Minimizing I/O in Toom-Cook Algorithms

Roy Nissim, Oded Schwartz, Yuval Spiizer

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Long integer multiplication is a fundamental kernel in many linear algebra and cryptography computations. Toom-Cook-k (k∈N) are a family of fast long integer multiplication algorithms frequently used in many applications, particularly for small k sizes (2, 3, and 4). Previous studies focus on minimizing Toom-Cook’s arithmetic cost, sometimes at the expense of asymptotically higher communication costs and memory footprint. For many high-performance computing applications, the bottleneck is communication rather than arithmetic. We propose new versions of Toom-Cook-k algorithms that simultaneously reduce their arithmetic cost, communication cost, and memory footprint. We obtain these results by utilizing the alternative basis and Toom-Graph techniques. The arithmetic costs of the new algorithms are only slightly higher than that of the best previous solution, while the communication costs and memory footprint are significantly reduced and proved to be optimal.

Original languageEnglish
Title of host publicationEuro-Par 2024
Subtitle of host publicationParallel Processing - 30th European Conference on Parallel and Distributed Processing, Proceedings
EditorsJesus Carretero, Javier Garcia-Blas, Sameer Shende, Ivona Brandic, Katzalin Olcoz, Martin Schreiber
PublisherSpringer Science and Business Media Deutschland GmbH
Pages59-73
Number of pages15
ISBN (Print)9783031695827
StatePublished - 2024
Event30th International Conference on Parallel and Distributed Computing, Euro-Par 2024 - Madrid, Spain
Duration: 26 Aug 202430 Aug 2024

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14803 LNCS

Conference

Conference30th International Conference on Parallel and Distributed Computing, Euro-Par 2024
Country/TerritorySpain
CityMadrid
Period26/08/2430/08/24

Keywords

  • Alternative Basis Method
  • Bilinear Algorithms
  • Fast Long Integer Multiplication
  • I/O Complexity
  • Toom-Cook
  • Toom-Graph

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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