Make epsilon an associated type on ApproxEq

src/angle.rs

@@ -80,7 +80,7 @@ pub trait Angle
 >
 :   Clone + Zero
 +   PartialEq + PartialOrd
-+   ApproxEq<S>
++   ApproxEq<Epsilon = S>
 +   Neg<Output=Self>
 +   Into<Rad<S>>
 +   Into<Deg<S>>
@@ -279,16 +279,18 @@ fmt::Debug for Deg<S> {
     }
 }
 
-impl<S: BaseFloat>
-ApproxEq<S> for Rad<S> {
+impl<S: BaseFloat> ApproxEq for Rad<S> {
+    type Epsilon = S;
+
     #[inline]
     fn approx_eq_eps(&self, other: &Rad<S>, epsilon: &S) -> bool {
         self.s.approx_eq_eps(&other.s, epsilon)
     }
 }
 
-impl<S: BaseFloat>
-ApproxEq<S> for Deg<S> {
+impl<S: BaseFloat> ApproxEq for Deg<S> {
+    type Epsilon = S;
+
     #[inline]
     fn approx_eq_eps(&self, other: &Deg<S>, epsilon: &S) -> bool {
         self.s.approx_eq_eps(&other.s, epsilon)

src/approx.rs

@@ -16,23 +16,26 @@
 use rust_num::{Float, NumCast};
 use rust_num::traits::cast;
 
-pub trait ApproxEq<T: NumCast + Float>: Sized {
-    fn approx_epsilon(_hack: Option<Self>) -> T {
+pub trait ApproxEq: Sized {
+    type Epsilon: NumCast + Float;
+
+    fn approx_epsilon() -> Self::Epsilon {
         cast(1.0e-5f64).unwrap()
     }
 
     fn approx_eq(&self, other: &Self) -> bool {
-        let eps: T = ApproxEq::approx_epsilon(None::<Self>);
-        self.approx_eq_eps(other, &eps)
+        self.approx_eq_eps(other, &Self::approx_epsilon())
     }
 
-    fn approx_eq_eps(&self, other: &Self, epsilon: &T) -> bool;
+    fn approx_eq_eps(&self, other: &Self, epsilon: &Self::Epsilon) -> bool;
 }
 
 
 macro_rules! approx_float(
     ($S:ident) => (
-        impl ApproxEq<$S> for $S {
+        impl ApproxEq for $S {
+            type Epsilon = $S;
+
              #[inline]
             fn approx_eq_eps(&self, other: &$S, epsilon: &$S) -> bool {
                  (*self - *other).abs() < *epsilon
@@ -62,9 +65,8 @@ macro_rules! assert_approx_eq(
     ($given: expr, $expected: expr) => ({
         let (given_val, expected_val) = (&($given), &($expected));
         if !given_val.approx_eq(expected_val) {
-            panic!("assertion failed: `left ≈ right` (left: `{:?}`, right: `{:?}`, tolerance: `{:?}`)",
-                *given_val, *expected_val,
-                ApproxEq::approx_epsilon(Some(*given_val))
+            panic!("assertion failed: `left ≈ right` (left: `{:?}`, right: `{:?}`)",
+                *given_val, *expected_val
             );
         }
     })

src/matrix.rs

@@ -249,7 +249,7 @@ impl<S: Copy + Neg<Output = S>> Matrix4<S> {
     }
 }
 
-pub trait Matrix<S: BaseFloat, V: Vector<S> + 'static>: Array2<V, V, S> + ApproxEq<S> + Sized // where
+pub trait Matrix<S: BaseFloat, V: Vector<S> + 'static>: Array2<V, V, S> + ApproxEq<Epsilon = S> + Sized // where
     // FIXME: blocked by rust-lang/rust#20671
     //
     // for<'a, 'b> &'a Self: Add<&'b Self, Output = Self>,
@@ -790,7 +790,9 @@ impl<S: BaseFloat> Matrix<S, Vector4<S>> for Matrix4<S> {
     }
 }
 
-impl<S: BaseFloat> ApproxEq<S> for Matrix2<S> {
+impl<S: BaseFloat> ApproxEq for Matrix2<S> {
+    type Epsilon = S;
+
     #[inline]
     fn approx_eq_eps(&self, other: &Matrix2<S>, epsilon: &S) -> bool {
         self[0].approx_eq_eps(&other[0], epsilon) &&
@@ -798,7 +800,9 @@ impl<S: BaseFloat> ApproxEq<S> for Matrix2<S> {
     }
 }
 
-impl<S: BaseFloat> ApproxEq<S> for Matrix3<S> {
+impl<S: BaseFloat> ApproxEq for Matrix3<S> {
+    type Epsilon = S;
+
     #[inline]
     fn approx_eq_eps(&self, other: &Matrix3<S>, epsilon: &S) -> bool {
         self[0].approx_eq_eps(&other[0], epsilon) &&
@@ -807,7 +811,9 @@ impl<S: BaseFloat> ApproxEq<S> for Matrix3<S> {
     }
 }
 
-impl<S: BaseFloat> ApproxEq<S> for Matrix4<S> {
+impl<S: BaseFloat> ApproxEq for Matrix4<S> {
+    type Epsilon = S;
+
     #[inline]
     fn approx_eq_eps(&self, other: &Matrix4<S>, epsilon: &S) -> bool {
         self[0].approx_eq_eps(&other[0], epsilon) &&

src/num.rs

@@ -110,7 +110,7 @@ impl BaseInt for u64 {}
 impl BaseInt for usize {}
 
 /// Base floating point types
-pub trait BaseFloat : BaseNum + Float + ApproxEq<Self> {}
+pub trait BaseFloat : BaseNum + Float + ApproxEq<Epsilon = Self> {}
 
 impl BaseFloat for f32 {}
 impl BaseFloat for f64 {}

src/point.rs

@@ -190,7 +190,9 @@ impl<S: BaseNum> Point<S> for Point2<S> {
     }
 }
 
-impl<S: BaseFloat> ApproxEq<S> for Point2<S> {
+impl<S: BaseFloat> ApproxEq for Point2<S> {
+    type Epsilon = S;
+
     #[inline]
     fn approx_eq_eps(&self, other: &Point2<S>, epsilon: &S) -> bool {
         self.x.approx_eq_eps(&other.x, epsilon) &&
@@ -270,7 +272,9 @@ impl<S: BaseNum> Point<S> for Point3<S> {
     }
 }
 
-impl<S: BaseFloat> ApproxEq<S> for Point3<S> {
+impl<S: BaseFloat> ApproxEq for Point3<S> {
+    type Epsilon = S;
+
     #[inline]
     fn approx_eq_eps(&self, other: &Point3<S>, epsilon: &S) -> bool {
         self.x.approx_eq_eps(&other.x, epsilon) &&

src/quaternion.rs

@@ -170,7 +170,9 @@ impl<'a, 'b, S: BaseFloat> Mul<&'b Quaternion<S>> for &'a Quaternion<S> {
     }
 }
 
-impl<S: BaseFloat> ApproxEq<S> for Quaternion<S> {
+impl<S: BaseFloat> ApproxEq for Quaternion<S> {
+    type Epsilon = S;
+
     #[inline]
     fn approx_eq_eps(&self, other: &Quaternion<S>, epsilon: &S) -> bool {
         self.s.approx_eq_eps(&other.s, epsilon) &&

src/rotation.rs

@@ -25,7 +25,7 @@ use vector::{Vector, Vector2, Vector3};
 
 /// A trait for a generic rotation. A rotation is a transformation that
 /// creates a circular motion, and preserves at least one point in the space.
-pub trait Rotation<S: BaseFloat, P: Point<S>>: PartialEq + ApproxEq<S> + Sized {
+pub trait Rotation<S: BaseFloat, P: Point<S>>: PartialEq + ApproxEq<Epsilon = S> + Sized {
     /// Create the identity transform (causes no transformation).
     fn one() -> Self;
 
@@ -206,7 +206,9 @@ impl<S: BaseFloat> Rotation<S, Point2<S>> for Basis2<S> {
     fn invert_self(&mut self) { self.mat.invert_self(); }
 }
 
-impl<S: BaseFloat> ApproxEq<S> for Basis2<S> {
+impl<S: BaseFloat> ApproxEq for Basis2<S> {
+    type Epsilon = S;
+
     #[inline]
     fn approx_eq_eps(&self, other: &Basis2<S>, epsilon: &S) -> bool {
         self.mat.approx_eq_eps(&other.mat, epsilon)
@@ -288,7 +290,9 @@ impl<S: BaseFloat> Rotation<S, Point3<S>> for Basis3<S> {
     fn invert_self(&mut self) { self.mat.invert_self(); }
 }
 
-impl<S: BaseFloat> ApproxEq<S> for Basis3<S> {
+impl<S: BaseFloat> ApproxEq for Basis3<S> {
+    type Epsilon = S;
+
     #[inline]
     fn approx_eq_eps(&self, other: &Basis3<S>, epsilon: &S) -> bool {
         self.mat.approx_eq_eps(&other.mat, epsilon)

src/vector.rs

@@ -287,7 +287,9 @@ macro_rules! vec {
             fn neg(self) -> $VectorN<S> { $VectorN::new($(-self.$field),+) }
         }
 
-        impl<S: BaseFloat> ApproxEq<S> for $VectorN<S> {
+        impl<S: BaseFloat> ApproxEq for $VectorN<S> {
+            type Epsilon = S;
+
             #[inline]
             fn approx_eq_eps(&self, other: &$VectorN<S>, epsilon: &S) -> bool {
                 $(self.$field.approx_eq_eps(&other.$field, epsilon))&&+
@@ -618,7 +620,7 @@ impl<S: BaseNum> Vector4<S> {
 /// Specifies geometric operations for vectors. This is only implemented for
 /// 2-dimensional and 3-dimensional vectors.
 pub trait EuclideanVector<S: BaseFloat>: Vector<S>
-                                       + ApproxEq<S>
+                                       + ApproxEq<Epsilon = S>
                                        + Sized {
     /// Returns `true` if the vector is perpendicular (at right angles) to the
     /// other vector.