Szudzik pairing for negative numbers

pair.py

import math
from typing import Tuple

def pair_negative(x: int) -> int:
    return 2 * x if x >= 0 else -2 * x - 1

def unpair_negative(z: int) -> int:
    return int(z / 2) if z % 2 == 0 else int((z + 1) / -2)
    
def pair_szudzik(x: int, y: int) -> int:
    a, b = pair_negative(x), pair_negative(y) 
    return a ** 2 + a + b if a >= b else b ** 2 + a

def unpair_szudzik(index: int) -> Tuple[int, int]:
    sqrtz = math.floor(math.sqrt(index))
    sqz = sqrtz * sqrtz
    a, b = (sqrtz, index - sqz - sqrtz) if (index - sqz) >= sqrtz else (index - sqz, sqrtz)
    return unpair_negative(a), unpair_negative(b)