Remove operator hacks

The LMul, RMul and Scalar* traits were only necessary due to language
limitations regarding trait bounds that are now gone. The Mat trait is now
expressed in terms of regular operator traits.

However, due to the removal of these traits this constitutes a breaking change.

src/lib.rs

@@ -122,7 +122,6 @@ pub use traits::{
     Inv,
     Iterable,
     IterableMut,
-    LMul,
     Mat,
     Mean,
     Norm,
@@ -133,11 +132,8 @@ pub use traits::{
     POrd,
     POrdering,
     PntAsVec,
-    RMul,
     Rotate, Rotation, RotationMatrix, RotationWithTranslation,
     Row,
-    ScalarAdd, ScalarSub,
-    ScalarMul, ScalarDiv,
     Shape,
     SquareMat,
     ToHomogeneous,

src/structs/pnt.rs

@@ -9,8 +9,7 @@ use std::iter::{Iterator, FromIterator, IntoIterator};
 use std::ops::{Add, Sub, Mul, Div, Neg, Index, IndexMut};
 use rand::{Rand, Rng};
 use num::{Zero, One};
-use traits::operations::{ApproxEq, POrd, POrdering, Axpy, ScalarAdd, ScalarSub, ScalarMul,
+use traits::operations::{ApproxEq, POrd, POrdering, Axpy};
-                         ScalarDiv};
 use traits::structure::{Cast, Dim, Indexable, Iterable, IterableMut, PntAsVec, Shape,
                         NumPnt, FloatPnt, BaseFloat, BaseNum, Bounded};
 use traits::geometry::{Orig, FromHomogeneous, ToHomogeneous};
@@ -66,7 +65,6 @@ pnt_sub_impl!(Pnt1, Vec1);
 neg_impl!(Pnt1, x);
 pnt_add_vec_impl!(Pnt1, Vec1, x);
 pnt_sub_vec_impl!(Pnt1, Vec1, x);
-scalar_ops_impl!(Pnt1, x);
 approx_eq_impl!(Pnt1, x);
 from_iterator_impl!(Pnt1, iterator);
 bounded_impl!(Pnt1, x);
@@ -109,7 +107,6 @@ pnt_sub_impl!(Pnt2, Vec2);
 neg_impl!(Pnt2, x, y);
 pnt_add_vec_impl!(Pnt2, Vec2, x, y);
 pnt_sub_vec_impl!(Pnt2, Vec2, x, y);
-scalar_ops_impl!(Pnt2, x, y);
 approx_eq_impl!(Pnt2, x, y);
 from_iterator_impl!(Pnt2, iterator, iterator);
 bounded_impl!(Pnt2, x, y);
@@ -154,7 +151,6 @@ pnt_sub_impl!(Pnt3, Vec3);
 neg_impl!(Pnt3, x, y, z);
 pnt_add_vec_impl!(Pnt3, Vec3, x, y, z);
 pnt_sub_vec_impl!(Pnt3, Vec3, x, y, z);
-scalar_ops_impl!(Pnt3, x, y, z);
 approx_eq_impl!(Pnt3, x, y, z);
 from_iterator_impl!(Pnt3, iterator, iterator, iterator);
 bounded_impl!(Pnt3, x, y, z);
@@ -201,7 +197,6 @@ pnt_sub_impl!(Pnt4, Vec4);
 neg_impl!(Pnt4, x, y, z, w);
 pnt_add_vec_impl!(Pnt4, Vec4, x, y, z, w);
 pnt_sub_vec_impl!(Pnt4, Vec4, x, y, z, w);
-scalar_ops_impl!(Pnt4, x, y, z, w);
 approx_eq_impl!(Pnt4, x, y, z, w);
 from_iterator_impl!(Pnt4, iterator, iterator, iterator, iterator);
 bounded_impl!(Pnt4, x, y, z, w);
@@ -250,7 +245,6 @@ pnt_sub_impl!(Pnt5, Vec5);
 neg_impl!(Pnt5, x, y, z, w, a);
 pnt_add_vec_impl!(Pnt5, Vec5, x, y, z, w, a);
 pnt_sub_vec_impl!(Pnt5, Vec5, x, y, z, w, a);
-scalar_ops_impl!(Pnt5, x, y, z, w, a);
 approx_eq_impl!(Pnt5, x, y, z, w, a);
 from_iterator_impl!(Pnt5, iterator, iterator, iterator, iterator, iterator);
 bounded_impl!(Pnt5, x, y, z, w, a);
@@ -301,7 +295,6 @@ pnt_sub_impl!(Pnt6, Vec6);
 neg_impl!(Pnt6, x, y, z, w, a, b);
 pnt_add_vec_impl!(Pnt6, Vec6, x, y, z, w, a, b);
 pnt_sub_vec_impl!(Pnt6, Vec6, x, y, z, w, a, b);
-scalar_ops_impl!(Pnt6, x, y, z, w, a, b);
 approx_eq_impl!(Pnt6, x, y, z, w, a, b);
 from_iterator_impl!(Pnt6, iterator, iterator, iterator, iterator, iterator, iterator);
 bounded_impl!(Pnt6, x, y, z, w, a, b);

src/structs/quat.rs

@@ -9,8 +9,7 @@ use std::iter::{FromIterator, IntoIterator};
 use rand::{Rand, Rng};
 use num::{Zero, One};
 use structs::{Vec3, Pnt3, Rot3, Mat3};
-use traits::operations::{ApproxEq, Inv, POrd, POrdering, Axpy, ScalarAdd, ScalarSub, ScalarMul,
+use traits::operations::{ApproxEq, Inv, POrd, POrdering, Axpy};
-                         ScalarDiv};
 use traits::structure::{Cast, Indexable, Iterable, IterableMut, Dim, Shape, BaseFloat, BaseNum,
                         Bounded};
 use traits::geometry::{Norm, Rotation, Rotate, Transform};
@@ -506,7 +505,6 @@ scalar_sub_impl!(Quat, w, i, j, k);
 scalar_mul_impl!(Quat, w, i, j, k);
 scalar_div_impl!(Quat, w, i, j, k);
 neg_impl!(Quat, w, i, j, k);
-scalar_ops_impl!(Quat, w, i, j, k);
 zero_one_impl!(Quat, w, i, j, k);
 approx_eq_impl!(Quat, w, i, j, k);
 from_iterator_impl!(Quat, iterator, iterator, iterator, iterator);

src/structs/vec.rs

@@ -9,8 +9,7 @@ use std::slice::{Iter, IterMut};
 use std::iter::{Iterator, FromIterator, IntoIterator};
 use rand::{Rand, Rng};
 use num::{Zero, One};
-use traits::operations::{ApproxEq, POrd, POrdering, Axpy, ScalarAdd, ScalarSub, ScalarMul,
+use traits::operations::{ApproxEq, POrd, POrdering, Axpy, Absolute};
-                         ScalarDiv, Absolute};
 use traits::geometry::{Transform, Rotate, FromHomogeneous, ToHomogeneous, Dot, Norm,
                        Translation, Translate};
 use traits::structure::{Basis, Cast, Dim, Indexable, Iterable, IterableMut, Shape, NumVec,
@@ -70,7 +69,6 @@ scalar_mul_impl!(Vec1, x);
 scalar_div_impl!(Vec1, x);
 neg_impl!(Vec1, x);
 dot_impl!(Vec1, x);
-scalar_ops_impl!(Vec1, x);
 translation_impl!(Vec1);
 norm_impl!(Vec1, x);
 approx_eq_impl!(Vec1, x);
@@ -124,7 +122,6 @@ scalar_mul_impl!(Vec2, x, y);
 scalar_div_impl!(Vec2, x, y);
 neg_impl!(Vec2, x, y);
 dot_impl!(Vec2, x, y);
-scalar_ops_impl!(Vec2, x, y);
 translation_impl!(Vec2);
 norm_impl!(Vec2, x, y);
 approx_eq_impl!(Vec2, x, y);
@@ -180,7 +177,6 @@ scalar_mul_impl!(Vec3, x, y, z);
 scalar_div_impl!(Vec3, x, y, z);
 neg_impl!(Vec3, x, y, z);
 dot_impl!(Vec3, x, y, z);
-scalar_ops_impl!(Vec3, x, y, z);
 translation_impl!(Vec3);
 norm_impl!(Vec3, x, y ,z);
 approx_eq_impl!(Vec3, x, y, z);
@@ -239,7 +235,6 @@ scalar_mul_impl!(Vec4, x, y, z, w);
 scalar_div_impl!(Vec4, x, y, z, w);
 neg_impl!(Vec4, x, y, z, w);
 dot_impl!(Vec4, x, y, z, w);
-scalar_ops_impl!(Vec4, x, y, z, w);
 translation_impl!(Vec4);
 norm_impl!(Vec4, x, y, z, w);
 approx_eq_impl!(Vec4, x, y, z, w);
@@ -299,7 +294,6 @@ scalar_mul_impl!(Vec5, x, y, z, w, a);
 scalar_div_impl!(Vec5, x, y, z, w, a);
 neg_impl!(Vec5, x, y, z, w, a);
 dot_impl!(Vec5, x, y, z, w, a);
-scalar_ops_impl!(Vec5, x, y, z, w, a);
 translation_impl!(Vec5);
 norm_impl!(Vec5, x, y, z, w, a);
 approx_eq_impl!(Vec5, x, y, z, w, a);
@@ -361,7 +355,6 @@ scalar_mul_impl!(Vec6, x, y, z, w, a, b);
 scalar_div_impl!(Vec6, x, y, z, w, a, b);
 neg_impl!(Vec6, x, y, z, w, a, b);
 dot_impl!(Vec6, x, y, z, w, a, b);
-scalar_ops_impl!(Vec6, x, y, z, w, a, b);
 translation_impl!(Vec6);
 norm_impl!(Vec6, x, y, z, w, a, b);
 approx_eq_impl!(Vec6, x, y, z, w, a, b);

src/structs/vec_macros.rs

@@ -504,38 +504,6 @@ macro_rules! dot_impl(
     )
 );
 
-macro_rules! scalar_ops_impl(
-    ($t: ident, $($compN: ident),+) => (
-        impl<N: Copy + Mul<N, Output = N>> ScalarMul<N> for $t<N> {
-            #[inline]
-            fn mul_s(&self, other: &N) -> $t<N> {
-                $t::new($(self.$compN * *other),+)
-            }
-        }
-
-        impl<N: Copy + Div<N, Output = N>> ScalarDiv<N> for $t<N> {
-            #[inline]
-            fn div_s(&self, other: &N) -> $t<N> {
-                $t::new($(self.$compN / *other),+)
-            }
-        }
-
-        impl<N: Copy + Add<N, Output = N>> ScalarAdd<N> for $t<N> {
-            #[inline]
-            fn add_s(&self, other: &N) -> $t<N> {
-                $t::new($(self.$compN + *other),+)
-            }
-        }
-
-        impl<N: Copy + Sub<N, Output = N>> ScalarSub<N> for $t<N> {
-            #[inline]
-            fn sub_s(&self, other: &N) -> $t<N> {
-                $t::new($(self.$compN - *other),+)
-            }
-        }
-    )
-);
-
 macro_rules! translation_impl(
     ($t: ident) => (
         impl<N: Copy + Add<N, Output = N> + Neg<Output = N>> Translation<$t<N>> for $t<N> {

src/traits/mod.rs

@@ -8,8 +8,8 @@ pub use traits::structure::{FloatVec, FloatPnt, Basis, Cast, Col, Dim, Indexable
                             IterableMut, Mat, SquareMat, Row, NumVec, NumPnt, PntAsVec, ColSlice,
                             RowSlice, Diag, Eye, Shape, BaseFloat, BaseNum, Bounded};
 
-pub use traits::operations::{Absolute, ApproxEq, Axpy, Cov, Det, Inv, LMul, Mean, Outer, POrd,
+pub use traits::operations::{Absolute, ApproxEq, Axpy, Cov, Det, Inv, Mean, Outer, POrd, Transpose,
-                             RMul, ScalarAdd, ScalarSub, ScalarMul, ScalarDiv, Transpose, EigenQR};
+                             EigenQR};
 pub use traits::operations::POrdering;
 
 pub mod geometry;

src/traits/operations.rs

@@ -1,7 +1,6 @@
 //! Low level operations on vectors and matrices.
 
 use num::{Float, Signed};
-use std::ops::Mul;
 use std::cmp::Ordering;
 use traits::structure::SquareMat;
 
@@ -337,68 +336,6 @@ pub trait EigenQR<N, V>: SquareMat<N, V> {
     fn eigen_qr(&self, eps: &N, niter: usize) -> (Self, V);
 }
 
-// XXX: those two traits should not exist since there is generalized operator overloading of Add
-// and Sub.
-// However, using the same trait multiple time as a trait bound (ex: impl<T: Add<N, V> + Add<V, V>)
-// does not work properly, mainly because the way we are doing generalized operator overloading is
-// verry hacky.
-//
-// Hopefully, this will be fixed on a future version of the language!
-/// Trait of objects having a right multiplication with another element.
-pub trait RMul<V> {
-    /// Computes `self * v`
-    fn rmul(&self, v: &V) -> V;
-}
-
-impl<M: Copy + Mul<T, Output = T>, T: Copy> RMul<T> for M {
-    fn rmul(&self, v: &T) -> T {
-        *self * *v
-    }
-}
-
-/// Trait of objects having a left multiplication with another element.
-pub trait LMul<V> {
-    /// Computes `v * self`
-    fn lmul(&self, &V) -> V;
-}
-
-impl<T: Copy + Mul<M, Output = T>, M: Copy> LMul<T> for M {
-    fn lmul(&self, v: &T) -> T {
-        *v * *self
-    }
-}
-
-// XXX: those traits should not exist since there is generalized operator overloading of Add and
-// Sub.
-// However, using the same trait multiple time as a trait bound (ex: impl<T: Add<N, V> + Add<V, V>)
-// does not work properly, mainly because the way we are doing generalized operator overloading is
-// verry hacky.
-//
-// Hopefully, this will be fixed on a future version of the language!
-/// Trait of objects having an addition with a scalar.
-pub trait ScalarAdd<N> {
-    /// Gets the result of `self + n`.
-    fn add_s(&self, n: &N) -> Self;
-}
-
-/// Trait of objects having a subtraction with a scalar.
-pub trait ScalarSub<N> {
-    /// Gets the result of `self - n`.
-    fn sub_s(&self, n: &N) -> Self;
-}
-
-/// Trait of objects having a multiplication with a scalar.
-pub trait ScalarMul<N> {
-    /// Gets the result of `self * n`.
-    fn mul_s(&self, n: &N) -> Self;
-}
-
-/// Trait of objects having a division by a scalar.
-pub trait ScalarDiv<N> {
-    /// Gets the result of `self / n`.
-    fn div_s(&self, n: &N) -> Self;
-}
-
 /// Trait of objects implementing the `y = ax + y` operation.
 pub trait Axpy<N> {
     /// Adds $$a * x$$ to `self`.

src/traits/structure.rs

@@ -4,7 +4,7 @@ use std::{f32, f64, i8, i16, i32, i64, u8, u16, u32, u64, isize, usize};
 use std::slice::{Iter, IterMut};
 use std::ops::{Add, Sub, Mul, Div, Rem, Index, IndexMut};
 use num::{Float, Zero, One};
-use traits::operations::{RMul, LMul, Axpy, Transpose, Inv, Absolute};
+use traits::operations::{Axpy, Transpose, Inv, Absolute};
 use traits::geometry::{Dot, Norm, Orig};
 
 /// Basic integral numeric trait.
@@ -59,11 +59,12 @@ pub trait Cast<T> {
 /// Trait of matrices.
 ///
 /// A matrix has rows and columns and are able to multiply them.
-pub trait Mat<N, R, C>: Row<R> + Col<C> + RMul<R> + LMul<C> + Index<(usize, usize), Output = N> { }
+pub trait Mat<N, R, C: Mul<Self>>: Row<R> + Col<C> + Mul<R> + Index<(usize, usize), Output = N> { }
 
 impl<N, M, R, C> Mat<N, R, C> for M
-    where M: Row<R> + Col<C> + RMul<R> + LMul<C> + Index<(usize, usize), Output = N> {
+    where M: Row<R> + Col<C> + Mul<R> + Index<(usize, usize), Output = N>,
-}
+          C: Mul<M>,
+{}
 
 /// Trait implemented by square matrices.
 pub trait SquareMat<N, V>: Mat<N, V, V> +