[Haskell-beginners] Performance of Prime Generator

[Zhi-Qiang Lei]

Hi,

I have bungled the Prime Generator on SPOJ for many times. Although the program is faster and faster on my machine, but it keeps "time limited exceeded" on SPOJ (6 seconds limit). Now my approach is for every number in the range, check if it is prime by checking if can be divided by all the primes smaller than or equal its square root. For the numbers between 999900000 and 1000000000, it take 0.64 seconds on my laptop. Could anyone give me some hints to enhance it? Thanks.

=== Test Data ===
1
999900000 1000000000
=== Test Data ===

=== Code ===
{-# OPTIONS_GHC -O2 -fno-cse #-}

import System.IO

data Wheel a = Wheel a [a]

roll :: Integral a => Wheel a -> [a]
roll (Wheel n rs) = [n*k+r | k <- [0..], r <- rs]

nextSize :: Integral a => Wheel a -> a -> Wheel a
nextSize (Wheel n rs) p =
  Wheel (p*n) [r' | k <- [0..(p-1)], r <- rs,
                      let r' = n*k+r, r' `mod` p /= 0]

mkWheel :: Integral a => [a] -> Wheel a
mkWheel ds = foldl nextSize (Wheel 1 [1]) ds

primes :: Integral a => [a]
primes = small ++ large where
    1:p:candidates = roll $ mkWheel small
    small          = [2,3,5,7]
    large          = p : filter isPrime candidates
    isPrime n      = all (not . divides n) 
                       $ takeWhile (\p -> p*p <= n) large

divides :: Integral a => a -> a -> Bool
divides n p = n `mod` p == 0

sqrt' :: Integral a => a -> a
sqrt' = floor . sqrt . fromIntegral

primesFromTo :: [Int] -> [Int]
primesFromTo [x, y] = filter isPrime [x..y]

isPrime :: Integral a => a -> Bool
isPrime 1 = False
isPrime 2 = True
isPrime n = all (not . divides n) $ takeWhile (<= sqrt' n) primes

main :: IO ()
main = do
    count <- fmap read getLine
    inputLines <- fmap (take count . lines) getContents
    let answers = map (primesFromTo . map read . words) inputLines
    putStr . unlines . map (unlines . map show) $ answers

=== Code ===

Best regards,
Zhi-Qiang Lei
zhiqiang.lei at gmail.com

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