QTIB: Quick bit-reversed permutations on CPUs

We present a fast algorithm for out-of-place bit-reversed permutation of large vectors for input to an FFT. It is an extension of two previously published methods with special consideration of advanced CPU hardware features. In particular, the method makes heavy use of cache prefetching, MMX and SSE units, and write-combining buffers. Implementations have been made in assembly language for 2-byte and 4-byte operands. In terms of efficiency the method significantly outperforms previously reported methods.

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