signed_magnitude.py

from typing import Literal


def unsigned_to_bytes(num: int, byteorder: Literal['big', 'little'] = 'big') -> bytes:
    """
    convert an unsigned int to the least number of bytes as possible.
    """
    # (0).bit_length() == 0
    return num.to_bytes((num.bit_length() + 7) // 8 or 1, byteorder)


def int_to_signed_magnitude(num: int, byteorder: Literal['big', 'little'] = 'big') -> bytes:
    """
    encode a signed integer with the signed-magnitude format
    """
    negative: bool = num < 0
    octets: bytearray = bytearray(unsigned_to_bytes(-num if negative else num, byteorder))
    significant: int = 0 if byteorder == 'big' else -1  # index of the most significant byte in octets
    if octets[significant] & 0x80:
        if byteorder == 'big':
            octets[0:0] = b'\x00'  # insert at the beginning
        else:
            octets += b'\x00'  # insert at the end
    if negative:
        octets[significant] |= 0x80
    return octets


if __name__ == '__main__':
    # big endian
    assert int_to_signed_magnitude(-129) == bytes.fromhex('80 81')  # 1000 0000 1000 0001
    assert int_to_signed_magnitude(-128) == bytes.fromhex('80 80')  # 1000 0000 1000 0000
    assert int_to_signed_magnitude(-127) == bytes.fromhex('ff')  # 1111 1111
    assert int_to_signed_magnitude(-1) == bytes.fromhex('81')  # 1000 0001
    assert int_to_signed_magnitude(0) == bytes.fromhex('00')  # 0000 0000
    assert int_to_signed_magnitude(1) == bytes.fromhex('01')  # 0000 0001
    assert int_to_signed_magnitude(127) == bytes.fromhex('7f')  # 0111 1111
    assert int_to_signed_magnitude(128) == bytes.fromhex('00 80')  # 0000 0000 1000 0000
    assert int_to_signed_magnitude(129) == bytes.fromhex('00 81')  # 0000 0000 1000 0001
    # little endian
    assert int_to_signed_magnitude(-129, 'little') == bytes.fromhex('81 80')
    assert int_to_signed_magnitude(-128, 'little') == bytes.fromhex('80 80')
    assert int_to_signed_magnitude(-127, 'little') == bytes.fromhex('ff')
    assert int_to_signed_magnitude(-1, 'little') == bytes.fromhex('81')
    assert int_to_signed_magnitude(0, 'little') == bytes.fromhex('00')
    assert int_to_signed_magnitude(1, 'little') == bytes.fromhex('01')
    assert int_to_signed_magnitude(127, 'little') == bytes.fromhex('7f')
    assert int_to_signed_magnitude(128, 'little') == bytes.fromhex('80 00')
    assert int_to_signed_magnitude(129, 'little') == bytes.fromhex('81 00')