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FFT ALGORITHMS FOR MULTIPLY-ADD ARCHITECTURES

FFTs are the single most important algorithms in science and engineering. To utilize current hardware architectures, special techniques are needed. This paper introduces newly developed radix-2n FFT kernels that efficiently take advantage of fused multiply-add (FMA) instructions. If a processor is provided with FMA instructions, the new radix-2n kernels reduce the number of required twiddle factors from 2n − 1 to n compared to conventional radix-2n FFT kernels. The reduction in the number of twiddle factors is accomplished by a “hidden” computation of the twiddle factors (instead of accessing a twiddle factor array) by hiding the additional arithmetic operations in FMA instructions. The new FFT kernels are fully compatible with conventional FFT kernels and can therefore easily be incorporated into existing FFT software, such as Fftw or Spiral.