diff options
Diffstat (limited to 'vendor/rand/src/distributions')
| -rw-r--r-- | vendor/rand/src/distributions/exponential.rs | 124 | ||||
| -rw-r--r-- | vendor/rand/src/distributions/gamma.rs | 386 | ||||
| -rw-r--r-- | vendor/rand/src/distributions/mod.rs | 409 | ||||
| -rw-r--r-- | vendor/rand/src/distributions/normal.rs | 201 | ||||
| -rw-r--r-- | vendor/rand/src/distributions/range.rs | 241 | ||||
| -rw-r--r-- | vendor/rand/src/distributions/ziggurat_tables.rs | 280 |
6 files changed, 0 insertions, 1641 deletions
diff --git a/vendor/rand/src/distributions/exponential.rs b/vendor/rand/src/distributions/exponential.rs deleted file mode 100644 index c3c924c..0000000 --- a/vendor/rand/src/distributions/exponential.rs +++ /dev/null @@ -1,124 +0,0 @@ -// Copyright 2013 The Rust Project Developers. See the COPYRIGHT -// file at the top-level directory of this distribution and at -// http://rust-lang.org/COPYRIGHT. -// -// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or -// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license -// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your -// option. This file may not be copied, modified, or distributed -// except according to those terms. - -//! The exponential distribution. - -use {Rng, Rand}; -use distributions::{ziggurat, ziggurat_tables, Sample, IndependentSample}; - -/// A wrapper around an `f64` to generate Exp(1) random numbers. -/// -/// 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*](http://www.doornik.com/research/ziggurat.pdf). Nuffield -/// College, Oxford -/// -/// # Example -/// -/// ```rust -/// use rand::distributions::exponential::Exp1; -/// -/// let Exp1(x) = rand::random(); -/// println!("{}", x); -/// ``` -#[derive(Clone, Copy, Debug)] -pub struct Exp1(pub f64); - -// This could be done via `-rng.gen::<f64>().ln()` but that is slower. -impl Rand for Exp1 { - #[inline] - fn rand<R:Rng>(rng: &mut R) -> Exp1 { - #[inline] - fn pdf(x: f64) -> f64 { - (-x).exp() - } - #[inline] - fn zero_case<R:Rng>(rng: &mut R, _u: f64) -> f64 { - ziggurat_tables::ZIG_EXP_R - rng.gen::<f64>().ln() - } - - Exp1(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`. -/// -/// # Example -/// -/// ```rust -/// use rand::distributions::{Exp, IndependentSample}; -/// -/// let exp = Exp::new(2.0); -/// let v = exp.ind_sample(&mut rand::thread_rng()); -/// println!("{} is from a Exp(2) distribution", v); -/// ``` -#[derive(Clone, Copy, Debug)] -pub struct Exp { - /// `lambda` stored as `1/lambda`, since this is what we scale by. - lambda_inverse: f64 -} - -impl Exp { - /// Construct a new `Exp` with the given shape parameter - /// `lambda`. Panics if `lambda <= 0`. - #[inline] - pub fn new(lambda: f64) -> Exp { - assert!(lambda > 0.0, "Exp::new called with `lambda` <= 0"); - Exp { lambda_inverse: 1.0 / lambda } - } -} - -impl Sample<f64> for Exp { - fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) } -} -impl IndependentSample<f64> for Exp { - fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 { - let Exp1(n) = rng.gen::<Exp1>(); - n * self.lambda_inverse - } -} - -#[cfg(test)] -mod test { - use distributions::{Sample, IndependentSample}; - use super::Exp; - - #[test] - fn test_exp() { - let mut exp = Exp::new(10.0); - let mut rng = ::test::rng(); - for _ in 0..1000 { - assert!(exp.sample(&mut rng) >= 0.0); - assert!(exp.ind_sample(&mut rng) >= 0.0); - } - } - #[test] - #[should_panic] - fn test_exp_invalid_lambda_zero() { - Exp::new(0.0); - } - #[test] - #[should_panic] - fn test_exp_invalid_lambda_neg() { - Exp::new(-10.0); - } -} diff --git a/vendor/rand/src/distributions/gamma.rs b/vendor/rand/src/distributions/gamma.rs deleted file mode 100644 index 2806495..0000000 --- a/vendor/rand/src/distributions/gamma.rs +++ /dev/null @@ -1,386 +0,0 @@ -// Copyright 2013 The Rust Project Developers. See the COPYRIGHT -// file at the top-level directory of this distribution and at -// http://rust-lang.org/COPYRIGHT. -// -// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or -// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license -// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your -// option. This file may not be copied, modified, or distributed -// except according to those terms. -// -// ignore-lexer-test FIXME #15679 - -//! The Gamma and derived distributions. - -use self::GammaRepr::*; -use self::ChiSquaredRepr::*; - -use {Rng, Open01}; -use super::normal::StandardNormal; -use super::{IndependentSample, Sample, Exp}; - -/// 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 [1] for -/// `shape < 1`. -/// -/// # Example -/// -/// ```rust -/// use rand::distributions::{IndependentSample, Gamma}; -/// -/// let gamma = Gamma::new(2.0, 5.0); -/// let v = gamma.ind_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](http://doi.acm.org/10.1145/358407.358414) -#[derive(Clone, Copy, Debug)] -pub struct Gamma { - repr: GammaRepr, -} - -#[derive(Clone, Copy, Debug)] -enum GammaRepr { - Large(GammaLargeShape), - One(Exp), - Small(GammaSmallShape) -} - -// These two helpers could be made public, but saving the -// match-on-Gamma-enum branch from using them directly (e.g. if one -// knows that the shape is always > 1) doesn't appear to be much -// faster. - -/// Gamma distribution where the shape parameter is less than 1. -/// -/// Note, samples from this require a compulsory floating-point `pow` -/// call, which makes it significantly slower than sampling from a -/// gamma distribution where the shape parameter is greater than or -/// equal to 1. -/// -/// See `Gamma` for sampling from a Gamma distribution with general -/// shape parameters. -#[derive(Clone, Copy, Debug)] -struct GammaSmallShape { - inv_shape: f64, - large_shape: GammaLargeShape -} - -/// Gamma distribution where the shape parameter is larger than 1. -/// -/// See `Gamma` for sampling from a Gamma distribution with general -/// shape parameters. -#[derive(Clone, Copy, Debug)] -struct GammaLargeShape { - scale: f64, - c: f64, - d: f64 -} - -impl Gamma { - /// Construct an object representing the `Gamma(shape, scale)` - /// distribution. - /// - /// Panics if `shape <= 0` or `scale <= 0`. - #[inline] - pub fn new(shape: f64, scale: f64) -> Gamma { - assert!(shape > 0.0, "Gamma::new called with shape <= 0"); - assert!(scale > 0.0, "Gamma::new called with scale <= 0"); - - let repr = if shape == 1.0 { - One(Exp::new(1.0 / scale)) - } else if shape < 1.0 { - Small(GammaSmallShape::new_raw(shape, scale)) - } else { - Large(GammaLargeShape::new_raw(shape, scale)) - }; - Gamma { repr: repr } - } -} - -impl GammaSmallShape { - fn new_raw(shape: f64, scale: f64) -> GammaSmallShape { - GammaSmallShape { - inv_shape: 1. / shape, - large_shape: GammaLargeShape::new_raw(shape + 1.0, scale) - } - } -} - -impl GammaLargeShape { - fn new_raw(shape: f64, scale: f64) -> GammaLargeShape { - let d = shape - 1. / 3.; - GammaLargeShape { - scale: scale, - c: 1. / (9. * d).sqrt(), - d: d - } - } -} - -impl Sample<f64> for Gamma { - fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) } -} -impl Sample<f64> for GammaSmallShape { - fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) } -} -impl Sample<f64> for GammaLargeShape { - fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) } -} - -impl IndependentSample<f64> for Gamma { - fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 { - match self.repr { - Small(ref g) => g.ind_sample(rng), - One(ref g) => g.ind_sample(rng), - Large(ref g) => g.ind_sample(rng), - } - } -} -impl IndependentSample<f64> for GammaSmallShape { - fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 { - let Open01(u) = rng.gen::<Open01<f64>>(); - - self.large_shape.ind_sample(rng) * u.powf(self.inv_shape) - } -} -impl IndependentSample<f64> for GammaLargeShape { - fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 { - loop { - let StandardNormal(x) = rng.gen::<StandardNormal>(); - let v_cbrt = 1.0 + self.c * x; - if v_cbrt <= 0.0 { // a^3 <= 0 iff a <= 0 - continue - } - - let v = v_cbrt * v_cbrt * v_cbrt; - let Open01(u) = rng.gen::<Open01<f64>>(); - - let x_sqr = x * x; - if u < 1.0 - 0.0331 * x_sqr * x_sqr || - u.ln() < 0.5 * x_sqr + self.d * (1.0 - v + v.ln()) { - return self.d * v * self.scale - } - } - } -} - -/// The chi-squared distribution `χ²(k)`, where `k` is the degrees of -/// freedom. -/// -/// For `k > 0` integral, this distribution is the sum of the squares -/// of `k` independent standard normal random variables. For other -/// `k`, this uses the equivalent characterisation -/// `χ²(k) = Gamma(k/2, 2)`. -/// -/// # Example -/// -/// ```rust -/// use rand::distributions::{ChiSquared, IndependentSample}; -/// -/// let chi = ChiSquared::new(11.0); -/// let v = chi.ind_sample(&mut rand::thread_rng()); -/// println!("{} is from a χ²(11) distribution", v) -/// ``` -#[derive(Clone, Copy, Debug)] -pub struct ChiSquared { - repr: ChiSquaredRepr, -} - -#[derive(Clone, Copy, Debug)] -enum ChiSquaredRepr { - // k == 1, Gamma(alpha, ..) is particularly slow for alpha < 1, - // e.g. when alpha = 1/2 as it would be for this case, so special- - // casing and using the definition of N(0,1)^2 is faster. - DoFExactlyOne, - DoFAnythingElse(Gamma), -} - -impl ChiSquared { - /// Create a new chi-squared distribution with degrees-of-freedom - /// `k`. Panics if `k < 0`. - pub fn new(k: f64) -> ChiSquared { - let repr = if k == 1.0 { - DoFExactlyOne - } else { - assert!(k > 0.0, "ChiSquared::new called with `k` < 0"); - DoFAnythingElse(Gamma::new(0.5 * k, 2.0)) - }; - ChiSquared { repr: repr } - } -} -impl Sample<f64> for ChiSquared { - fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) } -} -impl IndependentSample<f64> for ChiSquared { - fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 { - match self.repr { - DoFExactlyOne => { - // k == 1 => N(0,1)^2 - let StandardNormal(norm) = rng.gen::<StandardNormal>(); - norm * norm - } - DoFAnythingElse(ref g) => g.ind_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 -/// -/// ```rust -/// use rand::distributions::{FisherF, IndependentSample}; -/// -/// let f = FisherF::new(2.0, 32.0); -/// let v = f.ind_sample(&mut rand::thread_rng()); -/// println!("{} is from an F(2, 32) distribution", v) -/// ``` -#[derive(Clone, Copy, Debug)] -pub struct FisherF { - numer: ChiSquared, - denom: ChiSquared, - // denom_dof / numer_dof so that this can just be a straight - // multiplication, rather than a division. - dof_ratio: f64, -} - -impl FisherF { - /// Create a new `FisherF` distribution, with the given - /// parameter. Panics if either `m` or `n` are not positive. - pub fn new(m: f64, n: f64) -> FisherF { - assert!(m > 0.0, "FisherF::new called with `m < 0`"); - assert!(n > 0.0, "FisherF::new called with `n < 0`"); - - FisherF { - numer: ChiSquared::new(m), - denom: ChiSquared::new(n), - dof_ratio: n / m - } - } -} -impl Sample<f64> for FisherF { - fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) } -} -impl IndependentSample<f64> for FisherF { - fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 { - self.numer.ind_sample(rng) / self.denom.ind_sample(rng) * self.dof_ratio - } -} - -/// The Student t distribution, `t(nu)`, where `nu` is the degrees of -/// freedom. -/// -/// # Example -/// -/// ```rust -/// use rand::distributions::{StudentT, IndependentSample}; -/// -/// let t = StudentT::new(11.0); -/// let v = t.ind_sample(&mut rand::thread_rng()); -/// println!("{} is from a t(11) distribution", v) -/// ``` -#[derive(Clone, Copy, Debug)] -pub struct StudentT { - chi: ChiSquared, - dof: f64 -} - -impl StudentT { - /// Create a new Student t distribution with `n` degrees of - /// freedom. Panics if `n <= 0`. - pub fn new(n: f64) -> StudentT { - assert!(n > 0.0, "StudentT::new called with `n <= 0`"); - StudentT { - chi: ChiSquared::new(n), - dof: n - } - } -} -impl Sample<f64> for StudentT { - fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) } -} -impl IndependentSample<f64> for StudentT { - fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 { - let StandardNormal(norm) = rng.gen::<StandardNormal>(); - norm * (self.dof / self.chi.ind_sample(rng)).sqrt() - } -} - -#[cfg(test)] -mod test { - use distributions::{Sample, IndependentSample}; - use super::{ChiSquared, StudentT, FisherF}; - - #[test] - fn test_chi_squared_one() { - let mut chi = ChiSquared::new(1.0); - let mut rng = ::test::rng(); - for _ in 0..1000 { - chi.sample(&mut rng); - chi.ind_sample(&mut rng); - } - } - #[test] - fn test_chi_squared_small() { - let mut chi = ChiSquared::new(0.5); - let mut rng = ::test::rng(); - for _ in 0..1000 { - chi.sample(&mut rng); - chi.ind_sample(&mut rng); - } - } - #[test] - fn test_chi_squared_large() { - let mut chi = ChiSquared::new(30.0); - let mut rng = ::test::rng(); - for _ in 0..1000 { - chi.sample(&mut rng); - chi.ind_sample(&mut rng); - } - } - #[test] - #[should_panic] - fn test_chi_squared_invalid_dof() { - ChiSquared::new(-1.0); - } - - #[test] - fn test_f() { - let mut f = FisherF::new(2.0, 32.0); - let mut rng = ::test::rng(); - for _ in 0..1000 { - f.sample(&mut rng); - f.ind_sample(&mut rng); - } - } - - #[test] - fn test_t() { - let mut t = StudentT::new(11.0); - let mut rng = ::test::rng(); - for _ in 0..1000 { - t.sample(&mut rng); - t.ind_sample(&mut rng); - } - } -} diff --git a/vendor/rand/src/distributions/mod.rs b/vendor/rand/src/distributions/mod.rs deleted file mode 100644 index 5de8efb..0000000 --- a/vendor/rand/src/distributions/mod.rs +++ /dev/null @@ -1,409 +0,0 @@ -// Copyright 2013 The Rust Project Developers. See the COPYRIGHT -// file at the top-level directory of this distribution and at -// http://rust-lang.org/COPYRIGHT. -// -// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or -// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license -// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your -// option. This file may not be copied, modified, or distributed -// except according to those terms. - -//! Sampling from random distributions. -//! -//! This is a generalization of `Rand` to allow parameters to control the -//! exact properties of the generated values, e.g. the mean and standard -//! deviation of a normal distribution. The `Sample` trait is the most -//! general, and allows for generating values that change some state -//! internally. The `IndependentSample` trait is for generating values -//! that do not need to record state. - -use core::marker; - -use {Rng, Rand}; - -pub use self::range::Range; -#[cfg(feature="std")] -pub use self::gamma::{Gamma, ChiSquared, FisherF, StudentT}; -#[cfg(feature="std")] -pub use self::normal::{Normal, LogNormal}; -#[cfg(feature="std")] -pub use self::exponential::Exp; - -pub mod range; -#[cfg(feature="std")] -pub mod gamma; -#[cfg(feature="std")] -pub mod normal; -#[cfg(feature="std")] -pub mod exponential; - -#[cfg(feature="std")] -mod ziggurat_tables; - -/// Types that can be used to create a random instance of `Support`. -pub trait Sample<Support> { - /// Generate a random value of `Support`, using `rng` as the - /// source of randomness. - fn sample<R: Rng>(&mut self, rng: &mut R) -> Support; -} - -/// `Sample`s that do not require keeping track of state. -/// -/// Since no state is recorded, each sample is (statistically) -/// independent of all others, assuming the `Rng` used has this -/// property. -// FIXME maybe having this separate is overkill (the only reason is to -// take &self rather than &mut self)? or maybe this should be the -// trait called `Sample` and the other should be `DependentSample`. -pub trait IndependentSample<Support>: Sample<Support> { - /// Generate a random value. - fn ind_sample<R: Rng>(&self, &mut R) -> Support; -} - -/// A wrapper for generating types that implement `Rand` via the -/// `Sample` & `IndependentSample` traits. -#[derive(Debug)] -pub struct RandSample<Sup> { - _marker: marker::PhantomData<fn() -> Sup>, -} - -impl<Sup> Copy for RandSample<Sup> {} -impl<Sup> Clone for RandSample<Sup> { - fn clone(&self) -> Self { *self } -} - -impl<Sup: Rand> Sample<Sup> for RandSample<Sup> { - fn sample<R: Rng>(&mut self, rng: &mut R) -> Sup { self.ind_sample(rng) } -} - -impl<Sup: Rand> IndependentSample<Sup> for RandSample<Sup> { - fn ind_sample<R: Rng>(&self, rng: &mut R) -> Sup { - rng.gen() - } -} - -impl<Sup> RandSample<Sup> { - pub fn new() -> RandSample<Sup> { - RandSample { _marker: marker::PhantomData } - } -} - -/// A value with a particular weight for use with `WeightedChoice`. -#[derive(Copy, Clone, Debug)] -pub struct Weighted<T> { - /// The numerical weight of this item - pub weight: u32, - /// The actual item which is being weighted - pub item: T, -} - -/// A distribution that selects from a finite collection of weighted items. -/// -/// Each item has an associated weight that influences how likely it -/// is to be chosen: higher weight is more likely. -/// -/// The `Clone` restriction is a limitation of the `Sample` and -/// `IndependentSample` traits. Note that `&T` is (cheaply) `Clone` for -/// all `T`, as is `u32`, so one can store references or indices into -/// another vector. -/// -/// # Example -/// -/// ```rust -/// use rand::distributions::{Weighted, WeightedChoice, IndependentSample}; -/// -/// let mut items = vec!(Weighted { weight: 2, item: 'a' }, -/// Weighted { weight: 4, item: 'b' }, -/// Weighted { weight: 1, item: 'c' }); -/// let wc = WeightedChoice::new(&mut items); -/// let mut rng = rand::thread_rng(); -/// for _ in 0..16 { -/// // on average prints 'a' 4 times, 'b' 8 and 'c' twice. -/// println!("{}", wc.ind_sample(&mut rng)); -/// } -/// ``` -#[derive(Debug)] -pub struct WeightedChoice<'a, T:'a> { - items: &'a mut [Weighted<T>], - weight_range: Range<u32> -} - -impl<'a, T: Clone> WeightedChoice<'a, T> { - /// Create a new `WeightedChoice`. - /// - /// Panics if: - /// - /// - `items` is empty - /// - the total weight is 0 - /// - the total weight is larger than a `u32` can contain. - pub fn new(items: &'a mut [Weighted<T>]) -> WeightedChoice<'a, T> { - // strictly speaking, this is subsumed by the total weight == 0 case - assert!(!items.is_empty(), "WeightedChoice::new called with no items"); - - let mut running_total: u32 = 0; - - // we convert the list from individual weights to cumulative - // weights so we can binary search. This *could* drop elements - // with weight == 0 as an optimisation. - for item in items.iter_mut() { - running_total = match running_total.checked_add(item.weight) { - Some(n) => n, - None => panic!("WeightedChoice::new called with a total weight \ - larger than a u32 can contain") - }; - - item.weight = running_total; - } - assert!(running_total != 0, "WeightedChoice::new called with a total weight of 0"); - - WeightedChoice { - items: items, - // we're likely to be generating numbers in this range - // relatively often, so might as well cache it - weight_range: Range::new(0, running_total) - } - } -} - -impl<'a, T: Clone> Sample<T> for WeightedChoice<'a, T> { - fn sample<R: Rng>(&mut self, rng: &mut R) -> T { self.ind_sample(rng) } -} - -impl<'a, T: Clone> IndependentSample<T> for WeightedChoice<'a, T> { - fn ind_sample<R: Rng>(&self, rng: &mut R) -> T { - // we want to find the first element that has cumulative - // weight > sample_weight, which we do by binary since the - // cumulative weights of self.items are sorted. - - // choose a weight in [0, total_weight) - let sample_weight = self.weight_range.ind_sample(rng); - - // short circuit when it's the first item - if sample_weight < self.items[0].weight { - return self.items[0].item.clone(); - } - - let mut idx = 0; - let mut modifier = self.items.len(); - - // now we know that every possibility has an element to the - // left, so we can just search for the last element that has - // cumulative weight <= sample_weight, then the next one will - // be "it". (Note that this greatest element will never be the - // last element of the vector, since sample_weight is chosen - // in [0, total_weight) and the cumulative weight of the last - // one is exactly the total weight.) - while modifier > 1 { - let i = idx + modifier / 2; - if self.items[i].weight <= sample_weight { - // we're small, so look to the right, but allow this - // exact element still. - idx = i; - // we need the `/ 2` to round up otherwise we'll drop - // the trailing elements when `modifier` is odd. - modifier += 1; - } else { - // otherwise we're too big, so go left. (i.e. do - // nothing) - } - modifier /= 2; - } - return self.items[idx + 1].item.clone(); - } -} - -/// Sample a random number using the Ziggurat method (specifically the -/// ZIGNOR variant from Doornik 2005). Most of the arguments are -/// directly from the paper: -/// -/// * `rng`: source of randomness -/// * `symmetric`: whether this is a symmetric distribution, or one-sided with P(x < 0) = 0. -/// * `X`: the $x_i$ abscissae. -/// * `F`: precomputed values of the PDF at the $x_i$, (i.e. $f(x_i)$) -/// * `F_DIFF`: precomputed values of $f(x_i) - f(x_{i+1})$ -/// * `pdf`: the probability density function -/// * `zero_case`: manual sampling from the tail when we chose the -/// bottom box (i.e. i == 0) - -// the perf improvement (25-50%) is definitely worth the extra code -// size from force-inlining. -#[cfg(feature="std")] -#[inline(always)] -fn ziggurat<R: Rng, 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 { - const SCALE: f64 = (1u64 << 53) as f64; - loop { - // reimplement the f64 generation as an optimisation suggested - // by the Doornik paper: we have a lot of precision-space - // (i.e. there are 11 bits of the 64 of a u64 to use after - // creating a f64), so we might as well reuse some to save - // generating a whole extra random number. (Seems to be 15% - // faster.) - // - // This unfortunately misses out on the benefits of direct - // floating point generation if an RNG like dSMFT is - // used. (That is, such RNGs create floats directly, highly - // efficiently and overload next_f32/f64, so by not calling it - // this may be slower than it would be otherwise.) - // FIXME: investigate/optimise for the above. - let bits: u64 = rng.gen(); - let i = (bits & 0xff) as usize; - let f = (bits >> 11) as f64 / SCALE; - - // u is either U(-1, 1) or U(0, 1) depending on if this is a - // symmetric distribution or not. - let u = if symmetric {2.0 * f - 1.0} else {f}; - 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; - } - } -} - -#[cfg(test)] -mod tests { - - use {Rng, Rand}; - use super::{RandSample, WeightedChoice, Weighted, Sample, IndependentSample}; - - #[derive(PartialEq, Debug)] - struct ConstRand(usize); - impl Rand for ConstRand { - fn rand<R: Rng>(_: &mut R) -> ConstRand { - ConstRand(0) - } - } - - // 0, 1, 2, 3, ... - struct CountingRng { i: u32 } - impl Rng for CountingRng { - fn next_u32(&mut self) -> u32 { - self.i += 1; - self.i - 1 - } - fn next_u64(&mut self) -> u64 { - self.next_u32() as u64 - } - } - - #[test] - fn test_rand_sample() { - let mut rand_sample = RandSample::<ConstRand>::new(); - - assert_eq!(rand_sample.sample(&mut ::test::rng()), ConstRand(0)); - assert_eq!(rand_sample.ind_sample(&mut ::test::rng()), ConstRand(0)); - } - #[test] - fn test_weighted_choice() { - // this makes assumptions about the internal implementation of - // WeightedChoice, specifically: it doesn't reorder the items, - // it doesn't do weird things to the RNG (so 0 maps to 0, 1 to - // 1, internally; modulo a modulo operation). - - macro_rules! t { - ($items:expr, $expected:expr) => {{ - let mut items = $items; - let wc = WeightedChoice::new(&mut items); - let expected = $expected; - - let mut rng = CountingRng { i: 0 }; - - for &val in expected.iter() { - assert_eq!(wc.ind_sample(&mut rng), val) - } - }} - } - - t!(vec!(Weighted { weight: 1, item: 10}), [10]); - - // skip some - t!(vec!(Weighted { weight: 0, item: 20}, - Weighted { weight: 2, item: 21}, - Weighted { weight: 0, item: 22}, - Weighted { weight: 1, item: 23}), - [21,21, 23]); - - // different weights - t!(vec!(Weighted { weight: 4, item: 30}, - Weighted { weight: 3, item: 31}), - [30,30,30,30, 31,31,31]); - - // check that we're binary searching - // correctly with some vectors of odd - // length. - t!(vec!(Weighted { weight: 1, item: 40}, - Weighted { weight: 1, item: 41}, - Weighted { weight: 1, item: 42}, - Weighted { weight: 1, item: 43}, - Weighted { weight: 1, item: 44}), - [40, 41, 42, 43, 44]); - t!(vec!(Weighted { weight: 1, item: 50}, - Weighted { weight: 1, item: 51}, - Weighted { weight: 1, item: 52}, - Weighted { weight: 1, item: 53}, - Weighted { weight: 1, item: 54}, - Weighted { weight: 1, item: 55}, - Weighted { weight: 1, item: 56}), - [50, 51, 52, 53, 54, 55, 56]); - } - - #[test] - fn test_weighted_clone_initialization() { - let initial : Weighted<u32> = Weighted {weight: 1, item: 1}; - let clone = initial.clone(); - assert_eq!(initial.weight, clone.weight); - assert_eq!(initial.item, clone.item); - } - - #[test] #[should_panic] - fn test_weighted_clone_change_weight() { - let initial : Weighted<u32> = Weighted {weight: 1, item: 1}; - let mut clone = initial.clone(); - clone.weight = 5; - assert_eq!(initial.weight, clone.weight); - } - - #[test] #[should_panic] - fn test_weighted_clone_change_item() { - let initial : Weighted<u32> = Weighted {weight: 1, item: 1}; - let mut clone = initial.clone(); - clone.item = 5; - assert_eq!(initial.item, clone.item); - - } - - #[test] #[should_panic] - fn test_weighted_choice_no_items() { - WeightedChoice::<isize>::new(&mut []); - } - #[test] #[should_panic] - fn test_weighted_choice_zero_weight() { - WeightedChoice::new(&mut [Weighted { weight: 0, item: 0}, - Weighted { weight: 0, item: 1}]); - } - #[test] #[should_panic] - fn test_weighted_choice_weight_overflows() { - let x = ::std::u32::MAX / 2; // x + x + 2 is the overflow - WeightedChoice::new(&mut [Weighted { weight: x, item: 0 }, - Weighted { weight: 1, item: 1 }, - Weighted { weight: x, item: 2 }, - Weighted { weight: 1, item: 3 }]); - } -} diff --git a/vendor/rand/src/distributions/normal.rs b/vendor/rand/src/distributions/normal.rs deleted file mode 100644 index 280613d..0000000 --- a/vendor/rand/src/distributions/normal.rs +++ /dev/null @@ -1,201 +0,0 @@ -// Copyright 2013 The Rust Project Developers. See the COPYRIGHT -// file at the top-level directory of this distribution and at -// http://rust-lang.org/COPYRIGHT. -// -// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or -// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license -// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your -// option. This file may not be copied, modified, or distributed -// except according to those terms. - -//! The normal and derived distributions. - -use {Rng, Rand, Open01}; -use distributions::{ziggurat, ziggurat_tables, Sample, IndependentSample}; - -/// A wrapper around an `f64` to generate N(0, 1) random numbers -/// (a.k.a. a standard normal, or Gaussian). -/// -/// 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*](http://www.doornik.com/research/ziggurat.pdf). Nuffield -/// College, Oxford -/// -/// # Example -/// -/// ```rust -/// use rand::distributions::normal::StandardNormal; -/// -/// let StandardNormal(x) = rand::random(); -/// println!("{}", x); -/// ``` -#[derive(Clone, Copy, Debug)] -pub struct StandardNormal(pub f64); - -impl Rand for StandardNormal { - fn rand<R:Rng>(rng: &mut R) -> StandardNormal { - #[inline] - fn pdf(x: f64) -> f64 { - (-x*x/2.0).exp() - } - #[inline] - fn zero_case<R:Rng>(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 Open01(x_) = rng.gen::<Open01<f64>>(); - let Open01(y_) = rng.gen::<Open01<f64>>(); - - 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 } - } - - StandardNormal(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. -/// -/// # Example -/// -/// ```rust -/// use rand::distributions::{Normal, IndependentSample}; -/// -/// // mean 2, standard deviation 3 -/// let normal = Normal::new(2.0, 3.0); -/// let v = normal.ind_sample(&mut rand::thread_rng()); -/// println!("{} is from a N(2, 9) distribution", v) -/// ``` -#[derive(Clone, Copy, Debug)] -pub struct Normal { - mean: f64, - std_dev: f64, -} - -impl Normal { - /// Construct a new `Normal` distribution with the given mean and - /// standard deviation. - /// - /// # Panics - /// - /// Panics if `std_dev < 0`. - #[inline] - pub fn new(mean: f64, std_dev: f64) -> Normal { - assert!(std_dev >= 0.0, "Normal::new called with `std_dev` < 0"); - Normal { - mean: mean, - std_dev: std_dev - } - } -} -impl Sample<f64> for Normal { - fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) } -} -impl IndependentSample<f64> for Normal { - fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 { - let StandardNormal(n) = rng.gen::<StandardNormal>(); - self.mean + self.std_dev * n - } -} - - -/// The log-normal distribution `ln N(mean, std_dev**2)`. -/// -/// If `X` is log-normal distributed, then `ln(X)` is `N(mean, -/// std_dev**2)` distributed. -/// -/// # Example -/// -/// ```rust -/// use rand::distributions::{LogNormal, IndependentSample}; -/// -/// // mean 2, standard deviation 3 -/// let log_normal = LogNormal::new(2.0, 3.0); -/// let v = log_normal.ind_sample(&mut rand::thread_rng()); -/// println!("{} is from an ln N(2, 9) distribution", v) -/// ``` -#[derive(Clone, Copy, Debug)] -pub struct LogNormal { - norm: Normal -} - -impl LogNormal { - /// Construct a new `LogNormal` distribution with the given mean - /// and standard deviation. - /// - /// # Panics - /// - /// Panics if `std_dev < 0`. - #[inline] - pub fn new(mean: f64, std_dev: f64) -> LogNormal { - assert!(std_dev >= 0.0, "LogNormal::new called with `std_dev` < 0"); - LogNormal { norm: Normal::new(mean, std_dev) } - } -} -impl Sample<f64> for LogNormal { - fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) } -} -impl IndependentSample<f64> for LogNormal { - fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 { - self.norm.ind_sample(rng).exp() - } -} - -#[cfg(test)] -mod tests { - use distributions::{Sample, IndependentSample}; - use super::{Normal, LogNormal}; - - #[test] - fn test_normal() { - let mut norm = Normal::new(10.0, 10.0); - let mut rng = ::test::rng(); - for _ in 0..1000 { - norm.sample(&mut rng); - norm.ind_sample(&mut rng); - } - } - #[test] - #[should_panic] - fn test_normal_invalid_sd() { - Normal::new(10.0, -1.0); - } - - - #[test] - fn test_log_normal() { - let mut lnorm = LogNormal::new(10.0, 10.0); - let mut rng = ::test::rng(); - for _ in 0..1000 { - lnorm.sample(&mut rng); - lnorm.ind_sample(&mut rng); - } - } - #[test] - #[should_panic] - fn test_log_normal_invalid_sd() { - LogNormal::new(10.0, -1.0); - } -} diff --git a/vendor/rand/src/distributions/range.rs b/vendor/rand/src/distributions/range.rs deleted file mode 100644 index 935a00a..0000000 --- a/vendor/rand/src/distributions/range.rs +++ /dev/null @@ -1,241 +0,0 @@ -// Copyright 2013 The Rust Project Developers. See the COPYRIGHT -// file at the top-level directory of this distribution and at -// http://rust-lang.org/COPYRIGHT. -// -// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or -// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license -// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your -// option. This file may not be copied, modified, or distributed -// except according to those terms. - -//! Generating numbers between two others. - -// this is surprisingly complicated to be both generic & correct - -use core::num::Wrapping as w; - -use Rng; -use distributions::{Sample, IndependentSample}; - -/// Sample values uniformly between two bounds. -/// -/// This gives a uniform distribution (assuming the RNG used to sample -/// it is itself uniform & the `SampleRange` implementation for the -/// given type is correct), even for edge cases like `low = 0u8`, -/// `high = 170u8`, for which a naive modulo operation would return -/// numbers less than 85 with double the probability to those greater -/// than 85. -/// -/// Types should attempt to sample in `[low, high)`, i.e., not -/// including `high`, but this may be very difficult. All the -/// primitive integer types satisfy this property, and the float types -/// normally satisfy it, but rounding may mean `high` can occur. -/// -/// # Example -/// -/// ```rust -/// use rand::distributions::{IndependentSample, Range}; -/// -/// fn main() { -/// let between = Range::new(10, 10000); -/// let mut rng = rand::thread_rng(); -/// let mut sum = 0; -/// for _ in 0..1000 { -/// sum += between.ind_sample(&mut rng); -/// } -/// println!("{}", sum); -/// } -/// ``` -#[derive(Clone, Copy, Debug)] -pub struct Range<X> { - low: X, - range: X, - accept_zone: X -} - -impl<X: SampleRange + PartialOrd> Range<X> { - /// Create a new `Range` instance that samples uniformly from - /// `[low, high)`. Panics if `low >= high`. - pub fn new(low: X, high: X) -> Range<X> { - assert!(low < high, "Range::new called with `low >= high`"); - SampleRange::construct_range(low, high) - } -} - -impl<Sup: SampleRange> Sample<Sup> for Range<Sup> { - #[inline] - fn sample<R: Rng>(&mut self, rng: &mut R) -> Sup { self.ind_sample(rng) } -} -impl<Sup: SampleRange> IndependentSample<Sup> for Range<Sup> { - fn ind_sample<R: Rng>(&self, rng: &mut R) -> Sup { - SampleRange::sample_range(self, rng) - } -} - -/// The helper trait for types that have a sensible way to sample -/// uniformly between two values. This should not be used directly, -/// and is only to facilitate `Range`. -pub trait SampleRange : Sized { - /// Construct the `Range` object that `sample_range` - /// requires. This should not ever be called directly, only via - /// `Range::new`, which will check that `low < high`, so this - /// function doesn't have to repeat the check. - fn construct_range(low: Self, high: Self) -> Range<Self>; - - /// Sample a value from the given `Range` with the given `Rng` as - /// a source of randomness. - fn sample_range<R: Rng>(r: &Range<Self>, rng: &mut R) -> Self; -} - -macro_rules! integer_impl { - ($ty:ty, $unsigned:ident) => { - impl SampleRange for $ty { - // we play free and fast with unsigned vs signed here - // (when $ty is signed), but that's fine, since the - // contract of this macro is for $ty and $unsigned to be - // "bit-equal", so casting between them is a no-op & a - // bijection. - - #[inline] - fn construct_range(low: $ty, high: $ty) -> Range<$ty> { - let range = (w(high as $unsigned) - w(low as $unsigned)).0; - let unsigned_max: $unsigned = ::core::$unsigned::MAX; - - // this is the largest number that fits into $unsigned - // that `range` divides evenly, so, if we've sampled - // `n` uniformly from this region, then `n % range` is - // uniform in [0, range) - let zone = unsigned_max - unsigned_max % range; - - Range { - low: low, - range: range as $ty, - accept_zone: zone as $ty - } - } - - #[inline] - fn sample_range<R: Rng>(r: &Range<$ty>, rng: &mut R) -> $ty { - loop { - // rejection sample - let v = rng.gen::<$unsigned>(); - // until we find something that fits into the - // region which r.range evenly divides (this will - // be uniformly distributed) - if v < r.accept_zone as $unsigned { - // and return it, with some adjustments - return (w(r.low) + w((v % r.range as $unsigned) as $ty)).0; - } - } - } - } - } -} - -integer_impl! { i8, u8 } -integer_impl! { i16, u16 } -integer_impl! { i32, u32 } -integer_impl! { i64, u64 } -#[cfg(feature = "i128_support")] -integer_impl! { i128, u128 } -integer_impl! { isize, usize } -integer_impl! { u8, u8 } -integer_impl! { u16, u16 } -integer_impl! { u32, u32 } -integer_impl! { u64, u64 } -#[cfg(feature = "i128_support")] -integer_impl! { u128, u128 } -integer_impl! { usize, usize } - -macro_rules! float_impl { - ($ty:ty) => { - impl SampleRange for $ty { - fn construct_range(low: $ty, high: $ty) -> Range<$ty> { - Range { - low: low, - range: high - low, - accept_zone: 0.0 // unused - } - } - fn sample_range<R: Rng>(r: &Range<$ty>, rng: &mut R) -> $ty { - r.low + r.range * rng.gen::<$ty>() - } - } - } -} - -float_impl! { f32 } -float_impl! { f64 } - -#[cfg(test)] -mod tests { - use distributions::{Sample, IndependentSample}; - use super::Range as Range; - - #[should_panic] - #[test] - fn test_range_bad_limits_equal() { - Range::new(10, 10); - } - #[should_panic] - #[test] - fn test_range_bad_limits_flipped() { - Range::new(10, 5); - } - - #[test] - fn test_integers() { - let mut rng = ::test::rng(); - macro_rules! t { - ($($ty:ident),*) => {{ - $( - let v: &[($ty, $ty)] = &[(0, 10), - (10, 127), - (::core::$ty::MIN, ::core::$ty::MAX)]; - for &(low, high) in v.iter() { - let mut sampler: Range<$ty> = Range::new(low, high); - for _ in 0..1000 { - let v = sampler.sample(&mut rng); - assert!(low <= v && v < high); - let v = sampler.ind_sample(&mut rng); - assert!(low <= v && v < high); - } - } - )* - }} - } - #[cfg(not(feature = "i128_support"))] - t!(i8, i16, i32, i64, isize, - u8, u16, u32, u64, usize); - #[cfg(feature = "i128_support")] - t!(i8, i16, i32, i64, i128, isize, - u8, u16, u32, u64, u128, usize); - } - - #[test] - fn test_floats() { - let mut rng = ::test::rng(); - macro_rules! t { - ($($ty:ty),*) => {{ - $( - let v: &[($ty, $ty)] = &[(0.0, 100.0), - (-1e35, -1e25), - (1e-35, 1e-25), - (-1e35, 1e35)]; - for &(low, high) in v.iter() { - let mut sampler: Range<$ty> = Range::new(low, high); - for _ in 0..1000 { - let v = sampler.sample(&mut rng); - assert!(low <= v && v < high); - let v = sampler.ind_sample(&mut rng); - assert!(low <= v && v < high); - } - } - )* - }} - } - - t!(f32, f64) - } - -} diff --git a/vendor/rand/src/distributions/ziggurat_tables.rs b/vendor/rand/src/distributions/ziggurat_tables.rs deleted file mode 100644 index b6de4bf..0000000 --- a/vendor/rand/src/distributions/ziggurat_tables.rs +++ /dev/null @@ -1,280 +0,0 @@ -// Copyright 2013 The Rust Project Developers. See the COPYRIGHT -// file at the top-level directory of this distribution and at -// http://rust-lang.org/COPYRIGHT. -// -// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or -// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license -// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your -// option. This file may not be copied, modified, or distributed -// except according to those terms. - -// Tables for distributions which are sampled using the ziggurat -// algorithm. Autogenerated by `ziggurat_tables.py`. - -pub type ZigTable = &'static [f64; 257]; -pub const ZIG_NORM_R: f64 = 3.654152885361008796; -pub static ZIG_NORM_X: [f64; 257] = - [3.910757959537090045, 3.654152885361008796, 3.449278298560964462, 3.320244733839166074, - 3.224575052047029100, 3.147889289517149969, 3.083526132001233044, 3.027837791768635434, - 2.978603279880844834, 2.934366867207854224, 2.894121053612348060, 2.857138730872132548, - 2.822877396825325125, 2.790921174000785765, 2.760944005278822555, 2.732685359042827056, - 2.705933656121858100, 2.680514643284522158, 2.656283037575502437, 2.633116393630324570, - 2.610910518487548515, 2.589575986706995181, 2.569035452680536569, 2.549221550323460761, - 2.530075232158516929, 2.511544441625342294, 2.493583041269680667, 2.476149939669143318, - 2.459208374333311298, 2.442725318198956774, 2.426670984935725972, 2.411018413899685520, - 2.395743119780480601, 2.380822795170626005, 2.366237056715818632, 2.351967227377659952, - 2.337996148795031370, 2.324308018869623016, 2.310888250599850036, 2.297723348901329565, - 2.284800802722946056, 2.272108990226823888, 2.259637095172217780, 2.247375032945807760, - 2.235313384928327984, 2.223443340090905718, 2.211756642882544366, 2.200245546609647995, - 2.188902771624720689, 2.177721467738641614, 2.166695180352645966, 2.155817819875063268, - 2.145083634046203613, 2.134487182844320152, 2.124023315687815661, 2.113687150684933957, - 2.103474055713146829, 2.093379631137050279, 2.083399693996551783, 2.073530263516978778, - 2.063767547809956415, 2.054107931648864849, 2.044547965215732788, 2.035084353727808715, - 2.025713947862032960, 2.016433734904371722, 2.007240830558684852, 1.998132471356564244, - 1.989106007615571325, 1.980158896898598364, 1.971288697931769640, 1.962493064942461896, - 1.953769742382734043, 1.945116560006753925, 1.936531428273758904, 1.928012334050718257, - 1.919557336591228847, 1.911164563769282232, 1.902832208548446369, 1.894558525668710081, - 1.886341828534776388, 1.878180486290977669, 1.870072921069236838, 1.862017605397632281, - 1.854013059758148119, 1.846057850283119750, 1.838150586580728607, 1.830289919680666566, - 1.822474540091783224, 1.814703175964167636, 1.806974591348693426, 1.799287584547580199, - 1.791640986550010028, 1.784033659547276329, 1.776464495522344977, 1.768932414909077933, - 1.761436365316706665, 1.753975320315455111, 1.746548278279492994, 1.739154261283669012, - 1.731792314050707216, 1.724461502945775715, 1.717160915015540690, 1.709889657069006086, - 1.702646854797613907, 1.695431651932238548, 1.688243209434858727, 1.681080704722823338, - 1.673943330923760353, 1.666830296159286684, 1.659740822855789499, 1.652674147080648526, - 1.645629517902360339, 1.638606196773111146, 1.631603456932422036, 1.624620582830568427, - 1.617656869570534228, 1.610711622367333673, 1.603784156023583041, 1.596873794420261339, - 1.589979870021648534, 1.583101723393471438, 1.576238702733332886, 1.569390163412534456, - 1.562555467528439657, 1.555733983466554893, 1.548925085471535512, 1.542128153226347553, - 1.535342571438843118, 1.528567729435024614, 1.521803020758293101, 1.515047842773992404, - 1.508301596278571965, 1.501563685112706548, 1.494833515777718391, 1.488110497054654369, - 1.481394039625375747, 1.474683555695025516, 1.467978458615230908, 1.461278162507407830, - 1.454582081885523293, 1.447889631277669675, 1.441200224845798017, 1.434513276002946425, - 1.427828197027290358, 1.421144398672323117, 1.414461289772464658, 1.407778276843371534, - 1.401094763676202559, 1.394410150925071257, 1.387723835686884621, 1.381035211072741964, - 1.374343665770030531, 1.367648583594317957, 1.360949343030101844, 1.354245316759430606, - 1.347535871177359290, 1.340820365893152122, 1.334098153216083604, 1.327368577624624679, - 1.320630975217730096, 1.313884673146868964, 1.307128989027353860, 1.300363230327433728, - 1.293586693733517645, 1.286798664489786415, 1.279998415710333237, 1.273185207661843732, - 1.266358287014688333, 1.259516886060144225, 1.252660221891297887, 1.245787495544997903, - 1.238897891102027415, 1.231990574742445110, 1.225064693752808020, 1.218119375481726552, - 1.211153726239911244, 1.204166830140560140, 1.197157747875585931, 1.190125515422801650, - 1.183069142678760732, 1.175987612011489825, 1.168879876726833800, 1.161744859441574240, - 1.154581450355851802, 1.147388505416733873, 1.140164844363995789, 1.132909248648336975, - 1.125620459211294389, 1.118297174115062909, 1.110938046009249502, 1.103541679420268151, - 1.096106627847603487, 1.088631390649514197, 1.081114409698889389, 1.073554065787871714, - 1.065948674757506653, 1.058296483326006454, 1.050595664586207123, 1.042844313139370538, - 1.035040439828605274, 1.027181966030751292, 1.019266717460529215, 1.011292417434978441, - 1.003256679539591412, 0.995156999629943084, 0.986990747093846266, 0.978755155288937750, - 0.970447311058864615, 0.962064143217605250, 0.953602409875572654, 0.945058684462571130, - 0.936429340280896860, 0.927710533396234771, 0.918898183643734989, 0.909987953490768997, - 0.900975224455174528, 0.891855070726792376, 0.882622229578910122, 0.873271068082494550, - 0.863795545546826915, 0.854189171001560554, 0.844444954902423661, 0.834555354079518752, - 0.824512208745288633, 0.814306670128064347, 0.803929116982664893, 0.793369058833152785, - 0.782615023299588763, 0.771654424216739354, 0.760473406422083165, 0.749056662009581653, - 0.737387211425838629, 0.725446140901303549, 0.713212285182022732, 0.700661841097584448, - 0.687767892786257717, 0.674499822827436479, 0.660822574234205984, 0.646695714884388928, - 0.632072236375024632, 0.616896989996235545, 0.601104617743940417, 0.584616766093722262, - 0.567338257040473026, 0.549151702313026790, 0.529909720646495108, 0.509423329585933393, - 0.487443966121754335, 0.463634336771763245, 0.437518402186662658, 0.408389134588000746, - 0.375121332850465727, 0.335737519180459465, 0.286174591747260509, 0.215241895913273806, - 0.000000000000000000]; -pub static ZIG_NORM_F: [f64; 257] = - [0.000477467764586655, 0.001260285930498598, 0.002609072746106363, 0.004037972593371872, - 0.005522403299264754, 0.007050875471392110, 0.008616582769422917, 0.010214971439731100, - 0.011842757857943104, 0.013497450601780807, 0.015177088307982072, 0.016880083152595839, - 0.018605121275783350, 0.020351096230109354, 0.022117062707379922, 0.023902203305873237, - 0.025705804008632656, 0.027527235669693315, 0.029365939758230111, 0.031221417192023690, - 0.033093219458688698, 0.034980941461833073, 0.036884215688691151, 0.038802707404656918, - 0.040736110656078753, 0.042684144916619378, 0.044646552251446536, 0.046623094902089664, - 0.048613553216035145, 0.050617723861121788, 0.052635418276973649, 0.054666461325077916, - 0.056710690106399467, 0.058767952921137984, 0.060838108349751806, 0.062921024437977854, - 0.065016577971470438, 0.067124653828023989, 0.069245144397250269, 0.071377949059141965, - 0.073522973714240991, 0.075680130359194964, 0.077849336702372207, 0.080030515814947509, - 0.082223595813495684, 0.084428509570654661, 0.086645194450867782, 0.088873592068594229, - 0.091113648066700734, 0.093365311913026619, 0.095628536713353335, 0.097903279039215627, - 0.100189498769172020, 0.102487158942306270, 0.104796225622867056, 0.107116667775072880, - 0.109448457147210021, 0.111791568164245583, 0.114145977828255210, 0.116511665626037014, - 0.118888613443345698, 0.121276805485235437, 0.123676228202051403, 0.126086870220650349, - 0.128508722280473636, 0.130941777174128166, 0.133386029692162844, 0.135841476571757352, - 0.138308116449064322, 0.140785949814968309, 0.143274978974047118, 0.145775208006537926, - 0.148286642733128721, 0.150809290682410169, 0.153343161060837674, 0.155888264725064563, - 0.158444614156520225, 0.161012223438117663, 0.163591108232982951, 0.166181285765110071, - 0.168782774801850333, 0.171395595638155623, 0.174019770082499359, 0.176655321444406654, - 0.179302274523530397, 0.181960655600216487, 0.184630492427504539, 0.187311814224516926, - 0.190004651671193070, 0.192709036904328807, 0.195425003514885592, 0.198152586546538112, - 0.200891822495431333, 0.203642749311121501, 0.206405406398679298, 0.209179834621935651, - 0.211966076307852941, 0.214764175252008499, 0.217574176725178370, 0.220396127481011589, - 0.223230075764789593, 0.226076071323264877, 0.228934165415577484, 0.231804410825248525, - 0.234686861873252689, 0.237581574432173676, 0.240488605941449107, 0.243408015423711988, - 0.246339863502238771, 0.249284212419516704, 0.252241126056943765, 0.255210669955677150, - 0.258192911338648023, 0.261187919133763713, 0.264195763998317568, 0.267216518344631837, - 0.270250256366959984, 0.273297054069675804, 0.276356989296781264, 0.279430141762765316, - 0.282516593084849388, 0.285616426816658109, 0.288729728483353931, 0.291856585618280984, - 0.294997087801162572, 0.298151326697901342, 0.301319396102034120, 0.304501391977896274, - 0.307697412505553769, 0.310907558127563710, 0.314131931597630143, 0.317370638031222396, - 0.320623784958230129, 0.323891482377732021, 0.327173842814958593, 0.330470981380537099, - 0.333783015832108509, 0.337110066638412809, 0.340452257045945450, 0.343809713148291340, - 0.347182563958251478, 0.350570941482881204, 0.353974980801569250, 0.357394820147290515, - 0.360830600991175754, 0.364282468130549597, 0.367750569780596226, 0.371235057669821344, - 0.374736087139491414, 0.378253817247238111, 0.381788410875031348, 0.385340034841733958, - 0.388908860020464597, 0.392495061461010764, 0.396098818517547080, 0.399720314981931668, - 0.403359739222868885, 0.407017284331247953, 0.410693148271983222, 0.414387534042706784, - 0.418100649839684591, 0.421832709231353298, 0.425583931339900579, 0.429354541031341519, - 0.433144769114574058, 0.436954852549929273, 0.440785034667769915, 0.444635565397727750, - 0.448506701509214067, 0.452398706863882505, 0.456311852680773566, 0.460246417814923481, - 0.464202689050278838, 0.468180961407822172, 0.472181538469883255, 0.476204732721683788, - 0.480250865911249714, 0.484320269428911598, 0.488413284707712059, 0.492530263646148658, - 0.496671569054796314, 0.500837575128482149, 0.505028667945828791, 0.509245245998136142, - 0.513487720749743026, 0.517756517232200619, 0.522052074674794864, 0.526374847174186700, - 0.530725304406193921, 0.535103932383019565, 0.539511234259544614, 0.543947731192649941, - 0.548413963257921133, 0.552910490428519918, 0.557437893621486324, 0.561996775817277916, - 0.566587763258951771, 0.571211506738074970, 0.575868682975210544, 0.580559996103683473, - 0.585286179266300333, 0.590047996335791969, 0.594846243770991268, 0.599681752622167719, - 0.604555390700549533, 0.609468064928895381, 0.614420723892076803, 0.619414360609039205, - 0.624450015550274240, 0.629528779928128279, 0.634651799290960050, 0.639820277456438991, - 0.645035480824251883, 0.650298743114294586, 0.655611470583224665, 0.660975147780241357, - 0.666391343912380640, 0.671861719900766374, 0.677388036222513090, 0.682972161648791376, - 0.688616083008527058, 0.694321916130032579, 0.700091918140490099, 0.705928501336797409, - 0.711834248882358467, 0.717811932634901395, 0.723864533472881599, 0.729995264565802437, - 0.736207598131266683, 0.742505296344636245, 0.748892447223726720, 0.755373506511754500, - 0.761953346841546475, 0.768637315803334831, 0.775431304986138326, 0.782341832659861902, - 0.789376143571198563, 0.796542330428254619, 0.803849483176389490, 0.811307874318219935, - 0.818929191609414797, 0.826726833952094231, 0.834716292992930375, 0.842915653118441077, - 0.851346258465123684, 0.860033621203008636, 0.869008688043793165, 0.878309655816146839, - 0.887984660763399880, 0.898095921906304051, 0.908726440060562912, 0.919991505048360247, - 0.932060075968990209, 0.945198953453078028, 0.959879091812415930, 0.977101701282731328, - 1.000000000000000000]; -pub const ZIG_EXP_R: f64 = 7.697117470131050077; -pub static ZIG_EXP_X: [f64; 257] = - [8.697117470131052741, 7.697117470131050077, 6.941033629377212577, 6.478378493832569696, - 6.144164665772472667, 5.882144315795399869, 5.666410167454033697, 5.482890627526062488, - 5.323090505754398016, 5.181487281301500047, 5.054288489981304089, 4.938777085901250530, - 4.832939741025112035, 4.735242996601741083, 4.644491885420085175, 4.559737061707351380, - 4.480211746528421912, 4.405287693473573185, 4.334443680317273007, 4.267242480277365857, - 4.203313713735184365, 4.142340865664051464, 4.084051310408297830, 4.028208544647936762, - 3.974606066673788796, 3.923062500135489739, 3.873417670399509127, 3.825529418522336744, - 3.779270992411667862, 3.734528894039797375, 3.691201090237418825, 3.649195515760853770, - 3.608428813128909507, 3.568825265648337020, 3.530315889129343354, 3.492837654774059608, - 3.456332821132760191, 3.420748357251119920, 3.386035442460300970, 3.352149030900109405, - 3.319047470970748037, 3.286692171599068679, 3.255047308570449882, 3.224079565286264160, - 3.193757903212240290, 3.164053358025972873, 3.134938858084440394, 3.106389062339824481, - 3.078380215254090224, 3.050890016615455114, 3.023897504455676621, 2.997382949516130601, - 2.971327759921089662, 2.945714394895045718, 2.920526286512740821, 2.895747768600141825, - 2.871364012015536371, 2.847360965635188812, 2.823725302450035279, 2.800444370250737780, - 2.777506146439756574, 2.754899196562344610, 2.732612636194700073, 2.710636095867928752, - 2.688959688741803689, 2.667573980773266573, 2.646469963151809157, 2.625639026797788489, - 2.605072938740835564, 2.584763820214140750, 2.564704126316905253, 2.544886627111869970, - 2.525304390037828028, 2.505950763528594027, 2.486819361740209455, 2.467904050297364815, - 2.449198932978249754, 2.430698339264419694, 2.412396812688870629, 2.394289099921457886, - 2.376370140536140596, 2.358635057409337321, 2.341079147703034380, 2.323697874390196372, - 2.306486858283579799, 2.289441870532269441, 2.272558825553154804, 2.255833774367219213, - 2.239262898312909034, 2.222842503111036816, 2.206569013257663858, 2.190438966723220027, - 2.174449009937774679, 2.158595893043885994, 2.142876465399842001, 2.127287671317368289, - 2.111826546019042183, 2.096490211801715020, 2.081275874393225145, 2.066180819490575526, - 2.051202409468584786, 2.036338080248769611, 2.021585338318926173, 2.006941757894518563, - 1.992404978213576650, 1.977972700957360441, 1.963642687789548313, 1.949412758007184943, - 1.935280786297051359, 1.921244700591528076, 1.907302480018387536, 1.893452152939308242, - 1.879691795072211180, 1.866019527692827973, 1.852433515911175554, 1.838931967018879954, - 1.825513128903519799, 1.812175288526390649, 1.798916770460290859, 1.785735935484126014, - 1.772631179231305643, 1.759600930889074766, 1.746643651946074405, 1.733757834985571566, - 1.720942002521935299, 1.708194705878057773, 1.695514524101537912, 1.682900062917553896, - 1.670349953716452118, 1.657862852574172763, 1.645437439303723659, 1.633072416535991334, - 1.620766508828257901, 1.608518461798858379, 1.596327041286483395, 1.584191032532688892, - 1.572109239386229707, 1.560080483527888084, 1.548103603714513499, 1.536177455041032092, - 1.524300908219226258, 1.512472848872117082, 1.500692176842816750, 1.488957805516746058, - 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