I need to implement fast two-level loops, and I am learning using seq to make calls tail-recursive.
I write programs to compute
main = print $ sum [i*j|i::Int<-[1..20000],j::Int<-[1..20000]]
This program (compiled with -O2) runs twenty times slower than the unoptimized (otherwise the loop gets optimized out) C version.
But it seems to run in constant memory, so I assume that it has been turned into loops.
#include
int main(){
int s=0;
for(int i=1;i<=20000;++i){
for(int j=1;j<=20000;++j){
s+=i*j;
}
}
printf("%d\n",s);
return 0;
}
Then I write
main = print $ f 1 where
f i = let x = g 1 in x `seq` (x + if i<20000 then f (i+1) else 0) :: Int where
g j = let x = i*j in x `seq` (x + if j<20000 then g (j+1) else 0) :: Int
This version runs out of memory. When I scale the numbers down to 10000, the program does run correctly, and takes lots of memory.
Even if I change the seqs into deepseqs, or use BangPatterns (f !i =... ; g !j = ...), the situation doesn't change.
A monadic version
import Control.Monad.ST.Strict
import Control.Monad
import Data.STRef.Strict
main = print $ runST $ do
s <- newSTRef (0::Int)
let g !i !j =
if (j<=10000) then modifySTRef s (+1)>>(g i (j+1)) else return ()
let f !i =
if (i<=10000) then g i 1>>(f $ i+1) else return ()
f 1
readSTRef s
also runs out of memory.
So how can I write a program that executes nested loops efficiently?
