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Algorithms for the Five Basic Operations

  • Jean-Michel Muller
  • Nicolas Brisebarre
  • Florent de Dinechin
  • Claude-Pierre Jeannerod
  • Vincent Lefèvre
  • Guillaume Melquiond
  • Nathalie Revol
  • Damien Stehlé
  • Serge Torres
Chapter

Abstract

Among the many operations that the IEEE 754 standards specify (see Chapter 3), we will focus here and in the next two chapters on the five basic arithmetic operations: addition, subtraction, multiplication, division, and square root. We will also study the fused multiply-add (FMA) operator. We review here some of the known properties and algorithms used to implement each of those operators. Chapter 9 and Chapter 10 will detail some examples of actual implementations in, respectively, hardware and software.

Keywords

Basic Operation Binary Encode Functional Iteration Nonzero Digit Digit Position 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2010

Authors and Affiliations

  • Jean-Michel Muller
    • 1
  • Nicolas Brisebarre
    • 1
  • Florent de Dinechin
    • 2
  • Claude-Pierre Jeannerod
    • 3
  • Vincent Lefèvre
    • 3
  • Guillaume Melquiond
    • 4
  • Nathalie Revol
    • 3
  • Damien Stehlé
    • 5
  • Serge Torres
    • 2
  1. 1.CNRS, Laboratoire LIPÉcole Normale Supérieure de LyonLyon Cedex 07France
  2. 2.ENSL, Laboratoire LIPÉcole Normale Supérieure de LyonLyon Cedex 07France
  3. 3.INRIA, Laboratoire LIPÉcole Normale Supérieure de LyonLyon Cedex 07France
  4. 4.INRIA Saclay – Île-de- FranceParc Orsay UniversitéOrsay CedexFrance
  5. 5.CNRSMacquarie University, and University of Sydney School of Mathematics and Statistics University of SydneySydneyAustralia

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