Abstract
Recent work showed that staging and abstract interpretation can be used to derive correct families of combinatorial circuits, and illustrated this technique with an in-depth analysis of the Fast Fourier Transform (FFT) for sizes 2n. While the quality of the generated code was promising, it used more floating-point operations than the well-known FFTW codelets and split-radix algorithm. This paper shows that staging and abstract interpretation can in fact be used to produce circuits with the same number of floating-point operations as each of split-radix and FFTW. In addition, choosing between two standard implementations of complex multiplication produces results that match each of the two algorithms. Thus, we provide a constructive method for deriving the two distinct algorithms.
Supported by NSF ITR-0113569 “Putting Multi-stage Annotations to Work” and Texas ATP 003604-0032-2003 “Advanced Languages Techniques for Device Drivers.”
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Kiselyov, O., Taha, W. (2005). Relating FFTW and Split-Radix. In: Wu, Z., Chen, C., Guo, M., Bu, J. (eds) Embedded Software and Systems. ICESS 2004. Lecture Notes in Computer Science, vol 3605. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11535409_71
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DOI: https://doi.org/10.1007/11535409_71
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