android / platform / external / rust / crates / rand / 136b6bcc1d41c54f690d735e8051b536afed35e3 / . / src / distributions / mod.rs

// 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 | |

//! [`random`]: crate::random | |

//! [`rand_distr`]: https://crates.io/crates/rand_distr | |

//! [`statrs`]: https://crates.io/crates/statrs | |

use crate::Rng; | |

use core::iter; | |

pub use self::bernoulli::{Bernoulli, BernoulliError}; | |

pub use self::float::{Open01, OpenClosed01}; | |

pub use self::other::Alphanumeric; | |

#[doc(inline)] pub use self::uniform::Uniform; | |

#[cfg(feature = "alloc")] | |

pub use self::weighted::{WeightedError, WeightedIndex}; | |

// The following are all deprecated after being moved to rand_distr | |

#[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::exponential::{Exp, Exp1}; | |

#[allow(deprecated)] | |

#[cfg(feature = "std")] | |

pub use self::gamma::{Beta, ChiSquared, FisherF, Gamma, StudentT}; | |

#[allow(deprecated)] | |

#[cfg(feature = "std")] | |

pub use self::normal::{LogNormal, Normal, StandardNormal}; | |

#[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::triangular::Triangular; | |

#[allow(deprecated)] | |

#[cfg(feature = "std")] | |

pub use self::unit_circle::UnitCircle; | |

#[allow(deprecated)] | |

#[cfg(feature = "std")] | |

pub use self::unit_sphere::UnitSphereSurface; | |

#[allow(deprecated)] | |

#[cfg(feature = "std")] | |

pub use self::weibull::Weibull; | |

mod bernoulli; | |

#[cfg(feature = "std")] mod binomial; | |

#[cfg(feature = "std")] mod cauchy; | |

#[cfg(feature = "std")] mod dirichlet; | |

#[cfg(feature = "std")] mod exponential; | |

#[cfg(feature = "std")] mod gamma; | |

#[cfg(feature = "std")] mod normal; | |

#[cfg(feature = "std")] mod pareto; | |

#[cfg(feature = "std")] mod poisson; | |

#[cfg(feature = "std")] mod triangular; | |

pub mod uniform; | |

#[cfg(feature = "std")] mod unit_circle; | |

#[cfg(feature = "std")] mod unit_sphere; | |

#[cfg(feature = "std")] mod weibull; | |

#[cfg(feature = "alloc")] pub mod weighted; | |

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. | |

/// | |

/// Implementations are typically expected to be portable with reproducible | |

/// results when used with a PRNG with fixed seed; see the | |

/// [portability chapter](https://rust-random.github.io/book/portability.html) | |

/// of The Rust Rand Book. In some cases this does not apply, e.g. the `usize` | |

/// type requires different sampling on 32-bit and 64-bit machines. | |

/// | |

/// [`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 24 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 super::{Distribution, Uniform}; | |

use crate::Rng; | |

#[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); | |

} | |

} |