1.4 As an alternative to the approach outlined in the preceding problem, we can use C's bitwise operators to implement the tree-structured global sum. In order to see how this works, it helps to write down the binary (base 2) representation of each of the core ranks, and note the pairings during each stage:
From the table we see that during the first stage each core is paired with the core whose rank differs in the rightmost or first bit. During the second stage cores that continue are paired with the core whose rank differs in the second bit, and during the third stage cores are paired with the core whose rank differs in the third bit. Thus, if we have a binary value bitmask that is 0012 for the first stage, 0102 for the second, and 1002 for the third, we can get the rank of the core we're paired with by "inverting" the bit in our rank that is nonzero in bitmask. This can be done using the bitwise exclusive or ^ operator. Implement this algorithm in pseudo-code using the bitwise exclusive or and the left-shift operator.