uni-m.cds-adv-prog/ex0.1/nbody/nbody.cc

/* 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
   modified by Vaclav Zeman
   modified by Vaclav Haisman to use explicit SSE2 intrinsics
*/

#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 dSquared = _mm_add_pd(
                _mm_add_pd(_mm_mul_pd(dx, dx), _mm_mul_pd(dy, dy)),
                _mm_mul_pd(dz, dz));

            __m128d distance =
                _mm_cvtps_pd(_mm_rsqrt_ps(_mm_cvtpd_ps(dSquared)));
            for(unsigned j=0;j<2;++j)
            {
                distance = _mm_sub_pd(
                    _mm_mul_pd(distance, _mm_set1_pd(1.5)),
                    _mm_mul_pd(
                        _mm_mul_pd(
                            _mm_mul_pd(_mm_set1_pd(0.5), dSquared),
                             distance),
                        _mm_mul_pd(distance, distance)
                    )
                );
            }

            __m128d dmag = _mm_mul_pd(
                _mm_div_pd(_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 = 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());
}