# n-body C gcc #2 program

## source code

```/* The Computer Language Benchmarks Game
* https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
*
* contributed by Christoph Bauer
* slightly sped up by Petr Prokhorenkov
*/

#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;
};

/*
* Here's one weird thing: inlining of this function
* decreases performance by 25%. (I.e. do not compile this with -O3)
* Advances with dt == 1.0
*/
void advance(int nbodies, struct planet * bodies)
{
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 inv_distance = 1.0/sqrt(dx * dx + dy * dy + dz * dz);
double mag = inv_distance * inv_distance * inv_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 += b->vx;
b->y += b->vy;
b->z += 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.vx = - px / solar_mass;
bodies.vy = - py / solar_mass;
bodies.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
}
};

#define DT 1e-2
#define RECIP_DT (1.0/DT)

/*
* Rescale certain properties of bodies. That allows doing
* consequential advance()'s as if dt were equal to 1.0.
*
* When all advances done, rescale bodies back to obtain correct energy.
*/
void scale_bodies(int nbodies, struct planet * bodies, double scale) {
int i;

for (i = 0; i < nbodies; i++) {
bodies[i].mass *= scale*scale;
bodies[i].vx *= scale;
bodies[i].vy *= scale;
bodies[i].vz *= scale;
}
}

int main(int argc, char ** argv)
{
int n = atoi(argv);
int i;

offset_momentum(NBODIES, bodies);
printf ("%.9f\n", energy(NBODIES, bodies));
scale_bodies(NBODIES, bodies, DT);
for (i = 1; i <= n; i++)  {
}
scale_bodies(NBODIES, bodies, RECIP_DT);
printf ("%.9f\n", energy(NBODIES, bodies));
return 0;
}
```

## notes, command-line, and program output

```NOTES:
gcc (Ubuntu 10.2.0-13ubuntu1) 10.2.0

Mon, 02 Nov 2020 19:30:31 GMT

MAKE:
/usr/bin/gcc -pipe -Wall -O3 -fomit-frame-pointer -march=ivybridge  nbody.gcc-2.c -o nbody.gcc-2.gcc_run -lm
rm nbody.gcc-2.c

1.81s to complete and log all make actions

COMMAND LINE:
./nbody.gcc-2.gcc_run 50000000

PROGRAM OUTPUT:
-0.169075164
-0.169059907
```