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Frank Filthaut 2019-10-30 09:02:41 +01:00
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ex0.1/nbody/nbody.cc Normal file
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/* 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());
}

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# The Computer Language Benchmarks Game
# https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
#
# originally by Kevin Carson
# modified by Tupteq, Fredrik Johansson, and Daniel Nanz
# modified by Maciej Fijalkowski
# 2to3
import sys
def combinations(l):
result = []
for x in range(len(l) - 1):
ls = l[x+1:]
for y in ls:
result.append((l[x],y))
return result
PI = 3.14159265358979323
SOLAR_MASS = 4 * PI * PI
DAYS_PER_YEAR = 365.24
BODIES = {
'sun': ([0.0, 0.0, 0.0], [0.0, 0.0, 0.0], SOLAR_MASS),
'jupiter': ([4.84143144246472090e+00,
-1.16032004402742839e+00,
-1.03622044471123109e-01],
[1.66007664274403694e-03 * DAYS_PER_YEAR,
7.69901118419740425e-03 * DAYS_PER_YEAR,
-6.90460016972063023e-05 * DAYS_PER_YEAR],
9.54791938424326609e-04 * SOLAR_MASS),
'saturn': ([8.34336671824457987e+00,
4.12479856412430479e+00,
-4.03523417114321381e-01],
[-2.76742510726862411e-03 * DAYS_PER_YEAR,
4.99852801234917238e-03 * DAYS_PER_YEAR,
2.30417297573763929e-05 * DAYS_PER_YEAR],
2.85885980666130812e-04 * SOLAR_MASS),
'uranus': ([1.28943695621391310e+01,
-1.51111514016986312e+01,
-2.23307578892655734e-01],
[2.96460137564761618e-03 * DAYS_PER_YEAR,
2.37847173959480950e-03 * DAYS_PER_YEAR,
-2.96589568540237556e-05 * DAYS_PER_YEAR],
4.36624404335156298e-05 * SOLAR_MASS),
'neptune': ([1.53796971148509165e+01,
-2.59193146099879641e+01,
1.79258772950371181e-01],
[2.68067772490389322e-03 * DAYS_PER_YEAR,
1.62824170038242295e-03 * DAYS_PER_YEAR,
-9.51592254519715870e-05 * DAYS_PER_YEAR],
5.15138902046611451e-05 * SOLAR_MASS) }
SYSTEM = list(BODIES.values())
PAIRS = combinations(SYSTEM)
def advance(dt, n, bodies=SYSTEM, pairs=PAIRS):
for i in range(n):
for (([x1, y1, z1], v1, m1),
([x2, y2, z2], v2, m2)) in pairs:
dx = x1 - x2
dy = y1 - y2
dz = z1 - z2
mag = dt * ((dx * dx + dy * dy + dz * dz) ** (-1.5))
b1m = m1 * mag
b2m = m2 * mag
v1[0] -= dx * b2m
v1[1] -= dy * b2m
v1[2] -= dz * b2m
v2[0] += dx * b1m
v2[1] += dy * b1m
v2[2] += dz * b1m
for (r, [vx, vy, vz], m) in bodies:
r[0] += dt * vx
r[1] += dt * vy
r[2] += dt * vz
def report_energy(bodies=SYSTEM, pairs=PAIRS, e=0.0):
for (((x1, y1, z1), v1, m1),
((x2, y2, z2), v2, m2)) in pairs:
dx = x1 - x2
dy = y1 - y2
dz = z1 - z2
e -= (m1 * m2) / ((dx * dx + dy * dy + dz * dz) ** 0.5)
for (r, [vx, vy, vz], m) in bodies:
e += m * (vx * vx + vy * vy + vz * vz) / 2.
print("%.9f" % e)
def offset_momentum(ref, bodies=SYSTEM, px=0.0, py=0.0, pz=0.0):
for (r, [vx, vy, vz], m) in bodies:
px -= vx * m
py -= vy * m
pz -= vz * m
(r, v, m) = ref
v[0] = px / m
v[1] = py / m
v[2] = pz / m
def main(n, ref='sun'):
offset_momentum(BODIES[ref])
report_energy()
advance(0.01, n)
report_energy()
if __name__ == '__main__':
main(int(sys.argv[1]))