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Iterative Toom-Cook methods for very unbalanced long integer multiplication

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Alberto ZanoniAuthors Info & Claims

ISSAC '10: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation

July 2010

Pages 319 - 323

https://doi.org/10.1145/1837934.1837995

Published: 25 July 2010 Publication History

Abstract

We consider the multiplication of long integers when one factor is much larger than the other one. We describe an iterative approach using Toom-Cook unbalanced methods, which results in the evaluation of the smaller integer only once. The particular case of Toom-2.5 is considered in full detail. A further optimization depending on the parity of the shortest operand evaluation in 1 is also described. A comparison with GMP library is also presented.

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Cited By

Nissim RSchwartz OSpiizer YAgrawal KPetrank E(2024)Fault-Tolerant Parallel Integer MultiplicationProceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3626183.3659961(207-218)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3626183.3659961
Bahig HFathy K(2023)Sequential and parallel sliding window algorithms for multiplying large integersJournal of King Saud University - Computer and Information Sciences10.1016/j.jksuci.2023.02.01135:3(131-140)Online publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1016/j.jksuci.2023.02.011
Bahig HAlghadhban AMahdi MAlutaibi KBahig H(2020)Speeding up the Multiplication Algorithm for Large IntegersEngineering, Technology & Applied Science Research10.48084/etasr.393210:6(6533-6541)Online publication date: 20-Dec-2020
https://doi.org/10.48084/etasr.3932
Show More Cited By

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Iterative Toom-Cook methods for very unbalanced long integer multiplication

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cover image ACM Other conferences

ISSAC '10: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation

July 2010

366 pages

ISBN:9781450301503

DOI:10.1145/1837934

Program Chair:
Wolfram Koepf
London, Ontario, Canada

Copyright © 2010 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 25 July 2010

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ISSAC '10: International Symposium on Symbolic and Algebraic Computation

July 25 - 28, 2010

Munich, Germany

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ISSAC '10 Paper Acceptance Rate 45 of 110 submissions, 41%;

Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Nissim RSchwartz OSpiizer YAgrawal KPetrank E(2024)Fault-Tolerant Parallel Integer MultiplicationProceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3626183.3659961(207-218)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3626183.3659961
Bahig HFathy K(2023)Sequential and parallel sliding window algorithms for multiplying large integersJournal of King Saud University - Computer and Information Sciences10.1016/j.jksuci.2023.02.01135:3(131-140)Online publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1016/j.jksuci.2023.02.011
Bahig HAlghadhban AMahdi MAlutaibi KBahig H(2020)Speeding up the Multiplication Algorithm for Large IntegersEngineering, Technology & Applied Science Research10.48084/etasr.393210:6(6533-6541)Online publication date: 20-Dec-2020
https://doi.org/10.48084/etasr.3932
Zitouni MAkbarinia RYahia SMasseglia F(2017)Massively Distributed Environments and Closed Itemset Mining: The DCIM ApproachAdvanced Information Systems Engineering10.1007/978-3-319-59536-8_15(231-246)Online publication date: 27-May-2017
https://doi.org/10.1007/978-3-319-59536-8_15
Bodrato MZanoni A(2011)Long Integers and Polynomial Evaluation with Estrin's SchemeProceedings of the 2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing10.1109/SYNASC.2011.17(39-46)Online publication date: 26-Sep-2011
https://dl.acm.org/doi/10.1109/SYNASC.2011.17
Bodrato M(2011)High Degree Toom'n'Half for Balanced and Unbalanced MultiplicationProceedings of the 2011 IEEE 20th Symposium on Computer Arithmetic10.1109/ARITH.2011.12(15-22)Online publication date: 25-Jul-2011
https://dl.acm.org/doi/10.1109/ARITH.2011.12

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