diff --git a/resources/examples/nbodies.c3 b/resources/examples/nbodies.c3 new file mode 100644 index 000000000..84b301141 --- /dev/null +++ b/resources/examples/nbodies.c3 @@ -0,0 +1,161 @@ +module nbodies; + +const PI = 3.141592653589793; +const SOLAR_MASS = 4 * PI * PI; +const DAYS_PER_YEAR = 365.24; +const DT = 1e-2; +const RECIP_DT = (1.0/DT); + +struct Planet +{ + double x, y, z; + double vx, vy, vz; + double mass; +} + +func void advance(Planet[] bodies) @noinline +{ + usize nbodies = bodies.len(); + foreach (i, Planet* &b : bodies) + { + for (usize j = i + 1; j < nbodies; j++) + { + 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; + } + } + foreach (&b : bodies) + { + b.x += b.vx; + b.y += b.vy; + b.z += b.vz; + } +} + +func double energy(Planet[] bodies) +{ + double e; + usize nbodies = bodies.len(); + + foreach (i, Planet* &b : bodies) + { + e += 0.5 * b.mass * (b.vx * b.vx + b.vy * b.vy + b.vz * b.vz); + for (usize j = i + 1; j < nbodies; j++) + { + 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; +} + +func void offset_momentum(Planet[] bodies) +{ + double px; + double py; + double pz; + foreach (&b : bodies) + { + px += b.vx * b.mass; + py += b.vy * b.mass; + pz += b.vz * b.mass; + } + bodies[0].vx = - px / SOLAR_MASS; + bodies[0].vy = - py / SOLAR_MASS; + bodies[0].vz = - pz / SOLAR_MASS; +} + +Planet[*] planet_bodies = { + { /* 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 + } +}; + + +/* + * 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. + */ +func void scale_bodies(Planet[] bodies, double scale) +{ + foreach (&b : bodies) + { + b.mass *= scale * scale; + b.vx *= scale; + b.vy *= scale; + b.vz *= scale; + } +} + +extern func int atoi(char *s); +extern func int printf(char *s, ...); +extern func double sqrt(double); + +func int main(int argc, char ** argv) +{ + int n = atoi(argv[1]); + + Planet[] bodies = &planet_bodies; + offset_momentum(bodies); + printf ("%.9f\n", energy(bodies)); + scale_bodies(bodies, DT); + for (int i = 1; i <= n; i++) + { + advance(bodies); + } + scale_bodies(bodies, RECIP_DT); + printf ("%.9f\n", energy(bodies)); + return 0; +}