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Ceylon Solution for the n-body problem
/* The Computer Language Benchmarks Game
http://benchmarksgame.alioth.debian.org/
contributed by Renato Athaydes
*/
import ceylon.math.decimal {
decimalNumber,
halfUp,
round
}
import ceylon.math.float {
pi,
sqrt
}
Float solarMass = 4 * pi * pi;
Float daysPerYear = 365.24;
shared void nbody() {
value arg = process.arguments.first;
assert (exists arg);
value n = parseInteger(arg);
assert (exists n);
function formatFloat(Float float, Integer precision) =>
decimalNumber(float, round(precision, halfUp)).string;
function printResult(Float float) => print(formatFloat(float, 9));
value bodies = NBodySystem();
printResult(bodies.energy());
for (_ in 1:n) {
bodies.advance(0.01);
}
printResult(bodies.energy());
}
shared class Body(shared variable Float x, shared variable Float y, shared variable Float z,
shared variable Float vx, shared variable Float vy, shared variable Float vz,
shared Float mass) {
shared Body offsetMomentum(Float px, Float py, Float pz) {
vx = -px / solarMass;
vy = -py / solarMass;
vz = -pz / solarMass;
return this;
}
}
object jupiter extends Body(4.84143144246472090e+00,
-1.16032004402742839e+00,
-1.03622044471123109e-01,
1.66007664274403694e-03 * daysPerYear,
7.69901118419740425e-03 * daysPerYear,
-6.90460016972063023e-05 * daysPerYear,
9.54791938424326609e-04 * solarMass) {}
object saturn extends Body(8.34336671824457987e+00,
4.12479856412430479e+00,
-4.03523417114321381e-01,
-2.76742510726862411e-03 * daysPerYear,
4.99852801234917238e-03 * daysPerYear,
2.30417297573763929e-05 * daysPerYear,
2.85885980666130812e-04 * solarMass) {}
object uranus extends Body(1.28943695621391310e+01,
-1.51111514016986312e+01,
-2.23307578892655734e-01,
2.96460137564761618e-03 * daysPerYear,
2.37847173959480950e-03 * daysPerYear,
-2.96589568540237556e-05 * daysPerYear,
4.36624404335156298e-05 * solarMass) {}
object neptune extends Body(1.53796971148509165e+01,
-2.59193146099879641e+01,
1.79258772950371181e-01,
2.68067772490389322e-03 * daysPerYear,
1.62824170038242295e-03 * daysPerYear,
-9.51592254519715870e-05 * daysPerYear,
5.15138902046611451e-05 * solarMass) {}
object sun extends Body(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, solarMass) {}
shared final class NBodySystem() {
value bodies = [sun, jupiter, saturn, uranus, neptune];
variable value px = 0.0;
variable value py = 0.0;
variable value pz = 0.0;
value iter = bodies.iterator();
while (!is Finished next = iter.next()) {
px += next.vx*next.mass;
py += next.vy*next.mass;
pz += next.vz*next.mass;
}
bodies.first.offsetMomentum(px, py, pz);
shared void advance(Float dt) {
value iter = bodies.iterator();
variable Body[] remaining = bodies.rest;
while (!is Finished iBody = iter.next()) {
value iter2 = remaining.iterator();
while (!is Finished other = iter2.next()) {
value dx = iBody.x - other.x;
value dy = iBody.y - other.y;
value dz = iBody.z - other.z;
value dSquared = dx*dx + dy*dy + dz*dz;
value distance = sqrt(dSquared);
value mag = dt / (dSquared * distance);
iBody.vx -= dx*other.mass*mag;
iBody.vy -= dy*other.mass*mag;
iBody.vz -= dz*other.mass*mag;
other.vx += dx*iBody.mass*mag;
other.vy += dy*iBody.mass*mag;
other.vz += dz*iBody.mass*mag;
}
remaining = remaining.rest;
}
for (body in bodies) {
body.x += dt*body.vx;
body.y += dt*body.vy;
body.z += dt*body.vz;
}
}
shared Float energy() {
variable Float e = 0.0;
value iter = bodies.iterator();
variable Body[] remaining = bodies.rest;
while (!is Finished iBody = iter.next()) {
value iter2 = remaining.iterator();
e += 0.5*iBody.mass *
(iBody.vx*iBody.vx
+ iBody.vy*iBody.vy
+ iBody.vz*iBody.vz);
while (!is Finished other = iter2.next()) {
value dx = iBody.x - other.x;
value dy = iBody.y - other.y;
value dz = iBody.z - other.z;
value distance = sqrt(dx*dx + dy*dy + dz*dz);
e -= (iBody.mass * other.mass) / distance;
}
remaining = remaining.rest;
}
return e;
}
}
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