Hi Daniel Thanks - the figures are very impressive for the stream fusion library. I knew the paper, but I hadn't looked at it the implementation. Making a stricter unfoldr by using a strictness annotation on the state and getting rid of the tuple is nowhere near stream fusion-lib, i.e: data Maybe2 a st = Nothing2 | Just2 a !st deriving (Eq,Show) Performance wise stream fusion even beats a monoidal unfoldr. A monoidal unfoldr seems reasonable to me for this problem as there is no need to generate a list. As a monoidal unfoldr is not in the 'standard' libraries some people might not consider it idiomatic though. I put in a fixed value for epsilon in all three version rather than used echo at the command line and compiled all with ghc --make -O2 -------------- module Main (main) where import Data.Monoid data Maybe2 a st = Nothing2 | Just2 a !st deriving (Eq,Show) dummy_eps :: Double dummy_eps = 0.00000001 main :: IO () main = do putStrLn "EPS: " eps <- return dummy_eps let mx = floor (4/eps) !k = (mx+1) `quot` 2 putStrLn $ "PI mit EPS " ++ (show eps) ++ " = " ++ show (leibniz k) leibniz n = (4 *) $ getSum $ step n step :: Integer -> Sum Double step times = unfoldrMon phi (0,True,1) where phi (i,_,_) | i == times = Nothing2 phi (i,sig,d) | sig = Just2 (Sum (1/d)) (i+1,False,d+2) | otherwise = Just2 (Sum (negate (1/d))) (i+1,True,d+2) unfoldrMon :: Monoid a => (b -> Maybe2 a b) -> b -> a unfoldrMon f b = case f b of Just2 a new_b -> a `mappend` unfoldrMon f new_b Nothing2 -> mempty -- --------------------------------------------------- Leibniz1 (stream fusion) --------------------------------------------------- $ ./Leibniz1 +RTS -sstderr -RTS d:\coding\haskell\cafe\Leibniz1.exe +RTS -sstderr EPS: PI mit EPS 1.0e-8 = 3.1415926445727678 24,404 bytes allocated in the heap 892 bytes copied during GC 3,068 bytes maximum residency (1 sample(s)) 13,316 bytes maximum slop 1 MB total memory in use (0 MB lost due to fragmentation) Generation 0: 0 collections, 0 parallel, 0.00s, 0.00s elapsed Generation 1: 1 collections, 0 parallel, 0.00s, 0.00s elapsed INIT time 0.03s ( 0.00s elapsed) MUT time 4.59s ( 4.59s elapsed) GC time 0.00s ( 0.00s elapsed) EXIT time 0.00s ( 0.00s elapsed) Total time 4.63s ( 4.59s elapsed) %GC time 0.0% (0.0% elapsed) Alloc rate 5,276 bytes per MUT second Productivity 99.3% of total user, 100.0% of total elapsed --------------------------------------------------- Leibniz3 (monoidal unfoldr) --------------------------------------------------- $ ./Leibniz3 +RTS -sstderr -RTS d:\coding\haskell\cafe\Leibniz3.exe +RTS -sstderr EPS: Stack space overflow: current size 8388608 bytes. Use `+RTS -Ksize -RTS' to increase it. 92,448,984 bytes allocated in the heap 15,368 bytes copied during GC 8,382,800 bytes maximum residency (5 sample(s)) 4,198,684 bytes maximum slop 17 MB total memory in use (0 MB lost due to fragmentation) Generation 0: 125 collections, 0 parallel, 1.66s, 1.66s elapsed Generation 1: 5 collections, 0 parallel, 0.03s, 0.03s elapsed INIT time 0.03s ( 0.00s elapsed) MUT time 3.50s ( 3.55s elapsed) GC time 1.69s ( 1.69s elapsed) EXIT time 0.00s ( 0.00s elapsed) Total time 5.22s ( 5.23s elapsed) %GC time 32.3% (32.2% elapsed) Alloc rate 26,180,243 bytes per MUT second Productivity 67.1% of total user, 66.9% of total elapsed --------------------------------------------------- Leibniz2 - no stream fusion, unfoldr with strictness annotation on the state --------------------------------------------------- $ ./Leibniz2 +RTS -sstderr -RTS d:\coding\haskell\cafe\Leibniz2.exe +RTS -sstderr EPS: PI mit EPS 1.0e-8 = 3.141592648589476 25,600,024,064 bytes allocated in the heap 2,152,224 bytes copied during GC 3,336 bytes maximum residency (1 sample(s)) 11,908 bytes maximum slop 1 MB total memory in use (0 MB lost due to fragmentation) Generation 0: 48828 collections, 0 parallel, 2.19s, 2.23s elapsed Generation 1: 1 collections, 0 parallel, 0.00s, 0.00s elapsed INIT time 0.02s ( 0.00s elapsed) MUT time 75.16s ( 76.22s elapsed) GC time 2.19s ( 2.23s elapsed) EXIT time 0.00s ( 0.00s elapsed) Total time 77.36s ( 78.45s elapsed) %GC time 2.8% (2.8% elapsed) Alloc rate 340,553,219 bytes per MUT second Productivity 97.2% of total user, 95.8% of total elapsed