From d8b0d424174f1da974b40490e152c0d7e12d74fd Mon Sep 17 00:00:00 2001
From: Vinzent Steinberg <Vinzent.Steinberg@gmail.com>
Date: Mon, 30 Jul 2018 15:17:54 +0200
Subject: [PATCH 1/2] Implement triangular distribution

---
 src/distributions/mod.rs        |  5 ++
 src/distributions/triangular.rs | 88 +++++++++++++++++++++++++++++++++
 2 files changed, 93 insertions(+)
 create mode 100644 src/distributions/triangular.rs

diff --git a/src/distributions/mod.rs b/src/distributions/mod.rs
index 082d22278f4..9afc2bc2e87 100644
--- a/src/distributions/mod.rs
+++ b/src/distributions/mod.rs
@@ -98,6 +98,8 @@
 //!   - [`ChiSquared`] distribution
 //!   - [`StudentT`] distribution
 //!   - [`FisherF`] distribution
+//! - Triangular distribution:
+//!  - [`Triangular`] distribution
 //! - Multivariate probability distributions
 //!   - [`Dirichlet`] distribution
 //!   - [`UnitSphereSurface`] distribution
@@ -168,6 +170,7 @@
 //! [`Standard`]: struct.Standard.html
 //! [`StandardNormal`]: struct.StandardNormal.html
 //! [`StudentT`]: struct.StudentT.html
+//! [`Triangular`]: struct.Triangular.html
 //! [`Uniform`]: struct.Uniform.html
 //! [`Uniform::new`]: struct.Uniform.html#method.new
 //! [`Uniform::new_inclusive`]: struct.Uniform.html#method.new_inclusive
@@ -192,6 +195,7 @@ pub use self::bernoulli::Bernoulli;
 #[cfg(feature="std")] pub use self::binomial::Binomial;
 #[cfg(feature="std")] pub use self::cauchy::Cauchy;
 #[cfg(feature="std")] pub use self::dirichlet::Dirichlet;
+#[cfg(feature="std")] pub use self::triangular::Triangular;
 
 pub mod uniform;
 mod bernoulli;
@@ -206,6 +210,7 @@ mod bernoulli;
 #[cfg(feature="std")] mod binomial;
 #[cfg(feature="std")] mod cauchy;
 #[cfg(feature="std")] mod dirichlet;
+#[cfg(feature="std")] mod triangular;
 
 mod float;
 mod integer;
diff --git a/src/distributions/triangular.rs b/src/distributions/triangular.rs
new file mode 100644
index 00000000000..5b4c467b68d
--- /dev/null
+++ b/src/distributions/triangular.rs
@@ -0,0 +1,88 @@
+// 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 triangular distribution.
+
+use Rng;
+use distributions::{Distribution, Standard};
+
+/// The triangular distribution.
+///
+/// # Example
+///
+/// ```rust
+/// use rand::distributions::{Triangular, Distribution};
+///
+/// let d = Triangular::new(0., 5., 2.5);
+/// let v = d.sample(&mut rand::thread_rng());
+/// println!("{} is from a triangular distribution", v);
+/// ```
+#[derive(Clone, Copy, Debug)]
+pub struct Triangular {
+    min: f64,
+    max: f64,
+    mode: f64,
+}
+
+impl Triangular {
+    /// Construct a new `Triangular` with minimum `min`, maximum `max` and mode
+    /// `mode`.
+    ///
+    /// # Panics
+    ///
+    /// If `max < mode`, `mode < max` or `max == min`.
+    ///
+    #[inline]
+    pub fn new(min: f64, max: f64, mode: f64) -> Triangular {
+        assert!(max >= mode);
+        assert!(mode >= min);
+        assert!(max != min);
+        Triangular { min, max, mode }
+    }
+}
+
+impl Distribution<f64> for Triangular {
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
+        let f: f64 = rng.sample(Standard);
+        let diff_mode_min = self.mode - self.min;
+        let diff_max_min = self.max - self.min;
+        if f < diff_mode_min / diff_max_min {
+            self.min + (f * diff_max_min * diff_mode_min).sqrt()
+        } else {
+            self.max - ((1. - f) * diff_max_min * (self.max - self.mode)).sqrt()
+        }
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use distributions::Distribution;
+    use super::Triangular;
+
+    #[test]
+    fn test_new() {
+        for &(min, max, mode) in &[
+            (-1., 1., 0.), (1., 2., 1.), (5., 25., 25.), (1e-5, 1e5, 1e-3),
+            (0., 1., 0.9), (-4., -0.5, -2.), (-13.039, 8.41, 1.17),
+        ] {
+            println!("{} {} {}", min, max, mode);
+            let _ = Triangular::new(min, max, mode);
+        }
+    }
+
+    #[test]
+    fn test_sample() {
+        let norm = Triangular::new(0., 1., 0.5);
+        let mut rng = ::test::rng(1);
+        for _ in 0..1000 {
+            norm.sample(&mut rng);
+        }
+    }
+}

From 7f1bf4efc3196c8bffbeee1bc9b9f5bdd4e58582 Mon Sep 17 00:00:00 2001
From: Vinzent Steinberg <Vinzent.Steinberg@gmail.com>
Date: Mon, 30 Jul 2018 15:22:53 +0200
Subject: [PATCH 2/2] Triangular: Avoid division

---
 src/distributions/triangular.rs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/distributions/triangular.rs b/src/distributions/triangular.rs
index 5b4c467b68d..27c5c59d0e9 100644
--- a/src/distributions/triangular.rs
+++ b/src/distributions/triangular.rs
@@ -53,7 +53,7 @@ impl Distribution<f64> for Triangular {
         let f: f64 = rng.sample(Standard);
         let diff_mode_min = self.mode - self.min;
         let diff_max_min = self.max - self.min;
-        if f < diff_mode_min / diff_max_min {
+        if f * diff_max_min < diff_mode_min {
             self.min + (f * diff_max_min * diff_mode_min).sqrt()
         } else {
             self.max - ((1. - f) * diff_max_min * (self.max - self.mode)).sqrt()