    module Data.Digest.MD5Aux
       (md5,  md5s,  md5i,
        MD5(..), ABCD(..),
        Zord64, Str(..), BoolList(..), WordList(..)) where

    import Data.Char
    import Data.Bits
    import Data.Word

    {-
    Nasty kludge to create a type Zord64 which is really a Word64 but works
    how we want in hugs ands nhc98 too...
    Also need a rotate left function that actually works.

    #ifdef __GLASGOW_HASKELL__
    #define rotL rotateL
    #include "Zord64_EASY.hs"
    #else

    > import Zord64_HARD

    > rotL :: Word32 -> Rotation -> Word32
    > rotL a s = shiftL a s .|. shiftL a (s-32)

    #endif
    -}

    rotL x = rotateL x
    type Zord64 = Word64

    -- ===================== TYPES AND CLASS DEFINTIONS ========================

    type XYZ = (Word32, Word32, Word32)
    type Rotation = Int
    newtype ABCD = ABCD (Word32, Word32, Word32, Word32) deriving (Eq, Show)
    newtype Str = Str String
    newtype BoolList = BoolList [Bool]
    newtype WordList = WordList ([Word32], Zord64)

    -- Anything we want to work out the MD5 of must be an instance of class MD5

    class MD5 a where
     get_next :: a -> ([Word32], Int, a) -- get the next blocks worth
     --                     \      \   \------ the rest of the input
     --                      \      \--------- the number of bits returned
     --                       \--------------- the bits returned in 32bit words
     len_pad :: Zord64 -> a -> a         -- append the padding and length
     finished :: a -> Bool               -- Have we run out of input yet?

    -- Mainly exists because it's fairly easy to do MD5s on input where the
    -- length is not a multiple of 8

    instance MD5 BoolList where
     get_next (BoolList s) = (bools_to_word32s ys, length ys, BoolList zs)
      where (ys, zs) = splitAt 512 s
     len_pad l (BoolList bs)
      = BoolList (bs ++ [True]
                     ++ replicate (fromIntegral $ (447 - l) .&. 511) False
                     ++ [l .&. (shiftL 1 x) > 0 | x <- (mangle [0..63])]
                 )
      where mangle [] = []
            mangle xs = reverse ys ++ mangle zs
             where (ys, zs) = splitAt 8 xs
     finished (BoolList s) = s == []

    -- The string instance is fairly straightforward

    instance MD5 Str where
     get_next (Str s) = (string_to_word32s ys, 8 * length ys, Str zs)
      where (ys, zs) = splitAt 64 s
     len_pad c64 (Str s) = Str (s ++ padding ++ l)
      where padding = '\128':replicate (fromIntegral zeros) '\000'
            zeros = shiftR ((440 - c64) .&. 511) 3
            l = length_to_chars 8 c64
     finished (Str s) = s == ""

    -- YA instance that is believed will be useful

    instance MD5 WordList where
     get_next (WordList (ws, l)) = (xs, fromIntegral taken, WordList (ys, l - taken))
      where (xs, ys) = splitAt 16 ws
            taken = if l > 511 then 512 else l .&. 511
     len_pad c64 (WordList (ws, l)) = WordList (beginning ++ nextish ++ blanks ++ size, newlen)
      where beginning = if length ws > 0 then start ++ lastone' else []
            start = init ws
            lastone = last ws
            offset = c64 .&. 31
            lastone' = [if offset > 0 then lastone + theone else lastone]
            theone = shiftL (shiftR 128 (fromIntegral $ offset .&. 7))
                            (fromIntegral $ offset .&. (31 - 7))
            nextish = if offset == 0 then [128] else []
            c64' = c64 + (32 - offset)
            num_blanks = (fromIntegral $ shiftR ((448 - c64') .&. 511) 5)
            blanks = replicate num_blanks 0
            lowsize = fromIntegral $ c64 .&. (shiftL 1 32 - 1)
            topsize = fromIntegral $ shiftR c64 32
            size = [lowsize, topsize]
            newlen = l .&. (complement 511)
                   + if c64 .&. 511 >= 448 then 1024 else 512
     finished (WordList (_, z)) = z == 0

    instance Num ABCD where
     ABCD (a1, b1, c1, d1) + ABCD (a2, b2, c2, d2) = ABCD (a1 + a2, b1 + b2, c1 + c2, d1 + d2)

    -- ===================== EXPORTED FUNCTIONS ========================

    -- The simplest function, gives you the MD5 of a string as 4-tuple of
    -- 32bit words.

    md5 :: (MD5 a) => a -> ABCD
    md5 m = md5_main False 0 magic_numbers m

    -- Returns a hex number ala the md5sum program

    md5s :: (MD5 a) => a -> String
    md5s = abcd_to_string . md5

    -- Returns an integer equivalent to the above hex number

    md5i :: (MD5 a) => a -> Integer
    md5i = abcd_to_integer . md5

    -- ===================== THE CORE ALGORITHM ========================

    -- Decides what to do. The first argument indicates if padding has been
    -- added. The second is the length mod 2^64 so far. Then we have the
    -- starting state, the rest of the string and the final state.

    md5_main :: (MD5 a) =>
                Bool   -- Have we added padding yet?
             -> Zord64 -- The length so far mod 2^64
             -> ABCD   -- The initial state
             -> a      -- The non-processed portion of the message
             -> ABCD   -- The resulting state
    md5_main padded ilen abcd m
     = if finished m && padded
       then abcd
       else md5_main padded' (ilen + 512) (abcd + abcd') m''
     where (m16, l, m') = get_next m
           len' = ilen + fromIntegral l
           ((m16', _, m''), padded') = if not padded && l < 512
                                       then (get_next $ len_pad len' m, True)
                                       else ((m16, l, m'), padded)
           abcd' = md5_do_block abcd m16'

    -- md5_do_block processes a 512 bit block by calling md5_round 4 times to
    -- apply each round with the correct constants and permutations of the
    -- block

    md5_do_block :: ABCD     -- Initial state
                 -> [Word32] -- The block to be processed - 16 32bit words
                 -> ABCD     -- Resulting state
    md5_do_block abcd0 w = abcd4
     where (r1, r2, r3, r4) = rounds
           {-
           map (\x -> w !! x) [1,6,11,0,5,10,15,4,9,14,3,8,13,2,7,12]
                           -- [(5 * x + 1) `mod` 16 | x <- [0..15]]
           map (\x -> w !! x) [5,8,11,14,1,4,7,10,13,0,3,6,9,12,15,2]
                           -- [(3 * x + 5) `mod` 16 | x <- [0..15]]
           map (\x -> w !! x) [0,7,14,5,12,3,10,1,8,15,6,13,4,11,2,9]
                           -- [(7 * x) `mod` 16 | x <- [0..15]]
           -}
           perm5 [c0,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15]
            = [c1,c6,c11,c0,c5,c10,c15,c4,c9,c14,c3,c8,c13,c2,c7,c12]
           perm5 _ = error "broke at perm5"
           perm3 [c0,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15]
            = [c5,c8,c11,c14,c1,c4,c7,c10,c13,c0,c3,c6,c9,c12,c15,c2]
           perm3 _ = error "broke at perm3"
           perm7 [c0,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15]
            = [c0,c7,c14,c5,c12,c3,c10,c1,c8,c15,c6,c13,c4,c11,c2,c9]
           perm7 _ = error "broke at perm7"
           abcd1 = md5_round md5_f abcd0        w  r1
           abcd2 = md5_round md5_g abcd1 (perm5 w) r2
           abcd3 = md5_round md5_h abcd2 (perm3 w) r3
           abcd4 = md5_round md5_i abcd3 (perm7 w) r4

    -- md5_round does one of the rounds. It takes an auxiliary function and foldls
    -- (md5_inner_function f) to repeatedly apply it to the initial state with the
    -- correct constants

    md5_round :: (XYZ -> Word32)      -- Auxiliary function (F, G, H or I
                                      -- for those of you with a copy of
                                      -- the prayer book^W^WRFC)
              -> ABCD                 -- Initial state
              -> [Word32]             -- The 16 32bit words of input
              -> [(Rotation, Word32)] -- The list of 16 rotations and
                                      -- additive constants
              -> ABCD                 -- Resulting state
    md5_round f abcd s ns = foldl (md5_inner_function f) abcd ns'
     where ns' = zipWith (\x (y, z) -> (y, x + z)) s ns

    -- Apply one of the functions md5_[fghi] and put the new ABCD together

    md5_inner_function :: (XYZ -> Word32)    -- Auxiliary function
                       -> ABCD               -- Initial state
                       -> (Rotation, Word32) -- The rotation and additive
                                             -- constant (X[i] + T[j])
                       -> ABCD               -- Resulting state
    md5_inner_function f (ABCD (a, b, c, d)) (s, ki) = ABCD (d, a', b, c)
     where mid_a = a + f(b,c,d) + ki
           rot_a = rotL mid_a s
           a' = b + rot_a

    -- The 4 auxiliary functions

    md5_f :: XYZ -> Word32
    md5_f (x, y, z) = z `xor` (x .&. (y `xor` z))
    {- optimised version of: (x .&. y) .|. ((complement x) .&. z) -}

    md5_g :: XYZ -> Word32
    md5_g (x, y, z) = md5_f (z, x, y)
    {- was: (x .&. z) .|. (y .&. (complement z)) -}

    md5_h :: XYZ -> Word32
    md5_h (x, y, z) = x `xor` y `xor` z

    md5_i :: XYZ -> Word32
    md5_i (x, y, z) = y `xor` (x .|. (complement z))

    -- The magic numbers from the RFC.

    magic_numbers :: ABCD
    magic_numbers = ABCD (0x67452301, 0xefcdab89, 0x98badcfe, 0x10325476)

    -- The 4 lists of (rotation, additive constant) tuples, one for each round

    rounds :: ([(Rotation, Word32)],
               [(Rotation, Word32)],
               [(Rotation, Word32)],
               [(Rotation, Word32)])
    rounds = (r1, r2, r3, r4)
     where r1 = [(s11, 0xd76aa478), (s12, 0xe8c7b756), (s13, 0x242070db),
                 (s14, 0xc1bdceee), (s11, 0xf57c0faf), (s12, 0x4787c62a),
                 (s13, 0xa8304613), (s14, 0xfd469501), (s11, 0x698098d8),
                 (s12, 0x8b44f7af), (s13, 0xffff5bb1), (s14, 0x895cd7be),
                 (s11, 0x6b901122), (s12, 0xfd987193), (s13, 0xa679438e),
                 (s14, 0x49b40821)]
           r2 = [(s21, 0xf61e2562), (s22, 0xc040b340), (s23, 0x265e5a51),
                 (s24, 0xe9b6c7aa), (s21, 0xd62f105d), (s22,  0x2441453),
                 (s23, 0xd8a1e681), (s24, 0xe7d3fbc8), (s21, 0x21e1cde6),
                 (s22, 0xc33707d6), (s23, 0xf4d50d87), (s24, 0x455a14ed),
                 (s21, 0xa9e3e905), (s22, 0xfcefa3f8), (s23, 0x676f02d9),
                 (s24, 0x8d2a4c8a)]
           r3 = [(s31, 0xfffa3942), (s32, 0x8771f681), (s33, 0x6d9d6122),
                 (s34, 0xfde5380c), (s31, 0xa4beea44), (s32, 0x4bdecfa9),
                 (s33, 0xf6bb4b60), (s34, 0xbebfbc70), (s31, 0x289b7ec6),
                 (s32, 0xeaa127fa), (s33, 0xd4ef3085), (s34,  0x4881d05),
                 (s31, 0xd9d4d039), (s32, 0xe6db99e5), (s33, 0x1fa27cf8),
                 (s34, 0xc4ac5665)]
           r4 = [(s41, 0xf4292244), (s42, 0x432aff97), (s43, 0xab9423a7),
                 (s44, 0xfc93a039), (s41, 0x655b59c3), (s42, 0x8f0ccc92),
                 (s43, 0xffeff47d), (s44, 0x85845dd1), (s41, 0x6fa87e4f),
                 (s42, 0xfe2ce6e0), (s43, 0xa3014314), (s44, 0x4e0811a1),
                 (s41, 0xf7537e82), (s42, 0xbd3af235), (s43, 0x2ad7d2bb),
                 (s44, 0xeb86d391)]
           s11 = 7
           s12 = 12
           s13 = 17
           s14 = 22
           s21 = 5
           s22 = 9
           s23 = 14
           s24 = 20
           s31 = 4
           s32 = 11
           s33 = 16
           s34 = 23
           s41 = 6
           s42 = 10
           s43 = 15
           s44 = 21

    -- ===================== CONVERSION FUNCTIONS ========================

    -- Turn the 4 32 bit words into a string representing the hex number they
    -- represent.

    abcd_to_string :: ABCD -> String
    abcd_to_string (ABCD (a,b,c,d)) = concat $ map display_32bits_as_hex [a,b,c,d]

    -- Split the 32 bit word up, swap the chunks over and convert the numbers
    -- to their hex equivalents.

    display_32bits_as_hex :: Word32 -> String
    display_32bits_as_hex w = swap_pairs cs
     where cs = map (\x -> getc $ (shiftR w (4*x)) .&. 15) [0..7]
           getc n = (['0'..'9'] ++ ['a'..'f']) !! (fromIntegral n)
           swap_pairs (x1:x2:xs) = x2:x1:swap_pairs xs
           swap_pairs _ = []

    -- Convert to an integer, performing endianness magic as we go

    abcd_to_integer :: ABCD -> Integer
    abcd_to_integer (ABCD (a,b,c,d)) = rev_num a * 2^(96 :: Int)
                                     + rev_num b * 2^(64 :: Int)
                                     + rev_num c * 2^(32 :: Int)
                                     + rev_num d

    rev_num :: Word32 -> Integer
    rev_num i = toInteger j `mod` (2^(32 :: Int))
     --         NHC's fault ~~~~~~~~~~~~~~~~~~~~~
     where j = foldl (\so_far next -> shiftL so_far 8 + (shiftR i next .&. 255))
                     0 [0,8,16,24]

    -- Used to convert a 64 byte string to 16 32bit words

    string_to_word32s :: String -> [Word32]
    string_to_word32s "" = []
    string_to_word32s ss = this:string_to_word32s ss'
     where (s, ss') = splitAt 4 ss
           this = foldr (\c w -> shiftL w 8 + (fromIntegral.ord) c) 0 s

    -- Used to convert a list of 512 bools to 16 32bit words

    bools_to_word32s :: [Bool] -> [Word32]
    bools_to_word32s [] = []
    bools_to_word32s bs = this:bools_to_word32s rest
     where (bs1, bs1') = splitAt 8 bs
           (bs2, bs2') = splitAt 8 bs1'
           (bs3, bs3') = splitAt 8 bs2'
           (bs4, rest) = splitAt 8 bs3'
           this = boolss_to_word32 [bs1, bs2, bs3, bs4]
           bools_to_word8 = foldl (\w b -> shiftL w 1 + if b then 1 else 0) 0
           boolss_to_word32 = foldr (\w8 w -> shiftL w 8 + bools_to_word8 w8) 0

    -- Convert the size into a list of characters used by the len_pad function
    -- for strings

    length_to_chars :: Int -> Zord64 -> String
    length_to_chars 0 _ = []
    length_to_chars p n = this:length_to_chars (p-1) (shiftR n 8)
             where this = chr $ fromIntegral $ n .&. 255