Crate zenith_float_num 

zenith-float implements arbitrary-precision software floating-point numbers.

Modules

ctx

Context is used in expressions returning ExactNum.

Structs

Ball

Enclosure mid ± rad used to certify that a rounded midpoint is unique.

CachedFBig

A float stored at extra working precision so later requests at lower (or equal) precision reuse the cache instead of recomputing.

ComplexBall

Disk enclosure in (\mathbb{C}): center mid, radius rad.

ConstCacheInfo

Snapshot of how many mantissa bits of each constant are currently cached.

Consts

Constants cache contains arbitrary-precision mathematical constants.

ExactComplex

Complex value re + i·im with software-limb real and imaginary parts.

ExactInt

Arbitrary-precision signed integer. Distinct from ExactNum, which is floating-point.

ExactNum

A floating point number of arbitrary precision.

ExactNumArray

Batch of ExactNum values at a shared precision p, row-major.

ExactNumPoly

Dense univariate polynomial c₀ + c₁ x + ⋯ + cₙ xⁿ.

ExactRational

Exact rational num/den. Distinct from ExactNum, which is floating-point.

Ieee32

Software IEEE-754 binary32 (24-bit significand, 8-bit exponent). Stored as u32 bits.

Ieee64

Software IEEE-754 binary64 (53-bit significand, 11-bit exponent). Stored as u64 bits.

Ieee32Array

Contiguous binary32 lanes (u32 bits), row-major.

Ieee64Array

Contiguous binary64 lanes (u64 bits), row-major.

InlineBinaryBuffer

Fixed 16-byte stack buffer for an inlined ExactNum.

Radix

Radix for parse/format (bases 2 through 36).

RadixFloat

A floating-point value with an associated parse/format radix.

SharedConsts

Thread-safe Consts for batch evaluation across threads (std only). Callers still take &mut Consts inside SharedConsts::with; the mutex serializes cache fills.

Enums

Error

Possible errors.

RoundingMode

Rounding modes.

Sign

Sign.

Constants

BINARY_FLAG_ARRAY

ExactNumArray record.

BINARY_FLAG_HEAP_NEG

Heap finite, negative.

BINARY_FLAG_HEAP_POS

Heap finite, positive.

BINARY_FLAG_INF_NEG

INF_NEG.

BINARY_FLAG_INF_POS

INF_POS.

BINARY_FLAG_NAN_BARE

NaN with no associated Error.

BINARY_FLAG_NAN_DIV0

NaN: Error::DivisionByZero.

BINARY_FORMAT_VERSION

First-byte version stored in every record.

BINARY_HEADER_LEN

Header bytes of a heap or array record (same size as the inline record).

BINARY_INLINE_LEN

Bytes in InlineBinaryBuffer / ExactNum::to_inline_bytes.

BINARY_INLINE_MANT_BITS

Mantissa bits that fit in the inline record (2 × 32).

BINARY_INLINE_U32_WORDS

u32 limbs in the inline mantissa field.

BINARY_MAX_ELEMS

Maximum array elements accepted by ExactNumArray::from_bytes.

BINARY_MAX_U32

Maximum u32 limbs accepted by ExactNum::from_bytes.

CHEBYSHEV_MAX_DEGREE

Maximum number of Chebyshev coefficients chebyshev_coeffs will compute.

CSV_MAX_COLS

Maximum columns accepted in one CSV row.

CSV_MAX_ROWS

Maximum data rows accepted by Ieee64Array::from_csv_str.

DSP_MAX_POINTS

Maximum real length for dct / idct / dst / idst and the window generators. Transforms use a 2N-point FFT, so this is half of FFT_MAX_POINTS.

EXPONENT_BIT_SIZE

The size of exponent type in bits.

EXPONENT_MAX

Maximum exponent value.

EXPONENT_MIN

Minimum exponent value.

IEEE_SIMD_LANE_WIDTH

Number of u32 lanes in one integer SIMD vector (128-bit register). Binary64 uses IEEE_SIMD_LANE_WIDTH / 2 u64 lanes. Scalar fallback uses the same width so wrappers can size buffers without cfg.

INF_NEG

Negative infinity.

INF_POS

Positive infinity.

INLINE_WORDS

Number of words kept on the stack before allocating.

JACOBI_AGM_MAX

AGM / descending Landen steps for am, sn, cn, dn.

MAX_PREC_RETRY

Maximum extra correct-rounding retries.

NAN

Not a number.

ODE_MAX_STEPS

Maximum accepted steps for any solver in this module.

ODE_MIN_STEP

Default minimum step exponent: h_min = 2^{ODE_MIN_STEP}.

ORTHOPOLY_N_MAX

Maximum degree for every family in this module. Larger n is NaN.

POLLARD_RHO_ITER_MAX

Maximum f evaluations in one pollard_rho run before None.

POLY_COMPANION_CLOSED_DEG

Highest degree whose companion eigenvalues have a closed form on this type.

PROPTEST_CASES

Cases per proptest property under cargo test (no mpfr-tests required).

QUADRATURE_MAX_NODES

Maximum number of Gauss nodes. Larger n is None.

ROOT_DEFAULT_TOL

Default absolute tolerance exponent: tol = 2^{ROOT_DEFAULT_TOL}.

ROOT_MAX_ITER

Maximum iterations for every method in this module.

TANH_SINH_LEVELS_MAX

Maximum tanh–sinh step halvings after the precision-based h.

WORD_BASE

Base of words.

WORD_BIT_SIZE

Size of a word in bits.

WORD_MAX

Maximum value of a word.

WORD_SIGNIFICANT_BIT

Word with the most significant bit set.

Traits

FromExt

A trait for conversion with additional arguments.

Functions

bisect

Bisection on [a, b]. None if f(a) and f(b) do not have opposite signs.

blackman_window

Symmetric Blackman: 0.42 − 0.5 cos(θ) + 0.08 cos(2θ), θ = 2πk/(n−1).

brent

Brent’s method (bisection + secant + inverse quadratic) on [a, b].

chebyshev_coeffs

Interpolation coefficients of f on [a, b] at the n Chebyshev–Gauss nodes.

chebyshev_error_bound

ℓ¹ tail Σ_{k≥1} |c_k| at precision p.

chebyshev_eval

Evaluate the Chebyshev expansion of coeffs at x ∈ [a, b].

clenshaw

Clenshaw recurrence for Σ_{k=0}^{n-1} c_k T_k(x) at precision p.

constant_time_eq

Timing-safe equality: always scans both slices; length mismatch is false.

dct

Discrete cosine transform, type II, via a 2N-point FFT.

dst

Discrete sine transform, type II, via a 2N-point FFT.

euler

Explicit Euler for y' = f(t, y) on [t0, t1] with n_steps equal steps.

fft_real

Unnormalized DFT of a real row or column. Output is (2, n) (row 0 real, row 1 imaginary). Same power-of-two rule as ExactNumArray::fft.

gauss_hermite

Gauss–Hermite quadrature: ∫_{-∞}^{∞} f(x) e^{-x²} dx with n nodes.

gauss_laguerre

Gauss–Laguerre quadrature: ∫₀^∞ f(x) e^{-x} dx with n nodes.

gauss_legendre

Gauss–Legendre quadrature of f on [a, b] with n nodes.

hamming_window

Symmetric Hamming: 0.54 − 0.46 cos(2πk/(n−1)). Endpoints are 0.08.

hann_window

Symmetric Hann: ½(1 − cos(2πk/(n−1))). n = 1 is [1].

hmac_sha256

HMAC-SHA-256 (key, data).

idct

Inverse of dct: type-III DCT scaled by 2/N so idct(dct(x)) = x.

idst

Inverse of dst: type-III DST scaled by 2/N so idst(dst(x)) = x.

ifft_real

Inverse of fft_real: ExactNumArray::ifft then the real row.

illinois

Illinois (modified regula falsi) on [a, b].

kaiser_window

Kaiser–Bessel: I_0(β √(1−t_k²)) / I_0(β) with t_k = (k−(n−1)/2)/((n−1)/2).

miller_rabin

Miller–Rabin on |n| with the given bases. n < 2 is false.

mod_inv

Modular inverse of a modulo modulus. None if not invertible.

mod_pow

base^exp mod modulus. exp < 0 or a zero modulus is None. |modulus| = 1 is 0.

newton

Newton–Raphson from x0 with exact derivative df.

ode_min_step

Minimum step 2^{ODE_MIN_STEP} at precision p.

pollard_rho

Brent Pollard ρ. A proper factor of |n|, or None if prime / cap hit.

rectangular_window

Rectangular window: n ones.

rk4

Classical RK4 for y' = f(t, y) on [t0, t1] with n_steps equal steps.

rk45_adaptive

Dormand–Prince RK5(4) with absolute / relative step control.

root_default_tol

Suggested absolute tolerance 2^{ROOT_DEFAULT_TOL} at precision p.

sha256

SHA-256 of data.

sha512

SHA-512 of data.

tanh_sinh

Tanh–sinh (double-exponential) quadrature of f on [a, b].

ziv_round

Evaluate compute at increasing working precision until the result rounds uniquely to p bits (try_set_precision). Same retry budget as the transcendental kernel (crate::MAX_PREC_RETRY).

ziv_round_vec

Same Ziv loop as ziv_round, with every input lifted to p_wrk before compute.

Type Aliases

ConstCache

Alias for Consts: a progressive cache of π, e, ln 2, ln 10, √2, φ, and γ.

Exponent

An exponent.

Word

A word.