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High-performance implementation of the level-3 BLAS

Published: 25 July 2008 Publication History

Abstract

A simple but highly effective approach for transforming high-performance implementations on cache-based architectures of matrix-matrix multiplication into implementations of other commonly used matrix-matrix computations (the level-3 BLAS) is presented. Exceptional performance is demonstrated on various architectures.

References

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Bientinesi, P. and van de Geijn, R. 2006. Representing dense linear algebra algorithms: A farewell to indices. FLAME Working Note #17 TR-2006-10, Department of Computer Sciences, The University of Texas at Austin.
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Dongarra, J. J., Du Croz, J., Hammarling, S., and Duff, I. 1990. A set of level 3 basic linear algebra subprograms. ACM Trans. Math. Softw. 16, 1, 1--17.
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Elmroth, E., Gustavson, F., Jonsson, I., and Kågström, B. 2004. Recursive blocked algorithms and hybrid data structures for dense matrix library software. SIAM Rev. 46, 1, 3--45.
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Goto, K. and van de Geijn, R. A. 2008. Anatomy of a high-performance matrix multiplication. ACM Trans. Math. Softw. 34, 3.
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Gunnels, J. A., Gustavson, F. G., Henry, G. M., and van de Geijn, R. A. 2001. FLAME: Formal linear algebra methods environment. ACM Trans. Math. Softw. 27, 4, 422--455.
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Kågström, B., Ling, P., and Loan, C. V. 1998. GEMM-based level 3 BLAS: High performance model implementations and performance evaluation benchmark. ACM Trans. Math. Softw. 24, 3, 268--302.
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Marker, B., Van Zee, F. G., Goto, K., Quintana-Ortí, G., and van de Geijn, R. A. 2007. Toward scalable matrix multiply on multithreaded architectures. In Proceedings of the International Euro-Par Conference. A.-M. Kermarrec, L. Bougé, and T. Priol, Eds. Lecture Notes on Computer Science, vol. 4641. 748--757.
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  • (2024)Detailed Analysis and Optimization of Irregular-Shaped Matrix Multiplication on Multi-Core DSPsProceedings of the 53rd International Conference on Parallel Processing10.1145/3673038.3673101(1176-1186)Online publication date: 12-Aug-2024
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  • (2024)Optimizing Full-Spectrum Matrix Multiplications on ARMv8 Multi-Core CPUsIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2024.335036835:3(439-454)Online publication date: Mar-2024
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    Published In

    cover image ACM Transactions on Mathematical Software
    ACM Transactions on Mathematical Software  Volume 35, Issue 1
    July 2008
    136 pages
    ISSN:0098-3500
    EISSN:1557-7295
    DOI:10.1145/1377603
    Issue’s Table of Contents
    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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    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 25 July 2008
    Accepted: 01 October 2007
    Revised: 01 April 2007
    Received: 01 May 2006
    Published in TOMS Volume 35, Issue 1

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    Author Tags

    1. Linear algebra
    2. basic linear algebra subprograms
    3. libraries
    4. matrix-matrix operations

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    Cited By

    View all
    • (2024)Detailed Analysis and Optimization of Irregular-Shaped Matrix Multiplication on Multi-Core DSPsProceedings of the 53rd International Conference on Parallel Processing10.1145/3673038.3673101(1176-1186)Online publication date: 12-Aug-2024
    • (2024)IrGEMM: An Input-Aware Tuning Framework for Irregular GEMM on ARM and X86 CPUsIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2024.343257935:9(1672-1689)Online publication date: 1-Sep-2024
    • (2024)Optimizing Full-Spectrum Matrix Multiplications on ARMv8 Multi-Core CPUsIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2024.335036835:3(439-454)Online publication date: Mar-2024
    • (2024)Optimizing General Matrix Multiplications on Modern Multi-core DSPs2024 IEEE International Parallel and Distributed Processing Symposium (IPDPS)10.1109/IPDPS57955.2024.00090(964-975)Online publication date: 27-May-2024
    • (2024)Uncut-GEMMs: Communication-Aware Matrix Multiplication on Multi-GPU Nodes2024 IEEE International Conference on Cluster Computing (CLUSTER)10.1109/CLUSTER59578.2024.00020(143-154)Online publication date: 24-Sep-2024
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    • (2024)Automatic generation of ARM NEON micro-kernels for matrix multiplicationThe Journal of Supercomputing10.1007/s11227-024-05955-880:10(13873-13899)Online publication date: 1-Jul-2024
    • (2023)A parallel numerical algorithm by combining MPI and OpenMP programming models with applications in gravity field recoveryFrontiers in Earth Science10.3389/feart.2023.108087911Online publication date: 23-Mar-2023
    • (2023)To Pack or Not to Pack: A Generalized Packing Analysis and TransformationProceedings of the 21st ACM/IEEE International Symposium on Code Generation and Optimization10.1145/3579990.3580024(14-27)Online publication date: 17-Feb-2023
    • (2023)Towards a Unified Implementation of GEMM in BLISProceedings of the 37th International Conference on Supercomputing10.1145/3577193.3593707(111-121)Online publication date: 21-Jun-2023
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