• DocumentCode
    2866704
  • Title

    Short Division of Long Integers

  • Author

    Harvey, David ; Zimmermann, Paul

  • Author_Institution
    Courant Inst. of Math. Sci., New York Univ., New York, NY, USA
  • fYear
    2011
  • fDate
    25-27 July 2011
  • Firstpage
    7
  • Lastpage
    14
  • Abstract
    We consider the problem of short division - i.e., approximate quotient - of multiple-precision integers. We present ready-to-implement algorithms that yield an approximation of the quotient, with tight and rigorous error bounds. We exhibit speedups of up to 30% with respect to GMP division with remainder, and up to 10% with respect to GMP short division, with room for further improvements. This work enables one to implement fast correctly rounded division routines in multiple-precision software tools.
  • Keywords
    approximation theory; floating point arithmetic; software tools; GMP division; approximation; error bounds; floating-point division; multiple-precision integers; multiple-precision software tools; ready-to-implement algorithms; short division; Algorithm design and analysis; Approximation algorithms; Approximation methods; Context; Error analysis; Libraries; Tuning; GNU MP; GNU MPFR; arbitrary precision; floating-point division;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Computer Arithmetic (ARITH), 2011 20th IEEE Symposium on
  • Conference_Location
    Tubingen
  • ISSN
    1063-6889
  • Print_ISBN
    978-1-4244-9457-6
  • Type

    conf

  • DOI
    10.1109/ARITH.2011.11
  • Filename
    5992103