Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Efficiency of Reproducible Level 1 BLAS

  • Conference paper
  • First Online:
Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9553))

Abstract

Numerical reproducibility failures appear in massively parallel floating-point computations. One way to guarantee this reproducibility is to extend the IEEE-754 correct rounding to larger computing sequences, e.g. to the BLAS. Is the extra cost for numerical reproducibility acceptable in practice? We present solutions and experiments for the level 1 BLAS and we conclude about their efficiency.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Similar content being viewed by others

References

  1. IEEE 754–2008, Standard for Floating-Point Arithmetic. Institute of Electrical and Electronics Engineers, New York (2008)

    Google Scholar 

  2. Bohlender, G.: Floating-point computation of functions with maximum accuracy. IEEE Trans. Comput. C-26(7), 621–632 (1977)

    Article  MathSciNet  Google Scholar 

  3. Chohra, C., Langlois, P., Parello, D.: Implementation and Efficiency of Reproducible Level 1 BLAS (2015). http://hal-lirmm.ccsd.cnrs.fr/lirmm-01179986

  4. Collange, C., Defour, D., Graillat, S., Iakimchuk, R.: Reproducible and accurate matrix multiplication in ExBLAS for high-performance computing. In: SCAN 2014, Würzburg, Germany (2014)

    Google Scholar 

  5. Dekker, T.J.: A floating-point technique for extending the available precision. Numer. Math. 18, 224–242 (1971)

    Article  MathSciNet  Google Scholar 

  6. Demmel, J.W., Nguyen, H.D.: Fast reproducible floating-point summation. In: Proceedings of 21th IEEE Symposium on Computer Arithmetic. Austin, Texas, USA (2013)

    Google Scholar 

  7. Intel Math Kernel Library. http://www.intel.com/software/products/mkl/

  8. Jézéquel, F., Langlois, P., Revol, N.: First steps towards more numerical reproducibility. ESAIM: Proc. 45, 229–238 (2013)

    Article  MathSciNet  Google Scholar 

  9. Muller, J.M., Brisebarre, N., de Dinechin, F., Jeannerod, C.P., Lefèvre, V., Melquiond, G., Revol, N., Stehlé, D., Torres, S.: Handbook of Floating-Point Arithmetic. Birkhäuser, Boston (2010)

    Book  Google Scholar 

  10. Ogita, T., Rump, S.M., Oishi, S.: Accurate sum and dot product. SIAM J. Sci. Comput. 26(6), 1955–1988 (2005)

    Article  MathSciNet  Google Scholar 

  11. Reinders, J.: Intel Threading Building Blocks, 1st edn. O’Reilly & Associates Inc., Sebastopol (2007)

    Google Scholar 

  12. http://webdali.univ-perp.fr/ReproducibleSoftware

  13. Rump, S.M.: Ultimately fast accurate summation. SIAM J. Sci. Comput. 31(5), 3466–3502 (2009)

    Article  MathSciNet  Google Scholar 

  14. Rump, S.M., Ogita, T., Oishi, S.: Accurate floating-point summation - part I: faithful rounding. SIAM J. Sci. Comput. 31(1), 189–224 (2008)

    Article  MathSciNet  Google Scholar 

  15. Story, S.: Numerical reproducibility in the Intel Math Kernel Library. Salt Lake City, November 2012

    Google Scholar 

  16. Van Zee, F.G., van de Geijn, R.A.: BLIS: a framework for rapidly instantiating BLAS functionality. ACM Trans. Math. Software 41(3), 14:1–14:33 (2015)

    MathSciNet  MATH  Google Scholar 

  17. Yamanaka, N., Ogita, T., Rump, S., Oishi, S.: A parallel algorithm for accurate dot product. Parallel Comput. 34(68), 392–410 (2008)

    Article  MathSciNet  Google Scholar 

  18. Zhu, Y.K., Hayes, W.B.: Correct rounding and hybrid approach to exact floating-point summation. SIAM J. Sci. Comput. 31(4), 2981–3001 (2009)

    Article  MathSciNet  Google Scholar 

  19. Zhu, Y.K., Hayes, W.B.: Algorithm 908: online exact summation of floating-point streams. ACM Trans. Math. Softw. 37(3), 37:1–37:13 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Digits, Architectures et Logiciels Informatiques, Univ. Perpignan Via Domitia, 66860, Perpignan, France

    Chemseddine Chohra, Philippe Langlois & David Parello

  2. Laboratoire d’Informatique Robotique et de Microélectronique de Montpellier, Univ. Montpellier II, UMR 5506, CNRS, 34095, Montpellier, France

    Chemseddine Chohra, Philippe Langlois & David Parello

Authors
  1. Chemseddine Chohra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Philippe Langlois
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David Parello
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chemseddine Chohra .

Editor information

Editors and Affiliations

  1. Institute of Computer Science, University of Würzburg, Würzburg, Germany

    Marco Nehmeier

  2. Universität Würzburg, Würzburg, Germany

    Jürgen Wolff von Gudenberg

  3. Department of Mathematics, Uppsala University, Uppsala, Sweden

    Warwick Tucker

Rights and permissions

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 2.5 International License (http://creativecommons.org/licenses/by-nc/2.5/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Chohra, C., Langlois, P., Parello, D. (2016). Efficiency of Reproducible Level 1 BLAS. In: Nehmeier, M., Wolff von Gudenberg, J., Tucker, W. (eds) Scientific Computing, Computer Arithmetic, and Validated Numerics. SCAN 2015. Lecture Notes in Computer Science(), vol 9553. Springer, Cham. https://doi.org/10.1007/978-3-319-31769-4_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-31769-4_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-31768-7

  • Online ISBN: 978-3-319-31769-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation