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Timothy Warren
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src/nbody-3.rs
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281
src/nbody-3.rs
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// The Computer Language Benchmarks Game
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// https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
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//
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// Contributed by Mark C. Lewis.
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// Modified slightly by Chad Whipkey.
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// Converted from Java to C++ and added SSE support by Branimir Maksimovic.
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// Converted from C++ to C by Alexey Medvedchikov.
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// Modified by Jeremy Zerfas.
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// Converted to Rust by Cliff L. Biffle
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#![allow(non_upper_case_globals, non_camel_case_types, non_snake_case)]
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use std::arch::x86_64::*;
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use std::f64::consts::PI;
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use std::mem;
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#[repr(C)]
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struct body {
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position: [f64; 3],
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velocity: [f64; 3],
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mass: f64,
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}
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const SOLAR_MASS: f64 = 4. * PI * PI;
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const DAYS_PER_YEAR: f64 = 365.24;
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const BODIES_COUNT: usize = 5;
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static mut solar_Bodies: [body; BODIES_COUNT] = [
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body {
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// Sun
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mass: SOLAR_MASS,
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position: [0.; 3],
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velocity: [0.; 3],
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},
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body {
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// Jupiter
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mass: 9.54791938424326609e-04 * SOLAR_MASS,
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position: [
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4.84143144246472090e+00,
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-1.16032004402742839e+00,
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-1.03622044471123109e-01,
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],
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velocity: [
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1.66007664274403694e-03 * DAYS_PER_YEAR,
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7.69901118419740425e-03 * DAYS_PER_YEAR,
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-6.90460016972063023e-05 * DAYS_PER_YEAR,
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],
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},
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body {
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// Saturn
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mass: 2.85885980666130812e-04 * SOLAR_MASS,
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position: [
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8.34336671824457987e+00,
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4.12479856412430479e+00,
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-4.03523417114321381e-01,
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],
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velocity: [
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-2.76742510726862411e-03 * DAYS_PER_YEAR,
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4.99852801234917238e-03 * DAYS_PER_YEAR,
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2.30417297573763929e-05 * DAYS_PER_YEAR,
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],
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},
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body {
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// Uranus
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mass: 4.36624404335156298e-05 * SOLAR_MASS,
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position: [
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1.28943695621391310e+01,
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-1.51111514016986312e+01,
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-2.23307578892655734e-01,
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],
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velocity: [
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2.96460137564761618e-03 * DAYS_PER_YEAR,
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2.37847173959480950e-03 * DAYS_PER_YEAR,
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-2.96589568540237556e-05 * DAYS_PER_YEAR,
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],
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},
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body {
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// Neptune
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mass: 5.15138902046611451e-05 * SOLAR_MASS,
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position: [
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1.53796971148509165e+01,
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-2.59193146099879641e+01,
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1.79258772950371181e-01,
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],
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velocity: [
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2.68067772490389322e-03 * DAYS_PER_YEAR,
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1.62824170038242295e-03 * DAYS_PER_YEAR,
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-9.51592254519715870e-05 * DAYS_PER_YEAR,
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],
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},
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];
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// Calculate the momentum of each body and conserve momentum of the system by
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// adding to the Sun's velocity the appropriate opposite velocity needed in
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// order to offset that body's momentum.
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fn offset_Momentum(bodies: &mut [body; BODIES_COUNT]) {
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for i in 0..BODIES_COUNT {
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for m in 0..3 {
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bodies[0].velocity[m] -= bodies[i].velocity[m] * bodies[i].mass / SOLAR_MASS;
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}
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}
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}
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// Output the total energy of the system.
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fn output_Energy(bodies: &mut [body; BODIES_COUNT]) {
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let mut energy = 0.;
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for i in 0..BODIES_COUNT {
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// Add the kinetic energy for each body.
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energy += 0.5
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* bodies[i].mass
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* (bodies[i].velocity[0] * bodies[i].velocity[0]
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+ bodies[i].velocity[1] * bodies[i].velocity[1]
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+ bodies[i].velocity[2] * bodies[i].velocity[2]);
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// Add the potential energy between this body and
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// every other body
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for j in i + 1..BODIES_COUNT {
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let mut position_Delta = [0.; 3];
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for m in 0..3 {
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position_Delta[m] = bodies[i].position[m] - bodies[j].position[m];
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}
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energy -= bodies[i].mass * bodies[j].mass
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/ f64::sqrt(
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position_Delta[0] * position_Delta[0]
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+ position_Delta[1] * position_Delta[1]
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+ position_Delta[2] * position_Delta[2],
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);
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}
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}
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// Output the total energy of the system
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println!("{:.9}", energy);
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}
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// Advance all the bodies in the system by one timestep. Calculate the
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// interactions between all the bodies, update each body's velocity based on
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// those interactions, and update each body's position by the distance it
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// travels in a timestep at it's updated velocity.
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unsafe fn advance(bodies: &mut [body; BODIES_COUNT]) {
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// Figure out how many total different interactions there are between each
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// body and every other body. Some of the calculations for these
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// interactions will be calculated two at a time by using x86 SSE
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// instructions and because of that it will also be useful to have a
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// ROUNDED_INTERACTIONS_COUNT that is equal to the next highest even number
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// which is equal to or greater than INTERACTIONS_COUNT.
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const INTERACTIONS_COUNT: usize = BODIES_COUNT * (BODIES_COUNT - 1) / 2;
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const ROUNDED_INTERACTIONS_COUNT: usize = INTERACTIONS_COUNT + INTERACTIONS_COUNT % 2;
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// It's useful to have two arrays to keep track of the position_Deltas
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// and magnitudes of force between the bodies for each interaction. For the
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// position_Deltas array, instead of using a one dimensional array of
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// structures that each contain the X, Y, and Z components for a position
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// delta, a two dimensional array is used instead which consists of three
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// arrays that each contain all of the X, Y, and Z components for all of the
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// position_Deltas. This allows for more efficient loading of this data into
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// SSE registers. Both of these arrays are also set to contain
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// ROUNDED_INTERACTIONS_COUNT elements to simplify one of the following
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// loops and to also keep the second and third arrays in position_Deltas
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// aligned properly.
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#[repr(align(16))]
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#[derive(Copy, Clone)]
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struct Align16([f64; ROUNDED_INTERACTIONS_COUNT]);
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static mut position_Deltas: [Align16; 3] = [Align16([0.; ROUNDED_INTERACTIONS_COUNT]); 3];
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static mut magnitudes: Align16 = Align16([0.; ROUNDED_INTERACTIONS_COUNT]);
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// Calculate the position_Deltas between the bodies for each interaction.
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{
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let mut k = 0;
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for i in 0..BODIES_COUNT - 1 {
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for j in i + 1..BODIES_COUNT {
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for m in 0..3 {
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position_Deltas[m].0[k] = bodies[i].position[m] - bodies[j].position[m];
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}
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k += 1;
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}
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}
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}
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// Calculate the magnitudes of force between the bodies for each
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// interaction. This loop processes two interactions at a time which is why
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// ROUNDED_INTERACTIONS_COUNT/2 iterations are done.
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for i in 0..ROUNDED_INTERACTIONS_COUNT / 2 {
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// Load position_Deltas of two bodies into position_Delta.
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let mut position_Delta = [mem::MaybeUninit::<__m128d>::uninit(); 3];
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for m in 0..3 {
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position_Delta[m]
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.as_mut_ptr()
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.write(*(&position_Deltas[m].0 as *const f64 as *const __m128d).add(i));
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}
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let position_Delta: [__m128d; 3] = mem::transmute(position_Delta);
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let distance_Squared: __m128d = _mm_add_pd(
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_mm_add_pd(
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_mm_mul_pd(position_Delta[0], position_Delta[0]),
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_mm_mul_pd(position_Delta[1], position_Delta[1]),
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),
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_mm_mul_pd(position_Delta[2], position_Delta[2]),
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);
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// Doing square roots normally using double precision floating point
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// math can be quite time consuming so SSE's much faster single
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// precision reciprocal square root approximation instruction is used as
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// a starting point instead. The precision isn't quite sufficient to get
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// acceptable results so two iterations of the Newton–Raphson method are
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// done to improve precision further.
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let mut distance_Reciprocal: __m128d =
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_mm_cvtps_pd(_mm_rsqrt_ps(_mm_cvtpd_ps(distance_Squared)));
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for _ in 0..2 {
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// Normally the last four multiplications in this equation would
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// have to be done sequentially but by placing the last
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// multiplication in parentheses, a compiler can then schedule that
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// multiplication earlier.
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distance_Reciprocal = _mm_sub_pd(
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_mm_mul_pd(distance_Reciprocal, _mm_set1_pd(1.5)),
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_mm_mul_pd(
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_mm_mul_pd(
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_mm_mul_pd(_mm_set1_pd(0.5), distance_Squared),
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distance_Reciprocal,
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),
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_mm_mul_pd(distance_Reciprocal, distance_Reciprocal),
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),
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);
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}
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// Calculate the magnitudes of force between the bodies. Typically this
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// calculation would probably be done by using a division by the cube of
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// the distance (or similarly a multiplication by the cube of its
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// reciprocal) but for better performance on modern computers it often
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// will make sense to do part of the calculation using a division by the
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// distance_Squared which was already calculated earlier. Additionally
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// this method is probably a little more accurate due to less rounding
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// as well.
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(magnitudes.0.as_mut_ptr() as *mut __m128d)
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.add(i)
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.write(_mm_mul_pd(
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_mm_div_pd(_mm_set1_pd(0.01), distance_Squared),
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distance_Reciprocal,
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));
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}
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// Use the calculated magnitudes of force to update the velocities for all
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// of the bodies.
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{
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let mut k = 0;
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for i in 0..BODIES_COUNT - 1 {
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for j in i + 1..BODIES_COUNT {
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let i_mass_magnitude = bodies[i].mass * magnitudes.0[k];
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let j_mass_magnitude = bodies[j].mass * magnitudes.0[k];
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for m in 0..3 {
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bodies[i].velocity[m] -= position_Deltas[m].0[k] * j_mass_magnitude;
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bodies[j].velocity[m] += position_Deltas[m].0[k] * i_mass_magnitude;
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}
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k += 1;
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}
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}
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}
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// Use the updated velocities to update the positions for all of the bodies.
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for i in 0..BODIES_COUNT {
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for m in 0..3 {
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bodies[i].position[m] += 0.01 * bodies[i].velocity[m];
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}
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}
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}
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fn main() {
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unsafe {
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offset_Momentum(&mut solar_Bodies);
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output_Energy(&mut solar_Bodies);
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let c = std::env::args().nth(1).unwrap().parse().unwrap();
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for _ in 0..c {
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advance(&mut solar_Bodies);
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}
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output_Energy(&mut solar_Bodies);
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}
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}
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