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</pre><pre class="rust"><code><span class="comment">// Copyright 2018 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="doccomment">//! The Bernoulli distribution.</span>
<span class="kw">use</span> <span class="ident"><span class="kw">crate</span>::distributions::Distribution</span>;
<span class="kw">use</span> <span class="ident"><span class="kw">crate</span>::Rng</span>;
<span class="kw">use</span> <span class="ident">core</span>::{<span class="ident">fmt</span>, <span class="ident">u64</span>};
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>)]</span>
<span class="kw">use</span> <span class="ident">serde</span>::{<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>};
<span class="doccomment">/// The Bernoulli distribution.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This is a special case of the Binomial distribution where `n = 1`.</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::{Bernoulli, Distribution};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let d = Bernoulli::new(0.3).unwrap();</span>
<span class="doccomment">/// let v = d.sample(&amp;mut rand::thread_rng());</span>
<span class="doccomment">/// println!(&quot;{} is from a Bernoulli distribution&quot;, v);</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Precision</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This `Bernoulli` distribution uses 64 bits from the RNG (a `u64`),</span>
<span class="doccomment">/// so only probabilities that are multiples of 2&lt;sup&gt;-64&lt;/sup&gt; can be</span>
<span class="doccomment">/// represented.</span>
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span>
<span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
<span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">Bernoulli</span> {
<span class="doccomment">/// Probability of success, relative to the maximal integer.</span>
<span class="ident">p_int</span>: <span class="ident">u64</span>,
}
<span class="comment">// To sample from the Bernoulli distribution we use a method that compares a</span>
<span class="comment">// random `u64` value `v &lt; (p * 2^64)`.</span>
<span class="comment">//</span>
<span class="comment">// If `p == 1.0`, the integer `v` to compare against can not represented as a</span>
<span class="comment">// `u64`. We manually set it to `u64::MAX` instead (2^64 - 1 instead of 2^64).</span>
<span class="comment">// Note that value of `p &lt; 1.0` can never result in `u64::MAX`, because an</span>
<span class="comment">// `f64` only has 53 bits of precision, and the next largest value of `p` will</span>
<span class="comment">// result in `2^64 - 2048`.</span>
<span class="comment">//</span>
<span class="comment">// Also there is a 100% theoretical concern: if someone consistently wants to</span>
<span class="comment">// generate `true` using the Bernoulli distribution (i.e. by using a probability</span>
<span class="comment">// of `1.0`), just using `u64::MAX` is not enough. On average it would return</span>
<span class="comment">// false once every 2^64 iterations. Some people apparently care about this</span>
<span class="comment">// case.</span>
<span class="comment">//</span>
<span class="comment">// That is why we special-case `u64::MAX` to always return `true`, without using</span>
<span class="comment">// the RNG, and pay the performance price for all uses that *are* reasonable.</span>
<span class="comment">// Luckily, if `new()` and `sample` are close, the compiler can optimize out the</span>
<span class="comment">// extra check.</span>
<span class="kw">const</span> <span class="ident">ALWAYS_TRUE</span>: <span class="ident">u64</span> <span class="op">=</span> <span class="ident">u64::MAX</span>;
<span class="comment">// This is just `2.0.powi(64)`, but written this way because it is not available</span>
<span class="comment">// in `no_std` mode.</span>
<span class="kw">const</span> <span class="ident">SCALE</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.0</span> <span class="op">*</span> (<span class="number">1u64</span> <span class="op">&lt;</span><span class="op">&lt;</span> <span class="number">63</span>) <span class="kw">as</span> <span class="ident">f64</span>;
<span class="doccomment">/// Error type returned from `Bernoulli::new`.</span>
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>, <span class="ident">PartialEq</span>, <span class="ident">Eq</span>)]</span>
<span class="kw">pub</span> <span class="kw">enum</span> <span class="ident">BernoulliError</span> {
<span class="doccomment">/// `p &lt; 0` or `p &gt; 1`.</span>
<span class="ident">InvalidProbability</span>,
}
<span class="kw">impl</span> <span class="ident">fmt::Display</span> <span class="kw">for</span> <span class="ident">BernoulliError</span> {
<span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&amp;mut</span> <span class="ident">fmt::Formatter</span><span class="op">&lt;</span><span class="lifetime">&#39;_</span><span class="op">&gt;</span>) -&gt; <span class="ident">fmt::Result</span> {
<span class="ident">f</span>.<span class="ident">write_str</span>(<span class="kw">match</span> <span class="self">self</span> {
<span class="ident">BernoulliError::InvalidProbability</span> =&gt; <span class="string">&quot;p is outside [0, 1] in Bernoulli distribution&quot;</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">impl</span> <span class="ident">::std::error::Error</span> <span class="kw">for</span> <span class="ident">BernoulliError</span> {}
<span class="kw">impl</span> <span class="ident">Bernoulli</span> {
<span class="doccomment">/// Construct a new `Bernoulli` with the given probability of success `p`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Precision</span>
<span class="doccomment">///</span>
<span class="doccomment">/// For `p = 1.0`, the resulting distribution will always generate true.</span>
<span class="doccomment">/// For `p = 0.0`, the resulting distribution will always generate false.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This method is accurate for any input `p` in the range `[0, 1]` which is</span>
<span class="doccomment">/// a multiple of 2&lt;sup&gt;-64&lt;/sup&gt;. (Note that not all multiples of</span>
<span class="doccomment">/// 2&lt;sup&gt;-64&lt;/sup&gt; in `[0, 1]` can be represented as a `f64`.)</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">p</span>: <span class="ident">f64</span>) -&gt; <span class="prelude-ty">Result</span><span class="op">&lt;</span><span class="ident">Bernoulli</span>, <span class="ident">BernoulliError</span><span class="op">&gt;</span> {
<span class="kw">if</span> <span class="op">!</span>(<span class="number">0.0</span>..<span class="number">1.0</span>).<span class="ident">contains</span>(<span class="kw-2">&amp;</span><span class="ident">p</span>) {
<span class="kw">if</span> <span class="ident">p</span> <span class="op">==</span> <span class="number">1.0</span> {
<span class="kw">return</span> <span class="prelude-val">Ok</span>(<span class="ident">Bernoulli</span> { <span class="ident">p_int</span>: <span class="ident">ALWAYS_TRUE</span> });
}
<span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">BernoulliError::InvalidProbability</span>);
}
<span class="prelude-val">Ok</span>(<span class="ident">Bernoulli</span> {
<span class="ident">p_int</span>: (<span class="ident">p</span> <span class="op">*</span> <span class="ident">SCALE</span>) <span class="kw">as</span> <span class="ident">u64</span>,
})
}
<span class="doccomment">/// Construct a new `Bernoulli` with the probability of success of</span>
<span class="doccomment">/// `numerator`-in-`denominator`. I.e. `new_ratio(2, 3)` will return</span>
<span class="doccomment">/// a `Bernoulli` with a 2-in-3 chance, or about 67%, of returning `true`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// return `true`. If `numerator == 0` it will always return `false`.</span>
<span class="doccomment">/// For `numerator &gt; denominator` and `denominator == 0`, this returns an</span>
<span class="doccomment">/// error. Otherwise, for `numerator == denominator`, samples are always</span>
<span class="doccomment">/// true; for `numerator == 0` samples are always false.</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">from_ratio</span>(<span class="ident">numerator</span>: <span class="ident">u32</span>, <span class="ident">denominator</span>: <span class="ident">u32</span>) -&gt; <span class="prelude-ty">Result</span><span class="op">&lt;</span><span class="ident">Bernoulli</span>, <span class="ident">BernoulliError</span><span class="op">&gt;</span> {
<span class="kw">if</span> <span class="ident">numerator</span> <span class="op">&gt;</span> <span class="ident">denominator</span> <span class="op">|</span><span class="op">|</span> <span class="ident">denominator</span> <span class="op">==</span> <span class="number">0</span> {
<span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">BernoulliError::InvalidProbability</span>);
}
<span class="kw">if</span> <span class="ident">numerator</span> <span class="op">==</span> <span class="ident">denominator</span> {
<span class="kw">return</span> <span class="prelude-val">Ok</span>(<span class="ident">Bernoulli</span> { <span class="ident">p_int</span>: <span class="ident">ALWAYS_TRUE</span> });
}
<span class="kw">let</span> <span class="ident">p_int</span> <span class="op">=</span> ((<span class="ident">f64::from</span>(<span class="ident">numerator</span>) <span class="op">/</span> <span class="ident">f64::from</span>(<span class="ident">denominator</span>)) <span class="op">*</span> <span class="ident">SCALE</span>) <span class="kw">as</span> <span class="ident">u64</span>;
<span class="prelude-val">Ok</span>(<span class="ident">Bernoulli</span> { <span class="ident">p_int</span> })
}
}
<span class="kw">impl</span> <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">bool</span><span class="op">&gt;</span> <span class="kw">for</span> <span class="ident">Bernoulli</span> {
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="kw">fn</span> <span class="ident">sample</span><span class="op">&lt;</span><span class="ident">R</span>: <span class="ident">Rng</span> <span class="op">+</span> <span class="question-mark">?</span><span class="ident">Sized</span><span class="op">&gt;</span>(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&amp;mut</span> <span class="ident">R</span>) -&gt; <span class="ident">bool</span> {
<span class="comment">// Make sure to always return true for p = 1.0.</span>
<span class="kw">if</span> <span class="self">self</span>.<span class="ident">p_int</span> <span class="op">==</span> <span class="ident">ALWAYS_TRUE</span> {
<span class="kw">return</span> <span class="bool-val">true</span>;
}
<span class="kw">let</span> <span class="ident">v</span>: <span class="ident">u64</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">gen</span>();
<span class="ident">v</span> <span class="op">&lt;</span> <span class="self">self</span>.<span class="ident">p_int</span>
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span>
<span class="kw">mod</span> <span class="ident">test</span> {
<span class="kw">use</span> <span class="ident"><span class="kw">super</span>::Bernoulli</span>;
<span class="kw">use</span> <span class="ident"><span class="kw">crate</span>::distributions::Distribution</span>;
<span class="kw">use</span> <span class="ident"><span class="kw">crate</span>::Rng</span>;
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span><span class="op">=</span><span class="string">&quot;serde1&quot;</span>)]</span>
<span class="kw">fn</span> <span class="ident">test_serializing_deserializing_bernoulli</span>() {
<span class="kw">let</span> <span class="ident">coin_flip</span> <span class="op">=</span> <span class="ident">Bernoulli::new</span>(<span class="number">0.5</span>).<span class="ident">unwrap</span>();
<span class="kw">let</span> <span class="ident">de_coin_flip</span> : <span class="ident">Bernoulli</span> <span class="op">=</span> <span class="ident">bincode::deserialize</span>(<span class="kw-2">&amp;</span><span class="ident">bincode::serialize</span>(<span class="kw-2">&amp;</span><span class="ident">coin_flip</span>).<span class="ident">unwrap</span>()).<span class="ident">unwrap</span>();
<span class="macro">assert_eq!</span>(<span class="ident">coin_flip</span>.<span class="ident">p_int</span>, <span class="ident">de_coin_flip</span>.<span class="ident">p_int</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_trivial</span>() {
<span class="comment">// We prefer to be explicit here.</span>
<span class="attribute">#![<span class="ident">allow</span>(<span class="ident">clippy::bool_assert_comparison</span>)]</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">r</span> <span class="op">=</span> <span class="ident"><span class="kw">crate</span>::test::rng</span>(<span class="number">1</span>);
<span class="kw">let</span> <span class="ident">always_false</span> <span class="op">=</span> <span class="ident">Bernoulli::new</span>(<span class="number">0.0</span>).<span class="ident">unwrap</span>();
<span class="kw">let</span> <span class="ident">always_true</span> <span class="op">=</span> <span class="ident">Bernoulli::new</span>(<span class="number">1.0</span>).<span class="ident">unwrap</span>();
<span class="kw">for</span> <span class="kw">_</span> <span class="kw">in</span> <span class="number">0</span>..<span class="number">5</span> {
<span class="macro">assert_eq!</span>(<span class="ident">r</span>.<span class="ident">sample</span>::<span class="op">&lt;</span><span class="ident">bool</span>, <span class="kw">_</span><span class="op">&gt;</span>(<span class="kw-2">&amp;</span><span class="ident">always_false</span>), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>(<span class="ident">r</span>.<span class="ident">sample</span>::<span class="op">&lt;</span><span class="ident">bool</span>, <span class="kw">_</span><span class="op">&gt;</span>(<span class="kw-2">&amp;</span><span class="ident">always_true</span>), <span class="bool-val">true</span>);
<span class="macro">assert_eq!</span>(<span class="ident">Distribution</span>::<span class="op">&lt;</span><span class="ident">bool</span><span class="op">&gt;</span><span class="ident">::sample</span>(<span class="kw-2">&amp;</span><span class="ident">always_false</span>, <span class="kw-2">&amp;mut</span> <span class="ident">r</span>), <span class="bool-val">false</span>);
<span class="macro">assert_eq!</span>(<span class="ident">Distribution</span>::<span class="op">&lt;</span><span class="ident">bool</span><span class="op">&gt;</span><span class="ident">::sample</span>(<span class="kw-2">&amp;</span><span class="ident">always_true</span>, <span class="kw-2">&amp;mut</span> <span class="ident">r</span>), <span class="bool-val">true</span>);
}
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">miri</span>, <span class="ident">ignore</span>)]</span> <span class="comment">// Miri is too slow</span>
<span class="kw">fn</span> <span class="ident">test_average</span>() {
<span class="kw">const</span> <span class="ident">P</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">0.3</span>;
<span class="kw">const</span> <span class="ident">NUM</span>: <span class="ident">u32</span> <span class="op">=</span> <span class="number">3</span>;
<span class="kw">const</span> <span class="ident">DENOM</span>: <span class="ident">u32</span> <span class="op">=</span> <span class="number">10</span>;
<span class="kw">let</span> <span class="ident">d1</span> <span class="op">=</span> <span class="ident">Bernoulli::new</span>(<span class="ident">P</span>).<span class="ident">unwrap</span>();
<span class="kw">let</span> <span class="ident">d2</span> <span class="op">=</span> <span class="ident">Bernoulli::from_ratio</span>(<span class="ident">NUM</span>, <span class="ident">DENOM</span>).<span class="ident">unwrap</span>();
<span class="kw">const</span> <span class="ident">N</span>: <span class="ident">u32</span> <span class="op">=</span> <span class="number">100_000</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">sum1</span>: <span class="ident">u32</span> <span class="op">=</span> <span class="number">0</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">sum2</span>: <span class="ident">u32</span> <span class="op">=</span> <span class="number">0</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> <span class="ident"><span class="kw">crate</span>::test::rng</span>(<span class="number">2</span>);
<span class="kw">for</span> <span class="kw">_</span> <span class="kw">in</span> <span class="number">0</span>..<span class="ident">N</span> {
<span class="kw">if</span> <span class="ident">d1</span>.<span class="ident">sample</span>(<span class="kw-2">&amp;mut</span> <span class="ident">rng</span>) {
<span class="ident">sum1</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>;
}
<span class="kw">if</span> <span class="ident">d2</span>.<span class="ident">sample</span>(<span class="kw-2">&amp;mut</span> <span class="ident">rng</span>) {
<span class="ident">sum2</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>;
}
}
<span class="kw">let</span> <span class="ident">avg1</span> <span class="op">=</span> (<span class="ident">sum1</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">/</span> (<span class="ident">N</span> <span class="kw">as</span> <span class="ident">f64</span>);
<span class="macro">assert!</span>((<span class="ident">avg1</span> <span class="op">-</span> <span class="ident">P</span>).<span class="ident">abs</span>() <span class="op">&lt;</span> <span class="number">5e-3</span>);
<span class="kw">let</span> <span class="ident">avg2</span> <span class="op">=</span> (<span class="ident">sum2</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">/</span> (<span class="ident">N</span> <span class="kw">as</span> <span class="ident">f64</span>);
<span class="macro">assert!</span>((<span class="ident">avg2</span> <span class="op">-</span> (<span class="ident">NUM</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">/</span> (<span class="ident">DENOM</span> <span class="kw">as</span> <span class="ident">f64</span>)).<span class="ident">abs</span>() <span class="op">&lt;</span> <span class="number">5e-3</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">value_stability</span>() {
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> <span class="ident"><span class="kw">crate</span>::test::rng</span>(<span class="number">3</span>);
<span class="kw">let</span> <span class="ident">distr</span> <span class="op">=</span> <span class="ident">Bernoulli::new</span>(<span class="number">0.4532</span>).<span class="ident">unwrap</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">buf</span> <span class="op">=</span> [<span class="bool-val">false</span>; <span class="number">10</span>];
<span class="kw">for</span> <span class="ident">x</span> <span class="kw">in</span> <span class="kw-2">&amp;mut</span> <span class="ident">buf</span> {
<span class="kw-2">*</span><span class="ident">x</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">sample</span>(<span class="kw-2">&amp;</span><span class="ident">distr</span>);
}
<span class="macro">assert_eq!</span>(<span class="ident">buf</span>, [
<span class="bool-val">true</span>, <span class="bool-val">false</span>, <span class="bool-val">false</span>, <span class="bool-val">true</span>, <span class="bool-val">false</span>, <span class="bool-val">false</span>, <span class="bool-val">true</span>, <span class="bool-val">true</span>, <span class="bool-val">true</span>, <span class="bool-val">true</span>
]);
}
}
</code></pre></div>
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