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``````// Copyright 2018 Developers of the Rand project.
//
// option. This file may not be copied, modified, or distributed
// except according to those terms.

//! The Bernoulli distribution `Bernoulli(p)`.

use crate::distr::Distribution;
use crate::Rng;
use core::fmt;

#[cfg(feature = "serde")]
use serde::{Deserialize, Serialize};

/// The [Bernoulli distribution](https://en.wikipedia.org/wiki/Bernoulli_distribution) `Bernoulli(p)`.
///
/// This distribution describes a single boolean random variable, which is true
/// with probability `p` and false with probability `1 - p`.
/// It is a special case of the Binomial distribution with `n = 1`.
///
/// # Plot
///
/// The following plot shows the Bernoulli distribution with `p = 0.1`,
/// `p = 0.5`, and `p = 0.9`.
///
/// ![Bernoulli distribution](https://raw.githubusercontent.com/rust-random/charts/main/charts/bernoulli.svg)
///
/// # Example
///
/// ```rust
/// use rand::distr::{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.
#[derive(Clone, Copy, Debug, PartialEq)]
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
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 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
// 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 = 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;

/// Error type returned from [`Bernoulli::new`].
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum BernoulliError {
/// `p < 0` or `p > 1`.
InvalidProbability,
}

impl fmt::Display for BernoulliError {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
f.write_str(match self {
BernoulliError::InvalidProbability => "p is outside [0, 1] in Bernoulli distribution",
})
}
}

#[cfg(feature = "std")]
impl std::error::Error for BernoulliError {}

impl Bernoulli {
/// 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`.)
#[inline]
pub fn new(p: f64) -> Result<Bernoulli, BernoulliError> {
if !(0.0..1.0).contains(&p) {
if p == 1.0 {
return Ok(Bernoulli { p_int: ALWAYS_TRUE });
}
return Err(BernoulliError::InvalidProbability);
}
Ok(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`.
///
/// 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.
#[inline]
pub fn from_ratio(numerator: u32, denominator: u32) -> Result<Bernoulli, BernoulliError> {
if numerator > denominator || denominator == 0 {
return Err(BernoulliError::InvalidProbability);
}
if numerator == denominator {
return Ok(Bernoulli { p_int: ALWAYS_TRUE });
}
let p_int = ((f64::from(numerator) / f64::from(denominator)) * SCALE) as u64;
Ok(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.random();
v < self.p_int
}
}

#[cfg(test)]
mod test {
use super::Bernoulli;
use crate::distr::Distribution;
use crate::Rng;

#[test]
#[cfg(feature = "serde")]
fn test_serializing_deserializing_bernoulli() {
let coin_flip = Bernoulli::new(0.5).unwrap();
let de_coin_flip: Bernoulli =
bincode::deserialize(&bincode::serialize(&coin_flip).unwrap()).unwrap();

assert_eq!(coin_flip.p_int, de_coin_flip.p_int);
}

#[test]
fn test_trivial() {
// We prefer to be explicit here.
#![allow(clippy::bool_assert_comparison)]

let mut r = crate::test::rng(1);
let always_false = Bernoulli::new(0.0).unwrap();
let always_true = Bernoulli::new(1.0).unwrap();
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]
#[cfg_attr(miri, ignore)] // Miri is too slow
fn test_average() {
const P: f64 = 0.3;
const NUM: u32 = 3;
const DENOM: u32 = 10;
let d1 = Bernoulli::new(P).unwrap();
let d2 = Bernoulli::from_ratio(NUM, DENOM).unwrap();
const N: u32 = 100_000;

let mut sum1: u32 = 0;
let mut sum2: u32 = 0;
let mut rng = crate::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);
}

#[test]
fn value_stability() {
let mut rng = crate::test::rng(3);
let distr = Bernoulli::new(0.4532).unwrap();
let mut buf = [false; 10];
for x in &mut buf {
*x = rng.sample(distr);
}
assert_eq!(
buf,
[true, false, false, true, false, false, true, true, true, true]
);
}

#[test]
fn bernoulli_distributions_can_be_compared() {
assert_eq!(Bernoulli::new(1.0), Bernoulli::new(1.0));
}
}
``````