//! 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 { 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 { 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.horizontal_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)] = &[ // 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 }