# Shootout/Pidigits

### From HaskellWiki

A Shootout Entry for the pidigits benchmark. It looks like the current entry is affected by this bug in GHC 6.10.1 in which allocating large objects doesn't trigger a GC. Hopefully GHC 6.10.2 will fix this bug and roughly double the speed of the entry.

## Contents |

## 1 Proposed Entry

Avoids more multiplications by 0 by ommiting the third element of F all together. A bit faster, and this makes comp1 and comp2 identical again making the code a bit shorter too.

{-# OPTIONS -O2 -optc-O3 #-} -- -- The Great Computer Language Shootout -- http://shootout.alioth.debian.org/ -- by Don Stewart, Einar Karttunen, Branimir Maksimovic, -- Bertram Felgenhauer, and Darren Smith -- import System data F = F !Integer !Integer !Integer main = loop 10 0 . flip take (str (F 1 0 1) ns) . read . head =<< getArgs ns = [ F k (4*k+2) (2*k+1) | k <- [1..] ] loop n s [] = putStrLn $ replicate n ' ' ++ "\t:" ++ show s loop 0 s xs = putStrLn ("\t:"++show s) >> loop 10 s xs loop n s (x:xs) = putStr (show x) >> loop (n-1) (s+1) xs flr x (F q r t) = (q*x + r) `div` t comp (F q r t) (F u v x) = F (q*u) (q*v+r*x) (t*x) str z (x:xs) | y == flr 4 z = y : str (comp (F 10 (-10*y) 1) z) (x:xs) | otherwise = str (comp z x) xs where y = flr 3 z

## 2 Current Entry

Avoid multiplications by 0 (as seen in C entry). A bit faster.

{-# OPTIONS -O2 -optc-O3 #-} -- -- The Great Computer Language Shootout -- http://shootout.alioth.debian.org/ -- by Don Stewart, Einar Karttunen, Branimir Maksimovic and Bertram Felgenhauer -- import System data F = F !Integer !Integer !Integer !Integer main = loop 10 0 . flip take (str (F 1 0 0 1) ns) . read . head =<< getArgs ns = [ F k (4*k+2) 0 (2*k+1) | k <- [1..] ] loop n s [] = putStrLn $ replicate n ' ' ++ "\t:" ++ show s loop 0 s xs = putStrLn ("\t:"++show s) >> loop 10 s xs loop n s (x:xs) = putStr (show x) >> loop (n-1) (s+1) xs flr x (F q r s t) = (q*x + r) `div` (s*x + t) comp1 (F q r s t) (F u v w x) = F (q*u+r*w) (q*v+r*x) (t*w) (t*x) comp2 (F q r s t) (F u v w x) = F (q*u) (q*v+r*x) (s*u) (s*v+t*x) str z (x:xs) | y == flr 4 z = y : str (comp1 (F 10 (-10*y) 0 1) z) (x:xs) | otherwise = str (comp2 z x) xs where y = flr 3 z

## 3 Old Entry

Shorter still.

{-# OPTIONS -O2 -optc-O3 #-} -- -- The Great Computer Language Shootout -- http://shootout.alioth.debian.org/ -- by Don Stewart, Einar Karttunen and Branimir Maksimovic -- import System data F = F !Integer !Integer !Integer !Integer main = loop 10 0 . flip take (str (F 1 0 0 1) ns) . read . head =<< getArgs ns = [ F k (4*k+2) 0 (2*k+1) | k <- [1..] ] loop n s [] = putStrLn $ replicate n ' ' ++ "\t:" ++ show s loop 0 s xs = putStrLn ("\t:"++show s) >> loop 10 s xs loop n s (x:xs) = putStr (show x) >> loop (n-1) (s+1) xs flr x (F q r s t) = (q*x + r) `div` (s*x + t) comp (F q r s t) (F u v w x) = F (q*u+r*w) (q*v+r*x) (s*u+t*w) (s*v+t*x) str z (x:xs) | y == flr 4 z = y : str (comp (F 10 (-10*y) 0 1) z) (x:xs) | otherwise = str (comp z x) xs where y = flr 3 z

## 4 Older entry

A shorter combination of the Einar's and Branimir's two entries. Same performance. Compile with -O2. At 15 loc, it is by a very long way, the shortest entry, with really good performance. Lesson: arbitrary precsision arithmetic sucks in many other languages.

import System data LFT = LFT !Integer !Integer !Integer !Integer floorEx x (LFT q r s t) = (f q * f x + f r) `div` (f s * f x + f t) where f = fromInteger comp (LFT q r s t) (LFT u v w x) = LFT (q*u+r*w) (q*v+r*x) (s*u+t*w) (s*v+t*x) pi = stream (LFT 1 0 0 1) lfts (floorEx 3) ((==).floorEx 4) prod comp where prod z n = comp (LFT 10 (-10*n) 0 1) z lfts = [ LFT k (4*k+2) 0 (2*k+1) | k <- [1..] ] stream z (x:xs) f g h i | g z y = y : stream (h z y) (x:xs) f g h i | otherwise = stream (i z x) xs f g h i where y = f z main = getArgs >>= loop 10 0 . flip take Main.pi . read . head where loop n sum [] = putStrLn $ replicate n ' ' ++ "\t:" ++ show sum loop 0 sum xs = putStrLn ("\t:"++show sum) >> loop 10 sum xs loop n sum (x:xs) = putStr (show x) >> loop (n-1) (sum+1) xs

## 5 Original entry

musasabi's entry:

{-# OPTIONS -O2 -optc-O3 #-} -- The Great Computer Language Shootout -- http://shootout.alioth.debian.org/ -- contributed by Einar Karttunen -- adapted from the OCaml version. import System floor_ev (q, r, s, t) x = (q*x + r) `div` (s*x + t) comp (q,r,s,t) (q',r',s',t') = (q*q' + r*s', q*r' + r*t', s*q' + t*s', s*r' + t*t') next z = floor_ev z 3 safe z n = n == floor_ev z 4 prod z n = comp (10,-10 * n, 0, 1) z cons z k = let den = 2*k+1 in comp z (fromIntegral k, fromIntegral (2*den), 0, fromIntegral den) digit :: Int -> (Integer,Integer,Integer,Integer) -> Int -> Int -> Int -> IO () digit k z 0 row col = putStrLn (take (10-col) " "++"\t:"++show (row+col)) digit k z n row col = if safe z y then if col == 10 then do let row' = row + 10 putStr ("\t:"++show row'++"\n"++show y) digit k (prod z y) (n-1) row' 1 else putStr (show y) >> digit k (prod z y) (n-1) row (col+1) else digit (k+1) (cons z k) n row col where y = next z main = do [n] <- getArgs digit 1 (1,0,0,1) (read n) 0 0

## 6 Branimir's Idea

An alternative implementation submitted by Branimir Maksimovic

{-# OPTIONS -O2 -optc-O3 #-} {- original Haskell implementation from spigot.pdf document - I've just added printPi and main, also replaced floor and / with div - because for some reason div is much faster -} module Main where import System main = do [n] <- getArgs printPi $ take (read n) Main.pi printPi digits = printPi' digits 10 0 where printPi' [] ndigs sum' = do mapM_ (\_ -> putChar ' ') [1..ndigs] putStr $ "\t:" ++ show sum' ++ "\n" printPi' xxs 0 sum' = do putStr $ "\t:" ++ show sum' ++ "\n" printPi' xxs 10 sum' printPi' (x:xs) ndigs sum' = do putStr $ show x printPi' xs (ndigs-1) (sum'+1) stream :: (b->c) -> (b->c->Bool) -> (b->c->b) -> (b->a->b) -> b -> [a] -> [c] stream next safe prod cons z (x:xs) = if safe z y then y : stream next safe prod cons (prod z y) (x:xs) else stream next safe prod cons (cons z x) xs where y = next z type LFT = (Integer, Integer, Integer, Integer) floorExtr :: LFT -> Integer -> Integer floorExtr (q,r,s,t) x = ((fromInteger q) * fromInteger x + (fromInteger r)) `div` ((fromInteger s) * fromInteger x + (fromInteger t)) unit :: LFT unit = (1,0,0,1) comp :: LFT -> LFT -> LFT comp (q,r,s,t) (u,v,w,x) = (q*u+r*w,q*v+r*x,s*u+t*w,s*v+t*x) pi = stream next safe prod cons init lfts where init = unit lfts = [(k, 4*k+2, 0, 2*k+1) | k<-[1..]] next z = floorExtr z 3 safe z n = (n == floorExtr z 4) prod z n = comp (10, -10*n, 0, 1) z cons z z' = comp z z'