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| </pre><pre class="rust"><code><span class="comment">// Copyright 2018 Developers of the Rand project.</span> |
| <span class="comment">// Copyright 2013-2017 The Rust Project Developers.</span> |
| <span class="comment">//</span> |
| <span class="comment">// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or</span> |
| <span class="comment">// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license</span> |
| <span class="comment">// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your</span> |
| <span class="comment">// option. This file may not be copied, modified, or distributed</span> |
| <span class="comment">// except according to those terms.</span> |
| |
| <span class="doccomment">//! Generating random samples from probability distributions</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! This module is the home of the [`Distribution`] trait and several of its</span> |
| <span class="doccomment">//! implementations. It is the workhorse behind some of the convenient</span> |
| <span class="doccomment">//! functionality of the [`Rng`] trait, e.g. [`Rng::gen`] and of course</span> |
| <span class="doccomment">//! [`Rng::sample`].</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! Abstractly, a [probability distribution] describes the probability of</span> |
| <span class="doccomment">//! occurrence of each value in its sample space.</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! More concretely, an implementation of `Distribution<T>` for type `X` is an</span> |
| <span class="doccomment">//! algorithm for choosing values from the sample space (a subset of `T`)</span> |
| <span class="doccomment">//! according to the distribution `X` represents, using an external source of</span> |
| <span class="doccomment">//! randomness (an RNG supplied to the `sample` function).</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! A type `X` may implement `Distribution<T>` for multiple types `T`.</span> |
| <span class="doccomment">//! Any type implementing [`Distribution`] is stateless (i.e. immutable),</span> |
| <span class="doccomment">//! but it may have internal parameters set at construction time (for example,</span> |
| <span class="doccomment">//! [`Uniform`] allows specification of its sample space as a range within `T`).</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! # The `Standard` distribution</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! The [`Standard`] distribution is important to mention. This is the</span> |
| <span class="doccomment">//! distribution used by [`Rng::gen`] and represents the "default" way to</span> |
| <span class="doccomment">//! produce a random value for many different types, including most primitive</span> |
| <span class="doccomment">//! types, tuples, arrays, and a few derived types. See the documentation of</span> |
| <span class="doccomment">//! [`Standard`] for more details.</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! Implementing `Distribution<T>` for [`Standard`] for user types `T` makes it</span> |
| <span class="doccomment">//! possible to generate type `T` with [`Rng::gen`], and by extension also</span> |
| <span class="doccomment">//! with the [`random`] function.</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! ## Random characters</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! [`Alphanumeric`] is a simple distribution to sample random letters and</span> |
| <span class="doccomment">//! numbers of the `char` type; in contrast [`Standard`] may sample any valid</span> |
| <span class="doccomment">//! `char`.</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! # Uniform numeric ranges</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! The [`Uniform`] distribution is more flexible than [`Standard`], but also</span> |
| <span class="doccomment">//! more specialised: it supports fewer target types, but allows the sample</span> |
| <span class="doccomment">//! space to be specified as an arbitrary range within its target type `T`.</span> |
| <span class="doccomment">//! Both [`Standard`] and [`Uniform`] are in some sense uniform distributions.</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! Values may be sampled from this distribution using [`Rng::sample(Range)`] or</span> |
| <span class="doccomment">//! by creating a distribution object with [`Uniform::new`],</span> |
| <span class="doccomment">//! [`Uniform::new_inclusive`] or `From<Range>`. When the range limits are not</span> |
| <span class="doccomment">//! known at compile time it is typically faster to reuse an existing</span> |
| <span class="doccomment">//! `Uniform` object than to call [`Rng::sample(Range)`].</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! User types `T` may also implement `Distribution<T>` for [`Uniform`],</span> |
| <span class="doccomment">//! although this is less straightforward than for [`Standard`] (see the</span> |
| <span class="doccomment">//! documentation in the [`uniform`] module). Doing so enables generation of</span> |
| <span class="doccomment">//! values of type `T` with [`Rng::sample(Range)`].</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! ## Open and half-open ranges</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! There are surprisingly many ways to uniformly generate random floats. A</span> |
| <span class="doccomment">//! range between 0 and 1 is standard, but the exact bounds (open vs closed)</span> |
| <span class="doccomment">//! and accuracy differ. In addition to the [`Standard`] distribution Rand offers</span> |
| <span class="doccomment">//! [`Open01`] and [`OpenClosed01`]. See "Floating point implementation" section of</span> |
| <span class="doccomment">//! [`Standard`] documentation for more details.</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! # Non-uniform sampling</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! Sampling a simple true/false outcome with a given probability has a name:</span> |
| <span class="doccomment">//! the [`Bernoulli`] distribution (this is used by [`Rng::gen_bool`]).</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! For weighted sampling from a sequence of discrete values, use the</span> |
| <span class="doccomment">//! [`WeightedIndex`] distribution.</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! This crate no longer includes other non-uniform distributions; instead</span> |
| <span class="doccomment">//! it is recommended that you use either [`rand_distr`] or [`statrs`].</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//!</span> |
| <span class="doccomment">//! [probability distribution]: https://en.wikipedia.org/wiki/Probability_distribution</span> |
| <span class="doccomment">//! [`rand_distr`]: https://crates.io/crates/rand_distr</span> |
| <span class="doccomment">//! [`statrs`]: https://crates.io/crates/statrs</span> |
| |
| <span class="doccomment">//! [`random`]: crate::random</span> |
| <span class="doccomment">//! [`rand_distr`]: https://crates.io/crates/rand_distr</span> |
| <span class="doccomment">//! [`statrs`]: https://crates.io/crates/statrs</span> |
| |
| <span class="kw">mod</span> <span class="ident">bernoulli</span>; |
| <span class="kw">mod</span> <span class="ident">distribution</span>; |
| <span class="kw">mod</span> <span class="ident">float</span>; |
| <span class="kw">mod</span> <span class="ident">integer</span>; |
| <span class="kw">mod</span> <span class="ident">other</span>; |
| <span class="kw">mod</span> <span class="ident">slice</span>; |
| <span class="kw">mod</span> <span class="ident">utils</span>; |
| <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"alloc"</span>)]</span> |
| <span class="kw">mod</span> <span class="ident">weighted_index</span>; |
| |
| <span class="attribute">#[<span class="ident">doc</span>(<span class="ident">hidden</span>)]</span> |
| <span class="kw">pub</span> <span class="kw">mod</span> <span class="ident">hidden_export</span> { |
| <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="kw">super</span>::float::IntoFloat</span>; <span class="comment">// used by rand_distr</span> |
| } |
| <span class="kw">pub</span> <span class="kw">mod</span> <span class="ident">uniform</span>; |
| <span class="attribute">#[<span class="ident">deprecated</span>( |
| <span class="ident">since</span> <span class="op">=</span> <span class="string">"0.8.0"</span>, |
| <span class="ident">note</span> <span class="op">=</span> <span class="string">"use rand::distributions::{WeightedIndex, WeightedError} instead"</span> |
| )]</span> |
| <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"alloc"</span>)]</span> |
| <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">doc_cfg</span>, <span class="ident">doc</span>(<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"alloc"</span>)))]</span> |
| <span class="kw">pub</span> <span class="kw">mod</span> <span class="ident">weighted</span>; |
| |
| <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::bernoulli</span>::{<span class="ident">Bernoulli</span>, <span class="ident">BernoulliError</span>}; |
| <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::distribution</span>::{<span class="ident">Distribution</span>, <span class="ident">DistIter</span>, <span class="ident">DistMap</span>}; |
| <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"alloc"</span>)]</span> |
| <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::distribution::DistString</span>; |
| <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::float</span>::{<span class="ident">Open01</span>, <span class="ident">OpenClosed01</span>}; |
| <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::other::Alphanumeric</span>; |
| <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::slice::Slice</span>; |
| <span class="attribute">#[<span class="ident">doc</span>(<span class="ident">inline</span>)]</span> |
| <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::uniform::Uniform</span>; |
| <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"alloc"</span>)]</span> |
| <span class="kw">pub</span> <span class="kw">use</span> <span class="ident"><span class="self">self</span>::weighted_index</span>::{<span class="ident">WeightedError</span>, <span class="ident">WeightedIndex</span>}; |
| |
| <span class="attribute">#[<span class="ident">allow</span>(<span class="ident">unused</span>)]</span> |
| <span class="kw">use</span> <span class="ident"><span class="kw">crate</span>::Rng</span>; |
| |
| <span class="doccomment">/// A generic random value distribution, implemented for many primitive types.</span> |
| <span class="doccomment">/// Usually generates values with a numerically uniform distribution, and with a</span> |
| <span class="doccomment">/// range appropriate to the type.</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// ## Provided implementations</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// Assuming the provided `Rng` is well-behaved, these implementations</span> |
| <span class="doccomment">/// generate values with the following ranges and distributions:</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// * Integers (`i32`, `u32`, `isize`, `usize`, etc.): Uniformly distributed</span> |
| <span class="doccomment">/// over all values of the type.</span> |
| <span class="doccomment">/// * `char`: Uniformly distributed over all Unicode scalar values, i.e. all</span> |
| <span class="doccomment">/// code points in the range `0...0x10_FFFF`, except for the range</span> |
| <span class="doccomment">/// `0xD800...0xDFFF` (the surrogate code points). This includes</span> |
| <span class="doccomment">/// unassigned/reserved code points.</span> |
| <span class="doccomment">/// * `bool`: Generates `false` or `true`, each with probability 0.5.</span> |
| <span class="doccomment">/// * Floating point types (`f32` and `f64`): Uniformly distributed in the</span> |
| <span class="doccomment">/// half-open range `[0, 1)`. See notes below.</span> |
| <span class="doccomment">/// * Wrapping integers (`Wrapping<T>`), besides the type identical to their</span> |
| <span class="doccomment">/// normal integer variants.</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// The `Standard` distribution also supports generation of the following</span> |
| <span class="doccomment">/// compound types where all component types are supported:</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// * Tuples (up to 12 elements): each element is generated sequentially.</span> |
| <span class="doccomment">/// * Arrays (up to 32 elements): each element is generated sequentially;</span> |
| <span class="doccomment">/// see also [`Rng::fill`] which supports arbitrary array length for integer</span> |
| <span class="doccomment">/// types and tends to be faster for `u32` and smaller types.</span> |
| <span class="doccomment">/// When using `rustc` ≥ 1.51, enable the `min_const_gen` feature to support</span> |
| <span class="doccomment">/// arrays larger than 32 elements.</span> |
| <span class="doccomment">/// Note that [`Rng::fill`] and `Standard`'s array support are *not* equivalent:</span> |
| <span class="doccomment">/// the former is optimised for integer types (using fewer RNG calls for</span> |
| <span class="doccomment">/// element types smaller than the RNG word size), while the latter supports</span> |
| <span class="doccomment">/// any element type supported by `Standard`.</span> |
| <span class="doccomment">/// * `Option<T>` first generates a `bool`, and if true generates and returns</span> |
| <span class="doccomment">/// `Some(value)` where `value: T`, otherwise returning `None`.</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// ## Custom implementations</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// The [`Standard`] distribution may be implemented for user types as follows:</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// ```</span> |
| <span class="doccomment">/// # #![allow(dead_code)]</span> |
| <span class="doccomment">/// use rand::Rng;</span> |
| <span class="doccomment">/// use rand::distributions::{Distribution, Standard};</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// struct MyF32 {</span> |
| <span class="doccomment">/// x: f32,</span> |
| <span class="doccomment">/// }</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// impl Distribution<MyF32> for Standard {</span> |
| <span class="doccomment">/// fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> MyF32 {</span> |
| <span class="doccomment">/// MyF32 { x: rng.gen() }</span> |
| <span class="doccomment">/// }</span> |
| <span class="doccomment">/// }</span> |
| <span class="doccomment">/// ```</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// ## Example usage</span> |
| <span class="doccomment">/// ```</span> |
| <span class="doccomment">/// use rand::prelude::*;</span> |
| <span class="doccomment">/// use rand::distributions::Standard;</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// let val: f32 = StdRng::from_entropy().sample(Standard);</span> |
| <span class="doccomment">/// println!("f32 from [0, 1): {}", val);</span> |
| <span class="doccomment">/// ```</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// # Floating point implementation</span> |
| <span class="doccomment">/// The floating point implementations for `Standard` generate a random value in</span> |
| <span class="doccomment">/// the half-open interval `[0, 1)`, i.e. including 0 but not 1.</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// All values that can be generated are of the form `n * ε/2`. For `f32`</span> |
| <span class="doccomment">/// the 24 most significant random bits of a `u32` are used and for `f64` the</span> |
| <span class="doccomment">/// 53 most significant bits of a `u64` are used. The conversion uses the</span> |
| <span class="doccomment">/// multiplicative method: `(rng.gen::<$uty>() >> N) as $ty * (ε/2)`.</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// See also: [`Open01`] which samples from `(0, 1)`, [`OpenClosed01`] which</span> |
| <span class="doccomment">/// samples from `(0, 1]` and `Rng::gen_range(0..1)` which also samples from</span> |
| <span class="doccomment">/// `[0, 1)`. Note that `Open01` uses transmute-based methods which yield 1 bit</span> |
| <span class="doccomment">/// less precision but may perform faster on some architectures (on modern Intel</span> |
| <span class="doccomment">/// CPUs all methods have approximately equal performance).</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// [`Uniform`]: uniform::Uniform</span> |
| <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span> |
| <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"serde1"</span>, <span class="ident">derive</span>(<span class="ident">serde::Serialize</span>, <span class="ident">serde::Deserialize</span>))]</span> |
| <span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">Standard</span>; |
| </code></pre></div> |
| </section><section id="search" class="content hidden"></section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-current-crate="rand" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.60.0-nightly (1bd4fdc94 2022-01-12)" ></div> |
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