Bitreflecting

Bitreflecting is a term sometimes used in computer science and digital signal processing to describe the reversal of the order of bits within a byte or a larger binary word. For example, if a byte has the binary representation 10110010, its bit-reflected value would be 01001101. This operation is not a standard arithmetic or logical operation found in most processor instruction sets, but it is a fundamental component of certain algorithms.

The most common application of bit-reflecting is within the Fast Fourier Transform (FFT) algorithm, particularly the Cooley-Tukey radix-2 algorithm. In this context, bit-reflecting is used to reorder the input data points in a specific way before the main FFT computation begins. This reordering ensures that the data is arranged in the correct sequence for the butterfly operations that form the core of the FFT.

While not a direct processor instruction, bit-reflecting can be implemented efficiently in software using a combination of bitwise operations, shifts, and look-up tables. The specific implementation details can vary depending on the desired word size and performance requirements. Beyond FFT, bit-reflecting can also appear in other algorithms that rely on specific bit permutations, such as certain error correction codes or cryptographic functions.