Infinite loop while adding two integers using bitwise operations?

Python 3 has arbitrary-precision integers ("bignums"). This means that anytime x is negative, x << 1 will make x a negative number with twice the magnitude. Zeros shifting in from the right will just push the number larger and larger.

In two's complement, positive numbers have a 0 in the highest bit and negative numbers have a 1 in the highest bit. That means that, when only one of a and b is negative, the top bits of a and b will differ. Therefore, x will be positive (1 & 0 = 0) and y will be negative (1 ^ 0 = 1). Thus the new a will be positive (x<<1) and the new b will be negative (y).

Now: arbitrary-precision negative integers actually have an infinite number of leading 1 bits, at least mathematicallly. So a is a larger and larger positive number, expanding by 2 each iteration. b keeps getting more and more leading 1 bits added to be able to carry out the bitwise & and ^ with a. Thus whatever bits of a are turned on line up with one of the added 1 bits of b, so a & b is always true, so the loop runs forever.