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Generating high performance pruned FFT implementations

We derive a recursive general-radix pruned Cooley-Tukey fast Fourier transform (FFT) algorithm in Kronecker product notation. The algorithm is compatible with vectorization and parallelization required on state-of-the-art multicore CPUs. We include the pruned FFT algorithm into the program generation system Spiral, and automatically generate optimized implementations of the pruned FFT for the Intel Core2Duo multicore processor. Experimental results show that using the pruned FFT can indeed speed up the fastest available FFT implementations by up to 30% when the problem size and the pattern of unused inputs and outputs are known in advance.