This doesn't work because you're not left-shifting (doubling) the carry. But when adding the shifted carry to (x ^ y) we're back to potentially overflowing the

This doesn't work because you're not left-shifting (doubling) the carry. But when adding the shifted carry to (x ^ y) we're back to potentially overflowing the highest bits. The solution is to add the highest and the lower bits separately: lower = 0x7f7f7f7f; highest = ~lower; z = ((x & lower) + (y & lower)) ^ ((x ^ y) & highest); Note this only improves performance for larger container integers.