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Computing with Real Numbers

II. A Domain Framework for Computational Geometry

I. The LFT Approach to Real Number Computation

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Applied Semantics (APPSEM 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2395))

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Abstract

We introduce, in Part I, a number representation suitable for exact real number computation, consisting of an exponent and a mantissa, which is an infinite stream of signed digits, based on the interval [−1,1]. Numerical operations are implemented in terms of linear fractional transformations (LFT’s). We derive lower and upper bounds for the number of argument digits that are needed to obtain a desired number of result digits of a computation, which imply that the complexity of LFT application is that of multiplying n-bit integers. In Part II, we present an accessible account of a domain-theoretic approach to computational geometry and solid modelling which provides a data-type for designing robust geometric algorithms, illustrated here by the convex hull algorithm.

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Author information

Authors and Affiliations

  1. Department of Computing, Imperial College, 180 Queens Gate, London, SW7 2BZ, UK

    Abbas Edalat

  2. AbsInt Angewandte Informatik GmbH, Stuhlsatzenhausweg 69, D-66123, Saarbrücken, Germany

    Reinhold Heckmann

Authors
  1. Abbas Edalat
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  2. Reinhold Heckmann
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Editor information

Editors and Affiliations

  1. Projet Lemme, INRIA Sophia-Antipolis, 2004 Route des Lucioles, BP 93, 06902, Sophia Antipolis Cedex, France

    Gilles Barthe

  2. Department of Computing Science, Chalmers University of Technology, 412 96, Göteborg, Sweden

    Peter Dybjer

  3. Departamento de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    Luís Pinto

  4. Departamento de Informática, Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    João Saraiva

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© 2002 Springer-Verlag Berlin Heidelberg

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Edalat, A., Heckmann, R. (2002). Computing with Real Numbers. In: Barthe, G., Dybjer, P., Pinto, L., Saraiva, J. (eds) Applied Semantics. APPSEM 2000. Lecture Notes in Computer Science, vol 2395. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45699-6_5

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  • DOI: https://doi.org/10.1007/3-540-45699-6_5

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