content: {-# LANGUAGE BangPatterns, CPP, FlexibleInstances #-}
  -- |Pure implementations of the SHA suite of hash functions. The implementation
  -- is basically an unoptimized translation of FIPS 180-2 into Haskell. If you're
  -- looking for performance, you probably won't find it here.
  module Cryptol.SHA
         ( SHA256State(..), SHA512State(..)
         , SHA256Block(..), SHA512Block(..)
  
           -- * Raw SHA block functions
         , processSHA512Block
         , processSHA256Block
  
         , initialSHA224State
         , initialSHA256State
         , initialSHA384State
         , initialSHA512State
  
           -- * Internal routines included for testing
         , toBigEndianSBS, fromBigEndianSBS
         , calc_k
         , padSHA1, padSHA512
         , padSHA1Chunks, padSHA512Chunks
         )
   where
   
  import Data.Bits
  import Data.ByteString.Lazy(ByteString)
  import Data.Word (Word32, Word64)
  import qualified Data.ByteString.Lazy as BS
  import qualified Data.ByteString as SBS
  
  -- --------------------------------------------------------------------------
  --
  -- State Definitions and Initial States
  --
  -- --------------------------------------------------------------------------
  
  data SHA256State = SHA256S !Word32 !Word32 !Word32 !Word32
                             !Word32 !Word32 !Word32 !Word32
  
  initialSHA224State :: SHA256State
  initialSHA224State = SHA256S 0xc1059ed8 0x367cd507 0x3070dd17 0xf70e5939
                               0xffc00b31 0x68581511 0x64f98fa7 0xbefa4fa4
  
  initialSHA256State :: SHA256State
  initialSHA256State = SHA256S 0x6a09e667 0xbb67ae85 0x3c6ef372 0xa54ff53a
                               0x510e527f 0x9b05688c 0x1f83d9ab 0x5be0cd19
  
  data SHA512State = SHA512S !Word64 !Word64 !Word64 !Word64
                             !Word64 !Word64 !Word64 !Word64
  
  initialSHA384State :: SHA512State
  initialSHA384State = SHA512S 0xcbbb9d5dc1059ed8 0x629a292a367cd507
                               0x9159015a3070dd17 0x152fecd8f70e5939
                               0x67332667ffc00b31 0x8eb44a8768581511
                               0xdb0c2e0d64f98fa7 0x47b5481dbefa4fa4
  
  initialSHA512State :: SHA512State
  initialSHA512State = SHA512S 0x6a09e667f3bcc908 0xbb67ae8584caa73b
                               0x3c6ef372fe94f82b 0xa54ff53a5f1d36f1
                               0x510e527fade682d1 0x9b05688c2b3e6c1f
                               0x1f83d9abfb41bd6b 0x5be0cd19137e2179
  
  
  -- --------------------------------------------------------------------------
  --
  -- Padding
  --
  -- --------------------------------------------------------------------------
  
  padSHA1 :: ByteString -> ByteString
  padSHA1 = generic_pad 448 512 64
  
  padSHA1Chunks :: Int -> [SBS.ByteString]
  padSHA1Chunks = generic_pad_chunks 448 512 64
  
  padSHA512 :: ByteString -> ByteString
  padSHA512 = generic_pad 896 1024 128
  
  padSHA512Chunks :: Int -> [SBS.ByteString]
  padSHA512Chunks = generic_pad_chunks 896 1024 128
  
  generic_pad :: Word64 -> Word64 -> Int -> ByteString -> ByteString
  generic_pad a b lSize bs =
    BS.fromChunks $! go 0 chunks
   where
    chunks = BS.toChunks bs
  
    -- Generates the padded ByteString at the same time it computes the length
    -- of input. If the length is computed before the computation of the hash, it
    -- will break the lazy evaluation of the input and no longer run in constant
    -- memory space.
    go !len [] = generic_pad_chunks a b lSize len
    go !len (c:cs) = c : go (len + SBS.length c) cs
  
  generic_pad_chunks :: Word64 -> Word64 -> Int -> Int -> [SBS.ByteString]
  generic_pad_chunks a b lSize len =
    let lenBits = fromIntegral $ len * 8
        k = calc_k a b lenBits
        -- INVARIANT: k is necessarily > 0, and (k + 1) is a multiple of 8.
        kBytes = (k + 1) `div` 8
        nZeroBytes = fromIntegral $! kBytes - 1
        padLength = toBigEndianSBS lSize lenBits
    in [SBS.singleton 0x80, SBS.replicate nZeroBytes 0, padLength]
  
  -- Given a, b, and l, calculate the smallest k such that (l + 1 + k) mod b = a.
  calc_k :: Word64 -> Word64 -> Word64 -> Word64
  calc_k a b l =
    if r <= -1
      then fromIntegral r + b
      else fromIntegral r
   where
    r = toInteger a - toInteger l `mod` toInteger b - 1
  
  toBigEndianSBS :: (Integral a, Bits a) => Int -> a -> SBS.ByteString
  toBigEndianSBS s val = SBS.pack $ map getBits [s - 8, s - 16 .. 0]
   where
     getBits x = fromIntegral $ (val `shiftR` x) .&. 0xFF
  
  fromBigEndianSBS :: (Integral a, Bits a) => SBS.ByteString -> a
  fromBigEndianSBS =
    SBS.foldl (\ acc x -> (acc `shiftL` 8) + fromIntegral x) 0
  
  -- --------------------------------------------------------------------------
  --
  -- SHA Functions
  --
  -- --------------------------------------------------------------------------
  
  {-# SPECIALIZE ch :: Word32 -> Word32 -> Word32 -> Word32 #-}
  {-# SPECIALIZE ch :: Word64 -> Word64 -> Word64 -> Word64 #-}
  ch :: Bits a => a -> a -> a -> a
  ch x y z = (x .&. y) `xor` (complement x .&. z)
  
  {-# SPECIALIZE maj :: Word32 -> Word32 -> Word32 -> Word32 #-}
  {-# SPECIALIZE maj :: Word64 -> Word64 -> Word64 -> Word64 #-}
  maj :: Bits a => a -> a -> a -> a
  maj x y z = (x .&. (y .|. z)) .|. (y .&. z)
  -- note:
  --   the original functions is (x & y) ^ (x & z) ^ (y & z)
  --   if you fire off truth tables, this is equivalent to 
  --     (x & y) | (x & z) | (y & z)
  --   which you can the use distribution on:
  --     (x & (y | z)) | (y & z)
  --   which saves us one operation.
  
  bsig256_0 :: Word32 -> Word32
  bsig256_0 x = rotateR x 2 `xor` rotateR x 13 `xor` rotateR x 22
  
  bsig256_1 :: Word32 -> Word32
  bsig256_1 x = rotateR x 6 `xor` rotateR x 11 `xor` rotateR x 25
  
  lsig256_0 :: Word32 -> Word32
  lsig256_0 x = rotateR x 7 `xor` rotateR x 18 `xor` shiftR x 3
  
  lsig256_1 :: Word32 -> Word32
  lsig256_1 x = rotateR x 17 `xor` rotateR x 19 `xor` shiftR x 10
  
  bsig512_0 :: Word64 -> Word64
  bsig512_0 x = rotateR x 28 `xor` rotateR x 34 `xor` rotateR x 39
  
  bsig512_1 :: Word64 -> Word64
  bsig512_1 x = rotateR x 14 `xor` rotateR x 18 `xor` rotateR x 41
  
  lsig512_0 :: Word64 -> Word64
  lsig512_0 x = rotateR x 1 `xor` rotateR x 8 `xor` shiftR x 7
  
  lsig512_1 :: Word64 -> Word64
  lsig512_1 x = rotateR x 19 `xor` rotateR x 61 `xor` shiftR x 6
  
  -- --------------------------------------------------------------------------
  --
  -- Message Schedules
  --
  -- --------------------------------------------------------------------------
  
  
  data SHA256Block = SHA256Block !Word32 !Word32 !Word32 !Word32 !Word32 -- 00-04
                                 !Word32 !Word32 !Word32 !Word32 !Word32 -- 05-09
                                 !Word32 !Word32 !Word32 !Word32 !Word32 -- 10-14
                                 !Word32
  
  data SHA256Sched = SHA256Sched !Word32 !Word32 !Word32 !Word32 !Word32 -- 00-04
                                 !Word32 !Word32 !Word32 !Word32 !Word32 -- 05-09
                                 !Word32 !Word32 !Word32 !Word32 !Word32 -- 10-14
                                 !Word32 !Word32 !Word32 !Word32 !Word32 -- 15-19
                                 !Word32 !Word32 !Word32 !Word32 !Word32 -- 20-24
                                 !Word32 !Word32 !Word32 !Word32 !Word32 -- 25-29
                                 !Word32 !Word32 !Word32 !Word32 !Word32 -- 30-34
                                 !Word32 !Word32 !Word32 !Word32 !Word32 -- 35-39
                                 !Word32 !Word32 !Word32 !Word32 !Word32 -- 40-44
                                 !Word32 !Word32 !Word32 !Word32 !Word32 -- 45-49
                                 !Word32 !Word32 !Word32 !Word32 !Word32 -- 50-54
                                 !Word32 !Word32 !Word32 !Word32 !Word32 -- 55-59
                                 !Word32 !Word32 !Word32 !Word32         -- 60-63
  
  getSHA256Sched :: SHA256Block -> SHA256Sched
  getSHA256Sched (SHA256Block w00 w01 w02 w03
                              w04 w05 w06 w07
                              w08 w09 w10 w11
                              w12 w13 w14 w15) =
    let w16 = lsig256_1 w14 + w09 + lsig256_0 w01 + w00
        w17 = lsig256_1 w15 + w10 + lsig256_0 w02 + w01
        w18 = lsig256_1 w16 + w11 + lsig256_0 w03 + w02
        w19 = lsig256_1 w17 + w12 + lsig256_0 w04 + w03
        w20 = lsig256_1 w18 + w13 + lsig256_0 w05 + w04
        w21 = lsig256_1 w19 + w14 + lsig256_0 w06 + w05
        w22 = lsig256_1 w20 + w15 + lsig256_0 w07 + w06
        w23 = lsig256_1 w21 + w16 + lsig256_0 w08 + w07
        w24 = lsig256_1 w22 + w17 + lsig256_0 w09 + w08
        w25 = lsig256_1 w23 + w18 + lsig256_0 w10 + w09
        w26 = lsig256_1 w24 + w19 + lsig256_0 w11 + w10
        w27 = lsig256_1 w25 + w20 + lsig256_0 w12 + w11
        w28 = lsig256_1 w26 + w21 + lsig256_0 w13 + w12
        w29 = lsig256_1 w27 + w22 + lsig256_0 w14 + w13
        w30 = lsig256_1 w28 + w23 + lsig256_0 w15 + w14
        w31 = lsig256_1 w29 + w24 + lsig256_0 w16 + w15
        w32 = lsig256_1 w30 + w25 + lsig256_0 w17 + w16
        w33 = lsig256_1 w31 + w26 + lsig256_0 w18 + w17
        w34 = lsig256_1 w32 + w27 + lsig256_0 w19 + w18
        w35 = lsig256_1 w33 + w28 + lsig256_0 w20 + w19
        w36 = lsig256_1 w34 + w29 + lsig256_0 w21 + w20
        w37 = lsig256_1 w35 + w30 + lsig256_0 w22 + w21
        w38 = lsig256_1 w36 + w31 + lsig256_0 w23 + w22
        w39 = lsig256_1 w37 + w32 + lsig256_0 w24 + w23
        w40 = lsig256_1 w38 + w33 + lsig256_0 w25 + w24
        w41 = lsig256_1 w39 + w34 + lsig256_0 w26 + w25
        w42 = lsig256_1 w40 + w35 + lsig256_0 w27 + w26
        w43 = lsig256_1 w41 + w36 + lsig256_0 w28 + w27
        w44 = lsig256_1 w42 + w37 + lsig256_0 w29 + w28
        w45 = lsig256_1 w43 + w38 + lsig256_0 w30 + w29
        w46 = lsig256_1 w44 + w39 + lsig256_0 w31 + w30
        w47 = lsig256_1 w45 + w40 + lsig256_0 w32 + w31
        w48 = lsig256_1 w46 + w41 + lsig256_0 w33 + w32
        w49 = lsig256_1 w47 + w42 + lsig256_0 w34 + w33
        w50 = lsig256_1 w48 + w43 + lsig256_0 w35 + w34
        w51 = lsig256_1 w49 + w44 + lsig256_0 w36 + w35
        w52 = lsig256_1 w50 + w45 + lsig256_0 w37 + w36
        w53 = lsig256_1 w51 + w46 + lsig256_0 w38 + w37
        w54 = lsig256_1 w52 + w47 + lsig256_0 w39 + w38
        w55 = lsig256_1 w53 + w48 + lsig256_0 w40 + w39
        w56 = lsig256_1 w54 + w49 + lsig256_0 w41 + w40
        w57 = lsig256_1 w55 + w50 + lsig256_0 w42 + w41
        w58 = lsig256_1 w56 + w51 + lsig256_0 w43 + w42
        w59 = lsig256_1 w57 + w52 + lsig256_0 w44 + w43
        w60 = lsig256_1 w58 + w53 + lsig256_0 w45 + w44
        w61 = lsig256_1 w59 + w54 + lsig256_0 w46 + w45
        w62 = lsig256_1 w60 + w55 + lsig256_0 w47 + w46
        w63 = lsig256_1 w61 + w56 + lsig256_0 w48 + w47
      in SHA256Sched w00 w01 w02 w03 w04 w05 w06 w07 w08 w09
                          w10 w11 w12 w13 w14 w15 w16 w17 w18 w19
                          w20 w21 w22 w23 w24 w25 w26 w27 w28 w29
                          w30 w31 w32 w33 w34 w35 w36 w37 w38 w39
                          w40 w41 w42 w43 w44 w45 w46 w47 w48 w49
                          w50 w51 w52 w53 w54 w55 w56 w57 w58 w59
                          w60 w61 w62 w63
  
  data SHA512Block = SHA512Block !Word64 !Word64 !Word64 !Word64 !Word64 --  0- 4
                                 !Word64 !Word64 !Word64 !Word64 !Word64 --  5- 9
                                 !Word64 !Word64 !Word64 !Word64 !Word64 -- 10-14
                                 !Word64 -- 15
  
  data SHA512Sched = SHA512Sched !Word64 !Word64 !Word64 !Word64 !Word64 --  0- 4
                                 !Word64 !Word64 !Word64 !Word64 !Word64 --  5- 9
                                 !Word64 !Word64 !Word64 !Word64 !Word64 -- 10-14
                                 !Word64 !Word64 !Word64 !Word64 !Word64 -- 15-19
                                 !Word64 !Word64 !Word64 !Word64 !Word64 -- 20-24
                                 !Word64 !Word64 !Word64 !Word64 !Word64 -- 25-29
                                 !Word64 !Word64 !Word64 !Word64 !Word64 -- 30-34
                                 !Word64 !Word64 !Word64 !Word64 !Word64 -- 35-39
                                 !Word64 !Word64 !Word64 !Word64 !Word64 -- 40-44
                                 !Word64 !Word64 !Word64 !Word64 !Word64 -- 45-49
                                 !Word64 !Word64 !Word64 !Word64 !Word64 -- 50-54
                                 !Word64 !Word64 !Word64 !Word64 !Word64 -- 55-59
                                 !Word64 !Word64 !Word64 !Word64 !Word64 -- 60-64
                                 !Word64 !Word64 !Word64 !Word64 !Word64 -- 65-69
                                 !Word64 !Word64 !Word64 !Word64 !Word64 -- 70-74
                                 !Word64 !Word64 !Word64 !Word64 !Word64 -- 75-79
  
  getSHA512Sched :: SHA512Block -> SHA512Sched
  getSHA512Sched (SHA512Block w00 w01 w02 w03
                              w04 w05 w06 w07
                              w08 w09 w10 w11
                              w12 w13 w14 w15) =
    let w16 = lsig512_1 w14 + w09 + lsig512_0 w01 + w00
        w17 = lsig512_1 w15 + w10 + lsig512_0 w02 + w01
        w18 = lsig512_1 w16 + w11 + lsig512_0 w03 + w02
        w19 = lsig512_1 w17 + w12 + lsig512_0 w04 + w03
        w20 = lsig512_1 w18 + w13 + lsig512_0 w05 + w04
        w21 = lsig512_1 w19 + w14 + lsig512_0 w06 + w05
        w22 = lsig512_1 w20 + w15 + lsig512_0 w07 + w06
        w23 = lsig512_1 w21 + w16 + lsig512_0 w08 + w07
        w24 = lsig512_1 w22 + w17 + lsig512_0 w09 + w08
        w25 = lsig512_1 w23 + w18 + lsig512_0 w10 + w09
        w26 = lsig512_1 w24 + w19 + lsig512_0 w11 + w10
        w27 = lsig512_1 w25 + w20 + lsig512_0 w12 + w11
        w28 = lsig512_1 w26 + w21 + lsig512_0 w13 + w12
        w29 = lsig512_1 w27 + w22 + lsig512_0 w14 + w13
        w30 = lsig512_1 w28 + w23 + lsig512_0 w15 + w14
        w31 = lsig512_1 w29 + w24 + lsig512_0 w16 + w15
        w32 = lsig512_1 w30 + w25 + lsig512_0 w17 + w16
        w33 = lsig512_1 w31 + w26 + lsig512_0 w18 + w17
        w34 = lsig512_1 w32 + w27 + lsig512_0 w19 + w18
        w35 = lsig512_1 w33 + w28 + lsig512_0 w20 + w19
        w36 = lsig512_1 w34 + w29 + lsig512_0 w21 + w20
        w37 = lsig512_1 w35 + w30 + lsig512_0 w22 + w21
        w38 = lsig512_1 w36 + w31 + lsig512_0 w23 + w22
        w39 = lsig512_1 w37 + w32 + lsig512_0 w24 + w23
        w40 = lsig512_1 w38 + w33 + lsig512_0 w25 + w24
        w41 = lsig512_1 w39 + w34 + lsig512_0 w26 + w25
        w42 = lsig512_1 w40 + w35 + lsig512_0 w27 + w26
        w43 = lsig512_1 w41 + w36 + lsig512_0 w28 + w27
        w44 = lsig512_1 w42 + w37 + lsig512_0 w29 + w28
        w45 = lsig512_1 w43 + w38 + lsig512_0 w30 + w29
        w46 = lsig512_1 w44 + w39 + lsig512_0 w31 + w30
        w47 = lsig512_1 w45 + w40 + lsig512_0 w32 + w31
        w48 = lsig512_1 w46 + w41 + lsig512_0 w33 + w32
        w49 = lsig512_1 w47 + w42 + lsig512_0 w34 + w33
        w50 = lsig512_1 w48 + w43 + lsig512_0 w35 + w34
        w51 = lsig512_1 w49 + w44 + lsig512_0 w36 + w35
        w52 = lsig512_1 w50 + w45 + lsig512_0 w37 + w36
        w53 = lsig512_1 w51 + w46 + lsig512_0 w38 + w37
        w54 = lsig512_1 w52 + w47 + lsig512_0 w39 + w38
        w55 = lsig512_1 w53 + w48 + lsig512_0 w40 + w39
        w56 = lsig512_1 w54 + w49 + lsig512_0 w41 + w40
        w57 = lsig512_1 w55 + w50 + lsig512_0 w42 + w41
        w58 = lsig512_1 w56 + w51 + lsig512_0 w43 + w42
        w59 = lsig512_1 w57 + w52 + lsig512_0 w44 + w43
        w60 = lsig512_1 w58 + w53 + lsig512_0 w45 + w44
        w61 = lsig512_1 w59 + w54 + lsig512_0 w46 + w45
        w62 = lsig512_1 w60 + w55 + lsig512_0 w47 + w46
        w63 = lsig512_1 w61 + w56 + lsig512_0 w48 + w47
        w64 = lsig512_1 w62 + w57 + lsig512_0 w49 + w48
        w65 = lsig512_1 w63 + w58 + lsig512_0 w50 + w49
        w66 = lsig512_1 w64 + w59 + lsig512_0 w51 + w50
        w67 = lsig512_1 w65 + w60 + lsig512_0 w52 + w51
        w68 = lsig512_1 w66 + w61 + lsig512_0 w53 + w52
        w69 = lsig512_1 w67 + w62 + lsig512_0 w54 + w53
        w70 = lsig512_1 w68 + w63 + lsig512_0 w55 + w54
        w71 = lsig512_1 w69 + w64 + lsig512_0 w56 + w55
        w72 = lsig512_1 w70 + w65 + lsig512_0 w57 + w56
        w73 = lsig512_1 w71 + w66 + lsig512_0 w58 + w57
        w74 = lsig512_1 w72 + w67 + lsig512_0 w59 + w58
        w75 = lsig512_1 w73 + w68 + lsig512_0 w60 + w59
        w76 = lsig512_1 w74 + w69 + lsig512_0 w61 + w60
        w77 = lsig512_1 w75 + w70 + lsig512_0 w62 + w61
        w78 = lsig512_1 w76 + w71 + lsig512_0 w63 + w62
        w79 = lsig512_1 w77 + w72 + lsig512_0 w64 + w63
      in SHA512Sched w00 w01 w02 w03 w04 w05 w06 w07 w08 w09
                          w10 w11 w12 w13 w14 w15 w16 w17 w18 w19
                          w20 w21 w22 w23 w24 w25 w26 w27 w28 w29
                          w30 w31 w32 w33 w34 w35 w36 w37 w38 w39
                          w40 w41 w42 w43 w44 w45 w46 w47 w48 w49
                          w50 w51 w52 w53 w54 w55 w56 w57 w58 w59
                          w60 w61 w62 w63 w64 w65 w66 w67 w68 w69
                          w70 w71 w72 w73 w74 w75 w76 w77 w78 w79
  
  -- --------------------------------------------------------------------------
  --
  -- SHA Block Processors
  --
  -- --------------------------------------------------------------------------
  
  
  processSHA256Block :: SHA256State -> SHA256Block -> SHA256State
  processSHA256Block !s00@(SHA256S a00 b00 c00 d00 e00 f00 g00 h00) !blk = do
    let (SHA256Sched w00 w01 w02 w03 w04 w05 w06 w07 w08 w09
                 w10 w11 w12 w13 w14 w15 w16 w17 w18 w19
                 w20 w21 w22 w23 w24 w25 w26 w27 w28 w29
                 w30 w31 w32 w33 w34 w35 w36 w37 w38 w39
                 w40 w41 w42 w43 w44 w45 w46 w47 w48 w49
                 w50 w51 w52 w53 w54 w55 w56 w57 w58 w59
                 w60 w61 w62 w63) = getSHA256Sched blk
        s01 = step256 s00 0x428a2f98 w00
        s02 = step256 s01 0x71374491 w01
        s03 = step256 s02 0xb5c0fbcf w02
        s04 = step256 s03 0xe9b5dba5 w03
        s05 = step256 s04 0x3956c25b w04
        s06 = step256 s05 0x59f111f1 w05
        s07 = step256 s06 0x923f82a4 w06
        s08 = step256 s07 0xab1c5ed5 w07
        s09 = step256 s08 0xd807aa98 w08
        s10 = step256 s09 0x12835b01 w09
        s11 = step256 s10 0x243185be w10
        s12 = step256 s11 0x550c7dc3 w11
        s13 = step256 s12 0x72be5d74 w12
        s14 = step256 s13 0x80deb1fe w13
        s15 = step256 s14 0x9bdc06a7 w14
        s16 = step256 s15 0xc19bf174 w15
        s17 = step256 s16 0xe49b69c1 w16
        s18 = step256 s17 0xefbe4786 w17
        s19 = step256 s18 0x0fc19dc6 w18
        s20 = step256 s19 0x240ca1cc w19
        s21 = step256 s20 0x2de92c6f w20
        s22 = step256 s21 0x4a7484aa w21
        s23 = step256 s22 0x5cb0a9dc w22
        s24 = step256 s23 0x76f988da w23
        s25 = step256 s24 0x983e5152 w24
        s26 = step256 s25 0xa831c66d w25
        s27 = step256 s26 0xb00327c8 w26
        s28 = step256 s27 0xbf597fc7 w27
        s29 = step256 s28 0xc6e00bf3 w28
        s30 = step256 s29 0xd5a79147 w29
        s31 = step256 s30 0x06ca6351 w30
        s32 = step256 s31 0x14292967 w31
        s33 = step256 s32 0x27b70a85 w32
        s34 = step256 s33 0x2e1b2138 w33
        s35 = step256 s34 0x4d2c6dfc w34
        s36 = step256 s35 0x53380d13 w35
        s37 = step256 s36 0x650a7354 w36
        s38 = step256 s37 0x766a0abb w37
        s39 = step256 s38 0x81c2c92e w38
        s40 = step256 s39 0x92722c85 w39
        s41 = step256 s40 0xa2bfe8a1 w40
        s42 = step256 s41 0xa81a664b w41
        s43 = step256 s42 0xc24b8b70 w42
        s44 = step256 s43 0xc76c51a3 w43
        s45 = step256 s44 0xd192e819 w44
        s46 = step256 s45 0xd6990624 w45
        s47 = step256 s46 0xf40e3585 w46
        s48 = step256 s47 0x106aa070 w47
        s49 = step256 s48 0x19a4c116 w48
        s50 = step256 s49 0x1e376c08 w49
        s51 = step256 s50 0x2748774c w50
        s52 = step256 s51 0x34b0bcb5 w51
        s53 = step256 s52 0x391c0cb3 w52
        s54 = step256 s53 0x4ed8aa4a w53
        s55 = step256 s54 0x5b9cca4f w54
        s56 = step256 s55 0x682e6ff3 w55
        s57 = step256 s56 0x748f82ee w56
        s58 = step256 s57 0x78a5636f w57
        s59 = step256 s58 0x84c87814 w58
        s60 = step256 s59 0x8cc70208 w59
        s61 = step256 s60 0x90befffa w60
        s62 = step256 s61 0xa4506ceb w61
        s63 = step256 s62 0xbef9a3f7 w62
        s64 = step256 s63 0xc67178f2 w63
        SHA256S a64 b64 c64 d64 e64 f64 g64 h64 = s64
      in SHA256S (a00 + a64) (b00 + b64) (c00 + c64) (d00 + d64)
                 (e00 + e64) (f00 + f64) (g00 + g64) (h00 + h64)
  
  {-# INLINE step256 #-}
  step256 :: SHA256State -> Word32 -> Word32 -> SHA256State
  step256 !(SHA256S a b c d e f g h) k w = SHA256S a' b' c' d' e' f' g' h'
   where
    t1 = h + bsig256_1 e + ch e f g + k + w
    t2 = bsig256_0 a + maj a b c
    h' = g
    g' = f
    f' = e
    e' = d + t1
    d' = c
    c' = b
    b' = a
    a' = t1 + t2
  
  processSHA512Block :: SHA512State -> SHA512Block -> SHA512State
  processSHA512Block !s00@(SHA512S a00 b00 c00 d00 e00 f00 g00 h00) !blk =
    let (SHA512Sched w00 w01 w02 w03 w04 w05 w06 w07 w08 w09
                 w10 w11 w12 w13 w14 w15 w16 w17 w18 w19
                 w20 w21 w22 w23 w24 w25 w26 w27 w28 w29
                 w30 w31 w32 w33 w34 w35 w36 w37 w38 w39
                 w40 w41 w42 w43 w44 w45 w46 w47 w48 w49
                 w50 w51 w52 w53 w54 w55 w56 w57 w58 w59
                 w60 w61 w62 w63 w64 w65 w66 w67 w68 w69
                 w70 w71 w72 w73 w74 w75 w76 w77 w78 w79) = getSHA512Sched blk
        s01 = step512 s00 0x428a2f98d728ae22 w00
        s02 = step512 s01 0x7137449123ef65cd w01
        s03 = step512 s02 0xb5c0fbcfec4d3b2f w02
        s04 = step512 s03 0xe9b5dba58189dbbc w03
        s05 = step512 s04 0x3956c25bf348b538 w04
        s06 = step512 s05 0x59f111f1b605d019 w05
        s07 = step512 s06 0x923f82a4af194f9b w06
        s08 = step512 s07 0xab1c5ed5da6d8118 w07
        s09 = step512 s08 0xd807aa98a3030242 w08
        s10 = step512 s09 0x12835b0145706fbe w09
        s11 = step512 s10 0x243185be4ee4b28c w10
        s12 = step512 s11 0x550c7dc3d5ffb4e2 w11
        s13 = step512 s12 0x72be5d74f27b896f w12
        s14 = step512 s13 0x80deb1fe3b1696b1 w13
        s15 = step512 s14 0x9bdc06a725c71235 w14
        s16 = step512 s15 0xc19bf174cf692694 w15
        s17 = step512 s16 0xe49b69c19ef14ad2 w16
        s18 = step512 s17 0xefbe4786384f25e3 w17
        s19 = step512 s18 0x0fc19dc68b8cd5b5 w18
        s20 = step512 s19 0x240ca1cc77ac9c65 w19
        s21 = step512 s20 0x2de92c6f592b0275 w20
        s22 = step512 s21 0x4a7484aa6ea6e483 w21
        s23 = step512 s22 0x5cb0a9dcbd41fbd4 w22
        s24 = step512 s23 0x76f988da831153b5 w23
        s25 = step512 s24 0x983e5152ee66dfab w24
        s26 = step512 s25 0xa831c66d2db43210 w25
        s27 = step512 s26 0xb00327c898fb213f w26
        s28 = step512 s27 0xbf597fc7beef0ee4 w27
        s29 = step512 s28 0xc6e00bf33da88fc2 w28
        s30 = step512 s29 0xd5a79147930aa725 w29
        s31 = step512 s30 0x06ca6351e003826f w30
        s32 = step512 s31 0x142929670a0e6e70 w31
        s33 = step512 s32 0x27b70a8546d22ffc w32
        s34 = step512 s33 0x2e1b21385c26c926 w33
        s35 = step512 s34 0x4d2c6dfc5ac42aed w34
        s36 = step512 s35 0x53380d139d95b3df w35
        s37 = step512 s36 0x650a73548baf63de w36
        s38 = step512 s37 0x766a0abb3c77b2a8 w37
        s39 = step512 s38 0x81c2c92e47edaee6 w38
        s40 = step512 s39 0x92722c851482353b w39
        s41 = step512 s40 0xa2bfe8a14cf10364 w40
        s42 = step512 s41 0xa81a664bbc423001 w41
        s43 = step512 s42 0xc24b8b70d0f89791 w42
        s44 = step512 s43 0xc76c51a30654be30 w43
        s45 = step512 s44 0xd192e819d6ef5218 w44
        s46 = step512 s45 0xd69906245565a910 w45
        s47 = step512 s46 0xf40e35855771202a w46
        s48 = step512 s47 0x106aa07032bbd1b8 w47
        s49 = step512 s48 0x19a4c116b8d2d0c8 w48
        s50 = step512 s49 0x1e376c085141ab53 w49
        s51 = step512 s50 0x2748774cdf8eeb99 w50
        s52 = step512 s51 0x34b0bcb5e19b48a8 w51
        s53 = step512 s52 0x391c0cb3c5c95a63 w52
        s54 = step512 s53 0x4ed8aa4ae3418acb w53
        s55 = step512 s54 0x5b9cca4f7763e373 w54
        s56 = step512 s55 0x682e6ff3d6b2b8a3 w55
        s57 = step512 s56 0x748f82ee5defb2fc w56
        s58 = step512 s57 0x78a5636f43172f60 w57
        s59 = step512 s58 0x84c87814a1f0ab72 w58
        s60 = step512 s59 0x8cc702081a6439ec w59
        s61 = step512 s60 0x90befffa23631e28 w60
        s62 = step512 s61 0xa4506cebde82bde9 w61
        s63 = step512 s62 0xbef9a3f7b2c67915 w62
        s64 = step512 s63 0xc67178f2e372532b w63
        s65 = step512 s64 0xca273eceea26619c w64
        s66 = step512 s65 0xd186b8c721c0c207 w65
        s67 = step512 s66 0xeada7dd6cde0eb1e w66
        s68 = step512 s67 0xf57d4f7fee6ed178 w67
        s69 = step512 s68 0x06f067aa72176fba w68
        s70 = step512 s69 0x0a637dc5a2c898a6 w69
        s71 = step512 s70 0x113f9804bef90dae w70
        s72 = step512 s71 0x1b710b35131c471b w71
        s73 = step512 s72 0x28db77f523047d84 w72
        s74 = step512 s73 0x32caab7b40c72493 w73
        s75 = step512 s74 0x3c9ebe0a15c9bebc w74
        s76 = step512 s75 0x431d67c49c100d4c w75
        s77 = step512 s76 0x4cc5d4becb3e42b6 w76
        s78 = step512 s77 0x597f299cfc657e2a w77
        s79 = step512 s78 0x5fcb6fab3ad6faec w78
        s80 = step512 s79 0x6c44198c4a475817 w79
        SHA512S a80 b80 c80 d80 e80 f80 g80 h80 = s80
      in SHA512S (a00 + a80) (b00 + b80) (c00 + c80) (d00 + d80)
                 (e00 + e80) (f00 + f80) (g00 + g80) (h00 + h80)
  
  {-# INLINE step512 #-}
  step512 :: SHA512State -> Word64 -> Word64 -> SHA512State
  step512 !(SHA512S a b c d e f g h) k w = SHA512S a' b' c' d' e' f' g' h'
   where
    t1 = h + bsig512_1 e + ch e f g + k + w
    t2 = bsig512_0 a + maj a b c
    h' = g
    g' = f
    f' = e
    e' = d + t1
    d' = c
    c' = b
    b' = a
    a' = t1 + t2
  