1 // Copyright 2013 The Rust Project Developers. See the COPYRIGHT
2 // file at the top-level directory of this distribution and at
3 // http://rust-lang.org/COPYRIGHT.
5 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
6 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
7 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
8 // option. This file may not be copied, modified, or distributed
9 // except according to those terms.
11 //! Sampling from random distributions.
13 //! This is a generalization of `Rand` to allow parameters to control the
14 //! exact properties of the generated values, e.g. the mean and standard
15 //! deviation of a normal distribution. The `Sample` trait is the most
16 //! general, and allows for generating values that change some state
17 //! internally. The `IndependentSample` trait is for generating values
18 //! that do not need to record state.
22 #[cfg(not(test))] // only necessary for no_std
25 use core::marker::PhantomData;
29 pub use self::range::Range;
30 pub use self::gamma::{ChiSquared, FisherF, Gamma, StudentT};
31 pub use self::normal::{LogNormal, Normal};
32 pub use self::exponential::Exp;
39 /// Types that can be used to create a random instance of `Support`.
40 pub trait Sample<Support> {
41 /// Generate a random value of `Support`, using `rng` as the
42 /// source of randomness.
43 fn sample<R: Rng>(&mut self, rng: &mut R) -> Support;
46 /// `Sample`s that do not require keeping track of state.
48 /// Since no state is recorded, each sample is (statistically)
49 /// independent of all others, assuming the `Rng` used has this
51 // FIXME maybe having this separate is overkill (the only reason is to
52 // take &self rather than &mut self)? or maybe this should be the
53 // trait called `Sample` and the other should be `DependentSample`.
54 pub trait IndependentSample<Support>: Sample<Support> {
55 /// Generate a random value.
56 fn ind_sample<R: Rng>(&self, _: &mut R) -> Support;
59 /// A wrapper for generating types that implement `Rand` via the
60 /// `Sample` & `IndependentSample` traits.
61 pub struct RandSample<Sup> {
62 _marker: PhantomData<Sup>,
65 impl<Sup> RandSample<Sup> {
66 pub fn new() -> RandSample<Sup> {
67 RandSample { _marker: PhantomData }
71 impl<Sup: Rand> Sample<Sup> for RandSample<Sup> {
72 fn sample<R: Rng>(&mut self, rng: &mut R) -> Sup {
77 impl<Sup: Rand> IndependentSample<Sup> for RandSample<Sup> {
78 fn ind_sample<R: Rng>(&self, rng: &mut R) -> Sup {
83 impl<Sup> fmt::Debug for RandSample<Sup> {
84 fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
85 f.pad("RandSample { .. }")
89 /// A value with a particular weight for use with `WeightedChoice`.
90 pub struct Weighted<T> {
91 /// The numerical weight of this item
93 /// The actual item which is being weighted
97 impl<T: fmt::Debug> fmt::Debug for Weighted<T> {
98 fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
99 f.debug_struct("Weighted")
100 .field("weight", &self.weight)
101 .field("item", &self.item)
106 /// A distribution that selects from a finite collection of weighted items.
108 /// Each item has an associated weight that influences how likely it
109 /// is to be chosen: higher weight is more likely.
111 /// The `Clone` restriction is a limitation of the `Sample` and
112 /// `IndependentSample` traits. Note that `&T` is (cheaply) `Clone` for
113 /// all `T`, as is `usize`, so one can store references or indices into
115 pub struct WeightedChoice<'a, T: 'a> {
116 items: &'a mut [Weighted<T>],
117 weight_range: Range<usize>,
120 impl<'a, T: Clone> WeightedChoice<'a, T> {
121 /// Create a new `WeightedChoice`.
125 /// - the total weight is 0
126 /// - the total weight is larger than a `usize` can contain.
127 pub fn new(items: &'a mut [Weighted<T>]) -> WeightedChoice<'a, T> {
128 // strictly speaking, this is subsumed by the total weight == 0 case
129 assert!(!items.is_empty(),
130 "WeightedChoice::new called with no items");
132 let mut running_total = 0_usize;
134 // we convert the list from individual weights to cumulative
135 // weights so we can binary search. This *could* drop elements
136 // with weight == 0 as an optimisation.
137 for item in &mut *items {
138 running_total = match running_total.checked_add(item.weight) {
141 panic!("WeightedChoice::new called with a total weight larger than a usize \
146 item.weight = running_total;
148 assert!(running_total != 0,
149 "WeightedChoice::new called with a total weight of 0");
153 // we're likely to be generating numbers in this range
154 // relatively often, so might as well cache it
155 weight_range: Range::new(0, running_total),
160 impl<'a, T: Clone> Sample<T> for WeightedChoice<'a, T> {
161 fn sample<R: Rng>(&mut self, rng: &mut R) -> T {
166 impl<'a, T: Clone> IndependentSample<T> for WeightedChoice<'a, T> {
167 fn ind_sample<R: Rng>(&self, rng: &mut R) -> T {
168 // we want to find the first element that has cumulative
169 // weight > sample_weight, which we do by binary since the
170 // cumulative weights of self.items are sorted.
172 // choose a weight in [0, total_weight)
173 let sample_weight = self.weight_range.ind_sample(rng);
175 // short circuit when it's the first item
176 if sample_weight < self.items[0].weight {
177 return self.items[0].item.clone();
181 let mut modifier = self.items.len();
183 // now we know that every possibility has an element to the
184 // left, so we can just search for the last element that has
185 // cumulative weight <= sample_weight, then the next one will
186 // be "it". (Note that this greatest element will never be the
187 // last element of the vector, since sample_weight is chosen
188 // in [0, total_weight) and the cumulative weight of the last
189 // one is exactly the total weight.)
191 let i = idx + modifier / 2;
192 if self.items[i].weight <= sample_weight {
193 // we're small, so look to the right, but allow this
194 // exact element still.
196 // we need the `/ 2` to round up otherwise we'll drop
197 // the trailing elements when `modifier` is odd.
200 // otherwise we're too big, so go left. (i.e. do
205 return self.items[idx + 1].item.clone();
209 impl<'a, T: fmt::Debug> fmt::Debug for WeightedChoice<'a, T> {
210 fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
211 f.debug_struct("WeightedChoice")
212 .field("items", &self.items)
213 .field("weight_range", &self.weight_range)
220 /// Sample a random number using the Ziggurat method (specifically the
221 /// ZIGNOR variant from Doornik 2005). Most of the arguments are
222 /// directly from the paper:
224 /// * `rng`: source of randomness
225 /// * `symmetric`: whether this is a symmetric distribution, or one-sided with P(x < 0) = 0.
226 /// * `X`: the $x_i$ abscissae.
227 /// * `F`: precomputed values of the PDF at the $x_i$, (i.e. $f(x_i)$)
228 /// * `F_DIFF`: precomputed values of $f(x_i) - f(x_{i+1})$
229 /// * `pdf`: the probability density function
230 /// * `zero_case`: manual sampling from the tail when we chose the
231 /// bottom box (i.e. i == 0)
232 // the perf improvement (25-50%) is definitely worth the extra code
233 // size from force-inlining.
235 fn ziggurat<R: Rng, P, Z>(rng: &mut R,
237 x_tab: ziggurat_tables::ZigTable,
238 f_tab: ziggurat_tables::ZigTable,
242 where P: FnMut(f64) -> f64,
243 Z: FnMut(&mut R, f64) -> f64
245 const SCALE: f64 = (1u64 << 53) as f64;
247 // reimplement the f64 generation as an optimisation suggested
248 // by the Doornik paper: we have a lot of precision-space
249 // (i.e. there are 11 bits of the 64 of a u64 to use after
250 // creating a f64), so we might as well reuse some to save
251 // generating a whole extra random number. (Seems to be 15%
254 // This unfortunately misses out on the benefits of direct
255 // floating point generation if an RNG like dSMFT is
256 // used. (That is, such RNGs create floats directly, highly
257 // efficiently and overload next_f32/f64, so by not calling it
258 // this may be slower than it would be otherwise.)
259 // FIXME: investigate/optimise for the above.
260 let bits: u64 = rng.gen();
261 let i = (bits & 0xff) as usize;
262 let f = (bits >> 11) as f64 / SCALE;
264 // u is either U(-1, 1) or U(0, 1) depending on if this is a
265 // symmetric distribution or not.
266 let u = if symmetric { 2.0 * f - 1.0 } else { f };
267 let x = u * x_tab[i];
269 let test_x = if symmetric { x.abs() } else { x };
271 // algebraically equivalent to |u| < x_tab[i+1]/x_tab[i] (or u < x_tab[i+1]/x_tab[i])
272 if test_x < x_tab[i + 1] {
276 return zero_case(rng, u);
278 // algebraically equivalent to f1 + DRanU()*(f0 - f1) < 1
279 if f_tab[i + 1] + (f_tab[i] - f_tab[i + 1]) * rng.gen::<f64>() < pdf(x) {
288 use super::{IndependentSample, RandSample, Sample, Weighted, WeightedChoice};
290 #[derive(PartialEq, Debug)]
291 struct ConstRand(usize);
292 impl Rand for ConstRand {
293 fn rand<R: Rng>(_: &mut R) -> ConstRand {
302 impl Rng for CountingRng {
303 fn next_u32(&mut self) -> u32 {
307 fn next_u64(&mut self) -> u64 {
308 self.next_u32() as u64
313 fn test_rand_sample() {
314 let mut rand_sample = RandSample::<ConstRand>::new();
316 assert_eq!(rand_sample.sample(&mut ::test::rng()), ConstRand(0));
317 assert_eq!(rand_sample.ind_sample(&mut ::test::rng()), ConstRand(0));
321 fn test_weighted_choice() {
322 // this makes assumptions about the internal implementation of
323 // WeightedChoice, specifically: it doesn't reorder the items,
324 // it doesn't do weird things to the RNG (so 0 maps to 0, 1 to
325 // 1, internally; modulo a modulo operation).
328 ($items:expr, $expected:expr) => {{
329 let mut items = $items;
330 let wc = WeightedChoice::new(&mut items);
331 let expected = $expected;
333 let mut rng = CountingRng { i: 0 };
335 for &val in &expected {
336 assert_eq!(wc.ind_sample(&mut rng), val)
341 t!(vec![Weighted { weight: 1, item: 10 }],
345 t!(vec![Weighted { weight: 0, item: 20 },
346 Weighted { weight: 2, item: 21 },
347 Weighted { weight: 0, item: 22 },
348 Weighted { weight: 1, item: 23 }],
352 t!(vec![Weighted { weight: 4, item: 30 },
353 Weighted { weight: 3, item: 31 }],
354 [30, 30, 30, 30, 31, 31, 31]);
356 // check that we're binary searching
357 // correctly with some vectors of odd
359 t!(vec![Weighted { weight: 1, item: 40 },
360 Weighted { weight: 1, item: 41 },
361 Weighted { weight: 1, item: 42 },
362 Weighted { weight: 1, item: 43 },
363 Weighted { weight: 1, item: 44 }],
364 [40, 41, 42, 43, 44]);
365 t!(vec![Weighted { weight: 1, item: 50 },
366 Weighted { weight: 1, item: 51 },
367 Weighted { weight: 1, item: 52 },
368 Weighted { weight: 1, item: 53 },
369 Weighted { weight: 1, item: 54 },
370 Weighted { weight: 1, item: 55 },
371 Weighted { weight: 1, item: 56 }],
372 [50, 51, 52, 53, 54, 55, 56]);
377 fn test_weighted_choice_no_items() {
378 WeightedChoice::<isize>::new(&mut []);
383 fn test_weighted_choice_zero_weight() {
384 WeightedChoice::new(&mut [Weighted { weight: 0, item: 0 },
385 Weighted { weight: 0, item: 1 }]);
390 fn test_weighted_choice_weight_overflows() {
391 let x = (!0) as usize / 2; // x + x + 2 is the overflow
392 WeightedChoice::new(&mut [Weighted { weight: x, item: 0 },
393 Weighted { weight: 1, item: 1 },
394 Weighted { weight: x, item: 2 },
395 Weighted { weight: 1, item: 3 }]);