source code
! The Computer Language Benchmarks Game
! https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
!
! contributed by Simon Geard, translated from Mark C. Williams nbody.java
!
! ifort -O3 -static-libcxa -o nbody nbody.f90
!
program nbody
implicit none
integer result, num, i, k
character(len=8) argv
real*8, parameter :: tstep = 0.01d0
real*8, parameter :: PI = 3.141592653589793d0
real*8, parameter :: SOLAR_MASS = 4 * PI * PI
real*8, parameter :: DAYS_PER_YEAR = 365.24d0
real*8 :: e
type body
real*8 x, y, z, vx, vy, vz, mass
end type body
type(body), parameter :: jupiter = body( &
4.84143144246472090d0, -1.16032004402742839d0, &
-1.03622044471123109d-01, 1.66007664274403694d-03 * DAYS_PER_YEAR, &
7.69901118419740425d-03 * DAYS_PER_YEAR, -6.90460016972063023d-05 * DAYS_PER_YEAR, &
9.54791938424326609d-04 * SOLAR_MASS)
type(body), parameter :: saturn = body( &
8.34336671824457987d+00, &
4.12479856412430479d+00, &
-4.03523417114321381d-01, &
-2.76742510726862411d-03 * DAYS_PER_YEAR, &
4.99852801234917238d-03 * DAYS_PER_YEAR, &
2.30417297573763929d-05 * DAYS_PER_YEAR, &
2.85885980666130812d-04 * SOLAR_MASS)
type(body), parameter :: uranus = body( &
1.28943695621391310d+01, &
-1.51111514016986312d+01, &
-2.23307578892655734d-01, &
2.96460137564761618d-03 * DAYS_PER_YEAR, &
2.37847173959480950d-03 * DAYS_PER_YEAR, &
-2.96589568540237556d-05 * DAYS_PER_YEAR, &
4.36624404335156298d-05 * SOLAR_MASS )
type(body), parameter :: neptune = body( &
1.53796971148509165d+01, &
-2.59193146099879641d+01, &
1.79258772950371181d-01, &
2.68067772490389322d-03 * DAYS_PER_YEAR, &
1.62824170038242295d-03 * DAYS_PER_YEAR, &
-9.51592254519715870d-05 * DAYS_PER_YEAR, &
5.15138902046611451d-05 * SOLAR_MASS)
type(body), parameter :: sun = body(0.0d0, 0.0d0, 0.0d0, 0.0d0, 0.0d0, 0.0d0, SOLAR_MASS)
type(body), dimension(5) :: bodies
bodies = (/ sun, jupiter, saturn, uranus, neptune /)
call getarg(1,argv)
read(argv,*) num
call offsetMomentum(1,bodies)
e = energy(bodies)
write(*,'(f12.9)') e
do i=1,num
call advance(tstep, bodies)
end do
e = energy(bodies)
write(*,'(f12.9)') e
contains
subroutine offsetMomentum(k, bodies)
integer, intent(in) :: k
type(body), dimension(:), intent(inout) :: bodies
real*8 :: px, py, pz
px = 0.0d0
py = 0.0d0
pz = 0.0d0
do i=1,size(bodies)
px = px + bodies(i)%vx * bodies(i)%mass;
py = py + bodies(i)%vy * bodies(i)%mass;
pz = pz + bodies(i)%vz * bodies(i)%mass;
end do
bodies(k)%vx = -px/SOLAR_MASS
bodies(k)%vy = -py/SOLAR_MASS
bodies(k)%vz = -pz/SOLAR_MASS
end subroutine offsetMomentum
subroutine advance(tstep, bodies)
real*8, intent(in) :: tstep
type(body), dimension(:), intent(inout) :: bodies
real*8 dx, dy, dz, distance, mag
integer i, j
do i=1,size(bodies)
do j=i+1,size(bodies)
dx = bodies(i)%x - bodies(j)%x
dy = bodies(i)%y - bodies(j)%y
dz = bodies(i)%z - bodies(j)%z
distance = sqrt(dx*dx + dy*dy + dz*dz)
mag = tstep / (distance * distance * distance)
bodies(i)%vx = bodies(i)%vx - dx * bodies(j)%mass * mag
bodies(i)%vy = bodies(i)%vy - dy * bodies(j)%mass * mag
bodies(i)%vz = bodies(i)%vz - dz * bodies(j)%mass * mag
bodies(j)%vx = bodies(j)%vx + dx * bodies(i)%mass * mag
bodies(j)%vy = bodies(j)%vy + dy * bodies(i)%mass * mag
bodies(j)%vz = bodies(j)%vz + dz * bodies(i)%mass * mag
end do
end do
do i=1,size(bodies)
bodies(i)%x = bodies(i)%x + tstep * bodies(i)%vx
bodies(i)%y = bodies(i)%y + tstep * bodies(i)%vy
bodies(i)%z = bodies(i)%z + tstep * bodies(i)%vz
end do
end subroutine advance
real*8 function energy(bodies)
type(body), dimension(:), intent(in) :: bodies
real*8 dx, dy, dz, distance
integer i, j
energy = 0.0d0
do i=1,size(bodies)
energy = energy + 0.5d0 * bodies(i)%mass * &
( bodies(i)%vx * bodies(i)%vx + &
bodies(i)%vy * bodies(i)%vy + &
bodies(i)%vz * bodies(i)%vz)
do j=i+1,size(bodies)
dx = bodies(i)%x - bodies(j)%x
dy = bodies(i)%y - bodies(j)%y
dz = bodies(i)%z - bodies(j)%z
distance = sqrt(dx*dx + dy*dy + dz*dz)
energy = energy - (bodies(i)%mass * bodies(j)%mass) / distance;
end do
end do
end function energy
end program nbody