nbody.cc

/* The Computer Language Benchmarks Game
   http://benchmarksgame.alioth.debian.org/
 
   contributed by Mark C. Lewis
   modified slightly by Chad Whipkey
   converted from java to c++,added sse support, by Branimir Maksimovic 
   modified by Vaclav Zeman
*/

#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <array>
#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;

        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::array<Body, 5> 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);
        }

        void advance(double dt) {
            const unsigned N = (bodies.size()-1)*bodies.size()/2;
            struct __attribute__((aligned(16))) 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;
            }
        }

        double energy(){
            double e = 0.0;

            for (unsigned i=0; i < bodies.size(); ++i) {
                Body const & iBody = bodies[i];
                double dx, dy, dz, distance;
                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 const & 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 = 5000000;
    if (argc > 1) 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());
}