We blogAlternating without a branch
Suppose you want to achieve the effect of a variable repeatedly alternating between two values
(for example inside a loop) without using a branch. If the variables are just bit patterns such as integers or references (pointers) then you may use bitwise exclusive-or (exor) as follows, and eliminate the branch.
Of course, the exor of a and b can be precomputed outside the loop. This relies upon exor being not only commutative and associative, but also acting as its own inverse as follows.
Informally speaking, exor acts as its own inverse; it is both addition and subtraction in its domain.
Soon (after doing some real work) I will say how to alternate cyclically between three different values in a loop, without branching ... this is a little more amusing.