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</pre><pre class='rust '>
<span class='comment'>// Copyright 2013 The Rust Project Developers. See the COPYRIGHT</span>
<span class='comment'>// file at the top-level directory of this distribution and at</span>
<span class='comment'>// http://rust-lang.org/COPYRIGHT.</span>
<span class='comment'>//</span>
<span class='comment'>// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or</span>
<span class='comment'>// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license</span>
<span class='comment'>// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your</span>
<span class='comment'>// option. This file may not be copied, modified, or distributed</span>
<span class='comment'>// except according to those terms.</span>
<span class='doccomment'>//! Sampling from random distributions.</span>
<span class='doccomment'>//!</span>
<span class='doccomment'>//! This is a generalization of `Rand` to allow parameters to control the</span>
<span class='doccomment'>//! exact properties of the generated values, e.g. the mean and standard</span>
<span class='doccomment'>//! deviation of a normal distribution. The `Sample` trait is the most</span>
<span class='doccomment'>//! general, and allows for generating values that change some state</span>
<span class='doccomment'>//! internally. The `IndependentSample` trait is for generating values</span>
<span class='doccomment'>//! that do not need to record state.</span>
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>marker</span>;
<span class='kw'>use</span> {<span class='ident'>Rng</span>, <span class='ident'>Rand</span>};
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='self'>self</span>::<span class='ident'>range</span>::<span class='ident'>Range</span>;
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='self'>self</span>::<span class='ident'>gamma</span>::{<span class='ident'>Gamma</span>, <span class='ident'>ChiSquared</span>, <span class='ident'>FisherF</span>, <span class='ident'>StudentT</span>};
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='self'>self</span>::<span class='ident'>normal</span>::{<span class='ident'>Normal</span>, <span class='ident'>LogNormal</span>};
<span class='kw'>pub</span> <span class='kw'>use</span> <span class='self'>self</span>::<span class='ident'>exponential</span>::<span class='ident'>Exp</span>;
<span class='kw'>pub</span> <span class='kw'>mod</span> <span class='ident'>range</span>;
<span class='kw'>pub</span> <span class='kw'>mod</span> <span class='ident'>gamma</span>;
<span class='kw'>pub</span> <span class='kw'>mod</span> <span class='ident'>normal</span>;
<span class='kw'>pub</span> <span class='kw'>mod</span> <span class='ident'>exponential</span>;
<span class='doccomment'>/// Types that can be used to create a random instance of `Support`.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Sample</span><span class='op'><</span><span class='ident'>Support</span><span class='op'>></span> {
<span class='doccomment'>/// Generate a random value of `Support`, using `rng` as the</span>
<span class='doccomment'>/// source of randomness.</span>
<span class='kw'>fn</span> <span class='ident'>sample</span><span class='op'><</span><span class='ident'>R</span>: <span class='ident'>Rng</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>rng</span>: <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>R</span>) <span class='op'>-></span> <span class='ident'>Support</span>;
}
<span class='doccomment'>/// `Sample`s that do not require keeping track of state.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// Since no state is recorded, each sample is (statistically)</span>
<span class='doccomment'>/// independent of all others, assuming the `Rng` used has this</span>
<span class='doccomment'>/// property.</span>
<span class='comment'>// FIXME maybe having this separate is overkill (the only reason is to</span>
<span class='comment'>// take &self rather than &mut self)? or maybe this should be the</span>
<span class='comment'>// trait called `Sample` and the other should be `DependentSample`.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>IndependentSample</span><span class='op'><</span><span class='ident'>Support</span><span class='op'>></span>: <span class='ident'>Sample</span><span class='op'><</span><span class='ident'>Support</span><span class='op'>></span> {
<span class='doccomment'>/// Generate a random value.</span>
<span class='kw'>fn</span> <span class='ident'>ind_sample</span><span class='op'><</span><span class='ident'>R</span>: <span class='ident'>Rng</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>R</span>) <span class='op'>-></span> <span class='ident'>Support</span>;
}
<span class='doccomment'>/// A wrapper for generating types that implement `Rand` via the</span>
<span class='doccomment'>/// `Sample` & `IndependentSample` traits.</span>
<span class='kw'>pub</span> <span class='kw'>struct</span> <span class='ident'>RandSample</span><span class='op'><</span><span class='ident'>Sup</span><span class='op'>></span> {
<span class='ident'>_marker</span>: <span class='ident'>marker</span>::<span class='ident'>PhantomData</span><span class='op'><</span><span class='kw'>fn</span>() <span class='op'>-></span> <span class='ident'>Sup</span><span class='op'>></span>,
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>Sup</span><span class='op'>></span> <span class='ident'>Copy</span> <span class='kw'>for</span> <span class='ident'>RandSample</span><span class='op'><</span><span class='ident'>Sup</span><span class='op'>></span> {}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>Sup</span><span class='op'>></span> <span class='ident'>Clone</span> <span class='kw'>for</span> <span class='ident'>RandSample</span><span class='op'><</span><span class='ident'>Sup</span><span class='op'>></span> {
<span class='kw'>fn</span> <span class='ident'>clone</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span> { <span class='kw-2'>*</span><span class='self'>self</span> }
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>Sup</span>: <span class='ident'>Rand</span><span class='op'>></span> <span class='ident'>Sample</span><span class='op'><</span><span class='ident'>Sup</span><span class='op'>></span> <span class='kw'>for</span> <span class='ident'>RandSample</span><span class='op'><</span><span class='ident'>Sup</span><span class='op'>></span> {
<span class='kw'>fn</span> <span class='ident'>sample</span><span class='op'><</span><span class='ident'>R</span>: <span class='ident'>Rng</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>rng</span>: <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>R</span>) <span class='op'>-></span> <span class='ident'>Sup</span> { <span class='self'>self</span>.<span class='ident'>ind_sample</span>(<span class='ident'>rng</span>) }
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>Sup</span>: <span class='ident'>Rand</span><span class='op'>></span> <span class='ident'>IndependentSample</span><span class='op'><</span><span class='ident'>Sup</span><span class='op'>></span> <span class='kw'>for</span> <span class='ident'>RandSample</span><span class='op'><</span><span class='ident'>Sup</span><span class='op'>></span> {
<span class='kw'>fn</span> <span class='ident'>ind_sample</span><span class='op'><</span><span class='ident'>R</span>: <span class='ident'>Rng</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>rng</span>: <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>R</span>) <span class='op'>-></span> <span class='ident'>Sup</span> {
<span class='ident'>rng</span>.<span class='ident'>gen</span>()
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>Sup</span><span class='op'>></span> <span class='ident'>RandSample</span><span class='op'><</span><span class='ident'>Sup</span><span class='op'>></span> {
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>new</span>() <span class='op'>-></span> <span class='ident'>RandSample</span><span class='op'><</span><span class='ident'>Sup</span><span class='op'>></span> {
<span class='ident'>RandSample</span> { <span class='ident'>_marker</span>: <span class='ident'>marker</span>::<span class='ident'>PhantomData</span> }
}
}
<span class='doccomment'>/// A value with a particular weight for use with `WeightedChoice`.</span>
<span class='attribute'>#[<span class='ident'>derive</span>(<span class='ident'>Copy</span>)]</span>
<span class='attribute'>#[<span class='ident'>derive</span>(<span class='ident'>Clone</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>struct</span> <span class='ident'>Weighted</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='doccomment'>/// The numerical weight of this item</span>
<span class='kw'>pub</span> <span class='ident'>weight</span>: <span class='ident'>u32</span>,
<span class='doccomment'>/// The actual item which is being weighted</span>
<span class='kw'>pub</span> <span class='ident'>item</span>: <span class='ident'>T</span>,
}
<span class='doccomment'>/// A distribution that selects from a finite collection of weighted items.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// Each item has an associated weight that influences how likely it</span>
<span class='doccomment'>/// is to be chosen: higher weight is more likely.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// The `Clone` restriction is a limitation of the `Sample` and</span>
<span class='doccomment'>/// `IndependentSample` traits. Note that `&T` is (cheaply) `Clone` for</span>
<span class='doccomment'>/// all `T`, as is `u32`, so one can store references or indices into</span>
<span class='doccomment'>/// another vector.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// # Example</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// ```rust</span>
<span class='doccomment'>/// use rand::distributions::{Weighted, WeightedChoice, IndependentSample};</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// let mut items = vec!(Weighted { weight: 2, item: 'a' },</span>
<span class='doccomment'>/// Weighted { weight: 4, item: 'b' },</span>
<span class='doccomment'>/// Weighted { weight: 1, item: 'c' });</span>
<span class='doccomment'>/// let wc = WeightedChoice::new(&mut items);</span>
<span class='doccomment'>/// let mut rng = rand::thread_rng();</span>
<span class='doccomment'>/// for _ in 0..16 {</span>
<span class='doccomment'>/// // on average prints 'a' 4 times, 'b' 8 and 'c' twice.</span>
<span class='doccomment'>/// println!("{}", wc.ind_sample(&mut rng));</span>
<span class='doccomment'>/// }</span>
<span class='doccomment'>/// ```</span>
<span class='kw'>pub</span> <span class='kw'>struct</span> <span class='ident'>WeightedChoice</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='ident'>T</span>:<span class='lifetime'>'a</span><span class='op'>></span> {
<span class='ident'>items</span>: <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='kw-2'>mut</span> [<span class='ident'>Weighted</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>],
<span class='ident'>weight_range</span>: <span class='ident'>Range</span><span class='op'><</span><span class='ident'>u32</span><span class='op'>></span>
}
<span class='kw'>impl</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='ident'>T</span>: <span class='ident'>Clone</span><span class='op'>></span> <span class='ident'>WeightedChoice</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='ident'>T</span><span class='op'>></span> {
<span class='doccomment'>/// Create a new `WeightedChoice`.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// Panics if:</span>
<span class='doccomment'>/// - `v` is empty</span>
<span class='doccomment'>/// - the total weight is 0</span>
<span class='doccomment'>/// - the total weight is larger than a `u32` can contain.</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>new</span>(<span class='ident'>items</span>: <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='kw-2'>mut</span> [<span class='ident'>Weighted</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span>]) <span class='op'>-></span> <span class='ident'>WeightedChoice</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='ident'>T</span><span class='op'>></span> {
<span class='comment'>// strictly speaking, this is subsumed by the total weight == 0 case</span>
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='op'>!</span><span class='ident'>items</span>.<span class='ident'>is_empty</span>(), <span class='string'>"WeightedChoice::new called with no items"</span>);
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>running_total</span>: <span class='ident'>u32</span> <span class='op'>=</span> <span class='number'>0</span>;
<span class='comment'>// we convert the list from individual weights to cumulative</span>
<span class='comment'>// weights so we can binary search. This *could* drop elements</span>
<span class='comment'>// with weight == 0 as an optimisation.</span>
<span class='kw'>for</span> <span class='ident'>item</span> <span class='kw'>in</span> <span class='ident'>items</span>.<span class='ident'>iter_mut</span>() {
<span class='ident'>running_total</span> <span class='op'>=</span> <span class='kw'>match</span> <span class='ident'>running_total</span>.<span class='ident'>checked_add</span>(<span class='ident'>item</span>.<span class='ident'>weight</span>) {
<span class='prelude-val'>Some</span>(<span class='ident'>n</span>) <span class='op'>=></span> <span class='ident'>n</span>,
<span class='prelude-val'>None</span> <span class='op'>=></span> <span class='macro'>panic</span><span class='macro'>!</span>(<span class='string'>"WeightedChoice::new called with a total weight \
larger than a u32 can contain"</span>)
};
<span class='ident'>item</span>.<span class='ident'>weight</span> <span class='op'>=</span> <span class='ident'>running_total</span>;
}
<span class='macro'>assert</span><span class='macro'>!</span>(<span class='ident'>running_total</span> <span class='op'>!=</span> <span class='number'>0</span>, <span class='string'>"WeightedChoice::new called with a total weight of 0"</span>);
<span class='ident'>WeightedChoice</span> {
<span class='ident'>items</span>: <span class='ident'>items</span>,
<span class='comment'>// we're likely to be generating numbers in this range</span>
<span class='comment'>// relatively often, so might as well cache it</span>
<span class='ident'>weight_range</span>: <span class='ident'>Range</span>::<span class='ident'>new</span>(<span class='number'>0</span>, <span class='ident'>running_total</span>)
}
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='ident'>T</span>: <span class='ident'>Clone</span><span class='op'>></span> <span class='ident'>Sample</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> <span class='kw'>for</span> <span class='ident'>WeightedChoice</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='ident'>T</span><span class='op'>></span> {
<span class='kw'>fn</span> <span class='ident'>sample</span><span class='op'><</span><span class='ident'>R</span>: <span class='ident'>Rng</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>rng</span>: <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>R</span>) <span class='op'>-></span> <span class='ident'>T</span> { <span class='self'>self</span>.<span class='ident'>ind_sample</span>(<span class='ident'>rng</span>) }
}
<span class='kw'>impl</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='ident'>T</span>: <span class='ident'>Clone</span><span class='op'>></span> <span class='ident'>IndependentSample</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> <span class='kw'>for</span> <span class='ident'>WeightedChoice</span><span class='op'><</span><span class='lifetime'>'a</span>, <span class='ident'>T</span><span class='op'>></span> {
<span class='kw'>fn</span> <span class='ident'>ind_sample</span><span class='op'><</span><span class='ident'>R</span>: <span class='ident'>Rng</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>rng</span>: <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>R</span>) <span class='op'>-></span> <span class='ident'>T</span> {
<span class='comment'>// we want to find the first element that has cumulative</span>
<span class='comment'>// weight > sample_weight, which we do by binary since the</span>
<span class='comment'>// cumulative weights of self.items are sorted.</span>
<span class='comment'>// choose a weight in [0, total_weight)</span>
<span class='kw'>let</span> <span class='ident'>sample_weight</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>weight_range</span>.<span class='ident'>ind_sample</span>(<span class='ident'>rng</span>);
<span class='comment'>// short circuit when it's the first item</span>
<span class='kw'>if</span> <span class='ident'>sample_weight</span> <span class='op'><</span> <span class='self'>self</span>.<span class='ident'>items</span>[<span class='number'>0</span>].<span class='ident'>weight</span> {
<span class='kw'>return</span> <span class='self'>self</span>.<span class='ident'>items</span>[<span class='number'>0</span>].<span class='ident'>item</span>.<span class='ident'>clone</span>();
}
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>idx</span> <span class='op'>=</span> <span class='number'>0</span>;
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>modifier</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>items</span>.<span class='ident'>len</span>();
<span class='comment'>// now we know that every possibility has an element to the</span>
<span class='comment'>// left, so we can just search for the last element that has</span>
<span class='comment'>// cumulative weight <= sample_weight, then the next one will</span>
<span class='comment'>// be "it". (Note that this greatest element will never be the</span>
<span class='comment'>// last element of the vector, since sample_weight is chosen</span>
<span class='comment'>// in [0, total_weight) and the cumulative weight of the last</span>
<span class='comment'>// one is exactly the total weight.)</span>
<span class='kw'>while</span> <span class='ident'>modifier</span> <span class='op'>></span> <span class='number'>1</span> {
<span class='kw'>let</span> <span class='ident'>i</span> <span class='op'>=</span> <span class='ident'>idx</span> <span class='op'>+</span> <span class='ident'>modifier</span> <span class='op'>/</span> <span class='number'>2</span>;
<span class='kw'>if</span> <span class='self'>self</span>.<span class='ident'>items</span>[<span class='ident'>i</span>].<span class='ident'>weight</span> <span class='op'><=</span> <span class='ident'>sample_weight</span> {
<span class='comment'>// we're small, so look to the right, but allow this</span>
<span class='comment'>// exact element still.</span>
<span class='ident'>idx</span> <span class='op'>=</span> <span class='ident'>i</span>;
<span class='comment'>// we need the `/ 2` to round up otherwise we'll drop</span>
<span class='comment'>// the trailing elements when `modifier` is odd.</span>
<span class='ident'>modifier</span> <span class='op'>+=</span> <span class='number'>1</span>;
} <span class='kw'>else</span> {
<span class='comment'>// otherwise we're too big, so go left. (i.e. do</span>
<span class='comment'>// nothing)</span>
}
<span class='ident'>modifier</span> <span class='op'>/=</span> <span class='number'>2</span>;
}
<span class='kw'>return</span> <span class='self'>self</span>.<span class='ident'>items</span>[<span class='ident'>idx</span> <span class='op'>+</span> <span class='number'>1</span>].<span class='ident'>item</span>.<span class='ident'>clone</span>();
}
}
<span class='kw'>mod</span> <span class='ident'>ziggurat_tables</span>;
<span class='doccomment'>/// Sample a random number using the Ziggurat method (specifically the</span>
<span class='doccomment'>/// ZIGNOR variant from Doornik 2005). Most of the arguments are</span>
<span class='doccomment'>/// directly from the paper:</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// * `rng`: source of randomness</span>
<span class='doccomment'>/// * `symmetric`: whether this is a symmetric distribution, or one-sided with P(x < 0) = 0.</span>
<span class='doccomment'>/// * `X`: the $x_i$ abscissae.</span>
<span class='doccomment'>/// * `F`: precomputed values of the PDF at the $x_i$, (i.e. $f(x_i)$)</span>
<span class='doccomment'>/// * `F_DIFF`: precomputed values of $f(x_i) - f(x_{i+1})$</span>
<span class='doccomment'>/// * `pdf`: the probability density function</span>
<span class='doccomment'>/// * `zero_case`: manual sampling from the tail when we chose the</span>
<span class='doccomment'>/// bottom box (i.e. i == 0)</span>
<span class='comment'>// the perf improvement (25-50%) is definitely worth the extra code</span>
<span class='comment'>// size from force-inlining.</span>
<span class='attribute'>#[<span class='ident'>inline</span>(<span class='ident'>always</span>)]</span>
<span class='kw'>fn</span> <span class='ident'>ziggurat</span><span class='op'><</span><span class='ident'>R</span>: <span class='ident'>Rng</span>, <span class='ident'>P</span>, <span class='ident'>Z</span><span class='op'>></span>(
<span class='ident'>rng</span>: <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>R</span>,
<span class='ident'>symmetric</span>: <span class='ident'>bool</span>,
<span class='ident'>x_tab</span>: <span class='ident'>ziggurat_tables</span>::<span class='ident'>ZigTable</span>,
<span class='ident'>f_tab</span>: <span class='ident'>ziggurat_tables</span>::<span class='ident'>ZigTable</span>,
<span class='kw-2'>mut</span> <span class='ident'>pdf</span>: <span class='ident'>P</span>,
<span class='kw-2'>mut</span> <span class='ident'>zero_case</span>: <span class='ident'>Z</span>)
<span class='op'>-></span> <span class='ident'>f64</span> <span class='kw'>where</span> <span class='ident'>P</span>: <span class='ident'>FnMut</span>(<span class='ident'>f64</span>) <span class='op'>-></span> <span class='ident'>f64</span>, <span class='ident'>Z</span>: <span class='ident'>FnMut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>R</span>, <span class='ident'>f64</span>) <span class='op'>-></span> <span class='ident'>f64</span> {
<span class='kw'>const</span> <span class='ident'>SCALE</span>: <span class='ident'>f64</span> <span class='op'>=</span> (<span class='number'>1u64</span> <span class='op'><<</span> <span class='number'>53</span>) <span class='kw'>as</span> <span class='ident'>f64</span>;
<span class='kw'>loop</span> {
<span class='comment'>// reimplement the f64 generation as an optimisation suggested</span>
<span class='comment'>// by the Doornik paper: we have a lot of precision-space</span>
<span class='comment'>// (i.e. there are 11 bits of the 64 of a u64 to use after</span>
<span class='comment'>// creating a f64), so we might as well reuse some to save</span>
<span class='comment'>// generating a whole extra random number. (Seems to be 15%</span>
<span class='comment'>// faster.)</span>
<span class='comment'>//</span>
<span class='comment'>// This unfortunately misses out on the benefits of direct</span>
<span class='comment'>// floating point generation if an RNG like dSMFT is</span>
<span class='comment'>// used. (That is, such RNGs create floats directly, highly</span>
<span class='comment'>// efficiently and overload next_f32/f64, so by not calling it</span>
<span class='comment'>// this may be slower than it would be otherwise.)</span>
<span class='comment'>// FIXME: investigate/optimise for the above.</span>
<span class='kw'>let</span> <span class='ident'>bits</span>: <span class='ident'>u64</span> <span class='op'>=</span> <span class='ident'>rng</span>.<span class='ident'>gen</span>();
<span class='kw'>let</span> <span class='ident'>i</span> <span class='op'>=</span> (<span class='ident'>bits</span> <span class='op'>&</span> <span class='number'>0xff</span>) <span class='kw'>as</span> <span class='ident'>usize</span>;
<span class='kw'>let</span> <span class='ident'>f</span> <span class='op'>=</span> (<span class='ident'>bits</span> <span class='op'>>></span> <span class='number'>11</span>) <span class='kw'>as</span> <span class='ident'>f64</span> <span class='op'>/</span> <span class='ident'>SCALE</span>;
<span class='comment'>// u is either U(-1, 1) or U(0, 1) depending on if this is a</span>
<span class='comment'>// symmetric distribution or not.</span>
<span class='kw'>let</span> <span class='ident'>u</span> <span class='op'>=</span> <span class='kw'>if</span> <span class='ident'>symmetric</span> {<span class='number'>2.0</span> <span class='op'>*</span> <span class='ident'>f</span> <span class='op'>-</span> <span class='number'>1.0</span>} <span class='kw'>else</span> {<span class='ident'>f</span>};
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> <span class='ident'>u</span> <span class='op'>*</span> <span class='ident'>x_tab</span>[<span class='ident'>i</span>];
<span class='kw'>let</span> <span class='ident'>test_x</span> <span class='op'>=</span> <span class='kw'>if</span> <span class='ident'>symmetric</span> { <span class='ident'>x</span>.<span class='ident'>abs</span>() } <span class='kw'>else</span> {<span class='ident'>x</span>};
<span class='comment'>// algebraically equivalent to |u| < x_tab[i+1]/x_tab[i] (or u < x_tab[i+1]/x_tab[i])</span>
<span class='kw'>if</span> <span class='ident'>test_x</span> <span class='op'><</span> <span class='ident'>x_tab</span>[<span class='ident'>i</span> <span class='op'>+</span> <span class='number'>1</span>] {
<span class='kw'>return</span> <span class='ident'>x</span>;
}
<span class='kw'>if</span> <span class='ident'>i</span> <span class='op'>==</span> <span class='number'>0</span> {
<span class='kw'>return</span> <span class='ident'>zero_case</span>(<span class='ident'>rng</span>, <span class='ident'>u</span>);
}
<span class='comment'>// algebraically equivalent to f1 + DRanU()*(f0 - f1) < 1</span>
<span class='kw'>if</span> <span class='ident'>f_tab</span>[<span class='ident'>i</span> <span class='op'>+</span> <span class='number'>1</span>] <span class='op'>+</span> (<span class='ident'>f_tab</span>[<span class='ident'>i</span>] <span class='op'>-</span> <span class='ident'>f_tab</span>[<span class='ident'>i</span> <span class='op'>+</span> <span class='number'>1</span>]) <span class='op'>*</span> <span class='ident'>rng</span>.<span class='ident'>gen</span>::<span class='op'><</span><span class='ident'>f64</span><span class='op'>></span>() <span class='op'><</span> <span class='ident'>pdf</span>(<span class='ident'>x</span>) {
<span class='kw'>return</span> <span class='ident'>x</span>;
}
}
}
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>test</span>)]</span>
<span class='kw'>mod</span> <span class='ident'>tests</span> {
<span class='kw'>use</span> {<span class='ident'>Rng</span>, <span class='ident'>Rand</span>};
<span class='kw'>use</span> <span class='kw'>super</span>::{<span class='ident'>RandSample</span>, <span class='ident'>WeightedChoice</span>, <span class='ident'>Weighted</span>, <span class='ident'>Sample</span>, <span class='ident'>IndependentSample</span>};
<span class='attribute'>#[<span class='ident'>derive</span>(<span class='ident'>PartialEq</span>, <span class='ident'>Debug</span>)]</span>
<span class='kw'>struct</span> <span class='ident'>ConstRand</span>(<span class='ident'>usize</span>);
<span class='kw'>impl</span> <span class='ident'>Rand</span> <span class='kw'>for</span> <span class='ident'>ConstRand</span> {
<span class='kw'>fn</span> <span class='ident'>rand</span><span class='op'><</span><span class='ident'>R</span>: <span class='ident'>Rng</span><span class='op'>></span>(_: <span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>R</span>) <span class='op'>-></span> <span class='ident'>ConstRand</span> {
<span class='ident'>ConstRand</span>(<span class='number'>0</span>)
}
}
<span class='comment'>// 0, 1, 2, 3, ...</span>
<span class='kw'>struct</span> <span class='ident'>CountingRng</span> { <span class='ident'>i</span>: <span class='ident'>u32</span> }
<span class='kw'>impl</span> <span class='ident'>Rng</span> <span class='kw'>for</span> <span class='ident'>CountingRng</span> {
<span class='kw'>fn</span> <span class='ident'>next_u32</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>u32</span> {
<span class='self'>self</span>.<span class='ident'>i</span> <span class='op'>+=</span> <span class='number'>1</span>;
<span class='self'>self</span>.<span class='ident'>i</span> <span class='op'>-</span> <span class='number'>1</span>
}
<span class='kw'>fn</span> <span class='ident'>next_u64</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>u64</span> {
<span class='self'>self</span>.<span class='ident'>next_u32</span>() <span class='kw'>as</span> <span class='ident'>u64</span>
}
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_rand_sample</span>() {
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>rand_sample</span> <span class='op'>=</span> <span class='ident'>RandSample</span>::<span class='op'><</span><span class='ident'>ConstRand</span><span class='op'>></span>::<span class='ident'>new</span>();
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>rand_sample</span>.<span class='ident'>sample</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> ::<span class='ident'>test</span>::<span class='ident'>rng</span>()), <span class='ident'>ConstRand</span>(<span class='number'>0</span>));
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>rand_sample</span>.<span class='ident'>ind_sample</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> ::<span class='ident'>test</span>::<span class='ident'>rng</span>()), <span class='ident'>ConstRand</span>(<span class='number'>0</span>));
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_weighted_choice</span>() {
<span class='comment'>// this makes assumptions about the internal implementation of</span>
<span class='comment'>// WeightedChoice, specifically: it doesn't reorder the items,</span>
<span class='comment'>// it doesn't do weird things to the RNG (so 0 maps to 0, 1 to</span>
<span class='comment'>// 1, internally; modulo a modulo operation).</span>
<span class='macro'>macro_rules</span><span class='macro'>!</span> <span class='ident'>t</span> {
(<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>items</span>:<span class='ident'>expr</span>, <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>expected</span>:<span class='ident'>expr</span>) <span class='op'>=></span> {{
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>items</span> <span class='op'>=</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>items</span>;
<span class='kw'>let</span> <span class='ident'>wc</span> <span class='op'>=</span> <span class='ident'>WeightedChoice</span>::<span class='ident'>new</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>items</span>);
<span class='kw'>let</span> <span class='ident'>expected</span> <span class='op'>=</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>expected</span>;
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>rng</span> <span class='op'>=</span> <span class='ident'>CountingRng</span> { <span class='ident'>i</span>: <span class='number'>0</span> };
<span class='kw'>for</span> <span class='kw-2'>&</span><span class='ident'>val</span> <span class='kw'>in</span> <span class='ident'>expected</span>.<span class='ident'>iter</span>() {
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>wc</span>.<span class='ident'>ind_sample</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='ident'>rng</span>), <span class='ident'>val</span>)
}
}}
}
<span class='macro'>t</span><span class='macro'>!</span>(<span class='macro'>vec</span><span class='macro'>!</span>(<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>10</span>}), [<span class='number'>10</span>]);
<span class='comment'>// skip some</span>
<span class='macro'>t</span><span class='macro'>!</span>(<span class='macro'>vec</span><span class='macro'>!</span>(<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>0</span>, <span class='ident'>item</span>: <span class='number'>20</span>},
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>2</span>, <span class='ident'>item</span>: <span class='number'>21</span>},
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>0</span>, <span class='ident'>item</span>: <span class='number'>22</span>},
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>23</span>}),
[<span class='number'>21</span>,<span class='number'>21</span>, <span class='number'>23</span>]);
<span class='comment'>// different weights</span>
<span class='macro'>t</span><span class='macro'>!</span>(<span class='macro'>vec</span><span class='macro'>!</span>(<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>4</span>, <span class='ident'>item</span>: <span class='number'>30</span>},
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>3</span>, <span class='ident'>item</span>: <span class='number'>31</span>}),
[<span class='number'>30</span>,<span class='number'>30</span>,<span class='number'>30</span>,<span class='number'>30</span>, <span class='number'>31</span>,<span class='number'>31</span>,<span class='number'>31</span>]);
<span class='comment'>// check that we're binary searching</span>
<span class='comment'>// correctly with some vectors of odd</span>
<span class='comment'>// length.</span>
<span class='macro'>t</span><span class='macro'>!</span>(<span class='macro'>vec</span><span class='macro'>!</span>(<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>40</span>},
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>41</span>},
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>42</span>},
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>43</span>},
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>44</span>}),
[<span class='number'>40</span>, <span class='number'>41</span>, <span class='number'>42</span>, <span class='number'>43</span>, <span class='number'>44</span>]);
<span class='macro'>t</span><span class='macro'>!</span>(<span class='macro'>vec</span><span class='macro'>!</span>(<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>50</span>},
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>51</span>},
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>52</span>},
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>53</span>},
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>54</span>},
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>55</span>},
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>56</span>}),
[<span class='number'>50</span>, <span class='number'>51</span>, <span class='number'>52</span>, <span class='number'>53</span>, <span class='number'>54</span>, <span class='number'>55</span>, <span class='number'>56</span>]);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_weighted_clone_initialization</span>() {
<span class='kw'>let</span> <span class='ident'>initial</span> : <span class='ident'>Weighted</span><span class='op'><</span><span class='ident'>u32</span><span class='op'>></span> <span class='op'>=</span> <span class='ident'>Weighted</span> {<span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>1</span>};
<span class='kw'>let</span> <span class='ident'>clone</span> <span class='op'>=</span> <span class='ident'>initial</span>.<span class='ident'>clone</span>();
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>initial</span>.<span class='ident'>weight</span>, <span class='ident'>clone</span>.<span class='ident'>weight</span>);
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>initial</span>.<span class='ident'>item</span>, <span class='ident'>clone</span>.<span class='ident'>item</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span> <span class='attribute'>#[<span class='ident'>should_panic</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_weighted_clone_change_weight</span>() {
<span class='kw'>let</span> <span class='ident'>initial</span> : <span class='ident'>Weighted</span><span class='op'><</span><span class='ident'>u32</span><span class='op'>></span> <span class='op'>=</span> <span class='ident'>Weighted</span> {<span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>1</span>};
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>clone</span> <span class='op'>=</span> <span class='ident'>initial</span>.<span class='ident'>clone</span>();
<span class='ident'>clone</span>.<span class='ident'>weight</span> <span class='op'>=</span> <span class='number'>5</span>;
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>initial</span>.<span class='ident'>weight</span>, <span class='ident'>clone</span>.<span class='ident'>weight</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span> <span class='attribute'>#[<span class='ident'>should_panic</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_weighted_clone_change_item</span>() {
<span class='kw'>let</span> <span class='ident'>initial</span> : <span class='ident'>Weighted</span><span class='op'><</span><span class='ident'>u32</span><span class='op'>></span> <span class='op'>=</span> <span class='ident'>Weighted</span> {<span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>1</span>};
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>clone</span> <span class='op'>=</span> <span class='ident'>initial</span>.<span class='ident'>clone</span>();
<span class='ident'>clone</span>.<span class='ident'>item</span> <span class='op'>=</span> <span class='number'>5</span>;
<span class='macro'>assert_eq</span><span class='macro'>!</span>(<span class='ident'>initial</span>.<span class='ident'>item</span>, <span class='ident'>clone</span>.<span class='ident'>item</span>);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span> <span class='attribute'>#[<span class='ident'>should_panic</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_weighted_choice_no_items</span>() {
<span class='ident'>WeightedChoice</span>::<span class='op'><</span><span class='ident'>isize</span><span class='op'>></span>::<span class='ident'>new</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> []);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span> <span class='attribute'>#[<span class='ident'>should_panic</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_weighted_choice_zero_weight</span>() {
<span class='ident'>WeightedChoice</span>::<span class='ident'>new</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> [<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>0</span>, <span class='ident'>item</span>: <span class='number'>0</span>},
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>0</span>, <span class='ident'>item</span>: <span class='number'>1</span>}]);
}
<span class='attribute'>#[<span class='ident'>test</span>]</span> <span class='attribute'>#[<span class='ident'>should_panic</span>]</span>
<span class='kw'>fn</span> <span class='ident'>test_weighted_choice_weight_overflows</span>() {
<span class='kw'>let</span> <span class='ident'>x</span> <span class='op'>=</span> ::<span class='ident'>std</span>::<span class='ident'>u32</span>::<span class='ident'>MAX</span> <span class='op'>/</span> <span class='number'>2</span>; <span class='comment'>// x + x + 2 is the overflow</span>
<span class='ident'>WeightedChoice</span>::<span class='ident'>new</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> [<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='ident'>x</span>, <span class='ident'>item</span>: <span class='number'>0</span> },
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>1</span> },
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='ident'>x</span>, <span class='ident'>item</span>: <span class='number'>2</span> },
<span class='ident'>Weighted</span> { <span class='ident'>weight</span>: <span class='number'>1</span>, <span class='ident'>item</span>: <span class='number'>3</span> }]);
}
}
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