Merge pull request #254 from bjz/matrix-and-array-api-changes

Matrix and Array api changes

src/array.rs

@@ -13,85 +13,47 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-use std::mem;
 use std::ptr;
 use std::ops::*;
 
+use num::PartialOrd;
+
 /// An array containing elements of type `Element`
-pub trait Array1 where
+pub trait Array where
     // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
-    Self: Index<usize, Output = <Self as Array1>::Element>,
+    Self: Index<usize, Output = <Self as Array>::Element>,
-    Self: IndexMut<usize, Output = <Self as Array1>::Element>,
+    Self: IndexMut<usize, Output = <Self as Array>::Element>,
 {
     type Element: Copy;
 
     /// Get the pointer to the first element of the array.
-    fn ptr<'a>(&'a self) -> &'a Self::Element {
+    #[inline]
+    fn as_ptr(&self) -> *const Self::Element {
         &self[0]
     }
 
     /// Get a mutable pointer to the first element of the array.
-    fn mut_ptr<'a>(&'a mut self) -> &'a mut Self::Element {
+    #[inline]
+    fn as_mut_ptr(&mut self) -> *mut Self::Element {
         &mut self[0]
     }
 
     /// Swap the elements at indices `i` and `j` in-place.
     #[inline]
-    fn swap_elems(&mut self, i: usize, j: usize) {
+    fn swap_elements(&mut self, i: usize, j: usize) {
         // Yeah, ok borrow checker – I know what I'm doing here
         unsafe { ptr::swap(&mut self[i], &mut self[j]) };
     }
 
-    /// Replace an element in the array.
+    /// The sum of the elements of the array.
-    #[inline]
+    fn sum(self) -> Self::Element where Self::Element: Add<Output = <Self as Array>::Element>;
-    fn replace_elem(&mut self, i: usize, src: Self::Element) -> Self::Element {
-        mem::replace(&mut self[i], src)
-    }
-}
 
-/// A column-major array
+    /// The product of the elements of the array.
-pub trait Array2 where
+    fn product(self) -> Self::Element where Self::Element: Mul<Output = <Self as Array>::Element>;
-    // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
-    Self: Index<usize, Output = <Self as Array2>::Column>,
-    Self: IndexMut<usize, Output = <Self as Array2>::Column>,
-{
-    type Element: Copy;
-    type Column: Array1<Element = Self::Element>;
-    type Row: Array1<Element = Self::Element>;
 
-    /// Get the pointer to the first element of the array.
+    /// The minimum element of the array.
-    fn ptr<'a>(&'a self) -> &'a Self::Element {
+    fn min(self) -> Self::Element where Self::Element: PartialOrd;
-        &self[0][0]
+
-    }
+    /// The maximum element of the array.
-
+    fn max(self) -> Self::Element where Self::Element: PartialOrd;
-    /// Get a mutable pointer to the first element of the array.
-    fn mut_ptr<'a>(&'a mut self) -> &'a mut Self::Element {
-        &mut self[0][0]
-    }
-
-    /// Swap two columns of this array.
-    #[inline]
-    fn swap_cols(&mut self, a: usize, b: usize) {
-        unsafe { ptr::swap(&mut self[a], &mut self[b]) };
-    }
-
-    /// Replace a column in the array.
-    #[inline]
-    fn replace_col(&mut self, c: usize, src: Self::Column) -> Self::Column {
-        mem::replace(&mut self[c], src)
-    }
-
-    /// Get a row from this array by-value.
-    fn row(&self, r: usize) -> Self::Row;
-
-    /// Swap two rows of this array.
-    fn swap_rows(&mut self, a: usize, b: usize);
-
-    /// Swap the values at index `a` and `b`
-    #[inline]
-    fn swap_elems(&mut self, a: (usize, usize), b: (usize, usize)) {
-        let (ac, ar) = a;
-        let (bc, br) = b;
-        unsafe { ptr::swap(&mut self[ac][ar], &mut self[bc][br]) };
-    }
 }

src/matrix.rs

@@ -18,6 +18,7 @@
 use std::fmt;
 use std::mem;
 use std::ops::*;
+use std::ptr;
 
 use rand::{Rand, Rng};
 
@@ -26,7 +27,7 @@ use rust_num::traits::cast;
 
 use angle::{Rad, sin, cos, sin_cos};
 use approx::ApproxEq;
-use array::{Array1, Array2};
+use array::Array;
 use num::{BaseFloat, BaseNum};
 use point::{Point, Point3};
 use quaternion::Quaternion;
@@ -249,15 +250,12 @@ impl<S: Copy + Neg<Output = S>> Matrix4<S> {
     }
 }
 
+/// A column-major matrix of arbitrary dimensions.
 pub trait Matrix  where
     // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
-    Self: Array2<
+    Self: Index<usize, Output = <Self as Matrix>::Column>,
-        Element = <<Self as Matrix>::ColumnRow as Vector>::Scalar,
+    Self: IndexMut<usize, Output = <Self as Matrix>::Column>,
-        Column = <Self as Matrix>::ColumnRow,
+    Self: ApproxEq<Epsilon = <Self as Matrix>::Element>,
-        Row = <Self as Matrix>::ColumnRow,
-    >,
-    Self: ApproxEq<Epsilon = <<Self as Matrix>::ColumnRow as Vector>::Scalar> + Sized,
-    Self::Element: BaseFloat,
     // FIXME: blocked by rust-lang/rust#20671
     //
     // for<'a, 'b> &'a Self: Add<&'b Self, Output = Self>,
@@ -269,65 +267,106 @@ pub trait Matrix where
     // for<'a> &'a Self: Div<S, Output = Self>,
     // for<'a> &'a Self: Rem<S, Output = Self>,
 {
-    // FIXME: Will not be needed once equality constraints in where clauses is implemented
+    /// The type of the elements in the matrix.
-    type ColumnRow: Vector;
+    type Element: BaseFloat;
+
+    /// The row vector of the matrix.
+    type Row: Array<Element = Self::Element>;
+    /// The column vector of the matrix.
+    type Column: Array<Element = Self::Element>;
+
+    /// The type of the transposed matrix
+    type Transpose: Matrix<Element = Self::Element, Row = Self::Column, Column = Self::Row>;
+
+    /// Get the pointer to the first element of the array.
+    #[inline]
+    fn as_ptr(&self) -> *const Self::Element {
+        &self[0][0]
+    }
+
+    /// Get a mutable pointer to the first element of the array.
+    #[inline]
+    fn as_mut_ptr(&mut self) -> *mut Self::Element {
+        &mut self[0][0]
+    }
+
+    /// Replace a column in the array.
+    #[inline]
+    fn replace_col(&mut self, c: usize, src: Self::Column) -> Self::Column {
+        mem::replace(&mut self[c], src)
+    }
+
+    /// Get a row from this matrix by-value.
+    fn row(&self, r: usize) -> Self::Row;
+
+    /// Swap two rows of this array.
+    fn swap_rows(&mut self, a: usize, b: usize);
+    /// Swap two columns of this array.
+    fn swap_columns(&mut self, a: usize, b: usize);
+    /// Swap the values at index `a` and `b`
+    fn swap_elements(&mut self, a: (usize, usize), b: (usize, usize));
+
+    /// Create a matrix with all of the elements set to zero.
+    fn zero() -> Self;
+
+    /// Multiply the matrix by another matrix,
+    fn mul_m(&self, other: &Self::Transpose) -> Self;
+
+    /// Multiply the matrix by a column vector.
+    fn mul_v(&self, column: Self::Column) -> Self::Column;
+
+    /// Multiply this matrix by a scalar, returning the new matrix.
+    fn mul_s(&self, scalar: Self::Element) -> Self;
+    /// Divide this matrix by a scalar, returning the new matrix.
+    fn div_s(&self, scalar: Self::Element) -> Self;
+
+    /// Multiply this matrix by a scalar, in-place.
+    fn mul_self_s(&mut self, scalar: Self::Element);
+    /// Divide this matrix by a scalar, in-place.
+    fn div_self_s(&mut self, scalar: Self::Element);
+
+    /// Transpose this matrix, returning a new matrix.
+    fn transpose(&self) -> Self::Transpose;
+}
+
+/// A column-major major matrix where the rows and column vectors are of the same dimensions.
+pub trait SquareMatrix where
+    Self: Matrix<
+        // FIXME: Can be cleaned up once equality constraints in where clauses are implemented
+        Column = <Self as SquareMatrix>::ColumnRow,
+        Row = <Self as SquareMatrix>::ColumnRow,
+        Transpose = Self,
+    >,
+{
+    // FIXME: Will not be needed once equality constraints in where clauses are implemented
+    /// The row/column vector of the matrix.
+    ///
+    /// This is used to constrain the column and rows to be of the same type in lieu of equality
+    /// constraints being implemented for `where` clauses. Once those are added, this type will
+    /// likely go away.
+    type ColumnRow: Array<Element = Self::Element>;
 
     /// Create a new diagonal matrix using the supplied value.
     fn from_value(value: Self::Element) -> Self;
     /// Create a matrix from a non-uniform scale
     fn from_diagonal(diagonal: Self::Column) -> Self;
 
-    /// Create a matrix with all elements equal to zero.
-    #[inline]
-    fn zero() -> Self { Self::from_value(Self::Element::zero()) }
     /// Create a matrix where the each element of the diagonal is equal to one.
-    #[inline]
+    fn one() -> Self;
-    fn one() -> Self { Self::from_value(Self::Element::one()) }
-
-    /// Multiply this matrix by a scalar, returning the new matrix.
-    #[must_use]
-    fn mul_s(&self, s: Self::Element) -> Self;
-    /// Divide this matrix by a scalar, returning the new matrix.
-    #[must_use]
-    fn div_s(&self, s: Self::Element) -> Self;
-    /// Take the remainder of this matrix by a scalar, returning the new
-    /// matrix.
-    #[must_use]
-    fn rem_s(&self, s: Self::Element) -> Self;
 
     /// Add this matrix with another matrix, returning the new metrix.
-    #[must_use]
     fn add_m(&self, m: &Self) -> Self;
     /// Subtract another matrix from this matrix, returning the new matrix.
-    #[must_use]
     fn sub_m(&self, m: &Self) -> Self;
 
-    /// Multiplay a vector by this matrix, returning a new vector.
-    fn mul_v(&self, v: Self::Column) -> Self::Column;
-
-    /// Multiply this matrix by another matrix, returning the new matrix.
-    #[must_use]
-    fn mul_m(&self, m: &Self) -> Self;
-
-    /// Multiply this matrix by a scalar, in-place.
-    fn mul_self_s(&mut self, s: Self::Element);
-    /// Divide this matrix by a scalar, in-place.
-    fn div_self_s(&mut self, s: Self::Element);
-    /// Take the remainder of this matrix, in-place.
-    fn rem_self_s(&mut self, s: Self::Element);
-
     /// Add this matrix with another matrix, in-place.
     fn add_self_m(&mut self, m: &Self);
     /// Subtract another matrix from this matrix, in-place.
     fn sub_self_m(&mut self, m: &Self);
 
     /// Multiply this matrix by another matrix, in-place.
-    #[inline]
     fn mul_self_m(&mut self, m: &Self) { *self = self.mul_m(m); }
 
-    /// Transpose this matrix, returning a new matrix.
-    #[must_use]
-    fn transpose(&self) -> Self;
     /// Transpose this matrix in-place.
     fn transpose_self(&mut self);
     /// Take the determinant of this matrix.
@@ -370,10 +409,11 @@ pub trait Matrix where
     fn is_symmetric(&self) -> bool;
 }
 
-impl<S: Copy> Array2 for Matrix2<S> {
+impl<S: BaseFloat> Matrix for Matrix2<S> {
     type Element = S;
     type Column = Vector2<S>;
     type Row = Vector2<S>;
+    type Transpose = Matrix2<S>;
 
     #[inline]
     fn row(&self, r: usize) -> Vector2<S> {
@@ -383,54 +423,59 @@ impl<S: Copy> Array2 for Matrix2<S> {
 
     #[inline]
     fn swap_rows(&mut self, a: usize, b: usize) {
-        self[0].swap_elems(a, b);
+        self[0].swap_elements(a, b);
-        self[1].swap_elems(a, b);
+        self[1].swap_elements(a, b);
-    }
-}
-
-impl<S: Copy> Array2 for Matrix3<S> {
-    type Element = S;
-    type Column = Vector3<S>;
-    type Row = Vector3<S>;
-
-    #[inline]
-    fn row(&self, r: usize) -> Vector3<S> {
-        Vector3::new(self[0][r],
-                     self[1][r],
-                     self[2][r])
     }
 
     #[inline]
-    fn swap_rows(&mut self, a: usize, b: usize) {
+    fn swap_columns(&mut self, a: usize, b: usize) {
-        self[0].swap_elems(a, b);
+        unsafe { ptr::swap(&mut self[a], &mut self[b]) };
-        self[1].swap_elems(a, b);
-        self[2].swap_elems(a, b);
-    }
-}
-
-impl<S: Copy> Array2 for Matrix4<S> {
-    type Element = S;
-    type Column = Vector4<S>;
-    type Row = Vector4<S>;
-
-    #[inline]
-    fn row(&self, r: usize) -> Vector4<S> {
-        Vector4::new(self[0][r],
-                     self[1][r],
-                     self[2][r],
-                     self[3][r])
     }
 
     #[inline]
-    fn swap_rows(&mut self, a: usize, b: usize) {
+    fn swap_elements(&mut self, a: (usize, usize), b: (usize, usize)) {
-        self[0].swap_elems(a, b);
+        let (ac, ar) = a;
-        self[1].swap_elems(a, b);
+        let (bc, br) = b;
-        self[2].swap_elems(a, b);
+        unsafe { ptr::swap(&mut self[ac][ar], &mut self[bc][br]) };
-        self[3].swap_elems(a, b);
+    }
+
+    #[inline]
+    fn zero() -> Matrix2<S> {
+        Matrix2::new(S::zero(), S::zero(),
+                     S::zero(), S::zero())
+    }
+
+    #[inline]
+    fn mul_m(&self, other: &Matrix2<S>) -> Matrix2<S> { self * other }
+
+    #[inline]
+    fn mul_v(&self, v: Vector2<S>) -> Vector2<S> { self * v }
+
+    #[inline]
+    fn mul_s(&self, s: S) -> Matrix2<S> { self * s }
+
+    #[inline]
+    fn div_s(&self, s: S) -> Matrix2<S> { self / s }
+
+    #[inline]
+    fn mul_self_s(&mut self, s: S) {
+        self[0].mul_self_s(s);
+        self[1].mul_self_s(s);
+    }
+
+    #[inline]
+    fn div_self_s(&mut self, s: S) {
+        self[0].div_self_s(s);
+        self[1].div_self_s(s);
+    }
+
+    fn transpose(&self) -> Matrix2<S> {
+        Matrix2::new(self[0][0], self[1][0],
+                     self[0][1], self[1][1])
     }
 }
 
-impl<S: BaseFloat> Matrix for Matrix2<S> {
+impl<S: BaseFloat> SquareMatrix for Matrix2<S> {
     type ColumnRow = Vector2<S>;
 
     #[inline]
@@ -445,31 +490,17 @@ impl<S: BaseFloat> Matrix for Matrix2<S> {
                      S::zero(), value.y)
     }
 
-    #[inline] fn mul_s(&self, s: S) -> Matrix2<S> { self * s }
-    #[inline] fn div_s(&self, s: S) -> Matrix2<S> { self / s }
-    #[inline] fn rem_s(&self, s: S) -> Matrix2<S> { self % s }
-    #[inline] fn add_m(&self, m: &Matrix2<S>) -> Matrix2<S> { self + m }
-    #[inline] fn sub_m(&self, m: &Matrix2<S>) -> Matrix2<S> { self - m }
-    fn mul_m(&self, other: &Matrix2<S>) -> Matrix2<S> { self * other }
-    #[inline] fn mul_v(&self, v: Vector2<S>) -> Vector2<S> { self * v }
-
     #[inline]
-    fn mul_self_s(&mut self, s: S) {
+    fn one() -> Matrix2<S> {
-        self[0].mul_self_s(s);
+        Matrix2::new(S::one(), S::zero(),
-        self[1].mul_self_s(s);
+                     S::zero(), S::one())
     }
 
     #[inline]
-    fn div_self_s(&mut self, s: S) {
+    fn add_m(&self, m: &Matrix2<S>) -> Matrix2<S> { self + m }
-        self[0].div_self_s(s);
-        self[1].div_self_s(s);
-    }
 
     #[inline]
-    fn rem_self_s(&mut self, s: S) {
+    fn sub_m(&self, m: &Matrix2<S>) -> Matrix2<S> { self - m }
-        self[0].rem_self_s(s);
-        self[1].rem_self_s(s);
-    }
 
     #[inline]
     fn add_self_m(&mut self, m: &Matrix2<S>) {
@@ -483,14 +514,9 @@ impl<S: BaseFloat> Matrix for Matrix2<S> {
         self[1].sub_self_v(m[1]);
     }
 
-    fn transpose(&self) -> Matrix2<S> {
-        Matrix2::new(self[0][0], self[1][0],
-                     self[0][1], self[1][1])
-    }
-
     #[inline]
     fn transpose_self(&mut self) {
-        self.swap_elems((0, 1), (1, 0));
+        self.swap_elements((0, 1), (1, 0));
     }
 
     #[inline]
@@ -530,6 +556,78 @@ impl<S: BaseFloat> Matrix for Matrix2<S> {
 }
 
 impl<S: BaseFloat> Matrix for Matrix3<S> {
+    type Element = S;
+    type Column = Vector3<S>;
+    type Row = Vector3<S>;
+    type Transpose = Matrix3<S>;
+
+    #[inline]
+    fn row(&self, r: usize) -> Vector3<S> {
+        Vector3::new(self[0][r],
+                     self[1][r],
+                     self[2][r])
+    }
+
+    #[inline]
+    fn swap_rows(&mut self, a: usize, b: usize) {
+        self[0].swap_elements(a, b);
+        self[1].swap_elements(a, b);
+        self[2].swap_elements(a, b);
+    }
+
+    #[inline]
+    fn swap_columns(&mut self, a: usize, b: usize) {
+        unsafe { ptr::swap(&mut self[a], &mut self[b]) };
+    }
+
+    #[inline]
+    fn swap_elements(&mut self, a: (usize, usize), b: (usize, usize)) {
+        let (ac, ar) = a;
+        let (bc, br) = b;
+        unsafe { ptr::swap(&mut self[ac][ar], &mut self[bc][br]) };
+    }
+
+    #[inline]
+    fn zero() -> Matrix3<S> {
+        Matrix3::new(S::zero(), S::zero(), S::zero(),
+                     S::zero(), S::zero(), S::zero(),
+                     S::zero(), S::zero(), S::zero())
+    }
+
+    #[inline]
+    fn mul_m(&self, other: &Matrix3<S>) -> Matrix3<S> { self * other }
+
+    #[inline]
+    fn mul_v(&self, v: Vector3<S>) -> Vector3<S> { self * v}
+
+    #[inline]
+    fn mul_s(&self, s: S) -> Matrix3<S> { self * s }
+
+    #[inline]
+    fn div_s(&self, s: S) -> Matrix3<S> { self / s }
+
+    #[inline]
+    fn mul_self_s(&mut self, s: S) {
+        self[0].mul_self_s(s);
+        self[1].mul_self_s(s);
+        self[2].mul_self_s(s);
+    }
+
+    #[inline]
+    fn div_self_s(&mut self, s: S) {
+        self[0].div_self_s(s);
+        self[1].div_self_s(s);
+        self[2].div_self_s(s);
+    }
+
+    fn transpose(&self) -> Matrix3<S> {
+        Matrix3::new(self[0][0], self[1][0], self[2][0],
+                     self[0][1], self[1][1], self[2][1],
+                     self[0][2], self[1][2], self[2][2])
+    }
+}
+
+impl<S: BaseFloat> SquareMatrix for Matrix3<S> {
     type ColumnRow = Vector3<S>;
 
     #[inline]
@@ -546,34 +644,18 @@ impl<S: BaseFloat> Matrix for Matrix3<S> {
                      S::zero(), S::zero(), value.z)
     }
 
-    #[inline] fn mul_s(&self, s: S) -> Matrix3<S> { self * s }
-    #[inline] fn div_s(&self, s: S) -> Matrix3<S> { self / s }
-    #[inline] fn rem_s(&self, s: S) -> Matrix3<S> { self % s }
-    #[inline] fn add_m(&self, m: &Matrix3<S>) -> Matrix3<S> { self + m }
-    #[inline] fn sub_m(&self, m: &Matrix3<S>) -> Matrix3<S> { self - m }
-    fn mul_m(&self, other: &Matrix3<S>) -> Matrix3<S> { self * other }
-    #[inline] fn mul_v(&self, v: Vector3<S>) -> Vector3<S> { self * v}
-
     #[inline]
-    fn mul_self_s(&mut self, s: S) {
+    fn one() -> Matrix3<S> {
-        self[0].mul_self_s(s);
+        Matrix3::new(S::one(), S::zero(), S::zero(),
-        self[1].mul_self_s(s);
+                     S::zero(), S::one(), S::zero(),
-        self[2].mul_self_s(s);
+                     S::zero(), S::zero(), S::one())
     }
 
     #[inline]
-    fn div_self_s(&mut self, s: S) {
+    fn add_m(&self, m: &Matrix3<S>) -> Matrix3<S> { self + m }
-        self[0].div_self_s(s);
-        self[1].div_self_s(s);
-        self[2].div_self_s(s);
-    }
 
     #[inline]
-    fn rem_self_s(&mut self, s: S) {
+    fn sub_m(&self, m: &Matrix3<S>) -> Matrix3<S> { self - m }
-        self[0].rem_self_s(s);
-        self[1].rem_self_s(s);
-        self[2].rem_self_s(s);
-    }
 
     #[inline]
     fn add_self_m(&mut self, m: &Matrix3<S>) {
@@ -589,17 +671,11 @@ impl<S: BaseFloat> Matrix for Matrix3<S> {
         self[2].sub_self_v(m[2]);
     }
 
-    fn transpose(&self) -> Matrix3<S> {
-        Matrix3::new(self[0][0], self[1][0], self[2][0],
-                     self[0][1], self[1][1], self[2][1],
-                     self[0][2], self[1][2], self[2][2])
-    }
-
     #[inline]
     fn transpose_self(&mut self) {
-        self.swap_elems((0, 1), (1, 0));
+        self.swap_elements((0, 1), (1, 0));
-        self.swap_elems((0, 2), (2, 0));
+        self.swap_elements((0, 2), (2, 0));
-        self.swap_elems((1, 2), (2, 1));
+        self.swap_elements((1, 2), (2, 1));
     }
 
     fn determinant(&self) -> S {
@@ -648,6 +724,84 @@ impl<S: BaseFloat> Matrix for Matrix3<S> {
 }
 
 impl<S: BaseFloat> Matrix for Matrix4<S> {
+    type Element = S;
+    type Column = Vector4<S>;
+    type Row = Vector4<S>;
+    type Transpose = Matrix4<S>;
+
+    #[inline]
+    fn row(&self, r: usize) -> Vector4<S> {
+        Vector4::new(self[0][r],
+                     self[1][r],
+                     self[2][r],
+                     self[3][r])
+    }
+
+    #[inline]
+    fn swap_rows(&mut self, a: usize, b: usize) {
+        self[0].swap_elements(a, b);
+        self[1].swap_elements(a, b);
+        self[2].swap_elements(a, b);
+        self[3].swap_elements(a, b);
+    }
+
+    #[inline]
+    fn swap_columns(&mut self, a: usize, b: usize) {
+        unsafe { ptr::swap(&mut self[a], &mut self[b]) };
+    }
+
+    #[inline]
+    fn swap_elements(&mut self, a: (usize, usize), b: (usize, usize)) {
+        let (ac, ar) = a;
+        let (bc, br) = b;
+        unsafe { ptr::swap(&mut self[ac][ar], &mut self[bc][br]) };
+    }
+
+    #[inline]
+    fn zero() -> Matrix4<S> {
+        Matrix4::new(S::zero(), S::zero(), S::zero(), S::zero(),
+                     S::zero(), S::zero(), S::zero(), S::zero(),
+                     S::zero(), S::zero(), S::zero(), S::zero(),
+                     S::zero(), S::zero(), S::zero(), S::zero())
+    }
+
+    #[inline]
+    fn mul_m(&self, other: &Matrix4<S>) -> Matrix4<S> { self * other }
+
+    #[inline]
+    fn mul_v(&self, v: Vector4<S>) -> Vector4<S> { self * v }
+
+    #[inline]
+    fn mul_s(&self, s: S) -> Matrix4<S> { self * s }
+
+    #[inline]
+    fn div_s(&self, s: S) -> Matrix4<S> { self / s }
+
+    #[inline]
+    fn mul_self_s(&mut self, s: S) {
+        self[0].mul_self_s(s);
+        self[1].mul_self_s(s);
+        self[2].mul_self_s(s);
+        self[3].mul_self_s(s);
+    }
+
+    #[inline]
+    fn div_self_s(&mut self, s: S) {
+        self[0].div_self_s(s);
+        self[1].div_self_s(s);
+        self[2].div_self_s(s);
+        self[3].div_self_s(s);
+    }
+
+    fn transpose(&self) -> Matrix4<S> {
+        Matrix4::new(self[0][0], self[1][0], self[2][0], self[3][0],
+                     self[0][1], self[1][1], self[2][1], self[3][1],
+                     self[0][2], self[1][2], self[2][2], self[3][2],
+                     self[0][3], self[1][3], self[2][3], self[3][3])
+    }
+}
+
+impl<S: BaseFloat> SquareMatrix for Matrix4<S> {
     type ColumnRow = Vector4<S>;
 
     #[inline]
@@ -666,37 +820,19 @@ impl<S: BaseFloat> Matrix for Matrix4<S> {
                      S::zero(), S::zero(), S::zero(), value.w)
     }
 
-    #[inline] fn mul_s(&self, s: S) -> Matrix4<S> { self * s }
-    #[inline] fn div_s(&self, s: S) -> Matrix4<S> { self / s }
-    #[inline] fn rem_s(&self, s: S) -> Matrix4<S> { self % s }
-    #[inline] fn add_m(&self, m: &Matrix4<S>) -> Matrix4<S> { self + m }
-    #[inline] fn sub_m(&self, m: &Matrix4<S>) -> Matrix4<S> { self - m }
-    fn mul_m(&self, other: &Matrix4<S>) -> Matrix4<S> { self * other }
-    #[inline] fn mul_v(&self, v: Vector4<S>) -> Vector4<S> { self * v }
-
     #[inline]
-    fn mul_self_s(&mut self, s: S) {
+    fn one() -> Matrix4<S> {
-        self[0].mul_self_s(s);
+        Matrix4::new(S::one(), S::zero(), S::zero(), S::zero(),
-        self[1].mul_self_s(s);
+                     S::zero(), S::one(), S::zero(), S::zero(),
-        self[2].mul_self_s(s);
+                     S::zero(), S::zero(), S::one(), S::zero(),
-        self[3].mul_self_s(s);
+                     S::zero(), S::zero(), S::zero(), S::one())
     }
 
     #[inline]
-    fn div_self_s(&mut self, s: S) {
+    fn add_m(&self, m: &Matrix4<S>) -> Matrix4<S> { self + m }
-        self[0].div_self_s(s);
-        self[1].div_self_s(s);
-        self[2].div_self_s(s);
-        self[3].div_self_s(s);
-    }
 
     #[inline]
-    fn rem_self_s(&mut self, s: S) {
+    fn sub_m(&self, m: &Matrix4<S>) -> Matrix4<S> { self - m }
-        self[0].rem_self_s(s);
-        self[1].rem_self_s(s);
-        self[2].rem_self_s(s);
-        self[3].rem_self_s(s);
-    }
 
     #[inline]
     fn add_self_m(&mut self, m: &Matrix4<S>) {
@@ -714,20 +850,13 @@ impl<S: BaseFloat> Matrix for Matrix4<S> {
         self[3].sub_self_v(m[3]);
     }
 
-    fn transpose(&self) -> Matrix4<S> {
-        Matrix4::new(self[0][0], self[1][0], self[2][0], self[3][0],
-                     self[0][1], self[1][1], self[2][1], self[3][1],
-                     self[0][2], self[1][2], self[2][2], self[3][2],
-                     self[0][3], self[1][3], self[2][3], self[3][3])
-    }
-
     fn transpose_self(&mut self) {
-        self.swap_elems((0, 1), (1, 0));
+        self.swap_elements((0, 1), (1, 0));
-        self.swap_elems((0, 2), (2, 0));
+        self.swap_elements((0, 2), (2, 0));
-        self.swap_elems((0, 3), (3, 0));
+        self.swap_elements((0, 3), (3, 0));
-        self.swap_elems((1, 2), (2, 1));
+        self.swap_elements((1, 2), (2, 1));
-        self.swap_elems((1, 3), (3, 1));
+        self.swap_elements((1, 3), (3, 1));
-        self.swap_elems((2, 3), (3, 2));
+        self.swap_elements((2, 3), (3, 2));
     }
 
     fn determinant(&self) -> S {
@@ -852,7 +981,7 @@ impl<S: BaseFloat> ApproxEq for Matrix4<S> {
     }
 }
 
-impl<S: Neg<Output = S>> Neg for Matrix2<S> {
+impl<S: BaseFloat> Neg for Matrix2<S> {
     type Output = Matrix2<S>;
 
     #[inline]
@@ -861,7 +990,7 @@ impl<S: Neg<Output = S>> Neg for Matrix2<S> {
     }
 }
 
-impl<S: Neg<Output = S>> Neg for Matrix3<S> {
+impl<S: BaseFloat> Neg for Matrix3<S> {
     type Output = Matrix3<S>;
 
     #[inline]
@@ -870,7 +999,7 @@ impl<S: Neg<Output = S>> Neg for Matrix3<S> {
     }
 }
 
-impl<S: Neg<Output = S>> Neg for Matrix4<S> {
+impl<S: BaseFloat> Neg for Matrix4<S> {
     type Output = Matrix4<S>;
 
     #[inline]
@@ -881,7 +1010,7 @@ impl<S: Neg<Output = S>> Neg for Matrix4<S> {
 
 macro_rules! impl_scalar_binary_operator {
     ($Binop:ident :: $binop:ident, $MatrixN:ident { $($field:ident),+ }) => {
-        impl<'a, S: BaseNum> $Binop<S> for &'a $MatrixN<S> {
+        impl<'a, S: BaseFloat> $Binop<S> for &'a $MatrixN<S> {
             type Output = $MatrixN<S>;
 
             #[inline]
@@ -904,7 +1033,7 @@ impl_scalar_binary_operator!(Rem::rem, Matrix4 { x, y, z, w });
 
 macro_rules! impl_binary_operator {
     ($Binop:ident :: $binop:ident, $MatrixN:ident { $($field:ident),+ }) => {
-        impl<'a, 'b, S: BaseNum> $Binop<&'a $MatrixN<S>> for &'b $MatrixN<S> {
+        impl<'a, 'b, S: BaseFloat> $Binop<&'a $MatrixN<S>> for &'b $MatrixN<S> {
             type Output = $MatrixN<S>;
 
             #[inline]
@@ -924,7 +1053,7 @@ impl_binary_operator!(Sub::sub, Matrix4 { x, y, z, w });
 
 macro_rules! impl_vector_mul_operators {
     ($MatrixN:ident, $VectorN:ident { $($row_index:expr),+ }) => {
-        impl<'a, S: BaseNum> Mul<$VectorN<S>> for &'a $MatrixN<S> {
+        impl<'a, S: BaseFloat> Mul<$VectorN<S>> for &'a $MatrixN<S> {
             type Output = $VectorN<S>;
 
             fn mul(self, v: $VectorN<S>) -> $VectorN<S> {
@@ -932,7 +1061,7 @@ macro_rules! impl_vector_mul_operators {
             }
         }
 
-        impl<'a, 'b, S: BaseNum> Mul<&'a $VectorN<S>> for &'b $MatrixN<S> {
+        impl<'a, 'b, S: BaseFloat> Mul<&'a $VectorN<S>> for &'b $MatrixN<S> {
             type Output = $VectorN<S>;
 
             fn mul(self, v: &'a $VectorN<S>) -> $VectorN<S> {
@@ -946,7 +1075,7 @@ impl_vector_mul_operators!(Matrix2, Vector2 { 0, 1 });
 impl_vector_mul_operators!(Matrix3, Vector3 { 0, 1, 2 });
 impl_vector_mul_operators!(Matrix4, Vector4 { 0, 1, 2, 3 });
 
-impl<'a, 'b, S: BaseNum> Mul<&'a Matrix2<S>> for &'b Matrix2<S> {
+impl<'a, 'b, S: BaseFloat> Mul<&'a Matrix2<S>> for &'b Matrix2<S> {
     type Output = Matrix2<S>;
 
     fn mul(self, other: &'a Matrix2<S>) -> Matrix2<S> {
@@ -955,7 +1084,7 @@ impl<'a, 'b, S: BaseNum> Mul<&'a Matrix2<S>> for &'b Matrix2<S> {
     }
 }
 
-impl<'a, 'b, S: BaseNum> Mul<&'a Matrix3<S>> for &'b Matrix3<S> {
+impl<'a, 'b, S: BaseFloat> Mul<&'a Matrix3<S>> for &'b Matrix3<S> {
     type Output = Matrix3<S>;
 
     fn mul(self, other: &'a Matrix3<S>) -> Matrix3<S> {
@@ -965,7 +1094,7 @@ impl<'a, 'b, S: BaseNum> Mul<&'a Matrix3<S>> for &'b Matrix3<S> {
     }
 }
 
-impl<'a, 'b, S: BaseNum> Mul<&'a Matrix4<S>> for &'b Matrix4<S> {
+impl<'a, 'b, S: BaseFloat> Mul<&'a Matrix4<S>> for &'b Matrix4<S> {
     type Output = Matrix4<S>;
 
     fn mul(self, other: &'a Matrix4<S>) -> Matrix4<S> {

src/point.rs

@@ -24,7 +24,7 @@ use std::ops::*;
 use rust_num::{One, Zero};
 
 use approx::ApproxEq;
-use array::Array1;
+use array::Array;
 use matrix::Matrix;
 use num::{BaseNum, BaseFloat};
 use vector::*;
@@ -68,7 +68,7 @@ impl<S: BaseNum> Point3<S> {
 /// Specifies the numeric operations for point types.
 pub trait Point: Copy + Clone where
     // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
-    Self: Array1<Element = <Self as Point>::Scalar>,
+    Self: Array<Element = <Self as Point>::Scalar>,
     // FIXME: blocked by rust-lang/rust#20671
     //
     // for<'a, 'b> &'a Self: Add<&'b V, Output = Self>,
@@ -130,8 +130,24 @@ pub trait Point: Copy + Clone where
     fn max(self, p: Self) -> Self;
 }
 
-impl<S: BaseNum> Array1 for Point2<S> {
+impl<S: BaseNum> Array for Point2<S> {
     type Element = S;
+
+    fn sum(self) -> S {
+        self.x + self.y
+    }
+
+    fn product(self) -> S {
+        self.x * self.y
+    }
+
+    fn min(self) -> S {
+        self.x.partial_min(self.y)
+    }
+
+    fn max(self) -> S {
+        self.x.partial_max(self.y)
+    }
 }
 
 impl<S: BaseNum> Point for Point2<S> {
@@ -210,8 +226,24 @@ impl<S: BaseFloat> ApproxEq for Point2<S> {
     }
 }
 
-impl<S: BaseNum> Array1 for Point3<S> {
+impl<S: BaseNum> Array for Point3<S> {
     type Element = S;
+
+    fn sum(self) -> S {
+        self.x + self.y + self.z
+    }
+
+    fn product(self) -> S {
+        self.x * self.y * self.z
+    }
+
+    fn min(self) -> S {
+        self.x.partial_min(self.y).partial_min(self.z)
+    }
+
+    fn max(self) -> S {
+        self.x.partial_max(self.y).partial_max(self.z)
+    }
 }
 
 impl<S: BaseNum> Point for Point3<S> {

src/quaternion.rs

@@ -24,7 +24,6 @@ use rust_num::traits::cast;
 
 use angle::{Angle, Rad, acos, sin, sin_cos, rad};
 use approx::ApproxEq;
-use array::Array1;
 use matrix::{Matrix3, Matrix4};
 use num::BaseFloat;
 use point::Point3;
@@ -40,10 +39,6 @@ pub struct Quaternion<S> {
     pub v: Vector3<S>,
 }
 
-impl<S: Copy + BaseFloat> Array1 for Quaternion<S> {
-    type Element = S;
-}
-
 impl<S: BaseFloat> Quaternion<S> {
     /// Construct a new quaternion from one scalar component and three
     /// imaginary components

src/rotation.rs

@@ -15,9 +15,8 @@
 
 use angle::{Rad, acos};
 use approx::ApproxEq;
-use matrix::Matrix;
+use matrix::{Matrix, SquareMatrix};
-use matrix::Matrix2;
+use matrix::{Matrix2, Matrix3};
-use matrix::Matrix3;
 use num::BaseFloat;
 use point::{Point, Point2, Point3};
 use quaternion::Quaternion;

src/vector.rs

@@ -88,7 +88,7 @@
 //!
 //! Several other useful methods are provided as well. Vector fields can be
 //! accessed using array syntax (i.e. `vector[0] == vector.x`), or by using
-//! the methods provided by the [`Array1`](../array/trait.Array1.html) trait.
+//! the methods provided by the [`Array`](../array/trait.Array.html) trait.
 //! This trait also provides a `map()` method for applying arbitrary functions.
 //!
 //! The [`Vector`](../trait.Vector.html) trait presents the most general
@@ -105,15 +105,15 @@ use rust_num::{NumCast, Zero, One};
 
 use angle::{Rad, atan2, acos};
 use approx::ApproxEq;
-use array::Array1;
+use array::Array;
-use num::{BaseNum, BaseFloat};
+use num::{BaseNum, BaseFloat, PartialOrd};
 
 /// A trait that specifies a range of numeric operations for vectors. Not all
 /// of these make sense from a linear algebra point of view, but are included
 /// for pragmatic reasons.
 pub trait Vector: Copy + Clone where
     // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
-    Self: Array1<Element = <Self as Vector>::Scalar>,
+    Self: Array<Element = <Self as Vector>::Scalar>,
     // FIXME: blocked by rust-lang/rust#20671
     //
     // for<'a, 'b> &'a Self: Add<&'b Self, Output = Self>,
@@ -196,19 +196,8 @@ pub trait Vector: Copy + Clone where
     /// Take the remainder of this vector by another, in-place.
     fn rem_self_v(&mut self, v: Self);
 
-    /// The sum of the components of the vector.
+    /// Vector dot product
-    fn sum(self) -> Self::Scalar;
+    fn dot(self, other: Self) -> Self::Scalar;
-    /// The product of the components of the vector.
-    fn product(self) -> Self::Scalar;
-
-    /// Vector dot product.
-    #[inline]
-    fn dot(self, v: Self) -> Self::Scalar { self.mul_v(v).sum() }
-
-    /// The minimum component of the vector.
-    fn comp_min(self) -> Self::Scalar;
-    /// The maximum component of the vector.
-    fn comp_max(self) -> Self::Scalar;
 }
 
 /// Dot product of two vectors.
@@ -250,8 +239,13 @@ macro_rules! vec {
             }
         }
 
-        impl<S: Copy> Array1 for $VectorN<S> {
+        impl<S: Copy> Array for $VectorN<S> {
             type Element = S;
+
+            #[inline] fn sum(self) -> S where S: Add<Output = S> { fold!(add, { $(self.$field),+ }) }
+            #[inline] fn product(self) -> S where S: Mul<Output = S> { fold!(mul, { $(self.$field),+ }) }
+            #[inline] fn min(self) -> S where S: PartialOrd { fold!(partial_min, { $(self.$field),+ }) }
+            #[inline] fn max(self) -> S where S: PartialOrd { fold!(partial_max, { $(self.$field),+ }) }
         }
 
         impl<S: BaseNum> Vector for $VectorN<S> {
@@ -283,10 +277,7 @@ macro_rules! vec {
             #[inline] fn div_self_v(&mut self, v: $VectorN<S>) { *self = &*self / v; }
             #[inline] fn rem_self_v(&mut self, v: $VectorN<S>) { *self = &*self % v; }
 
-            #[inline] fn sum(self) -> S { fold!(add, { $(self.$field),+ }) }
+            #[inline] fn dot(self, other: $VectorN<S>) -> S { (self * other).sum() }
-            #[inline] fn product(self) -> S { fold!(mul, { $(self.$field),+ }) }
-            #[inline] fn comp_min(self) -> S { fold!(partial_min, { $(self.$field),+ }) }
-            #[inline] fn comp_max(self) -> S { fold!(partial_max, { $(self.$field),+ }) }
         }
 
         impl<S: Neg<Output = S>> Neg for $VectorN<S> {

tests/vector.rs

@@ -63,25 +63,25 @@ fn test_product() {
 }
 
 #[test]
-fn test_comp_min() {
+fn test_min() {
-    assert_eq!(Vector2::new(1isize, 2isize).comp_min(), 1isize);
+    assert_eq!(Vector2::new(1isize, 2isize).min(), 1isize);
-    assert_eq!(Vector3::new(1isize, 2isize, 3isize).comp_min(), 1isize);
+    assert_eq!(Vector3::new(1isize, 2isize, 3isize).min(), 1isize);
-    assert_eq!(Vector4::new(1isize, 2isize, 3isize, 4isize).comp_min(), 1isize);
+    assert_eq!(Vector4::new(1isize, 2isize, 3isize, 4isize).min(), 1isize);
 
-    assert_eq!(Vector2::new(3.0f64, 4.0f64).comp_min(), 3.0f64);
+    assert_eq!(Vector2::new(3.0f64, 4.0f64).min(), 3.0f64);
-    assert_eq!(Vector3::new(4.0f64, 5.0f64, 6.0f64).comp_min(), 4.0f64);
+    assert_eq!(Vector3::new(4.0f64, 5.0f64, 6.0f64).min(), 4.0f64);
-    assert_eq!(Vector4::new(5.0f64, 6.0f64, 7.0f64, 8.0f64).comp_min(), 5.0f64);
+    assert_eq!(Vector4::new(5.0f64, 6.0f64, 7.0f64, 8.0f64).min(), 5.0f64);
 }
 
 #[test]
-fn test_comp_max() {
+fn test_max() {
-    assert_eq!(Vector2::new(1isize, 2isize).comp_max(), 2isize);
+    assert_eq!(Vector2::new(1isize, 2isize).max(), 2isize);
-    assert_eq!(Vector3::new(1isize, 2isize, 3isize).comp_max(), 3isize);
+    assert_eq!(Vector3::new(1isize, 2isize, 3isize).max(), 3isize);
-    assert_eq!(Vector4::new(1isize, 2isize, 3isize, 4isize).comp_max(), 4isize);
+    assert_eq!(Vector4::new(1isize, 2isize, 3isize, 4isize).max(), 4isize);
 
-    assert_eq!(Vector2::new(3.0f64, 4.0f64).comp_max(), 4.0f64);
+    assert_eq!(Vector2::new(3.0f64, 4.0f64).max(), 4.0f64);
-    assert_eq!(Vector3::new(4.0f64, 5.0f64, 6.0f64).comp_max(), 6.0f64);
+    assert_eq!(Vector3::new(4.0f64, 5.0f64, 6.0f64).max(), 6.0f64);
-    assert_eq!(Vector4::new(5.0f64, 6.0f64, 7.0f64, 8.0f64).comp_max(), 8.0f64);
+    assert_eq!(Vector4::new(5.0f64, 6.0f64, 7.0f64, 8.0f64).max(), 8.0f64);
 }
 
 #[test]