# n-body Julia #4 program

## source code

```# The Computer Language Benchmarks Game
# https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
#
# Contributed by Andrei Fomiga, Stefan Karpinski, Viral B. Shah, Jeff
# Based on Mark C. Lewis's Java version.

using Printf

# Constants
const SOLAR_MASS = 4 * pi * pi
const DAYS_PER_YEAR = 365.24

# Use a struct instead of mutable struct since a struct can be stored
# inline in an array avoiding the overhead of following a pointer
struct Body
x::Float64
y::Float64
z::Float64
vx::Float64
vy::Float64
vz::Float64
m::Float64
end

function init_sun(bodies)
px = py = pz = 0.0
for b in bodies
px -= b.vx * b.m
py -= b.vy * b.m
pz -= b.vz * b.m
end
Body(0.0, 0.0, 0.0, px / SOLAR_MASS, py / SOLAR_MASS, pz / SOLAR_MASS, SOLAR_MASS)
end

n = length(bodies)
@inbounds for i=1:n-1
bi = bodies[i]

# Since the fields of bi aren't mutable, we track the changing
# value of bi's velocity outside of the Body struct
ivx = bi.vx
ivy = bi.vy
ivz = bi.vz

for j=i+1:n
bj = bodies[j]

dx = bi.x - bj.x
dy = bi.y - bj.y
dz = bi.z - bj.z

dsq = dx^2 + dy^2 + dz^2
mag = dt / (dsq * √dsq)

ivx -= dx * bj.m * mag
ivy -= dy * bj.m * mag
ivz -= dz * bj.m * mag

bodies[j] = Body(
bj.x, bj.y, bj.z,
bj.vx + dx * bi.m * mag,
bj.vy + dy * bi.m * mag,
bj.vz + dz * bi.m * mag,
bj.m
)
end

bodies[i] = Body(
bi.x, bi.y, bi.z,
ivx, ivy, ivz,
bi.m
)
end

@inbounds for i=1:n
bi = bodies[i]
bodies[i] = Body(
bi.x + dt * bi.vx, bi.y + dt * bi.vy, bi.z + dt * bi.vz,
bi.vx, bi.vy, bi.vz,
bi.m
)
end
end

function energy(bodies)
n = length(bodies)
e = 0.0
@inbounds for i=1:n
bi = bodies[i]

e += 0.5 * bi.m * (bi.vx^2 + bi.vy^2 + bi.vz^2)
for j=i+1:n
bj = bodies[j]

d = √((bi.x - bj.x)^2 + (bi.y - bj.y)^2 + (bi.z - bj.z)^2)
e -= bi.m * bodies[j].m / d
end
end
e
end

function nbody(n)
jupiter = Body( 4.84143144246472090e+0,                   # x
-1.16032004402742839e+0,                   # y
-1.03622044471123109e-1,                   # z
1.66007664274403694e-3 * DAYS_PER_YEAR,   # vx
7.69901118419740425e-3 * DAYS_PER_YEAR,   # vy
-6.90460016972063023e-5 * DAYS_PER_YEAR,   # vz
9.54791938424326609e-4 * SOLAR_MASS)      # mass

saturn = Body( 8.34336671824457987e+0,
4.12479856412430479e+0,
-4.03523417114321381e-1,
-2.76742510726862411e-3 * DAYS_PER_YEAR,
4.99852801234917238e-3 * DAYS_PER_YEAR,
2.30417297573763929e-5 * DAYS_PER_YEAR,
2.85885980666130812e-4 * SOLAR_MASS)

uranus = Body( 1.28943695621391310e+1,
-1.51111514016986312e+1,
-2.23307578892655734e-1,
2.96460137564761618e-3 * DAYS_PER_YEAR,
2.37847173959480950e-3 * DAYS_PER_YEAR,
-2.96589568540237556e-5 * DAYS_PER_YEAR,
4.36624404335156298e-5 * SOLAR_MASS)

neptune = Body( 1.53796971148509165e+1,
-2.59193146099879641e+1,
1.79258772950371181e-1,
2.68067772490389322e-3 * DAYS_PER_YEAR,
1.62824170038242295e-3 * DAYS_PER_YEAR,
-9.51592254519715870e-5 * DAYS_PER_YEAR,
5.15138902046611451e-5 * SOLAR_MASS)

bodies = [jupiter, saturn, uranus, neptune]
pushfirst!(bodies, init_sun(bodies))

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

isinteractive() || nbody(parse(Int, ARGS[1]))
```

## notes, command-line, and program output

```NOTES:
julia version build 19.0.1+10-21

Wed, 25 Jan 2023 02:49:48 GMT

MAKE: