Question

For a FFT function I need to permutate or shuffle the elements within an array in a bit-reversed way. That’s a common task with FFTs because most power of two sized FFT functions either expect or return their data in a bit-reversed way.

E.g. assume that the array has 256 elements I’d like to swap each element with it’s bit-reversed pattern. Here are two examples (in binary):

Element 00000001b should be swapped with element 10000000b
Element 00010111b should be swapped with element 11101000b

and so on.

Any idea how to do this fast and more important: in-place?

I already have a function that does this swap. It’s not hard to write one. Since this is such a common operation in DSP I have the feeling that there are more clever ways to do it than my very naiive loop.

Language in question is C, but any language is fine.

Answer 1

To swap in place with a single pass, iterate once through all elements in increasing index. Perform a swap only if the index is less-than the reversed index — this will skip the double swap problem and also palindrome cases (elements 00000000b, 10000001b, 10100101b) which inverse to the same value and no swap is required.

// Let data[256] be your element array 
for (i=0; i<256; i++)
    j = bit_reverse(i);
    if (i < j)
    {
        swap(data[i],data[j]);
    }

The bit_reverse() can be using Nathaneil’s bit-operations trick.
The bit_reverse() will be called 256 times but the swap() will be called less than 128 times.