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/*

Redistribution and use in source and binary forms, with or without

modification, are permitted provided that the following conditions are met:

    * Redistributions of source code must retain the above copyright

    notice, this list of conditions and the following disclaimer.

    * Redistributions in binary form must reproduce the above copyright

    notice, this list of conditions and the following disclaimer in the

    documentation and/or other materials provided with the distribution.

    * Neither the name of "The Computer Language Benchmarks Game" nor the

    name of "The Computer Language Shootout Benchmarks" nor the names of

    its contributors may be used to endorse or promote products derived

    from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"

AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE

IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE

ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE

LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR

CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF

SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS

INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN

CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)

ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE

POSSIBILITY OF SUCH DAMAGE.

*/

/*

 * The Great Computer Language Shootout

 * http://shootout.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 = 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;

}