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
11use crate::distributions::utils::FloatSIMDUtils;
12use crate::distributions::{Distribution, Standard};
13use crate::Rng;
14use core::mem;
15#[cfg(feature = "simd_support")] use packed_simd::*;
16
17#[cfg(feature = "serde1")]
18use serde::{Serialize, Deserialize};
19
20/// A distribution to sample floating point numbers uniformly in the half-open
21/// interval `(0, 1]`, i.e. including 1 but not 0.
22///
23/// All values that can be generated are of the form `n * ε/2`. For `f32`
24/// the 24 most significant random bits of a `u32` are used and for `f64` the
25/// 53 most significant bits of a `u64` are used. The conversion uses the
26/// multiplicative method.
27///
28/// See also: [`Standard`] which samples from `[0, 1)`, [`Open01`]
29/// which samples from `(0, 1)` and [`Uniform`] which samples from arbitrary
30/// ranges.
31///
32/// # Example
33/// ```
34/// use rand::{thread_rng, Rng};
35/// use rand::distributions::OpenClosed01;
36///
37/// let val: f32 = thread_rng().sample(OpenClosed01);
38/// println!("f32 from (0, 1): {}", val);
39/// ```
40///
41/// [`Standard`]: crate::distributions::Standard
42/// [`Open01`]: crate::distributions::Open01
43/// [`Uniform`]: crate::distributions::uniform::Uniform
44#[derive(Clone, Copy, Debug)]
45#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
46pub struct OpenClosed01;
47
48/// A distribution to sample floating point numbers uniformly in the open
49/// interval `(0, 1)`, i.e. not including either endpoint.
50///
51/// All values that can be generated are of the form `n * ε + ε/2`. For `f32`
52/// the 23 most significant random bits of an `u32` are used, for `f64` 52 from
53/// an `u64`. The conversion uses a transmute-based method.
54///
55/// See also: [`Standard`] which samples from `[0, 1)`, [`OpenClosed01`]
56/// which samples from `(0, 1]` and [`Uniform`] which samples from arbitrary
57/// ranges.
58///
59/// # Example
60/// ```
61/// use rand::{thread_rng, Rng};
62/// use rand::distributions::Open01;
63///
64/// let val: f32 = thread_rng().sample(Open01);
65/// println!("f32 from (0, 1): {}", val);
66/// ```
67///
68/// [`Standard`]: crate::distributions::Standard
69/// [`OpenClosed01`]: crate::distributions::OpenClosed01
70/// [`Uniform`]: crate::distributions::uniform::Uniform
71#[derive(Clone, Copy, Debug)]
72#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
73pub struct Open01;
74
75
76// This trait is needed by both this lib and rand_distr hence is a hidden export
77#[doc(hidden)]
78pub trait IntoFloat {
79 type F;
80
81 /// Helper method to combine the fraction and a constant exponent into a
82 /// float.
83 ///
84 /// Only the least significant bits of `self` may be set, 23 for `f32` and
85 /// 52 for `f64`.
86 /// The resulting value will fall in a range that depends on the exponent.
87 /// As an example the range with exponent 0 will be
88 /// [2<sup>0</sup>..2<sup>1</sup>), which is [1..2).
89 fn into_float_with_exponent(self, exponent: i32) -> Self::F;
90}
91
92macro_rules! float_impls {
93 ($ty:ident, $uty:ident, $f_scalar:ident, $u_scalar:ty,
94 $fraction_bits:expr, $exponent_bias:expr) => {
95 impl IntoFloat for $uty {
96 type F = $ty;
97 #[inline(always)]
98 fn into_float_with_exponent(self, exponent: i32) -> $ty {
99 // The exponent is encoded using an offset-binary representation
100 let exponent_bits: $u_scalar =
101 (($exponent_bias + exponent) as $u_scalar) << $fraction_bits;
102 $ty::from_bits(self | exponent_bits)
103 }
104 }
105
106 impl Distribution<$ty> for Standard {
107 fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
108 // Multiply-based method; 24/53 random bits; [0, 1) interval.
109 // We use the most significant bits because for simple RNGs
110 // those are usually more random.
111 let float_size = mem::size_of::<$f_scalar>() as u32 * 8;
112 let precision = $fraction_bits + 1;
113 let scale = 1.0 / ((1 as $u_scalar << precision) as $f_scalar);
114
115 let value: $uty = rng.gen();
116 let value = value >> (float_size - precision);
117 scale * $ty::cast_from_int(value)
118 }
119 }
120
121 impl Distribution<$ty> for OpenClosed01 {
122 fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
123 // Multiply-based method; 24/53 random bits; (0, 1] interval.
124 // We use the most significant bits because for simple RNGs
125 // those are usually more random.
126 let float_size = mem::size_of::<$f_scalar>() as u32 * 8;
127 let precision = $fraction_bits + 1;
128 let scale = 1.0 / ((1 as $u_scalar << precision) as $f_scalar);
129
130 let value: $uty = rng.gen();
131 let value = value >> (float_size - precision);
132 // Add 1 to shift up; will not overflow because of right-shift:
133 scale * $ty::cast_from_int(value + 1)
134 }
135 }
136
137 impl Distribution<$ty> for Open01 {
138 fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
139 // Transmute-based method; 23/52 random bits; (0, 1) interval.
140 // We use the most significant bits because for simple RNGs
141 // those are usually more random.
142 use core::$f_scalar::EPSILON;
143 let float_size = mem::size_of::<$f_scalar>() as u32 * 8;
144
145 let value: $uty = rng.gen();
146 let fraction = value >> (float_size - $fraction_bits);
147 fraction.into_float_with_exponent(0) - (1.0 - EPSILON / 2.0)
148 }
149 }
150 }
151}
152
153float_impls! { f32, u32, f32, u32, 23, 127 }
154float_impls! { f64, u64, f64, u64, 52, 1023 }
155
156#[cfg(feature = "simd_support")]
157float_impls! { f32x2, u32x2, f32, u32, 23, 127 }
158#[cfg(feature = "simd_support")]
159float_impls! { f32x4, u32x4, f32, u32, 23, 127 }
160#[cfg(feature = "simd_support")]
161float_impls! { f32x8, u32x8, f32, u32, 23, 127 }
162#[cfg(feature = "simd_support")]
163float_impls! { f32x16, u32x16, f32, u32, 23, 127 }
164
165#[cfg(feature = "simd_support")]
166float_impls! { f64x2, u64x2, f64, u64, 52, 1023 }
167#[cfg(feature = "simd_support")]
168float_impls! { f64x4, u64x4, f64, u64, 52, 1023 }
169#[cfg(feature = "simd_support")]
170float_impls! { f64x8, u64x8, f64, u64, 52, 1023 }
171
172
173#[cfg(test)]
174mod tests {
175 use super::*;
176 use crate::rngs::mock::StepRng;
177
178 const EPSILON32: f32 = ::core::f32::EPSILON;
179 const EPSILON64: f64 = ::core::f64::EPSILON;
180
181 macro_rules! test_f32 {
182 ($fnn:ident, $ty:ident, $ZERO:expr, $EPSILON:expr) => {
183 #[test]
184 fn $fnn() {
185 // Standard
186 let mut zeros = StepRng::new(0, 0);
187 assert_eq!(zeros.gen::<$ty>(), $ZERO);
188 let mut one = StepRng::new(1 << 8 | 1 << (8 + 32), 0);
189 assert_eq!(one.gen::<$ty>(), $EPSILON / 2.0);
190 let mut max = StepRng::new(!0, 0);
191 assert_eq!(max.gen::<$ty>(), 1.0 - $EPSILON / 2.0);
192
193 // OpenClosed01
194 let mut zeros = StepRng::new(0, 0);
195 assert_eq!(zeros.sample::<$ty, _>(OpenClosed01), 0.0 + $EPSILON / 2.0);
196 let mut one = StepRng::new(1 << 8 | 1 << (8 + 32), 0);
197 assert_eq!(one.sample::<$ty, _>(OpenClosed01), $EPSILON);
198 let mut max = StepRng::new(!0, 0);
199 assert_eq!(max.sample::<$ty, _>(OpenClosed01), $ZERO + 1.0);
200
201 // Open01
202 let mut zeros = StepRng::new(0, 0);
203 assert_eq!(zeros.sample::<$ty, _>(Open01), 0.0 + $EPSILON / 2.0);
204 let mut one = StepRng::new(1 << 9 | 1 << (9 + 32), 0);
205 assert_eq!(one.sample::<$ty, _>(Open01), $EPSILON / 2.0 * 3.0);
206 let mut max = StepRng::new(!0, 0);
207 assert_eq!(max.sample::<$ty, _>(Open01), 1.0 - $EPSILON / 2.0);
208 }
209 };
210 }
211 test_f32! { f32_edge_cases, f32, 0.0, EPSILON32 }
212 #[cfg(feature = "simd_support")]
213 test_f32! { f32x2_edge_cases, f32x2, f32x2::splat(0.0), f32x2::splat(EPSILON32) }
214 #[cfg(feature = "simd_support")]
215 test_f32! { f32x4_edge_cases, f32x4, f32x4::splat(0.0), f32x4::splat(EPSILON32) }
216 #[cfg(feature = "simd_support")]
217 test_f32! { f32x8_edge_cases, f32x8, f32x8::splat(0.0), f32x8::splat(EPSILON32) }
218 #[cfg(feature = "simd_support")]
219 test_f32! { f32x16_edge_cases, f32x16, f32x16::splat(0.0), f32x16::splat(EPSILON32) }
220
221 macro_rules! test_f64 {
222 ($fnn:ident, $ty:ident, $ZERO:expr, $EPSILON:expr) => {
223 #[test]
224 fn $fnn() {
225 // Standard
226 let mut zeros = StepRng::new(0, 0);
227 assert_eq!(zeros.gen::<$ty>(), $ZERO);
228 let mut one = StepRng::new(1 << 11, 0);
229 assert_eq!(one.gen::<$ty>(), $EPSILON / 2.0);
230 let mut max = StepRng::new(!0, 0);
231 assert_eq!(max.gen::<$ty>(), 1.0 - $EPSILON / 2.0);
232
233 // OpenClosed01
234 let mut zeros = StepRng::new(0, 0);
235 assert_eq!(zeros.sample::<$ty, _>(OpenClosed01), 0.0 + $EPSILON / 2.0);
236 let mut one = StepRng::new(1 << 11, 0);
237 assert_eq!(one.sample::<$ty, _>(OpenClosed01), $EPSILON);
238 let mut max = StepRng::new(!0, 0);
239 assert_eq!(max.sample::<$ty, _>(OpenClosed01), $ZERO + 1.0);
240
241 // Open01
242 let mut zeros = StepRng::new(0, 0);
243 assert_eq!(zeros.sample::<$ty, _>(Open01), 0.0 + $EPSILON / 2.0);
244 let mut one = StepRng::new(1 << 12, 0);
245 assert_eq!(one.sample::<$ty, _>(Open01), $EPSILON / 2.0 * 3.0);
246 let mut max = StepRng::new(!0, 0);
247 assert_eq!(max.sample::<$ty, _>(Open01), 1.0 - $EPSILON / 2.0);
248 }
249 };
250 }
251 test_f64! { f64_edge_cases, f64, 0.0, EPSILON64 }
252 #[cfg(feature = "simd_support")]
253 test_f64! { f64x2_edge_cases, f64x2, f64x2::splat(0.0), f64x2::splat(EPSILON64) }
254 #[cfg(feature = "simd_support")]
255 test_f64! { f64x4_edge_cases, f64x4, f64x4::splat(0.0), f64x4::splat(EPSILON64) }
256 #[cfg(feature = "simd_support")]
257 test_f64! { f64x8_edge_cases, f64x8, f64x8::splat(0.0), f64x8::splat(EPSILON64) }
258
259 #[test]
260 fn value_stability() {
261 fn test_samples<T: Copy + core::fmt::Debug + PartialEq, D: Distribution<T>>(
262 distr: &D, zero: T, expected: &[T],
263 ) {
264 let mut rng = crate::test::rng(0x6f44f5646c2a7334);
265 let mut buf = [zero; 3];
266 for x in &mut buf {
267 *x = rng.sample(&distr);
268 }
269 assert_eq!(&buf, expected);
270 }
271
272 test_samples(&Standard, 0f32, &[0.0035963655, 0.7346052, 0.09778172]);
273 test_samples(&Standard, 0f64, &[
274 0.7346051961657583,
275 0.20298547462974248,
276 0.8166436635290655,
277 ]);
278
279 test_samples(&OpenClosed01, 0f32, &[0.003596425, 0.73460525, 0.09778178]);
280 test_samples(&OpenClosed01, 0f64, &[
281 0.7346051961657584,
282 0.2029854746297426,
283 0.8166436635290656,
284 ]);
285
286 test_samples(&Open01, 0f32, &[0.0035963655, 0.73460525, 0.09778172]);
287 test_samples(&Open01, 0f64, &[
288 0.7346051961657584,
289 0.20298547462974248,
290 0.8166436635290656,
291 ]);
292
293 #[cfg(feature = "simd_support")]
294 {
295 // We only test a sub-set of types here. Values are identical to
296 // non-SIMD types; we assume this pattern continues across all
297 // SIMD types.
298
299 test_samples(&Standard, f32x2::new(0.0, 0.0), &[
300 f32x2::new(0.0035963655, 0.7346052),
301 f32x2::new(0.09778172, 0.20298547),
302 f32x2::new(0.34296435, 0.81664366),
303 ]);
304
305 test_samples(&Standard, f64x2::new(0.0, 0.0), &[
306 f64x2::new(0.7346051961657583, 0.20298547462974248),
307 f64x2::new(0.8166436635290655, 0.7423708925400552),
308 f64x2::new(0.16387782224016323, 0.9087068770169618),
309 ]);
310 }
311 }
312}
313