From 4d129e4dfb29f2be4da572b929a2c0c839eea735 Mon Sep 17 00:00:00 2001
From: Diggory Hardy <git@dhardy.name>
Date: Fri, 10 May 2019 17:48:50 +0100
Subject: [PATCH 1/9] rand_distr: remove dependence on num-traits

A custom trait can be fine-tuned to our needs
---
 rand_distr/Cargo.toml         |  1 -
 rand_distr/src/exponential.rs |  7 +++--
 rand_distr/src/gamma.rs       | 28 ++++++++++----------
 rand_distr/src/lib.rs         |  1 +
 rand_distr/src/normal.rs      |  7 +++--
 rand_distr/src/utils.rs       | 48 ++++++++++++++++++++++++++++++++---
 6 files changed, 66 insertions(+), 26 deletions(-)

diff --git a/rand_distr/Cargo.toml b/rand_distr/Cargo.toml
index 526ea0bc124..d6e4931ce34 100644
--- a/rand_distr/Cargo.toml
+++ b/rand_distr/Cargo.toml
@@ -20,4 +20,3 @@ appveyor = { repository = "rust-random/rand" }
 
 [dependencies]
 rand = { path = "..", version = ">=0.5, <=0.7" }
-num-traits = "0.2"
diff --git a/rand_distr/src/exponential.rs b/rand_distr/src/exponential.rs
index bd832f8279d..a4f76194602 100644
--- a/rand_distr/src/exponential.rs
+++ b/rand_distr/src/exponential.rs
@@ -11,8 +11,7 @@
 
 use rand::Rng;
 use crate::{ziggurat_tables, Distribution};
-use crate::utils::ziggurat;
-use num_traits::Float;
+use crate::utils::{ziggurat, Float};
 
 /// Samples floating-point numbers according to the exponential distribution,
 /// with rate parameter `λ = 1`. This is equivalent to `Exp::new(1.0)` or
@@ -105,10 +104,10 @@ where Exp1: Distribution<N>
     /// `lambda`.
     #[inline]
     pub fn new(lambda: N) -> Result<Exp<N>, Error> {
-        if !(lambda > N::zero()) {
+        if !(lambda > N::from(0.0)) {
             return Err(Error::LambdaTooSmall);
         }
-        Ok(Exp { lambda_inverse: N::one() / lambda })
+        Ok(Exp { lambda_inverse: N::from(1.0) / lambda })
     }
 }
 
diff --git a/rand_distr/src/gamma.rs b/rand_distr/src/gamma.rs
index 6035f61107d..2dcbebe09cb 100644
--- a/rand_distr/src/gamma.rs
+++ b/rand_distr/src/gamma.rs
@@ -15,7 +15,7 @@ use self::ChiSquaredRepr::*;
 use rand::Rng;
 use crate::normal::StandardNormal;
 use crate::{Distribution, Exp1, Exp, Open01};
-use num_traits::Float;
+use crate::utils::Float;
 
 /// The Gamma distribution `Gamma(shape, scale)` distribution.
 ///
@@ -108,16 +108,16 @@ where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distributi
     /// distribution.
     #[inline]
     pub fn new(shape: N, scale: N) -> Result<Gamma<N>, Error> {
-        if !(shape > N::zero()) {
+        if !(shape > N::from(0.0)) {
             return Err(Error::ShapeTooSmall);
         }
-        if !(scale > N::zero()) {
+        if !(scale > N::from(0.0)) {
             return Err(Error::ScaleTooSmall);
         }
 
-        let repr = if shape == N::one() {
-            One(Exp::new(N::one() / scale).map_err(|_| Error::ScaleTooLarge)?)
-        } else if shape < N::one() {
+        let repr = if shape == N::from(1.0) {
+            One(Exp::new(N::from(1.0) / scale).map_err(|_| Error::ScaleTooLarge)?)
+        } else if shape < N::from(1.0) {
             Small(GammaSmallShape::new_raw(shape, scale))
         } else {
             Large(GammaLargeShape::new_raw(shape, scale))
@@ -131,8 +131,8 @@ where StandardNormal: Distribution<N>, Open01: Distribution<N>
 {
     fn new_raw(shape: N, scale: N) -> GammaSmallShape<N> {
         GammaSmallShape {
-            inv_shape: N::one() / shape,
-            large_shape: GammaLargeShape::new_raw(shape + N::one(), scale)
+            inv_shape: N::from(1.0) / shape,
+            large_shape: GammaLargeShape::new_raw(shape + N::from(1.0), scale)
         }
     }
 }
@@ -141,10 +141,10 @@ impl<N: Float> GammaLargeShape<N>
 where StandardNormal: Distribution<N>, Open01: Distribution<N>
 {
     fn new_raw(shape: N, scale: N) -> GammaLargeShape<N> {
-        let d = shape - N::from(1. / 3.).unwrap();
+        let d = shape - N::from(1. / 3.);
         GammaLargeShape {
             scale,
-            c: N::one() / (N::from(9.).unwrap() * d).sqrt(),
+            c: N::from(1.0) / (N::from(9.) * d).sqrt(),
             d
         }
     }
@@ -177,8 +177,8 @@ where StandardNormal: Distribution<N>, Open01: Distribution<N>
         // Marsaglia & Tsang method, 2000
         loop {
             let x: N = rng.sample(StandardNormal);
-            let v_cbrt = N::one() + self.c * x;
-            if v_cbrt <= N::zero() { // a^3 <= 0 iff a <= 0
+            let v_cbrt = N::from(1.0) + self.c * x;
+            if v_cbrt <= N::from(0.0) { // a^3 <= 0 iff a <= 0
                 continue
             }
 
@@ -186,8 +186,8 @@ where StandardNormal: Distribution<N>, Open01: Distribution<N>
             let u: N = rng.sample(Open01);
 
             let x_sqr = x * x;
-            if u < N::one() - N::from(0.0331).unwrap() * x_sqr * x_sqr ||
-                u.ln() < N::from(0.5).unwrap() * x_sqr + self.d * (N::one() - v + v.ln())
+            if u < N::from(1.0) - N::from(0.0331) * x_sqr * x_sqr ||
+                u.ln() < N::from(0.5) * x_sqr + self.d * (N::from(1.0) - v + v.ln())
             {
                 return self.d * v * self.scale
             }
diff --git a/rand_distr/src/lib.rs b/rand_distr/src/lib.rs
index d172854098e..32de237814c 100644
--- a/rand_distr/src/lib.rs
+++ b/rand_distr/src/lib.rs
@@ -75,6 +75,7 @@ pub use self::cauchy::{Cauchy, Error as CauchyError};
 pub use self::dirichlet::{Dirichlet, Error as DirichletError};
 pub use self::triangular::{Triangular, TriangularError};
 pub use self::weibull::{Weibull, Error as WeibullError};
+pub use self::utils::Float;
 
 mod unit_sphere;
 mod unit_circle;
diff --git a/rand_distr/src/normal.rs b/rand_distr/src/normal.rs
index ea700e54d8a..036edc20569 100644
--- a/rand_distr/src/normal.rs
+++ b/rand_distr/src/normal.rs
@@ -11,8 +11,7 @@
 
 use rand::Rng;
 use crate::{ziggurat_tables, Distribution, Open01};
-use crate::utils::ziggurat;
-use num_traits::Float;
+use crate::utils::{ziggurat, Float};
 
 /// Samples floating-point numbers according to the normal distribution
 /// `N(0, 1)` (a.k.a. a standard normal, or Gaussian). This is equivalent to
@@ -122,7 +121,7 @@ where StandardNormal: Distribution<N>
     /// standard deviation.
     #[inline]
     pub fn new(mean: N, std_dev: N) -> Result<Normal<N>, Error> {
-        if !(std_dev >= N::zero()) {
+        if !(std_dev >= N::from(0.0)) {
             return Err(Error::StdDevTooSmall);
         }
         Ok(Normal {
@@ -169,7 +168,7 @@ where StandardNormal: Distribution<N>
     /// and standard deviation of the logarithm of the distribution.
     #[inline]
     pub fn new(mean: N, std_dev: N) -> Result<LogNormal<N>, Error> {
-        if !(std_dev >= N::zero()) {
+        if !(std_dev >= N::from(0.0)) {
             return Err(Error::StdDevTooSmall);
         }
         Ok(LogNormal { norm: Normal::new(mean, std_dev).unwrap() })
diff --git a/rand_distr/src/utils.rs b/rand_distr/src/utils.rs
index fcd81a472bb..f7055944302 100644
--- a/rand_distr/src/utils.rs
+++ b/rand_distr/src/utils.rs
@@ -10,8 +10,50 @@
 
 use rand::Rng;
 use crate::ziggurat_tables;
-
 use rand::distributions::hidden_export::IntoFloat;
+use core::{cmp, ops};
+
+/// Trait for floating-point scalar types
+/// 
+/// This allows many distributions to work with `f32` or `f64` parameters and is
+/// potentially extensible. Note however that the `Exp1` and `StandardNormal`
+/// distributions are implemented exclusively for `f32` and `f64`.
+/// 
+/// The bounds and methods are based purely on internal
+/// requirements, and will change as needed.
+pub trait Float: Copy + Sized + cmp::PartialOrd
+    + ops::Add<Output = Self>
+    + ops::Sub<Output = Self>
+    + ops::Mul<Output = Self>
+    + ops::Div<Output = Self>
+{
+    /// Support approximate representation of a f64 value
+    fn from(x: f64) -> Self;
+    /// Take the exponential of self
+    fn exp(self) -> Self;
+    /// Take the natural logarithm of self
+    fn ln(self) -> Self;
+    /// Take square root of self
+    fn sqrt(self) -> Self;
+    /// Take self to a floating-point power
+    fn powf(self, power: Self) -> Self;
+}
+
+impl Float for f32 {
+    fn from(x: f64) -> Self { x as f32 }
+    fn exp(self) -> Self { self.exp() }
+    fn ln(self) -> Self { self.ln() }
+    fn sqrt(self) -> Self { self.sqrt() }
+    fn powf(self, power: Self) -> Self { self.powf(power) }
+}
+
+impl Float for f64 {
+    fn from(x: f64) -> Self { x }
+    fn exp(self) -> Self { self.exp() }
+    fn ln(self) -> Self { self.ln() }
+    fn sqrt(self) -> Self { self.sqrt() }
+    fn powf(self, power: Self) -> Self { self.powf(power) }
+}
 
 /// Calculates ln(gamma(x)) (natural logarithm of the gamma
 /// function) using the Lanczos approximation.
@@ -26,7 +68,7 @@ use rand::distributions::hidden_export::IntoFloat;
 /// `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.
-pub fn log_gamma(x: f64) -> f64 {
+pub(crate) fn log_gamma(x: f64) -> f64 {
     // precalculated 6 coefficients for the first 6 terms of the series
     let coefficients: [f64; 6] = [
         76.18009172947146,
@@ -71,7 +113,7 @@ pub fn log_gamma(x: f64) -> f64 {
 // the perf improvement (25-50%) is definitely worth the extra code
 // size from force-inlining.
 #[inline(always)]
-pub fn ziggurat<R: Rng + ?Sized, P, Z>(
+pub(crate) fn ziggurat<R: Rng + ?Sized, P, Z>(
             rng: &mut R,
             symmetric: bool,
             x_tab: ziggurat_tables::ZigTable,

From 49a26aa31427376fd3f809daf30fb9eea6c51fbe Mon Sep 17 00:00:00 2001
From: Diggory Hardy <git@dhardy.name>
Date: Fri, 10 May 2019 17:56:09 +0100
Subject: [PATCH 2/9] rand_distr: make Cauchy generic over Float type

---
 rand_distr/src/cauchy.rs | 30 +++++++++++++++++-------------
 rand_distr/src/utils.rs  | 21 +++++++++++++++++++++
 2 files changed, 38 insertions(+), 13 deletions(-)

diff --git a/rand_distr/src/cauchy.rs b/rand_distr/src/cauchy.rs
index 5ad36ae5f4b..a59ef842d3d 100644
--- a/rand_distr/src/cauchy.rs
+++ b/rand_distr/src/cauchy.rs
@@ -10,8 +10,8 @@
 //! The Cauchy distribution.
 
 use rand::Rng;
-use crate::Distribution;
-use std::f64::consts::PI;
+use crate::{Distribution, Standard};
+use crate::utils::Float;
 
 /// The Cauchy distribution `Cauchy(median, scale)`.
 ///
@@ -28,9 +28,9 @@ use std::f64::consts::PI;
 /// println!("{} is from a Cauchy(2, 5) distribution", v);
 /// ```
 #[derive(Clone, Copy, Debug)]
-pub struct Cauchy {
-    median: f64,
-    scale: f64
+pub struct Cauchy<N> {
+    median: N,
+    scale: N,
 }
 
 /// Error type returned from `Cauchy::new`.
@@ -40,11 +40,13 @@ pub enum Error {
     ScaleTooSmall,
 }
 
-impl Cauchy {
+impl<N: Float> Cauchy<N>
+where Standard: Distribution<N>
+{
     /// Construct a new `Cauchy` with the given shape parameters
     /// `median` the peak location and `scale` the scale factor.
-    pub fn new(median: f64, scale: f64) -> Result<Cauchy, Error> {
-        if !(scale > 0.0) {
+    pub fn new(median: N, scale: N) -> Result<Cauchy<N>, Error> {
+        if !(scale > N::from(0.0)) {
             return Err(Error::ScaleTooSmall);
         }
         Ok(Cauchy {
@@ -54,13 +56,15 @@ impl Cauchy {
     }
 }
 
-impl Distribution<f64> for Cauchy {
-    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+impl<N: Float> Distribution<N> for Cauchy<N>
+where Standard: Distribution<N>
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
         // sample from [0, 1)
-        let x = rng.gen::<f64>();
+        let x = Standard.sample(rng);
         // get standard cauchy random number
         // note that π/2 is not exactly representable, even if x=0.5 the result is finite
-        let comp_dev = (PI * x).tan();
+        let comp_dev = (N::pi() * x).tan();
         // shift and scale according to parameters
         let result = self.median + self.scale * comp_dev;
         result
@@ -99,7 +103,7 @@ mod test {
     fn test_cauchy_mean() {
         let cauchy = Cauchy::new(10.0, 5.0).unwrap();
         let mut rng = crate::test::rng(123);
-        let mut sum = 0.0;
+        let mut sum = 0.0f64;
         for _ in 0..1000 {
             sum += cauchy.sample(&mut rng);
         }
diff --git a/rand_distr/src/utils.rs b/rand_distr/src/utils.rs
index f7055944302..36714890a01 100644
--- a/rand_distr/src/utils.rs
+++ b/rand_distr/src/utils.rs
@@ -27,8 +27,14 @@ pub trait Float: Copy + Sized + cmp::PartialOrd
     + ops::Mul<Output = Self>
     + ops::Div<Output = Self>
 {
+    /// The constant π
+    fn pi() -> Self;
     /// Support approximate representation of a f64 value
     fn from(x: f64) -> Self;
+    
+    /// Take the absolute value of self
+    fn abs(self) -> Self;
+    
     /// Take the exponential of self
     fn exp(self) -> Self;
     /// Take the natural logarithm of self
@@ -37,22 +43,37 @@ pub trait Float: Copy + Sized + cmp::PartialOrd
     fn sqrt(self) -> Self;
     /// Take self to a floating-point power
     fn powf(self, power: Self) -> Self;
+    
+    /// Take the tangent of self
+    fn tan(self) -> Self;
 }
 
 impl Float for f32 {
+    fn pi() -> Self { core::f32::consts::PI }
     fn from(x: f64) -> Self { x as f32 }
+    
+    fn abs(self) -> Self { self.abs() }
+    
     fn exp(self) -> Self { self.exp() }
     fn ln(self) -> Self { self.ln() }
     fn sqrt(self) -> Self { self.sqrt() }
     fn powf(self, power: Self) -> Self { self.powf(power) }
+    
+    fn tan(self) -> Self { self.tan() }
 }
 
 impl Float for f64 {
+    fn pi() -> Self { core::f64::consts::PI }
     fn from(x: f64) -> Self { x }
+    
+    fn abs(self) -> Self { self.abs() }
+    
     fn exp(self) -> Self { self.exp() }
     fn ln(self) -> Self { self.ln() }
     fn sqrt(self) -> Self { self.sqrt() }
     fn powf(self, power: Self) -> Self { self.powf(power) }
+    
+    fn tan(self) -> Self { self.tan() }
 }
 
 /// Calculates ln(gamma(x)) (natural logarithm of the gamma

From 0290d42a494d433fd2a54bdf9bd1c75a90f24e53 Mon Sep 17 00:00:00 2001
From: Diggory Hardy <git@dhardy.name>
Date: Sat, 11 May 2019 12:56:55 +0100
Subject: [PATCH 3/9] rand_distr: make Dirichlet distr generic over float types

---
 rand_distr/src/dirichlet.rs | 34 +++++++++++++++++++---------------
 rand_distr/src/utils.rs     |  1 +
 2 files changed, 20 insertions(+), 15 deletions(-)

diff --git a/rand_distr/src/dirichlet.rs b/rand_distr/src/dirichlet.rs
index bb53cd7c79b..b4ef530c075 100644
--- a/rand_distr/src/dirichlet.rs
+++ b/rand_distr/src/dirichlet.rs
@@ -10,8 +10,8 @@
 //! The dirichlet distribution.
 
 use rand::Rng;
-use crate::Distribution;
-use crate::gamma::Gamma;
+use crate::{Distribution, Gamma, StandardNormal, Exp1, Open01};
+use crate::utils::Float;
 
 /// The dirichelet distribution `Dirichlet(alpha)`.
 ///
@@ -30,9 +30,9 @@ use crate::gamma::Gamma;
 /// println!("{:?} is from a Dirichlet([1.0, 2.0, 3.0]) distribution", samples);
 /// ```
 #[derive(Clone, Debug)]
-pub struct Dirichlet {
+pub struct Dirichlet<N> {
     /// Concentration parameters (alpha)
-    alpha: Vec<f64>,
+    alpha: Vec<N>,
 }
 
 /// Error type returned from `Dirchlet::new`.
@@ -46,18 +46,20 @@ pub enum Error {
     SizeTooSmall,
 }
 
-impl Dirichlet {
+impl<N: Float> Dirichlet<N>
+where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
+{
     /// Construct a new `Dirichlet` with the given alpha parameter `alpha`.
     ///
     /// Requires `alpha.len() >= 2`.
     #[inline]
-    pub fn new<V: Into<Vec<f64>>>(alpha: V) -> Result<Dirichlet, Error> {
+    pub fn new<V: Into<Vec<N>>>(alpha: V) -> Result<Dirichlet<N>, Error> {
         let a = alpha.into();
         if a.len() < 2 {
             return Err(Error::AlphaTooShort);
         }
         for i in 0..a.len() {
-            if !(a[i] > 0.0) {
+            if !(a[i] > N::from(0.0)) {
                 return Err(Error::AlphaTooSmall);
             }
         }
@@ -69,8 +71,8 @@ impl Dirichlet {
     ///
     /// Requires `size >= 2`.
     #[inline]
-    pub fn new_with_size(alpha: f64, size: usize) -> Result<Dirichlet, Error> {
-        if !(alpha > 0.0) {
+    pub fn new_with_size(alpha: N, size: usize) -> Result<Dirichlet<N>, Error> {
+        if !(alpha > N::from(0.0)) {
             return Err(Error::AlphaTooSmall);
         }
         if size < 2 {
@@ -82,18 +84,20 @@ impl Dirichlet {
     }
 }
 
-impl Distribution<Vec<f64>> for Dirichlet {
-    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Vec<f64> {
+impl<N: Float> Distribution<Vec<N>> for Dirichlet<N>
+where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Vec<N> {
         let n = self.alpha.len();
-        let mut samples = vec![0.0f64; n];
-        let mut sum = 0.0f64;
+        let mut samples = vec![N::from(0.0); n];
+        let mut sum = N::from(0.0);
 
         for i in 0..n {
-            let g = Gamma::new(self.alpha[i], 1.0).unwrap();
+            let g = Gamma::new(self.alpha[i], N::from(1.0)).unwrap();
             samples[i] = g.sample(rng);
             sum += samples[i];
         }
-        let invacc = 1.0 / sum;
+        let invacc = N::from(1.0) / sum;
         for i in 0..n {
             samples[i] *= invacc;
         }
diff --git a/rand_distr/src/utils.rs b/rand_distr/src/utils.rs
index 36714890a01..5a1c774ac8d 100644
--- a/rand_distr/src/utils.rs
+++ b/rand_distr/src/utils.rs
@@ -26,6 +26,7 @@ pub trait Float: Copy + Sized + cmp::PartialOrd
     + ops::Sub<Output = Self>
     + ops::Mul<Output = Self>
     + ops::Div<Output = Self>
+    + ops::AddAssign + ops::SubAssign + ops::MulAssign + ops::DivAssign
 {
     /// The constant π
     fn pi() -> Self;

From 127ba16f8e070c683ae268b81e351d5827bdba97 Mon Sep 17 00:00:00 2001
From: Diggory Hardy <git@dhardy.name>
Date: Sat, 11 May 2019 13:00:27 +0100
Subject: [PATCH 4/9] rand_distr: make Pareto generic over Float

---
 rand_distr/src/pareto.rs | 27 ++++++++++++++++-----------
 1 file changed, 16 insertions(+), 11 deletions(-)

diff --git a/rand_distr/src/pareto.rs b/rand_distr/src/pareto.rs
index 59977940915..134aaaa5e05 100644
--- a/rand_distr/src/pareto.rs
+++ b/rand_distr/src/pareto.rs
@@ -10,6 +10,7 @@
 
 use rand::Rng;
 use crate::{Distribution, OpenClosed01};
+use crate::utils::Float;
 
 /// Samples floating-point numbers according to the Pareto distribution
 ///
@@ -22,9 +23,9 @@ use crate::{Distribution, OpenClosed01};
 /// println!("{}", val);
 /// ```
 #[derive(Clone, Copy, Debug)]
-pub struct Pareto {
-    scale: f64,
-    inv_neg_shape: f64,
+pub struct Pareto<N> {
+    scale: N,
+    inv_neg_shape: N,
 }
 
 /// Error type returned from `Pareto::new`.
@@ -36,25 +37,29 @@ pub enum Error {
     ShapeTooSmall,
 }
 
-impl Pareto {
+impl<N: Float> Pareto<N>
+where OpenClosed01: Distribution<N>
+{
     /// Construct a new Pareto distribution with given `scale` and `shape`.
     ///
     /// In the literature, `scale` is commonly written as x<sub>m</sub> or k and
     /// `shape` is often written as α.
-    pub fn new(scale: f64, shape: f64) -> Result<Pareto, Error> {
-        if !(scale > 0.0) {
+    pub fn new(scale: N, shape: N) -> Result<Pareto<N>, Error> {
+        if !(scale > N::from(0.0)) {
             return Err(Error::ScaleTooSmall);
         }
-        if !(shape > 0.0) {
+        if !(shape > N::from(0.0)) {
             return Err(Error::ShapeTooSmall);
         }
-        Ok(Pareto { scale, inv_neg_shape: -1.0 / shape })
+        Ok(Pareto { scale, inv_neg_shape: N::from(-1.0) / shape })
     }
 }
 
-impl Distribution<f64> for Pareto {
-    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
-        let u: f64 = rng.sample(OpenClosed01);
+impl<N: Float> Distribution<N> for Pareto<N>
+where OpenClosed01: Distribution<N>
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
+        let u: N = OpenClosed01.sample(rng);
         self.scale * u.powf(self.inv_neg_shape)
     }
 }

From 5487157babe7f2b3956bb305c2e04070ca324d53 Mon Sep 17 00:00:00 2001
From: Diggory Hardy <git@dhardy.name>
Date: Sat, 11 May 2019 14:38:51 +0100
Subject: [PATCH 5/9] rand_distr: make ChiSquared, FisherF, StudentT, Beta and
 Pert distributions generic over Float

---
 rand_distr/src/gamma.rs | 94 ++++++++++++++++++++++++-----------------
 rand_distr/src/pert.rs  | 35 ++++++++-------
 2 files changed, 75 insertions(+), 54 deletions(-)

diff --git a/rand_distr/src/gamma.rs b/rand_distr/src/gamma.rs
index 2dcbebe09cb..4018361648e 100644
--- a/rand_distr/src/gamma.rs
+++ b/rand_distr/src/gamma.rs
@@ -213,8 +213,8 @@ where StandardNormal: Distribution<N>, Open01: Distribution<N>
 /// println!("{} is from a χ²(11) distribution", v)
 /// ```
 #[derive(Clone, Copy, Debug)]
-pub struct ChiSquared {
-    repr: ChiSquaredRepr,
+pub struct ChiSquared<N> {
+    repr: ChiSquaredRepr<N>,
 }
 
 /// Error type returned from `ChiSquared::new` and `StudentT::new`.
@@ -225,35 +225,39 @@ pub enum ChiSquaredError {
 }
 
 #[derive(Clone, Copy, Debug)]
-enum ChiSquaredRepr {
+enum ChiSquaredRepr<N> {
     // 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.
     DoFExactlyOne,
-    DoFAnythingElse(Gamma<f64>),
+    DoFAnythingElse(Gamma<N>),
 }
 
-impl ChiSquared {
+impl<N: Float> ChiSquared<N>
+where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
+{
     /// Create a new chi-squared distribution with degrees-of-freedom
     /// `k`.
-    pub fn new(k: f64) -> Result<ChiSquared, ChiSquaredError> {
-        let repr = if k == 1.0 {
+    pub fn new(k: N) -> Result<ChiSquared<N>, ChiSquaredError> {
+        let repr = if k == N::from(1.0) {
             DoFExactlyOne
         } else {
-            if !(0.5 * k > 0.0) {
+            if !(N::from(0.5) * k > N::from(0.0)) {
                 return Err(ChiSquaredError::DoFTooSmall);
             }
-            DoFAnythingElse(Gamma::new(0.5 * k, 2.0).unwrap())
+            DoFAnythingElse(Gamma::new(N::from(0.5) * k, N::from(2.0)).unwrap())
         };
         Ok(ChiSquared { repr })
     }
 }
-impl Distribution<f64> for ChiSquared {
-    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+impl<N: Float> Distribution<N> for ChiSquared<N>
+where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
         match self.repr {
             DoFExactlyOne => {
                 // k == 1 => N(0,1)^2
-                let norm: f64 = rng.sample(StandardNormal);
+                let norm: N = rng.sample(StandardNormal);
                 norm * norm
             }
             DoFAnythingElse(ref g) => g.sample(rng)
@@ -277,12 +281,12 @@ impl Distribution<f64> for ChiSquared {
 /// println!("{} is from an F(2, 32) distribution", v)
 /// ```
 #[derive(Clone, Copy, Debug)]
-pub struct FisherF {
-    numer: ChiSquared,
-    denom: ChiSquared,
+pub struct FisherF<N> {
+    numer: ChiSquared<N>,
+    denom: ChiSquared<N>,
     // denom_dof / numer_dof so that this can just be a straight
     // multiplication, rather than a division.
-    dof_ratio: f64,
+    dof_ratio: N,
 }
 
 /// Error type returned from `FisherF::new`.
@@ -294,13 +298,15 @@ pub enum FisherFError {
     NTooSmall,
 }
 
-impl FisherF {
+impl<N: Float> FisherF<N>
+where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
+{
     /// Create a new `FisherF` distribution, with the given parameter.
-    pub fn new(m: f64, n: f64) -> Result<FisherF, FisherFError> {
-        if !(m > 0.0) {
+    pub fn new(m: N, n: N) -> Result<FisherF<N>, FisherFError> {
+        if !(m > N::from(0.0)) {
             return Err(FisherFError::MTooSmall);
         }
-        if !(n > 0.0) {
+        if !(n > N::from(0.0)) {
             return Err(FisherFError::NTooSmall);
         }
 
@@ -311,8 +317,10 @@ impl FisherF {
         })
     }
 }
-impl Distribution<f64> for FisherF {
-    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+impl<N: Float> Distribution<N> for FisherF<N>
+where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
         self.numer.sample(rng) / self.denom.sample(rng) * self.dof_ratio
     }
 }
@@ -330,24 +338,28 @@ impl Distribution<f64> for FisherF {
 /// println!("{} is from a t(11) distribution", v)
 /// ```
 #[derive(Clone, Copy, Debug)]
-pub struct StudentT {
-    chi: ChiSquared,
-    dof: f64
+pub struct StudentT<N> {
+    chi: ChiSquared<N>,
+    dof: N
 }
 
-impl StudentT {
+impl<N: Float> StudentT<N>
+where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
+{
     /// Create a new Student t distribution with `n` degrees of
     /// freedom.
-    pub fn new(n: f64) -> Result<StudentT, ChiSquaredError> {
+    pub fn new(n: N) -> Result<StudentT<N>, ChiSquaredError> {
         Ok(StudentT {
             chi: ChiSquared::new(n)?,
             dof: n
         })
     }
 }
-impl Distribution<f64> for StudentT {
-    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
-        let norm: f64 = rng.sample(StandardNormal);
+impl<N: Float> Distribution<N> for StudentT<N>
+where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
+        let norm: N = rng.sample(StandardNormal);
         norm * (self.dof / self.chi.sample(rng)).sqrt()
     }
 }
@@ -364,9 +376,9 @@ impl Distribution<f64> for StudentT {
 /// println!("{} is from a Beta(2, 5) distribution", v);
 /// ```
 #[derive(Clone, Copy, Debug)]
-pub struct Beta {
-    gamma_a: Gamma<f64>,
-    gamma_b: Gamma<f64>,
+pub struct Beta<N> {
+    gamma_a: Gamma<N>,
+    gamma_b: Gamma<N>,
 }
 
 /// Error type returned from `Beta::new`.
@@ -378,21 +390,25 @@ pub enum BetaError {
     BetaTooSmall,
 }
 
-impl Beta {
+impl<N: Float> Beta<N>
+where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
+{
     /// Construct an object representing the `Beta(alpha, beta)`
     /// distribution.
-    pub fn new(alpha: f64, beta: f64) -> Result<Beta, BetaError> {
+    pub fn new(alpha: N, beta: N) -> Result<Beta<N>, BetaError> {
         Ok(Beta {
-            gamma_a: Gamma::new(alpha, 1.)
+            gamma_a: Gamma::new(alpha, N::from(1.))
                          .map_err(|_| BetaError::AlphaTooSmall)?,
-            gamma_b: Gamma::new(beta, 1.)
+            gamma_b: Gamma::new(beta, N::from(1.))
                          .map_err(|_| BetaError::BetaTooSmall)?,
         })
     }
 }
 
-impl Distribution<f64> for Beta {
-    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+impl<N: Float> Distribution<N> for Beta<N>
+where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
         let x = self.gamma_a.sample(rng);
         let y = self.gamma_b.sample(rng);
         x / (x + y)
diff --git a/rand_distr/src/pert.rs b/rand_distr/src/pert.rs
index 13d7faceca3..25d4c3a824c 100644
--- a/rand_distr/src/pert.rs
+++ b/rand_distr/src/pert.rs
@@ -8,7 +8,8 @@
 //! The PERT distribution.
 
 use rand::Rng;
-use crate::{Distribution, Beta};
+use crate::{Distribution, Beta, StandardNormal, Exp1, Open01};
+use crate::utils::Float;
 
 /// The PERT distribution.
 ///
@@ -27,10 +28,10 @@ use crate::{Distribution, Beta};
 /// println!("{} is from a PERT distribution", v);
 /// ```
 #[derive(Clone, Copy, Debug)]
-pub struct Pert {
-    min: f64,
-    range: f64,
-    beta: Beta,
+pub struct Pert<N> {
+    min: N,
+    range: N,
+    beta: Beta<N>,
 }
 
 /// Error type returned from [`Pert`] constructors.
@@ -44,34 +45,36 @@ pub enum PertError {
     ShapeTooSmall,
 }
 
-impl Pert {
+impl<N: Float> Pert<N>
+where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
+{
     /// Set up the PERT distribution with defined `min`, `max` and `mode`.
     ///
     /// This is equivalent to calling `Pert::new_shape` with `shape == 4.0`.
     #[inline]
-    pub fn new(min: f64, max: f64, mode: f64) -> Result<Pert, PertError> {
-        Pert::new_with_shape(min, max, mode, 4.)
+    pub fn new(min: N, max: N, mode: N) -> Result<Pert<N>, PertError> {
+        Pert::new_with_shape(min, max, mode, N::from(4.))
     }
     
     /// Set up the PERT distribution with defined `min`, `max`, `mode` and
     /// `shape`.
-    pub fn new_with_shape(min: f64, max: f64, mode: f64, shape: f64) -> Result<Pert, PertError> {
+    pub fn new_with_shape(min: N, max: N, mode: N, shape: N) -> Result<Pert<N>, PertError> {
         if !(max > min) {
             return Err(PertError::RangeTooSmall);
         }
         if !(mode >= min && max >= mode) {
             return Err(PertError::ModeRange);
         }
-        if !(shape >= 0.) {
+        if !(shape >= N::from(0.)) {
             return Err(PertError::ShapeTooSmall);
         }
         
         let range = max - min;
-        let mu = (min + max + shape * mode) / (shape + 2.);
+        let mu = (min + max + shape * mode) / (shape + N::from(2.));
         let v = if mu == mode {
-            shape * 0.5 + 1.
+            shape * N::from(0.5) + N::from(1.)
         } else {
-            (mu - min) * (2. * mode - min - max)
+            (mu - min) * (N::from(2.) * mode - min - max)
                 / ((mode - mu) * (max - min))
         };
         let w = v * (max - mu) / (mu - min);
@@ -80,9 +83,11 @@ impl Pert {
     }
 }
 
-impl Distribution<f64> for Pert {
+impl<N: Float> Distribution<N> for Pert<N>
+where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
+{
     #[inline]
-    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
         self.beta.sample(rng) * self.range + self.min
     }
 }

From 9f13fcf86f69ed1f175dd630e2a26392d7966486 Mon Sep 17 00:00:00 2001
From: Diggory Hardy <git@dhardy.name>
Date: Mon, 13 May 2019 11:30:25 +0100
Subject: [PATCH 6/9] rand_distr: make Triangular generic over Float

---
 rand_distr/src/triangular.rs | 23 ++++++++++++++---------
 1 file changed, 14 insertions(+), 9 deletions(-)

diff --git a/rand_distr/src/triangular.rs b/rand_distr/src/triangular.rs
index b735743b3ff..72d58c5f278 100644
--- a/rand_distr/src/triangular.rs
+++ b/rand_distr/src/triangular.rs
@@ -9,6 +9,7 @@
 
 use rand::Rng;
 use crate::{Distribution, Standard};
+use crate::utils::Float;
 
 /// The triangular distribution.
 /// 
@@ -28,10 +29,10 @@ use crate::{Distribution, Standard};
 /// println!("{} is from a triangular distribution", v);
 /// ```
 #[derive(Clone, Copy, Debug)]
-pub struct Triangular {
-    min: f64,
-    max: f64,
-    mode: f64,
+pub struct Triangular<N> {
+    min: N,
+    max: N,
+    mode: N,
 }
 
 /// Error type returned from [`Triangular::new`].
@@ -43,10 +44,12 @@ pub enum TriangularError {
     ModeRange,
 }
 
-impl Triangular {
+impl<N: Float> Triangular<N>
+where Standard: Distribution<N>
+{
     /// Set up the Triangular distribution with defined `min`, `max` and `mode`.
     #[inline]
-    pub fn new(min: f64, max: f64, mode: f64) -> Result<Triangular, TriangularError> {
+    pub fn new(min: N, max: N, mode: N) -> Result<Triangular<N>, TriangularError> {
         if !(max >= min) {
             return Err(TriangularError::RangeTooSmall);
         }
@@ -57,10 +60,12 @@ impl Triangular {
     }
 }
 
-impl Distribution<f64> for Triangular {
+impl<N: Float> Distribution<N> for Triangular<N>
+where Standard: Distribution<N>
+{
     #[inline]
-    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
-        let f: f64 = rng.sample(Standard);
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
+        let f: N = rng.sample(Standard);
         let diff_mode_min = self.mode - self.min;
         let range = self.max - self.min;
         let f_range = f * range;

From db795b5e97eaa764616c7602f6b0cd18d24027ab Mon Sep 17 00:00:00 2001
From: Diggory Hardy <git@dhardy.name>
Date: Mon, 13 May 2019 11:38:47 +0100
Subject: [PATCH 7/9] rand_distr: make UnitCircle and UnitSphereSurface generic
 over Float

---
 rand_distr/src/lib.rs         |  2 +-
 rand_distr/src/unit_circle.rs | 13 +++++++------
 rand_distr/src/unit_sphere.rs | 15 ++++++++-------
 3 files changed, 16 insertions(+), 14 deletions(-)

diff --git a/rand_distr/src/lib.rs b/rand_distr/src/lib.rs
index 32de237814c..0e333e7c9d6 100644
--- a/rand_distr/src/lib.rs
+++ b/rand_distr/src/lib.rs
@@ -59,7 +59,7 @@
 //!   - [`UnitCircle`] distribution
 
 pub use rand::distributions::{Distribution, DistIter, Standard,
-    Alphanumeric, Uniform, OpenClosed01, Open01, Bernoulli, weighted};
+    Alphanumeric, Uniform, OpenClosed01, Open01, Bernoulli, uniform, weighted};
 
 pub use self::unit_sphere::UnitSphereSurface;
 pub use self::unit_circle::UnitCircle;
diff --git a/rand_distr/src/unit_circle.rs b/rand_distr/src/unit_circle.rs
index 948cbccf68b..65ee234911b 100644
--- a/rand_distr/src/unit_circle.rs
+++ b/rand_distr/src/unit_circle.rs
@@ -7,7 +7,8 @@
 // except according to those terms.
 
 use rand::Rng;
-use crate::{Distribution, Uniform};
+use crate::{Distribution, Uniform, uniform::SampleUniform};
+use crate::utils::Float;
 
 /// Samples uniformly from the edge of the unit circle in two dimensions.
 ///
@@ -30,10 +31,10 @@ use crate::{Distribution, Uniform};
 #[derive(Clone, Copy, Debug)]
 pub struct UnitCircle;
 
-impl Distribution<[f64; 2]> for UnitCircle {
+impl<N: Float + SampleUniform> Distribution<[N; 2]> for UnitCircle {
     #[inline]
-    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [f64; 2] {
-        let uniform = Uniform::new(-1., 1.);
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [N; 2] {
+        let uniform = Uniform::new(N::from(-1.), N::from(1.));
         let mut x1;
         let mut x2;
         let mut sum;
@@ -41,12 +42,12 @@ impl Distribution<[f64; 2]> for UnitCircle {
             x1 = uniform.sample(rng);
             x2 = uniform.sample(rng);
             sum = x1*x1 + x2*x2;
-            if sum < 1. {
+            if sum < N::from(1.) {
                 break;
             }
         }
         let diff = x1*x1 - x2*x2;
-        [diff / sum, 2.*x1*x2 / sum]
+        [diff / sum, N::from(2.)*x1*x2 / sum]
     }
 }
 
diff --git a/rand_distr/src/unit_sphere.rs b/rand_distr/src/unit_sphere.rs
index 1680e9da7e1..f7d453c092d 100644
--- a/rand_distr/src/unit_sphere.rs
+++ b/rand_distr/src/unit_sphere.rs
@@ -7,7 +7,8 @@
 // except according to those terms.
 
 use rand::Rng;
-use crate::{Distribution, Uniform};
+use crate::{Distribution, Uniform, uniform::SampleUniform};
+use crate::utils::Float;
 
 /// Samples uniformly from the surface of the unit sphere in three dimensions.
 ///
@@ -29,18 +30,18 @@ use crate::{Distribution, Uniform};
 #[derive(Clone, Copy, Debug)]
 pub struct UnitSphereSurface;
 
-impl Distribution<[f64; 3]> for UnitSphereSurface {
+impl<N: Float + SampleUniform> Distribution<[N; 3]> for UnitSphereSurface {
     #[inline]
-    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [f64; 3] {
-        let uniform = Uniform::new(-1., 1.);
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> [N; 3] {
+        let uniform = Uniform::new(N::from(-1.), N::from(1.));
         loop {
             let (x1, x2) = (uniform.sample(rng), uniform.sample(rng));
             let sum = x1*x1 + x2*x2;
-            if sum >= 1. {
+            if sum >= N::from(1.) {
                 continue;
             }
-            let factor = 2. * (1.0_f64 - sum).sqrt();
-            return [x1 * factor, x2 * factor, 1. - 2.*sum];
+            let factor = N::from(2.) * (N::from(1.0) - sum).sqrt();
+            return [x1 * factor, x2 * factor, N::from(1.) - N::from(2.)*sum];
         }
     }
 }

From ef5961357b265d1f26868980e9880ec0c57538ce Mon Sep 17 00:00:00 2001
From: Diggory Hardy <git@dhardy.name>
Date: Mon, 13 May 2019 11:41:33 +0100
Subject: [PATCH 8/9] rand_distr: make Weibull generic over Float

---
 rand_distr/src/utils.rs   |  1 +
 rand_distr/src/weibull.rs | 27 ++++++++++++++++-----------
 2 files changed, 17 insertions(+), 11 deletions(-)

diff --git a/rand_distr/src/utils.rs b/rand_distr/src/utils.rs
index 5a1c774ac8d..e5f107f23e5 100644
--- a/rand_distr/src/utils.rs
+++ b/rand_distr/src/utils.rs
@@ -22,6 +22,7 @@ use core::{cmp, ops};
 /// The bounds and methods are based purely on internal
 /// requirements, and will change as needed.
 pub trait Float: Copy + Sized + cmp::PartialOrd
+    + ops::Neg<Output = Self>
     + ops::Add<Output = Self>
     + ops::Sub<Output = Self>
     + ops::Mul<Output = Self>
diff --git a/rand_distr/src/weibull.rs b/rand_distr/src/weibull.rs
index 8d3c66d8919..5a05da92dc5 100644
--- a/rand_distr/src/weibull.rs
+++ b/rand_distr/src/weibull.rs
@@ -10,6 +10,7 @@
 
 use rand::Rng;
 use crate::{Distribution, OpenClosed01};
+use crate::utils::Float;
 
 /// Samples floating-point numbers according to the Weibull distribution
 ///
@@ -22,9 +23,9 @@ use crate::{Distribution, OpenClosed01};
 /// println!("{}", val);
 /// ```
 #[derive(Clone, Copy, Debug)]
-pub struct Weibull {
-    inv_shape: f64,
-    scale: f64,
+pub struct Weibull<N> {
+    inv_shape: N,
+    scale: N,
 }
 
 /// Error type returned from `Weibull::new`.
@@ -36,22 +37,26 @@ pub enum Error {
     ShapeTooSmall,
 }
 
-impl Weibull {
+impl<N: Float> Weibull<N>
+where OpenClosed01: Distribution<N>
+{
     /// Construct a new `Weibull` distribution with given `scale` and `shape`.
-    pub fn new(scale: f64, shape: f64) -> Result<Weibull, Error> {
-        if !(scale > 0.0) {
+    pub fn new(scale: N, shape: N) -> Result<Weibull<N>, Error> {
+        if !(scale > N::from(0.0)) {
             return Err(Error::ScaleTooSmall);
         }
-        if !(shape > 0.0) {
+        if !(shape > N::from(0.0)) {
             return Err(Error::ShapeTooSmall);
         }
-        Ok(Weibull { inv_shape: 1./shape, scale })
+        Ok(Weibull { inv_shape: N::from(1.)/shape, scale })
     }
 }
 
-impl Distribution<f64> for Weibull {
-    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
-        let x: f64 = rng.sample(OpenClosed01);
+impl<N: Float> Distribution<N> for Weibull<N>
+where OpenClosed01: Distribution<N>
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
+        let x: N = rng.sample(OpenClosed01);
         self.scale * (-x.ln()).powf(self.inv_shape)
     }
 }

From b330c210014eed72ac1b859e8ef8525efc6ca2b9 Mon Sep 17 00:00:00 2001
From: Diggory Hardy <git@dhardy.name>
Date: Tue, 14 May 2019 12:54:26 +0100
Subject: [PATCH 9/9] rand_distr: fix unit circle and sphere type
 specifications

These are required as a side-effect of the previous generalisation.
---
 rand_distr/src/unit_circle.rs | 18 +++++++++++++-----
 rand_distr/src/unit_sphere.rs | 21 +++++++++++++--------
 2 files changed, 26 insertions(+), 13 deletions(-)

diff --git a/rand_distr/src/unit_circle.rs b/rand_distr/src/unit_circle.rs
index 65ee234911b..55cfe4ff60c 100644
--- a/rand_distr/src/unit_circle.rs
+++ b/rand_distr/src/unit_circle.rs
@@ -20,7 +20,7 @@ use crate::utils::Float;
 /// ```
 /// use rand_distr::{UnitCircle, Distribution};
 ///
-/// let v = UnitCircle.sample(&mut rand::thread_rng());
+/// let v: [f64; 2] = UnitCircle.sample(&mut rand::thread_rng());
 /// println!("{:?} is from the unit circle.", v)
 /// ```
 ///
@@ -76,7 +76,7 @@ mod tests {
     fn norm() {
         let mut rng = crate::test::rng(1);
         for _ in 0..1000 {
-            let x = UnitCircle.sample(&mut rng);
+            let x: [f64; 2] = UnitCircle.sample(&mut rng);
             assert_almost_eq!(x[0]*x[0] + x[1]*x[1], 1., 1e-15);
         }
     }
@@ -84,8 +84,16 @@ mod tests {
     #[test]
     fn value_stability() {
         let mut rng = crate::test::rng(2);
-        assert_eq!(UnitCircle.sample(&mut rng), [-0.8032118336637037, 0.5956935036263119]);
-        assert_eq!(UnitCircle.sample(&mut rng), [-0.4742919588505423, -0.880367615130018]);
-        assert_eq!(UnitCircle.sample(&mut rng), [0.9297328981467168, 0.368234623716601]);
+        let expected = [
+                [-0.8032118336637037, 0.5956935036263119],
+                [-0.4742919588505423, -0.880367615130018],
+                [0.9297328981467168, 0.368234623716601],
+            ];
+        let samples: [[f64; 2]; 3] = [
+                UnitCircle.sample(&mut rng),
+                UnitCircle.sample(&mut rng),
+                UnitCircle.sample(&mut rng),
+            ];
+        assert_eq!(samples, expected);
     }
 }
diff --git a/rand_distr/src/unit_sphere.rs b/rand_distr/src/unit_sphere.rs
index f7d453c092d..dad6f5f7e11 100644
--- a/rand_distr/src/unit_sphere.rs
+++ b/rand_distr/src/unit_sphere.rs
@@ -20,7 +20,7 @@ use crate::utils::Float;
 /// ```
 /// use rand_distr::{UnitSphereSurface, Distribution};
 ///
-/// let v = UnitSphereSurface.sample(&mut rand::thread_rng());
+/// let v: [f64; 3] = UnitSphereSurface.sample(&mut rand::thread_rng());
 /// println!("{:?} is from the unit sphere surface.", v)
 /// ```
 ///
@@ -71,7 +71,7 @@ mod tests {
     fn norm() {
         let mut rng = crate::test::rng(1);
         for _ in 0..1000 {
-            let x = UnitSphereSurface.sample(&mut rng);
+            let x: [f64; 3] = UnitSphereSurface.sample(&mut rng);
             assert_almost_eq!(x[0]*x[0] + x[1]*x[1] + x[2]*x[2], 1., 1e-15);
         }
     }
@@ -79,11 +79,16 @@ mod tests {
     #[test]
     fn value_stability() {
         let mut rng = crate::test::rng(2);
-        assert_eq!(UnitSphereSurface.sample(&mut rng),
-                   [-0.24950027180862533, -0.7552572587896719, 0.6060825747478084]);
-        assert_eq!(UnitSphereSurface.sample(&mut rng),
-                   [0.47604534507233487, -0.797200864987207, -0.3712837328763685]);
-        assert_eq!(UnitSphereSurface.sample(&mut rng),
-                   [0.9795722330927367, 0.18692349236651176, 0.07414747571708524]);
+        let expected = [
+                [-0.24950027180862533, -0.7552572587896719, 0.6060825747478084],
+                [0.47604534507233487, -0.797200864987207, -0.3712837328763685],
+                [0.9795722330927367, 0.18692349236651176, 0.07414747571708524],
+            ];
+        let samples: [[f64; 3]; 3] = [
+                UnitSphereSurface.sample(&mut rng),
+                UnitSphereSurface.sample(&mut rng),
+                UnitSphereSurface.sample(&mut rng),
+            ];
+        assert_eq!(samples, expected);
     }
 }