Cantor pairing function for three integers(negative allowed)

cantor.py

# https://www.vertexfragment.com/ramblings/cantor-szudzik-pairing-functions/
# https://stackoverflow.com/questions/38965931/hash-function-for-3-integers
# https://math.stackexchange.com/questions/222709/inverting-the-cantor-pairing-function

def normalize(x):
    # this function make cantor pairing function work for negative numbers
    return 2*x if (x>=0) else (-2*x-1)

def normalize_inv(x):
    return x//2 if (x % 2 == 0) else -(x+1)//2

def cantor(a, b):
    return (a+b)*(a+b+1)//2 + b

def cantor_inv(z):
    n = (-1+pow(1+8*z, 0.5))//2
    b = z - n*(n+1)//2
    a = n - b
    return a, b

if __name__ == "__main__":
    n = 3
    for a in range(-n, n+1):
        for b in range(-n, n+1):
            for c in range(-n, n+1):
                na = normalize(a)
                nb = normalize(b)
                nc = normalize(c)
                z = cantor(cantor(na, nb), nc)
                inab, inc = cantor_inv(z)
                ic = normalize_inv(inc)
                ina, inb = cantor_inv(inab)
                ia = normalize_inv(ina)
                ib = normalize_inv(inb)
                print(a, b, c, " -> ", z, " -> ", ia, ib, ic)
                print("===============")