-speck-round">#</a> <code>speck_round</code></h3>
<p><code>speck_round</code> — operation <code>speck round</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p speck_round $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spectral-density-estimate">
<h3><a class="doc-anchor" href="#doc-spectral-density-estimate">#</a> <code>spectral_density_estimate</code></h3>
<p><code>spectral_density_estimate</code> — operation <code>spectral density estimate</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p spectral_density_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spectral-kappa-minus53">
<h3><a class="doc-anchor" href="#doc-spectral-kappa-minus53">#</a> <code>spectral_kappa_minus53</code></h3>
<p><code>spectral_kappa_minus53</code> — operation <code>spectral kappa minus53</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p spectral_kappa_minus53 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spectral-radius">
<h3><a class="doc-anchor" href="#doc-spectral-radius">#</a> <code>spectral_radius</code></h3>
<p><code>spectral_radius</code> — operation <code>spectral radius</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p spectral_radius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spectral-signature-match">
<h3><a class="doc-anchor" href="#doc-spectral-signature-match">#</a> <code>spectral_signature_match</code></h3>
<p><code>spectral_signature_match</code> — operation <code>spectral signature match</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p spectral_signature_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spectro">
<h3><a class="doc-anchor" href="#doc-spectro">#</a> <code>spectro</code></h3>
<p><code>spectro</code> — operation <code>spectro</code>. Alias for <code>spectrogram</code>. Category: *dsp / signal (extended)*.</p>
<pre><code class="lang-perl">p spectro $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spectrogram">
<h3><a class="doc-anchor" href="#doc-spectrogram">#</a> <code>spectrogram</code></h3>
<p><code>spectrogram(\@signal, $window_size, $hop_size)</code> (alias <code>stft</code>) — computes Short-Time Fourier Transform. Returns a 2D arrayref where each row is the spectrum of a windowed segment. Useful for time-frequency analysis.</p>
<pre><code class="lang-perl">my $spec = stft(\@audio, 1024, 512)
# $spec->[t][f] is magnitude at time t, frequency f
</code></pre>
</article>
<article class="doc-entry" id="doc-spectrogram-simple">
<h3><a class="doc-anchor" href="#doc-spectrogram-simple">#</a> <code>spectrogram_simple</code></h3>
<p><code>spectrogram_simple</code> — operation <code>spectrogram simple</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p spectrogram_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spectrophotometer-beer-lambert">
<h3><a class="doc-anchor" href="#doc-spectrophotometer-beer-lambert">#</a> <code>spectrophotometer_beer_lambert</code></h3>
<p><code>spectrophotometer_beer_lambert</code> — operation <code>spectrophotometer beer lambert</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p spectrophotometer_beer_lambert $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spectroscopic-factor">
<h3><a class="doc-anchor" href="#doc-spectroscopic-factor">#</a> <code>spectroscopic_factor</code></h3>
<p><code>spectroscopic_factor</code> — factor of <code>spectroscopic</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p spectroscopic_factor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-speed-distance-time">
<h3><a class="doc-anchor" href="#doc-speed-distance-time">#</a> <code>speed_distance_time</code></h3>
<p><code>speed_distance_time</code> — operation <code>speed distance time</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p speed_distance_time $x
</code></pre>
</article>
<article class="doc-entry" id="doc-speed-of-light">
<h3><a class="doc-anchor" href="#doc-speed-of-light">#</a> <code>speed_of_light</code></h3>
<p><code>speed_of_light</code> — operation <code>speed of light</code>. Category: *math / physics constants*.</p>
<pre><code class="lang-perl">p speed_of_light $x
</code></pre>
</article>
<article class="doc-entry" id="doc-speed-of-sound-ideal">
<h3><a class="doc-anchor" href="#doc-speed-of-sound-ideal">#</a> <code>speed_of_sound_ideal</code></h3>
<p><code>speed_of_sound_ideal</code> — operation <code>speed of sound ideal</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p speed_of_sound_ideal $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spew">
<h3><a class="doc-anchor" href="#doc-spew">#</a> <code>spew</code></h3>
<p><code>spew</code> — operation <code>spew</code>. Alias for <code>spurt</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p spew $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sph-harm">
<h3><a class="doc-anchor" href="#doc-sph-harm">#</a> <code>sph_harm</code></h3>
<p><code>sph_harm</code> — operation <code>sph harm</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p sph_harm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sphenic-q">
<h3><a class="doc-anchor" href="#doc-sphenic-q">#</a> <code>sphenic_q</code></h3>
<p><code>sphenic_q</code> — operation <code>sphenic q</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p sphenic_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sphere-aabb-intersect">
<h3><a class="doc-anchor" href="#doc-sphere-aabb-intersect">#</a> <code>sphere_aabb_intersect</code></h3>
<p><code>sphere_aabb_intersect(center, radius, aabb) → 0|1</code> — 1 if the sphere overlaps the AABB.</p>
</article>
<article class="doc-entry" id="doc-sphere-of-influence">
<h3><a class="doc-anchor" href="#doc-sphere-of-influence">#</a> <code>sphere_of_influence</code></h3>
<p><code>sphere_of_influence</code> — operation <code>sphere of influence</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p sphere_of_influence $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sphere-sphere-intersect">
<h3><a class="doc-anchor" href="#doc-sphere-sphere-intersect">#</a> <code>sphere_sphere_intersect</code></h3>
<p><code>sphere_sphere_intersect(c1, r1, c2, r2) → 0|1</code> — 1 if <code>|c1-c2| ≤ r1+r2</code>.</p>
</article>
<article class="doc-entry" id="doc-sphere-surface">
<h3><a class="doc-anchor" href="#doc-sphere-surface">#</a> <code>sphere_surface</code></h3>
<p><code>sphere_surface</code> — operation <code>sphere surface</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p sphere_surface $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sphere-surface-area">
<h3><a class="doc-anchor" href="#doc-sphere-surface-area">#</a> <code>sphere_surface_area</code></h3>
<p><code>sphere_surface_area</code> — operation <code>sphere surface area</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p sphere_surface_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sphere-volume">
<h3><a class="doc-anchor" href="#doc-sphere-volume">#</a> <code>sphere_volume</code></h3>
<p><code>sphere_volume</code> — operation <code>sphere volume</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p sphere_volume $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spherical-bessel-j0">
<h3><a class="doc-anchor" href="#doc-spherical-bessel-j0">#</a> <code>spherical_bessel_j0</code></h3>
<p><code>spherical_bessel_j0</code> — operation <code>spherical bessel j0</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p spherical_bessel_j0 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spherical-bessel-j1">
<h3><a class="doc-anchor" href="#doc-spherical-bessel-j1">#</a> <code>spherical_bessel_j1</code></h3>
<p><code>spherical_bessel_j1</code> — operation <code>spherical bessel j1</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p spherical_bessel_j1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spherical-bessel-y0">
<h3><a class="doc-anchor" href="#doc-spherical-bessel-y0">#</a> <code>spherical_bessel_y0</code></h3>
<p><code>spherical_bessel_y0</code> — operation <code>spherical bessel y0</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p spherical_bessel_y0 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spherical-bessel-y1">
<h3><a class="doc-anchor" href="#doc-spherical-bessel-y1">#</a> <code>spherical_bessel_y1</code></h3>
<p><code>spherical_bessel_y1</code> — operation <code>spherical bessel y1</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p spherical_bessel_y1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spherical-jn">
<h3><a class="doc-anchor" href="#doc-spherical-jn">#</a> <code>spherical_jn</code></h3>
<p><code>spherical_jn</code> — operation <code>spherical jn</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p spherical_jn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spherical-to-cartesian">
<h3><a class="doc-anchor" href="#doc-spherical-to-cartesian">#</a> <code>spherical_to_cartesian</code></h3>
<p><code>spherical_to_cartesian</code> — convert from <code>spherical</code> to <code>cartesian</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p spherical_to_cartesian $value
</code></pre>
</article>
<article class="doc-entry" id="doc-spherical-triangle-area">
<h3><a class="doc-anchor" href="#doc-spherical-triangle-area">#</a> <code>spherical_triangle_area</code></h3>
<p><code>spherical_triangle_area</code> — operation <code>spherical triangle area</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p spherical_triangle_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spherical-yn">
<h3><a class="doc-anchor" href="#doc-spherical-yn">#</a> <code>spherical_yn</code></h3>
<p><code>spherical_yn</code> — operation <code>spherical yn</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p spherical_yn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sphsurf">
<h3><a class="doc-anchor" href="#doc-sphsurf">#</a> <code>sphsurf</code></h3>
<p><code>sphsurf</code> — operation <code>sphsurf</code>. Alias for <code>sphere_surface</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p sphsurf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sphvol">
<h3><a class="doc-anchor" href="#doc-sphvol">#</a> <code>sphvol</code></h3>
<p><code>sphvol</code> — operation <code>sphvol</code>. Alias for <code>sphere_volume</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p sphvol $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spin-casimir">
<h3><a class="doc-anchor" href="#doc-spin-casimir">#</a> <code>spin_casimir</code></h3>
<p><code>spin_casimir</code> — operation <code>spin casimir</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p spin_casimir $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spin-orbit-coupling-term">
<h3><a class="doc-anchor" href="#doc-spin-orbit-coupling-term">#</a> <code>spin_orbit_coupling_term</code></h3>
<p><code>spin_orbit_coupling_term</code> — operation <code>spin orbit coupling term</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p spin_orbit_coupling_term $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spin-spin-coupling-term">
<h3><a class="doc-anchor" href="#doc-spin-spin-coupling-term">#</a> <code>spin_spin_coupling_term</code></h3>
<p><code>spin_spin_coupling_term</code> — operation <code>spin spin coupling term</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p spin_spin_coupling_term $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spinner-start">
<h3><a class="doc-anchor" href="#doc-spinner-start">#</a> <code>spinner_start</code></h3>
<p><code>spinner_start</code> — operation <code>spinner start</code>. Category: *pipeline / string helpers*.</p>
<pre><code class="lang-perl">p spinner_start $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spinner-stop">
<h3><a class="doc-anchor" href="#doc-spinner-stop">#</a> <code>spinner_stop</code></h3>
<p><code>spinner_stop</code> — operation <code>spinner stop</code>. Category: *pipeline / string helpers*.</p>
<pre><code class="lang-perl">p spinner_stop $x
</code></pre>
</article>
<article class="doc-entry" id="doc-split-at">
<h3><a class="doc-anchor" href="#doc-split-at">#</a> <code>split_at</code></h3>
<p><code>split_at</code> — operation <code>split at</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p split_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-split-on">
<h3><a class="doc-anchor" href="#doc-split-on">#</a> <code>split_on</code></h3>
<p><code>split_on</code> — operation <code>split on</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p split_on $x
</code></pre>
</article>
<article class="doc-entry" id="doc-split-regex">
<h3><a class="doc-anchor" href="#doc-split-regex">#</a> <code>split_regex</code></h3>
<p><code>split_regex</code> — operation <code>split regex</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p split_regex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-split-with">
<h3><a class="doc-anchor" href="#doc-split-with">#</a> <code>split_with</code></h3>
<p><code>split_with</code> — operation <code>split with</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p split_with $x
</code></pre>
</article>
<article class="doc-entry" id="doc-splitmix64-next">
<h3><a class="doc-anchor" href="#doc-splitmix64-next">#</a> <code>splitmix64_next</code></h3>
<p><code>splitmix64_next(seed) → int</code> — SplitMix64 step. Used for seeding other PRNGs.</p>
</article>
<article class="doc-entry" id="doc-splitmix64-step">
<h3><a class="doc-anchor" href="#doc-splitmix64-step">#</a> <code>splitmix64_step</code></h3>
<p><code>splitmix64_step</code> — single-step update of <code>splitmix64</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p splitmix64_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-splre">
<h3><a class="doc-anchor" href="#doc-splre">#</a> <code>splre</code></h3>
<p><code>splre</code> — operation <code>splre</code>. Alias for <code>split_regex</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p splre $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spmc-new">
<h3><a class="doc-anchor" href="#doc-spmc-new">#</a> <code>spmc_new</code></h3>
<p><code>spmc_new</code> — constructor of <code>spmc</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p spmc_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spon">
<h3><a class="doc-anchor" href="#doc-spon">#</a> <code>spon</code></h3>
<p><code>spon</code> — operation <code>spon</code>. Alias for <code>split_on</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p spon $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spookyhash-128">
<h3><a class="doc-anchor" href="#doc-spookyhash-128">#</a> <code>spookyhash_128</code></h3>
<p><code>spookyhash_128</code> — operation <code>spookyhash 128</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p spookyhash_128 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spop">
<h3><a class="doc-anchor" href="#doc-spop">#</a> <code>spop</code></h3>
<p><code>spop</code> — operation <code>spop</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p spop $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spring-energy">
<h3><a class="doc-anchor" href="#doc-spring-energy">#</a> <code>spring_energy</code></h3>
<p><code>spring_energy</code> — operation <code>spring energy</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p spring_energy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spring-force">
<h3><a class="doc-anchor" href="#doc-spring-force">#</a> <code>spring_force</code></h3>
<p><code>spring_force</code> — operation <code>spring force</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p spring_force $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spring-oscillator-pos">
<h3><a class="doc-anchor" href="#doc-spring-oscillator-pos">#</a> <code>spring_oscillator_pos</code></h3>
<p><code>spring_oscillator_pos(amplitude, omega, phase=0, t) → number</code> — <code>A·cos(ωt + φ)</code>.</p>
</article>
<article class="doc-entry" id="doc-spring-period">
<h3><a class="doc-anchor" href="#doc-spring-period">#</a> <code>spring_period</code></h3>
<p><code>spring_period</code> — operation <code>spring period</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p spring_period $x
</code></pre>
</article>
<article class="doc-entry" id="doc-springpe">
<h3><a class="doc-anchor" href="#doc-springpe">#</a> <code>springpe</code></h3>
<p><code>springpe</code> — operation <code>springpe</code>. Alias for <code>spring_energy</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p springpe $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spt-n-correction">
<h3><a class="doc-anchor" href="#doc-spt-n-correction">#</a> <code>spt_n_correction</code></h3>
<p><code>spt_n_correction</code> — operation <code>spt n correction</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p spt_n_correction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-spw">
<h3><a class="doc-anchor" href="#doc-spw">#</a> <code>spw</code></h3>
<p><code>spw</code> — operation <code>spw</code>. Alias for <code>split_with</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p spw $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sql">
<h3><a class="doc-anchor" href="#doc-sql">#</a> <code>sql</code></h3>
<p><code>sql</code> — operation <code>sql</code>. Alias for <code>sqlite</code>. Category: *data / network*.</p>
<pre><code class="lang-perl">p sql $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sqr">
<h3><a class="doc-anchor" href="#doc-sqr">#</a> <code>sqr</code></h3>
<p><code>sqr</code> — operation <code>sqr</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p sqr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sqrt2">
<h3><a class="doc-anchor" href="#doc-sqrt2">#</a> <code>sqrt2</code></h3>
<p><code>sqrt2</code> — operation <code>sqrt2</code>. Category: *math / physics constants*.</p>
<pre><code class="lang-perl">p sqrt2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sqrt-each">
<h3><a class="doc-anchor" href="#doc-sqrt-each">#</a> <code>sqrt_each</code></h3>
<p><code>sqrt_each</code> — square-root helper <code>each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p sqrt_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sqrt-swap-gate">
<h3><a class="doc-anchor" href="#doc-sqrt-swap-gate">#</a> <code>sqrt_swap_gate</code></h3>
<p><code>sqrt_swap_gate</code> — square-root helper <code>swap gate</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p sqrt_swap_gate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-square-each">
<h3><a class="doc-anchor" href="#doc-square-each">#</a> <code>square_each</code></h3>
<p><code>square_each</code> — operation <code>square each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p square_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-square-free">
<h3><a class="doc-anchor" href="#doc-square-free">#</a> <code>square_free</code></h3>
<p><code>square_free</code> — release / destroy of <code>square</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p square_free $x
</code></pre>
</article>
<article class="doc-entry" id="doc-square-pyramidal">
<h3><a class="doc-anchor" href="#doc-square-pyramidal">#</a> <code>square_pyramidal</code></h3>
<p><code>square_pyramidal(n) → int</code> — <code>n·(n+1)·(2n+1) / 6</code>.</p>
</article>
<article class="doc-entry" id="doc-square-pyramidal-number">
<h3><a class="doc-anchor" href="#doc-square-pyramidal-number">#</a> <code>square_pyramidal_number</code></h3>
<p><code>square_pyramidal_number</code> — operation <code>square pyramidal number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p square_pyramidal_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-square-root">
<h3><a class="doc-anchor" href="#doc-square-root">#</a> <code>square_root</code></h3>
<p><code>square_root</code> — operation <code>square root</code>. Category: *math functions*.</p>
<pre><code class="lang-perl">p square_root $x
</code></pre>
</article>
<article class="doc-entry" id="doc-squared-hinge">
<h3><a class="doc-anchor" href="#doc-squared-hinge">#</a> <code>squared_hinge</code></h3>
<p><code>squared_hinge</code> — operation <code>squared hinge</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p squared_hinge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-squared-triangular">
<h3><a class="doc-anchor" href="#doc-squared-triangular">#</a> <code>squared_triangular</code></h3>
<p><code>squared_triangular</code> — operation <code>squared triangular</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p squared_triangular $x
</code></pre>
</article>
<article class="doc-entry" id="doc-squares-seq">
<h3><a class="doc-anchor" href="#doc-squares-seq">#</a> <code>squares_seq</code></h3>
<p><code>squares_seq</code> — operation <code>squares seq</code>. Category: *sequences*.</p>
<pre><code class="lang-perl">p squares_seq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-squeezing-db">
<h3><a class="doc-anchor" href="#doc-squeezing-db">#</a> <code>squeezing_db</code></h3>
<p><code>squeezing_db</code> — operation <code>squeezing db</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p squeezing_db $x
</code></pre>
</article>
<article class="doc-entry" id="doc-squish">
<h3><a class="doc-anchor" href="#doc-squish">#</a> <code>squish</code></h3>
<p><code>squish</code> — operation <code>squish</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p squish $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sregex">
<h3><a class="doc-anchor" href="#doc-sregex">#</a> <code>sregex</code></h3>
<p><code>sregex</code> — operation <code>sregex</code>. Alias for <code>stress_regex</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p sregex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-srem">
<h3><a class="doc-anchor" href="#doc-srem">#</a> <code>srem</code></h3>
<p><code>srem</code> — operation <code>srem</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p srem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-srgb-to-rgb">
<h3><a class="doc-anchor" href="#doc-srgb-to-rgb">#</a> <code>srgb_to_rgb</code></h3>
<p><code>srgb_to_rgb</code> — convert from <code>srgb</code> to <code>rgb</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p srgb_to_rgb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-srgb-to-xyz">
<h3><a class="doc-anchor" href="#doc-srgb-to-xyz">#</a> <code>srgb_to_xyz</code></h3>
<p><code>srgb_to_xyz</code> — convert from <code>srgb</code> to <code>xyz</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p srgb_to_xyz $value
</code></pre>
</article>
<article class="doc-entry" id="doc-srton">
<h3><a class="doc-anchor" href="#doc-srton">#</a> <code>srton</code></h3>
<p><code>srton</code> — operation <code>srton</code>. Alias for <code>sort_on</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p srton $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ssa-phi-insert">
<h3><a class="doc-anchor" href="#doc-ssa-phi-insert">#</a> <code>ssa_phi_insert</code></h3>
<p><code>ssa_phi_insert</code> — operation <code>ssa phi insert</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p ssa_phi_insert $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ssn-check">
<h3><a class="doc-anchor" href="#doc-ssn-check">#</a> <code>ssn_check</code></h3>
<p><code>ssn_check</code> — operation <code>ssn check</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p ssn_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ssort">
<h3><a class="doc-anchor" href="#doc-ssort">#</a> <code>ssort</code></h3>
<p><code>ssort</code> — operation <code>ssort</code>. Alias for <code>stress_sort</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p ssort $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sst-anomaly-step">
<h3><a class="doc-anchor" href="#doc-sst-anomaly-step">#</a> <code>sst_anomaly_step</code></h3>
<p><code>sst_anomaly_step</code> — single-step update of <code>sst anomaly</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p sst_anomaly_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stable-matching-count">
<h3><a class="doc-anchor" href="#doc-stable-matching-count">#</a> <code>stable_matching_count</code></h3>
<p><code>stable_matching_count</code> — count of <code>stable matching</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p stable_matching_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stack-new">
<h3><a class="doc-anchor" href="#doc-stack-new">#</a> <code>stack_new</code></h3>
<p><code>stack_new</code> — stack op <code>new</code>. Category: *data structure helpers*.</p>
<pre><code class="lang-perl">p stack_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stackelberg-eq">
<h3><a class="doc-anchor" href="#doc-stackelberg-eq">#</a> <code>stackelberg_eq</code></h3>
<p><code>stackelberg_eq</code> — operation <code>stackelberg eq</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p stackelberg_eq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stackelberg-step">
<h3><a class="doc-anchor" href="#doc-stackelberg-step">#</a> <code>stackelberg_step</code></h3>
<p><code>stackelberg_step</code> — single-step update of <code>stackelberg</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p stackelberg_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stag-hunt-payoff">
<h3><a class="doc-anchor" href="#doc-stag-hunt-payoff">#</a> <code>stag_hunt_payoff</code></h3>
<p><code>stag_hunt_payoff</code> — operation <code>stag hunt payoff</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p stag_hunt_payoff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-standard-error">
<h3><a class="doc-anchor" href="#doc-standard-error">#</a> <code>standard_error</code></h3>
<p><code>standard_error</code> — operation <code>standard error</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p standard_error $x
</code></pre>
</article>
<article class="doc-entry" id="doc-standardized-mortality-smr">
<h3><a class="doc-anchor" href="#doc-standardized-mortality-smr">#</a> <code>standardized_mortality_smr</code></h3>
<p><code>standardized_mortality_smr</code> — operation <code>standardized mortality smr</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p standardized_mortality_smr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-standing-wave-fundamental">
<h3><a class="doc-anchor" href="#doc-standing-wave-fundamental">#</a> <code>standing_wave_fundamental</code></h3>
<p><code>standing_wave_fundamental</code> — operation <code>standing wave fundamental</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p standing_wave_fundamental $x
</code></pre>
</article>
<article class="doc-entry" id="doc-star-number">
<h3><a class="doc-anchor" href="#doc-star-number">#</a> <code>star_number</code></h3>
<p><code>star_number</code> — operation <code>star number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p star_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stark-shift-linear">
<h3><a class="doc-anchor" href="#doc-stark-shift-linear">#</a> <code>stark_shift_linear</code></h3>
<p><code>stark_shift_linear</code> — operation <code>stark shift linear</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p stark_shift_linear $x
</code></pre>
</article>
<article class="doc-entry" id="doc-starmap">
<h3><a class="doc-anchor" href="#doc-starmap">#</a> <code>starmap</code></h3>
<p><code>starmap</code> — operation <code>starmap</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p starmap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-start-of-day">
<h3><a class="doc-anchor" href="#doc-start-of-day">#</a> <code>start_of_day</code></h3>
<p><code>start_of_day</code> — operation <code>start of day</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p start_of_day $x
</code></pre>
</article>
<article class="doc-entry" id="doc-start-of-hour">
<h3><a class="doc-anchor" href="#doc-start-of-hour">#</a> <code>start_of_hour</code></h3>
<p><code>start_of_hour</code> — operation <code>start of hour</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p start_of_hour $x
</code></pre>
</article>
<article class="doc-entry" id="doc-start-of-minute">
<h3><a class="doc-anchor" href="#doc-start-of-minute">#</a> <code>start_of_minute</code></h3>
<p><code>start_of_minute</code> — operation <code>start of minute</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p start_of_minute $x
</code></pre>
</article>
<article class="doc-entry" id="doc-starts-with">
<h3><a class="doc-anchor" href="#doc-starts-with">#</a> <code>starts_with</code></h3>
<p><code>starts_with</code> — operation <code>starts with</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p starts_with $x
</code></pre>
</article>
<article class="doc-entry" id="doc-starts-with-any">
<h3><a class="doc-anchor" href="#doc-starts-with-any">#</a> <code>starts_with_any</code></h3>
<p><code>starts_with_any</code> — operation <code>starts with any</code>. Category: *string*.</p>
<pre><code class="lang-perl">p starts_with_any $x
</code></pre>
</article>
<article class="doc-entry" id="doc-state-norm">
<h3><a class="doc-anchor" href="#doc-state-norm">#</a> <code>state_norm</code></h3>
<p><code>state_norm</code> — norm (vector length-like) of <code>state</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p state_norm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-state-normalize">
<h3><a class="doc-anchor" href="#doc-state-normalize">#</a> <code>state_normalize</code></h3>
<p><code>state_normalize</code> — operation <code>state normalize</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p state_normalize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-state-of-charge-kalman">
<h3><a class="doc-anchor" href="#doc-state-of-charge-kalman">#</a> <code>state_of_charge_kalman</code></h3>
<p><code>state_of_charge_kalman</code> — operation <code>state of charge kalman</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p state_of_charge_kalman $x
</code></pre>
</article>
<article class="doc-entry" id="doc-state-space-kalman">
<h3><a class="doc-anchor" href="#doc-state-space-kalman">#</a> <code>state_space_kalman</code></h3>
<p><code>state_space_kalman</code> — operation <code>state space kalman</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p state_space_kalman $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stats-describe">
<h3><a class="doc-anchor" href="#doc-stats-describe">#</a> <code>stats_describe</code></h3>
<p><code>stats_describe</code> — operation <code>stats describe</code>. Alias for <code>describe</code>. Category: *statistics (extended)*.</p>
<pre><code class="lang-perl">p stats_describe $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stderr-stat">
<h3><a class="doc-anchor" href="#doc-stderr-stat">#</a> <code>stderr_stat</code></h3>
<p><code>stderr_stat</code> — operation <code>stderr stat</code>. Alias for <code>standard_error</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p stderr_stat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stefan-boltzmann">
<h3><a class="doc-anchor" href="#doc-stefan-boltzmann">#</a> <code>stefan_boltzmann</code></h3>
<p><code>stefan_boltzmann</code> — operation <code>stefan boltzmann</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p stefan_boltzmann $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stefan-boltzmann-constant">
<h3><a class="doc-anchor" href="#doc-stefan-boltzmann-constant">#</a> <code>stefan_boltzmann_constant</code></h3>
<p><code>stefan_boltzmann_constant</code> — operation <code>stefan boltzmann constant</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p stefan_boltzmann_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stefan-boltzmann-radiation">
<h3><a class="doc-anchor" href="#doc-stefan-boltzmann-radiation">#</a> <code>stefan_boltzmann_radiation</code></h3>
<p><code>stefan_boltzmann_radiation</code> — operation <code>stefan boltzmann radiation</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p stefan_boltzmann_radiation $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stefan-boltzmann-si">
<h3><a class="doc-anchor" href="#doc-stefan-boltzmann-si">#</a> <code>stefan_boltzmann_si</code></h3>
<p><code>stefan_boltzmann_si</code> — operation <code>stefan boltzmann si</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p stefan_boltzmann_si $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stefboltz">
<h3><a class="doc-anchor" href="#doc-stefboltz">#</a> <code>stefboltz</code></h3>
<p><code>stefboltz</code> — operation <code>stefboltz</code>. Alias for <code>stefan_boltzmann</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p stefboltz $x
</code></pre>
</article>
<article class="doc-entry" id="doc-steffensen">
<h3><a class="doc-anchor" href="#doc-steffensen">#</a> <code>steffensen</code></h3>
<p><code>steffensen</code> — operation <code>steffensen</code>. Alias for <code>steffensen_root</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p steffensen $x
</code></pre>
</article>
<article class="doc-entry" id="doc-steffensen-root">
<h3><a class="doc-anchor" href="#doc-steffensen-root">#</a> <code>steffensen_root</code></h3>
<p><code>steffensen_root</code> — operation <code>steffensen root</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p steffensen_root $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stem-lancaster">
<h3><a class="doc-anchor" href="#doc-stem-lancaster">#</a> <code>stem_lancaster</code></h3>
<p><code>stem_lancaster</code> — operation <code>stem lancaster</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p stem_lancaster $x
</code></pre>
</article>
<article class="doc-entry" id="doc-step">
<h3><a class="doc-anchor" href="#doc-step">#</a> <code>step</code></h3>
<p><code>step</code> — operation <code>step</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stern-layer-capacitance">
<h3><a class="doc-anchor" href="#doc-stern-layer-capacitance">#</a> <code>stern_layer_capacitance</code></h3>
<p><code>stern_layer_capacitance</code> — operation <code>stern layer capacitance</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p stern_layer_capacitance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stft-step">
<h3><a class="doc-anchor" href="#doc-stft-step">#</a> <code>stft_step</code></h3>
<p><code>stft_step</code> — single-step update of <code>stft</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p stft_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sthread">
<h3><a class="doc-anchor" href="#doc-sthread">#</a> <code>sthread</code></h3>
<p><code>sthread</code> — operation <code>sthread</code>. Alias for <code>stress_thread</code>. Category: *stress / telemetry extensions*.</p>
<pre><code class="lang-perl">p sthread $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stiffness-ratio">
<h3><a class="doc-anchor" href="#doc-stiffness-ratio">#</a> <code>stiffness_ratio</code></h3>
<p><code>stiffness_ratio</code> — ratio of <code>stiffness</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p stiffness_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stirling">
<h3><a class="doc-anchor" href="#doc-stirling">#</a> <code>stirling</code></h3>
<p><code>stirling</code> — operation <code>stirling</code>. Alias for <code>stirling_approx</code>. Category: *math formulas*.</p>
<pre><code class="lang-perl">p stirling $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stirling2">
<h3><a class="doc-anchor" href="#doc-stirling2">#</a> <code>stirling2</code></h3>
<p><code>stirling2</code> (alias <code>stirling_second</code>) computes the Stirling number of the second kind S(n,k) — the number of ways to partition n elements into k non-empty subsets.</p>
<pre><code class="lang-perl">p stirling2(4, 2) # 7
p stirling2(5, 3) # 25
</code></pre>
</article>
<article class="doc-entry" id="doc-stirling-1">
<h3><a class="doc-anchor" href="#doc-stirling-1">#</a> <code>stirling_1</code></h3>
<p><code>stirling_1</code> — operation <code>stirling 1</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p stirling_1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stirling-2">
<h3><a class="doc-anchor" href="#doc-stirling-2">#</a> <code>stirling_2</code></h3>
<p><code>stirling_2</code> — operation <code>stirling 2</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p stirling_2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stirling-approx">
<h3><a class="doc-anchor" href="#doc-stirling-approx">#</a> <code>stirling_approx</code></h3>
<p><code>stirling_approx</code> — operation <code>stirling approx</code>. Category: *math formulas*.</p>
<pre><code class="lang-perl">p stirling_approx $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stl-decompose">
<h3><a class="doc-anchor" href="#doc-stl-decompose">#</a> <code>stl_decompose</code></h3>
<p><code>stl_decompose</code> — operation <code>stl decompose</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p stl_decompose $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stoch-rsi">
<h3><a class="doc-anchor" href="#doc-stoch-rsi">#</a> <code>stoch_rsi</code></h3>
<p><code>stoch_rsi(prices, period=14) → array</code> — stochastic RSI: normalises RSI to [0,1] by <code>(rsi - min) / (max - min)</code> over its own window.</p>
<pre><code class="lang-perl">p stoch_rsi(\@closes, 14)
</code></pre>
</article>
<article class="doc-entry" id="doc-stoer-wagner-step">
<h3><a class="doc-anchor" href="#doc-stoer-wagner-step">#</a> <code>stoer_wagner_step</code></h3>
<p><code>stoer_wagner_step</code> — single-step update of <code>stoer wagner</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p stoer_wagner_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stone-to-kg">
<h3><a class="doc-anchor" href="#doc-stone-to-kg">#</a> <code>stone_to_kg</code></h3>
<p><code>stone_to_kg</code> — convert from <code>stone</code> to <code>kg</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p stone_to_kg $value
</code></pre>
</article>
<article class="doc-entry" id="doc-stormer-verlet-step">
<h3><a class="doc-anchor" href="#doc-stormer-verlet-step">#</a> <code>stormer_verlet_step</code></h3>
<p><code>stormer_verlet_step</code> — single-step update of <code>stormer verlet</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p stormer_verlet_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-aho-corasick">
<h3><a class="doc-anchor" href="#doc-str-aho-corasick">#</a> <code>str_aho_corasick</code></h3>
<p><code>str_aho_corasick</code> — operation <code>str aho corasick</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_aho_corasick $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-boyer-moore">
<h3><a class="doc-anchor" href="#doc-str-boyer-moore">#</a> <code>str_boyer_moore</code></h3>
<p><code>str_boyer_moore</code> — operation <code>str boyer moore</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_boyer_moore $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-compress-lzss">
<h3><a class="doc-anchor" href="#doc-str-compress-lzss">#</a> <code>str_compress_lzss</code></h3>
<p><code>str_compress_lzss</code> — operation <code>str compress lzss</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_compress_lzss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-compress-rle">
<h3><a class="doc-anchor" href="#doc-str-compress-rle">#</a> <code>str_compress_rle</code></h3>
<p><code>str_compress_rle</code> — operation <code>str compress rle</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_compress_rle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-decompress-lzss">
<h3><a class="doc-anchor" href="#doc-str-decompress-lzss">#</a> <code>str_decompress_lzss</code></h3>
<p><code>str_decompress_lzss</code> — operation <code>str decompress lzss</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_decompress_lzss $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-decompress-rle">
<h3><a class="doc-anchor" href="#doc-str-decompress-rle">#</a> <code>str_decompress_rle</code></h3>
<p><code>str_decompress_rle</code> — operation <code>str decompress rle</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_decompress_rle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-huffman-decode">
<h3><a class="doc-anchor" href="#doc-str-huffman-decode">#</a> <code>str_huffman_decode</code></h3>
<p><code>str_huffman_decode</code> — decode of <code>str huffman</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_huffman_decode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-huffman-encode">
<h3><a class="doc-anchor" href="#doc-str-huffman-encode">#</a> <code>str_huffman_encode</code></h3>
<p><code>str_huffman_encode</code> — encode of <code>str huffman</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_huffman_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-isogram">
<h3><a class="doc-anchor" href="#doc-str-isogram">#</a> <code>str_isogram</code></h3>
<p><code>str_isogram</code> — operation <code>str isogram</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_isogram $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-kmp">
<h3><a class="doc-anchor" href="#doc-str-kmp">#</a> <code>str_kmp</code></h3>
<p><code>str_kmp</code> — operation <code>str kmp</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_kmp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-lcs">
<h3><a class="doc-anchor" href="#doc-str-lcs">#</a> <code>str_lcs</code></h3>
<p><code>str_lcs</code> — operation <code>str lcs</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_lcs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-lcs-length">
<h3><a class="doc-anchor" href="#doc-str-lcs-length">#</a> <code>str_lcs_length</code></h3>
<p><code>str_lcs_length</code> — operation <code>str lcs length</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_lcs_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-longest-common-substring">
<h3><a class="doc-anchor" href="#doc-str-longest-common-substring">#</a> <code>str_longest_common_substring</code></h3>
<p><code>str_longest_common_substring</code> — operation <code>str longest common substring</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_longest_common_substring $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-rabin-karp">
<h3><a class="doc-anchor" href="#doc-str-rabin-karp">#</a> <code>str_rabin_karp</code></h3>
<p><code>str_rabin_karp</code> — operation <code>str rabin karp</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_rabin_karp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-rotations">
<h3><a class="doc-anchor" href="#doc-str-rotations">#</a> <code>str_rotations</code></h3>
<p><code>str_rotations</code> — operation <code>str rotations</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_rotations $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-suffix-array">
<h3><a class="doc-anchor" href="#doc-str-suffix-array">#</a> <code>str_suffix_array</code></h3>
<p><code>str_suffix_array</code> — operation <code>str suffix array</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_suffix_array $x
</code></pre>
</article>
<article class="doc-entry" id="doc-str-z-array">
<h3><a class="doc-anchor" href="#doc-str-z-array">#</a> <code>str_z_array</code></h3>
<p><code>str_z_array</code> — operation <code>str z array</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p str_z_array $x
</code></pre>
</article>
<article class="doc-entry" id="doc-strang-split">
<h3><a class="doc-anchor" href="#doc-strang-split">#</a> <code>strang_split</code></h3>
<p><code>strang_split</code> — operation <code>strang split</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p strang_split $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stratonovich-correction">
<h3><a class="doc-anchor" href="#doc-stratonovich-correction">#</a> <code>stratonovich_correction</code></h3>
<p><code>stratonovich_correction</code> — operation <code>stratonovich correction</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p stratonovich_correction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-strdist">
<h3><a class="doc-anchor" href="#doc-strdist">#</a> <code>strdist</code></h3>
<p><code>strdist</code> — operation <code>strdist</code>. Alias for <code>string_distance</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p strdist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-streak-color-index">
<h3><a class="doc-anchor" href="#doc-streak-color-index">#</a> <code>streak_color_index</code></h3>
<p><code>streak_color_index</code> — index of <code>streak color</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p streak_color_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-stream-prompt-cb">
<h3><a class="doc-anchor" href="#doc-stream-prompt-cb">#</a> <code>stream_prompt_cb</code></h3>
<p><code>stream_prompt_cb</code> — operation <code>stream prompt cb</code>. Category: *ai primitives (docs/ai_primitives.md)*.</p>
<pre><code class="lang-perl">p stream_prompt_cb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-streamfunction-step">
<h3><a class="doc-anchor" href="#doc-streamfunction-step">#</a> <code>streamfunction_step</code></h3>
<p><code>streamfunction_step</code> — single-step update of <code>streamfunction</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p streamfunction_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-strehl-ratio">
<h3><a class="doc-anchor" href="#doc-strehl-ratio">#</a> <code>strehl_ratio</code></h3>
<p><code>strehl_ratio</code> — ratio of <code>strehl</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p strehl_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-strict-word-similarity">
<h3><a class="doc-anchor" href="#doc-strict-word-similarity">#</a> <code>strict_word_similarity</code></h3>
<p><code>strict_word_similarity</code> — similarity metric of <code>strict word</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p strict_word_similarity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-strikethrough">
<h3><a class="doc-anchor" href="#doc-strikethrough">#</a> <code>strikethrough</code></h3>
<p><code>strikethrough</code> — operation <code>strikethrough</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p strikethrough $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-agg">
<h3><a class="doc-anchor" href="#doc-string-agg">#</a> <code>string_agg</code></h3>
<p><code>string_agg</code> — string helper <code>agg</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p string_agg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-camel-to-snake">
<h3><a class="doc-anchor" href="#doc-string-camel-to-snake">#</a> <code>string_camel_to_snake</code></h3>
<p><code>string_camel_to_snake</code> — convert from <code>string camel</code> to <code>snake</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_camel_to_snake $value
</code></pre>
</article>
<article class="doc-entry" id="doc-string-chars">
<h3><a class="doc-anchor" href="#doc-string-chars">#</a> <code>string_chars</code></h3>
<p><code>string_chars</code> — string helper <code>chars</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_chars $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-count">
<h3><a class="doc-anchor" href="#doc-string-count">#</a> <code>string_count</code></h3>
<p><code>string_count</code> — string helper <code>count</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p string_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-distance">
<h3><a class="doc-anchor" href="#doc-string-distance">#</a> <code>string_distance</code></h3>
<p><code>string_distance</code> — string helper <code>distance</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p string_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-drop-first">
<h3><a class="doc-anchor" href="#doc-string-drop-first">#</a> <code>string_drop_first</code></h3>
<p><code>string_drop_first</code> — string helper <code>drop first</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_drop_first $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-drop-last">
<h3><a class="doc-anchor" href="#doc-string-drop-last">#</a> <code>string_drop_last</code></h3>
<p><code>string_drop_last</code> — string helper <code>drop last</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_drop_last $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-drop-while">
<h3><a class="doc-anchor" href="#doc-string-drop-while">#</a> <code>string_drop_while</code></h3>
<p><code>string_drop_while</code> — string helper <code>drop while</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_drop_while $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-expand-tabs">
<h3><a class="doc-anchor" href="#doc-string-expand-tabs">#</a> <code>string_expand_tabs</code></h3>
<p><code>string_expand_tabs</code> — string helper <code>expand tabs</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_expand_tabs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-intersperse">
<h3><a class="doc-anchor" href="#doc-string-intersperse">#</a> <code>string_intersperse</code></h3>
<p><code>string_intersperse</code> — string helper <code>intersperse</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_intersperse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-kebab-to-snake">
<h3><a class="doc-anchor" href="#doc-string-kebab-to-snake">#</a> <code>string_kebab_to_snake</code></h3>
<p><code>string_kebab_to_snake</code> — convert from <code>string kebab</code> to <code>snake</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_kebab_to_snake $value
</code></pre>
</article>
<article class="doc-entry" id="doc-string-letter-frequency">
<h3><a class="doc-anchor" href="#doc-string-letter-frequency">#</a> <code>string_letter_frequency</code></h3>
<p><code>string_letter_frequency</code> — string helper <code>letter frequency</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_letter_frequency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-lines-count">
<h3><a class="doc-anchor" href="#doc-string-lines-count">#</a> <code>string_lines_count</code></h3>
<p><code>string_lines_count</code> — string helper <code>lines count</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_lines_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-multiply">
<h3><a class="doc-anchor" href="#doc-string-multiply">#</a> <code>string_multiply</code></h3>
<p><code>string_multiply</code> — string helper <code>multiply</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p string_multiply $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-normalize-spaces">
<h3><a class="doc-anchor" href="#doc-string-normalize-spaces">#</a> <code>string_normalize_spaces</code></h3>
<p><code>string_normalize_spaces</code> — string helper <code>normalize spaces</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_normalize_spaces $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-partition-at-word">
<h3><a class="doc-anchor" href="#doc-string-partition-at-word">#</a> <code>string_partition_at_word</code></h3>
<p><code>string_partition_at_word</code> — string helper <code>partition at word</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_partition_at_word $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-replicate">
<h3><a class="doc-anchor" href="#doc-string-replicate">#</a> <code>string_replicate</code></h3>
<p><code>string_replicate</code> — string helper <code>replicate</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_replicate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-snake-to-camel">
<h3><a class="doc-anchor" href="#doc-string-snake-to-camel">#</a> <code>string_snake_to_camel</code></h3>
<p><code>string_snake_to_camel</code> — convert from <code>string snake</code> to <code>camel</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_snake_to_camel $value
</code></pre>
</article>
<article class="doc-entry" id="doc-string-snake-to-kebab">
<h3><a class="doc-anchor" href="#doc-string-snake-to-kebab">#</a> <code>string_snake_to_kebab</code></h3>
<p><code>string_snake_to_kebab</code> — convert from <code>string snake</code> to <code>kebab</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_snake_to_kebab $value
</code></pre>
</article>
<article class="doc-entry" id="doc-string-sort">
<h3><a class="doc-anchor" href="#doc-string-sort">#</a> <code>string_sort</code></h3>
<p><code>string_sort</code> — string helper <code>sort</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p string_sort $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-split-at-first">
<h3><a class="doc-anchor" href="#doc-string-split-at-first">#</a> <code>string_split_at_first</code></h3>
<p><code>string_split_at_first</code> — string helper <code>split at first</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_split_at_first $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-take-first">
<h3><a class="doc-anchor" href="#doc-string-take-first">#</a> <code>string_take_first</code></h3>
<p><code>string_take_first</code> — string helper <code>take first</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_take_first $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-take-last">
<h3><a class="doc-anchor" href="#doc-string-take-last">#</a> <code>string_take_last</code></h3>
<p><code>string_take_last</code> — string helper <code>take last</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_take_last $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-take-while">
<h3><a class="doc-anchor" href="#doc-string-take-while">#</a> <code>string_take_while</code></h3>
<p><code>string_take_while</code> — string helper <code>take while</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_take_while $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-to-charcodes">
<h3><a class="doc-anchor" href="#doc-string-to-charcodes">#</a> <code>string_to_charcodes</code></h3>
<p><code>string_to_charcodes</code> — convert from <code>string</code> to <code>charcodes</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_to_charcodes $value
</code></pre>
</article>
<article class="doc-entry" id="doc-string-to-chars">
<h3><a class="doc-anchor" href="#doc-string-to-chars">#</a> <code>string_to_chars</code></h3>
<p><code>string_to_chars</code> — convert from <code>string</code> to <code>chars</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p string_to_chars $value
</code></pre>
</article>
<article class="doc-entry" id="doc-string-truncate-ellipsis">
<h3><a class="doc-anchor" href="#doc-string-truncate-ellipsis">#</a> <code>string_truncate_ellipsis</code></h3>
<p><code>string_truncate_ellipsis</code> — string helper <code>truncate ellipsis</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_truncate_ellipsis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-uniq-chars">
<h3><a class="doc-anchor" href="#doc-string-uniq-chars">#</a> <code>string_uniq_chars</code></h3>
<p><code>string_uniq_chars</code> — string helper <code>uniq chars</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_uniq_chars $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-unique-chars">
<h3><a class="doc-anchor" href="#doc-string-unique-chars">#</a> <code>string_unique_chars</code></h3>
<p><code>string_unique_chars</code> — string helper <code>unique chars</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p string_unique_chars $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-words-count">
<h3><a class="doc-anchor" href="#doc-string-words-count">#</a> <code>string_words_count</code></h3>
<p><code>string_words_count</code> — string helper <code>words count</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_words_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-string-xor">
<h3><a class="doc-anchor" href="#doc-string-xor">#</a> <code>string_xor</code></h3>
<p><code>string_xor</code> — string helper <code>xor</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p string_xor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-strip-ansi">
<h3><a class="doc-anchor" href="#doc-strip-ansi">#</a> <code>strip_ansi</code></h3>
<p><code>strip_ansi</code> — operation <code>strip ansi</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p strip_ansi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-strip-html">
<h3><a class="doc-anchor" href="#doc-strip-html">#</a> <code>strip_html</code></h3>
<p><code>strip_html</code> — operation <code>strip html</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p strip_html $x
</code></pre>
</article>
<article class="doc-entry" id="doc-strip-indent">
<h3><a class="doc-anchor" href="#doc-strip-indent">#</a> <code>strip_indent</code></h3>
<p><code>strip_indent(s) → string</code> — remove the common leading whitespace from every non-empty line.</p>
<pre><code class="lang-perl">p strip_indent(" a\n b\n")
</code></pre>
</article>
<article class="doc-entry" id="doc-strip-prefix">
<h3><a class="doc-anchor" href="#doc-strip-prefix">#</a> <code>strip_prefix</code></h3>
<p><code>strip_prefix</code> — operation <code>strip prefix</code>. Category: *path helpers*.</p>
<pre><code class="lang-perl">p strip_prefix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-strip-suffix">
<h3><a class="doc-anchor" href="#doc-strip-suffix">#</a> <code>strip_suffix</code></h3>
<p><code>strip_suffix</code> — operation <code>strip suffix</code>. Category: *path helpers*.</p>
<pre><code class="lang-perl">p strip_suffix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-strlen">
<h3><a class="doc-anchor" href="#doc-strlen">#</a> <code>strlen</code></h3>
<p><code>strlen</code> — operation <code>strlen</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p strlen $x
</code></pre>
</article>
<article class="doc-entry" id="doc-strmul">
<h3><a class="doc-anchor" href="#doc-strmul">#</a> <code>strmul</code></h3>
<p><code>strmul</code> — operation <code>strmul</code>. Alias for <code>string_multiply</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p strmul $x
</code></pre>
</article>
<article class="doc-entry" id="doc-strong-pseudoprime">
<h3><a class="doc-anchor" href="#doc-strong-pseudoprime">#</a> <code>strong_pseudoprime</code></h3>
<p><code>strong_pseudoprime</code> — operation <code>strong pseudoprime</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p strong_pseudoprime $x
</code></pre>
</article>
<article class="doc-entry" id="doc-strouhal-full">
<h3><a class="doc-anchor" href="#doc-strouhal-full">#</a> <code>strouhal_full</code></h3>
<p><code>strouhal_full</code> — operation <code>strouhal full</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p strouhal_full $x
</code></pre>
</article>
<article class="doc-entry" id="doc-strsm">
<h3><a class="doc-anchor" href="#doc-strsm">#</a> <code>strsm</code></h3>
<p><code>strsm</code> — operation <code>strsm</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p strsm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-struve-h0">
<h3><a class="doc-anchor" href="#doc-struve-h0">#</a> <code>struve_h0</code></h3>
<p><code>struve_h0</code> — operation <code>struve h0</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p struve_h0 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-struve-h1">
<h3><a class="doc-anchor" href="#doc-struve-h1">#</a> <code>struve_h1</code></h3>
<p><code>struve_h1</code> — operation <code>struve h1</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p struve_h1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-student-pdf">
<h3><a class="doc-anchor" href="#doc-student-pdf">#</a> <code>student_pdf</code></h3>
<p><code>t_pdf</code> (alias <code>tpdf</code>) evaluates Student's t-distribution PDF at x with nu degrees of freedom.</p>
<pre><code class="lang-perl">p tpdf(0, 10) # peak of t(10)
p tpdf(2.228, 10)
</code></pre>
</article>
<article class="doc-entry" id="doc-stulz-min-call">
<h3><a class="doc-anchor" href="#doc-stulz-min-call">#</a> <code>stulz_min_call</code></h3>
<p><code>stulz_min_call</code> — operation <code>stulz min call</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p stulz_min_call $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sturmian-word">
<h3><a class="doc-anchor" href="#doc-sturmian-word">#</a> <code>sturmian_word</code></h3>
<p><code>sturmian_word</code> — operation <code>sturmian word</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p sturmian_word $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sub">
<h3><a class="doc-anchor" href="#doc-sub">#</a> <code>sub</code></h3>
<p>The <code>sub</code> keyword is not supported in stryke. Use <code>fn</code> instead to define functions.</p>
</article>
<article class="doc-entry" id="doc-sub-script">
<h3><a class="doc-anchor" href="#doc-sub-script">#</a> <code>sub_script</code></h3>
<p><code>sub_script</code> — operation <code>sub script</code>. Alias for <code>subscript</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p sub_script $x
</code></pre>
</article>
<article class="doc-entry" id="doc-subfact">
<h3><a class="doc-anchor" href="#doc-subfact">#</a> <code>subfact</code></h3>
<p><code>subfact</code> — operation <code>subfact</code>. Alias for <code>subfactorial</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p subfact $x
</code></pre>
</article>
<article class="doc-entry" id="doc-subfactorial">
<h3><a class="doc-anchor" href="#doc-subfactorial">#</a> <code>subfactorial</code></h3>
<p><code>subfactorial</code> — operation <code>subfactorial</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p subfactorial $x
</code></pre>
</article>
<article class="doc-entry" id="doc-subgame-perfect-eq">
<h3><a class="doc-anchor" href="#doc-subgame-perfect-eq">#</a> <code>subgame_perfect_eq</code></h3>
<p><code>subgame_perfect_eq</code> — operation <code>subgame perfect eq</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p subgame_perfect_eq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-subgradient-step-size">
<h3><a class="doc-anchor" href="#doc-subgradient-step-size">#</a> <code>subgradient_step_size</code></h3>
<p><code>subgradient_step_size</code> — operation <code>subgradient step size</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p subgradient_step_size $x
</code></pre>
</article>
<article class="doc-entry" id="doc-subgraph-isomorphism">
<h3><a class="doc-anchor" href="#doc-subgraph-isomorphism">#</a> <code>subgraph_isomorphism</code></h3>
<p><code>subgraph_isomorphism</code> — operation <code>subgraph isomorphism</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p subgraph_isomorphism $x
</code></pre>
</article>
<article class="doc-entry" id="doc-submodular-curvature-bound">
<h3><a class="doc-anchor" href="#doc-submodular-curvature-bound">#</a> <code>submodular_curvature_bound</code></h3>
<p><code>submodular_curvature_bound</code> — operation <code>submodular curvature bound</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p submodular_curvature_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-submodular-greedy-step">
<h3><a class="doc-anchor" href="#doc-submodular-greedy-step">#</a> <code>submodular_greedy_step</code></h3>
<p><code>submodular_greedy_step</code> — single-step update of <code>submodular greedy</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p submodular_greedy_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-subname">
<h3><a class="doc-anchor" href="#doc-subname">#</a> <code>subname</code></h3>
<p><code>subname</code> — operation <code>subname</code>. Category: *list / aggregate*.</p>
<pre><code class="lang-perl">p subname $x
</code></pre>
</article>
<article class="doc-entry" id="doc-subscript">
<h3><a class="doc-anchor" href="#doc-subscript">#</a> <code>subscript</code></h3>
<p><code>subscript</code> — operation <code>subscript</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p subscript $x
</code></pre>
</article>
<article class="doc-entry" id="doc-subseqs">
<h3><a class="doc-anchor" href="#doc-subseqs">#</a> <code>subseqs</code></h3>
<p><code>subseqs</code> — operation <code>subseqs</code>. Alias for <code>subsequences</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p subseqs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-subsequences">
<h3><a class="doc-anchor" href="#doc-subsequences">#</a> <code>subsequences</code></h3>
<p><code>subsequences</code> — operation <code>subsequences</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p subsequences $x
</code></pre>
</article>
<article class="doc-entry" id="doc-subset-construction">
<h3><a class="doc-anchor" href="#doc-subset-construction">#</a> <code>subset_construction</code></h3>
<p><code>subset_construction</code> — operation <code>subset construction</code>. Category: *compilers / parsing*.</p>
<pre><code class="lang-perl">p subset_construction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-substitution-encrypt">
<h3><a class="doc-anchor" href="#doc-substitution-encrypt">#</a> <code>substitution_encrypt</code></h3>
<p><code>substitution_encrypt</code> — encrypt of <code>substitution</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p substitution_encrypt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-substring">
<h3><a class="doc-anchor" href="#doc-substring">#</a> <code>substring</code></h3>
<p><code>substring</code> — operation <code>substring</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p substring $x
</code></pre>
</article>
<article class="doc-entry" id="doc-substring-count">
<h3><a class="doc-anchor" href="#doc-substring-count">#</a> <code>substring_count</code></h3>
<p><code>substring_count</code> — count of <code>substring</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p substring_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-substring-similarity">
<h3><a class="doc-anchor" href="#doc-substring-similarity">#</a> <code>substring_similarity</code></h3>
<p><code>substring_similarity</code> — similarity metric of <code>substring</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p substring_similarity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-subsumption-check">
<h3><a class="doc-anchor" href="#doc-subsumption-check">#</a> <code>subsumption_check</code></h3>
<p><code>subsumption_check</code> — operation <code>subsumption check</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p subsumption_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-succ">
<h3><a class="doc-anchor" href="#doc-succ">#</a> <code>succ</code></h3>
<p><code>succ</code> — operation <code>succ</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p succ $x
</code></pre>
</article>
<article class="doc-entry" id="doc-suffix-array-naive">
<h3><a class="doc-anchor" href="#doc-suffix-array-naive">#</a> <code>suffix_array_naive</code></h3>
<p><code>suffix_array_naive</code> — operation <code>suffix array naive</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p suffix_array_naive $x
</code></pre>
</article>
<article class="doc-entry" id="doc-suffix-sums">
<h3><a class="doc-anchor" href="#doc-suffix-sums">#</a> <code>suffix_sums</code></h3>
<p><code>suffix_sums</code> — operation <code>suffix sums</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p suffix_sums $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sum-by">
<h3><a class="doc-anchor" href="#doc-sum-by">#</a> <code>sum_by</code></h3>
<p><code>sum_by</code> — operation <code>sum by</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p sum_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sum-degrees">
<h3><a class="doc-anchor" href="#doc-sum-degrees">#</a> <code>sum_degrees</code></h3>
<p><code>sum_degrees</code> — operation <code>sum degrees</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p sum_degrees $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sum-digits">
<h3><a class="doc-anchor" href="#doc-sum-digits">#</a> <code>sum_digits</code></h3>
<p><code>sum_digits</code> — operation <code>sum digits</code>. Category: *math / number theory extras*.</p>
<pre><code class="lang-perl">p sum_digits $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sum-divisors">
<h3><a class="doc-anchor" href="#doc-sum-divisors">#</a> <code>sum_divisors</code></h3>
<p><code>sum_divisors</code> — operation <code>sum divisors</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p sum_divisors $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sum-list">
<h3><a class="doc-anchor" href="#doc-sum-list">#</a> <code>sum_list</code></h3>
<p><code>sum_list</code> — operation <code>sum list</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p sum_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sum-of">
<h3><a class="doc-anchor" href="#doc-sum-of">#</a> <code>sum_of</code></h3>
<p><code>sum_of</code> — operation <code>sum of</code>. Category: *more list helpers*.</p>
<pre><code class="lang-perl">p sum_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sum-squares">
<h3><a class="doc-anchor" href="#doc-sum-squares">#</a> <code>sum_squares</code></h3>
<p><code>sum_squares</code> — operation <code>sum squares</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p sum_squares $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sum-two-squares">
<h3><a class="doc-anchor" href="#doc-sum-two-squares">#</a> <code>sum_two_squares</code></h3>
<p><code>sum_two_squares</code> — operation <code>sum two squares</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p sum_two_squares $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sumb">
<h3><a class="doc-anchor" href="#doc-sumb">#</a> <code>sumb</code></h3>
<p><code>sumb</code> — operation <code>sumb</code>. Alias for <code>sum_by</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p sumb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sumif">
<h3><a class="doc-anchor" href="#doc-sumif">#</a> <code>sumif</code></h3>
<p><code>sumif</code> — operation <code>sumif</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p sumif $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sumifs">
<h3><a class="doc-anchor" href="#doc-sumifs">#</a> <code>sumifs</code></h3>
<p><code>sumifs</code> — operation <code>sumifs</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p sumifs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sumproduct">
<h3><a class="doc-anchor" href="#doc-sumproduct">#</a> <code>sumproduct</code></h3>
<p><code>sumproduct</code> — operation <code>sumproduct</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p sumproduct $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sumsq">
<h3><a class="doc-anchor" href="#doc-sumsq">#</a> <code>sumsq</code></h3>
<p><code>sumsq</code> — operation <code>sumsq</code>. Alias for <code>sum_squares</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p sumsq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sun-distance-au">
<h3><a class="doc-anchor" href="#doc-sun-distance-au">#</a> <code>sun_distance_au</code></h3>
<p><code>sun_distance_au</code> — solar astronomy helper <code>distance au</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p sun_distance_au $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sun-position-low">
<h3><a class="doc-anchor" href="#doc-sun-position-low">#</a> <code>sun_position_low</code></h3>
<p><code>sun_position_low</code> — solar astronomy helper <code>position low</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p sun_position_low $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sun-radius">
<h3><a class="doc-anchor" href="#doc-sun-radius">#</a> <code>sun_radius</code></h3>
<p><code>sun_radius</code> — solar astronomy helper <code>radius</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p sun_radius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sun-rise-unix">
<h3><a class="doc-anchor" href="#doc-sun-rise-unix">#</a> <code>sun_rise_unix</code></h3>
<p><code>sun_rise_unix(lat, lon, unix_today) → int</code> — sunrise unix timestamp at given coords for that date. Uses solar declination from day-of-year, hour angle from <code>acos(−tan(φ)·tan(δ))</code>, and equation-of-time correction. Returns UNDEF for polar day/night (|−tan(φ)·tan(δ)| > 1).</p>
<pre><code class="lang-perl">p sun_rise_unix(37.7749, -122.4194, time())
</code></pre>
</article>
<article class="doc-entry" id="doc-sun-set-unix">
<h3><a class="doc-anchor" href="#doc-sun-set-unix">#</a> <code>sun_set_unix</code></h3>
<p><code>sun_set_unix(lat, lon, unix_today) → int</code> — sunset unix timestamp at given coords for that date. Same model as <code>sun_rise_unix</code> with EoT correction; returns UNDEF for polar day/night.</p>
<pre><code class="lang-perl">p sun_set_unix(37.7749, -122.4194, time())
</code></pre>
</article>
<article class="doc-entry" id="doc-sunion">
<h3><a class="doc-anchor" href="#doc-sunion">#</a> <code>sunion</code></h3>
<p><code>sunion</code> — operation <code>sunion</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p sunion $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sunny-16-rule">
<h3><a class="doc-anchor" href="#doc-sunny-16-rule">#</a> <code>sunny_16_rule</code></h3>
<p><code>sunny_16_rule(iso=100) → {aperture, shutter, iso}</code> — Sunny 16: f/16 at 1/ISO seconds in bright sun.</p>
<pre><code class="lang-perl">p sunny_16_rule(100) # {aperture: 16, shutter: 0.01, iso: 100}
</code></pre>
</article>
<article class="doc-entry" id="doc-sunspot-relative-number">
<h3><a class="doc-anchor" href="#doc-sunspot-relative-number">#</a> <code>sunspot_relative_number</code></h3>
<p><code>sunspot_relative_number</code> — operation <code>sunspot relative number</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p sunspot_relative_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sup">
<h3><a class="doc-anchor" href="#doc-sup">#</a> <code>sup</code></h3>
<p><code>sup</code> — operation <code>sup</code>. Alias for <code>superscript</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p sup $x
</code></pre>
</article>
<article class="doc-entry" id="doc-super-factorial">
<h3><a class="doc-anchor" href="#doc-super-factorial">#</a> <code>super_factorial</code></h3>
<p><code>super_factorial(n) → int</code> — <code>1! · 2! · … · n!</code>.</p>
</article>
<article class="doc-entry" id="doc-superbee-limiter">
<h3><a class="doc-anchor" href="#doc-superbee-limiter">#</a> <code>superbee_limiter</code></h3>
<p><code>superbee_limiter</code> — operation <code>superbee limiter</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p superbee_limiter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-superdense-coding">
<h3><a class="doc-anchor" href="#doc-superdense-coding">#</a> <code>superdense_coding</code></h3>
<p><code>superdense_coding</code> — operation <code>superdense coding</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p superdense_coding $x
</code></pre>
</article>
<article class="doc-entry" id="doc-supergolden">
<h3><a class="doc-anchor" href="#doc-supergolden">#</a> <code>supergolden</code></h3>
<p><code>supergolden</code> — operation <code>supergolden</code>. Alias for <code>supergolden_ratio</code>. Category: *math constants*.</p>
<pre><code class="lang-perl">p supergolden $x
</code></pre>
</article>
<article class="doc-entry" id="doc-supergolden-ratio">
<h3><a class="doc-anchor" href="#doc-supergolden-ratio">#</a> <code>supergolden_ratio</code></h3>
<p><code>supergolden_ratio</code> — ratio of <code>supergolden</code>. Category: *math constants*.</p>
<pre><code class="lang-perl">p supergolden_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-superscript">
<h3><a class="doc-anchor" href="#doc-superscript">#</a> <code>superscript</code></h3>
<p><code>superscript</code> — operation <code>superscript</code>. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p superscript $x
</code></pre>
</article>
<article class="doc-entry" id="doc-supply-elasticity">
<h3><a class="doc-anchor" href="#doc-supply-elasticity">#</a> <code>supply_elasticity</code></h3>
<p><code>supply_elasticity</code> — operation <code>supply elasticity</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p supply_elasticity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-support-level">
<h3><a class="doc-anchor" href="#doc-support-level">#</a> <code>support_level</code></h3>
<p><code>support_level(prices, period=20) → number</code> — rolling min over <code>period</code>; the most recent local floor.</p>
<pre><code class="lang-perl">p support_level(\@closes, 20)
</code></pre>
</article>
<article class="doc-entry" id="doc-surf-keypoints">
<h3><a class="doc-anchor" href="#doc-surf-keypoints">#</a> <code>surf_keypoints</code></h3>
<p><code>surf_keypoints</code> — operation <code>surf keypoints</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p surf_keypoints $x
</code></pre>
</article>
<article class="doc-entry" id="doc-surface-wave-ms">
<h3><a class="doc-anchor" href="#doc-surface-wave-ms">#</a> <code>surface_wave_ms</code></h3>
<p><code>surface_wave_ms</code> — operation <code>surface wave ms</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p surface_wave_ms $x
</code></pre>
</article>
<article class="doc-entry" id="doc-susceptible-to-infected">
<h3><a class="doc-anchor" href="#doc-susceptible-to-infected">#</a> <code>susceptible_to_infected</code></h3>
<p><code>susceptible_to_infected</code> — convert from <code>susceptible</code> to <code>infected</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p susceptible_to_infected $value
</code></pre>
</article>
<article class="doc-entry" id="doc-sw">
<h3><a class="doc-anchor" href="#doc-sw">#</a> <code>sw</code></h3>
<p><code>sw</code> — operation <code>sw</code>. Alias for <code>starts_with</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p sw $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sw-score">
<h3><a class="doc-anchor" href="#doc-sw-score">#</a> <code>sw_score</code></h3>
<p><code>sw_score(a, b, match=2, mismatch=-1, gap=-2) → number</code> — Smith-Waterman local alignment score (max non-negative cell in DP matrix).</p>
<pre><code class="lang-perl">p sw_score("XXACGTYY", "ZZACGTWW")
</code></pre>
</article>
<article class="doc-entry" id="doc-swamee-jain-factor">
<h3><a class="doc-anchor" href="#doc-swamee-jain-factor">#</a> <code>swamee_jain_factor</code></h3>
<p><code>swamee_jain_factor</code> — factor of <code>swamee jain</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p swamee_jain_factor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-swampland-distance-check">
<h3><a class="doc-anchor" href="#doc-swampland-distance-check">#</a> <code>swampland_distance_check</code></h3>
<p><code>swampland_distance_check</code> — operation <code>swampland distance check</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p swampland_distance_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-swap-bits">
<h3><a class="doc-anchor" href="#doc-swap-bits">#</a> <code>swap_bits</code></h3>
<p><code>swap_bits</code> — operation <code>swap bits</code>. Alias for <code>swap_bits_pos</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p swap_bits $x
</code></pre>
</article>
<article class="doc-entry" id="doc-swap-bits-pos">
<h3><a class="doc-anchor" href="#doc-swap-bits-pos">#</a> <code>swap_bits_pos</code></h3>
<p><code>swap_bits_pos</code> — operation <code>swap bits pos</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p swap_bits_pos $x
</code></pre>
</article>
<article class="doc-entry" id="doc-swap-case">
<h3><a class="doc-anchor" href="#doc-swap-case">#</a> <code>swap_case</code></h3>
<p><code>swap_case</code> — operation <code>swap case</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p swap_case $x
</code></pre>
</article>
<article class="doc-entry" id="doc-swap-free">
<h3><a class="doc-anchor" href="#doc-swap-free">#</a> <code>swap_free</code></h3>
<p><code>swap_free</code> — free swap space in bytes.</p>
<pre><code class="lang-perl">p format_bytes(swap_free)
my $pct = swap_total > 0 ? int(swap_free / swap_total * 100) : 100
p "$pct% swap free"
</code></pre>
</article>
<article class="doc-entry" id="doc-swap-indices">
<h3><a class="doc-anchor" href="#doc-swap-indices">#</a> <code>swap_indices</code></h3>
<p><code>swap_indices</code> — operation <code>swap indices</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p swap_indices $x
</code></pre>
</article>
<article class="doc-entry" id="doc-swap-pairs">
<h3><a class="doc-anchor" href="#doc-swap-pairs">#</a> <code>swap_pairs</code></h3>
<p><code>swap_pairs</code> — operation <code>swap pairs</code>. Category: *collection helpers (trivial)*.</p>
<pre><code class="lang-perl">p swap_pairs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-swap-total">
<h3><a class="doc-anchor" href="#doc-swap-total">#</a> <code>swap_total</code></h3>
<p><code>swap_total</code> — total swap space in bytes. Linux: <code>/proc/meminfo SwapTotal</code>. macOS: <code>vm.swapusage</code> sysctl. Returns 0 if swap is disabled, <code>undef</code> on unsupported platforms.</p>
<pre><code class="lang-perl">p swap_total # 8589934592
p format_bytes(swap_total) # 8.0 GiB
</code></pre>
</article>
<article class="doc-entry" id="doc-swap-used">
<h3><a class="doc-anchor" href="#doc-swap-used">#</a> <code>swap_used</code></h3>
<p><code>swap_used</code> — used swap space in bytes (total - free).</p>
<pre><code class="lang-perl">p format_bytes(swap_used)
p "swap pressure" if swap_used > swap_total * 0.8
</code></pre>
</article>
<article class="doc-entry" id="doc-swave-velocity-depth">
<h3><a class="doc-anchor" href="#doc-swave-velocity-depth">#</a> <code>swave_velocity_depth</code></h3>
<p><code>swave_velocity_depth</code> — operation <code>swave velocity depth</code>. Category: *geology, seismology, mineralogy*.</p>
<pre><code class="lang-perl">p swave_velocity_depth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-swelling-strain-step">
<h3><a class="doc-anchor" href="#doc-swelling-strain-step">#</a> <code>swelling_strain_step</code></h3>
<p><code>swelling_strain_step</code> — single-step update of <code>swelling strain</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p swelling_strain_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-swiss-pairing">
<h3><a class="doc-anchor" href="#doc-swiss-pairing">#</a> <code>swiss_pairing</code></h3>
<p><code>swiss_pairing(scores, played) → array</code> — greedy Swiss-system pairings; avoids rematches.</p>
<pre><code class="lang-perl">p swiss_pairing([3, 3, 2, 2, 1, 1], $played)
</code></pre>
</article>
<article class="doc-entry" id="doc-sym4-coeffs">
<h3><a class="doc-anchor" href="#doc-sym4-coeffs">#</a> <code>sym4_coeffs</code></h3>
<p><code>sym4_coeffs</code> — operation <code>sym4 coeffs</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p sym4_coeffs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sym-check">
<h3><a class="doc-anchor" href="#doc-sym-check">#</a> <code>sym_check</code></h3>
<p><code>sym_check</code> — operation <code>sym check</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p sym_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sym-links">
<h3><a class="doc-anchor" href="#doc-sym-links">#</a> <code>sym_links</code></h3>
<p><code>sym_links</code> — operation <code>sym links</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p sym_links $x
</code></pre>
</article>
<article class="doc-entry" id="doc-symmetric-diff">
<h3><a class="doc-anchor" href="#doc-symmetric-diff">#</a> <code>symmetric_diff</code></h3>
<p><code>symmetric_diff</code> — operation <code>symmetric diff</code>. Category: *collection*.</p>
<pre><code class="lang-perl">p symmetric_diff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-symplectic-euler-step">
<h3><a class="doc-anchor" href="#doc-symplectic-euler-step">#</a> <code>symplectic_euler_step</code></h3>
<p><code>symplectic_euler_step</code> — single-step update of <code>symplectic euler</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p symplectic_euler_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-synge-world-function">
<h3><a class="doc-anchor" href="#doc-synge-world-function">#</a> <code>synge_world_function</code></h3>
<p><code>synge_world_function</code> — operation <code>synge world function</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p synge_world_function $x
</code></pre>
</article>
<article class="doc-entry" id="doc-synodic-period">
<h3><a class="doc-anchor" href="#doc-synodic-period">#</a> <code>synodic_period</code></h3>
<p><code>synodic_period</code> — operation <code>synodic period</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p synodic_period $x
</code></pre>
</article>
<article class="doc-entry" id="doc-sys-uptime">
<h3><a class="doc-anchor" href="#doc-sys-uptime">#</a> <code>sys_uptime</code></h3>
<p><code>sys_uptime</code> — system uptime in seconds (float). On Linux reads <code>/proc/uptime</code>. On macOS uses <code>kern.boottime</code> sysctl. This is the wall-clock uptime of the machine, not the stryke process (see <code>uptime_secs</code> for process uptime).</p>
<pre><code class="lang-perl">p sys_uptime # 147951.5
my $days = int(sys_uptime / 86400)
p "up $days days"
</code></pre>
</article>
<article class="doc-entry" id="doc-t1ha">
<h3><a class="doc-anchor" href="#doc-t1ha">#</a> <code>t1ha</code></h3>
<p><code>t1ha</code> — operation <code>t1ha</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p t1ha $x
</code></pre>
</article>
<article class="doc-entry" id="doc-t-test-one-sample">
<h3><a class="doc-anchor" href="#doc-t-test-one-sample">#</a> <code>t_test_one_sample</code></h3>
<p><code>t_test_one_sample($mu, @sample)</code> (alias <code>ttest1</code>) — performs a one-sample t-test comparing a sample mean against a hypothesized population mean mu. Returns [t_statistic, degrees_of_freedom]. Use t-distribution tables for p-value lookup.</p>
<pre><code class="lang-perl">my @sample = (5.1, 4.9, 5.2, 5.0, 4.8)
my $result = ttest1(5.0, @sample)
p "t=$result->[0] df=$result->[1]"
</code></pre>
</article>
<article class="doc-entry" id="doc-t-test-paired">
<h3><a class="doc-anchor" href="#doc-t-test-paired">#</a> <code>t_test_paired</code></h3>
<p><code>t_test_paired(a, b) → {statistic, df, p_value}</code> — paired t-test on equal-length samples; tests <code>H0: mean(a-b) = 0</code>.</p>
<pre><code class="lang-perl">p t_test_paired(\@before, \@after)
</code></pre>
</article>
<article class="doc-entry" id="doc-t-test-two-sample">
<h3><a class="doc-anchor" href="#doc-t-test-two-sample">#</a> <code>t_test_two_sample</code></h3>
<p><code>t_test_two_sample(\@a, \@b)</code> (alias <code>ttest2</code>) — performs an independent two-sample t-test comparing means of two samples. Assumes equal variances. Returns [t_statistic, degrees_of_freedom].</p>
<pre><code class="lang-perl">my @a = (5.1, 5.3, 4.9)
my @b = (4.2, 4.5, 4.1)
my $r = ttest2(\@a, \@b)
p "t=$r->[0] df=$r->[1]"
</code></pre>
</article>
<article class="doc-entry" id="doc-tableau-branch-close">
<h3><a class="doc-anchor" href="#doc-tableau-branch-close">#</a> <code>tableau_branch_close</code></h3>
<p><code>tableau_branch_close</code> — close handle of <code>tableau branch</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p tableau_branch_close $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tabu-search-move-score">
<h3><a class="doc-anchor" href="#doc-tabu-search-move-score">#</a> <code>tabu_search_move_score</code></h3>
<p><code>tabu_search_move_score</code> — score of <code>tabu search move</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p tabu_search_move_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tabulate">
<h3><a class="doc-anchor" href="#doc-tabulate">#</a> <code>tabulate</code></h3>
<p><code>tabulate</code> — frequency table of values. Returns hash of value => count. Like R's table().</p>
<pre><code class="lang-perl">my %t = %{tabulate([qw(a b a c b a)])}
p $t{a} # 3
</code></pre>
</article>
<article class="doc-entry" id="doc-tackle-efficiency">
<h3><a class="doc-anchor" href="#doc-tackle-efficiency">#</a> <code>tackle_efficiency</code></h3>
<p><code>tackle_efficiency</code> — operation <code>tackle efficiency</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p tackle_efficiency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tafel-anodic-current">
<h3><a class="doc-anchor" href="#doc-tafel-anodic-current">#</a> <code>tafel_anodic_current</code></h3>
<p><code>tafel_anodic_current</code> — operation <code>tafel anodic current</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p tafel_anodic_current $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tafel-cathodic-current">
<h3><a class="doc-anchor" href="#doc-tafel-cathodic-current">#</a> <code>tafel_cathodic_current</code></h3>
<p><code>tafel_cathodic_current</code> — operation <code>tafel cathodic current</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p tafel_cathodic_current $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tail-lines">
<h3><a class="doc-anchor" href="#doc-tail-lines">#</a> <code>tail_lines</code></h3>
<p><code>tail_lines</code> — operation <code>tail lines</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p tail_lines $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tail-n">
<h3><a class="doc-anchor" href="#doc-tail-n">#</a> <code>tail_n</code></h3>
<p><code>tail_n</code> — operation <code>tail n</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p tail_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tail-str">
<h3><a class="doc-anchor" href="#doc-tail-str">#</a> <code>tail_str</code></h3>
<p><code>tail_str</code> — operation <code>tail str</code>. Alias for <code>right_str</code>. Category: *string*.</p>
<pre><code class="lang-perl">p tail_str $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tails">
<h3><a class="doc-anchor" href="#doc-tails">#</a> <code>tails</code></h3>
<p><code>tails</code> — operation <code>tails</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p tails $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tajimas-d">
<h3><a class="doc-anchor" href="#doc-tajimas-d">#</a> <code>tajimas_d</code></h3>
<p><code>tajimas_d</code> — operation <code>tajimas d</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p tajimas_d $x
</code></pre>
</article>
<article class="doc-entry" id="doc-take-every">
<h3><a class="doc-anchor" href="#doc-take-every">#</a> <code>take_every</code></h3>
<p><code>take_every</code> — operation <code>take every</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p take_every $x
</code></pre>
</article>
<article class="doc-entry" id="doc-take-last">
<h3><a class="doc-anchor" href="#doc-take-last">#</a> <code>take_last</code></h3>
<p><code>take_last</code> — operation <code>take last</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p take_last $x
</code></pre>
</article>
<article class="doc-entry" id="doc-take-n">
<h3><a class="doc-anchor" href="#doc-take-n">#</a> <code>take_n</code></h3>
<p><code>take_n</code> — operation <code>take n</code>. Category: *collection helpers (trivial)*.</p>
<pre><code class="lang-perl">p take_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-take-n-random">
<h3><a class="doc-anchor" href="#doc-take-n-random">#</a> <code>take_n_random</code></h3>
<p><code>take_n_random</code> — operation <code>take n random</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p take_n_random $x
</code></pre>
</article>
<article class="doc-entry" id="doc-talb">
<h3><a class="doc-anchor" href="#doc-talb">#</a> <code>talb</code></h3>
<p><code>talb</code> — operation <code>talb</code>. Alias for <code>tally_by</code>. Category: *ruby enumerable extras*.</p>
<pre><code class="lang-perl">p talb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tally-by">
<h3><a class="doc-anchor" href="#doc-tally-by">#</a> <code>tally_by</code></h3>
<p><code>tally_by</code> — operation <code>tally by</code>. Category: *ruby enumerable extras*.</p>
<pre><code class="lang-perl">p tally_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tan">
<h3><a class="doc-anchor" href="#doc-tan">#</a> <code>tan</code></h3>
<p><code>tan</code> — operation <code>tan</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p tan $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tanh">
<h3><a class="doc-anchor" href="#doc-tanh">#</a> <code>tanh</code></h3>
<p><code>tanh</code> — operation <code>tanh</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p tanh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tanh-grad">
<h3><a class="doc-anchor" href="#doc-tanh-grad">#</a> <code>tanh_grad</code></h3>
<p><code>tanh_grad</code> — operation <code>tanh grad</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p tanh_grad $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tanimoto-bits">
<h3><a class="doc-anchor" href="#doc-tanimoto-bits">#</a> <code>tanimoto_bits</code></h3>
<p><code>tanimoto_bits</code> — operation <code>tanimoto bits</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p tanimoto_bits $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tanimoto-coeff">
<h3><a class="doc-anchor" href="#doc-tanimoto-coeff">#</a> <code>tanimoto_coeff</code></h3>
<p><code>tanimoto_coeff(a, b) → number</code> — Tanimoto on numeric vectors: <code>a·b / (|a|² + |b|² - a·b)</code>.</p>
</article>
<article class="doc-entry" id="doc-tap-debug">
<h3><a class="doc-anchor" href="#doc-tap-debug">#</a> <code>tap_debug</code></h3>
<p><code>tap_debug</code> — operation <code>tap debug</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p tap_debug $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tap-val">
<h3><a class="doc-anchor" href="#doc-tap-val">#</a> <code>tap_val</code></h3>
<p><code>tap_val</code> — operation <code>tap val</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p tap_val $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tapply">
<h3><a class="doc-anchor" href="#doc-tapply">#</a> <code>tapply</code></h3>
<p><code>tapply</code> — apply a function by group. Takes data, group labels, and function. Returns hash. Like R's tapply().</p>
<pre><code class="lang-perl">my %means = %{tapply([1,2,3,4], ["a","a","b","b"], fn { avg(@{$_[0]}) })}
p $means{a} # 1.5
p $means{b} # 3.5
</code></pre>
</article>
<article class="doc-entry" id="doc-tar-header-checksum">
<h3><a class="doc-anchor" href="#doc-tar-header-checksum">#</a> <code>tar_header_checksum</code></h3>
<p><code>tar_header_checksum</code> — operation <code>tar header checksum</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p tar_header_checksum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tar-header-read">
<h3><a class="doc-anchor" href="#doc-tar-header-read">#</a> <code>tar_header_read</code></h3>
<p><code>tar_header_read(hex_bytes) → hash</code> — parse ustar header → <code>{name, size}</code> (octal size decoded).</p>
</article>
<article class="doc-entry" id="doc-tar-member-record">
<h3><a class="doc-anchor" href="#doc-tar-member-record">#</a> <code>tar_member_record</code></h3>
<p><code>tar_member_record</code> — operation <code>tar member record</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p tar_member_record $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tar-pad-512">
<h3><a class="doc-anchor" href="#doc-tar-pad-512">#</a> <code>tar_pad_512</code></h3>
<p><code>tar_pad_512</code> — operation <code>tar pad 512</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p tar_pad_512 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-target-heart-rate">
<h3><a class="doc-anchor" href="#doc-target-heart-rate">#</a> <code>target_heart_rate</code></h3>
<p><code>target_heart_rate</code> — rate of <code>target heart</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p target_heart_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tarjan-scc-step">
<h3><a class="doc-anchor" href="#doc-tarjan-scc-step">#</a> <code>tarjan_scc_step</code></h3>
<p><code>tarjan_scc_step</code> — single-step update of <code>tarjan scc</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p tarjan_scc_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tau">
<h3><a class="doc-anchor" href="#doc-tau">#</a> <code>tau</code></h3>
<p><code>tau</code> — operation <code>tau</code>. Category: *constants*.</p>
<pre><code class="lang-perl">p tau $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tax">
<h3><a class="doc-anchor" href="#doc-tax">#</a> <code>tax</code></h3>
<p><code>tax</code> — operation <code>tax</code>. Category: *finance*.</p>
<pre><code class="lang-perl">p tax $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tax-amount">
<h3><a class="doc-anchor" href="#doc-tax-amount">#</a> <code>tax_amount</code></h3>
<p><code>tax_amount</code> — operation <code>tax amount</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p tax_amount $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tax-incidence">
<h3><a class="doc-anchor" href="#doc-tax-incidence">#</a> <code>tax_incidence</code></h3>
<p><code>tax_incidence</code> — operation <code>tax incidence</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p tax_incidence $x
</code></pre>
</article>
<article class="doc-entry" id="doc-taylor-diagram-score">
<h3><a class="doc-anchor" href="#doc-taylor-diagram-score">#</a> <code>taylor_diagram_score</code></h3>
<p><code>taylor_diagram_score</code> — score of <code>taylor diagram</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p taylor_diagram_score $x
</code></pre>
</article>
<article class="doc-entry" id="doc-taylor-microscale-step">
<h3><a class="doc-anchor" href="#doc-taylor-microscale-step">#</a> <code>taylor_microscale_step</code></h3>
<p><code>taylor_microscale_step</code> — single-step update of <code>taylor microscale</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p taylor_microscale_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-taylor-window">
<h3><a class="doc-anchor" href="#doc-taylor-window">#</a> <code>taylor_window</code></h3>
<p><code>taylor_window</code> — operation <code>taylor window</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p taylor_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tcrossprod">
<h3><a class="doc-anchor" href="#doc-tcrossprod">#</a> <code>tcrossprod</code></h3>
<p><code>tcrossprod</code> — M * t(M) (R's tcrossprod).</p>
<pre><code class="lang-perl">my $aat = tcrossprod([[1,2],[3,4]]) # [[5,11],[11,25]]
</code></pre>
</article>
<article class="doc-entry" id="doc-td">
<h3><a class="doc-anchor" href="#doc-td">#</a> <code>td</code></h3>
<p><code>td</code> — operation <code>td</code>. Alias for <code>toml_decode</code>. Category: *serialization (stryke-only encoders)*.</p>
<pre><code class="lang-perl">p td $x
</code></pre>
</article>
<article class="doc-entry" id="doc-td-lambda-update">
<h3><a class="doc-anchor" href="#doc-td-lambda-update">#</a> <code>td_lambda_update</code></h3>
<p><code>td_lambda_update</code> — update step of <code>td lambda</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p td_lambda_update $x
</code></pre>
</article>
<article class="doc-entry" id="doc-td-zero-update">
<h3><a class="doc-anchor" href="#doc-td-zero-update">#</a> <code>td_zero_update</code></h3>
<p><code>td_zero_update</code> — update step of <code>td zero</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p td_zero_update $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tdigest-add">
<h3><a class="doc-anchor" href="#doc-tdigest-add">#</a> <code>tdigest_add</code></h3>
<p><code>tdigest_add</code> — operation <code>tdigest add</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p tdigest_add $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tdigest-new">
<h3><a class="doc-anchor" href="#doc-tdigest-new">#</a> <code>tdigest_new</code></h3>
<p><code>tdigest_new</code> — constructor of <code>tdigest</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p tdigest_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tdigest-quantile">
<h3><a class="doc-anchor" href="#doc-tdigest-quantile">#</a> <code>tdigest_quantile</code></h3>
<p><code>tdigest_quantile</code> — operation <code>tdigest quantile</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p tdigest_quantile $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tdilate">
<h3><a class="doc-anchor" href="#doc-tdilate">#</a> <code>tdilate</code></h3>
<p><code>time_dilation($proper_time, $velocity)</code> (alias <code>tdilate</code>) — dilated time Δt = Δt₀ × γ. Time appears to slow for moving objects.</p>
<pre><code class="lang-perl">p tdilate(1, 0.99 * 3e8) # ~7.09 s (1 second at 99% c)
</code></pre>
</article>
<article class="doc-entry" id="doc-te">
<h3><a class="doc-anchor" href="#doc-te">#</a> <code>te</code></h3>
<p><code>te</code> — operation <code>te</code>. Alias for <code>toml_encode</code>. Category: *serialization (stryke-only encoders)*.</p>
<pre><code class="lang-perl">p te $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tee-iter">
<h3><a class="doc-anchor" href="#doc-tee-iter">#</a> <code>tee_iter</code></h3>
<p><code>tee_iter</code> — operation <code>tee iter</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p tee_iter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-teei">
<h3><a class="doc-anchor" href="#doc-teei">#</a> <code>teei</code></h3>
<p><code>teei</code> — operation <code>teei</code>. Alias for <code>tee_iter</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p teei $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tema">
<h3><a class="doc-anchor" href="#doc-tema">#</a> <code>tema</code></h3>
<p><code>tema(prices, period=10) → array</code> — triple EMA: <code>3·EMA − 3·EMA(EMA) + EMA(EMA(EMA))</code>. Designed to remove EMA lag with no extra phase shift.</p>
<pre><code class="lang-perl">p tema(\@prices, 21)
</code></pre>
</article>
<article class="doc-entry" id="doc-temp-dir">
<h3><a class="doc-anchor" href="#doc-temp-dir">#</a> <code>temp_dir</code></h3>
<p><code>temp_dir</code> — operation <code>temp dir</code>. Category: *system introspection*.</p>
<pre><code class="lang-perl">p temp_dir $x
</code></pre>
</article>
<article class="doc-entry" id="doc-template-match">
<h3><a class="doc-anchor" href="#doc-template-match">#</a> <code>template_match</code></h3>
<p><code>template_match</code> — operation <code>template match</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p template_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tempo-to-ms">
<h3><a class="doc-anchor" href="#doc-tempo-to-ms">#</a> <code>tempo_to_ms</code></h3>
<p><code>tempo_to_ms</code> — convert from <code>tempo</code> to <code>ms</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p tempo_to_ms $value
</code></pre>
</article>
<article class="doc-entry" id="doc-tempo-to-ms-per-beat">
<h3><a class="doc-anchor" href="#doc-tempo-to-ms-per-beat">#</a> <code>tempo_to_ms_per_beat</code></h3>
<p><code>tempo_to_ms_per_beat(bpm) → number</code> — <code>60000 / bpm</code>. Common for sequencer math.</p>
<pre><code class="lang-perl">p tempo_to_ms_per_beat(120) # 500
</code></pre>
</article>
<article class="doc-entry" id="doc-tempplanck">
<h3><a class="doc-anchor" href="#doc-tempplanck">#</a> <code>tempplanck</code></h3>
<p><code>tempplanck</code> — operation <code>tempplanck</code>. Alias for <code>planck_temperature</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p tempplanck $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tensor-antisymmetrize-two">
<h3><a class="doc-anchor" href="#doc-tensor-antisymmetrize-two">#</a> <code>tensor_antisymmetrize_two</code></h3>
<p><code>tensor_antisymmetrize_two</code> — operation <code>tensor antisymmetrize two</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p tensor_antisymmetrize_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tensor-contract-two">
<h3><a class="doc-anchor" href="#doc-tensor-contract-two">#</a> <code>tensor_contract_two</code></h3>
<p><code>tensor_contract_two</code> — operation <code>tensor contract two</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p tensor_contract_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tensor-outer-two">
<h3><a class="doc-anchor" href="#doc-tensor-outer-two">#</a> <code>tensor_outer_two</code></h3>
<p><code>tensor_outer_two</code> — operation <code>tensor outer two</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p tensor_outer_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tensor-symmetrize-two">
<h3><a class="doc-anchor" href="#doc-tensor-symmetrize-two">#</a> <code>tensor_symmetrize_two</code></h3>
<p><code>tensor_symmetrize_two</code> — operation <code>tensor symmetrize two</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p tensor_symmetrize_two $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tensor-trace-index">
<h3><a class="doc-anchor" href="#doc-tensor-trace-index">#</a> <code>tensor_trace_index</code></h3>
<p><code>tensor_trace_index</code> — index of <code>tensor trace</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p tensor_trace_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-term-life-a-n-t">
<h3><a class="doc-anchor" href="#doc-term-life-a-n-t">#</a> <code>term_life_a_n_t</code></h3>
<p><code>term_life_a_n_t</code> — operation <code>term life a n t</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p term_life_a_n_t $x
</code></pre>
</article>
<article class="doc-entry" id="doc-terminal-velocity">
<h3><a class="doc-anchor" href="#doc-terminal-velocity">#</a> <code>terminal_velocity</code></h3>
<p><code>terminal_velocity</code> — operation <code>terminal velocity</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p terminal_velocity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ternary-search">
<h3><a class="doc-anchor" href="#doc-ternary-search">#</a> <code>ternary_search</code></h3>
<p><code>ternary_search(sorted, target) → int</code> — divides search range into thirds; <code>O(log n)</code> like binary search.</p>
<pre><code class="lang-perl">p ternary_search([1,3,5,7,9,11,13], 9) # 4
</code></pre>
</article>
<article class="doc-entry" id="doc-test-skip">
<h3><a class="doc-anchor" href="#doc-test-skip">#</a> <code>test_skip</code></h3>
<p><code>test_skip</code> — testing helper <code>skip</code>. Category: *testing framework*.</p>
<pre><code class="lang-perl">p test_skip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tetrahedral">
<h3><a class="doc-anchor" href="#doc-tetrahedral">#</a> <code>tetrahedral</code></h3>
<p><code>tetrahedral(n) → int</code> — <code>n·(n+1)·(n+2) / 6</code>.</p>
</article>
<article class="doc-entry" id="doc-tetrahedral-number">
<h3><a class="doc-anchor" href="#doc-tetrahedral-number">#</a> <code>tetrahedral_number</code></h3>
<p><code>tetrahedral_number</code> — operation <code>tetrahedral number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p tetrahedral_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tetranacci">
<h3><a class="doc-anchor" href="#doc-tetranacci">#</a> <code>tetranacci</code></h3>
<p><code>tetranacci(n) → int</code> — like Fibonacci but summing the previous four terms.</p>
</article>
<article class="doc-entry" id="doc-text-after">
<h3><a class="doc-anchor" href="#doc-text-after">#</a> <code>text_after</code></h3>
<p><code>text_after</code> — text helper <code>after</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p text_after $x
</code></pre>
</article>
<article class="doc-entry" id="doc-text-after-last">
<h3><a class="doc-anchor" href="#doc-text-after-last">#</a> <code>text_after_last</code></h3>
<p><code>text_after_last</code> — text helper <code>after last</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p text_after_last $x
</code></pre>
</article>
<article class="doc-entry" id="doc-text-before">
<h3><a class="doc-anchor" href="#doc-text-before">#</a> <code>text_before</code></h3>
<p><code>text_before</code> — text helper <code>before</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p text_before $x
</code></pre>
</article>
<article class="doc-entry" id="doc-text-before-last">
<h3><a class="doc-anchor" href="#doc-text-before-last">#</a> <code>text_before_last</code></h3>
<p><code>text_before_last</code> — text helper <code>before last</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p text_before_last $x
</code></pre>
</article>
<article class="doc-entry" id="doc-text-between">
<h3><a class="doc-anchor" href="#doc-text-between">#</a> <code>text_between</code></h3>
<p><code>text_between</code> — text helper <code>between</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p text_between $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tf2sos-step">
<h3><a class="doc-anchor" href="#doc-tf2sos-step">#</a> <code>tf2sos_step</code></h3>
<p><code>tf2sos_step</code> — single-step update of <code>tf2sos</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p tf2sos_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tf2zpk-step">
<h3><a class="doc-anchor" href="#doc-tf2zpk-step">#</a> <code>tf2zpk_step</code></h3>
<p><code>tf2zpk_step</code> — single-step update of <code>tf2zpk</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p tf2zpk_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tfidf-compute">
<h3><a class="doc-anchor" href="#doc-tfidf-compute">#</a> <code>tfidf_compute</code></h3>
<p><code>tfidf_compute(docs) → {vocab, matrix}</code> — TF-IDF matrix <code>[doc][term]</code>. Each row is a document's TF-IDF vector.</p>
<pre><code class="lang-perl">my $r = tfidf_compute([["the","cat"], ["a","dog"]])
</code></pre>
</article>
<article class="doc-entry" id="doc-tfld">
<h3><a class="doc-anchor" href="#doc-tfld">#</a> <code>tfld</code></h3>
<p><code>tfld</code> — operation <code>tfld</code>. Alias for <code>try_fold</code>. Category: *rust iterator methods*.</p>
<pre><code class="lang-perl">p tfld $x
</code></pre>
</article>
<article class="doc-entry" id="doc-theil-sen-slope">
<h3><a class="doc-anchor" href="#doc-theil-sen-slope">#</a> <code>theil_sen_slope</code></h3>
<p><code>theil_sen_slope</code> — operation <code>theil sen slope</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p theil_sen_slope $x
</code></pre>
</article>
<article class="doc-entry" id="doc-then-fn">
<h3><a class="doc-anchor" href="#doc-then-fn">#</a> <code>then_fn</code></h3>
<p><code>then_fn</code> — operation <code>then fn</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p then_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-thermal-mean-photons">
<h3><a class="doc-anchor" href="#doc-thermal-mean-photons">#</a> <code>thermal_mean_photons</code></h3>
<p><code>thermal_mean_photons</code> — operation <code>thermal mean photons</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p thermal_mean_photons $x
</code></pre>
</article>
<article class="doc-entry" id="doc-thermal-runaway-threshold">
<h3><a class="doc-anchor" href="#doc-thermal-runaway-threshold">#</a> <code>thermal_runaway_threshold</code></h3>
<p><code>thermal_runaway_threshold</code> — operation <code>thermal runaway threshold</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p thermal_runaway_threshold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-thermal-wind-step">
<h3><a class="doc-anchor" href="#doc-thermal-wind-step">#</a> <code>thermal_wind_step</code></h3>
<p><code>thermal_wind_step</code> — single-step update of <code>thermal wind</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p thermal_wind_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-theta2">
<h3><a class="doc-anchor" href="#doc-theta2">#</a> <code>theta2</code></h3>
<p><code>theta2</code> — operation <code>theta2</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p theta2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-theta3">
<h3><a class="doc-anchor" href="#doc-theta3">#</a> <code>theta3</code></h3>
<p><code>theta3</code> — operation <code>theta3</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p theta3 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-thfn">
<h3><a class="doc-anchor" href="#doc-thfn">#</a> <code>thfn</code></h3>
<p><code>thfn</code> — operation <code>thfn</code>. Alias for <code>then_fn</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p thfn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-thin-lens">
<h3><a class="doc-anchor" href="#doc-thin-lens">#</a> <code>thin_lens</code></h3>
<p><code>thin_lens($object_dist, $focal_length)</code> (alias <code>thinlens</code>) — image distance using 1/f = 1/do + 1/di.</p>
<pre><code class="lang-perl">p thinlens(30, 20) # 60 cm (real image)
p thinlens(10, 20) # -20 cm (virtual image)
</code></pre>
</article>
<article class="doc-entry" id="doc-thin-lens-v">
<h3><a class="doc-anchor" href="#doc-thin-lens-v">#</a> <code>thin_lens_v</code></h3>
<p><code>thin_lens_v</code> — operation <code>thin lens v</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p thin_lens_v $x
</code></pre>
</article>
<article class="doc-entry" id="doc-third-elem">
<h3><a class="doc-anchor" href="#doc-third-elem">#</a> <code>third_elem</code></h3>
<p><code>third_elem</code> — operation <code>third elem</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p third_elem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-thompson-beta-choose">
<h3><a class="doc-anchor" href="#doc-thompson-beta-choose">#</a> <code>thompson_beta_choose</code></h3>
<p><code>thompson_beta_choose(alphas, betas, seed=0) → int</code> — Thompson sampling from per-arm Beta posteriors.</p>
</article>
<article class="doc-entry" id="doc-thompson-sample-beta">
<h3><a class="doc-anchor" href="#doc-thompson-sample-beta">#</a> <code>thompson_sample_beta</code></h3>
<p><code>thompson_sample_beta</code> — operation <code>thompson sample beta</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p thompson_sample_beta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-three-opt-delta">
<h3><a class="doc-anchor" href="#doc-three-opt-delta">#</a> <code>three_opt_delta</code></h3>
<p><code>three_opt_delta</code> — operation <code>three opt delta</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p three_opt_delta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-threshold-act">
<h3><a class="doc-anchor" href="#doc-threshold-act">#</a> <code>threshold_act</code></h3>
<p><code>threshold_act</code> — operation <code>threshold act</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p threshold_act $x
</code></pre>
</article>
<article class="doc-entry" id="doc-threshold-hard-value">
<h3><a class="doc-anchor" href="#doc-threshold-hard-value">#</a> <code>threshold_hard_value</code></h3>
<p><code>threshold_hard_value</code> — value of <code>threshold hard</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p threshold_hard_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-threshold-soft-value">
<h3><a class="doc-anchor" href="#doc-threshold-soft-value">#</a> <code>threshold_soft_value</code></h3>
<p><code>threshold_soft_value</code> — value of <code>threshold soft</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p threshold_soft_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-thue-morse-string">
<h3><a class="doc-anchor" href="#doc-thue-morse-string">#</a> <code>thue_morse_string</code></h3>
<p><code>thue_morse_string</code> — operation <code>thue morse string</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p thue_morse_string $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ti2">
<h3><a class="doc-anchor" href="#doc-ti2">#</a> <code>ti2</code></h3>
<p><code>ti2</code> — operation <code>ti2</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p ti2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tidal-force">
<h3><a class="doc-anchor" href="#doc-tidal-force">#</a> <code>tidal_force</code></h3>
<p><code>tidal_force</code> — operation <code>tidal force</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p tidal_force $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tied">
<h3><a class="doc-anchor" href="#doc-tied">#</a> <code>tied</code></h3>
<p><code>tied</code> — operation <code>tied</code>. Category: *type / reflection*.</p>
<pre><code class="lang-perl">p tied $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tile-xyz-to-lat-lng">
<h3><a class="doc-anchor" href="#doc-tile-xyz-to-lat-lng">#</a> <code>tile_xyz_to_lat_lng</code></h3>
<p><code>tile_xyz_to_lat_lng</code> — convert from <code>tile xyz</code> to <code>lat lng</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p tile_xyz_to_lat_lng $value
</code></pre>
</article>
<article class="doc-entry" id="doc-time-sig-subdivision">
<h3><a class="doc-anchor" href="#doc-time-sig-subdivision">#</a> <code>time_sig_subdivision</code></h3>
<p><code>time_sig_subdivision</code> — operation <code>time sig subdivision</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p time_sig_subdivision $x
</code></pre>
</article>
<article class="doc-entry" id="doc-times-fn">
<h3><a class="doc-anchor" href="#doc-times-fn">#</a> <code>times_fn</code></h3>
<p><code>times_fn</code> — operation <code>times fn</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p times_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-timf">
<h3><a class="doc-anchor" href="#doc-timf">#</a> <code>timf</code></h3>
<p><code>timf</code> — operation <code>timf</code>. Alias for <code>times_fn</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p timf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tip">
<h3><a class="doc-anchor" href="#doc-tip">#</a> <code>tip</code></h3>
<p><code>tip</code> — operation <code>tip</code>. Category: *finance*.</p>
<pre><code class="lang-perl">p tip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tip-amount">
<h3><a class="doc-anchor" href="#doc-tip-amount">#</a> <code>tip_amount</code></h3>
<p><code>tip_amount</code> — operation <code>tip amount</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p tip_amount $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tisserand-param">
<h3><a class="doc-anchor" href="#doc-tisserand-param">#</a> <code>tisserand_param</code></h3>
<p><code>tisserand_param</code> — operation <code>tisserand param</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p tisserand_param $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tit-for-tat-step">
<h3><a class="doc-anchor" href="#doc-tit-for-tat-step">#</a> <code>tit_for_tat_step</code></h3>
<p><code>tit_for_tat_step</code> — single-step update of <code>tit for tat</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p tit_for_tat_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-title">
<h3><a class="doc-anchor" href="#doc-title">#</a> <code>title</code></h3>
<p><code>title</code> — operation <code>title</code>. Alias for <code>title_case</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p title $x
</code></pre>
</article>
<article class="doc-entry" id="doc-title-case">
<h3><a class="doc-anchor" href="#doc-title-case">#</a> <code>title_case</code></h3>
<p><code>title_case</code> — operation <code>title case</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p title_case $x
</code></pre>
</article>
<article class="doc-entry" id="doc-title-words">
<h3><a class="doc-anchor" href="#doc-title-words">#</a> <code>title_words</code></h3>
<p><code>title_words</code> — operation <code>title words</code>. Alias for <code>capitalize_words</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p title_words $x
</code></pre>
</article>
<article class="doc-entry" id="doc-titration-endpoint-index">
<h3><a class="doc-anchor" href="#doc-titration-endpoint-index">#</a> <code>titration_endpoint_index</code></h3>
<p><code>titration_endpoint_index</code> — index of <code>titration endpoint</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p titration_endpoint_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-titration-ph-endpoint">
<h3><a class="doc-anchor" href="#doc-titration-ph-endpoint">#</a> <code>titration_ph_endpoint</code></h3>
<p><code>titration_ph_endpoint</code> — operation <code>titration ph endpoint</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p titration_ph_endpoint $x
</code></pre>
</article>
<article class="doc-entry" id="doc-titration-volume">
<h3><a class="doc-anchor" href="#doc-titration-volume">#</a> <code>titration_volume</code></h3>
<p><code>titration_volume</code> — operation <code>titration volume</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p titration_volume $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tkeys">
<h3><a class="doc-anchor" href="#doc-tkeys">#</a> <code>tkeys</code></h3>
<p><code>tkeys</code> — operation <code>tkeys</code>. Alias for <code>transform_keys</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p tkeys $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tle-mean-motion">
<h3><a class="doc-anchor" href="#doc-tle-mean-motion">#</a> <code>tle_mean_motion</code></h3>
<p><code>tle_mean_motion</code> — operation <code>tle mean motion</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p tle_mean_motion $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tm-marmur">
<h3><a class="doc-anchor" href="#doc-tm-marmur">#</a> <code>tm_marmur</code></h3>
<p><code>tm_marmur</code> — operation <code>tm marmur</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p tm_marmur $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tm-wallace">
<h3><a class="doc-anchor" href="#doc-tm-wallace">#</a> <code>tm_wallace</code></h3>
<p><code>tm_wallace</code> — operation <code>tm wallace</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p tm_wallace $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-array">
<h3><a class="doc-anchor" href="#doc-to-array">#</a> <code>to_array</code></h3>
<p><code>to_array</code> — convert input to array form. Category: *list helpers*.</p>
<pre><code class="lang-perl">p to_array $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-ascii">
<h3><a class="doc-anchor" href="#doc-to-ascii">#</a> <code>to_ascii</code></h3>
<p><code>to_ascii</code> — convert input to ascii form. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p to_ascii $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-base">
<h3><a class="doc-anchor" href="#doc-to-base">#</a> <code>to_base</code></h3>
<p><code>to_base</code> — convert input to base form. Category: *base conversion*.</p>
<pre><code class="lang-perl">p to_base $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-bin">
<h3><a class="doc-anchor" href="#doc-to-bin">#</a> <code>to_bin</code></h3>
<p><code>to_bin</code> — convert input to bin form. Category: *base conversion*.</p>
<pre><code class="lang-perl">p to_bin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-bool">
<h3><a class="doc-anchor" href="#doc-to-bool">#</a> <code>to_bool</code></h3>
<p><code>to_bool</code> — convert input to bool form. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p to_bool $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-csv-line">
<h3><a class="doc-anchor" href="#doc-to-csv-line">#</a> <code>to_csv_line</code></h3>
<p><code>to_csv_line</code> — convert input to csv line form. Category: *string helpers*.</p>
<pre><code class="lang-perl">p to_csv_line $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-emoji-num">
<h3><a class="doc-anchor" href="#doc-to-emoji-num">#</a> <code>to_emoji_num</code></h3>
<p><code>to_emoji_num</code> — convert input to emoji num form. Category: *encoding / phonetics*.</p>
<pre><code class="lang-perl">p to_emoji_num $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-float">
<h3><a class="doc-anchor" href="#doc-to-float">#</a> <code>to_float</code></h3>
<p><code>to_float</code> — convert input to float form. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p to_float $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-float-each">
<h3><a class="doc-anchor" href="#doc-to-float-each">#</a> <code>to_float_each</code></h3>
<p><code>to_float_each</code> — convert input to float each form. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p to_float_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-hash">
<h3><a class="doc-anchor" href="#doc-to-hash">#</a> <code>to_hash</code></h3>
<p><code>to_hash LIST</code> — collect a flat list of key-value pairs into a Perl hash.</p>
<p>The list is consumed two elements at a time: odd-positioned elements become keys and even-positioned elements become values. If there is an odd number of elements, the last key maps to <code>undef</code>. This is a terminal operation that materializes the full stream. Useful for converting pipeline output into a lookup table.</p>
<pre><code class="lang-perl">my %h = qw(a 1 b 2) |> to_hash
@pairs |> to_hash
my %freq = @words |> map { _, 1 } |> to_hash
</code></pre>
</article>
<article class="doc-entry" id="doc-to-hex">
<h3><a class="doc-anchor" href="#doc-to-hex">#</a> <code>to_hex</code></h3>
<p><code>to_hex</code> — convert input to hex form. Category: *base conversion*.</p>
<pre><code class="lang-perl">p to_hex $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-int">
<h3><a class="doc-anchor" href="#doc-to-int">#</a> <code>to_int</code></h3>
<p><code>to_int</code> — convert input to int form. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p to_int $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-int-each">
<h3><a class="doc-anchor" href="#doc-to-int-each">#</a> <code>to_int_each</code></h3>
<p><code>to_int_each</code> — convert input to int each form. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p to_int_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-oct">
<h3><a class="doc-anchor" href="#doc-to-oct">#</a> <code>to_oct</code></h3>
<p><code>to_oct</code> — convert input to oct form. Category: *base conversion*.</p>
<pre><code class="lang-perl">p to_oct $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-pairs">
<h3><a class="doc-anchor" href="#doc-to-pairs">#</a> <code>to_pairs</code></h3>
<p><code>to_pairs</code> — convert input to pairs form. Category: *list helpers*.</p>
<pre><code class="lang-perl">p to_pairs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-reversed">
<h3><a class="doc-anchor" href="#doc-to-reversed">#</a> <code>to_reversed</code></h3>
<p><code>to_reversed</code> — convert input to reversed form. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p to_reversed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-set">
<h3><a class="doc-anchor" href="#doc-to-set">#</a> <code>to_set</code></h3>
<p><code>to_set LIST</code> — collect a list or iterator into a <code>set</code> object with O(1) membership testing.</p>
<p>The resulting set contains only unique elements (duplicates are discarded). This is a terminal operation that materializes the full stream. The returned set supports <code>->contains($val)</code>, <code>->union($other)</code>, <code>->intersection($other)</code>, and <code>->difference($other)</code>. Use this when you need fast repeated lookups against a collection of values.</p>
<pre><code class="lang-perl">my $s = 1:5 |> to_set
@words |> to_set # deduplicated set
my $allowed = to_set @whitelist
p $allowed->contains("foo")
</code></pre>
</article>
<article class="doc-entry" id="doc-to-sorted">
<h3><a class="doc-anchor" href="#doc-to-sorted">#</a> <code>to_sorted</code></h3>
<p><code>to_sorted</code> — convert input to sorted form. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p to_sorted $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-spliced">
<h3><a class="doc-anchor" href="#doc-to-spliced">#</a> <code>to_spliced</code></h3>
<p><code>to_spliced</code> — convert input to spliced form. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p to_spliced $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-string">
<h3><a class="doc-anchor" href="#doc-to-string">#</a> <code>to_string</code></h3>
<p><code>to_string</code> — convert input to string form. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p to_string $x
</code></pre>
</article>
<article class="doc-entry" id="doc-to-string-val">
<h3><a class="doc-anchor" href="#doc-to-string-val">#</a> <code>to_string_val</code></h3>
<p><code>to_string_val</code> — convert input to string val form. Category: *misc / utility*.</p>
<pre><code class="lang-perl">p to_string_val $x
</code></pre>
</article>
<article class="doc-entry" id="doc-toasc">
<h3><a class="doc-anchor" href="#doc-toasc">#</a> <code>toasc</code></h3>
<p><code>toasc</code> — operation <code>toasc</code>. Alias for <code>to_ascii</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p toasc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tobit-log-likelihood">
<h3><a class="doc-anchor" href="#doc-tobit-log-likelihood">#</a> <code>tobit_log_likelihood</code></h3>
<p><code>tobit_log_likelihood</code> — operation <code>tobit log likelihood</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p tobit_log_likelihood $x
</code></pre>
</article>
<article class="doc-entry" id="doc-today">
<h3><a class="doc-anchor" href="#doc-today">#</a> <code>today</code></h3>
<p><code>today</code> — operation <code>today</code>. Category: *date*.</p>
<pre><code class="lang-perl">p today $x
</code></pre>
</article>
<article class="doc-entry" id="doc-todd-genus-eval">
<h3><a class="doc-anchor" href="#doc-todd-genus-eval">#</a> <code>todd_genus_eval</code></h3>
<p><code>todd_genus_eval</code> — operation <code>todd genus eval</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p todd_genus_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-toffoli-gate">
<h3><a class="doc-anchor" href="#doc-toffoli-gate">#</a> <code>toffoli_gate</code></h3>
<p><code>toffoli_gate</code> — operation <code>toffoli gate</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p toffoli_gate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-token">
<h3><a class="doc-anchor" href="#doc-token">#</a> <code>token</code></h3>
<p><code>token</code> — operation <code>token</code>. Category: *id helpers*.</p>
<pre><code class="lang-perl">p token $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tokenize-bpe">
<h3><a class="doc-anchor" href="#doc-tokenize-bpe">#</a> <code>tokenize_bpe</code></h3>
<p><code>tokenize_bpe(s, merges) → array</code> — Byte-Pair Encoding tokenisation against a merge table.</p>
</article>
<article class="doc-entry" id="doc-tokenize-sentencepiece">
<h3><a class="doc-anchor" href="#doc-tokenize-sentencepiece">#</a> <code>tokenize_sentencepiece</code></h3>
<p><code>tokenize_sentencepiece(s) → array</code> — SentencePiece-like tokenisation; prepends ▁ to word starts.</p>
<pre><code class="lang-perl">p tokenize_sentencepiece("hello world") # ["▁hello", "▁world"]
</code></pre>
</article>
<article class="doc-entry" id="doc-tokenize-simple">
<h3><a class="doc-anchor" href="#doc-tokenize-simple">#</a> <code>tokenize_simple</code></h3>
<p><code>tokenize_simple(s) → array</code> — split on whitespace and basic punctuation.</p>
</article>
<article class="doc-entry" id="doc-tokenize-subword">
<h3><a class="doc-anchor" href="#doc-tokenize-subword">#</a> <code>tokenize_subword</code></h3>
<p><code>tokenize_subword(s, max_len=4) → array</code> — naive subword tokenisation: splits on non-alphanumeric boundaries, then chunks long words into pieces of at most <code>max_len</code> characters.</p>
</article>
<article class="doc-entry" id="doc-tokenize-word">
<h3><a class="doc-anchor" href="#doc-tokenize-word">#</a> <code>tokenize_word</code></h3>
<p><code>tokenize_word(s) → array</code> — whitespace tokeniser.</p>
</article>
<article class="doc-entry" id="doc-tomorrow">
<h3><a class="doc-anchor" href="#doc-tomorrow">#</a> <code>tomorrow</code></h3>
<p><code>tomorrow</code> — operation <code>tomorrow</code>. Category: *date*.</p>
<pre><code class="lang-perl">p tomorrow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-top">
<h3><a class="doc-anchor" href="#doc-top">#</a> <code>top</code></h3>
<p><code>top</code> — operation <code>top</code>. Category: *pipeline / string helpers*.</p>
<pre><code class="lang-perl">p top $x
</code></pre>
</article>
<article class="doc-entry" id="doc-top-hat-transform">
<h3><a class="doc-anchor" href="#doc-top-hat-transform">#</a> <code>top_hat_transform</code></h3>
<p><code>top_hat_transform(image, size=3) → matrix</code> — <code>image - opening</code>. Extracts bright details smaller than the structuring element.</p>
</article>
<article class="doc-entry" id="doc-top-k-indices">
<h3><a class="doc-anchor" href="#doc-top-k-indices">#</a> <code>top_k_indices</code></h3>
<p><code>top_k_indices(values, k=5) → array</code> — indices of the <code>k</code> largest values, sorted descending.</p>
<pre><code class="lang-perl">p top_k_indices([3,1,4,1,5,9,2,6], 3) # [5, 7, 4]
</code></pre>
</article>
<article class="doc-entry" id="doc-top-k-min-heap">
<h3><a class="doc-anchor" href="#doc-top-k-min-heap">#</a> <code>top_k_min_heap</code></h3>
<p><code>top_k_min_heap</code> — operation <code>top k min heap</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p top_k_min_heap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-top-n-by">
<h3><a class="doc-anchor" href="#doc-top-n-by">#</a> <code>top_n_by</code></h3>
<p><code>top_n_by</code> — operation <code>top n by</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p top_n_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-top-trading-cycle">
<h3><a class="doc-anchor" href="#doc-top-trading-cycle">#</a> <code>top_trading_cycle</code></h3>
<p><code>top_trading_cycle</code> — operation <code>top trading cycle</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p top_trading_cycle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-top-trading-cycles-step">
<h3><a class="doc-anchor" href="#doc-top-trading-cycles-step">#</a> <code>top_trading_cycles_step</code></h3>
<p><code>top_trading_cycles_step</code> — single-step update of <code>top trading cycles</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p top_trading_cycles_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-topk-indices">
<h3><a class="doc-anchor" href="#doc-topk-indices">#</a> <code>topk_indices</code></h3>
<p><code>topk_indices</code> — top-K sketch op <code>indices</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p topk_indices $x
</code></pre>
</article>
<article class="doc-entry" id="doc-topo-kahn-step">
<h3><a class="doc-anchor" href="#doc-topo-kahn-step">#</a> <code>topo_kahn_step</code></h3>
<p><code>topo_kahn_step</code> — single-step update of <code>topo kahn</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p topo_kahn_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-topological-sort">
<h3><a class="doc-anchor" href="#doc-topological-sort">#</a> <code>topological_sort</code></h3>
<p><code>topological_sort</code> — operation <code>topological sort</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p topological_sort $x
</code></pre>
</article>
<article class="doc-entry" id="doc-topological-sort-kahn">
<h3><a class="doc-anchor" href="#doc-topological-sort-kahn">#</a> <code>topological_sort_kahn</code></h3>
<p><code>topological_sort_kahn</code> — operation <code>topological sort kahn</code>. Category: *graph algorithms*.</p>
<pre><code class="lang-perl">p topological_sort_kahn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-toposort">
<h3><a class="doc-anchor" href="#doc-toposort">#</a> <code>toposort</code></h3>
<p><code>toposort</code> — operation <code>toposort</code>. Alias for <code>topological_sort</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p toposort $x
</code></pre>
</article>
<article class="doc-entry" id="doc-torque">
<h3><a class="doc-anchor" href="#doc-torque">#</a> <code>torque</code></h3>
<p><code>torque($force, $lever_arm, $angle)</code> — compute torque τ = r×F×sin(θ) (N⋅m). Angle in degrees, default 90.</p>
<pre><code class="lang-perl">p torque(50, 0.5) # 25 N⋅m (perpendicular force)
p torque(50, 0.5, 30) # 12.5 N⋅m
</code></pre>
</article>
<article class="doc-entry" id="doc-torque-arm">
<h3><a class="doc-anchor" href="#doc-torque-arm">#</a> <code>torque_arm</code></h3>
<p><code>torque_arm(force, radius, angle_deg=90) → number</code> — <code>F · r · sin(θ)</code>.</p>
</article>
<article class="doc-entry" id="doc-torsion-coefficient">
<h3><a class="doc-anchor" href="#doc-torsion-coefficient">#</a> <code>torsion_coefficient</code></h3>
<p><code>torsion_coefficient</code> — operation <code>torsion coefficient</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p torsion_coefficient $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tortuosity-estimate-bruggeman">
<h3><a class="doc-anchor" href="#doc-tortuosity-estimate-bruggeman">#</a> <code>tortuosity_estimate_bruggeman</code></h3>
<p><code>tortuosity_estimate_bruggeman</code> — operation <code>tortuosity estimate bruggeman</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p tortuosity_estimate_bruggeman $x
</code></pre>
</article>
<article class="doc-entry" id="doc-torus-surface">
<h3><a class="doc-anchor" href="#doc-torus-surface">#</a> <code>torus_surface</code></h3>
<p><code>torus_surface($major_r, $minor_r)</code> — computes the surface area of a torus. Returns <code>4π²Rr</code>.</p>
<pre><code class="lang-perl">p torus_surface(10, 2) # ~789.6
</code></pre>
</article>
<article class="doc-entry" id="doc-torus-surface-area">
<h3><a class="doc-anchor" href="#doc-torus-surface-area">#</a> <code>torus_surface_area</code></h3>
<p><code>torus_surface_area</code> — operation <code>torus surface area</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p torus_surface_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-torus-volume">
<h3><a class="doc-anchor" href="#doc-torus-volume">#</a> <code>torus_volume</code></h3>
<p><code>torus_volume($major_r, $minor_r)</code> — computes the volume of a torus with major radius R (center to tube center) and minor radius r (tube radius). Returns <code>2π²Rr²</code>.</p>
<pre><code class="lang-perl">p torus_volume(10, 2) # ~789.6
</code></pre>
</article>
<article class="doc-entry" id="doc-torussurf">
<h3><a class="doc-anchor" href="#doc-torussurf">#</a> <code>torussurf</code></h3>
<p><code>torussurf</code> — operation <code>torussurf</code>. Alias for <code>torus_surface</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p torussurf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-torusvol">
<h3><a class="doc-anchor" href="#doc-torusvol">#</a> <code>torusvol</code></h3>
<p><code>torusvol</code> — operation <code>torusvol</code>. Alias for <code>torus_volume</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p torusvol $x
</code></pre>
</article>
<article class="doc-entry" id="doc-total-solar-irradiance-step">
<h3><a class="doc-anchor" href="#doc-total-solar-irradiance-step">#</a> <code>total_solar_irradiance_step</code></h3>
<p><code>total_solar_irradiance_step</code> — single-step update of <code>total solar irradiance</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p total_solar_irradiance_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-total-variation-distance">
<h3><a class="doc-anchor" href="#doc-total-variation-distance">#</a> <code>total_variation_distance</code></h3>
<p><code>total_variation_distance</code> — distance / dissimilarity metric of <code>total variation</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p total_variation_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-totient-sum">
<h3><a class="doc-anchor" href="#doc-totient-sum">#</a> <code>totient_sum</code></h3>
<p><code>totient_sum</code> — Euler totient helper <code>sum</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p totient_sum @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-totsum">
<h3><a class="doc-anchor" href="#doc-totsum">#</a> <code>totsum</code></h3>
<p><code>totsum</code> — operation <code>totsum</code>. Alias for <code>totient_sum</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p totsum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-touch">
<h3><a class="doc-anchor" href="#doc-touch">#</a> <code>touch</code></h3>
<p><code>touch</code> — operation <code>touch</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p touch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tournament-score">
<h3><a class="doc-anchor" href="#doc-tournament-score">#</a> <code>tournament_score</code></h3>
<p><code>tournament_score(wins, draws, losses) → number</code> — <code>wins + 0.5·draws</code>.</p>
</article>
<article class="doc-entry" id="doc-tov-mass-limit">
<h3><a class="doc-anchor" href="#doc-tov-mass-limit">#</a> <code>tov_mass_limit</code></h3>
<p><code>tov_mass_limit</code> — operation <code>tov mass limit</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p tov_mass_limit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tower-of-hanoi">
<h3><a class="doc-anchor" href="#doc-tower-of-hanoi">#</a> <code>tower_of_hanoi</code></h3>
<p><code>tower_of_hanoi</code> — operation <code>tower of hanoi</code>. Category: *algorithms / puzzles*.</p>
<pre><code class="lang-perl">p tower_of_hanoi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tplanck">
<h3><a class="doc-anchor" href="#doc-tplanck">#</a> <code>tplanck</code></h3>
<p><code>tplanck</code> — operation <code>tplanck</code>. Alias for <code>planck_time</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p tplanck $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trace-distance">
<h3><a class="doc-anchor" href="#doc-trace-distance">#</a> <code>trace_distance</code></h3>
<p><code>trace_distance</code> — distance / dissimilarity metric of <code>trace</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p trace_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trade-wind-speed">
<h3><a class="doc-anchor" href="#doc-trade-wind-speed">#</a> <code>trade_wind_speed</code></h3>
<p><code>trade_wind_speed</code> — operation <code>trade wind speed</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p trade_wind_speed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tragedy-commons-metric">
<h3><a class="doc-anchor" href="#doc-tragedy-commons-metric">#</a> <code>tragedy_commons_metric</code></h3>
<p><code>tragedy_commons_metric</code> — metric of <code>tragedy commons</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p tragedy_commons_metric $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trailing-zeros">
<h3><a class="doc-anchor" href="#doc-trailing-zeros">#</a> <code>trailing_zeros</code></h3>
<p><code>trailing_zeros</code> — operation <code>trailing zeros</code>. Category: *base conversion*.</p>
<pre><code class="lang-perl">p trailing_zeros $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trait">
<h3><a class="doc-anchor" href="#doc-trait">#</a> <code>trait</code></h3>
<p><code>trait</code> declares an interface that classes can implement via <code>impl</code>. Traits define method signatures that implementing classes must provide.</p>
<p><strong>Declaration:</strong></p>
<pre><code class="lang-perl">trait Printable {
fn to_str # required (no body)
fn debug { ... } # optional default impl
}
</code></pre>
<p><strong>Implementation:</strong></p>
<pre><code class="lang-perl">class Item impl Printable {
name: Str
fn to_str { $self->name }
}
</code></pre>
<p><strong>Multiple traits:</strong></p>
<pre><code class="lang-perl">class Widget impl Printable, Comparable {
...
}
</code></pre>
<p>Note: trait method bodies provide default implementations; classes can override them.</p>
</article>
<article class="doc-entry" id="doc-trans-check">
<h3><a class="doc-anchor" href="#doc-trans-check">#</a> <code>trans_check</code></h3>
<p><code>trans_check</code> — operation <code>trans check</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p trans_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-transcribe-dna-rna">
<h3><a class="doc-anchor" href="#doc-transcribe-dna-rna">#</a> <code>transcribe_dna_rna</code></h3>
<p><code>transcribe_dna_rna</code> — operation <code>transcribe dna rna</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p transcribe_dna_rna $x
</code></pre>
</article>
<article class="doc-entry" id="doc-transform-keys">
<h3><a class="doc-anchor" href="#doc-transform-keys">#</a> <code>transform_keys</code></h3>
<p><code>transform_keys</code> — operation <code>transform keys</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p transform_keys $x
</code></pre>
</article>
<article class="doc-entry" id="doc-transform-values">
<h3><a class="doc-anchor" href="#doc-transform-values">#</a> <code>transform_values</code></h3>
<p><code>transform_values</code> — operation <code>transform values</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p transform_values $x
</code></pre>
</article>
<article class="doc-entry" id="doc-transition-arc-eager">
<h3><a class="doc-anchor" href="#doc-transition-arc-eager">#</a> <code>transition_arc_eager</code></h3>
<p><code>transition_arc_eager</code> — operation <code>transition arc eager</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p transition_arc_eager $x
</code></pre>
</article>
<article class="doc-entry" id="doc-transition-arc-standard">
<h3><a class="doc-anchor" href="#doc-transition-arc-standard">#</a> <code>transition_arc_standard</code></h3>
<p><code>transition_arc_standard</code> — operation <code>transition arc standard</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p transition_arc_standard $x
</code></pre>
</article>
<article class="doc-entry" id="doc-transitivity">
<h3><a class="doc-anchor" href="#doc-transitivity">#</a> <code>transitivity</code></h3>
<p><code>transitivity</code> — operation <code>transitivity</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p transitivity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-translate">
<h3><a class="doc-anchor" href="#doc-translate">#</a> <code>translate</code></h3>
<p><code>translate</code> — operation <code>translate</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p translate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-translate-dna">
<h3><a class="doc-anchor" href="#doc-translate-dna">#</a> <code>translate_dna</code></h3>
<p><code>translate_dna</code> — operation <code>translate dna</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p translate_dna $x
</code></pre>
</article>
<article class="doc-entry" id="doc-translate-point">
<h3><a class="doc-anchor" href="#doc-translate-point">#</a> <code>translate_point</code></h3>
<p><code>translate_point($x, $y, $dx, $dy)</code> — translates a 2D point by offset (dx, dy). Returns [$x+$dx, $y+$dy]. Basic vector addition.</p>
<pre><code class="lang-perl">my $p = translate_point(1, 2, 3, 4)
p @$p # (4, 6)
</code></pre>
</article>
<article class="doc-entry" id="doc-transmission-pair-index">
<h3><a class="doc-anchor" href="#doc-transmission-pair-index">#</a> <code>transmission_pair_index</code></h3>
<p><code>transmission_pair_index</code> — index of <code>transmission pair</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p transmission_pair_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-transmittance">
<h3><a class="doc-anchor" href="#doc-transmittance">#</a> <code>transmittance</code></h3>
<p><code>transmittance</code> — operation <code>transmittance</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p transmittance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-transmittance-to-a">
<h3><a class="doc-anchor" href="#doc-transmittance-to-a">#</a> <code>transmittance_to_a</code></h3>
<p><code>transmittance_to_a</code> — convert from <code>transmittance</code> to <code>a</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p transmittance_to_a $value
</code></pre>
</article>
<article class="doc-entry" id="doc-transpose">
<h3><a class="doc-anchor" href="#doc-transpose">#</a> <code>transpose</code></h3>
<p><code>transpose</code> — operation <code>transpose</code>. Category: *collection more*.</p>
<pre><code class="lang-perl">p transpose $x
</code></pre>
</article>
<article class="doc-entry" id="doc-transpose-axis">
<h3><a class="doc-anchor" href="#doc-transpose-axis">#</a> <code>transpose_axis</code></h3>
<p><code>transpose_axis</code> — operation <code>transpose axis</code>. Category: *apl/j/k array primitives*.</p>
<pre><code class="lang-perl">p transpose_axis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-transpose-freq-semitones">
<h3><a class="doc-anchor" href="#doc-transpose-freq-semitones">#</a> <code>transpose_freq_semitones</code></h3>
<p><code>transpose_freq_semitones</code> — operation <code>transpose freq semitones</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p transpose_freq_semitones $x
</code></pre>
</article>
<article class="doc-entry" id="doc-transpose-note">
<h3><a class="doc-anchor" href="#doc-transpose-note">#</a> <code>transpose_note</code></h3>
<p><code>transpose_note</code> — operation <code>transpose note</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p transpose_note $x
</code></pre>
</article>
<article class="doc-entry" id="doc-transpose-semi">
<h3><a class="doc-anchor" href="#doc-transpose-semi">#</a> <code>transpose_semi</code></h3>
<p><code>transpose_semi</code> — operation <code>transpose semi</code>. Alias for <code>transpose_freq_semitones</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p transpose_semi $x
</code></pre>
</article>
<article class="doc-entry" id="doc-transpt">
<h3><a class="doc-anchor" href="#doc-transpt">#</a> <code>transpt</code></h3>
<p><code>transpt</code> — operation <code>transpt</code>. Alias for <code>translate_point</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p transpt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trapezoid">
<h3><a class="doc-anchor" href="#doc-trapezoid">#</a> <code>trapezoid</code></h3>
<p><code>trapz</code> (alias <code>trapezoid</code>) integrates evenly-spaced samples using the trapezoidal rule. Optional dx (default 1).</p>
<pre><code class="lang-perl">my @y = map { _ ** 2 } 0:100
p trapz(\@y, 0.01) # ≈ 0.3333
</code></pre>
</article>
<article class="doc-entry" id="doc-trapezoidal-integrate">
<h3><a class="doc-anchor" href="#doc-trapezoidal-integrate">#</a> <code>trapezoidal_integrate</code></h3>
<p><code>trapezoidal_integrate(ys, dx=1) → number</code> — composite trapezoidal rule on pre-computed <code>y</code> samples spaced <code>dx</code> apart.</p>
<pre><code class="lang-perl">p trapezoidal_integrate([0,1,4,9,16], 1) # 16
</code></pre>
</article>
<article class="doc-entry" id="doc-trapezoidal-lte">
<h3><a class="doc-anchor" href="#doc-trapezoidal-lte">#</a> <code>trapezoidal_lte</code></h3>
<p><code>trapezoidal_lte</code> — operation <code>trapezoidal lte</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p trapezoidal_lte $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trapped-surface-check">
<h3><a class="doc-anchor" href="#doc-trapped-surface-check">#</a> <code>trapped_surface_check</code></h3>
<p><code>trapped_surface_check</code> — operation <code>trapped surface check</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p trapped_surface_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trasatti-voltammetry-charge">
<h3><a class="doc-anchor" href="#doc-trasatti-voltammetry-charge">#</a> <code>trasatti_voltammetry_charge</code></h3>
<p><code>trasatti_voltammetry_charge</code> — operation <code>trasatti voltammetry charge</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p trasatti_voltammetry_charge $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tree-kernel-collins">
<h3><a class="doc-anchor" href="#doc-tree-kernel-collins">#</a> <code>tree_kernel_collins</code></h3>
<p><code>tree_kernel_collins</code> — operation <code>tree kernel collins</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p tree_kernel_collins $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trend-line">
<h3><a class="doc-anchor" href="#doc-trend-line">#</a> <code>trend_line</code></h3>
<p><code>trend_line(prices) → hash</code> — OLS linear regression through index <code>(0..n)</code> vs <code>prices</code>. Returns <code>{slope, intercept}</code>.</p>
<pre><code class="lang-perl">my $t = trend_line(\@closes); p $t->{slope}
</code></pre>
</article>
<article class="doc-entry" id="doc-trev">
<h3><a class="doc-anchor" href="#doc-trev">#</a> <code>trev</code></h3>
<p><code>trev</code> — operation <code>trev</code>. Alias for <code>to_reversed</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p trev $x
</code></pre>
</article>
<article class="doc-entry" id="doc-treynor">
<h3><a class="doc-anchor" href="#doc-treynor">#</a> <code>treynor</code></h3>
<p><code>treynor(portfolio_return, beta, rf=0) → number</code> — <code>(return - rf) / beta</code>. Excess return per unit of market risk.</p>
<pre><code class="lang-perl">p treynor(0.12, 1.2, 0.03)
</code></pre>
</article>
<article class="doc-entry" id="doc-treynor-ratio">
<h3><a class="doc-anchor" href="#doc-treynor-ratio">#</a> <code>treynor_ratio</code></h3>
<p><code>treynor_ratio</code> — ratio of <code>treynor</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p treynor_ratio $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trial-smallest-factor">
<h3><a class="doc-anchor" href="#doc-trial-smallest-factor">#</a> <code>trial_smallest_factor</code></h3>
<p><code>trial_smallest_factor</code> — factor of <code>trial smallest</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p trial_smallest_factor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-triangle-area">
<h3><a class="doc-anchor" href="#doc-triangle-area">#</a> <code>triangle_area</code></h3>
<p><code>triangle_area</code> — triangle geometry op <code>area</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p triangle_area $x
</code></pre>
</article>
<article class="doc-entry" id="doc-triangle-area-3d">
<h3><a class="doc-anchor" href="#doc-triangle-area-3d">#</a> <code>triangle_area_3d</code></h3>
<p><code>triangle_area_3d(a, b, c) → number</code> — area of triangle in 3D = <code>0.5 · |AB × AC|</code>.</p>
</article>
<article class="doc-entry" id="doc-triangle-area-heron">
<h3><a class="doc-anchor" href="#doc-triangle-area-heron">#</a> <code>triangle_area_heron</code></h3>
<p><code>triangle_area_heron</code> — triangle geometry op <code>area heron</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p triangle_area_heron $x
</code></pre>
</article>
<article class="doc-entry" id="doc-triangle-area-pts">
<h3><a class="doc-anchor" href="#doc-triangle-area-pts">#</a> <code>triangle_area_pts</code></h3>
<p><code>triangle_area_pts</code> — triangle geometry op <code>area pts</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p triangle_area_pts $x
</code></pre>
</article>
<article class="doc-entry" id="doc-triangle-centroid">
<h3><a class="doc-anchor" href="#doc-triangle-centroid">#</a> <code>triangle_centroid</code></h3>
<p><code>triangle_centroid</code> — triangle geometry op <code>centroid</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p triangle_centroid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-triangle-circumcircle">
<h3><a class="doc-anchor" href="#doc-triangle-circumcircle">#</a> <code>triangle_circumcircle</code></h3>
<p><code>triangle_circumcircle</code> — triangle geometry op <code>circumcircle</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p triangle_circumcircle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-triangle-circumradius">
<h3><a class="doc-anchor" href="#doc-triangle-circumradius">#</a> <code>triangle_circumradius</code></h3>
<p><code>triangle_circumradius</code> — triangle geometry op <code>circumradius</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p triangle_circumradius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-triangle-contains-point">
<h3><a class="doc-anchor" href="#doc-triangle-contains-point">#</a> <code>triangle_contains_point</code></h3>
<p><code>triangle_contains_point</code> — triangle geometry op <code>contains point</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p triangle_contains_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-triangle-hypotenuse">
<h3><a class="doc-anchor" href="#doc-triangle-hypotenuse">#</a> <code>triangle_hypotenuse</code></h3>
<p><code>triangle_hypotenuse</code> — triangle geometry op <code>hypotenuse</code>. Category: *geometry / physics*.</p>
<pre><code class="lang-perl">p triangle_hypotenuse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-triangle-incircle">
<h3><a class="doc-anchor" href="#doc-triangle-incircle">#</a> <code>triangle_incircle</code></h3>
<p><code>triangle_incircle</code> — triangle geometry op <code>incircle</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p triangle_incircle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-triangle-inradius">
<h3><a class="doc-anchor" href="#doc-triangle-inradius">#</a> <code>triangle_inradius</code></h3>
<p><code>triangle_inradius</code> — triangle geometry op <code>inradius</code>. Category: *geometry / topology*.</p>
<pre><code class="lang-perl">p triangle_inradius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-triangle-normal">
<h3><a class="doc-anchor" href="#doc-triangle-normal">#</a> <code>triangle_normal</code></h3>
<p><code>triangle_normal(a, b, c) → [x,y,z]</code> — unit normal of triangle ABC via cross product.</p>
</article>
<article class="doc-entry" id="doc-triangles-count">
<h3><a class="doc-anchor" href="#doc-triangles-count">#</a> <code>triangles_count</code></h3>
<p><code>triangles_count</code> — count of <code>triangles</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p triangles_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-triangular-number">
<h3><a class="doc-anchor" href="#doc-triangular-number">#</a> <code>triangular_number</code></h3>
<p><code>triangular_number</code> — operation <code>triangular number</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p triangular_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-triangular-seq">
<h3><a class="doc-anchor" href="#doc-triangular-seq">#</a> <code>triangular_seq</code></h3>
<p><code>triangular_seq</code> — operation <code>triangular seq</code>. Category: *sequences*.</p>
<pre><code class="lang-perl">p triangular_seq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trib">
<h3><a class="doc-anchor" href="#doc-trib">#</a> <code>trib</code></h3>
<p><code>trib</code> — operation <code>trib</code>. Alias for <code>tribonacci</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p trib $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tribonacci">
<h3><a class="doc-anchor" href="#doc-tribonacci">#</a> <code>tribonacci</code></h3>
<p><code>tribonacci</code> — operation <code>tribonacci</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p tribonacci $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trie-count">
<h3><a class="doc-anchor" href="#doc-trie-count">#</a> <code>trie_count</code></h3>
<p><code>trie_count(trie) → int</code> — number of stored words.</p>
</article>
<article class="doc-entry" id="doc-trie-insert">
<h3><a class="doc-anchor" href="#doc-trie-insert">#</a> <code>trie_insert</code></h3>
<p><code>trie_insert(trie, word) → trie</code> — insert word; returns trie (mutates in place but lets you chain).</p>
<pre><code class="lang-perl">my $t = trie_new()
$t = trie_insert($t, "hello")
</code></pre>
</article>
<article class="doc-entry" id="doc-trie-keys">
<h3><a class="doc-anchor" href="#doc-trie-keys">#</a> <code>trie_keys</code></h3>
<p><code>trie_keys(trie) → array</code> — all words stored in the trie (empty prefix search).</p>
</article>
<article class="doc-entry" id="doc-trie-lookup">
<h3><a class="doc-anchor" href="#doc-trie-lookup">#</a> <code>trie_lookup</code></h3>
<p><code>trie_lookup(trie, word) → 0|1</code> — 1 if word is in the trie.</p>
</article>
<article class="doc-entry" id="doc-trie-new">
<h3><a class="doc-anchor" href="#doc-trie-new">#</a> <code>trie_new</code></h3>
<p><code>trie_new() → trie</code> — empty trie root: <code>{end: 0, children: {}}</code>.</p>
</article>
<article class="doc-entry" id="doc-trie-prefix-search">
<h3><a class="doc-anchor" href="#doc-trie-prefix-search">#</a> <code>trie_prefix_search</code></h3>
<p><code>trie_prefix_search(trie, prefix) → array</code> — all stored words sharing the given prefix.</p>
<pre><code class="lang-perl">p trie_prefix_search($t, "hel")
</code></pre>
</article>
<article class="doc-entry" id="doc-trie-remove">
<h3><a class="doc-anchor" href="#doc-trie-remove">#</a> <code>trie_remove</code></h3>
<p><code>trie_remove(trie, word) → trie</code> — clear the <code>end</code> flag for the given path; keeps structure for shared prefixes.</p>
</article>
<article class="doc-entry" id="doc-trigamma">
<h3><a class="doc-anchor" href="#doc-trigamma">#</a> <code>trigamma</code></h3>
<p><code>trigamma</code> — operation <code>trigamma</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p trigamma $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trigger-strategy-payoff">
<h3><a class="doc-anchor" href="#doc-trigger-strategy-payoff">#</a> <code>trigger_strategy_payoff</code></h3>
<p><code>trigger_strategy_payoff</code> — operation <code>trigger strategy payoff</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p trigger_strategy_payoff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trigram">
<h3><a class="doc-anchor" href="#doc-trigram">#</a> <code>trigram</code></h3>
<p><code>trigram</code> — operation <code>trigram</code>. Alias for <code>trigrams</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p trigram $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trigram-perplexity">
<h3><a class="doc-anchor" href="#doc-trigram-perplexity">#</a> <code>trigram_perplexity</code></h3>
<p><code>trigram_perplexity</code> — operation <code>trigram perplexity</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p trigram_perplexity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trigrams">
<h3><a class="doc-anchor" href="#doc-trigrams">#</a> <code>trigrams</code></h3>
<p><code>trigrams</code> — operation <code>trigrams</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p trigrams $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trim-each">
<h3><a class="doc-anchor" href="#doc-trim-each">#</a> <code>trim_each</code></h3>
<p><code>trim_each</code> — operation <code>trim each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p trim_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trim-left">
<h3><a class="doc-anchor" href="#doc-trim-left">#</a> <code>trim_left</code></h3>
<p><code>trim_left</code> — operation <code>trim left</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p trim_left $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trim-right">
<h3><a class="doc-anchor" href="#doc-trim-right">#</a> <code>trim_right</code></h3>
<p><code>trim_right</code> — operation <code>trim right</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p trim_right $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trimmed-mean">
<h3><a class="doc-anchor" href="#doc-trimmed-mean">#</a> <code>trimmed_mean</code></h3>
<p><code>trimmed_mean</code> — arithmetic mean of <code>trimmed</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p trimmed_mean @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-trinomial-call">
<h3><a class="doc-anchor" href="#doc-trinomial-call">#</a> <code>trinomial_call</code></h3>
<p><code>trinomial_call</code> — operation <code>trinomial call</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p trinomial_call $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trinum">
<h3><a class="doc-anchor" href="#doc-trinum">#</a> <code>trinum</code></h3>
<p><code>trinum</code> — operation <code>trinum</code>. Alias for <code>triangular_number</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p trinum $x
</code></pre>
</article>
<article class="doc-entry" id="doc-triple">
<h3><a class="doc-anchor" href="#doc-triple">#</a> <code>triple</code></h3>
<p><code>triple</code> — operation <code>triple</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p triple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-triples">
<h3><a class="doc-anchor" href="#doc-triples">#</a> <code>triples</code></h3>
<p><code>triples</code> — operation <code>triples</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p triples $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trix">
<h3><a class="doc-anchor" href="#doc-trix">#</a> <code>trix</code></h3>
<p><code>trix(prices, period=15) → array</code> — 1-period rate-of-change of a triple EMA. Returns percent change between consecutive triple-smoothed values.</p>
<pre><code class="lang-perl">p trix(\@prices, 15)
</code></pre>
</article>
<article class="doc-entry" id="doc-trpo-kl-constraint">
<h3><a class="doc-anchor" href="#doc-trpo-kl-constraint">#</a> <code>trpo_kl_constraint</code></h3>
<p><code>trpo_kl_constraint</code> — operation <code>trpo kl constraint</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p trpo_kl_constraint $x
</code></pre>
</article>
<article class="doc-entry" id="doc-true-range">
<h3><a class="doc-anchor" href="#doc-true-range">#</a> <code>true_range</code></h3>
<p><code>true_range(highs, lows, closes) → array</code> — <code>max(high−low, |high−prev_close|, |low−prev_close|)</code> per bar. Input to <code>atr</code>.</p>
<pre><code class="lang-perl">p true_range([12,13], [9,10], [10,11])
</code></pre>
</article>
<article class="doc-entry" id="doc-trueskill-match-quality">
<h3><a class="doc-anchor" href="#doc-trueskill-match-quality">#</a> <code>trueskill_match_quality</code></h3>
<p><code>trueskill_match_quality</code> — operation <code>trueskill match quality</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p trueskill_match_quality $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trueskill-simple">
<h3><a class="doc-anchor" href="#doc-trueskill-simple">#</a> <code>trueskill_simple</code></h3>
<p><code>trueskill_simple(mu_w, sigma_w, mu_l, sigma_l) → {winner_mu, winner_sigma, loser_mu, loser_sigma}</code> — 1v1 TrueSkill update.</p>
</article>
<article class="doc-entry" id="doc-trueskill-update">
<h3><a class="doc-anchor" href="#doc-trueskill-update">#</a> <code>trueskill_update</code></h3>
<p><code>trueskill_update</code> — update step of <code>trueskill</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p trueskill_update $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trunc">
<h3><a class="doc-anchor" href="#doc-trunc">#</a> <code>trunc</code></h3>
<p><code>trunc</code> — operation <code>trunc</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p trunc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-truncate-at">
<h3><a class="doc-anchor" href="#doc-truncate-at">#</a> <code>truncate_at</code></h3>
<p><code>truncate_at</code> — operation <code>truncate at</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p truncate_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-truncate-middle">
<h3><a class="doc-anchor" href="#doc-truncate-middle">#</a> <code>truncate_middle</code></h3>
<p><code>truncate_middle(s, width=20) → string</code> — truncate keeping head and tail, replacing the middle with <code>…</code>. Preserves visual ends.</p>
<pre><code class="lang-perl">p truncate_middle("averyverylongstring", 10)
</code></pre>
</article>
<article class="doc-entry" id="doc-truncn">
<h3><a class="doc-anchor" href="#doc-truncn">#</a> <code>truncn</code></h3>
<p><code>truncn</code> — operation <code>truncn</code>. Alias for <code>trunc</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p truncn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-trust-game-repayment">
<h3><a class="doc-anchor" href="#doc-trust-game-repayment">#</a> <code>trust_game_repayment</code></h3>
<p><code>trust_game_repayment</code> — operation <code>trust game repayment</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p trust_game_repayment $x
</code></pre>
</article>
<article class="doc-entry" id="doc-truth-table">
<h3><a class="doc-anchor" href="#doc-truth-table">#</a> <code>truth_table</code></h3>
<p><code>truth_table</code> — lookup table of <code>truth</code>. Category: *algorithms / puzzles*.</p>
<pre><code class="lang-perl">p truth_table $x
</code></pre>
</article>
<article class="doc-entry" id="doc-truthful-mechanism-check">
<h3><a class="doc-anchor" href="#doc-truthful-mechanism-check">#</a> <code>truthful_mechanism_check</code></h3>
<p><code>truthful_mechanism_check</code> — operation <code>truthful mechanism check</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p truthful_mechanism_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-truthy-count">
<h3><a class="doc-anchor" href="#doc-truthy-count">#</a> <code>truthy_count</code></h3>
<p><code>truthy_count</code> — count of <code>truthy</code>. Category: *counters*.</p>
<pre><code class="lang-perl">p truthy_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-try-fn">
<h3><a class="doc-anchor" href="#doc-try-fn">#</a> <code>try_fn</code></h3>
<p><code>try_fn</code> — operation <code>try fn</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p try_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-try-fold">
<h3><a class="doc-anchor" href="#doc-try-fold">#</a> <code>try_fold</code></h3>
<p><code>try_fold</code> — operation <code>try fold</code>. Category: *rust iterator methods*.</p>
<pre><code class="lang-perl">p try_fold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ts-headline">
<h3><a class="doc-anchor" href="#doc-ts-headline">#</a> <code>ts_headline</code></h3>
<p><code>ts_headline</code> — operation <code>ts headline</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p ts_headline $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ts-match">
<h3><a class="doc-anchor" href="#doc-ts-match">#</a> <code>ts_match</code></h3>
<p><code>ts_match</code> — operation <code>ts match</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p ts_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ts-rank">
<h3><a class="doc-anchor" href="#doc-ts-rank">#</a> <code>ts_rank</code></h3>
<p><code>ts_rank</code> — operation <code>ts rank</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p ts_rank $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tsirelson-bound">
<h3><a class="doc-anchor" href="#doc-tsirelson-bound">#</a> <code>tsirelson_bound</code></h3>
<p><code>tsirelson_bound</code> — operation <code>tsirelson bound</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p tsirelson_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tsp-2opt">
<h3><a class="doc-anchor" href="#doc-tsp-2opt">#</a> <code>tsp_2opt</code></h3>
<p><code>tsp_2opt(distance_matrix) → array</code> — improve a TSP tour using iterative 2-opt swaps until stable.</p>
<pre><code class="lang-perl">p tsp_2opt([[0,1,5,7],[1,0,3,4],[5,3,0,2],[7,4,2,0]])
</code></pre>
</article>
<article class="doc-entry" id="doc-tsp-christofides">
<h3><a class="doc-anchor" href="#doc-tsp-christofides">#</a> <code>tsp_christofides</code></h3>
<p><code>tsp_christofides</code> — Travelling Salesman heuristic <code>christofides</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p tsp_christofides $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tsp-held-karp">
<h3><a class="doc-anchor" href="#doc-tsp-held-karp">#</a> <code>tsp_held_karp</code></h3>
<p><code>tsp_held_karp</code> — Travelling Salesman heuristic <code>held karp</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p tsp_held_karp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tsp-held-karp-step">
<h3><a class="doc-anchor" href="#doc-tsp-held-karp-step">#</a> <code>tsp_held_karp_step</code></h3>
<p><code>tsp_held_karp_step</code> — Travelling Salesman heuristic <code>held karp step</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p tsp_held_karp_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tsp-lower-bound-mst">
<h3><a class="doc-anchor" href="#doc-tsp-lower-bound-mst">#</a> <code>tsp_lower_bound_mst</code></h3>
<p><code>tsp_lower_bound_mst</code> — Travelling Salesman heuristic <code>lower bound mst</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p tsp_lower_bound_mst $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tsp-nn-step">
<h3><a class="doc-anchor" href="#doc-tsp-nn-step">#</a> <code>tsp_nn_step</code></h3>
<p><code>tsp_nn_step</code> — Travelling Salesman heuristic <code>nn step</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p tsp_nn_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tspl">
<h3><a class="doc-anchor" href="#doc-tspl">#</a> <code>tspl</code></h3>
<p><code>tspl</code> — operation <code>tspl</code>. Alias for <code>to_spliced</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p tspl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tsrt">
<h3><a class="doc-anchor" href="#doc-tsrt">#</a> <code>tsrt</code></h3>
<p><code>tsrt</code> — operation <code>tsrt</code>. Alias for <code>to_sorted</code>. Category: *javascript array/object methods*.</p>
<pre><code class="lang-perl">p tsrt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tstr">
<h3><a class="doc-anchor" href="#doc-tstr">#</a> <code>tstr</code></h3>
<p><code>tstr</code> — operation <code>tstr</code>. Alias for <code>to_string_val</code>. Category: *misc / utility*.</p>
<pre><code class="lang-perl">p tstr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tt-to-tdb">
<h3><a class="doc-anchor" href="#doc-tt-to-tdb">#</a> <code>tt_to_tdb</code></h3>
<p><code>tt_to_tdb</code> — convert from <code>tt</code> to <code>tdb</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p tt_to_tdb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-ttable">
<h3><a class="doc-anchor" href="#doc-ttable">#</a> <code>ttable</code></h3>
<p><code>ttable</code> — operation <code>ttable</code>. Alias for <code>truth_table</code>. Category: *algorithms / puzzles*.</p>
<pre><code class="lang-perl">p ttable $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ttl">
<h3><a class="doc-anchor" href="#doc-ttl">#</a> <code>ttl</code></h3>
<p><code>ttl</code> — operation <code>ttl</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p ttl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tukey-lambda-quantile">
<h3><a class="doc-anchor" href="#doc-tukey-lambda-quantile">#</a> <code>tukey_lambda_quantile</code></h3>
<p><code>tukey_lambda_quantile</code> — operation <code>tukey lambda quantile</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p tukey_lambda_quantile $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tukey-w">
<h3><a class="doc-anchor" href="#doc-tukey-w">#</a> <code>tukey_w</code></h3>
<p><code>tukey_w</code> — operation <code>tukey w</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p tukey_w $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tukey-window">
<h3><a class="doc-anchor" href="#doc-tukey-window">#</a> <code>tukey_window</code></h3>
<p><code>tukey_window</code> — operation <code>tukey window</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p tukey_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tunneling-prob">
<h3><a class="doc-anchor" href="#doc-tunneling-prob">#</a> <code>tunneling_prob</code></h3>
<p><code>tunneling_prob</code> — operation <code>tunneling prob</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p tunneling_prob $x
</code></pre>
</article>
<article class="doc-entry" id="doc-turaev-alexander-step">
<h3><a class="doc-anchor" href="#doc-turaev-alexander-step">#</a> <code>turaev_alexander_step</code></h3>
<p><code>turaev_alexander_step</code> — single-step update of <code>turaev alexander</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p turaev_alexander_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-turbulence-intensity-step">
<h3><a class="doc-anchor" href="#doc-turbulence-intensity-step">#</a> <code>turbulence_intensity_step</code></h3>
<p><code>turbulence_intensity_step</code> — single-step update of <code>turbulence intensity</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p turbulence_intensity_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-turbulence-noise-2d">
<h3><a class="doc-anchor" href="#doc-turbulence-noise-2d">#</a> <code>turbulence_noise_2d</code></h3>
<p><code>turbulence_noise_2d(x, y, octaves=4) → number</code> — sum of <code>|perlin|</code> octaves with halving amplitude.</p>
</article>
<article class="doc-entry" id="doc-turbulent-dissipation-eps">
<h3><a class="doc-anchor" href="#doc-turbulent-dissipation-eps">#</a> <code>turbulent_dissipation_eps</code></h3>
<p><code>turbulent_dissipation_eps</code> — operation <code>turbulent dissipation eps</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p turbulent_dissipation_eps $x
</code></pre>
</article>
<article class="doc-entry" id="doc-turbulent-kinetic-energy-step">
<h3><a class="doc-anchor" href="#doc-turbulent-kinetic-energy-step">#</a> <code>turbulent_kinetic_energy_step</code></h3>
<p><code>turbulent_kinetic_energy_step</code> — single-step update of <code>turbulent kinetic energy</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p turbulent_kinetic_energy_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tvals">
<h3><a class="doc-anchor" href="#doc-tvals">#</a> <code>tvals</code></h3>
<p><code>tvals</code> — operation <code>tvals</code>. Alias for <code>transform_values</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p tvals $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tversky">
<h3><a class="doc-anchor" href="#doc-tversky">#</a> <code>tversky</code></h3>
<p><code>tversky</code> — operation <code>tversky</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p tversky $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tversky-index">
<h3><a class="doc-anchor" href="#doc-tversky-index">#</a> <code>tversky_index</code></h3>
<p><code>tversky_index(a, b, alpha=1, beta=1) → number</code> — asymmetric similarity; α/β weight the differences.</p>
</article>
<article class="doc-entry" id="doc-twap">
<h3><a class="doc-anchor" href="#doc-twap">#</a> <code>twap</code></h3>
<p><code>twap(prices) → array</code> — Time-Weighted Average Price: cumulative arithmetic mean across the series.</p>
<pre><code class="lang-perl">p twap(\@prices)
</code></pre>
</article>
<article class="doc-entry" id="doc-twin-primes">
<h3><a class="doc-anchor" href="#doc-twin-primes">#</a> <code>twin_primes</code></h3>
<p><code>twin_primes</code> — operation <code>twin primes</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p twin_primes $x
</code></pre>
</article>
<article class="doc-entry" id="doc-twinp">
<h3><a class="doc-anchor" href="#doc-twinp">#</a> <code>twinp</code></h3>
<p><code>twinp</code> — operation <code>twinp</code>. Alias for <code>twin_primes</code>. Category: *number theory / primes*.</p>
<pre><code class="lang-perl">p twinp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-twist-tensor-step">
<h3><a class="doc-anchor" href="#doc-twist-tensor-step">#</a> <code>twist_tensor_step</code></h3>
<p><code>twist_tensor_step</code> — single-step update of <code>twist tensor</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p twist_tensor_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-two-opt-swap-delta">
<h3><a class="doc-anchor" href="#doc-two-opt-swap-delta">#</a> <code>two_opt_swap_delta</code></h3>
<p><code>two_opt_swap_delta</code> — operation <code>two opt swap delta</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p two_opt_swap_delta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-two-sls-iv">
<h3><a class="doc-anchor" href="#doc-two-sls-iv">#</a> <code>two_sls_iv</code></h3>
<p><code>two_sls_iv</code> — operation <code>two sls iv</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p two_sls_iv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-two-watched-literals">
<h3><a class="doc-anchor" href="#doc-two-watched-literals">#</a> <code>two_watched_literals</code></h3>
<p><code>two_watched_literals</code> — operation <code>two watched literals</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p two_watched_literals $x
</code></pre>
</article>
<article class="doc-entry" id="doc-txaft">
<h3><a class="doc-anchor" href="#doc-txaft">#</a> <code>txaft</code></h3>
<p><code>txaft</code> — operation <code>txaft</code>. Alias for <code>text_after</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p txaft $x
</code></pre>
</article>
<article class="doc-entry" id="doc-txaftl">
<h3><a class="doc-anchor" href="#doc-txaftl">#</a> <code>txaftl</code></h3>
<p><code>txaftl</code> — operation <code>txaftl</code>. Alias for <code>text_after_last</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p txaftl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-txbef">
<h3><a class="doc-anchor" href="#doc-txbef">#</a> <code>txbef</code></h3>
<p><code>txbef</code> — operation <code>txbef</code>. Alias for <code>text_before</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p txbef $x
</code></pre>
</article>
<article class="doc-entry" id="doc-txbefl">
<h3><a class="doc-anchor" href="#doc-txbefl">#</a> <code>txbefl</code></h3>
<p><code>txbefl</code> — operation <code>txbefl</code>. Alias for <code>text_before_last</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p txbefl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-txbtwn">
<h3><a class="doc-anchor" href="#doc-txbtwn">#</a> <code>txbtwn</code></h3>
<p><code>txbtwn</code> — operation <code>txbtwn</code>. Alias for <code>text_between</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p txbtwn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-type">
<h3><a class="doc-anchor" href="#doc-type">#</a> <code>type</code></h3>
<p><code>type</code> — operation <code>type</code>. Alias for <code>type_of</code>. Category: *misc / utility*.</p>
<pre><code class="lang-perl">p type $x
</code></pre>
</article>
<article class="doc-entry" id="doc-type-each">
<h3><a class="doc-anchor" href="#doc-type-each">#</a> <code>type_each</code></h3>
<p><code>type_each</code> — operation <code>type each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p type_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-type-of">
<h3><a class="doc-anchor" href="#doc-type-of">#</a> <code>type_of</code></h3>
<p><code>type_of</code> — operation <code>type of</code>. Category: *misc / utility*.</p>
<pre><code class="lang-perl">p type_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-type-redis">
<h3><a class="doc-anchor" href="#doc-type-redis">#</a> <code>type_redis</code></h3>
<p><code>type_redis</code> — operation <code>type redis</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p type_redis $x
</code></pre>
</article>
<article class="doc-entry" id="doc-typeof">
<h3><a class="doc-anchor" href="#doc-typeof">#</a> <code>typeof</code></h3>
<p><code>typeof</code> — operation <code>typeof</code>. Alias for <code>type_of</code>. Category: *misc / utility*.</p>
<pre><code class="lang-perl">p typeof $x
</code></pre>
</article>
<article class="doc-entry" id="doc-tz">
<h3><a class="doc-anchor" href="#doc-tz">#</a> <code>tz</code></h3>
<p><code>tz</code> — operation <code>tz</code>. Alias for <code>trailing_zeros</code>. Category: *base conversion*.</p>
<pre><code class="lang-perl">p tz $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ubound">
<h3><a class="doc-anchor" href="#doc-ubound">#</a> <code>ubound</code></h3>
<p><code>ubound</code> — operation <code>ubound</code>. Alias for <code>upper_bound</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p ubound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ucb1-action-value">
<h3><a class="doc-anchor" href="#doc-ucb1-action-value">#</a> <code>ucb1_action_value</code></h3>
<p><code>ucb1_action_value</code> — value of <code>ucb1 action</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ucb1_action_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ucb1-choose">
<h3><a class="doc-anchor" href="#doc-ucb1-choose">#</a> <code>ucb1_choose</code></h3>
<p><code>ucb1_choose(q_values, counts, c=√2) → int</code> — UCB1 selection: <code>Q + c·√(ln(N)/n_i)</code>. Unvisited arms get +∞.</p>
</article>
<article class="doc-entry" id="doc-ucm-unobserved-components">
<h3><a class="doc-anchor" href="#doc-ucm-unobserved-components">#</a> <code>ucm_unobserved_components</code></h3>
<p><code>ucm_unobserved_components</code> — operation <code>ucm unobserved components</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p ucm_unobserved_components $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ud">
<h3><a class="doc-anchor" href="#doc-ud">#</a> <code>ud</code></h3>
<p><code>ud</code> — operation <code>ud</code>. Alias for <code>url_decode</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p ud $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ue">
<h3><a class="doc-anchor" href="#doc-ue">#</a> <code>ue</code></h3>
<p><code>ue</code> — operation <code>ue</code>. Alias for <code>url_encode</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p ue $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ugz">
<h3><a class="doc-anchor" href="#doc-ugz">#</a> <code>ugz</code></h3>
<p><code>ugz</code> — operation <code>ugz</code>. Alias for <code>gunzip</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p ugz $x
</code></pre>
</article>
<article class="doc-entry" id="doc-uid">
<h3><a class="doc-anchor" href="#doc-uid">#</a> <code>uid</code></h3>
<p><code>uid</code> — operation <code>uid</code>. Category: *system introspection*.</p>
<pre><code class="lang-perl">p uid $x
</code></pre>
</article>
<article class="doc-entry" id="doc-uin">
<h3><a class="doc-anchor" href="#doc-uin">#</a> <code>uin</code></h3>
<p><code>uin</code> — operation <code>uin</code>. Alias for <code>update_in</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p uin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ulcer-index">
<h3><a class="doc-anchor" href="#doc-ulcer-index">#</a> <code>ulcer_index</code></h3>
<p><code>ulcer_index(prices) → number</code> — Peter Martin's measure of downside risk: <code>√(mean(drawdown_pct²))</code>. Heavier penalty on deep, lasting drawdowns than stddev.</p>
<pre><code class="lang-perl">p ulcer_index(\@equity_curve)
</code></pre>
</article>
<article class="doc-entry" id="doc-ultimatum-acceptance-prob">
<h3><a class="doc-anchor" href="#doc-ultimatum-acceptance-prob">#</a> <code>ultimatum_acceptance_prob</code></h3>
<p><code>ultimatum_acceptance_prob</code> — operation <code>ultimatum acceptance prob</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p ultimatum_acceptance_prob $x
</code></pre>
</article>
<article class="doc-entry" id="doc-uncertainty-position">
<h3><a class="doc-anchor" href="#doc-uncertainty-position">#</a> <code>uncertainty_position</code></h3>
<p><code>uncertainty_position</code> — operation <code>uncertainty position</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p uncertainty_position $x
</code></pre>
</article>
<article class="doc-entry" id="doc-undef-count">
<h3><a class="doc-anchor" href="#doc-undef-count">#</a> <code>undef_count</code></h3>
<p><code>undef_count</code> — count of <code>undef</code>. Category: *counters*.</p>
<pre><code class="lang-perl">p undef_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-underline">
<h3><a class="doc-anchor" href="#doc-underline">#</a> <code>underline</code></h3>
<p><code>underline</code> — operation <code>underline</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p underline $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unfold">
<h3><a class="doc-anchor" href="#doc-unfold">#</a> <code>unfold</code></h3>
<p><code>unfold</code> — operation <code>unfold</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p unfold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unfoldr">
<h3><a class="doc-anchor" href="#doc-unfoldr">#</a> <code>unfoldr</code></h3>
<p><code>unfoldr</code> — operation <code>unfoldr</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p unfoldr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unfr">
<h3><a class="doc-anchor" href="#doc-unfr">#</a> <code>unfr</code></h3>
<p><code>unfr</code> — operation <code>unfr</code>. Alias for <code>unfoldr</code>. Category: *haskell list functions*.</p>
<pre><code class="lang-perl">p unfr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unicode-codepoints">
<h3><a class="doc-anchor" href="#doc-unicode-codepoints">#</a> <code>unicode_codepoints</code></h3>
<p><code>unicode_codepoints(s) → array</code> — array of Unicode code points (integers).</p>
<pre><code class="lang-perl">p unicode_codepoints("hi") # [104, 105]
</code></pre>
</article>
<article class="doc-entry" id="doc-unicode-to-native">
<h3><a class="doc-anchor" href="#doc-unicode-to-native">#</a> <code>unicode_to_native</code></h3>
<p><code>unicode_to_native</code> — convert from <code>unicode</code> to <code>native</code>. Category: *list / aggregate*.</p>
<pre><code class="lang-perl">p unicode_to_native $value
</code></pre>
</article>
<article class="doc-entry" id="doc-unification-robinson">
<h3><a class="doc-anchor" href="#doc-unification-robinson">#</a> <code>unification_robinson</code></h3>
<p><code>unification_robinson</code> — operation <code>unification robinson</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p unification_robinson $x
</code></pre>
</article>
<article class="doc-entry" id="doc-union-find-components">
<h3><a class="doc-anchor" href="#doc-union-find-components">#</a> <code>union_find_components</code></h3>
<p><code>union_find_components(uf) → int</code> — number of disjoint components.</p>
</article>
<article class="doc-entry" id="doc-union-find-find">
<h3><a class="doc-anchor" href="#doc-union-find-find">#</a> <code>union_find_find</code></h3>
<p><code>union_find_find(uf, x) → int</code> — root of x with path compression.</p>
</article>
<article class="doc-entry" id="doc-union-find-new">
<h3><a class="doc-anchor" href="#doc-union-find-new">#</a> <code>union_find_new</code></h3>
<p><code>union_find_new(n) → {parent, rank}</code> — disjoint-set forest of n singletons.</p>
</article>
<article class="doc-entry" id="doc-union-find-union">
<h3><a class="doc-anchor" href="#doc-union-find-union">#</a> <code>union_find_union</code></h3>
<p><code>union_find_union(uf, x, y) → uf</code> — union by rank.</p>
<pre><code class="lang-perl">my $uf = union_find_new(5)
$uf = union_find_union($uf, 0, 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-union-list">
<h3><a class="doc-anchor" href="#doc-union-list">#</a> <code>union_list</code></h3>
<p><code>union_list</code> — operation <code>union list</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p union_list $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unionl">
<h3><a class="doc-anchor" href="#doc-unionl">#</a> <code>unionl</code></h3>
<p><code>unionl</code> — operation <code>unionl</code>. Alias for <code>union_list</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p unionl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-uniq-by">
<h3><a class="doc-anchor" href="#doc-uniq-by">#</a> <code>uniq_by</code></h3>
<p><code>uniq_by</code> — operation <code>uniq by</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p uniq_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unique-by">
<h3><a class="doc-anchor" href="#doc-unique-by">#</a> <code>unique_by</code></h3>
<p><code>unique_by</code> — operation <code>unique by</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p unique_by $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unique-consecutive">
<h3><a class="doc-anchor" href="#doc-unique-consecutive">#</a> <code>unique_consecutive</code></h3>
<p><code>unique_consecutive</code> — operation <code>unique consecutive</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p unique_consecutive $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unique-count">
<h3><a class="doc-anchor" href="#doc-unique-count">#</a> <code>unique_count</code></h3>
<p><code>unique_count</code> — count of <code>unique</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p unique_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unique-count-of">
<h3><a class="doc-anchor" href="#doc-unique-count-of">#</a> <code>unique_count_of</code></h3>
<p><code>unique_count_of</code> — operation <code>unique count of</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p unique_count_of $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unique-words">
<h3><a class="doc-anchor" href="#doc-unique-words">#</a> <code>unique_words</code></h3>
<p><code>unique_words</code> — operation <code>unique words</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p unique_words $x
</code></pre>
</article>
<article class="doc-entry" id="doc-uniqw">
<h3><a class="doc-anchor" href="#doc-uniqw">#</a> <code>uniqw</code></h3>
<p><code>uniqw</code> — operation <code>uniqw</code>. Alias for <code>unique_words</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p uniqw $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unit-energy">
<h3><a class="doc-anchor" href="#doc-unit-energy">#</a> <code>unit_energy</code></h3>
<p><code>unit_energy(value, from, to) → number</code> — energy conversion. Units: J/joule, kJ, cal, kcal, Wh, kWh, eV, BTU.</p>
<pre><code class="lang-perl">p unit_energy(1, "kwh", "j") # 3.6e6
</code></pre>
</article>
<article class="doc-entry" id="doc-unit-pressure">
<h3><a class="doc-anchor" href="#doc-unit-pressure">#</a> <code>unit_pressure</code></h3>
<p><code>unit_pressure(value, from, to) → number</code> — pressure conversion. Units: Pa, kPa, MPa, bar, atm, torr/mmHg, psi.</p>
</article>
<article class="doc-entry" id="doc-unit-temperature">
<h3><a class="doc-anchor" href="#doc-unit-temperature">#</a> <code>unit_temperature</code></h3>
<p><code>unit_temperature(value, from, to) → number</code> — temperature conversion. Units: C/celsius, F/fahrenheit, K/kelvin, R/rankine.</p>
<pre><code class="lang-perl">p unit_temperature(100, "c", "f") # 212
</code></pre>
</article>
<article class="doc-entry" id="doc-unit-vec">
<h3><a class="doc-anchor" href="#doc-unit-vec">#</a> <code>unit_vec</code></h3>
<p><code>unit_vec</code> — unit conversion <code>vec</code>. Alias for <code>vec_normalize</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p unit_vec $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unit-vector">
<h3><a class="doc-anchor" href="#doc-unit-vector">#</a> <code>unit_vector</code></h3>
<p><code>unit_vector</code> — unit conversion <code>vector</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p unit_vector $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unit-volume-metric-to-us">
<h3><a class="doc-anchor" href="#doc-unit-volume-metric-to-us">#</a> <code>unit_volume_metric_to_us</code></h3>
<p><code>unit_volume_metric_to_us(ml, unit) → number</code> — inverse: milliliters to specified US unit.</p>
</article>
<article class="doc-entry" id="doc-unit-volume-us-to-metric">
<h3><a class="doc-anchor" href="#doc-unit-volume-us-to-metric">#</a> <code>unit_volume_us_to_metric</code></h3>
<p><code>unit_volume_us_to_metric(value, unit) → number</code> — convert US volume unit to milliliters. Units: tsp, tbsp, fl_oz, cup, pint, quart, gallon.</p>
<pre><code class="lang-perl">p unit_volume_us_to_metric(1, "cup") # 236.588
</code></pre>
</article>
<article class="doc-entry" id="doc-universal-code-length">
<h3><a class="doc-anchor" href="#doc-universal-code-length">#</a> <code>universal_code_length</code></h3>
<p><code>universal_code_length</code> — operation <code>universal code length</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p universal_code_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-universal-enveloping-dim">
<h3><a class="doc-anchor" href="#doc-universal-enveloping-dim">#</a> <code>universal_enveloping_dim</code></h3>
<p><code>universal_enveloping_dim</code> — operation <code>universal enveloping dim</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p universal_enveloping_dim $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unix-epoch">
<h3><a class="doc-anchor" href="#doc-unix-epoch">#</a> <code>unix_epoch</code></h3>
<p><code>unix_epoch</code> — operation <code>unix epoch</code>. Category: *now / timestamp*.</p>
<pre><code class="lang-perl">p unix_epoch $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unix-epoch-ms">
<h3><a class="doc-anchor" href="#doc-unix-epoch-ms">#</a> <code>unix_epoch_ms</code></h3>
<p><code>unix_epoch_ms</code> — operation <code>unix epoch ms</code>. Category: *now / timestamp*.</p>
<pre><code class="lang-perl">p unix_epoch_ms $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unix-epoch-to-iso">
<h3><a class="doc-anchor" href="#doc-unix-epoch-to-iso">#</a> <code>unix_epoch_to_iso</code></h3>
<p><code>unix_epoch_to_iso</code> — convert from <code>unix epoch</code> to <code>iso</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p unix_epoch_to_iso $value
</code></pre>
</article>
<article class="doc-entry" id="doc-unix-to-julian">
<h3><a class="doc-anchor" href="#doc-unix-to-julian">#</a> <code>unix_to_julian</code></h3>
<p><code>unix_to_julian(unix) → number</code> — convert unix timestamp to Julian Date. JD 2440587.5 is unix 0.</p>
<pre><code class="lang-perl">p unix_to_julian(0) # 2440587.5
</code></pre>
</article>
<article class="doc-entry" id="doc-unlines">
<h3><a class="doc-anchor" href="#doc-unlines">#</a> <code>unlines</code></h3>
<p><code>unlines</code> — operation <code>unlines</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p unlines $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unlns">
<h3><a class="doc-anchor" href="#doc-unlns">#</a> <code>unlns</code></h3>
<p><code>unlns</code> — operation <code>unlns</code>. Alias for <code>unlines</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p unlns $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unquote">
<h3><a class="doc-anchor" href="#doc-unquote">#</a> <code>unquote</code></h3>
<p><code>unquote</code> — operation <code>unquote</code>. Category: *string quote / escape*.</p>
<pre><code class="lang-perl">p unquote $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unruh-temperature-full">
<h3><a class="doc-anchor" href="#doc-unruh-temperature-full">#</a> <code>unruh_temperature_full</code></h3>
<p><code>unruh_temperature_full</code> — operation <code>unruh temperature full</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p unruh_temperature_full $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unscented-sigma-point">
<h3><a class="doc-anchor" href="#doc-unscented-sigma-point">#</a> <code>unscented_sigma_point</code></h3>
<p><code>unscented_sigma_point</code> — operation <code>unscented sigma point</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p unscented_sigma_point $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unsharp-mask-kernel">
<h3><a class="doc-anchor" href="#doc-unsharp-mask-kernel">#</a> <code>unsharp_mask_kernel</code></h3>
<p><code>unsharp_mask_kernel</code> — convolution kernel of <code>unsharp mask</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p unsharp_mask_kernel $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unsharp-mask-step">
<h3><a class="doc-anchor" href="#doc-unsharp-mask-step">#</a> <code>unsharp_mask_step</code></h3>
<p><code>unsharp_mask_step</code> — single-step update of <code>unsharp mask</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p unsharp_mask_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-untie">
<h3><a class="doc-anchor" href="#doc-untie">#</a> <code>untie</code></h3>
<p><code>untie</code> — operation <code>untie</code>. Category: *type / reflection*.</p>
<pre><code class="lang-perl">p untie $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unwds">
<h3><a class="doc-anchor" href="#doc-unwds">#</a> <code>unwds</code></h3>
<p><code>unwds</code> — operation <code>unwds</code>. Alias for <code>unwords</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p unwds $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unweaken">
<h3><a class="doc-anchor" href="#doc-unweaken">#</a> <code>unweaken</code></h3>
<p><code>unweaken</code> — operation <code>unweaken</code>. Category: *list / aggregate*.</p>
<pre><code class="lang-perl">p unweaken $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unwords">
<h3><a class="doc-anchor" href="#doc-unwords">#</a> <code>unwords</code></h3>
<p><code>unwords</code> — operation <code>unwords</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p unwords $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unzip">
<h3><a class="doc-anchor" href="#doc-unzip">#</a> <code>unzip</code></h3>
<p><code>unzip</code> — operation <code>unzip</code>. Category: *collection more*.</p>
<pre><code class="lang-perl">p unzip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unzip3">
<h3><a class="doc-anchor" href="#doc-unzip3">#</a> <code>unzip3</code></h3>
<p><code>unzip3</code> — operation <code>unzip3</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p unzip3 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unzip-archive">
<h3><a class="doc-anchor" href="#doc-unzip-archive">#</a> <code>unzip_archive</code></h3>
<p><code>unzip_archive</code> — operation <code>unzip archive</code>. Alias for <code>zip_extract</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p unzip_archive $x
</code></pre>
</article>
<article class="doc-entry" id="doc-unzip-pairs">
<h3><a class="doc-anchor" href="#doc-unzip-pairs">#</a> <code>unzip_pairs</code></h3>
<p><code>unzip_pairs</code> — operation <code>unzip pairs</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p unzip_pairs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-upc-check">
<h3><a class="doc-anchor" href="#doc-upc-check">#</a> <code>upc_check</code></h3>
<p><code>upc_check</code> — operation <code>upc check</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p upc_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-upcase-each">
<h3><a class="doc-anchor" href="#doc-upcase-each">#</a> <code>upcase_each</code></h3>
<p><code>upcase_each</code> — operation <code>upcase each</code>. Category: *trivial numeric helpers*.</p>
<pre><code class="lang-perl">p upcase_each $x
</code></pre>
</article>
<article class="doc-entry" id="doc-upda">
<h3><a class="doc-anchor" href="#doc-upda">#</a> <code>upda</code></h3>
<p><code>upda</code> — operation <code>upda</code>. Alias for <code>update_at</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p upda $x
</code></pre>
</article>
<article class="doc-entry" id="doc-update-at">
<h3><a class="doc-anchor" href="#doc-update-at">#</a> <code>update_at</code></h3>
<p><code>update_at</code> — operation <code>update at</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p update_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-update-in">
<h3><a class="doc-anchor" href="#doc-update-in">#</a> <code>update_in</code></h3>
<p><code>update_in</code> — operation <code>update in</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p update_in $x
</code></pre>
</article>
<article class="doc-entry" id="doc-upfirdn-step">
<h3><a class="doc-anchor" href="#doc-upfirdn-step">#</a> <code>upfirdn_step</code></h3>
<p><code>upfirdn_step</code> — single-step update of <code>upfirdn</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p upfirdn_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-upper-bound">
<h3><a class="doc-anchor" href="#doc-upper-bound">#</a> <code>upper_bound</code></h3>
<p><code>upper_bound</code> — operation <code>upper bound</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p upper_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-upper-snake">
<h3><a class="doc-anchor" href="#doc-upper-snake">#</a> <code>upper_snake</code></h3>
<p><code>upper_snake</code> — operation <code>upper snake</code>. Alias for <code>constant_case</code>. Category: *string*.</p>
<pre><code class="lang-perl">p upper_snake $x
</code></pre>
</article>
<article class="doc-entry" id="doc-upper-triangular-q">
<h3><a class="doc-anchor" href="#doc-upper-triangular-q">#</a> <code>upper_triangular_q</code></h3>
<p><code>upper_triangular_q</code> — operation <code>upper triangular q</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p upper_triangular_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-uppercase">
<h3><a class="doc-anchor" href="#doc-uppercase">#</a> <code>uppercase</code></h3>
<p><code>uppercase</code> — operation <code>uppercase</code>. Category: *string*.</p>
<pre><code class="lang-perl">p uppercase $x
</code></pre>
</article>
<article class="doc-entry" id="doc-upsample">
<h3><a class="doc-anchor" href="#doc-upsample">#</a> <code>upsample</code></h3>
<p><code>upsample(\@signal, $factor)</code> (alias <code>interpolate</code>) — increases sample rate by inserting zeros and filtering. Factor must be positive integer.</p>
<pre><code class="lang-perl">my $upsampled = interpolate(\@signal, 4) # 4x sample rate
</code></pre>
</article>
<article class="doc-entry" id="doc-uptime-secs">
<h3><a class="doc-anchor" href="#doc-uptime-secs">#</a> <code>uptime_secs</code></h3>
<p><code>uptime_secs</code> — operation <code>uptime secs</code>. Category: *more process / system*.</p>
<pre><code class="lang-perl">p uptime_secs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-upto">
<h3><a class="doc-anchor" href="#doc-upto">#</a> <code>upto</code></h3>
<p><code>upto</code> — operation <code>upto</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p upto $x
</code></pre>
</article>
<article class="doc-entry" id="doc-uqb">
<h3><a class="doc-anchor" href="#doc-uqb">#</a> <code>uqb</code></h3>
<p><code>uqb</code> — operation <code>uqb</code>. Alias for <code>uniq_by</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p uqb $x
</code></pre>
</article>
<article class="doc-entry" id="doc-uri-normalize">
<h3><a class="doc-anchor" href="#doc-uri-normalize">#</a> <code>uri_normalize</code></h3>
<p><code>uri_normalize</code> — URI helper <code>normalize</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p uri_normalize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-uri-resolve">
<h3><a class="doc-anchor" href="#doc-uri-resolve">#</a> <code>uri_resolve</code></h3>
<p><code>uri_resolve</code> — URI helper <code>resolve</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p uri_resolve $x
</code></pre>
</article>
<article class="doc-entry" id="doc-uri-template-expand">
<h3><a class="doc-anchor" href="#doc-uri-template-expand">#</a> <code>uri_template_expand</code></h3>
<p><code>uri_template_expand</code> — URI helper <code>template expand</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p uri_template_expand $x
</code></pre>
</article>
<article class="doc-entry" id="doc-url-decode-form">
<h3><a class="doc-anchor" href="#doc-url-decode-form">#</a> <code>url_decode_form</code></h3>
<p><code>url_decode_form</code> — URL helper <code>decode form</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p url_decode_form $x
</code></pre>
</article>
<article class="doc-entry" id="doc-url-encode-form">
<h3><a class="doc-anchor" href="#doc-url-encode-form">#</a> <code>url_encode_form</code></h3>
<p><code>url_encode_form</code> — URL helper <code>encode form</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p url_encode_form $x
</code></pre>
</article>
<article class="doc-entry" id="doc-url-host">
<h3><a class="doc-anchor" href="#doc-url-host">#</a> <code>url_host</code></h3>
<p><code>url_host</code> — URL helper <code>host</code>. Category: *url / email parts*.</p>
<pre><code class="lang-perl">p url_host $x
</code></pre>
</article>
<article class="doc-entry" id="doc-url-origin">
<h3><a class="doc-anchor" href="#doc-url-origin">#</a> <code>url_origin</code></h3>
<p><code>url_origin</code> — URL helper <code>origin</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p url_origin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-url-path">
<h3><a class="doc-anchor" href="#doc-url-path">#</a> <code>url_path</code></h3>
<p><code>url_path</code> — URL helper <code>path</code>. Category: *url / email parts*.</p>
<pre><code class="lang-perl">p url_path $x
</code></pre>
</article>
<article class="doc-entry" id="doc-url-query">
<h3><a class="doc-anchor" href="#doc-url-query">#</a> <code>url_query</code></h3>
<p><code>url_query</code> — URL helper <code>query</code>. Category: *url / email parts*.</p>
<pre><code class="lang-perl">p url_query $x
</code></pre>
</article>
<article class="doc-entry" id="doc-url-scheme">
<h3><a class="doc-anchor" href="#doc-url-scheme">#</a> <code>url_scheme</code></h3>
<p><code>url_scheme</code> — URL helper <code>scheme</code>. Category: *url / email parts*.</p>
<pre><code class="lang-perl">p url_scheme $x
</code></pre>
</article>
<article class="doc-entry" id="doc-urld">
<h3><a class="doc-anchor" href="#doc-urld">#</a> <code>urld</code></h3>
<p><code>urld</code> — operation <code>urld</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p urld $x
</code></pre>
</article>
<article class="doc-entry" id="doc-urle">
<h3><a class="doc-anchor" href="#doc-urle">#</a> <code>urle</code></h3>
<p><code>urle</code> — operation <code>urle</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p urle $x
</code></pre>
</article>
<article class="doc-entry" id="doc-us-to-ns">
<h3><a class="doc-anchor" href="#doc-us-to-ns">#</a> <code>us_to_ns</code></h3>
<p><code>us_to_ns</code> — convert from <code>us</code> to <code>ns</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p us_to_ns $value
</code></pre>
</article>
<article class="doc-entry" id="doc-usamp">
<h3><a class="doc-anchor" href="#doc-usamp">#</a> <code>usamp</code></h3>
<p><code>usamp</code> — operation <code>usamp</code>. Alias for <code>upsample</code>. Category: *dsp / signal (extended)*.</p>
<pre><code class="lang-perl">p usamp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-username">
<h3><a class="doc-anchor" href="#doc-username">#</a> <code>username</code></h3>
<p><code>username</code> — operation <code>username</code>. Category: *system introspection*.</p>
<pre><code class="lang-perl">p username $x
</code></pre>
</article>
<article class="doc-entry" id="doc-utc">
<h3><a class="doc-anchor" href="#doc-utc">#</a> <code>utc</code></h3>
<p><code>utc</code> — operation <code>utc</code>. Alias for <code>datetime_utc</code>. Category: *date / time*.</p>
<pre><code class="lang-perl">p utc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-utci-simple">
<h3><a class="doc-anchor" href="#doc-utci-simple">#</a> <code>utci_simple</code></h3>
<p><code>utci_simple</code> — operation <code>utci simple</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p utci_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-utilitarian-solution">
<h3><a class="doc-anchor" href="#doc-utilitarian-solution">#</a> <code>utilitarian_solution</code></h3>
<p><code>utilitarian_solution</code> — operation <code>utilitarian solution</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p utilitarian_solution $x
</code></pre>
</article>
<article class="doc-entry" id="doc-utm-from-lat-lng">
<h3><a class="doc-anchor" href="#doc-utm-from-lat-lng">#</a> <code>utm_from_lat_lng</code></h3>
<p><code>utm_from_lat_lng</code> — operation <code>utm from lat lng</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p utm_from_lat_lng $x
</code></pre>
</article>
<article class="doc-entry" id="doc-utm-to-lat-lng">
<h3><a class="doc-anchor" href="#doc-utm-to-lat-lng">#</a> <code>utm_to_lat_lng</code></h3>
<p><code>utm_to_lat_lng</code> — convert from <code>utm</code> to <code>lat lng</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p utm_to_lat_lng $value
</code></pre>
</article>
<article class="doc-entry" id="doc-utm-to-lat-lon">
<h3><a class="doc-anchor" href="#doc-utm-to-lat-lon">#</a> <code>utm_to_lat_lon</code></h3>
<p><code>utm_to_lat_lon(zone, easting, northing, hemi) → [lat, lon]</code> — UTM → geographic inverse.</p>
<pre><code class="lang-perl">p utm_to_lat_lon(18, 583959, 4507351, "N")
</code></pre>
</article>
<article class="doc-entry" id="doc-utm-zone">
<h3><a class="doc-anchor" href="#doc-utm-zone">#</a> <code>utm_zone</code></h3>
<p><code>utm_zone(lon_deg) → int</code> — UTM zone number 1-60 for given longitude.</p>
<pre><code class="lang-perl">p utm_zone(-122.4) # 10
</code></pre>
</article>
<article class="doc-entry" id="doc-uuencode-step">
<h3><a class="doc-anchor" href="#doc-uuencode-step">#</a> <code>uuencode_step</code></h3>
<p><code>uuencode_step</code> — single-step update of <code>uuencode</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p uuencode_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-uuid-v4">
<h3><a class="doc-anchor" href="#doc-uuid-v4">#</a> <code>uuid_v4</code></h3>
<p><code>uuid_v4</code> — operation <code>uuid v4</code>. Category: *id helpers*.</p>
<pre><code class="lang-perl">p uuid_v4 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-uzp">
<h3><a class="doc-anchor" href="#doc-uzp">#</a> <code>uzp</code></h3>
<p><code>uzp</code> — operation <code>uzp</code>. Alias for <code>unzip_pairs</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p uzp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-uzst">
<h3><a class="doc-anchor" href="#doc-uzst">#</a> <code>uzst</code></h3>
<p><code>uzst</code> — operation <code>uzst</code>. Alias for <code>zstd_decode</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p uzst $x
</code></pre>
</article>
<article class="doc-entry" id="doc-v-polynomial-eval">
<h3><a class="doc-anchor" href="#doc-v-polynomial-eval">#</a> <code>v_polynomial_eval</code></h3>
<p><code>v_polynomial_eval</code> — operation <code>v polynomial eval</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p v_polynomial_eval $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vaccination-coverage-required">
<h3><a class="doc-anchor" href="#doc-vaccination-coverage-required">#</a> <code>vaccination_coverage_required</code></h3>
<p><code>vaccination_coverage_required</code> — operation <code>vaccination coverage required</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p vaccination_coverage_required $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vacuum-energy-density">
<h3><a class="doc-anchor" href="#doc-vacuum-energy-density">#</a> <code>vacuum_energy_density</code></h3>
<p><code>vacuum_energy_density</code> — operation <code>vacuum energy density</code>. Category: *cosmology / gr / flrw*.</p>
<pre><code class="lang-perl">p vacuum_energy_density $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vacuum-permeability">
<h3><a class="doc-anchor" href="#doc-vacuum-permeability">#</a> <code>vacuum_permeability</code></h3>
<p><code>vacuum_permeability</code> — operation <code>vacuum permeability</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p vacuum_permeability $x
</code></pre>
</article>
<article class="doc-entry" id="doc-value-iteration-step">
<h3><a class="doc-anchor" href="#doc-value-iteration-step">#</a> <code>value_iteration_step</code></h3>
<p><code>value_iteration_step</code> — single-step update of <code>value iteration</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p value_iteration_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-value-noise-2d">
<h3><a class="doc-anchor" href="#doc-value-noise-2d">#</a> <code>value_noise_2d</code></h3>
<p><code>value_noise_2d(x, y) → number</code> — interpolated random-value lattice. Cheaper than Perlin, more grid-aligned.</p>
</article>
<article class="doc-entry" id="doc-values-at">
<h3><a class="doc-anchor" href="#doc-values-at">#</a> <code>values_at</code></h3>
<p><code>values_at</code> — operation <code>values at</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p values_at $x
</code></pre>
</article>
<article class="doc-entry" id="doc-values-sorted">
<h3><a class="doc-anchor" href="#doc-values-sorted">#</a> <code>values_sorted</code></h3>
<p><code>values_sorted</code> — operation <code>values sorted</code>. Category: *hash ops*.</p>
<pre><code class="lang-perl">p values_sorted $x
</code></pre>
</article>
<article class="doc-entry" id="doc-van-leer-limiter">
<h3><a class="doc-anchor" href="#doc-van-leer-limiter">#</a> <code>van_leer_limiter</code></h3>
<p><code>van_leer_limiter</code> — operation <code>van leer limiter</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p van_leer_limiter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-van-t-hoff-kp">
<h3><a class="doc-anchor" href="#doc-van-t-hoff-kp">#</a> <code>van_t_hoff_kp</code></h3>
<p><code>van_t_hoff_kp</code> — operation <code>van t hoff kp</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p van_t_hoff_kp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vang">
<h3><a class="doc-anchor" href="#doc-vang">#</a> <code>vang</code></h3>
<p><code>vang</code> — operation <code>vang</code>. Alias for <code>vector_angle</code>. Category: *geometry (extended)*.</p>
<pre><code class="lang-perl">p vang $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vant-hoff">
<h3><a class="doc-anchor" href="#doc-vant-hoff">#</a> <code>vant_hoff</code></h3>
<p><code>vant_hoff</code> — operation <code>vant hoff</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p vant_hoff $x
</code></pre>
</article>
<article class="doc-entry" id="doc-var-fit">
<h3><a class="doc-anchor" href="#doc-var-fit">#</a> <code>var_fit</code></h3>
<p><code>var_fit</code> — operation <code>var fit</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p var_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-var-historical">
<h3><a class="doc-anchor" href="#doc-var-historical">#</a> <code>var_historical</code></h3>
<p><code>var_historical</code> — operation <code>var historical</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p var_historical $x
</code></pre>
</article>
<article class="doc-entry" id="doc-variance-decomposition">
<h3><a class="doc-anchor" href="#doc-variance-decomposition">#</a> <code>variance_decomposition</code></h3>
<p><code>variance_decomposition</code> — operation <code>variance decomposition</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p variance_decomposition $x
</code></pre>
</article>
<article class="doc-entry" id="doc-varint-decode">
<h3><a class="doc-anchor" href="#doc-varint-decode">#</a> <code>varint_decode</code></h3>
<p><code>varint_decode(bytes) → int</code> — inverse varint decode.</p>
</article>
<article class="doc-entry" id="doc-varint-encode">
<h3><a class="doc-anchor" href="#doc-varint-encode">#</a> <code>varint_encode</code></h3>
<p><code>varint_encode(n) → array</code> — Protobuf-style variable-length 7-bit-per-byte encoding with high-bit continuation flag.</p>
<pre><code class="lang-perl">p varint_encode(300) # [0xAC, 0x02]
</code></pre>
</article>
<article class="doc-entry" id="doc-vary-match">
<h3><a class="doc-anchor" href="#doc-vary-match">#</a> <code>vary_match</code></h3>
<p><code>vary_match</code> — operation <code>vary match</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p vary_match $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vasicek-bond">
<h3><a class="doc-anchor" href="#doc-vasicek-bond">#</a> <code>vasicek_bond</code></h3>
<p><code>vasicek_bond</code> — operation <code>vasicek bond</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p vasicek_bond $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vat">
<h3><a class="doc-anchor" href="#doc-vat">#</a> <code>vat</code></h3>
<p><code>vat</code> — operation <code>vat</code>. Alias for <code>values_at</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p vat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vcg-payment">
<h3><a class="doc-anchor" href="#doc-vcg-payment">#</a> <code>vcg_payment</code></h3>
<p><code>vcg_payment</code> — operation <code>vcg payment</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p vcg_payment $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vcg-payment-step">
<h3><a class="doc-anchor" href="#doc-vcg-payment-step">#</a> <code>vcg_payment_step</code></h3>
<p><code>vcg_payment_step</code> — single-step update of <code>vcg payment</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p vcg_payment_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vcross">
<h3><a class="doc-anchor" href="#doc-vcross">#</a> <code>vcross</code></h3>
<p><code>vector_cross(\@a, \@b)</code> (alias <code>vcross</code>) — computes the cross product of two 3D vectors. Returns a 3-element arrayref perpendicular to both inputs.</p>
<pre><code class="lang-perl">my $c = vcross([1,0,0], [0,1,0])
p @$c # (0, 0, 1)
</code></pre>
</article>
<article class="doc-entry" id="doc-vdot">
<h3><a class="doc-anchor" href="#doc-vdot">#</a> <code>vdot</code></h3>
<p><code>vector_dot(\@a, \@b)</code> (alias <code>vdot</code>) — computes the dot product of two vectors. Returns the scalar sum of element-wise products.</p>
<pre><code class="lang-perl">p vdot([1,2,3], [4,5,6]) # 32
</code></pre>
</article>
<article class="doc-entry" id="doc-vec3-add">
<h3><a class="doc-anchor" href="#doc-vec3-add">#</a> <code>vec3_add</code></h3>
<p><code>vec3_add(a, b) → [x,y,z]</code> — componentwise vector addition.</p>
<pre><code class="lang-perl">p vec3_add([1,2,3], [4,5,6]) # [5,7,9]
</code></pre>
</article>
<article class="doc-entry" id="doc-vec3-cross">
<h3><a class="doc-anchor" href="#doc-vec3-cross">#</a> <code>vec3_cross</code></h3>
<p><code>vec3_cross(a, b) → [x,y,z]</code> — cross product <code>a × b</code>.</p>
<pre><code class="lang-perl">p vec3_cross([1,0,0], [0,1,0]) # [0,0,1]
</code></pre>
</article>
<article class="doc-entry" id="doc-vec3-distance">
<h3><a class="doc-anchor" href="#doc-vec3-distance">#</a> <code>vec3_distance</code></h3>
<p><code>vec3_distance(a, b) → number</code> — Euclidean distance between two points.</p>
</article>
<article class="doc-entry" id="doc-vec3-dot">
<h3><a class="doc-anchor" href="#doc-vec3-dot">#</a> <code>vec3_dot</code></h3>
<p><code>vec3_dot(a, b) → number</code> — dot product <code>Σ aᵢ·bᵢ</code>.</p>
<pre><code class="lang-perl">p vec3_dot([1,0,0], [0,1,0]) # 0
</code></pre>
</article>
<article class="doc-entry" id="doc-vec3-length">
<h3><a class="doc-anchor" href="#doc-vec3-length">#</a> <code>vec3_length</code></h3>
<p><code>vec3_length(v) → number</code> — Euclidean magnitude.</p>
<pre><code class="lang-perl">p vec3_length([3,0,4]) # 5
</code></pre>
</article>
<article class="doc-entry" id="doc-vec3-lerp">
<h3><a class="doc-anchor" href="#doc-vec3-lerp">#</a> <code>vec3_lerp</code></h3>
<p><code>vec3_lerp(a, b, t) → [x,y,z]</code> — linear interpolation with <code>t</code> clamped to [0,1].</p>
</article>
<article class="doc-entry" id="doc-vec3-normalize">
<h3><a class="doc-anchor" href="#doc-vec3-normalize">#</a> <code>vec3_normalize</code></h3>
<p><code>vec3_normalize(v) → [x,y,z]</code> — unit-length direction; returns [0,0,0] for zero vector.</p>
</article>
<article class="doc-entry" id="doc-vec3-project">
<h3><a class="doc-anchor" href="#doc-vec3-project">#</a> <code>vec3_project</code></h3>
<p><code>vec3_project(v, u) → [x,y,z]</code> — projection of <code>v</code> onto direction <code>u</code>: <code>(v·u/|u|²)·u</code>.</p>
</article>
<article class="doc-entry" id="doc-vec3-reflect">
<h3><a class="doc-anchor" href="#doc-vec3-reflect">#</a> <code>vec3_reflect</code></h3>
<p><code>vec3_reflect(v, n) → [x,y,z]</code> — reflect <code>v</code> about unit-normal <code>n</code>.</p>
</article>
<article class="doc-entry" id="doc-vec3-refract">
<h3><a class="doc-anchor" href="#doc-vec3-refract">#</a> <code>vec3_refract</code></h3>
<p><code>vec3_refract(v, n, eta) → [x,y,z]</code> — Snell's law refraction with index ratio <code>eta</code>; returns 0 vector for total internal reflection.</p>
</article>
<article class="doc-entry" id="doc-vec3-scale">
<h3><a class="doc-anchor" href="#doc-vec3-scale">#</a> <code>vec3_scale</code></h3>
<p><code>vec3_scale(v, s) → [x,y,z]</code> — scalar multiplication.</p>
</article>
<article class="doc-entry" id="doc-vec3-sub">
<h3><a class="doc-anchor" href="#doc-vec3-sub">#</a> <code>vec3_sub</code></h3>
<p><code>vec3_sub(a, b) → [x,y,z]</code> — componentwise subtraction.</p>
</article>
<article class="doc-entry" id="doc-vec4-add">
<h3><a class="doc-anchor" href="#doc-vec4-add">#</a> <code>vec4_add</code></h3>
<p><code>vec4_add(a, b) → [x,y,z,w]</code> — 4-component componentwise addition.</p>
</article>
<article class="doc-entry" id="doc-vec4-dot">
<h3><a class="doc-anchor" href="#doc-vec4-dot">#</a> <code>vec4_dot</code></h3>
<p><code>vec4_dot(a, b) → number</code> — 4-component dot product.</p>
</article>
<article class="doc-entry" id="doc-vec4-length">
<h3><a class="doc-anchor" href="#doc-vec4-length">#</a> <code>vec4_length</code></h3>
<p><code>vec4_length(v) → number</code> — 4-component magnitude.</p>
</article>
<article class="doc-entry" id="doc-vec4-scale">
<h3><a class="doc-anchor" href="#doc-vec4-scale">#</a> <code>vec4_scale</code></h3>
<p><code>vec4_scale(v, s) → [x,y,z,w]</code> — scalar multiply.</p>
</article>
<article class="doc-entry" id="doc-vec4-sub">
<h3><a class="doc-anchor" href="#doc-vec4-sub">#</a> <code>vec4_sub</code></h3>
<p><code>vec4_sub(a, b) → [x,y,z,w]</code> — 4-component subtraction.</p>
</article>
<article class="doc-entry" id="doc-vec-add">
<h3><a class="doc-anchor" href="#doc-vec-add">#</a> <code>vec_add</code></h3>
<p><code>vec_add</code> — operation <code>vec add</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p vec_add $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vec-clj">
<h3><a class="doc-anchor" href="#doc-vec-clj">#</a> <code>vec_clj</code></h3>
<p><code>vec_clj</code> — operation <code>vec clj</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p vec_clj $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vec-dot">
<h3><a class="doc-anchor" href="#doc-vec-dot">#</a> <code>vec_dot</code></h3>
<p><code>vec_dot</code> — operation <code>vec dot</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p vec_dot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vec-l2">
<h3><a class="doc-anchor" href="#doc-vec-l2">#</a> <code>vec_l2</code></h3>
<p><code>vec_l2</code> — operation <code>vec l2</code>. Alias for <code>l2_norm</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p vec_l2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vec-normalize">
<h3><a class="doc-anchor" href="#doc-vec-normalize">#</a> <code>vec_normalize</code></h3>
<p><code>vec_normalize</code> — operation <code>vec normalize</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p vec_normalize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vec-outer">
<h3><a class="doc-anchor" href="#doc-vec-outer">#</a> <code>vec_outer</code></h3>
<p><code>vec_outer</code> — operation <code>vec outer</code>. Alias for <code>outer_product</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p vec_outer $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vec-scale">
<h3><a class="doc-anchor" href="#doc-vec-scale">#</a> <code>vec_scale</code></h3>
<p><code>vec_scale</code> — operation <code>vec scale</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p vec_scale $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vec-set-value">
<h3><a class="doc-anchor" href="#doc-vec-set-value">#</a> <code>vec_set_value</code></h3>
<p><code>vec_set_value</code> — value of <code>vec set</code>. Category: *internal*.</p>
<pre><code class="lang-perl">p vec_set_value $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vec-sub">
<h3><a class="doc-anchor" href="#doc-vec-sub">#</a> <code>vec_sub</code></h3>
<p><code>vec_sub</code> — operation <code>vec sub</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p vec_sub $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vecc">
<h3><a class="doc-anchor" href="#doc-vecc">#</a> <code>vecc</code></h3>
<p><code>vecc</code> — operation <code>vecc</code>. Alias for <code>vec_clj</code>. Category: *algebraic match*.</p>
<pre><code class="lang-perl">p vecc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vecm-alpha-beta">
<h3><a class="doc-anchor" href="#doc-vecm-alpha-beta">#</a> <code>vecm_alpha_beta</code></h3>
<p><code>vecm_alpha_beta</code> — operation <code>vecm alpha beta</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p vecm_alpha_beta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vecm-fit">
<h3><a class="doc-anchor" href="#doc-vecm-fit">#</a> <code>vecm_fit</code></h3>
<p><code>vecm_fit</code> — operation <code>vecm fit</code>. Category: *statsmodels*.</p>
<pre><code class="lang-perl">p vecm_fit $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vector2-add">
<h3><a class="doc-anchor" href="#doc-vector2-add">#</a> <code>vector2_add</code></h3>
<p><code>vector2_add</code> — operation <code>vector2 add</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p vector2_add $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vector2-cross">
<h3><a class="doc-anchor" href="#doc-vector2-cross">#</a> <code>vector2_cross</code></h3>
<p><code>vector2_cross</code> — operation <code>vector2 cross</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p vector2_cross $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vector2-distance">
<h3><a class="doc-anchor" href="#doc-vector2-distance">#</a> <code>vector2_distance</code></h3>
<p><code>vector2_distance</code> — distance / dissimilarity metric of <code>vector2</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p vector2_distance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vector2-dot">
<h3><a class="doc-anchor" href="#doc-vector2-dot">#</a> <code>vector2_dot</code></h3>
<p><code>vector2_dot</code> — operation <code>vector2 dot</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p vector2_dot $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vector2-length">
<h3><a class="doc-anchor" href="#doc-vector2-length">#</a> <code>vector2_length</code></h3>
<p><code>vector2_length</code> — operation <code>vector2 length</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p vector2_length $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vector2-new">
<h3><a class="doc-anchor" href="#doc-vector2-new">#</a> <code>vector2_new</code></h3>
<p><code>vector2_new</code> — constructor of <code>vector2</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p vector2_new $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vector2-normalize">
<h3><a class="doc-anchor" href="#doc-vector2-normalize">#</a> <code>vector2_normalize</code></h3>
<p><code>vector2_normalize</code> — operation <code>vector2 normalize</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p vector2_normalize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vector2-rotate">
<h3><a class="doc-anchor" href="#doc-vector2-rotate">#</a> <code>vector2_rotate</code></h3>
<p><code>vector2_rotate</code> — operation <code>vector2 rotate</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p vector2_rotate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vector2-scale">
<h3><a class="doc-anchor" href="#doc-vector2-scale">#</a> <code>vector2_scale</code></h3>
<p><code>vector2_scale</code> — operation <code>vector2 scale</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p vector2_scale $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vector2-sub">
<h3><a class="doc-anchor" href="#doc-vector2-sub">#</a> <code>vector2_sub</code></h3>
<p><code>vector2_sub</code> — operation <code>vector2 sub</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p vector2_sub $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vector-add">
<h3><a class="doc-anchor" href="#doc-vector-add">#</a> <code>vector_add</code></h3>
<p><code>vector_add(a, b) → array</code> — componentwise addition.</p>
</article>
<article class="doc-entry" id="doc-vector-angle">
<h3><a class="doc-anchor" href="#doc-vector-angle">#</a> <code>vector_angle</code></h3>
<p><code>vector_angle(\@a, \@b)</code> (alias <code>vangle</code>) — computes the angle in radians between two vectors using the dot product formula.</p>
<pre><code class="lang-perl">p vangle([1,0], [0,1]) # ~1.5708 (π/2)
p vangle([1,0], [1,0]) # 0
</code></pre>
</article>
<article class="doc-entry" id="doc-vector-magnitude">
<h3><a class="doc-anchor" href="#doc-vector-magnitude">#</a> <code>vector_magnitude</code></h3>
<p><code>vector_magnitude(\@v)</code> (alias <code>vmag</code>) — computes the Euclidean length (L2 norm) of a vector.</p>
<pre><code class="lang-perl">p vmag([3, 4]) # 5
p vmag([1, 2, 2]) # 3
</code></pre>
</article>
<article class="doc-entry" id="doc-vector-mean">
<h3><a class="doc-anchor" href="#doc-vector-mean">#</a> <code>vector_mean</code></h3>
<p><code>vector_mean(v) → number</code> — arithmetic mean.</p>
</article>
<article class="doc-entry" id="doc-vector-normalize">
<h3><a class="doc-anchor" href="#doc-vector-normalize">#</a> <code>vector_normalize</code></h3>
<p><code>vector_normalize(\@v)</code> (alias <code>vnorm</code>) — returns a unit vector in the same direction. Divides by magnitude.</p>
<pre><code class="lang-perl">my $u = vnorm([3, 4])
p @$u # (0.6, 0.8)
</code></pre>
</article>
<article class="doc-entry" id="doc-vector-project">
<h3><a class="doc-anchor" href="#doc-vector-project">#</a> <code>vector_project</code></h3>
<p><code>vector_project</code> — operation <code>vector project</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p vector_project $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vector-reject">
<h3><a class="doc-anchor" href="#doc-vector-reject">#</a> <code>vector_reject</code></h3>
<p><code>vector_reject</code> — operation <code>vector reject</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p vector_reject $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vector-scale">
<h3><a class="doc-anchor" href="#doc-vector-scale">#</a> <code>vector_scale</code></h3>
<p><code>vector_scale(v, s) → array</code> — scalar multiply.</p>
</article>
<article class="doc-entry" id="doc-vector-sub">
<h3><a class="doc-anchor" href="#doc-vector-sub">#</a> <code>vector_sub</code></h3>
<p><code>vector_sub(a, b) → array</code> — componentwise subtraction.</p>
</article>
<article class="doc-entry" id="doc-velocity-potential-step">
<h3><a class="doc-anchor" href="#doc-velocity-potential-step">#</a> <code>velocity_potential_step</code></h3>
<p><code>velocity_potential_step</code> — single-step update of <code>velocity potential</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p velocity_potential_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-verlinde-count-step">
<h3><a class="doc-anchor" href="#doc-verlinde-count-step">#</a> <code>verlinde_count_step</code></h3>
<p><code>verlinde_count_step</code> — single-step update of <code>verlinde count</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p verlinde_count_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-verma-character-step">
<h3><a class="doc-anchor" href="#doc-verma-character-step">#</a> <code>verma_character_step</code></h3>
<p><code>verma_character_step</code> — single-step update of <code>verma character</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p verma_character_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-verner-8-combine">
<h3><a class="doc-anchor" href="#doc-verner-8-combine">#</a> <code>verner_8_combine</code></h3>
<p><code>verner_8_combine</code> — operation <code>verner 8 combine</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p verner_8_combine $x
</code></pre>
</article>
<article class="doc-entry" id="doc-versin">
<h3><a class="doc-anchor" href="#doc-versin">#</a> <code>versin</code></h3>
<p><code>versin</code> — operation <code>versin</code>. Category: *trig extensions*.</p>
<pre><code class="lang-perl">p versin $x
</code></pre>
</article>
<article class="doc-entry" id="doc-versine">
<h3><a class="doc-anchor" href="#doc-versine">#</a> <code>versine</code></h3>
<p><code>versine</code> — operation <code>versine</code>. Alias for <code>versin</code>. Category: *trig extensions*.</p>
<pre><code class="lang-perl">p versine $x
</code></pre>
</article>
<article class="doc-entry" id="doc-versine-fn">
<h3><a class="doc-anchor" href="#doc-versine-fn">#</a> <code>versine_fn</code></h3>
<p><code>versine_fn</code> — operation <code>versine fn</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p versine_fn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-version-cmp">
<h3><a class="doc-anchor" href="#doc-version-cmp">#</a> <code>version_cmp</code></h3>
<p><code>version_cmp</code> — operation <code>version cmp</code>. Alias for <code>compare_versions</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p version_cmp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vertex-connectivity">
<h3><a class="doc-anchor" href="#doc-vertex-connectivity">#</a> <code>vertex_connectivity</code></h3>
<p><code>vertex_connectivity</code> — operation <code>vertex connectivity</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p vertex_connectivity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vertex-cover-lp-round">
<h3><a class="doc-anchor" href="#doc-vertex-cover-lp-round">#</a> <code>vertex_cover_lp_round</code></h3>
<p><code>vertex_cover_lp_round</code> — operation <code>vertex cover lp round</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p vertex_cover_lp_round $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vf2-consistent">
<h3><a class="doc-anchor" href="#doc-vf2-consistent">#</a> <code>vf2_consistent</code></h3>
<p><code>vf2_consistent</code> — operation <code>vf2 consistent</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p vf2_consistent $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vickrey-auction">
<h3><a class="doc-anchor" href="#doc-vickrey-auction">#</a> <code>vickrey_auction</code></h3>
<p><code>vickrey_auction</code> — operation <code>vickrey auction</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p vickrey_auction $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vigenere-decrypt">
<h3><a class="doc-anchor" href="#doc-vigenere-decrypt">#</a> <code>vigenere_decrypt</code></h3>
<p><code>vigenere_decrypt</code> — decrypt of <code>vigenere</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p vigenere_decrypt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vigenere-encrypt">
<h3><a class="doc-anchor" href="#doc-vigenere-encrypt">#</a> <code>vigenere_encrypt</code></h3>
<p><code>vigenere_encrypt</code> — encrypt of <code>vigenere</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p vigenere_encrypt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vin-check">
<h3><a class="doc-anchor" href="#doc-vin-check">#</a> <code>vin_check</code></h3>
<p><code>vin_check</code> — operation <code>vin check</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p vin_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vin-decode">
<h3><a class="doc-anchor" href="#doc-vin-decode">#</a> <code>vin_decode</code></h3>
<p><code>vin_decode</code> — decode of <code>vin</code>. Category: *validation / input checks*.</p>
<pre><code class="lang-perl">p vin_decode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vincenty-bearing">
<h3><a class="doc-anchor" href="#doc-vincenty-bearing">#</a> <code>vincenty_bearing</code></h3>
<p><code>vincenty_bearing(lat1, lon1, lat2, lon2) → number</code> — initial great-circle bearing in degrees (0-360, north = 0).</p>
<pre><code class="lang-perl">p vincenty_bearing(40.71, -74.00, 51.51, -0.13) # ~51°
</code></pre>
</article>
<article class="doc-entry" id="doc-vincenty-dist">
<h3><a class="doc-anchor" href="#doc-vincenty-dist">#</a> <code>vincenty_dist</code></h3>
<p><code>vincenty_dist</code> — operation <code>vincenty dist</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p vincenty_dist $x
</code></pre>
</article>
<article class="doc-entry" id="doc-virtual-temperature-full">
<h3><a class="doc-anchor" href="#doc-virtual-temperature-full">#</a> <code>virtual_temperature_full</code></h3>
<p><code>virtual_temperature_full</code> — operation <code>virtual temperature full</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p virtual_temperature_full $x
</code></pre>
</article>
<article class="doc-entry" id="doc-viterbi-decode">
<h3><a class="doc-anchor" href="#doc-viterbi-decode">#</a> <code>viterbi_decode</code></h3>
<p><code>viterbi_decode(obs, init, trans, emit) → array</code> — most likely HMM state path; log-space Viterbi.</p>
<pre><code class="lang-perl">p viterbi_decode([0,1,0], \@pi, \@A, \@B)
</code></pre>
</article>
<article class="doc-entry" id="doc-viterbi-pos-tag">
<h3><a class="doc-anchor" href="#doc-viterbi-pos-tag">#</a> <code>viterbi_pos_tag</code></h3>
<p><code>viterbi_pos_tag</code> — operation <code>viterbi pos tag</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p viterbi_pos_tag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vlookup">
<h3><a class="doc-anchor" href="#doc-vlookup">#</a> <code>vlookup</code></h3>
<p><code>vlookup</code> — operation <code>vlookup</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p vlookup $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vo2-max-estimate">
<h3><a class="doc-anchor" href="#doc-vo2-max-estimate">#</a> <code>vo2_max_estimate</code></h3>
<p><code>vo2_max_estimate</code> — operation <code>vo2 max estimate</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p vo2_max_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-void">
<h3><a class="doc-anchor" href="#doc-void">#</a> <code>void</code></h3>
<p><code>void</code> — operation <code>void</code>. Category: *conversion / utility*.</p>
<pre><code class="lang-perl">p void $x
</code></pre>
</article>
<article class="doc-entry" id="doc-voigt-profile">
<h3><a class="doc-anchor" href="#doc-voigt-profile">#</a> <code>voigt_profile</code></h3>
<p><code>voigt_profile</code> — operation <code>voigt profile</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p voigt_profile $x
</code></pre>
</article>
<article class="doc-entry" id="doc-voigt-profile-simple">
<h3><a class="doc-anchor" href="#doc-voigt-profile-simple">#</a> <code>voigt_profile_simple</code></h3>
<p><code>voigt_profile_simple</code> — operation <code>voigt profile simple</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p voigt_profile_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-volatility-annualized">
<h3><a class="doc-anchor" href="#doc-volatility-annualized">#</a> <code>volatility_annualized</code></h3>
<p><code>volatility_annualized(returns, periods_per_year=252) → number</code> — <code>stddev(returns) · √periods_per_year</code>. Standard equity-return annualisation.</p>
<pre><code class="lang-perl">p volatility_annualized(\@daily_returns)
</code></pre>
</article>
<article class="doc-entry" id="doc-volatility-realized">
<h3><a class="doc-anchor" href="#doc-volatility-realized">#</a> <code>volatility_realized</code></h3>
<p><code>volatility_realized</code> — operation <code>volatility realized</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p volatility_realized $x
</code></pre>
</article>
<article class="doc-entry" id="doc-voltage-divider">
<h3><a class="doc-anchor" href="#doc-voltage-divider">#</a> <code>voltage_divider</code></h3>
<p><code>voltage_divider</code> — operation <code>voltage divider</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p voltage_divider $x
</code></pre>
</article>
<article class="doc-entry" id="doc-voltaic-efficiency">
<h3><a class="doc-anchor" href="#doc-voltaic-efficiency">#</a> <code>voltaic_efficiency</code></h3>
<p><code>voltaic_efficiency</code> — operation <code>voltaic efficiency</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p voltaic_efficiency $x
</code></pre>
</article>
<article class="doc-entry" id="doc-volume-form-riemannian">
<h3><a class="doc-anchor" href="#doc-volume-form-riemannian">#</a> <code>volume_form_riemannian</code></h3>
<p><code>volume_form_riemannian</code> — operation <code>volume form riemannian</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p volume_form_riemannian $x
</code></pre>
</article>
<article class="doc-entry" id="doc-voronoi-cell-2d">
<h3><a class="doc-anchor" href="#doc-voronoi-cell-2d">#</a> <code>voronoi_cell_2d</code></h3>
<p><code>voronoi_cell_2d(point, others, bbox=[xmin,ymin,xmax,ymax]) → array</code> — Voronoi cell of <code>point</code> as intersection of half-planes within bounding box.</p>
</article>
<article class="doc-entry" id="doc-vqe-step">
<h3><a class="doc-anchor" href="#doc-vqe-step">#</a> <code>vqe_step</code></h3>
<p><code>vqe_step</code> — single-step update of <code>vqe</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p vqe_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vsepr-geometry">
<h3><a class="doc-anchor" href="#doc-vsepr-geometry">#</a> <code>vsepr_geometry</code></h3>
<p><code>vsepr_geometry</code> — operation <code>vsepr geometry</code>. Category: *chemistry & biochemistry*.</p>
<pre><code class="lang-perl">p vsepr_geometry $x
</code></pre>
</article>
<article class="doc-entry" id="doc-vwap">
<h3><a class="doc-anchor" href="#doc-vwap">#</a> <code>vwap</code></h3>
<p><code>vwap(highs, lows, closes, volumes) → array</code> — Volume-Weighted Average Price: cumulative <code>Σ(typical·vol) / Σ(vol)</code>.</p>
<pre><code class="lang-perl">p vwap(\@hi, \@lo, \@cl, \@vol)
</code></pre>
</article>
<article class="doc-entry" id="doc-w-state">
<h3><a class="doc-anchor" href="#doc-w-state">#</a> <code>w_state</code></h3>
<p><code>w_state</code> — operation <code>w state</code>. Category: *quantum*.</p>
<pre><code class="lang-perl">p w_state $x
</code></pre>
</article>
<article class="doc-entry" id="doc-w-state-n">
<h3><a class="doc-anchor" href="#doc-w-state-n">#</a> <code>w_state_n</code></h3>
<p><code>w_state_n</code> — operation <code>w state n</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p w_state_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wacc">
<h3><a class="doc-anchor" href="#doc-wacc">#</a> <code>wacc</code></h3>
<p><code>wacc($equity, $debt, $cost_equity, $cost_debt, $tax_rate)</code> — computes Weighted Average Cost of Capital. Returns the blended cost of capital accounting for the tax shield on debt.</p>
<pre><code class="lang-perl">p wacc(60, 40, 0.10, 0.05, 0.25) # ~7.5%
</code></pre>
</article>
<article class="doc-entry" id="doc-wald-test-stat">
<h3><a class="doc-anchor" href="#doc-wald-test-stat">#</a> <code>wald_test_stat</code></h3>
<p><code>wald_test_stat</code> — operation <code>wald test stat</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p wald_test_stat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-walden-product">
<h3><a class="doc-anchor" href="#doc-walden-product">#</a> <code>walden_product</code></h3>
<p><code>walden_product</code> — operation <code>walden product</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p walden_product $x
</code></pre>
</article>
<article class="doc-entry" id="doc-walker-circulation-step">
<h3><a class="doc-anchor" href="#doc-walker-circulation-step">#</a> <code>walker_circulation_step</code></h3>
<p><code>walker_circulation_step</code> — single-step update of <code>walker circulation</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p walker_circulation_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-walksat-step">
<h3><a class="doc-anchor" href="#doc-walksat-step">#</a> <code>walksat_step</code></h3>
<p><code>walksat_step</code> — single-step update of <code>walksat</code>. Category: *logic, proof, sat/smt, type theory*.</p>
<pre><code class="lang-perl">p walksat_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-war-above-replacement">
<h3><a class="doc-anchor" href="#doc-war-above-replacement">#</a> <code>war_above_replacement</code></h3>
<p><code>war_above_replacement</code> — operation <code>war above replacement</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p war_above_replacement $x
</code></pre>
</article>
<article class="doc-entry" id="doc-warburg-impedance">
<h3><a class="doc-anchor" href="#doc-warburg-impedance">#</a> <code>warburg_impedance</code></h3>
<p><code>warburg_impedance</code> — operation <code>warburg impedance</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p warburg_impedance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-warped-product-step-zero">
<h3><a class="doc-anchor" href="#doc-warped-product-step-zero">#</a> <code>warped_product_step_zero</code></h3>
<p><code>warped_product_step_zero</code> — operation <code>warped product step zero</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p warped_product_step_zero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-warshall-step">
<h3><a class="doc-anchor" href="#doc-warshall-step">#</a> <code>warshall_step</code></h3>
<p><code>warshall_step</code> — single-step update of <code>warshall</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p warshall_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wasserstein-dist-emp">
<h3><a class="doc-anchor" href="#doc-wasserstein-dist-emp">#</a> <code>wasserstein_dist_emp</code></h3>
<p><code>wasserstein_dist_emp</code> — operation <code>wasserstein dist emp</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p wasserstein_dist_emp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-watershed-segment">
<h3><a class="doc-anchor" href="#doc-watershed-segment">#</a> <code>watershed_segment</code></h3>
<p><code>watershed_segment</code> — operation <code>watershed segment</code>. Category: *pil/opencv image processing*.</p>
<pre><code class="lang-perl">p watershed_segment $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wattersons-theta">
<h3><a class="doc-anchor" href="#doc-wattersons-theta">#</a> <code>wattersons_theta</code></h3>
<p><code>wattersons_theta</code> — operation <code>wattersons theta</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p wattersons_theta $x
</code></pre>
</article>
<article class="doc-entry" id="doc-watts-to-hp">
<h3><a class="doc-anchor" href="#doc-watts-to-hp">#</a> <code>watts_to_hp</code></h3>
<p><code>watts_to_hp</code> — convert from <code>watts</code> to <code>hp</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p watts_to_hp $value
</code></pre>
</article>
<article class="doc-entry" id="doc-wav-header-read">
<h3><a class="doc-anchor" href="#doc-wav-header-read">#</a> <code>wav_header_read</code></h3>
<p><code>wav_header_read(hex_bytes) → hash</code> — parse WAV RIFF/fmt → <code>{format, channels, sample_rate, bits_per_sample}</code>.</p>
</article>
<article class="doc-entry" id="doc-wave-string-speed">
<h3><a class="doc-anchor" href="#doc-wave-string-speed">#</a> <code>wave_string_speed</code></h3>
<p><code>wave_string_speed</code> — operation <code>wave string speed</code>. Category: *em / optics / relativity*.</p>
<pre><code class="lang-perl">p wave_string_speed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wavelength-freq">
<h3><a class="doc-anchor" href="#doc-wavelength-freq">#</a> <code>wavelength_freq</code></h3>
<p><code>wavelength_freq</code> — operation <code>wavelength freq</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p wavelength_freq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wavetable-synth">
<h3><a class="doc-anchor" href="#doc-wavetable-synth">#</a> <code>wavetable_synth</code></h3>
<p><code>wavetable_synth(table, freq=440, sr=44100, dur=1) → array</code> — wavetable oscillator with linear interpolation; returns float samples.</p>
<pre><code class="lang-perl">my @sine = map { sin(2*3.14159*$_/256) } 0..255
p wavetable_synth(\@sine, 440, 44100, 0.1)
</code></pre>
</article>
<article class="doc-entry" id="doc-wc">
<h3><a class="doc-anchor" href="#doc-wc">#</a> <code>wc</code></h3>
<p><code>wc</code> — operation <code>wc</code>. Alias for <code>word_count</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p wc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wcag-contrast">
<h3><a class="doc-anchor" href="#doc-wcag-contrast">#</a> <code>wcag_contrast</code></h3>
<p><code>wcag_contrast</code> — operation <code>wcag contrast</code>. Alias for <code>contrast_ratio_wcag</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p wcag_contrast $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wcag-luminance">
<h3><a class="doc-anchor" href="#doc-wcag-luminance">#</a> <code>wcag_luminance</code></h3>
<p><code>wcag_luminance</code> — operation <code>wcag luminance</code>. Alias for <code>relative_luminance</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p wcag_luminance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wcag-pass">
<h3><a class="doc-anchor" href="#doc-wcag-pass">#</a> <code>wcag_pass</code></h3>
<p><code>wcag_pass</code> — operation <code>wcag pass</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p wcag_pass $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wcount">
<h3><a class="doc-anchor" href="#doc-wcount">#</a> <code>wcount</code></h3>
<p><code>wcount</code> — operation <code>wcount</code>. Alias for <code>count_words</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p wcount $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weak-composition-count">
<h3><a class="doc-anchor" href="#doc-weak-composition-count">#</a> <code>weak_composition_count</code></h3>
<p><code>weak_composition_count</code> — count of <code>weak composition</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p weak_composition_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weaken">
<h3><a class="doc-anchor" href="#doc-weaken">#</a> <code>weaken</code></h3>
<p><code>weaken</code> — operation <code>weaken</code>. Category: *list / aggregate*.</p>
<pre><code class="lang-perl">p weaken $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weave-n">
<h3><a class="doc-anchor" href="#doc-weave-n">#</a> <code>weave_n</code></h3>
<p><code>weave_n</code> — operation <code>weave n</code>. Category: *iterator + string-distance extras*.</p>
<pre><code class="lang-perl">p weave_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weber-number">
<h3><a class="doc-anchor" href="#doc-weber-number">#</a> <code>weber_number</code></h3>
<p><code>weber_number</code> — operation <code>weber number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p weber_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weber-number-step">
<h3><a class="doc-anchor" href="#doc-weber-number-step">#</a> <code>weber_number_step</code></h3>
<p><code>weber_number_step</code> — single-step update of <code>weber number</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p weber_number_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-week-number-iso">
<h3><a class="doc-anchor" href="#doc-week-number-iso">#</a> <code>week_number_iso</code></h3>
<p><code>week_number_iso</code> — operation <code>week number iso</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p week_number_iso $x
</code></pre>
</article>
<article class="doc-entry" id="doc-week-of-year">
<h3><a class="doc-anchor" href="#doc-week-of-year">#</a> <code>week_of_year</code></h3>
<p><code>week_of_year</code> — operation <code>week of year</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p week_of_year $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weekday-name">
<h3><a class="doc-anchor" href="#doc-weekday-name">#</a> <code>weekday_name</code></h3>
<p><code>weekday_name</code> — operation <code>weekday name</code>. Category: *date helpers*.</p>
<pre><code class="lang-perl">p weekday_name $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weekday-name-short">
<h3><a class="doc-anchor" href="#doc-weekday-name-short">#</a> <code>weekday_name_short</code></h3>
<p><code>weekday_name_short</code> — operation <code>weekday name short</code>. Category: *calendrical algorithms*.</p>
<pre><code class="lang-perl">p weekday_name_short $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weekday-short">
<h3><a class="doc-anchor" href="#doc-weekday-short">#</a> <code>weekday_short</code></h3>
<p><code>weekday_short</code> — operation <code>weekday short</code>. Category: *date helpers*.</p>
<pre><code class="lang-perl">p weekday_short $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weeks-between">
<h3><a class="doc-anchor" href="#doc-weeks-between">#</a> <code>weeks_between</code></h3>
<p><code>weeks_between</code> — operation <code>weeks between</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p weeks_between $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weibpdf">
<h3><a class="doc-anchor" href="#doc-weibpdf">#</a> <code>weibpdf</code></h3>
<p><code>weibull_pdf</code> (alias <code>weibpdf</code>) evaluates the Weibull distribution PDF at x with shape k and scale lambda.</p>
<pre><code class="lang-perl">p weibpdf(1.0, 1.5, 1.0)
</code></pre>
</article>
<article class="doc-entry" id="doc-weighted-match-kuhn-step">
<h3><a class="doc-anchor" href="#doc-weighted-match-kuhn-step">#</a> <code>weighted_match_kuhn_step</code></h3>
<p><code>weighted_match_kuhn_step</code> — single-step update of <code>weighted match kuhn</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p weighted_match_kuhn_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weighted-mean">
<h3><a class="doc-anchor" href="#doc-weighted-mean">#</a> <code>weighted_mean</code></h3>
<p><code>weighted_mean</code> — arithmetic mean of <code>weighted</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p weighted_mean @xs
</code></pre>
</article>
<article class="doc-entry" id="doc-weighted-sample">
<h3><a class="doc-anchor" href="#doc-weighted-sample">#</a> <code>weighted_sample</code></h3>
<p><code>weighted_sample</code> — operation <code>weighted sample</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p weighted_sample $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weighted-set-cover-step">
<h3><a class="doc-anchor" href="#doc-weighted-set-cover-step">#</a> <code>weighted_set_cover_step</code></h3>
<p><code>weighted_set_cover_step</code> — single-step update of <code>weighted set cover</code>. Category: *combinatorial optimization, scheduling*.</p>
<pre><code class="lang-perl">p weighted_set_cover_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weighted-var">
<h3><a class="doc-anchor" href="#doc-weighted-var">#</a> <code>weighted_var</code></h3>
<p><code>weighted_var</code> — weighted variance. Args: values, weights.</p>
<pre><code class="lang-perl">p wvar([1,2,3,4], [1,1,1,1]) # same as var
</code></pre>
</article>
<article class="doc-entry" id="doc-weiler-atherton-clip">
<h3><a class="doc-anchor" href="#doc-weiler-atherton-clip">#</a> <code>weiler_atherton_clip</code></h3>
<p><code>weiler_atherton_clip</code> — operation <code>weiler atherton clip</code>. Category: *test runner*.</p>
<pre><code class="lang-perl">p weiler_atherton_clip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weingarten-map-step">
<h3><a class="doc-anchor" href="#doc-weingarten-map-step">#</a> <code>weingarten_map_step</code></h3>
<p><code>weingarten_map_step</code> — single-step update of <code>weingarten map</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p weingarten_map_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-welch-psd-avg">
<h3><a class="doc-anchor" href="#doc-welch-psd-avg">#</a> <code>welch_psd_avg</code></h3>
<p><code>welch_psd_avg</code> — operation <code>welch psd avg</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p welch_psd_avg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-welch-ttest">
<h3><a class="doc-anchor" href="#doc-welch-ttest">#</a> <code>welch_ttest</code></h3>
<p><code>welch_ttest</code> (alias <code>welcht</code>) performs Welch's t-test for two independent samples with unequal variances. Returns [t-statistic, degrees of freedom].</p>
<pre><code class="lang-perl">my ($t, $df) = @{welcht([1,2,3,4,5], [3,4,5,6,7])}
p "t=$t df=$df"
</code></pre>
</article>
<article class="doc-entry" id="doc-welch-window">
<h3><a class="doc-anchor" href="#doc-welch-window">#</a> <code>welch_window</code></h3>
<p><code>welch_window</code> — operation <code>welch window</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p welch_window $x
</code></pre>
</article>
<article class="doc-entry" id="doc-welsh-powell">
<h3><a class="doc-anchor" href="#doc-welsh-powell">#</a> <code>welsh_powell</code></h3>
<p><code>welsh_powell</code> — operation <code>welsh powell</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p welsh_powell $x
</code></pre>
</article>
<article class="doc-entry" id="doc-werckmeister-iii">
<h3><a class="doc-anchor" href="#doc-werckmeister-iii">#</a> <code>werckmeister_iii</code></h3>
<p><code>werckmeister_iii</code> — operation <code>werckmeister iii</code>. Category: *music theory*.</p>
<pre><code class="lang-perl">p werckmeister_iii $x
</code></pre>
</article>
<article class="doc-entry" id="doc-westerlies-jet-speed">
<h3><a class="doc-anchor" href="#doc-westerlies-jet-speed">#</a> <code>westerlies_jet_speed</code></h3>
<p><code>westerlies_jet_speed</code> — operation <code>westerlies jet speed</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p westerlies_jet_speed $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wet-bulb-potential">
<h3><a class="doc-anchor" href="#doc-wet-bulb-potential">#</a> <code>wet_bulb_potential</code></h3>
<p><code>wet_bulb_potential</code> — operation <code>wet bulb potential</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p wet_bulb_potential $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weyl-group-order">
<h3><a class="doc-anchor" href="#doc-weyl-group-order">#</a> <code>weyl_group_order</code></h3>
<p><code>weyl_group_order</code> — operation <code>weyl group order</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p weyl_group_order $x
</code></pre>
</article>
<article class="doc-entry" id="doc-weyl-tensor-step-zero">
<h3><a class="doc-anchor" href="#doc-weyl-tensor-step-zero">#</a> <code>weyl_tensor_step_zero</code></h3>
<p><code>weyl_tensor_step_zero</code> — operation <code>weyl tensor step zero</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p weyl_tensor_step_zero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wfrm">
<h3><a class="doc-anchor" href="#doc-wfrm">#</a> <code>wfrm</code></h3>
<p><code>wfrm</code> — operation <code>wfrm</code>. Alias for <code>words_from</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p wfrm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wh">
<h3><a class="doc-anchor" href="#doc-wh">#</a> <code>wh</code></h3>
<p><code>wh</code> — operation <code>wh</code>. Alias for <code>which</code>. Category: *filesystem extensions*.</p>
<pre><code class="lang-perl">p wh $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wha">
<h3><a class="doc-anchor" href="#doc-wha">#</a> <code>wha</code></h3>
<p>Return a list of all absolute paths matching the given command name across every directory in <code>PATH</code>, not just the first match. The short alias <code>wha</code> keeps things concise. This is useful for detecting shadowed executables or auditing which versions of a tool are installed.</p>
<pre><code class="lang-perl">my @all = which_all("python3")
@all |> e p # /usr/local/bin/python3
# /usr/bin/python3
p scalar wha("perl") # number of perls on PATH
</code></pre>
</article>
<article class="doc-entry" id="doc-when-false">
<h3><a class="doc-anchor" href="#doc-when-false">#</a> <code>when_false</code></h3>
<p><code>when_false</code> — operation <code>when false</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p when_false $x
</code></pre>
</article>
<article class="doc-entry" id="doc-when-true">
<h3><a class="doc-anchor" href="#doc-when-true">#</a> <code>when_true</code></h3>
<p><code>when_true</code> — operation <code>when true</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p when_true $x
</code></pre>
</article>
<article class="doc-entry" id="doc-which-fn">
<h3><a class="doc-anchor" href="#doc-which-fn">#</a> <code>which_fn</code></h3>
<p><code>which_fn</code> — return indices where a predicate is true. Like R's which().</p>
<pre><code class="lang-perl">my @idx = @{which_fn([1,5,3,8,2], fn { $_[0] > 3 })} # [1, 3]
</code></pre>
</article>
<article class="doc-entry" id="doc-white">
<h3><a class="doc-anchor" href="#doc-white">#</a> <code>white</code></h3>
<p><code>white</code> — operation <code>white</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p white $x
</code></pre>
</article>
<article class="doc-entry" id="doc-white-bold">
<h3><a class="doc-anchor" href="#doc-white-bold">#</a> <code>white_bold</code></h3>
<p><code>white_bold</code> — operation <code>white bold</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p white_bold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-white-point-d50">
<h3><a class="doc-anchor" href="#doc-white-point-d50">#</a> <code>white_point_d50</code></h3>
<p><code>white_point_d50</code> — operation <code>white point d50</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p white_point_d50 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-white-point-d65">
<h3><a class="doc-anchor" href="#doc-white-point-d65">#</a> <code>white_point_d65</code></h3>
<p><code>white_point_d65</code> — operation <code>white point d65</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p white_point_d65 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-white-robust-se">
<h3><a class="doc-anchor" href="#doc-white-robust-se">#</a> <code>white_robust_se</code></h3>
<p><code>white_robust_se</code> — operation <code>white robust se</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p white_robust_se $x
</code></pre>
</article>
<article class="doc-entry" id="doc-white-test-stat">
<h3><a class="doc-anchor" href="#doc-white-test-stat">#</a> <code>white_test_stat</code></h3>
<p><code>white_test_stat</code> — operation <code>white test stat</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p white_test_stat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-whittaker-m">
<h3><a class="doc-anchor" href="#doc-whittaker-m">#</a> <code>whittaker_m</code></h3>
<p><code>whittaker_m</code> — operation <code>whittaker m</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p whittaker_m $x
</code></pre>
</article>
<article class="doc-entry" id="doc-whole-life-a">
<h3><a class="doc-anchor" href="#doc-whole-life-a">#</a> <code>whole_life_a</code></h3>
<p><code>whole_life_a</code> — operation <code>whole life a</code>. Category: *actuarial science*.</p>
<pre><code class="lang-perl">p whole_life_a $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wieferich-check">
<h3><a class="doc-anchor" href="#doc-wieferich-check">#</a> <code>wieferich_check</code></h3>
<p><code>wieferich_check</code> — operation <code>wieferich check</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p wieferich_check $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wien">
<h3><a class="doc-anchor" href="#doc-wien">#</a> <code>wien</code></h3>
<p><code>wien</code> — operation <code>wien</code>. Alias for <code>wien_displacement</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p wien $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wien-constant">
<h3><a class="doc-anchor" href="#doc-wien-constant">#</a> <code>wien_constant</code></h3>
<p><code>wien_constant</code> — operation <code>wien constant</code>. Category: *physics constants*.</p>
<pre><code class="lang-perl">p wien_constant $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wien-displacement">
<h3><a class="doc-anchor" href="#doc-wien-displacement">#</a> <code>wien_displacement</code></h3>
<p><code>wien_displacement</code> — operation <code>wien displacement</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p wien_displacement $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wiener-filter">
<h3><a class="doc-anchor" href="#doc-wiener-filter">#</a> <code>wiener_filter</code></h3>
<p><code>wiener_filter</code> — filter op of <code>wiener</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p wiener_filter $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wigner-3j-bound">
<h3><a class="doc-anchor" href="#doc-wigner-3j-bound">#</a> <code>wigner_3j_bound</code></h3>
<p><code>wigner_3j_bound</code> — operation <code>wigner 3j bound</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p wigner_3j_bound $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wilcoxon">
<h3><a class="doc-anchor" href="#doc-wilcoxon">#</a> <code>wilcoxon</code></h3>
<p><code>wilcoxon</code> — operation <code>wilcoxon</code>. Category: *r / scipy distributions and tests*.</p>
<pre><code class="lang-perl">p wilcoxon $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wilcoxon-signed-rank">
<h3><a class="doc-anchor" href="#doc-wilcoxon-signed-rank">#</a> <code>wilcoxon_signed_rank</code></h3>
<p><code>wilcoxon_signed_rank(a, b) → {statistic, df, p_value}</code> — paired non-parametric test on ranks of <code>|a-b|</code>.</p>
<pre><code class="lang-perl">p wilcoxon_signed_rank(\@before, \@after)
</code></pre>
</article>
<article class="doc-entry" id="doc-williams-r">
<h3><a class="doc-anchor" href="#doc-williams-r">#</a> <code>williams_r</code></h3>
<p><code>williams_r(highs, lows, closes, period=14) → array</code> — Williams %R: <code>-100 · (highest_high − close) / (highest_high − lowest_low)</code>. Mirrors stochastic-K in [-100, 0].</p>
<pre><code class="lang-perl">p williams_r(\@hi, \@lo, \@cl, 14)
</code></pre>
</article>
<article class="doc-entry" id="doc-wilson-test">
<h3><a class="doc-anchor" href="#doc-wilson-test">#</a> <code>wilson_test</code></h3>
<p><code>wilson_test</code> — statistical test of <code>wilson</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p wilson_test $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wilson-theta-step">
<h3><a class="doc-anchor" href="#doc-wilson-theta-step">#</a> <code>wilson_theta_step</code></h3>
<p><code>wilson_theta_step</code> — single-step update of <code>wilson theta</code>. Category: *ode advanced*.</p>
<pre><code class="lang-perl">p wilson_theta_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-win-probability">
<h3><a class="doc-anchor" href="#doc-win-probability">#</a> <code>win_probability</code></h3>
<p><code>win_probability</code> — operation <code>win probability</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p win_probability $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wincirc">
<h3><a class="doc-anchor" href="#doc-wincirc">#</a> <code>wincirc</code></h3>
<p><code>wincirc</code> — operation <code>wincirc</code>. Alias for <code>windowed_circular</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p wincirc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wind-chill">
<h3><a class="doc-anchor" href="#doc-wind-chill">#</a> <code>wind_chill</code></h3>
<p><code>wind_chill</code> — operation <code>wind chill</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p wind_chill $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wind-chill-celsius">
<h3><a class="doc-anchor" href="#doc-wind-chill-celsius">#</a> <code>wind_chill_celsius</code></h3>
<p><code>wind_chill_celsius</code> — operation <code>wind chill celsius</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p wind_chill_celsius $x
</code></pre>
</article>
<article class="doc-entry" id="doc-window-bartlett">
<h3><a class="doc-anchor" href="#doc-window-bartlett">#</a> <code>window_bartlett</code></h3>
<p><code>window_bartlett(n) → array</code> — triangular (Bartlett) window; zero at endpoints.</p>
</article>
<article class="doc-entry" id="doc-window-blackman-harris">
<h3><a class="doc-anchor" href="#doc-window-blackman-harris">#</a> <code>window_blackman_harris</code></h3>
<p><code>window_blackman_harris(n) → array</code> — 4-term Blackman-Harris window. Very low side-lobes (~-92 dB).</p>
</article>
<article class="doc-entry" id="doc-window-flat-top">
<h3><a class="doc-anchor" href="#doc-window-flat-top">#</a> <code>window_flat_top</code></h3>
<p><code>window_flat_top(n) → array</code> — flat-top window. Trades wider main-lobe for flat passband (amplitude calibration).</p>
</article>
<article class="doc-entry" id="doc-window-gaussian">
<h3><a class="doc-anchor" href="#doc-window-gaussian">#</a> <code>window_gaussian</code></h3>
<p><code>window_gaussian(n, sigma=0.4) → array</code> — Gaussian window of length <code>n</code>.</p>
</article>
<article class="doc-entry" id="doc-window-n">
<h3><a class="doc-anchor" href="#doc-window-n">#</a> <code>window_n</code></h3>
<p><code>window_n</code> — windowing function for DSP / FFT <code>n</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p window_n $x
</code></pre>
</article>
<article class="doc-entry" id="doc-window-tukey">
<h3><a class="doc-anchor" href="#doc-window-tukey">#</a> <code>window_tukey</code></h3>
<p><code>window_tukey</code> — windowing function for DSP / FFT <code>tukey</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p window_tukey $x
</code></pre>
</article>
<article class="doc-entry" id="doc-window-welch">
<h3><a class="doc-anchor" href="#doc-window-welch">#</a> <code>window_welch</code></h3>
<p><code>window_welch(n) → array</code> — Welch (parabolic) window.</p>
</article>
<article class="doc-entry" id="doc-windowed-circular">
<h3><a class="doc-anchor" href="#doc-windowed-circular">#</a> <code>windowed_circular</code></h3>
<p><code>windowed_circular</code> — operation <code>windowed circular</code>. Category: *additional missing stdlib functions*.</p>
<pre><code class="lang-perl">p windowed_circular $x
</code></pre>
</article>
<article class="doc-entry" id="doc-winn">
<h3><a class="doc-anchor" href="#doc-winn">#</a> <code>winn</code></h3>
<p><code>winn</code> — operation <code>winn</code>. Alias for <code>window_n</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p winn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-winsor">
<h3><a class="doc-anchor" href="#doc-winsor">#</a> <code>winsor</code></h3>
<p><code>winsor</code> — operation <code>winsor</code>. Alias for <code>winsorize</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p winsor $x
</code></pre>
</article>
<article class="doc-entry" id="doc-winsorize">
<h3><a class="doc-anchor" href="#doc-winsorize">#</a> <code>winsorize</code></h3>
<p><code>winsorize</code> — operation <code>winsorize</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p winsorize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-winsorized-variance-arr">
<h3><a class="doc-anchor" href="#doc-winsorized-variance-arr">#</a> <code>winsorized_variance_arr</code></h3>
<p><code>winsorized_variance_arr</code> — operation <code>winsorized variance arr</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p winsorized_variance_arr $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wire-resistance">
<h3><a class="doc-anchor" href="#doc-wire-resistance">#</a> <code>wire_resistance</code></h3>
<p><code>wire_resistance</code> — operation <code>wire resistance</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p wire_resistance $x
</code></pre>
</article>
<article class="doc-entry" id="doc-without">
<h3><a class="doc-anchor" href="#doc-without">#</a> <code>without</code></h3>
<p><code>without</code> — operation <code>without</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p without $x
</code></pre>
</article>
<article class="doc-entry" id="doc-without-nth">
<h3><a class="doc-anchor" href="#doc-without-nth">#</a> <code>without_nth</code></h3>
<p><code>without_nth</code> — operation <code>without nth</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p without_nth $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wma">
<h3><a class="doc-anchor" href="#doc-wma">#</a> <code>wma</code></h3>
<p><code>wma(prices, period=10) → array</code> — weighted moving average. Newer values get higher linear weights (1, 2, …, period); divides by triangular-number total.</p>
<pre><code class="lang-perl">p wma([10,11,12,13,14], 3)
</code></pre>
</article>
<article class="doc-entry" id="doc-wmean">
<h3><a class="doc-anchor" href="#doc-wmean">#</a> <code>wmean</code></h3>
<p><code>wmean</code> — operation <code>wmean</code>. Alias for <code>weighted_mean</code>. Category: *math / numeric extras*.</p>
<pre><code class="lang-perl">p wmean $x
</code></pre>
</article>
<article class="doc-entry" id="doc-woba-weight">
<h3><a class="doc-anchor" href="#doc-woba-weight">#</a> <code>woba_weight</code></h3>
<p><code>woba_weight</code> — operation <code>woba weight</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p woba_weight $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wofz">
<h3><a class="doc-anchor" href="#doc-wofz">#</a> <code>wofz</code></h3>
<p><code>wofz</code> — operation <code>wofz</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p wofz $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wolfe-strong-q">
<h3><a class="doc-anchor" href="#doc-wolfe-strong-q">#</a> <code>wolfe_strong_q</code></h3>
<p><code>wolfe_strong_q</code> — operation <code>wolfe strong q</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p wolfe_strong_q $x
</code></pre>
</article>
<article class="doc-entry" id="doc-woodall-number">
<h3><a class="doc-anchor" href="#doc-woodall-number">#</a> <code>woodall_number</code></h3>
<p><code>woodall_number</code> — operation <code>woodall number</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p woodall_number $x
</code></pre>
</article>
<article class="doc-entry" id="doc-word-alignment-ibm1">
<h3><a class="doc-anchor" href="#doc-word-alignment-ibm1">#</a> <code>word_alignment_ibm1</code></h3>
<p><code>word_alignment_ibm1</code> — operation <code>word alignment ibm1</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p word_alignment_ibm1 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-word-alignment-ibm2">
<h3><a class="doc-anchor" href="#doc-word-alignment-ibm2">#</a> <code>word_alignment_ibm2</code></h3>
<p><code>word_alignment_ibm2</code> — operation <code>word alignment ibm2</code>. Category: *computational linguistics*.</p>
<pre><code class="lang-perl">p word_alignment_ibm2 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-word-count">
<h3><a class="doc-anchor" href="#doc-word-count">#</a> <code>word_count</code></h3>
<p><code>word_count</code> — count of <code>word</code>. Category: *trivial string ops*.</p>
<pre><code class="lang-perl">p word_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-word-count-simple">
<h3><a class="doc-anchor" href="#doc-word-count-simple">#</a> <code>word_count_simple</code></h3>
<p><code>word_count_simple</code> — operation <code>word count simple</code>. Alias for <code>string_words_count</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p word_count_simple $x
</code></pre>
</article>
<article class="doc-entry" id="doc-word-frequencies">
<h3><a class="doc-anchor" href="#doc-word-frequencies">#</a> <code>word_frequencies</code></h3>
<p><code>word_frequencies</code> — operation <code>word frequencies</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p word_frequencies $x
</code></pre>
</article>
<article class="doc-entry" id="doc-word-similarity">
<h3><a class="doc-anchor" href="#doc-word-similarity">#</a> <code>word_similarity</code></h3>
<p><code>word_similarity</code> — similarity metric of <code>word</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p word_similarity $x
</code></pre>
</article>
<article class="doc-entry" id="doc-word-wrap">
<h3><a class="doc-anchor" href="#doc-word-wrap">#</a> <code>word_wrap</code></h3>
<p><code>word_wrap(s, width=80) → string</code> — break a string into lines no longer than <code>width</code>, splitting on whitespace.</p>
<pre><code class="lang-perl">p word_wrap("the quick brown fox", 10)
</code></pre>
</article>
<article class="doc-entry" id="doc-word-wrap-text">
<h3><a class="doc-anchor" href="#doc-word-wrap-text">#</a> <code>word_wrap_text</code></h3>
<p><code>word_wrap_text</code> — operation <code>word wrap text</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p word_wrap_text $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wordfreq">
<h3><a class="doc-anchor" href="#doc-wordfreq">#</a> <code>wordfreq</code></h3>
<p><code>wordfreq</code> — operation <code>wordfreq</code>. Alias for <code>word_frequencies</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p wordfreq $x
</code></pre>
</article>
<article class="doc-entry" id="doc-words-from">
<h3><a class="doc-anchor" href="#doc-words-from">#</a> <code>words_from</code></h3>
<p><code>words_from</code> — operation <code>words from</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p words_from $x
</code></pre>
</article>
<article class="doc-entry" id="doc-work">
<h3><a class="doc-anchor" href="#doc-work">#</a> <code>work</code></h3>
<p><code>work($force, $distance, $angle)</code> — compute work W = F×d×cos(θ) (Joules). Angle in degrees, default 0.</p>
<pre><code class="lang-perl">p work(100, 10) # 1000 J (force parallel to motion)
p work(100, 10, 60) # 500 J (force at 60°)
</code></pre>
</article>
<article class="doc-entry" id="doc-worley-2d">
<h3><a class="doc-anchor" href="#doc-worley-2d">#</a> <code>worley_2d</code></h3>
<p><code>worley_2d(x, y) → number</code> — F1 cellular (Worley) noise: distance to nearest random feature point.</p>
</article>
<article class="doc-entry" id="doc-woy">
<h3><a class="doc-anchor" href="#doc-woy">#</a> <code>woy</code></h3>
<p><code>woy</code> — operation <code>woy</code>. Alias for <code>week_of_year</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p woy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wpa">
<h3><a class="doc-anchor" href="#doc-wpa">#</a> <code>wpa</code></h3>
<p><code>wpa</code> — operation <code>wpa</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p wpa $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wrap-around">
<h3><a class="doc-anchor" href="#doc-wrap-around">#</a> <code>wrap_around</code></h3>
<p><code>wrap_around</code> — operation <code>wrap around</code>. Category: *trig / math*.</p>
<pre><code class="lang-perl">p wrap_around $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wrap-index">
<h3><a class="doc-anchor" href="#doc-wrap-index">#</a> <code>wrap_index</code></h3>
<p><code>wrap_index</code> — index of <code>wrap</code>. Category: *list helpers*.</p>
<pre><code class="lang-perl">p wrap_index $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wrap-range">
<h3><a class="doc-anchor" href="#doc-wrap-range">#</a> <code>wrap_range</code></h3>
<p><code>wrap_range</code> — operation <code>wrap range</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p wrap_range $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wrap-text">
<h3><a class="doc-anchor" href="#doc-wrap-text">#</a> <code>wrap_text</code></h3>
<p><code>wrap_text</code> — operation <code>wrap text</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p wrap_text $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wrc-plus">
<h3><a class="doc-anchor" href="#doc-wrc-plus">#</a> <code>wrc_plus</code></h3>
<p><code>wrc_plus</code> — operation <code>wrc plus</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p wrc_plus $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wright-omega">
<h3><a class="doc-anchor" href="#doc-wright-omega">#</a> <code>wright_omega</code></h3>
<p><code>wright_omega</code> — operation <code>wright omega</code>. Category: *special functions extra*.</p>
<pre><code class="lang-perl">p wright_omega $x
</code></pre>
</article>
<article class="doc-entry" id="doc-writhe-polygon">
<h3><a class="doc-anchor" href="#doc-writhe-polygon">#</a> <code>writhe_polygon</code></h3>
<p><code>writhe_polygon</code> — operation <code>writhe polygon</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p writhe_polygon $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wrprng">
<h3><a class="doc-anchor" href="#doc-wrprng">#</a> <code>wrprng</code></h3>
<p><code>wrprng</code> — operation <code>wrprng</code>. Alias for <code>wrap_range</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p wrprng $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wrpt">
<h3><a class="doc-anchor" href="#doc-wrpt">#</a> <code>wrpt</code></h3>
<p><code>wrpt</code> — operation <code>wrpt</code>. Alias for <code>wrap_text</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p wrpt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ws-close-frame">
<h3><a class="doc-anchor" href="#doc-ws-close-frame">#</a> <code>ws_close_frame</code></h3>
<p><code>ws_close_frame</code> — WebSocket helper <code>close frame</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ws_close_frame $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ws-frame-decode">
<h3><a class="doc-anchor" href="#doc-ws-frame-decode">#</a> <code>ws_frame_decode</code></h3>
<p><code>ws_frame_decode</code> — WebSocket helper <code>frame decode</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ws_frame_decode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ws-frame-encode">
<h3><a class="doc-anchor" href="#doc-ws-frame-encode">#</a> <code>ws_frame_encode</code></h3>
<p><code>ws_frame_encode</code> — WebSocket helper <code>frame encode</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ws_frame_encode $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ws-handshake-accept">
<h3><a class="doc-anchor" href="#doc-ws-handshake-accept">#</a> <code>ws_handshake_accept</code></h3>
<p><code>ws_handshake_accept</code> — WebSocket helper <code>handshake accept</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ws_handshake_accept $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ws-handshake-key">
<h3><a class="doc-anchor" href="#doc-ws-handshake-key">#</a> <code>ws_handshake_key</code></h3>
<p><code>ws_handshake_key</code> — WebSocket helper <code>handshake key</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ws_handshake_key $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ws-mask">
<h3><a class="doc-anchor" href="#doc-ws-mask">#</a> <code>ws_mask</code></h3>
<p><code>ws_mask</code> — WebSocket helper <code>mask</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ws_mask $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ws-unmask">
<h3><a class="doc-anchor" href="#doc-ws-unmask">#</a> <code>ws_unmask</code></h3>
<p><code>ws_unmask</code> — WebSocket helper <code>unmask</code>. Category: *network / ip / cidr*.</p>
<pre><code class="lang-perl">p ws_unmask $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wsamp">
<h3><a class="doc-anchor" href="#doc-wsamp">#</a> <code>wsamp</code></h3>
<p><code>wsamp</code> — operation <code>wsamp</code>. Alias for <code>weighted_sample</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p wsamp $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wwrap">
<h3><a class="doc-anchor" href="#doc-wwrap">#</a> <code>wwrap</code></h3>
<p><code>wwrap</code> — operation <code>wwrap</code>. Alias for <code>word_wrap_text</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p wwrap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-www-auth-parse">
<h3><a class="doc-anchor" href="#doc-www-auth-parse">#</a> <code>www_auth_parse</code></h3>
<p><code>www_auth_parse</code> — operation <code>www auth parse</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p www_auth_parse $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wyhash-mix">
<h3><a class="doc-anchor" href="#doc-wyhash-mix">#</a> <code>wyhash_mix</code></h3>
<p><code>wyhash_mix</code> — operation <code>wyhash mix</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p wyhash_mix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-wynn-epsilon">
<h3><a class="doc-anchor" href="#doc-wynn-epsilon">#</a> <code>wynn_epsilon</code></h3>
<p><code>wynn_epsilon</code> — operation <code>wynn epsilon</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p wynn_epsilon $x
</code></pre>
</article>
<article class="doc-entry" id="doc-x25519-field-mul">
<h3><a class="doc-anchor" href="#doc-x25519-field-mul">#</a> <code>x25519_field_mul</code></h3>
<p><code>x25519_field_mul</code> — operation <code>x25519 field mul</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p x25519_field_mul $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xadd">
<h3><a class="doc-anchor" href="#doc-xadd">#</a> <code>xadd</code></h3>
<p><code>xadd</code> — operation <code>xadd</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p xadd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xattr-get">
<h3><a class="doc-anchor" href="#doc-xattr-get">#</a> <code>xattr_get</code></h3>
<p><code>xattr_get(path, name) → string</code> — read an extended attribute value.</p>
</article>
<article class="doc-entry" id="doc-xattr-list">
<h3><a class="doc-anchor" href="#doc-xattr-list">#</a> <code>xattr_list</code></h3>
<p><code>xattr_list(path) → array</code> — names of all extended attributes.</p>
</article>
<article class="doc-entry" id="doc-xattr-set">
<h3><a class="doc-anchor" href="#doc-xattr-set">#</a> <code>xattr_set</code></h3>
<p><code>xattr_set(path, name, value) → 0|1</code> — write an extended attribute.</p>
</article>
<article class="doc-entry" id="doc-xd">
<h3><a class="doc-anchor" href="#doc-xd">#</a> <code>xd</code></h3>
<p><code>xd</code> — operation <code>xd</code>. Alias for <code>xml_decode</code>. Category: *serialization (stryke-only encoders)*.</p>
<pre><code class="lang-perl">p xd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xe">
<h3><a class="doc-anchor" href="#doc-xe">#</a> <code>xe</code></h3>
<p><code>xe</code> — operation <code>xe</code>. Alias for <code>xml_encode</code>. Category: *serialization (stryke-only encoders)*.</p>
<pre><code class="lang-perl">p xe $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xentropy">
<h3><a class="doc-anchor" href="#doc-xentropy">#</a> <code>xentropy</code></h3>
<p><code>xentropy</code> — operation <code>xentropy</code>. Alias for <code>cross_entropy</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p xentropy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xfip">
<h3><a class="doc-anchor" href="#doc-xfip">#</a> <code>xfip</code></h3>
<p><code>xfip</code> — operation <code>xfip</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p xfip $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xirr">
<h3><a class="doc-anchor" href="#doc-xirr">#</a> <code>xirr</code></h3>
<p><code>xirr(\@cashflows, \@dates)</code> — computes IRR for irregularly-spaced cash flows. Dates can be epoch timestamps or date strings. More accurate than <code>irr</code> for real-world investments.</p>
<pre><code class="lang-perl">my @cf = (-1000, 500, 600)
my @dates = ('2020-01-01', '2020-07-01', '2021-01-01')
p xirr(\@cf, \@dates)
</code></pre>
</article>
<article class="doc-entry" id="doc-xlen">
<h3><a class="doc-anchor" href="#doc-xlen">#</a> <code>xlen</code></h3>
<p><code>xlen</code> — operation <code>xlen</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p xlen $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xlookup">
<h3><a class="doc-anchor" href="#doc-xlookup">#</a> <code>xlookup</code></h3>
<p><code>xlookup</code> — operation <code>xlookup</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p xlookup $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xml-attrs">
<h3><a class="doc-anchor" href="#doc-xml-attrs">#</a> <code>xml_attrs</code></h3>
<p><code>xml_attrs</code> — XML helper <code>attrs</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p xml_attrs $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xml-canonicalize">
<h3><a class="doc-anchor" href="#doc-xml-canonicalize">#</a> <code>xml_canonicalize</code></h3>
<p><code>xml_canonicalize</code> — XML helper <code>canonicalize</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p xml_canonicalize $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xml-children-by-tag">
<h3><a class="doc-anchor" href="#doc-xml-children-by-tag">#</a> <code>xml_children_by_tag</code></h3>
<p><code>xml_children_by_tag</code> — XML helper <code>children by tag</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p xml_children_by_tag $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xml-minify">
<h3><a class="doc-anchor" href="#doc-xml-minify">#</a> <code>xml_minify</code></h3>
<p><code>xml_minify</code> — XML helper <code>minify</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p xml_minify $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xml-namespace">
<h3><a class="doc-anchor" href="#doc-xml-namespace">#</a> <code>xml_namespace</code></h3>
<p><code>xml_namespace</code> — XML helper <code>namespace</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p xml_namespace $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xml-pretty">
<h3><a class="doc-anchor" href="#doc-xml-pretty">#</a> <code>xml_pretty</code></h3>
<p><code>xml_pretty</code> — XML helper <code>pretty</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p xml_pretty $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xml-root">
<h3><a class="doc-anchor" href="#doc-xml-root">#</a> <code>xml_root</code></h3>
<p><code>xml_root</code> — XML helper <code>root</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p xml_root $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xml-text">
<h3><a class="doc-anchor" href="#doc-xml-text">#</a> <code>xml_text</code></h3>
<p><code>xml_text</code> — XML helper <code>text</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p xml_text $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xml-to-json">
<h3><a class="doc-anchor" href="#doc-xml-to-json">#</a> <code>xml_to_json</code></h3>
<p><code>xml_to_json</code> — convert from <code>xml</code> to <code>json</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p xml_to_json $value
</code></pre>
</article>
<article class="doc-entry" id="doc-xmlagg">
<h3><a class="doc-anchor" href="#doc-xmlagg">#</a> <code>xmlagg</code></h3>
<p><code>xmlagg</code> — operation <code>xmlagg</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p xmlagg $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xmlforest">
<h3><a class="doc-anchor" href="#doc-xmlforest">#</a> <code>xmlforest</code></h3>
<p><code>xmlforest</code> — operation <code>xmlforest</code>. Category: *postgres sql strings, json, aggregates*.</p>
<pre><code class="lang-perl">p xmlforest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xnpv">
<h3><a class="doc-anchor" href="#doc-xnpv">#</a> <code>xnpv</code></h3>
<p><code>xnpv</code> — operation <code>xnpv</code>. Category: *excel/sheets + bond/loan financial*.</p>
<pre><code class="lang-perl">p xnpv $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xor-bool">
<h3><a class="doc-anchor" href="#doc-xor-bool">#</a> <code>xor_bool</code></h3>
<p><code>xor_bool</code> — operation <code>xor bool</code>. Category: *boolean combinators*.</p>
<pre><code class="lang-perl">p xor_bool $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xor-break-singlebyte">
<h3><a class="doc-anchor" href="#doc-xor-break-singlebyte">#</a> <code>xor_break_singlebyte</code></h3>
<p><code>xor_break_singlebyte</code> — operation <code>xor break singlebyte</code>. Category: *cryptanalysis & number theory deep*.</p>
<pre><code class="lang-perl">p xor_break_singlebyte $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xor-brute-keylen">
<h3><a class="doc-anchor" href="#doc-xor-brute-keylen">#</a> <code>xor_brute_keylen</code></h3>
<p><code>xor_brute_keylen</code> — operation <code>xor brute keylen</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p xor_brute_keylen $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xor-byte-string">
<h3><a class="doc-anchor" href="#doc-xor-byte-string">#</a> <code>xor_byte_string</code></h3>
<p><code>xor_byte_string</code> — operation <code>xor byte string</code>. Category: *more extensions (2)*.</p>
<pre><code class="lang-perl">p xor_byte_string $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xor-cipher-byte">
<h3><a class="doc-anchor" href="#doc-xor-cipher-byte">#</a> <code>xor_cipher_byte</code></h3>
<p><code>xor_cipher_byte</code> — operation <code>xor cipher byte</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p xor_cipher_byte $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xor-strings">
<h3><a class="doc-anchor" href="#doc-xor-strings">#</a> <code>xor_strings</code></h3>
<p><code>xor_strings</code> — operation <code>xor strings</code>. Category: *string helpers*.</p>
<pre><code class="lang-perl">p xor_strings $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xorshift32">
<h3><a class="doc-anchor" href="#doc-xorshift32">#</a> <code>xorshift32</code></h3>
<p><code>xorshift32</code> — operation <code>xorshift32</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p xorshift32 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xorshift32-next">
<h3><a class="doc-anchor" href="#doc-xorshift32-next">#</a> <code>xorshift32_next</code></h3>
<p><code>xorshift32_next(seed) → int</code> — Marsaglia's xorshift32 step.</p>
</article>
<article class="doc-entry" id="doc-xorshift32-step">
<h3><a class="doc-anchor" href="#doc-xorshift32-step">#</a> <code>xorshift32_step</code></h3>
<p><code>xorshift32_step</code> — single-step update of <code>xorshift32</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p xorshift32_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xorshift64">
<h3><a class="doc-anchor" href="#doc-xorshift64">#</a> <code>xorshift64</code></h3>
<p><code>xorshift64</code> — operation <code>xorshift64</code>. Category: *cryptography deep*.</p>
<pre><code class="lang-perl">p xorshift64 $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xpath-attribute">
<h3><a class="doc-anchor" href="#doc-xpath-attribute">#</a> <code>xpath_attribute</code></h3>
<p><code>xpath_attribute</code> — operation <code>xpath attribute</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p xpath_attribute $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xpath-select-one">
<h3><a class="doc-anchor" href="#doc-xpath-select-one">#</a> <code>xpath_select_one</code></h3>
<p><code>xpath_select_one</code> — operation <code>xpath select one</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p xpath_select_one $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xpath-text">
<h3><a class="doc-anchor" href="#doc-xpath-text">#</a> <code>xpath_text</code></h3>
<p><code>xpath_text</code> — operation <code>xpath text</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p xpath_text $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xpath-to-selector">
<h3><a class="doc-anchor" href="#doc-xpath-to-selector">#</a> <code>xpath_to_selector</code></h3>
<p><code>xpath_to_selector</code> — convert from <code>xpath</code> to <code>selector</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p xpath_to_selector $value
</code></pre>
</article>
<article class="doc-entry" id="doc-xrange">
<h3><a class="doc-anchor" href="#doc-xrange">#</a> <code>xrange</code></h3>
<p><code>xrange</code> — operation <code>xrange</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p xrange $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xtea-round">
<h3><a class="doc-anchor" href="#doc-xtea-round">#</a> <code>xtea_round</code></h3>
<p><code>xtea_round</code> — operation <code>xtea round</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p xtea_round $x
</code></pre>
</article>
<article class="doc-entry" id="doc-xyz-d50-to-d65">
<h3><a class="doc-anchor" href="#doc-xyz-d50-to-d65">#</a> <code>xyz_d50_to_d65</code></h3>
<p><code>xyz_d50_to_d65</code> — convert from <code>xyz d50</code> to <code>d65</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p xyz_d50_to_d65 $value
</code></pre>
</article>
<article class="doc-entry" id="doc-xyz-d65-to-d50">
<h3><a class="doc-anchor" href="#doc-xyz-d65-to-d50">#</a> <code>xyz_d65_to_d50</code></h3>
<p><code>xyz_d65_to_d50</code> — convert from <code>xyz d65</code> to <code>d50</code>. Category: *complex / geom / color / trig*.</p>
<pre><code class="lang-perl">p xyz_d65_to_d50 $value
</code></pre>
</article>
<article class="doc-entry" id="doc-xyz-to-lab">
<h3><a class="doc-anchor" href="#doc-xyz-to-lab">#</a> <code>xyz_to_lab</code></h3>
<p><code>xyz_to_lab</code> — convert from <code>xyz</code> to <code>lab</code>. Category: *astronomy / music / color / units*.</p>
<pre><code class="lang-perl">p xyz_to_lab $value
</code></pre>
</article>
<article class="doc-entry" id="doc-xyz-to-rgb">
<h3><a class="doc-anchor" href="#doc-xyz-to-rgb">#</a> <code>xyz_to_rgb</code></h3>
<p><code>xyz_to_rgb</code> — convert from <code>xyz</code> to <code>rgb</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p xyz_to_rgb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-yamanouchi-word-count">
<h3><a class="doc-anchor" href="#doc-yamanouchi-word-count">#</a> <code>yamanouchi_word_count</code></h3>
<p><code>yamanouchi_word_count</code> — count of <code>yamanouchi word</code>. Category: *econometrics*.</p>
<pre><code class="lang-perl">p yamanouchi_word_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-yards-per-attempt">
<h3><a class="doc-anchor" href="#doc-yards-per-attempt">#</a> <code>yards_per_attempt</code></h3>
<p><code>yards_per_attempt</code> — operation <code>yards per attempt</code>. Category: *astronomy / astrometry*.</p>
<pre><code class="lang-perl">p yards_per_attempt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-yards-to-m">
<h3><a class="doc-anchor" href="#doc-yards-to-m">#</a> <code>yards_to_m</code></h3>
<p><code>yards_to_m</code> — convert from <code>yards</code> to <code>m</code>. Category: *unit conversions*.</p>
<pre><code class="lang-perl">p yards_to_m $value
</code></pre>
</article>
<article class="doc-entry" id="doc-yd">
<h3><a class="doc-anchor" href="#doc-yd">#</a> <code>yd</code></h3>
<p><code>yd</code> — operation <code>yd</code>. Alias for <code>yaml_decode</code>. Category: *serialization (stryke-only encoders)*.</p>
<pre><code class="lang-perl">p yd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ye">
<h3><a class="doc-anchor" href="#doc-ye">#</a> <code>ye</code></h3>
<p><code>ye</code> — operation <code>ye</code>. Alias for <code>yaml_encode</code>. Category: *serialization (stryke-only encoders)*.</p>
<pre><code class="lang-perl">p ye $x
</code></pre>
</article>
<article class="doc-entry" id="doc-years-between">
<h3><a class="doc-anchor" href="#doc-years-between">#</a> <code>years_between</code></h3>
<p><code>years_between</code> — operation <code>years between</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p years_between $x
</code></pre>
</article>
<article class="doc-entry" id="doc-yellow">
<h3><a class="doc-anchor" href="#doc-yellow">#</a> <code>yellow</code></h3>
<p><code>yellow</code> — operation <code>yellow</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p yellow $x
</code></pre>
</article>
<article class="doc-entry" id="doc-yellow-bold">
<h3><a class="doc-anchor" href="#doc-yellow-bold">#</a> <code>yellow_bold</code></h3>
<p><code>yellow_bold</code> — operation <code>yellow bold</code>. Alias for <code>red</code>. Category: *color / ansi*.</p>
<pre><code class="lang-perl">p yellow_bold $x
</code></pre>
</article>
<article class="doc-entry" id="doc-yen-k-shortest">
<h3><a class="doc-anchor" href="#doc-yen-k-shortest">#</a> <code>yen_k_shortest</code></h3>
<p><code>yen_k_shortest</code> — operation <code>yen k shortest</code>. Category: *networkx graph algorithms*.</p>
<pre><code class="lang-perl">p yen_k_shortest $x
</code></pre>
</article>
<article class="doc-entry" id="doc-yesterday">
<h3><a class="doc-anchor" href="#doc-yesterday">#</a> <code>yesterday</code></h3>
<p><code>yesterday</code> — operation <code>yesterday</code>. Category: *date*.</p>
<pre><code class="lang-perl">p yesterday $x
</code></pre>
</article>
<article class="doc-entry" id="doc-yield-to-maturity">
<h3><a class="doc-anchor" href="#doc-yield-to-maturity">#</a> <code>yield_to_maturity</code></h3>
<p><code>yield_to_maturity(coupons, face_value, price) → number</code> — discount rate that equates bond price to PV of coupon + face cashflows (Newton solver).</p>
<pre><code class="lang-perl">p yield_to_maturity([50,50,50], 1000, 950)
</code></pre>
</article>
<article class="doc-entry" id="doc-yielddisc">
<h3><a class="doc-anchor" href="#doc-yielddisc">#</a> <code>yielddisc</code></h3>
<p><code>yielddisc</code> — operation <code>yielddisc</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p yielddisc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-yieldmat">
<h3><a class="doc-anchor" href="#doc-yieldmat">#</a> <code>yieldmat</code></h3>
<p><code>yieldmat</code> — operation <code>yieldmat</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p yieldmat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ylll-pml">
<h3><a class="doc-anchor" href="#doc-ylll-pml">#</a> <code>ylll_pml</code></h3>
<p><code>ylll_pml</code> — operation <code>ylll pml</code>. Category: *epidemiology / public health*.</p>
<pre><code class="lang-perl">p ylll_pml $x
</code></pre>
</article>
<article class="doc-entry" id="doc-yn">
<h3><a class="doc-anchor" href="#doc-yn">#</a> <code>yn</code></h3>
<p><code>yn</code> — operation <code>yn</code>. Category: *numpy + scipy.special*.</p>
<pre><code class="lang-perl">p yn $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ytm-newton">
<h3><a class="doc-anchor" href="#doc-ytm-newton">#</a> <code>ytm_newton</code></h3>
<p><code>ytm_newton</code> — operation <code>ytm newton</code>. Category: *financial pricing models*.</p>
<pre><code class="lang-perl">p ytm_newton $x
</code></pre>
</article>
<article class="doc-entry" id="doc-yuv-to-rgb">
<h3><a class="doc-anchor" href="#doc-yuv-to-rgb">#</a> <code>yuv_to_rgb</code></h3>
<p><code>yuv_to_rgb</code> — convert from <code>yuv</code> to <code>rgb</code>. Category: *b82-misc-utility*.</p>
<pre><code class="lang-perl">p yuv_to_rgb $value
</code></pre>
</article>
<article class="doc-entry" id="doc-z85-decode">
<h3><a class="doc-anchor" href="#doc-z85-decode">#</a> <code>z85_decode</code></h3>
<p><code>z85_decode(s) → string</code> — ZeroMQ Base85 decode; input length must be a multiple of 5.</p>
</article>
<article class="doc-entry" id="doc-z85-encode">
<h3><a class="doc-anchor" href="#doc-z85-encode">#</a> <code>z85_encode</code></h3>
<p><code>z85_encode(s) → string</code> — ZeroMQ Base85 (RFC 32/Z85). Input length must be a multiple of 4.</p>
<pre><code class="lang-perl">p z85_encode("12345678")
</code></pre>
</article>
<article class="doc-entry" id="doc-z-array">
<h3><a class="doc-anchor" href="#doc-z-array">#</a> <code>z_array</code></h3>
<p><code>z_array</code> — operation <code>z array</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p z_array $x
</code></pre>
</article>
<article class="doc-entry" id="doc-z-func">
<h3><a class="doc-anchor" href="#doc-z-func">#</a> <code>z_func</code></h3>
<p><code>z_func</code> — operation <code>z func</code>. Alias for <code>z_array</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p z_func $x
</code></pre>
</article>
<article class="doc-entry" id="doc-z-function-alt">
<h3><a class="doc-anchor" href="#doc-z-function-alt">#</a> <code>z_function_alt</code></h3>
<p><code>z_function_alt</code> — operation <code>z function alt</code>. Category: *more extensions*.</p>
<pre><code class="lang-perl">p z_function_alt $x
</code></pre>
</article>
<article class="doc-entry" id="doc-z-score">
<h3><a class="doc-anchor" href="#doc-z-score">#</a> <code>z_score</code></h3>
<p><code>z_score($value, $mean, $stddev)</code> — computes the z-score (standard score) of a value given the population mean and standard deviation. Returns how many standard deviations the value is from the mean. Useful for standardizing data and detecting outliers.</p>
<pre><code class="lang-perl">my $z = z_score(85, 75, 10)
p $z # 1 (one stddev above mean)
p z_score(50, 60, 5) # -2
</code></pre>
</article>
<article class="doc-entry" id="doc-z-score-robust">
<h3><a class="doc-anchor" href="#doc-z-score-robust">#</a> <code>z_score_robust</code></h3>
<p><code>z_score_robust</code> — operation <code>z score robust</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p z_score_robust $x
</code></pre>
</article>
<article class="doc-entry" id="doc-z-scores">
<h3><a class="doc-anchor" href="#doc-z-scores">#</a> <code>z_scores</code></h3>
<p><code>z_scores(@data)</code> — computes z-scores for all values in a list, returning an arrayref of standardized values. Each z-score indicates how many standard deviations that value is from the mean of the dataset. Useful for comparing values across different scales.</p>
<pre><code class="lang-perl">my @grades = (70, 80, 90)
my $zs = z_scores(@grades)
p @$zs # (-1, 0, 1)
@data |> z_scores |> e p
</code></pre>
</article>
<article class="doc-entry" id="doc-zadd">
<h3><a class="doc-anchor" href="#doc-zadd">#</a> <code>zadd</code></h3>
<p><code>zadd</code> — operation <code>zadd</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p zadd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zalgo">
<h3><a class="doc-anchor" href="#doc-zalgo">#</a> <code>zalgo</code></h3>
<p><code>zalgo</code> — operation <code>zalgo</code>. Category: *string processing extras*.</p>
<pre><code class="lang-perl">p zalgo $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zall">
<h3><a class="doc-anchor" href="#doc-zall">#</a> <code>zall</code></h3>
<p><code>zall</code> — operation <code>zall</code>. Alias for <code>zip_all</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p zall $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zcard">
<h3><a class="doc-anchor" href="#doc-zcard">#</a> <code>zcard</code></h3>
<p><code>zcard</code> — operation <code>zcard</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p zcard $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zcount">
<h3><a class="doc-anchor" href="#doc-zcount">#</a> <code>zcount</code></h3>
<p><code>zcount</code> — operation <code>zcount</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p zcount $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zcross">
<h3><a class="doc-anchor" href="#doc-zcross">#</a> <code>zcross</code></h3>
<p><code>zcross</code> — operation <code>zcross</code>. Alias for <code>zero_crossings</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p zcross $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zeeman-energy">
<h3><a class="doc-anchor" href="#doc-zeeman-energy">#</a> <code>zeeman_energy</code></h3>
<p><code>zeeman_energy</code> — operation <code>zeeman energy</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p zeeman_energy $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zeller-day-of-week">
<h3><a class="doc-anchor" href="#doc-zeller-day-of-week">#</a> <code>zeller_day_of_week</code></h3>
<p><code>zeller_day_of_week</code> — operation <code>zeller day of week</code>. Category: *misc*.</p>
<pre><code class="lang-perl">p zeller_day_of_week $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zeno-survival">
<h3><a class="doc-anchor" href="#doc-zeno-survival">#</a> <code>zeno_survival</code></h3>
<p><code>zeno_survival</code> — operation <code>zeno survival</code>. Category: *quantum mechanics deep*.</p>
<pre><code class="lang-perl">p zeno_survival $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zernike-radial">
<h3><a class="doc-anchor" href="#doc-zernike-radial">#</a> <code>zernike_radial</code></h3>
<p><code>zernike_radial(n, m, rho) → number</code> — Zernike radial polynomial <code>R_n^|m|(ρ)</code>. Returns 0 if <code>(n−|m|)</code> is odd or <code>|m| > n</code>. Negative <code>m</code> is accepted and uses <code>|m|</code> per the convention <code>R_n^m = R_n^{−m}</code>.</p>
</article>
<article class="doc-entry" id="doc-zero">
<h3><a class="doc-anchor" href="#doc-zero">#</a> <code>zero</code></h3>
<p><code>zero</code> — operation <code>zero</code>. Category: *trivial numeric / predicate builtins*.</p>
<pre><code class="lang-perl">p zero $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zero-crossing-rate">
<h3><a class="doc-anchor" href="#doc-zero-crossing-rate">#</a> <code>zero_crossing_rate</code></h3>
<p><code>zero_crossing_rate</code> — rate of <code>zero crossing</code>. Category: *extras*.</p>
<pre><code class="lang-perl">p zero_crossing_rate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zero-crossings">
<h3><a class="doc-anchor" href="#doc-zero-crossings">#</a> <code>zero_crossings</code></h3>
<p><code>zero_crossings</code> — operation <code>zero crossings</code>. Category: *array / list operations extras*.</p>
<pre><code class="lang-perl">p zero_crossings $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zero-order-concentration">
<h3><a class="doc-anchor" href="#doc-zero-order-concentration">#</a> <code>zero_order_concentration</code></h3>
<p><code>zero_order_concentration</code> — operation <code>zero order concentration</code>. Category: *chemistry*.</p>
<pre><code class="lang-perl">p zero_order_concentration $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zero-pad">
<h3><a class="doc-anchor" href="#doc-zero-pad">#</a> <code>zero_pad</code></h3>
<p><code>zero_pad</code> — operation <code>zero pad</code>. Category: *signal processing*.</p>
<pre><code class="lang-perl">p zero_pad $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zero-sum-minmax">
<h3><a class="doc-anchor" href="#doc-zero-sum-minmax">#</a> <code>zero_sum_minmax</code></h3>
<p><code>zero_sum_minmax</code> — operation <code>zero sum minmax</code>. Category: *climate, fluids, atmospheric*.</p>
<pre><code class="lang-perl">p zero_sum_minmax $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zero-sum-value">
<h3><a class="doc-anchor" href="#doc-zero-sum-value">#</a> <code>zero_sum_value</code></h3>
<p><code>zero_sum_value(payoff) → number</code> — value of a two-player zero-sum game. Returns the saddle-point value when maximin == minmax, the 2×2 mixed-strategy value (ad − bc)/(a + d − b − c) otherwise, or UNDEF for larger matrices with no saddle (caller should use LP).</p>
</article>
<article class="doc-entry" id="doc-zeros">
<h3><a class="doc-anchor" href="#doc-zeros">#</a> <code>zeros</code></h3>
<p><code>zeros</code> — operation <code>zeros</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p zeros $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zeros-mat">
<h3><a class="doc-anchor" href="#doc-zeros-mat">#</a> <code>zeros_mat</code></h3>
<p><code>zeros_mat</code> — operation <code>zeros mat</code>. Alias for <code>zeros_matrix</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p zeros_mat $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zeros-matrix">
<h3><a class="doc-anchor" href="#doc-zeros-matrix">#</a> <code>zeros_matrix</code></h3>
<p><code>zeros_matrix</code> — operation <code>zeros matrix</code>. Category: *matrix / linear algebra*.</p>
<pre><code class="lang-perl">p zeros_matrix $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zeta-potential-estimate">
<h3><a class="doc-anchor" href="#doc-zeta-potential-estimate">#</a> <code>zeta_potential_estimate</code></h3>
<p><code>zeta_potential_estimate</code> — operation <code>zeta potential estimate</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p zeta_potential_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zeta-riemann">
<h3><a class="doc-anchor" href="#doc-zeta-riemann">#</a> <code>zeta_riemann</code></h3>
<p><code>zeta_riemann(s) → number</code> — Riemann zeta <code>ζ(s) = Σ 1/n^s</code> for n=1..∞ (truncated series).</p>
<pre><code class="lang-perl">p zeta_riemann(2) # π²/6 ≈ 1.645
</code></pre>
</article>
<article class="doc-entry" id="doc-zfill">
<h3><a class="doc-anchor" href="#doc-zfill">#</a> <code>zfill</code></h3>
<p><code>zfill</code> — operation <code>zfill</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p zfill $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zfill-num">
<h3><a class="doc-anchor" href="#doc-zfill-num">#</a> <code>zfill_num</code></h3>
<p><code>zfill_num</code> — operation <code>zfill num</code>. Category: *extended stdlib*.</p>
<pre><code class="lang-perl">p zfill_num $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zgemm">
<h3><a class="doc-anchor" href="#doc-zgemm">#</a> <code>zgemm</code></h3>
<p><code>zgemm</code> — operation <code>zgemm</code>. Category: *blas / lapack*.</p>
<pre><code class="lang-perl">p zgemm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zigzag-decode">
<h3><a class="doc-anchor" href="#doc-zigzag-decode">#</a> <code>zigzag_decode</code></h3>
<p><code>zigzag_decode(n) → int</code> — inverse ZigZag.</p>
</article>
<article class="doc-entry" id="doc-zigzag-encode">
<h3><a class="doc-anchor" href="#doc-zigzag-encode">#</a> <code>zigzag_encode</code></h3>
<p><code>zigzag_encode(n) → int</code> — map signed int to unsigned via Protobuf ZigZag: <code>(n << 1) ^ (n >> 63)</code>. Lets small magnitudes pack into few bytes.</p>
<pre><code class="lang-perl">p zigzag_encode(-1) # 1
p zigzag_encode(1) # 2
</code></pre>
</article>
<article class="doc-entry" id="doc-zincrby">
<h3><a class="doc-anchor" href="#doc-zincrby">#</a> <code>zincrby</code></h3>
<p><code>zincrby</code> — operation <code>zincrby</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p zincrby $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zip-all">
<h3><a class="doc-anchor" href="#doc-zip-all">#</a> <code>zip_all</code></h3>
<p><code>zip_all</code> — operation <code>zip all</code>. Category: *go/general functional utilities*.</p>
<pre><code class="lang-perl">p zip_all $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zip-apply">
<h3><a class="doc-anchor" href="#doc-zip-apply">#</a> <code>zip_apply</code></h3>
<p><code>zip_apply</code> — operation <code>zip apply</code>. Category: *functional combinators*.</p>
<pre><code class="lang-perl">p zip_apply $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zip-archive">
<h3><a class="doc-anchor" href="#doc-zip-archive">#</a> <code>zip_archive</code></h3>
<p><code>zip_archive</code> — operation <code>zip archive</code>. Alias for <code>zip_create</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p zip_archive $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zip-central-dir">
<h3><a class="doc-anchor" href="#doc-zip-central-dir">#</a> <code>zip_central_dir</code></h3>
<p><code>zip_central_dir</code> — operation <code>zip central dir</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p zip_central_dir $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zip-central-directory">
<h3><a class="doc-anchor" href="#doc-zip-central-directory">#</a> <code>zip_central_directory</code></h3>
<p><code>zip_central_directory(hex_bytes) → hash</code> — scan for EOCD signature, return <code>{entries, cd_size, cd_offset}</code>.</p>
</article>
<article class="doc-entry" id="doc-zip-eocd">
<h3><a class="doc-anchor" href="#doc-zip-eocd">#</a> <code>zip_eocd</code></h3>
<p><code>zip_eocd</code> — operation <code>zip eocd</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p zip_eocd $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zip-fill">
<h3><a class="doc-anchor" href="#doc-zip-fill">#</a> <code>zip_fill</code></h3>
<p><code>zip_fill</code> — operation <code>zip fill</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p zip_fill $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zip-local-file-header">
<h3><a class="doc-anchor" href="#doc-zip-local-file-header">#</a> <code>zip_local_file_header</code></h3>
<p><code>zip_local_file_header(hex_bytes) → hash</code> — parse local file header → <code>{compression, crc32, compressed_size, uncompressed_size}</code>.</p>
</article>
<article class="doc-entry" id="doc-zip-local-header">
<h3><a class="doc-anchor" href="#doc-zip-local-header">#</a> <code>zip_local_header</code></h3>
<p><code>zip_local_header</code> — operation <code>zip local header</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p zip_local_header $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zip-with">
<h3><a class="doc-anchor" href="#doc-zip-with">#</a> <code>zip_with</code></h3>
<p><code>zip_with</code> — operation <code>zip with</code>. Alias for <code>take_while</code>. Category: *functional / iterator*.</p>
<pre><code class="lang-perl">p zip_with $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zipf">
<h3><a class="doc-anchor" href="#doc-zipf">#</a> <code>zipf</code></h3>
<p><code>zipf</code> — operation <code>zipf</code>. Alias for <code>zip_fill</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p zipf $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zipl">
<h3><a class="doc-anchor" href="#doc-zipl">#</a> <code>zipl</code></h3>
<p><code>zipl</code> — operation <code>zipl</code>. Category: *python/ruby stdlib*.</p>
<pre><code class="lang-perl">p zipl $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zipmap">
<h3><a class="doc-anchor" href="#doc-zipmap">#</a> <code>zipmap</code></h3>
<p><code>zipmap</code> — operation <code>zipmap</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p zipmap $x
</code></pre>
</article>
<article class="doc-entry" id="doc-ziv-lempel-estimate">
<h3><a class="doc-anchor" href="#doc-ziv-lempel-estimate">#</a> <code>ziv_lempel_estimate</code></h3>
<p><code>ziv_lempel_estimate</code> — operation <code>ziv lempel estimate</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p ziv_lempel_estimate $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zlexcount">
<h3><a class="doc-anchor" href="#doc-zlexcount">#</a> <code>zlexcount</code></h3>
<p><code>zlexcount</code> — operation <code>zlexcount</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p zlexcount $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zodiac-sign">
<h3><a class="doc-anchor" href="#doc-zodiac-sign">#</a> <code>zodiac_sign</code></h3>
<p><code>zodiac_sign(month, day) → string</code> — Western tropical zodiac sign for a given month/day.</p>
<pre><code class="lang-perl">p zodiac_sign(7, 15) # Cancer
</code></pre>
</article>
<article class="doc-entry" id="doc-zpk2sos-step">
<h3><a class="doc-anchor" href="#doc-zpk2sos-step">#</a> <code>zpk2sos_step</code></h3>
<p><code>zpk2sos_step</code> — single-step update of <code>zpk2sos</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p zpk2sos_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zpk2tf-step">
<h3><a class="doc-anchor" href="#doc-zpk2tf-step">#</a> <code>zpk2tf_step</code></h3>
<p><code>zpk2tf_step</code> — single-step update of <code>zpk2tf</code>. Category: *economics + game theory*.</p>
<pre><code class="lang-perl">p zpk2tf_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zrangebyscore">
<h3><a class="doc-anchor" href="#doc-zrangebyscore">#</a> <code>zrangebyscore</code></h3>
<p><code>zrangebyscore</code> — operation <code>zrangebyscore</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p zrangebyscore $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zrank">
<h3><a class="doc-anchor" href="#doc-zrank">#</a> <code>zrank</code></h3>
<p><code>zrank</code> — operation <code>zrank</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p zrank $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zrem">
<h3><a class="doc-anchor" href="#doc-zrem">#</a> <code>zrem</code></h3>
<p><code>zrem</code> — operation <code>zrem</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p zrem $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zrevrank">
<h3><a class="doc-anchor" href="#doc-zrevrank">#</a> <code>zrevrank</code></h3>
<p><code>zrevrank</code> — operation <code>zrevrank</code>. Category: *redis-flavour primitives*.</p>
<pre><code class="lang-perl">p zrevrank $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zrlc">
<h3><a class="doc-anchor" href="#doc-zrlc">#</a> <code>zrlc</code></h3>
<p><code>zrlc</code> — operation <code>zrlc</code>. Alias for <code>impedance_rlc</code>. Category: *physics formulas*.</p>
<pre><code class="lang-perl">p zrlc $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zscore">
<h3><a class="doc-anchor" href="#doc-zscore">#</a> <code>zscore</code></h3>
<p><code>zscore</code> — operation <code>zscore</code>. Category: *file stat / path*.</p>
<pre><code class="lang-perl">p zscore $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zscore-count">
<h3><a class="doc-anchor" href="#doc-zscore-count">#</a> <code>zscore_count</code></h3>
<p><code>zscore_count</code> — count of <code>zscore</code>. Category: *bioinformatics deep*.</p>
<pre><code class="lang-perl">p zscore_count $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zscore-norm">
<h3><a class="doc-anchor" href="#doc-zscore-norm">#</a> <code>zscore_norm</code></h3>
<p><code>zscore_norm</code> — norm (vector length-like) of <code>zscore</code>. Category: *ml extensions*.</p>
<pre><code class="lang-perl">p zscore_norm $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zscores">
<h3><a class="doc-anchor" href="#doc-zscores">#</a> <code>zscores</code></h3>
<p><code>zscores</code> — operation <code>zscores</code>. Alias for <code>z_scores</code>. Category: *statistics (extended)*.</p>
<pre><code class="lang-perl">p zscores $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zst">
<h3><a class="doc-anchor" href="#doc-zst">#</a> <code>zst</code></h3>
<p><code>zst</code> — operation <code>zst</code>. Alias for <code>zstd</code>. Category: *crypto / encoding*.</p>
<pre><code class="lang-perl">p zst $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zstd-encode-step">
<h3><a class="doc-anchor" href="#doc-zstd-encode-step">#</a> <code>zstd_encode_step</code></h3>
<p><code>zstd_encode_step</code> — single-step update of <code>zstd encode</code>. Category: *b81-misc-utility*.</p>
<pre><code class="lang-perl">p zstd_encode_step $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zstd-frame-header">
<h3><a class="doc-anchor" href="#doc-zstd-frame-header">#</a> <code>zstd_frame_header</code></h3>
<p><code>zstd_frame_header</code> — operation <code>zstd frame header</code>. Category: *archive/encoding format primitives*.</p>
<pre><code class="lang-perl">p zstd_frame_header $x
</code></pre>
</article>
<article class="doc-entry" id="doc-zstd-window-size-log">
<h3><a class="doc-anchor" href="#doc-zstd-window-size-log">#</a> <code>zstd_window_size_log</code></h3>
<p><code>zstd_window_size_log</code> — operation <code>zstd window size log</code>. Category: *electrochemistry, batteries, fuel cells*.</p>
<pre><code class="lang-perl">p zstd_window_size_log $x
</code></pre>
</article>
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