Import rand-0.7.3
Change-Id: Ib8c6100a9c5f516a04a5c045c6303942cd6db316
diff --git a/src/distributions/bernoulli.rs b/src/distributions/bernoulli.rs
new file mode 100644
index 0000000..a1fa86e
--- /dev/null
+++ b/src/distributions/bernoulli.rs
@@ -0,0 +1,199 @@
+// 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 crate::distributions::Distribution;
+use crate::Rng;
+use core::{fmt, u64};
+
+/// 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.
+#[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 = 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 !(p >= 0.0 && p < 1.0) {
+ 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.gen();
+ v < self.p_int
+ }
+}
+
+#[cfg(test)]
+mod test {
+ use super::Bernoulli;
+ use crate::distributions::Distribution;
+ use crate::Rng;
+
+ #[test]
+ fn test_trivial() {
+ 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
+ ]);
+ }
+}
diff --git a/src/distributions/binomial.rs b/src/distributions/binomial.rs
new file mode 100644
index 0000000..c096e4a
--- /dev/null
+++ b/src/distributions/binomial.rs
@@ -0,0 +1,321 @@
+// Copyright 2018 Developers of the Rand project.
+// Copyright 2016-2017 The Rust Project Developers.
+//
+// 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 binomial distribution.
+#![allow(deprecated)]
+#![allow(clippy::all)]
+
+use crate::distributions::{Distribution, Uniform};
+use crate::Rng;
+
+/// The binomial distribution `Binomial(n, p)`.
+///
+/// This distribution has density function:
+/// `f(k) = n!/(k! (n-k)!) p^k (1-p)^(n-k)` for `k >= 0`.
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct Binomial {
+ /// Number of trials.
+ n: u64,
+ /// Probability of success.
+ p: f64,
+}
+
+impl Binomial {
+ /// Construct a new `Binomial` with the given shape parameters `n` (number
+ /// of trials) and `p` (probability of success).
+ ///
+ /// Panics if `p < 0` or `p > 1`.
+ pub fn new(n: u64, p: f64) -> Binomial {
+ assert!(p >= 0.0, "Binomial::new called with p < 0");
+ assert!(p <= 1.0, "Binomial::new called with p > 1");
+ Binomial { n, p }
+ }
+}
+
+/// Convert a `f64` to an `i64`, panicing on overflow.
+// In the future (Rust 1.34), this might be replaced with `TryFrom`.
+fn f64_to_i64(x: f64) -> i64 {
+ assert!(x < (::std::i64::MAX as f64));
+ x as i64
+}
+
+impl Distribution<u64> for Binomial {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
+ // Handle these values directly.
+ if self.p == 0.0 {
+ return 0;
+ } else if self.p == 1.0 {
+ return self.n;
+ }
+
+ // The binomial distribution is symmetrical with respect to p -> 1-p,
+ // k -> n-k switch p so that it is less than 0.5 - this allows for lower
+ // expected values we will just invert the result at the end
+ let p = if self.p <= 0.5 { self.p } else { 1.0 - self.p };
+
+ let result;
+ let q = 1. - p;
+
+ // For small n * min(p, 1 - p), the BINV algorithm based on the inverse
+ // transformation of the binomial distribution is efficient. Otherwise,
+ // the BTPE algorithm is used.
+ //
+ // Voratas Kachitvichyanukul and Bruce W. Schmeiser. 1988. Binomial
+ // random variate generation. Commun. ACM 31, 2 (February 1988),
+ // 216-222. http://dx.doi.org/10.1145/42372.42381
+
+ // Threshold for prefering the BINV algorithm. The paper suggests 10,
+ // Ranlib uses 30, and GSL uses 14.
+ const BINV_THRESHOLD: f64 = 10.;
+
+ if (self.n as f64) * p < BINV_THRESHOLD && self.n <= (::std::i32::MAX as u64) {
+ // Use the BINV algorithm.
+ let s = p / q;
+ let a = ((self.n + 1) as f64) * s;
+ let mut r = q.powi(self.n as i32);
+ let mut u: f64 = rng.gen();
+ let mut x = 0;
+ while u > r as f64 {
+ u -= r;
+ x += 1;
+ r *= a / (x as f64) - s;
+ }
+ result = x;
+ } else {
+ // Use the BTPE algorithm.
+
+ // Threshold for using the squeeze algorithm. This can be freely
+ // chosen based on performance. Ranlib and GSL use 20.
+ const SQUEEZE_THRESHOLD: i64 = 20;
+
+ // Step 0: Calculate constants as functions of `n` and `p`.
+ let n = self.n as f64;
+ let np = n * p;
+ let npq = np * q;
+ let f_m = np + p;
+ let m = f64_to_i64(f_m);
+ // radius of triangle region, since height=1 also area of region
+ let p1 = (2.195 * npq.sqrt() - 4.6 * q).floor() + 0.5;
+ // tip of triangle
+ let x_m = (m as f64) + 0.5;
+ // left edge of triangle
+ let x_l = x_m - p1;
+ // right edge of triangle
+ let x_r = x_m + p1;
+ let c = 0.134 + 20.5 / (15.3 + (m as f64));
+ // p1 + area of parallelogram region
+ let p2 = p1 * (1. + 2. * c);
+
+ fn lambda(a: f64) -> f64 {
+ a * (1. + 0.5 * a)
+ }
+
+ let lambda_l = lambda((f_m - x_l) / (f_m - x_l * p));
+ let lambda_r = lambda((x_r - f_m) / (x_r * q));
+ // p1 + area of left tail
+ let p3 = p2 + c / lambda_l;
+ // p1 + area of right tail
+ let p4 = p3 + c / lambda_r;
+
+ // return value
+ let mut y: i64;
+
+ let gen_u = Uniform::new(0., p4);
+ let gen_v = Uniform::new(0., 1.);
+
+ loop {
+ // Step 1: Generate `u` for selecting the region. If region 1 is
+ // selected, generate a triangularly distributed variate.
+ let u = gen_u.sample(rng);
+ let mut v = gen_v.sample(rng);
+ if !(u > p1) {
+ y = f64_to_i64(x_m - p1 * v + u);
+ break;
+ }
+
+ if !(u > p2) {
+ // Step 2: Region 2, parallelograms. Check if region 2 is
+ // used. If so, generate `y`.
+ let x = x_l + (u - p1) / c;
+ v = v * c + 1.0 - (x - x_m).abs() / p1;
+ if v > 1. {
+ continue;
+ } else {
+ y = f64_to_i64(x);
+ }
+ } else if !(u > p3) {
+ // Step 3: Region 3, left exponential tail.
+ y = f64_to_i64(x_l + v.ln() / lambda_l);
+ if y < 0 {
+ continue;
+ } else {
+ v *= (u - p2) * lambda_l;
+ }
+ } else {
+ // Step 4: Region 4, right exponential tail.
+ y = f64_to_i64(x_r - v.ln() / lambda_r);
+ if y > 0 && (y as u64) > self.n {
+ continue;
+ } else {
+ v *= (u - p3) * lambda_r;
+ }
+ }
+
+ // Step 5: Acceptance/rejection comparison.
+
+ // Step 5.0: Test for appropriate method of evaluating f(y).
+ let k = (y - m).abs();
+ if !(k > SQUEEZE_THRESHOLD && (k as f64) < 0.5 * npq - 1.) {
+ // Step 5.1: Evaluate f(y) via the recursive relationship. Start the
+ // search from the mode.
+ let s = p / q;
+ let a = s * (n + 1.);
+ let mut f = 1.0;
+ if m < y {
+ let mut i = m;
+ loop {
+ i += 1;
+ f *= a / (i as f64) - s;
+ if i == y {
+ break;
+ }
+ }
+ } else if m > y {
+ let mut i = y;
+ loop {
+ i += 1;
+ f /= a / (i as f64) - s;
+ if i == m {
+ break;
+ }
+ }
+ }
+ if v > f {
+ continue;
+ } else {
+ break;
+ }
+ }
+
+ // Step 5.2: Squeezing. Check the value of ln(v) againts upper and
+ // lower bound of ln(f(y)).
+ let k = k as f64;
+ let rho = (k / npq) * ((k * (k / 3. + 0.625) + 1. / 6.) / npq + 0.5);
+ let t = -0.5 * k * k / npq;
+ let alpha = v.ln();
+ if alpha < t - rho {
+ break;
+ }
+ if alpha > t + rho {
+ continue;
+ }
+
+ // Step 5.3: Final acceptance/rejection test.
+ let x1 = (y + 1) as f64;
+ let f1 = (m + 1) as f64;
+ let z = (f64_to_i64(n) + 1 - m) as f64;
+ let w = (f64_to_i64(n) - y + 1) as f64;
+
+ fn stirling(a: f64) -> f64 {
+ let a2 = a * a;
+ (13860. - (462. - (132. - (99. - 140. / a2) / a2) / a2) / a2) / a / 166320.
+ }
+
+ if alpha
+ > x_m * (f1 / x1).ln()
+ + (n - (m as f64) + 0.5) * (z / w).ln()
+ + ((y - m) as f64) * (w * p / (x1 * q)).ln()
+ // We use the signs from the GSL implementation, which are
+ // different than the ones in the reference. According to
+ // the GSL authors, the new signs were verified to be
+ // correct by one of the original designers of the
+ // algorithm.
+ + stirling(f1)
+ + stirling(z)
+ - stirling(x1)
+ - stirling(w)
+ {
+ continue;
+ }
+
+ break;
+ }
+ assert!(y >= 0);
+ result = y as u64;
+ }
+
+ // Invert the result for p < 0.5.
+ if p != self.p {
+ self.n - result
+ } else {
+ result
+ }
+ }
+}
+
+#[cfg(test)]
+mod test {
+ use super::Binomial;
+ use crate::distributions::Distribution;
+ use crate::Rng;
+
+ fn test_binomial_mean_and_variance<R: Rng>(n: u64, p: f64, rng: &mut R) {
+ let binomial = Binomial::new(n, p);
+
+ let expected_mean = n as f64 * p;
+ let expected_variance = n as f64 * p * (1.0 - p);
+
+ let mut results = [0.0; 1000];
+ for i in results.iter_mut() {
+ *i = binomial.sample(rng) as f64;
+ }
+
+ let mean = results.iter().sum::<f64>() / results.len() as f64;
+ assert!(
+ (mean as f64 - expected_mean).abs() < expected_mean / 50.0,
+ "mean: {}, expected_mean: {}",
+ mean,
+ expected_mean
+ );
+
+ let variance =
+ results.iter().map(|x| (x - mean) * (x - mean)).sum::<f64>() / results.len() as f64;
+ assert!(
+ (variance - expected_variance).abs() < expected_variance / 10.0,
+ "variance: {}, expected_variance: {}",
+ variance,
+ expected_variance
+ );
+ }
+
+ #[test]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_binomial() {
+ let mut rng = crate::test::rng(351);
+ test_binomial_mean_and_variance(150, 0.1, &mut rng);
+ test_binomial_mean_and_variance(70, 0.6, &mut rng);
+ test_binomial_mean_and_variance(40, 0.5, &mut rng);
+ test_binomial_mean_and_variance(20, 0.7, &mut rng);
+ test_binomial_mean_and_variance(20, 0.5, &mut rng);
+ }
+
+ #[test]
+ fn test_binomial_end_points() {
+ let mut rng = crate::test::rng(352);
+ assert_eq!(rng.sample(Binomial::new(20, 0.0)), 0);
+ assert_eq!(rng.sample(Binomial::new(20, 1.0)), 20);
+ }
+
+ #[test]
+ #[should_panic]
+ fn test_binomial_invalid_lambda_neg() {
+ Binomial::new(20, -10.0);
+ }
+}
diff --git a/src/distributions/cauchy.rs b/src/distributions/cauchy.rs
new file mode 100644
index 0000000..dc54c98
--- /dev/null
+++ b/src/distributions/cauchy.rs
@@ -0,0 +1,99 @@
+// Copyright 2018 Developers of the Rand project.
+// Copyright 2016-2017 The Rust Project Developers.
+//
+// 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 Cauchy distribution.
+#![allow(deprecated)]
+#![allow(clippy::all)]
+
+use crate::distributions::Distribution;
+use crate::Rng;
+use std::f64::consts::PI;
+
+/// The Cauchy distribution `Cauchy(median, scale)`.
+///
+/// This distribution has a density function:
+/// `f(x) = 1 / (pi * scale * (1 + ((x - median) / scale)^2))`
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct Cauchy {
+ median: f64,
+ scale: f64,
+}
+
+impl Cauchy {
+ /// Construct a new `Cauchy` with the given shape parameters
+ /// `median` the peak location and `scale` the scale factor.
+ /// Panics if `scale <= 0`.
+ pub fn new(median: f64, scale: f64) -> Cauchy {
+ assert!(scale > 0.0, "Cauchy::new called with scale factor <= 0");
+ Cauchy { median, scale }
+ }
+}
+
+impl Distribution<f64> for Cauchy {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ // sample from [0, 1)
+ let x = rng.gen::<f64>();
+ // get standard cauchy random number
+ // note that π/2 is not exactly representable, even if x=0.5 the result is finite
+ let comp_dev = (PI * x).tan();
+ // shift and scale according to parameters
+ let result = self.median + self.scale * comp_dev;
+ result
+ }
+}
+
+#[cfg(test)]
+mod test {
+ use super::Cauchy;
+ use crate::distributions::Distribution;
+
+ fn median(mut numbers: &mut [f64]) -> f64 {
+ sort(&mut numbers);
+ let mid = numbers.len() / 2;
+ numbers[mid]
+ }
+
+ fn sort(numbers: &mut [f64]) {
+ numbers.sort_by(|a, b| a.partial_cmp(b).unwrap());
+ }
+
+ #[test]
+ fn test_cauchy_averages() {
+ // NOTE: given that the variance and mean are undefined,
+ // this test does not have any rigorous statistical meaning.
+ let cauchy = Cauchy::new(10.0, 5.0);
+ let mut rng = crate::test::rng(123);
+ let mut numbers: [f64; 1000] = [0.0; 1000];
+ let mut sum = 0.0;
+ for i in 0..1000 {
+ numbers[i] = cauchy.sample(&mut rng);
+ sum += numbers[i];
+ }
+ let median = median(&mut numbers);
+ println!("Cauchy median: {}", median);
+ assert!((median - 10.0).abs() < 0.4); // not 100% certain, but probable enough
+ let mean = sum / 1000.0;
+ println!("Cauchy mean: {}", mean);
+ // for a Cauchy distribution the mean should not converge
+ assert!((mean - 10.0).abs() > 0.4); // not 100% certain, but probable enough
+ }
+
+ #[test]
+ #[should_panic]
+ fn test_cauchy_invalid_scale_zero() {
+ Cauchy::new(0.0, 0.0);
+ }
+
+ #[test]
+ #[should_panic]
+ fn test_cauchy_invalid_scale_neg() {
+ Cauchy::new(0.0, -10.0);
+ }
+}
diff --git a/src/distributions/dirichlet.rs b/src/distributions/dirichlet.rs
new file mode 100644
index 0000000..a75678a
--- /dev/null
+++ b/src/distributions/dirichlet.rs
@@ -0,0 +1,126 @@
+// Copyright 2018 Developers of the Rand project.
+// Copyright 2013 The Rust Project Developers.
+//
+// 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 dirichlet distribution.
+#![allow(deprecated)]
+#![allow(clippy::all)]
+
+use crate::distributions::gamma::Gamma;
+use crate::distributions::Distribution;
+use crate::Rng;
+
+/// The dirichelet distribution `Dirichlet(alpha)`.
+///
+/// The Dirichlet distribution is a family of continuous multivariate
+/// probability distributions parameterized by a vector alpha of positive reals.
+/// It is a multivariate generalization of the beta distribution.
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Debug)]
+pub struct Dirichlet {
+ /// Concentration parameters (alpha)
+ alpha: Vec<f64>,
+}
+
+impl Dirichlet {
+ /// Construct a new `Dirichlet` with the given alpha parameter `alpha`.
+ ///
+ /// # Panics
+ /// - if `alpha.len() < 2`
+ #[inline]
+ pub fn new<V: Into<Vec<f64>>>(alpha: V) -> Dirichlet {
+ let a = alpha.into();
+ assert!(a.len() > 1);
+ for i in 0..a.len() {
+ assert!(a[i] > 0.0);
+ }
+
+ Dirichlet { alpha: a }
+ }
+
+ /// Construct a new `Dirichlet` with the given shape parameter `alpha` and `size`.
+ ///
+ /// # Panics
+ /// - if `alpha <= 0.0`
+ /// - if `size < 2`
+ #[inline]
+ pub fn new_with_param(alpha: f64, size: usize) -> Dirichlet {
+ assert!(alpha > 0.0);
+ assert!(size > 1);
+ Dirichlet {
+ alpha: vec![alpha; size],
+ }
+ }
+}
+
+impl Distribution<Vec<f64>> for Dirichlet {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Vec<f64> {
+ let n = self.alpha.len();
+ let mut samples = vec![0.0f64; n];
+ let mut sum = 0.0f64;
+
+ for i in 0..n {
+ let g = Gamma::new(self.alpha[i], 1.0);
+ samples[i] = g.sample(rng);
+ sum += samples[i];
+ }
+ let invacc = 1.0 / sum;
+ for i in 0..n {
+ samples[i] *= invacc;
+ }
+ samples
+ }
+}
+
+#[cfg(test)]
+mod test {
+ use super::Dirichlet;
+ use crate::distributions::Distribution;
+
+ #[test]
+ fn test_dirichlet() {
+ let d = Dirichlet::new(vec![1.0, 2.0, 3.0]);
+ let mut rng = crate::test::rng(221);
+ let samples = d.sample(&mut rng);
+ let _: Vec<f64> = samples
+ .into_iter()
+ .map(|x| {
+ assert!(x > 0.0);
+ x
+ })
+ .collect();
+ }
+
+ #[test]
+ fn test_dirichlet_with_param() {
+ let alpha = 0.5f64;
+ let size = 2;
+ let d = Dirichlet::new_with_param(alpha, size);
+ let mut rng = crate::test::rng(221);
+ let samples = d.sample(&mut rng);
+ let _: Vec<f64> = samples
+ .into_iter()
+ .map(|x| {
+ assert!(x > 0.0);
+ x
+ })
+ .collect();
+ }
+
+ #[test]
+ #[should_panic]
+ fn test_dirichlet_invalid_length() {
+ Dirichlet::new_with_param(0.5f64, 1);
+ }
+
+ #[test]
+ #[should_panic]
+ fn test_dirichlet_invalid_alpha() {
+ Dirichlet::new_with_param(0.0f64, 2);
+ }
+}
diff --git a/src/distributions/exponential.rs b/src/distributions/exponential.rs
new file mode 100644
index 0000000..5fdf7aa
--- /dev/null
+++ b/src/distributions/exponential.rs
@@ -0,0 +1,114 @@
+// Copyright 2018 Developers of the Rand project.
+// Copyright 2013 The Rust Project Developers.
+//
+// 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 exponential distribution.
+#![allow(deprecated)]
+
+use crate::distributions::utils::ziggurat;
+use crate::distributions::{ziggurat_tables, Distribution};
+use crate::Rng;
+
+/// Samples floating-point numbers according to the exponential distribution,
+/// with rate parameter `λ = 1`. This is equivalent to `Exp::new(1.0)` or
+/// sampling with `-rng.gen::<f64>().ln()`, but faster.
+///
+/// See `Exp` for the general exponential distribution.
+///
+/// Implemented via the ZIGNOR variant[^1] of the Ziggurat method. The exact
+/// description in the paper was adjusted to use tables for the exponential
+/// distribution rather than normal.
+///
+/// [^1]: Jurgen A. Doornik (2005). [*An Improved Ziggurat Method to
+/// Generate Normal Random Samples*](
+/// https://www.doornik.com/research/ziggurat.pdf).
+/// Nuffield College, Oxford
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct Exp1;
+
+// This could be done via `-rng.gen::<f64>().ln()` but that is slower.
+impl Distribution<f64> for Exp1 {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ #[inline]
+ fn pdf(x: f64) -> f64 {
+ (-x).exp()
+ }
+ #[inline]
+ fn zero_case<R: Rng + ?Sized>(rng: &mut R, _u: f64) -> f64 {
+ ziggurat_tables::ZIG_EXP_R - rng.gen::<f64>().ln()
+ }
+
+ ziggurat(
+ rng,
+ false,
+ &ziggurat_tables::ZIG_EXP_X,
+ &ziggurat_tables::ZIG_EXP_F,
+ pdf,
+ zero_case,
+ )
+ }
+}
+
+/// The exponential distribution `Exp(lambda)`.
+///
+/// This distribution has density function: `f(x) = lambda * exp(-lambda * x)`
+/// for `x > 0`.
+///
+/// Note that [`Exp1`](crate::distributions::Exp1) is an optimised implementation for `lambda = 1`.
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct Exp {
+ /// `lambda` stored as `1/lambda`, since this is what we scale by.
+ lambda_inverse: f64,
+}
+
+impl Exp {
+ /// Construct a new `Exp` with the given shape parameter
+ /// `lambda`. Panics if `lambda <= 0`.
+ #[inline]
+ pub fn new(lambda: f64) -> Exp {
+ assert!(lambda > 0.0, "Exp::new called with `lambda` <= 0");
+ Exp {
+ lambda_inverse: 1.0 / lambda,
+ }
+ }
+}
+
+impl Distribution<f64> for Exp {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ let n: f64 = rng.sample(Exp1);
+ n * self.lambda_inverse
+ }
+}
+
+#[cfg(test)]
+mod test {
+ use super::Exp;
+ use crate::distributions::Distribution;
+
+ #[test]
+ fn test_exp() {
+ let exp = Exp::new(10.0);
+ let mut rng = crate::test::rng(221);
+ for _ in 0..1000 {
+ assert!(exp.sample(&mut rng) >= 0.0);
+ }
+ }
+ #[test]
+ #[should_panic]
+ fn test_exp_invalid_lambda_zero() {
+ Exp::new(0.0);
+ }
+ #[test]
+ #[should_panic]
+ fn test_exp_invalid_lambda_neg() {
+ Exp::new(-10.0);
+ }
+}
diff --git a/src/distributions/float.rs b/src/distributions/float.rs
new file mode 100644
index 0000000..0a45f39
--- /dev/null
+++ b/src/distributions/float.rs
@@ -0,0 +1,307 @@
+// 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.
+
+//! Basic floating-point number distributions
+
+use crate::distributions::utils::FloatSIMDUtils;
+use crate::distributions::{Distribution, Standard};
+use crate::Rng;
+use core::mem;
+#[cfg(feature = "simd_support")] use packed_simd::*;
+
+/// A distribution to sample floating point numbers uniformly in the half-open
+/// interval `(0, 1]`, i.e. including 1 but not 0.
+///
+/// All values that can be generated are of the form `n * ε/2`. For `f32`
+/// the 24 most significant random bits of a `u32` are used and for `f64` the
+/// 53 most significant bits of a `u64` are used. The conversion uses the
+/// multiplicative method.
+///
+/// See also: [`Standard`] which samples from `[0, 1)`, [`Open01`]
+/// which samples from `(0, 1)` and [`Uniform`] which samples from arbitrary
+/// ranges.
+///
+/// # Example
+/// ```
+/// use rand::{thread_rng, Rng};
+/// use rand::distributions::OpenClosed01;
+///
+/// let val: f32 = thread_rng().sample(OpenClosed01);
+/// println!("f32 from (0, 1): {}", val);
+/// ```
+///
+/// [`Standard`]: crate::distributions::Standard
+/// [`Open01`]: crate::distributions::Open01
+/// [`Uniform`]: crate::distributions::uniform::Uniform
+#[derive(Clone, Copy, Debug)]
+pub struct OpenClosed01;
+
+/// A distribution to sample floating point numbers uniformly in the open
+/// interval `(0, 1)`, i.e. not including either endpoint.
+///
+/// All values that can be generated are of the form `n * ε + ε/2`. For `f32`
+/// the 23 most significant random bits of an `u32` are used, for `f64` 52 from
+/// an `u64`. The conversion uses a transmute-based method.
+///
+/// See also: [`Standard`] which samples from `[0, 1)`, [`OpenClosed01`]
+/// which samples from `(0, 1]` and [`Uniform`] which samples from arbitrary
+/// ranges.
+///
+/// # Example
+/// ```
+/// use rand::{thread_rng, Rng};
+/// use rand::distributions::Open01;
+///
+/// let val: f32 = thread_rng().sample(Open01);
+/// println!("f32 from (0, 1): {}", val);
+/// ```
+///
+/// [`Standard`]: crate::distributions::Standard
+/// [`OpenClosed01`]: crate::distributions::OpenClosed01
+/// [`Uniform`]: crate::distributions::uniform::Uniform
+#[derive(Clone, Copy, Debug)]
+pub struct Open01;
+
+
+// This trait is needed by both this lib and rand_distr hence is a hidden export
+#[doc(hidden)]
+pub trait IntoFloat {
+ type F;
+
+ /// Helper method to combine the fraction and a contant exponent into a
+ /// float.
+ ///
+ /// Only the least significant bits of `self` may be set, 23 for `f32` and
+ /// 52 for `f64`.
+ /// The resulting value will fall in a range that depends on the exponent.
+ /// As an example the range with exponent 0 will be
+ /// [2<sup>0</sup>..2<sup>1</sup>), which is [1..2).
+ fn into_float_with_exponent(self, exponent: i32) -> Self::F;
+}
+
+macro_rules! float_impls {
+ ($ty:ident, $uty:ident, $f_scalar:ident, $u_scalar:ty,
+ $fraction_bits:expr, $exponent_bias:expr) => {
+ impl IntoFloat for $uty {
+ type F = $ty;
+ #[inline(always)]
+ fn into_float_with_exponent(self, exponent: i32) -> $ty {
+ // The exponent is encoded using an offset-binary representation
+ let exponent_bits: $u_scalar =
+ (($exponent_bias + exponent) as $u_scalar) << $fraction_bits;
+ $ty::from_bits(self | exponent_bits)
+ }
+ }
+
+ impl Distribution<$ty> for Standard {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
+ // Multiply-based method; 24/53 random bits; [0, 1) interval.
+ // We use the most significant bits because for simple RNGs
+ // those are usually more random.
+ let float_size = mem::size_of::<$f_scalar>() as u32 * 8;
+ let precision = $fraction_bits + 1;
+ let scale = 1.0 / ((1 as $u_scalar << precision) as $f_scalar);
+
+ let value: $uty = rng.gen();
+ let value = value >> (float_size - precision);
+ scale * $ty::cast_from_int(value)
+ }
+ }
+
+ impl Distribution<$ty> for OpenClosed01 {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
+ // Multiply-based method; 24/53 random bits; (0, 1] interval.
+ // We use the most significant bits because for simple RNGs
+ // those are usually more random.
+ let float_size = mem::size_of::<$f_scalar>() as u32 * 8;
+ let precision = $fraction_bits + 1;
+ let scale = 1.0 / ((1 as $u_scalar << precision) as $f_scalar);
+
+ let value: $uty = rng.gen();
+ let value = value >> (float_size - precision);
+ // Add 1 to shift up; will not overflow because of right-shift:
+ scale * $ty::cast_from_int(value + 1)
+ }
+ }
+
+ impl Distribution<$ty> for Open01 {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
+ // Transmute-based method; 23/52 random bits; (0, 1) interval.
+ // We use the most significant bits because for simple RNGs
+ // those are usually more random.
+ use core::$f_scalar::EPSILON;
+ let float_size = mem::size_of::<$f_scalar>() as u32 * 8;
+
+ let value: $uty = rng.gen();
+ let fraction = value >> (float_size - $fraction_bits);
+ fraction.into_float_with_exponent(0) - (1.0 - EPSILON / 2.0)
+ }
+ }
+ }
+}
+
+float_impls! { f32, u32, f32, u32, 23, 127 }
+float_impls! { f64, u64, f64, u64, 52, 1023 }
+
+#[cfg(feature = "simd_support")]
+float_impls! { f32x2, u32x2, f32, u32, 23, 127 }
+#[cfg(feature = "simd_support")]
+float_impls! { f32x4, u32x4, f32, u32, 23, 127 }
+#[cfg(feature = "simd_support")]
+float_impls! { f32x8, u32x8, f32, u32, 23, 127 }
+#[cfg(feature = "simd_support")]
+float_impls! { f32x16, u32x16, f32, u32, 23, 127 }
+
+#[cfg(feature = "simd_support")]
+float_impls! { f64x2, u64x2, f64, u64, 52, 1023 }
+#[cfg(feature = "simd_support")]
+float_impls! { f64x4, u64x4, f64, u64, 52, 1023 }
+#[cfg(feature = "simd_support")]
+float_impls! { f64x8, u64x8, f64, u64, 52, 1023 }
+
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+ use crate::rngs::mock::StepRng;
+
+ const EPSILON32: f32 = ::core::f32::EPSILON;
+ const EPSILON64: f64 = ::core::f64::EPSILON;
+
+ macro_rules! test_f32 {
+ ($fnn:ident, $ty:ident, $ZERO:expr, $EPSILON:expr) => {
+ #[test]
+ fn $fnn() {
+ // Standard
+ let mut zeros = StepRng::new(0, 0);
+ assert_eq!(zeros.gen::<$ty>(), $ZERO);
+ let mut one = StepRng::new(1 << 8 | 1 << (8 + 32), 0);
+ assert_eq!(one.gen::<$ty>(), $EPSILON / 2.0);
+ let mut max = StepRng::new(!0, 0);
+ assert_eq!(max.gen::<$ty>(), 1.0 - $EPSILON / 2.0);
+
+ // OpenClosed01
+ let mut zeros = StepRng::new(0, 0);
+ assert_eq!(zeros.sample::<$ty, _>(OpenClosed01), 0.0 + $EPSILON / 2.0);
+ let mut one = StepRng::new(1 << 8 | 1 << (8 + 32), 0);
+ assert_eq!(one.sample::<$ty, _>(OpenClosed01), $EPSILON);
+ let mut max = StepRng::new(!0, 0);
+ assert_eq!(max.sample::<$ty, _>(OpenClosed01), $ZERO + 1.0);
+
+ // Open01
+ let mut zeros = StepRng::new(0, 0);
+ assert_eq!(zeros.sample::<$ty, _>(Open01), 0.0 + $EPSILON / 2.0);
+ let mut one = StepRng::new(1 << 9 | 1 << (9 + 32), 0);
+ assert_eq!(one.sample::<$ty, _>(Open01), $EPSILON / 2.0 * 3.0);
+ let mut max = StepRng::new(!0, 0);
+ assert_eq!(max.sample::<$ty, _>(Open01), 1.0 - $EPSILON / 2.0);
+ }
+ };
+ }
+ test_f32! { f32_edge_cases, f32, 0.0, EPSILON32 }
+ #[cfg(feature = "simd_support")]
+ test_f32! { f32x2_edge_cases, f32x2, f32x2::splat(0.0), f32x2::splat(EPSILON32) }
+ #[cfg(feature = "simd_support")]
+ test_f32! { f32x4_edge_cases, f32x4, f32x4::splat(0.0), f32x4::splat(EPSILON32) }
+ #[cfg(feature = "simd_support")]
+ test_f32! { f32x8_edge_cases, f32x8, f32x8::splat(0.0), f32x8::splat(EPSILON32) }
+ #[cfg(feature = "simd_support")]
+ test_f32! { f32x16_edge_cases, f32x16, f32x16::splat(0.0), f32x16::splat(EPSILON32) }
+
+ macro_rules! test_f64 {
+ ($fnn:ident, $ty:ident, $ZERO:expr, $EPSILON:expr) => {
+ #[test]
+ fn $fnn() {
+ // Standard
+ let mut zeros = StepRng::new(0, 0);
+ assert_eq!(zeros.gen::<$ty>(), $ZERO);
+ let mut one = StepRng::new(1 << 11, 0);
+ assert_eq!(one.gen::<$ty>(), $EPSILON / 2.0);
+ let mut max = StepRng::new(!0, 0);
+ assert_eq!(max.gen::<$ty>(), 1.0 - $EPSILON / 2.0);
+
+ // OpenClosed01
+ let mut zeros = StepRng::new(0, 0);
+ assert_eq!(zeros.sample::<$ty, _>(OpenClosed01), 0.0 + $EPSILON / 2.0);
+ let mut one = StepRng::new(1 << 11, 0);
+ assert_eq!(one.sample::<$ty, _>(OpenClosed01), $EPSILON);
+ let mut max = StepRng::new(!0, 0);
+ assert_eq!(max.sample::<$ty, _>(OpenClosed01), $ZERO + 1.0);
+
+ // Open01
+ let mut zeros = StepRng::new(0, 0);
+ assert_eq!(zeros.sample::<$ty, _>(Open01), 0.0 + $EPSILON / 2.0);
+ let mut one = StepRng::new(1 << 12, 0);
+ assert_eq!(one.sample::<$ty, _>(Open01), $EPSILON / 2.0 * 3.0);
+ let mut max = StepRng::new(!0, 0);
+ assert_eq!(max.sample::<$ty, _>(Open01), 1.0 - $EPSILON / 2.0);
+ }
+ };
+ }
+ test_f64! { f64_edge_cases, f64, 0.0, EPSILON64 }
+ #[cfg(feature = "simd_support")]
+ test_f64! { f64x2_edge_cases, f64x2, f64x2::splat(0.0), f64x2::splat(EPSILON64) }
+ #[cfg(feature = "simd_support")]
+ test_f64! { f64x4_edge_cases, f64x4, f64x4::splat(0.0), f64x4::splat(EPSILON64) }
+ #[cfg(feature = "simd_support")]
+ test_f64! { f64x8_edge_cases, f64x8, f64x8::splat(0.0), f64x8::splat(EPSILON64) }
+
+ #[test]
+ fn value_stability() {
+ fn test_samples<T: Copy + core::fmt::Debug + PartialEq, D: Distribution<T>>(
+ distr: &D, zero: T, expected: &[T],
+ ) {
+ let mut rng = crate::test::rng(0x6f44f5646c2a7334);
+ let mut buf = [zero; 3];
+ for x in &mut buf {
+ *x = rng.sample(&distr);
+ }
+ assert_eq!(&buf, expected);
+ }
+
+ test_samples(&Standard, 0f32, &[0.0035963655, 0.7346052, 0.09778172]);
+ test_samples(&Standard, 0f64, &[
+ 0.7346051961657583,
+ 0.20298547462974248,
+ 0.8166436635290655,
+ ]);
+
+ test_samples(&OpenClosed01, 0f32, &[0.003596425, 0.73460525, 0.09778178]);
+ test_samples(&OpenClosed01, 0f64, &[
+ 0.7346051961657584,
+ 0.2029854746297426,
+ 0.8166436635290656,
+ ]);
+
+ test_samples(&Open01, 0f32, &[0.0035963655, 0.73460525, 0.09778172]);
+ test_samples(&Open01, 0f64, &[
+ 0.7346051961657584,
+ 0.20298547462974248,
+ 0.8166436635290656,
+ ]);
+
+ #[cfg(feature = "simd_support")]
+ {
+ // We only test a sub-set of types here. Values are identical to
+ // non-SIMD types; we assume this pattern continues across all
+ // SIMD types.
+
+ test_samples(&Standard, f32x2::new(0.0, 0.0), &[
+ f32x2::new(0.0035963655, 0.7346052),
+ f32x2::new(0.09778172, 0.20298547),
+ f32x2::new(0.34296435, 0.81664366),
+ ]);
+
+ test_samples(&Standard, f64x2::new(0.0, 0.0), &[
+ f64x2::new(0.7346051961657583, 0.20298547462974248),
+ f64x2::new(0.8166436635290655, 0.7423708925400552),
+ f64x2::new(0.16387782224016323, 0.9087068770169618),
+ ]);
+ }
+ }
+}
diff --git a/src/distributions/gamma.rs b/src/distributions/gamma.rs
new file mode 100644
index 0000000..f19738d
--- /dev/null
+++ b/src/distributions/gamma.rs
@@ -0,0 +1,373 @@
+// Copyright 2018 Developers of the Rand project.
+// Copyright 2013 The Rust Project Developers.
+//
+// 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 Gamma and derived distributions.
+#![allow(deprecated)]
+
+use self::ChiSquaredRepr::*;
+use self::GammaRepr::*;
+
+use crate::distributions::normal::StandardNormal;
+use crate::distributions::{Distribution, Exp, Open01};
+use crate::Rng;
+
+/// The Gamma distribution `Gamma(shape, scale)` distribution.
+///
+/// The density function of this distribution is
+///
+/// ```text
+/// f(x) = x^(k - 1) * exp(-x / θ) / (Γ(k) * θ^k)
+/// ```
+///
+/// where `Γ` is the Gamma function, `k` is the shape and `θ` is the
+/// scale and both `k` and `θ` are strictly positive.
+///
+/// The algorithm used is that described by Marsaglia & Tsang 2000[^1],
+/// falling back to directly sampling from an Exponential for `shape
+/// == 1`, and using the boosting technique described in that paper for
+/// `shape < 1`.
+///
+/// [^1]: George Marsaglia and Wai Wan Tsang. 2000. "A Simple Method for
+/// Generating Gamma Variables" *ACM Trans. Math. Softw.* 26, 3
+/// (September 2000), 363-372.
+/// DOI:[10.1145/358407.358414](https://doi.acm.org/10.1145/358407.358414)
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct Gamma {
+ repr: GammaRepr,
+}
+
+#[derive(Clone, Copy, Debug)]
+enum GammaRepr {
+ Large(GammaLargeShape),
+ One(Exp),
+ Small(GammaSmallShape),
+}
+
+// These two helpers could be made public, but saving the
+// match-on-Gamma-enum branch from using them directly (e.g. if one
+// knows that the shape is always > 1) doesn't appear to be much
+// faster.
+
+/// Gamma distribution where the shape parameter is less than 1.
+///
+/// Note, samples from this require a compulsory floating-point `pow`
+/// call, which makes it significantly slower than sampling from a
+/// gamma distribution where the shape parameter is greater than or
+/// equal to 1.
+///
+/// See `Gamma` for sampling from a Gamma distribution with general
+/// shape parameters.
+#[derive(Clone, Copy, Debug)]
+struct GammaSmallShape {
+ inv_shape: f64,
+ large_shape: GammaLargeShape,
+}
+
+/// Gamma distribution where the shape parameter is larger than 1.
+///
+/// See `Gamma` for sampling from a Gamma distribution with general
+/// shape parameters.
+#[derive(Clone, Copy, Debug)]
+struct GammaLargeShape {
+ scale: f64,
+ c: f64,
+ d: f64,
+}
+
+impl Gamma {
+ /// Construct an object representing the `Gamma(shape, scale)`
+ /// distribution.
+ ///
+ /// Panics if `shape <= 0` or `scale <= 0`.
+ #[inline]
+ pub fn new(shape: f64, scale: f64) -> Gamma {
+ assert!(shape > 0.0, "Gamma::new called with shape <= 0");
+ assert!(scale > 0.0, "Gamma::new called with scale <= 0");
+
+ let repr = if shape == 1.0 {
+ One(Exp::new(1.0 / scale))
+ } else if shape < 1.0 {
+ Small(GammaSmallShape::new_raw(shape, scale))
+ } else {
+ Large(GammaLargeShape::new_raw(shape, scale))
+ };
+ Gamma { repr }
+ }
+}
+
+impl GammaSmallShape {
+ fn new_raw(shape: f64, scale: f64) -> GammaSmallShape {
+ GammaSmallShape {
+ inv_shape: 1. / shape,
+ large_shape: GammaLargeShape::new_raw(shape + 1.0, scale),
+ }
+ }
+}
+
+impl GammaLargeShape {
+ fn new_raw(shape: f64, scale: f64) -> GammaLargeShape {
+ let d = shape - 1. / 3.;
+ GammaLargeShape {
+ scale,
+ c: 1. / (9. * d).sqrt(),
+ d,
+ }
+ }
+}
+
+impl Distribution<f64> for Gamma {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ match self.repr {
+ Small(ref g) => g.sample(rng),
+ One(ref g) => g.sample(rng),
+ Large(ref g) => g.sample(rng),
+ }
+ }
+}
+impl Distribution<f64> for GammaSmallShape {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ let u: f64 = rng.sample(Open01);
+
+ self.large_shape.sample(rng) * u.powf(self.inv_shape)
+ }
+}
+impl Distribution<f64> for GammaLargeShape {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ loop {
+ let x = rng.sample(StandardNormal);
+ let v_cbrt = 1.0 + self.c * x;
+ if v_cbrt <= 0.0 {
+ // a^3 <= 0 iff a <= 0
+ continue;
+ }
+
+ let v = v_cbrt * v_cbrt * v_cbrt;
+ let u: f64 = rng.sample(Open01);
+
+ let x_sqr = x * x;
+ if u < 1.0 - 0.0331 * x_sqr * x_sqr
+ || u.ln() < 0.5 * x_sqr + self.d * (1.0 - v + v.ln())
+ {
+ return self.d * v * self.scale;
+ }
+ }
+ }
+}
+
+/// The chi-squared distribution `χ²(k)`, where `k` is the degrees of
+/// freedom.
+///
+/// For `k > 0` integral, this distribution is the sum of the squares
+/// of `k` independent standard normal random variables. For other
+/// `k`, this uses the equivalent characterisation
+/// `χ²(k) = Gamma(k/2, 2)`.
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct ChiSquared {
+ repr: ChiSquaredRepr,
+}
+
+#[derive(Clone, Copy, Debug)]
+enum ChiSquaredRepr {
+ // k == 1, Gamma(alpha, ..) is particularly slow for alpha < 1,
+ // e.g. when alpha = 1/2 as it would be for this case, so special-
+ // casing and using the definition of N(0,1)^2 is faster.
+ DoFExactlyOne,
+ DoFAnythingElse(Gamma),
+}
+
+impl ChiSquared {
+ /// Create a new chi-squared distribution with degrees-of-freedom
+ /// `k`. Panics if `k < 0`.
+ pub fn new(k: f64) -> ChiSquared {
+ let repr = if k == 1.0 {
+ DoFExactlyOne
+ } else {
+ assert!(k > 0.0, "ChiSquared::new called with `k` < 0");
+ DoFAnythingElse(Gamma::new(0.5 * k, 2.0))
+ };
+ ChiSquared { repr }
+ }
+}
+impl Distribution<f64> for ChiSquared {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ match self.repr {
+ DoFExactlyOne => {
+ // k == 1 => N(0,1)^2
+ let norm = rng.sample(StandardNormal);
+ norm * norm
+ }
+ DoFAnythingElse(ref g) => g.sample(rng),
+ }
+ }
+}
+
+/// The Fisher F distribution `F(m, n)`.
+///
+/// This distribution is equivalent to the ratio of two normalised
+/// chi-squared distributions, that is, `F(m,n) = (χ²(m)/m) /
+/// (χ²(n)/n)`.
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct FisherF {
+ numer: ChiSquared,
+ denom: ChiSquared,
+ // denom_dof / numer_dof so that this can just be a straight
+ // multiplication, rather than a division.
+ dof_ratio: f64,
+}
+
+impl FisherF {
+ /// Create a new `FisherF` distribution, with the given
+ /// parameter. Panics if either `m` or `n` are not positive.
+ pub fn new(m: f64, n: f64) -> FisherF {
+ assert!(m > 0.0, "FisherF::new called with `m < 0`");
+ assert!(n > 0.0, "FisherF::new called with `n < 0`");
+
+ FisherF {
+ numer: ChiSquared::new(m),
+ denom: ChiSquared::new(n),
+ dof_ratio: n / m,
+ }
+ }
+}
+impl Distribution<f64> for FisherF {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ self.numer.sample(rng) / self.denom.sample(rng) * self.dof_ratio
+ }
+}
+
+/// The Student t distribution, `t(nu)`, where `nu` is the degrees of
+/// freedom.
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct StudentT {
+ chi: ChiSquared,
+ dof: f64,
+}
+
+impl StudentT {
+ /// Create a new Student t distribution with `n` degrees of
+ /// freedom. Panics if `n <= 0`.
+ pub fn new(n: f64) -> StudentT {
+ assert!(n > 0.0, "StudentT::new called with `n <= 0`");
+ StudentT {
+ chi: ChiSquared::new(n),
+ dof: n,
+ }
+ }
+}
+impl Distribution<f64> for StudentT {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ let norm = rng.sample(StandardNormal);
+ norm * (self.dof / self.chi.sample(rng)).sqrt()
+ }
+}
+
+/// The Beta distribution with shape parameters `alpha` and `beta`.
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct Beta {
+ gamma_a: Gamma,
+ gamma_b: Gamma,
+}
+
+impl Beta {
+ /// Construct an object representing the `Beta(alpha, beta)`
+ /// distribution.
+ ///
+ /// Panics if `shape <= 0` or `scale <= 0`.
+ pub fn new(alpha: f64, beta: f64) -> Beta {
+ assert!((alpha > 0.) & (beta > 0.));
+ Beta {
+ gamma_a: Gamma::new(alpha, 1.),
+ gamma_b: Gamma::new(beta, 1.),
+ }
+ }
+}
+
+impl Distribution<f64> for Beta {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ let x = self.gamma_a.sample(rng);
+ let y = self.gamma_b.sample(rng);
+ x / (x + y)
+ }
+}
+
+#[cfg(test)]
+mod test {
+ use super::{Beta, ChiSquared, FisherF, StudentT};
+ use crate::distributions::Distribution;
+
+ const N: u32 = 100;
+
+ #[test]
+ fn test_chi_squared_one() {
+ let chi = ChiSquared::new(1.0);
+ let mut rng = crate::test::rng(201);
+ for _ in 0..N {
+ chi.sample(&mut rng);
+ }
+ }
+ #[test]
+ fn test_chi_squared_small() {
+ let chi = ChiSquared::new(0.5);
+ let mut rng = crate::test::rng(202);
+ for _ in 0..N {
+ chi.sample(&mut rng);
+ }
+ }
+ #[test]
+ fn test_chi_squared_large() {
+ let chi = ChiSquared::new(30.0);
+ let mut rng = crate::test::rng(203);
+ for _ in 0..N {
+ chi.sample(&mut rng);
+ }
+ }
+ #[test]
+ #[should_panic]
+ fn test_chi_squared_invalid_dof() {
+ ChiSquared::new(-1.0);
+ }
+
+ #[test]
+ fn test_f() {
+ let f = FisherF::new(2.0, 32.0);
+ let mut rng = crate::test::rng(204);
+ for _ in 0..N {
+ f.sample(&mut rng);
+ }
+ }
+
+ #[test]
+ fn test_t() {
+ let t = StudentT::new(11.0);
+ let mut rng = crate::test::rng(205);
+ for _ in 0..N {
+ t.sample(&mut rng);
+ }
+ }
+
+ #[test]
+ fn test_beta() {
+ let beta = Beta::new(1.0, 2.0);
+ let mut rng = crate::test::rng(201);
+ for _ in 0..N {
+ beta.sample(&mut rng);
+ }
+ }
+
+ #[test]
+ #[should_panic]
+ fn test_beta_invalid_dof() {
+ Beta::new(0., 0.);
+ }
+}
diff --git a/src/distributions/integer.rs b/src/distributions/integer.rs
new file mode 100644
index 0000000..f2db1f1
--- /dev/null
+++ b/src/distributions/integer.rs
@@ -0,0 +1,279 @@
+// 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 implementations of the `Standard` distribution for integer types.
+
+use crate::distributions::{Distribution, Standard};
+use crate::Rng;
+#[cfg(all(target_arch = "x86", feature = "nightly"))] use core::arch::x86::*;
+#[cfg(all(target_arch = "x86_64", feature = "nightly"))]
+use core::arch::x86_64::*;
+#[cfg(not(target_os = "emscripten"))] use core::num::NonZeroU128;
+use core::num::{NonZeroU16, NonZeroU32, NonZeroU64, NonZeroU8, NonZeroUsize};
+#[cfg(feature = "simd_support")] use packed_simd::*;
+
+impl Distribution<u8> for Standard {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u8 {
+ rng.next_u32() as u8
+ }
+}
+
+impl Distribution<u16> for Standard {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u16 {
+ rng.next_u32() as u16
+ }
+}
+
+impl Distribution<u32> for Standard {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u32 {
+ rng.next_u32()
+ }
+}
+
+impl Distribution<u64> for Standard {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
+ rng.next_u64()
+ }
+}
+
+#[cfg(not(target_os = "emscripten"))]
+impl Distribution<u128> for Standard {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u128 {
+ // Use LE; we explicitly generate one value before the next.
+ let x = u128::from(rng.next_u64());
+ let y = u128::from(rng.next_u64());
+ (y << 64) | x
+ }
+}
+
+impl Distribution<usize> for Standard {
+ #[inline]
+ #[cfg(any(target_pointer_width = "32", target_pointer_width = "16"))]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> usize {
+ rng.next_u32() as usize
+ }
+
+ #[inline]
+ #[cfg(target_pointer_width = "64")]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> usize {
+ rng.next_u64() as usize
+ }
+}
+
+macro_rules! impl_int_from_uint {
+ ($ty:ty, $uty:ty) => {
+ impl Distribution<$ty> for Standard {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
+ rng.gen::<$uty>() as $ty
+ }
+ }
+ };
+}
+
+impl_int_from_uint! { i8, u8 }
+impl_int_from_uint! { i16, u16 }
+impl_int_from_uint! { i32, u32 }
+impl_int_from_uint! { i64, u64 }
+#[cfg(not(target_os = "emscripten"))]
+impl_int_from_uint! { i128, u128 }
+impl_int_from_uint! { isize, usize }
+
+macro_rules! impl_nzint {
+ ($ty:ty, $new:path) => {
+ impl Distribution<$ty> for Standard {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
+ loop {
+ if let Some(nz) = $new(rng.gen()) {
+ break nz;
+ }
+ }
+ }
+ }
+ };
+}
+
+impl_nzint!(NonZeroU8, NonZeroU8::new);
+impl_nzint!(NonZeroU16, NonZeroU16::new);
+impl_nzint!(NonZeroU32, NonZeroU32::new);
+impl_nzint!(NonZeroU64, NonZeroU64::new);
+#[cfg(not(target_os = "emscripten"))]
+impl_nzint!(NonZeroU128, NonZeroU128::new);
+impl_nzint!(NonZeroUsize, NonZeroUsize::new);
+
+#[cfg(feature = "simd_support")]
+macro_rules! simd_impl {
+ ($(($intrinsic:ident, $vec:ty),)+) => {$(
+ impl Distribution<$intrinsic> for Standard {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $intrinsic {
+ $intrinsic::from_bits(rng.gen::<$vec>())
+ }
+ }
+ )+};
+
+ ($bits:expr,) => {};
+ ($bits:expr, $ty:ty, $($ty_more:ty,)*) => {
+ simd_impl!($bits, $($ty_more,)*);
+
+ impl Distribution<$ty> for Standard {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
+ let mut vec: $ty = Default::default();
+ unsafe {
+ let ptr = &mut vec;
+ let b_ptr = &mut *(ptr as *mut $ty as *mut [u8; $bits/8]);
+ rng.fill_bytes(b_ptr);
+ }
+ vec.to_le()
+ }
+ }
+ };
+}
+
+#[cfg(feature = "simd_support")]
+simd_impl!(16, u8x2, i8x2,);
+#[cfg(feature = "simd_support")]
+simd_impl!(32, u8x4, i8x4, u16x2, i16x2,);
+#[cfg(feature = "simd_support")]
+simd_impl!(64, u8x8, i8x8, u16x4, i16x4, u32x2, i32x2,);
+#[cfg(feature = "simd_support")]
+simd_impl!(128, u8x16, i8x16, u16x8, i16x8, u32x4, i32x4, u64x2, i64x2,);
+#[cfg(feature = "simd_support")]
+simd_impl!(256, u8x32, i8x32, u16x16, i16x16, u32x8, i32x8, u64x4, i64x4,);
+#[cfg(feature = "simd_support")]
+simd_impl!(512, u8x64, i8x64, u16x32, i16x32, u32x16, i32x16, u64x8, i64x8,);
+#[cfg(all(
+ feature = "simd_support",
+ feature = "nightly",
+ any(target_arch = "x86", target_arch = "x86_64")
+))]
+simd_impl!((__m64, u8x8), (__m128i, u8x16), (__m256i, u8x32),);
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+
+ #[test]
+ fn test_integers() {
+ let mut rng = crate::test::rng(806);
+
+ rng.sample::<isize, _>(Standard);
+ rng.sample::<i8, _>(Standard);
+ rng.sample::<i16, _>(Standard);
+ rng.sample::<i32, _>(Standard);
+ rng.sample::<i64, _>(Standard);
+ #[cfg(not(target_os = "emscripten"))]
+ rng.sample::<i128, _>(Standard);
+
+ rng.sample::<usize, _>(Standard);
+ rng.sample::<u8, _>(Standard);
+ rng.sample::<u16, _>(Standard);
+ rng.sample::<u32, _>(Standard);
+ rng.sample::<u64, _>(Standard);
+ #[cfg(not(target_os = "emscripten"))]
+ rng.sample::<u128, _>(Standard);
+ }
+
+ #[test]
+ fn value_stability() {
+ fn test_samples<T: Copy + core::fmt::Debug + PartialEq>(zero: T, expected: &[T])
+ where Standard: Distribution<T> {
+ let mut rng = crate::test::rng(807);
+ let mut buf = [zero; 3];
+ for x in &mut buf {
+ *x = rng.sample(Standard);
+ }
+ assert_eq!(&buf, expected);
+ }
+
+ test_samples(0u8, &[9, 247, 111]);
+ test_samples(0u16, &[32265, 42999, 38255]);
+ test_samples(0u32, &[2220326409, 2575017975, 2018088303]);
+ test_samples(0u64, &[
+ 11059617991457472009,
+ 16096616328739788143,
+ 1487364411147516184,
+ ]);
+ test_samples(0u128, &[
+ 296930161868957086625409848350820761097,
+ 145644820879247630242265036535529306392,
+ 111087889832015897993126088499035356354,
+ ]);
+ #[cfg(any(target_pointer_width = "32", target_pointer_width = "16"))]
+ test_samples(0usize, &[2220326409, 2575017975, 2018088303]);
+ #[cfg(target_pointer_width = "64")]
+ test_samples(0usize, &[
+ 11059617991457472009,
+ 16096616328739788143,
+ 1487364411147516184,
+ ]);
+
+ test_samples(0i8, &[9, -9, 111]);
+ // Skip further i* types: they are simple reinterpretation of u* samples
+
+ #[cfg(feature = "simd_support")]
+ {
+ // We only test a sub-set of types here and make assumptions about the rest.
+
+ test_samples(u8x2::default(), &[
+ u8x2::new(9, 126),
+ u8x2::new(247, 167),
+ u8x2::new(111, 149),
+ ]);
+ test_samples(u8x4::default(), &[
+ u8x4::new(9, 126, 87, 132),
+ u8x4::new(247, 167, 123, 153),
+ u8x4::new(111, 149, 73, 120),
+ ]);
+ test_samples(u8x8::default(), &[
+ u8x8::new(9, 126, 87, 132, 247, 167, 123, 153),
+ u8x8::new(111, 149, 73, 120, 68, 171, 98, 223),
+ u8x8::new(24, 121, 1, 50, 13, 46, 164, 20),
+ ]);
+
+ test_samples(i64x8::default(), &[
+ i64x8::new(
+ -7387126082252079607,
+ -2350127744969763473,
+ 1487364411147516184,
+ 7895421560427121838,
+ 602190064936008898,
+ 6022086574635100741,
+ -5080089175222015595,
+ -4066367846667249123,
+ ),
+ i64x8::new(
+ 9180885022207963908,
+ 3095981199532211089,
+ 6586075293021332726,
+ 419343203796414657,
+ 3186951873057035255,
+ 5287129228749947252,
+ 444726432079249540,
+ -1587028029513790706,
+ ),
+ i64x8::new(
+ 6075236523189346388,
+ 1351763722368165432,
+ -6192309979959753740,
+ -7697775502176768592,
+ -4482022114172078123,
+ 7522501477800909500,
+ -1837258847956201231,
+ -586926753024886735,
+ ),
+ ]);
+ }
+ }
+}
diff --git a/src/distributions/mod.rs b/src/distributions/mod.rs
new file mode 100644
index 0000000..4e1b1a6
--- /dev/null
+++ b/src/distributions/mod.rs
@@ -0,0 +1,406 @@
+// Copyright 2018 Developers of the Rand project.
+// Copyright 2013-2017 The Rust Project Developers.
+//
+// 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.
+
+//! Generating random samples from probability distributions
+//!
+//! This module is the home of the [`Distribution`] trait and several of its
+//! implementations. It is the workhorse behind some of the convenient
+//! functionality of the [`Rng`] trait, e.g. [`Rng::gen`], [`Rng::gen_range`] and
+//! of course [`Rng::sample`].
+//!
+//! Abstractly, a [probability distribution] describes the probability of
+//! occurance of each value in its sample space.
+//!
+//! More concretely, an implementation of `Distribution<T>` for type `X` is an
+//! algorithm for choosing values from the sample space (a subset of `T`)
+//! according to the distribution `X` represents, using an external source of
+//! randomness (an RNG supplied to the `sample` function).
+//!
+//! A type `X` may implement `Distribution<T>` for multiple types `T`.
+//! Any type implementing [`Distribution`] is stateless (i.e. immutable),
+//! but it may have internal parameters set at construction time (for example,
+//! [`Uniform`] allows specification of its sample space as a range within `T`).
+//!
+//!
+//! # The `Standard` distribution
+//!
+//! The [`Standard`] distribution is important to mention. This is the
+//! distribution used by [`Rng::gen`] and represents the "default" way to
+//! produce a random value for many different types, including most primitive
+//! types, tuples, arrays, and a few derived types. See the documentation of
+//! [`Standard`] for more details.
+//!
+//! Implementing `Distribution<T>` for [`Standard`] for user types `T` makes it
+//! possible to generate type `T` with [`Rng::gen`], and by extension also
+//! with the [`random`] function.
+//!
+//! ## Random characters
+//!
+//! [`Alphanumeric`] is a simple distribution to sample random letters and
+//! numbers of the `char` type; in contrast [`Standard`] may sample any valid
+//! `char`.
+//!
+//!
+//! # Uniform numeric ranges
+//!
+//! The [`Uniform`] distribution is more flexible than [`Standard`], but also
+//! more specialised: it supports fewer target types, but allows the sample
+//! space to be specified as an arbitrary range within its target type `T`.
+//! Both [`Standard`] and [`Uniform`] are in some sense uniform distributions.
+//!
+//! Values may be sampled from this distribution using [`Rng::gen_range`] or
+//! by creating a distribution object with [`Uniform::new`],
+//! [`Uniform::new_inclusive`] or `From<Range>`. When the range limits are not
+//! known at compile time it is typically faster to reuse an existing
+//! distribution object than to call [`Rng::gen_range`].
+//!
+//! User types `T` may also implement `Distribution<T>` for [`Uniform`],
+//! although this is less straightforward than for [`Standard`] (see the
+//! documentation in the [`uniform`] module. Doing so enables generation of
+//! values of type `T` with [`Rng::gen_range`].
+//!
+//! ## Open and half-open ranges
+//!
+//! There are surprisingly many ways to uniformly generate random floats. A
+//! range between 0 and 1 is standard, but the exact bounds (open vs closed)
+//! and accuracy differ. In addition to the [`Standard`] distribution Rand offers
+//! [`Open01`] and [`OpenClosed01`]. See "Floating point implementation" section of
+//! [`Standard`] documentation for more details.
+//!
+//! # Non-uniform sampling
+//!
+//! Sampling a simple true/false outcome with a given probability has a name:
+//! the [`Bernoulli`] distribution (this is used by [`Rng::gen_bool`]).
+//!
+//! For weighted sampling from a sequence of discrete values, use the
+//! [`weighted`] module.
+//!
+//! This crate no longer includes other non-uniform distributions; instead
+//! it is recommended that you use either [`rand_distr`] or [`statrs`].
+//!
+//!
+//! [probability distribution]: https://en.wikipedia.org/wiki/Probability_distribution
+//! [`rand_distr`]: https://crates.io/crates/rand_distr
+//! [`statrs`]: https://crates.io/crates/statrs
+
+//! [`random`]: crate::random
+//! [`rand_distr`]: https://crates.io/crates/rand_distr
+//! [`statrs`]: https://crates.io/crates/statrs
+
+use crate::Rng;
+use core::iter;
+
+pub use self::bernoulli::{Bernoulli, BernoulliError};
+pub use self::float::{Open01, OpenClosed01};
+pub use self::other::Alphanumeric;
+#[doc(inline)] pub use self::uniform::Uniform;
+#[cfg(feature = "alloc")]
+pub use self::weighted::{WeightedError, WeightedIndex};
+
+// The following are all deprecated after being moved to rand_distr
+#[allow(deprecated)]
+#[cfg(feature = "std")]
+pub use self::binomial::Binomial;
+#[allow(deprecated)]
+#[cfg(feature = "std")]
+pub use self::cauchy::Cauchy;
+#[allow(deprecated)]
+#[cfg(feature = "std")]
+pub use self::dirichlet::Dirichlet;
+#[allow(deprecated)]
+#[cfg(feature = "std")]
+pub use self::exponential::{Exp, Exp1};
+#[allow(deprecated)]
+#[cfg(feature = "std")]
+pub use self::gamma::{Beta, ChiSquared, FisherF, Gamma, StudentT};
+#[allow(deprecated)]
+#[cfg(feature = "std")]
+pub use self::normal::{LogNormal, Normal, StandardNormal};
+#[allow(deprecated)]
+#[cfg(feature = "std")]
+pub use self::pareto::Pareto;
+#[allow(deprecated)]
+#[cfg(feature = "std")]
+pub use self::poisson::Poisson;
+#[allow(deprecated)]
+#[cfg(feature = "std")]
+pub use self::triangular::Triangular;
+#[allow(deprecated)]
+#[cfg(feature = "std")]
+pub use self::unit_circle::UnitCircle;
+#[allow(deprecated)]
+#[cfg(feature = "std")]
+pub use self::unit_sphere::UnitSphereSurface;
+#[allow(deprecated)]
+#[cfg(feature = "std")]
+pub use self::weibull::Weibull;
+
+mod bernoulli;
+#[cfg(feature = "std")] mod binomial;
+#[cfg(feature = "std")] mod cauchy;
+#[cfg(feature = "std")] mod dirichlet;
+#[cfg(feature = "std")] mod exponential;
+#[cfg(feature = "std")] mod gamma;
+#[cfg(feature = "std")] mod normal;
+#[cfg(feature = "std")] mod pareto;
+#[cfg(feature = "std")] mod poisson;
+#[cfg(feature = "std")] mod triangular;
+pub mod uniform;
+#[cfg(feature = "std")] mod unit_circle;
+#[cfg(feature = "std")] mod unit_sphere;
+#[cfg(feature = "std")] mod weibull;
+#[cfg(feature = "alloc")] pub mod weighted;
+
+mod float;
+#[doc(hidden)]
+pub mod hidden_export {
+ pub use super::float::IntoFloat; // used by rand_distr
+}
+mod integer;
+mod other;
+mod utils;
+#[cfg(feature = "std")] mod ziggurat_tables;
+
+/// Types (distributions) that can be used to create a random instance of `T`.
+///
+/// It is possible to sample from a distribution through both the
+/// `Distribution` and [`Rng`] traits, via `distr.sample(&mut rng)` and
+/// `rng.sample(distr)`. They also both offer the [`sample_iter`] method, which
+/// produces an iterator that samples from the distribution.
+///
+/// All implementations are expected to be immutable; this has the significant
+/// advantage of not needing to consider thread safety, and for most
+/// distributions efficient state-less sampling algorithms are available.
+///
+/// Implementations are typically expected to be portable with reproducible
+/// results when used with a PRNG with fixed seed; see the
+/// [portability chapter](https://rust-random.github.io/book/portability.html)
+/// of The Rust Rand Book. In some cases this does not apply, e.g. the `usize`
+/// type requires different sampling on 32-bit and 64-bit machines.
+///
+/// [`sample_iter`]: Distribution::method.sample_iter
+pub trait Distribution<T> {
+ /// Generate a random value of `T`, using `rng` as the source of randomness.
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> T;
+
+ /// Create an iterator that generates random values of `T`, using `rng` as
+ /// the source of randomness.
+ ///
+ /// Note that this function takes `self` by value. This works since
+ /// `Distribution<T>` is impl'd for `&D` where `D: Distribution<T>`,
+ /// however borrowing is not automatic hence `distr.sample_iter(...)` may
+ /// need to be replaced with `(&distr).sample_iter(...)` to borrow or
+ /// `(&*distr).sample_iter(...)` to reborrow an existing reference.
+ ///
+ /// # Example
+ ///
+ /// ```
+ /// use rand::thread_rng;
+ /// use rand::distributions::{Distribution, Alphanumeric, Uniform, Standard};
+ ///
+ /// let rng = thread_rng();
+ ///
+ /// // Vec of 16 x f32:
+ /// let v: Vec<f32> = Standard.sample_iter(rng).take(16).collect();
+ ///
+ /// // String:
+ /// let s: String = Alphanumeric.sample_iter(rng).take(7).collect();
+ ///
+ /// // Dice-rolling:
+ /// let die_range = Uniform::new_inclusive(1, 6);
+ /// let mut roll_die = die_range.sample_iter(rng);
+ /// while roll_die.next().unwrap() != 6 {
+ /// println!("Not a 6; rolling again!");
+ /// }
+ /// ```
+ fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>
+ where
+ R: Rng,
+ Self: Sized,
+ {
+ DistIter {
+ distr: self,
+ rng,
+ phantom: ::core::marker::PhantomData,
+ }
+ }
+}
+
+impl<'a, T, D: Distribution<T>> Distribution<T> for &'a D {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> T {
+ (*self).sample(rng)
+ }
+}
+
+
+/// An iterator that generates random values of `T` with distribution `D`,
+/// using `R` as the source of randomness.
+///
+/// This `struct` is created by the [`sample_iter`] method on [`Distribution`].
+/// See its documentation for more.
+///
+/// [`sample_iter`]: Distribution::sample_iter
+#[derive(Debug)]
+pub struct DistIter<D, R, T> {
+ distr: D,
+ rng: R,
+ phantom: ::core::marker::PhantomData<T>,
+}
+
+impl<D, R, T> Iterator for DistIter<D, R, T>
+where
+ D: Distribution<T>,
+ R: Rng,
+{
+ type Item = T;
+
+ #[inline(always)]
+ fn next(&mut self) -> Option<T> {
+ // Here, self.rng may be a reference, but we must take &mut anyway.
+ // Even if sample could take an R: Rng by value, we would need to do this
+ // since Rng is not copyable and we cannot enforce that this is "reborrowable".
+ Some(self.distr.sample(&mut self.rng))
+ }
+
+ fn size_hint(&self) -> (usize, Option<usize>) {
+ (usize::max_value(), None)
+ }
+}
+
+impl<D, R, T> iter::FusedIterator for DistIter<D, R, T>
+where
+ D: Distribution<T>,
+ R: Rng,
+{
+}
+
+#[cfg(features = "nightly")]
+impl<D, R, T> iter::TrustedLen for DistIter<D, R, T>
+where
+ D: Distribution<T>,
+ R: Rng,
+{
+}
+
+
+/// A generic random value distribution, implemented for many primitive types.
+/// Usually generates values with a numerically uniform distribution, and with a
+/// range appropriate to the type.
+///
+/// ## Provided implementations
+///
+/// Assuming the provided `Rng` is well-behaved, these implementations
+/// generate values with the following ranges and distributions:
+///
+/// * Integers (`i32`, `u32`, `isize`, `usize`, etc.): Uniformly distributed
+/// over all values of the type.
+/// * `char`: Uniformly distributed over all Unicode scalar values, i.e. all
+/// code points in the range `0...0x10_FFFF`, except for the range
+/// `0xD800...0xDFFF` (the surrogate code points). This includes
+/// unassigned/reserved code points.
+/// * `bool`: Generates `false` or `true`, each with probability 0.5.
+/// * Floating point types (`f32` and `f64`): Uniformly distributed in the
+/// half-open range `[0, 1)`. See notes below.
+/// * Wrapping integers (`Wrapping<T>`), besides the type identical to their
+/// normal integer variants.
+///
+/// The `Standard` distribution also supports generation of the following
+/// compound types where all component types are supported:
+///
+/// * Tuples (up to 12 elements): each element is generated sequentially.
+/// * Arrays (up to 32 elements): each element is generated sequentially;
+/// see also [`Rng::fill`] which supports arbitrary array length for integer
+/// types and tends to be faster for `u32` and smaller types.
+/// * `Option<T>` first generates a `bool`, and if true generates and returns
+/// `Some(value)` where `value: T`, otherwise returning `None`.
+///
+/// ## Custom implementations
+///
+/// The [`Standard`] distribution may be implemented for user types as follows:
+///
+/// ```
+/// # #![allow(dead_code)]
+/// use rand::Rng;
+/// use rand::distributions::{Distribution, Standard};
+///
+/// struct MyF32 {
+/// x: f32,
+/// }
+///
+/// impl Distribution<MyF32> for Standard {
+/// fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> MyF32 {
+/// MyF32 { x: rng.gen() }
+/// }
+/// }
+/// ```
+///
+/// ## Example usage
+/// ```
+/// use rand::prelude::*;
+/// use rand::distributions::Standard;
+///
+/// let val: f32 = StdRng::from_entropy().sample(Standard);
+/// println!("f32 from [0, 1): {}", val);
+/// ```
+///
+/// # Floating point implementation
+/// The floating point implementations for `Standard` generate a random value in
+/// the half-open interval `[0, 1)`, i.e. including 0 but not 1.
+///
+/// All values that can be generated are of the form `n * ε/2`. For `f32`
+/// the 24 most significant random bits of a `u32` are used and for `f64` the
+/// 53 most significant bits of a `u64` are used. The conversion uses the
+/// multiplicative method: `(rng.gen::<$uty>() >> N) as $ty * (ε/2)`.
+///
+/// See also: [`Open01`] which samples from `(0, 1)`, [`OpenClosed01`] which
+/// samples from `(0, 1]` and `Rng::gen_range(0, 1)` which also samples from
+/// `[0, 1)`. Note that `Open01` and `gen_range` (which uses [`Uniform`]) use
+/// transmute-based methods which yield 1 bit less precision but may perform
+/// faster on some architectures (on modern Intel CPUs all methods have
+/// approximately equal performance).
+///
+/// [`Uniform`]: uniform::Uniform
+#[derive(Clone, Copy, Debug)]
+pub struct Standard;
+
+
+#[cfg(all(test, feature = "std"))]
+mod tests {
+ use super::{Distribution, Uniform};
+ use crate::Rng;
+
+ #[test]
+ fn test_distributions_iter() {
+ use crate::distributions::Open01;
+ let mut rng = crate::test::rng(210);
+ let distr = Open01;
+ let results: Vec<f32> = distr.sample_iter(&mut rng).take(100).collect();
+ println!("{:?}", results);
+ }
+
+ #[test]
+ fn test_make_an_iter() {
+ fn ten_dice_rolls_other_than_five<'a, R: Rng>(
+ rng: &'a mut R,
+ ) -> impl Iterator<Item = i32> + 'a {
+ Uniform::new_inclusive(1, 6)
+ .sample_iter(rng)
+ .filter(|x| *x != 5)
+ .take(10)
+ }
+
+ let mut rng = crate::test::rng(211);
+ let mut count = 0;
+ for val in ten_dice_rolls_other_than_five(&mut rng) {
+ assert!(val >= 1 && val <= 6 && val != 5);
+ count += 1;
+ }
+ assert_eq!(count, 10);
+ }
+}
diff --git a/src/distributions/normal.rs b/src/distributions/normal.rs
new file mode 100644
index 0000000..ec62fa9
--- /dev/null
+++ b/src/distributions/normal.rs
@@ -0,0 +1,177 @@
+// Copyright 2018 Developers of the Rand project.
+// Copyright 2013 The Rust Project Developers.
+//
+// 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 normal and derived distributions.
+#![allow(deprecated)]
+
+use crate::distributions::utils::ziggurat;
+use crate::distributions::{ziggurat_tables, Distribution, Open01};
+use crate::Rng;
+
+/// Samples floating-point numbers according to the normal distribution
+/// `N(0, 1)` (a.k.a. a standard normal, or Gaussian). This is equivalent to
+/// `Normal::new(0.0, 1.0)` but faster.
+///
+/// See `Normal` for the general normal distribution.
+///
+/// Implemented via the ZIGNOR variant[^1] of the Ziggurat method.
+///
+/// [^1]: Jurgen A. Doornik (2005). [*An Improved Ziggurat Method to
+/// Generate Normal Random Samples*](
+/// https://www.doornik.com/research/ziggurat.pdf).
+/// Nuffield College, Oxford
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct StandardNormal;
+
+impl Distribution<f64> for StandardNormal {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ #[inline]
+ fn pdf(x: f64) -> f64 {
+ (-x * x / 2.0).exp()
+ }
+ #[inline]
+ fn zero_case<R: Rng + ?Sized>(rng: &mut R, u: f64) -> f64 {
+ // compute a random number in the tail by hand
+
+ // strange initial conditions, because the loop is not
+ // do-while, so the condition should be true on the first
+ // run, they get overwritten anyway (0 < 1, so these are
+ // good).
+ let mut x = 1.0f64;
+ let mut y = 0.0f64;
+
+ while -2.0 * y < x * x {
+ let x_: f64 = rng.sample(Open01);
+ let y_: f64 = rng.sample(Open01);
+
+ x = x_.ln() / ziggurat_tables::ZIG_NORM_R;
+ y = y_.ln();
+ }
+
+ if u < 0.0 {
+ x - ziggurat_tables::ZIG_NORM_R
+ } else {
+ ziggurat_tables::ZIG_NORM_R - x
+ }
+ }
+
+ ziggurat(
+ rng,
+ true, // this is symmetric
+ &ziggurat_tables::ZIG_NORM_X,
+ &ziggurat_tables::ZIG_NORM_F,
+ pdf,
+ zero_case,
+ )
+ }
+}
+
+/// The normal distribution `N(mean, std_dev**2)`.
+///
+/// This uses the ZIGNOR variant of the Ziggurat method, see [`StandardNormal`]
+/// for more details.
+///
+/// Note that [`StandardNormal`] is an optimised implementation for mean 0, and
+/// standard deviation 1.
+///
+/// [`StandardNormal`]: crate::distributions::StandardNormal
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct Normal {
+ mean: f64,
+ std_dev: f64,
+}
+
+impl Normal {
+ /// Construct a new `Normal` distribution with the given mean and
+ /// standard deviation.
+ ///
+ /// # Panics
+ ///
+ /// Panics if `std_dev < 0`.
+ #[inline]
+ pub fn new(mean: f64, std_dev: f64) -> Normal {
+ assert!(std_dev >= 0.0, "Normal::new called with `std_dev` < 0");
+ Normal { mean, std_dev }
+ }
+}
+impl Distribution<f64> for Normal {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ let n = rng.sample(StandardNormal);
+ self.mean + self.std_dev * n
+ }
+}
+
+
+/// The log-normal distribution `ln N(mean, std_dev**2)`.
+///
+/// If `X` is log-normal distributed, then `ln(X)` is `N(mean, std_dev**2)`
+/// distributed.
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct LogNormal {
+ norm: Normal,
+}
+
+impl LogNormal {
+ /// Construct a new `LogNormal` distribution with the given mean
+ /// and standard deviation.
+ ///
+ /// # Panics
+ ///
+ /// Panics if `std_dev < 0`.
+ #[inline]
+ pub fn new(mean: f64, std_dev: f64) -> LogNormal {
+ assert!(std_dev >= 0.0, "LogNormal::new called with `std_dev` < 0");
+ LogNormal {
+ norm: Normal::new(mean, std_dev),
+ }
+ }
+}
+impl Distribution<f64> for LogNormal {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ self.norm.sample(rng).exp()
+ }
+}
+
+#[cfg(test)]
+mod tests {
+ use super::{LogNormal, Normal};
+ use crate::distributions::Distribution;
+
+ #[test]
+ fn test_normal() {
+ let norm = Normal::new(10.0, 10.0);
+ let mut rng = crate::test::rng(210);
+ for _ in 0..1000 {
+ norm.sample(&mut rng);
+ }
+ }
+ #[test]
+ #[should_panic]
+ fn test_normal_invalid_sd() {
+ Normal::new(10.0, -1.0);
+ }
+
+
+ #[test]
+ fn test_log_normal() {
+ let lnorm = LogNormal::new(10.0, 10.0);
+ let mut rng = crate::test::rng(211);
+ for _ in 0..1000 {
+ lnorm.sample(&mut rng);
+ }
+ }
+ #[test]
+ #[should_panic]
+ fn test_log_normal_invalid_sd() {
+ LogNormal::new(10.0, -1.0);
+ }
+}
diff --git a/src/distributions/other.rs b/src/distributions/other.rs
new file mode 100644
index 0000000..c95060e
--- /dev/null
+++ b/src/distributions/other.rs
@@ -0,0 +1,291 @@
+// 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 implementations of the `Standard` distribution for other built-in types.
+
+use core::char;
+use core::num::Wrapping;
+
+use crate::distributions::{Distribution, Standard, Uniform};
+use crate::Rng;
+
+// ----- Sampling distributions -----
+
+/// Sample a `char`, uniformly distributed over ASCII letters and numbers:
+/// a-z, A-Z and 0-9.
+///
+/// # Example
+///
+/// ```
+/// use std::iter;
+/// use rand::{Rng, thread_rng};
+/// use rand::distributions::Alphanumeric;
+///
+/// let mut rng = thread_rng();
+/// let chars: String = iter::repeat(())
+/// .map(|()| rng.sample(Alphanumeric))
+/// .take(7)
+/// .collect();
+/// println!("Random chars: {}", chars);
+/// ```
+#[derive(Debug)]
+pub struct Alphanumeric;
+
+
+// ----- Implementations of distributions -----
+
+impl Distribution<char> for Standard {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> char {
+ // A valid `char` is either in the interval `[0, 0xD800)` or
+ // `(0xDFFF, 0x11_0000)`. All `char`s must therefore be in
+ // `[0, 0x11_0000)` but not in the "gap" `[0xD800, 0xDFFF]` which is
+ // reserved for surrogates. This is the size of that gap.
+ const GAP_SIZE: u32 = 0xDFFF - 0xD800 + 1;
+
+ // Uniform::new(0, 0x11_0000 - GAP_SIZE) can also be used but it
+ // seemed slower.
+ let range = Uniform::new(GAP_SIZE, 0x11_0000);
+
+ let mut n = range.sample(rng);
+ if n <= 0xDFFF {
+ n -= GAP_SIZE;
+ }
+ unsafe { char::from_u32_unchecked(n) }
+ }
+}
+
+impl Distribution<char> for Alphanumeric {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> char {
+ const RANGE: u32 = 26 + 26 + 10;
+ const GEN_ASCII_STR_CHARSET: &[u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZ\
+ abcdefghijklmnopqrstuvwxyz\
+ 0123456789";
+ // We can pick from 62 characters. This is so close to a power of 2, 64,
+ // that we can do better than `Uniform`. Use a simple bitshift and
+ // rejection sampling. We do not use a bitmask, because for small RNGs
+ // the most significant bits are usually of higher quality.
+ loop {
+ let var = rng.next_u32() >> (32 - 6);
+ if var < RANGE {
+ return GEN_ASCII_STR_CHARSET[var as usize] as char;
+ }
+ }
+ }
+}
+
+impl Distribution<bool> for Standard {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> bool {
+ // We can compare against an arbitrary bit of an u32 to get a bool.
+ // Because the least significant bits of a lower quality RNG can have
+ // simple patterns, we compare against the most significant bit. This is
+ // easiest done using a sign test.
+ (rng.next_u32() as i32) < 0
+ }
+}
+
+macro_rules! tuple_impl {
+ // use variables to indicate the arity of the tuple
+ ($($tyvar:ident),* ) => {
+ // the trailing commas are for the 1 tuple
+ impl< $( $tyvar ),* >
+ Distribution<( $( $tyvar ),* , )>
+ for Standard
+ where $( Standard: Distribution<$tyvar> ),*
+ {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, _rng: &mut R) -> ( $( $tyvar ),* , ) {
+ (
+ // use the $tyvar's to get the appropriate number of
+ // repeats (they're not actually needed)
+ $(
+ _rng.gen::<$tyvar>()
+ ),*
+ ,
+ )
+ }
+ }
+ }
+}
+
+impl Distribution<()> for Standard {
+ #[allow(clippy::unused_unit)]
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, _: &mut R) -> () {
+ ()
+ }
+}
+tuple_impl! {A}
+tuple_impl! {A, B}
+tuple_impl! {A, B, C}
+tuple_impl! {A, B, C, D}
+tuple_impl! {A, B, C, D, E}
+tuple_impl! {A, B, C, D, E, F}
+tuple_impl! {A, B, C, D, E, F, G}
+tuple_impl! {A, B, C, D, E, F, G, H}
+tuple_impl! {A, B, C, D, E, F, G, H, I}
+tuple_impl! {A, B, C, D, E, F, G, H, I, J}
+tuple_impl! {A, B, C, D, E, F, G, H, I, J, K}
+tuple_impl! {A, B, C, D, E, F, G, H, I, J, K, L}
+
+macro_rules! array_impl {
+ // recursive, given at least one type parameter:
+ {$n:expr, $t:ident, $($ts:ident,)*} => {
+ array_impl!{($n - 1), $($ts,)*}
+
+ impl<T> Distribution<[T; $n]> for Standard where Standard: Distribution<T> {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, _rng: &mut R) -> [T; $n] {
+ [_rng.gen::<$t>(), $(_rng.gen::<$ts>()),*]
+ }
+ }
+ };
+ // empty case:
+ {$n:expr,} => {
+ impl<T> Distribution<[T; $n]> for Standard {
+ fn sample<R: Rng + ?Sized>(&self, _rng: &mut R) -> [T; $n] { [] }
+ }
+ };
+}
+
+array_impl! {32, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T,}
+
+impl<T> Distribution<Option<T>> for Standard
+where Standard: Distribution<T>
+{
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Option<T> {
+ // UFCS is needed here: https://github.com/rust-lang/rust/issues/24066
+ if rng.gen::<bool>() {
+ Some(rng.gen())
+ } else {
+ None
+ }
+ }
+}
+
+impl<T> Distribution<Wrapping<T>> for Standard
+where Standard: Distribution<T>
+{
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Wrapping<T> {
+ Wrapping(rng.gen())
+ }
+}
+
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+ use crate::RngCore;
+ #[cfg(all(not(feature = "std"), feature = "alloc"))] use alloc::string::String;
+
+ #[test]
+ fn test_misc() {
+ let rng: &mut dyn RngCore = &mut crate::test::rng(820);
+
+ rng.sample::<char, _>(Standard);
+ rng.sample::<bool, _>(Standard);
+ }
+
+ #[cfg(feature = "alloc")]
+ #[test]
+ fn test_chars() {
+ use core::iter;
+ let mut rng = crate::test::rng(805);
+
+ // Test by generating a relatively large number of chars, so we also
+ // take the rejection sampling path.
+ let word: String = iter::repeat(())
+ .map(|()| rng.gen::<char>())
+ .take(1000)
+ .collect();
+ assert!(word.len() != 0);
+ }
+
+ #[test]
+ fn test_alphanumeric() {
+ let mut rng = crate::test::rng(806);
+
+ // Test by generating a relatively large number of chars, so we also
+ // take the rejection sampling path.
+ let mut incorrect = false;
+ for _ in 0..100 {
+ let c = rng.sample(Alphanumeric);
+ incorrect |= !((c >= '0' && c <= '9') ||
+ (c >= 'A' && c <= 'Z') ||
+ (c >= 'a' && c <= 'z') );
+ }
+ assert!(incorrect == false);
+ }
+
+ #[test]
+ fn value_stability() {
+ fn test_samples<T: Copy + core::fmt::Debug + PartialEq, D: Distribution<T>>(
+ distr: &D, zero: T, expected: &[T],
+ ) {
+ let mut rng = crate::test::rng(807);
+ let mut buf = [zero; 5];
+ for x in &mut buf {
+ *x = rng.sample(&distr);
+ }
+ assert_eq!(&buf, expected);
+ }
+
+ test_samples(&Standard, 'a', &[
+ '\u{8cdac}',
+ '\u{a346a}',
+ '\u{80120}',
+ '\u{ed692}',
+ '\u{35888}',
+ ]);
+ test_samples(&Alphanumeric, 'a', &['h', 'm', 'e', '3', 'M']);
+ test_samples(&Standard, false, &[true, true, false, true, false]);
+ test_samples(&Standard, None as Option<bool>, &[
+ Some(true),
+ None,
+ Some(false),
+ None,
+ Some(false),
+ ]);
+ test_samples(&Standard, Wrapping(0i32), &[
+ Wrapping(-2074640887),
+ Wrapping(-1719949321),
+ Wrapping(2018088303),
+ Wrapping(-547181756),
+ Wrapping(838957336),
+ ]);
+
+ // We test only sub-sets of tuple and array impls
+ test_samples(&Standard, (), &[(), (), (), (), ()]);
+ test_samples(&Standard, (false,), &[
+ (true,),
+ (true,),
+ (false,),
+ (true,),
+ (false,),
+ ]);
+ test_samples(&Standard, (false, false), &[
+ (true, true),
+ (false, true),
+ (false, false),
+ (true, false),
+ (false, false),
+ ]);
+
+ test_samples(&Standard, [0u8; 0], &[[], [], [], [], []]);
+ test_samples(&Standard, [0u8; 3], &[
+ [9, 247, 111],
+ [68, 24, 13],
+ [174, 19, 194],
+ [172, 69, 213],
+ [149, 207, 29],
+ ]);
+ }
+}
diff --git a/src/distributions/pareto.rs b/src/distributions/pareto.rs
new file mode 100644
index 0000000..ac5473b
--- /dev/null
+++ b/src/distributions/pareto.rs
@@ -0,0 +1,70 @@
+// 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 Pareto distribution.
+#![allow(deprecated)]
+
+use crate::distributions::{Distribution, OpenClosed01};
+use crate::Rng;
+
+/// Samples floating-point numbers according to the Pareto distribution
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct Pareto {
+ scale: f64,
+ inv_neg_shape: f64,
+}
+
+impl Pareto {
+ /// Construct a new Pareto distribution with given `scale` and `shape`.
+ ///
+ /// In the literature, `scale` is commonly written as x<sub>m</sub> or k and
+ /// `shape` is often written as α.
+ ///
+ /// # Panics
+ ///
+ /// `scale` and `shape` have to be non-zero and positive.
+ pub fn new(scale: f64, shape: f64) -> Pareto {
+ assert!((scale > 0.) & (shape > 0.));
+ Pareto {
+ scale,
+ inv_neg_shape: -1.0 / shape,
+ }
+ }
+}
+
+impl Distribution<f64> for Pareto {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ let u: f64 = rng.sample(OpenClosed01);
+ self.scale * u.powf(self.inv_neg_shape)
+ }
+}
+
+#[cfg(test)]
+mod tests {
+ use super::Pareto;
+ use crate::distributions::Distribution;
+
+ #[test]
+ #[should_panic]
+ fn invalid() {
+ Pareto::new(0., 0.);
+ }
+
+ #[test]
+ fn sample() {
+ let scale = 1.0;
+ let shape = 2.0;
+ let d = Pareto::new(scale, shape);
+ let mut rng = crate::test::rng(1);
+ for _ in 0..1000 {
+ let r = d.sample(&mut rng);
+ assert!(r >= scale);
+ }
+ }
+}
diff --git a/src/distributions/poisson.rs b/src/distributions/poisson.rs
new file mode 100644
index 0000000..ce94d75
--- /dev/null
+++ b/src/distributions/poisson.rs
@@ -0,0 +1,151 @@
+// Copyright 2018 Developers of the Rand project.
+// Copyright 2016-2017 The Rust Project Developers.
+//
+// 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 Poisson distribution.
+#![allow(deprecated)]
+
+use crate::distributions::utils::log_gamma;
+use crate::distributions::{Cauchy, Distribution};
+use crate::Rng;
+
+/// The Poisson distribution `Poisson(lambda)`.
+///
+/// This distribution has a density function:
+/// `f(k) = lambda^k * exp(-lambda) / k!` for `k >= 0`.
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct Poisson {
+ lambda: f64,
+ // precalculated values
+ exp_lambda: f64,
+ log_lambda: f64,
+ sqrt_2lambda: f64,
+ magic_val: f64,
+}
+
+impl Poisson {
+ /// Construct a new `Poisson` with the given shape parameter
+ /// `lambda`. Panics if `lambda <= 0`.
+ pub fn new(lambda: f64) -> Poisson {
+ assert!(lambda > 0.0, "Poisson::new called with lambda <= 0");
+ let log_lambda = lambda.ln();
+ Poisson {
+ lambda,
+ exp_lambda: (-lambda).exp(),
+ log_lambda,
+ sqrt_2lambda: (2.0 * lambda).sqrt(),
+ magic_val: lambda * log_lambda - log_gamma(1.0 + lambda),
+ }
+ }
+}
+
+impl Distribution<u64> for Poisson {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
+ // using the algorithm from Numerical Recipes in C
+
+ // for low expected values use the Knuth method
+ if self.lambda < 12.0 {
+ let mut result = 0;
+ let mut p = 1.0;
+ while p > self.exp_lambda {
+ p *= rng.gen::<f64>();
+ result += 1;
+ }
+ result - 1
+ }
+ // high expected values - rejection method
+ else {
+ let mut int_result: u64;
+
+ // we use the Cauchy distribution as the comparison distribution
+ // f(x) ~ 1/(1+x^2)
+ let cauchy = Cauchy::new(0.0, 1.0);
+
+ loop {
+ let mut result;
+ let mut comp_dev;
+
+ loop {
+ // draw from the Cauchy distribution
+ comp_dev = rng.sample(cauchy);
+ // shift the peak of the comparison ditribution
+ result = self.sqrt_2lambda * comp_dev + self.lambda;
+ // repeat the drawing until we are in the range of possible values
+ if result >= 0.0 {
+ break;
+ }
+ }
+ // now the result is a random variable greater than 0 with Cauchy distribution
+ // the result should be an integer value
+ result = result.floor();
+ int_result = result as u64;
+
+ // this is the ratio of the Poisson distribution to the comparison distribution
+ // the magic value scales the distribution function to a range of approximately 0-1
+ // since it is not exact, we multiply the ratio by 0.9 to avoid ratios greater than 1
+ // this doesn't change the resulting distribution, only increases the rate of failed drawings
+ let check = 0.9
+ * (1.0 + comp_dev * comp_dev)
+ * (result * self.log_lambda - log_gamma(1.0 + result) - self.magic_val).exp();
+
+ // check with uniform random value - if below the threshold, we are within the target distribution
+ if rng.gen::<f64>() <= check {
+ break;
+ }
+ }
+ int_result
+ }
+ }
+}
+
+#[cfg(test)]
+mod test {
+ use super::Poisson;
+ use crate::distributions::Distribution;
+
+ #[test]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_poisson_10() {
+ let poisson = Poisson::new(10.0);
+ let mut rng = crate::test::rng(123);
+ let mut sum = 0;
+ for _ in 0..1000 {
+ sum += poisson.sample(&mut rng);
+ }
+ let avg = (sum as f64) / 1000.0;
+ println!("Poisson average: {}", avg);
+ assert!((avg - 10.0).abs() < 0.5); // not 100% certain, but probable enough
+ }
+
+ #[test]
+ fn test_poisson_15() {
+ // Take the 'high expected values' path
+ let poisson = Poisson::new(15.0);
+ let mut rng = crate::test::rng(123);
+ let mut sum = 0;
+ for _ in 0..1000 {
+ sum += poisson.sample(&mut rng);
+ }
+ let avg = (sum as f64) / 1000.0;
+ println!("Poisson average: {}", avg);
+ assert!((avg - 15.0).abs() < 0.5); // not 100% certain, but probable enough
+ }
+
+ #[test]
+ #[should_panic]
+ fn test_poisson_invalid_lambda_zero() {
+ Poisson::new(0.0);
+ }
+
+ #[test]
+ #[should_panic]
+ fn test_poisson_invalid_lambda_neg() {
+ Poisson::new(-10.0);
+ }
+}
diff --git a/src/distributions/triangular.rs b/src/distributions/triangular.rs
new file mode 100644
index 0000000..37be198
--- /dev/null
+++ b/src/distributions/triangular.rs
@@ -0,0 +1,83 @@
+// 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 triangular distribution.
+#![allow(deprecated)]
+
+use crate::distributions::{Distribution, Standard};
+use crate::Rng;
+
+/// The triangular distribution.
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct Triangular {
+ min: f64,
+ max: f64,
+ mode: f64,
+}
+
+impl Triangular {
+ /// Construct a new `Triangular` with minimum `min`, maximum `max` and mode
+ /// `mode`.
+ ///
+ /// # Panics
+ ///
+ /// If `max < mode`, `mode < max` or `max == min`.
+ #[inline]
+ pub fn new(min: f64, max: f64, mode: f64) -> Triangular {
+ assert!(max >= mode);
+ assert!(mode >= min);
+ assert!(max != min);
+ Triangular { min, max, mode }
+ }
+}
+
+impl Distribution<f64> for Triangular {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ let f: f64 = rng.sample(Standard);
+ let diff_mode_min = self.mode - self.min;
+ let diff_max_min = self.max - self.min;
+ if f * diff_max_min < diff_mode_min {
+ self.min + (f * diff_max_min * diff_mode_min).sqrt()
+ } else {
+ self.max - ((1. - f) * diff_max_min * (self.max - self.mode)).sqrt()
+ }
+ }
+}
+
+#[cfg(test)]
+mod test {
+ use super::Triangular;
+ use crate::distributions::Distribution;
+
+ #[test]
+ fn test_new() {
+ for &(min, max, mode) in &[
+ (-1., 1., 0.),
+ (1., 2., 1.),
+ (5., 25., 25.),
+ (1e-5, 1e5, 1e-3),
+ (0., 1., 0.9),
+ (-4., -0.5, -2.),
+ (-13.039, 8.41, 1.17),
+ ] {
+ println!("{} {} {}", min, max, mode);
+ let _ = Triangular::new(min, max, mode);
+ }
+ }
+
+ #[test]
+ fn test_sample() {
+ let norm = Triangular::new(0., 1., 0.5);
+ let mut rng = crate::test::rng(1);
+ for _ in 0..1000 {
+ norm.sample(&mut rng);
+ }
+ }
+}
diff --git a/src/distributions/uniform.rs b/src/distributions/uniform.rs
new file mode 100644
index 0000000..8584152
--- /dev/null
+++ b/src/distributions/uniform.rs
@@ -0,0 +1,1380 @@
+// Copyright 2018 Developers of the Rand project.
+// Copyright 2017 The Rust Project Developers.
+//
+// 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.
+
+//! A distribution uniformly sampling numbers within a given range.
+//!
+//! [`Uniform`] is the standard distribution to sample uniformly from a range;
+//! e.g. `Uniform::new_inclusive(1, 6)` can sample integers from 1 to 6, like a
+//! standard die. [`Rng::gen_range`] supports any type supported by
+//! [`Uniform`].
+//!
+//! This distribution is provided with support for several primitive types
+//! (all integer and floating-point types) as well as [`std::time::Duration`],
+//! and supports extension to user-defined types via a type-specific *back-end*
+//! implementation.
+//!
+//! The types [`UniformInt`], [`UniformFloat`] and [`UniformDuration`] are the
+//! back-ends supporting sampling from primitive integer and floating-point
+//! ranges as well as from [`std::time::Duration`]; these types do not normally
+//! need to be used directly (unless implementing a derived back-end).
+//!
+//! # Example usage
+//!
+//! ```
+//! use rand::{Rng, thread_rng};
+//! use rand::distributions::Uniform;
+//!
+//! let mut rng = thread_rng();
+//! let side = Uniform::new(-10.0, 10.0);
+//!
+//! // sample between 1 and 10 points
+//! for _ in 0..rng.gen_range(1, 11) {
+//! // sample a point from the square with sides -10 - 10 in two dimensions
+//! let (x, y) = (rng.sample(side), rng.sample(side));
+//! println!("Point: {}, {}", x, y);
+//! }
+//! ```
+//!
+//! # Extending `Uniform` to support a custom type
+//!
+//! To extend [`Uniform`] to support your own types, write a back-end which
+//! implements the [`UniformSampler`] trait, then implement the [`SampleUniform`]
+//! helper trait to "register" your back-end. See the `MyF32` example below.
+//!
+//! At a minimum, the back-end needs to store any parameters needed for sampling
+//! (e.g. the target range) and implement `new`, `new_inclusive` and `sample`.
+//! Those methods should include an assert to check the range is valid (i.e.
+//! `low < high`). The example below merely wraps another back-end.
+//!
+//! The `new`, `new_inclusive` and `sample_single` functions use arguments of
+//! type SampleBorrow<X> in order to support passing in values by reference or
+//! by value. In the implementation of these functions, you can choose to
+//! simply use the reference returned by [`SampleBorrow::borrow`], or you can choose
+//! to copy or clone the value, whatever is appropriate for your type.
+//!
+//! ```
+//! use rand::prelude::*;
+//! use rand::distributions::uniform::{Uniform, SampleUniform,
+//! UniformSampler, UniformFloat, SampleBorrow};
+//!
+//! struct MyF32(f32);
+//!
+//! #[derive(Clone, Copy, Debug)]
+//! struct UniformMyF32(UniformFloat<f32>);
+//!
+//! impl UniformSampler for UniformMyF32 {
+//! type X = MyF32;
+//! fn new<B1, B2>(low: B1, high: B2) -> Self
+//! where B1: SampleBorrow<Self::X> + Sized,
+//! B2: SampleBorrow<Self::X> + Sized
+//! {
+//! UniformMyF32(UniformFloat::<f32>::new(low.borrow().0, high.borrow().0))
+//! }
+//! fn new_inclusive<B1, B2>(low: B1, high: B2) -> Self
+//! where B1: SampleBorrow<Self::X> + Sized,
+//! B2: SampleBorrow<Self::X> + Sized
+//! {
+//! UniformSampler::new(low, high)
+//! }
+//! fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
+//! MyF32(self.0.sample(rng))
+//! }
+//! }
+//!
+//! impl SampleUniform for MyF32 {
+//! type Sampler = UniformMyF32;
+//! }
+//!
+//! let (low, high) = (MyF32(17.0f32), MyF32(22.0f32));
+//! let uniform = Uniform::new(low, high);
+//! let x = uniform.sample(&mut thread_rng());
+//! ```
+//!
+//! [`SampleUniform`]: crate::distributions::uniform::SampleUniform
+//! [`UniformSampler`]: crate::distributions::uniform::UniformSampler
+//! [`UniformInt`]: crate::distributions::uniform::UniformInt
+//! [`UniformFloat`]: crate::distributions::uniform::UniformFloat
+//! [`UniformDuration`]: crate::distributions::uniform::UniformDuration
+//! [`SampleBorrow::borrow`]: crate::distributions::uniform::SampleBorrow::borrow
+
+#[cfg(not(feature = "std"))] use core::time::Duration;
+#[cfg(feature = "std")] use std::time::Duration;
+
+use crate::distributions::float::IntoFloat;
+use crate::distributions::utils::{BoolAsSIMD, FloatAsSIMD, FloatSIMDUtils, WideningMultiply};
+use crate::distributions::Distribution;
+use crate::Rng;
+
+#[cfg(not(feature = "std"))]
+#[allow(unused_imports)] // rustc doesn't detect that this is actually used
+use crate::distributions::utils::Float;
+
+
+#[cfg(feature = "simd_support")] use packed_simd::*;
+
+/// Sample values uniformly between two bounds.
+///
+/// [`Uniform::new`] and [`Uniform::new_inclusive`] construct a uniform
+/// distribution sampling from the given range; these functions may do extra
+/// work up front to make sampling of multiple values faster.
+///
+/// When sampling from a constant range, many calculations can happen at
+/// compile-time and all methods should be fast; for floating-point ranges and
+/// the full range of integer types this should have comparable performance to
+/// the `Standard` distribution.
+///
+/// Steps are taken to avoid bias which might be present in naive
+/// implementations; for example `rng.gen::<u8>() % 170` samples from the range
+/// `[0, 169]` but is twice as likely to select numbers less than 85 than other
+/// values. Further, the implementations here give more weight to the high-bits
+/// generated by the RNG than the low bits, since with some RNGs the low-bits
+/// are of lower quality than the high bits.
+///
+/// Implementations must sample in `[low, high)` range for
+/// `Uniform::new(low, high)`, i.e., excluding `high`. In particular care must
+/// be taken to ensure that rounding never results values `< low` or `>= high`.
+///
+/// # Example
+///
+/// ```
+/// use rand::distributions::{Distribution, Uniform};
+///
+/// fn main() {
+/// let between = Uniform::from(10..10000);
+/// let mut rng = rand::thread_rng();
+/// let mut sum = 0;
+/// for _ in 0..1000 {
+/// sum += between.sample(&mut rng);
+/// }
+/// println!("{}", sum);
+/// }
+/// ```
+///
+/// [`new`]: Uniform::new
+/// [`new_inclusive`]: Uniform::new_inclusive
+#[derive(Clone, Copy, Debug)]
+pub struct Uniform<X: SampleUniform>(X::Sampler);
+
+impl<X: SampleUniform> Uniform<X> {
+ /// Create a new `Uniform` instance which samples uniformly from the half
+ /// open range `[low, high)` (excluding `high`). Panics if `low >= high`.
+ pub fn new<B1, B2>(low: B1, high: B2) -> Uniform<X>
+ where
+ B1: SampleBorrow<X> + Sized,
+ B2: SampleBorrow<X> + Sized,
+ {
+ Uniform(X::Sampler::new(low, high))
+ }
+
+ /// Create a new `Uniform` instance which samples uniformly from the closed
+ /// range `[low, high]` (inclusive). Panics if `low > high`.
+ pub fn new_inclusive<B1, B2>(low: B1, high: B2) -> Uniform<X>
+ where
+ B1: SampleBorrow<X> + Sized,
+ B2: SampleBorrow<X> + Sized,
+ {
+ Uniform(X::Sampler::new_inclusive(low, high))
+ }
+}
+
+impl<X: SampleUniform> Distribution<X> for Uniform<X> {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> X {
+ self.0.sample(rng)
+ }
+}
+
+/// Helper trait for creating objects using the correct implementation of
+/// [`UniformSampler`] for the sampling type.
+///
+/// See the [module documentation] on how to implement [`Uniform`] range
+/// sampling for a custom type.
+///
+/// [module documentation]: crate::distributions::uniform
+pub trait SampleUniform: Sized {
+ /// The `UniformSampler` implementation supporting type `X`.
+ type Sampler: UniformSampler<X = Self>;
+}
+
+/// Helper trait handling actual uniform sampling.
+///
+/// See the [module documentation] on how to implement [`Uniform`] range
+/// sampling for a custom type.
+///
+/// Implementation of [`sample_single`] is optional, and is only useful when
+/// the implementation can be faster than `Self::new(low, high).sample(rng)`.
+///
+/// [module documentation]: crate::distributions::uniform
+/// [`sample_single`]: UniformSampler::sample_single
+pub trait UniformSampler: Sized {
+ /// The type sampled by this implementation.
+ type X;
+
+ /// Construct self, with inclusive lower bound and exclusive upper bound
+ /// `[low, high)`.
+ ///
+ /// Usually users should not call this directly but instead use
+ /// `Uniform::new`, which asserts that `low < high` before calling this.
+ fn new<B1, B2>(low: B1, high: B2) -> Self
+ where
+ B1: SampleBorrow<Self::X> + Sized,
+ B2: SampleBorrow<Self::X> + Sized;
+
+ /// Construct self, with inclusive bounds `[low, high]`.
+ ///
+ /// Usually users should not call this directly but instead use
+ /// `Uniform::new_inclusive`, which asserts that `low <= high` before
+ /// calling this.
+ fn new_inclusive<B1, B2>(low: B1, high: B2) -> Self
+ where
+ B1: SampleBorrow<Self::X> + Sized,
+ B2: SampleBorrow<Self::X> + Sized;
+
+ /// Sample a value.
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X;
+
+ /// Sample a single value uniformly from a range with inclusive lower bound
+ /// and exclusive upper bound `[low, high)`.
+ ///
+ /// By default this is implemented using
+ /// `UniformSampler::new(low, high).sample(rng)`. However, for some types
+ /// more optimal implementations for single usage may be provided via this
+ /// method (which is the case for integers and floats).
+ /// Results may not be identical.
+ ///
+ /// Note that to use this method in a generic context, the type needs to be
+ /// retrieved via `SampleUniform::Sampler` as follows:
+ /// ```
+ /// use rand::{thread_rng, distributions::uniform::{SampleUniform, UniformSampler}};
+ /// # #[allow(unused)]
+ /// fn sample_from_range<T: SampleUniform>(lb: T, ub: T) -> T {
+ /// let mut rng = thread_rng();
+ /// <T as SampleUniform>::Sampler::sample_single(lb, ub, &mut rng)
+ /// }
+ /// ```
+ fn sample_single<R: Rng + ?Sized, B1, B2>(low: B1, high: B2, rng: &mut R) -> Self::X
+ where
+ B1: SampleBorrow<Self::X> + Sized,
+ B2: SampleBorrow<Self::X> + Sized,
+ {
+ let uniform: Self = UniformSampler::new(low, high);
+ uniform.sample(rng)
+ }
+}
+
+impl<X: SampleUniform> From<::core::ops::Range<X>> for Uniform<X> {
+ fn from(r: ::core::ops::Range<X>) -> Uniform<X> {
+ Uniform::new(r.start, r.end)
+ }
+}
+
+impl<X: SampleUniform> From<::core::ops::RangeInclusive<X>> for Uniform<X> {
+ fn from(r: ::core::ops::RangeInclusive<X>) -> Uniform<X> {
+ Uniform::new_inclusive(r.start(), r.end())
+ }
+}
+
+/// Helper trait similar to [`Borrow`] but implemented
+/// only for SampleUniform and references to SampleUniform in
+/// order to resolve ambiguity issues.
+///
+/// [`Borrow`]: std::borrow::Borrow
+pub trait SampleBorrow<Borrowed> {
+ /// Immutably borrows from an owned value. See [`Borrow::borrow`]
+ ///
+ /// [`Borrow::borrow`]: std::borrow::Borrow::borrow
+ fn borrow(&self) -> &Borrowed;
+}
+impl<Borrowed> SampleBorrow<Borrowed> for Borrowed
+where Borrowed: SampleUniform
+{
+ #[inline(always)]
+ fn borrow(&self) -> &Borrowed {
+ self
+ }
+}
+impl<'a, Borrowed> SampleBorrow<Borrowed> for &'a Borrowed
+where Borrowed: SampleUniform
+{
+ #[inline(always)]
+ fn borrow(&self) -> &Borrowed {
+ *self
+ }
+}
+
+////////////////////////////////////////////////////////////////////////////////
+
+// What follows are all back-ends.
+
+
+/// The back-end implementing [`UniformSampler`] for integer types.
+///
+/// Unless you are implementing [`UniformSampler`] for your own type, this type
+/// should not be used directly, use [`Uniform`] instead.
+///
+/// # Implementation notes
+///
+/// For simplicity, we use the same generic struct `UniformInt<X>` for all
+/// integer types `X`. This gives us only one field type, `X`; to store unsigned
+/// values of this size, we take use the fact that these conversions are no-ops.
+///
+/// For a closed range, the number of possible numbers we should generate is
+/// `range = (high - low + 1)`. To avoid bias, we must ensure that the size of
+/// our sample space, `zone`, is a multiple of `range`; other values must be
+/// rejected (by replacing with a new random sample).
+///
+/// As a special case, we use `range = 0` to represent the full range of the
+/// result type (i.e. for `new_inclusive($ty::MIN, $ty::MAX)`).
+///
+/// The optimum `zone` is the largest product of `range` which fits in our
+/// (unsigned) target type. We calculate this by calculating how many numbers we
+/// must reject: `reject = (MAX + 1) % range = (MAX - range + 1) % range`. Any (large)
+/// product of `range` will suffice, thus in `sample_single` we multiply by a
+/// power of 2 via bit-shifting (faster but may cause more rejections).
+///
+/// The smallest integer PRNGs generate is `u32`. For 8- and 16-bit outputs we
+/// use `u32` for our `zone` and samples (because it's not slower and because
+/// it reduces the chance of having to reject a sample). In this case we cannot
+/// store `zone` in the target type since it is too large, however we know
+/// `ints_to_reject < range <= $unsigned::MAX`.
+///
+/// An alternative to using a modulus is widening multiply: After a widening
+/// multiply by `range`, the result is in the high word. Then comparing the low
+/// word against `zone` makes sure our distribution is uniform.
+#[derive(Clone, Copy, Debug)]
+pub struct UniformInt<X> {
+ low: X,
+ range: X,
+ z: X, // either ints_to_reject or zone depending on implementation
+}
+
+macro_rules! uniform_int_impl {
+ ($ty:ty, $unsigned:ident, $u_large:ident) => {
+ impl SampleUniform for $ty {
+ type Sampler = UniformInt<$ty>;
+ }
+
+ impl UniformSampler for UniformInt<$ty> {
+ // We play free and fast with unsigned vs signed here
+ // (when $ty is signed), but that's fine, since the
+ // contract of this macro is for $ty and $unsigned to be
+ // "bit-equal", so casting between them is a no-op.
+
+ type X = $ty;
+
+ #[inline] // if the range is constant, this helps LLVM to do the
+ // calculations at compile-time.
+ fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
+ where
+ B1: SampleBorrow<Self::X> + Sized,
+ B2: SampleBorrow<Self::X> + Sized,
+ {
+ let low = *low_b.borrow();
+ let high = *high_b.borrow();
+ assert!(low < high, "Uniform::new called with `low >= high`");
+ UniformSampler::new_inclusive(low, high - 1)
+ }
+
+ #[inline] // if the range is constant, this helps LLVM to do the
+ // calculations at compile-time.
+ fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
+ where
+ B1: SampleBorrow<Self::X> + Sized,
+ B2: SampleBorrow<Self::X> + Sized,
+ {
+ let low = *low_b.borrow();
+ let high = *high_b.borrow();
+ assert!(
+ low <= high,
+ "Uniform::new_inclusive called with `low > high`"
+ );
+ let unsigned_max = ::core::$u_large::MAX;
+
+ let range = high.wrapping_sub(low).wrapping_add(1) as $unsigned;
+ let ints_to_reject = if range > 0 {
+ let range = $u_large::from(range);
+ (unsigned_max - range + 1) % range
+ } else {
+ 0
+ };
+
+ UniformInt {
+ low: low,
+ // These are really $unsigned values, but store as $ty:
+ range: range as $ty,
+ z: ints_to_reject as $unsigned as $ty,
+ }
+ }
+
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
+ let range = self.range as $unsigned as $u_large;
+ if range > 0 {
+ let unsigned_max = ::core::$u_large::MAX;
+ let zone = unsigned_max - (self.z as $unsigned as $u_large);
+ loop {
+ let v: $u_large = rng.gen();
+ let (hi, lo) = v.wmul(range);
+ if lo <= zone {
+ return self.low.wrapping_add(hi as $ty);
+ }
+ }
+ } else {
+ // Sample from the entire integer range.
+ rng.gen()
+ }
+ }
+
+ fn sample_single<R: Rng + ?Sized, B1, B2>(low_b: B1, high_b: B2, rng: &mut R) -> Self::X
+ where
+ B1: SampleBorrow<Self::X> + Sized,
+ B2: SampleBorrow<Self::X> + Sized,
+ {
+ let low = *low_b.borrow();
+ let high = *high_b.borrow();
+ assert!(low < high, "UniformSampler::sample_single: low >= high");
+ let range = high.wrapping_sub(low) as $unsigned as $u_large;
+ let zone = if ::core::$unsigned::MAX <= ::core::u16::MAX as $unsigned {
+ // Using a modulus is faster than the approximation for
+ // i8 and i16. I suppose we trade the cost of one
+ // modulus for near-perfect branch prediction.
+ let unsigned_max: $u_large = ::core::$u_large::MAX;
+ let ints_to_reject = (unsigned_max - range + 1) % range;
+ unsigned_max - ints_to_reject
+ } else {
+ // conservative but fast approximation. `- 1` is necessary to allow the
+ // same comparison without bias.
+ (range << range.leading_zeros()).wrapping_sub(1)
+ };
+
+ loop {
+ let v: $u_large = rng.gen();
+ let (hi, lo) = v.wmul(range);
+ if lo <= zone {
+ return low.wrapping_add(hi as $ty);
+ }
+ }
+ }
+ }
+ };
+}
+
+uniform_int_impl! { i8, u8, u32 }
+uniform_int_impl! { i16, u16, u32 }
+uniform_int_impl! { i32, u32, u32 }
+uniform_int_impl! { i64, u64, u64 }
+#[cfg(not(target_os = "emscripten"))]
+uniform_int_impl! { i128, u128, u128 }
+uniform_int_impl! { isize, usize, usize }
+uniform_int_impl! { u8, u8, u32 }
+uniform_int_impl! { u16, u16, u32 }
+uniform_int_impl! { u32, u32, u32 }
+uniform_int_impl! { u64, u64, u64 }
+uniform_int_impl! { usize, usize, usize }
+#[cfg(not(target_os = "emscripten"))]
+uniform_int_impl! { u128, u128, u128 }
+
+#[cfg(all(feature = "simd_support", feature = "nightly"))]
+macro_rules! uniform_simd_int_impl {
+ ($ty:ident, $unsigned:ident, $u_scalar:ident) => {
+ // The "pick the largest zone that can fit in an `u32`" optimization
+ // is less useful here. Multiple lanes complicate things, we don't
+ // know the PRNG's minimal output size, and casting to a larger vector
+ // is generally a bad idea for SIMD performance. The user can still
+ // implement it manually.
+
+ // TODO: look into `Uniform::<u32x4>::new(0u32, 100)` functionality
+ // perhaps `impl SampleUniform for $u_scalar`?
+ impl SampleUniform for $ty {
+ type Sampler = UniformInt<$ty>;
+ }
+
+ impl UniformSampler for UniformInt<$ty> {
+ type X = $ty;
+
+ #[inline] // if the range is constant, this helps LLVM to do the
+ // calculations at compile-time.
+ fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
+ where B1: SampleBorrow<Self::X> + Sized,
+ B2: SampleBorrow<Self::X> + Sized
+ {
+ let low = *low_b.borrow();
+ let high = *high_b.borrow();
+ assert!(low.lt(high).all(), "Uniform::new called with `low >= high`");
+ UniformSampler::new_inclusive(low, high - 1)
+ }
+
+ #[inline] // if the range is constant, this helps LLVM to do the
+ // calculations at compile-time.
+ fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
+ where B1: SampleBorrow<Self::X> + Sized,
+ B2: SampleBorrow<Self::X> + Sized
+ {
+ let low = *low_b.borrow();
+ let high = *high_b.borrow();
+ assert!(low.le(high).all(),
+ "Uniform::new_inclusive called with `low > high`");
+ let unsigned_max = ::core::$u_scalar::MAX;
+
+ // NOTE: these may need to be replaced with explicitly
+ // wrapping operations if `packed_simd` changes
+ let range: $unsigned = ((high - low) + 1).cast();
+ // `% 0` will panic at runtime.
+ let not_full_range = range.gt($unsigned::splat(0));
+ // replacing 0 with `unsigned_max` allows a faster `select`
+ // with bitwise OR
+ let modulo = not_full_range.select(range, $unsigned::splat(unsigned_max));
+ // wrapping addition
+ let ints_to_reject = (unsigned_max - range + 1) % modulo;
+ // When `range` is 0, `lo` of `v.wmul(range)` will always be
+ // zero which means only one sample is needed.
+ let zone = unsigned_max - ints_to_reject;
+
+ UniformInt {
+ low: low,
+ // These are really $unsigned values, but store as $ty:
+ range: range.cast(),
+ z: zone.cast(),
+ }
+ }
+
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
+ let range: $unsigned = self.range.cast();
+ let zone: $unsigned = self.z.cast();
+
+ // This might seem very slow, generating a whole new
+ // SIMD vector for every sample rejection. For most uses
+ // though, the chance of rejection is small and provides good
+ // general performance. With multiple lanes, that chance is
+ // multiplied. To mitigate this, we replace only the lanes of
+ // the vector which fail, iteratively reducing the chance of
+ // rejection. The replacement method does however add a little
+ // overhead. Benchmarking or calculating probabilities might
+ // reveal contexts where this replacement method is slower.
+ let mut v: $unsigned = rng.gen();
+ loop {
+ let (hi, lo) = v.wmul(range);
+ let mask = lo.le(zone);
+ if mask.all() {
+ let hi: $ty = hi.cast();
+ // wrapping addition
+ let result = self.low + hi;
+ // `select` here compiles to a blend operation
+ // When `range.eq(0).none()` the compare and blend
+ // operations are avoided.
+ let v: $ty = v.cast();
+ return range.gt($unsigned::splat(0)).select(result, v);
+ }
+ // Replace only the failing lanes
+ v = mask.select(v, rng.gen());
+ }
+ }
+ }
+ };
+
+ // bulk implementation
+ ($(($unsigned:ident, $signed:ident),)+ $u_scalar:ident) => {
+ $(
+ uniform_simd_int_impl!($unsigned, $unsigned, $u_scalar);
+ uniform_simd_int_impl!($signed, $unsigned, $u_scalar);
+ )+
+ };
+}
+
+#[cfg(all(feature = "simd_support", feature = "nightly"))]
+uniform_simd_int_impl! {
+ (u64x2, i64x2),
+ (u64x4, i64x4),
+ (u64x8, i64x8),
+ u64
+}
+
+#[cfg(all(feature = "simd_support", feature = "nightly"))]
+uniform_simd_int_impl! {
+ (u32x2, i32x2),
+ (u32x4, i32x4),
+ (u32x8, i32x8),
+ (u32x16, i32x16),
+ u32
+}
+
+#[cfg(all(feature = "simd_support", feature = "nightly"))]
+uniform_simd_int_impl! {
+ (u16x2, i16x2),
+ (u16x4, i16x4),
+ (u16x8, i16x8),
+ (u16x16, i16x16),
+ (u16x32, i16x32),
+ u16
+}
+
+#[cfg(all(feature = "simd_support", feature = "nightly"))]
+uniform_simd_int_impl! {
+ (u8x2, i8x2),
+ (u8x4, i8x4),
+ (u8x8, i8x8),
+ (u8x16, i8x16),
+ (u8x32, i8x32),
+ (u8x64, i8x64),
+ u8
+}
+
+
+/// The back-end implementing [`UniformSampler`] for floating-point types.
+///
+/// Unless you are implementing [`UniformSampler`] for your own type, this type
+/// should not be used directly, use [`Uniform`] instead.
+///
+/// # Implementation notes
+///
+/// Instead of generating a float in the `[0, 1)` range using [`Standard`], the
+/// `UniformFloat` implementation converts the output of an PRNG itself. This
+/// way one or two steps can be optimized out.
+///
+/// The floats are first converted to a value in the `[1, 2)` interval using a
+/// transmute-based method, and then mapped to the expected range with a
+/// multiply and addition. Values produced this way have what equals 23 bits of
+/// random digits for an `f32`, and 52 for an `f64`.
+///
+/// [`new`]: UniformSampler::new
+/// [`new_inclusive`]: UniformSampler::new_inclusive
+/// [`Standard`]: crate::distributions::Standard
+#[derive(Clone, Copy, Debug)]
+pub struct UniformFloat<X> {
+ low: X,
+ scale: X,
+}
+
+macro_rules! uniform_float_impl {
+ ($ty:ty, $uty:ident, $f_scalar:ident, $u_scalar:ident, $bits_to_discard:expr) => {
+ impl SampleUniform for $ty {
+ type Sampler = UniformFloat<$ty>;
+ }
+
+ impl UniformSampler for UniformFloat<$ty> {
+ type X = $ty;
+
+ fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
+ where
+ B1: SampleBorrow<Self::X> + Sized,
+ B2: SampleBorrow<Self::X> + Sized,
+ {
+ let low = *low_b.borrow();
+ let high = *high_b.borrow();
+ assert!(low.all_lt(high), "Uniform::new called with `low >= high`");
+ assert!(
+ low.all_finite() && high.all_finite(),
+ "Uniform::new called with non-finite boundaries"
+ );
+ let max_rand = <$ty>::splat(
+ (::core::$u_scalar::MAX >> $bits_to_discard).into_float_with_exponent(0) - 1.0,
+ );
+
+ let mut scale = high - low;
+
+ loop {
+ let mask = (scale * max_rand + low).ge_mask(high);
+ if mask.none() {
+ break;
+ }
+ scale = scale.decrease_masked(mask);
+ }
+
+ debug_assert!(<$ty>::splat(0.0).all_le(scale));
+
+ UniformFloat { low, scale }
+ }
+
+ fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
+ where
+ B1: SampleBorrow<Self::X> + Sized,
+ B2: SampleBorrow<Self::X> + Sized,
+ {
+ let low = *low_b.borrow();
+ let high = *high_b.borrow();
+ assert!(
+ low.all_le(high),
+ "Uniform::new_inclusive called with `low > high`"
+ );
+ assert!(
+ low.all_finite() && high.all_finite(),
+ "Uniform::new_inclusive called with non-finite boundaries"
+ );
+ let max_rand = <$ty>::splat(
+ (::core::$u_scalar::MAX >> $bits_to_discard).into_float_with_exponent(0) - 1.0,
+ );
+
+ let mut scale = (high - low) / max_rand;
+
+ loop {
+ let mask = (scale * max_rand + low).gt_mask(high);
+ if mask.none() {
+ break;
+ }
+ scale = scale.decrease_masked(mask);
+ }
+
+ debug_assert!(<$ty>::splat(0.0).all_le(scale));
+
+ UniformFloat { low, scale }
+ }
+
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
+ // Generate a value in the range [1, 2)
+ let value1_2 = (rng.gen::<$uty>() >> $bits_to_discard).into_float_with_exponent(0);
+
+ // Get a value in the range [0, 1) in order to avoid
+ // overflowing into infinity when multiplying with scale
+ let value0_1 = value1_2 - 1.0;
+
+ // We don't use `f64::mul_add`, because it is not available with
+ // `no_std`. Furthermore, it is slower for some targets (but
+ // faster for others). However, the order of multiplication and
+ // addition is important, because on some platforms (e.g. ARM)
+ // it will be optimized to a single (non-FMA) instruction.
+ value0_1 * self.scale + self.low
+ }
+
+ #[inline]
+ fn sample_single<R: Rng + ?Sized, B1, B2>(low_b: B1, high_b: B2, rng: &mut R) -> Self::X
+ where
+ B1: SampleBorrow<Self::X> + Sized,
+ B2: SampleBorrow<Self::X> + Sized,
+ {
+ let low = *low_b.borrow();
+ let high = *high_b.borrow();
+ assert!(
+ low.all_lt(high),
+ "UniformSampler::sample_single: low >= high"
+ );
+ let mut scale = high - low;
+
+ loop {
+ // Generate a value in the range [1, 2)
+ let value1_2 =
+ (rng.gen::<$uty>() >> $bits_to_discard).into_float_with_exponent(0);
+
+ // Get a value in the range [0, 1) in order to avoid
+ // overflowing into infinity when multiplying with scale
+ let value0_1 = value1_2 - 1.0;
+
+ // Doing multiply before addition allows some architectures
+ // to use a single instruction.
+ let res = value0_1 * scale + low;
+
+ debug_assert!(low.all_le(res) || !scale.all_finite());
+ if res.all_lt(high) {
+ return res;
+ }
+
+ // This handles a number of edge cases.
+ // * `low` or `high` is NaN. In this case `scale` and
+ // `res` are going to end up as NaN.
+ // * `low` is negative infinity and `high` is finite.
+ // `scale` is going to be infinite and `res` will be
+ // NaN.
+ // * `high` is positive infinity and `low` is finite.
+ // `scale` is going to be infinite and `res` will
+ // be infinite or NaN (if value0_1 is 0).
+ // * `low` is negative infinity and `high` is positive
+ // infinity. `scale` will be infinite and `res` will
+ // be NaN.
+ // * `low` and `high` are finite, but `high - low`
+ // overflows to infinite. `scale` will be infinite
+ // and `res` will be infinite or NaN (if value0_1 is 0).
+ // So if `high` or `low` are non-finite, we are guaranteed
+ // to fail the `res < high` check above and end up here.
+ //
+ // While we technically should check for non-finite `low`
+ // and `high` before entering the loop, by doing the checks
+ // here instead, we allow the common case to avoid these
+ // checks. But we are still guaranteed that if `low` or
+ // `high` are non-finite we'll end up here and can do the
+ // appropriate checks.
+ //
+ // Likewise `high - low` overflowing to infinity is also
+ // rare, so handle it here after the common case.
+ let mask = !scale.finite_mask();
+ if mask.any() {
+ assert!(
+ low.all_finite() && high.all_finite(),
+ "Uniform::sample_single: low and high must be finite"
+ );
+ scale = scale.decrease_masked(mask);
+ }
+ }
+ }
+ }
+ };
+}
+
+uniform_float_impl! { f32, u32, f32, u32, 32 - 23 }
+uniform_float_impl! { f64, u64, f64, u64, 64 - 52 }
+
+#[cfg(feature = "simd_support")]
+uniform_float_impl! { f32x2, u32x2, f32, u32, 32 - 23 }
+#[cfg(feature = "simd_support")]
+uniform_float_impl! { f32x4, u32x4, f32, u32, 32 - 23 }
+#[cfg(feature = "simd_support")]
+uniform_float_impl! { f32x8, u32x8, f32, u32, 32 - 23 }
+#[cfg(feature = "simd_support")]
+uniform_float_impl! { f32x16, u32x16, f32, u32, 32 - 23 }
+
+#[cfg(feature = "simd_support")]
+uniform_float_impl! { f64x2, u64x2, f64, u64, 64 - 52 }
+#[cfg(feature = "simd_support")]
+uniform_float_impl! { f64x4, u64x4, f64, u64, 64 - 52 }
+#[cfg(feature = "simd_support")]
+uniform_float_impl! { f64x8, u64x8, f64, u64, 64 - 52 }
+
+
+/// The back-end implementing [`UniformSampler`] for `Duration`.
+///
+/// Unless you are implementing [`UniformSampler`] for your own types, this type
+/// should not be used directly, use [`Uniform`] instead.
+#[derive(Clone, Copy, Debug)]
+pub struct UniformDuration {
+ mode: UniformDurationMode,
+ offset: u32,
+}
+
+#[derive(Debug, Copy, Clone)]
+enum UniformDurationMode {
+ Small {
+ secs: u64,
+ nanos: Uniform<u32>,
+ },
+ Medium {
+ nanos: Uniform<u64>,
+ },
+ Large {
+ max_secs: u64,
+ max_nanos: u32,
+ secs: Uniform<u64>,
+ },
+}
+
+impl SampleUniform for Duration {
+ type Sampler = UniformDuration;
+}
+
+impl UniformSampler for UniformDuration {
+ type X = Duration;
+
+ #[inline]
+ fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
+ where
+ B1: SampleBorrow<Self::X> + Sized,
+ B2: SampleBorrow<Self::X> + Sized,
+ {
+ let low = *low_b.borrow();
+ let high = *high_b.borrow();
+ assert!(low < high, "Uniform::new called with `low >= high`");
+ UniformDuration::new_inclusive(low, high - Duration::new(0, 1))
+ }
+
+ #[inline]
+ fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
+ where
+ B1: SampleBorrow<Self::X> + Sized,
+ B2: SampleBorrow<Self::X> + Sized,
+ {
+ let low = *low_b.borrow();
+ let high = *high_b.borrow();
+ assert!(
+ low <= high,
+ "Uniform::new_inclusive called with `low > high`"
+ );
+
+ let low_s = low.as_secs();
+ let low_n = low.subsec_nanos();
+ let mut high_s = high.as_secs();
+ let mut high_n = high.subsec_nanos();
+
+ if high_n < low_n {
+ high_s -= 1;
+ high_n += 1_000_000_000;
+ }
+
+ let mode = if low_s == high_s {
+ UniformDurationMode::Small {
+ secs: low_s,
+ nanos: Uniform::new_inclusive(low_n, high_n),
+ }
+ } else {
+ let max = high_s
+ .checked_mul(1_000_000_000)
+ .and_then(|n| n.checked_add(u64::from(high_n)));
+
+ if let Some(higher_bound) = max {
+ let lower_bound = low_s * 1_000_000_000 + u64::from(low_n);
+ UniformDurationMode::Medium {
+ nanos: Uniform::new_inclusive(lower_bound, higher_bound),
+ }
+ } else {
+ // An offset is applied to simplify generation of nanoseconds
+ let max_nanos = high_n - low_n;
+ UniformDurationMode::Large {
+ max_secs: high_s,
+ max_nanos,
+ secs: Uniform::new_inclusive(low_s, high_s),
+ }
+ }
+ };
+ UniformDuration {
+ mode,
+ offset: low_n,
+ }
+ }
+
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Duration {
+ match self.mode {
+ UniformDurationMode::Small { secs, nanos } => {
+ let n = nanos.sample(rng);
+ Duration::new(secs, n)
+ }
+ UniformDurationMode::Medium { nanos } => {
+ let nanos = nanos.sample(rng);
+ Duration::new(nanos / 1_000_000_000, (nanos % 1_000_000_000) as u32)
+ }
+ UniformDurationMode::Large {
+ max_secs,
+ max_nanos,
+ secs,
+ } => {
+ // constant folding means this is at least as fast as `gen_range`
+ let nano_range = Uniform::new(0, 1_000_000_000);
+ loop {
+ let s = secs.sample(rng);
+ let n = nano_range.sample(rng);
+ if !(s == max_secs && n > max_nanos) {
+ let sum = n + self.offset;
+ break Duration::new(s, sum);
+ }
+ }
+ }
+ }
+ }
+}
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+ use crate::rngs::mock::StepRng;
+
+ #[should_panic]
+ #[test]
+ fn test_uniform_bad_limits_equal_int() {
+ Uniform::new(10, 10);
+ }
+
+ #[test]
+ fn test_uniform_good_limits_equal_int() {
+ let mut rng = crate::test::rng(804);
+ let dist = Uniform::new_inclusive(10, 10);
+ for _ in 0..20 {
+ assert_eq!(rng.sample(dist), 10);
+ }
+ }
+
+ #[should_panic]
+ #[test]
+ fn test_uniform_bad_limits_flipped_int() {
+ Uniform::new(10, 5);
+ }
+
+ #[test]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_integers() {
+ #[cfg(not(target_os = "emscripten"))] use core::{i128, u128};
+ use core::{i16, i32, i64, i8, isize};
+ use core::{u16, u32, u64, u8, usize};
+
+ let mut rng = crate::test::rng(251);
+ macro_rules! t {
+ ($ty:ident, $v:expr, $le:expr, $lt:expr) => {{
+ for &(low, high) in $v.iter() {
+ let my_uniform = Uniform::new(low, high);
+ for _ in 0..1000 {
+ let v: $ty = rng.sample(my_uniform);
+ assert!($le(low, v) && $lt(v, high));
+ }
+
+ let my_uniform = Uniform::new_inclusive(low, high);
+ for _ in 0..1000 {
+ let v: $ty = rng.sample(my_uniform);
+ assert!($le(low, v) && $le(v, high));
+ }
+
+ let my_uniform = Uniform::new(&low, high);
+ for _ in 0..1000 {
+ let v: $ty = rng.sample(my_uniform);
+ assert!($le(low, v) && $lt(v, high));
+ }
+
+ let my_uniform = Uniform::new_inclusive(&low, &high);
+ for _ in 0..1000 {
+ let v: $ty = rng.sample(my_uniform);
+ assert!($le(low, v) && $le(v, high));
+ }
+
+ for _ in 0..1000 {
+ let v: $ty = rng.gen_range(low, high);
+ assert!($le(low, v) && $lt(v, high));
+ }
+ }
+ }};
+
+ // scalar bulk
+ ($($ty:ident),*) => {{
+ $(t!(
+ $ty,
+ [(0, 10), (10, 127), ($ty::MIN, $ty::MAX)],
+ |x, y| x <= y,
+ |x, y| x < y
+ );)*
+ }};
+
+ // simd bulk
+ ($($ty:ident),* => $scalar:ident) => {{
+ $(t!(
+ $ty,
+ [
+ ($ty::splat(0), $ty::splat(10)),
+ ($ty::splat(10), $ty::splat(127)),
+ ($ty::splat($scalar::MIN), $ty::splat($scalar::MAX)),
+ ],
+ |x: $ty, y| x.le(y).all(),
+ |x: $ty, y| x.lt(y).all()
+ );)*
+ }};
+ }
+ t!(i8, i16, i32, i64, isize, u8, u16, u32, u64, usize);
+ #[cfg(not(target_os = "emscripten"))]
+ t!(i128, u128);
+
+ #[cfg(all(feature = "simd_support", feature = "nightly"))]
+ {
+ t!(u8x2, u8x4, u8x8, u8x16, u8x32, u8x64 => u8);
+ t!(i8x2, i8x4, i8x8, i8x16, i8x32, i8x64 => i8);
+ t!(u16x2, u16x4, u16x8, u16x16, u16x32 => u16);
+ t!(i16x2, i16x4, i16x8, i16x16, i16x32 => i16);
+ t!(u32x2, u32x4, u32x8, u32x16 => u32);
+ t!(i32x2, i32x4, i32x8, i32x16 => i32);
+ t!(u64x2, u64x4, u64x8 => u64);
+ t!(i64x2, i64x4, i64x8 => i64);
+ }
+ }
+
+ #[test]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_floats() {
+ let mut rng = crate::test::rng(252);
+ let mut zero_rng = StepRng::new(0, 0);
+ let mut max_rng = StepRng::new(0xffff_ffff_ffff_ffff, 0);
+ macro_rules! t {
+ ($ty:ty, $f_scalar:ident, $bits_shifted:expr) => {{
+ let v: &[($f_scalar, $f_scalar)] = &[
+ (0.0, 100.0),
+ (-1e35, -1e25),
+ (1e-35, 1e-25),
+ (-1e35, 1e35),
+ (<$f_scalar>::from_bits(0), <$f_scalar>::from_bits(3)),
+ (-<$f_scalar>::from_bits(10), -<$f_scalar>::from_bits(1)),
+ (-<$f_scalar>::from_bits(5), 0.0),
+ (-<$f_scalar>::from_bits(7), -0.0),
+ (10.0, ::core::$f_scalar::MAX),
+ (-100.0, ::core::$f_scalar::MAX),
+ (-::core::$f_scalar::MAX / 5.0, ::core::$f_scalar::MAX),
+ (-::core::$f_scalar::MAX, ::core::$f_scalar::MAX / 5.0),
+ (-::core::$f_scalar::MAX * 0.8, ::core::$f_scalar::MAX * 0.7),
+ (-::core::$f_scalar::MAX, ::core::$f_scalar::MAX),
+ ];
+ for &(low_scalar, high_scalar) in v.iter() {
+ for lane in 0..<$ty>::lanes() {
+ let low = <$ty>::splat(0.0 as $f_scalar).replace(lane, low_scalar);
+ let high = <$ty>::splat(1.0 as $f_scalar).replace(lane, high_scalar);
+ let my_uniform = Uniform::new(low, high);
+ let my_incl_uniform = Uniform::new_inclusive(low, high);
+ for _ in 0..100 {
+ let v = rng.sample(my_uniform).extract(lane);
+ assert!(low_scalar <= v && v < high_scalar);
+ let v = rng.sample(my_incl_uniform).extract(lane);
+ assert!(low_scalar <= v && v <= high_scalar);
+ let v = rng.gen_range(low, high).extract(lane);
+ assert!(low_scalar <= v && v < high_scalar);
+ }
+
+ assert_eq!(
+ rng.sample(Uniform::new_inclusive(low, low)).extract(lane),
+ low_scalar
+ );
+
+ assert_eq!(zero_rng.sample(my_uniform).extract(lane), low_scalar);
+ assert_eq!(zero_rng.sample(my_incl_uniform).extract(lane), low_scalar);
+ assert_eq!(zero_rng.gen_range(low, high).extract(lane), low_scalar);
+ assert!(max_rng.sample(my_uniform).extract(lane) < high_scalar);
+ assert!(max_rng.sample(my_incl_uniform).extract(lane) <= high_scalar);
+
+ // Don't run this test for really tiny differences between high and low
+ // since for those rounding might result in selecting high for a very
+ // long time.
+ if (high_scalar - low_scalar) > 0.0001 {
+ let mut lowering_max_rng = StepRng::new(
+ 0xffff_ffff_ffff_ffff,
+ (-1i64 << $bits_shifted) as u64,
+ );
+ assert!(
+ lowering_max_rng.gen_range(low, high).extract(lane) < high_scalar
+ );
+ }
+ }
+ }
+
+ assert_eq!(
+ rng.sample(Uniform::new_inclusive(
+ ::core::$f_scalar::MAX,
+ ::core::$f_scalar::MAX
+ )),
+ ::core::$f_scalar::MAX
+ );
+ assert_eq!(
+ rng.sample(Uniform::new_inclusive(
+ -::core::$f_scalar::MAX,
+ -::core::$f_scalar::MAX
+ )),
+ -::core::$f_scalar::MAX
+ );
+ }};
+ }
+
+ t!(f32, f32, 32 - 23);
+ t!(f64, f64, 64 - 52);
+ #[cfg(feature = "simd_support")]
+ {
+ t!(f32x2, f32, 32 - 23);
+ t!(f32x4, f32, 32 - 23);
+ t!(f32x8, f32, 32 - 23);
+ t!(f32x16, f32, 32 - 23);
+ t!(f64x2, f64, 64 - 52);
+ t!(f64x4, f64, 64 - 52);
+ t!(f64x8, f64, 64 - 52);
+ }
+ }
+
+ #[test]
+ #[cfg(all(
+ feature = "std",
+ not(target_arch = "wasm32"),
+ not(target_arch = "asmjs")
+ ))]
+ fn test_float_assertions() {
+ use super::SampleUniform;
+ use std::panic::catch_unwind;
+ fn range<T: SampleUniform>(low: T, high: T) {
+ let mut rng = crate::test::rng(253);
+ rng.gen_range(low, high);
+ }
+
+ macro_rules! t {
+ ($ty:ident, $f_scalar:ident) => {{
+ let v: &[($f_scalar, $f_scalar)] = &[
+ (::std::$f_scalar::NAN, 0.0),
+ (1.0, ::std::$f_scalar::NAN),
+ (::std::$f_scalar::NAN, ::std::$f_scalar::NAN),
+ (1.0, 0.5),
+ (::std::$f_scalar::MAX, -::std::$f_scalar::MAX),
+ (::std::$f_scalar::INFINITY, ::std::$f_scalar::INFINITY),
+ (
+ ::std::$f_scalar::NEG_INFINITY,
+ ::std::$f_scalar::NEG_INFINITY,
+ ),
+ (::std::$f_scalar::NEG_INFINITY, 5.0),
+ (5.0, ::std::$f_scalar::INFINITY),
+ (::std::$f_scalar::NAN, ::std::$f_scalar::INFINITY),
+ (::std::$f_scalar::NEG_INFINITY, ::std::$f_scalar::NAN),
+ (::std::$f_scalar::NEG_INFINITY, ::std::$f_scalar::INFINITY),
+ ];
+ for &(low_scalar, high_scalar) in v.iter() {
+ for lane in 0..<$ty>::lanes() {
+ let low = <$ty>::splat(0.0 as $f_scalar).replace(lane, low_scalar);
+ let high = <$ty>::splat(1.0 as $f_scalar).replace(lane, high_scalar);
+ assert!(catch_unwind(|| range(low, high)).is_err());
+ assert!(catch_unwind(|| Uniform::new(low, high)).is_err());
+ assert!(catch_unwind(|| Uniform::new_inclusive(low, high)).is_err());
+ assert!(catch_unwind(|| range(low, low)).is_err());
+ assert!(catch_unwind(|| Uniform::new(low, low)).is_err());
+ }
+ }
+ }};
+ }
+
+ t!(f32, f32);
+ t!(f64, f64);
+ #[cfg(feature = "simd_support")]
+ {
+ t!(f32x2, f32);
+ t!(f32x4, f32);
+ t!(f32x8, f32);
+ t!(f32x16, f32);
+ t!(f64x2, f64);
+ t!(f64x4, f64);
+ t!(f64x8, f64);
+ }
+ }
+
+
+ #[test]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_durations() {
+ #[cfg(not(feature = "std"))] use core::time::Duration;
+ #[cfg(feature = "std")] use std::time::Duration;
+
+ let mut rng = crate::test::rng(253);
+
+ let v = &[
+ (Duration::new(10, 50000), Duration::new(100, 1234)),
+ (Duration::new(0, 100), Duration::new(1, 50)),
+ (
+ Duration::new(0, 0),
+ Duration::new(u64::max_value(), 999_999_999),
+ ),
+ ];
+ for &(low, high) in v.iter() {
+ let my_uniform = Uniform::new(low, high);
+ for _ in 0..1000 {
+ let v = rng.sample(my_uniform);
+ assert!(low <= v && v < high);
+ }
+ }
+ }
+
+ #[test]
+ fn test_custom_uniform() {
+ use crate::distributions::uniform::{
+ SampleBorrow, SampleUniform, UniformFloat, UniformSampler,
+ };
+ #[derive(Clone, Copy, PartialEq, PartialOrd)]
+ struct MyF32 {
+ x: f32,
+ }
+ #[derive(Clone, Copy, Debug)]
+ struct UniformMyF32(UniformFloat<f32>);
+ impl UniformSampler for UniformMyF32 {
+ type X = MyF32;
+
+ fn new<B1, B2>(low: B1, high: B2) -> Self
+ where
+ B1: SampleBorrow<Self::X> + Sized,
+ B2: SampleBorrow<Self::X> + Sized,
+ {
+ UniformMyF32(UniformFloat::<f32>::new(low.borrow().x, high.borrow().x))
+ }
+
+ fn new_inclusive<B1, B2>(low: B1, high: B2) -> Self
+ where
+ B1: SampleBorrow<Self::X> + Sized,
+ B2: SampleBorrow<Self::X> + Sized,
+ {
+ UniformSampler::new(low, high)
+ }
+
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
+ MyF32 {
+ x: self.0.sample(rng),
+ }
+ }
+ }
+ impl SampleUniform for MyF32 {
+ type Sampler = UniformMyF32;
+ }
+
+ let (low, high) = (MyF32 { x: 17.0f32 }, MyF32 { x: 22.0f32 });
+ let uniform = Uniform::new(low, high);
+ let mut rng = crate::test::rng(804);
+ for _ in 0..100 {
+ let x: MyF32 = rng.sample(uniform);
+ assert!(low <= x && x < high);
+ }
+ }
+
+ #[test]
+ fn test_uniform_from_std_range() {
+ let r = Uniform::from(2u32..7);
+ assert_eq!(r.0.low, 2);
+ assert_eq!(r.0.range, 5);
+ let r = Uniform::from(2.0f64..7.0);
+ assert_eq!(r.0.low, 2.0);
+ assert_eq!(r.0.scale, 5.0);
+ }
+
+ #[test]
+ fn test_uniform_from_std_range_inclusive() {
+ let r = Uniform::from(2u32..=6);
+ assert_eq!(r.0.low, 2);
+ assert_eq!(r.0.range, 5);
+ let r = Uniform::from(2.0f64..=7.0);
+ assert_eq!(r.0.low, 2.0);
+ assert!(r.0.scale > 5.0);
+ assert!(r.0.scale < 5.0 + 1e-14);
+ }
+
+ #[test]
+ fn value_stability() {
+ fn test_samples<T: SampleUniform + Copy + core::fmt::Debug + PartialEq>(
+ lb: T, ub: T, expected_single: &[T], expected_multiple: &[T],
+ ) where Uniform<T>: Distribution<T> {
+ let mut rng = crate::test::rng(897);
+ let mut buf = [lb; 3];
+
+ for x in &mut buf {
+ *x = T::Sampler::sample_single(lb, ub, &mut rng);
+ }
+ assert_eq!(&buf, expected_single);
+
+ let distr = Uniform::new(lb, ub);
+ for x in &mut buf {
+ *x = rng.sample(&distr);
+ }
+ assert_eq!(&buf, expected_multiple);
+ }
+
+ // We test on a sub-set of types; possibly we should do more.
+ // TODO: SIMD types
+
+ test_samples(11u8, 219, &[17, 66, 214], &[181, 93, 165]);
+ test_samples(11u32, 219, &[17, 66, 214], &[181, 93, 165]);
+
+ test_samples(0f32, 1e-2f32, &[0.0003070104, 0.0026630748, 0.00979833], &[
+ 0.008194133,
+ 0.00398172,
+ 0.007428536,
+ ]);
+ test_samples(
+ -1e10f64,
+ 1e10f64,
+ &[-4673848682.871551, 6388267422.932352, 4857075081.198343],
+ &[1173375212.1808167, 1917642852.109581, 2365076174.3153973],
+ );
+
+ test_samples(
+ Duration::new(2, 0),
+ Duration::new(4, 0),
+ &[
+ Duration::new(2, 532615131),
+ Duration::new(3, 638826742),
+ Duration::new(3, 485707508),
+ ],
+ &[
+ Duration::new(3, 117337521),
+ Duration::new(3, 191764285),
+ Duration::new(3, 236507617),
+ ],
+ );
+ }
+}
diff --git a/src/distributions/unit_circle.rs b/src/distributions/unit_circle.rs
new file mode 100644
index 0000000..37885d8
--- /dev/null
+++ b/src/distributions/unit_circle.rs
@@ -0,0 +1,102 @@
+// 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.
+
+#![allow(deprecated)]
+#![allow(clippy::all)]
+
+use crate::distributions::{Distribution, Uniform};
+use crate::Rng;
+
+/// Samples uniformly from the edge of the unit circle in two dimensions.
+///
+/// Implemented via a method by von Neumann[^1].
+///
+/// [^1]: von Neumann, J. (1951) [*Various Techniques Used in Connection with
+/// Random Digits.*](https://mcnp.lanl.gov/pdf_files/nbs_vonneumann.pdf)
+/// NBS Appl. Math. Ser., No. 12. Washington, DC: U.S. Government Printing
+/// Office, pp. 36-38.
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct UnitCircle;
+
+impl UnitCircle {
+ /// Construct a new `UnitCircle` distribution.
+ #[inline]
+ pub fn new() -> UnitCircle {
+ UnitCircle
+ }
+}
+
+impl Distribution<[f64; 2]> for UnitCircle {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [f64; 2] {
+ let uniform = Uniform::new(-1., 1.);
+ let mut x1;
+ let mut x2;
+ let mut sum;
+ loop {
+ x1 = uniform.sample(rng);
+ x2 = uniform.sample(rng);
+ sum = x1 * x1 + x2 * x2;
+ if sum < 1. {
+ break;
+ }
+ }
+ let diff = x1 * x1 - x2 * x2;
+ [diff / sum, 2. * x1 * x2 / sum]
+ }
+}
+
+#[cfg(test)]
+mod tests {
+ use super::UnitCircle;
+ use crate::distributions::Distribution;
+
+ /// Assert that two numbers are almost equal to each other.
+ ///
+ /// On panic, this macro will print the values of the expressions with their
+ /// debug representations.
+ macro_rules! assert_almost_eq {
+ ($a:expr, $b:expr, $prec:expr) => {
+ let diff = ($a - $b).abs();
+ if diff > $prec {
+ panic!(format!(
+ "assertion failed: `abs(left - right) = {:.1e} < {:e}`, \
+ (left: `{}`, right: `{}`)",
+ diff, $prec, $a, $b
+ ));
+ }
+ };
+ }
+
+ #[test]
+ fn norm() {
+ let mut rng = crate::test::rng(1);
+ let dist = UnitCircle::new();
+ for _ in 0..1000 {
+ let x = dist.sample(&mut rng);
+ assert_almost_eq!(x[0] * x[0] + x[1] * x[1], 1., 1e-15);
+ }
+ }
+
+ #[test]
+ fn value_stability() {
+ let mut rng = crate::test::rng(2);
+ let expected = [
+ [-0.9965658683520504, -0.08280380447614634],
+ [-0.9790853270389644, -0.20345004884984505],
+ [-0.8449189758898707, 0.5348943112253227],
+ ];
+ let samples = [
+ UnitCircle.sample(&mut rng),
+ UnitCircle.sample(&mut rng),
+ UnitCircle.sample(&mut rng),
+ ];
+ assert_eq!(samples, expected);
+ }
+}
diff --git a/src/distributions/unit_sphere.rs b/src/distributions/unit_sphere.rs
new file mode 100644
index 0000000..5b8c8ad
--- /dev/null
+++ b/src/distributions/unit_sphere.rs
@@ -0,0 +1,97 @@
+// 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.
+
+#![allow(deprecated)]
+#![allow(clippy::all)]
+
+use crate::distributions::{Distribution, Uniform};
+use crate::Rng;
+
+/// Samples uniformly from the surface of the unit sphere in three dimensions.
+///
+/// Implemented via a method by Marsaglia[^1].
+///
+/// [^1]: Marsaglia, George (1972). [*Choosing a Point from the Surface of a
+/// Sphere.*](https://doi.org/10.1214/aoms/1177692644)
+/// Ann. Math. Statist. 43, no. 2, 645--646.
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct UnitSphereSurface;
+
+impl UnitSphereSurface {
+ /// Construct a new `UnitSphereSurface` distribution.
+ #[inline]
+ pub fn new() -> UnitSphereSurface {
+ UnitSphereSurface
+ }
+}
+
+impl Distribution<[f64; 3]> for UnitSphereSurface {
+ #[inline]
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [f64; 3] {
+ let uniform = Uniform::new(-1., 1.);
+ loop {
+ let (x1, x2) = (uniform.sample(rng), uniform.sample(rng));
+ let sum = x1 * x1 + x2 * x2;
+ if sum >= 1. {
+ continue;
+ }
+ let factor = 2. * (1.0_f64 - sum).sqrt();
+ return [x1 * factor, x2 * factor, 1. - 2. * sum];
+ }
+ }
+}
+
+#[cfg(test)]
+mod tests {
+ use super::UnitSphereSurface;
+ use crate::distributions::Distribution;
+
+ /// Assert that two numbers are almost equal to each other.
+ ///
+ /// On panic, this macro will print the values of the expressions with their
+ /// debug representations.
+ macro_rules! assert_almost_eq {
+ ($a:expr, $b:expr, $prec:expr) => {
+ let diff = ($a - $b).abs();
+ if diff > $prec {
+ panic!(format!(
+ "assertion failed: `abs(left - right) = {:.1e} < {:e}`, \
+ (left: `{}`, right: `{}`)",
+ diff, $prec, $a, $b
+ ));
+ }
+ };
+ }
+
+ #[test]
+ fn norm() {
+ let mut rng = crate::test::rng(1);
+ let dist = UnitSphereSurface::new();
+ for _ in 0..1000 {
+ let x = dist.sample(&mut rng);
+ assert_almost_eq!(x[0] * x[0] + x[1] * x[1] + x[2] * x[2], 1., 1e-15);
+ }
+ }
+
+ #[test]
+ fn value_stability() {
+ let mut rng = crate::test::rng(2);
+ let expected = [
+ [0.03247542860231647, -0.7830477442152738, 0.6211131755296027],
+ [-0.09978440840914075, 0.9706650829833128, -0.21875184231323952],
+ [0.2735582468624679, 0.9435374242279655, -0.1868234852870203],
+ ];
+ let samples = [
+ UnitSphereSurface.sample(&mut rng),
+ UnitSphereSurface.sample(&mut rng),
+ UnitSphereSurface.sample(&mut rng),
+ ];
+ assert_eq!(samples, expected);
+ }
+}
diff --git a/src/distributions/utils.rs b/src/distributions/utils.rs
new file mode 100644
index 0000000..2d36b02
--- /dev/null
+++ b/src/distributions/utils.rs
@@ -0,0 +1,547 @@
+// Copyright 2018 Developers of the Rand project.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+//! Math helper functions
+
+#[cfg(feature = "std")] use crate::distributions::ziggurat_tables;
+#[cfg(feature = "std")] use crate::Rng;
+#[cfg(feature = "simd_support")] use packed_simd::*;
+
+
+pub trait WideningMultiply<RHS = Self> {
+ type Output;
+
+ fn wmul(self, x: RHS) -> Self::Output;
+}
+
+macro_rules! wmul_impl {
+ ($ty:ty, $wide:ty, $shift:expr) => {
+ impl WideningMultiply for $ty {
+ type Output = ($ty, $ty);
+
+ #[inline(always)]
+ fn wmul(self, x: $ty) -> Self::Output {
+ let tmp = (self as $wide) * (x as $wide);
+ ((tmp >> $shift) as $ty, tmp as $ty)
+ }
+ }
+ };
+
+ // simd bulk implementation
+ ($(($ty:ident, $wide:ident),)+, $shift:expr) => {
+ $(
+ impl WideningMultiply for $ty {
+ type Output = ($ty, $ty);
+
+ #[inline(always)]
+ fn wmul(self, x: $ty) -> Self::Output {
+ // For supported vectors, this should compile to a couple
+ // supported multiply & swizzle instructions (no actual
+ // casting).
+ // TODO: optimize
+ let y: $wide = self.cast();
+ let x: $wide = x.cast();
+ let tmp = y * x;
+ let hi: $ty = (tmp >> $shift).cast();
+ let lo: $ty = tmp.cast();
+ (hi, lo)
+ }
+ }
+ )+
+ };
+}
+wmul_impl! { u8, u16, 8 }
+wmul_impl! { u16, u32, 16 }
+wmul_impl! { u32, u64, 32 }
+#[cfg(not(target_os = "emscripten"))]
+wmul_impl! { u64, u128, 64 }
+
+// This code is a translation of the __mulddi3 function in LLVM's
+// compiler-rt. It is an optimised variant of the common method
+// `(a + b) * (c + d) = ac + ad + bc + bd`.
+//
+// For some reason LLVM can optimise the C version very well, but
+// keeps shuffling registers in this Rust translation.
+macro_rules! wmul_impl_large {
+ ($ty:ty, $half:expr) => {
+ impl WideningMultiply for $ty {
+ type Output = ($ty, $ty);
+
+ #[inline(always)]
+ fn wmul(self, b: $ty) -> Self::Output {
+ const LOWER_MASK: $ty = !0 >> $half;
+ let mut low = (self & LOWER_MASK).wrapping_mul(b & LOWER_MASK);
+ let mut t = low >> $half;
+ low &= LOWER_MASK;
+ t += (self >> $half).wrapping_mul(b & LOWER_MASK);
+ low += (t & LOWER_MASK) << $half;
+ let mut high = t >> $half;
+ t = low >> $half;
+ low &= LOWER_MASK;
+ t += (b >> $half).wrapping_mul(self & LOWER_MASK);
+ low += (t & LOWER_MASK) << $half;
+ high += t >> $half;
+ high += (self >> $half).wrapping_mul(b >> $half);
+
+ (high, low)
+ }
+ }
+ };
+
+ // simd bulk implementation
+ (($($ty:ty,)+) $scalar:ty, $half:expr) => {
+ $(
+ impl WideningMultiply for $ty {
+ type Output = ($ty, $ty);
+
+ #[inline(always)]
+ fn wmul(self, b: $ty) -> Self::Output {
+ // needs wrapping multiplication
+ const LOWER_MASK: $scalar = !0 >> $half;
+ let mut low = (self & LOWER_MASK) * (b & LOWER_MASK);
+ let mut t = low >> $half;
+ low &= LOWER_MASK;
+ t += (self >> $half) * (b & LOWER_MASK);
+ low += (t & LOWER_MASK) << $half;
+ let mut high = t >> $half;
+ t = low >> $half;
+ low &= LOWER_MASK;
+ t += (b >> $half) * (self & LOWER_MASK);
+ low += (t & LOWER_MASK) << $half;
+ high += t >> $half;
+ high += (self >> $half) * (b >> $half);
+
+ (high, low)
+ }
+ }
+ )+
+ };
+}
+#[cfg(target_os = "emscripten")]
+wmul_impl_large! { u64, 32 }
+#[cfg(not(target_os = "emscripten"))]
+wmul_impl_large! { u128, 64 }
+
+macro_rules! wmul_impl_usize {
+ ($ty:ty) => {
+ impl WideningMultiply for usize {
+ type Output = (usize, usize);
+
+ #[inline(always)]
+ fn wmul(self, x: usize) -> Self::Output {
+ let (high, low) = (self as $ty).wmul(x as $ty);
+ (high as usize, low as usize)
+ }
+ }
+ };
+}
+#[cfg(target_pointer_width = "32")]
+wmul_impl_usize! { u32 }
+#[cfg(target_pointer_width = "64")]
+wmul_impl_usize! { u64 }
+
+#[cfg(all(feature = "simd_support", feature = "nightly"))]
+mod simd_wmul {
+ use super::*;
+ #[cfg(target_arch = "x86")] use core::arch::x86::*;
+ #[cfg(target_arch = "x86_64")] use core::arch::x86_64::*;
+
+ wmul_impl! {
+ (u8x2, u16x2),
+ (u8x4, u16x4),
+ (u8x8, u16x8),
+ (u8x16, u16x16),
+ (u8x32, u16x32),,
+ 8
+ }
+
+ wmul_impl! { (u16x2, u32x2),, 16 }
+ #[cfg(not(target_feature = "sse2"))]
+ wmul_impl! { (u16x4, u32x4),, 16 }
+ #[cfg(not(target_feature = "sse4.2"))]
+ wmul_impl! { (u16x8, u32x8),, 16 }
+ #[cfg(not(target_feature = "avx2"))]
+ wmul_impl! { (u16x16, u32x16),, 16 }
+
+ // 16-bit lane widths allow use of the x86 `mulhi` instructions, which
+ // means `wmul` can be implemented with only two instructions.
+ #[allow(unused_macros)]
+ macro_rules! wmul_impl_16 {
+ ($ty:ident, $intrinsic:ident, $mulhi:ident, $mullo:ident) => {
+ impl WideningMultiply for $ty {
+ type Output = ($ty, $ty);
+
+ #[inline(always)]
+ fn wmul(self, x: $ty) -> Self::Output {
+ let b = $intrinsic::from_bits(x);
+ let a = $intrinsic::from_bits(self);
+ let hi = $ty::from_bits(unsafe { $mulhi(a, b) });
+ let lo = $ty::from_bits(unsafe { $mullo(a, b) });
+ (hi, lo)
+ }
+ }
+ };
+ }
+
+ #[cfg(target_feature = "sse2")]
+ wmul_impl_16! { u16x4, __m64, _mm_mulhi_pu16, _mm_mullo_pi16 }
+ #[cfg(target_feature = "sse4.2")]
+ wmul_impl_16! { u16x8, __m128i, _mm_mulhi_epu16, _mm_mullo_epi16 }
+ #[cfg(target_feature = "avx2")]
+ wmul_impl_16! { u16x16, __m256i, _mm256_mulhi_epu16, _mm256_mullo_epi16 }
+ // FIXME: there are no `__m512i` types in stdsimd yet, so `wmul::<u16x32>`
+ // cannot use the same implementation.
+
+ wmul_impl! {
+ (u32x2, u64x2),
+ (u32x4, u64x4),
+ (u32x8, u64x8),,
+ 32
+ }
+
+ // TODO: optimize, this seems to seriously slow things down
+ wmul_impl_large! { (u8x64,) u8, 4 }
+ wmul_impl_large! { (u16x32,) u16, 8 }
+ wmul_impl_large! { (u32x16,) u32, 16 }
+ wmul_impl_large! { (u64x2, u64x4, u64x8,) u64, 32 }
+}
+#[cfg(all(feature = "simd_support", feature = "nightly"))]
+pub use self::simd_wmul::*;
+
+
+/// Helper trait when dealing with scalar and SIMD floating point types.
+pub(crate) trait FloatSIMDUtils {
+ // `PartialOrd` for vectors compares lexicographically. We want to compare all
+ // the individual SIMD lanes instead, and get the combined result over all
+ // lanes. This is possible using something like `a.lt(b).all()`, but we
+ // implement it as a trait so we can write the same code for `f32` and `f64`.
+ // Only the comparison functions we need are implemented.
+ fn all_lt(self, other: Self) -> bool;
+ fn all_le(self, other: Self) -> bool;
+ fn all_finite(self) -> bool;
+
+ type Mask;
+ fn finite_mask(self) -> Self::Mask;
+ fn gt_mask(self, other: Self) -> Self::Mask;
+ fn ge_mask(self, other: Self) -> Self::Mask;
+
+ // Decrease all lanes where the mask is `true` to the next lower value
+ // representable by the floating-point type. At least one of the lanes
+ // must be set.
+ fn decrease_masked(self, mask: Self::Mask) -> Self;
+
+ // Convert from int value. Conversion is done while retaining the numerical
+ // value, not by retaining the binary representation.
+ type UInt;
+ fn cast_from_int(i: Self::UInt) -> Self;
+}
+
+/// Implement functions available in std builds but missing from core primitives
+#[cfg(not(std))]
+pub(crate) trait Float: Sized {
+ fn is_nan(self) -> bool;
+ fn is_infinite(self) -> bool;
+ fn is_finite(self) -> bool;
+}
+
+/// Implement functions on f32/f64 to give them APIs similar to SIMD types
+pub(crate) trait FloatAsSIMD: Sized {
+ #[inline(always)]
+ fn lanes() -> usize {
+ 1
+ }
+ #[inline(always)]
+ fn splat(scalar: Self) -> Self {
+ scalar
+ }
+ #[inline(always)]
+ fn extract(self, index: usize) -> Self {
+ debug_assert_eq!(index, 0);
+ self
+ }
+ #[inline(always)]
+ fn replace(self, index: usize, new_value: Self) -> Self {
+ debug_assert_eq!(index, 0);
+ new_value
+ }
+}
+
+pub(crate) trait BoolAsSIMD: Sized {
+ fn any(self) -> bool;
+ fn all(self) -> bool;
+ fn none(self) -> bool;
+}
+
+impl BoolAsSIMD for bool {
+ #[inline(always)]
+ fn any(self) -> bool {
+ self
+ }
+
+ #[inline(always)]
+ fn all(self) -> bool {
+ self
+ }
+
+ #[inline(always)]
+ fn none(self) -> bool {
+ !self
+ }
+}
+
+macro_rules! scalar_float_impl {
+ ($ty:ident, $uty:ident) => {
+ #[cfg(not(std))]
+ impl Float for $ty {
+ #[inline]
+ fn is_nan(self) -> bool {
+ self != self
+ }
+
+ #[inline]
+ fn is_infinite(self) -> bool {
+ self == ::core::$ty::INFINITY || self == ::core::$ty::NEG_INFINITY
+ }
+
+ #[inline]
+ fn is_finite(self) -> bool {
+ !(self.is_nan() || self.is_infinite())
+ }
+ }
+
+ impl FloatSIMDUtils for $ty {
+ type Mask = bool;
+ type UInt = $uty;
+
+ #[inline(always)]
+ fn all_lt(self, other: Self) -> bool {
+ self < other
+ }
+
+ #[inline(always)]
+ fn all_le(self, other: Self) -> bool {
+ self <= other
+ }
+
+ #[inline(always)]
+ fn all_finite(self) -> bool {
+ self.is_finite()
+ }
+
+ #[inline(always)]
+ fn finite_mask(self) -> Self::Mask {
+ self.is_finite()
+ }
+
+ #[inline(always)]
+ fn gt_mask(self, other: Self) -> Self::Mask {
+ self > other
+ }
+
+ #[inline(always)]
+ fn ge_mask(self, other: Self) -> Self::Mask {
+ self >= other
+ }
+
+ #[inline(always)]
+ fn decrease_masked(self, mask: Self::Mask) -> Self {
+ debug_assert!(mask, "At least one lane must be set");
+ <$ty>::from_bits(self.to_bits() - 1)
+ }
+
+ #[inline]
+ fn cast_from_int(i: Self::UInt) -> Self {
+ i as $ty
+ }
+ }
+
+ impl FloatAsSIMD for $ty {}
+ };
+}
+
+scalar_float_impl!(f32, u32);
+scalar_float_impl!(f64, u64);
+
+
+#[cfg(feature = "simd_support")]
+macro_rules! simd_impl {
+ ($ty:ident, $f_scalar:ident, $mty:ident, $uty:ident) => {
+ impl FloatSIMDUtils for $ty {
+ type Mask = $mty;
+ type UInt = $uty;
+
+ #[inline(always)]
+ fn all_lt(self, other: Self) -> bool {
+ self.lt(other).all()
+ }
+
+ #[inline(always)]
+ fn all_le(self, other: Self) -> bool {
+ self.le(other).all()
+ }
+
+ #[inline(always)]
+ fn all_finite(self) -> bool {
+ self.finite_mask().all()
+ }
+
+ #[inline(always)]
+ fn finite_mask(self) -> Self::Mask {
+ // This can possibly be done faster by checking bit patterns
+ let neg_inf = $ty::splat(::core::$f_scalar::NEG_INFINITY);
+ let pos_inf = $ty::splat(::core::$f_scalar::INFINITY);
+ self.gt(neg_inf) & self.lt(pos_inf)
+ }
+
+ #[inline(always)]
+ fn gt_mask(self, other: Self) -> Self::Mask {
+ self.gt(other)
+ }
+
+ #[inline(always)]
+ fn ge_mask(self, other: Self) -> Self::Mask {
+ self.ge(other)
+ }
+
+ #[inline(always)]
+ fn decrease_masked(self, mask: Self::Mask) -> Self {
+ // Casting a mask into ints will produce all bits set for
+ // true, and 0 for false. Adding that to the binary
+ // representation of a float means subtracting one from
+ // the binary representation, resulting in the next lower
+ // value representable by $ty. This works even when the
+ // current value is infinity.
+ debug_assert!(mask.any(), "At least one lane must be set");
+ <$ty>::from_bits(<$uty>::from_bits(self) + <$uty>::from_bits(mask))
+ }
+
+ #[inline]
+ fn cast_from_int(i: Self::UInt) -> Self {
+ i.cast()
+ }
+ }
+ };
+}
+
+#[cfg(feature="simd_support")] simd_impl! { f32x2, f32, m32x2, u32x2 }
+#[cfg(feature="simd_support")] simd_impl! { f32x4, f32, m32x4, u32x4 }
+#[cfg(feature="simd_support")] simd_impl! { f32x8, f32, m32x8, u32x8 }
+#[cfg(feature="simd_support")] simd_impl! { f32x16, f32, m32x16, u32x16 }
+#[cfg(feature="simd_support")] simd_impl! { f64x2, f64, m64x2, u64x2 }
+#[cfg(feature="simd_support")] simd_impl! { f64x4, f64, m64x4, u64x4 }
+#[cfg(feature="simd_support")] simd_impl! { f64x8, f64, m64x8, u64x8 }
+
+/// Calculates ln(gamma(x)) (natural logarithm of the gamma
+/// function) using the Lanczos approximation.
+///
+/// The approximation expresses the gamma function as:
+/// `gamma(z+1) = sqrt(2*pi)*(z+g+0.5)^(z+0.5)*exp(-z-g-0.5)*Ag(z)`
+/// `g` is an arbitrary constant; we use the approximation with `g=5`.
+///
+/// Noting that `gamma(z+1) = z*gamma(z)` and applying `ln` to both sides:
+/// `ln(gamma(z)) = (z+0.5)*ln(z+g+0.5)-(z+g+0.5) + ln(sqrt(2*pi)*Ag(z)/z)`
+///
+/// `Ag(z)` is an infinite series with coefficients that can be calculated
+/// ahead of time - we use just the first 6 terms, which is good enough
+/// for most purposes.
+#[cfg(feature = "std")]
+pub fn log_gamma(x: f64) -> f64 {
+ // precalculated 6 coefficients for the first 6 terms of the series
+ let coefficients: [f64; 6] = [
+ 76.18009172947146,
+ -86.50532032941677,
+ 24.01409824083091,
+ -1.231739572450155,
+ 0.1208650973866179e-2,
+ -0.5395239384953e-5,
+ ];
+
+ // (x+0.5)*ln(x+g+0.5)-(x+g+0.5)
+ let tmp = x + 5.5;
+ let log = (x + 0.5) * tmp.ln() - tmp;
+
+ // the first few terms of the series for Ag(x)
+ let mut a = 1.000000000190015;
+ let mut denom = x;
+ for coeff in &coefficients {
+ denom += 1.0;
+ a += coeff / denom;
+ }
+
+ // get everything together
+ // a is Ag(x)
+ // 2.5066... is sqrt(2pi)
+ log + (2.5066282746310005 * a / x).ln()
+}
+
+/// Sample a random number using the Ziggurat method (specifically the
+/// ZIGNOR variant from Doornik 2005). Most of the arguments are
+/// directly from the paper:
+///
+/// * `rng`: source of randomness
+/// * `symmetric`: whether this is a symmetric distribution, or one-sided with P(x < 0) = 0.
+/// * `X`: the $x_i$ abscissae.
+/// * `F`: precomputed values of the PDF at the $x_i$, (i.e. $f(x_i)$)
+/// * `F_DIFF`: precomputed values of $f(x_i) - f(x_{i+1})$
+/// * `pdf`: the probability density function
+/// * `zero_case`: manual sampling from the tail when we chose the
+/// bottom box (i.e. i == 0)
+
+// the perf improvement (25-50%) is definitely worth the extra code
+// size from force-inlining.
+#[cfg(feature = "std")]
+#[inline(always)]
+pub fn ziggurat<R: Rng + ?Sized, P, Z>(
+ rng: &mut R,
+ symmetric: bool,
+ x_tab: ziggurat_tables::ZigTable,
+ f_tab: ziggurat_tables::ZigTable,
+ mut pdf: P,
+ mut zero_case: Z
+) -> f64
+where
+ P: FnMut(f64) -> f64,
+ Z: FnMut(&mut R, f64) -> f64,
+{
+ use crate::distributions::float::IntoFloat;
+ loop {
+ // As an optimisation we re-implement the conversion to a f64.
+ // From the remaining 12 most significant bits we use 8 to construct `i`.
+ // This saves us generating a whole extra random number, while the added
+ // precision of using 64 bits for f64 does not buy us much.
+ let bits = rng.next_u64();
+ let i = bits as usize & 0xff;
+
+ let u = if symmetric {
+ // Convert to a value in the range [2,4) and substract to get [-1,1)
+ // We can't convert to an open range directly, that would require
+ // substracting `3.0 - EPSILON`, which is not representable.
+ // It is possible with an extra step, but an open range does not
+ // seem neccesary for the ziggurat algorithm anyway.
+ (bits >> 12).into_float_with_exponent(1) - 3.0
+ } else {
+ // Convert to a value in the range [1,2) and substract to get (0,1)
+ (bits >> 12).into_float_with_exponent(0) - (1.0 - ::core::f64::EPSILON / 2.0)
+ };
+ let x = u * x_tab[i];
+
+ let test_x = if symmetric { x.abs() } else { x };
+
+ // algebraically equivalent to |u| < x_tab[i+1]/x_tab[i] (or u < x_tab[i+1]/x_tab[i])
+ if test_x < x_tab[i + 1] {
+ return x;
+ }
+ if i == 0 {
+ return zero_case(rng, u);
+ }
+ // algebraically equivalent to f1 + DRanU()*(f0 - f1) < 1
+ if f_tab[i + 1] + (f_tab[i] - f_tab[i + 1]) * rng.gen::<f64>() < pdf(x) {
+ return x;
+ }
+ }
+}
diff --git a/src/distributions/weibull.rs b/src/distributions/weibull.rs
new file mode 100644
index 0000000..ffbc93b
--- /dev/null
+++ b/src/distributions/weibull.rs
@@ -0,0 +1,67 @@
+// 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 Weibull distribution.
+#![allow(deprecated)]
+
+use crate::distributions::{Distribution, OpenClosed01};
+use crate::Rng;
+
+/// Samples floating-point numbers according to the Weibull distribution
+#[deprecated(since = "0.7.0", note = "moved to rand_distr crate")]
+#[derive(Clone, Copy, Debug)]
+pub struct Weibull {
+ inv_shape: f64,
+ scale: f64,
+}
+
+impl Weibull {
+ /// Construct a new `Weibull` distribution with given `scale` and `shape`.
+ ///
+ /// # Panics
+ ///
+ /// `scale` and `shape` have to be non-zero and positive.
+ pub fn new(scale: f64, shape: f64) -> Weibull {
+ assert!((scale > 0.) & (shape > 0.));
+ Weibull {
+ inv_shape: 1. / shape,
+ scale,
+ }
+ }
+}
+
+impl Distribution<f64> for Weibull {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+ let x: f64 = rng.sample(OpenClosed01);
+ self.scale * (-x.ln()).powf(self.inv_shape)
+ }
+}
+
+#[cfg(test)]
+mod tests {
+ use super::Weibull;
+ use crate::distributions::Distribution;
+
+ #[test]
+ #[should_panic]
+ fn invalid() {
+ Weibull::new(0., 0.);
+ }
+
+ #[test]
+ fn sample() {
+ let scale = 1.0;
+ let shape = 2.0;
+ let d = Weibull::new(scale, shape);
+ let mut rng = crate::test::rng(1);
+ for _ in 0..1000 {
+ let r = d.sample(&mut rng);
+ assert!(r >= 0.);
+ }
+ }
+}
diff --git a/src/distributions/weighted/alias_method.rs b/src/distributions/weighted/alias_method.rs
new file mode 100644
index 0000000..7d42a35
--- /dev/null
+++ b/src/distributions/weighted/alias_method.rs
@@ -0,0 +1,517 @@
+//! This module contains an implementation of alias method for sampling random
+//! indices with probabilities proportional to a collection of weights.
+
+use super::WeightedError;
+#[cfg(not(feature = "std"))] use crate::alloc::vec;
+#[cfg(not(feature = "std"))] use crate::alloc::vec::Vec;
+use crate::distributions::uniform::SampleUniform;
+use crate::distributions::Distribution;
+use crate::distributions::Uniform;
+use crate::Rng;
+use core::fmt;
+use core::iter::Sum;
+use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign};
+
+/// A distribution using weighted sampling to pick a discretely selected item.
+///
+/// Sampling a [`WeightedIndex<W>`] distribution returns the index of a randomly
+/// selected element from the vector used to create the [`WeightedIndex<W>`].
+/// The chance of a given element being picked is proportional to the value of
+/// the element. The weights can have any type `W` for which a implementation of
+/// [`Weight`] exists.
+///
+/// # Performance
+///
+/// Given that `n` is the number of items in the vector used to create an
+/// [`WeightedIndex<W>`], [`WeightedIndex<W>`] will require `O(n)` amount of
+/// memory. More specifically it takes up some constant amount of memory plus
+/// the vector used to create it and a [`Vec<u32>`] with capacity `n`.
+///
+/// Time complexity for the creation of a [`WeightedIndex<W>`] is `O(n)`.
+/// Sampling is `O(1)`, it makes a call to [`Uniform<u32>::sample`] and a call
+/// to [`Uniform<W>::sample`].
+///
+/// # Example
+///
+/// ```
+/// use rand::distributions::weighted::alias_method::WeightedIndex;
+/// use rand::prelude::*;
+///
+/// let choices = vec!['a', 'b', 'c'];
+/// let weights = vec![2, 1, 1];
+/// let dist = WeightedIndex::new(weights).unwrap();
+/// let mut rng = thread_rng();
+/// for _ in 0..100 {
+/// // 50% chance to print 'a', 25% chance to print 'b', 25% chance to print 'c'
+/// println!("{}", choices[dist.sample(&mut rng)]);
+/// }
+///
+/// let items = [('a', 0), ('b', 3), ('c', 7)];
+/// let dist2 = WeightedIndex::new(items.iter().map(|item| item.1).collect()).unwrap();
+/// for _ in 0..100 {
+/// // 0% chance to print 'a', 30% chance to print 'b', 70% chance to print 'c'
+/// println!("{}", items[dist2.sample(&mut rng)].0);
+/// }
+/// ```
+///
+/// [`WeightedIndex<W>`]: crate::distributions::weighted::alias_method::WeightedIndex
+/// [`Weight`]: crate::distributions::weighted::alias_method::Weight
+/// [`Vec<u32>`]: Vec
+/// [`Uniform<u32>::sample`]: Distribution::sample
+/// [`Uniform<W>::sample`]: Distribution::sample
+pub struct WeightedIndex<W: Weight> {
+ aliases: Vec<u32>,
+ no_alias_odds: Vec<W>,
+ uniform_index: Uniform<u32>,
+ uniform_within_weight_sum: Uniform<W>,
+}
+
+impl<W: Weight> WeightedIndex<W> {
+ /// Creates a new [`WeightedIndex`].
+ ///
+ /// Returns an error if:
+ /// - The vector is empty.
+ /// - The vector is longer than `u32::MAX`.
+ /// - For any weight `w`: `w < 0` or `w > max` where `max = W::MAX /
+ /// weights.len()`.
+ /// - The sum of weights is zero.
+ pub fn new(weights: Vec<W>) -> Result<Self, WeightedError> {
+ let n = weights.len();
+ if n == 0 {
+ return Err(WeightedError::NoItem);
+ } else if n > ::core::u32::MAX as usize {
+ return Err(WeightedError::TooMany);
+ }
+ let n = n as u32;
+
+ let max_weight_size = W::try_from_u32_lossy(n)
+ .map(|n| W::MAX / n)
+ .unwrap_or(W::ZERO);
+ if !weights
+ .iter()
+ .all(|&w| W::ZERO <= w && w <= max_weight_size)
+ {
+ return Err(WeightedError::InvalidWeight);
+ }
+
+ // The sum of weights will represent 100% of no alias odds.
+ let weight_sum = Weight::sum(weights.as_slice());
+ // Prevent floating point overflow due to rounding errors.
+ let weight_sum = if weight_sum > W::MAX {
+ W::MAX
+ } else {
+ weight_sum
+ };
+ if weight_sum == W::ZERO {
+ return Err(WeightedError::AllWeightsZero);
+ }
+
+ // `weight_sum` would have been zero if `try_from_lossy` causes an error here.
+ let n_converted = W::try_from_u32_lossy(n).unwrap();
+
+ let mut no_alias_odds = weights;
+ for odds in no_alias_odds.iter_mut() {
+ *odds *= n_converted;
+ // Prevent floating point overflow due to rounding errors.
+ *odds = if *odds > W::MAX { W::MAX } else { *odds };
+ }
+
+ /// This struct is designed to contain three data structures at once,
+ /// sharing the same memory. More precisely it contains two linked lists
+ /// and an alias map, which will be the output of this method. To keep
+ /// the three data structures from getting in each other's way, it must
+ /// be ensured that a single index is only ever in one of them at the
+ /// same time.
+ struct Aliases {
+ aliases: Vec<u32>,
+ smalls_head: u32,
+ bigs_head: u32,
+ }
+
+ impl Aliases {
+ fn new(size: u32) -> Self {
+ Aliases {
+ aliases: vec![0; size as usize],
+ smalls_head: ::core::u32::MAX,
+ bigs_head: ::core::u32::MAX,
+ }
+ }
+
+ fn push_small(&mut self, idx: u32) {
+ self.aliases[idx as usize] = self.smalls_head;
+ self.smalls_head = idx;
+ }
+
+ fn push_big(&mut self, idx: u32) {
+ self.aliases[idx as usize] = self.bigs_head;
+ self.bigs_head = idx;
+ }
+
+ fn pop_small(&mut self) -> u32 {
+ let popped = self.smalls_head;
+ self.smalls_head = self.aliases[popped as usize];
+ popped
+ }
+
+ fn pop_big(&mut self) -> u32 {
+ let popped = self.bigs_head;
+ self.bigs_head = self.aliases[popped as usize];
+ popped
+ }
+
+ fn smalls_is_empty(&self) -> bool {
+ self.smalls_head == ::core::u32::MAX
+ }
+
+ fn bigs_is_empty(&self) -> bool {
+ self.bigs_head == ::core::u32::MAX
+ }
+
+ fn set_alias(&mut self, idx: u32, alias: u32) {
+ self.aliases[idx as usize] = alias;
+ }
+ }
+
+ let mut aliases = Aliases::new(n);
+
+ // Split indices into those with small weights and those with big weights.
+ for (index, &odds) in no_alias_odds.iter().enumerate() {
+ if odds < weight_sum {
+ aliases.push_small(index as u32);
+ } else {
+ aliases.push_big(index as u32);
+ }
+ }
+
+ // Build the alias map by finding an alias with big weight for each index with
+ // small weight.
+ while !aliases.smalls_is_empty() && !aliases.bigs_is_empty() {
+ let s = aliases.pop_small();
+ let b = aliases.pop_big();
+
+ aliases.set_alias(s, b);
+ no_alias_odds[b as usize] =
+ no_alias_odds[b as usize] - weight_sum + no_alias_odds[s as usize];
+
+ if no_alias_odds[b as usize] < weight_sum {
+ aliases.push_small(b);
+ } else {
+ aliases.push_big(b);
+ }
+ }
+
+ // The remaining indices should have no alias odds of about 100%. This is due to
+ // numeric accuracy. Otherwise they would be exactly 100%.
+ while !aliases.smalls_is_empty() {
+ no_alias_odds[aliases.pop_small() as usize] = weight_sum;
+ }
+ while !aliases.bigs_is_empty() {
+ no_alias_odds[aliases.pop_big() as usize] = weight_sum;
+ }
+
+ // Prepare distributions for sampling. Creating them beforehand improves
+ // sampling performance.
+ let uniform_index = Uniform::new(0, n);
+ let uniform_within_weight_sum = Uniform::new(W::ZERO, weight_sum);
+
+ Ok(Self {
+ aliases: aliases.aliases,
+ no_alias_odds,
+ uniform_index,
+ uniform_within_weight_sum,
+ })
+ }
+}
+
+impl<W: Weight> Distribution<usize> for WeightedIndex<W> {
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> usize {
+ let candidate = rng.sample(self.uniform_index);
+ if rng.sample(&self.uniform_within_weight_sum) < self.no_alias_odds[candidate as usize] {
+ candidate as usize
+ } else {
+ self.aliases[candidate as usize] as usize
+ }
+ }
+}
+
+impl<W: Weight> fmt::Debug for WeightedIndex<W>
+where
+ W: fmt::Debug,
+ Uniform<W>: fmt::Debug,
+{
+ fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+ f.debug_struct("WeightedIndex")
+ .field("aliases", &self.aliases)
+ .field("no_alias_odds", &self.no_alias_odds)
+ .field("uniform_index", &self.uniform_index)
+ .field("uniform_within_weight_sum", &self.uniform_within_weight_sum)
+ .finish()
+ }
+}
+
+impl<W: Weight> Clone for WeightedIndex<W>
+where Uniform<W>: Clone
+{
+ fn clone(&self) -> Self {
+ Self {
+ aliases: self.aliases.clone(),
+ no_alias_odds: self.no_alias_odds.clone(),
+ uniform_index: self.uniform_index.clone(),
+ uniform_within_weight_sum: self.uniform_within_weight_sum.clone(),
+ }
+ }
+}
+
+/// Trait that must be implemented for weights, that are used with
+/// [`WeightedIndex`]. Currently no guarantees on the correctness of
+/// [`WeightedIndex`] are given for custom implementations of this trait.
+pub trait Weight:
+ Sized
+ + Copy
+ + SampleUniform
+ + PartialOrd
+ + Add<Output = Self>
+ + AddAssign
+ + Sub<Output = Self>
+ + SubAssign
+ + Mul<Output = Self>
+ + MulAssign
+ + Div<Output = Self>
+ + DivAssign
+ + Sum
+{
+ /// Maximum number representable by `Self`.
+ const MAX: Self;
+
+ /// Element of `Self` equivalent to 0.
+ const ZERO: Self;
+
+ /// Produce an instance of `Self` from a `u32` value, or return `None` if
+ /// out of range. Loss of precision (where `Self` is a floating point type)
+ /// is acceptable.
+ fn try_from_u32_lossy(n: u32) -> Option<Self>;
+
+ /// Sums all values in slice `values`.
+ fn sum(values: &[Self]) -> Self {
+ values.iter().map(|x| *x).sum()
+ }
+}
+
+macro_rules! impl_weight_for_float {
+ ($T: ident) => {
+ impl Weight for $T {
+ const MAX: Self = ::core::$T::MAX;
+ const ZERO: Self = 0.0;
+
+ fn try_from_u32_lossy(n: u32) -> Option<Self> {
+ Some(n as $T)
+ }
+
+ fn sum(values: &[Self]) -> Self {
+ pairwise_sum(values)
+ }
+ }
+ };
+}
+
+/// In comparison to naive accumulation, the pairwise sum algorithm reduces
+/// rounding errors when there are many floating point values.
+fn pairwise_sum<T: Weight>(values: &[T]) -> T {
+ if values.len() <= 32 {
+ values.iter().map(|x| *x).sum()
+ } else {
+ let mid = values.len() / 2;
+ let (a, b) = values.split_at(mid);
+ pairwise_sum(a) + pairwise_sum(b)
+ }
+}
+
+macro_rules! impl_weight_for_int {
+ ($T: ident) => {
+ impl Weight for $T {
+ const MAX: Self = ::core::$T::MAX;
+ const ZERO: Self = 0;
+
+ fn try_from_u32_lossy(n: u32) -> Option<Self> {
+ let n_converted = n as Self;
+ if n_converted >= Self::ZERO && n_converted as u32 == n {
+ Some(n_converted)
+ } else {
+ None
+ }
+ }
+ }
+ };
+}
+
+impl_weight_for_float!(f64);
+impl_weight_for_float!(f32);
+impl_weight_for_int!(usize);
+#[cfg(not(target_os = "emscripten"))]
+impl_weight_for_int!(u128);
+impl_weight_for_int!(u64);
+impl_weight_for_int!(u32);
+impl_weight_for_int!(u16);
+impl_weight_for_int!(u8);
+impl_weight_for_int!(isize);
+#[cfg(not(target_os = "emscripten"))]
+impl_weight_for_int!(i128);
+impl_weight_for_int!(i64);
+impl_weight_for_int!(i32);
+impl_weight_for_int!(i16);
+impl_weight_for_int!(i8);
+
+#[cfg(test)]
+mod test {
+ use super::*;
+
+ #[test]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_weighted_index_f32() {
+ test_weighted_index(f32::into);
+
+ // Floating point special cases
+ assert_eq!(
+ WeightedIndex::new(vec![::core::f32::INFINITY]).unwrap_err(),
+ WeightedError::InvalidWeight
+ );
+ assert_eq!(
+ WeightedIndex::new(vec![-0_f32]).unwrap_err(),
+ WeightedError::AllWeightsZero
+ );
+ assert_eq!(
+ WeightedIndex::new(vec![-1_f32]).unwrap_err(),
+ WeightedError::InvalidWeight
+ );
+ assert_eq!(
+ WeightedIndex::new(vec![-::core::f32::INFINITY]).unwrap_err(),
+ WeightedError::InvalidWeight
+ );
+ assert_eq!(
+ WeightedIndex::new(vec![::core::f32::NAN]).unwrap_err(),
+ WeightedError::InvalidWeight
+ );
+ }
+
+ #[cfg(not(target_os = "emscripten"))]
+ #[test]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_weighted_index_u128() {
+ test_weighted_index(|x: u128| x as f64);
+ }
+
+ #[cfg(all(rustc_1_26, not(target_os = "emscripten")))]
+ #[test]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_weighted_index_i128() {
+ test_weighted_index(|x: i128| x as f64);
+
+ // Signed integer special cases
+ assert_eq!(
+ WeightedIndex::new(vec![-1_i128]).unwrap_err(),
+ WeightedError::InvalidWeight
+ );
+ assert_eq!(
+ WeightedIndex::new(vec![::core::i128::MIN]).unwrap_err(),
+ WeightedError::InvalidWeight
+ );
+ }
+
+ #[test]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_weighted_index_u8() {
+ test_weighted_index(u8::into);
+ }
+
+ #[test]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_weighted_index_i8() {
+ test_weighted_index(i8::into);
+
+ // Signed integer special cases
+ assert_eq!(
+ WeightedIndex::new(vec![-1_i8]).unwrap_err(),
+ WeightedError::InvalidWeight
+ );
+ assert_eq!(
+ WeightedIndex::new(vec![::core::i8::MIN]).unwrap_err(),
+ WeightedError::InvalidWeight
+ );
+ }
+
+ fn test_weighted_index<W: Weight, F: Fn(W) -> f64>(w_to_f64: F)
+ where WeightedIndex<W>: fmt::Debug {
+ const NUM_WEIGHTS: u32 = 10;
+ const ZERO_WEIGHT_INDEX: u32 = 3;
+ const NUM_SAMPLES: u32 = 15000;
+ let mut rng = crate::test::rng(0x9c9fa0b0580a7031);
+
+ let weights = {
+ let mut weights = Vec::with_capacity(NUM_WEIGHTS as usize);
+ let random_weight_distribution = crate::distributions::Uniform::new_inclusive(
+ W::ZERO,
+ W::MAX / W::try_from_u32_lossy(NUM_WEIGHTS).unwrap(),
+ );
+ for _ in 0..NUM_WEIGHTS {
+ weights.push(rng.sample(&random_weight_distribution));
+ }
+ weights[ZERO_WEIGHT_INDEX as usize] = W::ZERO;
+ weights
+ };
+ let weight_sum = weights.iter().map(|w| *w).sum::<W>();
+ let expected_counts = weights
+ .iter()
+ .map(|&w| w_to_f64(w) / w_to_f64(weight_sum) * NUM_SAMPLES as f64)
+ .collect::<Vec<f64>>();
+ let weight_distribution = WeightedIndex::new(weights).unwrap();
+
+ let mut counts = vec![0; NUM_WEIGHTS as usize];
+ for _ in 0..NUM_SAMPLES {
+ counts[rng.sample(&weight_distribution)] += 1;
+ }
+
+ assert_eq!(counts[ZERO_WEIGHT_INDEX as usize], 0);
+ for (count, expected_count) in counts.into_iter().zip(expected_counts) {
+ let difference = (count as f64 - expected_count).abs();
+ let max_allowed_difference = NUM_SAMPLES as f64 / NUM_WEIGHTS as f64 * 0.1;
+ assert!(difference <= max_allowed_difference);
+ }
+
+ assert_eq!(
+ WeightedIndex::<W>::new(vec![]).unwrap_err(),
+ WeightedError::NoItem
+ );
+ assert_eq!(
+ WeightedIndex::new(vec![W::ZERO]).unwrap_err(),
+ WeightedError::AllWeightsZero
+ );
+ assert_eq!(
+ WeightedIndex::new(vec![W::MAX, W::MAX]).unwrap_err(),
+ WeightedError::InvalidWeight
+ );
+ }
+
+ #[test]
+ fn value_stability() {
+ fn test_samples<W: Weight>(weights: Vec<W>, buf: &mut [usize], expected: &[usize]) {
+ assert_eq!(buf.len(), expected.len());
+ let distr = WeightedIndex::new(weights).unwrap();
+ let mut rng = crate::test::rng(0x9c9fa0b0580a7031);
+ for r in buf.iter_mut() {
+ *r = rng.sample(&distr);
+ }
+ assert_eq!(buf, expected);
+ }
+
+ let mut buf = [0; 10];
+ test_samples(vec![1i32, 1, 1, 1, 1, 1, 1, 1, 1], &mut buf, &[
+ 6, 5, 7, 5, 8, 7, 6, 2, 3, 7,
+ ]);
+ test_samples(vec![0.7f32, 0.1, 0.1, 0.1], &mut buf, &[
+ 2, 0, 0, 0, 0, 0, 0, 0, 1, 3,
+ ]);
+ test_samples(vec![1.0f64, 0.999, 0.998, 0.997], &mut buf, &[
+ 2, 1, 2, 3, 2, 1, 3, 2, 1, 1,
+ ]);
+ }
+}
diff --git a/src/distributions/weighted/mod.rs b/src/distributions/weighted/mod.rs
new file mode 100644
index 0000000..357e3a9
--- /dev/null
+++ b/src/distributions/weighted/mod.rs
@@ -0,0 +1,413 @@
+// 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.
+
+//! Weighted index sampling
+//!
+//! This module provides two implementations for sampling indices:
+//!
+//! * [`WeightedIndex`] allows `O(log N)` sampling
+//! * [`alias_method::WeightedIndex`] allows `O(1)` sampling, but with
+//! much greater set-up cost
+//!
+//! [`alias_method::WeightedIndex`]: alias_method/struct.WeightedIndex.html
+
+pub mod alias_method;
+
+use crate::distributions::uniform::{SampleBorrow, SampleUniform, UniformSampler};
+use crate::distributions::Distribution;
+use crate::Rng;
+use core::cmp::PartialOrd;
+use core::fmt;
+
+// Note that this whole module is only imported if feature="alloc" is enabled.
+#[cfg(not(feature = "std"))] use crate::alloc::vec::Vec;
+
+/// A distribution using weighted sampling to pick a discretely selected
+/// item.
+///
+/// Sampling a `WeightedIndex` distribution returns the index of a randomly
+/// selected element from the iterator used when the `WeightedIndex` was
+/// created. The chance of a given element being picked is proportional to the
+/// value of the element. The weights can use any type `X` for which an
+/// implementation of [`Uniform<X>`] exists.
+///
+/// # Performance
+///
+/// A `WeightedIndex<X>` contains a `Vec<X>` and a [`Uniform<X>`] and so its
+/// size is the sum of the size of those objects, possibly plus some alignment.
+///
+/// Creating a `WeightedIndex<X>` will allocate enough space to hold `N - 1`
+/// weights of type `X`, where `N` is the number of weights. However, since
+/// `Vec` doesn't guarantee a particular growth strategy, additional memory
+/// might be allocated but not used. Since the `WeightedIndex` object also
+/// contains, this might cause additional allocations, though for primitive
+/// types, ['Uniform<X>`] doesn't allocate any memory.
+///
+/// Time complexity of sampling from `WeightedIndex` is `O(log N)` where
+/// `N` is the number of weights.
+///
+/// Sampling from `WeightedIndex` will result in a single call to
+/// `Uniform<X>::sample` (method of the [`Distribution`] trait), which typically
+/// will request a single value from the underlying [`RngCore`], though the
+/// exact number depends on the implementaiton of `Uniform<X>::sample`.
+///
+/// # Example
+///
+/// ```
+/// use rand::prelude::*;
+/// use rand::distributions::WeightedIndex;
+///
+/// let choices = ['a', 'b', 'c'];
+/// let weights = [2, 1, 1];
+/// let dist = WeightedIndex::new(&weights).unwrap();
+/// let mut rng = thread_rng();
+/// for _ in 0..100 {
+/// // 50% chance to print 'a', 25% chance to print 'b', 25% chance to print 'c'
+/// println!("{}", choices[dist.sample(&mut rng)]);
+/// }
+///
+/// let items = [('a', 0), ('b', 3), ('c', 7)];
+/// let dist2 = WeightedIndex::new(items.iter().map(|item| item.1)).unwrap();
+/// for _ in 0..100 {
+/// // 0% chance to print 'a', 30% chance to print 'b', 70% chance to print 'c'
+/// println!("{}", items[dist2.sample(&mut rng)].0);
+/// }
+/// ```
+///
+/// [`Uniform<X>`]: crate::distributions::uniform::Uniform
+/// [`RngCore`]: crate::RngCore
+#[derive(Debug, Clone)]
+pub struct WeightedIndex<X: SampleUniform + PartialOrd> {
+ cumulative_weights: Vec<X>,
+ total_weight: X,
+ weight_distribution: X::Sampler,
+}
+
+impl<X: SampleUniform + PartialOrd> WeightedIndex<X> {
+ /// Creates a new a `WeightedIndex` [`Distribution`] using the values
+ /// in `weights`. The weights can use any type `X` for which an
+ /// implementation of [`Uniform<X>`] exists.
+ ///
+ /// Returns an error if the iterator is empty, if any weight is `< 0`, or
+ /// if its total value is 0.
+ ///
+ /// [`Uniform<X>`]: crate::distributions::uniform::Uniform
+ pub fn new<I>(weights: I) -> Result<WeightedIndex<X>, WeightedError>
+ where
+ I: IntoIterator,
+ I::Item: SampleBorrow<X>,
+ X: for<'a> ::core::ops::AddAssign<&'a X> + Clone + Default,
+ {
+ let mut iter = weights.into_iter();
+ let mut total_weight: X = iter.next().ok_or(WeightedError::NoItem)?.borrow().clone();
+
+ let zero = <X as Default>::default();
+ if total_weight < zero {
+ return Err(WeightedError::InvalidWeight);
+ }
+
+ let mut weights = Vec::<X>::with_capacity(iter.size_hint().0);
+ for w in iter {
+ if *w.borrow() < zero {
+ return Err(WeightedError::InvalidWeight);
+ }
+ weights.push(total_weight.clone());
+ total_weight += w.borrow();
+ }
+
+ if total_weight == zero {
+ return Err(WeightedError::AllWeightsZero);
+ }
+ let distr = X::Sampler::new(zero, total_weight.clone());
+
+ Ok(WeightedIndex {
+ cumulative_weights: weights,
+ total_weight,
+ weight_distribution: distr,
+ })
+ }
+
+ /// Update a subset of weights, without changing the number of weights.
+ ///
+ /// `new_weights` must be sorted by the index.
+ ///
+ /// Using this method instead of `new` might be more efficient if only a small number of
+ /// weights is modified. No allocations are performed, unless the weight type `X` uses
+ /// allocation internally.
+ ///
+ /// In case of error, `self` is not modified.
+ pub fn update_weights(&mut self, new_weights: &[(usize, &X)]) -> Result<(), WeightedError>
+ where X: for<'a> ::core::ops::AddAssign<&'a X>
+ + for<'a> ::core::ops::SubAssign<&'a X>
+ + Clone
+ + Default {
+ if new_weights.is_empty() {
+ return Ok(());
+ }
+
+ let zero = <X as Default>::default();
+
+ let mut total_weight = self.total_weight.clone();
+
+ // Check for errors first, so we don't modify `self` in case something
+ // goes wrong.
+ let mut prev_i = None;
+ for &(i, w) in new_weights {
+ if let Some(old_i) = prev_i {
+ if old_i >= i {
+ return Err(WeightedError::InvalidWeight);
+ }
+ }
+ if *w < zero {
+ return Err(WeightedError::InvalidWeight);
+ }
+ if i >= self.cumulative_weights.len() + 1 {
+ return Err(WeightedError::TooMany);
+ }
+
+ let mut old_w = if i < self.cumulative_weights.len() {
+ self.cumulative_weights[i].clone()
+ } else {
+ self.total_weight.clone()
+ };
+ if i > 0 {
+ old_w -= &self.cumulative_weights[i - 1];
+ }
+
+ total_weight -= &old_w;
+ total_weight += w;
+ prev_i = Some(i);
+ }
+ if total_weight == zero {
+ return Err(WeightedError::AllWeightsZero);
+ }
+
+ // Update the weights. Because we checked all the preconditions in the
+ // previous loop, this should never panic.
+ let mut iter = new_weights.iter();
+
+ let mut prev_weight = zero.clone();
+ let mut next_new_weight = iter.next();
+ let &(first_new_index, _) = next_new_weight.unwrap();
+ let mut cumulative_weight = if first_new_index > 0 {
+ self.cumulative_weights[first_new_index - 1].clone()
+ } else {
+ zero.clone()
+ };
+ for i in first_new_index..self.cumulative_weights.len() {
+ match next_new_weight {
+ Some(&(j, w)) if i == j => {
+ cumulative_weight += w;
+ next_new_weight = iter.next();
+ }
+ _ => {
+ let mut tmp = self.cumulative_weights[i].clone();
+ tmp -= &prev_weight; // We know this is positive.
+ cumulative_weight += &tmp;
+ }
+ }
+ prev_weight = cumulative_weight.clone();
+ core::mem::swap(&mut prev_weight, &mut self.cumulative_weights[i]);
+ }
+
+ self.total_weight = total_weight;
+ self.weight_distribution = X::Sampler::new(zero, self.total_weight.clone());
+
+ Ok(())
+ }
+}
+
+impl<X> Distribution<usize> for WeightedIndex<X>
+where X: SampleUniform + PartialOrd
+{
+ fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> usize {
+ use ::core::cmp::Ordering;
+ let chosen_weight = self.weight_distribution.sample(rng);
+ // Find the first item which has a weight *higher* than the chosen weight.
+ self.cumulative_weights
+ .binary_search_by(|w| {
+ if *w <= chosen_weight {
+ Ordering::Less
+ } else {
+ Ordering::Greater
+ }
+ })
+ .unwrap_err()
+ }
+}
+
+#[cfg(test)]
+mod test {
+ use super::*;
+
+ #[test]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_weightedindex() {
+ let mut r = crate::test::rng(700);
+ const N_REPS: u32 = 5000;
+ let weights = [1u32, 2, 3, 0, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7];
+ let total_weight = weights.iter().sum::<u32>() as f32;
+
+ let verify = |result: [i32; 14]| {
+ for (i, count) in result.iter().enumerate() {
+ let exp = (weights[i] * N_REPS) as f32 / total_weight;
+ let mut err = (*count as f32 - exp).abs();
+ if err != 0.0 {
+ err /= exp;
+ }
+ assert!(err <= 0.25);
+ }
+ };
+
+ // WeightedIndex from vec
+ let mut chosen = [0i32; 14];
+ let distr = WeightedIndex::new(weights.to_vec()).unwrap();
+ for _ in 0..N_REPS {
+ chosen[distr.sample(&mut r)] += 1;
+ }
+ verify(chosen);
+
+ // WeightedIndex from slice
+ chosen = [0i32; 14];
+ let distr = WeightedIndex::new(&weights[..]).unwrap();
+ for _ in 0..N_REPS {
+ chosen[distr.sample(&mut r)] += 1;
+ }
+ verify(chosen);
+
+ // WeightedIndex from iterator
+ chosen = [0i32; 14];
+ let distr = WeightedIndex::new(weights.iter()).unwrap();
+ for _ in 0..N_REPS {
+ chosen[distr.sample(&mut r)] += 1;
+ }
+ verify(chosen);
+
+ for _ in 0..5 {
+ assert_eq!(WeightedIndex::new(&[0, 1]).unwrap().sample(&mut r), 1);
+ assert_eq!(WeightedIndex::new(&[1, 0]).unwrap().sample(&mut r), 0);
+ assert_eq!(
+ WeightedIndex::new(&[0, 0, 0, 0, 10, 0])
+ .unwrap()
+ .sample(&mut r),
+ 4
+ );
+ }
+
+ assert_eq!(
+ WeightedIndex::new(&[10][0..0]).unwrap_err(),
+ WeightedError::NoItem
+ );
+ assert_eq!(
+ WeightedIndex::new(&[0]).unwrap_err(),
+ WeightedError::AllWeightsZero
+ );
+ assert_eq!(
+ WeightedIndex::new(&[10, 20, -1, 30]).unwrap_err(),
+ WeightedError::InvalidWeight
+ );
+ assert_eq!(
+ WeightedIndex::new(&[-10, 20, 1, 30]).unwrap_err(),
+ WeightedError::InvalidWeight
+ );
+ assert_eq!(
+ WeightedIndex::new(&[-10]).unwrap_err(),
+ WeightedError::InvalidWeight
+ );
+ }
+
+ #[test]
+ fn test_update_weights() {
+ let data = [
+ (
+ &[10u32, 2, 3, 4][..],
+ &[(1, &100), (2, &4)][..], // positive change
+ &[10, 100, 4, 4][..],
+ ),
+ (
+ &[1u32, 2, 3, 0, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7][..],
+ &[(2, &1), (5, &1), (13, &100)][..], // negative change and last element
+ &[1u32, 2, 1, 0, 5, 1, 7, 1, 2, 3, 4, 5, 6, 100][..],
+ ),
+ ];
+
+ for (weights, update, expected_weights) in data.iter() {
+ let total_weight = weights.iter().sum::<u32>();
+ let mut distr = WeightedIndex::new(weights.to_vec()).unwrap();
+ assert_eq!(distr.total_weight, total_weight);
+
+ distr.update_weights(update).unwrap();
+ let expected_total_weight = expected_weights.iter().sum::<u32>();
+ let expected_distr = WeightedIndex::new(expected_weights.to_vec()).unwrap();
+ assert_eq!(distr.total_weight, expected_total_weight);
+ assert_eq!(distr.total_weight, expected_distr.total_weight);
+ assert_eq!(distr.cumulative_weights, expected_distr.cumulative_weights);
+ }
+ }
+
+ #[test]
+ fn value_stability() {
+ fn test_samples<X: SampleUniform + PartialOrd, I>(
+ weights: I, buf: &mut [usize], expected: &[usize],
+ ) where
+ I: IntoIterator,
+ I::Item: SampleBorrow<X>,
+ X: for<'a> ::core::ops::AddAssign<&'a X> + Clone + Default,
+ {
+ assert_eq!(buf.len(), expected.len());
+ let distr = WeightedIndex::new(weights).unwrap();
+ let mut rng = crate::test::rng(701);
+ for r in buf.iter_mut() {
+ *r = rng.sample(&distr);
+ }
+ assert_eq!(buf, expected);
+ }
+
+ let mut buf = [0; 10];
+ test_samples(&[1i32, 1, 1, 1, 1, 1, 1, 1, 1], &mut buf, &[
+ 0, 6, 2, 6, 3, 4, 7, 8, 2, 5,
+ ]);
+ test_samples(&[0.7f32, 0.1, 0.1, 0.1], &mut buf, &[
+ 0, 0, 0, 1, 0, 0, 2, 3, 0, 0,
+ ]);
+ test_samples(&[1.0f64, 0.999, 0.998, 0.997], &mut buf, &[
+ 2, 2, 1, 3, 2, 1, 3, 3, 2, 1,
+ ]);
+ }
+}
+
+/// Error type returned from `WeightedIndex::new`.
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+pub enum WeightedError {
+ /// The provided weight collection contains no items.
+ NoItem,
+
+ /// A weight is either less than zero, greater than the supported maximum or
+ /// otherwise invalid.
+ InvalidWeight,
+
+ /// All items in the provided weight collection are zero.
+ AllWeightsZero,
+
+ /// Too many weights are provided (length greater than `u32::MAX`)
+ TooMany,
+}
+
+#[cfg(feature = "std")]
+impl ::std::error::Error for WeightedError {}
+
+impl fmt::Display for WeightedError {
+ fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+ match *self {
+ WeightedError::NoItem => write!(f, "No weights provided."),
+ WeightedError::InvalidWeight => write!(f, "A weight is invalid."),
+ WeightedError::AllWeightsZero => write!(f, "All weights are zero."),
+ WeightedError::TooMany => write!(f, "Too many weights (hit u32::MAX)"),
+ }
+ }
+}
diff --git a/src/distributions/ziggurat_tables.rs b/src/distributions/ziggurat_tables.rs
new file mode 100644
index 0000000..f830a60
--- /dev/null
+++ b/src/distributions/ziggurat_tables.rs
@@ -0,0 +1,283 @@
+// Copyright 2018 Developers of the Rand project.
+// Copyright 2013 The Rust Project Developers.
+//
+// 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.
+
+// Tables for distributions which are sampled using the ziggurat
+// algorithm. Autogenerated by `ziggurat_tables.py`.
+
+pub type ZigTable = &'static [f64; 257];
+pub const ZIG_NORM_R: f64 = 3.654152885361008796;
+#[rustfmt::skip]
+pub static ZIG_NORM_X: [f64; 257] =
+ [3.910757959537090045, 3.654152885361008796, 3.449278298560964462, 3.320244733839166074,
+ 3.224575052047029100, 3.147889289517149969, 3.083526132001233044, 3.027837791768635434,
+ 2.978603279880844834, 2.934366867207854224, 2.894121053612348060, 2.857138730872132548,
+ 2.822877396825325125, 2.790921174000785765, 2.760944005278822555, 2.732685359042827056,
+ 2.705933656121858100, 2.680514643284522158, 2.656283037575502437, 2.633116393630324570,
+ 2.610910518487548515, 2.589575986706995181, 2.569035452680536569, 2.549221550323460761,
+ 2.530075232158516929, 2.511544441625342294, 2.493583041269680667, 2.476149939669143318,
+ 2.459208374333311298, 2.442725318198956774, 2.426670984935725972, 2.411018413899685520,
+ 2.395743119780480601, 2.380822795170626005, 2.366237056715818632, 2.351967227377659952,
+ 2.337996148795031370, 2.324308018869623016, 2.310888250599850036, 2.297723348901329565,
+ 2.284800802722946056, 2.272108990226823888, 2.259637095172217780, 2.247375032945807760,
+ 2.235313384928327984, 2.223443340090905718, 2.211756642882544366, 2.200245546609647995,
+ 2.188902771624720689, 2.177721467738641614, 2.166695180352645966, 2.155817819875063268,
+ 2.145083634046203613, 2.134487182844320152, 2.124023315687815661, 2.113687150684933957,
+ 2.103474055713146829, 2.093379631137050279, 2.083399693996551783, 2.073530263516978778,
+ 2.063767547809956415, 2.054107931648864849, 2.044547965215732788, 2.035084353727808715,
+ 2.025713947862032960, 2.016433734904371722, 2.007240830558684852, 1.998132471356564244,
+ 1.989106007615571325, 1.980158896898598364, 1.971288697931769640, 1.962493064942461896,
+ 1.953769742382734043, 1.945116560006753925, 1.936531428273758904, 1.928012334050718257,
+ 1.919557336591228847, 1.911164563769282232, 1.902832208548446369, 1.894558525668710081,
+ 1.886341828534776388, 1.878180486290977669, 1.870072921069236838, 1.862017605397632281,
+ 1.854013059758148119, 1.846057850283119750, 1.838150586580728607, 1.830289919680666566,
+ 1.822474540091783224, 1.814703175964167636, 1.806974591348693426, 1.799287584547580199,
+ 1.791640986550010028, 1.784033659547276329, 1.776464495522344977, 1.768932414909077933,
+ 1.761436365316706665, 1.753975320315455111, 1.746548278279492994, 1.739154261283669012,
+ 1.731792314050707216, 1.724461502945775715, 1.717160915015540690, 1.709889657069006086,
+ 1.702646854797613907, 1.695431651932238548, 1.688243209434858727, 1.681080704722823338,
+ 1.673943330923760353, 1.666830296159286684, 1.659740822855789499, 1.652674147080648526,
+ 1.645629517902360339, 1.638606196773111146, 1.631603456932422036, 1.624620582830568427,
+ 1.617656869570534228, 1.610711622367333673, 1.603784156023583041, 1.596873794420261339,
+ 1.589979870021648534, 1.583101723393471438, 1.576238702733332886, 1.569390163412534456,
+ 1.562555467528439657, 1.555733983466554893, 1.548925085471535512, 1.542128153226347553,
+ 1.535342571438843118, 1.528567729435024614, 1.521803020758293101, 1.515047842773992404,
+ 1.508301596278571965, 1.501563685112706548, 1.494833515777718391, 1.488110497054654369,
+ 1.481394039625375747, 1.474683555695025516, 1.467978458615230908, 1.461278162507407830,
+ 1.454582081885523293, 1.447889631277669675, 1.441200224845798017, 1.434513276002946425,
+ 1.427828197027290358, 1.421144398672323117, 1.414461289772464658, 1.407778276843371534,
+ 1.401094763676202559, 1.394410150925071257, 1.387723835686884621, 1.381035211072741964,
+ 1.374343665770030531, 1.367648583594317957, 1.360949343030101844, 1.354245316759430606,
+ 1.347535871177359290, 1.340820365893152122, 1.334098153216083604, 1.327368577624624679,
+ 1.320630975217730096, 1.313884673146868964, 1.307128989027353860, 1.300363230327433728,
+ 1.293586693733517645, 1.286798664489786415, 1.279998415710333237, 1.273185207661843732,
+ 1.266358287014688333, 1.259516886060144225, 1.252660221891297887, 1.245787495544997903,
+ 1.238897891102027415, 1.231990574742445110, 1.225064693752808020, 1.218119375481726552,
+ 1.211153726239911244, 1.204166830140560140, 1.197157747875585931, 1.190125515422801650,
+ 1.183069142678760732, 1.175987612011489825, 1.168879876726833800, 1.161744859441574240,
+ 1.154581450355851802, 1.147388505416733873, 1.140164844363995789, 1.132909248648336975,
+ 1.125620459211294389, 1.118297174115062909, 1.110938046009249502, 1.103541679420268151,
+ 1.096106627847603487, 1.088631390649514197, 1.081114409698889389, 1.073554065787871714,
+ 1.065948674757506653, 1.058296483326006454, 1.050595664586207123, 1.042844313139370538,
+ 1.035040439828605274, 1.027181966030751292, 1.019266717460529215, 1.011292417434978441,
+ 1.003256679539591412, 0.995156999629943084, 0.986990747093846266, 0.978755155288937750,
+ 0.970447311058864615, 0.962064143217605250, 0.953602409875572654, 0.945058684462571130,
+ 0.936429340280896860, 0.927710533396234771, 0.918898183643734989, 0.909987953490768997,
+ 0.900975224455174528, 0.891855070726792376, 0.882622229578910122, 0.873271068082494550,
+ 0.863795545546826915, 0.854189171001560554, 0.844444954902423661, 0.834555354079518752,
+ 0.824512208745288633, 0.814306670128064347, 0.803929116982664893, 0.793369058833152785,
+ 0.782615023299588763, 0.771654424216739354, 0.760473406422083165, 0.749056662009581653,
+ 0.737387211425838629, 0.725446140901303549, 0.713212285182022732, 0.700661841097584448,
+ 0.687767892786257717, 0.674499822827436479, 0.660822574234205984, 0.646695714884388928,
+ 0.632072236375024632, 0.616896989996235545, 0.601104617743940417, 0.584616766093722262,
+ 0.567338257040473026, 0.549151702313026790, 0.529909720646495108, 0.509423329585933393,
+ 0.487443966121754335, 0.463634336771763245, 0.437518402186662658, 0.408389134588000746,
+ 0.375121332850465727, 0.335737519180459465, 0.286174591747260509, 0.215241895913273806,
+ 0.000000000000000000];
+#[rustfmt::skip]
+pub static ZIG_NORM_F: [f64; 257] =
+ [0.000477467764586655, 0.001260285930498598, 0.002609072746106363, 0.004037972593371872,
+ 0.005522403299264754, 0.007050875471392110, 0.008616582769422917, 0.010214971439731100,
+ 0.011842757857943104, 0.013497450601780807, 0.015177088307982072, 0.016880083152595839,
+ 0.018605121275783350, 0.020351096230109354, 0.022117062707379922, 0.023902203305873237,
+ 0.025705804008632656, 0.027527235669693315, 0.029365939758230111, 0.031221417192023690,
+ 0.033093219458688698, 0.034980941461833073, 0.036884215688691151, 0.038802707404656918,
+ 0.040736110656078753, 0.042684144916619378, 0.044646552251446536, 0.046623094902089664,
+ 0.048613553216035145, 0.050617723861121788, 0.052635418276973649, 0.054666461325077916,
+ 0.056710690106399467, 0.058767952921137984, 0.060838108349751806, 0.062921024437977854,
+ 0.065016577971470438, 0.067124653828023989, 0.069245144397250269, 0.071377949059141965,
+ 0.073522973714240991, 0.075680130359194964, 0.077849336702372207, 0.080030515814947509,
+ 0.082223595813495684, 0.084428509570654661, 0.086645194450867782, 0.088873592068594229,
+ 0.091113648066700734, 0.093365311913026619, 0.095628536713353335, 0.097903279039215627,
+ 0.100189498769172020, 0.102487158942306270, 0.104796225622867056, 0.107116667775072880,
+ 0.109448457147210021, 0.111791568164245583, 0.114145977828255210, 0.116511665626037014,
+ 0.118888613443345698, 0.121276805485235437, 0.123676228202051403, 0.126086870220650349,
+ 0.128508722280473636, 0.130941777174128166, 0.133386029692162844, 0.135841476571757352,
+ 0.138308116449064322, 0.140785949814968309, 0.143274978974047118, 0.145775208006537926,
+ 0.148286642733128721, 0.150809290682410169, 0.153343161060837674, 0.155888264725064563,
+ 0.158444614156520225, 0.161012223438117663, 0.163591108232982951, 0.166181285765110071,
+ 0.168782774801850333, 0.171395595638155623, 0.174019770082499359, 0.176655321444406654,
+ 0.179302274523530397, 0.181960655600216487, 0.184630492427504539, 0.187311814224516926,
+ 0.190004651671193070, 0.192709036904328807, 0.195425003514885592, 0.198152586546538112,
+ 0.200891822495431333, 0.203642749311121501, 0.206405406398679298, 0.209179834621935651,
+ 0.211966076307852941, 0.214764175252008499, 0.217574176725178370, 0.220396127481011589,
+ 0.223230075764789593, 0.226076071323264877, 0.228934165415577484, 0.231804410825248525,
+ 0.234686861873252689, 0.237581574432173676, 0.240488605941449107, 0.243408015423711988,
+ 0.246339863502238771, 0.249284212419516704, 0.252241126056943765, 0.255210669955677150,
+ 0.258192911338648023, 0.261187919133763713, 0.264195763998317568, 0.267216518344631837,
+ 0.270250256366959984, 0.273297054069675804, 0.276356989296781264, 0.279430141762765316,
+ 0.282516593084849388, 0.285616426816658109, 0.288729728483353931, 0.291856585618280984,
+ 0.294997087801162572, 0.298151326697901342, 0.301319396102034120, 0.304501391977896274,
+ 0.307697412505553769, 0.310907558127563710, 0.314131931597630143, 0.317370638031222396,
+ 0.320623784958230129, 0.323891482377732021, 0.327173842814958593, 0.330470981380537099,
+ 0.333783015832108509, 0.337110066638412809, 0.340452257045945450, 0.343809713148291340,
+ 0.347182563958251478, 0.350570941482881204, 0.353974980801569250, 0.357394820147290515,
+ 0.360830600991175754, 0.364282468130549597, 0.367750569780596226, 0.371235057669821344,
+ 0.374736087139491414, 0.378253817247238111, 0.381788410875031348, 0.385340034841733958,
+ 0.388908860020464597, 0.392495061461010764, 0.396098818517547080, 0.399720314981931668,
+ 0.403359739222868885, 0.407017284331247953, 0.410693148271983222, 0.414387534042706784,
+ 0.418100649839684591, 0.421832709231353298, 0.425583931339900579, 0.429354541031341519,
+ 0.433144769114574058, 0.436954852549929273, 0.440785034667769915, 0.444635565397727750,
+ 0.448506701509214067, 0.452398706863882505, 0.456311852680773566, 0.460246417814923481,
+ 0.464202689050278838, 0.468180961407822172, 0.472181538469883255, 0.476204732721683788,
+ 0.480250865911249714, 0.484320269428911598, 0.488413284707712059, 0.492530263646148658,
+ 0.496671569054796314, 0.500837575128482149, 0.505028667945828791, 0.509245245998136142,
+ 0.513487720749743026, 0.517756517232200619, 0.522052074674794864, 0.526374847174186700,
+ 0.530725304406193921, 0.535103932383019565, 0.539511234259544614, 0.543947731192649941,
+ 0.548413963257921133, 0.552910490428519918, 0.557437893621486324, 0.561996775817277916,
+ 0.566587763258951771, 0.571211506738074970, 0.575868682975210544, 0.580559996103683473,
+ 0.585286179266300333, 0.590047996335791969, 0.594846243770991268, 0.599681752622167719,
+ 0.604555390700549533, 0.609468064928895381, 0.614420723892076803, 0.619414360609039205,
+ 0.624450015550274240, 0.629528779928128279, 0.634651799290960050, 0.639820277456438991,
+ 0.645035480824251883, 0.650298743114294586, 0.655611470583224665, 0.660975147780241357,
+ 0.666391343912380640, 0.671861719900766374, 0.677388036222513090, 0.682972161648791376,
+ 0.688616083008527058, 0.694321916130032579, 0.700091918140490099, 0.705928501336797409,
+ 0.711834248882358467, 0.717811932634901395, 0.723864533472881599, 0.729995264565802437,
+ 0.736207598131266683, 0.742505296344636245, 0.748892447223726720, 0.755373506511754500,
+ 0.761953346841546475, 0.768637315803334831, 0.775431304986138326, 0.782341832659861902,
+ 0.789376143571198563, 0.796542330428254619, 0.803849483176389490, 0.811307874318219935,
+ 0.818929191609414797, 0.826726833952094231, 0.834716292992930375, 0.842915653118441077,
+ 0.851346258465123684, 0.860033621203008636, 0.869008688043793165, 0.878309655816146839,
+ 0.887984660763399880, 0.898095921906304051, 0.908726440060562912, 0.919991505048360247,
+ 0.932060075968990209, 0.945198953453078028, 0.959879091812415930, 0.977101701282731328,
+ 1.000000000000000000];
+pub const ZIG_EXP_R: f64 = 7.697117470131050077;
+#[rustfmt::skip]
+pub static ZIG_EXP_X: [f64; 257] =
+ [8.697117470131052741, 7.697117470131050077, 6.941033629377212577, 6.478378493832569696,
+ 6.144164665772472667, 5.882144315795399869, 5.666410167454033697, 5.482890627526062488,
+ 5.323090505754398016, 5.181487281301500047, 5.054288489981304089, 4.938777085901250530,
+ 4.832939741025112035, 4.735242996601741083, 4.644491885420085175, 4.559737061707351380,
+ 4.480211746528421912, 4.405287693473573185, 4.334443680317273007, 4.267242480277365857,
+ 4.203313713735184365, 4.142340865664051464, 4.084051310408297830, 4.028208544647936762,
+ 3.974606066673788796, 3.923062500135489739, 3.873417670399509127, 3.825529418522336744,
+ 3.779270992411667862, 3.734528894039797375, 3.691201090237418825, 3.649195515760853770,
+ 3.608428813128909507, 3.568825265648337020, 3.530315889129343354, 3.492837654774059608,
+ 3.456332821132760191, 3.420748357251119920, 3.386035442460300970, 3.352149030900109405,
+ 3.319047470970748037, 3.286692171599068679, 3.255047308570449882, 3.224079565286264160,
+ 3.193757903212240290, 3.164053358025972873, 3.134938858084440394, 3.106389062339824481,
+ 3.078380215254090224, 3.050890016615455114, 3.023897504455676621, 2.997382949516130601,
+ 2.971327759921089662, 2.945714394895045718, 2.920526286512740821, 2.895747768600141825,
+ 2.871364012015536371, 2.847360965635188812, 2.823725302450035279, 2.800444370250737780,
+ 2.777506146439756574, 2.754899196562344610, 2.732612636194700073, 2.710636095867928752,
+ 2.688959688741803689, 2.667573980773266573, 2.646469963151809157, 2.625639026797788489,
+ 2.605072938740835564, 2.584763820214140750, 2.564704126316905253, 2.544886627111869970,
+ 2.525304390037828028, 2.505950763528594027, 2.486819361740209455, 2.467904050297364815,
+ 2.449198932978249754, 2.430698339264419694, 2.412396812688870629, 2.394289099921457886,
+ 2.376370140536140596, 2.358635057409337321, 2.341079147703034380, 2.323697874390196372,
+ 2.306486858283579799, 2.289441870532269441, 2.272558825553154804, 2.255833774367219213,
+ 2.239262898312909034, 2.222842503111036816, 2.206569013257663858, 2.190438966723220027,
+ 2.174449009937774679, 2.158595893043885994, 2.142876465399842001, 2.127287671317368289,
+ 2.111826546019042183, 2.096490211801715020, 2.081275874393225145, 2.066180819490575526,
+ 2.051202409468584786, 2.036338080248769611, 2.021585338318926173, 2.006941757894518563,
+ 1.992404978213576650, 1.977972700957360441, 1.963642687789548313, 1.949412758007184943,
+ 1.935280786297051359, 1.921244700591528076, 1.907302480018387536, 1.893452152939308242,
+ 1.879691795072211180, 1.866019527692827973, 1.852433515911175554, 1.838931967018879954,
+ 1.825513128903519799, 1.812175288526390649, 1.798916770460290859, 1.785735935484126014,
+ 1.772631179231305643, 1.759600930889074766, 1.746643651946074405, 1.733757834985571566,
+ 1.720942002521935299, 1.708194705878057773, 1.695514524101537912, 1.682900062917553896,
+ 1.670349953716452118, 1.657862852574172763, 1.645437439303723659, 1.633072416535991334,
+ 1.620766508828257901, 1.608518461798858379, 1.596327041286483395, 1.584191032532688892,
+ 1.572109239386229707, 1.560080483527888084, 1.548103603714513499, 1.536177455041032092,
+ 1.524300908219226258, 1.512472848872117082, 1.500692176842816750, 1.488957805516746058,
+ 1.477268661156133867, 1.465623682245745352, 1.454021818848793446, 1.442462031972012504,
+ 1.430943292938879674, 1.419464582769983219, 1.408024891569535697, 1.396623217917042137,
+ 1.385258568263121992, 1.373929956328490576, 1.362636402505086775, 1.351376933258335189,
+ 1.340150580529504643, 1.328956381137116560, 1.317793376176324749, 1.306660610415174117,
+ 1.295557131686601027, 1.284481990275012642, 1.273434238296241139, 1.262412929069615330,
+ 1.251417116480852521, 1.240445854334406572, 1.229498195693849105, 1.218573192208790124,
+ 1.207669893426761121, 1.196787346088403092, 1.185924593404202199, 1.175080674310911677,
+ 1.164254622705678921, 1.153445466655774743, 1.142652227581672841, 1.131873919411078511,
+ 1.121109547701330200, 1.110358108727411031, 1.099618588532597308, 1.088889961938546813,
+ 1.078171191511372307, 1.067461226479967662, 1.056759001602551429, 1.046063435977044209,
+ 1.035373431790528542, 1.024687873002617211, 1.014005623957096480, 1.003325527915696735,
+ 0.992646405507275897, 0.981967053085062602, 0.971286240983903260, 0.960602711668666509,
+ 0.949915177764075969, 0.939222319955262286, 0.928522784747210395, 0.917815182070044311,
+ 0.907098082715690257, 0.896370015589889935, 0.885629464761751528, 0.874874866291025066,
+ 0.864104604811004484, 0.853317009842373353, 0.842510351810368485, 0.831682837734273206,
+ 0.820832606554411814, 0.809957724057418282, 0.799056177355487174, 0.788125868869492430,
+ 0.777164609759129710, 0.766170112735434672, 0.755139984181982249, 0.744071715500508102,
+ 0.732962673584365398, 0.721810090308756203, 0.710611050909655040, 0.699362481103231959,
+ 0.688061132773747808, 0.676703568029522584, 0.665286141392677943, 0.653804979847664947,
+ 0.642255960424536365, 0.630634684933490286, 0.618936451394876075, 0.607156221620300030,
+ 0.595288584291502887, 0.583327712748769489, 0.571267316532588332, 0.559100585511540626,
+ 0.546820125163310577, 0.534417881237165604, 0.521885051592135052, 0.509211982443654398,
+ 0.496388045518671162, 0.483401491653461857, 0.470239275082169006, 0.456886840931420235,
+ 0.443327866073552401, 0.429543940225410703, 0.415514169600356364, 0.401214678896277765,
+ 0.386617977941119573, 0.371692145329917234, 0.356399760258393816, 0.340696481064849122,
+ 0.324529117016909452, 0.307832954674932158, 0.290527955491230394, 0.272513185478464703,
+ 0.253658363385912022, 0.233790483059674731, 0.212671510630966620, 0.189958689622431842,
+ 0.165127622564187282, 0.137304980940012589, 0.104838507565818778, 0.063852163815001570,
+ 0.000000000000000000];
+#[rustfmt::skip]
+pub static ZIG_EXP_F: [f64; 257] =
+ [0.000167066692307963, 0.000454134353841497, 0.000967269282327174, 0.001536299780301573,
+ 0.002145967743718907, 0.002788798793574076, 0.003460264777836904, 0.004157295120833797,
+ 0.004877655983542396, 0.005619642207205489, 0.006381905937319183, 0.007163353183634991,
+ 0.007963077438017043, 0.008780314985808977, 0.009614413642502212, 0.010464810181029981,
+ 0.011331013597834600, 0.012212592426255378, 0.013109164931254991, 0.014020391403181943,
+ 0.014945968011691148, 0.015885621839973156, 0.016839106826039941, 0.017806200410911355,
+ 0.018786700744696024, 0.019780424338009740, 0.020787204072578114, 0.021806887504283581,
+ 0.022839335406385240, 0.023884420511558174, 0.024942026419731787, 0.026012046645134221,
+ 0.027094383780955803, 0.028188948763978646, 0.029295660224637411, 0.030414443910466622,
+ 0.031545232172893622, 0.032687963508959555, 0.033842582150874358, 0.035009037697397431,
+ 0.036187284781931443, 0.037377282772959382, 0.038578995503074871, 0.039792391023374139,
+ 0.041017441380414840, 0.042254122413316254, 0.043502413568888197, 0.044762297732943289,
+ 0.046033761076175184, 0.047316792913181561, 0.048611385573379504, 0.049917534282706379,
+ 0.051235237055126281, 0.052564494593071685, 0.053905310196046080, 0.055257689676697030,
+ 0.056621641283742870, 0.057997175631200659, 0.059384305633420280, 0.060783046445479660,
+ 0.062193415408541036, 0.063615431999807376, 0.065049117786753805, 0.066494496385339816,
+ 0.067951593421936643, 0.069420436498728783, 0.070901055162371843, 0.072393480875708752,
+ 0.073897746992364746, 0.075413888734058410, 0.076941943170480517, 0.078481949201606435,
+ 0.080033947542319905, 0.081597980709237419, 0.083174093009632397, 0.084762330532368146,
+ 0.086362741140756927, 0.087975374467270231, 0.089600281910032886, 0.091237516631040197,
+ 0.092887133556043569, 0.094549189376055873, 0.096223742550432825, 0.097910853311492213,
+ 0.099610583670637132, 0.101322997425953631, 0.103048160171257702, 0.104786139306570145,
+ 0.106537004050001632, 0.108300825451033755, 0.110077676405185357, 0.111867631670056283,
+ 0.113670767882744286, 0.115487163578633506, 0.117316899211555525, 0.119160057175327641,
+ 0.121016721826674792, 0.122886979509545108, 0.124770918580830933, 0.126668629437510671,
+ 0.128580204545228199, 0.130505738468330773, 0.132445327901387494, 0.134399071702213602,
+ 0.136367070926428829, 0.138349428863580176, 0.140346251074862399, 0.142357645432472146,
+ 0.144383722160634720, 0.146424593878344889, 0.148480375643866735, 0.150551185001039839,
+ 0.152637142027442801, 0.154738369384468027, 0.156854992369365148, 0.158987138969314129,
+ 0.161134939917591952, 0.163298528751901734, 0.165478041874935922, 0.167673618617250081,
+ 0.169885401302527550, 0.172113535315319977, 0.174358169171353411, 0.176619454590494829,
+ 0.178897546572478278, 0.181192603475496261, 0.183504787097767436, 0.185834262762197083,
+ 0.188181199404254262, 0.190545769663195363, 0.192928149976771296, 0.195328520679563189,
+ 0.197747066105098818, 0.200183974691911210, 0.202639439093708962, 0.205113656293837654,
+ 0.207606827724221982, 0.210119159388988230, 0.212650861992978224, 0.215202151075378628,
+ 0.217773247148700472, 0.220364375843359439, 0.222975768058120111, 0.225607660116683956,
+ 0.228260293930716618, 0.230933917169627356, 0.233628783437433291, 0.236345152457059560,
+ 0.239083290262449094, 0.241843469398877131, 0.244625969131892024, 0.247431075665327543,
+ 0.250259082368862240, 0.253110290015629402, 0.255985007030415324, 0.258883549749016173,
+ 0.261806242689362922, 0.264753418835062149, 0.267725419932044739, 0.270722596799059967,
+ 0.273745309652802915, 0.276793928448517301, 0.279868833236972869, 0.282970414538780746,
+ 0.286099073737076826, 0.289255223489677693, 0.292439288161892630, 0.295651704281261252,
+ 0.298892921015581847, 0.302163400675693528, 0.305463619244590256, 0.308794066934560185,
+ 0.312155248774179606, 0.315547685227128949, 0.318971912844957239, 0.322428484956089223,
+ 0.325917972393556354, 0.329440964264136438, 0.332998068761809096, 0.336589914028677717,
+ 0.340217149066780189, 0.343880444704502575, 0.347580494621637148, 0.351318016437483449,
+ 0.355093752866787626, 0.358908472948750001, 0.362762973354817997, 0.366658079781514379,
+ 0.370594648435146223, 0.374573567615902381, 0.378595759409581067, 0.382662181496010056,
+ 0.386773829084137932, 0.390931736984797384, 0.395136981833290435, 0.399390684475231350,
+ 0.403694012530530555, 0.408048183152032673, 0.412454465997161457, 0.416914186433003209,
+ 0.421428728997616908, 0.425999541143034677, 0.430628137288459167, 0.435316103215636907,
+ 0.440065100842354173, 0.444876873414548846, 0.449753251162755330, 0.454696157474615836,
+ 0.459707615642138023, 0.464789756250426511, 0.469944825283960310, 0.475175193037377708,
+ 0.480483363930454543, 0.485871987341885248, 0.491343869594032867, 0.496901987241549881,
+ 0.502549501841348056, 0.508289776410643213, 0.514126393814748894, 0.520063177368233931,
+ 0.526104213983620062, 0.532253880263043655, 0.538516872002862246, 0.544898237672440056,
+ 0.551403416540641733, 0.558038282262587892, 0.564809192912400615, 0.571723048664826150,
+ 0.578787358602845359, 0.586010318477268366, 0.593400901691733762, 0.600968966365232560,
+ 0.608725382079622346, 0.616682180915207878, 0.624852738703666200, 0.633251994214366398,
+ 0.641896716427266423, 0.650805833414571433, 0.660000841079000145, 0.669506316731925177,
+ 0.679350572264765806, 0.689566496117078431, 0.700192655082788606, 0.711274760805076456,
+ 0.722867659593572465, 0.735038092431424039, 0.747868621985195658, 0.761463388849896838,
+ 0.775956852040116218, 0.791527636972496285, 0.808421651523009044, 0.826993296643051101,
+ 0.847785500623990496, 0.871704332381204705, 0.900469929925747703, 0.938143680862176477,
+ 1.000000000000000000];
diff --git a/src/lib.rs b/src/lib.rs
new file mode 100644
index 0000000..d42a79f
--- /dev/null
+++ b/src/lib.rs
@@ -0,0 +1,723 @@
+// Copyright 2018 Developers of the Rand project.
+// Copyright 2013-2017 The Rust Project Developers.
+//
+// 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.
+
+//! Utilities for random number generation
+//!
+//! Rand provides utilities to generate random numbers, to convert them to
+//! useful types and distributions, and some randomness-related algorithms.
+//!
+//! # Quick Start
+//!
+//! To get you started quickly, the easiest and highest-level way to get
+//! a random value is to use [`random()`]; alternatively you can use
+//! [`thread_rng()`]. The [`Rng`] trait provides a useful API on all RNGs, while
+//! the [`distributions`] and [`seq`] modules provide further
+//! functionality on top of RNGs.
+//!
+//! ```
+//! use rand::prelude::*;
+//!
+//! if rand::random() { // generates a boolean
+//! // Try printing a random unicode code point (probably a bad idea)!
+//! println!("char: {}", rand::random::<char>());
+//! }
+//!
+//! let mut rng = rand::thread_rng();
+//! let y: f64 = rng.gen(); // generates a float between 0 and 1
+//!
+//! let mut nums: Vec<i32> = (1..100).collect();
+//! nums.shuffle(&mut rng);
+//! ```
+//!
+//! # The Book
+//!
+//! For the user guide and futher documentation, please read
+//! [The Rust Rand Book](https://rust-random.github.io/book).
+
+#![doc(
+ html_logo_url = "https://www.rust-lang.org/logos/rust-logo-128x128-blk.png",
+ html_favicon_url = "https://www.rust-lang.org/favicon.ico",
+ html_root_url = "https://rust-random.github.io/rand/"
+)]
+#![deny(missing_docs)]
+#![deny(missing_debug_implementations)]
+#![doc(test(attr(allow(unused_variables), deny(warnings))))]
+#![cfg_attr(not(feature = "std"), no_std)]
+#![cfg_attr(all(feature = "simd_support", feature = "nightly"), feature(stdsimd))]
+#![allow(
+ clippy::excessive_precision,
+ clippy::unreadable_literal,
+ clippy::float_cmp
+)]
+
+#[cfg(all(feature = "alloc", not(feature = "std")))] extern crate alloc;
+
+#[allow(unused)]
+macro_rules! trace { ($($x:tt)*) => (
+ #[cfg(feature = "log")] {
+ log::trace!($($x)*)
+ }
+) }
+#[allow(unused)]
+macro_rules! debug { ($($x:tt)*) => (
+ #[cfg(feature = "log")] {
+ log::debug!($($x)*)
+ }
+) }
+#[allow(unused)]
+macro_rules! info { ($($x:tt)*) => (
+ #[cfg(feature = "log")] {
+ log::info!($($x)*)
+ }
+) }
+#[allow(unused)]
+macro_rules! warn { ($($x:tt)*) => (
+ #[cfg(feature = "log")] {
+ log::warn!($($x)*)
+ }
+) }
+#[allow(unused)]
+macro_rules! error { ($($x:tt)*) => (
+ #[cfg(feature = "log")] {
+ log::error!($($x)*)
+ }
+) }
+
+// Re-exports from rand_core
+pub use rand_core::{CryptoRng, Error, RngCore, SeedableRng};
+
+// Public exports
+#[cfg(feature = "std")] pub use crate::rngs::thread::thread_rng;
+
+// Public modules
+pub mod distributions;
+pub mod prelude;
+pub mod rngs;
+pub mod seq;
+
+
+use crate::distributions::uniform::{SampleBorrow, SampleUniform, UniformSampler};
+use crate::distributions::{Distribution, Standard};
+use core::num::Wrapping;
+use core::{mem, slice};
+
+/// An automatically-implemented extension trait on [`RngCore`] providing high-level
+/// generic methods for sampling values and other convenience methods.
+///
+/// This is the primary trait to use when generating random values.
+///
+/// # Generic usage
+///
+/// The basic pattern is `fn foo<R: Rng + ?Sized>(rng: &mut R)`. Some
+/// things are worth noting here:
+///
+/// - Since `Rng: RngCore` and every `RngCore` implements `Rng`, it makes no
+/// difference whether we use `R: Rng` or `R: RngCore`.
+/// - The `+ ?Sized` un-bounding allows functions to be called directly on
+/// type-erased references; i.e. `foo(r)` where `r: &mut RngCore`. Without
+/// this it would be necessary to write `foo(&mut r)`.
+///
+/// An alternative pattern is possible: `fn foo<R: Rng>(rng: R)`. This has some
+/// trade-offs. It allows the argument to be consumed directly without a `&mut`
+/// (which is how `from_rng(thread_rng())` works); also it still works directly
+/// on references (including type-erased references). Unfortunately within the
+/// function `foo` it is not known whether `rng` is a reference type or not,
+/// hence many uses of `rng` require an extra reference, either explicitly
+/// (`distr.sample(&mut rng)`) or implicitly (`rng.gen()`); one may hope the
+/// optimiser can remove redundant references later.
+///
+/// Example:
+///
+/// ```
+/// # use rand::thread_rng;
+/// use rand::Rng;
+///
+/// fn foo<R: Rng + ?Sized>(rng: &mut R) -> f32 {
+/// rng.gen()
+/// }
+///
+/// # let v = foo(&mut thread_rng());
+/// ```
+pub trait Rng: RngCore {
+ /// Return a random value supporting the [`Standard`] distribution.
+ ///
+ /// # Example
+ ///
+ /// ```
+ /// use rand::{thread_rng, Rng};
+ ///
+ /// let mut rng = thread_rng();
+ /// let x: u32 = rng.gen();
+ /// println!("{}", x);
+ /// println!("{:?}", rng.gen::<(f64, bool)>());
+ /// ```
+ ///
+ /// # Arrays and tuples
+ ///
+ /// The `rng.gen()` method is able to generate arrays (up to 32 elements)
+ /// and tuples (up to 12 elements), so long as all element types can be
+ /// generated.
+ ///
+ /// For arrays of integers, especially for those with small element types
+ /// (< 64 bit), it will likely be faster to instead use [`Rng::fill`].
+ ///
+ /// ```
+ /// use rand::{thread_rng, Rng};
+ ///
+ /// let mut rng = thread_rng();
+ /// let tuple: (u8, i32, char) = rng.gen(); // arbitrary tuple support
+ ///
+ /// let arr1: [f32; 32] = rng.gen(); // array construction
+ /// let mut arr2 = [0u8; 128];
+ /// rng.fill(&mut arr2); // array fill
+ /// ```
+ ///
+ /// [`Standard`]: distributions::Standard
+ #[inline]
+ fn gen<T>(&mut self) -> T
+ where Standard: Distribution<T> {
+ Standard.sample(self)
+ }
+
+ /// Generate a random value in the range [`low`, `high`), i.e. inclusive of
+ /// `low` and exclusive of `high`.
+ ///
+ /// This function is optimised for the case that only a single sample is
+ /// made from the given range. See also the [`Uniform`] distribution
+ /// type which may be faster if sampling from the same range repeatedly.
+ ///
+ /// # Panics
+ ///
+ /// Panics if `low >= high`.
+ ///
+ /// # Example
+ ///
+ /// ```
+ /// use rand::{thread_rng, Rng};
+ ///
+ /// let mut rng = thread_rng();
+ /// let n: u32 = rng.gen_range(0, 10);
+ /// println!("{}", n);
+ /// let m: f64 = rng.gen_range(-40.0f64, 1.3e5f64);
+ /// println!("{}", m);
+ /// ```
+ ///
+ /// [`Uniform`]: distributions::uniform::Uniform
+ fn gen_range<T: SampleUniform, B1, B2>(&mut self, low: B1, high: B2) -> T
+ where
+ B1: SampleBorrow<T> + Sized,
+ B2: SampleBorrow<T> + Sized,
+ {
+ T::Sampler::sample_single(low, high, self)
+ }
+
+ /// Sample a new value, using the given distribution.
+ ///
+ /// ### Example
+ ///
+ /// ```
+ /// use rand::{thread_rng, Rng};
+ /// use rand::distributions::Uniform;
+ ///
+ /// let mut rng = thread_rng();
+ /// let x = rng.sample(Uniform::new(10u32, 15));
+ /// // Type annotation requires two types, the type and distribution; the
+ /// // distribution can be inferred.
+ /// let y = rng.sample::<u16, _>(Uniform::new(10, 15));
+ /// ```
+ fn sample<T, D: Distribution<T>>(&mut self, distr: D) -> T {
+ distr.sample(self)
+ }
+
+ /// Create an iterator that generates values using the given distribution.
+ ///
+ /// Note that this function takes its arguments by value. This works since
+ /// `(&mut R): Rng where R: Rng` and
+ /// `(&D): Distribution where D: Distribution`,
+ /// however borrowing is not automatic hence `rng.sample_iter(...)` may
+ /// need to be replaced with `(&mut rng).sample_iter(...)`.
+ ///
+ /// # Example
+ ///
+ /// ```
+ /// use rand::{thread_rng, Rng};
+ /// use rand::distributions::{Alphanumeric, Uniform, Standard};
+ ///
+ /// let rng = thread_rng();
+ ///
+ /// // Vec of 16 x f32:
+ /// let v: Vec<f32> = rng.sample_iter(Standard).take(16).collect();
+ ///
+ /// // String:
+ /// let s: String = rng.sample_iter(Alphanumeric).take(7).collect();
+ ///
+ /// // Combined values
+ /// println!("{:?}", rng.sample_iter(Standard).take(5)
+ /// .collect::<Vec<(f64, bool)>>());
+ ///
+ /// // Dice-rolling:
+ /// let die_range = Uniform::new_inclusive(1, 6);
+ /// let mut roll_die = rng.sample_iter(die_range);
+ /// while roll_die.next().unwrap() != 6 {
+ /// println!("Not a 6; rolling again!");
+ /// }
+ /// ```
+ fn sample_iter<T, D>(self, distr: D) -> distributions::DistIter<D, Self, T>
+ where
+ D: Distribution<T>,
+ Self: Sized,
+ {
+ distr.sample_iter(self)
+ }
+
+ /// Fill `dest` entirely with random bytes (uniform value distribution),
+ /// where `dest` is any type supporting [`AsByteSliceMut`], namely slices
+ /// and arrays over primitive integer types (`i8`, `i16`, `u32`, etc.).
+ ///
+ /// On big-endian platforms this performs byte-swapping to ensure
+ /// portability of results from reproducible generators.
+ ///
+ /// This uses [`fill_bytes`] internally which may handle some RNG errors
+ /// implicitly (e.g. waiting if the OS generator is not ready), but panics
+ /// on other errors. See also [`try_fill`] which returns errors.
+ ///
+ /// # Example
+ ///
+ /// ```
+ /// use rand::{thread_rng, Rng};
+ ///
+ /// let mut arr = [0i8; 20];
+ /// thread_rng().fill(&mut arr[..]);
+ /// ```
+ ///
+ /// [`fill_bytes`]: RngCore::fill_bytes
+ /// [`try_fill`]: Rng::try_fill
+ fn fill<T: AsByteSliceMut + ?Sized>(&mut self, dest: &mut T) {
+ self.fill_bytes(dest.as_byte_slice_mut());
+ dest.to_le();
+ }
+
+ /// Fill `dest` entirely with random bytes (uniform value distribution),
+ /// where `dest` is any type supporting [`AsByteSliceMut`], namely slices
+ /// and arrays over primitive integer types (`i8`, `i16`, `u32`, etc.).
+ ///
+ /// On big-endian platforms this performs byte-swapping to ensure
+ /// portability of results from reproducible generators.
+ ///
+ /// This is identical to [`fill`] except that it uses [`try_fill_bytes`]
+ /// internally and forwards RNG errors.
+ ///
+ /// # Example
+ ///
+ /// ```
+ /// # use rand::Error;
+ /// use rand::{thread_rng, Rng};
+ ///
+ /// # fn try_inner() -> Result<(), Error> {
+ /// let mut arr = [0u64; 4];
+ /// thread_rng().try_fill(&mut arr[..])?;
+ /// # Ok(())
+ /// # }
+ ///
+ /// # try_inner().unwrap()
+ /// ```
+ ///
+ /// [`try_fill_bytes`]: RngCore::try_fill_bytes
+ /// [`fill`]: Rng::fill
+ fn try_fill<T: AsByteSliceMut + ?Sized>(&mut self, dest: &mut T) -> Result<(), Error> {
+ self.try_fill_bytes(dest.as_byte_slice_mut())?;
+ dest.to_le();
+ Ok(())
+ }
+
+ /// Return a bool with a probability `p` of being true.
+ ///
+ /// See also the [`Bernoulli`] distribution, which may be faster if
+ /// sampling from the same probability repeatedly.
+ ///
+ /// # Example
+ ///
+ /// ```
+ /// use rand::{thread_rng, Rng};
+ ///
+ /// let mut rng = thread_rng();
+ /// println!("{}", rng.gen_bool(1.0 / 3.0));
+ /// ```
+ ///
+ /// # Panics
+ ///
+ /// If `p < 0` or `p > 1`.
+ ///
+ /// [`Bernoulli`]: distributions::bernoulli::Bernoulli
+ #[inline]
+ fn gen_bool(&mut self, p: f64) -> bool {
+ let d = distributions::Bernoulli::new(p).unwrap();
+ self.sample(d)
+ }
+
+ /// Return a bool with a probability of `numerator/denominator` of being
+ /// true. I.e. `gen_ratio(2, 3)` has chance of 2 in 3, or about 67%, of
+ /// returning true. If `numerator == denominator`, then the returned value
+ /// is guaranteed to be `true`. If `numerator == 0`, then the returned
+ /// value is guaranteed to be `false`.
+ ///
+ /// See also the [`Bernoulli`] distribution, which may be faster if
+ /// sampling from the same `numerator` and `denominator` repeatedly.
+ ///
+ /// # Panics
+ ///
+ /// If `denominator == 0` or `numerator > denominator`.
+ ///
+ /// # Example
+ ///
+ /// ```
+ /// use rand::{thread_rng, Rng};
+ ///
+ /// let mut rng = thread_rng();
+ /// println!("{}", rng.gen_ratio(2, 3));
+ /// ```
+ ///
+ /// [`Bernoulli`]: distributions::bernoulli::Bernoulli
+ #[inline]
+ fn gen_ratio(&mut self, numerator: u32, denominator: u32) -> bool {
+ let d = distributions::Bernoulli::from_ratio(numerator, denominator).unwrap();
+ self.sample(d)
+ }
+}
+
+impl<R: RngCore + ?Sized> Rng for R {}
+
+/// Trait for casting types to byte slices
+///
+/// This is used by the [`Rng::fill`] and [`Rng::try_fill`] methods.
+pub trait AsByteSliceMut {
+ /// Return a mutable reference to self as a byte slice
+ fn as_byte_slice_mut(&mut self) -> &mut [u8];
+
+ /// Call `to_le` on each element (i.e. byte-swap on Big Endian platforms).
+ fn to_le(&mut self);
+}
+
+impl AsByteSliceMut for [u8] {
+ fn as_byte_slice_mut(&mut self) -> &mut [u8] {
+ self
+ }
+
+ fn to_le(&mut self) {}
+}
+
+macro_rules! impl_as_byte_slice {
+ () => {};
+ ($t:ty) => {
+ impl AsByteSliceMut for [$t] {
+ fn as_byte_slice_mut(&mut self) -> &mut [u8] {
+ if self.len() == 0 {
+ unsafe {
+ // must not use null pointer
+ slice::from_raw_parts_mut(0x1 as *mut u8, 0)
+ }
+ } else {
+ unsafe {
+ slice::from_raw_parts_mut(self.as_mut_ptr()
+ as *mut u8,
+ self.len() * mem::size_of::<$t>()
+ )
+ }
+ }
+ }
+
+ fn to_le(&mut self) {
+ for x in self {
+ *x = x.to_le();
+ }
+ }
+ }
+
+ impl AsByteSliceMut for [Wrapping<$t>] {
+ fn as_byte_slice_mut(&mut self) -> &mut [u8] {
+ if self.len() == 0 {
+ unsafe {
+ // must not use null pointer
+ slice::from_raw_parts_mut(0x1 as *mut u8, 0)
+ }
+ } else {
+ unsafe {
+ slice::from_raw_parts_mut(self.as_mut_ptr()
+ as *mut u8,
+ self.len() * mem::size_of::<$t>()
+ )
+ }
+ }
+ }
+
+ fn to_le(&mut self) {
+ for x in self {
+ *x = Wrapping(x.0.to_le());
+ }
+ }
+ }
+ };
+ ($t:ty, $($tt:ty,)*) => {
+ impl_as_byte_slice!($t);
+ // TODO: this could replace above impl once Rust #32463 is fixed
+ // impl_as_byte_slice!(Wrapping<$t>);
+ impl_as_byte_slice!($($tt,)*);
+ }
+}
+
+impl_as_byte_slice!(u16, u32, u64, usize,);
+#[cfg(not(target_os = "emscripten"))]
+impl_as_byte_slice!(u128);
+impl_as_byte_slice!(i8, i16, i32, i64, isize,);
+#[cfg(not(target_os = "emscripten"))]
+impl_as_byte_slice!(i128);
+
+macro_rules! impl_as_byte_slice_arrays {
+ ($n:expr,) => {};
+ ($n:expr, $N:ident) => {
+ impl<T> AsByteSliceMut for [T; $n] where [T]: AsByteSliceMut {
+ fn as_byte_slice_mut(&mut self) -> &mut [u8] {
+ self[..].as_byte_slice_mut()
+ }
+
+ fn to_le(&mut self) {
+ self[..].to_le()
+ }
+ }
+ };
+ ($n:expr, $N:ident, $($NN:ident,)*) => {
+ impl_as_byte_slice_arrays!($n, $N);
+ impl_as_byte_slice_arrays!($n - 1, $($NN,)*);
+ };
+ (!div $n:expr,) => {};
+ (!div $n:expr, $N:ident, $($NN:ident,)*) => {
+ impl_as_byte_slice_arrays!($n, $N);
+ impl_as_byte_slice_arrays!(!div $n / 2, $($NN,)*);
+ };
+}
+#[rustfmt::skip]
+impl_as_byte_slice_arrays!(32, N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,);
+impl_as_byte_slice_arrays!(!div 4096, N,N,N,N,N,N,N,);
+
+/// Generates a random value using the thread-local random number generator.
+///
+/// This is simply a shortcut for `thread_rng().gen()`. See [`thread_rng`] for
+/// documentation of the entropy source and [`Standard`] for documentation of
+/// distributions and type-specific generation.
+///
+/// # Examples
+///
+/// ```
+/// let x = rand::random::<u8>();
+/// println!("{}", x);
+///
+/// let y = rand::random::<f64>();
+/// println!("{}", y);
+///
+/// if rand::random() { // generates a boolean
+/// println!("Better lucky than good!");
+/// }
+/// ```
+///
+/// If you're calling `random()` in a loop, caching the generator as in the
+/// following example can increase performance.
+///
+/// ```
+/// use rand::Rng;
+///
+/// let mut v = vec![1, 2, 3];
+///
+/// for x in v.iter_mut() {
+/// *x = rand::random()
+/// }
+///
+/// // can be made faster by caching thread_rng
+///
+/// let mut rng = rand::thread_rng();
+///
+/// for x in v.iter_mut() {
+/// *x = rng.gen();
+/// }
+/// ```
+///
+/// [`Standard`]: distributions::Standard
+#[cfg(feature = "std")]
+#[inline]
+pub fn random<T>() -> T
+where Standard: Distribution<T> {
+ thread_rng().gen()
+}
+
+#[cfg(test)]
+mod test {
+ use super::*;
+ use crate::rngs::mock::StepRng;
+ #[cfg(all(not(feature = "std"), feature = "alloc"))] use alloc::boxed::Box;
+
+ /// Construct a deterministic RNG with the given seed
+ pub fn rng(seed: u64) -> impl RngCore {
+ // For tests, we want a statistically good, fast, reproducible RNG.
+ // PCG32 will do fine, and will be easy to embed if we ever need to.
+ const INC: u64 = 11634580027462260723;
+ rand_pcg::Pcg32::new(seed, INC)
+ }
+
+ #[test]
+ fn test_fill_bytes_default() {
+ let mut r = StepRng::new(0x11_22_33_44_55_66_77_88, 0);
+
+ // check every remainder mod 8, both in small and big vectors.
+ let lengths = [0, 1, 2, 3, 4, 5, 6, 7, 80, 81, 82, 83, 84, 85, 86, 87];
+ for &n in lengths.iter() {
+ let mut buffer = [0u8; 87];
+ let v = &mut buffer[0..n];
+ r.fill_bytes(v);
+
+ // use this to get nicer error messages.
+ for (i, &byte) in v.iter().enumerate() {
+ if byte == 0 {
+ panic!("byte {} of {} is zero", i, n)
+ }
+ }
+ }
+ }
+
+ #[test]
+ fn test_fill() {
+ let x = 9041086907909331047; // a random u64
+ let mut rng = StepRng::new(x, 0);
+
+ // Convert to byte sequence and back to u64; byte-swap twice if BE.
+ let mut array = [0u64; 2];
+ rng.fill(&mut array[..]);
+ assert_eq!(array, [x, x]);
+ assert_eq!(rng.next_u64(), x);
+
+ // Convert to bytes then u32 in LE order
+ let mut array = [0u32; 2];
+ rng.fill(&mut array[..]);
+ assert_eq!(array, [x as u32, (x >> 32) as u32]);
+ assert_eq!(rng.next_u32(), x as u32);
+
+ // Check equivalence using wrapped arrays
+ let mut warray = [Wrapping(0u32); 2];
+ rng.fill(&mut warray[..]);
+ assert_eq!(array[0], warray[0].0);
+ assert_eq!(array[1], warray[1].0);
+ }
+
+ #[test]
+ fn test_fill_empty() {
+ let mut array = [0u32; 0];
+ let mut rng = StepRng::new(0, 1);
+ rng.fill(&mut array);
+ rng.fill(&mut array[..]);
+ }
+
+ #[test]
+ fn test_gen_range() {
+ let mut r = rng(101);
+ for _ in 0..1000 {
+ let a = r.gen_range(-4711, 17);
+ assert!(a >= -4711 && a < 17);
+ let a = r.gen_range(-3i8, 42);
+ assert!(a >= -3i8 && a < 42i8);
+ let a = r.gen_range(&10u16, 99);
+ assert!(a >= 10u16 && a < 99u16);
+ let a = r.gen_range(-100i32, &2000);
+ assert!(a >= -100i32 && a < 2000i32);
+ let a = r.gen_range(&12u32, &24u32);
+ assert!(a >= 12u32 && a < 24u32);
+
+ assert_eq!(r.gen_range(0u32, 1), 0u32);
+ assert_eq!(r.gen_range(-12i64, -11), -12i64);
+ assert_eq!(r.gen_range(3_000_000, 3_000_001), 3_000_000);
+ }
+ }
+
+ #[test]
+ #[should_panic]
+ fn test_gen_range_panic_int() {
+ let mut r = rng(102);
+ r.gen_range(5, -2);
+ }
+
+ #[test]
+ #[should_panic]
+ fn test_gen_range_panic_usize() {
+ let mut r = rng(103);
+ r.gen_range(5, 2);
+ }
+
+ #[test]
+ fn test_gen_bool() {
+ let mut r = rng(105);
+ for _ in 0..5 {
+ assert_eq!(r.gen_bool(0.0), false);
+ assert_eq!(r.gen_bool(1.0), true);
+ }
+ }
+
+ #[test]
+ fn test_rng_trait_object() {
+ use crate::distributions::{Distribution, Standard};
+ let mut rng = rng(109);
+ let mut r = &mut rng as &mut dyn RngCore;
+ r.next_u32();
+ r.gen::<i32>();
+ assert_eq!(r.gen_range(0, 1), 0);
+ let _c: u8 = Standard.sample(&mut r);
+ }
+
+ #[test]
+ #[cfg(feature = "alloc")]
+ fn test_rng_boxed_trait() {
+ use crate::distributions::{Distribution, Standard};
+ let rng = rng(110);
+ let mut r = Box::new(rng) as Box<dyn RngCore>;
+ r.next_u32();
+ r.gen::<i32>();
+ assert_eq!(r.gen_range(0, 1), 0);
+ let _c: u8 = Standard.sample(&mut r);
+ }
+
+ #[test]
+ #[cfg(feature = "std")]
+ fn test_random() {
+ // not sure how to test this aside from just getting some values
+ let _n: usize = random();
+ let _f: f32 = random();
+ let _o: Option<Option<i8>> = random();
+ let _many: (
+ (),
+ (usize, isize, Option<(u32, (bool,))>),
+ (u8, i8, u16, i16, u32, i32, u64, i64),
+ (f32, (f64, (f64,))),
+ ) = random();
+ }
+
+ #[test]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_gen_ratio_average() {
+ const NUM: u32 = 3;
+ const DENOM: u32 = 10;
+ const N: u32 = 100_000;
+
+ let mut sum: u32 = 0;
+ let mut rng = rng(111);
+ for _ in 0..N {
+ if rng.gen_ratio(NUM, DENOM) {
+ sum += 1;
+ }
+ }
+ // Have Binomial(N, NUM/DENOM) distribution
+ let expected = (NUM * N) / DENOM; // exact integer
+ assert!(((sum - expected) as i32).abs() < 500);
+ }
+}
diff --git a/src/prelude.rs b/src/prelude.rs
new file mode 100644
index 0000000..98ae3bb
--- /dev/null
+++ b/src/prelude.rs
@@ -0,0 +1,33 @@
+// 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.
+
+//! Convenience re-export of common members
+//!
+//! Like the standard library's prelude, this module simplifies importing of
+//! common items. Unlike the standard prelude, the contents of this module must
+//! be imported manually:
+//!
+//! ```
+//! use rand::prelude::*;
+//! # let mut r = StdRng::from_rng(thread_rng()).unwrap();
+//! # let _: f32 = r.gen();
+//! ```
+
+#[doc(no_inline)] pub use crate::distributions::Distribution;
+#[cfg(feature = "small_rng")]
+#[doc(no_inline)]
+pub use crate::rngs::SmallRng;
+#[doc(no_inline)] pub use crate::rngs::StdRng;
+#[doc(no_inline)]
+#[cfg(feature = "std")]
+pub use crate::rngs::ThreadRng;
+#[doc(no_inline)] pub use crate::seq::{IteratorRandom, SliceRandom};
+#[doc(no_inline)]
+#[cfg(feature = "std")]
+pub use crate::{random, thread_rng};
+#[doc(no_inline)] pub use crate::{CryptoRng, Rng, RngCore, SeedableRng};
diff --git a/src/rngs/adapter/mod.rs b/src/rngs/adapter/mod.rs
new file mode 100644
index 0000000..45e56af
--- /dev/null
+++ b/src/rngs/adapter/mod.rs
@@ -0,0 +1,15 @@
+// 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.
+
+//! Wrappers / adapters forming RNGs
+
+#[cfg(feature = "std")] mod read;
+mod reseeding;
+
+#[cfg(feature = "std")] pub use self::read::{ReadError, ReadRng};
+pub use self::reseeding::ReseedingRng;
diff --git a/src/rngs/adapter/read.rs b/src/rngs/adapter/read.rs
new file mode 100644
index 0000000..9a4b55d
--- /dev/null
+++ b/src/rngs/adapter/read.rs
@@ -0,0 +1,155 @@
+// Copyright 2018 Developers of the Rand project.
+// Copyright 2013 The Rust Project Developers.
+//
+// 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.
+
+//! A wrapper around any Read to treat it as an RNG.
+
+use std::fmt;
+use std::io::Read;
+
+use rand_core::{impls, Error, RngCore};
+
+
+/// An RNG that reads random bytes straight from any type supporting
+/// [`std::io::Read`], for example files.
+///
+/// This will work best with an infinite reader, but that is not required.
+///
+/// This can be used with `/dev/urandom` on Unix but it is recommended to use
+/// [`OsRng`] instead.
+///
+/// # Panics
+///
+/// `ReadRng` uses [`std::io::Read::read_exact`], which retries on interrupts.
+/// All other errors from the underlying reader, including when it does not
+/// have enough data, will only be reported through [`try_fill_bytes`].
+/// The other [`RngCore`] methods will panic in case of an error.
+///
+/// # Example
+///
+/// ```
+/// use rand::Rng;
+/// use rand::rngs::adapter::ReadRng;
+///
+/// let data = vec![1, 2, 3, 4, 5, 6, 7, 8];
+/// let mut rng = ReadRng::new(&data[..]);
+/// println!("{:x}", rng.gen::<u32>());
+/// ```
+///
+/// [`OsRng`]: crate::rngs::OsRng
+/// [`try_fill_bytes`]: RngCore::try_fill_bytes
+#[derive(Debug)]
+pub struct ReadRng<R> {
+ reader: R,
+}
+
+impl<R: Read> ReadRng<R> {
+ /// Create a new `ReadRng` from a `Read`.
+ pub fn new(r: R) -> ReadRng<R> {
+ ReadRng { reader: r }
+ }
+}
+
+impl<R: Read> RngCore for ReadRng<R> {
+ fn next_u32(&mut self) -> u32 {
+ impls::next_u32_via_fill(self)
+ }
+
+ fn next_u64(&mut self) -> u64 {
+ impls::next_u64_via_fill(self)
+ }
+
+ fn fill_bytes(&mut self, dest: &mut [u8]) {
+ self.try_fill_bytes(dest).unwrap_or_else(|err| {
+ panic!(
+ "reading random bytes from Read implementation failed; error: {}",
+ err
+ )
+ });
+ }
+
+ fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
+ if dest.is_empty() {
+ return Ok(());
+ }
+ // Use `std::io::read_exact`, which retries on `ErrorKind::Interrupted`.
+ self.reader
+ .read_exact(dest)
+ .map_err(|e| Error::new(ReadError(e)))
+ }
+}
+
+/// `ReadRng` error type
+#[derive(Debug)]
+pub struct ReadError(std::io::Error);
+
+impl fmt::Display for ReadError {
+ fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+ write!(f, "ReadError: {}", self.0)
+ }
+}
+
+impl std::error::Error for ReadError {
+ fn source(&self) -> Option<&(dyn std::error::Error + 'static)> {
+ Some(&self.0)
+ }
+}
+
+
+#[cfg(test)]
+mod test {
+ use super::ReadRng;
+ use crate::RngCore;
+
+ #[test]
+ fn test_reader_rng_u64() {
+ // transmute from the target to avoid endianness concerns.
+ #[rustfmt::skip]
+ let v = vec![0u8, 0, 0, 0, 0, 0, 0, 1,
+ 0 , 0, 0, 0, 0, 0, 0, 2,
+ 0, 0, 0, 0, 0, 0, 0, 3];
+ let mut rng = ReadRng::new(&v[..]);
+
+ assert_eq!(rng.next_u64(), 1_u64.to_be());
+ assert_eq!(rng.next_u64(), 2_u64.to_be());
+ assert_eq!(rng.next_u64(), 3_u64.to_be());
+ }
+
+ #[test]
+ fn test_reader_rng_u32() {
+ let v = vec![0u8, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3];
+ let mut rng = ReadRng::new(&v[..]);
+
+ assert_eq!(rng.next_u32(), 1_u32.to_be());
+ assert_eq!(rng.next_u32(), 2_u32.to_be());
+ assert_eq!(rng.next_u32(), 3_u32.to_be());
+ }
+
+ #[test]
+ fn test_reader_rng_fill_bytes() {
+ let v = [1u8, 2, 3, 4, 5, 6, 7, 8];
+ let mut w = [0u8; 8];
+
+ let mut rng = ReadRng::new(&v[..]);
+ rng.fill_bytes(&mut w);
+
+ assert!(v == w);
+ }
+
+ #[test]
+ fn test_reader_rng_insufficient_bytes() {
+ let v = [1u8, 2, 3, 4, 5, 6, 7, 8];
+ let mut w = [0u8; 9];
+
+ let mut rng = ReadRng::new(&v[..]);
+
+ let result = rng.try_fill_bytes(&mut w);
+ assert!(result.is_err());
+ println!("Error: {}", result.unwrap_err());
+ }
+}
diff --git a/src/rngs/adapter/reseeding.rs b/src/rngs/adapter/reseeding.rs
new file mode 100644
index 0000000..5460e34
--- /dev/null
+++ b/src/rngs/adapter/reseeding.rs
@@ -0,0 +1,369 @@
+// Copyright 2018 Developers of the Rand project.
+// Copyright 2013 The Rust Project Developers.
+//
+// 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.
+
+//! A wrapper around another PRNG that reseeds it after it
+//! generates a certain number of random bytes.
+
+use core::mem::size_of;
+
+use rand_core::block::{BlockRng, BlockRngCore};
+use rand_core::{CryptoRng, Error, RngCore, SeedableRng};
+
+/// A wrapper around any PRNG that implements [`BlockRngCore`], that adds the
+/// ability to reseed it.
+///
+/// `ReseedingRng` reseeds the underlying PRNG in the following cases:
+///
+/// - On a manual call to [`reseed()`].
+/// - After `clone()`, the clone will be reseeded on first use.
+/// - After a process is forked, the RNG in the child process is reseeded within
+/// the next few generated values, depending on the block size of the
+/// underlying PRNG. For ChaCha and Hc128 this is a maximum of
+/// 15 `u32` values before reseeding.
+/// - After the PRNG has generated a configurable number of random bytes.
+///
+/// # When should reseeding after a fixed number of generated bytes be used?
+///
+/// Reseeding after a fixed number of generated bytes is never strictly
+/// *necessary*. Cryptographic PRNGs don't have a limited number of bytes they
+/// can output, or at least not a limit reachable in any practical way. There is
+/// no such thing as 'running out of entropy'.
+///
+/// Occasionally reseeding can be seen as some form of 'security in depth'. Even
+/// if in the future a cryptographic weakness is found in the CSPRNG being used,
+/// or a flaw in the implementation, occasionally reseeding should make
+/// exploiting it much more difficult or even impossible.
+///
+/// Use [`ReseedingRng::new`] with a `threshold` of `0` to disable reseeding
+/// after a fixed number of generated bytes.
+///
+/// # Error handling
+///
+/// Although unlikely, reseeding the wrapped PRNG can fail. `ReseedingRng` will
+/// never panic but try to handle the error intelligently through some
+/// combination of retrying and delaying reseeding until later.
+/// If handling the source error fails `ReseedingRng` will continue generating
+/// data from the wrapped PRNG without reseeding.
+///
+/// Manually calling [`reseed()`] will not have this retry or delay logic, but
+/// reports the error.
+///
+/// # Example
+///
+/// ```
+/// use rand::prelude::*;
+/// use rand_chacha::ChaCha20Core; // Internal part of ChaChaRng that
+/// // implements BlockRngCore
+/// use rand::rngs::OsRng;
+/// use rand::rngs::adapter::ReseedingRng;
+///
+/// let prng = ChaCha20Core::from_entropy();
+/// let mut reseeding_rng = ReseedingRng::new(prng, 0, OsRng);
+///
+/// println!("{}", reseeding_rng.gen::<u64>());
+///
+/// let mut cloned_rng = reseeding_rng.clone();
+/// assert!(reseeding_rng.gen::<u64>() != cloned_rng.gen::<u64>());
+/// ```
+///
+/// [`BlockRngCore`]: rand_core::block::BlockRngCore
+/// [`ReseedingRng::new`]: ReseedingRng::new
+/// [`reseed()`]: ReseedingRng::reseed
+#[derive(Debug)]
+pub struct ReseedingRng<R, Rsdr>(BlockRng<ReseedingCore<R, Rsdr>>)
+where
+ R: BlockRngCore + SeedableRng,
+ Rsdr: RngCore;
+
+impl<R, Rsdr> ReseedingRng<R, Rsdr>
+where
+ R: BlockRngCore + SeedableRng,
+ Rsdr: RngCore,
+{
+ /// Create a new `ReseedingRng` from an existing PRNG, combined with a RNG
+ /// to use as reseeder.
+ ///
+ /// `threshold` sets the number of generated bytes after which to reseed the
+ /// PRNG. Set it to zero to never reseed based on the number of generated
+ /// values.
+ pub fn new(rng: R, threshold: u64, reseeder: Rsdr) -> Self {
+ ReseedingRng(BlockRng::new(ReseedingCore::new(rng, threshold, reseeder)))
+ }
+
+ /// Reseed the internal PRNG.
+ pub fn reseed(&mut self) -> Result<(), Error> {
+ self.0.core.reseed()
+ }
+}
+
+// TODO: this should be implemented for any type where the inner type
+// implements RngCore, but we can't specify that because ReseedingCore is private
+impl<R, Rsdr: RngCore> RngCore for ReseedingRng<R, Rsdr>
+where
+ R: BlockRngCore<Item = u32> + SeedableRng,
+ <R as BlockRngCore>::Results: AsRef<[u32]> + AsMut<[u32]>,
+{
+ #[inline(always)]
+ fn next_u32(&mut self) -> u32 {
+ self.0.next_u32()
+ }
+
+ #[inline(always)]
+ fn next_u64(&mut self) -> u64 {
+ self.0.next_u64()
+ }
+
+ fn fill_bytes(&mut self, dest: &mut [u8]) {
+ self.0.fill_bytes(dest)
+ }
+
+ fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
+ self.0.try_fill_bytes(dest)
+ }
+}
+
+impl<R, Rsdr> Clone for ReseedingRng<R, Rsdr>
+where
+ R: BlockRngCore + SeedableRng + Clone,
+ Rsdr: RngCore + Clone,
+{
+ fn clone(&self) -> ReseedingRng<R, Rsdr> {
+ // Recreating `BlockRng` seems easier than cloning it and resetting
+ // the index.
+ ReseedingRng(BlockRng::new(self.0.core.clone()))
+ }
+}
+
+impl<R, Rsdr> CryptoRng for ReseedingRng<R, Rsdr>
+where
+ R: BlockRngCore + SeedableRng + CryptoRng,
+ Rsdr: RngCore + CryptoRng,
+{
+}
+
+#[derive(Debug)]
+struct ReseedingCore<R, Rsdr> {
+ inner: R,
+ reseeder: Rsdr,
+ threshold: i64,
+ bytes_until_reseed: i64,
+ fork_counter: usize,
+}
+
+impl<R, Rsdr> BlockRngCore for ReseedingCore<R, Rsdr>
+where
+ R: BlockRngCore + SeedableRng,
+ Rsdr: RngCore,
+{
+ type Item = <R as BlockRngCore>::Item;
+ type Results = <R as BlockRngCore>::Results;
+
+ fn generate(&mut self, results: &mut Self::Results) {
+ let global_fork_counter = fork::get_fork_counter();
+ if self.bytes_until_reseed <= 0 || self.is_forked(global_fork_counter) {
+ // We get better performance by not calling only `reseed` here
+ // and continuing with the rest of the function, but by directly
+ // returning from a non-inlined function.
+ return self.reseed_and_generate(results, global_fork_counter);
+ }
+ let num_bytes = results.as_ref().len() * size_of::<Self::Item>();
+ self.bytes_until_reseed -= num_bytes as i64;
+ self.inner.generate(results);
+ }
+}
+
+impl<R, Rsdr> ReseedingCore<R, Rsdr>
+where
+ R: BlockRngCore + SeedableRng,
+ Rsdr: RngCore,
+{
+ /// Create a new `ReseedingCore`.
+ fn new(rng: R, threshold: u64, reseeder: Rsdr) -> Self {
+ use ::core::i64::MAX;
+ fork::register_fork_handler();
+
+ // Because generating more values than `i64::MAX` takes centuries on
+ // current hardware, we just clamp to that value.
+ // Also we set a threshold of 0, which indicates no limit, to that
+ // value.
+ let threshold = if threshold == 0 {
+ MAX
+ } else if threshold <= MAX as u64 {
+ threshold as i64
+ } else {
+ MAX
+ };
+
+ ReseedingCore {
+ inner: rng,
+ reseeder,
+ threshold: threshold as i64,
+ bytes_until_reseed: threshold as i64,
+ fork_counter: 0,
+ }
+ }
+
+ /// Reseed the internal PRNG.
+ fn reseed(&mut self) -> Result<(), Error> {
+ R::from_rng(&mut self.reseeder).map(|result| {
+ self.bytes_until_reseed = self.threshold;
+ self.inner = result
+ })
+ }
+
+ fn is_forked(&self, global_fork_counter: usize) -> bool {
+ // In theory, on 32-bit platforms, it is possible for
+ // `global_fork_counter` to wrap around after ~4e9 forks.
+ //
+ // This check will detect a fork in the normal case where
+ // `fork_counter < global_fork_counter`, and also when the difference
+ // between both is greater than `isize::MAX` (wrapped around).
+ //
+ // It will still fail to detect a fork if there have been more than
+ // `isize::MAX` forks, without any reseed in between. Seems unlikely
+ // enough.
+ (self.fork_counter.wrapping_sub(global_fork_counter) as isize) < 0
+ }
+
+ #[inline(never)]
+ fn reseed_and_generate(
+ &mut self, results: &mut <Self as BlockRngCore>::Results, global_fork_counter: usize,
+ ) {
+ #![allow(clippy::if_same_then_else)] // false positive
+ if self.is_forked(global_fork_counter) {
+ info!("Fork detected, reseeding RNG");
+ } else {
+ trace!("Reseeding RNG (periodic reseed)");
+ }
+
+ let num_bytes = results.as_ref().len() * size_of::<<R as BlockRngCore>::Item>();
+
+ if let Err(e) = self.reseed() {
+ warn!("Reseeding RNG failed: {}", e);
+ let _ = e;
+ }
+ self.fork_counter = global_fork_counter;
+
+ self.bytes_until_reseed = self.threshold - num_bytes as i64;
+ self.inner.generate(results);
+ }
+}
+
+impl<R, Rsdr> Clone for ReseedingCore<R, Rsdr>
+where
+ R: BlockRngCore + SeedableRng + Clone,
+ Rsdr: RngCore + Clone,
+{
+ fn clone(&self) -> ReseedingCore<R, Rsdr> {
+ ReseedingCore {
+ inner: self.inner.clone(),
+ reseeder: self.reseeder.clone(),
+ threshold: self.threshold,
+ bytes_until_reseed: 0, // reseed clone on first use
+ fork_counter: self.fork_counter,
+ }
+ }
+}
+
+impl<R, Rsdr> CryptoRng for ReseedingCore<R, Rsdr>
+where
+ R: BlockRngCore + SeedableRng + CryptoRng,
+ Rsdr: RngCore + CryptoRng,
+{
+}
+
+
+#[cfg(all(unix, feature = "std", not(target_os = "emscripten")))]
+mod fork {
+ use core::sync::atomic::{AtomicUsize, Ordering};
+ use std::sync::Once;
+
+ // Fork protection
+ //
+ // We implement fork protection on Unix using `pthread_atfork`.
+ // When the process is forked, we increment `RESEEDING_RNG_FORK_COUNTER`.
+ // Every `ReseedingRng` stores the last known value of the static in
+ // `fork_counter`. If the cached `fork_counter` is less than
+ // `RESEEDING_RNG_FORK_COUNTER`, it is time to reseed this RNG.
+ //
+ // If reseeding fails, we don't deal with this by setting a delay, but just
+ // don't update `fork_counter`, so a reseed is attempted as soon as
+ // possible.
+
+ static RESEEDING_RNG_FORK_COUNTER: AtomicUsize = AtomicUsize::new(0);
+
+ pub fn get_fork_counter() -> usize {
+ RESEEDING_RNG_FORK_COUNTER.load(Ordering::Relaxed)
+ }
+
+ extern "C" fn fork_handler() {
+ // Note: fetch_add is defined to wrap on overflow
+ // (which is what we want).
+ RESEEDING_RNG_FORK_COUNTER.fetch_add(1, Ordering::Relaxed);
+ }
+
+ pub fn register_fork_handler() {
+ static REGISTER: Once = Once::new();
+ REGISTER.call_once(|| unsafe {
+ libc::pthread_atfork(None, None, Some(fork_handler));
+ });
+ }
+}
+
+#[cfg(not(all(unix, feature = "std", not(target_os = "emscripten"))))]
+mod fork {
+ pub fn get_fork_counter() -> usize {
+ 0
+ }
+ pub fn register_fork_handler() {}
+}
+
+
+#[cfg(test)]
+mod test {
+ use super::ReseedingRng;
+ use crate::rngs::mock::StepRng;
+ use crate::rngs::std::Core;
+ use crate::{Rng, SeedableRng};
+
+ #[test]
+ fn test_reseeding() {
+ let mut zero = StepRng::new(0, 0);
+ let rng = Core::from_rng(&mut zero).unwrap();
+ let thresh = 1; // reseed every time the buffer is exhausted
+ let mut reseeding = ReseedingRng::new(rng, thresh, zero);
+
+ // RNG buffer size is [u32; 64]
+ // Debug is only implemented up to length 32 so use two arrays
+ let mut buf = ([0u32; 32], [0u32; 32]);
+ reseeding.fill(&mut buf.0);
+ reseeding.fill(&mut buf.1);
+ let seq = buf;
+ for _ in 0..10 {
+ reseeding.fill(&mut buf.0);
+ reseeding.fill(&mut buf.1);
+ assert_eq!(buf, seq);
+ }
+ }
+
+ #[test]
+ fn test_clone_reseeding() {
+ let mut zero = StepRng::new(0, 0);
+ let rng = Core::from_rng(&mut zero).unwrap();
+ let mut rng1 = ReseedingRng::new(rng, 32 * 4, zero);
+
+ let first: u32 = rng1.gen();
+ for _ in 0..10 {
+ let _ = rng1.gen::<u32>();
+ }
+
+ let mut rng2 = rng1.clone();
+ assert_eq!(first, rng2.gen::<u32>());
+ }
+}
diff --git a/src/rngs/entropy.rs b/src/rngs/entropy.rs
new file mode 100644
index 0000000..9ad0d71
--- /dev/null
+++ b/src/rngs/entropy.rs
@@ -0,0 +1,76 @@
+// 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.
+
+//! Entropy generator, or wrapper around external generators
+
+#![allow(deprecated)] // whole module is deprecated
+
+use crate::rngs::OsRng;
+use rand_core::{CryptoRng, Error, RngCore};
+
+/// An interface returning random data from external source(s), provided
+/// specifically for securely seeding algorithmic generators (PRNGs).
+///
+/// This is deprecated. It is suggested you use [`rngs::OsRng`] instead.
+///
+/// [`rngs::OsRng`]: crate::rngs::OsRng
+#[derive(Debug)]
+#[deprecated(since = "0.7.0", note = "use rngs::OsRng instead")]
+pub struct EntropyRng {
+ source: OsRng,
+}
+
+impl EntropyRng {
+ /// Create a new `EntropyRng`.
+ ///
+ /// This method will do no system calls or other initialization routines,
+ /// those are done on first use. This is done to make `new` infallible,
+ /// and `try_fill_bytes` the only place to report errors.
+ pub fn new() -> Self {
+ EntropyRng { source: OsRng }
+ }
+}
+
+impl Default for EntropyRng {
+ fn default() -> Self {
+ EntropyRng::new()
+ }
+}
+
+impl RngCore for EntropyRng {
+ fn next_u32(&mut self) -> u32 {
+ self.source.next_u32()
+ }
+
+ fn next_u64(&mut self) -> u64 {
+ self.source.next_u64()
+ }
+
+ fn fill_bytes(&mut self, dest: &mut [u8]) {
+ self.source.fill_bytes(dest)
+ }
+
+ fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
+ self.source.try_fill_bytes(dest)
+ }
+}
+
+impl CryptoRng for EntropyRng {}
+
+
+#[cfg(test)]
+mod test {
+ use super::*;
+
+ #[test]
+ fn test_entropy() {
+ let mut rng = EntropyRng::new();
+ let n = (rng.next_u32() ^ rng.next_u32()).count_ones();
+ assert!(n >= 2); // p(failure) approx 1e-7
+ }
+}
diff --git a/src/rngs/mock.rs b/src/rngs/mock.rs
new file mode 100644
index 0000000..9a47264
--- /dev/null
+++ b/src/rngs/mock.rs
@@ -0,0 +1,67 @@
+// 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.
+
+//! Mock random number generator
+
+use rand_core::{impls, Error, RngCore};
+
+/// A simple implementation of `RngCore` for testing purposes.
+///
+/// This generates an arithmetic sequence (i.e. adds a constant each step)
+/// over a `u64` number, using wrapping arithmetic. If the increment is 0
+/// the generator yields a constant.
+///
+/// ```
+/// use rand::Rng;
+/// use rand::rngs::mock::StepRng;
+///
+/// let mut my_rng = StepRng::new(2, 1);
+/// let sample: [u64; 3] = my_rng.gen();
+/// assert_eq!(sample, [2, 3, 4]);
+/// ```
+#[derive(Debug, Clone)]
+pub struct StepRng {
+ v: u64,
+ a: u64,
+}
+
+impl StepRng {
+ /// Create a `StepRng`, yielding an arithmetic sequence starting with
+ /// `initial` and incremented by `increment` each time.
+ pub fn new(initial: u64, increment: u64) -> Self {
+ StepRng {
+ v: initial,
+ a: increment,
+ }
+ }
+}
+
+impl RngCore for StepRng {
+ #[inline]
+ fn next_u32(&mut self) -> u32 {
+ self.next_u64() as u32
+ }
+
+ #[inline]
+ fn next_u64(&mut self) -> u64 {
+ let result = self.v;
+ self.v = self.v.wrapping_add(self.a);
+ result
+ }
+
+ #[inline]
+ fn fill_bytes(&mut self, dest: &mut [u8]) {
+ impls::fill_bytes_via_next(self, dest);
+ }
+
+ #[inline]
+ fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
+ self.fill_bytes(dest);
+ Ok(())
+ }
+}
diff --git a/src/rngs/mod.rs b/src/rngs/mod.rs
new file mode 100644
index 0000000..1112196
--- /dev/null
+++ b/src/rngs/mod.rs
@@ -0,0 +1,116 @@
+// 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.
+
+//! Random number generators and adapters
+//!
+//! ## Background: Random number generators (RNGs)
+//!
+//! Computers cannot produce random numbers from nowhere. We classify
+//! random number generators as follows:
+//!
+//! - "True" random number generators (TRNGs) use hard-to-predict data sources
+//! (e.g. the high-resolution parts of event timings and sensor jitter) to
+//! harvest random bit-sequences, apply algorithms to remove bias and
+//! estimate available entropy, then combine these bits into a byte-sequence
+//! or an entropy pool. This job is usually done by the operating system or
+//! a hardware generator (HRNG).
+//! - "Pseudo"-random number generators (PRNGs) use algorithms to transform a
+//! seed into a sequence of pseudo-random numbers. These generators can be
+//! fast and produce well-distributed unpredictable random numbers (or not).
+//! They are usually deterministic: given algorithm and seed, the output
+//! sequence can be reproduced. They have finite period and eventually loop;
+//! with many algorithms this period is fixed and can be proven sufficiently
+//! long, while others are chaotic and the period depends on the seed.
+//! - "Cryptographically secure" pseudo-random number generators (CSPRNGs)
+//! are the sub-set of PRNGs which are secure. Security of the generator
+//! relies both on hiding the internal state and using a strong algorithm.
+//!
+//! ## Traits and functionality
+//!
+//! All RNGs implement the [`RngCore`] trait, as a consequence of which the
+//! [`Rng`] extension trait is automatically implemented. Secure RNGs may
+//! additionally implement the [`CryptoRng`] trait.
+//!
+//! All PRNGs require a seed to produce their random number sequence. The
+//! [`SeedableRng`] trait provides three ways of constructing PRNGs:
+//!
+//! - `from_seed` accepts a type specific to the PRNG
+//! - `from_rng` allows a PRNG to be seeded from any other RNG
+//! - `seed_from_u64` allows any PRNG to be seeded from a `u64` insecurely
+//! - `from_entropy` securely seeds a PRNG from fresh entropy
+//!
+//! Use the [`rand_core`] crate when implementing your own RNGs.
+//!
+//! ## Our generators
+//!
+//! This crate provides several random number generators:
+//!
+//! - [`OsRng`] is an interface to the operating system's random number
+//! source. Typically the operating system uses a CSPRNG with entropy
+//! provided by a TRNG and some type of on-going re-seeding.
+//! - [`ThreadRng`], provided by the [`thread_rng`] function, is a handle to a
+//! thread-local CSPRNG with periodic seeding from [`OsRng`]. Because this
+//! is local, it is typically much faster than [`OsRng`]. It should be
+//! secure, though the paranoid may prefer [`OsRng`].
+//! - [`StdRng`] is a CSPRNG chosen for good performance and trust of security
+//! (based on reviews, maturity and usage). The current algorithm is ChaCha20,
+//! which is well established and rigorously analysed.
+//! [`StdRng`] provides the algorithm used by [`ThreadRng`] but without
+//! periodic reseeding.
+//! - [`SmallRng`] is an **insecure** PRNG designed to be fast, simple, require
+//! little memory, and have good output quality.
+//!
+//! The algorithms selected for [`StdRng`] and [`SmallRng`] may change in any
+//! release and may be platform-dependent, therefore they should be considered
+//! **not reproducible**.
+//!
+//! ## Additional generators
+//!
+//! **TRNGs**: The [`rdrand`] crate provides an interface to the RDRAND and
+//! RDSEED instructions available in modern Intel and AMD CPUs.
+//! The [`rand_jitter`] crate provides a user-space implementation of
+//! entropy harvesting from CPU timer jitter, but is very slow and has
+//! [security issues](https://github.com/rust-random/rand/issues/699).
+//!
+//! **PRNGs**: Several companion crates are available, providing individual or
+//! families of PRNG algorithms. These provide the implementations behind
+//! [`StdRng`] and [`SmallRng`] but can also be used directly, indeed *should*
+//! be used directly when **reproducibility** matters.
+//! Some suggestions are: [`rand_chacha`], [`rand_pcg`], [`rand_xoshiro`].
+//! A full list can be found by searching for crates with the [`rng` tag].
+//!
+//! [`Rng`]: crate::Rng
+//! [`RngCore`]: crate::RngCore
+//! [`CryptoRng`]: crate::CryptoRng
+//! [`SeedableRng`]: crate::SeedableRng
+//! [`thread_rng`]: crate::thread_rng
+//! [`rdrand`]: https://crates.io/crates/rdrand
+//! [`rand_jitter`]: https://crates.io/crates/rand_jitter
+//! [`rand_chacha`]: https://crates.io/crates/rand_chacha
+//! [`rand_pcg`]: https://crates.io/crates/rand_pcg
+//! [`rand_xoshiro`]: https://crates.io/crates/rand_xoshiro
+//! [`rng` tag]: https://crates.io/keywords/rng
+
+pub mod adapter;
+
+#[cfg(feature = "std")] mod entropy;
+pub mod mock; // Public so we don't export `StepRng` directly, making it a bit
+ // more clear it is intended for testing.
+#[cfg(feature = "small_rng")] mod small;
+mod std;
+#[cfg(feature = "std")] pub(crate) mod thread;
+
+#[allow(deprecated)]
+#[cfg(feature = "std")]
+pub use self::entropy::EntropyRng;
+
+#[cfg(feature = "small_rng")] pub use self::small::SmallRng;
+pub use self::std::StdRng;
+#[cfg(feature = "std")] pub use self::thread::ThreadRng;
+
+#[cfg(feature = "getrandom")] pub use rand_core::OsRng;
diff --git a/src/rngs/small.rs b/src/rngs/small.rs
new file mode 100644
index 0000000..d676898
--- /dev/null
+++ b/src/rngs/small.rs
@@ -0,0 +1,113 @@
+// 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.
+
+//! A small fast RNG
+
+use rand_core::{Error, RngCore, SeedableRng};
+
+#[cfg(all(not(target_os = "emscripten"), target_pointer_width = "64"))]
+type Rng = rand_pcg::Pcg64Mcg;
+#[cfg(not(all(not(target_os = "emscripten"), target_pointer_width = "64")))]
+type Rng = rand_pcg::Pcg32;
+
+/// A small-state, fast non-crypto PRNG
+///
+/// `SmallRng` may be a good choice when a PRNG with small state, cheap
+/// initialization, good statistical quality and good performance are required.
+/// It is **not** a good choice when security against prediction or
+/// reproducibility are important.
+///
+/// This PRNG is **feature-gated**: to use, you must enable the crate feature
+/// `small_rng`.
+///
+/// The algorithm is deterministic but should not be considered reproducible
+/// due to dependence on platform and possible replacement in future
+/// library versions. For a reproducible generator, use a named PRNG from an
+/// external crate, e.g. [rand_pcg] or [rand_chacha].
+/// Refer also to [The Book](https://rust-random.github.io/book/guide-rngs.html).
+///
+/// The PRNG algorithm in `SmallRng` is chosen to be
+/// efficient on the current platform, without consideration for cryptography
+/// or security. The size of its state is much smaller than [`StdRng`].
+/// The current algorithm is [`Pcg64Mcg`](rand_pcg::Pcg64Mcg) on 64-bit
+/// platforms and [`Pcg32`](rand_pcg::Pcg32) on 32-bit platforms. Both are
+/// implemented by the [rand_pcg] crate.
+///
+/// # Examples
+///
+/// Initializing `SmallRng` with a random seed can be done using [`SeedableRng::from_entropy`]:
+///
+/// ```
+/// use rand::{Rng, SeedableRng};
+/// use rand::rngs::SmallRng;
+///
+/// // Create small, cheap to initialize and fast RNG with a random seed.
+/// // The randomness is supplied by the operating system.
+/// let mut small_rng = SmallRng::from_entropy();
+/// # let v: u32 = small_rng.gen();
+/// ```
+///
+/// When initializing a lot of `SmallRng`'s, using [`thread_rng`] can be more
+/// efficient:
+///
+/// ```
+/// use rand::{SeedableRng, thread_rng};
+/// use rand::rngs::SmallRng;
+///
+/// // Create a big, expensive to initialize and slower, but unpredictable RNG.
+/// // This is cached and done only once per thread.
+/// let mut thread_rng = thread_rng();
+/// // Create small, cheap to initialize and fast RNGs with random seeds.
+/// // One can generally assume this won't fail.
+/// let rngs: Vec<SmallRng> = (0..10)
+/// .map(|_| SmallRng::from_rng(&mut thread_rng).unwrap())
+/// .collect();
+/// ```
+///
+/// [`StdRng`]: crate::rngs::StdRng
+/// [`thread_rng`]: crate::thread_rng
+/// [rand_chacha]: https://crates.io/crates/rand_chacha
+/// [rand_pcg]: https://crates.io/crates/rand_pcg
+#[derive(Clone, Debug)]
+pub struct SmallRng(Rng);
+
+impl RngCore for SmallRng {
+ #[inline(always)]
+ fn next_u32(&mut self) -> u32 {
+ self.0.next_u32()
+ }
+
+ #[inline(always)]
+ fn next_u64(&mut self) -> u64 {
+ self.0.next_u64()
+ }
+
+ #[inline(always)]
+ fn fill_bytes(&mut self, dest: &mut [u8]) {
+ self.0.fill_bytes(dest);
+ }
+
+ #[inline(always)]
+ fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
+ self.0.try_fill_bytes(dest)
+ }
+}
+
+impl SeedableRng for SmallRng {
+ type Seed = <Rng as SeedableRng>::Seed;
+
+ #[inline(always)]
+ fn from_seed(seed: Self::Seed) -> Self {
+ SmallRng(Rng::from_seed(seed))
+ }
+
+ #[inline(always)]
+ fn from_rng<R: RngCore>(rng: R) -> Result<Self, Error> {
+ Rng::from_rng(rng).map(SmallRng)
+ }
+}
diff --git a/src/rngs/std.rs b/src/rngs/std.rs
new file mode 100644
index 0000000..8b07081
--- /dev/null
+++ b/src/rngs/std.rs
@@ -0,0 +1,103 @@
+// 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 standard RNG
+
+use crate::{CryptoRng, Error, RngCore, SeedableRng};
+
+#[cfg(all(any(test, feature = "std"), not(target_os = "emscripten")))]
+pub(crate) use rand_chacha::ChaCha20Core as Core;
+#[cfg(all(any(test, feature = "std"), target_os = "emscripten"))]
+pub(crate) use rand_hc::Hc128Core as Core;
+
+#[cfg(not(target_os = "emscripten"))] use rand_chacha::ChaCha20Rng as Rng;
+#[cfg(target_os = "emscripten")] use rand_hc::Hc128Rng as Rng;
+
+/// The standard RNG. The PRNG algorithm in `StdRng` is chosen to be efficient
+/// on the current platform, to be statistically strong and unpredictable
+/// (meaning a cryptographically secure PRNG).
+///
+/// The current algorithm used is the ChaCha block cipher with 20 rounds.
+/// This may change as new evidence of cipher security and performance
+/// becomes available.
+///
+/// The algorithm is deterministic but should not be considered reproducible
+/// due to dependence on configuration and possible replacement in future
+/// library versions. For a secure reproducible generator, we recommend use of
+/// the [rand_chacha] crate directly.
+///
+/// [rand_chacha]: https://crates.io/crates/rand_chacha
+#[derive(Clone, Debug)]
+pub struct StdRng(Rng);
+
+impl RngCore for StdRng {
+ #[inline(always)]
+ fn next_u32(&mut self) -> u32 {
+ self.0.next_u32()
+ }
+
+ #[inline(always)]
+ fn next_u64(&mut self) -> u64 {
+ self.0.next_u64()
+ }
+
+ #[inline(always)]
+ fn fill_bytes(&mut self, dest: &mut [u8]) {
+ self.0.fill_bytes(dest);
+ }
+
+ #[inline(always)]
+ fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
+ self.0.try_fill_bytes(dest)
+ }
+}
+
+impl SeedableRng for StdRng {
+ type Seed = <Rng as SeedableRng>::Seed;
+
+ #[inline(always)]
+ fn from_seed(seed: Self::Seed) -> Self {
+ StdRng(Rng::from_seed(seed))
+ }
+
+ #[inline(always)]
+ fn from_rng<R: RngCore>(rng: R) -> Result<Self, Error> {
+ Rng::from_rng(rng).map(StdRng)
+ }
+}
+
+impl CryptoRng for StdRng {}
+
+
+#[cfg(test)]
+mod test {
+ use crate::rngs::StdRng;
+ use crate::{RngCore, SeedableRng};
+
+ #[test]
+ fn test_stdrng_construction() {
+ // Test value-stability of StdRng. This is expected to break any time
+ // the algorithm is changed.
+ #[rustfmt::skip]
+ let seed = [1,0,0,0, 23,0,0,0, 200,1,0,0, 210,30,0,0,
+ 0,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0];
+
+ #[cfg(any(feature = "stdrng_strong", not(feature = "stdrng_fast")))]
+ let target = [3950704604716924505, 5573172343717151650];
+ #[cfg(all(not(feature = "stdrng_strong"), feature = "stdrng_fast"))]
+ let target = [10719222850664546238, 14064965282130556830];
+
+ let mut rng0 = StdRng::from_seed(seed);
+ let x0 = rng0.next_u64();
+
+ let mut rng1 = StdRng::from_rng(rng0).unwrap();
+ let x1 = rng1.next_u64();
+
+ assert_eq!([x0, x1], target);
+ }
+}
diff --git a/src/rngs/thread.rs b/src/rngs/thread.rs
new file mode 100644
index 0000000..91ed4c3
--- /dev/null
+++ b/src/rngs/thread.rs
@@ -0,0 +1,124 @@
+// 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.
+
+//! Thread-local random number generator
+
+use std::cell::UnsafeCell;
+use std::ptr::NonNull;
+
+use super::std::Core;
+use crate::rngs::adapter::ReseedingRng;
+use crate::rngs::OsRng;
+use crate::{CryptoRng, Error, RngCore, SeedableRng};
+
+// Rationale for using `UnsafeCell` in `ThreadRng`:
+//
+// Previously we used a `RefCell`, with an overhead of ~15%. There will only
+// ever be one mutable reference to the interior of the `UnsafeCell`, because
+// we only have such a reference inside `next_u32`, `next_u64`, etc. Within a
+// single thread (which is the definition of `ThreadRng`), there will only ever
+// be one of these methods active at a time.
+//
+// A possible scenario where there could be multiple mutable references is if
+// `ThreadRng` is used inside `next_u32` and co. But the implementation is
+// completely under our control. We just have to ensure none of them use
+// `ThreadRng` internally, which is nonsensical anyway. We should also never run
+// `ThreadRng` in destructors of its implementation, which is also nonsensical.
+
+
+// Number of generated bytes after which to reseed `ThreadRng`.
+// According to benchmarks, reseeding has a noticable impact with thresholds
+// of 32 kB and less. We choose 64 kB to avoid significant overhead.
+const THREAD_RNG_RESEED_THRESHOLD: u64 = 1024 * 64;
+
+/// The type returned by [`thread_rng`], essentially just a reference to the
+/// PRNG in thread-local memory.
+///
+/// `ThreadRng` uses the same PRNG as [`StdRng`] for security and performance.
+/// As hinted by the name, the generator is thread-local. `ThreadRng` is a
+/// handle to this generator and thus supports `Copy`, but not `Send` or `Sync`.
+///
+/// Unlike `StdRng`, `ThreadRng` uses the [`ReseedingRng`] wrapper to reseed
+/// the PRNG from fresh entropy every 64 kiB of random data.
+/// [`OsRng`] is used to provide seed data.
+///
+/// Note that the reseeding is done as an extra precaution against side-channel
+/// attacks and mis-use (e.g. if somehow weak entropy were supplied initially).
+/// The PRNG algorithms used are assumed to be secure.
+///
+/// [`ReseedingRng`]: crate::rngs::adapter::ReseedingRng
+/// [`StdRng`]: crate::rngs::StdRng
+#[derive(Copy, Clone, Debug)]
+pub struct ThreadRng {
+ // inner raw pointer implies type is neither Send nor Sync
+ rng: NonNull<ReseedingRng<Core, OsRng>>,
+}
+
+thread_local!(
+ static THREAD_RNG_KEY: UnsafeCell<ReseedingRng<Core, OsRng>> = {
+ let r = Core::from_rng(OsRng).unwrap_or_else(|err|
+ panic!("could not initialize thread_rng: {}", err));
+ let rng = ReseedingRng::new(r,
+ THREAD_RNG_RESEED_THRESHOLD,
+ OsRng);
+ UnsafeCell::new(rng)
+ }
+);
+
+/// Retrieve the lazily-initialized thread-local random number generator,
+/// seeded by the system. Intended to be used in method chaining style,
+/// e.g. `thread_rng().gen::<i32>()`, or cached locally, e.g.
+/// `let mut rng = thread_rng();`. Invoked by the `Default` trait, making
+/// `ThreadRng::default()` equivalent.
+///
+/// For more information see [`ThreadRng`].
+pub fn thread_rng() -> ThreadRng {
+ let raw = THREAD_RNG_KEY.with(|t| t.get());
+ let nn = NonNull::new(raw).unwrap();
+ ThreadRng { rng: nn }
+}
+
+impl Default for ThreadRng {
+ fn default() -> ThreadRng {
+ crate::prelude::thread_rng()
+ }
+}
+
+impl RngCore for ThreadRng {
+ #[inline(always)]
+ fn next_u32(&mut self) -> u32 {
+ unsafe { self.rng.as_mut().next_u32() }
+ }
+
+ #[inline(always)]
+ fn next_u64(&mut self) -> u64 {
+ unsafe { self.rng.as_mut().next_u64() }
+ }
+
+ fn fill_bytes(&mut self, dest: &mut [u8]) {
+ unsafe { self.rng.as_mut().fill_bytes(dest) }
+ }
+
+ fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
+ unsafe { self.rng.as_mut().try_fill_bytes(dest) }
+ }
+}
+
+impl CryptoRng for ThreadRng {}
+
+
+#[cfg(test)]
+mod test {
+ #[test]
+ fn test_thread_rng() {
+ use crate::Rng;
+ let mut r = crate::thread_rng();
+ r.gen::<i32>();
+ assert_eq!(r.gen_range(0, 1), 0);
+ }
+}
diff --git a/src/seq/index.rs b/src/seq/index.rs
new file mode 100644
index 0000000..551d409
--- /dev/null
+++ b/src/seq/index.rs
@@ -0,0 +1,438 @@
+// 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.
+
+//! Low-level API for sampling indices
+
+#[cfg(feature = "alloc")] use core::slice;
+
+#[cfg(all(feature = "alloc", not(feature = "std")))]
+use crate::alloc::vec::{self, Vec};
+#[cfg(feature = "std")] use std::vec;
+// BTreeMap is not as fast in tests, but better than nothing.
+#[cfg(all(feature = "alloc", not(feature = "std")))]
+use crate::alloc::collections::BTreeSet;
+#[cfg(feature = "std")] use std::collections::HashSet;
+
+#[cfg(feature = "alloc")]
+use crate::distributions::{uniform::SampleUniform, Distribution, Uniform};
+use crate::Rng;
+
+/// A vector of indices.
+///
+/// Multiple internal representations are possible.
+#[derive(Clone, Debug)]
+pub enum IndexVec {
+ #[doc(hidden)]
+ U32(Vec<u32>),
+ #[doc(hidden)]
+ USize(Vec<usize>),
+}
+
+impl IndexVec {
+ /// Returns the number of indices
+ #[inline]
+ pub fn len(&self) -> usize {
+ match *self {
+ IndexVec::U32(ref v) => v.len(),
+ IndexVec::USize(ref v) => v.len(),
+ }
+ }
+
+ /// Returns `true` if the length is 0.
+ #[inline]
+ pub fn is_empty(&self) -> bool {
+ match *self {
+ IndexVec::U32(ref v) => v.is_empty(),
+ IndexVec::USize(ref v) => v.is_empty(),
+ }
+ }
+
+ /// Return the value at the given `index`.
+ ///
+ /// (Note: we cannot implement [`std::ops::Index`] because of lifetime
+ /// restrictions.)
+ #[inline]
+ pub fn index(&self, index: usize) -> usize {
+ match *self {
+ IndexVec::U32(ref v) => v[index] as usize,
+ IndexVec::USize(ref v) => v[index],
+ }
+ }
+
+ /// Return result as a `Vec<usize>`. Conversion may or may not be trivial.
+ #[inline]
+ pub fn into_vec(self) -> Vec<usize> {
+ match self {
+ IndexVec::U32(v) => v.into_iter().map(|i| i as usize).collect(),
+ IndexVec::USize(v) => v,
+ }
+ }
+
+ /// Iterate over the indices as a sequence of `usize` values
+ #[inline]
+ pub fn iter(&self) -> IndexVecIter<'_> {
+ match *self {
+ IndexVec::U32(ref v) => IndexVecIter::U32(v.iter()),
+ IndexVec::USize(ref v) => IndexVecIter::USize(v.iter()),
+ }
+ }
+
+ /// Convert into an iterator over the indices as a sequence of `usize` values
+ #[inline]
+ pub fn into_iter(self) -> IndexVecIntoIter {
+ match self {
+ IndexVec::U32(v) => IndexVecIntoIter::U32(v.into_iter()),
+ IndexVec::USize(v) => IndexVecIntoIter::USize(v.into_iter()),
+ }
+ }
+}
+
+impl PartialEq for IndexVec {
+ fn eq(&self, other: &IndexVec) -> bool {
+ use self::IndexVec::*;
+ match (self, other) {
+ (&U32(ref v1), &U32(ref v2)) => v1 == v2,
+ (&USize(ref v1), &USize(ref v2)) => v1 == v2,
+ (&U32(ref v1), &USize(ref v2)) => {
+ (v1.len() == v2.len()) && (v1.iter().zip(v2.iter()).all(|(x, y)| *x as usize == *y))
+ }
+ (&USize(ref v1), &U32(ref v2)) => {
+ (v1.len() == v2.len()) && (v1.iter().zip(v2.iter()).all(|(x, y)| *x == *y as usize))
+ }
+ }
+ }
+}
+
+impl From<Vec<u32>> for IndexVec {
+ #[inline]
+ fn from(v: Vec<u32>) -> Self {
+ IndexVec::U32(v)
+ }
+}
+
+impl From<Vec<usize>> for IndexVec {
+ #[inline]
+ fn from(v: Vec<usize>) -> Self {
+ IndexVec::USize(v)
+ }
+}
+
+/// Return type of `IndexVec::iter`.
+#[derive(Debug)]
+pub enum IndexVecIter<'a> {
+ #[doc(hidden)]
+ U32(slice::Iter<'a, u32>),
+ #[doc(hidden)]
+ USize(slice::Iter<'a, usize>),
+}
+
+impl<'a> Iterator for IndexVecIter<'a> {
+ type Item = usize;
+
+ #[inline]
+ fn next(&mut self) -> Option<usize> {
+ use self::IndexVecIter::*;
+ match *self {
+ U32(ref mut iter) => iter.next().map(|i| *i as usize),
+ USize(ref mut iter) => iter.next().cloned(),
+ }
+ }
+
+ #[inline]
+ fn size_hint(&self) -> (usize, Option<usize>) {
+ match *self {
+ IndexVecIter::U32(ref v) => v.size_hint(),
+ IndexVecIter::USize(ref v) => v.size_hint(),
+ }
+ }
+}
+
+impl<'a> ExactSizeIterator for IndexVecIter<'a> {}
+
+/// Return type of `IndexVec::into_iter`.
+#[derive(Clone, Debug)]
+pub enum IndexVecIntoIter {
+ #[doc(hidden)]
+ U32(vec::IntoIter<u32>),
+ #[doc(hidden)]
+ USize(vec::IntoIter<usize>),
+}
+
+impl Iterator for IndexVecIntoIter {
+ type Item = usize;
+
+ #[inline]
+ fn next(&mut self) -> Option<Self::Item> {
+ use self::IndexVecIntoIter::*;
+ match *self {
+ U32(ref mut v) => v.next().map(|i| i as usize),
+ USize(ref mut v) => v.next(),
+ }
+ }
+
+ #[inline]
+ fn size_hint(&self) -> (usize, Option<usize>) {
+ use self::IndexVecIntoIter::*;
+ match *self {
+ U32(ref v) => v.size_hint(),
+ USize(ref v) => v.size_hint(),
+ }
+ }
+}
+
+impl ExactSizeIterator for IndexVecIntoIter {}
+
+
+/// Randomly sample exactly `amount` distinct indices from `0..length`, and
+/// return them in random order (fully shuffled).
+///
+/// This method is used internally by the slice sampling methods, but it can
+/// sometimes be useful to have the indices themselves so this is provided as
+/// an alternative.
+///
+/// The implementation used is not specified; we automatically select the
+/// fastest available algorithm for the `length` and `amount` parameters
+/// (based on detailed profiling on an Intel Haswell CPU). Roughly speaking,
+/// complexity is `O(amount)`, except that when `amount` is small, performance
+/// is closer to `O(amount^2)`, and when `length` is close to `amount` then
+/// `O(length)`.
+///
+/// Note that performance is significantly better over `u32` indices than over
+/// `u64` indices. Because of this we hide the underlying type behind an
+/// abstraction, `IndexVec`.
+///
+/// If an allocation-free `no_std` function is required, it is suggested
+/// to adapt the internal `sample_floyd` implementation.
+///
+/// Panics if `amount > length`.
+pub fn sample<R>(rng: &mut R, length: usize, amount: usize) -> IndexVec
+where R: Rng + ?Sized {
+ if amount > length {
+ panic!("`amount` of samples must be less than or equal to `length`");
+ }
+ if length > (::core::u32::MAX as usize) {
+ // We never want to use inplace here, but could use floyd's alg
+ // Lazy version: always use the cache alg.
+ return sample_rejection(rng, length, amount);
+ }
+ let amount = amount as u32;
+ let length = length as u32;
+
+ // Choice of algorithm here depends on both length and amount. See:
+ // https://github.com/rust-random/rand/pull/479
+ // We do some calculations with f32. Accuracy is not very important.
+
+ if amount < 163 {
+ const C: [[f32; 2]; 2] = [[1.6, 8.0 / 45.0], [10.0, 70.0 / 9.0]];
+ let j = if length < 500_000 { 0 } else { 1 };
+ let amount_fp = amount as f32;
+ let m4 = C[0][j] * amount_fp;
+ // Short-cut: when amount < 12, floyd's is always faster
+ if amount > 11 && (length as f32) < (C[1][j] + m4) * amount_fp {
+ sample_inplace(rng, length, amount)
+ } else {
+ sample_floyd(rng, length, amount)
+ }
+ } else {
+ const C: [f32; 2] = [270.0, 330.0 / 9.0];
+ let j = if length < 500_000 { 0 } else { 1 };
+ if (length as f32) < C[j] * (amount as f32) {
+ sample_inplace(rng, length, amount)
+ } else {
+ sample_rejection(rng, length, amount)
+ }
+ }
+}
+
+/// Randomly sample exactly `amount` indices from `0..length`, using Floyd's
+/// combination algorithm.
+///
+/// The output values are fully shuffled. (Overhead is under 50%.)
+///
+/// This implementation uses `O(amount)` memory and `O(amount^2)` time.
+fn sample_floyd<R>(rng: &mut R, length: u32, amount: u32) -> IndexVec
+where R: Rng + ?Sized {
+ // For small amount we use Floyd's fully-shuffled variant. For larger
+ // amounts this is slow due to Vec::insert performance, so we shuffle
+ // afterwards. Benchmarks show little overhead from extra logic.
+ let floyd_shuffle = amount < 50;
+
+ debug_assert!(amount <= length);
+ let mut indices = Vec::with_capacity(amount as usize);
+ for j in length - amount..length {
+ let t = rng.gen_range(0, j + 1);
+ if floyd_shuffle {
+ if let Some(pos) = indices.iter().position(|&x| x == t) {
+ indices.insert(pos, j);
+ continue;
+ }
+ } else if indices.contains(&t) {
+ indices.push(j);
+ continue;
+ }
+ indices.push(t);
+ }
+ if !floyd_shuffle {
+ // Reimplement SliceRandom::shuffle with smaller indices
+ for i in (1..amount).rev() {
+ // invariant: elements with index > i have been locked in place.
+ indices.swap(i as usize, rng.gen_range(0, i + 1) as usize);
+ }
+ }
+ IndexVec::from(indices)
+}
+
+/// Randomly sample exactly `amount` indices from `0..length`, using an inplace
+/// partial Fisher-Yates method.
+/// Sample an amount of indices using an inplace partial fisher yates method.
+///
+/// This allocates the entire `length` of indices and randomizes only the first `amount`.
+/// It then truncates to `amount` and returns.
+///
+/// This method is not appropriate for large `length` and potentially uses a lot
+/// of memory; because of this we only implement for `u32` index (which improves
+/// performance in all cases).
+///
+/// Set-up is `O(length)` time and memory and shuffling is `O(amount)` time.
+fn sample_inplace<R>(rng: &mut R, length: u32, amount: u32) -> IndexVec
+where R: Rng + ?Sized {
+ debug_assert!(amount <= length);
+ let mut indices: Vec<u32> = Vec::with_capacity(length as usize);
+ indices.extend(0..length);
+ for i in 0..amount {
+ let j: u32 = rng.gen_range(i, length);
+ indices.swap(i as usize, j as usize);
+ }
+ indices.truncate(amount as usize);
+ debug_assert_eq!(indices.len(), amount as usize);
+ IndexVec::from(indices)
+}
+
+trait UInt: Copy + PartialOrd + Ord + PartialEq + Eq + SampleUniform + core::hash::Hash {
+ fn zero() -> Self;
+ fn as_usize(self) -> usize;
+}
+impl UInt for u32 {
+ #[inline]
+ fn zero() -> Self {
+ 0
+ }
+
+ #[inline]
+ fn as_usize(self) -> usize {
+ self as usize
+ }
+}
+impl UInt for usize {
+ #[inline]
+ fn zero() -> Self {
+ 0
+ }
+
+ #[inline]
+ fn as_usize(self) -> usize {
+ self
+ }
+}
+
+/// Randomly sample exactly `amount` indices from `0..length`, using rejection
+/// sampling.
+///
+/// Since `amount <<< length` there is a low chance of a random sample in
+/// `0..length` being a duplicate. We test for duplicates and resample where
+/// necessary. The algorithm is `O(amount)` time and memory.
+///
+/// This function is generic over X primarily so that results are value-stable
+/// over 32-bit and 64-bit platforms.
+fn sample_rejection<X: UInt, R>(rng: &mut R, length: X, amount: X) -> IndexVec
+where
+ R: Rng + ?Sized,
+ IndexVec: From<Vec<X>>,
+{
+ debug_assert!(amount < length);
+ #[cfg(feature = "std")]
+ let mut cache = HashSet::with_capacity(amount.as_usize());
+ #[cfg(not(feature = "std"))]
+ let mut cache = BTreeSet::new();
+ let distr = Uniform::new(X::zero(), length);
+ let mut indices = Vec::with_capacity(amount.as_usize());
+ for _ in 0..amount.as_usize() {
+ let mut pos = distr.sample(rng);
+ while !cache.insert(pos) {
+ pos = distr.sample(rng);
+ }
+ indices.push(pos);
+ }
+
+ debug_assert_eq!(indices.len(), amount.as_usize());
+ IndexVec::from(indices)
+}
+
+#[cfg(test)]
+mod test {
+ use super::*;
+ #[cfg(all(feature = "alloc", not(feature = "std")))] use crate::alloc::vec;
+ #[cfg(feature = "std")] use std::vec;
+
+ #[test]
+ fn test_sample_boundaries() {
+ let mut r = crate::test::rng(404);
+
+ assert_eq!(sample_inplace(&mut r, 0, 0).len(), 0);
+ assert_eq!(sample_inplace(&mut r, 1, 0).len(), 0);
+ assert_eq!(sample_inplace(&mut r, 1, 1).into_vec(), vec![0]);
+
+ assert_eq!(sample_rejection(&mut r, 1u32, 0).len(), 0);
+
+ assert_eq!(sample_floyd(&mut r, 0, 0).len(), 0);
+ assert_eq!(sample_floyd(&mut r, 1, 0).len(), 0);
+ assert_eq!(sample_floyd(&mut r, 1, 1).into_vec(), vec![0]);
+
+ // These algorithms should be fast with big numbers. Test average.
+ let sum: usize = sample_rejection(&mut r, 1 << 25, 10u32).into_iter().sum();
+ assert!(1 << 25 < sum && sum < (1 << 25) * 25);
+
+ let sum: usize = sample_floyd(&mut r, 1 << 25, 10).into_iter().sum();
+ assert!(1 << 25 < sum && sum < (1 << 25) * 25);
+ }
+
+ #[test]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_sample_alg() {
+ let seed_rng = crate::test::rng;
+
+ // We can't test which algorithm is used directly, but Floyd's alg
+ // should produce different results from the others. (Also, `inplace`
+ // and `cached` currently use different sizes thus produce different results.)
+
+ // A small length and relatively large amount should use inplace
+ let (length, amount): (usize, usize) = (100, 50);
+ let v1 = sample(&mut seed_rng(420), length, amount);
+ let v2 = sample_inplace(&mut seed_rng(420), length as u32, amount as u32);
+ assert!(v1.iter().all(|e| e < length));
+ assert_eq!(v1, v2);
+
+ // Test Floyd's alg does produce different results
+ let v3 = sample_floyd(&mut seed_rng(420), length as u32, amount as u32);
+ assert!(v1 != v3);
+
+ // A large length and small amount should use Floyd
+ let (length, amount): (usize, usize) = (1 << 20, 50);
+ let v1 = sample(&mut seed_rng(421), length, amount);
+ let v2 = sample_floyd(&mut seed_rng(421), length as u32, amount as u32);
+ assert!(v1.iter().all(|e| e < length));
+ assert_eq!(v1, v2);
+
+ // A large length and larger amount should use cache
+ let (length, amount): (usize, usize) = (1 << 20, 600);
+ let v1 = sample(&mut seed_rng(422), length, amount);
+ let v2 = sample_rejection(&mut seed_rng(422), length as u32, amount as u32);
+ assert!(v1.iter().all(|e| e < length));
+ assert_eq!(v1, v2);
+ }
+}
diff --git a/src/seq/mod.rs b/src/seq/mod.rs
new file mode 100644
index 0000000..dabf329
--- /dev/null
+++ b/src/seq/mod.rs
@@ -0,0 +1,850 @@
+// 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.
+
+//! Sequence-related functionality
+//!
+//! This module provides:
+//!
+//! * [`SliceRandom`] slice sampling and mutation
+//! * [`IteratorRandom`] iterator sampling
+//! * [`index::sample`] low-level API to choose multiple indices from
+//! `0..length`
+//!
+//! Also see:
+//!
+//! * [`crate::distributions::weighted`] module which provides
+//! implementations of weighted index sampling.
+//!
+//! In order to make results reproducible across 32-64 bit architectures, all
+//! `usize` indices are sampled as a `u32` where possible (also providing a
+//! small performance boost in some cases).
+
+
+#[cfg(feature = "alloc")] pub mod index;
+
+#[cfg(feature = "alloc")] use core::ops::Index;
+
+#[cfg(all(feature = "alloc", not(feature = "std")))] use crate::alloc::vec::Vec;
+
+#[cfg(feature = "alloc")]
+use crate::distributions::uniform::{SampleBorrow, SampleUniform};
+#[cfg(feature = "alloc")] use crate::distributions::WeightedError;
+use crate::Rng;
+
+/// Extension trait on slices, providing random mutation and sampling methods.
+///
+/// This trait is implemented on all `[T]` slice types, providing several
+/// methods for choosing and shuffling elements. You must `use` this trait:
+///
+/// ```
+/// use rand::seq::SliceRandom;
+///
+/// fn main() {
+/// let mut rng = rand::thread_rng();
+/// let mut bytes = "Hello, random!".to_string().into_bytes();
+/// bytes.shuffle(&mut rng);
+/// let str = String::from_utf8(bytes).unwrap();
+/// println!("{}", str);
+/// }
+/// ```
+/// Example output (non-deterministic):
+/// ```none
+/// l,nmroHado !le
+/// ```
+pub trait SliceRandom {
+ /// The element type.
+ type Item;
+
+ /// Returns a reference to one random element of the slice, or `None` if the
+ /// slice is empty.
+ ///
+ /// For slices, complexity is `O(1)`.
+ ///
+ /// # Example
+ ///
+ /// ```
+ /// use rand::thread_rng;
+ /// use rand::seq::SliceRandom;
+ ///
+ /// let choices = [1, 2, 4, 8, 16, 32];
+ /// let mut rng = thread_rng();
+ /// println!("{:?}", choices.choose(&mut rng));
+ /// assert_eq!(choices[..0].choose(&mut rng), None);
+ /// ```
+ fn choose<R>(&self, rng: &mut R) -> Option<&Self::Item>
+ where R: Rng + ?Sized;
+
+ /// Returns a mutable reference to one random element of the slice, or
+ /// `None` if the slice is empty.
+ ///
+ /// For slices, complexity is `O(1)`.
+ fn choose_mut<R>(&mut self, rng: &mut R) -> Option<&mut Self::Item>
+ where R: Rng + ?Sized;
+
+ /// Chooses `amount` elements from the slice at random, without repetition,
+ /// and in random order. The returned iterator is appropriate both for
+ /// collection into a `Vec` and filling an existing buffer (see example).
+ ///
+ /// In case this API is not sufficiently flexible, use [`index::sample`].
+ ///
+ /// For slices, complexity is the same as [`index::sample`].
+ ///
+ /// # Example
+ /// ```
+ /// use rand::seq::SliceRandom;
+ ///
+ /// let mut rng = &mut rand::thread_rng();
+ /// let sample = "Hello, audience!".as_bytes();
+ ///
+ /// // collect the results into a vector:
+ /// let v: Vec<u8> = sample.choose_multiple(&mut rng, 3).cloned().collect();
+ ///
+ /// // store in a buffer:
+ /// let mut buf = [0u8; 5];
+ /// for (b, slot) in sample.choose_multiple(&mut rng, buf.len()).zip(buf.iter_mut()) {
+ /// *slot = *b;
+ /// }
+ /// ```
+ #[cfg(feature = "alloc")]
+ fn choose_multiple<R>(&self, rng: &mut R, amount: usize) -> SliceChooseIter<Self, Self::Item>
+ where R: Rng + ?Sized;
+
+ /// Similar to [`choose`], but where the likelihood of each outcome may be
+ /// specified.
+ ///
+ /// The specified function `weight` maps each item `x` to a relative
+ /// likelihood `weight(x)`. The probability of each item being selected is
+ /// therefore `weight(x) / s`, where `s` is the sum of all `weight(x)`.
+ ///
+ /// For slices of length `n`, complexity is `O(n)`.
+ /// See also [`choose_weighted_mut`], [`distributions::weighted`].
+ ///
+ /// # Example
+ ///
+ /// ```
+ /// use rand::prelude::*;
+ ///
+ /// let choices = [('a', 2), ('b', 1), ('c', 1)];
+ /// let mut rng = thread_rng();
+ /// // 50% chance to print 'a', 25% chance to print 'b', 25% chance to print 'c'
+ /// println!("{:?}", choices.choose_weighted(&mut rng, |item| item.1).unwrap().0);
+ /// ```
+ /// [`choose`]: SliceRandom::choose
+ /// [`choose_weighted_mut`]: SliceRandom::choose_weighted_mut
+ /// [`distributions::weighted`]: crate::distributions::weighted
+ #[cfg(feature = "alloc")]
+ fn choose_weighted<R, F, B, X>(
+ &self, rng: &mut R, weight: F,
+ ) -> Result<&Self::Item, WeightedError>
+ where
+ R: Rng + ?Sized,
+ F: Fn(&Self::Item) -> B,
+ B: SampleBorrow<X>,
+ X: SampleUniform
+ + for<'a> ::core::ops::AddAssign<&'a X>
+ + ::core::cmp::PartialOrd<X>
+ + Clone
+ + Default;
+
+ /// Similar to [`choose_mut`], but where the likelihood of each outcome may
+ /// be specified.
+ ///
+ /// The specified function `weight` maps each item `x` to a relative
+ /// likelihood `weight(x)`. The probability of each item being selected is
+ /// therefore `weight(x) / s`, where `s` is the sum of all `weight(x)`.
+ ///
+ /// For slices of length `n`, complexity is `O(n)`.
+ /// See also [`choose_weighted`], [`distributions::weighted`].
+ ///
+ /// [`choose_mut`]: SliceRandom::choose_mut
+ /// [`choose_weighted`]: SliceRandom::choose_weighted
+ /// [`distributions::weighted`]: crate::distributions::weighted
+ #[cfg(feature = "alloc")]
+ fn choose_weighted_mut<R, F, B, X>(
+ &mut self, rng: &mut R, weight: F,
+ ) -> Result<&mut Self::Item, WeightedError>
+ where
+ R: Rng + ?Sized,
+ F: Fn(&Self::Item) -> B,
+ B: SampleBorrow<X>,
+ X: SampleUniform
+ + for<'a> ::core::ops::AddAssign<&'a X>
+ + ::core::cmp::PartialOrd<X>
+ + Clone
+ + Default;
+
+ /// Shuffle a mutable slice in place.
+ ///
+ /// For slices of length `n`, complexity is `O(n)`.
+ ///
+ /// # Example
+ ///
+ /// ```
+ /// use rand::seq::SliceRandom;
+ /// use rand::thread_rng;
+ ///
+ /// let mut rng = thread_rng();
+ /// let mut y = [1, 2, 3, 4, 5];
+ /// println!("Unshuffled: {:?}", y);
+ /// y.shuffle(&mut rng);
+ /// println!("Shuffled: {:?}", y);
+ /// ```
+ fn shuffle<R>(&mut self, rng: &mut R)
+ where R: Rng + ?Sized;
+
+ /// Shuffle a slice in place, but exit early.
+ ///
+ /// Returns two mutable slices from the source slice. The first contains
+ /// `amount` elements randomly permuted. The second has the remaining
+ /// elements that are not fully shuffled.
+ ///
+ /// This is an efficient method to select `amount` elements at random from
+ /// the slice, provided the slice may be mutated.
+ ///
+ /// If you only need to choose elements randomly and `amount > self.len()/2`
+ /// then you may improve performance by taking
+ /// `amount = values.len() - amount` and using only the second slice.
+ ///
+ /// If `amount` is greater than the number of elements in the slice, this
+ /// will perform a full shuffle.
+ ///
+ /// For slices, complexity is `O(m)` where `m = amount`.
+ fn partial_shuffle<R>(
+ &mut self, rng: &mut R, amount: usize,
+ ) -> (&mut [Self::Item], &mut [Self::Item])
+ where R: Rng + ?Sized;
+}
+
+/// Extension trait on iterators, providing random sampling methods.
+///
+/// This trait is implemented on all sized iterators, providing methods for
+/// choosing one or more elements. You must `use` this trait:
+///
+/// ```
+/// use rand::seq::IteratorRandom;
+///
+/// fn main() {
+/// let mut rng = rand::thread_rng();
+///
+/// let faces = "😀😎😐😕😠😢";
+/// println!("I am {}!", faces.chars().choose(&mut rng).unwrap());
+/// }
+/// ```
+/// Example output (non-deterministic):
+/// ```none
+/// I am 😀!
+/// ```
+pub trait IteratorRandom: Iterator + Sized {
+ /// Choose one element at random from the iterator.
+ ///
+ /// Returns `None` if and only if the iterator is empty.
+ ///
+ /// This method uses [`Iterator::size_hint`] for optimisation. With an
+ /// accurate hint and where [`Iterator::nth`] is a constant-time operation
+ /// this method can offer `O(1)` performance. Where no size hint is
+ /// available, complexity is `O(n)` where `n` is the iterator length.
+ /// Partial hints (where `lower > 0`) also improve performance.
+ ///
+ /// For slices, prefer [`SliceRandom::choose`] which guarantees `O(1)`
+ /// performance.
+ fn choose<R>(mut self, rng: &mut R) -> Option<Self::Item>
+ where R: Rng + ?Sized {
+ let (mut lower, mut upper) = self.size_hint();
+ let mut consumed = 0;
+ let mut result = None;
+
+ if upper == Some(lower) {
+ return if lower == 0 {
+ None
+ } else {
+ self.nth(gen_index(rng, lower))
+ };
+ }
+
+ // Continue until the iterator is exhausted
+ loop {
+ if lower > 1 {
+ let ix = gen_index(rng, lower + consumed);
+ let skip = if ix < lower {
+ result = self.nth(ix);
+ lower - (ix + 1)
+ } else {
+ lower
+ };
+ if upper == Some(lower) {
+ return result;
+ }
+ consumed += lower;
+ if skip > 0 {
+ self.nth(skip - 1);
+ }
+ } else {
+ let elem = self.next();
+ if elem.is_none() {
+ return result;
+ }
+ consumed += 1;
+ let denom = consumed as f64; // accurate to 2^53 elements
+ if rng.gen_bool(1.0 / denom) {
+ result = elem;
+ }
+ }
+
+ let hint = self.size_hint();
+ lower = hint.0;
+ upper = hint.1;
+ }
+ }
+
+ /// Collects values at random from the iterator into a supplied buffer
+ /// until that buffer is filled.
+ ///
+ /// Although the elements are selected randomly, the order of elements in
+ /// the buffer is neither stable nor fully random. If random ordering is
+ /// desired, shuffle the result.
+ ///
+ /// Returns the number of elements added to the buffer. This equals the length
+ /// of the buffer unless the iterator contains insufficient elements, in which
+ /// case this equals the number of elements available.
+ ///
+ /// Complexity is `O(n)` where `n` is the length of the iterator.
+ /// For slices, prefer [`SliceRandom::choose_multiple`].
+ fn choose_multiple_fill<R>(mut self, rng: &mut R, buf: &mut [Self::Item]) -> usize
+ where R: Rng + ?Sized {
+ let amount = buf.len();
+ let mut len = 0;
+ while len < amount {
+ if let Some(elem) = self.next() {
+ buf[len] = elem;
+ len += 1;
+ } else {
+ // Iterator exhausted; stop early
+ return len;
+ }
+ }
+
+ // Continue, since the iterator was not exhausted
+ for (i, elem) in self.enumerate() {
+ let k = gen_index(rng, i + 1 + amount);
+ if let Some(slot) = buf.get_mut(k) {
+ *slot = elem;
+ }
+ }
+ len
+ }
+
+ /// Collects `amount` values at random from the iterator into a vector.
+ ///
+ /// This is equivalent to `choose_multiple_fill` except for the result type.
+ ///
+ /// Although the elements are selected randomly, the order of elements in
+ /// the buffer is neither stable nor fully random. If random ordering is
+ /// desired, shuffle the result.
+ ///
+ /// The length of the returned vector equals `amount` unless the iterator
+ /// contains insufficient elements, in which case it equals the number of
+ /// elements available.
+ ///
+ /// Complexity is `O(n)` where `n` is the length of the iterator.
+ /// For slices, prefer [`SliceRandom::choose_multiple`].
+ #[cfg(feature = "alloc")]
+ fn choose_multiple<R>(mut self, rng: &mut R, amount: usize) -> Vec<Self::Item>
+ where R: Rng + ?Sized {
+ let mut reservoir = Vec::with_capacity(amount);
+ reservoir.extend(self.by_ref().take(amount));
+
+ // Continue unless the iterator was exhausted
+ //
+ // note: this prevents iterators that "restart" from causing problems.
+ // If the iterator stops once, then so do we.
+ if reservoir.len() == amount {
+ for (i, elem) in self.enumerate() {
+ let k = gen_index(rng, i + 1 + amount);
+ if let Some(slot) = reservoir.get_mut(k) {
+ *slot = elem;
+ }
+ }
+ } else {
+ // Don't hang onto extra memory. There is a corner case where
+ // `amount` was much less than `self.len()`.
+ reservoir.shrink_to_fit();
+ }
+ reservoir
+ }
+}
+
+
+impl<T> SliceRandom for [T] {
+ type Item = T;
+
+ fn choose<R>(&self, rng: &mut R) -> Option<&Self::Item>
+ where R: Rng + ?Sized {
+ if self.is_empty() {
+ None
+ } else {
+ Some(&self[gen_index(rng, self.len())])
+ }
+ }
+
+ fn choose_mut<R>(&mut self, rng: &mut R) -> Option<&mut Self::Item>
+ where R: Rng + ?Sized {
+ if self.is_empty() {
+ None
+ } else {
+ let len = self.len();
+ Some(&mut self[gen_index(rng, len)])
+ }
+ }
+
+ #[cfg(feature = "alloc")]
+ fn choose_multiple<R>(&self, rng: &mut R, amount: usize) -> SliceChooseIter<Self, Self::Item>
+ where R: Rng + ?Sized {
+ let amount = ::core::cmp::min(amount, self.len());
+ SliceChooseIter {
+ slice: self,
+ _phantom: Default::default(),
+ indices: index::sample(rng, self.len(), amount).into_iter(),
+ }
+ }
+
+ #[cfg(feature = "alloc")]
+ fn choose_weighted<R, F, B, X>(
+ &self, rng: &mut R, weight: F,
+ ) -> Result<&Self::Item, WeightedError>
+ where
+ R: Rng + ?Sized,
+ F: Fn(&Self::Item) -> B,
+ B: SampleBorrow<X>,
+ X: SampleUniform
+ + for<'a> ::core::ops::AddAssign<&'a X>
+ + ::core::cmp::PartialOrd<X>
+ + Clone
+ + Default,
+ {
+ use crate::distributions::{Distribution, WeightedIndex};
+ let distr = WeightedIndex::new(self.iter().map(weight))?;
+ Ok(&self[distr.sample(rng)])
+ }
+
+ #[cfg(feature = "alloc")]
+ fn choose_weighted_mut<R, F, B, X>(
+ &mut self, rng: &mut R, weight: F,
+ ) -> Result<&mut Self::Item, WeightedError>
+ where
+ R: Rng + ?Sized,
+ F: Fn(&Self::Item) -> B,
+ B: SampleBorrow<X>,
+ X: SampleUniform
+ + for<'a> ::core::ops::AddAssign<&'a X>
+ + ::core::cmp::PartialOrd<X>
+ + Clone
+ + Default,
+ {
+ use crate::distributions::{Distribution, WeightedIndex};
+ let distr = WeightedIndex::new(self.iter().map(weight))?;
+ Ok(&mut self[distr.sample(rng)])
+ }
+
+ fn shuffle<R>(&mut self, rng: &mut R)
+ where R: Rng + ?Sized {
+ for i in (1..self.len()).rev() {
+ // invariant: elements with index > i have been locked in place.
+ self.swap(i, gen_index(rng, i + 1));
+ }
+ }
+
+ fn partial_shuffle<R>(
+ &mut self, rng: &mut R, amount: usize,
+ ) -> (&mut [Self::Item], &mut [Self::Item])
+ where R: Rng + ?Sized {
+ // This applies Durstenfeld's algorithm for the
+ // [Fisher–Yates shuffle](https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle#The_modern_algorithm)
+ // for an unbiased permutation, but exits early after choosing `amount`
+ // elements.
+
+ let len = self.len();
+ let end = if amount >= len { 0 } else { len - amount };
+
+ for i in (end..len).rev() {
+ // invariant: elements with index > i have been locked in place.
+ self.swap(i, gen_index(rng, i + 1));
+ }
+ let r = self.split_at_mut(end);
+ (r.1, r.0)
+ }
+}
+
+impl<I> IteratorRandom for I where I: Iterator + Sized {}
+
+
+/// An iterator over multiple slice elements.
+///
+/// This struct is created by
+/// [`SliceRandom::choose_multiple`](trait.SliceRandom.html#tymethod.choose_multiple).
+#[cfg(feature = "alloc")]
+#[derive(Debug)]
+pub struct SliceChooseIter<'a, S: ?Sized + 'a, T: 'a> {
+ slice: &'a S,
+ _phantom: ::core::marker::PhantomData<T>,
+ indices: index::IndexVecIntoIter,
+}
+
+#[cfg(feature = "alloc")]
+impl<'a, S: Index<usize, Output = T> + ?Sized + 'a, T: 'a> Iterator for SliceChooseIter<'a, S, T> {
+ type Item = &'a T;
+
+ fn next(&mut self) -> Option<Self::Item> {
+ // TODO: investigate using SliceIndex::get_unchecked when stable
+ self.indices.next().map(|i| &self.slice[i as usize])
+ }
+
+ fn size_hint(&self) -> (usize, Option<usize>) {
+ (self.indices.len(), Some(self.indices.len()))
+ }
+}
+
+#[cfg(feature = "alloc")]
+impl<'a, S: Index<usize, Output = T> + ?Sized + 'a, T: 'a> ExactSizeIterator
+ for SliceChooseIter<'a, S, T>
+{
+ fn len(&self) -> usize {
+ self.indices.len()
+ }
+}
+
+
+// Sample a number uniformly between 0 and `ubound`. Uses 32-bit sampling where
+// possible, primarily in order to produce the same output on 32-bit and 64-bit
+// platforms.
+#[inline]
+fn gen_index<R: Rng + ?Sized>(rng: &mut R, ubound: usize) -> usize {
+ if ubound <= (core::u32::MAX as usize) {
+ rng.gen_range(0, ubound as u32) as usize
+ } else {
+ rng.gen_range(0, ubound)
+ }
+}
+
+
+#[cfg(test)]
+mod test {
+ use super::*;
+ #[cfg(feature = "alloc")] use crate::Rng;
+ #[cfg(all(feature = "alloc", not(feature = "std")))] use alloc::vec::Vec;
+
+ #[test]
+ fn test_slice_choose() {
+ let mut r = crate::test::rng(107);
+ let chars = [
+ 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n',
+ ];
+ let mut chosen = [0i32; 14];
+ // The below all use a binomial distribution with n=1000, p=1/14.
+ // binocdf(40, 1000, 1/14) ~= 2e-5; 1-binocdf(106, ..) ~= 2e-5
+ for _ in 0..1000 {
+ let picked = *chars.choose(&mut r).unwrap();
+ chosen[(picked as usize) - ('a' as usize)] += 1;
+ }
+ for count in chosen.iter() {
+ assert!(40 < *count && *count < 106);
+ }
+
+ chosen.iter_mut().for_each(|x| *x = 0);
+ for _ in 0..1000 {
+ *chosen.choose_mut(&mut r).unwrap() += 1;
+ }
+ for count in chosen.iter() {
+ assert!(40 < *count && *count < 106);
+ }
+
+ let mut v: [isize; 0] = [];
+ assert_eq!(v.choose(&mut r), None);
+ assert_eq!(v.choose_mut(&mut r), None);
+ }
+
+ #[derive(Clone)]
+ struct UnhintedIterator<I: Iterator + Clone> {
+ iter: I,
+ }
+ impl<I: Iterator + Clone> Iterator for UnhintedIterator<I> {
+ type Item = I::Item;
+
+ fn next(&mut self) -> Option<Self::Item> {
+ self.iter.next()
+ }
+ }
+
+ #[derive(Clone)]
+ struct ChunkHintedIterator<I: ExactSizeIterator + Iterator + Clone> {
+ iter: I,
+ chunk_remaining: usize,
+ chunk_size: usize,
+ hint_total_size: bool,
+ }
+ impl<I: ExactSizeIterator + Iterator + Clone> Iterator for ChunkHintedIterator<I> {
+ type Item = I::Item;
+
+ fn next(&mut self) -> Option<Self::Item> {
+ if self.chunk_remaining == 0 {
+ self.chunk_remaining = ::core::cmp::min(self.chunk_size, self.iter.len());
+ }
+ self.chunk_remaining = self.chunk_remaining.saturating_sub(1);
+
+ self.iter.next()
+ }
+
+ fn size_hint(&self) -> (usize, Option<usize>) {
+ (
+ self.chunk_remaining,
+ if self.hint_total_size {
+ Some(self.iter.len())
+ } else {
+ None
+ },
+ )
+ }
+ }
+
+ #[derive(Clone)]
+ struct WindowHintedIterator<I: ExactSizeIterator + Iterator + Clone> {
+ iter: I,
+ window_size: usize,
+ hint_total_size: bool,
+ }
+ impl<I: ExactSizeIterator + Iterator + Clone> Iterator for WindowHintedIterator<I> {
+ type Item = I::Item;
+
+ fn next(&mut self) -> Option<Self::Item> {
+ self.iter.next()
+ }
+
+ fn size_hint(&self) -> (usize, Option<usize>) {
+ (
+ ::core::cmp::min(self.iter.len(), self.window_size),
+ if self.hint_total_size {
+ Some(self.iter.len())
+ } else {
+ None
+ },
+ )
+ }
+ }
+
+ #[test]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_iterator_choose() {
+ let r = &mut crate::test::rng(109);
+ fn test_iter<R: Rng + ?Sized, Iter: Iterator<Item = usize> + Clone>(r: &mut R, iter: Iter) {
+ let mut chosen = [0i32; 9];
+ for _ in 0..1000 {
+ let picked = iter.clone().choose(r).unwrap();
+ chosen[picked] += 1;
+ }
+ for count in chosen.iter() {
+ // Samples should follow Binomial(1000, 1/9)
+ // Octave: binopdf(x, 1000, 1/9) gives the prob of *count == x
+ // Note: have seen 153, which is unlikely but not impossible.
+ assert!(
+ 72 < *count && *count < 154,
+ "count not close to 1000/9: {}",
+ count
+ );
+ }
+ }
+
+ test_iter(r, 0..9);
+ test_iter(r, [0, 1, 2, 3, 4, 5, 6, 7, 8].iter().cloned());
+ #[cfg(feature = "alloc")]
+ test_iter(r, (0..9).collect::<Vec<_>>().into_iter());
+ test_iter(r, UnhintedIterator { iter: 0..9 });
+ test_iter(r, ChunkHintedIterator {
+ iter: 0..9,
+ chunk_size: 4,
+ chunk_remaining: 4,
+ hint_total_size: false,
+ });
+ test_iter(r, ChunkHintedIterator {
+ iter: 0..9,
+ chunk_size: 4,
+ chunk_remaining: 4,
+ hint_total_size: true,
+ });
+ test_iter(r, WindowHintedIterator {
+ iter: 0..9,
+ window_size: 2,
+ hint_total_size: false,
+ });
+ test_iter(r, WindowHintedIterator {
+ iter: 0..9,
+ window_size: 2,
+ hint_total_size: true,
+ });
+
+ assert_eq!((0..0).choose(r), None);
+ assert_eq!(UnhintedIterator { iter: 0..0 }.choose(r), None);
+ }
+
+ #[test]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_shuffle() {
+ let mut r = crate::test::rng(108);
+ let empty: &mut [isize] = &mut [];
+ empty.shuffle(&mut r);
+ let mut one = [1];
+ one.shuffle(&mut r);
+ let b: &[_] = &[1];
+ assert_eq!(one, b);
+
+ let mut two = [1, 2];
+ two.shuffle(&mut r);
+ assert!(two == [1, 2] || two == [2, 1]);
+
+ fn move_last(slice: &mut [usize], pos: usize) {
+ // use slice[pos..].rotate_left(1); once we can use that
+ let last_val = slice[pos];
+ for i in pos..slice.len() - 1 {
+ slice[i] = slice[i + 1];
+ }
+ *slice.last_mut().unwrap() = last_val;
+ }
+ let mut counts = [0i32; 24];
+ for _ in 0..10000 {
+ let mut arr: [usize; 4] = [0, 1, 2, 3];
+ arr.shuffle(&mut r);
+ let mut permutation = 0usize;
+ let mut pos_value = counts.len();
+ for i in 0..4 {
+ pos_value /= 4 - i;
+ let pos = arr.iter().position(|&x| x == i).unwrap();
+ assert!(pos < (4 - i));
+ permutation += pos * pos_value;
+ move_last(&mut arr, pos);
+ assert_eq!(arr[3], i);
+ }
+ for i in 0..4 {
+ assert_eq!(arr[i], i);
+ }
+ counts[permutation] += 1;
+ }
+ for count in counts.iter() {
+ // Binomial(10000, 1/24) with average 416.667
+ // Octave: binocdf(n, 10000, 1/24)
+ // 99.9% chance samples lie within this range:
+ assert!(352 <= *count && *count <= 483, "count: {}", count);
+ }
+ }
+
+ #[test]
+ fn test_partial_shuffle() {
+ let mut r = crate::test::rng(118);
+
+ let mut empty: [u32; 0] = [];
+ let res = empty.partial_shuffle(&mut r, 10);
+ assert_eq!((res.0.len(), res.1.len()), (0, 0));
+
+ let mut v = [1, 2, 3, 4, 5];
+ let res = v.partial_shuffle(&mut r, 2);
+ assert_eq!((res.0.len(), res.1.len()), (2, 3));
+ assert!(res.0[0] != res.0[1]);
+ // First elements are only modified if selected, so at least one isn't modified:
+ assert!(res.1[0] == 1 || res.1[1] == 2 || res.1[2] == 3);
+ }
+
+ #[test]
+ #[cfg(feature = "alloc")]
+ fn test_sample_iter() {
+ let min_val = 1;
+ let max_val = 100;
+
+ let mut r = crate::test::rng(401);
+ let vals = (min_val..max_val).collect::<Vec<i32>>();
+ let small_sample = vals.iter().choose_multiple(&mut r, 5);
+ let large_sample = vals.iter().choose_multiple(&mut r, vals.len() + 5);
+
+ assert_eq!(small_sample.len(), 5);
+ assert_eq!(large_sample.len(), vals.len());
+ // no randomization happens when amount >= len
+ assert_eq!(large_sample, vals.iter().collect::<Vec<_>>());
+
+ assert!(small_sample
+ .iter()
+ .all(|e| { **e >= min_val && **e <= max_val }));
+ }
+
+ #[test]
+ #[cfg(feature = "alloc")]
+ #[cfg_attr(miri, ignore)] // Miri is too slow
+ fn test_weighted() {
+ let mut r = crate::test::rng(406);
+ const N_REPS: u32 = 3000;
+ let weights = [1u32, 2, 3, 0, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7];
+ let total_weight = weights.iter().sum::<u32>() as f32;
+
+ let verify = |result: [i32; 14]| {
+ for (i, count) in result.iter().enumerate() {
+ let exp = (weights[i] * N_REPS) as f32 / total_weight;
+ let mut err = (*count as f32 - exp).abs();
+ if err != 0.0 {
+ err /= exp;
+ }
+ assert!(err <= 0.25);
+ }
+ };
+
+ // choose_weighted
+ fn get_weight<T>(item: &(u32, T)) -> u32 {
+ item.0
+ }
+ let mut chosen = [0i32; 14];
+ let mut items = [(0u32, 0usize); 14]; // (weight, index)
+ for (i, item) in items.iter_mut().enumerate() {
+ *item = (weights[i], i);
+ }
+ for _ in 0..N_REPS {
+ let item = items.choose_weighted(&mut r, get_weight).unwrap();
+ chosen[item.1] += 1;
+ }
+ verify(chosen);
+
+ // choose_weighted_mut
+ let mut items = [(0u32, 0i32); 14]; // (weight, count)
+ for (i, item) in items.iter_mut().enumerate() {
+ *item = (weights[i], 0);
+ }
+ for _ in 0..N_REPS {
+ items.choose_weighted_mut(&mut r, get_weight).unwrap().1 += 1;
+ }
+ for (ch, item) in chosen.iter_mut().zip(items.iter()) {
+ *ch = item.1;
+ }
+ verify(chosen);
+
+ // Check error cases
+ let empty_slice = &mut [10][0..0];
+ assert_eq!(
+ empty_slice.choose_weighted(&mut r, |_| 1),
+ Err(WeightedError::NoItem)
+ );
+ assert_eq!(
+ empty_slice.choose_weighted_mut(&mut r, |_| 1),
+ Err(WeightedError::NoItem)
+ );
+ assert_eq!(
+ ['x'].choose_weighted_mut(&mut r, |_| 0),
+ Err(WeightedError::AllWeightsZero)
+ );
+ assert_eq!(
+ [0, -1].choose_weighted_mut(&mut r, |x| *x),
+ Err(WeightedError::InvalidWeight)
+ );
+ assert_eq!(
+ [-1, 0].choose_weighted_mut(&mut r, |x| *x),
+ Err(WeightedError::InvalidWeight)
+ );
+ }
+}