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-// Copyright 2018 Developers of the Rand project.
-// Copyright 2013-2017 The Rust Project Developers.
-//
-// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
-// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
-// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
-// option. This file may not be copied, modified, or distributed
-// except according to those terms.
-
-//! Generating random samples from probability distributions
-//!
-//! This module is the home of the [`Distribution`] trait and several of its
-//! implementations. It is the workhorse behind some of the convenient
-//! functionality of the [`Rng`] trait, e.g. [`Rng::gen`], [`Rng::gen_range`] and
-//! of course [`Rng::sample`].
-//!
-//! Abstractly, a [probability distribution] describes the probability of
-//! occurance of each value in its sample space.
-//!
-//! More concretely, an implementation of `Distribution<T>` for type `X` is an
-//! algorithm for choosing values from the sample space (a subset of `T`)
-//! according to the distribution `X` represents, using an external source of
-//! randomness (an RNG supplied to the `sample` function).
-//!
-//! A type `X` may implement `Distribution<T>` for multiple types `T`.
-//! Any type implementing [`Distribution`] is stateless (i.e. immutable),
-//! but it may have internal parameters set at construction time (for example,
-//! [`Uniform`] allows specification of its sample space as a range within `T`).
-//!
-//!
-//! # The `Standard` distribution
-//!
-//! The [`Standard`] distribution is important to mention. This is the
-//! distribution used by [`Rng::gen()`] and represents the "default" way to
-//! produce a random value for many different types, including most primitive
-//! types, tuples, arrays, and a few derived types. See the documentation of
-//! [`Standard`] for more details.
-//!
-//! Implementing `Distribution<T>` for [`Standard`] for user types `T` makes it
-//! possible to generate type `T` with [`Rng::gen()`], and by extension also
-//! with the [`random()`] function.
-//!
-//! ## Random characters
-//!
-//! [`Alphanumeric`] is a simple distribution to sample random letters and
-//! numbers of the `char` type; in contrast [`Standard`] may sample any valid
-//! `char`.
-//!
-//!
-//! # Uniform numeric ranges
-//!
-//! The [`Uniform`] distribution is more flexible than [`Standard`], but also
-//! more specialised: it supports fewer target types, but allows the sample
-//! space to be specified as an arbitrary range within its target type `T`.
-//! Both [`Standard`] and [`Uniform`] are in some sense uniform distributions.
-//!
-//! Values may be sampled from this distribution using [`Rng::gen_range`] or
-//! by creating a distribution object with [`Uniform::new`],
-//! [`Uniform::new_inclusive`] or `From<Range>`. When the range limits are not
-//! known at compile time it is typically faster to reuse an existing
-//! distribution object than to call [`Rng::gen_range`].
-//!
-//! User types `T` may also implement `Distribution<T>` for [`Uniform`],
-//! although this is less straightforward than for [`Standard`] (see the
-//! documentation in the [`uniform`] module. Doing so enables generation of
-//! values of type `T` with [`Rng::gen_range`].
-//!
-//! ## Open and half-open ranges
-//!
-//! There are surprisingly many ways to uniformly generate random floats. A
-//! range between 0 and 1 is standard, but the exact bounds (open vs closed)
-//! and accuracy differ. In addition to the [`Standard`] distribution Rand offers
-//! [`Open01`] and [`OpenClosed01`]. See "Floating point implementation" section of
-//! [`Standard`] documentation for more details.
-//!
-//! # Non-uniform sampling
-//!
-//! Sampling a simple true/false outcome with a given probability has a name:
-//! the [`Bernoulli`] distribution (this is used by [`Rng::gen_bool`]).
-//!
-//! For weighted sampling from a sequence of discrete values, use the
-//! [`weighted`] module.
-//!
-//! This crate no longer includes other non-uniform distributions; instead
-//! it is recommended that you use either [`rand_distr`] or [`statrs`].
-//!
-//!
-//! [probability distribution]: https://en.wikipedia.org/wiki/Probability_distribution
-//! [`rand_distr`]: https://crates.io/crates/rand_distr
-//! [`statrs`]: https://crates.io/crates/statrs
-
-//! [`Alphanumeric`]: distributions::Alphanumeric
-//! [`Bernoulli`]: distributions::Bernoulli
-//! [`Open01`]: distributions::Open01
-//! [`OpenClosed01`]: distributions::OpenClosed01
-//! [`Standard`]: distributions::Standard
-//! [`Uniform`]: distributions::Uniform
-//! [`Uniform::new`]: distributions::Uniform::new
-//! [`Uniform::new_inclusive`]: distributions::Uniform::new_inclusive
-//! [`weighted`]: distributions::weighted
-//! [`rand_distr`]: https://crates.io/crates/rand_distr
-//! [`statrs`]: https://crates.io/crates/statrs
-
-use core::iter;
-use crate::Rng;
-
-pub use self::other::Alphanumeric;
-#[doc(inline)] pub use self::uniform::Uniform;
-pub use self::float::{OpenClosed01, Open01};
-pub use self::bernoulli::{Bernoulli, BernoulliError};
-#[cfg(feature="alloc")] pub use self::weighted::{WeightedIndex, WeightedError};
-
-// The following are all deprecated after being moved to rand_distr
-#[allow(deprecated)]
-#[cfg(feature="std")] pub use self::unit_sphere::UnitSphereSurface;
-#[allow(deprecated)]
-#[cfg(feature="std")] pub use self::unit_circle::UnitCircle;
-#[allow(deprecated)]
-#[cfg(feature="std")] pub use self::gamma::{Gamma, ChiSquared, FisherF,
- StudentT, Beta};
-#[allow(deprecated)]
-#[cfg(feature="std")] pub use self::normal::{Normal, LogNormal, StandardNormal};
-#[allow(deprecated)]
-#[cfg(feature="std")] pub use self::exponential::{Exp, Exp1};
-#[allow(deprecated)]
-#[cfg(feature="std")] pub use self::pareto::Pareto;
-#[allow(deprecated)]
-#[cfg(feature="std")] pub use self::poisson::Poisson;
-#[allow(deprecated)]
-#[cfg(feature="std")] pub use self::binomial::Binomial;
-#[allow(deprecated)]
-#[cfg(feature="std")] pub use self::cauchy::Cauchy;
-#[allow(deprecated)]
-#[cfg(feature="std")] pub use self::dirichlet::Dirichlet;
-#[allow(deprecated)]
-#[cfg(feature="std")] pub use self::triangular::Triangular;
-#[allow(deprecated)]
-#[cfg(feature="std")] pub use self::weibull::Weibull;
-
-pub mod uniform;
-mod bernoulli;
-#[cfg(feature="alloc")] pub mod weighted;
-#[cfg(feature="std")] mod unit_sphere;
-#[cfg(feature="std")] mod unit_circle;
-#[cfg(feature="std")] mod gamma;
-#[cfg(feature="std")] mod normal;
-#[cfg(feature="std")] mod exponential;
-#[cfg(feature="std")] mod pareto;
-#[cfg(feature="std")] mod poisson;
-#[cfg(feature="std")] mod binomial;
-#[cfg(feature="std")] mod cauchy;
-#[cfg(feature="std")] mod dirichlet;
-#[cfg(feature="std")] mod triangular;
-#[cfg(feature="std")] mod weibull;
-
-mod float;
-#[doc(hidden)] pub mod hidden_export {
- pub use super::float::IntoFloat; // used by rand_distr
-}
-mod integer;
-mod other;
-mod utils;
-#[cfg(feature="std")] mod ziggurat_tables;
-
-/// Types (distributions) that can be used to create a random instance of `T`.
-///
-/// It is possible to sample from a distribution through both the
-/// `Distribution` and [`Rng`] traits, via `distr.sample(&mut rng)` and
-/// `rng.sample(distr)`. They also both offer the [`sample_iter`] method, which
-/// produces an iterator that samples from the distribution.
-///
-/// All implementations are expected to be immutable; this has the significant
-/// advantage of not needing to consider thread safety, and for most
-/// distributions efficient state-less sampling algorithms are available.
-///
-/// [`sample_iter`]: Distribution::method.sample_iter
-pub trait Distribution<T> {
- /// Generate a random value of `T`, using `rng` as the source of randomness.
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> T;
-
- /// Create an iterator that generates random values of `T`, using `rng` as
- /// the source of randomness.
- ///
- /// Note that this function takes `self` by value. This works since
- /// `Distribution<T>` is impl'd for `&D` where `D: Distribution<T>`,
- /// however borrowing is not automatic hence `distr.sample_iter(...)` may
- /// need to be replaced with `(&distr).sample_iter(...)` to borrow or
- /// `(&*distr).sample_iter(...)` to reborrow an existing reference.
- ///
- /// # Example
- ///
- /// ```
- /// use rand::thread_rng;
- /// use rand::distributions::{Distribution, Alphanumeric, Uniform, Standard};
- ///
- /// let rng = thread_rng();
- ///
- /// // Vec of 16 x f32:
- /// let v: Vec<f32> = Standard.sample_iter(rng).take(16).collect();
- ///
- /// // String:
- /// let s: String = Alphanumeric.sample_iter(rng).take(7).collect();
- ///
- /// // Dice-rolling:
- /// let die_range = Uniform::new_inclusive(1, 6);
- /// let mut roll_die = die_range.sample_iter(rng);
- /// while roll_die.next().unwrap() != 6 {
- /// println!("Not a 6; rolling again!");
- /// }
- /// ```
- fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>
- where R: Rng, Self: Sized
- {
- DistIter {
- distr: self,
- rng,
- phantom: ::core::marker::PhantomData,
- }
- }
-}
-
-impl<'a, T, D: Distribution<T>> Distribution<T> for &'a D {
- fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> T {
- (*self).sample(rng)
- }
-}
-
-
-/// An iterator that generates random values of `T` with distribution `D`,
-/// using `R` as the source of randomness.
-///
-/// This `struct` is created by the [`sample_iter`] method on [`Distribution`].
-/// See its documentation for more.
-///
-/// [`sample_iter`]: Distribution::sample_iter
-#[derive(Debug)]
-pub struct DistIter<D, R, T> {
- distr: D,
- rng: R,
- phantom: ::core::marker::PhantomData<T>,
-}
-
-impl<D, R, T> Iterator for DistIter<D, R, T>
- where D: Distribution<T>, R: Rng
-{
- type Item = T;
-
- #[inline(always)]
- fn next(&mut self) -> Option<T> {
- // Here, self.rng may be a reference, but we must take &mut anyway.
- // Even if sample could take an R: Rng by value, we would need to do this
- // since Rng is not copyable and we cannot enforce that this is "reborrowable".
- Some(self.distr.sample(&mut self.rng))
- }
-
- fn size_hint(&self) -> (usize, Option<usize>) {
- (usize::max_value(), None)
- }
-}
-
-impl<D, R, T> iter::FusedIterator for DistIter<D, R, T>
- where D: Distribution<T>, R: Rng {}
-
-#[cfg(features = "nightly")]
-impl<D, R, T> iter::TrustedLen for DistIter<D, R, T>
- where D: Distribution<T>, R: Rng {}
-
-
-/// A generic random value distribution, implemented for many primitive types.
-/// Usually generates values with a numerically uniform distribution, and with a
-/// range appropriate to the type.
-///
-/// ## Provided implementations
-///
-/// Assuming the provided `Rng` is well-behaved, these implementations
-/// generate values with the following ranges and distributions:
-///
-/// * Integers (`i32`, `u32`, `isize`, `usize`, etc.): Uniformly distributed
-/// over all values of the type.
-/// * `char`: Uniformly distributed over all Unicode scalar values, i.e. all
-/// code points in the range `0...0x10_FFFF`, except for the range
-/// `0xD800...0xDFFF` (the surrogate code points). This includes
-/// unassigned/reserved code points.
-/// * `bool`: Generates `false` or `true`, each with probability 0.5.
-/// * Floating point types (`f32` and `f64`): Uniformly distributed in the
-/// half-open range `[0, 1)`. See notes below.
-/// * Wrapping integers (`Wrapping<T>`), besides the type identical to their
-/// normal integer variants.
-///
-/// The `Standard` distribution also supports generation of the following
-/// compound types where all component types are supported:
-///
-/// * Tuples (up to 12 elements): each element is generated sequentially.
-/// * Arrays (up to 32 elements): each element is generated sequentially;
-/// see also [`Rng::fill`] which supports arbitrary array length for integer
-/// types and tends to be faster for `u32` and smaller types.
-/// * `Option<T>` first generates a `bool`, and if true generates and returns
-/// `Some(value)` where `value: T`, otherwise returning `None`.
-///
-/// ## Custom implementations
-///
-/// The [`Standard`] distribution may be implemented for user types as follows:
-///
-/// ```
-/// # #![allow(dead_code)]
-/// use rand::Rng;
-/// use rand::distributions::{Distribution, Standard};
-///
-/// struct MyF32 {
-/// x: f32,
-/// }
-///
-/// impl Distribution<MyF32> for Standard {
-/// fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> MyF32 {
-/// MyF32 { x: rng.gen() }
-/// }
-/// }
-/// ```
-///
-/// ## Example usage
-/// ```
-/// use rand::prelude::*;
-/// use rand::distributions::Standard;
-///
-/// let val: f32 = StdRng::from_entropy().sample(Standard);
-/// println!("f32 from [0, 1): {}", val);
-/// ```
-///
-/// # Floating point implementation
-/// The floating point implementations for `Standard` generate a random value in
-/// the half-open interval `[0, 1)`, i.e. including 0 but not 1.
-///
-/// All values that can be generated are of the form `n * ε/2`. For `f32`
-/// the 23 most significant random bits of a `u32` are used and for `f64` the
-/// 53 most significant bits of a `u64` are used. The conversion uses the
-/// multiplicative method: `(rng.gen::<$uty>() >> N) as $ty * (ε/2)`.
-///
-/// See also: [`Open01`] which samples from `(0, 1)`, [`OpenClosed01`] which
-/// samples from `(0, 1]` and `Rng::gen_range(0, 1)` which also samples from
-/// `[0, 1)`. Note that `Open01` and `gen_range` (which uses [`Uniform`]) use
-/// transmute-based methods which yield 1 bit less precision but may perform
-/// faster on some architectures (on modern Intel CPUs all methods have
-/// approximately equal performance).
-///
-/// [`Uniform`]: uniform::Uniform
-#[derive(Clone, Copy, Debug)]
-pub struct Standard;
-
-
-#[cfg(all(test, feature = "std"))]
-mod tests {
- use crate::Rng;
- use super::{Distribution, Uniform};
-
- #[test]
- fn test_distributions_iter() {
- use crate::distributions::Open01;
- let mut rng = crate::test::rng(210);
- let distr = Open01;
- let results: Vec<f32> = distr.sample_iter(&mut rng).take(100).collect();
- println!("{:?}", results);
- }
-
- #[test]
- fn test_make_an_iter() {
- fn ten_dice_rolls_other_than_five<'a, R: Rng>(rng: &'a mut R) -> impl Iterator<Item = i32> + 'a {
- Uniform::new_inclusive(1, 6)
- .sample_iter(rng)
- .filter(|x| *x != 5)
- .take(10)
- }
-
- let mut rng = crate::test::rng(211);
- let mut count = 0;
- for val in ten_dice_rolls_other_than_five(&mut rng) {
- assert!(val >= 1 && val <= 6 && val != 5);
- count += 1;
- }
- assert_eq!(count, 10);
- }
-}