skip to main content
column

Fast parallel GCD algorithm of many integers

Published:28 January 2014Publication History
Skip Abstract Section

Abstract

We present a new parallel algorithm which computes the GCD of n integers of O(n) bits in O(n / log n) time with O(n2+ε) processors, for any ε > 0 on CRCW PRAM model.

References

  1. A. Borodin, J. von zur Gathen and J. Hopcroft, Fast parallel matrix and GCD computations, Information and Control, 52, 3, 1982, 241--256Google ScholarGoogle ScholarCross RefCross Ref
  2. B. Chor and O. Goldreich, An improved parallel algorithm for integer GCD, Algorithmica, 5, 1990, 1--10Google ScholarGoogle ScholarCross RefCross Ref
  3. G. Cooperman, S. Feisel, J. von zur Gathen and G. Havas, GCD of many integers, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, 1627 (1999), 310--317 Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. G. Havas, S. Majewski, Extended gcd calculation, Congressus Numerantium, 111, 1627 (1998), 104--114Google ScholarGoogle Scholar
  5. S.M. Sedjelmaci, On A Parallel Lehmer-Euclid GCD Algorithm, in Proc. of the International Symposium on Symbolic and Algebraic Computation (ISSAC'2001), 2001, 303--308 Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. S.M. Sedjelmaci, Fast Parallel GCD algorithm of many integers, lipn.univ-paris13.fr/~sedjelmaci, Rapport interne, LIPN, April, 2013Google ScholarGoogle Scholar
  7. J. Sorenson, Two Fast GCD Algorithms, J. of Algorithms, 16, 1994, 110--144 Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Fast parallel GCD algorithm of many integers

        Recommendations

        Comments

        Login options

        Check if you have access through your login credentials or your institution to get full access on this article.

        Sign in

        Full Access

        • Published in

          cover image ACM Communications in Computer Algebra
          ACM Communications in Computer Algebra  Volume 47, Issue 3/4
          September/December 2013
          116 pages
          ISSN:1932-2240
          DOI:10.1145/2576802
          Issue’s Table of Contents

          Copyright © 2014 Author

          Publisher

          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 28 January 2014

          Check for updates

          Qualifiers

          • column

        PDF Format

        View or Download as a PDF file.

        PDF

        eReader

        View online with eReader.

        eReader