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An Algorithm that Computes a Lower Bound on the Distance Between a Segment and ℤ2

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Developments in Reliable Computing

Abstract

We give a fast algorithm for computing a lower bound on the distance between a straight line and the points of a bounded regular grid. This algorithm is used to find worst cases when trying to round the elementary functions correctly in floating-point arithmetic. These worst cases are useful to design algorithms that guarantee the exact rounding of the elementary functions.

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References

  1. R Alessandri and V. Berthé. Three distance theorems and combinatorics on words. Research report, Institut de Mathématiques de Luminy, Marseille, France, 1997.

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Author information

Authors and Affiliations

  1. Laboratoire LIP, Project Arénaire, École Normale Supérieure de Lyon, France

    Vincent Lefèvre

Authors
  1. Vincent Lefèvre
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Editor information

Editors and Affiliations

  1. József Attila University, Szeged, Hungary

    Tibor Csendes

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© 1999 Springer Science+Business Media Dordrecht

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Lefèvre, V. (1999). An Algorithm that Computes a Lower Bound on the Distance Between a Segment and ℤ2 . In: Csendes, T. (eds) Developments in Reliable Computing. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1247-7_16

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  • DOI: https://doi.org/10.1007/978-94-017-1247-7_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5350-3

  • Online ISBN: 978-94-017-1247-7

  • eBook Packages: Springer Book Archive

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