Hide modules whose distributions we're exposing directly throguh rand…

…::distributions. Also move a couple of distribution helper functions into utils.rs.

src/distributions/binomial.rs

@@ -12,7 +12,7 @@
 
 use Rng;
 use distributions::{Distribution, Bernoulli, Cauchy};
-use distributions::log_gamma::log_gamma;
+use distributions::utils::log_gamma;
 
 /// The binomial distribution `Binomial(n, p)`.
 ///

src/distributions/exponential.rs

@@ -11,7 +11,8 @@
 //! The exponential distribution.
 
 use {Rng};
-use distributions::{ziggurat, ziggurat_tables, Distribution};
+use distributions::{ziggurat_tables, Distribution};
+use distributions::utils::ziggurat;
 
 /// Samples floating-point numbers according to the exponential distribution,
 /// with rate parameter `λ = 1`. This is equivalent to `Exp::new(1.0)` or

src/distributions/mod.rs

@@ -173,60 +173,37 @@
 
 use Rng;
 
-#[doc(inline)] pub use self::other::Alphanumeric;
+pub use self::other::Alphanumeric;
 #[doc(inline)] pub use self::uniform::Uniform;
-#[doc(inline)] pub use self::float::{OpenClosed01, Open01};
-#[cfg(feature="alloc")]
-#[doc(inline)] pub use self::weighted::WeightedIndex;
-#[cfg(feature="std")]
-#[doc(inline)] pub use self::gamma::{Gamma, ChiSquared, FisherF, StudentT};
-#[cfg(feature="std")]
-#[doc(inline)] pub use self::normal::{Normal, LogNormal, StandardNormal};
-#[cfg(feature="std")]
-#[doc(inline)] pub use self::exponential::{Exp, Exp1};
-#[cfg(feature="std")]
-#[doc(inline)] pub use self::pareto::Pareto;
-#[cfg(feature = "std")]
-#[doc(inline)] pub use self::poisson::Poisson;
-#[cfg(feature = "std")]
-#[doc(inline)] pub use self::binomial::Binomial;
-#[doc(inline)] pub use self::bernoulli::Bernoulli;
-#[cfg(feature = "std")]
-#[doc(inline)] pub use self::cauchy::Cauchy;
-#[cfg(feature = "std")]
-#[doc(inline)] pub use self::dirichlet::Dirichlet;
+pub use self::float::{OpenClosed01, Open01};
+pub use self::bernoulli::Bernoulli;
+#[cfg(feature="alloc")] pub use self::weighted::WeightedIndex;
+#[cfg(feature="std")] pub use self::gamma::{Gamma, ChiSquared, FisherF, StudentT};
+#[cfg(feature="std")] pub use self::normal::{Normal, LogNormal, StandardNormal};
+#[cfg(feature="std")] pub use self::exponential::{Exp, Exp1};
+#[cfg(feature="std")] pub use self::pareto::Pareto;
+#[cfg(feature="std")] pub use self::poisson::Poisson;
+#[cfg(feature="std")] pub use self::binomial::Binomial;
+#[cfg(feature="std")] pub use self::cauchy::Cauchy;
+#[cfg(feature="std")] pub use self::dirichlet::Dirichlet;
 
 pub mod uniform;
-#[cfg(feature="alloc")]
-#[doc(hidden)] pub mod weighted;
-#[cfg(feature="std")]
-#[doc(hidden)] pub mod gamma;
-#[cfg(feature="std")]
-#[doc(hidden)] pub mod normal;
-#[cfg(feature="std")]
-#[doc(hidden)] pub mod exponential;
-#[cfg(feature="std")]
-#[doc(hidden)] pub mod pareto;
-#[cfg(feature = "std")]
-#[doc(hidden)] pub mod poisson;
-#[cfg(feature = "std")]
-#[doc(hidden)] pub mod binomial;
-#[doc(hidden)] pub mod bernoulli;
-#[cfg(feature = "std")]
-#[doc(hidden)] pub mod cauchy;
-#[cfg(feature = "std")]
-#[doc(hidden)] pub mod dirichlet;
+mod bernoulli;
+#[cfg(feature="alloc")] mod weighted;
+#[cfg(feature="std")] mod gamma;
+#[cfg(feature="std")] mod normal;
+#[cfg(feature="std")] mod exponential;
+#[cfg(feature="std")] mod pareto;
+#[cfg(feature="std")] mod poisson;
+#[cfg(feature="std")] mod binomial;
+#[cfg(feature="std")] mod cauchy;
+#[cfg(feature="std")] mod dirichlet;
 
 mod float;
 mod integer;
-#[cfg(feature="std")]
-mod log_gamma;
 mod other;
 mod utils;
-#[cfg(feature="std")]
-mod ziggurat_tables;
-#[cfg(feature="std")]
-use distributions::float::IntoFloat;
+#[cfg(feature="std")] mod ziggurat_tables;
 
 /// Types (distributions) that can be used to create a random instance of `T`.
 ///
@@ -487,69 +464,6 @@ impl<'a, T: Clone> Distribution<T> for WeightedChoice<'a, T> {
     }
 }
 
-/// Sample a random number using the Ziggurat method (specifically the
-/// ZIGNOR variant from Doornik 2005). Most of the arguments are
-/// directly from the paper:
-///
-/// * `rng`: source of randomness
-/// * `symmetric`: whether this is a symmetric distribution, or one-sided with P(x < 0) = 0.
-/// * `X`: the $x_i$ abscissae.
-/// * `F`: precomputed values of the PDF at the $x_i$, (i.e. $f(x_i)$)
-/// * `F_DIFF`: precomputed values of $f(x_i) - f(x_{i+1})$
-/// * `pdf`: the probability density function
-/// * `zero_case`: manual sampling from the tail when we chose the
-///    bottom box (i.e. i == 0)
-
-// the perf improvement (25-50%) is definitely worth the extra code
-// size from force-inlining.
-#[cfg(feature="std")]
-#[inline(always)]
-fn ziggurat<R: Rng + ?Sized, P, Z>(
-            rng: &mut R,
-            symmetric: bool,
-            x_tab: ziggurat_tables::ZigTable,
-            f_tab: ziggurat_tables::ZigTable,
-            mut pdf: P,
-            mut zero_case: Z)
-            -> f64 where P: FnMut(f64) -> f64, Z: FnMut(&mut R, f64) -> f64 {
-    loop {
-        // As an optimisation we re-implement the conversion to a f64.
-        // From the remaining 12 most significant bits we use 8 to construct `i`.
-        // This saves us generating a whole extra random number, while the added
-        // precision of using 64 bits for f64 does not buy us much.
-        let bits = rng.next_u64();
-        let i = bits as usize & 0xff;
-
-        let u = if symmetric {
-            // Convert to a value in the range [2,4) and substract to get [-1,1)
-            // We can't convert to an open range directly, that would require
-            // substracting `3.0 - EPSILON`, which is not representable.
-            // It is possible with an extra step, but an open range does not
-            // seem neccesary for the ziggurat algorithm anyway.
-            (bits >> 12).into_float_with_exponent(1) - 3.0
-        } else {
-            // Convert to a value in the range [1,2) and substract to get (0,1)
-            (bits >> 12).into_float_with_exponent(0)
-            - (1.0 - ::core::f64::EPSILON / 2.0)
-        };
-        let x = u * x_tab[i];
-
-        let test_x = if symmetric { x.abs() } else {x};
-
-        // algebraically equivalent to |u| < x_tab[i+1]/x_tab[i] (or u < x_tab[i+1]/x_tab[i])
-        if test_x < x_tab[i + 1] {
-            return x;
-        }
-        if i == 0 {
-            return zero_case(rng, u);
-        }
-        // algebraically equivalent to f1 + DRanU()*(f0 - f1) < 1
-        if f_tab[i + 1] + (f_tab[i] - f_tab[i + 1]) * rng.gen::<f64>() < pdf(x) {
-            return x;
-        }
-    }
-}
-
 #[cfg(test)]
 mod tests {
     use rngs::mock::StepRng;

src/distributions/normal.rs

@@ -11,7 +11,8 @@
 //! The normal and derived distributions.
 
 use Rng;
-use distributions::{ziggurat, ziggurat_tables, Distribution, Open01};
+use distributions::{ziggurat_tables, Distribution, Open01};
+use distributions::utils::ziggurat;
 
 /// Samples floating-point numbers according to the normal distribution
 /// `N(0, 1)` (a.k.a. a standard normal, or Gaussian). This is equivalent to

src/distributions/poisson.rs

@@ -12,7 +12,7 @@
 
 use Rng;
 use distributions::{Distribution, Cauchy};
-use distributions::log_gamma::log_gamma;
+use distributions::utils::log_gamma;
 
 /// The Poisson distribution `Poisson(lambda)`.
 ///

src/distributions/utils.rs

@@ -12,6 +12,10 @@
 
 #[cfg(feature="simd_support")]
 use core::simd::*;
+#[cfg(feature="std")]
+use distributions::ziggurat_tables;
+#[cfg(feature="std")]
+use Rng;
 
 
 pub trait WideningMultiply<RHS = Self> {
@@ -162,3 +166,111 @@ macro_rules! simd_less_then {
 #[cfg(feature="simd_support")] simd_less_then! { f64x2 }
 #[cfg(feature="simd_support")] simd_less_then! { f64x4 }
 #[cfg(feature="simd_support")] simd_less_then! { f64x8 }
+
+/// Calculates ln(gamma(x)) (natural logarithm of the gamma
+/// function) using the Lanczos approximation.
+///
+/// The approximation expresses the gamma function as:
+/// `gamma(z+1) = sqrt(2*pi)*(z+g+0.5)^(z+0.5)*exp(-z-g-0.5)*Ag(z)`
+/// `g` is an arbitrary constant; we use the approximation with `g=5`.
+///
+/// Noting that `gamma(z+1) = z*gamma(z)` and applying `ln` to both sides:
+/// `ln(gamma(z)) = (z+0.5)*ln(z+g+0.5)-(z+g+0.5) + ln(sqrt(2*pi)*Ag(z)/z)`
+///
+/// `Ag(z)` is an infinite series with coefficients that can be calculated
+/// ahead of time - we use just the first 6 terms, which is good enough
+/// for most purposes.
+#[cfg(feature="std")]
+pub fn log_gamma(x: f64) -> f64 {
+    // precalculated 6 coefficients for the first 6 terms of the series
+    let coefficients: [f64; 6] = [
+        76.18009172947146,
+        -86.50532032941677,
+        24.01409824083091,
+        -1.231739572450155,
+        0.1208650973866179e-2,
+        -0.5395239384953e-5,
+    ];
+
+    // (x+0.5)*ln(x+g+0.5)-(x+g+0.5)
+    let tmp = x + 5.5;
+    let log = (x + 0.5) * tmp.ln() - tmp;
+
+    // the first few terms of the series for Ag(x)
+    let mut a = 1.000000000190015;
+    let mut denom = x;
+    for coeff in &coefficients {
+        denom += 1.0;
+        a += coeff / denom;
+    }
+
+    // get everything together
+    // a is Ag(x)
+    // 2.5066... is sqrt(2pi)
+    log + (2.5066282746310005 * a / x).ln()
+}
+
+/// Sample a random number using the Ziggurat method (specifically the
+/// ZIGNOR variant from Doornik 2005). Most of the arguments are
+/// directly from the paper:
+///
+/// * `rng`: source of randomness
+/// * `symmetric`: whether this is a symmetric distribution, or one-sided with P(x < 0) = 0.
+/// * `X`: the $x_i$ abscissae.
+/// * `F`: precomputed values of the PDF at the $x_i$, (i.e. $f(x_i)$)
+/// * `F_DIFF`: precomputed values of $f(x_i) - f(x_{i+1})$
+/// * `pdf`: the probability density function
+/// * `zero_case`: manual sampling from the tail when we chose the
+///    bottom box (i.e. i == 0)
+
+// the perf improvement (25-50%) is definitely worth the extra code
+// size from force-inlining.
+#[cfg(feature="std")]
+#[inline(always)]
+pub fn ziggurat<R: Rng + ?Sized, P, Z>(
+            rng: &mut R,
+            symmetric: bool,
+            x_tab: ziggurat_tables::ZigTable,
+            f_tab: ziggurat_tables::ZigTable,
+            mut pdf: P,
+            mut zero_case: Z)
+            -> f64 where P: FnMut(f64) -> f64, Z: FnMut(&mut R, f64) -> f64 {
+    use distributions::float::IntoFloat;
+    loop {
+        // As an optimisation we re-implement the conversion to a f64.
+        // From the remaining 12 most significant bits we use 8 to construct `i`.
+        // This saves us generating a whole extra random number, while the added
+        // precision of using 64 bits for f64 does not buy us much.
+        let bits = rng.next_u64();
+        let i = bits as usize & 0xff;
+
+        let u = if symmetric {
+            // Convert to a value in the range [2,4) and substract to get [-1,1)
+            // We can't convert to an open range directly, that would require
+            // substracting `3.0 - EPSILON`, which is not representable.
+            // It is possible with an extra step, but an open range does not
+            // seem neccesary for the ziggurat algorithm anyway.
+            (bits >> 12).into_float_with_exponent(1) - 3.0
+        } else {
+            // Convert to a value in the range [1,2) and substract to get (0,1)
+            (bits >> 12).into_float_with_exponent(0)
+            - (1.0 - ::core::f64::EPSILON / 2.0)
+        };
+        let x = u * x_tab[i];
+
+        let test_x = if symmetric { x.abs() } else {x};
+
+        // algebraically equivalent to |u| < x_tab[i+1]/x_tab[i] (or u < x_tab[i+1]/x_tab[i])
+        if test_x < x_tab[i + 1] {
+            return x;
+        }
+        if i == 0 {
+            return zero_case(rng, u);
+        }
+        // algebraically equivalent to f1 + DRanU()*(f0 - f1) < 1
+        if f_tab[i + 1] + (f_tab[i] - f_tab[i + 1]) * rng.gen::<f64>() < pdf(x) {
+            return x;
+        }
+    }
+}
+