# SHA-512 pure Python for MicroPython
# Based on public domain implementation
# Compact version optimized for MicroPython memory constraints

_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,
]

_M64 = 0xffffffffffffffff

def _rotr64(x, n):
    return ((x >> n) | (x << (64 - n))) & _M64

def _sha512_compress(state, block):
    w = list(block)
    for i in range(16, 80):
        s0 = _rotr64(w[i-15], 1) ^ _rotr64(w[i-15], 8) ^ (w[i-15] >> 7)
        s1 = _rotr64(w[i-2], 19) ^ _rotr64(w[i-2], 61) ^ (w[i-2] >> 6)
        w.append((w[i-16] + s0 + w[i-7] + s1) & _M64)

    a, b, c, d, e, f, g, h = state

    for i in range(80):
        S1   = _rotr64(e, 14) ^ _rotr64(e, 18) ^ _rotr64(e, 41)
        ch   = (e & f) ^ ((~e & _M64) & g)
        temp1 = (h + S1 + ch + _K[i] + w[i]) & _M64
        S0   = _rotr64(a, 28) ^ _rotr64(a, 34) ^ _rotr64(a, 39)
        maj  = (a & b) ^ (a & c) ^ (b & c)
        temp2 = (S0 + maj) & _M64

        h = g; g = f; f = e
        e = (d + temp1) & _M64
        d = c; c = b; b = a
        a = (temp1 + temp2) & _M64

    return [
        (state[0] + a) & _M64, (state[1] + b) & _M64,
        (state[2] + c) & _M64, (state[3] + d) & _M64,
        (state[4] + e) & _M64, (state[5] + f) & _M64,
        (state[6] + g) & _M64, (state[7] + h) & _M64,
    ]

def sha512(data: bytes) -> bytes:
    # Initial hash values
    state = [
        0x6a09e667f3bcc908, 0xbb67ae8584caa73b,
        0x3c6ef372fe94f82b, 0xa54ff53a5f1d36f1,
        0x510e527fade682d1, 0x9b05688c2b3e6c1f,
        0x1f83d9abfb41bd6b, 0x5be0cd19137e2179,
    ]

    msg    = bytearray(data)
    length = len(data) * 8
    msg.append(0x80)
    while len(msg) % 128 != 112:
        msg.append(0x00)
    # Append length as 128-bit big-endian (high 64 bits are 0)
    msg += (0).to_bytes(8, 'big')
    msg += length.to_bytes(8, 'big')

    for i in range(0, len(msg), 128):
        block = []
        for j in range(0, 128, 8):
            block.append(int.from_bytes(msg[i+j:i+j+8], 'big'))
        state = _sha512_compress(state, block)

    return b''.join(s.to_bytes(8, 'big') for s in state)