# n-body Julia #3 program

## source code

# The Computer Language Benchmarks Game
# https://salsa.debian.org/benchmarksgame-team/benchmarksgame/

# contributed by Isaac Yonemoto
# based on the version by Jarret Revels and Alex Arslan

module NBody

using Printf

# Constants
const solar_mass = 4 * pi * pi
const inv_solar_mass =  -1 / solar_mass
const days_per_year = 365.24

const ThreeSpace = NTuple{3, VecElement{Float64}}
Base.zero(::Type{ThreeSpace}) = (VecElement(0.0), VecElement(0.0), VecElement(0.0))

const threezero = Base.zero(ThreeSpace)

# A heavenly body in the system
mutable struct Body
pos::ThreeSpace
vel::ThreeSpace
mass::Float64
end

function offset_momentum(b::Body, pos :: ThreeSpace)
local vel::ThreeSpace = b.vel
b.vel = (VecElement(pos[1].value * inv_solar_mass),
VecElement(pos[2].value * inv_solar_mass),
VecElement(pos[3].value * inv_solar_mass))
end

function init_sun(bodies::Vector{Body})
local p = threezero
for b in bodies
vel = b.vel
end
offset_momentum(bodies[1], p)
end

for i = 1:length(bodies)
for j = i+1:length(bodies)
bodyipos = bodies[i].pos
bodyjpos = bodies[j].pos

dpos::ThreeSpace = (
VecElement(bodyipos[1].value - bodyjpos[1].value),
VecElement(bodyipos[2].value - bodyjpos[2].value),
VecElement(bodyipos[3].value - bodyjpos[3].value)
)

dsq::ThreeSpace = (
VecElement(dpos[1].value * dpos[1].value),
VecElement(dpos[2].value * dpos[2].value),
VecElement(dpos[3].value * dpos[3].value)
)

tdsq = dsq[1].value + dsq[2].value + dsq[3].value
distance = sqrt(tdsq)
mag = dt / (tdsq * distance)
imassmag = bodies[i].mass * mag
negjmassmag = - bodies[j].mass * mag

bodyivel = bodies[i].vel
bodyjvel = bodies[j].vel

bodyivel::ThreeSpace = (
)

bodyjvel::ThreeSpace = (
)

bodies[i].vel = bodyivel
bodies[j].vel = bodyjvel
end
end

for b in bodies
bodypos = b.pos
bodyvel = b.vel
newbodypos::ThreeSpace = (
)
b.pos = newbodypos
end
end

function energy(bodies::Vector{Body})
local e::Float64 = 0.0
for i = 1:length(bodies)
vel = bodies[i].vel
pos = bodies[i].pos

e += 0.5 * bodies[i].mass * (vel[1].value^2 + vel[2].value^2 + vel[3].value^2)

for j = i+1:length(bodies)
posj = bodies[j].pos

dx = pos[1].value - posj[1].value
dy = pos[2].value - posj[2].value
dz = pos[3].value - posj[3].value

distance = sqrt(dx^2 + dy^2 + dz^2)
e -= (bodies[i].mass * bodies[j].mass) / distance
end
end
e
end

function initbody(a,b,c,d,e,f,g)
Body((
VecElement(a),
VecElement(b),
VecElement(c)
),(
VecElement(d),
VecElement(e),
VecElement(f)
),
g)
end

function perf_nbody(N::Int=1000)
jupiter = initbody( 4.84143144246472090e+00,                  # x
-1.16032004402742839e+00,                  # y
-1.03622044471123109e-01,                  # z
1.66007664274403694e-03 * days_per_year,   # vx
7.69901118419740425e-03 * days_per_year,   # vy
-6.90460016972063023e-05 * days_per_year,  # vz
9.54791938424326609e-04 * solar_mass)      # mass

saturn = initbody( 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 = initbody( 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 = initbody( 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)

sun = initbody(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, solar_mass)

bodies = [sun, jupiter, saturn, uranus, neptune]

init_sun(bodies)

@printf("%.9f\n", energy(bodies))

for i = 1:N
end
@printf("%.9f\n", energy(bodies))
end

end # module

n = parse(Int,ARGS[1])
NBody.perf_nbody(n)

## notes, command-line, and program output

NOTES:
julia version build 19.0.1+10-21

Wed, 25 Jan 2023 02:38:46 GMT

MAKE: