Please have a look in the thread Minimum CUDA requirement for GFN. Iain explained the "z-transform".
____________
Best wishes. Knowledge is power. by jjwhalen

I called this new algorithm the "z-Transform" because of Georg Bruun paper:
z-Transform DFT Filters and FFT's, IEEE Trans. ASSP, ASSP-26, No. 1, February 1978.
http://orbit.dtu.dk/fedora/objects/orbit:20643/datastreams/file_4658740/content

If you have a look at Figure 4, you see that we can use half a FFT to "filter" with the z-transfer function z^-N/2 - 1. Because (z^-N - 1) / (z^-N/2 - 1) = z^-N/2 + 1, we compute modulo a GF polynomial.

That is faster than the DWT that was used in the previous versions of genefer:
http://www.ams.org/journals/mcom/1994-62-205/S0025-5718-1994-1185244-1/S0025-5718-1994-1185244-1.pdf
http://www.ams.org/journals/mcom/2002-71-238/S0025-5718-01-01350-3/S0025-5718-01-01350-3.pdf

This is not really "new math" but it is a new algorithm.

Note that the chapter VI of Bruun's paper is known as Bruun's FFT
http://en.wikipedia.org/wiki/Bruun's_FFT_algorithm
It is twice as fast as the complex z-Transform (for real data) but rouding error increases quickly with FFT size. Because of this inaccurate numerical precision, it cannot be used with 64-bit floating point type for GF test.

Yves

Will it have an effect on the search for GFPs of higher N/B values? How much faster is it?