Handbook of Floating-Point Arithmetic
Floating-point arithmetic is by far the most widely used way of implementing real-number arithmetic on modern computers. Although the basic principles of floating-point arithmetic can be explained in a short amount of time, making such an arithmetic relia
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Handbook of Floating-Point Arithmetic
Birkh¨auser Boston • Basel • Berlin
Jean-Michel Muller CNRS, Laboratoire LIP ´ Ecole Normale Sup´erieure de Lyon 46, all´ee d’Italie 69364 Lyon Cedex 07 France jean-michel.muller@ ens-lyon.fr
Nicolas Brisebarre CNRS, Laboratoire LIP ´ Ecole Normale Sup´erieure de Lyon 46, all´ee d’Italie 69364 Lyon Cedex 07 France nicolas.brisebarre@ ens-lyon.fr
Florent de Dinechin ENSL, Laboratoire LIP ´ Ecole Normale Sup´erieure de Lyon 46, all´ee d’Italie 69364 Lyon Cedex 07 France florent.de.dinechin@ ens-lyon.fr
Claude-Pierre Jeannerod INRIA, Laboratoire LIP ´ Ecole Normale Sup´erieure de Lyon 46, all´ee d’Italie 69364 Lyon Cedex 07 France claude-pierre.jeannerod@ ens-lyon.fr
Vincent Lef`evre INRIA, Laboratoire LIP ´ Ecole Normale Sup´erieure de Lyon 46, all´ee d’Italie 69364 Lyon Cedex 07 France [email protected]
Guillaume Melquiond INRIA Saclay – ˆIle-deFrance Parc Orsay Universit´e 4, rue Jacques Monod 91893 Orsay Cedex France guillaume.melquiond@ inria.fr
Nathalie Revol INRIA, Laboratoire LIP ´ Ecole Normale Sup´erieure de Lyon 46, all´ee d’Italie 69364 Lyon Cedex 07 France [email protected]
Damien Stehl´e CNRS, Macquarie University, and University of Sydney School of Mathematics and Statistics University of Sydney Sydney NSW 2006 Australia [email protected]
Serge Torres ENSL, Laboratoire LIP ´ Ecole Normale Sup´erieure de Lyon 46, all´ee d’Italie 69364 Lyon Cedex 07 France [email protected]
ISBN 978-0-8176-4704-9 DOI 10.1007/978-0-8176-4705-6
e-ISBN 978-0-8176-4705-6
Library of Congress Control Number: 2009939668 Mathematics Subject Classification (2000): 65Y99, 68N30 ACM Subject Classification: G.1.0, G.4 c Birkh¨auser Boston, a part of Springer Science+Business Media, LLC 2010
All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkh¨auser Boston, c/o Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Birkh¨auser Boston is part of Springer Science+Business Media (www.birkhauser.com)
Contents Preface
xv
List of Figures
xvii
List of Tables
xxi
I
Introduction, Basic Definitions, and Standards
1 Introduction 1.1 Some History . . . . . . . 1.2 Desirable Properties . . . . 1.3 Some Strange Behaviors . 1.3.1 Some famous bugs 1.3.2 Difficult problems
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2 Defini
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