FYI, I have these number on the Shootout nbody problem,
code below.
C: 9 seconds.
Felix: 43 seconds.
IMHO: the poor performance is because parallel assignment
is not implemented for assignments (only for tail recursion!).
I've played with the algorithm, mainly hoisting loop invariants,
but it doesn't seem to make much difference.
The Felix solution treats the coordinates as a single
vector (because the code is shorter and cleaner that way).
I actually translated the Oberon solution rather than
adapting the C or C++ solutions.. I was very tempted to
defined an Oberon DSSL (syntax extension) and run the Oberon
code 'as written' :)
///////////////////////////////////////////////////
#import <flx.flxh>
PI := 3.141592653589793;
SOLAR_MASS := 4.0 * PI * PI;
DAYS_PER_YEAR := 365.24;
typedef vec = array[double,3];
fun add(x:vec,y:vec)=>x.(0)+y.(0), x.(1)+y.(1), x.(2)+y.(2);
fun sub(x:vec,y:vec)=>x.(0)-y.(0), x.(1)-y.(1), x.(2)-y.(2);
fun neg(x:vec)=>-x.(0), -x.(1),-x.(2);
fun mul(x:vec,var y:double)=>x.(0)*y, x.(1)*y, x.(2)*y;
fun div(x:vec,var y:double)=>x.(0)/y, x.(1)/y, x.(2)/y;
fun mul(var y:double,x:vec)=>x.(0)*y, x.(1)*y, x.(2)*y;
fun sqr(x:vec)=>x.(0)*x.(0)+x.(1)*x.(1)+x.(2)*x.(2);
fun norm(x:vec)=>sqrt(sqr x);
struct Body { pos:vec; vel:vec; mass: double; };
proc Advance(dt: double){
var i: int; var j:int;
forall i in 0 upto nbodies-1 do
bimass := bodies.[i].mass;
var delta = 0.0,0.0,0.0;
forall j in i+1 upto nbodies-1 do
var d = bodies.[i].pos - bodies.[j].pos;
var distance = norm d;
var mag := dt / (distance * distance * distance);
delta = delta + d * (bodies.[j].mass * mag);
bodies.[j].vel = bodies.[j].vel + d * (bimass * mag);
done;
bodies.[i].vel = bodies.[i].vel - delta;
done;
forall i in 0 upto nbodies-1 do
bodies.[i].pos = bodies.[i].pos + dt * bodies.[i].vel;
done;
}
fun Energy(): double =
{
var i: int; var j: int;
var e = 0.0;
forall i in 0 upto nbodies-1 do
e = e + 0.5 * bodies.[i].mass * sqr bodies.[i].vel;
forall j in i+1 upto nbodies-1 do
d := bodies.[i].pos - bodies.[j].pos;
distance := norm d;
e = e - bodies.[i].mass * bodies.[j].mass / distance;
done;
done;
return e;
}
proc OffsetMomentum()
{
var i: int;
var p = (0.0,0.0,0.0);
forall i in 1 upto nbodies-1 do
p = p + bodies.[i].vel * bodies.[i].mass;
done;
bodies.[0].vel = -p / SOLAR_MASS;
}
nticks := atoi$ System::argv 1;
/* define planetary masses, initial positions, velocities */
jupiter := Body (
(4.84143144246472090e+00,
-1.16032004402742839e+00,
-1.03622044471123109e-01),
(1.66007664274403694e-03 * DAYS_PER_YEAR,
7.69901118419740425e-03 * DAYS_PER_YEAR,
-6.90460016972063023e-05 * DAYS_PER_YEAR),
9.54791938424326609e-04 * SOLAR_MASS
);
saturn := Body (
(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 := Body (
(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 := Body (
(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 := Body ((0.0, 0.0, 0.0), (0.0, 0.0, 0.0), SOLAR_MASS);
bodies := (sun,jupiter,saturn,uranus,neptune);
nbodies := 5;
OffsetMomentum();
println$ f"%.9f"$ Energy();
var i : int;
forall i in 1 upto nticks do Advance(0.01e+00); done;
println$ f"%.9f"$ Energy();
////////////////////////////////////////////////////////
--
John Skaller <skaller at users dot sf dot net>
Felix, successor to C++: http://felix.sf.net
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