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