Accelerating Big Integer Arithmetic Using Intel IFMA Extensions

Shay Gueron; Vlad Krasnov

doi:10.1109/ARITH.2016.22

Accelerating Big Integer Arithmetic Using Intel IFMA Extensions

Shay Gueron, Vlad Krasnov

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Intel has recently announced a new set of processor instructions, dubbed AVX512IFMA, that carry out Integer Fused Multiply Accumulate operations. These instructions operate on 512-bit registers and compute eight independent 52-bit unsigned integer multiplications, to generate eight 104-bit products, and accumulate their low/high halves into 64-bit containers. Using these instructions requires that inputs are converted to (redundant form) radix 2⁵², and outputs are converted to the desired representation. This paper demonstrates several techniques for leveraging the AVX512IFMA instructions in order to speed up big-integer multiplications. Although processors that support AVX512IFMA are not yet available at the time this paper is written, we show how currently available public tools can be used for estimating their potential performance benefits. For example, based on these tools, we expect a 2x speedup for 1024-bit integer multiplication, over the best currently available method.

Original language	English
Title of host publication	Proceedings - 2016 IEEE 23rd Symposium on Computer Arithmetic, ARITH 2016
Editors	Javier Hormigo, Nathalie Revol, Paolo Montuschi, Stuart Oberman, Michael Schulte
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	32-38
Number of pages	7
ISBN (Electronic)	9781509016150
DOIs	https://doi.org/10.1109/ARITH.2016.22
State	Published - 7 Sep 2016
Event	23rd IEEE Symposium on Computer Arithmetic, ARITH 2016 - Santa Clara, United States Duration: 10 Jul 2016 → 13 Jul 2016

Publication series

Name	Proceedings - Symposium on Computer Arithmetic
Volume	2016-September

Conference

Conference	23rd IEEE Symposium on Computer Arithmetic, ARITH 2016
Country/Territory	United States
City	Santa Clara
Period	10/07/16 → 13/07/16

Bibliographical note

Publisher Copyright:
© 2016 IEEE.

Keywords

AVX
AVX512
IFMA
SIMD
big integer arithmetic
processor instructions

ASJC Scopus subject areas

Hardware and Architecture
Software
Theoretical Computer Science

Access to Document

10.1109/ARITH.2016.22

Cite this

Gueron, S., & Krasnov, V. (2016). Accelerating Big Integer Arithmetic Using Intel IFMA Extensions. In J. Hormigo, N. Revol, P. Montuschi, S. Oberman, & M. Schulte (Eds.), Proceedings - 2016 IEEE 23rd Symposium on Computer Arithmetic, ARITH 2016 (pp. 32-38). Article 7563269 (Proceedings - Symposium on Computer Arithmetic; Vol. 2016-September). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ARITH.2016.22

Gueron, Shay ; Krasnov, Vlad. / Accelerating Big Integer Arithmetic Using Intel IFMA Extensions. Proceedings - 2016 IEEE 23rd Symposium on Computer Arithmetic, ARITH 2016. editor / Javier Hormigo ; Nathalie Revol ; Paolo Montuschi ; Stuart Oberman ; Michael Schulte. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 32-38 (Proceedings - Symposium on Computer Arithmetic).

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title = "Accelerating Big Integer Arithmetic Using Intel IFMA Extensions",

abstract = "Intel has recently announced a new set of processor instructions, dubbed AVX512IFMA, that carry out Integer Fused Multiply Accumulate operations. These instructions operate on 512-bit registers and compute eight independent 52-bit unsigned integer multiplications, to generate eight 104-bit products, and accumulate their low/high halves into 64-bit containers. Using these instructions requires that inputs are converted to (redundant form) radix 252, and outputs are converted to the desired representation. This paper demonstrates several techniques for leveraging the AVX512IFMA instructions in order to speed up big-integer multiplications. Although processors that support AVX512IFMA are not yet available at the time this paper is written, we show how currently available public tools can be used for estimating their potential performance benefits. For example, based on these tools, we expect a 2x speedup for 1024-bit integer multiplication, over the best currently available method.",

keywords = "AVX, AVX512, IFMA, SIMD, big integer arithmetic, processor instructions",

author = "Shay Gueron and Vlad Krasnov",

note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 23rd IEEE Symposium on Computer Arithmetic, ARITH 2016 ; Conference date: 10-07-2016 Through 13-07-2016",

year = "2016",

month = sep,

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doi = "10.1109/ARITH.2016.22",

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series = "Proceedings - Symposium on Computer Arithmetic",

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Gueron, S & Krasnov, V 2016, Accelerating Big Integer Arithmetic Using Intel IFMA Extensions. in J Hormigo, N Revol, P Montuschi, S Oberman & M Schulte (eds), Proceedings - 2016 IEEE 23rd Symposium on Computer Arithmetic, ARITH 2016., 7563269, Proceedings - Symposium on Computer Arithmetic, vol. 2016-September, Institute of Electrical and Electronics Engineers Inc., pp. 32-38, 23rd IEEE Symposium on Computer Arithmetic, ARITH 2016, Santa Clara, United States, 10/07/16. https://doi.org/10.1109/ARITH.2016.22

Accelerating Big Integer Arithmetic Using Intel IFMA Extensions. / Gueron, Shay; Krasnov, Vlad.
Proceedings - 2016 IEEE 23rd Symposium on Computer Arithmetic, ARITH 2016. ed. / Javier Hormigo; Nathalie Revol; Paolo Montuschi; Stuart Oberman; Michael Schulte. Institute of Electrical and Electronics Engineers Inc., 2016. p. 32-38 7563269 (Proceedings - Symposium on Computer Arithmetic; Vol. 2016-September).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Gueron S, Krasnov V. Accelerating Big Integer Arithmetic Using Intel IFMA Extensions. In Hormigo J, Revol N, Montuschi P, Oberman S, Schulte M, editors, Proceedings - 2016 IEEE 23rd Symposium on Computer Arithmetic, ARITH 2016. Institute of Electrical and Electronics Engineers Inc. 2016. p. 32-38. 7563269. (Proceedings - Symposium on Computer Arithmetic). doi: 10.1109/ARITH.2016.22

Accelerating Big Integer Arithmetic Using Intel IFMA Extensions

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this