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POHaskell - Optimizing differential equation solver
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copied!<p>I'm learning Haskell and am trying to write code as fast as I can do in C. For this exercise, I'm writing a <a href="http://en.wikipedia.org/wiki/Euler_method" rel="noreferrer">Euler integrator</a> for a simple one-dimensional physical system.</p> <ul> <li>The C code is compiled with GCC 4.5.4 and <code>-O3</code>. It runs in <b>1.166</b> seconds.</li> <li>The Haskell code is compiled with GHC 7.4.1 and <code>-O3</code>. It runs in <b>21.3</b> seconds.</li> <li>If I compile Haskell with <code>-O3 -fllvm</code>, it runs in <b>4.022</b> seconds.</li> </ul> <p>So, am I missing something to optimize my Haskell code?</p> <p><b>PS.:</b> I used the following arguments: <code>1e-8 5</code>.</p> <p>C code:</p> <pre><code>#include <stdio.h> double p, v, a, t; double func(double t) { return t * t; } void euler(double dt) { double nt = t + dt; double na = func(nt); double nv = v + na * dt; double np = p + nv * dt; p = np; v = nv; a = na; t = nt; } int main(int argc, char ** argv) { double dt, limit; sscanf(argv[1], "%lf", &dt); sscanf(argv[2], "%lf", &limit); p = 0.0; v = 0.0; a = 0.0; t = 0.0; while(t < limit) euler(dt); printf("%f %f %f %f\n", p, v, a, t); return 0; } </code></pre> <p>Haskell Code:</p> <pre><code>import System.Environment (getArgs) data EulerState = EulerState !Double !Double !Double !Double deriving(Show) type EulerFunction = Double -> Double main = do [dt, l] <- fmap (map read) getArgs print $ runEuler (EulerState 0 0 0 0) (**2) dt l runEuler :: EulerState -> EulerFunction -> Double -> Double -> EulerState runEuler s@(EulerState _ _ _ t) f dt limit = let s' = euler s f dt in case t `compare` limit of LT -> s' `seq` runEuler s' f dt limit _ -> s' euler :: EulerState -> EulerFunction -> Double -> EulerState euler (EulerState p v a t) f dt = (EulerState p' v' a' t') where t' = t + dt a' = f t' v' = v + a'*dt p' = p + v'*dt </code></pre>

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