Implement Bernoulli distribution

benches/misc.rs

@@ -11,14 +11,15 @@ use rand::prelude::*;
 use rand::seq::*;
 
 #[bench]
-fn misc_gen_bool(b: &mut Bencher) {
+fn misc_gen_bool_const(b: &mut Bencher) {
     let mut rng = SmallRng::from_rng(&mut thread_rng()).unwrap();
     b.iter(|| {
+        // Can be evaluated at compile time.
         let mut accum = true;
         for _ in 0..::RAND_BENCH_N {
             accum ^= rng.gen_bool(0.18);
         }
-        black_box(accum);
+        accum
     })
 }
 
@@ -27,12 +28,37 @@ fn misc_gen_bool_var(b: &mut Bencher) {
     let mut rng = SmallRng::from_rng(&mut thread_rng()).unwrap();
     b.iter(|| {
         let mut p = 0.18;
+        black_box(&mut p);  // Avoid constant folding.
+        for _ in 0..::RAND_BENCH_N {
+            black_box(rng.gen_bool(p));
+        }
+    })
+}
+
+#[bench]
+fn misc_bernoulli_const(b: &mut Bencher) {
+    let mut rng = SmallRng::from_rng(&mut thread_rng()).unwrap();
+    let d = rand::distributions::Bernoulli::new(0.18);
+    b.iter(|| {
+        // Can be evaluated at compile time.
         let mut accum = true;
         for _ in 0..::RAND_BENCH_N {
-            accum ^= rng.gen_bool(p);
-            p += 0.0001;
+            accum ^= rng.sample(d);
+        }
+        accum
+    })
+}
+
+#[bench]
+fn misc_bernoulli_var(b: &mut Bencher) {
+    let mut rng = SmallRng::from_rng(&mut thread_rng()).unwrap();
+    b.iter(|| {
+        let mut p = 0.18;
+        black_box(&mut p);  // Avoid constant folding.
+        let d = rand::distributions::Bernoulli::new(p);
+        for _ in 0..::RAND_BENCH_N {
+            black_box(rng.sample(d));
         }
-        black_box(accum);
     })
 }
 

src/distributions/bernoulli.rs

@@ -0,0 +1,120 @@
+// Copyright 2018 The Rust Project Developers. See the COPYRIGHT
+// file at the top-level directory of this distribution and at
+// https://rust-lang.org/COPYRIGHT.
+//
+// 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.
+//! The Bernoulli distribution.
+
+use Rng;
+use distributions::Distribution;
+
+/// The Bernoulli distribution.
+///
+/// This is a special case of the Binomial distribution where `n = 1`.
+///
+/// # Example
+///
+/// ```rust
+/// use rand::distributions::{Bernoulli, Distribution};
+///
+/// let d = Bernoulli::new(0.3);
+/// let v = d.sample(&mut rand::thread_rng());
+/// println!("{} is from a Bernoulli distribution", v);
+/// ```
+///
+/// # Precision
+///
+/// This `Bernoulli` distribution uses 64 bits from the RNG (a `u64`),
+/// so only probabilities that are multiples of 2<sup>-64</sup> can be
+/// represented.
+#[derive(Clone, Copy, Debug)]
+pub struct Bernoulli {
+    /// Probability of success, relative to the maximal integer.
+    p_int: u64,
+}
+
+impl Bernoulli {
+    /// Construct a new `Bernoulli` with the given probability of success `p`.
+    ///
+    /// # Panics
+    ///
+    /// If `p < 0` or `p > 1`.
+    ///
+    /// # Precision
+    ///
+    /// For `p = 1.0`, the resulting distribution will always generate true.
+    /// For `p = 0.0`, the resulting distribution will always generate false.
+    ///
+    /// This method is accurate for any input `p` in the range `[0, 1]` which is
+    /// a multiple of 2<sup>-64</sup>. (Note that not all multiples of
+    /// 2<sup>-64</sup> in `[0, 1]` can be represented as a `f64`.)
+    #[inline]
+    pub fn new(p: f64) -> Bernoulli {
+        assert!((p >= 0.0) & (p <= 1.0), "Bernoulli::new not called with 0 <= p <= 0");
+        // Technically, this should be 2^64 or `u64::MAX + 1` because we compare
+        // using `<` when sampling. However, `u64::MAX` rounds to an `f64`
+        // larger than `u64::MAX` anyway.
+        const MAX_P_INT: f64 = ::core::u64::MAX as f64;
+        let p_int = if p < 1.0 {
+            (p * MAX_P_INT) as u64
+        } else {
+            // Avoid overflow: `MAX_P_INT` cannot be represented as u64.
+            ::core::u64::MAX
+        };
+        Bernoulli { p_int }
+    }
+}
+
+impl Distribution<bool> for Bernoulli {
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> bool {
+        // Make sure to always return true for p = 1.0.
+        if self.p_int == ::core::u64::MAX {
+            return true;
+        }
+        let r: u64 = rng.gen();
+        r < self.p_int
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use Rng;
+    use distributions::Distribution;
+    use super::Bernoulli;
+
+    #[test]
+    fn test_trivial() {
+        let mut r = ::test::rng(1);
+        let always_false = Bernoulli::new(0.0);
+        let always_true = Bernoulli::new(1.0);
+        for _ in 0..5 {
+            assert_eq!(r.sample::<bool, _>(&always_false), false);
+            assert_eq!(r.sample::<bool, _>(&always_true), true);
+            assert_eq!(Distribution::<bool>::sample(&always_false, &mut r), false);
+            assert_eq!(Distribution::<bool>::sample(&always_true, &mut r), true);
+        }
+    }
+
+    #[test]
+    fn test_average() {
+        const P: f64 = 0.3;
+        let d = Bernoulli::new(P);
+        const N: u32 = 10_000_000;
+
+        let mut sum: u32 = 0;
+        let mut rng = ::test::rng(2);
+        for _ in 0..N {
+            if d.sample(&mut rng) {
+                sum += 1;
+            }
+        }
+        let avg = (sum as f64) / (N as f64);
+
+        assert!((avg - P).abs() < 1e-3);
+    }
+}

src/distributions/binomial.rs

@@ -31,13 +31,17 @@ use std::f64::consts::PI;
 /// ```
 #[derive(Clone, Copy, Debug)]
 pub struct Binomial {
-    n: u64, // number of trials
-    p: f64, // probability of success
+    /// Number of trials.
+    n: u64,
+    /// Probability of success.
+    p: f64,
 }
 
 impl Binomial {
-    /// Construct a new `Binomial` with the given shape parameters
-    /// `n`, `p`. Panics if `p <= 0` or `p >= 1`.
+    /// Construct a new `Binomial` with the given shape parameters `n` (number
+    /// of trials) and `p` (probability of success).
+    ///
+    /// Panics if `p <= 0` or `p >= 1`.
     pub fn new(n: u64, p: f64) -> Binomial {
         assert!(p > 0.0, "Binomial::new called with p <= 0");
         assert!(p < 1.0, "Binomial::new called with p >= 1");

src/distributions/mod.rs

@@ -178,6 +178,7 @@ pub use self::uniform::Uniform as Range;
 #[doc(inline)] pub use self::poisson::Poisson;
 #[cfg(feature = "std")]
 #[doc(inline)] pub use self::binomial::Binomial;
+#[doc(inline)] pub use self::bernoulli::Bernoulli;
 
 pub mod uniform;
 #[cfg(feature="std")]
@@ -190,6 +191,7 @@ pub mod uniform;
 #[doc(hidden)] pub mod poisson;
 #[cfg(feature = "std")]
 #[doc(hidden)] pub mod binomial;
+#[doc(hidden)] pub mod bernoulli;
 
 mod float;
 mod integer;

src/lib.rs

@@ -318,7 +318,6 @@ pub trait Rng: RngCore {
     /// println!("{}", x);
     /// println!("{:?}", rng.gen::<(f64, bool)>());
     /// ```
-    #[inline(always)]
     fn gen<T>(&mut self) -> T where Standard: Distribution<T> {
         Standard.sample(self)
     }
@@ -474,6 +473,8 @@ pub trait Rng: RngCore {
 
     /// Return a bool with a probability `p` of being true.
     ///
+    /// This is a wrapper around [`distributions::Bernoulli`].
+    ///
     /// # Example
     ///
     /// ```rust
@@ -483,20 +484,15 @@ pub trait Rng: RngCore {
     /// println!("{}", rng.gen_bool(1.0 / 3.0));
     /// ```
     ///
-    /// # Accuracy note
+    /// # Panics
+    ///
+    /// If `p` < 0 or `p` > 1.
     ///
-    /// `gen_bool` uses 32 bits of the RNG, so if you use it to generate close
-    /// to or more than `2^32` results, a tiny bias may become noticable.
-    /// A notable consequence of the method used here is that the worst case is
-    /// `rng.gen_bool(0.0)`: it has a chance of 1 in `2^32` of being true, while
-    /// it should always be false. But using `gen_bool` to consume *many* values
-    /// from an RNG just to consistently generate `false` does not match with
-    /// the intent of this method.
+    /// [`distributions::Bernoulli`]: distributions/bernoulli/struct.Bernoulli.html
+    #[inline]
     fn gen_bool(&mut self, p: f64) -> bool {
-        assert!(p >= 0.0 && p <= 1.0);
-        // If `p` is constant, this will be evaluated at compile-time.
-        let p_int = (p * f64::from(core::u32::MAX)) as u32;
-        self.gen::<u32>() <= p_int
+        let d = distributions::Bernoulli::new(p);
+        self.sample(d)
     }
 
     /// Return a random element from `values`.
@@ -897,7 +893,6 @@ pub fn weak_rng() -> XorShiftRng {
 /// [`thread_rng`]: fn.thread_rng.html
 /// [`Standard`]: distributions/struct.Standard.html
 #[cfg(feature="std")]
-#[inline]
 pub fn random<T>() -> T where Standard: Distribution<T> {
     thread_rng().gen()
 }
@@ -918,7 +913,6 @@ pub fn random<T>() -> T where Standard: Distribution<T> {
 /// println!("{:?}", sample);
 /// ```
 #[cfg(feature="std")]
-#[inline(always)]
 #[deprecated(since="0.4.0", note="renamed to seq::sample_iter")]
 pub fn sample<T, I, R>(rng: &mut R, iterable: I, amount: usize) -> Vec<T>
     where I: IntoIterator<Item=T>,

tests/bool.rs

@@ -0,0 +1,23 @@
+#![no_std]
+
+extern crate rand;
+
+use rand::SeedableRng;
+use rand::rngs::SmallRng;
+use rand::distributions::{Distribution, Bernoulli};
+
+/// This test should make sure that we don't accidentally have undefined
+/// behavior for large propabilties due to
+/// https://github.com/rust-lang/rust/issues/10184.
+/// Expressions like `1.0*(u64::MAX as f64) as u64` have to be avoided.
+#[test]
+fn large_probability() {
+    let p = 1. - ::core::f64::EPSILON / 2.;
+    assert!(p < 1.);
+    let d = Bernoulli::new(p);
+    let mut rng = SmallRng::from_seed(
+        [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]);
+    for _ in 0..10 {
+        assert!(d.sample(&mut rng), "extremely unlikely to fail by accident");
+    }
+}