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Basic Properties and Algorithms

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

Abstract

In this chapter, we present some short yet useful algorithms and some basic properties that can be derived from specifications of floating-point arithmetic systems, such as the ones given in the various successive IEEE standards. Thanks to these standards, we now have an accurate definition of floating-point formats and operations. The behavior of a sequence of operations becomes at least partially1 predictable (see Chapter 7) for more details on this). We therefore can build algorithms and proofs that use these specifications.

Keywords

Basic Property Complex Number Arithmetic Operation Naive Algorithm Complex Division 
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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