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Experiments in Parallel Matrix Multiplication on Multi-core Systems

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Algorithms and Architectures for Parallel Processing (ICA3PP 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7439))

Abstract

Matrix multiplication is an example of application that is both easy to specify and to provide a simple implementation. There exist numerous sophisticated algorithms or very efficient complex implementations. In this study we are rather interested in the design/programming overhead with respect to performance benefits. Starting from the naive sequential implementation, the implementation is first optimised by improving data accesses, then by using vector units of modern processors, and we finally propose a parallel version for multi-core architectures. The various proposed optimisations are experimented on several architectures and the trade-off software complexity versus efficiency is evaluated using Halstead metrics.

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References

  1. Albrecht, A.: Measuring Application Development Productivity. In: Press, I.B.M. (ed.) IBM Application Development Symp., pp. 83–92 (October 1979)

    Google Scholar 

  2. Cole, M.: Algorithmic Skeletons: Structured Management of Parallel Computation. MIT Press (1989), http://homepages.inf.ed.ac.uk/mic/Pubs

  3. Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation 9(3), 251–280 (1990), http://www.sciencedirect.com/science/article/pii/S0747717108800132

    Article  MathSciNet  MATH  Google Scholar 

  4. D’Alberto, P., Nicolau, A.: Adaptive strassen and atlas’s dgemm: A fast squarematrix multiply for modern high-performance systems. In: Proceedings of the Eighth International Conference on High-Performance Computing in Asia-Pacific Region. HPCASIA 2005, p. 45. IEEE Computer Society, Washington, DC (2005), doi:10.1109/HPCASIA.2005.18

    Google Scholar 

  5. Dongarra, J.J., Du Croz, J., Hammarling, S., Duff, I.S.: A set of level 3 basic linear algebra subprograms. ACM Trans. Math. Softw. 16(1), 1–17 (1990), http://doi.acm.org/10.1145/77626.79170

    Article  MATH  Google Scholar 

  6. Dongarra, J.J., Luszczek, P., Petitet, A.: The linpack benchmark: past, present and future. Concurrency and Computation: Practice and Experience 15(9), 803–820 (2003), doi:10.1002/cpe.728

    Article  Google Scholar 

  7. Gonzáalez-Vélez, H., Leyton, M.: A survey of algorithmic skeleton frameworks: highlevel structured parallel programming enablers. Software, Practrice & Experience 40(12), 1135–1160 (2010)

    Article  Google Scholar 

  8. Halstead, M.H.: Elements of Software Science. Operating and programming systems series. Elsevier Science Ltd. (1977)

    Google Scholar 

  9. Javed, N., Loulergue, F.: Parallel Programming and Performance Predictability with Orléans Skeleton Library. In: International Conference on High Performance Computing and Simulation (HPCS), pp. 257–263. IEEE (2011)

    Google Scholar 

  10. Kemerer, C.F.: An empirical validation of software cost estimation models. Commun. ACM 30(5), 416–429 (1987)

    Article  Google Scholar 

  11. Mccabe, T.J.: A complexity measure. In: ICSE 1976: Proceedings of the 2nd International Conference on Software Engineering. IEEE Computer Society Press, Los Alamitos (1976)

    Google Scholar 

  12. Peleg, A., Weiser, U.: MMX technology extension to the intel architecture. IEEE Micro 16(4), 42–50 (1996)

    Article  Google Scholar 

  13. Strassen, V.: Gaussian elimination is not optimal. Numerische Mathematik 13, 354–356 (1969), doi:10.1007/BF02165411, 10.1007/BF02165411

    Article  MathSciNet  MATH  Google Scholar 

  14. Strey, A., Bange, M.: Performance Analysis of Intel’s MMX and SSE: A Case Study. In: Sakellariou, R., Keane, J.A., Gurd, J.R., Freeman, L. (eds.) Euro-Par 2001. LNCS, vol. 2150, pp. 142–147. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. Touati, S.A.A., Worms, J., Briais, S.: The Speedup Test. Tech. Rep. inria-00443839, INRIA Saclay - Ile de France (2010), http://hal.inria.fr/inria-00443839

  16. Whaley, R.C., Petitet, A., Dongarra, J.J.: Automated empirical optimization of software and the ATLAS project. Parallel Computing 27(1-2), 3–35 (2001); also available as University of Tennessee LAPACKWorking Note #147, UT-CS-00-448 (2000), www.netlib.org/lapack/lawns/lawn147.ps

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. LIFO, University of Orléans, France

    Joeffrey Legaux, Sylvain Jubertie & Frédéric Loulergue

Authors
  1. Joeffrey Legaux
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  2. Sylvain Jubertie
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  3. Frédéric Loulergue
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Editor information

Editors and Affiliations

  1. School of Information Technology, Deakin University, Melbourne Burwood Campus, 221 Burwood Highway, 3125, Burwood, VIC, Australia

    Yang Xiang

  2. SEECS, University of Ottawa, 8, King Edward Ave, K1N 6N5, Ottawa, ON, Canada

    Ivan Stojmenovic

  3. Department of Intelligent Informatics, Kyushu Sangyo University, 2-3-1 Matsukadai, Higashi-ku, 813-8503, Fukuoka, Japan

    Bernady O. Apduhan

  4. School of Information Science and Engineering, Central South University, 410083, Changsha, Hunan Province, P.R. China

    Guojun Wang

  5. Department of Information Engineering, Hiroshima University, 1-4-1, Kagamiyama, 739-8527, Higashi-Hiroshima, Japan

    Koji Nakano

  6. School of Information Technologies, University of Sydney, Building J12, 2006, Sydney, NSW, Australia

    Albert Zomaya

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© 2012 Springer-Verlag Berlin Heidelberg

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Legaux, J., Jubertie, S., Loulergue, F. (2012). Experiments in Parallel Matrix Multiplication on Multi-core Systems. In: Xiang, Y., Stojmenovic, I., Apduhan, B.O., Wang, G., Nakano, K., Zomaya, A. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2012. Lecture Notes in Computer Science, vol 7439. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33078-0_26

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  • DOI: https://doi.org/10.1007/978-3-642-33078-0_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33077-3

  • Online ISBN: 978-3-642-33078-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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