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Diffstat (limited to 'rand/src/distributions')
22 files changed, 0 insertions, 5860 deletions
diff --git a/rand/src/distributions/bernoulli.rs b/rand/src/distributions/bernoulli.rs deleted file mode 100644 index eadd056..0000000 --- a/rand/src/distributions/bernoulli.rs +++ /dev/null @@ -1,166 +0,0 @@ -// 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::Rng; -use crate::distributions::Distribution; - -/// The Bernoulli distribution. -/// -/// This is a special case of the Binomial distribution where `n = 1`. -/// -/// # Example -/// -/// ```rust -/// use rand::distributions::{Bernoulli, Distribution}; -/// -/// let d = Bernoulli::new(0.3).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 = ::core::u64::MAX; - -// This is just `2.0.powi(64)`, but written this way because it is not available -// in `no_std` mode. -const SCALE: f64 = 2.0 * (1u64 << 63) as f64; - -/// Error type returned from `Bernoulli::new`. -#[derive(Clone, Copy, Debug, PartialEq, Eq)] -pub enum BernoulliError { - /// `p < 0` or `p > 1`. - InvalidProbability, -} - -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`. - /// - /// If `numerator == denominator` then the returned `Bernoulli` will always - /// return `true`. If `numerator == 0` it will always return `false`. - #[inline] - pub fn from_ratio(numerator: u32, denominator: u32) -> Result<Bernoulli, BernoulliError> { - if numerator > denominator { - 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 crate::Rng; - use crate::distributions::Distribution; - use super::Bernoulli; - - #[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(not(miri))] // 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); - } -} diff --git a/rand/src/distributions/binomial.rs b/rand/src/distributions/binomial.rs deleted file mode 100644 index 8fc290a..0000000 --- a/rand/src/distributions/binomial.rs +++ /dev/null @@ -1,313 +0,0 @@ -// 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::Rng; -use crate::distributions::{Distribution, Uniform}; - -/// 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 crate::Rng; - use crate::distributions::Distribution; - use super::Binomial; - - 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(not(miri))] // 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/rand/src/distributions/cauchy.rs b/rand/src/distributions/cauchy.rs deleted file mode 100644 index 0a5d149..0000000 --- a/rand/src/distributions/cauchy.rs +++ /dev/null @@ -1,103 +0,0 @@ -// 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::Rng; -use crate::distributions::Distribution; -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 crate::distributions::Distribution; - use super::Cauchy; - - 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] - #[cfg(not(miri))] // Miri doesn't support transcendental functions - 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/rand/src/distributions/dirichlet.rs b/rand/src/distributions/dirichlet.rs deleted file mode 100644 index 1ce01fd..0000000 --- a/rand/src/distributions/dirichlet.rs +++ /dev/null @@ -1,128 +0,0 @@ -// 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::Rng; -use crate::distributions::Distribution; -use crate::distributions::gamma::Gamma; - -/// 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/rand/src/distributions/exponential.rs b/rand/src/distributions/exponential.rs deleted file mode 100644 index 0278248..0000000 --- a/rand/src/distributions/exponential.rs +++ /dev/null @@ -1,108 +0,0 @@ -// 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::{Rng}; -use crate::distributions::{ziggurat_tables, Distribution}; -use crate::distributions::utils::ziggurat; - -/// 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 crate::distributions::Distribution; - use super::Exp; - - #[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/rand/src/distributions/float.rs b/rand/src/distributions/float.rs deleted file mode 100644 index bda523a..0000000 --- a/rand/src/distributions/float.rs +++ /dev/null @@ -1,259 +0,0 @@ -// 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 core::mem; -use crate::Rng; -use crate::distributions::{Distribution, Standard}; -use crate::distributions::utils::FloatSIMDUtils; -#[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 23 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 22 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 - $fraction_bits); - fraction.into_float_with_exponent(0) - (1.0 - EPSILON / 2.0) - } - } - } -} - -float_impls! { f32, u32, f32, u32, 23, 127 } -float_impls! { f64, u64, f64, u64, 52, 1023 } - -#[cfg(feature="simd_support")] -float_impls! { f32x2, u32x2, f32, u32, 23, 127 } -#[cfg(feature="simd_support")] -float_impls! { f32x4, u32x4, f32, u32, 23, 127 } -#[cfg(feature="simd_support")] -float_impls! { f32x8, u32x8, f32, u32, 23, 127 } -#[cfg(feature="simd_support")] -float_impls! { f32x16, u32x16, f32, u32, 23, 127 } - -#[cfg(feature="simd_support")] -float_impls! { f64x2, u64x2, f64, u64, 52, 1023 } -#[cfg(feature="simd_support")] -float_impls! { f64x4, u64x4, f64, u64, 52, 1023 } -#[cfg(feature="simd_support")] -float_impls! { f64x8, u64x8, f64, u64, 52, 1023 } - - -#[cfg(test)] -mod tests { - use crate::Rng; - use crate::distributions::{Open01, OpenClosed01}; - use crate::rngs::mock::StepRng; - #[cfg(feature="simd_support")] - use packed_simd::*; - - const EPSILON32: f32 = ::core::f32::EPSILON; - const EPSILON64: f64 = ::core::f64::EPSILON; - - macro_rules! test_f32 { - ($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) } -} diff --git a/rand/src/distributions/gamma.rs b/rand/src/distributions/gamma.rs deleted file mode 100644 index b5a97f5..0000000 --- a/rand/src/distributions/gamma.rs +++ /dev/null @@ -1,371 +0,0 @@ -// 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::GammaRepr::*; -use self::ChiSquaredRepr::*; - -use crate::Rng; -use crate::distributions::normal::StandardNormal; -use crate::distributions::{Distribution, Exp, Open01}; - -/// 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 crate::distributions::Distribution; - use super::{Beta, ChiSquared, StudentT, FisherF}; - - 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/rand/src/distributions/integer.rs b/rand/src/distributions/integer.rs deleted file mode 100644 index 5238339..0000000 --- a/rand/src/distributions/integer.rs +++ /dev/null @@ -1,184 +0,0 @@ -// 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::{Rng}; -use crate::distributions::{Distribution, Standard}; -use core::num::{NonZeroU8, NonZeroU16, NonZeroU32, NonZeroU64, NonZeroUsize}; -#[cfg(not(target_os = "emscripten"))] use core::num::NonZeroU128; -#[cfg(feature="simd_support")] -use packed_simd::*; -#[cfg(all(target_arch = "x86", feature="nightly"))] -use core::arch::x86::*; -#[cfg(all(target_arch = "x86_64", feature="nightly"))] -use core::arch::x86_64::*; - -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 crate::Rng; - use crate::distributions::{Standard}; - - #[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); - } -} diff --git a/rand/src/distributions/mod.rs b/rand/src/distributions/mod.rs deleted file mode 100644 index 02ece6f..0000000 --- a/rand/src/distributions/mod.rs +++ /dev/null @@ -1,381 +0,0 @@ -// 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 - -//! [`Alphanumeric`]: distributions::Alphanumeric -//! [`Bernoulli`]: distributions::Bernoulli -//! [`Open01`]: distributions::Open01 -//! [`OpenClosed01`]: distributions::OpenClosed01 -//! [`Standard`]: distributions::Standard -//! [`Uniform`]: distributions::Uniform -//! [`Uniform::new`]: distributions::Uniform::new -//! [`Uniform::new_inclusive`]: distributions::Uniform::new_inclusive -//! [`weighted`]: distributions::weighted -//! [`rand_distr`]: https://crates.io/crates/rand_distr -//! [`statrs`]: https://crates.io/crates/statrs - -use core::iter; -use crate::Rng; - -pub use self::other::Alphanumeric; -#[doc(inline)] pub use self::uniform::Uniform; -pub use self::float::{OpenClosed01, Open01}; -pub use self::bernoulli::{Bernoulli, BernoulliError}; -#[cfg(feature="alloc")] pub use self::weighted::{WeightedIndex, WeightedError}; - -// The following are all deprecated after being moved to rand_distr -#[allow(deprecated)] -#[cfg(feature="std")] pub use self::unit_sphere::UnitSphereSurface; -#[allow(deprecated)] -#[cfg(feature="std")] pub use self::unit_circle::UnitCircle; -#[allow(deprecated)] -#[cfg(feature="std")] pub use self::gamma::{Gamma, ChiSquared, FisherF, - StudentT, Beta}; -#[allow(deprecated)] -#[cfg(feature="std")] pub use self::normal::{Normal, LogNormal, StandardNormal}; -#[allow(deprecated)] -#[cfg(feature="std")] pub use self::exponential::{Exp, Exp1}; -#[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::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::triangular::Triangular; -#[allow(deprecated)] -#[cfg(feature="std")] pub use self::weibull::Weibull; - -pub mod uniform; -mod bernoulli; -#[cfg(feature="alloc")] pub mod weighted; -#[cfg(feature="std")] mod unit_sphere; -#[cfg(feature="std")] mod unit_circle; -#[cfg(feature="std")] mod gamma; -#[cfg(feature="std")] mod normal; -#[cfg(feature="std")] mod exponential; -#[cfg(feature="std")] mod pareto; -#[cfg(feature="std")] mod poisson; -#[cfg(feature="std")] mod binomial; -#[cfg(feature="std")] mod cauchy; -#[cfg(feature="std")] mod dirichlet; -#[cfg(feature="std")] mod triangular; -#[cfg(feature="std")] mod weibull; - -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. -/// -/// [`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 23 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 crate::Rng; - use super::{Distribution, Uniform}; - - #[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/rand/src/distributions/normal.rs b/rand/src/distributions/normal.rs deleted file mode 100644 index 7808baf..0000000 --- a/rand/src/distributions/normal.rs +++ /dev/null @@ -1,170 +0,0 @@ -// 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::Rng; -use crate::distributions::{ziggurat_tables, Distribution, Open01}; -use crate::distributions::utils::ziggurat; - -/// 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 crate::distributions::Distribution; - use super::{Normal, LogNormal}; - - #[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/rand/src/distributions/other.rs b/rand/src/distributions/other.rs deleted file mode 100644 index 6ec0473..0000000 --- a/rand/src/distributions/other.rs +++ /dev/null @@ -1,220 +0,0 @@ -// 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::Rng; -use crate::distributions::{Distribution, Standard, Uniform}; - -// ----- 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 crate::{Rng, RngCore, Standard}; - use crate::distributions::Alphanumeric; - #[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); - } -} diff --git a/rand/src/distributions/pareto.rs b/rand/src/distributions/pareto.rs deleted file mode 100644 index edc9122..0000000 --- a/rand/src/distributions/pareto.rs +++ /dev/null @@ -1,67 +0,0 @@ -// 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::Rng; -use crate::distributions::{Distribution, OpenClosed01}; - -/// 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 crate::distributions::Distribution; - use super::Pareto; - - #[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/rand/src/distributions/poisson.rs b/rand/src/distributions/poisson.rs deleted file mode 100644 index 9fd6e99..0000000 --- a/rand/src/distributions/poisson.rs +++ /dev/null @@ -1,151 +0,0 @@ -// 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::Rng; -use crate::distributions::{Distribution, Cauchy}; -use crate::distributions::utils::log_gamma; - -/// 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 crate::distributions::Distribution; - use super::Poisson; - - #[test] - #[cfg(not(miri))] // 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] - #[cfg(not(miri))] // Miri doesn't support transcendental functions - 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/rand/src/distributions/triangular.rs b/rand/src/distributions/triangular.rs deleted file mode 100644 index 3e8f8b0..0000000 --- a/rand/src/distributions/triangular.rs +++ /dev/null @@ -1,79 +0,0 @@ -// 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::Rng; -use crate::distributions::{Distribution, Standard}; - -/// 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 crate::distributions::Distribution; - use super::Triangular; - - #[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/rand/src/distributions/uniform.rs b/rand/src/distributions/uniform.rs deleted file mode 100644 index 8c90f4e..0000000 --- a/rand/src/distributions/uniform.rs +++ /dev/null @@ -1,1270 +0,0 @@ -// 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 { -//! inner: 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 { -//! inner: 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.inner.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(feature = "std")] -use std::time::Duration; -#[cfg(not(feature = "std"))] -use core::time::Duration; - -use crate::Rng; -use crate::distributions::Distribution; -use crate::distributions::float::IntoFloat; -use crate::distributions::utils::{WideningMultiply, FloatSIMDUtils, FloatAsSIMD, BoolAsSIMD}; - -#[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> { - inner: 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 { inner: 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 { inner: 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.inner.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. - 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, $u_scalar); - )+ - }; -} - -#[cfg(all(feature = "simd_support", feature = "nightly"))] -uniform_simd_int_impl! { - (u64x2, i64x2), - (u64x4, i64x4), - (u64x8, i64x8), - u64 -} - -#[cfg(all(feature = "simd_support", feature = "nightly"))] -uniform_simd_int_impl! { - (u32x2, i32x2), - (u32x4, i32x4), - (u32x8, i32x8), - (u32x16, i32x16), - u32 -} - -#[cfg(all(feature = "simd_support", feature = "nightly"))] -uniform_simd_int_impl! { - (u16x2, i16x2), - (u16x4, i16x4), - (u16x8, i16x8), - (u16x16, i16x16), - (u16x32, i16x32), - u16 -} - -#[cfg(all(feature = "simd_support", feature = "nightly"))] -uniform_simd_int_impl! { - (u8x2, i8x2), - (u8x4, i8x4), - (u8x8, i8x8), - (u8x16, i8x16), - (u8x32, i8x32), - (u8x64, i8x64), - u8 -} - - -/// The back-end implementing [`UniformSampler`] for floating-point types. -/// -/// Unless you are implementing [`UniformSampler`] for your own type, this type -/// should not be used directly, use [`Uniform`] instead. -/// -/// # Implementation notes -/// -/// Instead of generating a float in the `[0, 1)` range using [`Standard`], the -/// `UniformFloat` implementation converts the output of an PRNG itself. This -/// way one or two steps can be optimized out. -/// -/// The floats are first converted to a value in the `[1, 2)` interval using a -/// transmute-based method, and then mapped to the expected range with a -/// multiply and addition. Values produced this way have what equals 22 bits of -/// random digits for an `f32`, and 52 for an `f64`. -/// -/// [`new`]: UniformSampler::new -/// [`new_inclusive`]: UniformSampler::new_inclusive -/// [`Standard`]: crate::distributions::Standard -#[derive(Clone, Copy, Debug)] -pub struct UniformFloat<X> { - low: X, - scale: X, -} - -macro_rules! uniform_float_impl { - ($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 crate::Rng; - use crate::rngs::mock::StepRng; - use crate::distributions::uniform::Uniform; - use crate::distributions::utils::FloatAsSIMD; - #[cfg(feature="simd_support")] use packed_simd::*; - - #[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(not(miri))] // Miri is too slow - fn test_integers() { - use core::{i8, i16, i32, i64, isize}; - use core::{u8, u16, u32, u64, usize}; - #[cfg(not(target_os = "emscripten"))] - use core::{i128, u128}; - - 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: $ty, y| x.lt(y).all() - );)* - }}; - } - t!(i8, i16, i32, i64, isize, - u8, u16, u32, u64, usize); - #[cfg(not(target_os = "emscripten"))] - t!(i128, u128); - - #[cfg(all(feature = "simd_support", feature = "nightly"))] - { - t!(u8x2, u8x4, u8x8, u8x16, u8x32, u8x64 => u8); - t!(i8x2, i8x4, i8x8, i8x16, i8x32, i8x64 => i8); - t!(u16x2, u16x4, u16x8, u16x16, u16x32 => u16); - t!(i16x2, i16x4, i16x8, i16x16, i16x32 => i16); - t!(u32x2, u32x4, u32x8, u32x16 => u32); - t!(i32x2, i32x4, i32x8, i32x16 => i32); - t!(u64x2, u64x4, u64x8 => u64); - t!(i64x2, i64x4, i64x8 => i64); - } - } - - #[test] - #[cfg(not(miri))] // Miri is too slow - fn test_floats() { - let mut rng = crate::test::rng(252); - let mut zero_rng = StepRng::new(0, 0); - let mut max_rng = StepRng::new(0xffff_ffff_ffff_ffff, 0); - macro_rules! t { - ($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::$f_scalar::MAX); - }} - } - - t!(f32, f32, 32 - 23); - t!(f64, f64, 64 - 52); - #[cfg(feature="simd_support")] - { - t!(f32x2, f32, 32 - 23); - t!(f32x4, f32, 32 - 23); - t!(f32x8, f32, 32 - 23); - t!(f32x16, f32, 32 - 23); - t!(f64x2, f64, 64 - 52); - t!(f64x4, f64, 64 - 52); - t!(f64x8, f64, 64 - 52); - } - } - - #[test] - #[cfg(all(feature="std", - not(target_arch = "wasm32"), - not(target_arch = "asmjs")))] - #[cfg(not(miri))] // Miri does not support catching panics - fn test_float_assertions() { - use std::panic::catch_unwind; - use super::SampleUniform; - fn range<T: SampleUniform>(low: T, high: T) { - let mut rng = crate::test::rng(253); - rng.gen_range(low, high); - } - - macro_rules! t { - ($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(not(miri))] // Miri is too slow - fn test_durations() { - #[cfg(feature = "std")] - use std::time::Duration; - #[cfg(not(feature = "std"))] - use core::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::{UniformSampler, UniformFloat, SampleUniform, SampleBorrow}; - #[derive(Clone, Copy, PartialEq, PartialOrd)] - struct MyF32 { - x: f32, - } - #[derive(Clone, Copy, Debug)] - struct UniformMyF32 { - inner: 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 { - inner: 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.inner.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.inner.low, 2); - assert_eq!(r.inner.range, 5); - let r = Uniform::from(2.0f64..7.0); - assert_eq!(r.inner.low, 2.0); - assert_eq!(r.inner.scale, 5.0); - } - - #[test] - fn test_uniform_from_std_range_inclusive() { - let r = Uniform::from(2u32..=6); - assert_eq!(r.inner.low, 2); - assert_eq!(r.inner.range, 5); - let r = Uniform::from(2.0f64..=7.0); - assert_eq!(r.inner.low, 2.0); - assert!(r.inner.scale > 5.0); - assert!(r.inner.scale < 5.0 + 1e-14); - } -} diff --git a/rand/src/distributions/unit_circle.rs b/rand/src/distributions/unit_circle.rs deleted file mode 100644 index 56e75b6..0000000 --- a/rand/src/distributions/unit_circle.rs +++ /dev/null @@ -1,101 +0,0 @@ -// 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::Rng; -use crate::distributions::{Distribution, Uniform}; - -/// 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 crate::distributions::Distribution; - use super::UnitCircle; - - /// 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/rand/src/distributions/unit_sphere.rs b/rand/src/distributions/unit_sphere.rs deleted file mode 100644 index 188f48c..0000000 --- a/rand/src/distributions/unit_sphere.rs +++ /dev/null @@ -1,96 +0,0 @@ -// 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::Rng; -use crate::distributions::{Distribution, Uniform}; - -/// 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 crate::distributions::Distribution; - use super::UnitSphereSurface; - - /// 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, $b)); - } - ); - } - - #[test] - fn norm() { - let mut rng = crate::test::rng(1); - let dist = UnitSphereSurface::new(); - for _ in 0..1000 { - let x = dist.sample(&mut rng); - assert_almost_eq!(x[0]*x[0] + x[1]*x[1] + x[2]*x[2], 1., 1e-15); - } - } - - #[test] - fn value_stability() { - let mut rng = crate::test::rng(2); - let expected = [ - [0.03247542860231647, -0.7830477442152738, 0.6211131755296027], - [-0.09978440840914075, 0.9706650829833128, -0.21875184231323952], - [0.2735582468624679, 0.9435374242279655, -0.1868234852870203], - ]; - let samples = [ - UnitSphereSurface.sample(&mut rng), - UnitSphereSurface.sample(&mut rng), - UnitSphereSurface.sample(&mut rng), - ]; - assert_eq!(samples, expected); - } -} diff --git a/rand/src/distributions/utils.rs b/rand/src/distributions/utils.rs deleted file mode 100644 index 3af4e86..0000000 --- a/rand/src/distributions/utils.rs +++ /dev/null @@ -1,488 +0,0 @@ -// Copyright 2018 Developers of the Rand project. -// -// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or -// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license -// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your -// option. This file may not be copied, modified, or distributed -// except according to those terms. - -//! Math helper functions - -#[cfg(feature="simd_support")] -use packed_simd::*; -#[cfg(feature="std")] -use crate::distributions::ziggurat_tables; -#[cfg(feature="std")] -use crate::Rng; - - -pub trait WideningMultiply<RHS = Self> { - type Output; - - fn wmul(self, x: RHS) -> Self::Output; -} - -macro_rules! wmul_impl { - ($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 $ty); - (high as usize, low as usize) - } - } - } -} -#[cfg(target_pointer_width = "32")] -wmul_impl_usize! { u32 } -#[cfg(target_pointer_width = "64")] -wmul_impl_usize! { u64 } - -#[cfg(all(feature = "simd_support", feature = "nightly"))] -mod simd_wmul { - #[cfg(target_arch = "x86")] - use core::arch::x86::*; - #[cfg(target_arch = "x86_64")] - use core::arch::x86_64::*; - use super::*; - - wmul_impl! { - (u8x2, u16x2), - (u8x4, u16x4), - (u8x8, u16x8), - (u8x16, u16x16), - (u8x32, u16x32),, - 8 - } - - wmul_impl! { (u16x2, u32x2),, 16 } - #[cfg(not(target_feature = "sse2"))] - wmul_impl! { (u16x4, u32x4),, 16 } - #[cfg(not(target_feature = "sse4.2"))] - wmul_impl! { (u16x8, u32x8),, 16 } - #[cfg(not(target_feature = "avx2"))] - wmul_impl! { (u16x16, u32x16),, 16 } - - // 16-bit lane widths allow use of the x86 `mulhi` instructions, which - // means `wmul` can be implemented with only two instructions. - #[allow(unused_macros)] - macro_rules! wmul_impl_16 { - ($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 $ty { - type Mask = bool; - #[inline(always)] - fn all_lt(self, other: Self) -> bool { self < other } - #[inline(always)] - fn all_le(self, other: Self) -> bool { self <= other } - #[inline(always)] - fn all_finite(self) -> bool { self.is_finite() } - #[inline(always)] - fn finite_mask(self) -> Self::Mask { self.is_finite() } - #[inline(always)] - fn gt_mask(self, other: Self) -> Self::Mask { self > other } - #[inline(always)] - fn ge_mask(self, other: Self) -> Self::Mask { self >= other } - #[inline(always)] - fn decrease_masked(self, mask: Self::Mask) -> Self { - debug_assert!(mask, "At least one lane must be set"); - <$ty>::from_bits(self.to_bits() - 1) - } - type UInt = $uty; - 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; - #[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)) - } - type UInt = $uty; - #[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/rand/src/distributions/weibull.rs b/rand/src/distributions/weibull.rs deleted file mode 100644 index 483714f..0000000 --- a/rand/src/distributions/weibull.rs +++ /dev/null @@ -1,64 +0,0 @@ -// 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::Rng; -use crate::distributions::{Distribution, OpenClosed01}; - -/// 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 crate::distributions::Distribution; - use super::Weibull; - - #[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/rand/src/distributions/weighted/alias_method.rs b/rand/src/distributions/weighted/alias_method.rs deleted file mode 100644 index bdd4ba0..0000000 --- a/rand/src/distributions/weighted/alias_method.rs +++ /dev/null @@ -1,499 +0,0 @@ -//! 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::Vec; -#[cfg(not(feature = "std"))] -use crate::alloc::vec; -use core::fmt; -use core::iter::Sum; -use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign}; -use crate::distributions::uniform::SampleUniform; -use crate::distributions::Distribution; -use crate::distributions::Uniform; -use crate::Rng; - -/// 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(not(miri))] // 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(not(miri))] // 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(not(miri))] // 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(not(miri))] // Miri is too slow - fn test_weighted_index_u8() { - test_weighted_index(u8::into); - } - - #[test] - #[cfg(not(miri))] // 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 - ); - } -} diff --git a/rand/src/distributions/weighted/mod.rs b/rand/src/distributions/weighted/mod.rs deleted file mode 100644 index 2711637..0000000 --- a/rand/src/distributions/weighted/mod.rs +++ /dev/null @@ -1,363 +0,0 @@ -// 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::Rng; -use crate::distributions::Distribution; -use crate::distributions::uniform::{UniformSampler, SampleUniform, SampleBorrow}; -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(not(miri))] // 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.into_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); - } - } -} - -/// 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, -} - -impl WeightedError { - fn msg(&self) -> &str { - match *self { - WeightedError::NoItem => "No weights provided.", - WeightedError::InvalidWeight => "A weight is invalid.", - WeightedError::AllWeightsZero => "All weights are zero.", - WeightedError::TooMany => "Too many weights (hit u32::MAX)", - } - } -} - -#[cfg(feature="std")] -impl ::std::error::Error for WeightedError { - fn description(&self) -> &str { - self.msg() - } - fn cause(&self) -> Option<&dyn (::std::error::Error)> { - None - } -} - -impl fmt::Display for WeightedError { - fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { - write!(f, "{}", self.msg()) - } -} diff --git a/rand/src/distributions/ziggurat_tables.rs b/rand/src/distributions/ziggurat_tables.rs deleted file mode 100644 index ca1ce30..0000000 --- a/rand/src/distributions/ziggurat_tables.rs +++ /dev/null @@ -1,279 +0,0 @@ -// 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; -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]; -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; -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, - 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