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diff --git a/library/portable-simd/crates/core_simd/examples/matrix_inversion.rs b/library/portable-simd/crates/core_simd/examples/matrix_inversion.rs new file mode 100644 index 000000000..39f530f68 --- /dev/null +++ b/library/portable-simd/crates/core_simd/examples/matrix_inversion.rs @@ -0,0 +1,316 @@ +//! 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 +} diff --git a/library/portable-simd/crates/core_simd/examples/nbody.rs b/library/portable-simd/crates/core_simd/examples/nbody.rs new file mode 100644 index 000000000..df38a0096 --- /dev/null +++ b/library/portable-simd/crates/core_simd/examples/nbody.rs @@ -0,0 +1,193 @@ +#![feature(portable_simd)] +extern crate std_float; + +/// Benchmarks game nbody code +/// Taken from the `packed_simd` crate +/// Run this benchmark with `cargo test --example nbody` +mod nbody { + use core_simd::simd::*; + #[allow(unused)] // False positive? + use std_float::StdFloat; + + use std::f64::consts::PI; + const SOLAR_MASS: f64 = 4.0 * PI * PI; + const DAYS_PER_YEAR: f64 = 365.24; + + #[derive(Debug, Clone, Copy)] + struct Body { + pub x: f64x4, + pub v: f64x4, + pub mass: f64, + } + + const N_BODIES: usize = 5; + const BODIES: [Body; N_BODIES] = [ + // sun: + Body { + x: f64x4::from_array([0., 0., 0., 0.]), + v: f64x4::from_array([0., 0., 0., 0.]), + mass: SOLAR_MASS, + }, + // jupiter: + Body { + x: f64x4::from_array([ + 4.84143144246472090e+00, + -1.16032004402742839e+00, + -1.03622044471123109e-01, + 0., + ]), + v: f64x4::from_array([ + 1.66007664274403694e-03 * DAYS_PER_YEAR, + 7.69901118419740425e-03 * DAYS_PER_YEAR, + -6.90460016972063023e-05 * DAYS_PER_YEAR, + 0., + ]), + mass: 9.54791938424326609e-04 * SOLAR_MASS, + }, + // saturn: + Body { + x: f64x4::from_array([ + 8.34336671824457987e+00, + 4.12479856412430479e+00, + -4.03523417114321381e-01, + 0., + ]), + v: f64x4::from_array([ + -2.76742510726862411e-03 * DAYS_PER_YEAR, + 4.99852801234917238e-03 * DAYS_PER_YEAR, + 2.30417297573763929e-05 * DAYS_PER_YEAR, + 0., + ]), + mass: 2.85885980666130812e-04 * SOLAR_MASS, + }, + // uranus: + Body { + x: f64x4::from_array([ + 1.28943695621391310e+01, + -1.51111514016986312e+01, + -2.23307578892655734e-01, + 0., + ]), + v: f64x4::from_array([ + 2.96460137564761618e-03 * DAYS_PER_YEAR, + 2.37847173959480950e-03 * DAYS_PER_YEAR, + -2.96589568540237556e-05 * DAYS_PER_YEAR, + 0., + ]), + mass: 4.36624404335156298e-05 * SOLAR_MASS, + }, + // neptune: + Body { + x: f64x4::from_array([ + 1.53796971148509165e+01, + -2.59193146099879641e+01, + 1.79258772950371181e-01, + 0., + ]), + v: f64x4::from_array([ + 2.68067772490389322e-03 * DAYS_PER_YEAR, + 1.62824170038242295e-03 * DAYS_PER_YEAR, + -9.51592254519715870e-05 * DAYS_PER_YEAR, + 0., + ]), + mass: 5.15138902046611451e-05 * SOLAR_MASS, + }, + ]; + + fn offset_momentum(bodies: &mut [Body; N_BODIES]) { + let (sun, rest) = bodies.split_at_mut(1); + let sun = &mut sun[0]; + for body in rest { + let m_ratio = body.mass / SOLAR_MASS; + sun.v -= body.v * Simd::splat(m_ratio); + } + } + + fn energy(bodies: &[Body; N_BODIES]) -> f64 { + let mut e = 0.; + for i in 0..N_BODIES { + let bi = &bodies[i]; + e += bi.mass * (bi.v * bi.v).reduce_sum() * 0.5; + for bj in bodies.iter().take(N_BODIES).skip(i + 1) { + let dx = bi.x - bj.x; + e -= bi.mass * bj.mass / (dx * dx).reduce_sum().sqrt() + } + } + e + } + + fn advance(bodies: &mut [Body; N_BODIES], dt: f64) { + const N: usize = N_BODIES * (N_BODIES - 1) / 2; + + // compute distance between bodies: + let mut r = [f64x4::splat(0.); N]; + { + let mut i = 0; + for j in 0..N_BODIES { + for k in j + 1..N_BODIES { + r[i] = bodies[j].x - bodies[k].x; + i += 1; + } + } + } + + let mut mag = [0.0; N]; + for i in (0..N).step_by(2) { + let d2s = f64x2::from_array([ + (r[i] * r[i]).reduce_sum(), + (r[i + 1] * r[i + 1]).reduce_sum(), + ]); + let dmags = f64x2::splat(dt) / (d2s * d2s.sqrt()); + mag[i] = dmags[0]; + mag[i + 1] = dmags[1]; + } + + let mut i = 0; + for j in 0..N_BODIES { + for k in j + 1..N_BODIES { + let f = r[i] * Simd::splat(mag[i]); + bodies[j].v -= f * Simd::splat(bodies[k].mass); + bodies[k].v += f * Simd::splat(bodies[j].mass); + i += 1 + } + } + for body in bodies { + body.x += Simd::splat(dt) * body.v + } + } + + pub fn run(n: usize) -> (f64, f64) { + let mut bodies = BODIES; + offset_momentum(&mut bodies); + let energy_before = energy(&bodies); + for _ in 0..n { + advance(&mut bodies, 0.01); + } + let energy_after = energy(&bodies); + + (energy_before, energy_after) + } +} + +#[cfg(test)] +mod tests { + // Good enough for demonstration purposes, not going for strictness here. + fn approx_eq_f64(a: f64, b: f64) -> bool { + (a - b).abs() < 0.00001 + } + #[test] + fn test() { + const OUTPUT: [f64; 2] = [-0.169075164, -0.169087605]; + let (energy_before, energy_after) = super::nbody::run(1000); + assert!(approx_eq_f64(energy_before, OUTPUT[0])); + assert!(approx_eq_f64(energy_after, OUTPUT[1])); + } +} + +fn main() { + { + let (energy_before, energy_after) = nbody::run(1000); + println!("Energy before: {energy_before}"); + println!("Energy after: {energy_after}"); + } +} diff --git a/library/portable-simd/crates/core_simd/examples/spectral_norm.rs b/library/portable-simd/crates/core_simd/examples/spectral_norm.rs new file mode 100644 index 000000000..012182e09 --- /dev/null +++ b/library/portable-simd/crates/core_simd/examples/spectral_norm.rs @@ -0,0 +1,77 @@ +#![feature(portable_simd)] + +use core_simd::simd::*; + +fn a(i: usize, j: usize) -> f64 { + ((i + j) * (i + j + 1) / 2 + i + 1) as f64 +} + +fn mult_av(v: &[f64], out: &mut [f64]) { + assert!(v.len() == out.len()); + assert!(v.len() % 2 == 0); + + for (i, out) in out.iter_mut().enumerate() { + let mut sum = f64x2::splat(0.0); + + let mut j = 0; + while j < v.len() { + let b = f64x2::from_slice(&v[j..]); + let a = f64x2::from_array([a(i, j), a(i, j + 1)]); + sum += b / a; + j += 2 + } + *out = sum.reduce_sum(); + } +} + +fn mult_atv(v: &[f64], out: &mut [f64]) { + assert!(v.len() == out.len()); + assert!(v.len() % 2 == 0); + + for (i, out) in out.iter_mut().enumerate() { + let mut sum = f64x2::splat(0.0); + + let mut j = 0; + while j < v.len() { + let b = f64x2::from_slice(&v[j..]); + let a = f64x2::from_array([a(j, i), a(j + 1, i)]); + sum += b / a; + j += 2 + } + *out = sum.reduce_sum(); + } +} + +fn mult_atav(v: &[f64], out: &mut [f64], tmp: &mut [f64]) { + mult_av(v, tmp); + mult_atv(tmp, out); +} + +pub fn spectral_norm(n: usize) -> f64 { + assert!(n % 2 == 0, "only even lengths are accepted"); + + let mut u = vec![1.0; n]; + let mut v = u.clone(); + let mut tmp = u.clone(); + + for _ in 0..10 { + mult_atav(&u, &mut v, &mut tmp); + mult_atav(&v, &mut u, &mut tmp); + } + (dot(&u, &v) / dot(&v, &v)).sqrt() +} + +fn dot(x: &[f64], y: &[f64]) -> f64 { + // This is auto-vectorized: + x.iter().zip(y).map(|(&x, &y)| x * y).sum() +} + +#[cfg(test)] +#[test] +fn test() { + assert_eq!(&format!("{:.9}", spectral_norm(100)), "1.274219991"); +} + +fn main() { + // Empty main to make cargo happy +} |