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-rw-r--r--rand/src/distributions/bernoulli.rs165
-rw-r--r--rand/src/distributions/binomial.rs177
-rw-r--r--rand/src/distributions/cauchy.rs115
-rw-r--r--rand/src/distributions/dirichlet.rs137
-rw-r--r--rand/src/distributions/exponential.rs124
-rw-r--r--rand/src/distributions/float.rs259
-rw-r--r--rand/src/distributions/gamma.rs413
-rw-r--r--rand/src/distributions/integer.rs161
-rw-r--r--rand/src/distributions/mod.rs621
-rw-r--r--rand/src/distributions/normal.rs197
-rw-r--r--rand/src/distributions/other.rs219
-rw-r--r--rand/src/distributions/pareto.rs74
-rw-r--r--rand/src/distributions/poisson.rs157
-rw-r--r--rand/src/distributions/triangular.rs86
-rw-r--r--rand/src/distributions/uniform.rs1298
-rw-r--r--rand/src/distributions/unit_circle.rs101
-rw-r--r--rand/src/distributions/unit_sphere.rs99
-rw-r--r--rand/src/distributions/utils.rs504
-rw-r--r--rand/src/distributions/weibull.rs71
-rw-r--r--rand/src/distributions/weighted.rs232
-rw-r--r--rand/src/distributions/ziggurat_tables.rs279
21 files changed, 0 insertions, 5489 deletions
diff --git a/rand/src/distributions/bernoulli.rs b/rand/src/distributions/bernoulli.rs
deleted file mode 100644
index f49618c..0000000
--- a/rand/src/distributions/bernoulli.rs
+++ /dev/null
@@ -1,165 +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 Rng;
-use distributions::Distribution;
-
-/// The Bernoulli distribution.
-///
-/// This is a special case of the Binomial distribution where `n = 1`.
-///
-/// # Example
-///
-/// ```rust
-/// use rand::distributions::{Bernoulli, Distribution};
-///
-/// let d = Bernoulli::new(0.3);
-/// let v = d.sample(&mut rand::thread_rng());
-/// println!("{} is from a Bernoulli distribution", v);
-/// ```
-///
-/// # Precision
-///
-/// This `Bernoulli` distribution uses 64 bits from the RNG (a `u64`),
-/// so only probabilities that are multiples of 2<sup>-64</sup> can be
-/// represented.
-#[derive(Clone, Copy, Debug)]
-pub struct Bernoulli {
- /// Probability of success, relative to the maximal integer.
- p_int: u64,
-}
-
-// To sample from the Bernoulli distribution we use a method that compares a
-// random `u64` value `v < (p * 2^64)`.
-//
-// If `p == 1.0`, the integer `v` to compare against can not represented as a
-// `u64`. We manually set it to `u64::MAX` instead (2^64 - 1 instead of 2^64).
-// Note that value of `p < 1.0` can never result in `u64::MAX`, because an
-// `f64` only has 53 bits of precision, and the next largest value of `p` will
-// result in `2^64 - 2048`.
-//
-// Also there is a 100% theoretical concern: if someone consistenly wants to
-// generate `true` using the Bernoulli distribution (i.e. by using a probability
-// of `1.0`), just using `u64::MAX` is not enough. On average it would return
-// false once every 2^64 iterations. Some people apparently care about this
-// case.
-//
-// That is why we special-case `u64::MAX` to always return `true`, without using
-// the RNG, and pay the performance price for all uses that *are* reasonable.
-// Luckily, if `new()` and `sample` are close, the compiler can optimize out the
-// extra check.
-const ALWAYS_TRUE: u64 = ::core::u64::MAX;
-
-// This is just `2.0.powi(64)`, but written this way because it is not available
-// in `no_std` mode.
-const SCALE: f64 = 2.0 * (1u64 << 63) as f64;
-
-impl Bernoulli {
- /// Construct a new `Bernoulli` with the given probability of success `p`.
- ///
- /// # Panics
- ///
- /// If `p < 0` or `p > 1`.
- ///
- /// # Precision
- ///
- /// For `p = 1.0`, the resulting distribution will always generate true.
- /// For `p = 0.0`, the resulting distribution will always generate false.
- ///
- /// This method is accurate for any input `p` in the range `[0, 1]` which is
- /// a multiple of 2<sup>-64</sup>. (Note that not all multiples of
- /// 2<sup>-64</sup> in `[0, 1]` can be represented as a `f64`.)
- #[inline]
- pub fn new(p: f64) -> Bernoulli {
- if p < 0.0 || p >= 1.0 {
- if p == 1.0 { return Bernoulli { p_int: ALWAYS_TRUE } }
- panic!("Bernoulli::new not called with 0.0 <= p <= 1.0");
- }
- Bernoulli { p_int: (p * SCALE) as u64 }
- }
-
- /// Construct a new `Bernoulli` with the probability of success of
- /// `numerator`-in-`denominator`. I.e. `new_ratio(2, 3)` will return
- /// a `Bernoulli` with a 2-in-3 chance, or about 67%, of returning `true`.
- ///
- /// If `numerator == denominator` then the returned `Bernoulli` will always
- /// return `true`. If `numerator == 0` it will always return `false`.
- ///
- /// # Panics
- ///
- /// If `denominator == 0` or `numerator > denominator`.
- ///
- #[inline]
- pub fn from_ratio(numerator: u32, denominator: u32) -> Bernoulli {
- assert!(numerator <= denominator);
- if numerator == denominator {
- return Bernoulli { p_int: ::core::u64::MAX }
- }
- let p_int = ((numerator as f64 / denominator as f64) * SCALE) as u64;
- Bernoulli { p_int }
- }
-}
-
-impl Distribution<bool> for Bernoulli {
- #[inline]
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> bool {
- // Make sure to always return true for p = 1.0.
- if self.p_int == ALWAYS_TRUE { return true; }
- let v: u64 = rng.gen();
- v < self.p_int
- }
-}
-
-#[cfg(test)]
-mod test {
- use Rng;
- use distributions::Distribution;
- use super::Bernoulli;
-
- #[test]
- fn test_trivial() {
- let mut r = ::test::rng(1);
- let always_false = Bernoulli::new(0.0);
- let always_true = Bernoulli::new(1.0);
- for _ in 0..5 {
- assert_eq!(r.sample::<bool, _>(&always_false), false);
- assert_eq!(r.sample::<bool, _>(&always_true), true);
- assert_eq!(Distribution::<bool>::sample(&always_false, &mut r), false);
- assert_eq!(Distribution::<bool>::sample(&always_true, &mut r), true);
- }
- }
-
- #[test]
- fn test_average() {
- const P: f64 = 0.3;
- const NUM: u32 = 3;
- const DENOM: u32 = 10;
- let d1 = Bernoulli::new(P);
- let d2 = Bernoulli::from_ratio(NUM, DENOM);
- const N: u32 = 100_000;
-
- let mut sum1: u32 = 0;
- let mut sum2: u32 = 0;
- let mut rng = ::test::rng(2);
- for _ in 0..N {
- if d1.sample(&mut rng) {
- sum1 += 1;
- }
- if d2.sample(&mut rng) {
- sum2 += 1;
- }
- }
- let avg1 = (sum1 as f64) / (N as f64);
- assert!((avg1 - P).abs() < 5e-3);
-
- let avg2 = (sum2 as f64) / (N as f64);
- assert!((avg2 - (NUM as f64)/(DENOM as f64)).abs() < 5e-3);
- }
-}
diff --git a/rand/src/distributions/binomial.rs b/rand/src/distributions/binomial.rs
deleted file mode 100644
index 2df393e..0000000
--- a/rand/src/distributions/binomial.rs
+++ /dev/null
@@ -1,177 +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.
-
-use Rng;
-use distributions::{Distribution, Bernoulli, Cauchy};
-use distributions::utils::log_gamma;
-
-/// 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`.
-///
-/// # Example
-///
-/// ```
-/// use rand::distributions::{Binomial, Distribution};
-///
-/// let bin = Binomial::new(20, 0.3);
-/// let v = bin.sample(&mut rand::thread_rng());
-/// println!("{} is from a binomial distribution", v);
-/// ```
-#[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 }
- }
-}
-
-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;
- }
-
- // For low n, it is faster to sample directly. For both methods,
- // performance is independent of p. On Intel Haswell CPU this method
- // appears to be faster for approx n < 300.
- if self.n < 300 {
- let mut result = 0;
- let d = Bernoulli::new(self.p);
- for _ in 0 .. self.n {
- result += rng.sample(d) as u32;
- }
- return result as u64;
- }
-
- // 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
- };
-
- // prepare some cached values
- let float_n = self.n as f64;
- let ln_fact_n = log_gamma(float_n + 1.0);
- let pc = 1.0 - p;
- let log_p = p.ln();
- let log_pc = pc.ln();
- let expected = self.n as f64 * p;
- let sq = (expected * (2.0 * pc)).sqrt();
-
- let mut lresult;
-
- // 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 comp_dev: f64;
- loop {
- // draw from the Cauchy distribution
- comp_dev = rng.sample(cauchy);
- // shift the peak of the comparison ditribution
- lresult = expected + sq * comp_dev;
- // repeat the drawing until we are in the range of possible values
- if lresult >= 0.0 && lresult < float_n + 1.0 {
- break;
- }
- }
-
- // the result should be discrete
- lresult = lresult.floor();
-
- let log_binomial_dist = ln_fact_n - log_gamma(lresult+1.0) -
- log_gamma(float_n - lresult + 1.0) + lresult*log_p + (float_n - lresult)*log_pc;
- // this is the binomial probability divided by the comparison probability
- // we will generate a uniform random value and if it is larger than this,
- // we interpret it as a value falling out of the distribution and repeat
- let comparison_coeff = (log_binomial_dist.exp() * sq) * (1.2 * (1.0 + comp_dev*comp_dev));
-
- if comparison_coeff >= rng.gen() {
- break;
- }
- }
-
- // invert the result for p < 0.5
- if p != self.p {
- self.n - lresult as u64
- } else {
- lresult as u64
- }
- }
-}
-
-#[cfg(test)]
-mod test {
- use Rng;
- use 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);
-
- 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);
- }
-
- #[test]
- fn test_binomial() {
- let mut rng = ::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 = ::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 feef015..0000000
--- a/rand/src/distributions/cauchy.rs
+++ /dev/null
@@ -1,115 +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.
-
-use Rng;
-use 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))`
-///
-/// # Example
-///
-/// ```
-/// use rand::distributions::{Cauchy, Distribution};
-///
-/// let cau = Cauchy::new(2.0, 5.0);
-/// let v = cau.sample(&mut rand::thread_rng());
-/// println!("{} is from a Cauchy(2, 5) distribution", v);
-/// ```
-#[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 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]
- fn test_cauchy_median() {
- let cauchy = Cauchy::new(10.0, 5.0);
- let mut rng = ::test::rng(123);
- let mut numbers: [f64; 1000] = [0.0; 1000];
- for i in 0..1000 {
- numbers[i] = cauchy.sample(&mut rng);
- }
- let median = median(&mut numbers);
- println!("Cauchy median: {}", median);
- assert!((median - 10.0).abs() < 0.5); // not 100% certain, but probable enough
- }
-
- #[test]
- fn test_cauchy_mean() {
- let cauchy = Cauchy::new(10.0, 5.0);
- let mut rng = ::test::rng(123);
- let mut sum = 0.0;
- for _ in 0..1000 {
- sum += cauchy.sample(&mut rng);
- }
- let mean = sum / 1000.0;
- println!("Cauchy mean: {}", mean);
- // for a Cauchy distribution the mean should not converge
- assert!((mean - 10.0).abs() > 0.5); // 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 19384b8..0000000
--- a/rand/src/distributions/dirichlet.rs
+++ /dev/null
@@ -1,137 +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.
-
-use Rng;
-use distributions::Distribution;
-use 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.
-///
-/// # Example
-///
-/// ```
-/// use rand::prelude::*;
-/// use rand::distributions::Dirichlet;
-///
-/// let dirichlet = Dirichlet::new(vec![1.0, 2.0, 3.0]);
-/// let samples = dirichlet.sample(&mut rand::thread_rng());
-/// println!("{:?} is from a Dirichlet([1.0, 2.0, 3.0]) distribution", samples);
-/// ```
-
-#[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 distributions::Distribution;
-
- #[test]
- fn test_dirichlet() {
- let d = Dirichlet::new(vec![1.0, 2.0, 3.0]);
- let mut rng = ::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 = ::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 a7d0500..0000000
--- a/rand/src/distributions/exponential.rs
+++ /dev/null
@@ -1,124 +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.
-
-use {Rng};
-use distributions::{ziggurat_tables, Distribution};
-use 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
-///
-/// # Example
-/// ```
-/// use rand::prelude::*;
-/// use rand::distributions::Exp1;
-///
-/// let val: f64 = SmallRng::from_entropy().sample(Exp1);
-/// println!("{}", val);
-/// ```
-#[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`](struct.Exp1.html) is an optimised implementation for `lambda = 1`.
-///
-/// # Example
-///
-/// ```
-/// use rand::distributions::{Exp, Distribution};
-///
-/// let exp = Exp::new(2.0);
-/// let v = exp.sample(&mut rand::thread_rng());
-/// println!("{} is from a Exp(2) distribution", v);
-/// ```
-#[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 distributions::Distribution;
- use super::Exp;
-
- #[test]
- fn test_exp() {
- let exp = Exp::new(10.0);
- let mut rng = ::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 ece12f5..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 Rng;
-use distributions::{Distribution, Standard};
-use 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`]: struct.Standard.html
-/// [`Open01`]: struct.Open01.html
-/// [`Uniform`]: uniform/struct.Uniform.html
-#[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`]: struct.Standard.html
-/// [`OpenClosed01`]: struct.OpenClosed01.html
-/// [`Uniform`]: uniform/struct.Uniform.html
-#[derive(Clone, Copy, Debug)]
-pub struct Open01;
-
-
-pub(crate) 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;
- // TODO: use from_bits when min compiler > 1.25 (see #545)
- // $ty::from_bits(self | exponent_bits)
- unsafe{ mem::transmute(self | exponent_bits) }
- }
- }
-
- impl Distribution<$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 - $fraction_bits);
- fraction.into_float_with_exponent(0) - (1.0 - EPSILON / 2.0)
- }
- }
- }
-}
-
-float_impls! { f32, u32, f32, u32, 23, 127 }
-float_impls! { f64, u64, f64, u64, 52, 1023 }
-
-#[cfg(feature="simd_support")]
-float_impls! { f32x2, u32x2, f32, u32, 23, 127 }
-#[cfg(feature="simd_support")]
-float_impls! { f32x4, u32x4, f32, u32, 23, 127 }
-#[cfg(feature="simd_support")]
-float_impls! { f32x8, u32x8, f32, u32, 23, 127 }
-#[cfg(feature="simd_support")]
-float_impls! { f32x16, u32x16, f32, u32, 23, 127 }
-
-#[cfg(feature="simd_support")]
-float_impls! { f64x2, u64x2, f64, u64, 52, 1023 }
-#[cfg(feature="simd_support")]
-float_impls! { f64x4, u64x4, f64, u64, 52, 1023 }
-#[cfg(feature="simd_support")]
-float_impls! { f64x8, u64x8, f64, u64, 52, 1023 }
-
-
-#[cfg(test)]
-mod tests {
- use Rng;
- use distributions::{Open01, OpenClosed01};
- use rngs::mock::StepRng;
- #[cfg(feature="simd_support")]
- use packed_simd::*;
-
- const EPSILON32: f32 = ::core::f32::EPSILON;
- const EPSILON64: f64 = ::core::f64::EPSILON;
-
- macro_rules! test_f32 {
- ($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 43ac2bc..0000000
--- a/rand/src/distributions/gamma.rs
+++ /dev/null
@@ -1,413 +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.
-
-use self::GammaRepr::*;
-use self::ChiSquaredRepr::*;
-
-use Rng;
-use distributions::normal::StandardNormal;
-use 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`.
-///
-/// # Example
-///
-/// ```
-/// use rand::distributions::{Distribution, Gamma};
-///
-/// let gamma = Gamma::new(2.0, 5.0);
-/// let v = gamma.sample(&mut rand::thread_rng());
-/// println!("{} is from a Gamma(2, 5) distribution", v);
-/// ```
-///
-/// [^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)
-#[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)`.
-///
-/// # Example
-///
-/// ```
-/// use rand::distributions::{ChiSquared, Distribution};
-///
-/// let chi = ChiSquared::new(11.0);
-/// let v = chi.sample(&mut rand::thread_rng());
-/// println!("{} is from a χ²(11) distribution", v)
-/// ```
-#[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)`.
-///
-/// # Example
-///
-/// ```
-/// use rand::distributions::{FisherF, Distribution};
-///
-/// let f = FisherF::new(2.0, 32.0);
-/// let v = f.sample(&mut rand::thread_rng());
-/// println!("{} is from an F(2, 32) distribution", v)
-/// ```
-#[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.
-///
-/// # Example
-///
-/// ```
-/// use rand::distributions::{StudentT, Distribution};
-///
-/// let t = StudentT::new(11.0);
-/// let v = t.sample(&mut rand::thread_rng());
-/// println!("{} is from a t(11) distribution", v)
-/// ```
-#[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`.
-///
-/// # Example
-///
-/// ```
-/// use rand::distributions::{Distribution, Beta};
-///
-/// let beta = Beta::new(2.0, 5.0);
-/// let v = beta.sample(&mut rand::thread_rng());
-/// println!("{} is from a Beta(2, 5) distribution", v);
-/// ```
-#[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 distributions::Distribution;
- use super::{Beta, ChiSquared, StudentT, FisherF};
-
- #[test]
- fn test_chi_squared_one() {
- let chi = ChiSquared::new(1.0);
- let mut rng = ::test::rng(201);
- for _ in 0..1000 {
- chi.sample(&mut rng);
- }
- }
- #[test]
- fn test_chi_squared_small() {
- let chi = ChiSquared::new(0.5);
- let mut rng = ::test::rng(202);
- for _ in 0..1000 {
- chi.sample(&mut rng);
- }
- }
- #[test]
- fn test_chi_squared_large() {
- let chi = ChiSquared::new(30.0);
- let mut rng = ::test::rng(203);
- for _ in 0..1000 {
- 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 = ::test::rng(204);
- for _ in 0..1000 {
- f.sample(&mut rng);
- }
- }
-
- #[test]
- fn test_t() {
- let t = StudentT::new(11.0);
- let mut rng = ::test::rng(205);
- for _ in 0..1000 {
- t.sample(&mut rng);
- }
- }
-
- #[test]
- fn test_beta() {
- let beta = Beta::new(1.0, 2.0);
- let mut rng = ::test::rng(201);
- for _ in 0..1000 {
- 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 7e408db..0000000
--- a/rand/src/distributions/integer.rs
+++ /dev/null
@@ -1,161 +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 {Rng};
-use distributions::{Distribution, Standard};
-#[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(all(rustc_1_26, 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 = rng.next_u64() as u128;
- let y = rng.next_u64() as u128;
- (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 $ty
- }
- }
- }
-}
-
-impl_int_from_uint! { i8, u8 }
-impl_int_from_uint! { i16, u16 }
-impl_int_from_uint! { i32, u32 }
-impl_int_from_uint! { i64, u64 }
-#[cfg(all(rustc_1_26, not(target_os = "emscripten")))] impl_int_from_uint! { i128, u128 }
-impl_int_from_uint! { isize, usize }
-
-#[cfg(feature="simd_support")]
-macro_rules! simd_impl {
- ($(($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 Rng;
- use distributions::{Standard};
-
- #[test]
- fn test_integers() {
- let mut rng = ::test::rng(806);
-
- rng.sample::<isize, _>(Standard);
- rng.sample::<i8, _>(Standard);
- rng.sample::<i16, _>(Standard);
- rng.sample::<i32, _>(Standard);
- rng.sample::<i64, _>(Standard);
- #[cfg(all(rustc_1_26, 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(all(rustc_1_26, 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 5e879cb..0000000
--- a/rand/src/distributions/mod.rs
+++ /dev/null
@@ -1,621 +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, including [`gen`], [`gen_range`] and
-//! of course [`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.
-//!
-//!
-//! # Distribution to sample from a `Uniform` range
-//!
-//! 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`].
-//!
-//!
-//! # Other distributions
-//!
-//! 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] for
-//! more details.
-//!
-//! [`Alphanumeric`] is a simple distribution to sample random letters and
-//! numbers of the `char` type; in contrast [`Standard`] may sample any valid
-//! `char`.
-//!
-//! [`WeightedIndex`] can be used to do weighted sampling from a set of items,
-//! such as from an array.
-//!
-//! # Non-uniform probability distributions
-//!
-//! Rand currently provides the following probability distributions:
-//!
-//! - Related to real-valued quantities that grow linearly
-//! (e.g. errors, offsets):
-//! - [`Normal`] distribution, and [`StandardNormal`] as a primitive
-//! - [`Cauchy`] distribution
-//! - Related to Bernoulli trials (yes/no events, with a given probability):
-//! - [`Binomial`] distribution
-//! - [`Bernoulli`] distribution, similar to [`Rng::gen_bool`].
-//! - Related to positive real-valued quantities that grow exponentially
-//! (e.g. prices, incomes, populations):
-//! - [`LogNormal`] distribution
-//! - Related to the occurrence of independent events at a given rate:
-//! - [`Pareto`] distribution
-//! - [`Poisson`] distribution
-//! - [`Exp`]onential distribution, and [`Exp1`] as a primitive
-//! - [`Weibull`] distribution
-//! - Gamma and derived distributions:
-//! - [`Gamma`] distribution
-//! - [`ChiSquared`] distribution
-//! - [`StudentT`] distribution
-//! - [`FisherF`] distribution
-//! - Triangular distribution:
-//! - [`Beta`] distribution
-//! - [`Triangular`] distribution
-//! - Multivariate probability distributions
-//! - [`Dirichlet`] distribution
-//! - [`UnitSphereSurface`] distribution
-//! - [`UnitCircle`] distribution
-//!
-//! # Examples
-//!
-//! Sampling from a distribution:
-//!
-//! ```
-//! use rand::{thread_rng, Rng};
-//! use rand::distributions::Exp;
-//!
-//! let exp = Exp::new(2.0);
-//! let v = thread_rng().sample(exp);
-//! println!("{} is from an Exp(2) distribution", v);
-//! ```
-//!
-//! Implementing the [`Standard`] distribution for a user type:
-//!
-//! ```
-//! # #![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() }
-//! }
-//! }
-//! ```
-//!
-//!
-//! [probability distribution]: https://en.wikipedia.org/wiki/Probability_distribution
-//! [`Distribution`]: trait.Distribution.html
-//! [`gen_range`]: ../trait.Rng.html#method.gen_range
-//! [`gen`]: ../trait.Rng.html#method.gen
-//! [`sample`]: ../trait.Rng.html#method.sample
-//! [`new_inclusive`]: struct.Uniform.html#method.new_inclusive
-//! [`random()`]: ../fn.random.html
-//! [`Rng::gen_bool`]: ../trait.Rng.html#method.gen_bool
-//! [`Rng::gen_range`]: ../trait.Rng.html#method.gen_range
-//! [`Rng::gen()`]: ../trait.Rng.html#method.gen
-//! [`Rng`]: ../trait.Rng.html
-//! [`uniform` module]: uniform/index.html
-//! [Floating point implementation]: struct.Standard.html#floating-point-implementation
-// distributions
-//! [`Alphanumeric`]: struct.Alphanumeric.html
-//! [`Bernoulli`]: struct.Bernoulli.html
-//! [`Beta`]: struct.Beta.html
-//! [`Binomial`]: struct.Binomial.html
-//! [`Cauchy`]: struct.Cauchy.html
-//! [`ChiSquared`]: struct.ChiSquared.html
-//! [`Dirichlet`]: struct.Dirichlet.html
-//! [`Exp`]: struct.Exp.html
-//! [`Exp1`]: struct.Exp1.html
-//! [`FisherF`]: struct.FisherF.html
-//! [`Gamma`]: struct.Gamma.html
-//! [`LogNormal`]: struct.LogNormal.html
-//! [`Normal`]: struct.Normal.html
-//! [`Open01`]: struct.Open01.html
-//! [`OpenClosed01`]: struct.OpenClosed01.html
-//! [`Pareto`]: struct.Pareto.html
-//! [`Poisson`]: struct.Poisson.html
-//! [`Standard`]: struct.Standard.html
-//! [`StandardNormal`]: struct.StandardNormal.html
-//! [`StudentT`]: struct.StudentT.html
-//! [`Triangular`]: struct.Triangular.html
-//! [`Uniform`]: struct.Uniform.html
-//! [`Uniform::new`]: struct.Uniform.html#method.new
-//! [`Uniform::new_inclusive`]: struct.Uniform.html#method.new_inclusive
-//! [`UnitSphereSurface`]: struct.UnitSphereSurface.html
-//! [`UnitCircle`]: struct.UnitCircle.html
-//! [`Weibull`]: struct.Weibull.html
-//! [`WeightedIndex`]: struct.WeightedIndex.html
-
-#[cfg(any(rustc_1_26, features="nightly"))]
-use core::iter;
-use Rng;
-
-pub use self::other::Alphanumeric;
-#[doc(inline)] pub use self::uniform::Uniform;
-pub use self::float::{OpenClosed01, Open01};
-pub use self::bernoulli::Bernoulli;
-#[cfg(feature="alloc")] pub use self::weighted::{WeightedIndex, WeightedError};
-#[cfg(feature="std")] pub use self::unit_sphere::UnitSphereSurface;
-#[cfg(feature="std")] pub use self::unit_circle::UnitCircle;
-#[cfg(feature="std")] pub use self::gamma::{Gamma, ChiSquared, FisherF,
- StudentT, Beta};
-#[cfg(feature="std")] pub use self::normal::{Normal, LogNormal, StandardNormal};
-#[cfg(feature="std")] pub use self::exponential::{Exp, Exp1};
-#[cfg(feature="std")] pub use self::pareto::Pareto;
-#[cfg(feature="std")] pub use self::poisson::Poisson;
-#[cfg(feature="std")] pub use self::binomial::Binomial;
-#[cfg(feature="std")] pub use self::cauchy::Cauchy;
-#[cfg(feature="std")] pub use self::dirichlet::Dirichlet;
-#[cfg(feature="std")] pub use self::triangular::Triangular;
-#[cfg(feature="std")] pub use self::weibull::Weibull;
-
-pub mod uniform;
-mod bernoulli;
-#[cfg(feature="alloc")] 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;
-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.
-///
-/// [`Rng`]: ../trait.Rng.html
-/// [`sample_iter`]: trait.Distribution.html#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.
- ///
- /// # Example
- ///
- /// ```
- /// use rand::thread_rng;
- /// use rand::distributions::{Distribution, Alphanumeric, Uniform, Standard};
- ///
- /// let mut rng = thread_rng();
- ///
- /// // Vec of 16 x f32:
- /// let v: Vec<f32> = Standard.sample_iter(&mut rng).take(16).collect();
- ///
- /// // String:
- /// let s: String = Alphanumeric.sample_iter(&mut rng).take(7).collect();
- ///
- /// // Dice-rolling:
- /// let die_range = Uniform::new_inclusive(1, 6);
- /// let mut roll_die = die_range.sample_iter(&mut rng);
- /// while roll_die.next().unwrap() != 6 {
- /// println!("Not a 6; rolling again!");
- /// }
- /// ```
- fn sample_iter<'a, R>(&'a self, rng: &'a mut R) -> DistIter<'a, Self, R, T>
- where Self: Sized, R: Rng
- {
- DistIter {
- distr: self,
- rng: 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.
-///
-/// [`Distribution`]: trait.Distribution.html
-/// [`sample_iter`]: trait.Distribution.html#method.sample_iter
-#[derive(Debug)]
-pub struct DistIter<'a, D: 'a, R: 'a, T> {
- distr: &'a D,
- rng: &'a mut R,
- phantom: ::core::marker::PhantomData<T>,
-}
-
-impl<'a, D, R, T> Iterator for DistIter<'a, D, R, T>
- where D: Distribution<T>, R: Rng + 'a
-{
- type Item = T;
-
- #[inline(always)]
- fn next(&mut self) -> Option<T> {
- Some(self.distr.sample(self.rng))
- }
-
- fn size_hint(&self) -> (usize, Option<usize>) {
- (usize::max_value(), None)
- }
-}
-
-#[cfg(rustc_1_26)]
-impl<'a, D, R, T> iter::FusedIterator for DistIter<'a, D, R, T>
- where D: Distribution<T>, R: Rng + 'a {}
-
-#[cfg(features = "nightly")]
-impl<'a, D, R, T> iter::TrustedLen for DistIter<'a, D, R, T>
- where D: Distribution<T>, R: Rng + 'a {}
-
-
-/// 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.
-///
-/// ## Built-in 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 following aggregate types also implement the distribution `Standard` as
-/// long as their component types implement it:
-///
-/// * Tuples and arrays: Each element of the tuple or array is generated
-/// independently, using the `Standard` distribution recursively.
-/// * `Option<T>` where `Standard` is implemented for `T`: Returns `None` with
-/// probability 0.5; otherwise generates a random `x: T` and returns `Some(x)`.
-///
-/// # Example
-/// ```
-/// use rand::prelude::*;
-/// use rand::distributions::Standard;
-///
-/// let val: f32 = SmallRng::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).
-///
-/// [`Open01`]: struct.Open01.html
-/// [`OpenClosed01`]: struct.OpenClosed01.html
-/// [`Uniform`]: uniform/struct.Uniform.html
-#[derive(Clone, Copy, Debug)]
-pub struct Standard;
-
-
-/// A value with a particular weight for use with `WeightedChoice`.
-#[deprecated(since="0.6.0", note="use WeightedIndex instead")]
-#[allow(deprecated)]
-#[derive(Copy, Clone, Debug)]
-pub struct Weighted<T> {
- /// The numerical weight of this item
- pub weight: u32,
- /// The actual item which is being weighted
- pub item: T,
-}
-
-/// A distribution that selects from a finite collection of weighted items.
-///
-/// Deprecated: use [`WeightedIndex`] instead.
-///
-/// [`WeightedIndex`]: struct.WeightedIndex.html
-#[deprecated(since="0.6.0", note="use WeightedIndex instead")]
-#[allow(deprecated)]
-#[derive(Debug)]
-pub struct WeightedChoice<'a, T:'a> {
- items: &'a mut [Weighted<T>],
- weight_range: Uniform<u32>,
-}
-
-#[deprecated(since="0.6.0", note="use WeightedIndex instead")]
-#[allow(deprecated)]
-impl<'a, T: Clone> WeightedChoice<'a, T> {
- /// Create a new `WeightedChoice`.
- ///
- /// Panics if:
- ///
- /// - `items` is empty
- /// - the total weight is 0
- /// - the total weight is larger than a `u32` can contain.
- pub fn new(items: &'a mut [Weighted<T>]) -> WeightedChoice<'a, T> {
- // strictly speaking, this is subsumed by the total weight == 0 case
- assert!(!items.is_empty(), "WeightedChoice::new called with no items");
-
- let mut running_total: u32 = 0;
-
- // we convert the list from individual weights to cumulative
- // weights so we can binary search. This *could* drop elements
- // with weight == 0 as an optimisation.
- for item in items.iter_mut() {
- running_total = match running_total.checked_add(item.weight) {
- Some(n) => n,
- None => panic!("WeightedChoice::new called with a total weight \
- larger than a u32 can contain")
- };
-
- item.weight = running_total;
- }
- assert!(running_total != 0, "WeightedChoice::new called with a total weight of 0");
-
- WeightedChoice {
- items,
- // we're likely to be generating numbers in this range
- // relatively often, so might as well cache it
- weight_range: Uniform::new(0, running_total)
- }
- }
-}
-
-#[deprecated(since="0.6.0", note="use WeightedIndex instead")]
-#[allow(deprecated)]
-impl<'a, T: Clone> Distribution<T> for WeightedChoice<'a, T> {
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> T {
- // we want to find the first element that has cumulative
- // weight > sample_weight, which we do by binary since the
- // cumulative weights of self.items are sorted.
-
- // choose a weight in [0, total_weight)
- let sample_weight = self.weight_range.sample(rng);
-
- // short circuit when it's the first item
- if sample_weight < self.items[0].weight {
- return self.items[0].item.clone();
- }
-
- let mut idx = 0;
- let mut modifier = self.items.len();
-
- // now we know that every possibility has an element to the
- // left, so we can just search for the last element that has
- // cumulative weight <= sample_weight, then the next one will
- // be "it". (Note that this greatest element will never be the
- // last element of the vector, since sample_weight is chosen
- // in [0, total_weight) and the cumulative weight of the last
- // one is exactly the total weight.)
- while modifier > 1 {
- let i = idx + modifier / 2;
- if self.items[i].weight <= sample_weight {
- // we're small, so look to the right, but allow this
- // exact element still.
- idx = i;
- // we need the `/ 2` to round up otherwise we'll drop
- // the trailing elements when `modifier` is odd.
- modifier += 1;
- } else {
- // otherwise we're too big, so go left. (i.e. do
- // nothing)
- }
- modifier /= 2;
- }
- self.items[idx + 1].item.clone()
- }
-}
-
-#[cfg(test)]
-mod tests {
- use rngs::mock::StepRng;
- #[allow(deprecated)]
- use super::{WeightedChoice, Weighted, Distribution};
-
- #[test]
- #[allow(deprecated)]
- fn test_weighted_choice() {
- // this makes assumptions about the internal implementation of
- // WeightedChoice. It may fail when the implementation in
- // `distributions::uniform::UniformInt` changes.
-
- macro_rules! t {
- ($items:expr, $expected:expr) => {{
- let mut items = $items;
- let mut total_weight = 0;
- for item in &items { total_weight += item.weight; }
-
- let wc = WeightedChoice::new(&mut items);
- let expected = $expected;
-
- // Use extremely large steps between the random numbers, because
- // we test with small ranges and `UniformInt` is designed to prefer
- // the most significant bits.
- let mut rng = StepRng::new(0, !0 / (total_weight as u64));
-
- for &val in expected.iter() {
- assert_eq!(wc.sample(&mut rng), val)
- }
- }}
- }
-
- t!([Weighted { weight: 1, item: 10}], [10]);
-
- // skip some
- t!([Weighted { weight: 0, item: 20},
- Weighted { weight: 2, item: 21},
- Weighted { weight: 0, item: 22},
- Weighted { weight: 1, item: 23}],
- [21, 21, 23]);
-
- // different weights
- t!([Weighted { weight: 4, item: 30},
- Weighted { weight: 3, item: 31}],
- [30, 31, 30, 31, 30, 31, 30]);
-
- // check that we're binary searching
- // correctly with some vectors of odd
- // length.
- t!([Weighted { weight: 1, item: 40},
- Weighted { weight: 1, item: 41},
- Weighted { weight: 1, item: 42},
- Weighted { weight: 1, item: 43},
- Weighted { weight: 1, item: 44}],
- [40, 41, 42, 43, 44]);
- t!([Weighted { weight: 1, item: 50},
- Weighted { weight: 1, item: 51},
- Weighted { weight: 1, item: 52},
- Weighted { weight: 1, item: 53},
- Weighted { weight: 1, item: 54},
- Weighted { weight: 1, item: 55},
- Weighted { weight: 1, item: 56}],
- [50, 54, 51, 55, 52, 56, 53]);
- }
-
- #[test]
- #[allow(deprecated)]
- fn test_weighted_clone_initialization() {
- let initial : Weighted<u32> = Weighted {weight: 1, item: 1};
- let clone = initial.clone();
- assert_eq!(initial.weight, clone.weight);
- assert_eq!(initial.item, clone.item);
- }
-
- #[test] #[should_panic]
- #[allow(deprecated)]
- fn test_weighted_clone_change_weight() {
- let initial : Weighted<u32> = Weighted {weight: 1, item: 1};
- let mut clone = initial.clone();
- clone.weight = 5;
- assert_eq!(initial.weight, clone.weight);
- }
-
- #[test] #[should_panic]
- #[allow(deprecated)]
- fn test_weighted_clone_change_item() {
- let initial : Weighted<u32> = Weighted {weight: 1, item: 1};
- let mut clone = initial.clone();
- clone.item = 5;
- assert_eq!(initial.item, clone.item);
-
- }
-
- #[test] #[should_panic]
- #[allow(deprecated)]
- fn test_weighted_choice_no_items() {
- WeightedChoice::<isize>::new(&mut []);
- }
- #[test] #[should_panic]
- #[allow(deprecated)]
- fn test_weighted_choice_zero_weight() {
- WeightedChoice::new(&mut [Weighted { weight: 0, item: 0},
- Weighted { weight: 0, item: 1}]);
- }
- #[test] #[should_panic]
- #[allow(deprecated)]
- fn test_weighted_choice_weight_overflows() {
- let x = ::core::u32::MAX / 2; // x + x + 2 is the overflow
- WeightedChoice::new(&mut [Weighted { weight: x, item: 0 },
- Weighted { weight: 1, item: 1 },
- Weighted { weight: x, item: 2 },
- Weighted { weight: 1, item: 3 }]);
- }
-
- #[cfg(feature="std")]
- #[test]
- fn test_distributions_iter() {
- use distributions::Normal;
- let mut rng = ::test::rng(210);
- let distr = Normal::new(10.0, 10.0);
- let results: Vec<_> = distr.sample_iter(&mut rng).take(100).collect();
- println!("{:?}", results);
- }
-}
diff --git a/rand/src/distributions/normal.rs b/rand/src/distributions/normal.rs
deleted file mode 100644
index b8d632e..0000000
--- a/rand/src/distributions/normal.rs
+++ /dev/null
@@ -1,197 +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.
-
-use Rng;
-use distributions::{ziggurat_tables, Distribution, Open01};
-use 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
-///
-/// # Example
-/// ```
-/// use rand::prelude::*;
-/// use rand::distributions::StandardNormal;
-///
-/// let val: f64 = SmallRng::from_entropy().sample(StandardNormal);
-/// println!("{}", val);
-/// ```
-#[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.
-///
-/// # Example
-///
-/// ```
-/// use rand::distributions::{Normal, Distribution};
-///
-/// // mean 2, standard deviation 3
-/// let normal = Normal::new(2.0, 3.0);
-/// let v = normal.sample(&mut rand::thread_rng());
-/// println!("{} is from a N(2, 9) distribution", v)
-/// ```
-///
-/// [`StandardNormal`]: struct.StandardNormal.html
-#[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.
-///
-/// # Example
-///
-/// ```
-/// use rand::distributions::{LogNormal, Distribution};
-///
-/// // mean 2, standard deviation 3
-/// let log_normal = LogNormal::new(2.0, 3.0);
-/// let v = log_normal.sample(&mut rand::thread_rng());
-/// println!("{} is from an ln N(2, 9) distribution", v)
-/// ```
-#[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 distributions::Distribution;
- use super::{Normal, LogNormal};
-
- #[test]
- fn test_normal() {
- let norm = Normal::new(10.0, 10.0);
- let mut rng = ::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 = ::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 2295f79..0000000
--- a/rand/src/distributions/other.rs
+++ /dev/null
@@ -1,219 +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 {Rng};
-use 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 {
- #[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 {Rng, RngCore, Standard};
- use distributions::Alphanumeric;
- #[cfg(all(not(feature="std"), feature="alloc"))] use alloc::string::String;
-
- #[test]
- fn test_misc() {
- let rng: &mut RngCore = &mut ::test::rng(820);
-
- rng.sample::<char, _>(Standard);
- rng.sample::<bool, _>(Standard);
- }
-
- #[cfg(feature="alloc")]
- #[test]
- fn test_chars() {
- use core::iter;
- let mut rng = ::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 = ::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 744a157..0000000
--- a/rand/src/distributions/pareto.rs
+++ /dev/null
@@ -1,74 +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.
-
-use Rng;
-use distributions::{Distribution, OpenClosed01};
-
-/// Samples floating-point numbers according to the Pareto distribution
-///
-/// # Example
-/// ```
-/// use rand::prelude::*;
-/// use rand::distributions::Pareto;
-///
-/// let val: f64 = SmallRng::from_entropy().sample(Pareto::new(1., 2.));
-/// println!("{}", val);
-/// ```
-#[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 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 = ::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 1244caa..0000000
--- a/rand/src/distributions/poisson.rs
+++ /dev/null
@@ -1,157 +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.
-
-use Rng;
-use distributions::{Distribution, Cauchy};
-use 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`.
-///
-/// # Example
-///
-/// ```
-/// use rand::distributions::{Poisson, Distribution};
-///
-/// let poi = Poisson::new(2.0);
-/// let v = poi.sample(&mut rand::thread_rng());
-/// println!("{} is from a Poisson(2) distribution", v);
-/// ```
-#[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 distributions::Distribution;
- use super::Poisson;
-
- #[test]
- fn test_poisson_10() {
- let poisson = Poisson::new(10.0);
- let mut rng = ::test::rng(123);
- let mut sum = 0;
- for _ in 0..1000 {
- sum += poisson.sample(&mut rng);
- }
- let avg = (sum as f64) / 1000.0;
- println!("Poisson average: {}", avg);
- assert!((avg - 10.0).abs() < 0.5); // not 100% certain, but probable enough
- }
-
- #[test]
- fn test_poisson_15() {
- // Take the 'high expected values' path
- let poisson = Poisson::new(15.0);
- let mut rng = ::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 a6eef5c..0000000
--- a/rand/src/distributions/triangular.rs
+++ /dev/null
@@ -1,86 +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.
-
-use Rng;
-use distributions::{Distribution, Standard};
-
-/// The triangular distribution.
-///
-/// # Example
-///
-/// ```rust
-/// use rand::distributions::{Triangular, Distribution};
-///
-/// let d = Triangular::new(0., 5., 2.5);
-/// let v = d.sample(&mut rand::thread_rng());
-/// println!("{} is from a triangular distribution", v);
-/// ```
-#[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 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 = ::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 ceed77d..0000000
--- a/rand/src/distributions/uniform.rs
+++ /dev/null
@@ -1,1298 +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());
-//! ```
-//!
-//! [`Uniform`]: struct.Uniform.html
-//! [`Rng::gen_range`]: ../../trait.Rng.html#method.gen_range
-//! [`SampleUniform`]: trait.SampleUniform.html
-//! [`UniformSampler`]: trait.UniformSampler.html
-//! [`UniformInt`]: struct.UniformInt.html
-//! [`UniformFloat`]: struct.UniformFloat.html
-//! [`UniformDuration`]: struct.UniformDuration.html
-//! [`SampleBorrow::borrow`]: trait.SampleBorrow.html#method.borrow
-
-#[cfg(feature = "std")]
-use std::time::Duration;
-#[cfg(all(not(feature = "std"), rustc_1_25))]
-use core::time::Duration;
-
-use Rng;
-use distributions::Distribution;
-use distributions::float::IntoFloat;
-use distributions::utils::{WideningMultiply, FloatSIMDUtils, FloatAsSIMD, BoolAsSIMD};
-
-#[cfg(not(feature = "std"))]
-#[allow(unused_imports)] // rustc doesn't detect that this is actually used
-use 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);
-/// }
-/// ```
-///
-/// [`Uniform::new`]: struct.Uniform.html#method.new
-/// [`Uniform::new_inclusive`]: struct.Uniform.html#method.new_inclusive
-/// [`new`]: struct.Uniform.html#method.new
-/// [`new_inclusive`]: struct.Uniform.html#method.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.
-///
-/// [`UniformSampler`]: trait.UniformSampler.html
-/// [module documentation]: index.html
-/// [`Uniform`]: struct.Uniform.html
-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]: index.html
-/// [`Uniform`]: struct.Uniform.html
-/// [`sample_single`]: trait.UniformSampler.html#method.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)`.
- ///
- /// Usually users should not call this directly but instead use
- /// `Uniform::sample_single`, which asserts that `low < high` before calling
- /// this.
- ///
- /// Via this method, implementations can provide a method optimized for
- /// sampling only a single value from the specified range. The default
- /// implementation simply calls `UniformSampler::new` then `sample` on the
- /// result.
- 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)
- }
-}
-
-#[cfg(rustc_1_27)]
-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`]: https://doc.rust-lang.org/std/borrow/trait.Borrow.html
-pub trait SampleBorrow<Borrowed> {
- /// Immutably borrows from an owned value. See [`Borrow::borrow`]
- ///
- /// [`Borrow::borrow`]: https://doc.rust-lang.org/std/borrow/trait.Borrow.html#tymethod.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 a closed range, the number of possible numbers we should generate is
-/// `range = (high - low + 1)`. It is not possible to end up with a uniform
-/// distribution if we map *all* the random integers that can be generated to
-/// this range. We have to map integers from a `zone` that is a multiple of the
-/// range. The rest of the integers, that cause a bias, are rejected.
-///
-/// The problem with `range` is that to cover the full range of the type, it has
-/// to store `unsigned_max + 1`, which can't be represented. But if the range
-/// covers the full range of the type, no modulus is needed. A range of size 0
-/// can't exist, so we use that to represent this special case. Wrapping
-/// arithmetic even makes representing `unsigned_max + 1` as 0 simple.
-///
-/// We don't calculate `zone` directly, but first calculate the number of
-/// integers to reject. To handle `unsigned_max + 1` not fitting in the type,
-/// we use:
-/// `ints_to_reject = (unsigned_max + 1) % range;`
-/// `ints_to_reject = (unsigned_max - range + 1) % range;`
-///
-/// The smallest integer PRNGs generate is `u32`. That is why for small integer
-/// sizes (`i8`/`u8` and `i16`/`u16`) there is an optimization: don't pick the
-/// largest zone that can fit in the small type, but pick the largest zone that
-/// can fit in an `u32`. `ints_to_reject` is always less than half the size of
-/// the small integer. This means the first bit of `zone` is always 1, and so
-/// are all the other preceding bits of a larger integer. The easiest way to
-/// grow the `zone` for the larger type is to simply sign extend it.
-///
-/// 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.
-///
-/// [`UniformSampler`]: trait.UniformSampler.html
-/// [`Uniform`]: struct.Uniform.html
-#[derive(Clone, Copy, Debug)]
-pub struct UniformInt<X> {
- low: X,
- range: X,
- zone: X,
-}
-
-macro_rules! uniform_int_impl {
- ($ty:ty, $signed:ty, $unsigned:ident,
- $i_large: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 = $ty;
-
- #[inline] // if the range is constant, this helps LLVM to do the
- // calculations at compile-time.
- fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
- where B1: SampleBorrow<Self::X> + Sized,
- B2: SampleBorrow<Self::X> + Sized
- {
- let low = *low_b.borrow();
- let high = *high_b.borrow();
- assert!(low < high, "Uniform::new called with `low >= high`");
- UniformSampler::new_inclusive(low, high - 1)
- }
-
- #[inline] // if the range is constant, this helps LLVM to do the
- // calculations at compile-time.
- fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
- where B1: SampleBorrow<Self::X> + Sized,
- B2: SampleBorrow<Self::X> + Sized
- {
- let low = *low_b.borrow();
- let high = *high_b.borrow();
- assert!(low <= high,
- "Uniform::new_inclusive called with `low > high`");
- let unsigned_max = ::core::$unsigned::MAX;
-
- let range = high.wrapping_sub(low).wrapping_add(1) as $unsigned;
- let ints_to_reject =
- if range > 0 {
- (unsigned_max - range + 1) % range
- } else {
- 0
- };
- let zone = unsigned_max - ints_to_reject;
-
- UniformInt {
- low: low,
- // These are really $unsigned values, but store as $ty:
- range: range as $ty,
- zone: zone 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 {
- // Grow `zone` to fit a type of at least 32 bits, by
- // sign-extending it (the first bit is always 1, so are all
- // the preceding bits of the larger type).
- // For types that already have the right size, all the
- // casting is a no-op.
- let zone = self.zone as $signed as $i_large 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,
- "Uniform::sample_single called with 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 $ty);
- }
- }
- }
- }
- }
-}
-
-uniform_int_impl! { i8, i8, u8, i32, u32 }
-uniform_int_impl! { i16, i16, u16, i32, u32 }
-uniform_int_impl! { i32, i32, u32, i32, u32 }
-uniform_int_impl! { i64, i64, u64, i64, u64 }
-#[cfg(all(rustc_1_26, not(target_os = "emscripten")))]
-uniform_int_impl! { i128, i128, u128, u128, u128 }
-uniform_int_impl! { isize, isize, usize, isize, usize }
-uniform_int_impl! { u8, i8, u8, i32, u32 }
-uniform_int_impl! { u16, i16, u16, i32, u32 }
-uniform_int_impl! { u32, i32, u32, i32, u32 }
-uniform_int_impl! { u64, i64, u64, i64, u64 }
-uniform_int_impl! { usize, isize, usize, isize, usize }
-#[cfg(all(rustc_1_26, not(target_os = "emscripten")))]
-uniform_int_impl! { u128, u128, u128, i128, u128 }
-
-#[cfg(all(feature = "simd_support", feature = "nightly"))]
-macro_rules! uniform_simd_int_impl {
- ($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(),
- zone: zone.cast(),
- }
- }
-
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
- let range: $unsigned = self.range.cast();
- let zone: $unsigned = self.zone.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, $u_scalar);
- )+
- };
-}
-
-#[cfg(all(feature = "simd_support", feature = "nightly"))]
-uniform_simd_int_impl! {
- (u64x2, i64x2),
- (u64x4, i64x4),
- (u64x8, i64x8),
- u64
-}
-
-#[cfg(all(feature = "simd_support", feature = "nightly"))]
-uniform_simd_int_impl! {
- (u32x2, i32x2),
- (u32x4, i32x4),
- (u32x8, i32x8),
- (u32x16, i32x16),
- u32
-}
-
-#[cfg(all(feature = "simd_support", feature = "nightly"))]
-uniform_simd_int_impl! {
- (u16x2, i16x2),
- (u16x4, i16x4),
- (u16x8, i16x8),
- (u16x16, i16x16),
- (u16x32, i16x32),
- u16
-}
-
-#[cfg(all(feature = "simd_support", feature = "nightly"))]
-uniform_simd_int_impl! {
- (u8x2, i8x2),
- (u8x4, i8x4),
- (u8x8, i8x8),
- (u8x16, i8x16),
- (u8x32, i8x32),
- (u8x64, i8x64),
- u8
-}
-
-
-/// The back-end implementing [`UniformSampler`] for floating-point types.
-///
-/// Unless you are implementing [`UniformSampler`] for your own type, this type
-/// should not be used directly, use [`Uniform`] instead.
-///
-/// # Implementation notes
-///
-/// Instead of generating a float in the `[0, 1)` range using [`Standard`], the
-/// `UniformFloat` implementation converts the output of an PRNG itself. This
-/// way one or two steps can be optimized out.
-///
-/// The floats are first converted to a value in the `[1, 2)` interval using a
-/// transmute-based method, and then mapped to the expected range with a
-/// multiply and addition. Values produced this way have what equals 22 bits of
-/// random digits for an `f32`, and 52 for an `f64`.
-///
-/// [`UniformSampler`]: trait.UniformSampler.html
-/// [`new`]: trait.UniformSampler.html#tymethod.new
-/// [`new_inclusive`]: trait.UniformSampler.html#tymethod.new_inclusive
-/// [`Uniform`]: struct.Uniform.html
-/// [`Standard`]: ../struct.Standard.html
-#[derive(Clone, Copy, Debug)]
-pub struct UniformFloat<X> {
- low: X,
- scale: X,
-}
-
-macro_rules! uniform_float_impl {
- ($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>() >> $bits_to_discard)
- .into_float_with_exponent(0);
-
- // Get a value in the range [0, 1) in order to avoid
- // overflowing into infinity when multiplying with scale
- let value0_1 = value1_2 - 1.0;
-
- // We don't use `f64::mul_add`, because it is not available with
- // `no_std`. Furthermore, it is slower for some targets (but
- // faster for others). However, the order of multiplication and
- // addition is important, because on some platforms (e.g. ARM)
- // it will be optimized to a single (non-FMA) instruction.
- value0_1 * self.scale + self.low
- }
-
- #[inline]
- fn sample_single<R: Rng + ?Sized, B1, B2>(low_b: B1, high_b: B2, rng: &mut R)
- -> Self::X
- where B1: SampleBorrow<Self::X> + Sized,
- B2: SampleBorrow<Self::X> + Sized
- {
- let low = *low_b.borrow();
- let high = *high_b.borrow();
- assert!(low.all_lt(high),
- "Uniform::sample_single called with low >= high");
- let mut scale = high - low;
-
- loop {
- // Generate a value in the range [1, 2)
- let value1_2 = (rng.gen::<$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 called with non-finite boundaries");
- 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.
-///
-/// [`UniformSampler`]: trait.UniformSampler.html
-/// [`Uniform`]: struct.Uniform.html
-#[cfg(any(feature = "std", rustc_1_25))]
-#[derive(Clone, Copy, Debug)]
-pub struct UniformDuration {
- mode: UniformDurationMode,
- offset: u32,
-}
-
-#[cfg(any(feature = "std", rustc_1_25))]
-#[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>,
- }
-}
-
-#[cfg(any(feature = "std", rustc_1_25))]
-impl SampleUniform for Duration {
- type Sampler = UniformDuration;
-}
-
-#[cfg(any(feature = "std", rustc_1_25))]
-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 = high_s - 1;
- high_n = 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(high_n as u64));
-
- if let Some(higher_bound) = max {
- let lower_bound = low_s * 1_000_000_000 + low_n as u64;
- 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 Rng;
- use rngs::mock::StepRng;
- use distributions::uniform::Uniform;
- use 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 = ::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]
- fn test_integers() {
- use core::{i8, i16, i32, i64, isize};
- use core::{u8, u16, u32, u64, usize};
- #[cfg(all(rustc_1_26, not(target_os = "emscripten")))]
- use core::{i128, u128};
-
- let mut rng = ::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: $ty, y| x.lt(y).all()
- );)*
- }};
- }
- t!(i8, i16, i32, i64, isize,
- u8, u16, u32, u64, usize);
- #[cfg(all(rustc_1_26, not(target_os = "emscripten")))]
- t!(i128, u128);
-
- #[cfg(all(feature = "simd_support", feature = "nightly"))]
- {
- t!(u8x2, u8x4, u8x8, u8x16, u8x32, u8x64 => u8);
- t!(i8x2, i8x4, i8x8, i8x16, i8x32, i8x64 => i8);
- t!(u16x2, u16x4, u16x8, u16x16, u16x32 => u16);
- t!(i16x2, i16x4, i16x8, i16x16, i16x32 => i16);
- t!(u32x2, u32x4, u32x8, u32x16 => u32);
- t!(i32x2, i32x4, i32x8, i32x16 => i32);
- t!(u64x2, u64x4, u64x8 => u64);
- t!(i64x2, i64x4, i64x8 => i64);
- }
- }
-
- #[test]
- fn test_floats() {
- let mut rng = ::test::rng(252);
- let mut zero_rng = StepRng::new(0, 0);
- let mut max_rng = StepRng::new(0xffff_ffff_ffff_ffff, 0);
- macro_rules! t {
- ($ty:ty, $f_scalar:ident, $bits_shifted:expr) => {{
- let v: &[($f_scalar, $f_scalar)]=
- &[(0.0, 100.0),
- (-1e35, -1e25),
- (1e-35, 1e-25),
- (-1e35, 1e35),
- (<$f_scalar>::from_bits(0), <$f_scalar>::from_bits(3)),
- (-<$f_scalar>::from_bits(10), -<$f_scalar>::from_bits(1)),
- (-<$f_scalar>::from_bits(5), 0.0),
- (-<$f_scalar>::from_bits(7), -0.0),
- (10.0, ::core::$f_scalar::MAX),
- (-100.0, ::core::$f_scalar::MAX),
- (-::core::$f_scalar::MAX / 5.0, ::core::$f_scalar::MAX),
- (-::core::$f_scalar::MAX, ::core::$f_scalar::MAX / 5.0),
- (-::core::$f_scalar::MAX * 0.8, ::core::$f_scalar::MAX * 0.7),
- (-::core::$f_scalar::MAX, ::core::$f_scalar::MAX),
- ];
- for &(low_scalar, high_scalar) in v.iter() {
- for lane in 0..<$ty>::lanes() {
- let low = <$ty>::splat(0.0 as $f_scalar).replace(lane, low_scalar);
- let high = <$ty>::splat(1.0 as $f_scalar).replace(lane, high_scalar);
- let my_uniform = Uniform::new(low, high);
- let my_incl_uniform = Uniform::new_inclusive(low, high);
- for _ in 0..100 {
- let v = rng.sample(my_uniform).extract(lane);
- assert!(low_scalar <= v && v < high_scalar);
- let v = rng.sample(my_incl_uniform).extract(lane);
- assert!(low_scalar <= v && v <= high_scalar);
- let v = rng.gen_range(low, high).extract(lane);
- assert!(low_scalar <= v && v < high_scalar);
- }
-
- assert_eq!(rng.sample(Uniform::new_inclusive(low, low)).extract(lane), low_scalar);
-
- assert_eq!(zero_rng.sample(my_uniform).extract(lane), low_scalar);
- assert_eq!(zero_rng.sample(my_incl_uniform).extract(lane), low_scalar);
- assert_eq!(zero_rng.gen_range(low, high).extract(lane), low_scalar);
- assert!(max_rng.sample(my_uniform).extract(lane) < high_scalar);
- assert!(max_rng.sample(my_incl_uniform).extract(lane) <= high_scalar);
-
- // Don't run this test for really tiny differences between high and low
- // since for those rounding might result in selecting high for a very
- // long time.
- if (high_scalar - low_scalar) > 0.0001 {
- let mut lowering_max_rng =
- StepRng::new(0xffff_ffff_ffff_ffff,
- (-1i64 << $bits_shifted) as u64);
- assert!(lowering_max_rng.gen_range(low, high).extract(lane) < high_scalar);
- }
- }
- }
-
- assert_eq!(rng.sample(Uniform::new_inclusive(::core::$f_scalar::MAX,
- ::core::$f_scalar::MAX)),
- ::core::$f_scalar::MAX);
- assert_eq!(rng.sample(Uniform::new_inclusive(-::core::$f_scalar::MAX,
- -::core::$f_scalar::MAX)),
- -::core::$f_scalar::MAX);
- }}
- }
-
- t!(f32, f32, 32 - 23);
- t!(f64, f64, 64 - 52);
- #[cfg(feature="simd_support")]
- {
- t!(f32x2, f32, 32 - 23);
- t!(f32x4, f32, 32 - 23);
- t!(f32x8, f32, 32 - 23);
- t!(f32x16, f32, 32 - 23);
- t!(f64x2, f64, 64 - 52);
- t!(f64x4, f64, 64 - 52);
- t!(f64x8, f64, 64 - 52);
- }
- }
-
- #[test]
- #[cfg(all(feature="std",
- not(target_arch = "wasm32"),
- not(target_arch = "asmjs")))]
- fn test_float_assertions() {
- use std::panic::catch_unwind;
- use super::SampleUniform;
- fn range<T: SampleUniform>(low: T, high: T) {
- let mut rng = ::test::rng(253);
- rng.gen_range(low, high);
- }
-
- macro_rules! t {
- ($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(any(feature = "std", rustc_1_25))]
- fn test_durations() {
- #[cfg(feature = "std")]
- use std::time::Duration;
- #[cfg(all(not(feature = "std"), rustc_1_25))]
- use core::time::Duration;
-
- let mut rng = ::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 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 = ::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);
- }
-
- #[cfg(rustc_1_27)]
- #[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 01ab76a..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.
-
-use Rng;
-use distributions::{Distribution, Uniform};
-
-/// Samples uniformly from the edge of the unit circle in two dimensions.
-///
-/// Implemented via a method by von Neumann[^1].
-///
-///
-/// # Example
-///
-/// ```
-/// use rand::distributions::{UnitCircle, Distribution};
-///
-/// let circle = UnitCircle::new();
-/// let v = circle.sample(&mut rand::thread_rng());
-/// println!("{:?} is from the unit circle.", v)
-/// ```
-///
-/// [^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.
-#[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 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 = ::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 = ::test::rng(2);
- let dist = UnitCircle::new();
- assert_eq!(dist.sample(&mut rng), [-0.8032118336637037, 0.5956935036263119]);
- assert_eq!(dist.sample(&mut rng), [-0.4742919588505423, -0.880367615130018]);
- assert_eq!(dist.sample(&mut rng), [0.9297328981467168, 0.368234623716601]);
- }
-}
diff --git a/rand/src/distributions/unit_sphere.rs b/rand/src/distributions/unit_sphere.rs
deleted file mode 100644
index 37de88b..0000000
--- a/rand/src/distributions/unit_sphere.rs
+++ /dev/null
@@ -1,99 +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.
-
-use Rng;
-use distributions::{Distribution, Uniform};
-
-/// Samples uniformly from the surface of the unit sphere in three dimensions.
-///
-/// Implemented via a method by Marsaglia[^1].
-///
-///
-/// # Example
-///
-/// ```
-/// use rand::distributions::{UnitSphereSurface, Distribution};
-///
-/// let sphere = UnitSphereSurface::new();
-/// let v = sphere.sample(&mut rand::thread_rng());
-/// println!("{:?} is from the unit sphere surface.", v)
-/// ```
-///
-/// [^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.
-#[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 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, $b));
- }
- );
- }
-
- #[test]
- fn norm() {
- let mut rng = ::test::rng(1);
- let dist = UnitSphereSurface::new();
- for _ in 0..1000 {
- let x = dist.sample(&mut rng);
- assert_almost_eq!(x[0]*x[0] + x[1]*x[1] + x[2]*x[2], 1., 1e-15);
- }
- }
-
- #[test]
- fn value_stability() {
- let mut rng = ::test::rng(2);
- let dist = UnitSphereSurface::new();
- assert_eq!(dist.sample(&mut rng),
- [-0.24950027180862533, -0.7552572587896719, 0.6060825747478084]);
- assert_eq!(dist.sample(&mut rng),
- [0.47604534507233487, -0.797200864987207, -0.3712837328763685]);
- assert_eq!(dist.sample(&mut rng),
- [0.9795722330927367, 0.18692349236651176, 0.07414747571708524]);
- }
-}
diff --git a/rand/src/distributions/utils.rs b/rand/src/distributions/utils.rs
deleted file mode 100644
index d4d3642..0000000
--- a/rand/src/distributions/utils.rs
+++ /dev/null
@@ -1,504 +0,0 @@
-// Copyright 2018 Developers of the Rand project.
-//
-// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
-// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
-// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
-// option. This file may not be copied, modified, or distributed
-// except according to those terms.
-
-//! Math helper functions
-
-#[cfg(feature="simd_support")]
-use packed_simd::*;
-#[cfg(feature="std")]
-use distributions::ziggurat_tables;
-#[cfg(feature="std")]
-use Rng;
-
-
-pub trait WideningMultiply<RHS = Self> {
- type Output;
-
- fn wmul(self, x: RHS) -> Self::Output;
-}
-
-macro_rules! wmul_impl {
- ($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: $ty = tmp.cast();
- (hi, lo)
- }
- }
- )+
- };
-}
-wmul_impl! { u8, u16, 8 }
-wmul_impl! { u16, u32, 16 }
-wmul_impl! { u32, u64, 32 }
-#[cfg(all(rustc_1_26, not(target_os = "emscripten")))]
-wmul_impl! { u64, u128, 64 }
-
-// This code is a translation of the __mulddi3 function in LLVM's
-// compiler-rt. It is an optimised variant of the common method
-// `(a + b) * (c + d) = ac + ad + bc + bd`.
-//
-// For some reason LLVM can optimise the C version very well, but
-// keeps shuffling registers in this Rust translation.
-macro_rules! wmul_impl_large {
- ($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 >> $half);
-
- (high, low)
- }
- }
- )+
- };
-}
-#[cfg(not(all(rustc_1_26, not(target_os = "emscripten"))))]
-wmul_impl_large! { u64, 32 }
-#[cfg(all(rustc_1_26, not(target_os = "emscripten")))]
-wmul_impl_large! { u128, 64 }
-
-macro_rules! wmul_impl_usize {
- ($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 {
- type Bits;
-
- fn is_nan(self) -> bool;
- fn is_infinite(self) -> bool;
- fn is_finite(self) -> bool;
- fn to_bits(self) -> Self::Bits;
- fn from_bits(v: Self::Bits) -> Self;
-}
-
-/// 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 {
- type Bits = $uty;
-
- #[inline]
- fn is_nan(self) -> bool {
- self != self
- }
-
- #[inline]
- fn is_infinite(self) -> bool {
- self == ::core::$ty::INFINITY || self == ::core::$ty::NEG_INFINITY
- }
-
- #[inline]
- fn is_finite(self) -> bool {
- !(self.is_nan() || self.is_infinite())
- }
-
- #[inline]
- fn to_bits(self) -> Self::Bits {
- unsafe { ::core::mem::transmute(self) }
- }
-
- #[inline]
- fn from_bits(v: Self::Bits) -> Self {
- // It turns out the safety issues with sNaN were overblown! Hooray!
- unsafe { ::core::mem::transmute(v) }
- }
- }
-
- 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;
- 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 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 5fbe10a..0000000
--- a/rand/src/distributions/weibull.rs
+++ /dev/null
@@ -1,71 +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.
-
-use Rng;
-use distributions::{Distribution, OpenClosed01};
-
-/// Samples floating-point numbers according to the Weibull distribution
-///
-/// # Example
-/// ```
-/// use rand::prelude::*;
-/// use rand::distributions::Weibull;
-///
-/// let val: f64 = SmallRng::from_entropy().sample(Weibull::new(1., 10.));
-/// println!("{}", val);
-/// ```
-#[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 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 = ::test::rng(1);
- for _ in 0..1000 {
- let r = d.sample(&mut rng);
- assert!(r >= 0.);
- }
- }
-}
diff --git a/rand/src/distributions/weighted.rs b/rand/src/distributions/weighted.rs
deleted file mode 100644
index 01c8fe6..0000000
--- a/rand/src/distributions/weighted.rs
+++ /dev/null
@@ -1,232 +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.
-
-use Rng;
-use distributions::Distribution;
-use 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 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`], 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>`]: struct.Uniform.html
-/// [`Uniform<X>::sample`]: struct.Uniform.html#method.sample
-/// [`RngCore`]: ../trait.RngCore.html
-#[derive(Debug, Clone)]
-pub struct WeightedIndex<X: SampleUniform + PartialOrd> {
- cumulative_weights: Vec<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.
- ///
- /// [`Distribution`]: trait.Distribution.html
- /// [`Uniform<X>`]: struct.Uniform.html
- 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::NegativeWeight);
- }
-
- let mut weights = Vec::<X>::with_capacity(iter.size_hint().0);
- for w in iter {
- if *w.borrow() < zero {
- return Err(WeightedError::NegativeWeight);
- }
- 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);
-
- Ok(WeightedIndex { cumulative_weights: weights, weight_distribution: distr })
- }
-}
-
-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]
- fn test_weightedindex() {
- let mut r = ::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::NegativeWeight);
- assert_eq!(WeightedIndex::new(&[-10, 20, 1, 30]).unwrap_err(), WeightedError::NegativeWeight);
- assert_eq!(WeightedIndex::new(&[-10]).unwrap_err(), WeightedError::NegativeWeight);
- }
-}
-
-/// Error type returned from `WeightedIndex::new`.
-#[derive(Debug, Clone, Copy, PartialEq, Eq)]
-pub enum WeightedError {
- /// The provided iterator contained no items.
- NoItem,
-
- /// A weight lower than zero was used.
- NegativeWeight,
-
- /// All items in the provided iterator had a weight of zero.
- AllWeightsZero,
-}
-
-impl WeightedError {
- fn msg(&self) -> &str {
- match *self {
- WeightedError::NoItem => "No items found",
- WeightedError::NegativeWeight => "Item has negative weight",
- WeightedError::AllWeightsZero => "All items had weight zero",
- }
- }
-}
-
-#[cfg(feature="std")]
-impl ::std::error::Error for WeightedError {
- fn description(&self) -> &str {
- self.msg()
- }
- fn cause(&self) -> Option<&::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,
- 3.078380215254090224, 3.050890016615455114, 3.023897504455676621, 2.997382949516130601,
- 2.971327759921089662, 2.945714394895045718, 2.920526286512740821, 2.895747768600141825,
- 2.871364012015536371, 2.847360965635188812, 2.823725302450035279, 2.800444370250737780,
- 2.777506146439756574, 2.754899196562344610, 2.732612636194700073, 2.710636095867928752,
- 2.688959688741803689, 2.667573980773266573, 2.646469963151809157, 2.625639026797788489,
- 2.605072938740835564, 2.584763820214140750, 2.564704126316905253, 2.544886627111869970,
- 2.525304390037828028, 2.505950763528594027, 2.486819361740209455, 2.467904050297364815,
- 2.449198932978249754, 2.430698339264419694, 2.412396812688870629, 2.394289099921457886,
- 2.376370140536140596, 2.358635057409337321, 2.341079147703034380, 2.323697874390196372,
- 2.306486858283579799, 2.289441870532269441, 2.272558825553154804, 2.255833774367219213,
- 2.239262898312909034, 2.222842503111036816, 2.206569013257663858, 2.190438966723220027,
- 2.174449009937774679, 2.158595893043885994, 2.142876465399842001, 2.127287671317368289,
- 2.111826546019042183, 2.096490211801715020, 2.081275874393225145, 2.066180819490575526,
- 2.051202409468584786, 2.036338080248769611, 2.021585338318926173, 2.006941757894518563,
- 1.992404978213576650, 1.977972700957360441, 1.963642687789548313, 1.949412758007184943,
- 1.935280786297051359, 1.921244700591528076, 1.907302480018387536, 1.893452152939308242,
- 1.879691795072211180, 1.866019527692827973, 1.852433515911175554, 1.838931967018879954,
- 1.825513128903519799, 1.812175288526390649, 1.798916770460290859, 1.785735935484126014,
- 1.772631179231305643, 1.759600930889074766, 1.746643651946074405, 1.733757834985571566,
- 1.720942002521935299, 1.708194705878057773, 1.695514524101537912, 1.682900062917553896,
- 1.670349953716452118, 1.657862852574172763, 1.645437439303723659, 1.633072416535991334,
- 1.620766508828257901, 1.608518461798858379, 1.596327041286483395, 1.584191032532688892,
- 1.572109239386229707, 1.560080483527888084, 1.548103603714513499, 1.536177455041032092,
- 1.524300908219226258, 1.512472848872117082, 1.500692176842816750, 1.488957805516746058,
- 1.477268661156133867, 1.465623682245745352, 1.454021818848793446, 1.442462031972012504,
- 1.430943292938879674, 1.419464582769983219, 1.408024891569535697, 1.396623217917042137,
- 1.385258568263121992, 1.373929956328490576, 1.362636402505086775, 1.351376933258335189,
- 1.340150580529504643, 1.328956381137116560, 1.317793376176324749, 1.306660610415174117,
- 1.295557131686601027, 1.284481990275012642, 1.273434238296241139, 1.262412929069615330,
- 1.251417116480852521, 1.240445854334406572, 1.229498195693849105, 1.218573192208790124,
- 1.207669893426761121, 1.196787346088403092, 1.185924593404202199, 1.175080674310911677,
- 1.164254622705678921, 1.153445466655774743, 1.142652227581672841, 1.131873919411078511,
- 1.121109547701330200, 1.110358108727411031, 1.099618588532597308, 1.088889961938546813,
- 1.078171191511372307, 1.067461226479967662, 1.056759001602551429, 1.046063435977044209,
- 1.035373431790528542, 1.024687873002617211, 1.014005623957096480, 1.003325527915696735,
- 0.992646405507275897, 0.981967053085062602, 0.971286240983903260, 0.960602711668666509,
- 0.949915177764075969, 0.939222319955262286, 0.928522784747210395, 0.917815182070044311,
- 0.907098082715690257, 0.896370015589889935, 0.885629464761751528, 0.874874866291025066,
- 0.864104604811004484, 0.853317009842373353, 0.842510351810368485, 0.831682837734273206,
- 0.820832606554411814, 0.809957724057418282, 0.799056177355487174, 0.788125868869492430,
- 0.777164609759129710, 0.766170112735434672, 0.755139984181982249, 0.744071715500508102,
- 0.732962673584365398, 0.721810090308756203, 0.710611050909655040, 0.699362481103231959,
- 0.688061132773747808, 0.676703568029522584, 0.665286141392677943, 0.653804979847664947,
- 0.642255960424536365, 0.630634684933490286, 0.618936451394876075, 0.607156221620300030,
- 0.595288584291502887, 0.583327712748769489, 0.571267316532588332, 0.559100585511540626,
- 0.546820125163310577, 0.534417881237165604, 0.521885051592135052, 0.509211982443654398,
- 0.496388045518671162, 0.483401491653461857, 0.470239275082169006, 0.456886840931420235,
- 0.443327866073552401, 0.429543940225410703, 0.415514169600356364, 0.401214678896277765,
- 0.386617977941119573, 0.371692145329917234, 0.356399760258393816, 0.340696481064849122,
- 0.324529117016909452, 0.307832954674932158, 0.290527955491230394, 0.272513185478464703,
- 0.253658363385912022, 0.233790483059674731, 0.212671510630966620, 0.189958689622431842,
- 0.165127622564187282, 0.137304980940012589, 0.104838507565818778, 0.063852163815001570,
- 0.000000000000000000];
-pub static ZIG_EXP_F: [f64; 257] =
- [0.000167066692307963, 0.000454134353841497, 0.000967269282327174, 0.001536299780301573,
- 0.002145967743718907, 0.002788798793574076, 0.003460264777836904, 0.004157295120833797,
- 0.004877655983542396, 0.005619642207205489, 0.006381905937319183, 0.007163353183634991,
- 0.007963077438017043, 0.008780314985808977, 0.009614413642502212, 0.010464810181029981,
- 0.011331013597834600, 0.012212592426255378, 0.013109164931254991, 0.014020391403181943,
- 0.014945968011691148, 0.015885621839973156, 0.016839106826039941, 0.017806200410911355,
- 0.018786700744696024, 0.019780424338009740, 0.020787204072578114, 0.021806887504283581,
- 0.022839335406385240, 0.023884420511558174, 0.024942026419731787, 0.026012046645134221,
- 0.027094383780955803, 0.028188948763978646, 0.029295660224637411, 0.030414443910466622,
- 0.031545232172893622, 0.032687963508959555, 0.033842582150874358, 0.035009037697397431,
- 0.036187284781931443, 0.037377282772959382, 0.038578995503074871, 0.039792391023374139,
- 0.041017441380414840, 0.042254122413316254, 0.043502413568888197, 0.044762297732943289,
- 0.046033761076175184, 0.047316792913181561, 0.048611385573379504, 0.049917534282706379,
- 0.051235237055126281, 0.052564494593071685, 0.053905310196046080, 0.055257689676697030,
- 0.056621641283742870, 0.057997175631200659, 0.059384305633420280, 0.060783046445479660,
- 0.062193415408541036, 0.063615431999807376, 0.065049117786753805, 0.066494496385339816,
- 0.067951593421936643, 0.069420436498728783, 0.070901055162371843, 0.072393480875708752,
- 0.073897746992364746, 0.075413888734058410, 0.076941943170480517, 0.078481949201606435,
- 0.080033947542319905, 0.081597980709237419, 0.083174093009632397, 0.084762330532368146,
- 0.086362741140756927, 0.087975374467270231, 0.089600281910032886, 0.091237516631040197,
- 0.092887133556043569, 0.094549189376055873, 0.096223742550432825, 0.097910853311492213,
- 0.099610583670637132, 0.101322997425953631, 0.103048160171257702, 0.104786139306570145,
- 0.106537004050001632, 0.108300825451033755, 0.110077676405185357, 0.111867631670056283,
- 0.113670767882744286, 0.115487163578633506, 0.117316899211555525, 0.119160057175327641,
- 0.121016721826674792, 0.122886979509545108, 0.124770918580830933, 0.126668629437510671,
- 0.128580204545228199, 0.130505738468330773, 0.132445327901387494, 0.134399071702213602,
- 0.136367070926428829, 0.138349428863580176, 0.140346251074862399, 0.142357645432472146,
- 0.144383722160634720, 0.146424593878344889, 0.148480375643866735, 0.150551185001039839,
- 0.152637142027442801, 0.154738369384468027, 0.156854992369365148, 0.158987138969314129,
- 0.161134939917591952, 0.163298528751901734, 0.165478041874935922, 0.167673618617250081,
- 0.169885401302527550, 0.172113535315319977, 0.174358169171353411, 0.176619454590494829,
- 0.178897546572478278, 0.181192603475496261, 0.183504787097767436, 0.185834262762197083,
- 0.188181199404254262, 0.190545769663195363, 0.192928149976771296, 0.195328520679563189,
- 0.197747066105098818, 0.200183974691911210, 0.202639439093708962, 0.205113656293837654,
- 0.207606827724221982, 0.210119159388988230, 0.212650861992978224, 0.215202151075378628,
- 0.217773247148700472, 0.220364375843359439, 0.222975768058120111, 0.225607660116683956,
- 0.228260293930716618, 0.230933917169627356, 0.233628783437433291, 0.236345152457059560,
- 0.239083290262449094, 0.241843469398877131, 0.244625969131892024, 0.247431075665327543,
- 0.250259082368862240, 0.253110290015629402, 0.255985007030415324, 0.258883549749016173,
- 0.261806242689362922, 0.264753418835062149, 0.267725419932044739, 0.270722596799059967,
- 0.273745309652802915, 0.276793928448517301, 0.279868833236972869, 0.282970414538780746,
- 0.286099073737076826, 0.289255223489677693, 0.292439288161892630, 0.295651704281261252,
- 0.298892921015581847, 0.302163400675693528, 0.305463619244590256, 0.308794066934560185,
- 0.312155248774179606, 0.315547685227128949, 0.318971912844957239, 0.322428484956089223,
- 0.325917972393556354, 0.329440964264136438, 0.332998068761809096, 0.336589914028677717,
- 0.340217149066780189, 0.343880444704502575, 0.347580494621637148, 0.351318016437483449,
- 0.355093752866787626, 0.358908472948750001, 0.362762973354817997, 0.366658079781514379,
- 0.370594648435146223, 0.374573567615902381, 0.378595759409581067, 0.382662181496010056,
- 0.386773829084137932, 0.390931736984797384, 0.395136981833290435, 0.399390684475231350,
- 0.403694012530530555, 0.408048183152032673, 0.412454465997161457, 0.416914186433003209,
- 0.421428728997616908, 0.425999541143034677, 0.430628137288459167, 0.435316103215636907,
- 0.440065100842354173, 0.444876873414548846, 0.449753251162755330, 0.454696157474615836,
- 0.459707615642138023, 0.464789756250426511, 0.469944825283960310, 0.475175193037377708,
- 0.480483363930454543, 0.485871987341885248, 0.491343869594032867, 0.496901987241549881,
- 0.502549501841348056, 0.508289776410643213, 0.514126393814748894, 0.520063177368233931,
- 0.526104213983620062, 0.532253880263043655, 0.538516872002862246, 0.544898237672440056,
- 0.551403416540641733, 0.558038282262587892, 0.564809192912400615, 0.571723048664826150,
- 0.578787358602845359, 0.586010318477268366, 0.593400901691733762, 0.600968966365232560,
- 0.608725382079622346, 0.616682180915207878, 0.624852738703666200, 0.633251994214366398,
- 0.641896716427266423, 0.650805833414571433, 0.660000841079000145, 0.669506316731925177,
- 0.679350572264765806, 0.689566496117078431, 0.700192655082788606, 0.711274760805076456,
- 0.722867659593572465, 0.735038092431424039, 0.747868621985195658, 0.761463388849896838,
- 0.775956852040116218, 0.791527636972496285, 0.808421651523009044, 0.826993296643051101,
- 0.847785500623990496, 0.871704332381204705, 0.900469929925747703, 0.938143680862176477,
- 1.000000000000000000];
generated by cgit v1.2.1 (git 2.18.0) at 2024-05-18 08:36:01 +0000