Add traits `Distance` and `Norm` in order to provide abstract notions of distances between numbers.

The `Norm` trait provides a `norm` function for types that represent a normed vector space – e.g. the absolute value of a float or the norm of a complex number.

The `Distance` trait provides a `distance` function to still calculate the distance between two values if no sensible norm can be defined.

src/dist.rs

@@ -0,0 +1,73 @@
+use std::ops::{Sub, Div, DivAssign};
+
+use {Num};
+
+pub trait Distance {
+    type Output: Num;
+    fn distance(&self, other: &Self) -> Self::Output;
+}
+
+pub trait Norm: Sized  {
+    type Output: Num;
+    fn norm(&self) -> <Self as Norm>::Output;
+}
+
+pub fn normalize<T: Norm<Output=R> + DivAssign<R>, R: Num>(v: &mut T) {
+    *v /= v.norm();
+}
+
+pub fn normalized<T: Norm<Output=R> + Div<R, Output=T>, R: Num>(v: T) -> T {
+    let norm = v.norm();
+    v / norm
+}
+
+impl<T: Copy + Norm + Sub<Self, Output=Self>> Distance for T{
+    type Output = <Self as Norm>::Output;
+    fn distance(&self, other: &Self) -> <Self as Distance>::Output {
+        (*self - *other).norm()
+    }
+}
+
+
+macro_rules! norm_impl_self {
+    ($($t:ty)*) => ($(
+        impl Norm for $t {
+            type Output = Self;
+            fn norm(&self) -> <Self as Norm>::Output {
+                *self
+            }
+        }
+    )*)
+}
+
+macro_rules! norm_impl_abs {
+    ($($t:ty)*) => ($(
+        impl Norm for $t {
+            type Output = Self;
+            fn norm(&self) -> <Self as Norm>::Output {
+                self.abs()
+            }
+        }
+    )*)
+}
+
+macro_rules! norm_impl_unsigned_output {
+    ($($t:ty, $out:ty);*) => ($(
+        impl Norm for $t {
+            type Output = $out;
+            fn norm(&self) -> <Self as Norm>::Output {
+                self.abs() as $out
+            }
+        }
+    )*)
+}
+
+norm_impl_abs!(f32 f64);
+norm_impl_unsigned_output!(i8, u8; i16, u16; i32, u32; i64, u64; isize, usize);
+norm_impl_self!(u8 u16 u32 u64 usize);
+
+#[cfg(has_i128)]
+norm_impl_unsigned_output!(i128, u128);
+
+#[cfg(has_u128)]
+norm_impl_self!(u128);

src/lib.rs

@@ -48,6 +48,7 @@ mod macros;
 
 pub mod bounds;
 pub mod cast;
+pub mod dist;
 pub mod float;
 pub mod identities;
 pub mod int;