Faster algorithm to find unique element between two arrays?

Question

EDIT: For anyone new to this question, I have posted an answer clarifying what was going on. The accepted answer is the one I feel best answers my question

Answer 1

Caution, it is wrong to use the O(n + m) notation. There is but one size parameter which is n (in the asymptotic sense, n and n+1 are equal). You should just say O(n). [For m > n+1, the problem is different and more challenging.]

As pointed by others, this is optimal as you must read all values.

All you can do is reducing the asymptotic constant. There is little room for improvement, as the obvious solutions are already very efficient. The single loop in (10) is probably hard to beat. Unrolling it a bit should improve (slightly) by avoiding a branch.

If your goal is sheer performance, than you should turn to non-portable solutions such as vectorization (using the AXV instructions, 8 ints at a time) and parallelization on multicores or GPGPU. In good old dirty C and a 64 bits processor, you could map the data to an array of 64 bit ints and xor the elements two pairs at a time ;)