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Spiral-generated modular FFT algorithms

Published: 21 July 2010 Publication History

Abstract

This paper presents an extension of the Spiral system to automatically generate and optimize FFT algorithms for the discrete Fourier transform over finite fields. The generated code is intended to support modular algorithms for multivariate polynomial computations in the modpn library used by Maple. The resulting code provides an order of magnitude speedup over the original implementations in the modpn library, and the Spiral system provides the ability to automatically tune the FFT code to different computing platforms.

References

[1]
{FLMS06} A. Filatei, X. Li, M. Moreno Maza, and É. Schost. Implementation techniques for fast polynomial arithmetic in a high-level programming environment. In Proc. ISSAC'06, pp 93--100, New York, NY, USA, 2006. ACM Press.
[2]
{FVP06} Franz Franchetti, Yevgen Voronenko and Markus Püschel, "FFT Program Generation for Shared Memory: SMP and Multicore," Proc. Supercomputing (SC), 2006.
[3]
{FVP08} Franz Franchetti, Yevgen Voronenko and Markus Püschel, "A Rewriting System for the Vectorization of Signal Transforms," Proc. High Performance Computing for Computational Science (VECPAR), Lecture Notes in Computer Science, Springer, Vol. 4395, pp. 363--377, 2006.
[4]
{LM06} X. Li and M. Moreno Maza. Efficient implementation of polynomial arithmetic in a multiple-level programming environment. In A. Iglesias and N. Takayama, editors, Proc. International Congress of Mathematical Software - ICMS 2006, pp 12--23. Springer, 2006.
[5]
{LMP09} Xin Li, Marc Moreno Maza, and Wei Pan. Computations modulo regular chains. In ISSAC '09: Proceedings of the 2009 international symposium on Symbolic and algebraic computation, pp 239--246, New York, NY, USA, 2009. ACM.
[6]
{Mont85} P. L. Montgomery. Modular Multiplication Without Trial Division. Mathematics of Computation, vol. 44, no. 170, pp. 519--521, 1985.
[7]
{PMJ05} Markus Püschel, José M. F. Moura, Jeremy Johnson, David Padua, Manuela Veloso, Bryan Singer, Jianxin Xiong, Franz Franchetti, Aca Gacic, Yevgen Voronenko, Kang Chen, Robert W. Johnson, and Nick Rizzolo SPIRAL: Code Generation for DSP Transforms Proceedings of the IEEE special issue on "Program Generation, Optimization, and Adaptation," Vol. 93, No. 2, 2005, pp. 232--275.
[8]
{www.spiral.net} Spiral project website. http://www.spiral.net, 2010.

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  • (2024)SZKP: A Scalable Accelerator Architecture for Zero-Knowledge ProofsProceedings of the 2024 International Conference on Parallel Architectures and Compilation Techniques10.1145/3656019.3676898(271-283)Online publication date: 14-Oct-2024
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  • (2023)Generating High-Performance Number Theoretic Transform Implementations for Vector Architectures2023 IEEE High Performance Extreme Computing Conference (HPEC)10.1109/HPEC58863.2023.10363559(1-7)Online publication date: 25-Sep-2023
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cover image ACM Other conferences
PASCO '10: Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
July 2010
192 pages
ISBN:9781450300674
DOI:10.1145/1837210
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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  • Grenoble University: Grenoble University
  • Grenoble INP / ENSIMAG
  • INRIA: Institut Natl de Recherche en Info et en Automatique

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 21 July 2010

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Author Tags

  1. FFT
  2. autotuning
  3. code generation
  4. high performance computing
  5. modular arithmetic
  6. vectorization

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PASCO '10
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  • Grenoble University
  • INRIA

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Cited By

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  • (2024)SZKP: A Scalable Accelerator Architecture for Zero-Knowledge ProofsProceedings of the 2024 International Conference on Parallel Architectures and Compilation Techniques10.1145/3656019.3676898(271-283)Online publication date: 14-Oct-2024
  • (2023)RPU: The Ring Processing Unit2023 IEEE International Symposium on Performance Analysis of Systems and Software (ISPASS)10.1109/ISPASS57527.2023.00034(272-282)Online publication date: Apr-2023
  • (2023)Generating High-Performance Number Theoretic Transform Implementations for Vector Architectures2023 IEEE High Performance Extreme Computing Conference (HPEC)10.1109/HPEC58863.2023.10363559(1-7)Online publication date: 25-Sep-2023
  • (2022)An Implementation of Parallel Number-Theoretic Transform Using Intel AVX-512 InstructionsComputer Algebra in Scientific Computing10.1007/978-3-031-14788-3_18(318-332)Online publication date: 22-Aug-2022
  • (2020)Fast Multiple Montgomery Multiplications Using Intel AVX-512IFMA InstructionsComputational Science and Its Applications – ICCSA 202010.1007/978-3-030-58814-4_52(655-663)Online publication date: 1-Jul-2020
  • (2019)Big Prime Field FFT on Multi-core ProcessorsProceedings of the 2019 International Symposium on Symbolic and Algebraic Computation10.1145/3326229.3326273(106-113)Online publication date: 8-Jul-2019
  • (2018)SPIRAL: Extreme Performance PortabilityProceedings of the IEEE10.1109/JPROC.2018.2873289106:11(1935-1968)Online publication date: Nov-2018
  • (2018)Twin-SSB-OFDM Transmission Over Heterodyne W-Band Fiber-Wireless System With Real-Time Implementable Blind Carrier RecoveryJournal of Lightwave Technology10.1109/JLT.2018.287636836:23(5562-5572)Online publication date: 1-Dec-2018
  • (2017)Low communication FMM-accelerated FFT on GPUsProceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis10.1145/3126908.3126919(1-11)Online publication date: 12-Nov-2017
  • (2017)Fast, Dense Feature SDM on an iPhone2017 12th IEEE International Conference on Automatic Face & Gesture Recognition (FG 2017)10.1109/FG.2017.21(95-102)Online publication date: 30-May-2017
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