RosettaCodeData/Task/Legendre-prime-counting-fun.../Haskell/legendre-prime-counting-fun...

52 lines
2.0 KiB
Haskell

{-# OPTIONS_GHC -O2 -fllvm #-}
{-# LANGUAGE FlexibleContexts, BangPatterns #-}
import Data.Time.Clock.POSIX ( getPOSIXTime ) -- for timing
import Data.Int ( Int64 )
import Data.Word ( Word32, Word64 )
import Data.Bits ( Bits( (.&.), (.|.), shiftL, shiftR ) )
import Control.Monad ( unless, when, forM_ )
import Control.Monad.ST ( ST, runST )
import Data.Array.ST ( runSTUArray )
import Data.Array.Base ( UArray(..), IArray(unsafeAt), listArray, elems, assocs,
MArray( unsafeNewArray_, newArray, unsafeRead, unsafeWrite ),
STUArray, unsafeFreezeSTUArray, castSTUArray )
countPrimes :: Word64 -> Int64
countPrimes n =
if n < 3 then (if n < 2 then 0 else 1) else
let sqrtn = truncate $ sqrt $ fromIntegral n
qdrtn = truncate $ sqrt $ fromIntegral sqrtn
rtlmt = (sqrtn - 3) `div` 2
qrtlmt = (qdrtn - 3) `div` 2
oddPrimes@(UArray _ _ psz _) = runST $ do -- UArray of odd primes...
cmpsts <- newArray (0, rtlmt) False :: ST s (STUArray s Int Bool)
forM_ [ 0 .. qrtlmt ] $ \ i -> do
t <- unsafeRead cmpsts i
unless t $ do
let sqri = (i + i) * (i + 3) + 3
bp = i + i + 3
forM_ [ sqri, sqri + bp .. rtlmt ] $ \ c ->
unsafeWrite cmpsts c True
fcmpsts <- unsafeFreezeSTUArray cmpsts
let !numoprms = sum $ [ 1 | False <- elems fcmpsts ]
prms = [ fromIntegral $ i + i + 3 | (i, False) <- assocs fcmpsts ]
return $ listArray (0, numoprms - 1) prms :: ST s (UArray Int Word32)
phi x a =
if a < 1 then x - (x `shiftR` 1) else
let na = a - 1
p = fromIntegral $ unsafeAt oddPrimes na in
if x < p then 1 else
phi x na - phi (x `div` p) na
in fromIntegral (phi n psz) + fromIntegral psz
main :: IO ()
main = do
strt <- getPOSIXTime
mapM_ (\n -> putStrLn $ show n ++ "\t" ++ show (countPrimesx (10^n))) [ 0 .. 9 ]
stop <- getPOSIXTime
let elpsd = round $ 1e3 * (stop - strt) :: Int64
putStrLn $ "This took " ++ show elpsd ++ " milliseconds."