Peter Verswyvelen wrote:
The following code, when compiled with GHC 6.6.1 --make -O gives a stack overflow when I enter 1000000 as a command line argument:
(please don't look at the efficiency of the code, it can of course be improved a lot both in time performance and numeric precision...)
import System
leibnizPI :: Integer -> Double leibnizPI n = sum (map leibnizTerm [0..n]) where leibnizTerm n = let i = fromIntegral n in 4 * (((-1) ** i) / (2*i+1)) main = do args <- getArgs let n = read (head args) print (leibnizPI n)
However, if I replace
main = print (leibnizPI 1000000)
is does not stack overflow.
Now, if I leave the original main, but replace sum in leibnizPI by
mysum xs = aux 0 xs where aux s (x:xs) = aux (s+x) xs aux s [] = s
Then I don't get a stack overflow.
However, I do get a stack overflow when I compile it without -O, in all cases.
This puzzles me. I don't see any non-tail calls in my code...
I guess it has to do with strictness? http://www.haskell.org/haskellwiki/Performance/Strictness
Yes. The problem is that without optimizations, both sum and mysum build a large unevaluated expression of the form ((..((0+x1)+x2)+...)+xn) The stack overflow happens when this expression gets evaluated. At that point, the outermost (+) demands the result of the (+) on the next level, and so on. To prevent this you need a stricter version of sum. You can build one with foldl':
import Data.List
sum' :: Num a => [a] -> a sum' = foldl' (+) 0
Arguably this is the "correct" definition of sum. The problem you had is fairly common.
Why isn't it possible to annotate strictness on the type signature in Haskell as in Clean? Is this on the TODO list?
Strictness is independent from the type in Haskell (but see the fourth solution presented below). You can explicitely make one value at least as strict as another using seq:
mysum' xs = aux 0 xs where aux s (x:xs) = let s' = s+x in s' `seq` aux s' xs aux s [] = s
In ghc, you can mark arguments as strict
mysum'' xs = aux 0 xs where aux !s (x:xs) = aux (s+x) xs aux !s [] = s
This is a language extension, you need -fbang-patterns to allow it, or with a recent ghc (6.7, 6.9 or a 6.8 rc) a {-# LANGUAGE BangPatterns #-} pragma, or -XBangPatterns. A fourth possibility, which is Haskell 98 again, is to declare an auxiliary data type with a strict field:
data Strict a = Strict !a
mysum''' xs = aux (Strict 0) xs where aux (Strict s) (x:xs) = aux (Strict (s+x)) xs aux (Strict s) [] = s
Hope that helps, Bertram