1// Copyright 2018 Developers of the Rand project.
2// Copyright 2013-2017 The Rust Project Developers.
3//
4// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
5// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
6// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
7// option. This file may not be copied, modified, or distributed
8// except according to those terms.
9
10//! Generating random samples from probability distributions
11//!
12//! This module is the home of the [`Distribution`] trait and several of its
13//! implementations. It is the workhorse behind some of the convenient
14//! functionality of the [`Rng`] trait, e.g. [`Rng::gen`] and of course
15//! [`Rng::sample`].
16//!
17//! Abstractly, a [probability distribution] describes the probability of
18//! occurrence of each value in its sample space.
19//!
20//! More concretely, an implementation of `Distribution<T>` for type `X` is an
21//! algorithm for choosing values from the sample space (a subset of `T`)
22//! according to the distribution `X` represents, using an external source of
23//! randomness (an RNG supplied to the `sample` function).
24//!
25//! A type `X` may implement `Distribution<T>` for multiple types `T`.
26//! Any type implementing [`Distribution`] is stateless (i.e. immutable),
27//! but it may have internal parameters set at construction time (for example,
28//! [`Uniform`] allows specification of its sample space as a range within `T`).
29//!
30//!
31//! # The `Standard` distribution
32//!
33//! The [`Standard`] distribution is important to mention. This is the
34//! distribution used by [`Rng::gen`] and represents the "default" way to
35//! produce a random value for many different types, including most primitive
36//! types, tuples, arrays, and a few derived types. See the documentation of
37//! [`Standard`] for more details.
38//!
39//! Implementing `Distribution<T>` for [`Standard`] for user types `T` makes it
40//! possible to generate type `T` with [`Rng::gen`], and by extension also
41//! with the [`random`] function.
42//!
43//! ## Random characters
44//!
45//! [`Alphanumeric`] is a simple distribution to sample random letters and
46//! numbers of the `char` type; in contrast [`Standard`] may sample any valid
47//! `char`.
48//!
49//!
50//! # Uniform numeric ranges
51//!
52//! The [`Uniform`] distribution is more flexible than [`Standard`], but also
53//! more specialised: it supports fewer target types, but allows the sample
54//! space to be specified as an arbitrary range within its target type `T`.
55//! Both [`Standard`] and [`Uniform`] are in some sense uniform distributions.
56//!
57//! Values may be sampled from this distribution using [`Rng::sample(Range)`] or
58//! by creating a distribution object with [`Uniform::new`],
59//! [`Uniform::new_inclusive`] or `From<Range>`. When the range limits are not
60//! known at compile time it is typically faster to reuse an existing
61//! `Uniform` object than to call [`Rng::sample(Range)`].
62//!
63//! User types `T` may also implement `Distribution<T>` for [`Uniform`],
64//! although this is less straightforward than for [`Standard`] (see the
65//! documentation in the [`uniform`] module). Doing so enables generation of
66//! values of type `T` with [`Rng::sample(Range)`].
67//!
68//! ## Open and half-open ranges
69//!
70//! There are surprisingly many ways to uniformly generate random floats. A
71//! range between 0 and 1 is standard, but the exact bounds (open vs closed)
72//! and accuracy differ. In addition to the [`Standard`] distribution Rand offers
73//! [`Open01`] and [`OpenClosed01`]. See "Floating point implementation" section of
74//! [`Standard`] documentation for more details.
75//!
76//! # Non-uniform sampling
77//!
78//! Sampling a simple true/false outcome with a given probability has a name:
79//! the [`Bernoulli`] distribution (this is used by [`Rng::gen_bool`]).
80//!
81//! For weighted sampling from a sequence of discrete values, use the
82//! [`WeightedIndex`] distribution.
83//!
84//! This crate no longer includes other non-uniform distributions; instead
85//! it is recommended that you use either [`rand_distr`] or [`statrs`].
86//!
87//!
88//! [probability distribution]: https://en.wikipedia.org/wiki/Probability_distribution
89//! [`rand_distr`]: https://crates.io/crates/rand_distr
90//! [`statrs`]: https://crates.io/crates/statrs
91
92//! [`random`]: crate::random
93//! [`rand_distr`]: https://crates.io/crates/rand_distr
94//! [`statrs`]: https://crates.io/crates/statrs
95
96mod bernoulli;
97mod distribution;
98mod float;
99mod integer;
100mod other;
101mod slice;
102mod utils;
103#[cfg(feature = "alloc")]
104mod weighted_index;
105
106#[doc(hidden)]
107pub mod hidden_export {
108 pub use super::float::IntoFloat; // used by rand_distr
109}
110pub mod uniform;
111#[deprecated(
112 since = "0.8.0",
113 note = "use rand::distributions::{WeightedIndex, WeightedError} instead"
114)]
115#[cfg(feature = "alloc")]
116#[cfg_attr(doc_cfg, doc(cfg(feature = "alloc")))]
117pub mod weighted;
118
119pub use self::bernoulli::{Bernoulli, BernoulliError};
120pub use self::distribution::{Distribution, DistIter, DistMap};
121#[cfg(feature = "alloc")]
122pub use self::distribution::DistString;
123pub use self::float::{Open01, OpenClosed01};
124pub use self::other::Alphanumeric;
125pub use self::slice::Slice;
126#[doc(inline)]
127pub use self::uniform::Uniform;
128#[cfg(feature = "alloc")]
129pub use self::weighted_index::{WeightedError, WeightedIndex};
130
131#[allow(unused)]
132use crate::Rng;
133
134/// A generic random value distribution, implemented for many primitive types.
135/// Usually generates values with a numerically uniform distribution, and with a
136/// range appropriate to the type.
137///
138/// ## Provided implementations
139///
140/// Assuming the provided `Rng` is well-behaved, these implementations
141/// generate values with the following ranges and distributions:
142///
143/// * Integers (`i32`, `u32`, `isize`, `usize`, etc.): Uniformly distributed
144/// over all values of the type.
145/// * `char`: Uniformly distributed over all Unicode scalar values, i.e. all
146/// code points in the range `0...0x10_FFFF`, except for the range
147/// `0xD800...0xDFFF` (the surrogate code points). This includes
148/// unassigned/reserved code points.
149/// * `bool`: Generates `false` or `true`, each with probability 0.5.
150/// * Floating point types (`f32` and `f64`): Uniformly distributed in the
151/// half-open range `[0, 1)`. See notes below.
152/// * Wrapping integers (`Wrapping<T>`), besides the type identical to their
153/// normal integer variants.
154///
155/// The `Standard` distribution also supports generation of the following
156/// compound types where all component types are supported:
157///
158/// * Tuples (up to 12 elements): each element is generated sequentially.
159/// * Arrays (up to 32 elements): each element is generated sequentially;
160/// see also [`Rng::fill`] which supports arbitrary array length for integer
161/// and float types and tends to be faster for `u32` and smaller types.
162/// When using `rustc` ≥ 1.51, enable the `min_const_gen` feature to support
163/// arrays larger than 32 elements.
164/// Note that [`Rng::fill`] and `Standard`'s array support are *not* equivalent:
165/// the former is optimised for integer types (using fewer RNG calls for
166/// element types smaller than the RNG word size), while the latter supports
167/// any element type supported by `Standard`.
168/// * `Option<T>` first generates a `bool`, and if true generates and returns
169/// `Some(value)` where `value: T`, otherwise returning `None`.
170///
171/// ## Custom implementations
172///
173/// The [`Standard`] distribution may be implemented for user types as follows:
174///
175/// ```
176/// # #![allow(dead_code)]
177/// use rand::Rng;
178/// use rand::distributions::{Distribution, Standard};
179///
180/// struct MyF32 {
181/// x: f32,
182/// }
183///
184/// impl Distribution<MyF32> for Standard {
185/// fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> MyF32 {
186/// MyF32 { x: rng.gen() }
187/// }
188/// }
189/// ```
190///
191/// ## Example usage
192/// ```
193/// use rand::prelude::*;
194/// use rand::distributions::Standard;
195///
196/// let val: f32 = StdRng::from_entropy().sample(Standard);
197/// println!("f32 from [0, 1): {}", val);
198/// ```
199///
200/// # Floating point implementation
201/// The floating point implementations for `Standard` generate a random value in
202/// the half-open interval `[0, 1)`, i.e. including 0 but not 1.
203///
204/// All values that can be generated are of the form `n * ε/2`. For `f32`
205/// the 24 most significant random bits of a `u32` are used and for `f64` the
206/// 53 most significant bits of a `u64` are used. The conversion uses the
207/// multiplicative method: `(rng.gen::<$uty>() >> N) as $ty * (ε/2)`.
208///
209/// See also: [`Open01`] which samples from `(0, 1)`, [`OpenClosed01`] which
210/// samples from `(0, 1]` and `Rng::gen_range(0..1)` which also samples from
211/// `[0, 1)`. Note that `Open01` uses transmute-based methods which yield 1 bit
212/// less precision but may perform faster on some architectures (on modern Intel
213/// CPUs all methods have approximately equal performance).
214///
215/// [`Uniform`]: uniform::Uniform
216#[derive(Clone, Copy, Debug)]
217#[cfg_attr(feature = "serde1", derive(serde::Serialize, serde::Deserialize))]
218pub struct Standard;
219