Haskell math performance
- by Travis Brown
I'm in the middle of porting David Blei's original C implementation of Latent Dirichlet Allocation to Haskell, and I'm trying to decide whether to leave some of the low-level stuff in C. The following function is one example—it's an approximation of the second derivative of lgamma:
double trigamma(double x)
{
double p;
int i;
x=x+6;
p=1/(x*x);
p=(((((0.075757575757576*p-0.033333333333333)*p+0.0238095238095238)
*p-0.033333333333333)*p+0.166666666666667)*p+1)/x+0.5*p;
for (i=0; i<6 ;i++)
{
x=x-1;
p=1/(x*x)+p;
}
return(p);
}
I've translated this into more or less idiomatic Haskell as follows:
trigamma :: Double -> Double
trigamma x = snd $ last $ take 7 $ iterate next (x' - 1, p')
where
x' = x + 6
p = 1 / x' ^ 2
p' = p / 2 + c / x'
c = foldr1 (\a b -> (a + b * p)) [1, 1/6, -1/30, 1/42, -1/30, 5/66]
next (x, p) = (x - 1, 1 / x ^ 2 + p)
The problem is that when I run both through Criterion, my Haskell version is six or seven times slower (I'm compiling with -O2 on GHC 6.12.1). Some similar functions are even worse.
I know practically nothing about Haskell performance, and I'm not terribly interested in digging through Core or anything like that, since I can always just call the handful of math-intensive C functions through FFI.
But I'm curious about whether there's low-hanging fruit that I'm missing—some kind of extension or library or annotation that I could use to speed up this numeric stuff without making it too ugly.
