453 lines
13 KiB
Rust
453 lines
13 KiB
Rust
use core::cast::transmute;
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use core::cmp::Eq;
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use core::ptr::to_unsafe_ptr;
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use core::sys::size_of;
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use core::util::swap;
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use core::vec::raw::buf_as_slice;
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use std::cmp::{FuzzyEq, FUZZY_EPSILON};
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use numeric::*;
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use numeric::number::Number;
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use numeric::number::Number::{zero,one};
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use vec::{
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Vec2,
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Vector2,
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MutableVector,
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NumericVector,
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MutableNumericVector,
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vec2,
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dvec2,
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};
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use mat::{
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Mat3,
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Mat4,
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Matrix,
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Matrix2,
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Matrix3,
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Matrix4,
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MutableMatrix,
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};
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/**
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* A 2 x 2 column major matrix
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*
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* # Type parameters
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*
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* * `T` - The type of the elements of the matrix. Should be a floating point type.
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*
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* # Fields
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*
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* * `x` - the first column vector of the matrix
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* * `y` - the second column vector of the matrix
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* * `z` - the third column vector of the matrix
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*/
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#[deriving_eq]
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pub struct Mat2<T> { x: Vec2<T>, y: Vec2<T> }
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impl<T:Copy + Float + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> Matrix<T, Vec2<T>> for Mat2<T> {
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#[inline(always)]
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pure fn col(&self, i: uint) -> Vec2<T> { self[i] }
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#[inline(always)]
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pure fn row(&self, i: uint) -> Vec2<T> {
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Vector2::new(self[0][i],
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self[1][i])
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}
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/**
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* Construct a 2 x 2 diagonal matrix with the major diagonal set to `value`
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*
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* # Arguments
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*
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* * `value` - the value to set the major diagonal to
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*
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* ~~~
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* c0 c1
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* +-----+-----+
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* r0 | val | 0 |
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* +-----+-----+
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* r1 | 0 | val |
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* +-----+-----+
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* ~~~
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*/
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#[inline(always)]
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static pure fn from_value(value: T) -> Mat2<T> {
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Matrix2::new(value, zero(),
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zero(), value)
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}
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/**
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* Returns the multiplicative identity matrix
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* ~~~
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* c0 c1
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* +----+----+
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* r0 | 1 | 0 |
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* +----+----+
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* r1 | 0 | 1 |
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* +----+----+
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* ~~~
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*/
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#[inline(always)]
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static pure fn identity() -> Mat2<T> {
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Matrix2::new( one::<T>(), zero::<T>(),
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zero::<T>(), one::<T>())
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}
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/**
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* Returns the additive identity matrix
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* ~~~
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* c0 c1
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* +----+----+
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* r0 | 0 | 0 |
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* +----+----+
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* r1 | 0 | 0 |
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* +----+----+
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* ~~~
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*/
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#[inline(always)]
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static pure fn zero() -> Mat2<T> {
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Matrix2::new(zero::<T>(), zero::<T>(),
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zero::<T>(), zero::<T>())
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}
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#[inline(always)]
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pure fn mul_t(&self, value: T) -> Mat2<T> {
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Matrix2::from_cols(self[0].mul_t(value),
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self[1].mul_t(value))
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}
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#[inline(always)]
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pure fn mul_v(&self, vec: &Vec2<T>) -> Vec2<T> {
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Vector2::new(self.row(0).dot(vec),
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self.row(1).dot(vec))
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}
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#[inline(always)]
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pure fn add_m(&self, other: &Mat2<T>) -> Mat2<T> {
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Matrix2::from_cols(self[0].add_v(&other[0]),
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self[1].add_v(&other[1]))
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}
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#[inline(always)]
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pure fn sub_m(&self, other: &Mat2<T>) -> Mat2<T> {
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Matrix2::from_cols(self[0].sub_v(&other[0]),
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self[1].sub_v(&other[1]))
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}
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#[inline(always)]
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pure fn mul_m(&self, other: &Mat2<T>) -> Mat2<T> {
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Matrix2::new(self.row(0).dot(&other.col(0)), self.row(1).dot(&other.col(0)),
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self.row(0).dot(&other.col(1)), self.row(1).dot(&other.col(1)))
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}
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pure fn dot(&self, other: &Mat2<T>) -> T {
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other.transpose().mul_m(self).trace()
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}
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pure fn determinant(&self) -> T {
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self[0][0] * self[1][1] - self[1][0] * self[0][1]
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}
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pure fn trace(&self) -> T {
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self[0][0] + self[1][1]
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}
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#[inline(always)]
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pure fn inverse(&self) -> Option<Mat2<T>> {
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let d = self.determinant();
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if d.fuzzy_eq(&zero()) {
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None
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} else {
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Some(Matrix2::new( self[1][1]/d, -self[0][1]/d,
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-self[1][0]/d, self[0][0]/d))
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}
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}
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#[inline(always)]
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pure fn transpose(&self) -> Mat2<T> {
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Matrix2::new(self[0][0], self[1][0],
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self[0][1], self[1][1])
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}
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#[inline(always)]
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pure fn is_identity(&self) -> bool {
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self.fuzzy_eq(&Matrix::identity())
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}
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#[inline(always)]
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pure fn is_diagonal(&self) -> bool {
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self[0][1].fuzzy_eq(&zero()) &&
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self[1][0].fuzzy_eq(&zero())
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}
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#[inline(always)]
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pure fn is_rotated(&self) -> bool {
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!self.fuzzy_eq(&Matrix::identity())
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}
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#[inline(always)]
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pure fn is_symmetric(&self) -> bool {
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self[0][1].fuzzy_eq(&self[1][0]) &&
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self[1][0].fuzzy_eq(&self[0][1])
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}
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#[inline(always)]
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pure fn is_invertible(&self) -> bool {
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!self.determinant().fuzzy_eq(&zero())
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}
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#[inline(always)]
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pure fn to_ptr(&self) -> *T {
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unsafe {
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transmute::<*Mat2<T>, *T>(
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to_unsafe_ptr(self)
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)
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}
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}
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}
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impl<T:Copy + Float + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> MutableMatrix<T, Vec2<T> > for Mat2<T> {
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#[inline(always)]
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fn col_mut(&mut self, i: uint) -> &self/mut Vec2<T> {
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match i {
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0 => &mut self.x,
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1 => &mut self.y,
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_ => fail!(fmt!("index out of bounds: expected an index from 0 to 1, but found %u", i))
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}
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}
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#[inline(always)]
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fn swap_cols(&mut self, a: uint, b: uint) {
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swap(&mut self.x, &mut self.y);
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}
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#[inline(always)]
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fn swap_rows(&mut self, a: uint, b: uint) {
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self.x.swap(a, b);
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self.y.swap(a, b);
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}
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#[inline(always)]
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fn set(&mut self, other: &Mat2<T>) {
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(*self) = (*other);
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}
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#[inline(always)]
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fn to_identity(&mut self) {
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(*self) = Matrix::identity();
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}
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#[inline(always)]
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fn to_zero(&mut self) {
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(*self) = Matrix::zero();
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}
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#[inline(always)]
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fn mul_self_t(&mut self, value: T) {
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&mut self.x.mul_self_t(&value);
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&mut self.y.mul_self_t(&value);
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}
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#[inline(always)]
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fn add_self_m(&mut self, other: &Mat2<T>) {
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&mut self.x.add_self_v(&other[0]);
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&mut self.y.add_self_v(&other[1]);
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}
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#[inline(always)]
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fn sub_self_m(&mut self, other: &Mat2<T>) {
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&mut self.x.sub_self_v(&other[0]);
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&mut self.y.sub_self_v(&other[1]);
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}
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#[inline(always)]
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fn invert_self(&mut self) {
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match self.inverse() {
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Some(m) => (*self) = m,
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None => fail!(~"Couldn't invert the matrix!")
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}
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}
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#[inline(always)]
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fn transpose_self(&mut self) {
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&mut swap(&mut self.x.index_mut(1), &mut self.y.index_mut(0));
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&mut swap(&mut self.y.index_mut(0), &mut self.x.index_mut(1));
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}
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}
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impl<T:Copy + Float + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> Matrix2<T, Vec2<T>> for Mat2<T> {
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/**
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* Construct a 2 x 2 matrix
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*
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* # Arguments
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*
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* * `c0r0`, `c0r1` - the first column of the matrix
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* * `c1r0`, `c1r1` - the second column of the matrix
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*
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* ~~~
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* c0 c1
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* +------+------+
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* r0 | c0r0 | c1r0 |
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* +------+------+
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* r1 | c0r1 | c1r1 |
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* +------+------+
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* ~~~
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*/
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#[inline(always)]
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static pure fn new(c0r0: T, c0r1: T,
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c1r0: T, c1r1: T) -> Mat2<T> {
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Matrix2::from_cols(Vector2::new::<T,Vec2<T>>(c0r0, c0r1),
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Vector2::new::<T,Vec2<T>>(c1r0, c1r1))
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}
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/**
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* Construct a 2 x 2 matrix from column vectors
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*
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* # Arguments
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*
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* * `c0` - the first column vector of the matrix
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* * `c1` - the second column vector of the matrix
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*
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* ~~~
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* c0 c1
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* +------+------+
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* r0 | c0.x | c1.x |
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* +------+------+
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* r1 | c0.y | c1.y |
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* +------+------+
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* ~~~
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*/
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#[inline(always)]
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static pure fn from_cols(c0: Vec2<T>,
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c1: Vec2<T>) -> Mat2<T> {
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Mat2 { x: c0, y: c1 }
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}
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#[inline(always)]
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static pure fn from_angle(radians: T) -> Mat2<T> {
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let cos_theta = cos(radians);
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let sin_theta = sin(radians);
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Matrix2::new(cos_theta, -sin_theta,
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sin_theta, cos_theta)
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}
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/**
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* Returns the the matrix with an extra row and column added
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* ~~~
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* c0 c1 c0 c1 c2
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* +----+----+ +----+----+----+
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* r0 | a | b | r0 | a | b | 0 |
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* +----+----+ +----+----+----+
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* r1 | c | d | => r1 | c | d | 0 |
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* +----+----+ +----+----+----+
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* r2 | 0 | 0 | 1 |
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* +----+----+----+
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* ~~~
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*/
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#[inline(always)]
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pure fn to_mat3(&self) -> Mat3<T> {
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Matrix3::new(self[0][0], self[0][1], zero(),
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self[1][0], self[1][1], zero(),
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zero(), zero(), one())
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}
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/**
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* Returns the the matrix with an extra two rows and columns added
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* ~~~
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* c0 c1 c0 c1 c2 c3
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* +----+----+ +----+----+----+----+
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* r0 | a | b | r0 | a | b | 0 | 0 |
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* +----+----+ +----+----+----+----+
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* r1 | c | d | => r1 | c | d | 0 | 0 |
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* +----+----+ +----+----+----+----+
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* r2 | 0 | 0 | 1 | 0 |
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* +----+----+----+----+
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* r3 | 0 | 0 | 0 | 1 |
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* +----+----+----+----+
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* ~~~
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*/
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#[inline(always)]
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pure fn to_mat4(&self) -> Mat4<T> {
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Matrix4::new(self[0][0], self[0][1], zero(), zero(),
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self[1][0], self[1][1], zero(), zero(),
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zero(), zero(), one(), zero(),
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zero(), zero(), zero(), one())
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}
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}
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impl<T:Copy> Index<uint, Vec2<T>> for Mat2<T> {
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#[inline(always)]
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pure fn index(&self, i: uint) -> Vec2<T> {
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unsafe { do buf_as_slice(
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transmute::<*Mat2<T>, *Vec2<T>>(
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to_unsafe_ptr(self)), 2) |slice| { slice[i] }
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}
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}
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}
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impl<T:Copy + Float + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> Neg<Mat2<T>> for Mat2<T> {
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#[inline(always)]
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pure fn neg(&self) -> Mat2<T> {
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Matrix2::from_cols(-self[0], -self[1])
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}
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}
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impl<T:Copy + Float + FuzzyEq<T>> FuzzyEq<T> for Mat2<T> {
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#[inline(always)]
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pure fn fuzzy_eq(&self, other: &Mat2<T>) -> bool {
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self.fuzzy_eq_eps(other, &Number::from(FUZZY_EPSILON))
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}
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#[inline(always)]
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pure fn fuzzy_eq_eps(&self, other: &Mat2<T>, epsilon: &T) -> bool {
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self[0].fuzzy_eq_eps(&other[0], epsilon) &&
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self[1].fuzzy_eq_eps(&other[1], epsilon)
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}
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}
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// GLSL-style type aliases, corresponding to Section 4.1.6 of the [GLSL 4.30.6 specification]
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// (http://www.opengl.org/registry/doc/GLSLangSpec.4.30.6.pdf).
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pub type mat2 = Mat2<f32>; // a 2×2 single-precision floating-point matrix
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pub type dmat2 = Mat2<f64>; // a 2×2 double-precision floating-point matrix
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// Static method wrappers for GLSL-style types
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impl mat2 {
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#[inline(always)] static pure fn new(c0r0: f32, c0r1: f32, c1r0: f32, c1r1: f32)
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-> mat2 { Matrix2::new(c0r0, c0r1, c1r0, c1r1) }
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#[inline(always)] static pure fn from_cols(c0: vec2, c1: vec2)
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-> mat2 { Matrix2::from_cols(c0, c1) }
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#[inline(always)] static pure fn from_value(v: f32) -> mat2 { Matrix::from_value(v) }
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#[inline(always)] static pure fn identity() -> mat2 { Matrix::identity() }
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#[inline(always)] static pure fn zero() -> mat2 { Matrix::zero() }
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#[inline(always)] static pure fn from_angle(radians: f32) -> mat2 { Matrix2::from_angle(radians) }
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#[inline(always)] static pure fn dim() -> uint { 2 }
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#[inline(always)] static pure fn rows() -> uint { 2 }
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#[inline(always)] static pure fn cols() -> uint { 2 }
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#[inline(always)] static pure fn size_of() -> uint { size_of::<mat2>() }
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}
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impl dmat2 {
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#[inline(always)] static pure fn new(c0r0: f64, c0r1: f64, c1r0: f64, c1r1: f64)
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-> dmat2 { Matrix2::new(c0r0, c0r1, c1r0, c1r1) }
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#[inline(always)] static pure fn from_cols(c0: dvec2, c1: dvec2)
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-> dmat2 { Matrix2::from_cols(c0, c1) }
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#[inline(always)] static pure fn from_value(v: f64) -> dmat2 { Matrix::from_value(v) }
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#[inline(always)] static pure fn identity() -> dmat2 { Matrix::identity() }
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#[inline(always)] static pure fn zero() -> dmat2 { Matrix::zero() }
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#[inline(always)] static pure fn from_angle(radians: f64) -> dmat2 { Matrix2::from_angle(radians) }
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#[inline(always)] static pure fn dim() -> uint { 2 }
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#[inline(always)] static pure fn rows() -> uint { 2 }
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#[inline(always)] static pure fn cols() -> uint { 2 }
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#[inline(always)] static pure fn size_of() -> uint { size_of::<dmat2>() }
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}
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