Infinite loop while adding two integers using bitwise operations in Python 3 -

i trying solve question writing python code adding 2 integers without use of '+' or '-' operators. have following code works 2 positive numbers:

def getsum(self, a, b):      while (a & b):         x = & b         y = ^ b         = x << 1         b = y      return ^ b 

this piece of code works if input 2 positive integers or 2 negative integers fails when 1 number positive , other negative. goes infinite loop. idea why might happening ?

python 3 has arbitrary-precision integers ("bignums"). means anytime x negative, x << 1 make x negative number twice magnitude. zeros shifting in right push number larger , larger.

in two's complement, positive numbers have 0 in highest bit , negative numbers have 1 in highest bit. means that, when 1 of a , b negative, top bits of a , b differ. therefore, x positive (1 & 0 = 0) , y negative (1 ^ 0 = 1). new a positive (x<<1) , new b negative (y).

now: arbitrary-precision negative integers have infinite number of leading 1 bits, @ least mathematicallly. a larger , larger positive number, expanding 2 each iteration. b keeps getting more , more leading 1 bits added able carry out bitwise & , ^ a. whatever bits of a turned on line 1 of added 1 bits of b, a & b true, loop runs forever.