source code
/* 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++,added sse support, by Branimir Maksimovic
*/
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <immintrin.h>
static const double PI = 3.141592653589793;
static const double SOLAR_MASS = 4 * PI * PI;
static const double DAYS_PER_YEAR = 365.24;
class Body {
public: double x, y, z, filler, vx, vy, vz, mass;
public: Body(){}
static Body& jupiter(){
static Body p;
p.x = 4.84143144246472090e+00;
p.y = -1.16032004402742839e+00;
p.z = -1.03622044471123109e-01;
p.vx = 1.66007664274403694e-03 * DAYS_PER_YEAR;
p.vy = 7.69901118419740425e-03 * DAYS_PER_YEAR;
p.vz = -6.90460016972063023e-05 * DAYS_PER_YEAR;
p.mass = 9.54791938424326609e-04 * SOLAR_MASS;
return p;
}
static Body& saturn(){
static Body p;
p.x = 8.34336671824457987e+00;
p.y = 4.12479856412430479e+00;
p.z = -4.03523417114321381e-01;
p.vx = -2.76742510726862411e-03 * DAYS_PER_YEAR;
p.vy = 4.99852801234917238e-03 * DAYS_PER_YEAR;
p.vz = 2.30417297573763929e-05 * DAYS_PER_YEAR;
p.mass = 2.85885980666130812e-04 * SOLAR_MASS;
return p;
}
static Body& uranus(){
static Body p;
p.x = 1.28943695621391310e+01;
p.y = -1.51111514016986312e+01;
p.z = -2.23307578892655734e-01;
p.vx = 2.96460137564761618e-03 * DAYS_PER_YEAR;
p.vy = 2.37847173959480950e-03 * DAYS_PER_YEAR;
p.vz = -2.96589568540237556e-05 * DAYS_PER_YEAR;
p.mass = 4.36624404335156298e-05 * SOLAR_MASS;
return p;
}
static Body& neptune(){
static Body p;
p.x = 1.53796971148509165e+01;
p.y = -2.59193146099879641e+01;
p.z = 1.79258772950371181e-01;
p.vx = 2.68067772490389322e-03 * DAYS_PER_YEAR;
p.vy = 1.62824170038242295e-03 * DAYS_PER_YEAR;
p.vz = -9.51592254519715870e-05 * DAYS_PER_YEAR;
p.mass = 5.15138902046611451e-05 * SOLAR_MASS;
return p;
}
static Body& sun(){
static Body p;
p.mass = SOLAR_MASS;
return p;
}
Body& offsetMomentum(double px, double py, double pz){
vx = -px / SOLAR_MASS;
vy = -py / SOLAR_MASS;
vz = -pz / SOLAR_MASS;
return *this;
}
};
class NBodySystem {
private: std::vector<Body> bodies;
public: NBodySystem()
: bodies {
Body::sun(),
Body::jupiter(),
Body::saturn(),
Body::uranus(),
Body::neptune()
}
{
double px = 0.0;
double py = 0.0;
double pz = 0.0;
for(unsigned i=0; i < bodies.size(); ++i) {
px += bodies[i].vx * bodies[i].mass;
py += bodies[i].vy * bodies[i].mass;
pz += bodies[i].vz * bodies[i].mass;
}
bodies[0].offsetMomentum(px,py,pz);
}
public: void advance(double dt) {
unsigned N = (bodies.size()-1)*bodies.size()/2;
struct R{
double dx,dy,dz,filler;
};
static R r[1000];
static __attribute__((aligned(16))) double mag[1000];
for(unsigned i=0,k=0; i < bodies.size()-1; ++i) {
Body& iBody = bodies[i];
for(unsigned j=i+1; j < bodies.size(); ++j,++k) {
r[k].dx = iBody.x - bodies[j].x;
r[k].dy = iBody.y - bodies[j].y;
r[k].dz = iBody.z - bodies[j].z;
}
}
for(unsigned i=0; i < N; i+=2) {
__m128d dx,dy,dz;
dx = _mm_loadl_pd(dx,&r[i].dx);
dy = _mm_loadl_pd(dy,&r[i].dy);
dz = _mm_loadl_pd(dz,&r[i].dz);
dx = _mm_loadh_pd(dx,&r[i+1].dx);
dy = _mm_loadh_pd(dy,&r[i+1].dy);
dz = _mm_loadh_pd(dz,&r[i+1].dz);
__m128d dSquared = dx*dx + dy*dy + dz*dz;
__m128d distance =
_mm_cvtps_pd(_mm_rsqrt_ps(_mm_cvtpd_ps(dSquared)));
for(unsigned j=0;j<2;++j)
{
distance = distance * _mm_set1_pd(1.5) -
((_mm_set1_pd(0.5) * dSquared) * distance) *
(distance * distance);
}
__m128d dmag = _mm_set1_pd(dt)/(dSquared) * distance;
_mm_store_pd(&mag[i],dmag);
}
for(unsigned i=0,k=0; i < bodies.size()-1; ++i) {
Body& iBody = bodies[i];
for(unsigned j=i+1; j < bodies.size(); ++j,++k) {
iBody.vx -= r[k].dx * bodies[j].mass * mag[k];
iBody.vy -= r[k].dy * bodies[j].mass * mag[k];
iBody.vz -= r[k].dz * bodies[j].mass * mag[k];
bodies[j].vx += r[k].dx * iBody.mass * mag[k];
bodies[j].vy += r[k].dy * iBody.mass * mag[k];
bodies[j].vz += r[k].dz * iBody.mass * mag[k];
}
}
for (unsigned i = 0; i < bodies.size(); ++i) {
bodies[i].x += dt * bodies[i].vx;
bodies[i].y += dt * bodies[i].vy;
bodies[i].z += dt * bodies[i].vz;
}
}
public: double energy(){
double dx, dy, dz, distance;
double e = 0.0;
for (unsigned i=0; i < bodies.size(); ++i) {
Body& iBody = bodies[i];
e += 0.5 * iBody.mass *
( iBody.vx * iBody.vx
+ iBody.vy * iBody.vy
+ iBody.vz * iBody.vz );
for (unsigned j=i+1; j < bodies.size(); ++j) {
Body& jBody = bodies[j];
dx = iBody.x - jBody.x;
dy = iBody.y - jBody.y;
dz = iBody.z - jBody.z;
distance = sqrt(dx*dx + dy*dy + dz*dz);
e -= (iBody.mass * jBody.mass) / distance;
}
}
return e;
}
};
int main(int argc, char** argv) {
int n = atoi(argv[1]);
NBodySystem bodies;
printf("%.9f\n", bodies.energy());
for (int i=0; i<n; ++i)
bodies.advance(0.01);
printf("%.9f\n", bodies.energy());
}
notes, command-line, and program output
NOTES:
64-bit Ubuntu quad core
g++ (Ubuntu 9.3.0-10ubuntu2) 9.3.0
Mon, 04 May 2020 19:16:41 GMT
MAKE:
/usr/bin/g++ -c -pipe -O3 -fomit-frame-pointer -march=core2 nbody.gpp-5.c++ -o nbody.gpp-5.c++.o && \
/usr/bin/g++ nbody.gpp-5.c++.o -o nbody.gpp-5.gpp_run
rm nbody.gpp-5.c++
5.54s to complete and log all make actions
COMMAND LINE:
./nbody.gpp-5.gpp_run 50000000
PROGRAM OUTPUT:
-0.169075164
-0.169059907