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|
//! 4x4 matrix inverse
// Code ported from the `packed_simd` crate
// Run this code with `cargo test --example matrix_inversion`
#![feature(array_chunks, portable_simd)]
use core_simd::simd::*;
use Which::*;
// Gotta define our own 4x4 matrix since Rust doesn't ship multidim arrays yet :^)
#[derive(Copy, Clone, Debug, PartialEq, PartialOrd)]
pub struct Matrix4x4([[f32; 4]; 4]);
#[allow(clippy::too_many_lines)]
pub fn scalar_inv4x4(m: Matrix4x4) -> Option<Matrix4x4> {
let m = m.0;
#[rustfmt::skip]
let mut inv = [
// row 0:
[
// 0,0:
m[1][1] * m[2][2] * m[3][3] -
m[1][1] * m[2][3] * m[3][2] -
m[2][1] * m[1][2] * m[3][3] +
m[2][1] * m[1][3] * m[3][2] +
m[3][1] * m[1][2] * m[2][3] -
m[3][1] * m[1][3] * m[2][2],
// 0,1:
-m[0][1] * m[2][2] * m[3][3] +
m[0][1] * m[2][3] * m[3][2] +
m[2][1] * m[0][2] * m[3][3] -
m[2][1] * m[0][3] * m[3][2] -
m[3][1] * m[0][2] * m[2][3] +
m[3][1] * m[0][3] * m[2][2],
// 0,2:
m[0][1] * m[1][2] * m[3][3] -
m[0][1] * m[1][3] * m[3][2] -
m[1][1] * m[0][2] * m[3][3] +
m[1][1] * m[0][3] * m[3][2] +
m[3][1] * m[0][2] * m[1][3] -
m[3][1] * m[0][3] * m[1][2],
// 0,3:
-m[0][1] * m[1][2] * m[2][3] +
m[0][1] * m[1][3] * m[2][2] +
m[1][1] * m[0][2] * m[2][3] -
m[1][1] * m[0][3] * m[2][2] -
m[2][1] * m[0][2] * m[1][3] +
m[2][1] * m[0][3] * m[1][2],
],
// row 1
[
// 1,0:
-m[1][0] * m[2][2] * m[3][3] +
m[1][0] * m[2][3] * m[3][2] +
m[2][0] * m[1][2] * m[3][3] -
m[2][0] * m[1][3] * m[3][2] -
m[3][0] * m[1][2] * m[2][3] +
m[3][0] * m[1][3] * m[2][2],
// 1,1:
m[0][0] * m[2][2] * m[3][3] -
m[0][0] * m[2][3] * m[3][2] -
m[2][0] * m[0][2] * m[3][3] +
m[2][0] * m[0][3] * m[3][2] +
m[3][0] * m[0][2] * m[2][3] -
m[3][0] * m[0][3] * m[2][2],
// 1,2:
-m[0][0] * m[1][2] * m[3][3] +
m[0][0] * m[1][3] * m[3][2] +
m[1][0] * m[0][2] * m[3][3] -
m[1][0] * m[0][3] * m[3][2] -
m[3][0] * m[0][2] * m[1][3] +
m[3][0] * m[0][3] * m[1][2],
// 1,3:
m[0][0] * m[1][2] * m[2][3] -
m[0][0] * m[1][3] * m[2][2] -
m[1][0] * m[0][2] * m[2][3] +
m[1][0] * m[0][3] * m[2][2] +
m[2][0] * m[0][2] * m[1][3] -
m[2][0] * m[0][3] * m[1][2],
],
// row 2
[
// 2,0:
m[1][0] * m[2][1] * m[3][3] -
m[1][0] * m[2][3] * m[3][1] -
m[2][0] * m[1][1] * m[3][3] +
m[2][0] * m[1][3] * m[3][1] +
m[3][0] * m[1][1] * m[2][3] -
m[3][0] * m[1][3] * m[2][1],
// 2,1:
-m[0][0] * m[2][1] * m[3][3] +
m[0][0] * m[2][3] * m[3][1] +
m[2][0] * m[0][1] * m[3][3] -
m[2][0] * m[0][3] * m[3][1] -
m[3][0] * m[0][1] * m[2][3] +
m[3][0] * m[0][3] * m[2][1],
// 2,2:
m[0][0] * m[1][1] * m[3][3] -
m[0][0] * m[1][3] * m[3][1] -
m[1][0] * m[0][1] * m[3][3] +
m[1][0] * m[0][3] * m[3][1] +
m[3][0] * m[0][1] * m[1][3] -
m[3][0] * m[0][3] * m[1][1],
// 2,3:
-m[0][0] * m[1][1] * m[2][3] +
m[0][0] * m[1][3] * m[2][1] +
m[1][0] * m[0][1] * m[2][3] -
m[1][0] * m[0][3] * m[2][1] -
m[2][0] * m[0][1] * m[1][3] +
m[2][0] * m[0][3] * m[1][1],
],
// row 3
[
// 3,0:
-m[1][0] * m[2][1] * m[3][2] +
m[1][0] * m[2][2] * m[3][1] +
m[2][0] * m[1][1] * m[3][2] -
m[2][0] * m[1][2] * m[3][1] -
m[3][0] * m[1][1] * m[2][2] +
m[3][0] * m[1][2] * m[2][1],
// 3,1:
m[0][0] * m[2][1] * m[3][2] -
m[0][0] * m[2][2] * m[3][1] -
m[2][0] * m[0][1] * m[3][2] +
m[2][0] * m[0][2] * m[3][1] +
m[3][0] * m[0][1] * m[2][2] -
m[3][0] * m[0][2] * m[2][1],
// 3,2:
-m[0][0] * m[1][1] * m[3][2] +
m[0][0] * m[1][2] * m[3][1] +
m[1][0] * m[0][1] * m[3][2] -
m[1][0] * m[0][2] * m[3][1] -
m[3][0] * m[0][1] * m[1][2] +
m[3][0] * m[0][2] * m[1][1],
// 3,3:
m[0][0] * m[1][1] * m[2][2] -
m[0][0] * m[1][2] * m[2][1] -
m[1][0] * m[0][1] * m[2][2] +
m[1][0] * m[0][2] * m[2][1] +
m[2][0] * m[0][1] * m[1][2] -
m[2][0] * m[0][2] * m[1][1],
],
];
let det = m[0][0] * inv[0][0] + m[0][1] * inv[1][0] + m[0][2] * inv[2][0] + m[0][3] * inv[3][0];
if det == 0. {
return None;
}
let det_inv = 1. / det;
for row in &mut inv {
for elem in row.iter_mut() {
*elem *= det_inv;
}
}
Some(Matrix4x4(inv))
}
pub fn simd_inv4x4(m: Matrix4x4) -> Option<Matrix4x4> {
let m = m.0;
let m_0 = f32x4::from_array(m[0]);
let m_1 = f32x4::from_array(m[1]);
let m_2 = f32x4::from_array(m[2]);
let m_3 = f32x4::from_array(m[3]);
const SHUFFLE01: [Which; 4] = [First(0), First(1), Second(0), Second(1)];
const SHUFFLE02: [Which; 4] = [First(0), First(2), Second(0), Second(2)];
const SHUFFLE13: [Which; 4] = [First(1), First(3), Second(1), Second(3)];
const SHUFFLE23: [Which; 4] = [First(2), First(3), Second(2), Second(3)];
let tmp = simd_swizzle!(m_0, m_1, SHUFFLE01);
let row1 = simd_swizzle!(m_2, m_3, SHUFFLE01);
let row0 = simd_swizzle!(tmp, row1, SHUFFLE02);
let row1 = simd_swizzle!(row1, tmp, SHUFFLE13);
let tmp = simd_swizzle!(m_0, m_1, SHUFFLE23);
let row3 = simd_swizzle!(m_2, m_3, SHUFFLE23);
let row2 = simd_swizzle!(tmp, row3, SHUFFLE02);
let row3 = simd_swizzle!(row3, tmp, SHUFFLE13);
let tmp = (row2 * row3).reverse().rotate_lanes_right::<2>();
let minor0 = row1 * tmp;
let minor1 = row0 * tmp;
let tmp = tmp.rotate_lanes_right::<2>();
let minor0 = (row1 * tmp) - minor0;
let minor1 = (row0 * tmp) - minor1;
let minor1 = minor1.rotate_lanes_right::<2>();
let tmp = (row1 * row2).reverse().rotate_lanes_right::<2>();
let minor0 = (row3 * tmp) + minor0;
let minor3 = row0 * tmp;
let tmp = tmp.rotate_lanes_right::<2>();
let minor0 = minor0 - row3 * tmp;
let minor3 = row0 * tmp - minor3;
let minor3 = minor3.rotate_lanes_right::<2>();
let tmp = (row3 * row1.rotate_lanes_right::<2>())
.reverse()
.rotate_lanes_right::<2>();
let row2 = row2.rotate_lanes_right::<2>();
let minor0 = row2 * tmp + minor0;
let minor2 = row0 * tmp;
let tmp = tmp.rotate_lanes_right::<2>();
let minor0 = minor0 - row2 * tmp;
let minor2 = row0 * tmp - minor2;
let minor2 = minor2.rotate_lanes_right::<2>();
let tmp = (row0 * row1).reverse().rotate_lanes_right::<2>();
let minor2 = minor2 + row3 * tmp;
let minor3 = row2 * tmp - minor3;
let tmp = tmp.rotate_lanes_right::<2>();
let minor2 = row3 * tmp - minor2;
let minor3 = minor3 - row2 * tmp;
let tmp = (row0 * row3).reverse().rotate_lanes_right::<2>();
let minor1 = minor1 - row2 * tmp;
let minor2 = row1 * tmp + minor2;
let tmp = tmp.rotate_lanes_right::<2>();
let minor1 = row2 * tmp + minor1;
let minor2 = minor2 - row1 * tmp;
let tmp = (row0 * row2).reverse().rotate_lanes_right::<2>();
let minor1 = row3 * tmp + minor1;
let minor3 = minor3 - row1 * tmp;
let tmp = tmp.rotate_lanes_right::<2>();
let minor1 = minor1 - row3 * tmp;
let minor3 = row1 * tmp + minor3;
let det = row0 * minor0;
let det = det.rotate_lanes_right::<2>() + det;
let det = det.reverse().rotate_lanes_right::<2>() + det;
if det.reduce_sum() == 0. {
return None;
}
// calculate the reciprocal
let tmp = f32x4::splat(1.0) / det;
let det = tmp + tmp - det * tmp * tmp;
let res0 = minor0 * det;
let res1 = minor1 * det;
let res2 = minor2 * det;
let res3 = minor3 * det;
let mut m = m;
m[0] = res0.to_array();
m[1] = res1.to_array();
m[2] = res2.to_array();
m[3] = res3.to_array();
Some(Matrix4x4(m))
}
#[cfg(test)]
#[rustfmt::skip]
mod tests {
use super::*;
#[test]
fn test() {
let tests: &[(Matrix4x4, Option<Matrix4x4>)] = &[
// Identity:
(Matrix4x4([
[1., 0., 0., 0.],
[0., 1., 0., 0.],
[0., 0., 1., 0.],
[0., 0., 0., 1.],
]),
Some(Matrix4x4([
[1., 0., 0., 0.],
[0., 1., 0., 0.],
[0., 0., 1., 0.],
[0., 0., 0., 1.],
]))
),
// None:
(Matrix4x4([
[1., 2., 3., 4.],
[12., 11., 10., 9.],
[5., 6., 7., 8.],
[16., 15., 14., 13.],
]),
None
),
// Other:
(Matrix4x4([
[1., 1., 1., 0.],
[0., 3., 1., 2.],
[2., 3., 1., 0.],
[1., 0., 2., 1.],
]),
Some(Matrix4x4([
[-3., -0.5, 1.5, 1.0],
[ 1., 0.25, -0.25, -0.5],
[ 3., 0.25, -1.25, -0.5],
[-3., 0.0, 1.0, 1.0],
]))
),
];
for &(input, output) in tests {
assert_eq!(scalar_inv4x4(input), output);
assert_eq!(simd_inv4x4(input), output);
}
}
}
fn main() {
// Empty main to make cargo happy
}
|
