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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 crate::distributions::utils::FloatSIMDUtils; | |
12 | use crate::distributions::{Distribution, Standard}; | |
13 | use crate::Rng; | |
14 | use core::mem; | |
15 | #[cfg(feature = "simd_support")] use packed_simd::*; | |
16 | ||
17 | #[cfg(feature = "serde1")] | |
18 | use 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))] | |
46 | pub 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))] | |
73 | pub struct Open01; | |
74 | ||
75 | ||
76 | // This trait is needed by both this lib and rand_distr hence is a hidden export | |
77 | #[doc(hidden)] | |
78 | pub trait IntoFloat { | |
79 | type F; | |
80 | ||
04454e1e | 81 | /// Helper method to combine the fraction and a constant exponent into a |
cdc7bbd5 XL |
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 | ||
92 | macro_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 - $fraction_bits); | |
147 | fraction.into_float_with_exponent(0) - (1.0 - EPSILON / 2.0) | |
148 | } | |
149 | } | |
150 | } | |
151 | } | |
152 | ||
153 | float_impls! { f32, u32, f32, u32, 23, 127 } | |
154 | float_impls! { f64, u64, f64, u64, 52, 1023 } | |
155 | ||
156 | #[cfg(feature = "simd_support")] | |
157 | float_impls! { f32x2, u32x2, f32, u32, 23, 127 } | |
158 | #[cfg(feature = "simd_support")] | |
159 | float_impls! { f32x4, u32x4, f32, u32, 23, 127 } | |
160 | #[cfg(feature = "simd_support")] | |
161 | float_impls! { f32x8, u32x8, f32, u32, 23, 127 } | |
162 | #[cfg(feature = "simd_support")] | |
163 | float_impls! { f32x16, u32x16, f32, u32, 23, 127 } | |
164 | ||
165 | #[cfg(feature = "simd_support")] | |
166 | float_impls! { f64x2, u64x2, f64, u64, 52, 1023 } | |
167 | #[cfg(feature = "simd_support")] | |
168 | float_impls! { f64x4, u64x4, f64, u64, 52, 1023 } | |
169 | #[cfg(feature = "simd_support")] | |
170 | float_impls! { f64x8, u64x8, f64, u64, 52, 1023 } | |
171 | ||
172 | ||
173 | #[cfg(test)] | |
174 | mod tests { | |
175 | use super::*; | |
176 | use crate::rngs::mock::StepRng; | |
177 | ||
178 | const EPSILON32: f32 = ::core::f32::EPSILON; | |
179 | const EPSILON64: f64 = ::core::f64::EPSILON; | |
180 | ||
181 | macro_rules! test_f32 { | |
182 | ($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 | } |