// Provided by @sdwelle as a performance regression in issue #269

module SHA512 where

/*
sha512 : {b, a} (a*1024 == 128 + b + 1 + 1024 - (b+129) % 1024,
                 a*1024 % 1024 == 0,
                 a * 1024 - b >= 129,
                 2^^128 - 1 >= b,
                 fin (a + 1)) => [b] -> [512]

                 */
sha512 M = result
  where
    M' = (pad M)
    blocks = (groupBy`{1024} M')
    hash = [H0] # [ processBlock b h | b <- blocks | h <- hash ]
    result = (join (hash!0))

processBlock : [1024] -> [8][64] -> [8][64]
processBlock block Hprev = Hs
  where
    Mi = split block : [16][64]
    Ws = (messageSch Mi)
    round = [Hprev] # [ (step r (Ws@t) t) | t <- [0..79] | r <- round ]
    Hs = [ (x + H) | x <- (round!0) | H <- Hprev ]

step : [8][64] -> [64] -> [8] -> [8][64]
step [a, b, c, d, e, f, g, h] Wt t = [a', b', c', d', e', f', g', h']
  where
    T1 = h + (SIGMA1 e) + (Ch e f g) + (K@t) + Wt
    T2 = (SIGMA0 a) + (Maj a b c)
    h' = g
    g' = f
    f' = e
    e' = d + T1
    d' = c
    c' = b
    b' = a
    a' = T1 + T2

messageSch : [16][64] -> [80][64]
messageSch Mi = W
  where
    W = Mi # [ (sigma1 (W@(t-2))) + (W@(t-7)) + (sigma0 (W@(t-15))) + (W@(t-16)) | t <- [16..79] ]

pad : {l, k} (fin l,
              l <= ((2^^128) - 1),
              l >= 0,
              fin k,
              k - l >= 129,
              k == 128 + l + 1 + 1024 - ((l+129)%1024),
              k%1024 == 0) => [l] -> [k]
pad M = M # (1:[1]) # (0:[k-128-l-1]) # (`l:[128])

Ch : [64] -> [64] -> [64] -> [64]
Ch x y z = (x && y) ^ ((~x) && z)

Maj : [64] -> [64] -> [64] -> [64]
Maj x y z = (x && y) ^ (x && z) ^ (y && z)

SIGMA0 : [64] -> [64]
SIGMA0 x = (x >>> 28) ^ (x >>> 34) ^ (x >>> 39)

SIGMA1 : [64] -> [64]
SIGMA1 x = (x >>> 14) ^ (x >>> 18) ^ (x >>> 41)

sigma0 : [64] -> [64]
sigma0 x = (x >>> 1) ^ (x >>> 8) ^ (x >> 7)

sigma1 : [64] -> [64]
sigma1 x = (x >>> 19) ^ (x >>> 61) ^ (x >> 6)

H0 = [ 0x6a09e667f3bcc908, 0xbb67ae8584caa73b, 0x3c6ef372fe94f82b, 0xa54ff53a5f1d36f1,
       0x510e527fade682d1, 0x9b05688c2b3e6c1f, 0x1f83d9abfb41bd6b, 0x5be0cd19137e2179 ]

K = [
0x428a2f98d728ae22, 0x7137449123ef65cd, 0xb5c0fbcfec4d3b2f, 0xe9b5dba58189dbbc,
0x3956c25bf348b538, 0x59f111f1b605d019, 0x923f82a4af194f9b, 0xab1c5ed5da6d8118,
0xd807aa98a3030242, 0x12835b0145706fbe, 0x243185be4ee4b28c, 0x550c7dc3d5ffb4e2,
0x72be5d74f27b896f, 0x80deb1fe3b1696b1, 0x9bdc06a725c71235, 0xc19bf174cf692694,
0xe49b69c19ef14ad2, 0xefbe4786384f25e3, 0x0fc19dc68b8cd5b5, 0x240ca1cc77ac9c65,
0x2de92c6f592b0275, 0x4a7484aa6ea6e483, 0x5cb0a9dcbd41fbd4, 0x76f988da831153b5,
0x983e5152ee66dfab, 0xa831c66d2db43210, 0xb00327c898fb213f, 0xbf597fc7beef0ee4,
0xc6e00bf33da88fc2, 0xd5a79147930aa725, 0x06ca6351e003826f, 0x142929670a0e6e70,
0x27b70a8546d22ffc, 0x2e1b21385c26c926, 0x4d2c6dfc5ac42aed, 0x53380d139d95b3df,
0x650a73548baf63de, 0x766a0abb3c77b2a8, 0x81c2c92e47edaee6, 0x92722c851482353b,
0xa2bfe8a14cf10364, 0xa81a664bbc423001, 0xc24b8b70d0f89791, 0xc76c51a30654be30,
0xd192e819d6ef5218, 0xd69906245565a910, 0xf40e35855771202a, 0x106aa07032bbd1b8,
0x19a4c116b8d2d0c8, 0x1e376c085141ab53, 0x2748774cdf8eeb99, 0x34b0bcb5e19b48a8,
0x391c0cb3c5c95a63, 0x4ed8aa4ae3418acb, 0x5b9cca4f7763e373, 0x682e6ff3d6b2b8a3,
0x748f82ee5defb2fc, 0x78a5636f43172f60, 0x84c87814a1f0ab72, 0x8cc702081a6439ec,
0x90befffa23631e28, 0xa4506cebde82bde9, 0xbef9a3f7b2c67915, 0xc67178f2e372532b,
0xca273eceea26619c, 0xd186b8c721c0c207, 0xeada7dd6cde0eb1e, 0xf57d4f7fee6ed178,
0x06f067aa72176fba, 0x0a637dc5a2c898a6, 0x113f9804bef90dae, 0x1b710b35131c471b,
0x28db77f523047d84, 0x32caab7b40c72493, 0x3c9ebe0a15c9bebc, 0x431d67c49c100d4c,
0x4cc5d4becb3e42b6, 0x597f299cfc657e2a, 0x5fcb6fab3ad6faec, 0x6c44198c4a475817
]


property testVector1 x = sha512 0xfd2203e467574e834ab07c9097ae164532f24be1eb5d88f1af7748ceff0d2c67a21f4e4097f9d3bb4e9fbf97186e0db6db0100230a52b453d421f8ab9c9a6043aa3295ea20d2f06a2f37470d8a99075f1b8a8336f6228cf08b5942fc1fb4299c7d2480e8e82bce175540bdfad7752bc95b577f229515394f3ae5cec870a4b2f8 == 0xa21b1077d52b27ac545af63b32746c6e3c51cb0cb9f281eb9f3580a6d4996d5c9917d2a6e484627a9d5a06fa1b25327a9d710e027387fc3e07d7c4d14c6086cc