/* The Great Computer Language Shootout
   http://shootout.alioth.debian.org/
   contributed by Isaac Gouy */

var PI = 3.141592653589793;
var SOLAR_MASS = 4 * PI * PI;
var DAYS_PER_YEAR = 365.24;

function Body(x,y,z,vx,vy,vz,mass){
   this.x = x;
   this.y = y;
   this.z = z;
   this.vx = vx;
   this.vy = vy;
   this.vz = vz;
   this.mass = mass;
}

Body.prototype.offsetMomentum = function(px,py,pz) {
   this.vx = -px / SOLAR_MASS;
   this.vy = -py / SOLAR_MASS;
   this.vz = -pz / SOLAR_MASS;
   return this;
}

function Jupiter(){
   return new Body(
      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
   );
}

function Saturn(){
   return new Body(
      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
   );
}

function Uranus(){
   return new Body(
      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
   );
}

function Neptune(){
   return new Body(
      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
   );
}

function Sun(){
   return new Body(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, SOLAR_MASS);
}


function NBodySystem(bodies){
   this.bodies = bodies;
   var px = 0.0;
   var py = 0.0;
   var pz = 0.0;
   var size = this.bodies.length;
   for (var i=0; i<size; i++){
      var b = this.bodies[i];
      var m = b.mass;
      px += b.vx * m;
      py += b.vy * m;
      pz += b.vz * m;
   }
   this.bodies[0].offsetMomentum(px,py,pz);
}

NBodySystem.prototype.advance = function(dt){
   var dx, dy, dz, distance, mag;
   var size = this.bodies.length;

   for (var i=0; i<size; i++) {
      var bodyi = this.bodies[i];
      for (var j=i+1; j<size; j++) {
         var bodyj = this.bodies[j];
         dx = bodyi.x - bodyj.x;
         dy = bodyi.y - bodyj.y;
         dz = bodyi.z - bodyj.z;

         distance = Math.sqrt(dx*dx + dy*dy + dz*dz);
         mag = dt / (distance * distance * distance);

         bodyi.vx -= dx * bodyj.mass * mag;
         bodyi.vy -= dy * bodyj.mass * mag;
         bodyi.vz -= dz * bodyj.mass * mag;

         bodyj.vx += dx * bodyi.mass * mag;
         bodyj.vy += dy * bodyi.mass * mag;
         bodyj.vz += dz * bodyi.mass * mag;
      }
   }

   for (var i=0; i<size; i++) {
      var body = this.bodies[i];
      body.x += dt * body.vx;
      body.y += dt * body.vy;
      body.z += dt * body.vz;
   }
}

NBodySystem.prototype.energy = function(){
   var dx, dy, dz, distance;
   var e = 0.0;
   var size = this.bodies.length;

   for (var i=0; i<size; i++) {
      var bodyi = this.bodies[i];

      e += 0.5 * bodyi.mass *
         ( bodyi.vx * bodyi.vx
         + bodyi.vy * bodyi.vy
         + bodyi.vz * bodyi.vz );

      for (var j=i+1; j<size; j++) {
         var bodyj = this.bodies[j];
         dx = bodyi.x - bodyj.x;
         dy = bodyi.y - bodyj.y;
         dz = bodyi.z - bodyj.z;

         distance = Math.sqrt(dx*dx + dy*dy + dz*dz);
         e -= (bodyi.mass * bodyj.mass) / distance;
      }
   }
   return e;
}

var ret;

for ( var n = 3; n <= 24; n *= 2 ) {
    (function(){
        var bodies = new NBodySystem( Array(
           Sun(),Jupiter(),Saturn(),Uranus(),Neptune()
        ));
        var max = n * 100;
        
        ret = bodies.energy();
        for (var i=0; i<max; i++){
            bodies.advance(0.01);
        }
        ret = bodies.energy();
    })();
}

print(ret == -0.16906933525822856)
