313 lines
12 KiB
Rust
313 lines
12 KiB
Rust
// Copyright 2018 Developers of the Rand project.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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//! Basic floating-point number distributions
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use crate::distributions::utils::FloatSIMDUtils;
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use crate::distributions::{Distribution, Standard};
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use crate::Rng;
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use core::mem;
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#[cfg(feature = "simd_support")] use packed_simd::*;
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#[cfg(feature = "serde1")]
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use serde::{Serialize, Deserialize};
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/// A distribution to sample floating point numbers uniformly in the half-open
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/// interval `(0, 1]`, i.e. including 1 but not 0.
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///
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/// All values that can be generated are of the form `n * ε/2`. For `f32`
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/// the 24 most significant random bits of a `u32` are used and for `f64` the
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/// 53 most significant bits of a `u64` are used. The conversion uses the
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/// multiplicative method.
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///
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/// See also: [`Standard`] which samples from `[0, 1)`, [`Open01`]
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/// which samples from `(0, 1)` and [`Uniform`] which samples from arbitrary
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/// ranges.
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///
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/// # Example
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/// ```
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/// use rand::{thread_rng, Rng};
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/// use rand::distributions::OpenClosed01;
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///
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/// let val: f32 = thread_rng().sample(OpenClosed01);
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/// println!("f32 from (0, 1): {}", val);
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/// ```
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///
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/// [`Standard`]: crate::distributions::Standard
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/// [`Open01`]: crate::distributions::Open01
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/// [`Uniform`]: crate::distributions::uniform::Uniform
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#[derive(Clone, Copy, Debug)]
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#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
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pub struct OpenClosed01;
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/// A distribution to sample floating point numbers uniformly in the open
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/// interval `(0, 1)`, i.e. not including either endpoint.
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///
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/// All values that can be generated are of the form `n * ε + ε/2`. For `f32`
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/// the 23 most significant random bits of an `u32` are used, for `f64` 52 from
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/// an `u64`. The conversion uses a transmute-based method.
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///
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/// See also: [`Standard`] which samples from `[0, 1)`, [`OpenClosed01`]
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/// which samples from `(0, 1]` and [`Uniform`] which samples from arbitrary
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/// ranges.
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///
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/// # Example
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/// ```
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/// use rand::{thread_rng, Rng};
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/// use rand::distributions::Open01;
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///
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/// let val: f32 = thread_rng().sample(Open01);
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/// println!("f32 from (0, 1): {}", val);
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/// ```
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///
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/// [`Standard`]: crate::distributions::Standard
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/// [`OpenClosed01`]: crate::distributions::OpenClosed01
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/// [`Uniform`]: crate::distributions::uniform::Uniform
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#[derive(Clone, Copy, Debug)]
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#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
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pub struct Open01;
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// This trait is needed by both this lib and rand_distr hence is a hidden export
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#[doc(hidden)]
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pub trait IntoFloat {
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type F;
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/// Helper method to combine the fraction and a constant exponent into a
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/// float.
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///
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/// Only the least significant bits of `self` may be set, 23 for `f32` and
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/// 52 for `f64`.
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/// The resulting value will fall in a range that depends on the exponent.
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/// As an example the range with exponent 0 will be
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/// [2<sup>0</sup>..2<sup>1</sup>), which is [1..2).
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fn into_float_with_exponent(self, exponent: i32) -> Self::F;
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}
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macro_rules! float_impls {
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($ty:ident, $uty:ident, $f_scalar:ident, $u_scalar:ty,
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$fraction_bits:expr, $exponent_bias:expr) => {
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impl IntoFloat for $uty {
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type F = $ty;
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#[inline(always)]
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fn into_float_with_exponent(self, exponent: i32) -> $ty {
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// The exponent is encoded using an offset-binary representation
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let exponent_bits: $u_scalar =
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(($exponent_bias + exponent) as $u_scalar) << $fraction_bits;
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$ty::from_bits(self | exponent_bits)
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}
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}
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impl Distribution<$ty> for Standard {
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fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
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// Multiply-based method; 24/53 random bits; [0, 1) interval.
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// We use the most significant bits because for simple RNGs
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// those are usually more random.
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let float_size = mem::size_of::<$f_scalar>() as u32 * 8;
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let precision = $fraction_bits + 1;
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let scale = 1.0 / ((1 as $u_scalar << precision) as $f_scalar);
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let value: $uty = rng.gen();
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let value = value >> (float_size - precision);
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scale * $ty::cast_from_int(value)
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}
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}
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impl Distribution<$ty> for OpenClosed01 {
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fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
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// Multiply-based method; 24/53 random bits; (0, 1] interval.
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// We use the most significant bits because for simple RNGs
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// those are usually more random.
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let float_size = mem::size_of::<$f_scalar>() as u32 * 8;
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let precision = $fraction_bits + 1;
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let scale = 1.0 / ((1 as $u_scalar << precision) as $f_scalar);
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let value: $uty = rng.gen();
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let value = value >> (float_size - precision);
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// Add 1 to shift up; will not overflow because of right-shift:
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scale * $ty::cast_from_int(value + 1)
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}
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}
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impl Distribution<$ty> for Open01 {
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fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
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// Transmute-based method; 23/52 random bits; (0, 1) interval.
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// We use the most significant bits because for simple RNGs
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// those are usually more random.
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use core::$f_scalar::EPSILON;
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let float_size = mem::size_of::<$f_scalar>() as u32 * 8;
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let value: $uty = rng.gen();
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let fraction = value >> (float_size - $fraction_bits);
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fraction.into_float_with_exponent(0) - (1.0 - EPSILON / 2.0)
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}
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}
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}
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}
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float_impls! { f32, u32, f32, u32, 23, 127 }
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float_impls! { f64, u64, f64, u64, 52, 1023 }
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#[cfg(feature = "simd_support")]
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float_impls! { f32x2, u32x2, f32, u32, 23, 127 }
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#[cfg(feature = "simd_support")]
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float_impls! { f32x4, u32x4, f32, u32, 23, 127 }
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#[cfg(feature = "simd_support")]
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float_impls! { f32x8, u32x8, f32, u32, 23, 127 }
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#[cfg(feature = "simd_support")]
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float_impls! { f32x16, u32x16, f32, u32, 23, 127 }
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#[cfg(feature = "simd_support")]
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float_impls! { f64x2, u64x2, f64, u64, 52, 1023 }
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#[cfg(feature = "simd_support")]
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float_impls! { f64x4, u64x4, f64, u64, 52, 1023 }
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#[cfg(feature = "simd_support")]
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float_impls! { f64x8, u64x8, f64, u64, 52, 1023 }
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#[cfg(test)]
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mod tests {
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use super::*;
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use crate::rngs::mock::StepRng;
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const EPSILON32: f32 = ::core::f32::EPSILON;
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const EPSILON64: f64 = ::core::f64::EPSILON;
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macro_rules! test_f32 {
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($fnn:ident, $ty:ident, $ZERO:expr, $EPSILON:expr) => {
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#[test]
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fn $fnn() {
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// Standard
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let mut zeros = StepRng::new(0, 0);
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assert_eq!(zeros.gen::<$ty>(), $ZERO);
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let mut one = StepRng::new(1 << 8 | 1 << (8 + 32), 0);
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assert_eq!(one.gen::<$ty>(), $EPSILON / 2.0);
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let mut max = StepRng::new(!0, 0);
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assert_eq!(max.gen::<$ty>(), 1.0 - $EPSILON / 2.0);
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// OpenClosed01
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let mut zeros = StepRng::new(0, 0);
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assert_eq!(zeros.sample::<$ty, _>(OpenClosed01), 0.0 + $EPSILON / 2.0);
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let mut one = StepRng::new(1 << 8 | 1 << (8 + 32), 0);
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assert_eq!(one.sample::<$ty, _>(OpenClosed01), $EPSILON);
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let mut max = StepRng::new(!0, 0);
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assert_eq!(max.sample::<$ty, _>(OpenClosed01), $ZERO + 1.0);
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// Open01
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let mut zeros = StepRng::new(0, 0);
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assert_eq!(zeros.sample::<$ty, _>(Open01), 0.0 + $EPSILON / 2.0);
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let mut one = StepRng::new(1 << 9 | 1 << (9 + 32), 0);
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assert_eq!(one.sample::<$ty, _>(Open01), $EPSILON / 2.0 * 3.0);
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let mut max = StepRng::new(!0, 0);
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assert_eq!(max.sample::<$ty, _>(Open01), 1.0 - $EPSILON / 2.0);
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}
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};
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}
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test_f32! { f32_edge_cases, f32, 0.0, EPSILON32 }
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#[cfg(feature = "simd_support")]
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test_f32! { f32x2_edge_cases, f32x2, f32x2::splat(0.0), f32x2::splat(EPSILON32) }
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#[cfg(feature = "simd_support")]
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test_f32! { f32x4_edge_cases, f32x4, f32x4::splat(0.0), f32x4::splat(EPSILON32) }
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#[cfg(feature = "simd_support")]
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test_f32! { f32x8_edge_cases, f32x8, f32x8::splat(0.0), f32x8::splat(EPSILON32) }
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#[cfg(feature = "simd_support")]
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test_f32! { f32x16_edge_cases, f32x16, f32x16::splat(0.0), f32x16::splat(EPSILON32) }
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macro_rules! test_f64 {
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($fnn:ident, $ty:ident, $ZERO:expr, $EPSILON:expr) => {
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#[test]
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fn $fnn() {
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// Standard
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let mut zeros = StepRng::new(0, 0);
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assert_eq!(zeros.gen::<$ty>(), $ZERO);
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let mut one = StepRng::new(1 << 11, 0);
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assert_eq!(one.gen::<$ty>(), $EPSILON / 2.0);
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let mut max = StepRng::new(!0, 0);
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assert_eq!(max.gen::<$ty>(), 1.0 - $EPSILON / 2.0);
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// OpenClosed01
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let mut zeros = StepRng::new(0, 0);
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assert_eq!(zeros.sample::<$ty, _>(OpenClosed01), 0.0 + $EPSILON / 2.0);
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let mut one = StepRng::new(1 << 11, 0);
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assert_eq!(one.sample::<$ty, _>(OpenClosed01), $EPSILON);
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let mut max = StepRng::new(!0, 0);
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assert_eq!(max.sample::<$ty, _>(OpenClosed01), $ZERO + 1.0);
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// Open01
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let mut zeros = StepRng::new(0, 0);
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assert_eq!(zeros.sample::<$ty, _>(Open01), 0.0 + $EPSILON / 2.0);
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let mut one = StepRng::new(1 << 12, 0);
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assert_eq!(one.sample::<$ty, _>(Open01), $EPSILON / 2.0 * 3.0);
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let mut max = StepRng::new(!0, 0);
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assert_eq!(max.sample::<$ty, _>(Open01), 1.0 - $EPSILON / 2.0);
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}
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};
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}
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test_f64! { f64_edge_cases, f64, 0.0, EPSILON64 }
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#[cfg(feature = "simd_support")]
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test_f64! { f64x2_edge_cases, f64x2, f64x2::splat(0.0), f64x2::splat(EPSILON64) }
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#[cfg(feature = "simd_support")]
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test_f64! { f64x4_edge_cases, f64x4, f64x4::splat(0.0), f64x4::splat(EPSILON64) }
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#[cfg(feature = "simd_support")]
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test_f64! { f64x8_edge_cases, f64x8, f64x8::splat(0.0), f64x8::splat(EPSILON64) }
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#[test]
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fn value_stability() {
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fn test_samples<T: Copy + core::fmt::Debug + PartialEq, D: Distribution<T>>(
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distr: &D, zero: T, expected: &[T],
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) {
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let mut rng = crate::test::rng(0x6f44f5646c2a7334);
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let mut buf = [zero; 3];
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for x in &mut buf {
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*x = rng.sample(&distr);
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}
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assert_eq!(&buf, expected);
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}
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test_samples(&Standard, 0f32, &[0.0035963655, 0.7346052, 0.09778172]);
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test_samples(&Standard, 0f64, &[
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0.7346051961657583,
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0.20298547462974248,
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0.8166436635290655,
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]);
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test_samples(&OpenClosed01, 0f32, &[0.003596425, 0.73460525, 0.09778178]);
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test_samples(&OpenClosed01, 0f64, &[
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0.7346051961657584,
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0.2029854746297426,
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0.8166436635290656,
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]);
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test_samples(&Open01, 0f32, &[0.0035963655, 0.73460525, 0.09778172]);
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test_samples(&Open01, 0f64, &[
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0.7346051961657584,
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0.20298547462974248,
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0.8166436635290656,
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]);
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#[cfg(feature = "simd_support")]
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{
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// We only test a sub-set of types here. Values are identical to
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// non-SIMD types; we assume this pattern continues across all
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// SIMD types.
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test_samples(&Standard, f32x2::new(0.0, 0.0), &[
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f32x2::new(0.0035963655, 0.7346052),
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f32x2::new(0.09778172, 0.20298547),
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f32x2::new(0.34296435, 0.81664366),
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]);
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test_samples(&Standard, f64x2::new(0.0, 0.0), &[
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f64x2::new(0.7346051961657583, 0.20298547462974248),
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f64x2::new(0.8166436635290655, 0.7423708925400552),
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f64x2::new(0.16387782224016323, 0.9087068770169618),
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]);
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}
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}
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}
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