nbody.c

# The Computer Language Benchmarks Game
# http://benchmarksgame.alioth.debian.org/
#
# originally by Kevin Carson
# modified by Tupteq, Fredrik Johansson, and Daniel Nanz
# modified by Maciej Fijalkowski
# 2to3

from libc.math cimport pow, sqrt
import sys

PI = 3.14159265358979323
SOLAR_MASS = 4 * PI * PI
DAYS_PER_YEAR = 365.24

cdef struct body_t:
    double x[3]
    double v[3]
    double m

DEF NBODIES = 5

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)
        }

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

cdef void make_cbodies(list bodies, body_t *cbodies, int num_cbodies):
    cdef body_t *cbody
    for i, body in enumerate(bodies):
        if i >= num_cbodies:
            break
        (x, v, m) = body
        cbody = &cbodies[i]
        cbody.x[0], cbody.x[1], cbody.x[2] = x
        cbody.v[0], cbody.v[1], cbody.v[2] = v
        cbodies[i].m = m

cdef list make_pybodies(body_t *cbodies, int num_cbodies):
    pybodies = []
    for i in range(num_cbodies):
        x = [cbodies[i].x[0], cbodies[i].x[1], cbodies[i].x[2]]
        v = [cbodies[i].v[0], cbodies[i].v[1], cbodies[i].v[2]]
        pybodies.append((x, v, cbodies[i].m))
    return pybodies


def advance(double dt, int n, bodies):
    # Note that this does not take a `pairs` argument, and *returns* a new
    # `bodies` list.  This is slightly different from the original pure-Python
    # version of `advance`.

    cdef:
        int i, ii, jj
        double dx, dy, dz, mag, b1m, b2m, ds
        body_t *body1
        body_t *body2
        body_t cbodies[NBODIES]

    make_cbodies(bodies, cbodies, NBODIES)

    for i in range(n):
        for ii in range(NBODIES-1):
            body1 = &cbodies[ii]
            for jj in range(ii+1, NBODIES):
                body2 = &cbodies[jj]
                dx = body1.x[0] - body2.x[0]
                dy = body1.x[1] - body2.x[1]
                dz = body1.x[2] - body2.x[2]
                ds = dx * dx + dy * dy + dz * dz
                mag = dt / (ds * sqrt(ds))
                b1m = body1.m * mag
                b2m = body2.m * mag
                body1.v[0] -= dx * b2m
                body1.v[1] -= dy * b2m
                body1.v[2] -= dz * b2m
                body2.v[0] += dx * b1m
                body2.v[1] += dy * b1m
                body2.v[2] += dz * b1m
        for ii in range(NBODIES):
            body2 = &cbodies[ii]
            body2.x[0] += dt * body2.v[0]
            body2.x[1] += dt * body2.v[1]
            body2.x[2] += dt * body2.v[2]

    return make_pybodies(cbodies, NBODIES)


def report_energy(bodies):
    # Note that this takes just a `bodies` list, and computes `pairs`
    # internally, which is a slight modification from the original pure-Python
    # version of `report_energy`.

    e = 0.0

    pairs = combinations(bodies)

    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):

    px = py = 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, bodies=BODIES, ref='sun'):
    system = list(bodies.values())
    offset_momentum(bodies[ref], system)
    report_energy(system)
    system = advance(0.01, n, system)
    report_energy(system)
[chris@Vonbrigdum 02-cython]$ cd ../03-pure-c/
[chris@Vonbrigdum 03-pure-c]$ ls
Makefile  nbody.c
[chris@Vonbrigdum 03-pure-c]$ cat nbody.c
/* The Computer Language Benchmarks Game
 * http://benchmarksgame.alioth.debian.org/
 *
 * 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[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
  }
};

#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[1]);
  int i;

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