vendor/rand/src/distributions/float.rs

   1 // Copyright 2018 Developers of the Rand project.
   2 //
   3 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
   4 // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
   5 // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
   6 // option. This file may not be copied, modified, or distributed
   7 // except according to those terms.
   8
   9 //! Basic floating-point number distributions
  10
  11 use core::mem;
  12 use crate::Rng;
  13 use crate::distributions::{Distribution, Standard};
  14 use crate::distributions::utils::FloatSIMDUtils;
  15 #[cfg(feature="simd_support")]
  16 use packed_simd::*;
  17
  18 /// A distribution to sample floating point numbers uniformly in the half-open
  19 /// interval `(0, 1]`, i.e. including 1 but not 0.
  20 ///
  21 /// All values that can be generated are of the form `n * ε/2`. For `f32`
  22 /// the 23 most significant random bits of a `u32` are used and for `f64` the
  23 /// 53 most significant bits of a `u64` are used. The conversion uses the
  24 /// multiplicative method.
  25 ///
  26 /// See also: [`Standard`] which samples from `[0, 1)`, [`Open01`]
  27 /// which samples from `(0, 1)` and [`Uniform`] which samples from arbitrary
  28 /// ranges.
  29 ///
  30 /// # Example
  31 /// ```
  32 /// use rand::{thread_rng, Rng};
  33 /// use rand::distributions::OpenClosed01;
  34 ///
  35 /// let val: f32 = thread_rng().sample(OpenClosed01);
  36 /// println!("f32 from (0, 1): {}", val);
  37 /// ```
  38 ///
  39 /// [`Standard`]: crate::distributions::Standard
  40 /// [`Open01`]: crate::distributions::Open01
  41 /// [`Uniform`]: crate::distributions::uniform::Uniform
  42 #[derive(Clone, Copy, Debug)]
  43 pub struct OpenClosed01;
  44
  45 /// A distribution to sample floating point numbers uniformly in the open
  46 /// interval `(0, 1)`, i.e. not including either endpoint.
  47 ///
  48 /// All values that can be generated are of the form `n * ε + ε/2`. For `f32`
  49 /// the 22 most significant random bits of an `u32` are used, for `f64` 52 from
  50 /// an `u64`. The conversion uses a transmute-based method.
  51 ///
  52 /// See also: [`Standard`] which samples from `[0, 1)`, [`OpenClosed01`]
  53 /// which samples from `(0, 1]` and [`Uniform`] which samples from arbitrary
  54 /// ranges.
  55 ///
  56 /// # Example
  57 /// ```
  58 /// use rand::{thread_rng, Rng};
  59 /// use rand::distributions::Open01;
  60 ///
  61 /// let val: f32 = thread_rng().sample(Open01);
  62 /// println!("f32 from (0, 1): {}", val);
  63 /// ```
  64 ///
  65 /// [`Standard`]: crate::distributions::Standard
  66 /// [`OpenClosed01`]: crate::distributions::OpenClosed01
  67 /// [`Uniform`]: crate::distributions::uniform::Uniform
  68 #[derive(Clone, Copy, Debug)]
  69 pub struct Open01;
  70
  71
  72 // This trait is needed by both this lib and rand_distr hence is a hidden export
  73 #[doc(hidden)]
  74 pub trait IntoFloat {
  75     type F;
  76
  77     /// Helper method to combine the fraction and a contant exponent into a
  78     /// float.
  79     ///
  80     /// Only the least significant bits of `self` may be set, 23 for `f32` and
  81     /// 52 for `f64`.
  82     /// The resulting value will fall in a range that depends on the exponent.
  83     /// As an example the range with exponent 0 will be
  84     /// [2<sup>0</sup>..2<sup>1</sup>), which is [1..2).
  85     fn into_float_with_exponent(self, exponent: i32) -> Self::F;
  86 }
  87
  88 macro_rules! float_impls {
  89     ($ty:ident, $uty:ident, $f_scalar:ident, $u_scalar:ty,
  90      $fraction_bits:expr, $exponent_bias:expr) => {
  91         impl IntoFloat for $uty {
  92             type F = $ty;
  93             #[inline(always)]
  94             fn into_float_with_exponent(self, exponent: i32) -> $ty {
  95                 // The exponent is encoded using an offset-binary representation
  96                 let exponent_bits: $u_scalar =
  97                     (($exponent_bias + exponent) as $u_scalar) << $fraction_bits;
  98                 // TODO: use from_bits when min compiler > 1.25 (see #545)
  99                 // $ty::from_bits(self | exponent_bits)
 100                 unsafe{ mem::transmute(self | exponent_bits) }
 101             }
 102         }
 103
 104         impl Distribution<$ty> for Standard {
 105             fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
 106                 // Multiply-based method; 24/53 random bits; [0, 1) interval.
 107                 // We use the most significant bits because for simple RNGs
 108                 // those are usually more random.
 109                 let float_size = mem::size_of::<$f_scalar>() as u32 * 8;
 110                 let precision = $fraction_bits + 1;
 111                 let scale = 1.0 / ((1 as $u_scalar << precision) as $f_scalar);
 112
 113                 let value: $uty = rng.gen();
 114                 let value = value >> (float_size - precision);
 115                 scale * $ty::cast_from_int(value)
 116             }
 117         }
 118
 119         impl Distribution<$ty> for OpenClosed01 {
 120             fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
 121                 // Multiply-based method; 24/53 random bits; (0, 1] interval.
 122                 // We use the most significant bits because for simple RNGs
 123                 // those are usually more random.
 124                 let float_size = mem::size_of::<$f_scalar>() as u32 * 8;
 125                 let precision = $fraction_bits + 1;
 126                 let scale = 1.0 / ((1 as $u_scalar << precision) as $f_scalar);
 127
 128                 let value: $uty = rng.gen();
 129                 let value = value >> (float_size - precision);
 130                 // Add 1 to shift up; will not overflow because of right-shift:
 131                 scale * $ty::cast_from_int(value + 1)
 132             }
 133         }
 134
 135         impl Distribution<$ty> for Open01 {
 136             fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
 137                 // Transmute-based method; 23/52 random bits; (0, 1) interval.
 138                 // We use the most significant bits because for simple RNGs
 139                 // those are usually more random.
 140                 use core::$f_scalar::EPSILON;
 141                 let float_size = mem::size_of::<$f_scalar>() as u32 * 8;
 142
 143                 let value: $uty = rng.gen();
 144                 let fraction = value >> (float_size - $fraction_bits);
 145                 fraction.into_float_with_exponent(0) - (1.0 - EPSILON / 2.0)
 146             }
 147         }
 148     }
 149 }
 150
 151 float_impls! { f32, u32, f32, u32, 23, 127 }
 152 float_impls! { f64, u64, f64, u64, 52, 1023 }
 153
 154 #[cfg(feature="simd_support")]
 155 float_impls! { f32x2, u32x2, f32, u32, 23, 127 }
 156 #[cfg(feature="simd_support")]
 157 float_impls! { f32x4, u32x4, f32, u32, 23, 127 }
 158 #[cfg(feature="simd_support")]
 159 float_impls! { f32x8, u32x8, f32, u32, 23, 127 }
 160 #[cfg(feature="simd_support")]
 161 float_impls! { f32x16, u32x16, f32, u32, 23, 127 }
 162
 163 #[cfg(feature="simd_support")]
 164 float_impls! { f64x2, u64x2, f64, u64, 52, 1023 }
 165 #[cfg(feature="simd_support")]
 166 float_impls! { f64x4, u64x4, f64, u64, 52, 1023 }
 167 #[cfg(feature="simd_support")]
 168 float_impls! { f64x8, u64x8, f64, u64, 52, 1023 }
 169
 170
 171 #[cfg(test)]
 172 mod tests {
 173     use crate::Rng;
 174     use crate::distributions::{Open01, OpenClosed01};
 175     use crate::rngs::mock::StepRng;
 176     #[cfg(feature="simd_support")]
 177     use packed_simd::*;
 178
 179     const EPSILON32: f32 = ::core::f32::EPSILON;
 180     const EPSILON64: f64 = ::core::f64::EPSILON;
 181
 182     macro_rules! test_f32 {
 183         ($fnn:ident, $ty:ident, $ZERO:expr, $EPSILON:expr) => {
 184             #[test]
 185             fn $fnn() {
 186                 // Standard
 187                 let mut zeros = StepRng::new(0, 0);
 188                 assert_eq!(zeros.gen::<$ty>(), $ZERO);
 189                 let mut one = StepRng::new(1 << 8 | 1 << (8 + 32), 0);
 190                 assert_eq!(one.gen::<$ty>(), $EPSILON / 2.0);
 191                 let mut max = StepRng::new(!0, 0);
 192                 assert_eq!(max.gen::<$ty>(), 1.0 - $EPSILON / 2.0);
 193
 194                 // OpenClosed01
 195                 let mut zeros = StepRng::new(0, 0);
 196                 assert_eq!(zeros.sample::<$ty, _>(OpenClosed01),
 197                            0.0 + $EPSILON / 2.0);
 198                 let mut one = StepRng::new(1 << 8 | 1 << (8 + 32), 0);
 199                 assert_eq!(one.sample::<$ty, _>(OpenClosed01), $EPSILON);
 200                 let mut max = StepRng::new(!0, 0);
 201                 assert_eq!(max.sample::<$ty, _>(OpenClosed01), $ZERO + 1.0);
 202
 203                 // Open01
 204                 let mut zeros = StepRng::new(0, 0);
 205                 assert_eq!(zeros.sample::<$ty, _>(Open01), 0.0 + $EPSILON / 2.0);
 206                 let mut one = StepRng::new(1 << 9 | 1 << (9 + 32), 0);
 207                 assert_eq!(one.sample::<$ty, _>(Open01), $EPSILON / 2.0 * 3.0);
 208                 let mut max = StepRng::new(!0, 0);
 209                 assert_eq!(max.sample::<$ty, _>(Open01), 1.0 - $EPSILON / 2.0);
 210             }
 211         }
 212     }
 213     test_f32! { f32_edge_cases, f32, 0.0, EPSILON32 }
 214     #[cfg(feature="simd_support")]
 215     test_f32! { f32x2_edge_cases, f32x2, f32x2::splat(0.0), f32x2::splat(EPSILON32) }
 216     #[cfg(feature="simd_support")]
 217     test_f32! { f32x4_edge_cases, f32x4, f32x4::splat(0.0), f32x4::splat(EPSILON32) }
 218     #[cfg(feature="simd_support")]
 219     test_f32! { f32x8_edge_cases, f32x8, f32x8::splat(0.0), f32x8::splat(EPSILON32) }
 220     #[cfg(feature="simd_support")]
 221     test_f32! { f32x16_edge_cases, f32x16, f32x16::splat(0.0), f32x16::splat(EPSILON32) }
 222
 223     macro_rules! test_f64 {
 224         ($fnn:ident, $ty:ident, $ZERO:expr, $EPSILON:expr) => {
 225             #[test]
 226             fn $fnn() {
 227                 // Standard
 228                 let mut zeros = StepRng::new(0, 0);
 229                 assert_eq!(zeros.gen::<$ty>(), $ZERO);
 230                 let mut one = StepRng::new(1 << 11, 0);
 231                 assert_eq!(one.gen::<$ty>(), $EPSILON / 2.0);
 232                 let mut max = StepRng::new(!0, 0);
 233                 assert_eq!(max.gen::<$ty>(), 1.0 - $EPSILON / 2.0);
 234
 235                 // OpenClosed01
 236                 let mut zeros = StepRng::new(0, 0);
 237                 assert_eq!(zeros.sample::<$ty, _>(OpenClosed01),
 238                            0.0 + $EPSILON / 2.0);
 239                 let mut one = StepRng::new(1 << 11, 0);
 240                 assert_eq!(one.sample::<$ty, _>(OpenClosed01), $EPSILON);
 241                 let mut max = StepRng::new(!0, 0);
 242                 assert_eq!(max.sample::<$ty, _>(OpenClosed01), $ZERO + 1.0);
 243
 244                 // Open01
 245                 let mut zeros = StepRng::new(0, 0);
 246                 assert_eq!(zeros.sample::<$ty, _>(Open01), 0.0 + $EPSILON / 2.0);
 247                 let mut one = StepRng::new(1 << 12, 0);
 248                 assert_eq!(one.sample::<$ty, _>(Open01), $EPSILON / 2.0 * 3.0);
 249                 let mut max = StepRng::new(!0, 0);
 250                 assert_eq!(max.sample::<$ty, _>(Open01), 1.0 - $EPSILON / 2.0);
 251             }
 252         }
 253     }
 254     test_f64! { f64_edge_cases, f64, 0.0, EPSILON64 }
 255     #[cfg(feature="simd_support")]
 256     test_f64! { f64x2_edge_cases, f64x2, f64x2::splat(0.0), f64x2::splat(EPSILON64) }
 257     #[cfg(feature="simd_support")]
 258     test_f64! { f64x4_edge_cases, f64x4, f64x4::splat(0.0), f64x4::splat(EPSILON64) }
 259     #[cfg(feature="simd_support")]
 260     test_f64! { f64x8_edge_cases, f64x8, f64x8::splat(0.0), f64x8::splat(EPSILON64) }
 261 }