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.
Comments
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.