Appendix: Number Theory Tools for Floating-Point Arithmetic

Jean-Michel Muller (), Nicolas Brisebarre (), Florent de Dinechin (), Claude-Pierre Jeannerod (), Vincent Lefèvre (), Guillaume Melquiond (), Nathalie Revol (), Damien Stehlé () and Serge Torres ()
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Jean-Michel Muller: École Normale Supérieure de Lyon, CNRS, Laboratoire LIP
Nicolas Brisebarre: École Normale Supérieure de Lyon, CNRS, Laboratoire LIP
Florent de Dinechin: École Normale Supérieure de Lyon, ENSL, Laboratoire LIP
Claude-Pierre Jeannerod: École Normale Supérieure de Lyon, INRIA, Laboratoire LIP
Vincent Lefèvre: École Normale Supérieure de Lyon, INRIA, Laboratoire LIP
Guillaume Melquiond: Parc Orsay Université, INRIA Saclay – Île-de- France
Nathalie Revol: École Normale Supérieure de Lyon, INRIA, Laboratoire LIP
Damien Stehlé: Macquarie University, and University of Sydney School of Mathematics and Statistics University of Sydney, CNRS
Serge Torres: École Normale Supérieure de Lyon, ENSL, Laboratoire LIP

Chapter Chapter 16 in Handbook of Floating-Point Arithmetic, 2010, pp 521-528 from Springer

Abstract: Abstract Continued fractions make it possible to build very good (indeed, the best possible, in a sense that will be made explicit by Theorems 49 and 50) rational approximations to real numbers. As such, they naturally appear in many problems of number theory, discrete mathematics, and computer science. Since floating-point numbers are rational approximations to real numbers, it is not surprising that continued fractions play a role in some areas of floating-point arithmetic.

Date: 2010
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DOI: 10.1007/978-0-8176-4705-6_16

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