Relating FFTW and Split-Radix
Relating FFTW and Split-Radix. Proc. of ICESS'04, the First International Conference on Embedded Software and System, December 9-10 2004, Hangzhou (Zhejiang), China.
This ongoing attempt to reproduce an efficient implementation of FFT using staging and abstract interpretation attempts to answer the question "How can we get the raw performance of hardware without giving up the expressivity and clarity of software?"
Here's how Oleg describes the contribution of this paper,
One may think that generating truly optimal power-of-two FFT is straightforward: we generate the naive radix-2 FFT code, and then optimize it, removing trivial multiplications (x*1), trivial additions (x+0), etc. That was the approach demonstrated previously.
Oleg points out that the point isn't that they managed to reproduced the FFTW results. The crucial point is that we know exactly which identities (i.e., axioms) contributed to the optimum. The search was principled rather heuristic, and the code is generated in only one pass. There are no manipulations on the code: it is generated just right.
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