Bit-reversal permutation

Summary

In applied mathematics, a bit-reversal permutation is a permutation of a sequence of $n$ items, where $n=2^k$ is a power of two. It is defined by indexing the elements of the sequence by the numbers from $0$ to $n-1$, representing each of these numbers by its binary representation (padded to have length exactly $k$), and mapping each item to the item whose representation has the same bits in the reversed order.