[mgraczyk]

The author seems to misunderstand the idea of asymptotic complexity. All of the reversal operations are O(1) because the number of bits being flipped is a constant. If he were concerned with flipping the bits in an arbitrary precision number, then his different solutions might deserve "Big-O" classifications.

Second point: The reason that the original solution is slow is because a mod operation by a number that is not a power of two involves a floating point divide, or several multiply accumulates at extended precision. Either of those two operations are slower than any of the other methods.