// Copyright 2018 Developers of the Rand project.
// Copyright 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.
//! A distribution uniformly sampling numbers within a given range.
//!
//! [`Uniform`] is the standard distribution to sample uniformly from a range;
//! e.g. `Uniform::new_inclusive(1, 6)` can sample integers from 1 to 6, like a
//! standard die. [`Rng::gen_range`] supports any type supported by
//! [`Uniform`].
//!
//! This distribution is provided with support for several primitive types
//! (all integer and floating-point types) as well as `std::time::Duration`,
//! and supports extension to user-defined types via a type-specific *back-end*
//! implementation.
//!
//! The types [`UniformInt`], [`UniformFloat`] and [`UniformDuration`] are the
//! back-ends supporting sampling from primitive integer and floating-point
//! ranges as well as from `std::time::Duration`; these types do not normally
//! need to be used directly (unless implementing a derived back-end).
//!
//! # Example usage
//!
//! ```
//! use rand::{Rng, thread_rng};
//! use rand::distributions::Uniform;
//!
//! let mut rng = thread_rng();
//! let side = Uniform::new(-10.0, 10.0);
//!
//! // sample between 1 and 10 points
//! for _ in 0..rng.gen_range(1, 11) {
//! // sample a point from the square with sides -10 - 10 in two dimensions
//! let (x, y) = (rng.sample(side), rng.sample(side));
//! println!("Point: {}, {}", x, y);
//! }
//! ```
//!
//! # Extending `Uniform` to support a custom type
//!
//! To extend [`Uniform`] to support your own types, write a back-end which
//! implements the [`UniformSampler`] trait, then implement the [`SampleUniform`]
//! helper trait to "register" your back-end. See the `MyF32` example below.
//!
//! At a minimum, the back-end needs to store any parameters needed for sampling
//! (e.g. the target range) and implement `new`, `new_inclusive` and `sample`.
//! Those methods should include an assert to check the range is valid (i.e.
//! `low < high`). The example below merely wraps another back-end.
//!
//! The `new`, `new_inclusive` and `sample_single` functions use arguments of
//! type SampleBorrow<X> in order to support passing in values by reference or
//! by value. In the implementation of these functions, you can choose to
//! simply use the reference returned by [`SampleBorrow::borrow`], or you can choose
//! to copy or clone the value, whatever is appropriate for your type.
//!
//! ```
//! use rand::prelude::*;
//! use rand::distributions::uniform::{Uniform, SampleUniform,
//! UniformSampler, UniformFloat, SampleBorrow};
//!
//! struct MyF32(f32);
//!
//! #[derive(Clone, Copy, Debug)]
//! struct UniformMyF32 {
//! inner: UniformFloat<f32>,
//! }
//!
//! impl UniformSampler for UniformMyF32 {
//! type X = MyF32;
//! fn new<B1, B2>(low: B1, high: B2) -> Self
//! where B1: SampleBorrow<Self::X> + Sized,
//! B2: SampleBorrow<Self::X> + Sized
//! {
//! UniformMyF32 {
//! inner: UniformFloat::<f32>::new(low.borrow().0, high.borrow().0),
//! }
//! }
//! fn new_inclusive<B1, B2>(low: B1, high: B2) -> Self
//! where B1: SampleBorrow<Self::X> + Sized,
//! B2: SampleBorrow<Self::X> + Sized
//! {
//! UniformSampler::new(low, high)
//! }
//! fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
//! MyF32(self.inner.sample(rng))
//! }
//! }
//!
//! impl SampleUniform for MyF32 {
//! type Sampler = UniformMyF32;
//! }
//!
//! let (low, high) = (MyF32(17.0f32), MyF32(22.0f32));
//! let uniform = Uniform::new(low, high);
//! let x = uniform.sample(&mut thread_rng());
//! ```
//!
//! [`Uniform`]: struct.Uniform.html
//! [`Rng::gen_range`]: ../../trait.Rng.html#method.gen_range
//! [`SampleUniform`]: trait.SampleUniform.html
//! [`UniformSampler`]: trait.UniformSampler.html
//! [`UniformInt`]: struct.UniformInt.html
//! [`UniformFloat`]: struct.UniformFloat.html
//! [`UniformDuration`]: struct.UniformDuration.html
//! [`SampleBorrow::borrow`]: trait.SampleBorrow.html#method.borrow
#[cfg(feature = "std")]
use std::time::Duration;
#[cfg(all(not(feature = "std"), rustc_1_25))]
use core::time::Duration;
use Rng;
use distributions::Distribution;
use distributions::float::IntoFloat;
use distributions::utils::{WideningMultiply, FloatSIMDUtils, FloatAsSIMD, BoolAsSIMD};
#[cfg(not(feature = "std"))]
#[allow(unused_imports)] // rustc doesn't detect that this is actually used
use distributions::utils::Float;
#[cfg(feature="simd_support")]
use packed_simd::*;
/// Sample values uniformly between two bounds.
///
/// [`Uniform::new`] and [`Uniform::new_inclusive`] construct a uniform
/// distribution sampling from the given range; these functions may do extra
/// work up front to make sampling of multiple values faster.
///
/// When sampling from a constant range, many calculations can happen at
/// compile-time and all methods should be fast; for floating-point ranges and
/// the full range of integer types this should have comparable performance to
/// the `Standard` distribution.
///
/// Steps are taken to avoid bias which might be present in naive
/// implementations; for example `rng.gen::<u8>() % 170` samples from the range
/// `[0, 169]` but is twice as likely to select numbers less than 85 than other
/// values. Further, the implementations here give more weight to the high-bits
/// generated by the RNG than the low bits, since with some RNGs the low-bits
/// are of lower quality than the high bits.
///
/// Implementations must sample in `[low, high)` range for
/// `Uniform::new(low, high)`, i.e., excluding `high`. In particular care must
/// be taken to ensure that rounding never results values `< low` or `>= high`.
///
/// # Example
///
/// ```
/// use rand::distributions::{Distribution, Uniform};
///
/// fn main() {
/// let between = Uniform::from(10..10000);
/// let mut rng = rand::thread_rng();
/// let mut sum = 0;
/// for _ in 0..1000 {
/// sum += between.sample(&mut rng);
/// }
/// println!("{}", sum);
/// }
/// ```
///
/// [`Uniform::new`]: struct.Uniform.html#method.new
/// [`Uniform::new_inclusive`]: struct.Uniform.html#method.new_inclusive
/// [`new`]: struct.Uniform.html#method.new
/// [`new_inclusive`]: struct.Uniform.html#method.new_inclusive
#[derive(Clone, Copy, Debug)]
pub struct Uniform<X: SampleUniform> {
inner: X::Sampler,
}
impl<X: SampleUniform> Uniform<X> {
/// Create a new `Uniform` instance which samples uniformly from the half
/// open range `[low, high)` (excluding `high`). Panics if `low >= high`.
pub fn new<B1, B2>(low: B1, high: B2) -> Uniform<X>
where B1: SampleBorrow<X> + Sized,
B2: SampleBorrow<X> + Sized
{
Uniform { inner: X::Sampler::new(low, high) }
}
/// Create a new `Uniform` instance which samples uniformly from the closed
/// range `[low, high]` (inclusive). Panics if `low > high`.
pub fn new_inclusive<B1, B2>(low: B1, high: B2) -> Uniform<X>
where B1: SampleBorrow<X> + Sized,
B2: SampleBorrow<X> + Sized
{
Uniform { inner: X::Sampler::new_inclusive(low, high) }
}
}
impl<X: SampleUniform> Distribution<X> for Uniform<X> {
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> X {
self.inner.sample(rng)
}
}
/// Helper trait for creating objects using the correct implementation of
/// [`UniformSampler`] for the sampling type.
///
/// See the [module documentation] on how to implement [`Uniform`] range
/// sampling for a custom type.
///
/// [`UniformSampler`]: trait.UniformSampler.html
/// [module documentation]: index.html
/// [`Uniform`]: struct.Uniform.html
pub trait SampleUniform: Sized {
/// The `UniformSampler` implementation supporting type `X`.
type Sampler: UniformSampler<X = Self>;
}
/// Helper trait handling actual uniform sampling.
///
/// See the [module documentation] on how to implement [`Uniform`] range
/// sampling for a custom type.
///
/// Implementation of [`sample_single`] is optional, and is only useful when
/// the implementation can be faster than `Self::new(low, high).sample(rng)`.
///
/// [module documentation]: index.html
/// [`Uniform`]: struct.Uniform.html
/// [`sample_single`]: trait.UniformSampler.html#method.sample_single
pub trait UniformSampler: Sized {
/// The type sampled by this implementation.
type X;
/// Construct self, with inclusive lower bound and exclusive upper bound
/// `[low, high)`.
///
/// Usually users should not call this directly but instead use
/// `Uniform::new`, which asserts that `low < high` before calling this.
fn new<B1, B2>(low: B1, high: B2) -> Self
where B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized;
/// Construct self, with inclusive bounds `[low, high]`.
///
/// Usually users should not call this directly but instead use
/// `Uniform::new_inclusive`, which asserts that `low <= high` before
/// calling this.
fn new_inclusive<B1, B2>(low: B1, high: B2) -> Self
where B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized;
/// Sample a value.
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X;
/// Sample a single value uniformly from a range with inclusive lower bound
/// and exclusive upper bound `[low, high)`.
///
/// Usually users should not call this directly but instead use
/// `Uniform::sample_single`, which asserts that `low < high` before calling
/// this.
///
/// Via this method, implementations can provide a method optimized for
/// sampling only a single value from the specified range. The default
/// implementation simply calls `UniformSampler::new` then `sample` on the
/// result.
fn sample_single<R: Rng + ?Sized, B1, B2>(low: B1, high: B2, rng: &mut R)
-> Self::X
where B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized
{
let uniform: Self = UniformSampler::new(low, high);
uniform.sample(rng)
}
}
impl<X: SampleUniform> From<::core::ops::Range<X>> for Uniform<X> {
fn from(r: ::core::ops::Range<X>) -> Uniform<X> {
Uniform::new(r.start, r.end)
}
}
#[cfg(rustc_1_27)]
impl<X: SampleUniform> From<::core::ops::RangeInclusive<X>> for Uniform<X> {
fn from(r: ::core::ops::RangeInclusive<X>) -> Uniform<X> {
Uniform::new_inclusive(r.start(), r.end())
}
}
/// Helper trait similar to [`Borrow`] but implemented
/// only for SampleUniform and references to SampleUniform in
/// order to resolve ambiguity issues.
///
/// [`Borrow`]: https://doc.rust-lang.org/std/borrow/trait.Borrow.html
pub trait SampleBorrow<Borrowed> {
/// Immutably borrows from an owned value. See [`Borrow::borrow`]
///
/// [`Borrow::borrow`]: https://doc.rust-lang.org/std/borrow/trait.Borrow.html#tymethod.borrow
fn borrow(&self) -> &Borrowed;
}
impl<Borrowed> SampleBorrow<Borrowed> for Borrowed where Borrowed: SampleUniform {
#[inline(always)]
fn borrow(&self) -> &Borrowed { self }
}
impl<'a, Borrowed> SampleBorrow<Borrowed> for &'a Borrowed where Borrowed: SampleUniform {
#[inline(always)]
fn borrow(&self) -> &Borrowed { *self }
}
////////////////////////////////////////////////////////////////////////////////
// What follows are all back-ends.
/// The back-end implementing [`UniformSampler`] for integer types.
///
/// Unless you are implementing [`UniformSampler`] for your own type, this type
/// should not be used directly, use [`Uniform`] instead.
///
/// # Implementation notes
///
/// For a closed range, the number of possible numbers we should generate is
/// `range = (high - low + 1)`. It is not possible to end up with a uniform
/// distribution if we map *all* the random integers that can be generated to
/// this range. We have to map integers from a `zone` that is a multiple of the
/// range. The rest of the integers, that cause a bias, are rejected.
///
/// The problem with `range` is that to cover the full range of the type, it has
/// to store `unsigned_max + 1`, which can't be represented. But if the range
/// covers the full range of the type, no modulus is needed. A range of size 0
/// can't exist, so we use that to represent this special case. Wrapping
/// arithmetic even makes representing `unsigned_max + 1` as 0 simple.
///
/// We don't calculate `zone` directly, but first calculate the number of
/// integers to reject. To handle `unsigned_max + 1` not fitting in the type,
/// we use:
/// `ints_to_reject = (unsigned_max + 1) % range;`
/// `ints_to_reject = (unsigned_max - range + 1) % range;`
///
/// The smallest integer PRNGs generate is `u32`. That is why for small integer
/// sizes (`i8`/`u8` and `i16`/`u16`) there is an optimization: don't pick the
/// largest zone that can fit in the small type, but pick the largest zone that
/// can fit in an `u32`. `ints_to_reject` is always less than half the size of
/// the small integer. This means the first bit of `zone` is always 1, and so
/// are all the other preceding bits of a larger integer. The easiest way to
/// grow the `zone` for the larger type is to simply sign extend it.
///
/// An alternative to using a modulus is widening multiply: After a widening
/// multiply by `range`, the result is in the high word. Then comparing the low
/// word against `zone` makes sure our distribution is uniform.
///
/// [`UniformSampler`]: trait.UniformSampler.html
/// [`Uniform`]: struct.Uniform.html
#[derive(Clone, Copy, Debug)]
pub struct UniformInt<X> {
low: X,
range: X,
zone: X,
}
macro_rules! uniform_int_impl {
($ty:ty, $signed:ty, $unsigned:ident,
$i_large:ident, $u_large:ident) => {
impl SampleUniform for $ty {
type Sampler = UniformInt<$ty>;
}
impl UniformSampler for UniformInt<$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.
type X = $ty;
#[inline] // if the range is constant, this helps LLVM to do the
// calculations at compile-time.
fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
where B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized
{
let low = *low_b.borrow();
let high = *high_b.borrow();
assert!(low < high, "Uniform::new called with `low >= high`");
UniformSampler::new_inclusive(low, high - 1)
}
#[inline] // if the range is constant, this helps LLVM to do the
// calculations at compile-time.
fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
where B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized
{
let low = *low_b.borrow();
let high = *high_b.borrow();
assert!(low <= high,
"Uniform::new_inclusive called with `low > high`");
let unsigned_max = ::core::$unsigned::MAX;
let range = high.wrapping_sub(low).wrapping_add(1) as $unsigned;
let ints_to_reject =
if range > 0 {
(unsigned_max - range + 1) % range
} else {
0
};
let zone = unsigned_max - ints_to_reject;
UniformInt {
low: low,
// These are really $unsigned values, but store as $ty:
range: range as $ty,
zone: zone as $ty
}
}
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
let range = self.range as $unsigned as $u_large;
if range > 0 {
// Grow `zone` to fit a type of at least 32 bits, by
// sign-extending it (the first bit is always 1, so are all
// the preceding bits of the larger type).
// For types that already have the right size, all the
// casting is a no-op.
let zone = self.zone as $signed as $i_large as $u_large;
loop {
let v: $u_large = rng.gen();
let (hi, lo) = v.wmul(range);
if lo <= zone {
return self.low.wrapping_add(hi as $ty);
}
}
} else {
// Sample from the entire integer range.
rng.gen()
}
}
fn sample_single<R: Rng + ?Sized, B1, B2>(low_b: B1, high_b: B2, rng: &mut R)
-> Self::X
where B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized
{
let low = *low_b.borrow();
let high = *high_b.borrow();
assert!(low < high,
"Uniform::sample_single called with low >= high");
let range = high.wrapping_sub(low) as $unsigned as $u_large;
let zone =
if ::core::$unsigned::MAX <= ::core::u16::MAX as $unsigned {
// Using a modulus is faster than the approximation for
// i8 and i16. I suppose we trade the cost of one
// modulus for near-perfect branch prediction.
let unsigned_max: $u_large = ::core::$u_large::MAX;
let ints_to_reject = (unsigned_max - range + 1) % range;
unsigned_max - ints_to_reject
} else {
// conservative but fast approximation. `- 1` is necessary to allow the
// same comparison without bias.
(range << range.leading_zeros()).wrapping_sub(1)
};
loop {
let v: $u_large = rng.gen();
let (hi, lo) = v.wmul(range);
if lo <= zone {
return low.wrapping_add(hi as $ty);
}
}
}
}
}
}
uniform_int_impl! { i8, i8, u8, i32, u32 }
uniform_int_impl! { i16, i16, u16, i32, u32 }
uniform_int_impl! { i32, i32, u32, i32, u32 }
uniform_int_impl! { i64, i64, u64, i64, u64 }
#[cfg(all(rustc_1_26, not(target_os = "emscripten")))]
uniform_int_impl! { i128, i128, u128, u128, u128 }
uniform_int_impl! { isize, isize, usize, isize, usize }
uniform_int_impl! { u8, i8, u8, i32, u32 }
uniform_int_impl! { u16, i16, u16, i32, u32 }
uniform_int_impl! { u32, i32, u32, i32, u32 }
uniform_int_impl! { u64, i64, u64, i64, u64 }
uniform_int_impl! { usize, isize, usize, isize, usize }
#[cfg(all(rustc_1_26, not(target_os = "emscripten")))]
uniform_int_impl! { u128, u128, u128, i128, u128 }
#[cfg(all(feature = "simd_support", feature = "nightly"))]
macro_rules! uniform_simd_int_impl {
($ty:ident, $unsigned:ident, $u_scalar:ident) => {
// The "pick the largest zone that can fit in an `u32`" optimization
// is less useful here. Multiple lanes complicate things, we don't
// know the PRNG's minimal output size, and casting to a larger vector
// is generally a bad idea for SIMD performance. The user can still
// implement it manually.
// TODO: look into `Uniform::<u32x4>::new(0u32, 100)` functionality
// perhaps `impl SampleUniform for $u_scalar`?
impl SampleUniform for $ty {
type Sampler = UniformInt<$ty>;
}
impl UniformSampler for UniformInt<$ty> {
type X = $ty;
#[inline] // if the range is constant, this helps LLVM to do the
// calculations at compile-time.
fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
where B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized
{
let low = *low_b.borrow();
let high = *high_b.borrow();
assert!(low.lt(high).all(), "Uniform::new called with `low >= high`");
UniformSampler::new_inclusive(low, high - 1)
}
#[inline] // if the range is constant, this helps LLVM to do the
// calculations at compile-time.
fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
where B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized
{
let low = *low_b.borrow();
let high = *high_b.borrow();
assert!(low.le(high).all(),
"Uniform::new_inclusive called with `low > high`");
let unsigned_max = ::core::$u_scalar::MAX;
// NOTE: these may need to be replaced with explicitly
// wrapping operations if `packed_simd` changes
let range: $unsigned = ((high - low) + 1).cast();
// `% 0` will panic at runtime.
let not_full_range = range.gt($unsigned::splat(0));
// replacing 0 with `unsigned_max` allows a faster `select`
// with bitwise OR
let modulo = not_full_range.select(range, $unsigned::splat(unsigned_max));
// wrapping addition
let ints_to_reject = (unsigned_max - range + 1) % modulo;
// When `range` is 0, `lo` of `v.wmul(range)` will always be
// zero which means only one sample is needed.
let zone = unsigned_max - ints_to_reject;
UniformInt {
low: low,
// These are really $unsigned values, but store as $ty:
range: range.cast(),
zone: zone.cast(),
}
}
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
let range: $unsigned = self.range.cast();
let zone: $unsigned = self.zone.cast();
// This might seem very slow, generating a whole new
// SIMD vector for every sample rejection. For most uses
// though, the chance of rejection is small and provides good
// general performance. With multiple lanes, that chance is
// multiplied. To mitigate this, we replace only the lanes of
// the vector which fail, iteratively reducing the chance of
// rejection. The replacement method does however add a little
// overhead. Benchmarking or calculating probabilities might
// reveal contexts where this replacement method is slower.
let mut v: $unsigned = rng.gen();
loop {
let (hi, lo) = v.wmul(range);
let mask = lo.le(zone);
if mask.all() {
let hi: $ty = hi.cast();
// wrapping addition
let result = self.low + hi;
// `select` here compiles to a blend operation
// When `range.eq(0).none()` the compare and blend
// operations are avoided.
let v: $ty = v.cast();
return range.gt($unsigned::splat(0)).select(result, v);
}
// Replace only the failing lanes
v = mask.select(v, rng.gen());
}
}
}
};
// bulk implementation
($(($unsigned:ident, $signed:ident),)+ $u_scalar:ident) => {
$(
uniform_simd_int_impl!($unsigned, $unsigned, $u_scalar);
uniform_simd_int_impl!($signed, $unsigned, $u_scalar);
)+
};
}
#[cfg(all(feature = "simd_support", feature = "nightly"))]
uniform_simd_int_impl! {
(u64x2, i64x2),
(u64x4, i64x4),
(u64x8, i64x8),
u64
}
#[cfg(all(feature = "simd_support", feature = "nightly"))]
uniform_simd_int_impl! {
(u32x2, i32x2),
(u32x4, i32x4),
(u32x8, i32x8),
(u32x16, i32x16),
u32
}
#[cfg(all(feature = "simd_support", feature = "nightly"))]
uniform_simd_int_impl! {
(u16x2, i16x2),
(u16x4, i16x4),
(u16x8, i16x8),
(u16x16, i16x16),
(u16x32, i16x32),
u16
}
#[cfg(all(feature = "simd_support", feature = "nightly"))]
uniform_simd_int_impl! {
(u8x2, i8x2),
(u8x4, i8x4),
(u8x8, i8x8),
(u8x16, i8x16),
(u8x32, i8x32),
(u8x64, i8x64),
u8
}
/// The back-end implementing [`UniformSampler`] for floating-point types.
///
/// Unless you are implementing [`UniformSampler`] for your own type, this type
/// should not be used directly, use [`Uniform`] instead.
///
/// # Implementation notes
///
/// Instead of generating a float in the `[0, 1)` range using [`Standard`], the
/// `UniformFloat` implementation converts the output of an PRNG itself. This
/// way one or two steps can be optimized out.
///
/// The floats are first converted to a value in the `[1, 2)` interval using a
/// transmute-based method, and then mapped to the expected range with a
/// multiply and addition. Values produced this way have what equals 22 bits of
/// random digits for an `f32`, and 52 for an `f64`.
///
/// [`UniformSampler`]: trait.UniformSampler.html
/// [`new`]: trait.UniformSampler.html#tymethod.new
/// [`new_inclusive`]: trait.UniformSampler.html#tymethod.new_inclusive
/// [`Uniform`]: struct.Uniform.html
/// [`Standard`]: ../struct.Standard.html
#[derive(Clone, Copy, Debug)]
pub struct UniformFloat<X> {
low: X,
scale: X,
}
macro_rules! uniform_float_impl {
($ty:ty, $uty:ident, $f_scalar:ident, $u_scalar:ident, $bits_to_discard:expr) => {
impl SampleUniform for $ty {
type Sampler = UniformFloat<$ty>;
}
impl UniformSampler for UniformFloat<$ty> {
type X = $ty;
fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
where B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized
{
let low = *low_b.borrow();
let high = *high_b.borrow();
assert!(low.all_lt(high),
"Uniform::new called with `low >= high`");
assert!(low.all_finite() && high.all_finite(),
"Uniform::new called with non-finite boundaries");
let max_rand = <$ty>::splat((::core::$u_scalar::MAX >> $bits_to_discard)
.into_float_with_exponent(0) - 1.0);
let mut scale = high - low;
loop {
let mask = (scale * max_rand + low).ge_mask(high);
if mask.none() {
break;
}
scale = scale.decrease_masked(mask);
}
debug_assert!(<$ty>::splat(0.0).all_le(scale));
UniformFloat { low, scale }
}
fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
where B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized
{
let low = *low_b.borrow();
let high = *high_b.borrow();
assert!(low.all_le(high),
"Uniform::new_inclusive called with `low > high`");
assert!(low.all_finite() && high.all_finite(),
"Uniform::new_inclusive called with non-finite boundaries");
let max_rand = <$ty>::splat((::core::$u_scalar::MAX >> $bits_to_discard)
.into_float_with_exponent(0) - 1.0);
let mut scale = (high - low) / max_rand;
loop {
let mask = (scale * max_rand + low).gt_mask(high);
if mask.none() {
break;
}
scale = scale.decrease_masked(mask);
}
debug_assert!(<$ty>::splat(0.0).all_le(scale));
UniformFloat { low, scale }
}
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
// Generate a value in the range [1, 2)
let value1_2 = (rng.gen::<$uty>() >> $bits_to_discard)
.into_float_with_exponent(0);
// Get a value in the range [0, 1) in order to avoid
// overflowing into infinity when multiplying with scale
let value0_1 = value1_2 - 1.0;
// We don't use `f64::mul_add`, because it is not available with
// `no_std`. Furthermore, it is slower for some targets (but
// faster for others). However, the order of multiplication and
// addition is important, because on some platforms (e.g. ARM)
// it will be optimized to a single (non-FMA) instruction.
value0_1 * self.scale + self.low
}
#[inline]
fn sample_single<R: Rng + ?Sized, B1, B2>(low_b: B1, high_b: B2, rng: &mut R)
-> Self::X
where B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized
{
let low = *low_b.borrow();
let high = *high_b.borrow();
assert!(low.all_lt(high),
"Uniform::sample_single called with low >= high");
let mut scale = high - low;
loop {
// Generate a value in the range [1, 2)
let value1_2 = (rng.gen::<$uty>() >> $bits_to_discard)
.into_float_with_exponent(0);
// Get a value in the range [0, 1) in order to avoid
// overflowing into infinity when multiplying with scale
let value0_1 = value1_2 - 1.0;
// Doing multiply before addition allows some architectures
// to use a single instruction.
let res = value0_1 * scale + low;
debug_assert!(low.all_le(res) || !scale.all_finite());
if res.all_lt(high) {
return res;
}
// This handles a number of edge cases.
// * `low` or `high` is NaN. In this case `scale` and
// `res` are going to end up as NaN.
// * `low` is negative infinity and `high` is finite.
// `scale` is going to be infinite and `res` will be
// NaN.
// * `high` is positive infinity and `low` is finite.
// `scale` is going to be infinite and `res` will
// be infinite or NaN (if value0_1 is 0).
// * `low` is negative infinity and `high` is positive
// infinity. `scale` will be infinite and `res` will
// be NaN.
// * `low` and `high` are finite, but `high - low`
// overflows to infinite. `scale` will be infinite
// and `res` will be infinite or NaN (if value0_1 is 0).
// So if `high` or `low` are non-finite, we are guaranteed
// to fail the `res < high` check above and end up here.
//
// While we technically should check for non-finite `low`
// and `high` before entering the loop, by doing the checks
// here instead, we allow the common case to avoid these
// checks. But we are still guaranteed that if `low` or
// `high` are non-finite we'll end up here and can do the
// appropriate checks.
//
// Likewise `high - low` overflowing to infinity is also
// rare, so handle it here after the common case.
let mask = !scale.finite_mask();
if mask.any() {
assert!(low.all_finite() && high.all_finite(),
"Uniform::sample_single called with non-finite boundaries");
scale = scale.decrease_masked(mask);
}
}
}
}
}
}
uniform_float_impl! { f32, u32, f32, u32, 32 - 23 }
uniform_float_impl! { f64, u64, f64, u64, 64 - 52 }
#[cfg(feature="simd_support")]
uniform_float_impl! { f32x2, u32x2, f32, u32, 32 - 23 }
#[cfg(feature="simd_support")]
uniform_float_impl! { f32x4, u32x4, f32, u32, 32 - 23 }
#[cfg(feature="simd_support")]
uniform_float_impl! { f32x8, u32x8, f32, u32, 32 - 23 }
#[cfg(feature="simd_support")]
uniform_float_impl! { f32x16, u32x16, f32, u32, 32 - 23 }
#[cfg(feature="simd_support")]
uniform_float_impl! { f64x2, u64x2, f64, u64, 64 - 52 }
#[cfg(feature="simd_support")]
uniform_float_impl! { f64x4, u64x4, f64, u64, 64 - 52 }
#[cfg(feature="simd_support")]
uniform_float_impl! { f64x8, u64x8, f64, u64, 64 - 52 }
/// The back-end implementing [`UniformSampler`] for `Duration`.
///
/// Unless you are implementing [`UniformSampler`] for your own types, this type
/// should not be used directly, use [`Uniform`] instead.
///
/// [`UniformSampler`]: trait.UniformSampler.html
/// [`Uniform`]: struct.Uniform.html
#[cfg(any(feature = "std", rustc_1_25))]
#[derive(Clone, Copy, Debug)]
pub struct UniformDuration {
mode: UniformDurationMode,
offset: u32,
}
#[cfg(any(feature = "std", rustc_1_25))]
#[derive(Debug, Copy, Clone)]
enum UniformDurationMode {
Small {
secs: u64,
nanos: Uniform<u32>,
},
Medium {
nanos: Uniform<u64>,
},
Large {
max_secs: u64,
max_nanos: u32,
secs: Uniform<u64>,
}
}
#[cfg(any(feature = "std", rustc_1_25))]
impl SampleUniform for Duration {
type Sampler = UniformDuration;
}
#[cfg(any(feature = "std", rustc_1_25))]
impl UniformSampler for UniformDuration {
type X = Duration;
#[inline]
fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
where B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized
{
let low = *low_b.borrow();
let high = *high_b.borrow();
assert!(low < high, "Uniform::new called with `low >= high`");
UniformDuration::new_inclusive(low, high - Duration::new(0, 1))
}
#[inline]
fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
where B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized
{
let low = *low_b.borrow();
let high = *high_b.borrow();
assert!(low <= high, "Uniform::new_inclusive called with `low > high`");
let low_s = low.as_secs();
let low_n = low.subsec_nanos();
let mut high_s = high.as_secs();
let mut high_n = high.subsec_nanos();
if high_n < low_n {
high_s = high_s - 1;
high_n = high_n + 1_000_000_000;
}
let mode = if low_s == high_s {
UniformDurationMode::Small {
secs: low_s,
nanos: Uniform::new_inclusive(low_n, high_n),
}
} else {
let max = high_s
.checked_mul(1_000_000_000)
.and_then(|n| n.checked_add(high_n as u64));
if let Some(higher_bound) = max {
let lower_bound = low_s * 1_000_000_000 + low_n as u64;
UniformDurationMode::Medium {
nanos: Uniform::new_inclusive(lower_bound, higher_bound),
}
} else {
// An offset is applied to simplify generation of nanoseconds
let max_nanos = high_n - low_n;
UniformDurationMode::Large {
max_secs: high_s,
max_nanos,
secs: Uniform::new_inclusive(low_s, high_s),
}
}
};
UniformDuration {
mode,
offset: low_n,
}
}
#[inline]
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Duration {
match self.mode {
UniformDurationMode::Small { secs, nanos } => {
let n = nanos.sample(rng);
Duration::new(secs, n)
}
UniformDurationMode::Medium { nanos } => {
let nanos = nanos.sample(rng);
Duration::new(nanos / 1_000_000_000, (nanos % 1_000_000_000) as u32)
}
UniformDurationMode::Large { max_secs, max_nanos, secs } => {
// constant folding means this is at least as fast as `gen_range`
let nano_range = Uniform::new(0, 1_000_000_000);
loop {
let s = secs.sample(rng);
let n = nano_range.sample(rng);
if !(s == max_secs && n > max_nanos) {
let sum = n + self.offset;
break Duration::new(s, sum);
}
}
}
}
}
}
#[cfg(test)]
mod tests {
use Rng;
use rngs::mock::StepRng;
use distributions::uniform::Uniform;
use distributions::utils::FloatAsSIMD;
#[cfg(feature="simd_support")] use packed_simd::*;
#[should_panic]
#[test]
fn test_uniform_bad_limits_equal_int() {
Uniform::new(10, 10);
}
#[test]
fn test_uniform_good_limits_equal_int() {
let mut rng = ::test::rng(804);
let dist = Uniform::new_inclusive(10, 10);
for _ in 0..20 {
assert_eq!(rng.sample(dist), 10);
}
}
#[should_panic]
#[test]
fn test_uniform_bad_limits_flipped_int() {
Uniform::new(10, 5);
}
#[test]
fn test_integers() {
use core::{i8, i16, i32, i64, isize};
use core::{u8, u16, u32, u64, usize};
#[cfg(all(rustc_1_26, not(target_os = "emscripten")))]
use core::{i128, u128};
let mut rng = ::test::rng(251);
macro_rules! t {
($ty:ident, $v:expr, $le:expr, $lt:expr) => {{
for &(low, high) in $v.iter() {
let my_uniform = Uniform::new(low, high);
for _ in 0..1000 {
let v: $ty = rng.sample(my_uniform);
assert!($le(low, v) && $lt(v, high));
}
let my_uniform = Uniform::new_inclusive(low, high);
for _ in 0..1000 {
let v: $ty = rng.sample(my_uniform);
assert!($le(low, v) && $le(v, high));
}
let my_uniform = Uniform::new(&low, high);
for _ in 0..1000 {
let v: $ty = rng.sample(my_uniform);
assert!($le(low, v) && $lt(v, high));
}
let my_uniform = Uniform::new_inclusive(&low, &high);
for _ in 0..1000 {
let v: $ty = rng.sample(my_uniform);
assert!($le(low, v) && $le(v, high));
}
for _ in 0..1000 {
let v: $ty = rng.gen_range(low, high);
assert!($le(low, v) && $lt(v, high));
}
}
}};
// scalar bulk
($($ty:ident),*) => {{
$(t!(
$ty,
[(0, 10), (10, 127), ($ty::MIN, $ty::MAX)],
|x, y| x <= y,
|x, y| x < y
);)*
}};
// simd bulk
($($ty:ident),* => $scalar:ident) => {{
$(t!(
$ty,
[
($ty::splat(0), $ty::splat(10)),
($ty::splat(10), $ty::splat(127)),
($ty::splat($scalar::MIN), $ty::splat($scalar::MAX)),
],
|x: $ty, y| x.le(y).all(),
|x: $ty, y| x.lt(y).all()
);)*
}};
}
t!(i8, i16, i32, i64, isize,
u8, u16, u32, u64, usize);
#[cfg(all(rustc_1_26, not(target_os = "emscripten")))]
t!(i128, u128);
#[cfg(all(feature = "simd_support", feature = "nightly"))]
{
t!(u8x2, u8x4, u8x8, u8x16, u8x32, u8x64 => u8);
t!(i8x2, i8x4, i8x8, i8x16, i8x32, i8x64 => i8);
t!(u16x2, u16x4, u16x8, u16x16, u16x32 => u16);
t!(i16x2, i16x4, i16x8, i16x16, i16x32 => i16);
t!(u32x2, u32x4, u32x8, u32x16 => u32);
t!(i32x2, i32x4, i32x8, i32x16 => i32);
t!(u64x2, u64x4, u64x8 => u64);
t!(i64x2, i64x4, i64x8 => i64);
}
}
#[test]
fn test_floats() {
let mut rng = ::test::rng(252);
let mut zero_rng = StepRng::new(0, 0);
let mut max_rng = StepRng::new(0xffff_ffff_ffff_ffff, 0);
macro_rules! t {
($ty:ty, $f_scalar:ident, $bits_shifted:expr) => {{
let v: &[($f_scalar, $f_scalar)]=
&[(0.0, 100.0),
(-1e35, -1e25),
(1e-35, 1e-25),
(-1e35, 1e35),
(<$f_scalar>::from_bits(0), <$f_scalar>::from_bits(3)),
(-<$f_scalar>::from_bits(10), -<$f_scalar>::from_bits(1)),
(-<$f_scalar>::from_bits(5), 0.0),
(-<$f_scalar>::from_bits(7), -0.0),
(10.0, ::core::$f_scalar::MAX),
(-100.0, ::core::$f_scalar::MAX),
(-::core::$f_scalar::MAX / 5.0, ::core::$f_scalar::MAX),
(-::core::$f_scalar::MAX, ::core::$f_scalar::MAX / 5.0),
(-::core::$f_scalar::MAX * 0.8, ::core::$f_scalar::MAX * 0.7),
(-::core::$f_scalar::MAX, ::core::$f_scalar::MAX),
];
for &(low_scalar, high_scalar) in v.iter() {
for lane in 0..<$ty>::lanes() {
let low = <$ty>::splat(0.0 as $f_scalar).replace(lane, low_scalar);
let high = <$ty>::splat(1.0 as $f_scalar).replace(lane, high_scalar);
let my_uniform = Uniform::new(low, high);
let my_incl_uniform = Uniform::new_inclusive(low, high);
for _ in 0..100 {
let v = rng.sample(my_uniform).extract(lane);
assert!(low_scalar <= v && v < high_scalar);
let v = rng.sample(my_incl_uniform).extract(lane);
assert!(low_scalar <= v && v <= high_scalar);
let v = rng.gen_range(low, high).extract(lane);
assert!(low_scalar <= v && v < high_scalar);
}
assert_eq!(rng.sample(Uniform::new_inclusive(low, low)).extract(lane), low_scalar);
assert_eq!(zero_rng.sample(my_uniform).extract(lane), low_scalar);
assert_eq!(zero_rng.sample(my_incl_uniform).extract(lane), low_scalar);
assert_eq!(zero_rng.gen_range(low, high).extract(lane), low_scalar);
assert!(max_rng.sample(my_uniform).extract(lane) < high_scalar);
assert!(max_rng.sample(my_incl_uniform).extract(lane) <= high_scalar);
// Don't run this test for really tiny differences between high and low
// since for those rounding might result in selecting high for a very
// long time.
if (high_scalar - low_scalar) > 0.0001 {
let mut lowering_max_rng =
StepRng::new(0xffff_ffff_ffff_ffff,
(-1i64 << $bits_shifted) as u64);
assert!(lowering_max_rng.gen_range(low, high).extract(lane) < high_scalar);
}
}
}
assert_eq!(rng.sample(Uniform::new_inclusive(::core::$f_scalar::MAX,
::core::$f_scalar::MAX)),
::core::$f_scalar::MAX);
assert_eq!(rng.sample(Uniform::new_inclusive(-::core::$f_scalar::MAX,
-::core::$f_scalar::MAX)),
-::core::$f_scalar::MAX);
}}
}
t!(f32, f32, 32 - 23);
t!(f64, f64, 64 - 52);
#[cfg(feature="simd_support")]
{
t!(f32x2, f32, 32 - 23);
t!(f32x4, f32, 32 - 23);
t!(f32x8, f32, 32 - 23);
t!(f32x16, f32, 32 - 23);
t!(f64x2, f64, 64 - 52);
t!(f64x4, f64, 64 - 52);
t!(f64x8, f64, 64 - 52);
}
}
#[test]
#[cfg(all(feature="std",
not(target_arch = "wasm32"),
not(target_arch = "asmjs")))]
fn test_float_assertions() {
use std::panic::catch_unwind;
use super::SampleUniform;
fn range<T: SampleUniform>(low: T, high: T) {
let mut rng = ::test::rng(253);
rng.gen_range(low, high);
}
macro_rules! t {
($ty:ident, $f_scalar:ident) => {{
let v: &[($f_scalar, $f_scalar)] =
&[(::std::$f_scalar::NAN, 0.0),
(1.0, ::std::$f_scalar::NAN),
(::std::$f_scalar::NAN, ::std::$f_scalar::NAN),
(1.0, 0.5),
(::std::$f_scalar::MAX, -::std::$f_scalar::MAX),
(::std::$f_scalar::INFINITY, ::std::$f_scalar::INFINITY),
(::std::$f_scalar::NEG_INFINITY, ::std::$f_scalar::NEG_INFINITY),
(::std::$f_scalar::NEG_INFINITY, 5.0),
(5.0, ::std::$f_scalar::INFINITY),
(::std::$f_scalar::NAN, ::std::$f_scalar::INFINITY),
(::std::$f_scalar::NEG_INFINITY, ::std::$f_scalar::NAN),
(::std::$f_scalar::NEG_INFINITY, ::std::$f_scalar::INFINITY),
];
for &(low_scalar, high_scalar) in v.iter() {
for lane in 0..<$ty>::lanes() {
let low = <$ty>::splat(0.0 as $f_scalar).replace(lane, low_scalar);
let high = <$ty>::splat(1.0 as $f_scalar).replace(lane, high_scalar);
assert!(catch_unwind(|| range(low, high)).is_err());
assert!(catch_unwind(|| Uniform::new(low, high)).is_err());
assert!(catch_unwind(|| Uniform::new_inclusive(low, high)).is_err());
assert!(catch_unwind(|| range(low, low)).is_err());
assert!(catch_unwind(|| Uniform::new(low, low)).is_err());
}
}
}}
}
t!(f32, f32);
t!(f64, f64);
#[cfg(feature="simd_support")]
{
t!(f32x2, f32);
t!(f32x4, f32);
t!(f32x8, f32);
t!(f32x16, f32);
t!(f64x2, f64);
t!(f64x4, f64);
t!(f64x8, f64);
}
}
#[test]
#[cfg(any(feature = "std", rustc_1_25))]
fn test_durations() {
#[cfg(feature = "std")]
use std::time::Duration;
#[cfg(all(not(feature = "std"), rustc_1_25))]
use core::time::Duration;
let mut rng = ::test::rng(253);
let v = &[(Duration::new(10, 50000), Duration::new(100, 1234)),
(Duration::new(0, 100), Duration::new(1, 50)),
(Duration::new(0, 0), Duration::new(u64::max_value(), 999_999_999))];
for &(low, high) in v.iter() {
let my_uniform = Uniform::new(low, high);
for _ in 0..1000 {
let v = rng.sample(my_uniform);
assert!(low <= v && v < high);
}
}
}
#[test]
fn test_custom_uniform() {
use distributions::uniform::{UniformSampler, UniformFloat, SampleUniform, SampleBorrow};
#[derive(Clone, Copy, PartialEq, PartialOrd)]
struct MyF32 {
x: f32,
}
#[derive(Clone, Copy, Debug)]
struct UniformMyF32 {
inner: UniformFloat<f32>,
}
impl UniformSampler for UniformMyF32 {
type X = MyF32;
fn new<B1, B2>(low: B1, high: B2) -> Self
where B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized
{
UniformMyF32 {
inner: UniformFloat::<f32>::new(low.borrow().x, high.borrow().x),
}
}
fn new_inclusive<B1, B2>(low: B1, high: B2) -> Self
where B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized
{
UniformSampler::new(low, high)
}
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
MyF32 { x: self.inner.sample(rng) }
}
}
impl SampleUniform for MyF32 {
type Sampler = UniformMyF32;
}
let (low, high) = (MyF32{ x: 17.0f32 }, MyF32{ x: 22.0f32 });
let uniform = Uniform::new(low, high);
let mut rng = ::test::rng(804);
for _ in 0..100 {
let x: MyF32 = rng.sample(uniform);
assert!(low <= x && x < high);
}
}
#[test]
fn test_uniform_from_std_range() {
let r = Uniform::from(2u32..7);
assert_eq!(r.inner.low, 2);
assert_eq!(r.inner.range, 5);
let r = Uniform::from(2.0f64..7.0);
assert_eq!(r.inner.low, 2.0);
assert_eq!(r.inner.scale, 5.0);
}
#[cfg(rustc_1_27)]
#[test]
fn test_uniform_from_std_range_inclusive() {
let r = Uniform::from(2u32..=6);
assert_eq!(r.inner.low, 2);
assert_eq!(r.inner.range, 5);
let r = Uniform::from(2.0f64..=7.0);
assert_eq!(r.inner.low, 2.0);
assert!(r.inner.scale > 5.0);
assert!(r.inner.scale < 5.0 + 1e-14);
}
}