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Computing predecessor and successor in rounding to nearest

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Abstract

We give simple and efficient methods to compute and/or estimate the predecessor and successor of a floating-point number using only floating-point operations in rounding to nearest. This may be used to simulate interval operations, in which case the quality in terms of the diameter of the result is significantly improved compared to existing approaches.

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Authors and Affiliations

  1. Institute for Reliable Computing, Hamburg University of Technology, Schwarzenbergstraße 95, 21071, Hamburg, Germany

    Siegfried M. Rump

  2. Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Siegfried M. Rump

  3. Centre de Recherche INRIA Nancy–Grand Est, Équipe-projet CACAO, Bâtiment A, 615 rue du jardin botanique, 54600, Villers-lès-Nancy, France

    Paul Zimmermann

  4. INRIA Saclay–Île-de-France, Parc Orsay Université–ZAC des Vignes, 4 rue Jacques Monod–Bâtiment N, 91893, Orsay Cedex, France

    Sylvie Boldo

  5. Centre de recherche commun INRIA–Microsoft Research, 28 rue Jean Rostand, 91893, Orsay Cedex, France

    Guillaume Melquiond

Authors
  1. Siegfried M. Rump
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  2. Paul Zimmermann
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  3. Sylvie Boldo
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  4. Guillaume Melquiond
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Corresponding author

Correspondence to Siegfried M. Rump.

Additional information

Communicated by Axel Ruhe.

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Rump, S.M., Zimmermann, P., Boldo, S. et al. Computing predecessor and successor in rounding to nearest. Bit Numer Math 49, 419–431 (2009). https://doi.org/10.1007/s10543-009-0218-z

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  • DOI: https://doi.org/10.1007/s10543-009-0218-z

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