Skip to main content

Highly Scalable Multiplication for Distributed Sparse Multivariate Polynomials on Many-Core Systems

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8136))

Abstract

We present a highly scalable algorithm for multiplying sparse multivariate polynomials represented in a distributed format. This algorithm targets not only the shared memory multicore computers, but also computers clusters or specialized hardware attached to a host computer, such as graphics processing units or many-core coprocessors. The scalability on the large number of cores is ensured by the lacks of synchronizations, locks and false-sharing during the main parallel step.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gastineau, M.: Parallel operations of sparse polynomials on multicores: I. multiplication and poisson bracket. In: Moreno Maza, M., Roch, J.L. (eds.) PASCO 2010: Proceedings of the 4th International Workshop on Parallel and Symbolic Computation, pp. 44–52. ACM, New York (2010)

    Google Scholar 

  2. Monagan, M., Pearce, R.: Parallel sparse polynomial multiplication using heaps. In: Johnson, J., Park, H., Kaltofen, E. (eds.) ISSAC 2009: Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, pp. 263–270. ACM, New York (2009)

    Chapter  Google Scholar 

  3. Biscani, F.: Parallel sparse polynomial multiplication on modern hardware architectures. In: van der Hoeven, J., van Hoeij, M. (eds.) Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation. ISSAC 2012, pp. 83–90. ACM, New York (2012)

    Chapter  Google Scholar 

  4. Biscani, F.: Design and implementation of a modern algebraic manipulator for Celestial Mechanics. PhD thesis, Centro Interdipartimentale Studi e Attivita Spaziali,Universita degli Studi di Padova, Padova (May 2008)

    Google Scholar 

  5. Wang, P.S.: Parallel polynomial operations on smps: an overview. J. Symb. Comput. 21(4-6), 397–410 (1996)

    Article  MATH  Google Scholar 

  6. Gastineau, M., Laskar, J.: Trip: a computer algebra system dedicated to celestial mechanics and perturbation series. ACM Commun. Comput. Algebra 44(3/4), 194–197 (2011)

    Google Scholar 

  7. Horowitz, E.: A sorting algorithm for polynomial multiplication. J. ACM 22(4), 450–462 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  8. Blumofe, R.D., Leiserson, C.E.: Scheduling multithreaded computations by work stealing. J. ACM 46(5), 720–748 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. Frigo, M., Strumpen, V.: The cache complexity of multithreaded cache oblivious algorithms. In: Gibbons, P.B., Vishkin, U. (eds.) Proceedings of the Eighteenth Annual ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2006, pp. 271–280. ACM, New York (2006)

    Chapter  Google Scholar 

  10. Johnson, S.C.: Sparse polynomial arithmetic. SIGSAM Bull. 8(3), 63–71 (1974)

    Article  Google Scholar 

  11. Monagan, M., Pearce, R.: Parallel sparse polynomial division using heaps. In: Moreno Maza, M., Roch, J.L. (eds.) Proceedings of the 4th International Workshop on Parallel and Symbolic Computation, PASCO 2010, pp. 105–111. ACM, New York (2010)

    Google Scholar 

  12. Fateman, R.: Comparing the speed of programs for sparse polynomial multiplication. SIGSAM Bull. 37(1), 4–15 (2003)

    Article  MATH  Google Scholar 

  13. OpenMP Architecture Review Board: OpenMP application program interface version 3.0 (May 2008)

    Google Scholar 

  14. Reinders, J.: Intel threading building blocks, 1st edn. Reilly & Associates, Inc., Sebastopol (2007)

    Google Scholar 

  15. Monagan, M., Pearce, R.: Sparse polynomial multiplication and division in maple 14. ACM Commun. Comput. Algebra 44(3/4), 205–209 (2011)

    Google Scholar 

  16. Granlund, T.: GNU multiple precision arithmetic library 4.2.4 (September 2008), http://swox.com/gmp/

  17. Sanders, J., Kandrot, E.: CUDA by Example: An Introduction to General-Purpose GPU Programming, 1st edn. Addison-Wesley Professional (2010)

    Google Scholar 

  18. Augonnet, C., Thibault, S., Namyst, R., Wacrenier, P.A.: Starpu: a unified platform for task scheduling on heterogeneous multicore architectures. Concurrency and Computation: Practice and Experience 23(2), 187–198 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this paper

Cite this paper

Gastineau, M., Laskar, J. (2013). Highly Scalable Multiplication for Distributed Sparse Multivariate Polynomials on Many-Core Systems. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2013. Lecture Notes in Computer Science, vol 8136. Springer, Cham. https://doi.org/10.1007/978-3-319-02297-0_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-02297-0_8

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02296-3

  • Online ISBN: 978-3-319-02297-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics