Vendor dependencies for 0.3.0 release

vendor/rand_distr/src/binomial.rs

@@ -0,0 +1,350 @@
+// 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 crate::{Distribution, Uniform};
+use rand::Rng;
+use core::fmt;
+use core::cmp::Ordering;
+#[allow(unused_imports)]
+use num_traits::Float;
+
+/// 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_distr::{Binomial, Distribution};
+///
+/// let bin = Binomial::new(20, 0.3).unwrap();
+/// let v = bin.sample(&mut rand::thread_rng());
+/// println!("{} is from a binomial distribution", v);
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct Binomial {
+    /// Number of trials.
+    n: u64,
+    /// Probability of success.
+    p: f64,
+}
+
+/// Error type returned from `Binomial::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// `p < 0` or `nan`.
+    ProbabilityTooSmall,
+    /// `p > 1`.
+    ProbabilityTooLarge,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::ProbabilityTooSmall => "p < 0 or is NaN in binomial distribution",
+            Error::ProbabilityTooLarge => "p > 1 in binomial distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+impl Binomial {
+    /// Construct a new `Binomial` with the given shape parameters `n` (number
+    /// of trials) and `p` (probability of success).
+    pub fn new(n: u64, p: f64) -> Result<Binomial, Error> {
+        if !(p >= 0.0) {
+            return Err(Error::ProbabilityTooSmall);
+        }
+        if !(p <= 1.0) {
+            return Err(Error::ProbabilityTooLarge);
+        }
+        Ok(Binomial { n, p })
+    }
+}
+
+/// Convert a `f64` to an `i64`, panicking on overflow.
+fn f64_to_i64(x: f64) -> i64 {
+    assert!(x < (core::i64::MAX as f64));
+    x as i64
+}
+
+impl Distribution<u64> for Binomial {
+    #[allow(clippy::many_single_char_names)] // Same names as in the reference.
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
+        // Handle these values directly.
+        if self.p == 0.0 {
+            return 0;
+        } else if self.p == 1.0 {
+            return self.n;
+        }
+
+        // The binomial distribution is symmetrical with respect to p -> 1-p,
+        // k -> n-k switch p so that it is less than 0.5 - this allows for lower
+        // expected values we will just invert the result at the end
+        let p = if self.p <= 0.5 { self.p } else { 1.0 - self.p };
+
+        let result;
+        let q = 1. - p;
+
+        // For small n * min(p, 1 - p), the BINV algorithm based on the inverse
+        // transformation of the binomial distribution is efficient. Otherwise,
+        // the BTPE algorithm is used.
+        //
+        // Voratas Kachitvichyanukul and Bruce W. Schmeiser. 1988. Binomial
+        // random variate generation. Commun. ACM 31, 2 (February 1988),
+        // 216-222. http://dx.doi.org/10.1145/42372.42381
+
+        // Threshold for preferring the BINV algorithm. The paper suggests 10,
+        // Ranlib uses 30, and GSL uses 14.
+        const BINV_THRESHOLD: f64 = 10.;
+
+        if (self.n as f64) * p < BINV_THRESHOLD && self.n <= (core::i32::MAX as u64) {
+            // Use the BINV algorithm.
+            let s = p / q;
+            let a = ((self.n + 1) as f64) * s;
+            let mut r = q.powi(self.n as i32);
+            let mut u: f64 = rng.gen();
+            let mut x = 0;
+            while u > r as f64 {
+                u -= r;
+                x += 1;
+                r *= a / (x as f64) - s;
+            }
+            result = x;
+        } else {
+            // Use the BTPE algorithm.
+
+            // Threshold for using the squeeze algorithm. This can be freely
+            // chosen based on performance. Ranlib and GSL use 20.
+            const SQUEEZE_THRESHOLD: i64 = 20;
+
+            // Step 0: Calculate constants as functions of `n` and `p`.
+            let n = self.n as f64;
+            let np = n * p;
+            let npq = np * q;
+            let f_m = np + p;
+            let m = f64_to_i64(f_m);
+            // radius of triangle region, since height=1 also area of region
+            let p1 = (2.195 * npq.sqrt() - 4.6 * q).floor() + 0.5;
+            // tip of triangle
+            let x_m = (m as f64) + 0.5;
+            // left edge of triangle
+            let x_l = x_m - p1;
+            // right edge of triangle
+            let x_r = x_m + p1;
+            let c = 0.134 + 20.5 / (15.3 + (m as f64));
+            // p1 + area of parallelogram region
+            let p2 = p1 * (1. + 2. * c);
+
+            fn lambda(a: f64) -> f64 {
+                a * (1. + 0.5 * a)
+            }
+
+            let lambda_l = lambda((f_m - x_l) / (f_m - x_l * p));
+            let lambda_r = lambda((x_r - f_m) / (x_r * q));
+            // p1 + area of left tail
+            let p3 = p2 + c / lambda_l;
+            // p1 + area of right tail
+            let p4 = p3 + c / lambda_r;
+
+            // return value
+            let mut y: i64;
+
+            let gen_u = Uniform::new(0., p4);
+            let gen_v = Uniform::new(0., 1.);
+
+            loop {
+                // Step 1: Generate `u` for selecting the region. If region 1 is
+                // selected, generate a triangularly distributed variate.
+                let u = gen_u.sample(rng);
+                let mut v = gen_v.sample(rng);
+                if !(u > p1) {
+                    y = f64_to_i64(x_m - p1 * v + u);
+                    break;
+                }
+
+                if !(u > p2) {
+                    // Step 2: Region 2, parallelograms. Check if region 2 is
+                    // used. If so, generate `y`.
+                    let x = x_l + (u - p1) / c;
+                    v = v * c + 1.0 - (x - x_m).abs() / p1;
+                    if v > 1. {
+                        continue;
+                    } else {
+                        y = f64_to_i64(x);
+                    }
+                } else if !(u > p3) {
+                    // Step 3: Region 3, left exponential tail.
+                    y = f64_to_i64(x_l + v.ln() / lambda_l);
+                    if y < 0 {
+                        continue;
+                    } else {
+                        v *= (u - p2) * lambda_l;
+                    }
+                } else {
+                    // Step 4: Region 4, right exponential tail.
+                    y = f64_to_i64(x_r - v.ln() / lambda_r);
+                    if y > 0 && (y as u64) > self.n {
+                        continue;
+                    } else {
+                        v *= (u - p3) * lambda_r;
+                    }
+                }
+
+                // Step 5: Acceptance/rejection comparison.
+
+                // Step 5.0: Test for appropriate method of evaluating f(y).
+                let k = (y - m).abs();
+                if !(k > SQUEEZE_THRESHOLD && (k as f64) < 0.5 * npq - 1.) {
+                    // Step 5.1: Evaluate f(y) via the recursive relationship. Start the
+                    // search from the mode.
+                    let s = p / q;
+                    let a = s * (n + 1.);
+                    let mut f = 1.0;
+                    match m.cmp(&y) {
+                        Ordering::Less => {
+                            let mut i = m;
+                            loop {
+                                i += 1;
+                                f *= a / (i as f64) - s;
+                                if i == y {
+                                    break;
+                                }
+                            }
+                        },
+                        Ordering::Greater => {
+                            let mut i = y;
+                            loop {
+                                i += 1;
+                                f /= a / (i as f64) - s;
+                                if i == m {
+                                    break;
+                                }
+                            }
+                        },
+                        Ordering::Equal => {},
+                    }
+                    if v > f {
+                        continue;
+                    } else {
+                        break;
+                    }
+                }
+
+                // Step 5.2: Squeezing. Check the value of ln(v) against upper and
+                // lower bound of ln(f(y)).
+                let k = k as f64;
+                let rho = (k / npq) * ((k * (k / 3. + 0.625) + 1. / 6.) / npq + 0.5);
+                let t = -0.5 * k * k / npq;
+                let alpha = v.ln();
+                if alpha < t - rho {
+                    break;
+                }
+                if alpha > t + rho {
+                    continue;
+                }
+
+                // Step 5.3: Final acceptance/rejection test.
+                let x1 = (y + 1) as f64;
+                let f1 = (m + 1) as f64;
+                let z = (f64_to_i64(n) + 1 - m) as f64;
+                let w = (f64_to_i64(n) - y + 1) as f64;
+
+                fn stirling(a: f64) -> f64 {
+                    let a2 = a * a;
+                    (13860. - (462. - (132. - (99. - 140. / a2) / a2) / a2) / a2) / a / 166320.
+                }
+
+                if alpha
+                    > x_m * (f1 / x1).ln()
+                        + (n - (m as f64) + 0.5) * (z / w).ln()
+                        + ((y - m) as f64) * (w * p / (x1 * q)).ln()
+                        // We use the signs from the GSL implementation, which are
+                        // different than the ones in the reference. According to
+                        // the GSL authors, the new signs were verified to be
+                        // correct by one of the original designers of the
+                        // algorithm.
+                        + stirling(f1)
+                        + stirling(z)
+                        - stirling(x1)
+                        - stirling(w)
+                {
+                    continue;
+                }
+
+                break;
+            }
+            assert!(y >= 0);
+            result = y as u64;
+        }
+
+        // Invert the result for p < 0.5.
+        if p != self.p {
+            self.n - result
+        } else {
+            result
+        }
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::Binomial;
+    use crate::Distribution;
+    use rand::Rng;
+
+    fn test_binomial_mean_and_variance<R: Rng>(n: u64, p: f64, rng: &mut R) {
+        let binomial = Binomial::new(n, p).unwrap();
+
+        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 = crate::test::rng(351);
+        test_binomial_mean_and_variance(150, 0.1, &mut rng);
+        test_binomial_mean_and_variance(70, 0.6, &mut rng);
+        test_binomial_mean_and_variance(40, 0.5, &mut rng);
+        test_binomial_mean_and_variance(20, 0.7, &mut rng);
+        test_binomial_mean_and_variance(20, 0.5, &mut rng);
+    }
+
+    #[test]
+    fn test_binomial_end_points() {
+        let mut rng = crate::test::rng(352);
+        assert_eq!(rng.sample(Binomial::new(20, 0.0).unwrap()), 0);
+        assert_eq!(rng.sample(Binomial::new(20, 1.0).unwrap()), 20);
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_binomial_invalid_lambda_neg() {
+        Binomial::new(20, -10.0).unwrap();
+    }
+}

vendor/rand_distr/src/cauchy.rs

@@ -0,0 +1,167 @@
+// 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 num_traits::{Float, FloatConst};
+use crate::{Distribution, Standard};
+use rand::Rng;
+use core::fmt;
+
+/// The Cauchy distribution `Cauchy(median, scale)`.
+///
+/// This distribution has a density function:
+/// `f(x) = 1 / (pi * scale * (1 + ((x - median) / scale)^2))`
+///
+/// Note that at least for `f32`, results are not fully portable due to minor
+/// differences in the target system's *tan* implementation, `tanf`.
+///
+/// # Example
+///
+/// ```
+/// use rand_distr::{Cauchy, Distribution};
+///
+/// let cau = Cauchy::new(2.0, 5.0).unwrap();
+/// let v = cau.sample(&mut rand::thread_rng());
+/// println!("{} is from a Cauchy(2, 5) distribution", v);
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct Cauchy<F>
+where F: Float + FloatConst, Standard: Distribution<F>
+{
+    median: F,
+    scale: F,
+}
+
+/// Error type returned from `Cauchy::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// `scale <= 0` or `nan`.
+    ScaleTooSmall,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::ScaleTooSmall => "scale is not positive in Cauchy distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+impl<F> Cauchy<F>
+where F: Float + FloatConst, Standard: Distribution<F>
+{
+    /// Construct a new `Cauchy` with the given shape parameters
+    /// `median` the peak location and `scale` the scale factor.
+    pub fn new(median: F, scale: F) -> Result<Cauchy<F>, Error> {
+        if !(scale > F::zero()) {
+            return Err(Error::ScaleTooSmall);
+        }
+        Ok(Cauchy { median, scale })
+    }
+}
+
+impl<F> Distribution<F> for Cauchy<F>
+where F: Float + FloatConst, Standard: Distribution<F>
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        // sample from [0, 1)
+        let x = Standard.sample(rng);
+        // 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 = (F::PI() * x).tan();
+        // shift and scale according to parameters
+        self.median + self.scale * comp_dev
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    fn median(numbers: &mut [f64]) -> f64 {
+        sort(numbers);
+        let mid = numbers.len() / 2;
+        numbers[mid]
+    }
+
+    fn sort(numbers: &mut [f64]) {
+        numbers.sort_by(|a, b| a.partial_cmp(b).unwrap());
+    }
+
+    #[test]
+    fn test_cauchy_averages() {
+        // NOTE: given that the variance and mean are undefined,
+        // this test does not have any rigorous statistical meaning.
+        let cauchy = Cauchy::new(10.0, 5.0).unwrap();
+        let mut rng = crate::test::rng(123);
+        let mut numbers: [f64; 1000] = [0.0; 1000];
+        let mut sum = 0.0;
+        for number in &mut numbers[..] {
+            *number = cauchy.sample(&mut rng);
+            sum += *number;
+        }
+        let median = median(&mut numbers);
+        #[cfg(feature = "std")]
+        std::println!("Cauchy median: {}", median);
+        assert!((median - 10.0).abs() < 0.4); // not 100% certain, but probable enough
+        let mean = sum / 1000.0;
+        #[cfg(feature = "std")]
+        std::println!("Cauchy mean: {}", mean);
+        // for a Cauchy distribution the mean should not converge
+        assert!((mean - 10.0).abs() > 0.4); // not 100% certain, but probable enough
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_cauchy_invalid_scale_zero() {
+        Cauchy::new(0.0, 0.0).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_cauchy_invalid_scale_neg() {
+        Cauchy::new(0.0, -10.0).unwrap();
+    }
+
+    #[test]
+    fn value_stability() {
+        fn gen_samples<F: Float + FloatConst + core::fmt::Debug>(m: F, s: F, buf: &mut [F])
+        where Standard: Distribution<F> {
+            let distr = Cauchy::new(m, s).unwrap();
+            let mut rng = crate::test::rng(353);
+            for x in buf {
+                *x = rng.sample(&distr);
+            }
+        }
+
+        let mut buf = [0.0; 4];
+        gen_samples(100f64, 10.0, &mut buf);
+        assert_eq!(&buf, &[
+            77.93369152808678,
+            90.1606912098641,
+            125.31516221323625,
+            86.10217834773925
+        ]);
+
+        // Unfortunately this test is not fully portable due to reliance on the
+        // system's implementation of tanf (see doc on Cauchy struct).
+        let mut buf = [0.0; 4];
+        gen_samples(10f32, 7.0, &mut buf);
+        let expected = [15.023088, -5.446413, 3.7092876, 3.112482];
+        for (a, b) in buf.iter().zip(expected.iter()) {
+            assert_almost_eq!(*a, *b, 1e-5);
+        }
+    }
+}

vendor/rand_distr/src/dirichlet.rs

@@ -0,0 +1,186 @@
+// 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.
+#![cfg(feature = "alloc")]
+use num_traits::Float;
+use crate::{Distribution, Exp1, Gamma, Open01, StandardNormal};
+use rand::Rng;
+use core::fmt;
+use alloc::{boxed::Box, vec, vec::Vec};
+
+/// The Dirichlet 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_distr::Dirichlet;
+///
+/// let dirichlet = Dirichlet::new(&[1.0, 2.0, 3.0]).unwrap();
+/// let samples = dirichlet.sample(&mut rand::thread_rng());
+/// println!("{:?} is from a Dirichlet([1.0, 2.0, 3.0]) distribution", samples);
+/// ```
+#[cfg_attr(doc_cfg, doc(cfg(feature = "alloc")))]
+#[derive(Clone, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct Dirichlet<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    /// Concentration parameters (alpha)
+    alpha: Box<[F]>,
+}
+
+/// Error type returned from `Dirchlet::new`.
+#[cfg_attr(doc_cfg, doc(cfg(feature = "alloc")))]
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// `alpha.len() < 2`.
+    AlphaTooShort,
+    /// `alpha <= 0.0` or `nan`.
+    AlphaTooSmall,
+    /// `size < 2`.
+    SizeTooSmall,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::AlphaTooShort | Error::SizeTooSmall => {
+                "less than 2 dimensions in Dirichlet distribution"
+            }
+            Error::AlphaTooSmall => "alpha is not positive in Dirichlet distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+impl<F> Dirichlet<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    /// Construct a new `Dirichlet` with the given alpha parameter `alpha`.
+    ///
+    /// Requires `alpha.len() >= 2`.
+    #[inline]
+    pub fn new(alpha: &[F]) -> Result<Dirichlet<F>, Error> {
+        if alpha.len() < 2 {
+            return Err(Error::AlphaTooShort);
+        }
+        for &ai in alpha.iter() {
+            if !(ai > F::zero()) {
+                return Err(Error::AlphaTooSmall);
+            }
+        }
+
+        Ok(Dirichlet { alpha: alpha.to_vec().into_boxed_slice() })
+    }
+
+    /// Construct a new `Dirichlet` with the given shape parameter `alpha` and `size`.
+    ///
+    /// Requires `size >= 2`.
+    #[inline]
+    pub fn new_with_size(alpha: F, size: usize) -> Result<Dirichlet<F>, Error> {
+        if !(alpha > F::zero()) {
+            return Err(Error::AlphaTooSmall);
+        }
+        if size < 2 {
+            return Err(Error::SizeTooSmall);
+        }
+        Ok(Dirichlet {
+            alpha: vec![alpha; size].into_boxed_slice(),
+        })
+    }
+}
+
+impl<F> Distribution<Vec<F>> for Dirichlet<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Vec<F> {
+        let n = self.alpha.len();
+        let mut samples = vec![F::zero(); n];
+        let mut sum = F::zero();
+
+        for (s, &a) in samples.iter_mut().zip(self.alpha.iter()) {
+            let g = Gamma::new(a, F::one()).unwrap();
+            *s = g.sample(rng);
+            sum =  sum + (*s);
+        }
+        let invacc = F::one() / sum;
+        for s in samples.iter_mut() {
+            *s = (*s)*invacc;
+        }
+        samples
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    fn test_dirichlet() {
+        let d = Dirichlet::new(&[1.0, 2.0, 3.0]).unwrap();
+        let mut rng = crate::test::rng(221);
+        let samples = d.sample(&mut rng);
+        let _: Vec<f64> = samples
+            .into_iter()
+            .map(|x| {
+                assert!(x > 0.0);
+                x
+            })
+            .collect();
+    }
+
+    #[test]
+    fn test_dirichlet_with_param() {
+        let alpha = 0.5f64;
+        let size = 2;
+        let d = Dirichlet::new_with_size(alpha, size).unwrap();
+        let mut rng = crate::test::rng(221);
+        let samples = d.sample(&mut rng);
+        let _: Vec<f64> = samples
+            .into_iter()
+            .map(|x| {
+                assert!(x > 0.0);
+                x
+            })
+            .collect();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_dirichlet_invalid_length() {
+        Dirichlet::new_with_size(0.5f64, 1).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_dirichlet_invalid_alpha() {
+        Dirichlet::new_with_size(0.0f64, 2).unwrap();
+    }
+}

vendor/rand_distr/src/exponential.rs

@@ -0,0 +1,181 @@
+// 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 crate::utils::ziggurat;
+use num_traits::Float;
+use crate::{ziggurat_tables, Distribution};
+use rand::Rng;
+use core::fmt;
+
+/// 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_distr::Exp1;
+///
+/// let val: f64 = thread_rng().sample(Exp1);
+/// println!("{}", val);
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct Exp1;
+
+impl Distribution<f32> for Exp1 {
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f32 {
+        // TODO: use optimal 32-bit implementation
+        let x: f64 = self.sample(rng);
+        x as f32
+    }
+}
+
+// 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`, when `lambda > 0`. For `lambda = 0`, all samples yield infinity.
+///
+/// Note that [`Exp1`](crate::Exp1) is an optimised implementation for `lambda = 1`.
+///
+/// # Example
+///
+/// ```
+/// use rand_distr::{Exp, Distribution};
+///
+/// let exp = Exp::new(2.0).unwrap();
+/// let v = exp.sample(&mut rand::thread_rng());
+/// println!("{} is from a Exp(2) distribution", v);
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct Exp<F>
+where F: Float, Exp1: Distribution<F>
+{
+    /// `lambda` stored as `1/lambda`, since this is what we scale by.
+    lambda_inverse: F,
+}
+
+/// Error type returned from `Exp::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// `lambda < 0` or `nan`.
+    LambdaTooSmall,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::LambdaTooSmall => "lambda is negative or NaN in exponential distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+impl<F: Float> Exp<F>
+where F: Float, Exp1: Distribution<F>
+{
+    /// Construct a new `Exp` with the given shape parameter
+    /// `lambda`.
+    /// 
+    /// # Remarks
+    /// 
+    /// For custom types `N` implementing the [`Float`] trait,
+    /// the case `lambda = 0` is handled as follows: each sample corresponds
+    /// to a sample from an `Exp1` multiplied by `1 / 0`. Primitive types 
+    /// yield infinity, since `1 / 0 = infinity`.
+    #[inline]
+    pub fn new(lambda: F) -> Result<Exp<F>, Error> {
+        if !(lambda >= F::zero()) {
+            return Err(Error::LambdaTooSmall);
+        }
+        Ok(Exp {
+            lambda_inverse: F::one() / lambda,
+        })
+    }
+}
+
+impl<F> Distribution<F> for Exp<F>
+where F: Float, Exp1: Distribution<F>
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        rng.sample(Exp1) * self.lambda_inverse
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    fn test_exp() {
+        let exp = Exp::new(10.0).unwrap();
+        let mut rng = crate::test::rng(221);
+        for _ in 0..1000 {
+            assert!(exp.sample(&mut rng) >= 0.0);
+        }
+    }
+    #[test]
+    fn test_zero() {
+        let d = Exp::new(0.0).unwrap();
+        assert_eq!(d.sample(&mut crate::test::rng(21)), f64::infinity());
+    }
+    #[test]
+    #[should_panic]
+    fn test_exp_invalid_lambda_neg() {
+        Exp::new(-10.0).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_exp_invalid_lambda_nan() {
+        Exp::new(f64::nan()).unwrap();
+    }
+}

vendor/rand_distr/src/frechet.rs

@@ -0,0 +1,185 @@
+// Copyright 2021 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 Fréchet distribution.
+
+use crate::{Distribution, OpenClosed01};
+use core::fmt;
+use num_traits::Float;
+use rand::Rng;
+
+/// Samples floating-point numbers according to the Fréchet distribution
+///
+/// This distribution has density function:
+/// `f(x) = [(x - μ) / σ]^(-1 - α) exp[-(x - μ) / σ]^(-α) α / σ`,
+/// where `μ` is the location parameter, `σ` the scale parameter, and `α` the shape parameter.
+///
+/// # Example
+/// ```
+/// use rand::prelude::*;
+/// use rand_distr::Frechet;
+///
+/// let val: f64 = thread_rng().sample(Frechet::new(0.0, 1.0, 1.0).unwrap());
+/// println!("{}", val);
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct Frechet<F>
+where
+    F: Float,
+    OpenClosed01: Distribution<F>,
+{
+    location: F,
+    scale: F,
+    shape: F,
+}
+
+/// Error type returned from `Frechet::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// location is infinite or NaN
+    LocationNotFinite,
+    /// scale is not finite positive number
+    ScaleNotPositive,
+    /// shape is not finite positive number
+    ShapeNotPositive,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::LocationNotFinite => "location is not finite in Frechet distribution",
+            Error::ScaleNotPositive => "scale is not positive and finite in Frechet distribution",
+            Error::ShapeNotPositive => "shape is not positive and finite in Frechet distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+impl<F> Frechet<F>
+where
+    F: Float,
+    OpenClosed01: Distribution<F>,
+{
+    /// Construct a new `Frechet` distribution with given `location`, `scale`, and `shape`.
+    pub fn new(location: F, scale: F, shape: F) -> Result<Frechet<F>, Error> {
+        if scale <= F::zero() || scale.is_infinite() || scale.is_nan() {
+            return Err(Error::ScaleNotPositive);
+        }
+        if shape <= F::zero() || shape.is_infinite() || shape.is_nan() {
+            return Err(Error::ShapeNotPositive);
+        }
+        if location.is_infinite() || location.is_nan() {
+            return Err(Error::LocationNotFinite);
+        }
+        Ok(Frechet {
+            location,
+            scale,
+            shape,
+        })
+    }
+}
+
+impl<F> Distribution<F> for Frechet<F>
+where
+    F: Float,
+    OpenClosed01: Distribution<F>,
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        let x: F = rng.sample(OpenClosed01);
+        self.location + self.scale * (-x.ln()).powf(-self.shape.recip())
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    #[should_panic]
+    fn test_zero_scale() {
+        Frechet::new(0.0, 0.0, 1.0).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_infinite_scale() {
+        Frechet::new(0.0, core::f64::INFINITY, 1.0).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_nan_scale() {
+        Frechet::new(0.0, core::f64::NAN, 1.0).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_zero_shape() {
+        Frechet::new(0.0, 1.0, 0.0).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_infinite_shape() {
+        Frechet::new(0.0, 1.0, core::f64::INFINITY).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_nan_shape() {
+        Frechet::new(0.0, 1.0, core::f64::NAN).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_infinite_location() {
+        Frechet::new(core::f64::INFINITY, 1.0, 1.0).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_nan_location() {
+        Frechet::new(core::f64::NAN, 1.0, 1.0).unwrap();
+    }
+
+    #[test]
+    fn test_sample_against_cdf() {
+        fn quantile_function(x: f64) -> f64 {
+            (-x.ln()).recip()
+        }
+        let location = 0.0;
+        let scale = 1.0;
+        let shape = 1.0;
+        let iterations = 100_000;
+        let increment = 1.0 / iterations as f64;
+        let probabilities = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9];
+        let mut quantiles = [0.0; 9];
+        for (i, p) in probabilities.iter().enumerate() {
+            quantiles[i] = quantile_function(*p);
+        }
+        let mut proportions = [0.0; 9];
+        let d = Frechet::new(location, scale, shape).unwrap();
+        let mut rng = crate::test::rng(1);
+        for _ in 0..iterations {
+            let replicate = d.sample(&mut rng);
+            for (i, q) in quantiles.iter().enumerate() {
+                if replicate < *q {
+                    proportions[i] += increment;
+                }
+            }
+        }
+        assert!(proportions
+            .iter()
+            .zip(&probabilities)
+            .all(|(p_hat, p)| (p_hat - p).abs() < 0.003))
+    }
+}

vendor/rand_distr/src/gamma.rs

@@ -0,0 +1,814 @@
+// 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.
+
+// We use the variable names from the published reference, therefore this
+// warning is not helpful.
+#![allow(clippy::many_single_char_names)]
+
+use self::ChiSquaredRepr::*;
+use self::GammaRepr::*;
+
+use crate::normal::StandardNormal;
+use num_traits::Float;
+use crate::{Distribution, Exp, Exp1, Open01};
+use rand::Rng;
+use core::fmt;
+#[cfg(feature = "serde1")]
+use serde::{Serialize, Deserialize};
+
+/// 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_distr::{Distribution, Gamma};
+///
+/// let gamma = Gamma::new(2.0, 5.0).unwrap();
+/// 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)]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+pub struct Gamma<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    repr: GammaRepr<F>,
+}
+
+/// Error type returned from `Gamma::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// `shape <= 0` or `nan`.
+    ShapeTooSmall,
+    /// `scale <= 0` or `nan`.
+    ScaleTooSmall,
+    /// `1 / scale == 0`.
+    ScaleTooLarge,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::ShapeTooSmall => "shape is not positive in gamma distribution",
+            Error::ScaleTooSmall => "scale is not positive in gamma distribution",
+            Error::ScaleTooLarge => "scale is infinity in gamma distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+enum GammaRepr<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    Large(GammaLargeShape<F>),
+    One(Exp<F>),
+    Small(GammaSmallShape<F>),
+}
+
+// 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)]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+struct GammaSmallShape<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    inv_shape: F,
+    large_shape: GammaLargeShape<F>,
+}
+
+/// 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)]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+struct GammaLargeShape<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    scale: F,
+    c: F,
+    d: F,
+}
+
+impl<F> Gamma<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    /// Construct an object representing the `Gamma(shape, scale)`
+    /// distribution.
+    #[inline]
+    pub fn new(shape: F, scale: F) -> Result<Gamma<F>, Error> {
+        if !(shape > F::zero()) {
+            return Err(Error::ShapeTooSmall);
+        }
+        if !(scale > F::zero()) {
+            return Err(Error::ScaleTooSmall);
+        }
+
+        let repr = if shape == F::one() {
+            One(Exp::new(F::one() / scale).map_err(|_| Error::ScaleTooLarge)?)
+        } else if shape < F::one() {
+            Small(GammaSmallShape::new_raw(shape, scale))
+        } else {
+            Large(GammaLargeShape::new_raw(shape, scale))
+        };
+        Ok(Gamma { repr })
+    }
+}
+
+impl<F> GammaSmallShape<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    fn new_raw(shape: F, scale: F) -> GammaSmallShape<F> {
+        GammaSmallShape {
+            inv_shape: F::one() / shape,
+            large_shape: GammaLargeShape::new_raw(shape + F::one(), scale),
+        }
+    }
+}
+
+impl<F> GammaLargeShape<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    fn new_raw(shape: F, scale: F) -> GammaLargeShape<F> {
+        let d = shape - F::from(1. / 3.).unwrap();
+        GammaLargeShape {
+            scale,
+            c: F::one() / (F::from(9.).unwrap() * d).sqrt(),
+            d,
+        }
+    }
+}
+
+impl<F> Distribution<F> for Gamma<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        match self.repr {
+            Small(ref g) => g.sample(rng),
+            One(ref g) => g.sample(rng),
+            Large(ref g) => g.sample(rng),
+        }
+    }
+}
+impl<F> Distribution<F> for GammaSmallShape<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        let u: F = rng.sample(Open01);
+
+        self.large_shape.sample(rng) * u.powf(self.inv_shape)
+    }
+}
+impl<F> Distribution<F> for GammaLargeShape<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        // Marsaglia & Tsang method, 2000
+        loop {
+            let x: F = rng.sample(StandardNormal);
+            let v_cbrt = F::one() + self.c * x;
+            if v_cbrt <= F::zero() {
+                // a^3 <= 0 iff a <= 0
+                continue;
+            }
+
+            let v = v_cbrt * v_cbrt * v_cbrt;
+            let u: F = rng.sample(Open01);
+
+            let x_sqr = x * x;
+            if u < F::one() - F::from(0.0331).unwrap() * x_sqr * x_sqr
+                || u.ln() < F::from(0.5).unwrap() * x_sqr + self.d * (F::one() - 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_distr::{ChiSquared, Distribution};
+///
+/// let chi = ChiSquared::new(11.0).unwrap();
+/// let v = chi.sample(&mut rand::thread_rng());
+/// println!("{} is from a χ²(11) distribution", v)
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+pub struct ChiSquared<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    repr: ChiSquaredRepr<F>,
+}
+
+/// Error type returned from `ChiSquared::new` and `StudentT::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+pub enum ChiSquaredError {
+    /// `0.5 * k <= 0` or `nan`.
+    DoFTooSmall,
+}
+
+impl fmt::Display for ChiSquaredError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            ChiSquaredError::DoFTooSmall => {
+                "degrees-of-freedom k is not positive in chi-squared distribution"
+            }
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for ChiSquaredError {}
+
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+enum ChiSquaredRepr<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    // 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<F>),
+}
+
+impl<F> ChiSquared<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    /// Create a new chi-squared distribution with degrees-of-freedom
+    /// `k`.
+    pub fn new(k: F) -> Result<ChiSquared<F>, ChiSquaredError> {
+        let repr = if k == F::one() {
+            DoFExactlyOne
+        } else {
+            if !(F::from(0.5).unwrap() * k > F::zero()) {
+                return Err(ChiSquaredError::DoFTooSmall);
+            }
+            DoFAnythingElse(Gamma::new(F::from(0.5).unwrap() * k, F::from(2.0).unwrap()).unwrap())
+        };
+        Ok(ChiSquared { repr })
+    }
+}
+impl<F> Distribution<F> for ChiSquared<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        match self.repr {
+            DoFExactlyOne => {
+                // k == 1 => N(0,1)^2
+                let norm: F = 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_distr::{FisherF, Distribution};
+///
+/// let f = FisherF::new(2.0, 32.0).unwrap();
+/// let v = f.sample(&mut rand::thread_rng());
+/// println!("{} is from an F(2, 32) distribution", v)
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+pub struct FisherF<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    numer: ChiSquared<F>,
+    denom: ChiSquared<F>,
+    // denom_dof / numer_dof so that this can just be a straight
+    // multiplication, rather than a division.
+    dof_ratio: F,
+}
+
+/// Error type returned from `FisherF::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+pub enum FisherFError {
+    /// `m <= 0` or `nan`.
+    MTooSmall,
+    /// `n <= 0` or `nan`.
+    NTooSmall,
+}
+
+impl fmt::Display for FisherFError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            FisherFError::MTooSmall => "m is not positive in Fisher F distribution",
+            FisherFError::NTooSmall => "n is not positive in Fisher F distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for FisherFError {}
+
+impl<F> FisherF<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    /// Create a new `FisherF` distribution, with the given parameter.
+    pub fn new(m: F, n: F) -> Result<FisherF<F>, FisherFError> {
+        let zero = F::zero();
+        if !(m > zero) {
+            return Err(FisherFError::MTooSmall);
+        }
+        if !(n > zero) {
+            return Err(FisherFError::NTooSmall);
+        }
+
+        Ok(FisherF {
+            numer: ChiSquared::new(m).unwrap(),
+            denom: ChiSquared::new(n).unwrap(),
+            dof_ratio: n / m,
+        })
+    }
+}
+impl<F> Distribution<F> for FisherF<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        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_distr::{StudentT, Distribution};
+///
+/// let t = StudentT::new(11.0).unwrap();
+/// let v = t.sample(&mut rand::thread_rng());
+/// println!("{} is from a t(11) distribution", v)
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+pub struct StudentT<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    chi: ChiSquared<F>,
+    dof: F,
+}
+
+impl<F> StudentT<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    /// Create a new Student t distribution with `n` degrees of
+    /// freedom.
+    pub fn new(n: F) -> Result<StudentT<F>, ChiSquaredError> {
+        Ok(StudentT {
+            chi: ChiSquared::new(n)?,
+            dof: n,
+        })
+    }
+}
+impl<F> Distribution<F> for StudentT<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        let norm: F = rng.sample(StandardNormal);
+        norm * (self.dof / self.chi.sample(rng)).sqrt()
+    }
+}
+
+/// The algorithm used for sampling the Beta distribution.
+///
+/// Reference:
+///
+/// R. C. H. Cheng (1978).
+/// Generating beta variates with nonintegral shape parameters.
+/// Communications of the ACM 21, 317-322.
+/// https://doi.org/10.1145/359460.359482
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+enum BetaAlgorithm<N> {
+    BB(BB<N>),
+    BC(BC<N>),
+}
+
+/// Algorithm BB for `min(alpha, beta) > 1`.
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+struct BB<N> {
+    alpha: N,
+    beta: N,
+    gamma: N,
+}
+
+/// Algorithm BC for `min(alpha, beta) <= 1`.
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+struct BC<N> {
+    alpha: N,
+    beta: N,
+    delta: N,
+    kappa1: N,
+    kappa2: N,
+}
+
+/// The Beta distribution with shape parameters `alpha` and `beta`.
+///
+/// # Example
+///
+/// ```
+/// use rand_distr::{Distribution, Beta};
+///
+/// let beta = Beta::new(2.0, 5.0).unwrap();
+/// let v = beta.sample(&mut rand::thread_rng());
+/// println!("{} is from a Beta(2, 5) distribution", v);
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+pub struct Beta<F>
+where
+    F: Float,
+    Open01: Distribution<F>,
+{
+    a: F, b: F, switched_params: bool,
+    algorithm: BetaAlgorithm<F>,
+}
+
+/// Error type returned from `Beta::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+pub enum BetaError {
+    /// `alpha <= 0` or `nan`.
+    AlphaTooSmall,
+    /// `beta <= 0` or `nan`.
+    BetaTooSmall,
+}
+
+impl fmt::Display for BetaError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            BetaError::AlphaTooSmall => "alpha is not positive in beta distribution",
+            BetaError::BetaTooSmall => "beta is not positive in beta distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for BetaError {}
+
+impl<F> Beta<F>
+where
+    F: Float,
+    Open01: Distribution<F>,
+{
+    /// Construct an object representing the `Beta(alpha, beta)`
+    /// distribution.
+    pub fn new(alpha: F, beta: F) -> Result<Beta<F>, BetaError> {
+        if !(alpha > F::zero()) {
+            return Err(BetaError::AlphaTooSmall);
+        }
+        if !(beta > F::zero()) {
+            return Err(BetaError::BetaTooSmall);
+        }
+        // From now on, we use the notation from the reference,
+        // i.e. `alpha` and `beta` are renamed to `a0` and `b0`.
+        let (a0, b0) = (alpha, beta);
+        let (a, b, switched_params) = if a0 < b0 {
+            (a0, b0, false)
+        } else {
+            (b0, a0, true)
+        };
+        if a > F::one() {
+            // Algorithm BB
+            let alpha = a + b;
+            let beta = ((alpha - F::from(2.).unwrap())
+                        / (F::from(2.).unwrap()*a*b - alpha)).sqrt();
+            let gamma = a + F::one() / beta;
+
+            Ok(Beta {
+                a, b, switched_params,
+                algorithm: BetaAlgorithm::BB(BB {
+                    alpha, beta, gamma,
+                })
+            })
+        } else {
+            // Algorithm BC
+            //
+            // Here `a` is the maximum instead of the minimum.
+            let (a, b, switched_params) = (b, a, !switched_params);
+            let alpha = a + b;
+            let beta = F::one() / b;
+            let delta = F::one() + a - b;
+            let kappa1 = delta
+                * (F::from(1. / 18. / 4.).unwrap() + F::from(3. / 18. / 4.).unwrap()*b)
+                / (a*beta - F::from(14. / 18.).unwrap());
+            let kappa2 = F::from(0.25).unwrap()
+                + (F::from(0.5).unwrap() + F::from(0.25).unwrap()/delta)*b;
+
+            Ok(Beta {
+                a, b, switched_params,
+                algorithm: BetaAlgorithm::BC(BC {
+                    alpha, beta, delta, kappa1, kappa2,
+                })
+            })
+        }
+    }
+}
+
+impl<F> Distribution<F> for Beta<F>
+where
+    F: Float,
+    Open01: Distribution<F>,
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        let mut w;
+        match self.algorithm {
+            BetaAlgorithm::BB(algo) => {
+                loop {
+                    // 1.
+                    let u1 = rng.sample(Open01);
+                    let u2 = rng.sample(Open01);
+                    let v = algo.beta * (u1 / (F::one() - u1)).ln();
+                    w = self.a * v.exp();
+                    let z = u1*u1 * u2;
+                    let r = algo.gamma * v - F::from(4.).unwrap().ln();
+                    let s = self.a + r - w;
+                    // 2.
+                    if s + F::one() + F::from(5.).unwrap().ln()
+                        >= F::from(5.).unwrap() * z {
+                        break;
+                    }
+                    // 3.
+                    let t = z.ln();
+                    if s >= t {
+                        break;
+                    }
+                    // 4.
+                    if !(r + algo.alpha * (algo.alpha / (self.b + w)).ln() < t) {
+                        break;
+                    }
+                }
+            },
+            BetaAlgorithm::BC(algo) => {
+                loop {
+                    let z;
+                    // 1.
+                    let u1 = rng.sample(Open01);
+                    let u2 = rng.sample(Open01);
+                    if u1 < F::from(0.5).unwrap() {
+                        // 2.
+                        let y = u1 * u2;
+                        z = u1 * y;
+                        if F::from(0.25).unwrap() * u2 + z - y >= algo.kappa1 {
+                            continue;
+                        }
+                    } else {
+                        // 3.
+                        z = u1 * u1 * u2;
+                        if z <= F::from(0.25).unwrap() {
+                            let v = algo.beta * (u1 / (F::one() - u1)).ln();
+                            w = self.a * v.exp();
+                            break;
+                        }
+                        // 4.
+                        if z >= algo.kappa2 {
+                            continue;
+                        }
+                    }
+                    // 5.
+                    let v = algo.beta * (u1 / (F::one() - u1)).ln();
+                    w = self.a * v.exp();
+                    if !(algo.alpha * ((algo.alpha / (self.b + w)).ln() + v)
+                         - F::from(4.).unwrap().ln() < z.ln()) {
+                        break;
+                    };
+                }
+            },
+        };
+        // 5. for BB, 6. for BC
+        if !self.switched_params {
+            if w == F::infinity() {
+                // Assuming `b` is finite, for large `w`:
+                return F::one();
+            }
+            w / (self.b + w)
+        } else {
+            self.b / (self.b + w)
+        }
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    fn test_chi_squared_one() {
+        let chi = ChiSquared::new(1.0).unwrap();
+        let mut rng = crate::test::rng(201);
+        for _ in 0..1000 {
+            chi.sample(&mut rng);
+        }
+    }
+    #[test]
+    fn test_chi_squared_small() {
+        let chi = ChiSquared::new(0.5).unwrap();
+        let mut rng = crate::test::rng(202);
+        for _ in 0..1000 {
+            chi.sample(&mut rng);
+        }
+    }
+    #[test]
+    fn test_chi_squared_large() {
+        let chi = ChiSquared::new(30.0).unwrap();
+        let mut rng = crate::test::rng(203);
+        for _ in 0..1000 {
+            chi.sample(&mut rng);
+        }
+    }
+    #[test]
+    #[should_panic]
+    fn test_chi_squared_invalid_dof() {
+        ChiSquared::new(-1.0).unwrap();
+    }
+
+    #[test]
+    fn test_f() {
+        let f = FisherF::new(2.0, 32.0).unwrap();
+        let mut rng = crate::test::rng(204);
+        for _ in 0..1000 {
+            f.sample(&mut rng);
+        }
+    }
+
+    #[test]
+    fn test_t() {
+        let t = StudentT::new(11.0).unwrap();
+        let mut rng = crate::test::rng(205);
+        for _ in 0..1000 {
+            t.sample(&mut rng);
+        }
+    }
+
+    #[test]
+    fn test_beta() {
+        let beta = Beta::new(1.0, 2.0).unwrap();
+        let mut rng = crate::test::rng(201);
+        for _ in 0..1000 {
+            beta.sample(&mut rng);
+        }
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_beta_invalid_dof() {
+        Beta::new(0., 0.).unwrap();
+    }
+
+    #[test]
+    fn test_beta_small_param() {
+        let beta = Beta::<f64>::new(1e-3, 1e-3).unwrap();
+        let mut rng = crate::test::rng(206);
+        for i in 0..1000 {
+            assert!(!beta.sample(&mut rng).is_nan(), "failed at i={}", i);
+        }
+    }
+}

vendor/rand_distr/src/geometric.rs

@@ -0,0 +1,238 @@
+//! The geometric distribution.
+
+use crate::Distribution;
+use rand::Rng;
+use core::fmt;
+#[allow(unused_imports)]
+use num_traits::Float;
+
+/// The geometric distribution `Geometric(p)` bounded to `[0, u64::MAX]`.
+/// 
+/// This is the probability distribution of the number of failures before the
+/// first success in a series of Bernoulli trials. It has the density function
+/// `f(k) = (1 - p)^k p` for `k >= 0`, where `p` is the probability of success
+/// on each trial.
+/// 
+/// This is the discrete analogue of the [exponential distribution](crate::Exp).
+/// 
+/// Note that [`StandardGeometric`](crate::StandardGeometric) is an optimised
+/// implementation for `p = 0.5`.
+///
+/// # Example
+///
+/// ```
+/// use rand_distr::{Geometric, Distribution};
+///
+/// let geo = Geometric::new(0.25).unwrap();
+/// let v = geo.sample(&mut rand::thread_rng());
+/// println!("{} is from a Geometric(0.25) distribution", v);
+/// ```
+#[derive(Copy, Clone, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct Geometric
+{
+    p: f64,
+    pi: f64,
+    k: u64
+}
+
+/// Error type returned from `Geometric::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// `p < 0 || p > 1` or `nan`
+    InvalidProbability,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::InvalidProbability => "p is NaN or outside the interval [0, 1] in geometric distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+impl Geometric {
+    /// Construct a new `Geometric` with the given shape parameter `p`
+    /// (probability of success on each trial).
+    pub fn new(p: f64) -> Result<Self, Error> {
+        if !p.is_finite() || p < 0.0 || p > 1.0 {
+            Err(Error::InvalidProbability)
+        } else if p == 0.0 || p >= 2.0 / 3.0 {
+            Ok(Geometric { p, pi: p, k: 0 })
+        } else {
+            let (pi, k) = {
+                // choose smallest k such that pi = (1 - p)^(2^k) <= 0.5
+                let mut k = 1;
+                let mut pi = (1.0 - p).powi(2);
+                while pi > 0.5 {
+                    k += 1;
+                    pi = pi * pi;
+                }
+                (pi, k)
+            };
+
+            Ok(Geometric { p, pi, k })
+        }
+    }
+}
+
+impl Distribution<u64> for Geometric
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
+        if self.p >= 2.0 / 3.0 {
+            // use the trivial algorithm:
+            let mut failures = 0;
+            loop {
+                let u = rng.gen::<f64>();
+                if u <= self.p { break; }
+                failures += 1;
+            }
+            return failures;
+        }
+        
+        if self.p == 0.0 { return core::u64::MAX; }
+
+        let Geometric { p, pi, k } = *self;
+
+        // Based on the algorithm presented in section 3 of
+        // Karl Bringmann and Tobias Friedrich (July 2013) - Exact and Efficient
+        // Generation of Geometric Random Variates and Random Graphs, published
+        // in International Colloquium on Automata, Languages and Programming
+        // (pp.267-278)
+        // https://people.mpi-inf.mpg.de/~kbringma/paper/2013ICALP-1.pdf
+
+        // Use the trivial algorithm to sample D from Geo(pi) = Geo(p) / 2^k:
+        let d = {
+            let mut failures = 0;
+            while rng.gen::<f64>() < pi {
+                failures += 1;
+            }
+            failures
+        };
+
+        // Use rejection sampling for the remainder M from Geo(p) % 2^k:
+        // choose M uniformly from [0, 2^k), but reject with probability (1 - p)^M
+        // NOTE: The paper suggests using bitwise sampling here, which is 
+        // currently unsupported, but should improve performance by requiring
+        // fewer iterations on average.                 ~ October 28, 2020
+        let m = loop {
+            let m = rng.gen::<u64>() & ((1 << k) - 1);
+            let p_reject = if m <= core::i32::MAX as u64 {
+                (1.0 - p).powi(m as i32)
+            } else {
+                (1.0 - p).powf(m as f64)
+            };
+            
+            let u = rng.gen::<f64>();
+            if u < p_reject {
+                break m;
+            }
+        };
+
+        (d << k) + m
+    }
+}
+
+/// Samples integers according to the geometric distribution with success
+/// probability `p = 0.5`. This is equivalent to `Geometeric::new(0.5)`,
+/// but faster.
+/// 
+/// See [`Geometric`](crate::Geometric) for the general geometric distribution.
+/// 
+/// Implemented via iterated [Rng::gen::<u64>().leading_zeros()].
+/// 
+/// # Example
+/// ```
+/// use rand::prelude::*;
+/// use rand_distr::StandardGeometric;
+/// 
+/// let v = StandardGeometric.sample(&mut thread_rng());
+/// println!("{} is from a Geometric(0.5) distribution", v);
+/// ```
+#[derive(Copy, Clone, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct StandardGeometric;
+
+impl Distribution<u64> for StandardGeometric {
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
+        let mut result = 0;
+        loop {
+            let x = rng.gen::<u64>().leading_zeros() as u64;
+            result += x;
+            if x < 64 { break; }
+        }
+        result
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    fn test_geo_invalid_p() {
+        assert!(Geometric::new(core::f64::NAN).is_err());
+        assert!(Geometric::new(core::f64::INFINITY).is_err());
+        assert!(Geometric::new(core::f64::NEG_INFINITY).is_err());
+
+        assert!(Geometric::new(-0.5).is_err());
+        assert!(Geometric::new(0.0).is_ok());
+        assert!(Geometric::new(1.0).is_ok());
+        assert!(Geometric::new(2.0).is_err());
+    }
+
+    fn test_geo_mean_and_variance<R: Rng>(p: f64, rng: &mut R) {
+        let distr = Geometric::new(p).unwrap();
+
+        let expected_mean = (1.0 - p) / p;
+        let expected_variance = (1.0 - p) / (p * p);
+
+        let mut results = [0.0; 10000];
+        for i in results.iter_mut() {
+            *i = distr.sample(rng) as f64;
+        }
+
+        let mean = results.iter().sum::<f64>() / results.len() as f64;
+        assert!((mean as f64 - expected_mean).abs() < expected_mean / 40.0);
+
+        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_geometric() {
+        let mut rng = crate::test::rng(12345);
+
+        test_geo_mean_and_variance(0.10, &mut rng);
+        test_geo_mean_and_variance(0.25, &mut rng);
+        test_geo_mean_and_variance(0.50, &mut rng);
+        test_geo_mean_and_variance(0.75, &mut rng);
+        test_geo_mean_and_variance(0.90, &mut rng);
+    }
+
+    #[test]
+    fn test_standard_geometric() {
+        let mut rng = crate::test::rng(654321);
+
+        let distr = StandardGeometric;
+        let expected_mean = 1.0;
+        let expected_variance = 2.0;
+
+        let mut results = [0.0; 1000];
+        for i in results.iter_mut() {
+            *i = distr.sample(&mut 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);
+    }
+}

vendor/rand_distr/src/gumbel.rs

@@ -0,0 +1,155 @@
+// Copyright 2021 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 Gumbel distribution.
+
+use crate::{Distribution, OpenClosed01};
+use core::fmt;
+use num_traits::Float;
+use rand::Rng;
+
+/// Samples floating-point numbers according to the Gumbel distribution
+///
+/// This distribution has density function:
+/// `f(x) = exp(-(z + exp(-z))) / σ`, where `z = (x - μ) / σ`,
+/// `μ` is the location parameter, and `σ` the scale parameter.
+///
+/// # Example
+/// ```
+/// use rand::prelude::*;
+/// use rand_distr::Gumbel;
+///
+/// let val: f64 = thread_rng().sample(Gumbel::new(0.0, 1.0).unwrap());
+/// println!("{}", val);
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct Gumbel<F>
+where
+    F: Float,
+    OpenClosed01: Distribution<F>,
+{
+    location: F,
+    scale: F,
+}
+
+/// Error type returned from `Gumbel::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// location is infinite or NaN
+    LocationNotFinite,
+    /// scale is not finite positive number
+    ScaleNotPositive,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::ScaleNotPositive => "scale is not positive and finite in Gumbel distribution",
+            Error::LocationNotFinite => "location is not finite in Gumbel distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+impl<F> Gumbel<F>
+where
+    F: Float,
+    OpenClosed01: Distribution<F>,
+{
+    /// Construct a new `Gumbel` distribution with given `location` and `scale`.
+    pub fn new(location: F, scale: F) -> Result<Gumbel<F>, Error> {
+        if scale <= F::zero() || scale.is_infinite() || scale.is_nan() {
+            return Err(Error::ScaleNotPositive);
+        }
+        if location.is_infinite() || location.is_nan() {
+            return Err(Error::LocationNotFinite);
+        }
+        Ok(Gumbel { location, scale })
+    }
+}
+
+impl<F> Distribution<F> for Gumbel<F>
+where
+    F: Float,
+    OpenClosed01: Distribution<F>,
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        let x: F = rng.sample(OpenClosed01);
+        self.location - self.scale * (-x.ln()).ln()
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    #[should_panic]
+    fn test_zero_scale() {
+        Gumbel::new(0.0, 0.0).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_infinite_scale() {
+        Gumbel::new(0.0, core::f64::INFINITY).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_nan_scale() {
+        Gumbel::new(0.0, core::f64::NAN).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_infinite_location() {
+        Gumbel::new(core::f64::INFINITY, 1.0).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_nan_location() {
+        Gumbel::new(core::f64::NAN, 1.0).unwrap();
+    }
+
+    #[test]
+    fn test_sample_against_cdf() {
+        fn neg_log_log(x: f64) -> f64 {
+            -(-x.ln()).ln()
+        }
+        let location = 0.0;
+        let scale = 1.0;
+        let iterations = 100_000;
+        let increment = 1.0 / iterations as f64;
+        let probabilities = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9];
+        let mut quantiles = [0.0; 9];
+        for (i, p) in probabilities.iter().enumerate() {
+            quantiles[i] = neg_log_log(*p);
+        }
+        let mut proportions = [0.0; 9];
+        let d = Gumbel::new(location, scale).unwrap();
+        let mut rng = crate::test::rng(1);
+        for _ in 0..iterations {
+            let replicate = d.sample(&mut rng);
+            for (i, q) in quantiles.iter().enumerate() {
+                if replicate < *q {
+                    proportions[i] += increment;
+                }
+            }
+        }
+        assert!(proportions
+            .iter()
+            .zip(&probabilities)
+            .all(|(p_hat, p)| (p_hat - p).abs() < 0.003))
+    }
+}

vendor/rand_distr/src/hypergeometric.rs

@@ -0,0 +1,422 @@
+//! The hypergeometric distribution.
+
+use crate::Distribution;
+use rand::Rng;
+use rand::distributions::uniform::Uniform;
+use core::fmt;
+#[allow(unused_imports)]
+use num_traits::Float;
+
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+enum SamplingMethod {
+    InverseTransform{ initial_p: f64, initial_x: i64 },
+    RejectionAcceptance{
+        m: f64,
+        a: f64,
+        lambda_l: f64,
+        lambda_r: f64,
+        x_l: f64,
+        x_r: f64,
+        p1: f64,
+        p2: f64,
+        p3: f64
+    },
+}
+
+/// The hypergeometric distribution `Hypergeometric(N, K, n)`.
+/// 
+/// This is the distribution of successes in samples of size `n` drawn without
+/// replacement from a population of size `N` containing `K` success states.
+/// It has the density function:
+/// `f(k) = binomial(K, k) * binomial(N-K, n-k) / binomial(N, n)`,
+/// where `binomial(a, b) = a! / (b! * (a - b)!)`.
+/// 
+/// The [binomial distribution](crate::Binomial) is the analogous distribution
+/// for sampling with replacement. It is a good approximation when the population
+/// size is much larger than the sample size.
+/// 
+/// # Example
+/// 
+/// ```
+/// use rand_distr::{Distribution, Hypergeometric};
+///
+/// let hypergeo = Hypergeometric::new(60, 24, 7).unwrap();
+/// let v = hypergeo.sample(&mut rand::thread_rng());
+/// println!("{} is from a hypergeometric distribution", v);
+/// ```
+#[derive(Copy, Clone, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct Hypergeometric {
+    n1: u64,
+    n2: u64,
+    k: u64,
+    offset_x: i64,
+    sign_x: i64,
+    sampling_method: SamplingMethod,
+}
+
+/// Error type returned from `Hypergeometric::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// `total_population_size` is too large, causing floating point underflow.
+    PopulationTooLarge,
+    /// `population_with_feature > total_population_size`.
+    ProbabilityTooLarge,
+    /// `sample_size > total_population_size`.
+    SampleSizeTooLarge,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::PopulationTooLarge => "total_population_size is too large causing underflow in geometric distribution",
+            Error::ProbabilityTooLarge => "population_with_feature > total_population_size in geometric distribution",
+            Error::SampleSizeTooLarge => "sample_size > total_population_size in geometric distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+// evaluate fact(numerator.0)*fact(numerator.1) / fact(denominator.0)*fact(denominator.1)
+fn fraction_of_products_of_factorials(numerator: (u64, u64), denominator: (u64, u64)) -> f64 {
+    let min_top = u64::min(numerator.0, numerator.1);
+    let min_bottom = u64::min(denominator.0, denominator.1);
+    // the factorial of this will cancel out:
+    let min_all = u64::min(min_top, min_bottom);
+
+    let max_top = u64::max(numerator.0, numerator.1);
+    let max_bottom = u64::max(denominator.0, denominator.1);
+    let max_all = u64::max(max_top, max_bottom);
+
+    let mut result = 1.0;
+    for i in (min_all + 1)..=max_all {
+        if i <= min_top {
+            result *= i as f64;
+        }
+        
+        if i <= min_bottom {
+            result /= i as f64;
+        }
+        
+        if i <= max_top {
+            result *= i as f64;
+        }
+        
+        if i <= max_bottom {
+            result /= i as f64;
+        }
+    }
+    
+    result
+}
+
+fn ln_of_factorial(v: f64) -> f64 {
+    // the paper calls for ln(v!), but also wants to pass in fractions,
+    // so we need to use Stirling's approximation to fill in the gaps:
+    v * v.ln() - v
+}
+
+impl Hypergeometric {
+    /// Constructs a new `Hypergeometric` with the shape parameters
+    /// `N = total_population_size`,
+    /// `K = population_with_feature`,
+    /// `n = sample_size`.
+    #[allow(clippy::many_single_char_names)] // Same names as in the reference.
+    pub fn new(total_population_size: u64, population_with_feature: u64, sample_size: u64) -> Result<Self, Error> {
+        if population_with_feature > total_population_size {
+            return Err(Error::ProbabilityTooLarge);
+        }
+
+        if sample_size > total_population_size {
+            return Err(Error::SampleSizeTooLarge);
+        }
+
+        // set-up constants as function of original parameters
+        let n = total_population_size;
+        let (mut sign_x, mut offset_x) = (1, 0);
+        let (n1, n2) = {
+            // switch around success and failure states if necessary to ensure n1 <= n2
+            let population_without_feature = n - population_with_feature;
+            if population_with_feature > population_without_feature {
+                sign_x = -1;
+                offset_x = sample_size as i64;
+                (population_without_feature, population_with_feature)
+            } else {
+                (population_with_feature, population_without_feature)
+            }
+        };
+        // when sampling more than half the total population, take the smaller
+        // group as sampled instead (we can then return n1-x instead).
+        // 
+        // Note: the boundary condition given in the paper is `sample_size < n / 2`;
+        // we're deviating here, because when n is even, it doesn't matter whether
+        // we switch here or not, but when n is odd `n/2 < n - n/2`, so switching
+        // when `k == n/2`, we'd actually be taking the _larger_ group as sampled.
+        let k = if sample_size <= n / 2 {
+            sample_size
+        } else {
+            offset_x += n1 as i64 * sign_x;
+            sign_x *= -1;
+            n - sample_size
+        };
+
+        // Algorithm H2PE has bounded runtime only if `M - max(0, k-n2) >= 10`,
+        // where `M` is the mode of the distribution.
+        // Use algorithm HIN for the remaining parameter space.
+        // 
+        // Voratas Kachitvichyanukul and Bruce W. Schmeiser. 1985. Computer
+        // generation of hypergeometric random variates.
+        // J. Statist. Comput. Simul. Vol.22 (August 1985), 127-145
+        // https://www.researchgate.net/publication/233212638
+        const HIN_THRESHOLD: f64 = 10.0;
+        let m = ((k + 1) as f64 * (n1 + 1) as f64 / (n + 2) as f64).floor();
+        let sampling_method = if m - f64::max(0.0, k as f64 - n2 as f64) < HIN_THRESHOLD {
+            let (initial_p, initial_x) = if k < n2 {
+                (fraction_of_products_of_factorials((n2, n - k), (n, n2 - k)), 0)
+            } else {
+                (fraction_of_products_of_factorials((n1, k), (n, k - n2)), (k - n2) as i64)
+            };
+
+            if initial_p <= 0.0 || !initial_p.is_finite() {
+                return Err(Error::PopulationTooLarge);
+            }
+
+            SamplingMethod::InverseTransform { initial_p, initial_x }
+        } else {
+            let a = ln_of_factorial(m) +
+                ln_of_factorial(n1 as f64 - m) +
+                ln_of_factorial(k as f64 - m) +
+                ln_of_factorial((n2 - k) as f64 + m);
+
+            let numerator = (n - k) as f64 * k as f64 * n1 as f64 * n2 as f64;
+            let denominator = (n - 1) as f64 * n as f64 * n as f64;
+            let d = 1.5 * (numerator / denominator).sqrt() + 0.5;
+
+            let x_l = m - d + 0.5;
+            let x_r = m + d + 0.5;
+
+            let k_l = f64::exp(a -
+                ln_of_factorial(x_l) -
+                ln_of_factorial(n1 as f64 - x_l) -
+                ln_of_factorial(k as f64 - x_l) -
+                ln_of_factorial((n2 - k) as f64 + x_l));
+            let k_r = f64::exp(a -
+                ln_of_factorial(x_r - 1.0) -
+                ln_of_factorial(n1 as f64 - x_r + 1.0) -
+                ln_of_factorial(k as f64 - x_r + 1.0) -
+                ln_of_factorial((n2 - k) as f64 + x_r - 1.0));
+            
+            let numerator = x_l * ((n2 - k) as f64 + x_l);
+            let denominator = (n1 as f64 - x_l + 1.0) * (k as f64 - x_l + 1.0);
+            let lambda_l = -((numerator / denominator).ln());
+
+            let numerator = (n1 as f64 - x_r + 1.0) * (k as f64 - x_r + 1.0);
+            let denominator = x_r * ((n2 - k) as f64 + x_r);
+            let lambda_r = -((numerator / denominator).ln());
+
+            // the paper literally gives `p2 + kL/lambdaL` where it (probably)
+            // should have been `p2 <- p1 + kL/lambdaL`; another print error?!
+            let p1 = 2.0 * d;
+            let p2 = p1 + k_l / lambda_l;
+            let p3 = p2 + k_r / lambda_r;
+
+            SamplingMethod::RejectionAcceptance {
+                m, a, lambda_l, lambda_r, x_l, x_r, p1, p2, p3
+            }
+        };
+
+        Ok(Hypergeometric { n1, n2, k, offset_x, sign_x, sampling_method })
+    }
+}
+
+impl Distribution<u64> for Hypergeometric {
+    #[allow(clippy::many_single_char_names)] // Same names as in the reference.
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
+        use SamplingMethod::*;
+
+        let Hypergeometric { n1, n2, k, sign_x, offset_x, sampling_method } = *self;
+        let x = match sampling_method {
+            InverseTransform { initial_p: mut p, initial_x: mut x } => {
+                let mut u = rng.gen::<f64>();
+                while u > p && x < k as i64 { // the paper erroneously uses `until n < p`, which doesn't make any sense
+                    u -= p;
+                    p *= ((n1 as i64 - x as i64) * (k as i64 - x as i64)) as f64;
+                    p /= ((x as i64 + 1) * (n2 as i64 - k as i64 + 1 + x as i64)) as f64;
+                    x += 1;
+                }
+                x
+            },
+            RejectionAcceptance { m, a, lambda_l, lambda_r, x_l, x_r, p1, p2, p3 } => {
+                let distr_region_select = Uniform::new(0.0, p3);
+                loop {
+                    let (y, v) = loop {
+                        let u = distr_region_select.sample(rng);
+                        let v = rng.gen::<f64>(); // for the accept/reject decision
+            
+                        if u <= p1 {
+                            // Region 1, central bell
+                            let y = (x_l + u).floor();
+                            break (y, v);
+                        } else if u <= p2 {
+                            // Region 2, left exponential tail
+                            let y = (x_l + v.ln() / lambda_l).floor();
+                            if y as i64 >= i64::max(0, k as i64 - n2 as i64) {
+                                let v = v * (u - p1) * lambda_l;
+                                break (y, v);
+                            }
+                        } else {
+                            // Region 3, right exponential tail
+                            let y = (x_r - v.ln() / lambda_r).floor();
+                            if y as u64 <= u64::min(n1, k) {
+                                let v = v * (u - p2) * lambda_r;
+                                break (y, v);
+                            }
+                        }
+                    };
+        
+                    // Step 4: Acceptance/Rejection Comparison
+                    if m < 100.0 || y <= 50.0 {
+                        // Step 4.1: evaluate f(y) via recursive relationship
+                        let mut f = 1.0;
+                        if m < y {
+                            for i in (m as u64 + 1)..=(y as u64) {
+                                f *= (n1 - i + 1) as f64 * (k - i + 1) as f64;
+                                f /= i as f64 * (n2 - k + i) as f64;
+                            }
+                        } else {
+                            for i in (y as u64 + 1)..=(m as u64) {
+                                f *= i as f64 * (n2 - k + i) as f64;
+                                f /= (n1 - i) as f64 * (k - i) as f64;
+                            }
+                        }
+        
+                        if v <= f { break y as i64; }
+                    } else {
+                        // Step 4.2: Squeezing
+                        let y1 = y + 1.0;
+                        let ym = y - m;
+                        let yn = n1 as f64 - y + 1.0;
+                        let yk = k as f64 - y + 1.0;
+                        let nk = n2 as f64 - k as f64 + y1;
+                        let r = -ym / y1;
+                        let s = ym / yn;
+                        let t = ym / yk;
+                        let e = -ym / nk;
+                        let g = yn * yk / (y1 * nk) - 1.0;
+                        let dg = if g < 0.0 {
+                            1.0 + g
+                        } else {
+                            1.0
+                        };
+                        let gu = g * (1.0 + g * (-0.5 + g / 3.0));
+                        let gl = gu - g.powi(4) / (4.0 * dg);
+                        let xm = m + 0.5;
+                        let xn = n1 as f64 - m + 0.5;
+                        let xk = k as f64 - m + 0.5;
+                        let nm = n2 as f64 - k as f64 + xm;
+                        let ub = xm * r * (1.0 + r * (-0.5 + r / 3.0)) +
+                            xn * s * (1.0 + s * (-0.5 + s / 3.0)) +
+                            xk * t * (1.0 + t * (-0.5 + t / 3.0)) +
+                            nm * e * (1.0 + e * (-0.5 + e / 3.0)) +
+                            y * gu - m * gl + 0.0034;
+                        let av = v.ln();
+                        if av > ub { continue; }
+                        let dr = if r < 0.0 {
+                            xm * r.powi(4) / (1.0 + r)
+                        } else {
+                            xm * r.powi(4)
+                        };
+                        let ds = if s < 0.0 {
+                            xn * s.powi(4) / (1.0 + s)
+                        } else {
+                            xn * s.powi(4)
+                        };
+                        let dt = if t < 0.0 {
+                            xk * t.powi(4) / (1.0 + t)
+                        } else {
+                            xk * t.powi(4)
+                        };
+                        let de = if e < 0.0 {
+                            nm * e.powi(4) / (1.0 + e)
+                        } else {
+                            nm * e.powi(4)
+                        };
+        
+                        if av < ub - 0.25*(dr + ds + dt + de) + (y + m)*(gl - gu) - 0.0078 {
+                            break y as i64;
+                        }
+        
+                        // Step 4.3: Final Acceptance/Rejection Test
+                        let av_critical = a -
+                            ln_of_factorial(y) -
+                            ln_of_factorial(n1 as f64 - y) - 
+                            ln_of_factorial(k as f64 - y) - 
+                            ln_of_factorial((n2 - k) as f64 + y);
+                        if v.ln() <= av_critical {
+                            break y as i64;
+                        }
+                    }
+                }
+            }
+        };
+
+        (offset_x + sign_x * x) as u64
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    fn test_hypergeometric_invalid_params() {
+        assert!(Hypergeometric::new(100, 101, 5).is_err());
+        assert!(Hypergeometric::new(100, 10, 101).is_err());
+        assert!(Hypergeometric::new(100, 101, 101).is_err());
+        assert!(Hypergeometric::new(100, 10, 5).is_ok());
+    }
+
+    fn test_hypergeometric_mean_and_variance<R: Rng>(n: u64, k: u64, s: u64, rng: &mut R)
+    {
+        let distr = Hypergeometric::new(n, k, s).unwrap();
+
+        let expected_mean = s as f64 * k as f64 / n as f64;
+        let expected_variance = {
+            let numerator = (s * k * (n - k) * (n - s)) as f64;
+            let denominator = (n * n * (n - 1)) as f64;
+            numerator / denominator
+        };
+
+        let mut results = [0.0; 1000];
+        for i in results.iter_mut() {
+            *i = distr.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_hypergeometric() {
+        let mut rng = crate::test::rng(737);
+
+        // exercise algorithm HIN:
+        test_hypergeometric_mean_and_variance(500, 400, 30, &mut rng);
+        test_hypergeometric_mean_and_variance(250, 200, 230, &mut rng);
+        test_hypergeometric_mean_and_variance(100, 20, 6, &mut rng);
+        test_hypergeometric_mean_and_variance(50, 10, 47, &mut rng);
+
+        // exercise algorithm H2PE
+        test_hypergeometric_mean_and_variance(5000, 2500, 500, &mut rng);
+        test_hypergeometric_mean_and_variance(10100, 10000, 1000, &mut rng);
+        test_hypergeometric_mean_and_variance(100100, 100, 10000, &mut rng);
+    }
+}

vendor/rand_distr/src/inverse_gaussian.rs

@@ -0,0 +1,112 @@
+use crate::{Distribution, Standard, StandardNormal};
+use num_traits::Float;
+use rand::Rng;
+use core::fmt;
+
+/// Error type returned from `InverseGaussian::new`
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+pub enum Error {
+    /// `mean <= 0` or `nan`.
+    MeanNegativeOrNull,
+    /// `shape <= 0` or `nan`.
+    ShapeNegativeOrNull,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::MeanNegativeOrNull => "mean <= 0 or is NaN in inverse Gaussian distribution",
+            Error::ShapeNegativeOrNull => "shape <= 0 or is NaN in inverse Gaussian distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+/// The [inverse Gaussian distribution](https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution)
+#[derive(Debug, Clone, Copy)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct InverseGaussian<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Standard: Distribution<F>,
+{
+    mean: F,
+    shape: F,
+}
+
+impl<F> InverseGaussian<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Standard: Distribution<F>,
+{
+    /// Construct a new `InverseGaussian` distribution with the given mean and
+    /// shape.
+    pub fn new(mean: F, shape: F) -> Result<InverseGaussian<F>, Error> {
+        let zero = F::zero();
+        if !(mean > zero) {
+            return Err(Error::MeanNegativeOrNull);
+        }
+
+        if !(shape > zero) {
+            return Err(Error::ShapeNegativeOrNull);
+        }
+
+        Ok(Self { mean, shape })
+    }
+}
+
+impl<F> Distribution<F> for InverseGaussian<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Standard: Distribution<F>,
+{
+    #[allow(clippy::many_single_char_names)]
+    fn sample<R>(&self, rng: &mut R) -> F
+    where R: Rng + ?Sized {
+        let mu = self.mean;
+        let l = self.shape;
+
+        let v: F = rng.sample(StandardNormal);
+        let y = mu * v * v;
+
+        let mu_2l = mu / (F::from(2.).unwrap() * l);
+
+        let x = mu + mu_2l * (y - (F::from(4.).unwrap() * l * y + y * y).sqrt());
+
+        let u: F = rng.gen();
+
+        if u <= mu / (mu + x) {
+            return x;
+        }
+
+        mu * mu / x
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_inverse_gaussian() {
+        let inv_gauss = InverseGaussian::new(1.0, 1.0).unwrap();
+        let mut rng = crate::test::rng(210);
+        for _ in 0..1000 {
+            inv_gauss.sample(&mut rng);
+        }
+    }
+
+    #[test]
+    fn test_inverse_gaussian_invalid_param() {
+        assert!(InverseGaussian::new(-1.0, 1.0).is_err());
+        assert!(InverseGaussian::new(-1.0, -1.0).is_err());
+        assert!(InverseGaussian::new(1.0, -1.0).is_err());
+        assert!(InverseGaussian::new(1.0, 1.0).is_ok());
+    }
+}

vendor/rand_distr/src/lib.rs

@@ -0,0 +1,213 @@
+// Copyright 2019 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.
+
+#![doc(
+    html_logo_url = "https://www.rust-lang.org/logos/rust-logo-128x128-blk.png",
+    html_favicon_url = "https://www.rust-lang.org/favicon.ico",
+    html_root_url = "https://rust-random.github.io/rand/"
+)]
+#![deny(missing_docs)]
+#![deny(missing_debug_implementations)]
+#![allow(
+    clippy::excessive_precision,
+    clippy::float_cmp,
+    clippy::unreadable_literal
+)]
+#![allow(clippy::neg_cmp_op_on_partial_ord)] // suggested fix too verbose
+#![no_std]
+#![cfg_attr(doc_cfg, feature(doc_cfg))]
+
+//! Generating random samples from probability distributions.
+//!
+//! ## Re-exports
+//!
+//! This crate is a super-set of the [`rand::distributions`] module. See the
+//! [`rand::distributions`] module documentation for an overview of the core
+//! [`Distribution`] trait and implementations.
+//!
+//! The following are re-exported:
+//!
+//! - The [`Distribution`] trait and [`DistIter`] helper type
+//! - The [`Standard`], [`Alphanumeric`], [`Uniform`], [`OpenClosed01`],
+//! [`Open01`], [`Bernoulli`], and [`WeightedIndex`] distributions
+//!
+//! ## Distributions
+//!
+//! This crate provides the following probability distributions:
+//!
+//! - Related to real-valued quantities that grow linearly
+//!   (e.g. errors, offsets):
+//!   - [`Normal`] distribution, and [`StandardNormal`] as a primitive
+//!   - [`SkewNormal`] distribution
+//!   - [`Cauchy`] distribution
+//! - Related to Bernoulli trials (yes/no events, with a given probability):
+//!   - [`Binomial`] distribution
+//!   - [`Geometric`] distribution
+//!   - [`Hypergeometric`] distribution
+//! - 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
+//!   - [`Gumbel`] distribution
+//!   - [`Frechet`] distribution
+//!   - [`Zeta`] distribution
+//!   - [`Zipf`] distribution
+//! - Gamma and derived distributions:
+//!   - [`Gamma`] distribution
+//!   - [`ChiSquared`] distribution
+//!   - [`StudentT`] distribution
+//!   - [`FisherF`] distribution
+//! - Triangular distribution:
+//!   - [`Beta`] distribution
+//!   - [`Triangular`] distribution
+//! - Multivariate probability distributions
+//!   - [`Dirichlet`] distribution
+//!   - [`UnitSphere`] distribution
+//!   - [`UnitBall`] distribution
+//!   - [`UnitCircle`] distribution
+//!   - [`UnitDisc`] distribution
+//! - Alternative implementation for weighted index sampling
+//!   - [`WeightedAliasIndex`] distribution
+//! - Misc. distributions
+//!   - [`InverseGaussian`] distribution
+//!   - [`NormalInverseGaussian`] distribution
+
+#[cfg(feature = "alloc")]
+extern crate alloc;
+
+#[cfg(feature = "std")]
+extern crate std;
+
+// This is used for doc links:
+#[allow(unused)]
+use rand::Rng;
+
+pub use rand::distributions::{
+    uniform, Alphanumeric, Bernoulli, BernoulliError, DistIter, Distribution, Open01, OpenClosed01,
+    Standard, Uniform,
+};
+
+pub use self::binomial::{Binomial, Error as BinomialError};
+pub use self::cauchy::{Cauchy, Error as CauchyError};
+#[cfg(feature = "alloc")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "alloc")))]
+pub use self::dirichlet::{Dirichlet, Error as DirichletError};
+pub use self::exponential::{Error as ExpError, Exp, Exp1};
+pub use self::frechet::{Error as FrechetError, Frechet};
+pub use self::gamma::{
+    Beta, BetaError, ChiSquared, ChiSquaredError, Error as GammaError, FisherF, FisherFError,
+    Gamma, StudentT,
+};
+pub use self::geometric::{Error as GeoError, Geometric, StandardGeometric};
+pub use self::gumbel::{Error as GumbelError, Gumbel};
+pub use self::hypergeometric::{Error as HyperGeoError, Hypergeometric};
+pub use self::inverse_gaussian::{Error as InverseGaussianError, InverseGaussian};
+pub use self::normal::{Error as NormalError, LogNormal, Normal, StandardNormal};
+pub use self::normal_inverse_gaussian::{
+    Error as NormalInverseGaussianError, NormalInverseGaussian,
+};
+pub use self::pareto::{Error as ParetoError, Pareto};
+pub use self::pert::{Pert, PertError};
+pub use self::poisson::{Error as PoissonError, Poisson};
+pub use self::skew_normal::{Error as SkewNormalError, SkewNormal};
+pub use self::triangular::{Triangular, TriangularError};
+pub use self::unit_ball::UnitBall;
+pub use self::unit_circle::UnitCircle;
+pub use self::unit_disc::UnitDisc;
+pub use self::unit_sphere::UnitSphere;
+pub use self::weibull::{Error as WeibullError, Weibull};
+pub use self::zipf::{Zeta, ZetaError, Zipf, ZipfError};
+#[cfg(feature = "alloc")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "alloc")))]
+pub use rand::distributions::{WeightedError, WeightedIndex};
+#[cfg(feature = "alloc")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "alloc")))]
+pub use weighted_alias::WeightedAliasIndex;
+
+pub use num_traits;
+
+#[cfg(test)]
+#[macro_use]
+mod test {
+    // Notes on testing
+    //
+    // Testing random number distributions correctly is hard. The following
+    // testing is desired:
+    //
+    // - Construction: test initialisation with a few valid parameter sets.
+    // - Erroneous usage: test that incorrect usage generates an error.
+    // - Vector: test that usage with fixed inputs (including RNG) generates a
+    //   fixed output sequence on all platforms.
+    // - Correctness at fixed points (optional): using a specific mock RNG,
+    //   check that specific values are sampled (e.g. end-points and median of
+    //   distribution).
+    // - Correctness of PDF (extra): generate a histogram of samples within a
+    //   certain range, and check this approximates the PDF. These tests are
+    //   expected to be expensive, and should be behind a feature-gate.
+    //
+    // TODO: Vector and correctness tests are largely absent so far.
+    // NOTE: Some distributions have tests checking only that samples can be
+    // generated. This is redundant with vector and correctness tests.
+
+    /// Construct a deterministic RNG with the given seed
+    pub fn rng(seed: u64) -> impl rand::RngCore {
+        // For tests, we want a statistically good, fast, reproducible RNG.
+        // PCG32 will do fine, and will be easy to embed if we ever need to.
+        const INC: u64 = 11634580027462260723;
+        rand_pcg::Pcg32::new(seed, INC)
+    }
+
+    /// 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();
+            assert!(diff <= $prec,
+                "assertion failed: `abs(left - right) = {:.1e} < {:e}`, \
+                    (left: `{}`, right: `{}`)",
+                diff, $prec, $a, $b
+            );
+        };
+    }
+}
+
+#[cfg(feature = "alloc")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "alloc")))]
+pub mod weighted_alias;
+
+mod binomial;
+mod cauchy;
+mod dirichlet;
+mod exponential;
+mod frechet;
+mod gamma;
+mod geometric;
+mod gumbel;
+mod hypergeometric;
+mod inverse_gaussian;
+mod normal;
+mod normal_inverse_gaussian;
+mod pareto;
+mod pert;
+mod poisson;
+mod skew_normal;
+mod triangular;
+mod unit_ball;
+mod unit_circle;
+mod unit_disc;
+mod unit_sphere;
+mod utils;
+mod weibull;
+mod ziggurat_tables;
+mod zipf;

vendor/rand_distr/src/normal.rs

@@ -0,0 +1,371 @@
+// 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 crate::utils::ziggurat;
+use num_traits::Float;
+use crate::{ziggurat_tables, Distribution, Open01};
+use rand::Rng;
+use core::fmt;
+
+/// 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_distr::StandardNormal;
+///
+/// let val: f64 = thread_rng().sample(StandardNormal);
+/// println!("{}", val);
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct StandardNormal;
+
+impl Distribution<f32> for StandardNormal {
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f32 {
+        // TODO: use optimal 32-bit implementation
+        let x: f64 = self.sample(rng);
+        x as f32
+    }
+}
+
+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_distr::{Normal, Distribution};
+///
+/// // mean 2, standard deviation 3
+/// let normal = Normal::new(2.0, 3.0).unwrap();
+/// let v = normal.sample(&mut rand::thread_rng());
+/// println!("{} is from a N(2, 9) distribution", v)
+/// ```
+///
+/// [`StandardNormal`]: crate::StandardNormal
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct Normal<F>
+where F: Float, StandardNormal: Distribution<F>
+{
+    mean: F,
+    std_dev: F,
+}
+
+/// Error type returned from `Normal::new` and `LogNormal::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// The mean value is too small (log-normal samples must be positive)
+    MeanTooSmall,
+    /// The standard deviation or other dispersion parameter is not finite.
+    BadVariance,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::MeanTooSmall => "mean < 0 or NaN in log-normal distribution",
+            Error::BadVariance => "variation parameter is non-finite in (log)normal distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+impl<F> Normal<F>
+where F: Float, StandardNormal: Distribution<F>
+{
+    /// Construct, from mean and standard deviation
+    ///
+    /// Parameters:
+    ///
+    /// -   mean (`μ`, unrestricted)
+    /// -   standard deviation (`σ`, must be finite)
+    #[inline]
+    pub fn new(mean: F, std_dev: F) -> Result<Normal<F>, Error> {
+        if !std_dev.is_finite() {
+            return Err(Error::BadVariance);
+        }
+        Ok(Normal { mean, std_dev })
+    }
+
+    /// Construct, from mean and coefficient of variation
+    ///
+    /// Parameters:
+    ///
+    /// -   mean (`μ`, unrestricted)
+    /// -   coefficient of variation (`cv = abs(σ / μ)`)
+    #[inline]
+    pub fn from_mean_cv(mean: F, cv: F) -> Result<Normal<F>, Error> {
+        if !cv.is_finite() || cv < F::zero() {
+            return Err(Error::BadVariance);
+        }
+        let std_dev = cv * mean;
+        Ok(Normal { mean, std_dev })
+    }
+
+    /// Sample from a z-score
+    ///
+    /// This may be useful for generating correlated samples `x1` and `x2`
+    /// from two different distributions, as follows.
+    /// ```
+    /// # use rand::prelude::*;
+    /// # use rand_distr::{Normal, StandardNormal};
+    /// let mut rng = thread_rng();
+    /// let z = StandardNormal.sample(&mut rng);
+    /// let x1 = Normal::new(0.0, 1.0).unwrap().from_zscore(z);
+    /// let x2 = Normal::new(2.0, -3.0).unwrap().from_zscore(z);
+    /// ```
+    #[inline]
+    pub fn from_zscore(&self, zscore: F) -> F {
+        self.mean + self.std_dev * zscore
+    }
+
+    /// Returns the mean (`μ`) of the distribution.
+    pub fn mean(&self) -> F {
+        self.mean
+    }
+
+    /// Returns the standard deviation (`σ`) of the distribution.
+    pub fn std_dev(&self) -> F {
+        self.std_dev
+    }
+}
+
+impl<F> Distribution<F> for Normal<F>
+where F: Float, StandardNormal: Distribution<F>
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        self.from_zscore(rng.sample(StandardNormal))
+    }
+}
+
+
+/// 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_distr::{LogNormal, Distribution};
+///
+/// // mean 2, standard deviation 3
+/// let log_normal = LogNormal::new(2.0, 3.0).unwrap();
+/// let v = log_normal.sample(&mut rand::thread_rng());
+/// println!("{} is from an ln N(2, 9) distribution", v)
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct LogNormal<F>
+where F: Float, StandardNormal: Distribution<F>
+{
+    norm: Normal<F>,
+}
+
+impl<F> LogNormal<F>
+where F: Float, StandardNormal: Distribution<F>
+{
+    /// Construct, from (log-space) mean and standard deviation
+    ///
+    /// Parameters are the "standard" log-space measures (these are the mean
+    /// and standard deviation of the logarithm of samples):
+    ///
+    /// -   `mu` (`μ`, unrestricted) is the mean of the underlying distribution
+    /// -   `sigma` (`σ`, must be finite) is the standard deviation of the
+    ///     underlying Normal distribution
+    #[inline]
+    pub fn new(mu: F, sigma: F) -> Result<LogNormal<F>, Error> {
+        let norm = Normal::new(mu, sigma)?;
+        Ok(LogNormal { norm })
+    }
+
+    /// Construct, from (linear-space) mean and coefficient of variation
+    ///
+    /// Parameters are linear-space measures:
+    ///
+    /// -   mean (`μ > 0`) is the (real) mean of the distribution
+    /// -   coefficient of variation (`cv = σ / μ`, requiring `cv ≥ 0`) is a
+    ///     standardized measure of dispersion
+    ///
+    /// As a special exception, `μ = 0, cv = 0` is allowed (samples are `-inf`).
+    #[inline]
+    pub fn from_mean_cv(mean: F, cv: F) -> Result<LogNormal<F>, Error> {
+        if cv == F::zero() {
+            let mu = mean.ln();
+            let norm = Normal::new(mu, F::zero()).unwrap();
+            return Ok(LogNormal { norm });
+        }
+        if !(mean > F::zero()) {
+            return Err(Error::MeanTooSmall);
+        }
+        if !(cv >= F::zero()) {
+            return Err(Error::BadVariance);
+        }
+
+        // Using X ~ lognormal(μ, σ), CV² = Var(X) / E(X)²
+        // E(X) = exp(μ + σ² / 2) = exp(μ) × exp(σ² / 2)
+        // Var(X) = exp(2μ + σ²)(exp(σ²) - 1) = E(X)² × (exp(σ²) - 1)
+        // but Var(X) = (CV × E(X))² so CV² = exp(σ²) - 1
+        // thus σ² = log(CV² + 1)
+        // and exp(μ) = E(X) / exp(σ² / 2) = E(X) / sqrt(CV² + 1)
+        let a = F::one() + cv * cv; // e
+        let mu = F::from(0.5).unwrap() * (mean * mean / a).ln();
+        let sigma = a.ln().sqrt();
+        let norm = Normal::new(mu, sigma)?;
+        Ok(LogNormal { norm })
+    }
+
+    /// Sample from a z-score
+    ///
+    /// This may be useful for generating correlated samples `x1` and `x2`
+    /// from two different distributions, as follows.
+    /// ```
+    /// # use rand::prelude::*;
+    /// # use rand_distr::{LogNormal, StandardNormal};
+    /// let mut rng = thread_rng();
+    /// let z = StandardNormal.sample(&mut rng);
+    /// let x1 = LogNormal::from_mean_cv(3.0, 1.0).unwrap().from_zscore(z);
+    /// let x2 = LogNormal::from_mean_cv(2.0, 4.0).unwrap().from_zscore(z);
+    /// ```
+    #[inline]
+    pub fn from_zscore(&self, zscore: F) -> F {
+        self.norm.from_zscore(zscore).exp()
+    }
+}
+
+impl<F> Distribution<F> for LogNormal<F>
+where F: Float, StandardNormal: Distribution<F>
+{
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        self.norm.sample(rng).exp()
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_normal() {
+        let norm = Normal::new(10.0, 10.0).unwrap();
+        let mut rng = crate::test::rng(210);
+        for _ in 0..1000 {
+            norm.sample(&mut rng);
+        }
+    }
+    #[test]
+    fn test_normal_cv() {
+        let norm = Normal::from_mean_cv(1024.0, 1.0 / 256.0).unwrap();
+        assert_eq!((norm.mean, norm.std_dev), (1024.0, 4.0));
+    }
+    #[test]
+    fn test_normal_invalid_sd() {
+        assert!(Normal::from_mean_cv(10.0, -1.0).is_err());
+    }
+
+    #[test]
+    fn test_log_normal() {
+        let lnorm = LogNormal::new(10.0, 10.0).unwrap();
+        let mut rng = crate::test::rng(211);
+        for _ in 0..1000 {
+            lnorm.sample(&mut rng);
+        }
+    }
+    #[test]
+    fn test_log_normal_cv() {
+        let lnorm = LogNormal::from_mean_cv(0.0, 0.0).unwrap();
+        assert_eq!((lnorm.norm.mean, lnorm.norm.std_dev), (-core::f64::INFINITY, 0.0));
+
+        let lnorm = LogNormal::from_mean_cv(1.0, 0.0).unwrap();
+        assert_eq!((lnorm.norm.mean, lnorm.norm.std_dev), (0.0, 0.0));
+
+        let e = core::f64::consts::E;
+        let lnorm = LogNormal::from_mean_cv(e.sqrt(), (e - 1.0).sqrt()).unwrap();
+        assert_almost_eq!(lnorm.norm.mean, 0.0, 2e-16);
+        assert_almost_eq!(lnorm.norm.std_dev, 1.0, 2e-16);
+
+        let lnorm = LogNormal::from_mean_cv(e.powf(1.5), (e - 1.0).sqrt()).unwrap();
+        assert_almost_eq!(lnorm.norm.mean, 1.0, 1e-15);
+        assert_eq!(lnorm.norm.std_dev, 1.0);
+    }
+    #[test]
+    fn test_log_normal_invalid_sd() {
+        assert!(LogNormal::from_mean_cv(-1.0, 1.0).is_err());
+        assert!(LogNormal::from_mean_cv(0.0, 1.0).is_err());
+        assert!(LogNormal::from_mean_cv(1.0, -1.0).is_err());
+    }
+}

vendor/rand_distr/src/normal_inverse_gaussian.rs

@@ -0,0 +1,107 @@
+use crate::{Distribution, InverseGaussian, Standard, StandardNormal};
+use num_traits::Float;
+use rand::Rng;
+use core::fmt;
+
+/// Error type returned from `NormalInverseGaussian::new`
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+pub enum Error {
+    /// `alpha <= 0` or `nan`.
+    AlphaNegativeOrNull,
+    /// `|beta| >= alpha` or `nan`.
+    AbsoluteBetaNotLessThanAlpha,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::AlphaNegativeOrNull => "alpha <= 0 or is NaN in normal inverse Gaussian distribution",
+            Error::AbsoluteBetaNotLessThanAlpha => "|beta| >= alpha or is NaN in normal inverse Gaussian distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+/// The [normal-inverse Gaussian distribution](https://en.wikipedia.org/wiki/Normal-inverse_Gaussian_distribution)
+#[derive(Debug, Clone, Copy)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct NormalInverseGaussian<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Standard: Distribution<F>,
+{
+    alpha: F,
+    beta: F,
+    inverse_gaussian: InverseGaussian<F>,
+}
+
+impl<F> NormalInverseGaussian<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Standard: Distribution<F>,
+{
+    /// Construct a new `NormalInverseGaussian` distribution with the given alpha (tail heaviness) and
+    /// beta (asymmetry) parameters.
+    pub fn new(alpha: F, beta: F) -> Result<NormalInverseGaussian<F>, Error> {
+        if !(alpha > F::zero()) {
+            return Err(Error::AlphaNegativeOrNull);
+        }
+
+        if !(beta.abs() < alpha) {
+            return Err(Error::AbsoluteBetaNotLessThanAlpha);
+        }
+
+        let gamma = (alpha * alpha - beta * beta).sqrt();
+
+        let mu = F::one() / gamma;
+
+        let inverse_gaussian = InverseGaussian::new(mu, F::one()).unwrap();
+
+        Ok(Self {
+            alpha,
+            beta,
+            inverse_gaussian,
+        })
+    }
+}
+
+impl<F> Distribution<F> for NormalInverseGaussian<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Standard: Distribution<F>,
+{
+    fn sample<R>(&self, rng: &mut R) -> F
+    where R: Rng + ?Sized {
+        let inv_gauss = rng.sample(&self.inverse_gaussian);
+
+        self.beta * inv_gauss + inv_gauss.sqrt() * rng.sample(StandardNormal)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_normal_inverse_gaussian() {
+        let norm_inv_gauss = NormalInverseGaussian::new(2.0, 1.0).unwrap();
+        let mut rng = crate::test::rng(210);
+        for _ in 0..1000 {
+            norm_inv_gauss.sample(&mut rng);
+        }
+    }
+
+    #[test]
+    fn test_normal_inverse_gaussian_invalid_param() {
+        assert!(NormalInverseGaussian::new(-1.0, 1.0).is_err());
+        assert!(NormalInverseGaussian::new(-1.0, -1.0).is_err());
+        assert!(NormalInverseGaussian::new(1.0, 2.0).is_err());
+        assert!(NormalInverseGaussian::new(2.0, 1.0).is_ok());
+    }
+}

vendor/rand_distr/src/pareto.rs

@@ -0,0 +1,134 @@
+// 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 num_traits::Float;
+use crate::{Distribution, OpenClosed01};
+use rand::Rng;
+use core::fmt;
+
+/// Samples floating-point numbers according to the Pareto distribution
+///
+/// # Example
+/// ```
+/// use rand::prelude::*;
+/// use rand_distr::Pareto;
+///
+/// let val: f64 = thread_rng().sample(Pareto::new(1., 2.).unwrap());
+/// println!("{}", val);
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct Pareto<F>
+where F: Float, OpenClosed01: Distribution<F>
+{
+    scale: F,
+    inv_neg_shape: F,
+}
+
+/// Error type returned from `Pareto::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// `scale <= 0` or `nan`.
+    ScaleTooSmall,
+    /// `shape <= 0` or `nan`.
+    ShapeTooSmall,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::ScaleTooSmall => "scale is not positive in Pareto distribution",
+            Error::ShapeTooSmall => "shape is not positive in Pareto distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+impl<F> Pareto<F>
+where F: Float, OpenClosed01: Distribution<F>
+{
+    /// 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.
+    pub fn new(scale: F, shape: F) -> Result<Pareto<F>, Error> {
+        let zero = F::zero();
+
+        if !(scale > zero) {
+            return Err(Error::ScaleTooSmall);
+        }
+        if !(shape > zero) {
+            return Err(Error::ShapeTooSmall);
+        }
+        Ok(Pareto {
+            scale,
+            inv_neg_shape: F::from(-1.0).unwrap() / shape,
+        })
+    }
+}
+
+impl<F> Distribution<F> for Pareto<F>
+where F: Float, OpenClosed01: Distribution<F>
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        let u: F = OpenClosed01.sample(rng);
+        self.scale * u.powf(self.inv_neg_shape)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use core::fmt::{Debug, Display, LowerExp};
+
+    #[test]
+    #[should_panic]
+    fn invalid() {
+        Pareto::new(0., 0.).unwrap();
+    }
+
+    #[test]
+    fn sample() {
+        let scale = 1.0;
+        let shape = 2.0;
+        let d = Pareto::new(scale, shape).unwrap();
+        let mut rng = crate::test::rng(1);
+        for _ in 0..1000 {
+            let r = d.sample(&mut rng);
+            assert!(r >= scale);
+        }
+    }
+
+    #[test]
+    fn value_stability() {
+        fn test_samples<F: Float + Debug + Display + LowerExp, D: Distribution<F>>(
+            distr: D, thresh: F, expected: &[F],
+        ) {
+            let mut rng = crate::test::rng(213);
+            for v in expected {
+                let x = rng.sample(&distr);
+                assert_almost_eq!(x, *v, thresh);
+            }
+        }
+
+        test_samples(Pareto::new(1f32, 1.0).unwrap(), 1e-6, &[
+            1.0423688, 2.1235929, 4.132709, 1.4679428,
+        ]);
+        test_samples(Pareto::new(2.0, 0.5).unwrap(), 1e-14, &[
+            9.019295276219136,
+            4.3097126018270595,
+            6.837815045397157,
+            105.8826669383772,
+        ]);
+    }
+}

vendor/rand_distr/src/pert.rs

@@ -0,0 +1,149 @@
+// 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 PERT distribution.
+
+use num_traits::Float;
+use crate::{Beta, Distribution, Exp1, Open01, StandardNormal};
+use rand::Rng;
+use core::fmt;
+
+/// The PERT distribution.
+///
+/// Similar to the [`Triangular`] distribution, the PERT distribution is
+/// parameterised by a range and a mode within that range. Unlike the
+/// [`Triangular`] distribution, the probability density function of the PERT
+/// distribution is smooth, with a configurable weighting around the mode.
+///
+/// # Example
+///
+/// ```rust
+/// use rand_distr::{Pert, Distribution};
+///
+/// let d = Pert::new(0., 5., 2.5).unwrap();
+/// let v = d.sample(&mut rand::thread_rng());
+/// println!("{} is from a PERT distribution", v);
+/// ```
+///
+/// [`Triangular`]: crate::Triangular
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct Pert<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    min: F,
+    range: F,
+    beta: Beta<F>,
+}
+
+/// Error type returned from [`Pert`] constructors.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum PertError {
+    /// `max < min` or `min` or `max` is NaN.
+    RangeTooSmall,
+    /// `mode < min` or `mode > max` or `mode` is NaN.
+    ModeRange,
+    /// `shape < 0` or `shape` is NaN
+    ShapeTooSmall,
+}
+
+impl fmt::Display for PertError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            PertError::RangeTooSmall => "requirement min < max is not met in PERT distribution",
+            PertError::ModeRange => "mode is outside [min, max] in PERT distribution",
+            PertError::ShapeTooSmall => "shape < 0 or is NaN in PERT distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for PertError {}
+
+impl<F> Pert<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    /// Set up the PERT distribution with defined `min`, `max` and `mode`.
+    ///
+    /// This is equivalent to calling `Pert::new_shape` with `shape == 4.0`.
+    #[inline]
+    pub fn new(min: F, max: F, mode: F) -> Result<Pert<F>, PertError> {
+        Pert::new_with_shape(min, max, mode, F::from(4.).unwrap())
+    }
+
+    /// Set up the PERT distribution with defined `min`, `max`, `mode` and
+    /// `shape`.
+    pub fn new_with_shape(min: F, max: F, mode: F, shape: F) -> Result<Pert<F>, PertError> {
+        if !(max > min) {
+            return Err(PertError::RangeTooSmall);
+        }
+        if !(mode >= min && max >= mode) {
+            return Err(PertError::ModeRange);
+        }
+        if !(shape >= F::from(0.).unwrap()) {
+            return Err(PertError::ShapeTooSmall);
+        }
+
+        let range = max - min;
+        let mu = (min + max + shape * mode) / (shape + F::from(2.).unwrap());
+        let v = if mu == mode {
+            shape * F::from(0.5).unwrap() + F::from(1.).unwrap()
+        } else {
+            (mu - min) * (F::from(2.).unwrap() * mode - min - max) / ((mode - mu) * (max - min))
+        };
+        let w = v * (max - mu) / (mu - min);
+        let beta = Beta::new(v, w).map_err(|_| PertError::RangeTooSmall)?;
+        Ok(Pert { min, range, beta })
+    }
+}
+
+impl<F> Distribution<F> for Pert<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+    Exp1: Distribution<F>,
+    Open01: Distribution<F>,
+{
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        self.beta.sample(rng) * self.range + self.min
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    fn test_pert() {
+        for &(min, max, mode) in &[
+            (-1., 1., 0.),
+            (1., 2., 1.),
+            (5., 25., 25.),
+        ] {
+            let _distr = Pert::new(min, max, mode).unwrap();
+            // TODO: test correctness
+        }
+
+        for &(min, max, mode) in &[
+            (-1., 1., 2.),
+            (-1., 1., -2.),
+            (2., 1., 1.),
+        ] {
+            assert!(Pert::new(min, max, mode).is_err());
+        }
+    }
+}

vendor/rand_distr/src/poisson.rs

@@ -0,0 +1,181 @@
+// 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 num_traits::{Float, FloatConst};
+use crate::{Cauchy, Distribution, Standard};
+use rand::Rng;
+use core::fmt;
+
+/// The Poisson distribution `Poisson(lambda)`.
+///
+/// This distribution has a density function:
+/// `f(k) = lambda^k * exp(-lambda) / k!` for `k >= 0`.
+///
+/// # Example
+///
+/// ```
+/// use rand_distr::{Poisson, Distribution};
+///
+/// let poi = Poisson::new(2.0).unwrap();
+/// let v = poi.sample(&mut rand::thread_rng());
+/// println!("{} is from a Poisson(2) distribution", v);
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct Poisson<F>
+where F: Float + FloatConst, Standard: Distribution<F>
+{
+    lambda: F,
+    // precalculated values
+    exp_lambda: F,
+    log_lambda: F,
+    sqrt_2lambda: F,
+    magic_val: F,
+}
+
+/// Error type returned from `Poisson::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// `lambda <= 0` or `nan`.
+    ShapeTooSmall,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::ShapeTooSmall => "lambda is not positive in Poisson distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+impl<F> Poisson<F>
+where F: Float + FloatConst, Standard: Distribution<F>
+{
+    /// Construct a new `Poisson` with the given shape parameter
+    /// `lambda`.
+    pub fn new(lambda: F) -> Result<Poisson<F>, Error> {
+        if !(lambda > F::zero()) {
+            return Err(Error::ShapeTooSmall);
+        }
+        let log_lambda = lambda.ln();
+        Ok(Poisson {
+            lambda,
+            exp_lambda: (-lambda).exp(),
+            log_lambda,
+            sqrt_2lambda: (F::from(2.0).unwrap() * lambda).sqrt(),
+            magic_val: lambda * log_lambda - crate::utils::log_gamma(F::one() + lambda),
+        })
+    }
+}
+
+impl<F> Distribution<F> for Poisson<F>
+where F: Float + FloatConst, Standard: Distribution<F>
+{
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        // using the algorithm from Numerical Recipes in C
+
+        // for low expected values use the Knuth method
+        if self.lambda < F::from(12.0).unwrap() {
+            let mut result = F::zero();
+            let mut p = F::one();
+            while p > self.exp_lambda {
+                p = p*rng.gen::<F>();
+                result = result + F::one();
+            }
+            result - F::one()
+        }
+        // high expected values - rejection method
+        else {
+            // we use the Cauchy distribution as the comparison distribution
+            // f(x) ~ 1/(1+x^2)
+            let cauchy = Cauchy::new(F::zero(), F::one()).unwrap();
+            let mut result;
+
+            loop {
+                let mut comp_dev;
+
+                loop {
+                    // draw from the Cauchy distribution
+                    comp_dev = rng.sample(cauchy);
+                    // shift the peak of the comparison distribution
+                    result = self.sqrt_2lambda * comp_dev + self.lambda;
+                    // repeat the drawing until we are in the range of possible values
+                    if result >= F::zero() {
+                        break;
+                    }
+                }
+                // now the result is a random variable greater than 0 with Cauchy distribution
+                // the result should be an integer value
+                result = result.floor();
+
+                // 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 = F::from(0.9).unwrap()
+                    * (F::one() + comp_dev * comp_dev)
+                    * (result * self.log_lambda
+                        - crate::utils::log_gamma(F::one() + result)
+                        - self.magic_val)
+                        .exp();
+
+                // check with uniform random value - if below the threshold, we are within the target distribution
+                if rng.gen::<F>() <= check {
+                    break;
+                }
+            }
+            result
+        }
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    fn test_poisson_avg_gen<F: Float + FloatConst>(lambda: F, tol: F)
+        where Standard: Distribution<F>
+    {
+        let poisson = Poisson::new(lambda).unwrap();
+        let mut rng = crate::test::rng(123);
+        let mut sum = F::zero();
+        for _ in 0..1000 {
+            sum = sum + poisson.sample(&mut rng);
+        }
+        let avg = sum / F::from(1000.0).unwrap();
+        assert!((avg - lambda).abs() < tol);
+    }
+
+    #[test]
+    fn test_poisson_avg() {
+        test_poisson_avg_gen::<f64>(10.0, 0.5);
+        test_poisson_avg_gen::<f64>(15.0, 0.5);
+        test_poisson_avg_gen::<f32>(10.0, 0.5);
+        test_poisson_avg_gen::<f32>(15.0, 0.5);
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_poisson_invalid_lambda_zero() {
+        Poisson::new(0.0).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_poisson_invalid_lambda_neg() {
+        Poisson::new(-10.0).unwrap();
+    }
+}

vendor/rand_distr/src/skew_normal.rs

@@ -0,0 +1,256 @@
+// Copyright 2021 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 Skew Normal distribution.
+
+use crate::{Distribution, StandardNormal};
+use core::fmt;
+use num_traits::Float;
+use rand::Rng;
+
+/// The [skew normal distribution] `SN(location, scale, shape)`.
+///
+/// The skew normal distribution is a generalization of the
+/// [`Normal`] distribution to allow for non-zero skewness.
+///
+/// It has the density function, for `scale > 0`,
+/// `f(x) = 2 / scale * phi((x - location) / scale) * Phi(alpha * (x - location) / scale)`
+/// where `phi` and `Phi` are the density and distribution of a standard normal variable.
+///
+/// # Example
+///
+/// ```
+/// use rand_distr::{SkewNormal, Distribution};
+///
+/// // location 2, scale 3, shape 1
+/// let skew_normal = SkewNormal::new(2.0, 3.0, 1.0).unwrap();
+/// let v = skew_normal.sample(&mut rand::thread_rng());
+/// println!("{} is from a SN(2, 3, 1) distribution", v)
+/// ```
+///
+/// # Implementation details
+///
+/// We are using the algorithm from [A Method to Simulate the Skew Normal Distribution].
+///
+/// [skew normal distribution]: https://en.wikipedia.org/wiki/Skew_normal_distribution
+/// [`Normal`]: struct.Normal.html
+/// [A Method to Simulate the Skew Normal Distribution]: https://dx.doi.org/10.4236/am.2014.513201
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct SkewNormal<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+{
+    location: F,
+    scale: F,
+    shape: F,
+}
+
+/// Error type returned from `SkewNormal::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// The scale parameter is not finite or it is less or equal to zero.
+    ScaleTooSmall,
+    /// The shape parameter is not finite.
+    BadShape,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::ScaleTooSmall => {
+                "scale parameter is either non-finite or it is less or equal to zero in skew normal distribution"
+            }
+            Error::BadShape => "shape parameter is non-finite in skew normal distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+impl<F> SkewNormal<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+{
+    /// Construct, from location, scale and shape.
+    ///
+    /// Parameters:
+    ///
+    /// -   location (unrestricted)
+    /// -   scale (must be finite and larger than zero)
+    /// -   shape (must be finite)
+    #[inline]
+    pub fn new(location: F, scale: F, shape: F) -> Result<SkewNormal<F>, Error> {
+        if !scale.is_finite() || !(scale > F::zero()) {
+            return Err(Error::ScaleTooSmall);
+        }
+        if !shape.is_finite() {
+            return Err(Error::BadShape);
+        }
+        Ok(SkewNormal {
+            location,
+            scale,
+            shape,
+        })
+    }
+
+    /// Returns the location of the distribution.
+    pub fn location(&self) -> F {
+        self.location
+    }
+
+    /// Returns the scale of the distribution.
+    pub fn scale(&self) -> F {
+        self.scale
+    }
+
+    /// Returns the shape of the distribution.
+    pub fn shape(&self) -> F {
+        self.shape
+    }
+}
+
+impl<F> Distribution<F> for SkewNormal<F>
+where
+    F: Float,
+    StandardNormal: Distribution<F>,
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        let linear_map = |x: F| -> F { x * self.scale + self.location };
+        let u_1: F = rng.sample(StandardNormal);
+        if self.shape == F::zero() {
+            linear_map(u_1)
+        } else {
+            let u_2 = rng.sample(StandardNormal);
+            let (u, v) = (u_1.max(u_2), u_1.min(u_2));
+            if self.shape == -F::one() {
+                linear_map(v)
+            } else if self.shape == F::one() {
+                linear_map(u)
+            } else {
+                let normalized = ((F::one() + self.shape) * u + (F::one() - self.shape) * v)
+                    / ((F::one() + self.shape * self.shape).sqrt()
+                        * F::from(core::f64::consts::SQRT_2).unwrap());
+                linear_map(normalized)
+            }
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn test_samples<F: Float + core::fmt::Debug, D: Distribution<F>>(
+        distr: D, zero: F, expected: &[F],
+    ) {
+        let mut rng = crate::test::rng(213);
+        let mut buf = [zero; 4];
+        for x in &mut buf {
+            *x = rng.sample(&distr);
+        }
+        assert_eq!(buf, expected);
+    }
+
+    #[test]
+    #[should_panic]
+    fn invalid_scale_nan() {
+        SkewNormal::new(0.0, core::f64::NAN, 0.0).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn invalid_scale_zero() {
+        SkewNormal::new(0.0, 0.0, 0.0).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn invalid_scale_negative() {
+        SkewNormal::new(0.0, -1.0, 0.0).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn invalid_scale_infinite() {
+        SkewNormal::new(0.0, core::f64::INFINITY, 0.0).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn invalid_shape_nan() {
+        SkewNormal::new(0.0, 1.0, core::f64::NAN).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn invalid_shape_infinite() {
+        SkewNormal::new(0.0, 1.0, core::f64::INFINITY).unwrap();
+    }
+
+    #[test]
+    fn valid_location_nan() {
+        SkewNormal::new(core::f64::NAN, 1.0, 0.0).unwrap();
+    }
+
+    #[test]
+    fn skew_normal_value_stability() {
+        test_samples(
+            SkewNormal::new(0.0, 1.0, 0.0).unwrap(),
+            0f32,
+            &[-0.11844189, 0.781378, 0.06563994, -1.1932899],
+        );
+        test_samples(
+            SkewNormal::new(0.0, 1.0, 0.0).unwrap(),
+            0f64,
+            &[
+                -0.11844188827977231,
+                0.7813779637772346,
+                0.06563993969580051,
+                -1.1932899004186373,
+            ],
+        );
+        test_samples(
+            SkewNormal::new(core::f64::INFINITY, 1.0, 0.0).unwrap(),
+            0f64,
+            &[
+                core::f64::INFINITY,
+                core::f64::INFINITY,
+                core::f64::INFINITY,
+                core::f64::INFINITY,
+            ],
+        );
+        test_samples(
+            SkewNormal::new(core::f64::NEG_INFINITY, 1.0, 0.0).unwrap(),
+            0f64,
+            &[
+                core::f64::NEG_INFINITY,
+                core::f64::NEG_INFINITY,
+                core::f64::NEG_INFINITY,
+                core::f64::NEG_INFINITY,
+            ],
+        );
+    }
+
+    #[test]
+    fn skew_normal_value_location_nan() {
+        let skew_normal = SkewNormal::new(core::f64::NAN, 1.0, 0.0).unwrap();
+        let mut rng = crate::test::rng(213);
+        let mut buf = [0.0; 4];
+        for x in &mut buf {
+            *x = rng.sample(&skew_normal);
+        }
+        for value in buf.iter() {
+            assert!(value.is_nan());
+        }
+    }
+}

vendor/rand_distr/src/triangular.rs

@@ -0,0 +1,133 @@
+// 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 num_traits::Float;
+use crate::{Distribution, Standard};
+use rand::Rng;
+use core::fmt;
+
+/// The triangular distribution.
+///
+/// A continuous probability distribution parameterised by a range, and a mode
+/// (most likely value) within that range.
+///
+/// The probability density function is triangular. For a similar distribution
+/// with a smooth PDF, see the [`Pert`] distribution.
+///
+/// # Example
+///
+/// ```rust
+/// use rand_distr::{Triangular, Distribution};
+///
+/// let d = Triangular::new(0., 5., 2.5).unwrap();
+/// let v = d.sample(&mut rand::thread_rng());
+/// println!("{} is from a triangular distribution", v);
+/// ```
+///
+/// [`Pert`]: crate::Pert
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct Triangular<F>
+where F: Float, Standard: Distribution<F>
+{
+    min: F,
+    max: F,
+    mode: F,
+}
+
+/// Error type returned from [`Triangular::new`].
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum TriangularError {
+    /// `max < min` or `min` or `max` is NaN.
+    RangeTooSmall,
+    /// `mode < min` or `mode > max` or `mode` is NaN.
+    ModeRange,
+}
+
+impl fmt::Display for TriangularError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            TriangularError::RangeTooSmall => {
+                "requirement min <= max is not met in triangular distribution"
+            }
+            TriangularError::ModeRange => "mode is outside [min, max] in triangular distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for TriangularError {}
+
+impl<F> Triangular<F>
+where F: Float, Standard: Distribution<F>
+{
+    /// Set up the Triangular distribution with defined `min`, `max` and `mode`.
+    #[inline]
+    pub fn new(min: F, max: F, mode: F) -> Result<Triangular<F>, TriangularError> {
+        if !(max >= min) {
+            return Err(TriangularError::RangeTooSmall);
+        }
+        if !(mode >= min && max >= mode) {
+            return Err(TriangularError::ModeRange);
+        }
+        Ok(Triangular { min, max, mode })
+    }
+}
+
+impl<F> Distribution<F> for Triangular<F>
+where F: Float, Standard: Distribution<F>
+{
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        let f: F = rng.sample(Standard);
+        let diff_mode_min = self.mode - self.min;
+        let range = self.max - self.min;
+        let f_range = f * range;
+        if f_range < diff_mode_min {
+            self.min + (f_range * diff_mode_min).sqrt()
+        } else {
+            self.max - ((range - f_range) * (self.max - self.mode)).sqrt()
+        }
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+    use rand::{rngs::mock, Rng};
+
+    #[test]
+    fn test_triangular() {
+        let mut half_rng = mock::StepRng::new(0x8000_0000_0000_0000, 0);
+        assert_eq!(half_rng.gen::<f64>(), 0.5);
+        for &(min, max, mode, median) in &[
+            (-1., 1., 0., 0.),
+            (1., 2., 1., 2. - 0.5f64.sqrt()),
+            (5., 25., 25., 5. + 200f64.sqrt()),
+            (1e-5, 1e5, 1e-3, 1e5 - 4999999949.5f64.sqrt()),
+            (0., 1., 0.9, 0.45f64.sqrt()),
+            (-4., -0.5, -2., -4.0 + 3.5f64.sqrt()),
+        ] {
+            #[cfg(feature = "std")]
+            std::println!("{} {} {} {}", min, max, mode, median);
+            let distr = Triangular::new(min, max, mode).unwrap();
+            // Test correct value at median:
+            assert_eq!(distr.sample(&mut half_rng), median);
+        }
+
+        for &(min, max, mode) in &[
+            (-1., 1., 2.),
+            (-1., 1., -2.),
+            (2., 1., 1.),
+        ] {
+            assert!(Triangular::new(min, max, mode).is_err());
+        }
+    }
+}

vendor/rand_distr/src/unit_ball.rs

@@ -0,0 +1,48 @@
+// Copyright 2019 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 num_traits::Float;
+use crate::{uniform::SampleUniform, Distribution, Uniform};
+use rand::Rng;
+
+/// Samples uniformly from the unit ball (surface and interior) in three
+/// dimensions.
+///
+/// Implemented via rejection sampling.
+///
+///
+/// # Example
+///
+/// ```
+/// use rand_distr::{UnitBall, Distribution};
+///
+/// let v: [f64; 3] = UnitBall.sample(&mut rand::thread_rng());
+/// println!("{:?} is from the unit ball.", v)
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct UnitBall;
+
+impl<F: Float + SampleUniform> Distribution<[F; 3]> for UnitBall {
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [F; 3] {
+        let uniform = Uniform::new(F::from(-1.).unwrap(), F::from(1.).unwrap());
+        let mut x1;
+        let mut x2;
+        let mut x3;
+        loop {
+            x1 = uniform.sample(rng);
+            x2 = uniform.sample(rng);
+            x3 = uniform.sample(rng);
+            if x1 * x1 + x2 * x2 + x3 * x3 <= F::from(1.).unwrap() {
+                break;
+            }
+        }
+        [x1, x2, x3]
+    }
+}

vendor/rand_distr/src/unit_circle.rs

@@ -0,0 +1,68 @@
+// 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 num_traits::Float;
+use crate::{uniform::SampleUniform, Distribution, Uniform};
+use rand::Rng;
+
+/// Samples uniformly from the edge of the unit circle in two dimensions.
+///
+/// Implemented via a method by von Neumann[^1].
+///
+///
+/// # Example
+///
+/// ```
+/// use rand_distr::{UnitCircle, Distribution};
+///
+/// let v: [f64; 2] = UnitCircle.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)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct UnitCircle;
+
+impl<F: Float + SampleUniform> Distribution<[F; 2]> for UnitCircle {
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [F; 2] {
+        let uniform = Uniform::new(F::from(-1.).unwrap(), F::from(1.).unwrap());
+        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 < F::from(1.).unwrap() {
+                break;
+            }
+        }
+        let diff = x1 * x1 - x2 * x2;
+        [diff / sum, F::from(2.).unwrap() * x1 * x2 / sum]
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::UnitCircle;
+    use crate::Distribution;
+
+    #[test]
+    fn norm() {
+        let mut rng = crate::test::rng(1);
+        for _ in 0..1000 {
+            let x: [f64; 2] = UnitCircle.sample(&mut rng);
+            assert_almost_eq!(x[0] * x[0] + x[1] * x[1], 1., 1e-15);
+        }
+    }
+}

vendor/rand_distr/src/unit_disc.rs

@@ -0,0 +1,45 @@
+// Copyright 2019 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 num_traits::Float;
+use crate::{uniform::SampleUniform, Distribution, Uniform};
+use rand::Rng;
+
+/// Samples uniformly from the unit disc in two dimensions.
+///
+/// Implemented via rejection sampling.
+///
+///
+/// # Example
+///
+/// ```
+/// use rand_distr::{UnitDisc, Distribution};
+///
+/// let v: [f64; 2] = UnitDisc.sample(&mut rand::thread_rng());
+/// println!("{:?} is from the unit Disc.", v)
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct UnitDisc;
+
+impl<F: Float + SampleUniform> Distribution<[F; 2]> for UnitDisc {
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [F; 2] {
+        let uniform = Uniform::new(F::from(-1.).unwrap(), F::from(1.).unwrap());
+        let mut x1;
+        let mut x2;
+        loop {
+            x1 = uniform.sample(rng);
+            x2 = uniform.sample(rng);
+            if x1 * x1 + x2 * x2 <= F::from(1.).unwrap() {
+                break;
+            }
+        }
+        [x1, x2]
+    }
+}

vendor/rand_distr/src/unit_sphere.rs

@@ -0,0 +1,63 @@
+// Copyright 2018-2019 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 num_traits::Float;
+use crate::{uniform::SampleUniform, Distribution, Uniform};
+use rand::Rng;
+
+/// Samples uniformly from the surface of the unit sphere in three dimensions.
+///
+/// Implemented via a method by Marsaglia[^1].
+///
+///
+/// # Example
+///
+/// ```
+/// use rand_distr::{UnitSphere, Distribution};
+///
+/// let v: [f64; 3] = UnitSphere.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)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct UnitSphere;
+
+impl<F: Float + SampleUniform> Distribution<[F; 3]> for UnitSphere {
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [F; 3] {
+        let uniform = Uniform::new(F::from(-1.).unwrap(), F::from(1.).unwrap());
+        loop {
+            let (x1, x2) = (uniform.sample(rng), uniform.sample(rng));
+            let sum = x1 * x1 + x2 * x2;
+            if sum >= F::from(1.).unwrap() {
+                continue;
+            }
+            let factor = F::from(2.).unwrap() * (F::one() - sum).sqrt();
+            return [x1 * factor, x2 * factor, F::from(1.).unwrap() - F::from(2.).unwrap() * sum];
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::UnitSphere;
+    use crate::Distribution;
+
+    #[test]
+    fn norm() {
+        let mut rng = crate::test::rng(1);
+        for _ in 0..1000 {
+            let x: [f64; 3] = UnitSphere.sample(&mut rng);
+            assert_almost_eq!(x[0] * x[0] + x[1] * x[1] + x[2] * x[2], 1., 1e-15);
+        }
+    }
+}

vendor/rand_distr/src/utils.rs

@@ -0,0 +1,121 @@
+// 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
+
+use crate::ziggurat_tables;
+use rand::distributions::hidden_export::IntoFloat;
+use rand::Rng;
+use num_traits::Float;
+
+/// 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.
+pub(crate) fn log_gamma<F: Float>(x: F) -> F {
+    // precalculated 6 coefficients for the first 6 terms of the series
+    let coefficients: [F; 6] = [
+        F::from(76.18009172947146).unwrap(),
+        F::from(-86.50532032941677).unwrap(),
+        F::from(24.01409824083091).unwrap(),
+        F::from(-1.231739572450155).unwrap(),
+        F::from(0.1208650973866179e-2).unwrap(),
+        F::from(-0.5395239384953e-5).unwrap(),
+    ];
+
+    // (x+0.5)*ln(x+g+0.5)-(x+g+0.5)
+    let tmp = x + F::from(5.5).unwrap();
+    let log = (x + F::from(0.5).unwrap()) * tmp.ln() - tmp;
+
+    // the first few terms of the series for Ag(x)
+    let mut a = F::from(1.000000000190015).unwrap();
+    let mut denom = x;
+    for &coeff in &coefficients {
+        denom = denom + F::one();
+        a = a + (coeff / denom);
+    }
+
+    // get everything together
+    // a is Ag(x)
+    // 2.5066... is sqrt(2pi)
+    log + (F::from(2.5066282746310005).unwrap() * 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.
+#[inline(always)]
+pub(crate) 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,
+{
+    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 subtract to get [-1,1)
+            // We can't convert to an open range directly, that would require
+            // subtracting `3.0 - EPSILON`, which is not representable.
+            // It is possible with an extra step, but an open range does not
+            // seem necessary 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 subtract 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;
+        }
+    }
+}

vendor/rand_distr/src/weibull.rs

@@ -0,0 +1,132 @@
+// 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 num_traits::Float;
+use crate::{Distribution, OpenClosed01};
+use rand::Rng;
+use core::fmt;
+
+/// Samples floating-point numbers according to the Weibull distribution
+///
+/// # Example
+/// ```
+/// use rand::prelude::*;
+/// use rand_distr::Weibull;
+///
+/// let val: f64 = thread_rng().sample(Weibull::new(1., 10.).unwrap());
+/// println!("{}", val);
+/// ```
+#[derive(Clone, Copy, Debug)]
+#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
+pub struct Weibull<F>
+where F: Float, OpenClosed01: Distribution<F>
+{
+    inv_shape: F,
+    scale: F,
+}
+
+/// Error type returned from `Weibull::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// `scale <= 0` or `nan`.
+    ScaleTooSmall,
+    /// `shape <= 0` or `nan`.
+    ShapeTooSmall,
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            Error::ScaleTooSmall => "scale is not positive in Weibull distribution",
+            Error::ShapeTooSmall => "shape is not positive in Weibull distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for Error {}
+
+impl<F> Weibull<F>
+where F: Float, OpenClosed01: Distribution<F>
+{
+    /// Construct a new `Weibull` distribution with given `scale` and `shape`.
+    pub fn new(scale: F, shape: F) -> Result<Weibull<F>, Error> {
+        if !(scale > F::zero()) {
+            return Err(Error::ScaleTooSmall);
+        }
+        if !(shape > F::zero()) {
+            return Err(Error::ShapeTooSmall);
+        }
+        Ok(Weibull {
+            inv_shape: F::from(1.).unwrap() / shape,
+            scale,
+        })
+    }
+}
+
+impl<F> Distribution<F> for Weibull<F>
+where F: Float, OpenClosed01: Distribution<F>
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        let x: F = rng.sample(OpenClosed01);
+        self.scale * (-x.ln()).powf(self.inv_shape)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    #[should_panic]
+    fn invalid() {
+        Weibull::new(0., 0.).unwrap();
+    }
+
+    #[test]
+    fn sample() {
+        let scale = 1.0;
+        let shape = 2.0;
+        let d = Weibull::new(scale, shape).unwrap();
+        let mut rng = crate::test::rng(1);
+        for _ in 0..1000 {
+            let r = d.sample(&mut rng);
+            assert!(r >= 0.);
+        }
+    }
+
+    #[test]
+    fn value_stability() {
+        fn test_samples<F: Float + core::fmt::Debug, D: Distribution<F>>(
+            distr: D, zero: F, expected: &[F],
+        ) {
+            let mut rng = crate::test::rng(213);
+            let mut buf = [zero; 4];
+            for x in &mut buf {
+                *x = rng.sample(&distr);
+            }
+            assert_eq!(buf, expected);
+        }
+
+        test_samples(Weibull::new(1.0, 1.0).unwrap(), 0f32, &[
+            0.041495778,
+            0.7531094,
+            1.4189332,
+            0.38386202,
+        ]);
+        test_samples(Weibull::new(2.0, 0.5).unwrap(), 0f64, &[
+            1.1343478702739669,
+            0.29470010050655226,
+            0.7556151370284702,
+            7.877212340241561,
+        ]);
+    }
+}

vendor/rand_distr/src/weighted_alias.rs

@@ -0,0 +1,524 @@
+// Copyright 2019 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.
+
+//! This module contains an implementation of alias method for sampling random
+//! indices with probabilities proportional to a collection of weights.
+
+use super::WeightedError;
+use crate::{uniform::SampleUniform, Distribution, Uniform};
+use core::fmt;
+use core::iter::Sum;
+use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign};
+use rand::Rng;
+use alloc::{boxed::Box, vec, vec::Vec};
+#[cfg(feature = "serde1")]
+use serde::{Serialize, Deserialize};
+
+/// A distribution using weighted sampling to pick a discretely selected item.
+///
+/// Sampling a [`WeightedAliasIndex<W>`] distribution returns the index of a randomly
+/// selected element from the vector used to create the [`WeightedAliasIndex<W>`].
+/// The chance of a given element being picked is proportional to the value of
+/// the element. The weights can have any type `W` for which a implementation of
+/// [`AliasableWeight`] exists.
+///
+/// # Performance
+///
+/// Given that `n` is the number of items in the vector used to create an
+/// [`WeightedAliasIndex<W>`], it will require `O(n)` amount of memory.
+/// More specifically it takes up some constant amount of memory plus
+/// the vector used to create it and a [`Vec<u32>`] with capacity `n`.
+///
+/// Time complexity for the creation of a [`WeightedAliasIndex<W>`] is `O(n)`.
+/// Sampling is `O(1)`, it makes a call to [`Uniform<u32>::sample`] and a call
+/// to [`Uniform<W>::sample`].
+///
+/// # Example
+///
+/// ```
+/// use rand_distr::WeightedAliasIndex;
+/// use rand::prelude::*;
+///
+/// let choices = vec!['a', 'b', 'c'];
+/// let weights = vec![2, 1, 1];
+/// let dist = WeightedAliasIndex::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 = WeightedAliasIndex::new(items.iter().map(|item| item.1).collect()).unwrap();
+/// for _ in 0..100 {
+///     // 0% chance to print 'a', 30% chance to print 'b', 70% chance to print 'c'
+///     println!("{}", items[dist2.sample(&mut rng)].0);
+/// }
+/// ```
+///
+/// [`WeightedAliasIndex<W>`]: WeightedAliasIndex
+/// [`Vec<u32>`]: Vec
+/// [`Uniform<u32>::sample`]: Distribution::sample
+/// [`Uniform<W>::sample`]: Distribution::sample
+#[cfg_attr(doc_cfg, doc(cfg(feature = "alloc")))]
+#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
+#[cfg_attr(feature = "serde1", serde(bound(serialize = "W: Serialize, W::Sampler: Serialize")))]
+#[cfg_attr(feature = "serde1", serde(bound(deserialize = "W: Deserialize<'de>, W::Sampler: Deserialize<'de>")))]
+pub struct WeightedAliasIndex<W: AliasableWeight> {
+    aliases: Box<[u32]>,
+    no_alias_odds: Box<[W]>,
+    uniform_index: Uniform<u32>,
+    uniform_within_weight_sum: Uniform<W>,
+}
+
+impl<W: AliasableWeight> WeightedAliasIndex<W> {
+    /// Creates a new [`WeightedAliasIndex`].
+    ///
+    /// Returns an error if:
+    /// - The vector is empty.
+    /// - The vector is longer than `u32::MAX`.
+    /// - For any weight `w`: `w < 0` or `w > max` where `max = W::MAX /
+    ///   weights.len()`.
+    /// - The sum of weights is zero.
+    pub fn new(weights: Vec<W>) -> Result<Self, WeightedError> {
+        let n = weights.len();
+        if n == 0 {
+            return Err(WeightedError::NoItem);
+        } else if n > ::core::u32::MAX as usize {
+            return Err(WeightedError::TooMany);
+        }
+        let n = n as u32;
+
+        let max_weight_size = W::try_from_u32_lossy(n)
+            .map(|n| W::MAX / n)
+            .unwrap_or(W::ZERO);
+        if !weights
+            .iter()
+            .all(|&w| W::ZERO <= w && w <= max_weight_size)
+        {
+            return Err(WeightedError::InvalidWeight);
+        }
+
+        // The sum of weights will represent 100% of no alias odds.
+        let weight_sum = AliasableWeight::sum(weights.as_slice());
+        // Prevent floating point overflow due to rounding errors.
+        let weight_sum = if weight_sum > W::MAX {
+            W::MAX
+        } else {
+            weight_sum
+        };
+        if weight_sum == W::ZERO {
+            return Err(WeightedError::AllWeightsZero);
+        }
+
+        // `weight_sum` would have been zero if `try_from_lossy` causes an error here.
+        let n_converted = W::try_from_u32_lossy(n).unwrap();
+
+        let mut no_alias_odds = weights.into_boxed_slice();
+        for odds in no_alias_odds.iter_mut() {
+            *odds *= n_converted;
+            // Prevent floating point overflow due to rounding errors.
+            *odds = if *odds > W::MAX { W::MAX } else { *odds };
+        }
+
+        /// This struct is designed to contain three data structures at once,
+        /// sharing the same memory. More precisely it contains two linked lists
+        /// and an alias map, which will be the output of this method. To keep
+        /// the three data structures from getting in each other's way, it must
+        /// be ensured that a single index is only ever in one of them at the
+        /// same time.
+        struct Aliases {
+            aliases: Box<[u32]>,
+            smalls_head: u32,
+            bigs_head: u32,
+        }
+
+        impl Aliases {
+            fn new(size: u32) -> Self {
+                Aliases {
+                    aliases: vec![0; size as usize].into_boxed_slice(),
+                    smalls_head: ::core::u32::MAX,
+                    bigs_head: ::core::u32::MAX,
+                }
+            }
+
+            fn push_small(&mut self, idx: u32) {
+                self.aliases[idx as usize] = self.smalls_head;
+                self.smalls_head = idx;
+            }
+
+            fn push_big(&mut self, idx: u32) {
+                self.aliases[idx as usize] = self.bigs_head;
+                self.bigs_head = idx;
+            }
+
+            fn pop_small(&mut self) -> u32 {
+                let popped = self.smalls_head;
+                self.smalls_head = self.aliases[popped as usize];
+                popped
+            }
+
+            fn pop_big(&mut self) -> u32 {
+                let popped = self.bigs_head;
+                self.bigs_head = self.aliases[popped as usize];
+                popped
+            }
+
+            fn smalls_is_empty(&self) -> bool {
+                self.smalls_head == ::core::u32::MAX
+            }
+
+            fn bigs_is_empty(&self) -> bool {
+                self.bigs_head == ::core::u32::MAX
+            }
+
+            fn set_alias(&mut self, idx: u32, alias: u32) {
+                self.aliases[idx as usize] = alias;
+            }
+        }
+
+        let mut aliases = Aliases::new(n);
+
+        // Split indices into those with small weights and those with big weights.
+        for (index, &odds) in no_alias_odds.iter().enumerate() {
+            if odds < weight_sum {
+                aliases.push_small(index as u32);
+            } else {
+                aliases.push_big(index as u32);
+            }
+        }
+
+        // Build the alias map by finding an alias with big weight for each index with
+        // small weight.
+        while !aliases.smalls_is_empty() && !aliases.bigs_is_empty() {
+            let s = aliases.pop_small();
+            let b = aliases.pop_big();
+
+            aliases.set_alias(s, b);
+            no_alias_odds[b as usize] =
+                no_alias_odds[b as usize] - weight_sum + no_alias_odds[s as usize];
+
+            if no_alias_odds[b as usize] < weight_sum {
+                aliases.push_small(b);
+            } else {
+                aliases.push_big(b);
+            }
+        }
+
+        // The remaining indices should have no alias odds of about 100%. This is due to
+        // numeric accuracy. Otherwise they would be exactly 100%.
+        while !aliases.smalls_is_empty() {
+            no_alias_odds[aliases.pop_small() as usize] = weight_sum;
+        }
+        while !aliases.bigs_is_empty() {
+            no_alias_odds[aliases.pop_big() as usize] = weight_sum;
+        }
+
+        // Prepare distributions for sampling. Creating them beforehand improves
+        // sampling performance.
+        let uniform_index = Uniform::new(0, n);
+        let uniform_within_weight_sum = Uniform::new(W::ZERO, weight_sum);
+
+        Ok(Self {
+            aliases: aliases.aliases,
+            no_alias_odds,
+            uniform_index,
+            uniform_within_weight_sum,
+        })
+    }
+}
+
+impl<W: AliasableWeight> Distribution<usize> for WeightedAliasIndex<W> {
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> usize {
+        let candidate = rng.sample(self.uniform_index);
+        if rng.sample(&self.uniform_within_weight_sum) < self.no_alias_odds[candidate as usize] {
+            candidate as usize
+        } else {
+            self.aliases[candidate as usize] as usize
+        }
+    }
+}
+
+impl<W: AliasableWeight> fmt::Debug for WeightedAliasIndex<W>
+where
+    W: fmt::Debug,
+    Uniform<W>: fmt::Debug,
+{
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        f.debug_struct("WeightedAliasIndex")
+            .field("aliases", &self.aliases)
+            .field("no_alias_odds", &self.no_alias_odds)
+            .field("uniform_index", &self.uniform_index)
+            .field("uniform_within_weight_sum", &self.uniform_within_weight_sum)
+            .finish()
+    }
+}
+
+impl<W: AliasableWeight> Clone for WeightedAliasIndex<W>
+where Uniform<W>: Clone
+{
+    fn clone(&self) -> Self {
+        Self {
+            aliases: self.aliases.clone(),
+            no_alias_odds: self.no_alias_odds.clone(),
+            uniform_index: self.uniform_index,
+            uniform_within_weight_sum: self.uniform_within_weight_sum.clone(),
+        }
+    }
+}
+
+/// Trait that must be implemented for weights, that are used with
+/// [`WeightedAliasIndex`]. Currently no guarantees on the correctness of
+/// [`WeightedAliasIndex`] are given for custom implementations of this trait.
+#[cfg_attr(doc_cfg, doc(cfg(feature = "alloc")))]
+pub trait AliasableWeight:
+    Sized
+    + Copy
+    + SampleUniform
+    + PartialOrd
+    + Add<Output = Self>
+    + AddAssign
+    + Sub<Output = Self>
+    + SubAssign
+    + Mul<Output = Self>
+    + MulAssign
+    + Div<Output = Self>
+    + DivAssign
+    + Sum
+{
+    /// Maximum number representable by `Self`.
+    const MAX: Self;
+
+    /// Element of `Self` equivalent to 0.
+    const ZERO: Self;
+
+    /// Produce an instance of `Self` from a `u32` value, or return `None` if
+    /// out of range. Loss of precision (where `Self` is a floating point type)
+    /// is acceptable.
+    fn try_from_u32_lossy(n: u32) -> Option<Self>;
+
+    /// Sums all values in slice `values`.
+    fn sum(values: &[Self]) -> Self {
+        values.iter().copied().sum()
+    }
+}
+
+macro_rules! impl_weight_for_float {
+    ($T: ident) => {
+        impl AliasableWeight for $T {
+            const MAX: Self = ::core::$T::MAX;
+            const ZERO: Self = 0.0;
+
+            fn try_from_u32_lossy(n: u32) -> Option<Self> {
+                Some(n as $T)
+            }
+
+            fn sum(values: &[Self]) -> Self {
+                pairwise_sum(values)
+            }
+        }
+    };
+}
+
+/// In comparison to naive accumulation, the pairwise sum algorithm reduces
+/// rounding errors when there are many floating point values.
+fn pairwise_sum<T: AliasableWeight>(values: &[T]) -> T {
+    if values.len() <= 32 {
+        values.iter().copied().sum()
+    } else {
+        let mid = values.len() / 2;
+        let (a, b) = values.split_at(mid);
+        pairwise_sum(a) + pairwise_sum(b)
+    }
+}
+
+macro_rules! impl_weight_for_int {
+    ($T: ident) => {
+        impl AliasableWeight for $T {
+            const MAX: Self = ::core::$T::MAX;
+            const ZERO: Self = 0;
+
+            fn try_from_u32_lossy(n: u32) -> Option<Self> {
+                let n_converted = n as Self;
+                if n_converted >= Self::ZERO && n_converted as u32 == n {
+                    Some(n_converted)
+                } else {
+                    None
+                }
+            }
+        }
+    };
+}
+
+impl_weight_for_float!(f64);
+impl_weight_for_float!(f32);
+impl_weight_for_int!(usize);
+impl_weight_for_int!(u128);
+impl_weight_for_int!(u64);
+impl_weight_for_int!(u32);
+impl_weight_for_int!(u16);
+impl_weight_for_int!(u8);
+impl_weight_for_int!(isize);
+impl_weight_for_int!(i128);
+impl_weight_for_int!(i64);
+impl_weight_for_int!(i32);
+impl_weight_for_int!(i16);
+impl_weight_for_int!(i8);
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    #[cfg_attr(miri, ignore)] // Miri is too slow
+    fn test_weighted_index_f32() {
+        test_weighted_index(f32::into);
+
+        // Floating point special cases
+        assert_eq!(
+            WeightedAliasIndex::new(vec![::core::f32::INFINITY]).unwrap_err(),
+            WeightedError::InvalidWeight
+        );
+        assert_eq!(
+            WeightedAliasIndex::new(vec![-0_f32]).unwrap_err(),
+            WeightedError::AllWeightsZero
+        );
+        assert_eq!(
+            WeightedAliasIndex::new(vec![-1_f32]).unwrap_err(),
+            WeightedError::InvalidWeight
+        );
+        assert_eq!(
+            WeightedAliasIndex::new(vec![-::core::f32::INFINITY]).unwrap_err(),
+            WeightedError::InvalidWeight
+        );
+        assert_eq!(
+            WeightedAliasIndex::new(vec![::core::f32::NAN]).unwrap_err(),
+            WeightedError::InvalidWeight
+        );
+    }
+
+    #[test]
+    #[cfg_attr(miri, ignore)] // Miri is too slow
+    fn test_weighted_index_u128() {
+        test_weighted_index(|x: u128| x as f64);
+    }
+
+    #[test]
+    #[cfg_attr(miri, ignore)] // Miri is too slow
+    fn test_weighted_index_i128() {
+        test_weighted_index(|x: i128| x as f64);
+
+        // Signed integer special cases
+        assert_eq!(
+            WeightedAliasIndex::new(vec![-1_i128]).unwrap_err(),
+            WeightedError::InvalidWeight
+        );
+        assert_eq!(
+            WeightedAliasIndex::new(vec![::core::i128::MIN]).unwrap_err(),
+            WeightedError::InvalidWeight
+        );
+    }
+
+    #[test]
+    #[cfg_attr(miri, ignore)] // Miri is too slow
+    fn test_weighted_index_u8() {
+        test_weighted_index(u8::into);
+    }
+
+    #[test]
+    #[cfg_attr(miri, ignore)] // Miri is too slow
+    fn test_weighted_index_i8() {
+        test_weighted_index(i8::into);
+
+        // Signed integer special cases
+        assert_eq!(
+            WeightedAliasIndex::new(vec![-1_i8]).unwrap_err(),
+            WeightedError::InvalidWeight
+        );
+        assert_eq!(
+            WeightedAliasIndex::new(vec![::core::i8::MIN]).unwrap_err(),
+            WeightedError::InvalidWeight
+        );
+    }
+
+    fn test_weighted_index<W: AliasableWeight, F: Fn(W) -> f64>(w_to_f64: F)
+    where WeightedAliasIndex<W>: fmt::Debug {
+        const NUM_WEIGHTS: u32 = 10;
+        const ZERO_WEIGHT_INDEX: u32 = 3;
+        const NUM_SAMPLES: u32 = 15000;
+        let mut rng = crate::test::rng(0x9c9fa0b0580a7031);
+
+        let weights = {
+            let mut weights = Vec::with_capacity(NUM_WEIGHTS as usize);
+            let random_weight_distribution = Uniform::new_inclusive(
+                W::ZERO,
+                W::MAX / W::try_from_u32_lossy(NUM_WEIGHTS).unwrap(),
+            );
+            for _ in 0..NUM_WEIGHTS {
+                weights.push(rng.sample(&random_weight_distribution));
+            }
+            weights[ZERO_WEIGHT_INDEX as usize] = W::ZERO;
+            weights
+        };
+        let weight_sum = weights.iter().copied().sum::<W>();
+        let expected_counts = weights
+            .iter()
+            .map(|&w| w_to_f64(w) / w_to_f64(weight_sum) * NUM_SAMPLES as f64)
+            .collect::<Vec<f64>>();
+        let weight_distribution = WeightedAliasIndex::new(weights).unwrap();
+
+        let mut counts = vec![0; NUM_WEIGHTS as usize];
+        for _ in 0..NUM_SAMPLES {
+            counts[rng.sample(&weight_distribution)] += 1;
+        }
+
+        assert_eq!(counts[ZERO_WEIGHT_INDEX as usize], 0);
+        for (count, expected_count) in counts.into_iter().zip(expected_counts) {
+            let difference = (count as f64 - expected_count).abs();
+            let max_allowed_difference = NUM_SAMPLES as f64 / NUM_WEIGHTS as f64 * 0.1;
+            assert!(difference <= max_allowed_difference);
+        }
+
+        assert_eq!(
+            WeightedAliasIndex::<W>::new(vec![]).unwrap_err(),
+            WeightedError::NoItem
+        );
+        assert_eq!(
+            WeightedAliasIndex::new(vec![W::ZERO]).unwrap_err(),
+            WeightedError::AllWeightsZero
+        );
+        assert_eq!(
+            WeightedAliasIndex::new(vec![W::MAX, W::MAX]).unwrap_err(),
+            WeightedError::InvalidWeight
+        );
+    }
+
+    #[test]
+    fn value_stability() {
+        fn test_samples<W: AliasableWeight>(weights: Vec<W>, buf: &mut [usize], expected: &[usize]) {
+            assert_eq!(buf.len(), expected.len());
+            let distr = WeightedAliasIndex::new(weights).unwrap();
+            let mut rng = crate::test::rng(0x9c9fa0b0580a7031);
+            for r in buf.iter_mut() {
+                *r = rng.sample(&distr);
+            }
+            assert_eq!(buf, expected);
+        }
+
+        let mut buf = [0; 10];
+        test_samples(vec![1i32, 1, 1, 1, 1, 1, 1, 1, 1], &mut buf, &[
+            6, 5, 7, 5, 8, 7, 6, 2, 3, 7,
+        ]);
+        test_samples(vec![0.7f32, 0.1, 0.1, 0.1], &mut buf, &[
+            2, 0, 0, 0, 0, 0, 0, 0, 1, 3,
+        ]);
+        test_samples(vec![1.0f64, 0.999, 0.998, 0.997], &mut buf, &[
+            2, 1, 2, 3, 2, 1, 3, 2, 1, 1,
+        ]);
+    }
+}

vendor/rand_distr/src/ziggurat_tables.rs

@@ -0,0 +1,283 @@
+// Copyright 2018 Developers of the Rand project.
+// Copyright 2013 The Rust Project Developers.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+// Tables for distributions which are sampled using the ziggurat
+// algorithm. Autogenerated by `ziggurat_tables.py`.
+
+pub type ZigTable = &'static [f64; 257];
+pub const ZIG_NORM_R: f64 = 3.654152885361008796;
+#[rustfmt::skip]
+pub static ZIG_NORM_X: [f64; 257] =
+    [3.910757959537090045, 3.654152885361008796, 3.449278298560964462, 3.320244733839166074,
+     3.224575052047029100, 3.147889289517149969, 3.083526132001233044, 3.027837791768635434,
+     2.978603279880844834, 2.934366867207854224, 2.894121053612348060, 2.857138730872132548,
+     2.822877396825325125, 2.790921174000785765, 2.760944005278822555, 2.732685359042827056,
+     2.705933656121858100, 2.680514643284522158, 2.656283037575502437, 2.633116393630324570,
+     2.610910518487548515, 2.589575986706995181, 2.569035452680536569, 2.549221550323460761,
+     2.530075232158516929, 2.511544441625342294, 2.493583041269680667, 2.476149939669143318,
+     2.459208374333311298, 2.442725318198956774, 2.426670984935725972, 2.411018413899685520,
+     2.395743119780480601, 2.380822795170626005, 2.366237056715818632, 2.351967227377659952,
+     2.337996148795031370, 2.324308018869623016, 2.310888250599850036, 2.297723348901329565,
+     2.284800802722946056, 2.272108990226823888, 2.259637095172217780, 2.247375032945807760,
+     2.235313384928327984, 2.223443340090905718, 2.211756642882544366, 2.200245546609647995,
+     2.188902771624720689, 2.177721467738641614, 2.166695180352645966, 2.155817819875063268,
+     2.145083634046203613, 2.134487182844320152, 2.124023315687815661, 2.113687150684933957,
+     2.103474055713146829, 2.093379631137050279, 2.083399693996551783, 2.073530263516978778,
+     2.063767547809956415, 2.054107931648864849, 2.044547965215732788, 2.035084353727808715,
+     2.025713947862032960, 2.016433734904371722, 2.007240830558684852, 1.998132471356564244,
+     1.989106007615571325, 1.980158896898598364, 1.971288697931769640, 1.962493064942461896,
+     1.953769742382734043, 1.945116560006753925, 1.936531428273758904, 1.928012334050718257,
+     1.919557336591228847, 1.911164563769282232, 1.902832208548446369, 1.894558525668710081,
+     1.886341828534776388, 1.878180486290977669, 1.870072921069236838, 1.862017605397632281,
+     1.854013059758148119, 1.846057850283119750, 1.838150586580728607, 1.830289919680666566,
+     1.822474540091783224, 1.814703175964167636, 1.806974591348693426, 1.799287584547580199,
+     1.791640986550010028, 1.784033659547276329, 1.776464495522344977, 1.768932414909077933,
+     1.761436365316706665, 1.753975320315455111, 1.746548278279492994, 1.739154261283669012,
+     1.731792314050707216, 1.724461502945775715, 1.717160915015540690, 1.709889657069006086,
+     1.702646854797613907, 1.695431651932238548, 1.688243209434858727, 1.681080704722823338,
+     1.673943330923760353, 1.666830296159286684, 1.659740822855789499, 1.652674147080648526,
+     1.645629517902360339, 1.638606196773111146, 1.631603456932422036, 1.624620582830568427,
+     1.617656869570534228, 1.610711622367333673, 1.603784156023583041, 1.596873794420261339,
+     1.589979870021648534, 1.583101723393471438, 1.576238702733332886, 1.569390163412534456,
+     1.562555467528439657, 1.555733983466554893, 1.548925085471535512, 1.542128153226347553,
+     1.535342571438843118, 1.528567729435024614, 1.521803020758293101, 1.515047842773992404,
+     1.508301596278571965, 1.501563685112706548, 1.494833515777718391, 1.488110497054654369,
+     1.481394039625375747, 1.474683555695025516, 1.467978458615230908, 1.461278162507407830,
+     1.454582081885523293, 1.447889631277669675, 1.441200224845798017, 1.434513276002946425,
+     1.427828197027290358, 1.421144398672323117, 1.414461289772464658, 1.407778276843371534,
+     1.401094763676202559, 1.394410150925071257, 1.387723835686884621, 1.381035211072741964,
+     1.374343665770030531, 1.367648583594317957, 1.360949343030101844, 1.354245316759430606,
+     1.347535871177359290, 1.340820365893152122, 1.334098153216083604, 1.327368577624624679,
+     1.320630975217730096, 1.313884673146868964, 1.307128989027353860, 1.300363230327433728,
+     1.293586693733517645, 1.286798664489786415, 1.279998415710333237, 1.273185207661843732,
+     1.266358287014688333, 1.259516886060144225, 1.252660221891297887, 1.245787495544997903,
+     1.238897891102027415, 1.231990574742445110, 1.225064693752808020, 1.218119375481726552,
+     1.211153726239911244, 1.204166830140560140, 1.197157747875585931, 1.190125515422801650,
+     1.183069142678760732, 1.175987612011489825, 1.168879876726833800, 1.161744859441574240,
+     1.154581450355851802, 1.147388505416733873, 1.140164844363995789, 1.132909248648336975,
+     1.125620459211294389, 1.118297174115062909, 1.110938046009249502, 1.103541679420268151,
+     1.096106627847603487, 1.088631390649514197, 1.081114409698889389, 1.073554065787871714,
+     1.065948674757506653, 1.058296483326006454, 1.050595664586207123, 1.042844313139370538,
+     1.035040439828605274, 1.027181966030751292, 1.019266717460529215, 1.011292417434978441,
+     1.003256679539591412, 0.995156999629943084, 0.986990747093846266, 0.978755155288937750,
+     0.970447311058864615, 0.962064143217605250, 0.953602409875572654, 0.945058684462571130,
+     0.936429340280896860, 0.927710533396234771, 0.918898183643734989, 0.909987953490768997,
+     0.900975224455174528, 0.891855070726792376, 0.882622229578910122, 0.873271068082494550,
+     0.863795545546826915, 0.854189171001560554, 0.844444954902423661, 0.834555354079518752,
+     0.824512208745288633, 0.814306670128064347, 0.803929116982664893, 0.793369058833152785,
+     0.782615023299588763, 0.771654424216739354, 0.760473406422083165, 0.749056662009581653,
+     0.737387211425838629, 0.725446140901303549, 0.713212285182022732, 0.700661841097584448,
+     0.687767892786257717, 0.674499822827436479, 0.660822574234205984, 0.646695714884388928,
+     0.632072236375024632, 0.616896989996235545, 0.601104617743940417, 0.584616766093722262,
+     0.567338257040473026, 0.549151702313026790, 0.529909720646495108, 0.509423329585933393,
+     0.487443966121754335, 0.463634336771763245, 0.437518402186662658, 0.408389134588000746,
+     0.375121332850465727, 0.335737519180459465, 0.286174591747260509, 0.215241895913273806,
+     0.000000000000000000];
+#[rustfmt::skip]
+pub static ZIG_NORM_F: [f64; 257] =
+    [0.000477467764586655, 0.001260285930498598, 0.002609072746106363, 0.004037972593371872,
+     0.005522403299264754, 0.007050875471392110, 0.008616582769422917, 0.010214971439731100,
+     0.011842757857943104, 0.013497450601780807, 0.015177088307982072, 0.016880083152595839,
+     0.018605121275783350, 0.020351096230109354, 0.022117062707379922, 0.023902203305873237,
+     0.025705804008632656, 0.027527235669693315, 0.029365939758230111, 0.031221417192023690,
+     0.033093219458688698, 0.034980941461833073, 0.036884215688691151, 0.038802707404656918,
+     0.040736110656078753, 0.042684144916619378, 0.044646552251446536, 0.046623094902089664,
+     0.048613553216035145, 0.050617723861121788, 0.052635418276973649, 0.054666461325077916,
+     0.056710690106399467, 0.058767952921137984, 0.060838108349751806, 0.062921024437977854,
+     0.065016577971470438, 0.067124653828023989, 0.069245144397250269, 0.071377949059141965,
+     0.073522973714240991, 0.075680130359194964, 0.077849336702372207, 0.080030515814947509,
+     0.082223595813495684, 0.084428509570654661, 0.086645194450867782, 0.088873592068594229,
+     0.091113648066700734, 0.093365311913026619, 0.095628536713353335, 0.097903279039215627,
+     0.100189498769172020, 0.102487158942306270, 0.104796225622867056, 0.107116667775072880,
+     0.109448457147210021, 0.111791568164245583, 0.114145977828255210, 0.116511665626037014,
+     0.118888613443345698, 0.121276805485235437, 0.123676228202051403, 0.126086870220650349,
+     0.128508722280473636, 0.130941777174128166, 0.133386029692162844, 0.135841476571757352,
+     0.138308116449064322, 0.140785949814968309, 0.143274978974047118, 0.145775208006537926,
+     0.148286642733128721, 0.150809290682410169, 0.153343161060837674, 0.155888264725064563,
+     0.158444614156520225, 0.161012223438117663, 0.163591108232982951, 0.166181285765110071,
+     0.168782774801850333, 0.171395595638155623, 0.174019770082499359, 0.176655321444406654,
+     0.179302274523530397, 0.181960655600216487, 0.184630492427504539, 0.187311814224516926,
+     0.190004651671193070, 0.192709036904328807, 0.195425003514885592, 0.198152586546538112,
+     0.200891822495431333, 0.203642749311121501, 0.206405406398679298, 0.209179834621935651,
+     0.211966076307852941, 0.214764175252008499, 0.217574176725178370, 0.220396127481011589,
+     0.223230075764789593, 0.226076071323264877, 0.228934165415577484, 0.231804410825248525,
+     0.234686861873252689, 0.237581574432173676, 0.240488605941449107, 0.243408015423711988,
+     0.246339863502238771, 0.249284212419516704, 0.252241126056943765, 0.255210669955677150,
+     0.258192911338648023, 0.261187919133763713, 0.264195763998317568, 0.267216518344631837,
+     0.270250256366959984, 0.273297054069675804, 0.276356989296781264, 0.279430141762765316,
+     0.282516593084849388, 0.285616426816658109, 0.288729728483353931, 0.291856585618280984,
+     0.294997087801162572, 0.298151326697901342, 0.301319396102034120, 0.304501391977896274,
+     0.307697412505553769, 0.310907558127563710, 0.314131931597630143, 0.317370638031222396,
+     0.320623784958230129, 0.323891482377732021, 0.327173842814958593, 0.330470981380537099,
+     0.333783015832108509, 0.337110066638412809, 0.340452257045945450, 0.343809713148291340,
+     0.347182563958251478, 0.350570941482881204, 0.353974980801569250, 0.357394820147290515,
+     0.360830600991175754, 0.364282468130549597, 0.367750569780596226, 0.371235057669821344,
+     0.374736087139491414, 0.378253817247238111, 0.381788410875031348, 0.385340034841733958,
+     0.388908860020464597, 0.392495061461010764, 0.396098818517547080, 0.399720314981931668,
+     0.403359739222868885, 0.407017284331247953, 0.410693148271983222, 0.414387534042706784,
+     0.418100649839684591, 0.421832709231353298, 0.425583931339900579, 0.429354541031341519,
+     0.433144769114574058, 0.436954852549929273, 0.440785034667769915, 0.444635565397727750,
+     0.448506701509214067, 0.452398706863882505, 0.456311852680773566, 0.460246417814923481,
+     0.464202689050278838, 0.468180961407822172, 0.472181538469883255, 0.476204732721683788,
+     0.480250865911249714, 0.484320269428911598, 0.488413284707712059, 0.492530263646148658,
+     0.496671569054796314, 0.500837575128482149, 0.505028667945828791, 0.509245245998136142,
+     0.513487720749743026, 0.517756517232200619, 0.522052074674794864, 0.526374847174186700,
+     0.530725304406193921, 0.535103932383019565, 0.539511234259544614, 0.543947731192649941,
+     0.548413963257921133, 0.552910490428519918, 0.557437893621486324, 0.561996775817277916,
+     0.566587763258951771, 0.571211506738074970, 0.575868682975210544, 0.580559996103683473,
+     0.585286179266300333, 0.590047996335791969, 0.594846243770991268, 0.599681752622167719,
+     0.604555390700549533, 0.609468064928895381, 0.614420723892076803, 0.619414360609039205,
+     0.624450015550274240, 0.629528779928128279, 0.634651799290960050, 0.639820277456438991,
+     0.645035480824251883, 0.650298743114294586, 0.655611470583224665, 0.660975147780241357,
+     0.666391343912380640, 0.671861719900766374, 0.677388036222513090, 0.682972161648791376,
+     0.688616083008527058, 0.694321916130032579, 0.700091918140490099, 0.705928501336797409,
+     0.711834248882358467, 0.717811932634901395, 0.723864533472881599, 0.729995264565802437,
+     0.736207598131266683, 0.742505296344636245, 0.748892447223726720, 0.755373506511754500,
+     0.761953346841546475, 0.768637315803334831, 0.775431304986138326, 0.782341832659861902,
+     0.789376143571198563, 0.796542330428254619, 0.803849483176389490, 0.811307874318219935,
+     0.818929191609414797, 0.826726833952094231, 0.834716292992930375, 0.842915653118441077,
+     0.851346258465123684, 0.860033621203008636, 0.869008688043793165, 0.878309655816146839,
+     0.887984660763399880, 0.898095921906304051, 0.908726440060562912, 0.919991505048360247,
+     0.932060075968990209, 0.945198953453078028, 0.959879091812415930, 0.977101701282731328,
+     1.000000000000000000];
+pub const ZIG_EXP_R: f64 = 7.697117470131050077;
+#[rustfmt::skip]
+pub static ZIG_EXP_X: [f64; 257] =
+    [8.697117470131052741, 7.697117470131050077, 6.941033629377212577, 6.478378493832569696,
+     6.144164665772472667, 5.882144315795399869, 5.666410167454033697, 5.482890627526062488,
+     5.323090505754398016, 5.181487281301500047, 5.054288489981304089, 4.938777085901250530,
+     4.832939741025112035, 4.735242996601741083, 4.644491885420085175, 4.559737061707351380,
+     4.480211746528421912, 4.405287693473573185, 4.334443680317273007, 4.267242480277365857,
+     4.203313713735184365, 4.142340865664051464, 4.084051310408297830, 4.028208544647936762,
+     3.974606066673788796, 3.923062500135489739, 3.873417670399509127, 3.825529418522336744,
+     3.779270992411667862, 3.734528894039797375, 3.691201090237418825, 3.649195515760853770,
+     3.608428813128909507, 3.568825265648337020, 3.530315889129343354, 3.492837654774059608,
+     3.456332821132760191, 3.420748357251119920, 3.386035442460300970, 3.352149030900109405,
+     3.319047470970748037, 3.286692171599068679, 3.255047308570449882, 3.224079565286264160,
+     3.193757903212240290, 3.164053358025972873, 3.134938858084440394, 3.106389062339824481,
+     3.078380215254090224, 3.050890016615455114, 3.023897504455676621, 2.997382949516130601,
+     2.971327759921089662, 2.945714394895045718, 2.920526286512740821, 2.895747768600141825,
+     2.871364012015536371, 2.847360965635188812, 2.823725302450035279, 2.800444370250737780,
+     2.777506146439756574, 2.754899196562344610, 2.732612636194700073, 2.710636095867928752,
+     2.688959688741803689, 2.667573980773266573, 2.646469963151809157, 2.625639026797788489,
+     2.605072938740835564, 2.584763820214140750, 2.564704126316905253, 2.544886627111869970,
+     2.525304390037828028, 2.505950763528594027, 2.486819361740209455, 2.467904050297364815,
+     2.449198932978249754, 2.430698339264419694, 2.412396812688870629, 2.394289099921457886,
+     2.376370140536140596, 2.358635057409337321, 2.341079147703034380, 2.323697874390196372,
+     2.306486858283579799, 2.289441870532269441, 2.272558825553154804, 2.255833774367219213,
+     2.239262898312909034, 2.222842503111036816, 2.206569013257663858, 2.190438966723220027,
+     2.174449009937774679, 2.158595893043885994, 2.142876465399842001, 2.127287671317368289,
+     2.111826546019042183, 2.096490211801715020, 2.081275874393225145, 2.066180819490575526,
+     2.051202409468584786, 2.036338080248769611, 2.021585338318926173, 2.006941757894518563,
+     1.992404978213576650, 1.977972700957360441, 1.963642687789548313, 1.949412758007184943,
+     1.935280786297051359, 1.921244700591528076, 1.907302480018387536, 1.893452152939308242,
+     1.879691795072211180, 1.866019527692827973, 1.852433515911175554, 1.838931967018879954,
+     1.825513128903519799, 1.812175288526390649, 1.798916770460290859, 1.785735935484126014,
+     1.772631179231305643, 1.759600930889074766, 1.746643651946074405, 1.733757834985571566,
+     1.720942002521935299, 1.708194705878057773, 1.695514524101537912, 1.682900062917553896,
+     1.670349953716452118, 1.657862852574172763, 1.645437439303723659, 1.633072416535991334,
+     1.620766508828257901, 1.608518461798858379, 1.596327041286483395, 1.584191032532688892,
+     1.572109239386229707, 1.560080483527888084, 1.548103603714513499, 1.536177455041032092,
+     1.524300908219226258, 1.512472848872117082, 1.500692176842816750, 1.488957805516746058,
+     1.477268661156133867, 1.465623682245745352, 1.454021818848793446, 1.442462031972012504,
+     1.430943292938879674, 1.419464582769983219, 1.408024891569535697, 1.396623217917042137,
+     1.385258568263121992, 1.373929956328490576, 1.362636402505086775, 1.351376933258335189,
+     1.340150580529504643, 1.328956381137116560, 1.317793376176324749, 1.306660610415174117,
+     1.295557131686601027, 1.284481990275012642, 1.273434238296241139, 1.262412929069615330,
+     1.251417116480852521, 1.240445854334406572, 1.229498195693849105, 1.218573192208790124,
+     1.207669893426761121, 1.196787346088403092, 1.185924593404202199, 1.175080674310911677,
+     1.164254622705678921, 1.153445466655774743, 1.142652227581672841, 1.131873919411078511,
+     1.121109547701330200, 1.110358108727411031, 1.099618588532597308, 1.088889961938546813,
+     1.078171191511372307, 1.067461226479967662, 1.056759001602551429, 1.046063435977044209,
+     1.035373431790528542, 1.024687873002617211, 1.014005623957096480, 1.003325527915696735,
+     0.992646405507275897, 0.981967053085062602, 0.971286240983903260, 0.960602711668666509,
+     0.949915177764075969, 0.939222319955262286, 0.928522784747210395, 0.917815182070044311,
+     0.907098082715690257, 0.896370015589889935, 0.885629464761751528, 0.874874866291025066,
+     0.864104604811004484, 0.853317009842373353, 0.842510351810368485, 0.831682837734273206,
+     0.820832606554411814, 0.809957724057418282, 0.799056177355487174, 0.788125868869492430,
+     0.777164609759129710, 0.766170112735434672, 0.755139984181982249, 0.744071715500508102,
+     0.732962673584365398, 0.721810090308756203, 0.710611050909655040, 0.699362481103231959,
+     0.688061132773747808, 0.676703568029522584, 0.665286141392677943, 0.653804979847664947,
+     0.642255960424536365, 0.630634684933490286, 0.618936451394876075, 0.607156221620300030,
+     0.595288584291502887, 0.583327712748769489, 0.571267316532588332, 0.559100585511540626,
+     0.546820125163310577, 0.534417881237165604, 0.521885051592135052, 0.509211982443654398,
+     0.496388045518671162, 0.483401491653461857, 0.470239275082169006, 0.456886840931420235,
+     0.443327866073552401, 0.429543940225410703, 0.415514169600356364, 0.401214678896277765,
+     0.386617977941119573, 0.371692145329917234, 0.356399760258393816, 0.340696481064849122,
+     0.324529117016909452, 0.307832954674932158, 0.290527955491230394, 0.272513185478464703,
+     0.253658363385912022, 0.233790483059674731, 0.212671510630966620, 0.189958689622431842,
+     0.165127622564187282, 0.137304980940012589, 0.104838507565818778, 0.063852163815001570,
+     0.000000000000000000];
+#[rustfmt::skip]
+pub static ZIG_EXP_F: [f64; 257] =
+    [0.000167066692307963, 0.000454134353841497, 0.000967269282327174, 0.001536299780301573,
+     0.002145967743718907, 0.002788798793574076, 0.003460264777836904, 0.004157295120833797,
+     0.004877655983542396, 0.005619642207205489, 0.006381905937319183, 0.007163353183634991,
+     0.007963077438017043, 0.008780314985808977, 0.009614413642502212, 0.010464810181029981,
+     0.011331013597834600, 0.012212592426255378, 0.013109164931254991, 0.014020391403181943,
+     0.014945968011691148, 0.015885621839973156, 0.016839106826039941, 0.017806200410911355,
+     0.018786700744696024, 0.019780424338009740, 0.020787204072578114, 0.021806887504283581,
+     0.022839335406385240, 0.023884420511558174, 0.024942026419731787, 0.026012046645134221,
+     0.027094383780955803, 0.028188948763978646, 0.029295660224637411, 0.030414443910466622,
+     0.031545232172893622, 0.032687963508959555, 0.033842582150874358, 0.035009037697397431,
+     0.036187284781931443, 0.037377282772959382, 0.038578995503074871, 0.039792391023374139,
+     0.041017441380414840, 0.042254122413316254, 0.043502413568888197, 0.044762297732943289,
+     0.046033761076175184, 0.047316792913181561, 0.048611385573379504, 0.049917534282706379,
+     0.051235237055126281, 0.052564494593071685, 0.053905310196046080, 0.055257689676697030,
+     0.056621641283742870, 0.057997175631200659, 0.059384305633420280, 0.060783046445479660,
+     0.062193415408541036, 0.063615431999807376, 0.065049117786753805, 0.066494496385339816,
+     0.067951593421936643, 0.069420436498728783, 0.070901055162371843, 0.072393480875708752,
+     0.073897746992364746, 0.075413888734058410, 0.076941943170480517, 0.078481949201606435,
+     0.080033947542319905, 0.081597980709237419, 0.083174093009632397, 0.084762330532368146,
+     0.086362741140756927, 0.087975374467270231, 0.089600281910032886, 0.091237516631040197,
+     0.092887133556043569, 0.094549189376055873, 0.096223742550432825, 0.097910853311492213,
+     0.099610583670637132, 0.101322997425953631, 0.103048160171257702, 0.104786139306570145,
+     0.106537004050001632, 0.108300825451033755, 0.110077676405185357, 0.111867631670056283,
+     0.113670767882744286, 0.115487163578633506, 0.117316899211555525, 0.119160057175327641,
+     0.121016721826674792, 0.122886979509545108, 0.124770918580830933, 0.126668629437510671,
+     0.128580204545228199, 0.130505738468330773, 0.132445327901387494, 0.134399071702213602,
+     0.136367070926428829, 0.138349428863580176, 0.140346251074862399, 0.142357645432472146,
+     0.144383722160634720, 0.146424593878344889, 0.148480375643866735, 0.150551185001039839,
+     0.152637142027442801, 0.154738369384468027, 0.156854992369365148, 0.158987138969314129,
+     0.161134939917591952, 0.163298528751901734, 0.165478041874935922, 0.167673618617250081,
+     0.169885401302527550, 0.172113535315319977, 0.174358169171353411, 0.176619454590494829,
+     0.178897546572478278, 0.181192603475496261, 0.183504787097767436, 0.185834262762197083,
+     0.188181199404254262, 0.190545769663195363, 0.192928149976771296, 0.195328520679563189,
+     0.197747066105098818, 0.200183974691911210, 0.202639439093708962, 0.205113656293837654,
+     0.207606827724221982, 0.210119159388988230, 0.212650861992978224, 0.215202151075378628,
+     0.217773247148700472, 0.220364375843359439, 0.222975768058120111, 0.225607660116683956,
+     0.228260293930716618, 0.230933917169627356, 0.233628783437433291, 0.236345152457059560,
+     0.239083290262449094, 0.241843469398877131, 0.244625969131892024, 0.247431075665327543,
+     0.250259082368862240, 0.253110290015629402, 0.255985007030415324, 0.258883549749016173,
+     0.261806242689362922, 0.264753418835062149, 0.267725419932044739, 0.270722596799059967,
+     0.273745309652802915, 0.276793928448517301, 0.279868833236972869, 0.282970414538780746,
+     0.286099073737076826, 0.289255223489677693, 0.292439288161892630, 0.295651704281261252,
+     0.298892921015581847, 0.302163400675693528, 0.305463619244590256, 0.308794066934560185,
+     0.312155248774179606, 0.315547685227128949, 0.318971912844957239, 0.322428484956089223,
+     0.325917972393556354, 0.329440964264136438, 0.332998068761809096, 0.336589914028677717,
+     0.340217149066780189, 0.343880444704502575, 0.347580494621637148, 0.351318016437483449,
+     0.355093752866787626, 0.358908472948750001, 0.362762973354817997, 0.366658079781514379,
+     0.370594648435146223, 0.374573567615902381, 0.378595759409581067, 0.382662181496010056,
+     0.386773829084137932, 0.390931736984797384, 0.395136981833290435, 0.399390684475231350,
+     0.403694012530530555, 0.408048183152032673, 0.412454465997161457, 0.416914186433003209,
+     0.421428728997616908, 0.425999541143034677, 0.430628137288459167, 0.435316103215636907,
+     0.440065100842354173, 0.444876873414548846, 0.449753251162755330, 0.454696157474615836,
+     0.459707615642138023, 0.464789756250426511, 0.469944825283960310, 0.475175193037377708,
+     0.480483363930454543, 0.485871987341885248, 0.491343869594032867, 0.496901987241549881,
+     0.502549501841348056, 0.508289776410643213, 0.514126393814748894, 0.520063177368233931,
+     0.526104213983620062, 0.532253880263043655, 0.538516872002862246, 0.544898237672440056,
+     0.551403416540641733, 0.558038282262587892, 0.564809192912400615, 0.571723048664826150,
+     0.578787358602845359, 0.586010318477268366, 0.593400901691733762, 0.600968966365232560,
+     0.608725382079622346, 0.616682180915207878, 0.624852738703666200, 0.633251994214366398,
+     0.641896716427266423, 0.650805833414571433, 0.660000841079000145, 0.669506316731925177,
+     0.679350572264765806, 0.689566496117078431, 0.700192655082788606, 0.711274760805076456,
+     0.722867659593572465, 0.735038092431424039, 0.747868621985195658, 0.761463388849896838,
+     0.775956852040116218, 0.791527636972496285, 0.808421651523009044, 0.826993296643051101,
+     0.847785500623990496, 0.871704332381204705, 0.900469929925747703, 0.938143680862176477,
+     1.000000000000000000];

vendor/rand_distr/src/zipf.rs

@@ -0,0 +1,374 @@
+// Copyright 2021 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 Zeta and related distributions.
+
+use num_traits::Float;
+use crate::{Distribution, Standard};
+use rand::{Rng, distributions::OpenClosed01};
+use core::fmt;
+
+/// Samples integers according to the [zeta distribution].
+///
+/// The zeta distribution is a limit of the [`Zipf`] distribution. Sometimes it
+/// is called one of the following: discrete Pareto, Riemann-Zeta, Zipf, or
+/// Zipf–Estoup distribution.
+///
+/// It has the density function `f(k) = k^(-a) / C(a)` for `k >= 1`, where `a`
+/// is the parameter and `C(a)` is the Riemann zeta function.
+///
+/// # Example
+/// ```
+/// use rand::prelude::*;
+/// use rand_distr::Zeta;
+///
+/// let val: f64 = thread_rng().sample(Zeta::new(1.5).unwrap());
+/// println!("{}", val);
+/// ```
+///
+/// # Remarks
+///
+/// The zeta distribution has no upper limit. Sampled values may be infinite.
+/// In particular, a value of infinity might be returned for the following
+/// reasons:
+/// 1. it is the best representation in the type `F` of the actual sample.
+/// 2. to prevent infinite loops for very small `a`.
+///
+/// # Implementation details
+///
+/// We are using the algorithm from [Non-Uniform Random Variate Generation],
+/// Section 6.1, page 551.
+///
+/// [zeta distribution]: https://en.wikipedia.org/wiki/Zeta_distribution
+/// [Non-Uniform Random Variate Generation]: https://doi.org/10.1007/978-1-4613-8643-8
+#[derive(Clone, Copy, Debug)]
+pub struct Zeta<F>
+where F: Float, Standard: Distribution<F>, OpenClosed01: Distribution<F>
+{
+    a_minus_1: F,
+    b: F,
+}
+
+/// Error type returned from `Zeta::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum ZetaError {
+    /// `a <= 1` or `nan`.
+    ATooSmall,
+}
+
+impl fmt::Display for ZetaError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            ZetaError::ATooSmall => "a <= 1 or is NaN in Zeta distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for ZetaError {}
+
+impl<F> Zeta<F>
+where F: Float, Standard: Distribution<F>, OpenClosed01: Distribution<F>
+{
+    /// Construct a new `Zeta` distribution with given `a` parameter.
+    #[inline]
+    pub fn new(a: F) -> Result<Zeta<F>, ZetaError> {
+        if !(a > F::one()) {
+            return Err(ZetaError::ATooSmall);
+        }
+        let a_minus_1 = a - F::one();
+        let two = F::one() + F::one();
+        Ok(Zeta {
+            a_minus_1,
+            b: two.powf(a_minus_1),
+        })
+    }
+}
+
+impl<F> Distribution<F> for Zeta<F>
+where F: Float, Standard: Distribution<F>, OpenClosed01: Distribution<F>
+{
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        loop {
+            let u = rng.sample(OpenClosed01);
+            let x = u.powf(-F::one() / self.a_minus_1).floor();
+            debug_assert!(x >= F::one());
+            if x.is_infinite() {
+                // For sufficiently small `a`, `x` will always be infinite,
+                // which is rejected, resulting in an infinite loop. We avoid
+                // this by always returning infinity instead.
+                return x;
+            }
+
+            let t = (F::one() + F::one() / x).powf(self.a_minus_1);
+
+            let v = rng.sample(Standard);
+            if v * x * (t - F::one()) * self.b <= t * (self.b - F::one()) {
+                return x;
+            }
+        }
+    }
+}
+
+/// Samples integers according to the Zipf distribution.
+///
+/// The samples follow Zipf's law: The frequency of each sample from a finite
+/// set of size `n` is inversely proportional to a power of its frequency rank
+/// (with exponent `s`).
+///
+/// For large `n`, this converges to the [`Zeta`] distribution.
+///
+/// For `s = 0`, this becomes a uniform distribution.
+///
+/// # Example
+/// ```
+/// use rand::prelude::*;
+/// use rand_distr::Zipf;
+///
+/// let val: f64 = thread_rng().sample(Zipf::new(10, 1.5).unwrap());
+/// println!("{}", val);
+/// ```
+///
+/// # Implementation details
+///
+/// Implemented via [rejection sampling](https://en.wikipedia.org/wiki/Rejection_sampling),
+/// due to Jason Crease[1].
+///
+/// [1]: https://jasoncrease.medium.com/rejection-sampling-the-zipf-distribution-6b359792cffa
+#[derive(Clone, Copy, Debug)]
+pub struct Zipf<F>
+where F: Float, Standard: Distribution<F> {
+    n: F,
+    s: F,
+    t: F,
+    q: F,
+}
+
+/// Error type returned from `Zipf::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum ZipfError {
+    /// `s < 0` or `nan`.
+    STooSmall,
+    /// `n < 1`.
+    NTooSmall,
+}
+
+impl fmt::Display for ZipfError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(match self {
+            ZipfError::STooSmall => "s < 0 or is NaN in Zipf distribution",
+            ZipfError::NTooSmall => "n < 1 in Zipf distribution",
+        })
+    }
+}
+
+#[cfg(feature = "std")]
+#[cfg_attr(doc_cfg, doc(cfg(feature = "std")))]
+impl std::error::Error for ZipfError {}
+
+impl<F> Zipf<F>
+where F: Float, Standard: Distribution<F> {
+    /// Construct a new `Zipf` distribution for a set with `n` elements and a
+    /// frequency rank exponent `s`.
+    ///
+    /// For large `n`, rounding may occur to fit the number into the float type.
+    #[inline]
+    pub fn new(n: u64, s: F) -> Result<Zipf<F>, ZipfError> {
+        if !(s >= F::zero()) {
+            return Err(ZipfError::STooSmall);
+        }
+        if n < 1 {
+            return Err(ZipfError::NTooSmall);
+        }
+        let n = F::from(n).unwrap();  // This does not fail.
+        let q = if s != F::one() {
+            // Make sure to calculate the division only once.
+            F::one() / (F::one() - s)
+        } else {
+            // This value is never used.
+            F::zero()
+        };
+        let t = if s != F::one() {
+            (n.powf(F::one() - s) - s) * q
+        } else {
+            F::one() + n.ln()
+        };
+        debug_assert!(t > F::zero());
+        Ok(Zipf {
+            n, s, t, q
+        })
+    }
+
+    /// Inverse cumulative density function
+    #[inline]
+    fn inv_cdf(&self, p: F) -> F {
+        let one = F::one();
+        let pt = p * self.t;
+        if pt <= one {
+            pt
+        } else if self.s != one {
+            (pt * (one - self.s) + self.s).powf(self.q)
+        } else {
+            (pt - one).exp()
+        }
+    }
+}
+
+impl<F> Distribution<F> for Zipf<F>
+where F: Float, Standard: Distribution<F>
+{
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
+        let one = F::one();
+        loop {
+            let inv_b = self.inv_cdf(rng.sample(Standard));
+            let x = (inv_b + one).floor();
+            let mut ratio = x.powf(-self.s);
+            if x > one {
+                ratio = ratio * inv_b.powf(self.s)
+            };
+
+            let y = rng.sample(Standard);
+            if y < ratio {
+                return x;
+            }
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn test_samples<F: Float + core::fmt::Debug, D: Distribution<F>>(
+        distr: D, zero: F, expected: &[F],
+    ) {
+        let mut rng = crate::test::rng(213);
+        let mut buf = [zero; 4];
+        for x in &mut buf {
+            *x = rng.sample(&distr);
+        }
+        assert_eq!(buf, expected);
+    }
+
+    #[test]
+    #[should_panic]
+    fn zeta_invalid() {
+        Zeta::new(1.).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn zeta_nan() {
+        Zeta::new(core::f64::NAN).unwrap();
+    }
+
+    #[test]
+    fn zeta_sample() {
+        let a = 2.0;
+        let d = Zeta::new(a).unwrap();
+        let mut rng = crate::test::rng(1);
+        for _ in 0..1000 {
+            let r = d.sample(&mut rng);
+            assert!(r >= 1.);
+        }
+    }
+
+    #[test]
+    fn zeta_small_a() {
+        let a = 1. + 1e-15;
+        let d = Zeta::new(a).unwrap();
+        let mut rng = crate::test::rng(2);
+        for _ in 0..1000 {
+            let r = d.sample(&mut rng);
+            assert!(r >= 1.);
+        }
+    }
+
+    #[test]
+    fn zeta_value_stability() {
+        test_samples(Zeta::new(1.5).unwrap(), 0f32, &[
+            1.0, 2.0, 1.0, 1.0,
+        ]);
+        test_samples(Zeta::new(2.0).unwrap(), 0f64, &[
+            2.0, 1.0, 1.0, 1.0,
+        ]);
+    }
+
+    #[test]
+    #[should_panic]
+    fn zipf_s_too_small() {
+        Zipf::new(10, -1.).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn zipf_n_too_small() {
+        Zipf::new(0, 1.).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn zipf_nan() {
+        Zipf::new(10, core::f64::NAN).unwrap();
+    }
+
+    #[test]
+    fn zipf_sample() {
+        let d = Zipf::new(10, 0.5).unwrap();
+        let mut rng = crate::test::rng(2);
+        for _ in 0..1000 {
+            let r = d.sample(&mut rng);
+            assert!(r >= 1.);
+        }
+    }
+
+    #[test]
+    fn zipf_sample_s_1() {
+        let d = Zipf::new(10, 1.).unwrap();
+        let mut rng = crate::test::rng(2);
+        for _ in 0..1000 {
+            let r = d.sample(&mut rng);
+            assert!(r >= 1.);
+        }
+    }
+
+    #[test]
+    fn zipf_sample_s_0() {
+        let d = Zipf::new(10, 0.).unwrap();
+        let mut rng = crate::test::rng(2);
+        for _ in 0..1000 {
+            let r = d.sample(&mut rng);
+            assert!(r >= 1.);
+        }
+        // TODO: verify that this is a uniform distribution
+    }
+
+    #[test]
+    fn zipf_sample_large_n() {
+        let d = Zipf::new(core::u64::MAX, 1.5).unwrap();
+        let mut rng = crate::test::rng(2);
+        for _ in 0..1000 {
+            let r = d.sample(&mut rng);
+            assert!(r >= 1.);
+        }
+        // TODO: verify that this is a zeta distribution
+    }
+
+    #[test]
+    fn zipf_value_stability() {
+        test_samples(Zipf::new(10, 0.5).unwrap(), 0f32, &[
+            10.0, 2.0, 6.0, 7.0
+        ]);
+        test_samples(Zipf::new(10, 2.0).unwrap(), 0f64, &[
+            1.0, 2.0, 3.0, 2.0
+        ]);
+    }
+}