Thanks for the correction, I fixed that and compared against C++ version by the OP. Here are the results which, again, show how powerful Julia is using SArrays:
C++ (with -Ofast
):
-0.169075164
-0.169083134
Process returned 0 (0x0) execution time : 0.485 s
Julia (with -O3 --check-bounds=no
):
-0.169075164
-0.169083134
0.391008 seconds (24 allocations: 1.125 KiB)
The full versions for reproducability:
using Printf
using StaticArrays
const planet = SVector{7, Float64}
const solar_mass = 4 * π^2
const days_per_year = 365.24
function advance(nbodies, bodies, dt)
for i = 1:nbodies
b = bodies[i]
for j = i+1:nbodies
b2 = bodies[j]
dx = b[1] - b2[1]
dy = b[2] - b2[2]
dz = b[3] - b2[3]
dsq = dx*dx + dy*dy + dz*dz
distance = sqrt(dsq)
mag = dt / (dsq * distance)
b4 = dx * b2[7] * mag
b5 = dy * b2[7] * mag
b6 = dz * b2[7] * mag
b24 = dx * b[7] * mag
b25 = dy * b[7] * mag
b26 = dz * b[7] * mag
bodies[i] -= planet(0, 0, 0, b4, b5, b6, 0)
bodies[j] += planet(0, 0, 0, b24,b25,b26, 0)
end
end
for i = 1:nbodies
b = bodies[i]
bodies[i] += planet(dt*b[4], dt*b[5], dt*b[6], 0, 0, 0, 0)
end
end
function energy(nbodies::Int, bodies)
e = 0.0
for i = 1:nbodies
b::planet = bodies[i]
e += 0.5 * b[7] * (b[4] * b[4] + b[5] * b[5] + b[6] * b[6])
for j = i + 1:nbodies
b2::planet = bodies[j]
dx = b[1] - b2[1]
dy = b[2] - b2[2]
dz = b[3] - b2[3]
distance = sqrt(dx*dx + dy*dy + dz*dz)
e -= (b[7] * b2[7]) / distance
end
end
return e
end
function offset_momentum(nbodies::Int, bodies::Vector{planet})
px = 0.0
py = 0.0
pz = 0.0
for i = 1:nbodies
px += bodies[i][4] * bodies[i][7]
py += bodies[i][5] * bodies[i][7]
pz += bodies[i][6] * bodies[i][7]
end
bodies[1] -= planet(0,0,0, px/solar_mass, py/solar_mass, pz/solar_mass, 0)
end
function main(iterations::Int)
NBODIES = 5
bodies = Array{planet}(undef, NBODIES)
bodies[1] = planet( # sun
0, 0, 0, 0, 0, 0, solar_mass
)
bodies[2] = planet( #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
)
bodies[3] = planet( #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
)
bodies[4] = planet( #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
)
bodies[5] = planet( #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
)
n = iterations
offset_momentum(NBODIES, bodies);
@printf("%.9f\n", energy(NBODIES, bodies))
for i = 1:n
advance(NBODIES, bodies, 0.01)
end
@printf("%.9f\n", energy(NBODIES, bodies))
end
main(500)
@time main(5_000_000)
and
/* The Computer Language Benchmarks Game
* http://benchmarksgame.alioth.debian.org/
*
* contributed by Christoph Bauer
*
*/
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define pi 3.141592653589793
#define solar_mass (4 * pi * pi)
#define days_per_year 365.24
struct planet {
double x, y, z;
double vx, vy, vz;
double mass;
};
void advance(int nbodies, struct planet * bodies, double dt)
{
int i, j;
for (i = 0; i < nbodies; i++) {
struct planet * b = &(bodies[i]);
for (j = i + 1; j < nbodies; j++) {
struct planet * b2 = &(bodies[j]);
double dx = b->x - b2->x;
double dy = b->y - b2->y;
double dz = b->z - b2->z;
double distance = sqrt(dx * dx + dy * dy + dz * dz);
double mag = dt / (distance * distance * distance);
b->vx -= dx * b2->mass * mag;
b->vy -= dy * b2->mass * mag;
b->vz -= dz * b2->mass * mag;
b2->vx += dx * b->mass * mag;
b2->vy += dy * b->mass * mag;
b2->vz += dz * b->mass * mag;
}
}
for (i = 0; i < nbodies; i++) {
struct planet * b = &(bodies[i]);
b->x += dt * b->vx;
b->y += dt * b->vy;
b->z += dt * b->vz;
}
}
double energy(int nbodies, struct planet * bodies)
{
double e;
int i, j;
e = 0.0;
for (i = 0; i < nbodies; i++) {
struct planet * b = &(bodies[i]);
e += 0.5 * b->mass * (b->vx * b->vx + b->vy * b->vy + b->vz * b->vz);
for (j = i + 1; j < nbodies; j++) {
struct planet * b2 = &(bodies[j]);
double dx = b->x - b2->x;
double dy = b->y - b2->y;
double dz = b->z - b2->z;
double distance = sqrt(dx * dx + dy * dy + dz * dz);
e -= (b->mass * b2->mass) / distance;
}
}
return e;
}
void offset_momentum(int nbodies, struct planet * bodies)
{
double px = 0.0, py = 0.0, pz = 0.0;
int i;
for (i = 0; i < nbodies; i++) {
px += bodies[i].vx * bodies[i].mass;
py += bodies[i].vy * bodies[i].mass;
pz += bodies[i].vz * bodies[i].mass;
}
bodies[0].vx = - px / solar_mass;
bodies[0].vy = - py / solar_mass;
bodies[0].vz = - pz / solar_mass;
}
#define NBODIES 5
struct planet bodies[NBODIES] = {
{ /* sun */
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
}
};
int main(int argc, char ** argv)
{
int n = 5000000; // atoi(argv[1]);
int i;
offset_momentum(NBODIES, bodies);
printf ("%.9f\n", energy(NBODIES, bodies));
for (i = 1; i <= n; i++)
advance(NBODIES, bodies, 0.01);
printf ("%.9f\n", energy(NBODIES, bodies));
return 0;
}