-- The Great Computer Language Shootout
-- http://shootout.alioth.debian.org/
-- contributed by Isaac Gouy, tuned by Mike Pall

local sqrt = math.sqrt

local PI = 3.141592653589793
local SOLAR_MASS = 4 * PI * PI
local DAYS_PER_YEAR = 365.24

local Jupiter = {
	x = 4.84143144246472090e+00,
	y = -1.16032004402742839e+00,
	z = -1.03622044471123109e-01,
	vx = 1.66007664274403694e-03 * DAYS_PER_YEAR,
	vy = 7.69901118419740425e-03 * DAYS_PER_YEAR,
	vz = -6.90460016972063023e-05 * DAYS_PER_YEAR,
	mass = 9.54791938424326609e-04 * SOLAR_MASS
}

local Saturn = {
	x = 8.34336671824457987e+00,
	y = 4.12479856412430479e+00,
	z = -4.03523417114321381e-01,
	vx = -2.76742510726862411e-03 * DAYS_PER_YEAR,
	vy = 4.99852801234917238e-03 * DAYS_PER_YEAR,
	vz = 2.30417297573763929e-05 * DAYS_PER_YEAR,
	mass = 2.85885980666130812e-04 * SOLAR_MASS
}

local Uranus = {
	x = 1.28943695621391310e+01,
	y = -1.51111514016986312e+01,
	z = -2.23307578892655734e-01,
	vx = 2.96460137564761618e-03 * DAYS_PER_YEAR,
	vy = 2.37847173959480950e-03 * DAYS_PER_YEAR,
	vz = -2.96589568540237556e-05 * DAYS_PER_YEAR,
	mass = 4.36624404335156298e-05 * SOLAR_MASS
}

local Neptune = {
	x = 1.53796971148509165e+01,
	y = -2.59193146099879641e+01,
	z = 1.79258772950371181e-01,
	vx = 2.68067772490389322e-03 * DAYS_PER_YEAR,
	vy = 1.62824170038242295e-03 * DAYS_PER_YEAR,
	vz = -9.51592254519715870e-05 * DAYS_PER_YEAR,
	mass = 5.15138902046611451e-05 * SOLAR_MASS
}

local Sun = {
	x = 0,
	y = 0,
	z = 0,
	vx = 0,
	vy = 0,
	vz = 0,
	mass = SOLAR_MASS
}

local function advance(bodies, nbody, dt)
	for i = 1, nbody do
		local bi = bodies[i]
		local bix, biy, biz, bimass = bi.x, bi.y, bi.z, bi.mass
		local bivx, bivy, bivz = bi.vx, bi.vy, bi.vz
		for j = i + 1, nbody do
			local bj = bodies[j]
			local dx, dy, dz = bix - bj.x, biy - bj.y, biz - bj.z
			local distance = sqrt(dx * dx + dy * dy + dz * dz)
			local mag = dt / (distance * distance * distance)
			local bim, bjm = bimass * mag, bj.mass * mag
			bivx = bivx - (dx * bjm)
			bivy = bivy - (dy * bjm)
			bivz = bivz - (dz * bjm)
			bj.vx = bj.vx + (dx * bim)
			bj.vy = bj.vy + (dy * bim)
			bj.vz = bj.vz + (dz * bim)
		end
		bi.vx = bivx
		bi.vy = bivy
		bi.vz = bivz
	end
	for i = 1, nbody do
		local bi = bodies[i]
		bi.x = bi.x + (dt * bi.vx)
		bi.y = bi.y + (dt * bi.vy)
		bi.z = bi.z + (dt * bi.vz)
	end
end


local function energy(bodies, nbody)
	local e = 0
	for i = 1, nbody do
		local bi = bodies[i]
		local vx, vy, vz, bim = bi.vx, bi.vy, bi.vz, bi.mass
		e = e + (0.5 * bim * (vx * vx + vy * vy + vz * vz))
		for j = i + 1, nbody do
			local bj = bodies[j]
			local dx, dy, dz = bi.x - bj.x, bi.y - bj.y, bi.z - bj.z
			local distance = sqrt(dx * dx + dy * dy + dz * dz)
			e = e - ((bim * bj.mass) / distance)
		end
	end
	return e
end


local function offsetMomentum(b, nbody)
	local px, py, pz = 0, 0, 0
	for i = 1, nbody do
		local bi = b[i]
		local bim = bi.mass
		px = px + (bi.vx * bim)
		py = py + (bi.vy * bim)
		pz = pz + (bi.vz * bim)
	end
	b[1].vx = -px / SOLAR_MASS
	b[1].vy = -py / SOLAR_MASS
	b[1].vz = -pz / SOLAR_MASS
end

local N = tonumber((...)) or 500000 -- normally 50000000
local bodies = { Sun, Jupiter, Saturn, Uranus, Neptune }
local nbody = table.getn(bodies)

offsetMomentum(bodies, nbody)
io.write(string.format("%0.9f", energy(bodies, nbody)), "\n")
for i = 1, N do advance(bodies, nbody, 0.01) end
io.write(string.format("%0.9f", energy(bodies, nbody)), "\n")
