32-bit Mersenne Twister in Haskell

mersenne32.hs

import Data.Bits
import Data.Word
import System.Random

mtN = 624
mtM = 397

data MersenneTwister = MersenneTwister [Word32] Int
    deriving Show

getMT :: Word32 -> MersenneTwister
mtNext :: [Word32] -> Int -> (Int, MersenneTwister)

instance RandomGen MersenneTwister where
    next (MersenneTwister cache i) = mtNext cache i
    split g = (g, g)


getMT init = MersenneTwister (scanl mtInitStep init [1..mtN-1]) mtN
    where mtInitStep :: Word32 -> Int -> Word32
          mtInitStep prev i = 1812433253 * (prev `xor` (prev `shiftR` 30)) + fromIntegral i

mtNext cache i
    | i < mtN = (shuffle (cache !! i), MersenneTwister cache (i + 1))
    | otherwise = (shuffle (head newcache), MersenneTwister newcache 1)
        where shuffle :: Word32 -> Int
              shuffle y = fromIntegral v
                  where y1 = y `xor` (y `shiftR` 11)
                        y2 = y1 `xor` ((y1 `shiftL` 7) .&. 0x9d2c5680)
                        y3 = y2 `xor` ((y2 `shiftL` 15) .&. 0xefc60000)
                        y4 = y3 `xor` (y3 `shiftR` 18)
                        v = toInteger y4 + toInteger (minBound :: Int)
              newcache = mtNextState cache

mtNextState :: [Word32] -> [Word32]
mtNextState state = allbutlast ++ [last]
      where part1 = map (setState1 state) [0 .. mtN - mtM - 1]
            allbutlast = makeall state part1 [mtN - 2, mtN - 3 .. mtN - mtM]
            makeall s ns [] = ns
            makeall s ns (i:is) = rs ++ [value]
              where value = setState2 s rs i
                    rs = makeall s ns is
            last = setState3 state allbutlast

            setState1 :: [Word32] -> Int -> Word32
            setState1 state i = (state !! (i + mtM)) `xor` twist (state !! i) (state !! (i + 1))
            
            setState2 :: [Word32] -> [Word32] -> Int -> Word32
            setState2 state newstate i = (newstate !! (i + mtM - mtN)) `xor` twist (state !! i) (state !! (i + 1))
            
            setState3 :: [Word32] -> [Word32] -> Word32
            setState3 state newstate = (newstate !! (mtM - 1)) `xor` twist (state !! (mtN - 1)) (head newstate)

            mixbits :: Word32 -> Word32 -> Word32
            mixbits u v = (u .&. 0x80000000) .|. (v .&. 0x7fffffff)
            
            twist :: Word32 -> Word32 -> Word32
            twist u v = (mixbits u v `shiftR` 1) `xor` n
                where n
                        | v .&. 1 == 1 = 0x9908b0df
                        | otherwise = 0