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Definitions and Basic Notions

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

Abstract

As said in the Introduction, roughly speaking, a radix-β floating-point number x is a number of the form m · β e , where β is the radix of the floating-point system, m such that |m| < β is the significand of x, and e is its exponent. And yet, portability, accuracy, and the ability to prove interesting and useful properties as well as to design smart algorithms require more rigorous definitions, and much care in the specifications. This is the first purpose of this chapter. The second one is to deal with basic problems: rounding, exceptions, properties of real arithmetic that become wrong in floating-point arithmetic, best choices for the radix, and radix conversions.

Keywords

Arithmetic Operation Basic Notion Interval Arithmetic Decimal Number Conversion Algorithm 
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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