auto merge of #10859 : huonw/rust/helper-dists, r=cmr

This moves `std::rand::distribitions::{Normal, StandardNormal}` to `...::distributions::normal`, reexporting `Normal` from `distributions` (and similarly for `Exp` and Exp1`), and adds:
- Log-normal
- Chi-squared
- F
- Student T

all of which are implemented in C++11's random library. Tests in huonw/random-tests@0424b8a. Note that these are approximately half documentation & half implementation (of which a significant portion is boilerplate `}`'s and so on).

Author: bors

src/libstd/rand/distributions/exponential.rs

@@ -0,0 +1,141 @@
+// Copyright 2013 The Rust Project Developers. See the COPYRIGHT
+// file at the top-level directory of this distribution and at
+// http://rust-lang.org/COPYRIGHT.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+//! The exponential distribution.
+
+use rand::{Rng, Rand};
+use rand::distributions::{ziggurat, ziggurat_tables, Sample, IndependentSample};
+
+/// A wrapper around an `f64` to generate Exp(1) random numbers.
+///
+/// See `Exp` for the general exponential distribution.Note that this
+ // has to be unwrapped before use as an `f64` (using either
+/// `*` or `cast::transmute` is safe).
+///
+/// Implemented via the ZIGNOR variant[1] of the Ziggurat method. The
+/// exact description in the paper was adjusted to use tables for the
+/// exponential distribution rather than normal.
+///
+/// [1]: Jurgen A. Doornik (2005). [*An Improved Ziggurat Method to
+/// Generate Normal Random
+/// Samples*](http://www.doornik.com/research/ziggurat.pdf). Nuffield
+/// College, Oxford
+pub struct Exp1(f64);
+
+// This could be done via `-rng.gen::<f64>().ln()` but that is slower.
+impl Rand for Exp1 {
+    #[inline]
+    fn rand<R:Rng>(rng: &mut R) -> Exp1 {
+        #[inline]
+        fn pdf(x: f64) -> f64 {
+            (-x).exp()
+        }
+        #[inline]
+        fn zero_case<R:Rng>(rng: &mut R, _u: f64) -> f64 {
+            ziggurat_tables::ZIG_EXP_R - rng.gen::<f64>().ln()
+        }
+
+        Exp1(ziggurat(rng, false,
+                      &ziggurat_tables::ZIG_EXP_X,
+                      &ziggurat_tables::ZIG_EXP_F,
+                      pdf, zero_case))
+    }
+}
+
+/// The exponential distribution `Exp(lambda)`.
+///
+/// This distribution has density function: `f(x) = lambda *
+/// exp(-lambda * x)` for `x > 0`.
+///
+/// # Example
+///
+/// ```rust
+/// use std::rand;
+/// use std::rand::distributions::{Exp, IndependentSample};
+///
+/// fn main() {
+///     let exp = Exp::new(2.0);
+///     let v = exp.ind_sample(&mut rand::task_rng());
+///     println!("{} is from a Exp(2) distribution", v);
+/// }
+/// ```
+pub struct Exp {
+    /// `lambda` stored as `1/lambda`, since this is what we scale by.
+    priv lambda_inverse: f64
+}
+
+impl Exp {
+    /// Construct a new `Exp` with the given shape parameter
+    /// `lambda`. Fails if `lambda <= 0`.
+    pub fn new(lambda: f64) -> Exp {
+        assert!(lambda > 0.0, "Exp::new called with `lambda` <= 0");
+        Exp { lambda_inverse: 1.0 / lambda }
+    }
+}
+
+impl Sample<f64> for Exp {
+    fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
+}
+impl IndependentSample<f64> for Exp {
+    fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
+        (*rng.gen::<Exp1>()) * self.lambda_inverse
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use rand::*;
+    use super::*;
+    use iter::range;
+    use option::{Some, None};
+
+    #[test]
+    fn test_exp() {
+        let mut exp = Exp::new(10.0);
+        let mut rng = task_rng();
+        for _ in range(0, 1000) {
+            assert!(exp.sample(&mut rng) >= 0.0);
+            assert!(exp.ind_sample(&mut rng) >= 0.0);
+        }
+    }
+    #[test]
+    #[should_fail]
+    fn test_exp_invalid_lambda_zero() {
+        Exp::new(0.0);
+    }
+    #[test]
+    #[should_fail]
+    fn test_exp_invalid_lambda_neg() {
+        Exp::new(-10.0);
+    }
+}
+
+#[cfg(test)]
+mod bench {
+    use extra::test::BenchHarness;
+    use rand::{XorShiftRng, RAND_BENCH_N};
+    use super::*;
+    use iter::range;
+    use option::{Some, None};
+    use mem::size_of;
+
+    #[bench]
+    fn rand_exp(bh: &mut BenchHarness) {
+        let mut rng = XorShiftRng::new();
+        let mut exp = Exp::new(2.71828 * 3.14159);
+
+        bh.iter(|| {
+            for _ in range(0, RAND_BENCH_N) {
+                exp.sample(&mut rng);
+            }
+        });
+        bh.bytes = size_of::<f64>() as u64 * RAND_BENCH_N;
+    }
+}

src/libstd/rand/distributions/gamma.rs

@@ -8,10 +8,11 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
-//! The Gamma distribution.
+//! The Gamma and derived distributions.
 
 use rand::{Rng, Open01};
-use super::{IndependentSample, Sample, StandardNormal, Exp};
+use super::{IndependentSample, Sample, Exp};
+use super::normal::StandardNormal;
 use num;
 
 /// The Gamma distribution `Gamma(shape, scale)` distribution.
@@ -168,6 +169,213 @@ impl IndependentSample<f64> for GammaLargeShape {
     }
 }
 
+/// The chi-squared distribution `χ²(k)`, where `k` is the degrees of
+/// freedom.
+///
+/// For `k > 0` integral, this distribution is the sum of the squares
+/// of `k` independent standard normal random variables. For other
+/// `k`, this uses the equivalent characterisation `χ²(k) = Gamma(k/2,
+/// 2)`.
+///
+/// # Example
+///
+/// ```rust
+/// use std::rand;
+/// use std::rand::distributions::{ChiSquared, IndependentSample};
+///
+/// fn main() {
+///     let chi = ChiSquared::new(11.0);
+///     let v = chi.ind_sample(&mut rand::task_rng());
+///     println!("{} is from a χ²(11) distribution", v)
+/// }
+/// ```
+pub enum ChiSquared {
+    // k == 1, Gamma(alpha, ..) is particularly slow for alpha < 1,
+    // e.g. when alpha = 1/2 as it would be for this case, so special-
+    // casing and using the definition of N(0,1)^2 is faster.
+    priv DoFExactlyOne,
+    priv DoFAnythingElse(Gamma)
+}
+
+impl ChiSquared {
+    /// Create a new chi-squared distribution with degrees-of-freedom
+    /// `k`. Fails if `k < 0`.
+    pub fn new(k: f64) -> ChiSquared {
+        if k == 1.0 {
+            DoFExactlyOne
+        } else {
+            assert!(k > 0.0, "ChiSquared::new called with `k` < 0");
+            DoFAnythingElse(Gamma::new(0.5 * k, 2.0))
+        }
+    }
+}
+impl Sample<f64> for ChiSquared {
+    fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
+}
+impl IndependentSample<f64> for ChiSquared {
+    fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
+        match *self {
+            DoFExactlyOne => {
+                // k == 1 => N(0,1)^2
+                let norm = *rng.gen::<StandardNormal>();
+                norm * norm
+            }
+            DoFAnythingElse(ref g) => g.ind_sample(rng)
+        }
+    }
+}
+
+/// The Fisher F distribution `F(m, n)`.
+///
+/// This distribution is equivalent to the ratio of two normalised
+/// chi-squared distributions, that is, `F(m,n) = (χ²(m)/m) /
+/// (χ²(n)/n)`.
+///
+/// # Example
+///
+/// ```rust
+/// use std::rand;
+/// use std::rand::distributions::{FisherF, IndependentSample};
+///
+/// fn main() {
+///     let f = FisherF::new(2.0, 32.0);
+///     let v = f.ind_sample(&mut rand::task_rng());
+///     println!("{} is from an F(2, 32) distribution", v)
+/// }
+/// ```
+pub struct FisherF {
+    priv numer: ChiSquared,
+    priv denom: ChiSquared,
+    // denom_dof / numer_dof so that this can just be a straight
+    // multiplication, rather than a division.
+    priv dof_ratio: f64,
+}
+
+impl FisherF {
+    /// Create a new `FisherF` distribution, with the given
+    /// parameter. Fails if either `m` or `n` are not positive.
+    pub fn new(m: f64, n: f64) -> FisherF {
+        assert!(m > 0.0, "FisherF::new called with `m < 0`");
+        assert!(n > 0.0, "FisherF::new called with `n < 0`");
+
+        FisherF {
+            numer: ChiSquared::new(m),
+            denom: ChiSquared::new(n),
+            dof_ratio: n / m
+        }
+    }
+}
+impl Sample<f64> for FisherF {
+    fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
+}
+impl IndependentSample<f64> for FisherF {
+    fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
+        self.numer.ind_sample(rng) / self.denom.ind_sample(rng) * self.dof_ratio
+    }
+}
+
+/// The Student t distribution, `t(nu)`, where `nu` is the degrees of
+/// freedom.
+///
+/// # Example
+///
+/// ```rust
+/// use std::rand;
+/// use std::rand::distributions::{StudentT, IndependentSample};
+///
+/// fn main() {
+///     let t = StudentT::new(11.0);
+///     let v = t.ind_sample(&mut rand::task_rng());
+///     println!("{} is from a t(11) distribution", v)
+/// }
+/// ```
+pub struct StudentT {
+    priv chi: ChiSquared,
+    priv dof: f64
+}
+
+impl StudentT {
+    /// Create a new Student t distribution with `n` degrees of
+    /// freedom. Fails if `n <= 0`.
+    pub fn new(n: f64) -> StudentT {
+        assert!(n > 0.0, "StudentT::new called with `n <= 0`");
+        StudentT {
+            chi: ChiSquared::new(n),
+            dof: n
+        }
+    }
+}
+impl Sample<f64> for StudentT {
+    fn sample<R: Rng>(&mut self, rng: &mut R) -> f64 { self.ind_sample(rng) }
+}
+impl IndependentSample<f64> for StudentT {
+    fn ind_sample<R: Rng>(&self, rng: &mut R) -> f64 {
+        let norm = *rng.gen::<StandardNormal>();
+        norm * (self.dof / self.chi.ind_sample(rng)).sqrt()
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use rand::*;
+    use super::*;
+    use iter::range;
+    use option::{Some, None};
+
+    #[test]
+    fn test_chi_squared_one() {
+        let mut chi = ChiSquared::new(1.0);
+        let mut rng = task_rng();
+        for _ in range(0, 1000) {
+            chi.sample(&mut rng);
+            chi.ind_sample(&mut rng);
+        }
+    }
+    #[test]
+    fn test_chi_squared_small() {
+        let mut chi = ChiSquared::new(0.5);
+        let mut rng = task_rng();
+        for _ in range(0, 1000) {
+            chi.sample(&mut rng);
+            chi.ind_sample(&mut rng);
+        }
+    }
+    #[test]
+    fn test_chi_squared_large() {
+        let mut chi = ChiSquared::new(30.0);
+        let mut rng = task_rng();
+        for _ in range(0, 1000) {
+            chi.sample(&mut rng);
+            chi.ind_sample(&mut rng);
+        }
+    }
+    #[test]
+    #[should_fail]
+    fn test_log_normal_invalid_dof() {
+        ChiSquared::new(-1.0);
+    }
+
+    #[test]
+    fn test_f() {
+        let mut f = FisherF::new(2.0, 32.0);
+        let mut rng = task_rng();
+        for _ in range(0, 1000) {
+            f.sample(&mut rng);
+            f.ind_sample(&mut rng);
+        }
+    }
+
+    #[test]
+    fn test_t() {
+        let mut t = StudentT::new(11.0);
+        let mut rng = task_rng();
+        for _ in range(0, 1000) {
+            t.sample(&mut rng);
+            t.ind_sample(&mut rng);
+        }
+    }
+}
+
 #[cfg(test)]
 mod bench {
     use super::*;