Remove Float bound from MetricSpace and InnerSpace; move Float bound to individual methods

This makes it possible to call methods like `dot` on integers.

src/structure.rs

@@ -195,7 +195,7 @@ where
 /// Examples are vectors, points, and quaternions.
 pub trait MetricSpace: Sized {
     /// The metric to be returned by the `distance` function.
-    type Metric: Float;
+    type Metric;
 
     /// Returns the squared distance.
     ///
@@ -205,7 +205,7 @@ pub trait MetricSpace: Sized {
     fn distance2(self, other: Self) -> Self::Metric;
 
     /// The distance between two values.
-    fn distance(self, other: Self) -> Self::Metric {
+    fn distance(self, other: Self) -> Self::Metric where Self::Metric: Float {
         Float::sqrt(Self::distance2(self, other))
     }
 }
@@ -219,7 +219,6 @@ pub trait MetricSpace: Sized {
 /// Examples include vectors and quaternions.
 pub trait InnerSpace: VectorSpace
 where
-    Self::Scalar: Float,
     // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
     Self: MetricSpace<Metric = <Self as VectorSpace>::Scalar>
 {
@@ -242,29 +241,11 @@ where
         Self::dot(self, self)
     }
 
-    /// The distance from the tail to the tip of the vector.
-    #[inline]
-    fn magnitude(self) -> Self::Scalar {
-        Float::sqrt(self.magnitude2())
-    }
-
     /// Returns the angle between two vectors in radians.
     fn angle(self, other: Self) -> Rad<Self::Scalar> where Self::Scalar: BaseFloat {
         Rad::acos(Self::dot(self, other) / (self.magnitude() * other.magnitude()))
     }
 
-    /// Returns a vector with the same direction, but with a magnitude of `1`.
-    #[inline]
-    fn normalize(self) -> Self {
-        self.normalize_to(Self::Scalar::one())
-    }
-
-    /// Returns a vector with the same direction and a given magnitude.
-    #[inline]
-    fn normalize_to(self, magnitude: Self::Scalar) -> Self {
-        self * (magnitude / self.magnitude())
-    }
-
     /// Returns the
     /// [vector projection](https://en.wikipedia.org/wiki/Vector_projection)
     /// of the current inner space projected onto the supplied argument.
@@ -272,6 +253,24 @@ where
     fn project_on(self, other: Self) -> Self {
         other * (self.dot(other) / other.magnitude2())
     }
+
+    /// The distance from the tail to the tip of the vector.
+    #[inline]
+    fn magnitude(self) -> Self::Scalar where Self::Scalar: Float {
+        Float::sqrt(self.magnitude2())
+    }
+
+    /// Returns a vector with the same direction, but with a magnitude of `1`.
+    #[inline]
+    fn normalize(self) -> Self where Self::Scalar: Float {
+        self.normalize_to(Self::Scalar::one())
+    }
+
+    /// Returns a vector with the same direction and a given magnitude.
+    #[inline]
+    fn normalize_to(self, magnitude: Self::Scalar) -> Self where Self::Scalar: Float {
+        self * (magnitude / self.magnitude())
+    }
 }
 
 /// Points in a [Euclidean space](https://en.wikipedia.org/wiki/Euclidean_space)

src/vector.rs

@@ -139,7 +139,7 @@ macro_rules! impl_vector {
             }
         }
 
-        impl<S: BaseNum + Float> MetricSpace for $VectorN<S> {
+        impl<S: BaseNum> MetricSpace for $VectorN<S> {
             type Metric = S;
 
             #[inline]
@@ -525,14 +525,14 @@ where
     V::dot(a, b)
 }
 
-impl<S: BaseNum + Float> InnerSpace for Vector1<S> {
+impl<S: BaseNum> InnerSpace for Vector1<S> {
     #[inline]
     fn dot(self, other: Vector1<S>) -> S {
         Vector1::mul_element_wise(self, other).sum()
     }
 }
 
-impl<S: BaseNum + Float> InnerSpace for Vector2<S> {
+impl<S: BaseNum> InnerSpace for Vector2<S> {
     #[inline]
     fn dot(self, other: Vector2<S>) -> S {
         Vector2::mul_element_wise(self, other).sum()
@@ -544,7 +544,7 @@ impl<S: BaseNum + Float> InnerSpace for Vector2<S> {
     }
 }
 
-impl<S: BaseNum + Float> InnerSpace for Vector3<S> {
+impl<S: BaseNum> InnerSpace for Vector3<S> {
     #[inline]
     fn dot(self, other: Vector3<S>) -> S {
         Vector3::mul_element_wise(self, other).sum()
@@ -556,7 +556,7 @@ impl<S: BaseNum + Float> InnerSpace for Vector3<S> {
     }
 }
 
-impl<S: BaseNum + Float> InnerSpace for Vector4<S> {
+impl<S: BaseNum> InnerSpace for Vector4<S> {
     #[inline]
     fn dot(self, other: Vector4<S>) -> S {
         Vector4::mul_element_wise(self, other).sum()
@@ -966,5 +966,11 @@ mod tests {
                 Vector4::new(-2, 1, 0, 1).zip(Vector4::new(-1, -1, -1, -1), |a, b| a < b)
             );
         }
+
+        #[test]
+        fn test_dot() {
+            assert_eq!(vec3(1.0, 2.0, 3.0).dot(vec3(4.0, 5.0, 6.0)), 32.0);
+            assert_eq!(vec3(1, 2, 3).dot(vec3(4, 5, 6)), 32);
+        }
     }
 }