diff options
Diffstat (limited to 'rand/src/distributions/bernoulli.rs')
| -rw-r--r-- | rand/src/distributions/bernoulli.rs | 165 |
1 files changed, 165 insertions, 0 deletions
diff --git a/rand/src/distributions/bernoulli.rs b/rand/src/distributions/bernoulli.rs new file mode 100644 index 0000000..f49618c --- /dev/null +++ b/rand/src/distributions/bernoulli.rs @@ -0,0 +1,165 @@ +// 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. + +//! The Bernoulli distribution. + +use Rng; +use distributions::Distribution; + +/// 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); +/// 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. +#[derive(Clone, Copy, Debug)] +pub struct Bernoulli { + /// Probability of success, relative to the maximal integer. + p_int: u64, +} + +// 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 consistenly 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. +const ALWAYS_TRUE: u64 = ::core::u64::MAX; + +// This is just `2.0.powi(64)`, but written this way because it is not available +// in `no_std` mode. +const SCALE: f64 = 2.0 * (1u64 << 63) as f64; + +impl Bernoulli { + /// Construct a new `Bernoulli` with the given probability of success `p`. + /// + /// # Panics + /// + /// If `p < 0` or `p > 1`. + /// + /// # 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`.) + #[inline] + pub fn new(p: f64) -> Bernoulli { + if p < 0.0 || p >= 1.0 { + if p == 1.0 { return Bernoulli { p_int: ALWAYS_TRUE } } + panic!("Bernoulli::new not called with 0.0 <= p <= 1.0"); + } + Bernoulli { p_int: (p * SCALE) as u64 } + } + + /// 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`. + /// + /// If `numerator == denominator` then the returned `Bernoulli` will always + /// return `true`. If `numerator == 0` it will always return `false`. + /// + /// # Panics + /// + /// If `denominator == 0` or `numerator > denominator`. + /// + #[inline] + pub fn from_ratio(numerator: u32, denominator: u32) -> Bernoulli { + assert!(numerator <= denominator); + if numerator == denominator { + return Bernoulli { p_int: ::core::u64::MAX } + } + let p_int = ((numerator as f64 / denominator as f64) * SCALE) as u64; + Bernoulli { p_int } + } +} + +impl Distribution<bool> for Bernoulli { + #[inline] + fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> bool { + // Make sure to always return true for p = 1.0. + if self.p_int == ALWAYS_TRUE { return true; } + let v: u64 = rng.gen(); + v < self.p_int + } +} + +#[cfg(test)] +mod test { + use Rng; + use distributions::Distribution; + use super::Bernoulli; + + #[test] + fn test_trivial() { + let mut r = ::test::rng(1); + let always_false = Bernoulli::new(0.0); + let always_true = Bernoulli::new(1.0); + for _ in 0..5 { + assert_eq!(r.sample::<bool, _>(&always_false), false); + assert_eq!(r.sample::<bool, _>(&always_true), true); + assert_eq!(Distribution::<bool>::sample(&always_false, &mut r), false); + assert_eq!(Distribution::<bool>::sample(&always_true, &mut r), true); + } + } + + #[test] + fn test_average() { + const P: f64 = 0.3; + const NUM: u32 = 3; + const DENOM: u32 = 10; + let d1 = Bernoulli::new(P); + let d2 = Bernoulli::from_ratio(NUM, DENOM); + const N: u32 = 100_000; + + let mut sum1: u32 = 0; + let mut sum2: u32 = 0; + let mut rng = ::test::rng(2); + for _ in 0..N { + if d1.sample(&mut rng) { + sum1 += 1; + } + if d2.sample(&mut rng) { + sum2 += 1; + } + } + let avg1 = (sum1 as f64) / (N as f64); + assert!((avg1 - P).abs() < 5e-3); + + let avg2 = (sum2 as f64) / (N as f64); + assert!((avg2 - (NUM as f64)/(DENOM as f64)).abs() < 5e-3); + } +} |