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Automatic Parallel Library Generation for General-Size Modular FFT Algorithms

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8136)

Abstract

This paper presents the automatic library generation for modular FFT algorithms with arbitrary input sizes. We show how to represent the transform and its algorithms at a high abstraction level. Symbolic manipulations and code optimizations that use rewriting systems can then be systematically applied to generate a library with recursive function closure. The generated library is automatically optimized for the target computing platforms, and is intended to support modular algorithms for multivariate polynomial computations in the modpn library used by modpn. The resulting scalar and vector codes provide comparable speedup to the fixed-size code presented in [LJF10], which is an order of magnitude faster over the hand-tuned modpn library. Thread-level parallelism has also been utilized by the generated library and delivers additional speedup.

Keywords

  • FFT
  • modular arithmetic
  • library generation
  • parallelization
  • autotuning

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Meng, L., Johnson, J. (2013). Automatic Parallel Library Generation for General-Size Modular FFT Algorithms. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2013. Lecture Notes in Computer Science, vol 8136. Springer, Cham. https://doi.org/10.1007/978-3-319-02297-0_21

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  • DOI: https://doi.org/10.1007/978-3-319-02297-0_21

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02296-3

  • Online ISBN: 978-3-319-02297-0

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