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