# Shootout/Pidigits

From HaskellWiki

A Shootout Entry for the pidigits benchmark. Currently Haskell is second!

## Proposed 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
```

## Current 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
```

## 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
```

## 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
```

## 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'
```