Document why we use an open interval

src/distributions/float.rs

@@ -45,15 +45,6 @@ macro_rules! float_impls {
         impl Distribution<$ty> for Uniform {
             /// Generate a floating point number in the open interval `(0, 1)`
             /// (not including either endpoint) with a uniform distribution.
-            ///
-            /// # Example
-            /// ```rust
-            /// use rand::{NewRng, SmallRng, Rng};
-            /// use rand::distributions::Uniform;
-            ///
-            /// let val: f32 = SmallRng::new().sample(Uniform);
-            /// println!("f32 from (0,1): {}", val);
-            /// ```
             fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> $ty {
                 const EPSILON: $ty = 1.0 / (1u64 << $fraction_bits) as $ty;
                 let float_size = mem::size_of::<$ty>() * 8;

src/distributions/mod.rs

@@ -177,7 +177,7 @@ impl<'a, T, D: Distribution<T>> Distribution<T> for &'a D {
 /// use rand::distributions::Uniform;
 ///
 /// let val: f32 = SmallRng::new().sample(Uniform);
-/// println!("f32 from [0,1): {}", val);
+/// println!("f32 from (0,1): {}", val);
 /// ```
 ///
 /// With dynamic dispatch (type erasure of `Rng`):
@@ -189,9 +189,29 @@ impl<'a, T, D: Distribution<T>> Distribution<T> for &'a D {
 /// let mut rng = thread_rng();
 /// let mut erased_rng: &mut RngCore = &mut rng;
 /// let val: f32 = erased_rng.sample(Uniform);
-/// println!("f32 from [0,1): {}", val);
+/// println!("f32 from (0,1): {}", val);
 /// ```
 ///
+/// # Open interval for floats
+/// In theory it is possible to choose between an open interval `(0, 1)`, and
+/// the half-open intervals `[0, 1)` and `(0, 1]`. All can give a distribution
+/// with perfectly uniform intervals. Many libraries in other programming
+/// languages default to the closed-open interval `[0, 1)`. We choose here to go
+/// with *open*, with the arguments:
+///
+/// - The chance to generate a specific value, like exactly 0.0, is *tiny*. No
+///   (or almost no) sensible code relies on an exact floating-point value to be
+///   generated with a very small chance (1 in ~8 million (2^23) for `f32`, and
+///   1 in 2^52 for `f64`). What is relied on is having a uniform distribution
+///   and a mean of `0.5`.
+/// - Several common algorithms rely on never seeing the value `0.0` generated,
+///   i.e. they rely on an open interval. For example when the logarithm of the
+///   value is taken, or used as a devisor.
+///
+/// In other words, the guarantee some value *could* be generated is less useful
+/// than the guarantee some value (`0.0`) is never generated. That makes an open
+/// interval a nicer choice.
+///
 /// [`Exp1`]: struct.Exp1.html
 /// [`StandardNormal`]: struct.StandardNormal.html
 #[derive(Debug)]

src/lib.rs

@@ -410,7 +410,7 @@ pub trait Rng: RngCore {
 
     /// Return a random value supporting the [`Uniform`] distribution.
     /// 
-    /// [`Uniform`]: struct.Uniform.html
+    /// [`Uniform`]: distributions/struct.Uniform.html
     ///
     /// # Example
     ///