124 lines
3.4 KiB
Lua
124 lines
3.4 KiB
Lua
-- The Computer Language Benchmarks Game
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-- https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
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-- contributed by Mike Pall
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-- modified by Geoff Leyland
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local sqrt = math.sqrt
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local PI = 3.141592653589793
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local SOLAR_MASS = 4 * PI * PI
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local DAYS_PER_YEAR = 365.24
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local bodies = {
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{ -- Sun
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x = 0,
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y = 0,
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z = 0,
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vx = 0,
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vy = 0,
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vz = 0,
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mass = SOLAR_MASS
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},
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{ -- Jupiter
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x = 4.84143144246472090e+00,
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y = -1.16032004402742839e+00,
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z = -1.03622044471123109e-01,
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vx = 1.66007664274403694e-03 * DAYS_PER_YEAR,
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vy = 7.69901118419740425e-03 * DAYS_PER_YEAR,
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vz = -6.90460016972063023e-05 * DAYS_PER_YEAR,
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mass = 9.54791938424326609e-04 * SOLAR_MASS
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},
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{ -- Saturn
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x = 8.34336671824457987e+00,
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y = 4.12479856412430479e+00,
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z = -4.03523417114321381e-01,
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vx = -2.76742510726862411e-03 * DAYS_PER_YEAR,
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vy = 4.99852801234917238e-03 * DAYS_PER_YEAR,
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vz = 2.30417297573763929e-05 * DAYS_PER_YEAR,
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mass = 2.85885980666130812e-04 * SOLAR_MASS
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},
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{ -- Uranus
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x = 1.28943695621391310e+01,
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y = -1.51111514016986312e+01,
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z = -2.23307578892655734e-01,
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vx = 2.96460137564761618e-03 * DAYS_PER_YEAR,
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vy = 2.37847173959480950e-03 * DAYS_PER_YEAR,
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vz = -2.96589568540237556e-05 * DAYS_PER_YEAR,
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mass = 4.36624404335156298e-05 * SOLAR_MASS
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},
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{ -- Neptune
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x = 1.53796971148509165e+01,
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y = -2.59193146099879641e+01,
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z = 1.79258772950371181e-01,
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vx = 2.68067772490389322e-03 * DAYS_PER_YEAR,
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vy = 1.62824170038242295e-03 * DAYS_PER_YEAR,
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vz = -9.51592254519715870e-05 * DAYS_PER_YEAR,
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mass = 5.15138902046611451e-05 * SOLAR_MASS
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}
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}
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local function advance(bodies, nbody, dt)
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for i=1,nbody do
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local bi = bodies[i]
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local bix, biy, biz, bimass = bi.x, bi.y, bi.z, bi.mass
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local bivx, bivy, bivz = bi.vx, bi.vy, bi.vz
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for j=i+1,nbody do
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local bj = bodies[j]
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local dx, dy, dz = bix-bj.x, biy-bj.y, biz-bj.z
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local mag = sqrt(dx*dx + dy*dy + dz*dz)
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mag = dt / (mag * mag * mag)
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local bm = bj.mass*mag
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bivx = bivx - (dx * bm)
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bivy = bivy - (dy * bm)
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bivz = bivz - (dz * bm)
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bm = bimass*mag
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bj.vx = bj.vx + (dx * bm)
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bj.vy = bj.vy + (dy * bm)
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bj.vz = bj.vz + (dz * bm)
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end
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bi.vx = bivx
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bi.vy = bivy
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bi.vz = bivz
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bi.x = bix + dt * bivx
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bi.y = biy + dt * bivy
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bi.z = biz + dt * bivz
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end
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end
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local function energy(bodies, nbody)
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local e = 0
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for i=1,nbody do
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local bi = bodies[i]
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local vx, vy, vz, bim = bi.vx, bi.vy, bi.vz, bi.mass
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e = e + (0.5 * bim * (vx*vx + vy*vy + vz*vz))
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for j=i+1,nbody do
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local bj = bodies[j]
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local dx, dy, dz = bi.x-bj.x, bi.y-bj.y, bi.z-bj.z
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local distance = sqrt(dx*dx + dy*dy + dz*dz)
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e = e - ((bim * bj.mass) / distance)
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end
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end
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return e
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end
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local function offsetMomentum(b, nbody)
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local px, py, pz = 0, 0, 0
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for i=1,nbody do
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local bi = b[i]
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local bim = bi.mass
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px = px + (bi.vx * bim)
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py = py + (bi.vy * bim)
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pz = pz + (bi.vz * bim)
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end
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b[1].vx = -px / SOLAR_MASS
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b[1].vy = -py / SOLAR_MASS
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b[1].vz = -pz / SOLAR_MASS
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end
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local N = tonumber(arg and arg[1]) or 1000
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local nbody = #bodies
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offsetMomentum(bodies, nbody)
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io.write( string.format("%0.9f",energy(bodies, nbody)), "\n")
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for i=1,N do advance(bodies, nbody, 0.01) end
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io.write( string.format("%0.9f",energy(bodies, nbody)), "\n")
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