Skip to main content
SpringerLink
Log in
Book cover

International Conference on Algorithms and Architectures for Parallel Processing

ICA3PP 2019: Algorithms and Architectures for Parallel Processing pp 60–74Cite as

Accelerating Large Integer Multiplication Using Intel AVX-512IFMA

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11944))

Abstract

In this study, we implemented large integer multiplication with Single Instruction Multiple Data (SIMD) instructions. We evaluated the implementation on a processor with Cannon Lake microarchitecture, containing Intel AVX-512IFMA (Integer Fused Multiply-Add) instructions. AVX-512IFMA can compute multiple 52-bit integer multiplication and addition operations through one instruction and it has the potential to process large integer multiplications faster than its conventional AVX-512 counterpart. Furthermore, the AVX-512IFMA instructions take three 52-bit integers of 64-bit spaces as operands, and we can use the remaining 12 bits effectively to accumulate carries (reduced-radix representation). For multiplication in the context of larger integers, we applied the Karatsuba and Basecase methods to our program. The former is known to be a faster algorithm than the latter. For evaluation purposes, we compared execution times against extant alternatives and the GNU Multiple Precision Arithmetic Library (GMP). This comparison showed that we were able to achieve a substantive improvement in performance. Specifically, our proposed approach was up to approximately 3.07 times faster than AVX-512F (Foundation) and approximately 2.97 times faster than GMP.

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

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 EPUB and 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

References

  1. GMP source code used in Mathematica. http://www.wolfram.com/LGPL/GMP

  2. The GNU MP. https://gmplib.org/

  3. Intel AVX-512 Instructions and Their Use in the Implementation of Math Functions, http://www.fit.vutbr.cz/~iklubal/IPA/AVX-512_Cornea.pdf

  4. Intel Intrinsics Guide. https://software.intel.com/sites/landingpage/IntrinsicsGuide/#avx512techs=AVX512IFMA52

  5. Mathematica. https://www.wolfram.com/mathematica/index.en.html

  6. Maxima. http://maxima.sourceforge.net

  7. Intel Xeon Phi Processor Product Brief. https://www.intel.com/content/dam/www/public/us/en/documents/product-briefs/xeon-phi-processor-product-brief.pdf (2016)

  8. Second Generation Intel Xeon Scalable Processors Specification Update. https://www.intel.com/content/dam/www/public/us/en/documents/specification-updates/2nd-gen-xeon-scalable-spec-update.pdf (May 2019)

  9. Brent, R., Zimmermann, P.: Modern Computer Arithmetic. Cambridge University Press (2010)

    Google Scholar 

  10. Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 297–301 (1965)

    Article  MathSciNet  Google Scholar 

  11. Drucker, N., Gueron, S.: Fast Modular Squaring with AVX512IFMA. In: Latifi, S. (ed.) 16th International Conference on Information Technology-New Generations (ITNG 2019), pp. 3–8. Springer International Publishing, Cham (2019)

    Chapter  Google Scholar 

  12. Edamatsu, T., Takahashi, D.: Acceleration of Large Integer Multiplication with Intel AVX-512 Instructions. In: 2018 IEEE 20th International Conference on High Performance Computing and Communications (HPCC). pp. 211–218 (2018)

    Google Scholar 

  13. Fürer, M.: Faster integer multiplication. SIAM J. Comput. 39, 979–1005 (2009)

    Article  MathSciNet  Google Scholar 

  14. Gueron, S., Krasnov, V.: Accelerating Big Integer Arithmetic Using Intel IFMA Extensions. In: Proc. 2016 IEEE 23rd Symposium on Computer Arithmetic (ARITH). pp. 32–38 (2016)

    Google Scholar 

  15. Harvey, D., van der Hoeven, J.: Integer multiplication in time \(O(n\) log \(n)\) (2019), https://hal.archives-ouvertes.fr/hal-02070778

  16. Intel Corporation: Using Streaming SIMD Extensions (SSE2) to Perform Big Multiplications, version 2.0. Technical Report AP-941 (248606–001) (2000), https://software.intel.com/sites/default/files/14/4f/24960

  17. Karatsuba, A., Ofman, Y.: Multiplication of multidigit numbers on automata. Soviet Physics Doklady 7, 595 (1963)

    Google Scholar 

  18. Keliris, A., Maniatakos, M.: Investigating Large Integer Arithmetic on Intel Xeon Phi SIMD Extensions. In: Proc. Design & Technology of Integrated Systems In Nanoscale Era (DTIS). pp. 1–6 (2014)

    Google Scholar 

  19. Miller, V.S.: Use of elliptic curves in cryptography. In: Williams, H.C. (ed.) Advances in Cryptology – CRYPTO ’85 Proceedings, pp. 417–426. Springer, Berlin, Heidelberg (1985)

    Google Scholar 

  20. Montgomery, P.L.: Modular multiplication without trial division. Math. Comput. 44, 519–521 (1985)

    Article  MathSciNet  Google Scholar 

  21. Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21, 120–126 (1978)

    Article  MathSciNet  Google Scholar 

  22. Schönhage, A., Strassen, V.: Schnelle Multiplikation großer Zahlen. Computing 7, 281–292 (1971)

    Article  MathSciNet  Google Scholar 

  23. Toom, A.L.: The complexity of a scheme of functional elements realizing the multiplication of integers. Soviet Mathematics Doklady 3, 714–716 (1963)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Takuya Edamatsu

  2. Center for Computational Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Daisuke Takahashi

Authors
  1. Takuya Edamatsu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daisuke Takahashi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Takuya Edamatsu .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Software Engineering, Swinburne University of Technology, Hawthorn, Melbourne, VIC, Australia

    Sheng Wen

  2. School of Computer Science, The University of Sydney, Camperdown, NSW, Australia

    Albert Zomaya

  3. Department of Computer Science, St. Francis Xavier University, Antigonish, NS, Canada

    Laurence T. Yang

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Edamatsu, T., Takahashi, D. (2020). Accelerating Large Integer Multiplication Using Intel AVX-512IFMA. In: Wen, S., Zomaya, A., Yang, L. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2019. Lecture Notes in Computer Science(), vol 11944. Springer, Cham. https://doi.org/10.1007/978-3-030-38991-8_5

Download citation

Publish with us

Policies and ethics

Search

Navigation