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 </pre><pre class="rust"><code><span class="comment">// Copyright 2019 Developers of the Rand project.</span>
 <span class="comment">//</span>
 <span class="comment">// Licensed under the Apache License, Version 2.0 &lt;LICENSE-APACHE or</span>
 <span class="comment">// https://www.apache.org/licenses/LICENSE-2.0&gt; or the MIT license</span>
 <span class="comment">// &lt;LICENSE-MIT or https://opensource.org/licenses/MIT&gt;, 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="attribute">#![<span class="ident">doc</span>(
     <span class="ident">html_logo_url</span> <span class="op">=</span> <span class="string">&quot;https://www.rust-lang.org/logos/rust-logo-128x128-blk.png&quot;</span>,
     <span class="ident">html_favicon_url</span> <span class="op">=</span> <span class="string">&quot;https://www.rust-lang.org/favicon.ico&quot;</span>,
     <span class="ident">html_root_url</span> <span class="op">=</span> <span class="string">&quot;https://rust-random.github.io/rand/&quot;</span>
 )]</span>
 <span class="attribute">#![<span class="ident">deny</span>(<span class="ident">missing_docs</span>)]</span>
 <span class="attribute">#![<span class="ident">deny</span>(<span class="ident">missing_debug_implementations</span>)]</span>
 <span class="attribute">#![<span class="ident">allow</span>(
     <span class="ident">clippy::excessive_precision</span>,
     <span class="ident">clippy::float_cmp</span>,
     <span class="ident">clippy::unreadable_literal</span>
 )]</span>
 <span class="attribute">#![<span class="ident">allow</span>(<span class="ident">clippy::neg_cmp_op_on_partial_ord</span>)]</span> <span class="comment">// suggested fix too verbose</span>
 <span class="attribute">#![<span class="ident">no_std</span>]</span>
 <span class="attribute">#![<span class="ident">cfg_attr</span>(<span class="ident">doc_cfg</span>, <span class="ident">feature</span>(<span class="ident">doc_cfg</span>))]</span>

 <span class="doccomment">//! Generating random samples from probability distributions.</span>
 <span class="doccomment">//!</span>
 <span class="doccomment">//! ## Re-exports</span>
 <span class="doccomment">//!</span>
 <span class="doccomment">//! This crate is a super-set of the [`rand::distributions`] module. See the</span>
 <span class="doccomment">//! [`rand::distributions`] module documentation for an overview of the core</span>
 <span class="doccomment">//! [`Distribution`] trait and implementations.</span>
 <span class="doccomment">//!</span>
 <span class="doccomment">//! The following are re-exported:</span>
 <span class="doccomment">//!</span>
 <span class="doccomment">//! - The [`Distribution`] trait and [`DistIter`] helper type</span>
 <span class="doccomment">//! - The [`Standard`], [`Alphanumeric`], [`Uniform`], [`OpenClosed01`],</span>
 <span class="doccomment">//! [`Open01`], [`Bernoulli`], and [`WeightedIndex`] distributions</span>
 <span class="doccomment">//!</span>
 <span class="doccomment">//! ## Distributions</span>
 <span class="doccomment">//!</span>
 <span class="doccomment">//! This crate provides the following probability distributions:</span>
 <span class="doccomment">//!</span>
 <span class="doccomment">//! - Related to real-valued quantities that grow linearly</span>
 <span class="doccomment">//!   (e.g. errors, offsets):</span>
 <span class="doccomment">//!   - [`Normal`] distribution, and [`StandardNormal`] as a primitive</span>
 <span class="doccomment">//!   - [`SkewNormal`] distribution</span>
 <span class="doccomment">//!   - [`Cauchy`] distribution</span>
 <span class="doccomment">//! - Related to Bernoulli trials (yes/no events, with a given probability):</span>
 <span class="doccomment">//!   - [`Binomial`] distribution</span>
 <span class="doccomment">//!   - [`Geometric`] distribution</span>
 <span class="doccomment">//!   - [`Hypergeometric`] distribution</span>
 <span class="doccomment">//! - Related to positive real-valued quantities that grow exponentially</span>
 <span class="doccomment">//!   (e.g. prices, incomes, populations):</span>
 <span class="doccomment">//!   - [`LogNormal`] distribution</span>
 <span class="doccomment">//! - Related to the occurrence of independent events at a given rate:</span>
 <span class="doccomment">//!   - [`Pareto`] distribution</span>
 <span class="doccomment">//!   - [`Poisson`] distribution</span>
 <span class="doccomment">//!   - [`Exp`]onential distribution, and [`Exp1`] as a primitive</span>
 <span class="doccomment">//!   - [`Weibull`] distribution</span>
 <span class="doccomment">//!   - [`Gumbel`] distribution</span>
 <span class="doccomment">//!   - [`Frechet`] distribution</span>
 <span class="doccomment">//!   - [`Zeta`] distribution</span>
 <span class="doccomment">//!   - [`Zipf`] distribution</span>
 <span class="doccomment">//! - Gamma and derived distributions:</span>
 <span class="doccomment">//!   - [`Gamma`] distribution</span>
 <span class="doccomment">//!   - [`ChiSquared`] distribution</span>
 <span class="doccomment">//!   - [`StudentT`] distribution</span>
 <span class="doccomment">//!   - [`FisherF`] distribution</span>
 <span class="doccomment">//! - Triangular distribution:</span>
 <span class="doccomment">//!   - [`Beta`] distribution</span>
 <span class="doccomment">//!   - [`Triangular`] distribution</span>
 <span class="doccomment">//! - Multivariate probability distributions</span>
 <span class="doccomment">//!   - [`Dirichlet`] distribution</span>
 <span class="doccomment">//!   - [`UnitSphere`] distribution</span>
 <span class="doccomment">//!   - [`UnitBall`] distribution</span>
 <span class="doccomment">//!   - [`UnitCircle`] distribution</span>
 <span class="doccomment">//!   - [`UnitDisc`] distribution</span>
 <span class="doccomment">//! - Alternative implementation for weighted index sampling</span>
 <span class="doccomment">//!   - [`WeightedAliasIndex`] distribution</span>
 <span class="doccomment">//! - Misc. distributions</span>
 <span class="doccomment">//!   - [`InverseGaussian`] distribution</span>
 <span class="doccomment">//!   - [`NormalInverseGaussian`] distribution</span>

 <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;alloc&quot;</span>)]</span>
 <span class="kw">extern</span> <span class="kw">crate</span> <span class="ident">alloc</span>;

 <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;std&quot;</span>)]</span>
 <span class="kw">extern</span> <span class="kw">crate</span> <span class="ident">std</span>;

 <span class="comment">// This is used for doc links:</span>
 <span class="attribute">#[<span class="ident">allow</span>(<span class="ident">unused</span>)]</span>
 <span class="kw">use</span> <span class="ident">rand::Rng</span>;

 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident">rand::distributions</span>::{
     <span class="ident">uniform</span>, <span class="ident">Alphanumeric</span>, <span class="ident">Bernoulli</span>, <span class="ident">BernoulliError</span>, <span class="ident">DistIter</span>, <span class="ident">Distribution</span>, <span class="ident">Open01</span>, <span class="ident">OpenClosed01</span>,
     <span class="ident">Standard</span>, <span class="ident">Uniform</span>,
 };

 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::binomial</span>::{<span class="ident">Binomial</span>, <span class="ident">Error</span> <span class="kw">as</span> <span class="ident">BinomialError</span>};
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::cauchy</span>::{<span class="ident">Cauchy</span>, <span class="ident">Error</span> <span class="kw">as</span> <span class="ident">CauchyError</span>};
 <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;alloc&quot;</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">doc_cfg</span>, <span class="ident">doc</span>(<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;alloc&quot;</span>)))]</span>
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::dirichlet</span>::{<span class="ident">Dirichlet</span>, <span class="ident">Error</span> <span class="kw">as</span> <span class="ident">DirichletError</span>};
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::exponential</span>::{<span class="ident">Error</span> <span class="kw">as</span> <span class="ident">ExpError</span>, <span class="ident">Exp</span>, <span class="ident">Exp1</span>};
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::frechet</span>::{<span class="ident">Error</span> <span class="kw">as</span> <span class="ident">FrechetError</span>, <span class="ident">Frechet</span>};
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::gamma</span>::{
     <span class="ident">Beta</span>, <span class="ident">BetaError</span>, <span class="ident">ChiSquared</span>, <span class="ident">ChiSquaredError</span>, <span class="ident">Error</span> <span class="kw">as</span> <span class="ident">GammaError</span>, <span class="ident">FisherF</span>, <span class="ident">FisherFError</span>,
     <span class="ident">Gamma</span>, <span class="ident">StudentT</span>,
 };
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::geometric</span>::{<span class="ident">Error</span> <span class="kw">as</span> <span class="ident">GeoError</span>, <span class="ident">Geometric</span>, <span class="ident">StandardGeometric</span>};
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::gumbel</span>::{<span class="ident">Error</span> <span class="kw">as</span> <span class="ident">GumbelError</span>, <span class="ident">Gumbel</span>};
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::hypergeometric</span>::{<span class="ident">Error</span> <span class="kw">as</span> <span class="ident">HyperGeoError</span>, <span class="ident">Hypergeometric</span>};
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::inverse_gaussian</span>::{<span class="ident">Error</span> <span class="kw">as</span> <span class="ident">InverseGaussianError</span>, <span class="ident">InverseGaussian</span>};
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::normal</span>::{<span class="ident">Error</span> <span class="kw">as</span> <span class="ident">NormalError</span>, <span class="ident">LogNormal</span>, <span class="ident">Normal</span>, <span class="ident">StandardNormal</span>};
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::normal_inverse_gaussian</span>::{
     <span class="ident">Error</span> <span class="kw">as</span> <span class="ident">NormalInverseGaussianError</span>, <span class="ident">NormalInverseGaussian</span>,
 };
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::pareto</span>::{<span class="ident">Error</span> <span class="kw">as</span> <span class="ident">ParetoError</span>, <span class="ident">Pareto</span>};
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::pert</span>::{<span class="ident">Pert</span>, <span class="ident">PertError</span>};
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::poisson</span>::{<span class="ident">Error</span> <span class="kw">as</span> <span class="ident">PoissonError</span>, <span class="ident">Poisson</span>};
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::skew_normal</span>::{<span class="ident">Error</span> <span class="kw">as</span> <span class="ident">SkewNormalError</span>, <span class="ident">SkewNormal</span>};
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::triangular</span>::{<span class="ident">Triangular</span>, <span class="ident">TriangularError</span>};
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::unit_ball::UnitBall</span>;
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::unit_circle::UnitCircle</span>;
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::unit_disc::UnitDisc</span>;
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::unit_sphere::UnitSphere</span>;
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::weibull</span>::{<span class="ident">Error</span> <span class="kw">as</span> <span class="ident">WeibullError</span>, <span class="ident">Weibull</span>};
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::zipf</span>::{<span class="ident">Zeta</span>, <span class="ident">ZetaError</span>, <span class="ident">Zipf</span>, <span class="ident">ZipfError</span>};
 <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;alloc&quot;</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">doc_cfg</span>, <span class="ident">doc</span>(<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;alloc&quot;</span>)))]</span>
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident">rand::distributions</span>::{<span class="ident">WeightedError</span>, <span class="ident">WeightedIndex</span>};
 <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;alloc&quot;</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">doc_cfg</span>, <span class="ident">doc</span>(<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;alloc&quot;</span>)))]</span>
 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident">weighted_alias::WeightedAliasIndex</span>;

 <span class="kw">pub</span> <span class="kw">use</span> <span class="ident">num_traits</span>;

 <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span>
 <span class="attribute">#[<span class="ident">macro_use</span>]</span>
 <span class="kw">mod</span> <span class="ident">test</span> {
     <span class="comment">// Notes on testing</span>
     <span class="comment">//</span>
     <span class="comment">// Testing random number distributions correctly is hard. The following</span>
     <span class="comment">// testing is desired:</span>
     <span class="comment">//</span>
     <span class="comment">// - Construction: test initialisation with a few valid parameter sets.</span>
     <span class="comment">// - Erroneous usage: test that incorrect usage generates an error.</span>
     <span class="comment">// - Vector: test that usage with fixed inputs (including RNG) generates a</span>
     <span class="comment">//   fixed output sequence on all platforms.</span>
     <span class="comment">// - Correctness at fixed points (optional): using a specific mock RNG,</span>
     <span class="comment">//   check that specific values are sampled (e.g. end-points and median of</span>
     <span class="comment">//   distribution).</span>
     <span class="comment">// - Correctness of PDF (extra): generate a histogram of samples within a</span>
     <span class="comment">//   certain range, and check this approximates the PDF. These tests are</span>
     <span class="comment">//   expected to be expensive, and should be behind a feature-gate.</span>
     <span class="comment">//</span>
     <span class="comment">// TODO: Vector and correctness tests are largely absent so far.</span>
     <span class="comment">// NOTE: Some distributions have tests checking only that samples can be</span>
     <span class="comment">// generated. This is redundant with vector and correctness tests.</span>

     <span class="doccomment">/// Construct a deterministic RNG with the given seed</span>
     <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">rng</span>(<span class="ident">seed</span>: <span class="ident">u64</span>) -&gt; <span class="kw">impl</span> <span class="ident">rand::RngCore</span> {
         <span class="comment">// For tests, we want a statistically good, fast, reproducible RNG.</span>
         <span class="comment">// PCG32 will do fine, and will be easy to embed if we ever need to.</span>
         <span class="kw">const</span> <span class="ident">INC</span>: <span class="ident">u64</span> <span class="op">=</span> <span class="number">11634580027462260723</span>;
         <span class="ident">rand_pcg::Pcg32::new</span>(<span class="ident">seed</span>, <span class="ident">INC</span>)
     }

     <span class="doccomment">/// Assert that two numbers are almost equal to each other.</span>
     <span class="doccomment">///</span>
     <span class="doccomment">/// On panic, this macro will print the values of the expressions with their</span>
     <span class="doccomment">/// debug representations.</span>
     <span class="macro">macro_rules!</span> <span class="ident">assert_almost_eq</span> {
         (<span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>:<span class="ident">expr</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">prec</span>:<span class="ident">expr</span>) =&gt; {
             <span class="kw">let</span> <span class="ident">diff</span> <span class="op">=</span> (<span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span> <span class="op">-</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>).<span class="ident">abs</span>();
             <span class="macro">assert!</span>(<span class="ident">diff</span> <span class="op">&lt;</span><span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">prec</span>,
                 <span class="string">&quot;assertion failed: `abs(left - right) = {:.1e} &lt; {:e}`, \
                     (left: `{}`, right: `{}`)&quot;</span>,
                 <span class="ident">diff</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">prec</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">a</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">b</span>
             );
         };
     }
 }

 <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;alloc&quot;</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">doc_cfg</span>, <span class="ident">doc</span>(<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;alloc&quot;</span>)))]</span>
 <span class="kw">pub</span> <span class="kw">mod</span> <span class="ident">weighted_alias</span>;

 <span class="kw">mod</span> <span class="ident">binomial</span>;
 <span class="kw">mod</span> <span class="ident">cauchy</span>;
 <span class="kw">mod</span> <span class="ident">dirichlet</span>;
 <span class="kw">mod</span> <span class="ident">exponential</span>;
 <span class="kw">mod</span> <span class="ident">frechet</span>;
 <span class="kw">mod</span> <span class="ident">gamma</span>;
 <span class="kw">mod</span> <span class="ident">geometric</span>;
 <span class="kw">mod</span> <span class="ident">gumbel</span>;
 <span class="kw">mod</span> <span class="ident">hypergeometric</span>;
 <span class="kw">mod</span> <span class="ident">inverse_gaussian</span>;
 <span class="kw">mod</span> <span class="ident">normal</span>;
 <span class="kw">mod</span> <span class="ident">normal_inverse_gaussian</span>;
 <span class="kw">mod</span> <span class="ident">pareto</span>;
 <span class="kw">mod</span> <span class="ident">pert</span>;
 <span class="kw">mod</span> <span class="ident">poisson</span>;
 <span class="kw">mod</span> <span class="ident">skew_normal</span>;
 <span class="kw">mod</span> <span class="ident">triangular</span>;
 <span class="kw">mod</span> <span class="ident">unit_ball</span>;
 <span class="kw">mod</span> <span class="ident">unit_circle</span>;
 <span class="kw">mod</span> <span class="ident">unit_disc</span>;
 <span class="kw">mod</span> <span class="ident">unit_sphere</span>;
 <span class="kw">mod</span> <span class="ident">utils</span>;
 <span class="kw">mod</span> <span class="ident">weibull</span>;
 <span class="kw">mod</span> <span class="ident">ziggurat_tables</span>;
 <span class="kw">mod</span> <span class="ident">zipf</span>;
 </code></pre></div>
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