    >{- |
    >   Module     : Data.Hash.MD5
    >   Copyright  : Copyright (C) 2001 Ian Lynagh
    >   License    : Either BSD or GPL
    >
    >   Maintainer : Ian Lynagh <igloo@earth.li>
    >   Stability  : provisional
    >   Portability: portable
    >
    >Generation of MD5sums
    >
    >Written by Ian Lynagh, igloo\@earth.li
    >-}

    > module Data.Hash.MD5 (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

    > type Zord64 = Word64

#else

    > import Data.Hash.MD5.Zord64_HARD

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

#endif ======================== 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 hex number from 'md5s'. -}
    > 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