Introduction

Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre, Guillaume Melquiond, Nathalie Revol and Serge Torres
Additional contact information
Jean-Michel Muller: CNRS - LIP
Nicolas Brunie: Kalray
Florent de Dinechin: INSA-Lyon - CITI
Claude-Pierre Jeannerod: Inria - LIP
Mioara Joldes: CNRS - LAAS
Vincent Lefèvre: Inria - LIP
Guillaume Melquiond: Inria - LRI
Nathalie Revol: Inria - LIP
Serge Torres: ENS-Lyon - LIP

Chapter Chapter 1 in Handbook of Floating-Point Arithmetic, 2018, pp 3-14 from Springer

Abstract: Abstract Representing and manipulating real numbers efficiently is required in many fields of science, engineering, finance, and more. Since the early years of electronic computing, many different ways of approximating real numbers on computers have been introduced. One can cite (this list is far from being exhaustive): fixed-point arithmetic, logarithmic [337, 585] and semi-logarithmic [444] number systems, intervals [428], continued fractions [349, 622], rational numbers [348] and possibly infinite strings of rational numbers [418], level-index number systems [100, 475], fixed-slash and floating-slash number systems [412], tapered floating-point arithmetic [432, 22], 2-adic numbers [623], and most recently unums and posits [228, 229].

Date: 2018
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DOI: 10.1007/978-3-319-76526-6_1

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