The Computer LanguageBenchmarks Game

n-body Pascal Free Pascal #2 program

source code

```{ The Computer Language Benchmarks Game
http://benchmarksgame.alioth.debian.org

contributed by Ian Osgood,
modified by Florian Klaempfl
modified by Ales Katona
modified by Vincent Snijders
modified by Jeppe Johansen
}

{\$mode objfpc}

program n_body;

uses Math;

type
Body = record
x, y, z,
vx, vy, vz,
mass : double;
end;
PBody = ^Body;

const pi = 3.141592653589793;
solarMass = 4 * sqr(pi);
daysPerYear = 365.24;

type
tbody = array[1..5] of Body;

const b : tbody = (
{ Sun }
( x:0; y:0; z:0;  vx:0; vy:0; vz:0;  mass: solarMass ),
{ Jupiter }
( x:    4.84143144246472090e+00;
y:   -1.16032004402742839e+00;
z:   -1.03622044471123109e-01;
vx:   1.66007664274403694e-03 * daysPerYear;
vy:   7.69901118419740425e-03 * daysPerYear;
vz:  -6.90460016972063023e-05 * daysPerYear;
mass: 9.54791938424326609e-04 * solarMass ),
{ Saturn }
( x:    8.34336671824457987e+00;
y:    4.12479856412430479e+00;
z:   -4.03523417114321381e-01;
vx:  -2.76742510726862411e-03 * daysPerYear;
vy:   4.99852801234917238e-03 * daysPerYear;
vz:   2.30417297573763929e-05 * daysPerYear;
mass: 2.85885980666130812e-04 * solarMass ),
{ Uranus }
( x:    1.28943695621391310e+01;
y:   -1.51111514016986312e+01;
z:   -2.23307578892655734e-01;
vx:   2.96460137564761618e-03 * daysPerYear;
vy:   2.37847173959480950e-03 * daysPerYear;
vz:  -2.96589568540237556e-05 * daysPerYear;
mass: 4.36624404335156298e-05 * solarMass ),
{ Neptune }
( x:    1.53796971148509165e+01;
y:   -2.59193146099879641e+01;
z:    1.79258772950371181e-01;
vx:   2.68067772490389322e-03 * daysPerYear;
vy:   1.62824170038242295e-03 * daysPerYear;
vz:  -9.51592254519715870e-05 * daysPerYear;
mass: 5.15138902046611451e-05 * solarMass )
);

procedure offsetMomentum;
var px,py,pz : double;
i : integer;
begin
px:=0.0; py:=0.0; pz:=0.0;
for i := low(b)+1 to high(b) do
with b[i] do
begin
px := px - vx * mass;
py := py - vy * mass;
pz := pz - vz * mass;
end;
b[low(b)].vx := px / solarMass;
b[low(b)].vy := py / solarMass;
b[low(b)].vz := pz / solarMass;
end;

function distance(i,j : integer) : double;
begin
distance := sqrt(sqr(b[i].x-b[j].x) + sqr(b[i].y-b[j].y) +
sqr(b[i].z-b[j].z));
end;

function energy : double;
var
i,j : integer;
begin
result := 0.0;
for i := low(b) to high(b) do
with b[i] do
begin
result := result + mass * (sqr(vx) + sqr(vy) + sqr(vz)) * 0.5;
for j := i+1 to high(b) do
result := result - mass * b[j].mass / distance(i,j);
end;
end;

var i,j : integer;
dx,dy,dz,mag,dsquared : double;
bi,bj : PBody;
begin
bi:=@b[low(b)];
for i := low(b) to high(b)-1 do begin
bj := bi;
for j := i+1 to high(b) do
begin
inc(bj);
dx := bi^.x - bj^.x;
dy := bi^.y - bj^.y;
dz := bi^.z - bj^.z;
dsquared := sqr(dx)+sqr(dy)+sqr(dz);
mag := dt / (sqrt(dsquared)*dsquared);
bi^.vx := bi^.vx - dx * bj^.mass * mag;
bi^.vy := bi^.vy - dy * bj^.mass * mag;
bi^.vz := bi^.vz - dz * bj^.mass * mag;
bj^.vx := bj^.vx + dx * bi^.mass * mag;
bj^.vy := bj^.vy + dy * bi^.mass * mag;
bj^.vz := bj^.vz + dz * bi^.mass * mag;
end;
inc(bi);
end;
bi:=@b[low(b)];
for i := low(b) to high(b) do begin
with bi^ do
begin
x := x + dt * vx;
y := y + dt * vy;
z := z + dt * vz;
end;
inc(bi);
end;
end;

var i : integer;
n : Integer;
begin
SetPrecisionMode(pmDouble);
offsetMomentum;
writeln(energy:0:9);
Val(ParamStr(1), n, i);
for i := 1 to n do advance(0.01);
writeln(energy:0:9);
end.
```

notes, command-line, and program output

```NOTES:
Free Pascal Compiler version 3.0.4 [2017/10/03] for x86_64

Sun, 10 Dec 2017 05:33:37 GMT

MAKE:
mv nbody.fpascal-2.fpascal nbody.fpascal-2.pas
/opt/src/fpc-3.0.4/bin/fpc -FuInclude/fpascal -XXs -O4 -Tlinux -CfSSE3 -oFPASCAL_RUN nbody.fpascal-2.pas
Free Pascal Compiler version 3.0.4 [2017/10/03] for x86_64
Copyright (c) 1993-2017 by Florian Klaempfl and others
Target OS: Linux for x86-64
Compiling nbody.fpascal-2.pas
/usr/bin/ld: warning: link.res contains output sections; did you forget -T?
152 lines compiled, 0.2 sec
mv FPASCAL_RUN nbody.fpascal-2.fpascal_run
rm nbody.fpascal-2.pas

0.21s to complete and log all make actions

COMMAND LINE:
./nbody.fpascal-2.fpascal_run 50000000

PROGRAM OUTPUT:
-0.169075164
-0.169059907
```