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Overcoming the memory wall in symbolic algebra: a faster permutation multiplication

Authors:

Gene Cooperman,

Xiaoqin MaAuthors Info & Claims

ACM SIGSAM Bulletin, Volume 36, Issue 4

Pages 1 - 4

https://doi.org/10.1145/641239.641241

Published: 01 December 2002 Publication History

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Abstract

The traditional permutation multiplication algorithm is now limited by memory latency and not by CPU speed. A new cache-aware permutation algorithm speeds up permutation multiplication by a factor of 3.4 on current CPUs. The new algorithm is limited by memory bandwidth, but not by memory latency. Current trends indicate improving memory bandwidth and stagnant memory latency. This makes the new algorithm especially important for future computer architectures. In addition, we believe this "memory wall" will soon force a redesign of other common algorithms of symbolic algebra.

References

[1]

Intel PC SDRAM Specification, Revision 1.7, November 1999. http://www.intel.com/technology/memory/pc133sdram/spec/sdram133.htm

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[2]

G. Cooperman and V. Grinberg, "Scalable Parallel Coset Enumeration: Bulk Definition and the Memory Wall", J. Symbolic Computation33, pp. 563--585.

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[3]

W.A. Wulf and S.A. McKee. Hitting the memory wall: Implications of the obvious. ACM Computer Architecture News, 23(1):20--24, 1995.

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Slavici VDong XKunkle DCooperman GKoepf W(2010)Fast multiplication of large permutations for disk, flash memory and RAMProceedings of the 2010 International Symposium on Symbolic and Algebraic Computation10.1145/1837934.1838001(355-362)Online publication date: 25-Jul-2010
https://dl.acm.org/doi/10.1145/1837934.1838001
Cooperman GRobinson EHong H(2003)Memory-based and disk-based algorithms for very high degree permutation groupsProceedings of the 2003 international symposium on Symbolic and algebraic computation10.1145/860854.860877(66-73)Online publication date: 3-Aug-2003
https://dl.acm.org/doi/10.1145/860854.860877
Wang YKaeli DBanerjee UGallivan KGonzalez A(2003)Profile-guided I/O partitioningProceedings of the 17th annual international conference on Supercomputing10.1145/782814.782850(252-260)Online publication date: 23-Jun-2003
https://dl.acm.org/doi/10.1145/782814.782850

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Published In

ACM SIGSAM Bulletin Volume 36, Issue 4

December 2002

32 pages

ISSN:0163-5824

DOI:10.1145/641239

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Association for Computing Machinery

New York, NY, United States

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Published: 01 December 2002

Published in SIGSAM Volume 36, Issue 4

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Slavici VDong XKunkle DCooperman GKoepf W(2010)Fast multiplication of large permutations for disk, flash memory and RAMProceedings of the 2010 International Symposium on Symbolic and Algebraic Computation10.1145/1837934.1838001(355-362)Online publication date: 25-Jul-2010
https://dl.acm.org/doi/10.1145/1837934.1838001
Cooperman GRobinson EHong H(2003)Memory-based and disk-based algorithms for very high degree permutation groupsProceedings of the 2003 international symposium on Symbolic and algebraic computation10.1145/860854.860877(66-73)Online publication date: 3-Aug-2003
https://dl.acm.org/doi/10.1145/860854.860877
Wang YKaeli DBanerjee UGallivan KGonzalez A(2003)Profile-guided I/O partitioningProceedings of the 17th annual international conference on Supercomputing10.1145/782814.782850(252-260)Online publication date: 23-Jun-2003
https://dl.acm.org/doi/10.1145/782814.782850

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