Monadic Eratosthenes Sieve

erat.hs

import System.Environment
import Control.Monad
import Data.Array
import Data.Array.ST

(^!) :: Num a => a -> Int -> a
(^!) x n = x^n

squareRoot :: Integer -> Integer
squareRoot 0 = 0
squareRoot 1 = 1
squareRoot n =
   let twopows = iterate (^!2) 2
       (lowerRoot, lowerN) =
          last $ takeWhile ((n>=) . snd) $ zip (1:twopows) twopows
       newtonStep x = div (x + div n x) 2
       iters = iterate newtonStep (squareRoot (div n lowerN) * lowerRoot)
       isRoot r  =  r^!2 <= n && n < (r+1)^!2
   in  head $ dropWhile (not . isRoot) iters

erat stop = runSTArray $
        newArray (2, stop) True >>=
        \sieve -> (mapM_ (\idx -> readArray sieve idx >>=
                                  \isPrime -> when isPrime $
                                                mapM_ (\k -> writeArray sieve k False)
                                                      [idx*2, idx*3 .. stop]) 
                         [2..stop] >>
                   return sieve)

primes max = [n | (n, isPrime) <- assocs (erat max), isPrime]

main = do
    args <- getArgs
    let maxPrime :: Integer 
        maxPrime = read (head args)
    let allPrimes = primes maxPrime
    print $ length allPrimes

erat1.hs

erat stop = runSTArray $ do
  sieve <- newArray (2, stop) True
  forM_ [2..stop] $ \idx ->
    do
      isPrime <- readArray sieve idx
      when isPrime $
           forM_ [idx*2, idx*3 .. stop] $ \k ->
             writeArray sieve k False
  return sieve

erat2.hs

erat stop = runSTArray $
        newArray (2, stop) True >>=
        \sieve -> (mapM_ (\idx -> readArray sieve idx >>=
                                  \isPrime -> when isPrime $
                                                mapM_ (\k -> writeArray sieve k False)
                                                      [idx*2, idx*3 .. stop]) 
                         [2..stop] >>
                   return sieve)

primes max = [n | (n, isPrime) <- assocs (erat max), isPrime]

ferat.hs

import Data.PSQueue
import Data.Maybe
import Control.Monad.State
import System.Environment

heappush :: (Ord k, Ord p) => k -> p -> State (PSQ k p) ()
heappush k p = state $ \pq -> ((), insert k p pq)

heapadjust :: (Ord k, Ord p) => k -> (p -> p) -> State (PSQ k p) ()
heapadjust k f = state $ \pq -> ((), adjust f k pq)

heapview :: (Ord k, Ord p) => State (PSQ k p) (k, p)
heapview = state $ \pq -> let Just b = findMin pq
                              k = key b
                              p = prio b
                          in ((k, p), pq)

heappop :: (Ord k, Ord p) => State (PSQ k p) (k, p)
heappop = state $ \pq -> heappop' pq
          where heappop' :: (Ord k, Ord p) => PSQ k p -> ((k, p), PSQ k p)
                heappop' pq = let Just (b, pq') = minView pq 
                              in ((key b, prio b), pq')

increasePegs :: Integer -> State (PSQ Integer Integer) ()
increasePegs n = do
    (k, m) <- heapview
    when (m == n) $
        heapadjust k (+k) >>
        increasePegs n

primesStep :: Integer -> State (PSQ Integer Integer) (Maybe Integer)
primesStep n = do
    (k, m) <- heapview
    if m == n
        then increasePegs n >>
             return Nothing
        else heappush n (n*n) >>
             return (Just n)

primes = let pq = singleton 2 4
             (ps, pq') = (runState $ mapM primesStep [3..]) pq
         in catMaybes ps

main = do
    args <- getArgs
    let maxPrime :: Integer 
        maxPrime = (read . head) args
    print . length $ takeWhile (<maxPrime) primes

herat.cabal

-- herat.cabal auto-generated by cabal init. For additional options,
-- see
-- http://www.haskell.org/cabal/release/cabal-latest/doc/users-guide/authors.html#pkg-descr.
-- The name of the package.
Name:                herat

-- The package version. See the Haskell package versioning policy
-- (http://www.haskell.org/haskellwiki/Package_versioning_policy) for
-- standards guiding when and how versions should be incremented.
Version:             0.1

-- A short (one-line) description of the package.
Synopsis:            Eratosthenes implementations

-- A longer description of the package.
-- Description:         

-- URL for the project homepage or repository.
Homepage:            https://gist.github.com/1171446

-- The license under which the package is released.
License:             BSD3

-- The file containing the license text.
License-file:        LICENSE

-- The package author(s).
Author:              Enrico Franchi

-- An email address to which users can send suggestions, bug reports,
-- and patches.
Maintainer:          [email protected]

-- A copyright notice.
Copyright: Enrico Franchi (c) 2011

Category:            Math

Build-type:          Simple

-- Extra files to be distributed with the package, such as examples or
-- a README.
-- Extra-source-files:  

-- Constraint on the version of Cabal needed to build this package.
Cabal-version:       >=1.2


Executable erat
  Main-is: erat.hs
  Build-depends: base, array
  
Executable ferat
    Main-is: ferat.hs
    Build-depends: base, PSQueue >= 1.1, mtl

LICENSE

Copyright (c)2011, Enrico Franchi

All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

    * Redistributions of source code must retain the above copyright
      notice, this list of conditions and the following disclaimer.

    * Redistributions in binary form must reproduce the above
      copyright notice, this list of conditions and the following
      disclaimer in the documentation and/or other materials provided
      with the distribution.

    * Neither the name of Enrico Franchi nor the names of other
      contributors may be used to endorse or promote products derived
      from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

merat.hs

import System.Environment
import Control.Monad
import Data.Array
import Data.Array.ST

(^!) :: Num a => a -> Int -> a
(^!) x n = x^n

squareRoot :: Integer -> Integer
squareRoot 0 = 0
squareRoot 1 = 1
squareRoot n =
   let twopows = iterate (^!2) 2
       (lowerRoot, lowerN) =
          last $ takeWhile ((n>=) . snd) $ zip (1:twopows) twopows
       newtonStep x = div (x + div n x) 2
       iters = iterate newtonStep (squareRoot (div n lowerN) * lowerRoot)
       isRoot r  =  r^!2 <= n && n < (r+1)^!2
   in  head $ dropWhile (not . isRoot) iters

erat stop = runSTArray $ do
  sieve <- newArray (2, stop) True
  forM_ [2..stop] $ \idx ->
    do
      isPrime <- readArray sieve idx
      when isPrime $
           forM_ [idx*2, idx*3 .. stop] $ \k ->
             writeArray sieve k False
  return sieve

primes max = [n | (n, isPrime) <- assocs (erat max), isPrime]

main = do
    args <- getArgs
    let maxPrime :: Integer 
        maxPrime = read (head args)
    let allPrimes = primes maxPrime
    print $ length allPrimes

Setup.hs

import Distribution.Simple
main = defaultMain