#!/usr/bin/env python3

class Serial:

    modulus = 2 ** 32

    @property
    def bitmask(self):
        return self.modulus - 1

    @property
    def signbit(self):
        return self.modulus >> 1

    def __init__(self, val):
        self._val = int(val) & self.bitmask

    def __add__(self, val):
        return type(self)(self._val + int(val))

    def __le__(self, other):
        return (self.modulus - int(self) + int(other)) & self.signbit == 0

    def __ge__(self, other):
        return (self.modulus + int(self) - int(other)) & self.signbit == 0

    def __eq__(self, other):
        return int(self) == int(other)

    def __ne__(self, other):
        return int(self) != int(other)

    def __lt__(self, other):
        return self != other and self <= other

    def __gt__(self, other):
        return self != other and self >= other

    def __int__(self):
        return self._val

    def __str__(self):
        return f"{int(self):{len(str(self.modulus))}d}"

def step(start, finish):
    if start < finish:
        return start, finish
    else:
        midpoint = start + ((Serial.modulus >> 1) - 2)
        assert start < midpoint and midpoint < finish
        return start, midpoint, finish

if __name__ == "__main__":
    from random import randint

    for test in range(100):
        i1 = Serial(randint(0, Serial.modulus - 1))
        i2 = Serial(randint(0, Serial.modulus - 1))

        assert i1 == i2 or \
            (i1 < i2 and not (i1 > i2)) or \
            (i1 > i2 and not (i1 < i2)) or \
            int(i1) & int(i2) == Serial.modulus >> 1

        print(f"{i1} => {i2}: {', '.join(str(s) for s in step(i1, i2))}")