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Handbook of Floating-Point Arithmetic pp 239–267Cite as

Algorithms for the Five Basic Operations

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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.

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Authors and Affiliations

  1. CNRS, Laboratoire LIP, École Normale Supérieure de Lyon, 46, allée d’Italie, 69364, Lyon Cedex 07, France

    Jean-Michel Muller & Nicolas Brisebarre

  2. ENSL, Laboratoire LIP, École Normale Supérieure de Lyon, 46, allée d’Italie, 69364, Lyon Cedex 07, France

    Florent de Dinechin & Serge Torres

  3. INRIA, Laboratoire LIP, École Normale Supérieure de Lyon, 46, allée d’Italie, 69364, Lyon Cedex 07, France

    Claude-Pierre Jeannerod, Vincent Lefèvre & Nathalie Revol

  4. INRIA Saclay – Île-de- France, Parc Orsay Université, 4, rue Jacques Monod, 91893, Orsay Cedex, France

    Guillaume Melquiond

  5. CNRS, Macquarie University, and University of Sydney School of Mathematics and Statistics University of Sydney, 2006, Sydney, NSW, Australia

    Damien Stehlé

Authors
  1. Jean-Michel Muller
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  2. Nicolas Brisebarre
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  3. Florent de Dinechin
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  4. Claude-Pierre Jeannerod
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  5. Vincent Lefèvre
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  6. Guillaume Melquiond
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  7. Nathalie Revol
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  8. Damien Stehlé
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  9. Serge Torres
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Corresponding author

Correspondence to Jean-Michel Muller .

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© 2010 Birkhäuser Boston

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Muller, JM. et al. (2010). Algorithms for the Five Basic Operations. In: Handbook of Floating-Point Arithmetic. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4705-6_8

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