Prime factor FFT for modern computers

In the paper construction of efficient prime factor FFT algorithms for computers with hierarchical memory and possibly more than one processor is addressed. Accordingly to observations done for FFTW, FFTs constructed of 32-point or similar-sized butterflies are the best, hence, it is postulated to implement highly efficient 15-, 31-, and 63-point DFT algorithms for the prime factor FFTs. The novel form of arithmetical complexity criterion is proposed, and applied in optimization of small-N DFT modules. The data transfer count analysis show that prime factor FFTs are much better from this point of view than common factor FFTs. It is then shown that indeed, prime factor FFTs containing 15-point, and especially 63-point modules may easily outperform FFTs for data sizes being powers of number 2.