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Generating symmetric DFTs and equivariant FFT algorithms

Published: 29 July 2007 Publication History

Abstract

This paper presents a code generator which produces efficient implementations of multi-dimensional fast Fourier transform (FFT) algorithms which utilize symmetries in the input data to reduce memory usage and the number of arithmetic operations. The FFT algorithms are constructed using a group theoretic version of the divide and conquer step in the FFT that is compatible with the group of symmetries. The GAP compute algebra system is used to perform the necessary group computations and the generated algorithm is represented as a symbolic matrix factorization, which is translated into efficient code using the SPIRAL system. Performance data is given that shows that the resulting code is significantly faster than state-of-the-art FFT implementations that do not utilize the symmetries.

References

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Cited By

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  • (2020)Accelerated Pseudo-Spectral Method of Self-Consistent Field Theory via Crystallographic Fast Fourier TransformMacromolecules10.1021/acs.macromol.0c0197453:22(9943-9952)Online publication date: 13-Nov-2020
  • (2017)The Frobenius FFTProceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation10.1145/3087604.3087633(437-444)Online publication date: 23-Jul-2017
  • (2013)Structured FFT and TFTProceedings of the 38th International Symposium on Symbolic and Algebraic Computation10.1145/2465506.2465526(355-362)Online publication date: 26-Jun-2013
  • Show More Cited By

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cover image ACM Conferences
ISSAC '07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation
July 2007
406 pages
ISBN:9781595937438
DOI:10.1145/1277548
  • General Chair:
  • Dongming Wang
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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Publication History

Published: 29 July 2007

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Author Tags

  1. code generation
  2. fast Fourier transform
  3. group symmetries
  4. matrix factorization
  5. multi-dimensional discrete fourier transform

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ISSAC07
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ISSAC07: International Symposium on Symbolic and Algebraic Computation
July 29 - August 1, 2007
Ontario, Waterloo, Canada

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

View all
  • (2020)Accelerated Pseudo-Spectral Method of Self-Consistent Field Theory via Crystallographic Fast Fourier TransformMacromolecules10.1021/acs.macromol.0c0197453:22(9943-9952)Online publication date: 13-Nov-2020
  • (2017)The Frobenius FFTProceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation10.1145/3087604.3087633(437-444)Online publication date: 23-Jul-2017
  • (2013)Structured FFT and TFTProceedings of the 38th International Symposium on Symbolic and Algebraic Computation10.1145/2465506.2465526(355-362)Online publication date: 26-Jun-2013
  • (2011)Multidimensional DFT IP Generator for FPGA PlatformsIEEE Transactions on Circuits and Systems I: Regular Papers10.1109/TCSI.2010.207875058:4(755-764)Online publication date: Apr-2011

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