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</pre><pre class="rust"><code><span class="doccomment">//! The geometric distribution.
</span><span class="kw">use </span><span class="kw">crate</span>::Distribution;
<span class="kw">use </span>rand::Rng;
<span class="kw">use </span>core::fmt;
<span class="attribute">#[allow(unused_imports)]
</span><span class="kw">use </span>num_traits::Float;
<span class="doccomment">/// The geometric distribution `Geometric(p)` bounded to `[0, u64::MAX]`.
///
/// This is the probability distribution of the number of failures before the
/// first success in a series of Bernoulli trials. It has the density function
/// `f(k) = (1 - p)^k p` for `k &gt;= 0`, where `p` is the probability of success
/// on each trial.
///
/// This is the discrete analogue of the [exponential distribution](crate::Exp).
///
/// Note that [`StandardGeometric`](crate::StandardGeometric) is an optimised
/// implementation for `p = 0.5`.
///
/// # Example
///
/// ```
/// use rand_distr::{Geometric, Distribution};
///
/// let geo = Geometric::new(0.25).unwrap();
/// let v = geo.sample(&amp;mut rand::thread_rng());
/// println!(&quot;{} is from a Geometric(0.25) distribution&quot;, v);
/// ```
</span><span class="attribute">#[derive(Copy, Clone, Debug)]
#[cfg_attr(feature = <span class="string">&quot;serde1&quot;</span>, derive(serde::Serialize, serde::Deserialize))]
</span><span class="kw">pub struct </span>Geometric
{
p: f64,
pi: f64,
k: u64
}
<span class="doccomment">/// Error type returned from `Geometric::new`.
</span><span class="attribute">#[derive(Clone, Copy, Debug, PartialEq, Eq)]
</span><span class="kw">pub enum </span>Error {
<span class="doccomment">/// `p &lt; 0 || p &gt; 1` or `nan`
</span>InvalidProbability,
}
<span class="kw">impl </span>fmt::Display <span class="kw">for </span>Error {
<span class="kw">fn </span>fmt(<span class="kw-2">&amp;</span><span class="self">self</span>, f: <span class="kw-2">&amp;mut </span>fmt::Formatter&lt;<span class="lifetime">&#39;_</span>&gt;) -&gt; fmt::Result {
f.write_str(<span class="kw">match </span><span class="self">self </span>{
Error::InvalidProbability =&gt; <span class="string">&quot;p is NaN or outside the interval [0, 1] in geometric distribution&quot;</span>,
})
}
}
<span class="attribute">#[cfg(feature = <span class="string">&quot;std&quot;</span>)]
#[cfg_attr(doc_cfg, doc(cfg(feature = <span class="string">&quot;std&quot;</span>)))]
</span><span class="kw">impl </span>std::error::Error <span class="kw">for </span>Error {}
<span class="kw">impl </span>Geometric {
<span class="doccomment">/// Construct a new `Geometric` with the given shape parameter `p`
/// (probability of success on each trial).
</span><span class="kw">pub fn </span>new(p: f64) -&gt; <span class="prelude-ty">Result</span>&lt;<span class="self">Self</span>, Error&gt; {
<span class="kw">if </span>!p.is_finite() || p &lt; <span class="number">0.0 </span>|| p &gt; <span class="number">1.0 </span>{
<span class="prelude-val">Err</span>(Error::InvalidProbability)
} <span class="kw">else if </span>p == <span class="number">0.0 </span>|| p &gt;= <span class="number">2.0 </span>/ <span class="number">3.0 </span>{
<span class="prelude-val">Ok</span>(Geometric { p, pi: p, k: <span class="number">0 </span>})
} <span class="kw">else </span>{
<span class="kw">let </span>(pi, k) = {
<span class="comment">// choose smallest k such that pi = (1 - p)^(2^k) &lt;= 0.5
</span><span class="kw">let </span><span class="kw-2">mut </span>k = <span class="number">1</span>;
<span class="kw">let </span><span class="kw-2">mut </span>pi = (<span class="number">1.0 </span>- p).powi(<span class="number">2</span>);
<span class="kw">while </span>pi &gt; <span class="number">0.5 </span>{
k += <span class="number">1</span>;
pi = pi * pi;
}
(pi, k)
};
<span class="prelude-val">Ok</span>(Geometric { p, pi, k })
}
}
}
<span class="kw">impl </span>Distribution&lt;u64&gt; <span class="kw">for </span>Geometric
{
<span class="kw">fn </span>sample&lt;R: Rng + <span class="question-mark">?</span>Sized&gt;(<span class="kw-2">&amp;</span><span class="self">self</span>, rng: <span class="kw-2">&amp;mut </span>R) -&gt; u64 {
<span class="kw">if </span><span class="self">self</span>.p &gt;= <span class="number">2.0 </span>/ <span class="number">3.0 </span>{
<span class="comment">// use the trivial algorithm:
</span><span class="kw">let </span><span class="kw-2">mut </span>failures = <span class="number">0</span>;
<span class="kw">loop </span>{
<span class="kw">let </span>u = rng.gen::&lt;f64&gt;();
<span class="kw">if </span>u &lt;= <span class="self">self</span>.p { <span class="kw">break</span>; }
failures += <span class="number">1</span>;
}
<span class="kw">return </span>failures;
}
<span class="kw">if </span><span class="self">self</span>.p == <span class="number">0.0 </span>{ <span class="kw">return </span>core::u64::MAX; }
<span class="kw">let </span>Geometric { p, pi, k } = <span class="kw-2">*</span><span class="self">self</span>;
<span class="comment">// Based on the algorithm presented in section 3 of
// Karl Bringmann and Tobias Friedrich (July 2013) - Exact and Efficient
// Generation of Geometric Random Variates and Random Graphs, published
// in International Colloquium on Automata, Languages and Programming
// (pp.267-278)
// https://people.mpi-inf.mpg.de/~kbringma/paper/2013ICALP-1.pdf
// Use the trivial algorithm to sample D from Geo(pi) = Geo(p) / 2^k:
</span><span class="kw">let </span>d = {
<span class="kw">let </span><span class="kw-2">mut </span>failures = <span class="number">0</span>;
<span class="kw">while </span>rng.gen::&lt;f64&gt;() &lt; pi {
failures += <span class="number">1</span>;
}
failures
};
<span class="comment">// Use rejection sampling for the remainder M from Geo(p) % 2^k:
// choose M uniformly from [0, 2^k), but reject with probability (1 - p)^M
// NOTE: The paper suggests using bitwise sampling here, which is
// currently unsupported, but should improve performance by requiring
// fewer iterations on average. ~ October 28, 2020
</span><span class="kw">let </span>m = <span class="kw">loop </span>{
<span class="kw">let </span>m = rng.gen::&lt;u64&gt;() &amp; ((<span class="number">1 </span>&lt;&lt; k) - <span class="number">1</span>);
<span class="kw">let </span>p_reject = <span class="kw">if </span>m &lt;= core::i32::MAX <span class="kw">as </span>u64 {
(<span class="number">1.0 </span>- p).powi(m <span class="kw">as </span>i32)
} <span class="kw">else </span>{
(<span class="number">1.0 </span>- p).powf(m <span class="kw">as </span>f64)
};
<span class="kw">let </span>u = rng.gen::&lt;f64&gt;();
<span class="kw">if </span>u &lt; p_reject {
<span class="kw">break </span>m;
}
};
(d &lt;&lt; k) + m
}
}
<span class="doccomment">/// Samples integers according to the geometric distribution with success
/// probability `p = 0.5`. This is equivalent to `Geometeric::new(0.5)`,
/// but faster.
///
/// See [`Geometric`](crate::Geometric) for the general geometric distribution.
///
/// Implemented via iterated [Rng::gen::&lt;u64&gt;().leading_zeros()].
///
/// # Example
/// ```
/// use rand::prelude::*;
/// use rand_distr::StandardGeometric;
///
/// let v = StandardGeometric.sample(&amp;mut thread_rng());
/// println!(&quot;{} is from a Geometric(0.5) distribution&quot;, v);
/// ```
</span><span class="attribute">#[derive(Copy, Clone, Debug)]
#[cfg_attr(feature = <span class="string">&quot;serde1&quot;</span>, derive(serde::Serialize, serde::Deserialize))]
</span><span class="kw">pub struct </span>StandardGeometric;
<span class="kw">impl </span>Distribution&lt;u64&gt; <span class="kw">for </span>StandardGeometric {
<span class="kw">fn </span>sample&lt;R: Rng + <span class="question-mark">?</span>Sized&gt;(<span class="kw-2">&amp;</span><span class="self">self</span>, rng: <span class="kw-2">&amp;mut </span>R) -&gt; u64 {
<span class="kw">let </span><span class="kw-2">mut </span>result = <span class="number">0</span>;
<span class="kw">loop </span>{
<span class="kw">let </span>x = rng.gen::&lt;u64&gt;().leading_zeros() <span class="kw">as </span>u64;
result += x;
<span class="kw">if </span>x &lt; <span class="number">64 </span>{ <span class="kw">break</span>; }
}
result
}
}
<span class="attribute">#[cfg(test)]
</span><span class="kw">mod </span>test {
<span class="kw">use super</span>::<span class="kw-2">*</span>;
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_geo_invalid_p() {
<span class="macro">assert!</span>(Geometric::new(core::f64::NAN).is_err());
<span class="macro">assert!</span>(Geometric::new(core::f64::INFINITY).is_err());
<span class="macro">assert!</span>(Geometric::new(core::f64::NEG_INFINITY).is_err());
<span class="macro">assert!</span>(Geometric::new(-<span class="number">0.5</span>).is_err());
<span class="macro">assert!</span>(Geometric::new(<span class="number">0.0</span>).is_ok());
<span class="macro">assert!</span>(Geometric::new(<span class="number">1.0</span>).is_ok());
<span class="macro">assert!</span>(Geometric::new(<span class="number">2.0</span>).is_err());
}
<span class="kw">fn </span>test_geo_mean_and_variance&lt;R: Rng&gt;(p: f64, rng: <span class="kw-2">&amp;mut </span>R) {
<span class="kw">let </span>distr = Geometric::new(p).unwrap();
<span class="kw">let </span>expected_mean = (<span class="number">1.0 </span>- p) / p;
<span class="kw">let </span>expected_variance = (<span class="number">1.0 </span>- p) / (p * p);
<span class="kw">let </span><span class="kw-2">mut </span>results = [<span class="number">0.0</span>; <span class="number">10000</span>];
<span class="kw">for </span>i <span class="kw">in </span>results.iter_mut() {
<span class="kw-2">*</span>i = distr.sample(rng) <span class="kw">as </span>f64;
}
<span class="kw">let </span>mean = results.iter().sum::&lt;f64&gt;() / results.len() <span class="kw">as </span>f64;
<span class="macro">assert!</span>((mean <span class="kw">as </span>f64 - expected_mean).abs() &lt; expected_mean / <span class="number">40.0</span>);
<span class="kw">let </span>variance =
results.iter().map(|x| (x - mean) * (x - mean)).sum::&lt;f64&gt;() / results.len() <span class="kw">as </span>f64;
<span class="macro">assert!</span>((variance - expected_variance).abs() &lt; expected_variance / <span class="number">10.0</span>);
}
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_geometric() {
<span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">12345</span>);
test_geo_mean_and_variance(<span class="number">0.10</span>, <span class="kw-2">&amp;mut </span>rng);
test_geo_mean_and_variance(<span class="number">0.25</span>, <span class="kw-2">&amp;mut </span>rng);
test_geo_mean_and_variance(<span class="number">0.50</span>, <span class="kw-2">&amp;mut </span>rng);
test_geo_mean_and_variance(<span class="number">0.75</span>, <span class="kw-2">&amp;mut </span>rng);
test_geo_mean_and_variance(<span class="number">0.90</span>, <span class="kw-2">&amp;mut </span>rng);
}
<span class="attribute">#[test]
</span><span class="kw">fn </span>test_standard_geometric() {
<span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">654321</span>);
<span class="kw">let </span>distr = StandardGeometric;
<span class="kw">let </span>expected_mean = <span class="number">1.0</span>;
<span class="kw">let </span>expected_variance = <span class="number">2.0</span>;
<span class="kw">let </span><span class="kw-2">mut </span>results = [<span class="number">0.0</span>; <span class="number">1000</span>];
<span class="kw">for </span>i <span class="kw">in </span>results.iter_mut() {
<span class="kw-2">*</span>i = distr.sample(<span class="kw-2">&amp;mut </span>rng) <span class="kw">as </span>f64;
}
<span class="kw">let </span>mean = results.iter().sum::&lt;f64&gt;() / results.len() <span class="kw">as </span>f64;
<span class="macro">assert!</span>((mean <span class="kw">as </span>f64 - expected_mean).abs() &lt; expected_mean / <span class="number">50.0</span>);
<span class="kw">let </span>variance =
results.iter().map(|x| (x - mean) * (x - mean)).sum::&lt;f64&gt;() / results.len() <span class="kw">as </span>f64;
<span class="macro">assert!</span>((variance - expected_variance).abs() &lt; expected_variance / <span class="number">10.0</span>);
}
}
</code></pre></div>
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