rand/distr/uniform_float.rs
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// Copyright 2018-2020 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.
//! `UniformFloat` implementation
use super::{Error, SampleBorrow, SampleUniform, UniformSampler};
use crate::distr::float::IntoFloat;
use crate::distr::utils::{BoolAsSIMD, FloatAsSIMD, FloatSIMDUtils, IntAsSIMD};
use crate::Rng;
#[cfg(feature = "simd_support")]
use core::simd::prelude::*;
// #[cfg(feature = "simd_support")]
// use core::simd::{LaneCount, SupportedLaneCount};
#[cfg(feature = "serde")]
use serde::{Deserialize, Serialize};
/// 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
///
/// `UniformFloat` implementations convert RNG output to a float in the range
/// `[1, 2)` via transmutation, map this to `[0, 1)`, then scale and translate
/// to the desired range. Values produced this way have what equals 23 bits of
/// random digits for an `f32` and 52 for an `f64`.
///
/// # Bias and range errors
///
/// Bias may be expected within the least-significant bit of the significand.
/// It is not guaranteed that exclusive limits of a range are respected; i.e.
/// when sampling the range `[a, b)` it is not guaranteed that `b` is never
/// sampled.
///
/// [`new`]: UniformSampler::new
/// [`new_inclusive`]: UniformSampler::new_inclusive
/// [`StandardUniform`]: crate::distr::StandardUniform
/// [`Uniform`]: super::Uniform
#[derive(Clone, Copy, Debug, PartialEq)]
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
pub struct UniformFloat<X> {
low: X,
scale: X,
}
macro_rules! uniform_float_impl {
($($meta:meta)?, $ty:ty, $uty:ident, $f_scalar:ident, $u_scalar:ident, $bits_to_discard:expr) => {
$(#[cfg($meta)])?
impl UniformFloat<$ty> {
/// Construct, reducing `scale` as required to ensure that rounding
/// can never yield values greater than `high`.
///
/// Note: though it may be tempting to use a variant of this method
/// to ensure that samples from `[low, high)` are always strictly
/// less than `high`, this approach may be very slow where
/// `scale.abs()` is much smaller than `high.abs()`
/// (example: `low=0.99999999997819644, high=1.`).
fn new_bounded(low: $ty, high: $ty, mut scale: $ty) -> Self {
let max_rand = <$ty>::splat(1.0 as $f_scalar - $f_scalar::EPSILON);
loop {
let mask = (scale * max_rand + low).gt_mask(high);
if !mask.any() {
break;
}
scale = scale.decrease_masked(mask);
}
debug_assert!(<$ty>::splat(0.0).all_le(scale));
UniformFloat { low, scale }
}
}
$(#[cfg($meta)])?
impl SampleUniform for $ty {
type Sampler = UniformFloat<$ty>;
}
$(#[cfg($meta)])?
impl UniformSampler for UniformFloat<$ty> {
type X = $ty;
fn new<B1, B2>(low_b: B1, high_b: B2) -> Result<Self, Error>
where
B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized,
{
let low = *low_b.borrow();
let high = *high_b.borrow();
#[cfg(debug_assertions)]
if !(low.all_finite()) || !(high.all_finite()) {
return Err(Error::NonFinite);
}
if !(low.all_lt(high)) {
return Err(Error::EmptyRange);
}
let scale = high - low;
if !(scale.all_finite()) {
return Err(Error::NonFinite);
}
Ok(Self::new_bounded(low, high, scale))
}
fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Result<Self, Error>
where
B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized,
{
let low = *low_b.borrow();
let high = *high_b.borrow();
#[cfg(debug_assertions)]
if !(low.all_finite()) || !(high.all_finite()) {
return Err(Error::NonFinite);
}
if !low.all_le(high) {
return Err(Error::EmptyRange);
}
let max_rand = <$ty>::splat(1.0 as $f_scalar - $f_scalar::EPSILON);
let scale = (high - low) / max_rand;
if !scale.all_finite() {
return Err(Error::NonFinite);
}
Ok(Self::new_bounded(low, high, scale))
}
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
// Generate a value in the range [1, 2)
let value1_2 = (rng.random::<$uty>() >> $uty::splat($bits_to_discard)).into_float_with_exponent(0);
// Get a value in the range [0, 1) to avoid overflow when multiplying by scale
let value0_1 = value1_2 - <$ty>::splat(1.0);
// We don't use `f64::mul_add`, because it is not available with
// `no_std`. Furthermore, it is slower for some targets (but
// faster for others). However, the order of multiplication and
// addition is important, because on some platforms (e.g. ARM)
// it will be optimized to a single (non-FMA) instruction.
value0_1 * self.scale + self.low
}
#[inline]
fn sample_single<R: Rng + ?Sized, B1, B2>(low_b: B1, high_b: B2, rng: &mut R) -> Result<Self::X, Error>
where
B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized,
{
Self::sample_single_inclusive(low_b, high_b, rng)
}
#[inline]
fn sample_single_inclusive<R: Rng + ?Sized, B1, B2>(low_b: B1, high_b: B2, rng: &mut R) -> Result<Self::X, Error>
where
B1: SampleBorrow<Self::X> + Sized,
B2: SampleBorrow<Self::X> + Sized,
{
let low = *low_b.borrow();
let high = *high_b.borrow();
#[cfg(debug_assertions)]
if !low.all_finite() || !high.all_finite() {
return Err(Error::NonFinite);
}
if !low.all_le(high) {
return Err(Error::EmptyRange);
}
let scale = high - low;
if !scale.all_finite() {
return Err(Error::NonFinite);
}
// Generate a value in the range [1, 2)
let value1_2 =
(rng.random::<$uty>() >> $uty::splat($bits_to_discard)).into_float_with_exponent(0);
// Get a value in the range [0, 1) to avoid overflow when multiplying by scale
let value0_1 = value1_2 - <$ty>::splat(1.0);
// Doing multiply before addition allows some architectures
// to use a single instruction.
Ok(value0_1 * scale + low)
}
}
};
}
uniform_float_impl! { , f32, u32, f32, u32, 32 - 23 }
uniform_float_impl! { , f64, u64, f64, u64, 64 - 52 }
#[cfg(feature = "simd_support")]
uniform_float_impl! { feature = "simd_support", f32x2, u32x2, f32, u32, 32 - 23 }
#[cfg(feature = "simd_support")]
uniform_float_impl! { feature = "simd_support", f32x4, u32x4, f32, u32, 32 - 23 }
#[cfg(feature = "simd_support")]
uniform_float_impl! { feature = "simd_support", f32x8, u32x8, f32, u32, 32 - 23 }
#[cfg(feature = "simd_support")]
uniform_float_impl! { feature = "simd_support", f32x16, u32x16, f32, u32, 32 - 23 }
#[cfg(feature = "simd_support")]
uniform_float_impl! { feature = "simd_support", f64x2, u64x2, f64, u64, 64 - 52 }
#[cfg(feature = "simd_support")]
uniform_float_impl! { feature = "simd_support", f64x4, u64x4, f64, u64, 64 - 52 }
#[cfg(feature = "simd_support")]
uniform_float_impl! { feature = "simd_support", f64x8, u64x8, f64, u64, 64 - 52 }
#[cfg(test)]
mod tests {
use super::*;
use crate::distr::{utils::FloatSIMDScalarUtils, Uniform};
use crate::rngs::mock::StepRng;
#[test]
#[cfg_attr(miri, ignore)] // Miri is too slow
fn test_floats() {
let mut rng = crate::test::rng(252);
let mut zero_rng = StepRng::new(0, 0);
let mut max_rng = StepRng::new(0xffff_ffff_ffff_ffff, 0);
macro_rules! t {
($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),
(0.1 * $f_scalar::MAX, $f_scalar::MAX),
(-$f_scalar::MAX * 0.2, $f_scalar::MAX * 0.7),
];
for &(low_scalar, high_scalar) in v.iter() {
for lane in 0..<$ty>::LEN {
let low = <$ty>::splat(0.0 as $f_scalar).replace(lane, low_scalar);
let high = <$ty>::splat(1.0 as $f_scalar).replace(lane, high_scalar);
let my_uniform = Uniform::new(low, high).unwrap();
let my_incl_uniform = Uniform::new_inclusive(low, high).unwrap();
for _ in 0..100 {
let v = rng.sample(my_uniform).extract(lane);
assert!(low_scalar <= v && v <= high_scalar);
let v = rng.sample(my_incl_uniform).extract(lane);
assert!(low_scalar <= v && v <= high_scalar);
let v =
<$ty as SampleUniform>::Sampler::sample_single(low, high, &mut rng)
.unwrap()
.extract(lane);
assert!(low_scalar <= v && v <= high_scalar);
let v = <$ty as SampleUniform>::Sampler::sample_single_inclusive(
low, high, &mut rng,
)
.unwrap()
.extract(lane);
assert!(low_scalar <= v && v <= high_scalar);
}
assert_eq!(
rng.sample(Uniform::new_inclusive(low, low).unwrap())
.extract(lane),
low_scalar
);
assert_eq!(zero_rng.sample(my_uniform).extract(lane), low_scalar);
assert_eq!(zero_rng.sample(my_incl_uniform).extract(lane), low_scalar);
assert_eq!(
<$ty as SampleUniform>::Sampler::sample_single(
low,
high,
&mut zero_rng
)
.unwrap()
.extract(lane),
low_scalar
);
assert_eq!(
<$ty as SampleUniform>::Sampler::sample_single_inclusive(
low,
high,
&mut zero_rng
)
.unwrap()
.extract(lane),
low_scalar
);
assert!(max_rng.sample(my_uniform).extract(lane) <= high_scalar);
assert!(max_rng.sample(my_incl_uniform).extract(lane) <= high_scalar);
// sample_single cannot cope with max_rng:
// assert!(<$ty as SampleUniform>::Sampler
// ::sample_single(low, high, &mut max_rng).unwrap()
// .extract(lane) <= high_scalar);
assert!(
<$ty as SampleUniform>::Sampler::sample_single_inclusive(
low,
high,
&mut max_rng
)
.unwrap()
.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 << $bits_shifted) as u64,
);
assert!(
<$ty as SampleUniform>::Sampler::sample_single(
low,
high,
&mut lowering_max_rng
)
.unwrap()
.extract(lane)
<= high_scalar
);
}
}
}
assert_eq!(
rng.sample(Uniform::new_inclusive($f_scalar::MAX, $f_scalar::MAX).unwrap()),
$f_scalar::MAX
);
assert_eq!(
rng.sample(Uniform::new_inclusive(-$f_scalar::MAX, -$f_scalar::MAX).unwrap()),
-$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]
fn test_float_overflow() {
assert_eq!(Uniform::try_from(f64::MIN..f64::MAX), Err(Error::NonFinite));
}
#[test]
#[should_panic]
fn test_float_overflow_single() {
let mut rng = crate::test::rng(252);
rng.random_range(f64::MIN..f64::MAX);
}
#[test]
#[cfg(all(feature = "std", panic = "unwind"))]
fn test_float_assertions() {
use super::SampleUniform;
fn range<T: SampleUniform>(low: T, high: T) -> Result<T, Error> {
let mut rng = crate::test::rng(253);
T::Sampler::sample_single(low, high, &mut rng)
}
macro_rules! t {
($ty:ident, $f_scalar:ident) => {{
let v: &[($f_scalar, $f_scalar)] = &[
($f_scalar::NAN, 0.0),
(1.0, $f_scalar::NAN),
($f_scalar::NAN, $f_scalar::NAN),
(1.0, 0.5),
($f_scalar::MAX, -$f_scalar::MAX),
($f_scalar::INFINITY, $f_scalar::INFINITY),
($f_scalar::NEG_INFINITY, $f_scalar::NEG_INFINITY),
($f_scalar::NEG_INFINITY, 5.0),
(5.0, $f_scalar::INFINITY),
($f_scalar::NAN, $f_scalar::INFINITY),
($f_scalar::NEG_INFINITY, $f_scalar::NAN),
($f_scalar::NEG_INFINITY, $f_scalar::INFINITY),
];
for &(low_scalar, high_scalar) in v.iter() {
for lane in 0..<$ty>::LEN {
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!(range(low, high).is_err());
assert!(Uniform::new(low, high).is_err());
assert!(Uniform::new_inclusive(low, high).is_err());
assert!(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]
fn test_uniform_from_std_range() {
let r = Uniform::try_from(2.0f64..7.0).unwrap();
assert_eq!(r.0.low, 2.0);
assert_eq!(r.0.scale, 5.0);
}
#[test]
fn test_uniform_from_std_range_bad_limits() {
#![allow(clippy::reversed_empty_ranges)]
assert!(Uniform::try_from(100.0..10.0).is_err());
assert!(Uniform::try_from(100.0..100.0).is_err());
}
#[test]
fn test_uniform_from_std_range_inclusive() {
let r = Uniform::try_from(2.0f64..=7.0).unwrap();
assert_eq!(r.0.low, 2.0);
assert!(r.0.scale > 5.0);
assert!(r.0.scale < 5.0 + 1e-14);
}
#[test]
fn test_uniform_from_std_range_inclusive_bad_limits() {
#![allow(clippy::reversed_empty_ranges)]
assert!(Uniform::try_from(100.0..=10.0).is_err());
assert!(Uniform::try_from(100.0..=99.0).is_err());
}
}