Shootout/Spectral

{-# OPTIONS -optc-O #-}
--
-- The Great Computer Language Shootout
-- http:--shootout.alioth.debian.org/
--
-- Contributed by Don Stewart
--
-- gcc miscompiles this program with -O3
-- 
 
import Monad
import System
import Numeric
import Data.Array.IO
import Data.Array.Base
 
main = getArgs >>= approximate . read . head >>= putStrLn . \s -> showFFloat (Just 9) s []
 
approximate n = do
    u <- newArray  (0,n-1) 1 :: IO (IOUArray Int Double)
    v <- newArray_ (0,n-1)   :: IO (IOUArray Int Double)
    sequence_ $ replicate 10 $ multiplyAtAv n u v >> multiplyAtAv n v u
    loop 0 0 0 n u v
 
loop vbv vv i n u v | vbv `seq` vv `seq` i `seq` n `seq` u `seq` v `seq` False = undefined
loop vbv vv i n u v | i >= n    = return $! sqrt (vbv/vv)
                    | otherwise = do ui <- unsafeRead u i
                                     vi <- unsafeRead v i
                                     loop (vbv + ui * vi) (vv + vi * vi) (i+1) n u v
 
-- return element i,j of infinite matrix A 
a i j | i `seq` j `seq` False = undefined
a i j = 1 / fromIntegral (x*(x+1) `div` 2 + i + 1) where x = i+j
 
-- multiply vector v by matrix A */
multiplyAv n v av | n `seq` v `seq` av `seq` False = undefined
multiplyAv n v av = loop 0
    where loop i  = when (i < n) $ loop' i 0 0 >>= unsafeWrite av i >> loop (i+1)
          loop' i j av | i `seq` j `seq` av `seq` False = undefined
          loop' i j av | j >= n    = return av 
                       | otherwise = do vj  <- v `unsafeRead` j
                                        loop' i (j+1) (av + a i j * vj)
 
-- multiply vector v by matrix A transposed
multiplyAtv n v atv | n `seq` v `seq` atv `seq` False = undefined
multiplyAtv n v atv = loop 0
    where loop i = when (i < n) $ loop' i 0 0 >>= unsafeWrite atv i >> loop (i+1)
          loop' i j atvi | j `seq` atvi `seq` False = undefined
          loop' i j atvi | j >= n    = return atvi 
                         | otherwise = do vj <- v `unsafeRead` j 
                                          loop' i (j+1) (atvi + a j i * vj)
 
-- multiply vector v by matrix A and then by matrix A transposed */
multiplyAtAv n v atav | n `seq` v `seq` atav `seq` False = undefined
multiplyAtAv n v atav = do u <- newArray_ (0,n-1) :: IO (IOUArray Int Double)
                           multiplyAv n v u >> multiplyAtv n u atav

-- The Great Computer Language Shootout
-- http:--shootout.alioth.debian.org/
--
-- Original C contributed by Sebastien Loisel
-- Conversion to C++ by Jon Harrop
-- Conversion to Haskell by Einar Karttunen
 
import Control.Monad.ST
import Data.Array.Base
import Data.Array.ST
import Numeric
import System
 
eval_A :: Int -> Int -> Double
eval_A i j = 1 / fromIntegral ((i+j)*(i+j+1) `div` 2 + i + 1)
 
plusAt :: STUArray s Int Double -> Int -> Double -> ST s ()
plusAt a i v = do o <- unsafeRead a i
                  unsafeWrite a i (v+o)
 
eval_A_Times_u :: STUArray s Int Double -> STUArray s Int Double -> ST s ()
eval_A_Times_u u au = outer (snd $ bounds u)
    where outer 0 = unsafeWrite au 0 0 >> inner 0 (snd $ bounds u)
          outer i = unsafeWrite au i 0 >> inner i (snd $ bounds u) >> outer (i-1)
          inner i 0 = unsafeRead u 0 >>= \uj -> plusAt au i (eval_A i 0 * uj)
          inner i j = unsafeRead u j >>= \uj -> plusAt au i (eval_A i j * uj) >> inner i (j-1)
 
eval_At_Times_u :: STUArray s Int Double -> STUArray s Int Double -> ST s ()
eval_At_Times_u u au = outer (snd $ bounds u)
    where outer 0 = unsafeWrite au 0 0 >> inner 0 (snd $ bounds u)
          outer i = unsafeWrite au i 0 >> inner i (snd $ bounds u) >> outer (i-1)
          inner i 0 = unsafeRead u 0 >>= \uj -> plusAt au i (eval_A 0 i * uj)
          inner i j = unsafeRead u j >>= \uj -> plusAt au i (eval_A j i * uj) >> inner i (j-1)
 
eval_AtA_Times_u u v = do w <- newArray (bounds u) 0
                          eval_A_Times_u u w >> eval_At_Times_u w v
 
main = do
  n <- getArgs >>= return.read.head
  let (vBv,vv) = runST (do u <- newArray (0,n-1) 1
                           v <- newArray (0,n-1) 0
                           sequence_ $ replicate 10 (eval_AtA_Times_u u v >> eval_AtA_Times_u v u)
                           vLoop u v n (0, 0))
  putStrLn $ showFFloat (Just 9) (sqrt (vBv/vv)) ""
 
vLoop :: STUArray s Int Double -> STUArray s Int Double -> Int -> (Double,Double) -> ST s (Double,Double)
vLoop u v 0 a            = return a
vLoop u v (i+1) (vBv,vv) = vLoop u v i =<< op
    where op = do ui <- unsafeRead u i
                  vi <- unsafeRead v i
                  return (vBv+(ui*vi),vv+(vi*vi))