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Four Easy Ways to a Faster FFT

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Journal of Mathematical Modelling and Algorithms

Abstract

The Fast Fourier Transform (FFT) was named one of the Top Ten algorithms of the 20th century , and continues to be a focus of current research. A problem with currently used FFT packages is that they require large, finely tuned, machine specific libraries, produced by highly skilled software developers. Therefore, these packages fail to perform well across a variety of architectures. Furthermore, many need to run repeated experiments in order to ‘re-program’ their code to its optimal performance based on a given machine's underlying hardware. Finally, it is difficult to know which radix to use given a particular vector size and machine configuration. We propose the use of monolithic array analysis as a way to remove the constraints imposed on performance by a machine's underlying hardware, by pre-optimizing array access patterns. In doing this we arrive at a single optimized program. We have achieved up to a 99.6% increase in performance, and the ability to run vectors up to 8 388 608 elements larger, on our experimental platforms. Preliminary experiments indicate different radices perform better relative to a machine's underlying architecture.

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Authors and Affiliations

  1. Computer Science Department, University at Albany, SUNY, Albany, NY, 12222, U.S.A.

    Lenore R. Mullin

  2. NY 12222, U.S.A.

    Sharon G. Small

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  1. Lenore R. Mullin
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Mullin, L.R., Small, S.G. Four Easy Ways to a Faster FFT. Journal of Mathematical Modelling and Algorithms 1, 193–214 (2002). https://doi.org/10.1023/A:1020590506372

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