Simultaneous Conversions with the Residue Number System Using Linear Algebra-Reference-Cited by-同舟云学术

Simultaneous Conversions with the Residue Number System Using Linear Algebra

Published:2018-04-26 Issue:3 Volume:44 Page:1-21
ISSN:0098-3500
Container-title:ACM Transactions on Mathematical Software
language:en
Short-container-title:ACM Trans. Math. Softw.

Author:

Doliskani Javad¹,Giorgi Pascal²,Lebreton Romain²,Schost Eric³

Affiliation:

1. Institute for Quantum Computing, University of Waterloo, Waterloo, Canada

2. LIRMM CNRS - University of Montpellier, France

3. University of Waterloo, Waterloo, Canada

Abstract

We present an algorithm for simultaneous conversions between a given set of integers and their Residue Number System representations based on linear algebra. We provide a highly optimized implementation of the algorithm that exploits the computational features of modern processors. The main application of our algorithm is matrix multiplication over integers. Our speed-up of the conversions to and from the Residue Number System significantly improves the overall running time of matrix multiplication.

Funder

French ANR

Canada Research Chairs program

NSERC

Publisher

Association for Computing Machinery (ACM)

Subject

Applied Mathematics,Software

Link

https://dl.acm.org/doi/pdf/10.1145/3145573

Reference42 articles.

1. A. V. Aho J. E. Hopcroft and J. D. Ullman. 1974. The Design and Analysis of Computer Algorithms. Addison-Wesley. A. V. Aho J. E. Hopcroft and J. D. Ullman. 1974. The Design and Analysis of Computer Algorithms. Addison-Wesley.

2. Lecture Notes in Computer Science;Barrett P.

3. D. J. Bernstein. 2004. Scaled remainder trees. Retrieved from https://cr.yp.to/arith/scaledmod-20040820.pdf. D. J. Bernstein. 2004. Scaled remainder trees. Retrieved from https://cr.yp.to/arith/scaledmod-20040820.pdf.

4. Fast modular transforms

5. The Magma Algebra System I: The User Language

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