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| </pre><pre class="rust"><code><span class="comment">// Copyright 2018 Developers of the Rand project. |
| // |
| // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or |
| // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license |
| // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your |
| // option. This file may not be copied, modified, or distributed |
| // except according to those terms. |
| |
| </span><span class="doccomment">//! The Bernoulli distribution. |
| |
| </span><span class="kw">use </span><span class="kw">crate</span>::distributions::Distribution; |
| <span class="kw">use </span><span class="kw">crate</span>::Rng; |
| <span class="kw">use </span>core::{fmt, u64}; |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"serde1"</span>)] |
| </span><span class="kw">use </span>serde::{Serialize, Deserialize}; |
| <span class="doccomment">/// The Bernoulli distribution. |
| /// |
| /// This is a special case of the Binomial distribution where `n = 1`. |
| /// |
| /// # Example |
| /// |
| /// ```rust |
| /// use rand::distributions::{Bernoulli, Distribution}; |
| /// |
| /// let d = Bernoulli::new(0.3).unwrap(); |
| /// let v = d.sample(&mut rand::thread_rng()); |
| /// println!("{} is from a Bernoulli distribution", v); |
| /// ``` |
| /// |
| /// # Precision |
| /// |
| /// This `Bernoulli` distribution uses 64 bits from the RNG (a `u64`), |
| /// so only probabilities that are multiples of 2<sup>-64</sup> can be |
| /// represented. |
| </span><span class="attribute">#[derive(Clone, Copy, Debug, PartialEq)] |
| #[cfg_attr(feature = <span class="string">"serde1"</span>, derive(Serialize, Deserialize))] |
| </span><span class="kw">pub struct </span>Bernoulli { |
| <span class="doccomment">/// Probability of success, relative to the maximal integer. |
| </span>p_int: u64, |
| } |
| |
| <span class="comment">// To sample from the Bernoulli distribution we use a method that compares a |
| // random `u64` value `v < (p * 2^64)`. |
| // |
| // If `p == 1.0`, the integer `v` to compare against can not represented as a |
| // `u64`. We manually set it to `u64::MAX` instead (2^64 - 1 instead of 2^64). |
| // Note that value of `p < 1.0` can never result in `u64::MAX`, because an |
| // `f64` only has 53 bits of precision, and the next largest value of `p` will |
| // result in `2^64 - 2048`. |
| // |
| // Also there is a 100% theoretical concern: if someone consistently wants to |
| // generate `true` using the Bernoulli distribution (i.e. by using a probability |
| // of `1.0`), just using `u64::MAX` is not enough. On average it would return |
| // false once every 2^64 iterations. Some people apparently care about this |
| // case. |
| // |
| // That is why we special-case `u64::MAX` to always return `true`, without using |
| // the RNG, and pay the performance price for all uses that *are* reasonable. |
| // Luckily, if `new()` and `sample` are close, the compiler can optimize out the |
| // extra check. |
| </span><span class="kw">const </span>ALWAYS_TRUE: u64 = u64::MAX; |
| |
| <span class="comment">// This is just `2.0.powi(64)`, but written this way because it is not available |
| // in `no_std` mode. |
| </span><span class="kw">const </span>SCALE: f64 = <span class="number">2.0 </span>* (<span class="number">1u64 </span><< <span class="number">63</span>) <span class="kw">as </span>f64; |
| |
| <span class="doccomment">/// Error type returned from `Bernoulli::new`. |
| </span><span class="attribute">#[derive(Clone, Copy, Debug, PartialEq, Eq)] |
| </span><span class="kw">pub enum </span>BernoulliError { |
| <span class="doccomment">/// `p < 0` or `p > 1`. |
| </span>InvalidProbability, |
| } |
| |
| <span class="kw">impl </span>fmt::Display <span class="kw">for </span>BernoulliError { |
| <span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> fmt::Result { |
| f.write_str(<span class="kw">match </span><span class="self">self </span>{ |
| BernoulliError::InvalidProbability => <span class="string">"p is outside [0, 1] in Bernoulli distribution"</span>, |
| }) |
| } |
| } |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| </span><span class="kw">impl </span>::std::error::Error <span class="kw">for </span>BernoulliError {} |
| |
| <span class="kw">impl </span>Bernoulli { |
| <span class="doccomment">/// Construct a new `Bernoulli` with the given probability of success `p`. |
| /// |
| /// # Precision |
| /// |
| /// For `p = 1.0`, the resulting distribution will always generate true. |
| /// For `p = 0.0`, the resulting distribution will always generate false. |
| /// |
| /// This method is accurate for any input `p` in the range `[0, 1]` which is |
| /// a multiple of 2<sup>-64</sup>. (Note that not all multiples of |
| /// 2<sup>-64</sup> in `[0, 1]` can be represented as a `f64`.) |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>new(p: f64) -> <span class="prelude-ty">Result</span><Bernoulli, BernoulliError> { |
| <span class="kw">if </span>!(<span class="number">0.0</span>..<span class="number">1.0</span>).contains(<span class="kw-2">&</span>p) { |
| <span class="kw">if </span>p == <span class="number">1.0 </span>{ |
| <span class="kw">return </span><span class="prelude-val">Ok</span>(Bernoulli { p_int: ALWAYS_TRUE }); |
| } |
| <span class="kw">return </span><span class="prelude-val">Err</span>(BernoulliError::InvalidProbability); |
| } |
| <span class="prelude-val">Ok</span>(Bernoulli { |
| p_int: (p * SCALE) <span class="kw">as </span>u64, |
| }) |
| } |
| |
| <span class="doccomment">/// Construct a new `Bernoulli` with the probability of success of |
| /// `numerator`-in-`denominator`. I.e. `new_ratio(2, 3)` will return |
| /// a `Bernoulli` with a 2-in-3 chance, or about 67%, of returning `true`. |
| /// |
| /// return `true`. If `numerator == 0` it will always return `false`. |
| /// For `numerator > denominator` and `denominator == 0`, this returns an |
| /// error. Otherwise, for `numerator == denominator`, samples are always |
| /// true; for `numerator == 0` samples are always false. |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>from_ratio(numerator: u32, denominator: u32) -> <span class="prelude-ty">Result</span><Bernoulli, BernoulliError> { |
| <span class="kw">if </span>numerator > denominator || denominator == <span class="number">0 </span>{ |
| <span class="kw">return </span><span class="prelude-val">Err</span>(BernoulliError::InvalidProbability); |
| } |
| <span class="kw">if </span>numerator == denominator { |
| <span class="kw">return </span><span class="prelude-val">Ok</span>(Bernoulli { p_int: ALWAYS_TRUE }); |
| } |
| <span class="kw">let </span>p_int = ((f64::from(numerator) / f64::from(denominator)) * SCALE) <span class="kw">as </span>u64; |
| <span class="prelude-val">Ok</span>(Bernoulli { p_int }) |
| } |
| } |
| |
| <span class="kw">impl </span>Distribution<bool> <span class="kw">for </span>Bernoulli { |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>sample<R: Rng + <span class="question-mark">?</span>Sized>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> bool { |
| <span class="comment">// Make sure to always return true for p = 1.0. |
| </span><span class="kw">if </span><span class="self">self</span>.p_int == ALWAYS_TRUE { |
| <span class="kw">return </span><span class="bool-val">true</span>; |
| } |
| <span class="kw">let </span>v: u64 = rng.gen(); |
| v < <span class="self">self</span>.p_int |
| } |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>test { |
| <span class="kw">use </span><span class="kw">super</span>::Bernoulli; |
| <span class="kw">use </span><span class="kw">crate</span>::distributions::Distribution; |
| <span class="kw">use </span><span class="kw">crate</span>::Rng; |
| |
| <span class="attribute">#[test] |
| #[cfg(feature=<span class="string">"serde1"</span>)] |
| </span><span class="kw">fn </span>test_serializing_deserializing_bernoulli() { |
| <span class="kw">let </span>coin_flip = Bernoulli::new(<span class="number">0.5</span>).unwrap(); |
| <span class="kw">let </span>de_coin_flip : Bernoulli = bincode::deserialize(<span class="kw-2">&</span>bincode::serialize(<span class="kw-2">&</span>coin_flip).unwrap()).unwrap(); |
| |
| <span class="macro">assert_eq!</span>(coin_flip.p_int, de_coin_flip.p_int); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>test_trivial() { |
| <span class="comment">// We prefer to be explicit here. |
| </span><span class="attribute">#![allow(clippy::bool_assert_comparison)] |
| |
| </span><span class="kw">let </span><span class="kw-2">mut </span>r = <span class="kw">crate</span>::test::rng(<span class="number">1</span>); |
| <span class="kw">let </span>always_false = Bernoulli::new(<span class="number">0.0</span>).unwrap(); |
| <span class="kw">let </span>always_true = Bernoulli::new(<span class="number">1.0</span>).unwrap(); |
| <span class="kw">for _ in </span><span class="number">0</span>..<span class="number">5 </span>{ |
| <span class="macro">assert_eq!</span>(r.sample::<bool, <span class="kw">_</span>>(<span class="kw-2">&</span>always_false), <span class="bool-val">false</span>); |
| <span class="macro">assert_eq!</span>(r.sample::<bool, <span class="kw">_</span>>(<span class="kw-2">&</span>always_true), <span class="bool-val">true</span>); |
| <span class="macro">assert_eq!</span>(Distribution::<bool>::sample(<span class="kw-2">&</span>always_false, <span class="kw-2">&mut </span>r), <span class="bool-val">false</span>); |
| <span class="macro">assert_eq!</span>(Distribution::<bool>::sample(<span class="kw-2">&</span>always_true, <span class="kw-2">&mut </span>r), <span class="bool-val">true</span>); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| #[cfg_attr(miri, ignore)] </span><span class="comment">// Miri is too slow |
| </span><span class="kw">fn </span>test_average() { |
| <span class="kw">const </span>P: f64 = <span class="number">0.3</span>; |
| <span class="kw">const </span>NUM: u32 = <span class="number">3</span>; |
| <span class="kw">const </span>DENOM: u32 = <span class="number">10</span>; |
| <span class="kw">let </span>d1 = Bernoulli::new(P).unwrap(); |
| <span class="kw">let </span>d2 = Bernoulli::from_ratio(NUM, DENOM).unwrap(); |
| <span class="kw">const </span>N: u32 = <span class="number">100_000</span>; |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>sum1: u32 = <span class="number">0</span>; |
| <span class="kw">let </span><span class="kw-2">mut </span>sum2: u32 = <span class="number">0</span>; |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">2</span>); |
| <span class="kw">for _ in </span><span class="number">0</span>..N { |
| <span class="kw">if </span>d1.sample(<span class="kw-2">&mut </span>rng) { |
| sum1 += <span class="number">1</span>; |
| } |
| <span class="kw">if </span>d2.sample(<span class="kw-2">&mut </span>rng) { |
| sum2 += <span class="number">1</span>; |
| } |
| } |
| <span class="kw">let </span>avg1 = (sum1 <span class="kw">as </span>f64) / (N <span class="kw">as </span>f64); |
| <span class="macro">assert!</span>((avg1 - P).abs() < <span class="number">5e-3</span>); |
| |
| <span class="kw">let </span>avg2 = (sum2 <span class="kw">as </span>f64) / (N <span class="kw">as </span>f64); |
| <span class="macro">assert!</span>((avg2 - (NUM <span class="kw">as </span>f64) / (DENOM <span class="kw">as </span>f64)).abs() < <span class="number">5e-3</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>value_stability() { |
| <span class="kw">let </span><span class="kw-2">mut </span>rng = <span class="kw">crate</span>::test::rng(<span class="number">3</span>); |
| <span class="kw">let </span>distr = Bernoulli::new(<span class="number">0.4532</span>).unwrap(); |
| <span class="kw">let </span><span class="kw-2">mut </span>buf = [<span class="bool-val">false</span>; <span class="number">10</span>]; |
| <span class="kw">for </span>x <span class="kw">in </span><span class="kw-2">&mut </span>buf { |
| <span class="kw-2">*</span>x = rng.sample(<span class="kw-2">&</span>distr); |
| } |
| <span class="macro">assert_eq!</span>(buf, [ |
| <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>]); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>bernoulli_distributions_can_be_compared() { |
| <span class="macro">assert_eq!</span>(Bernoulli::new(<span class="number">1.0</span>), Bernoulli::new(<span class="number">1.0</span>)); |
| } |
| } |
| </code></pre></div> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-current-crate="rand" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |
