Computing predecessor and successor in rounding to nearest (original) (raw)

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
2. Paul Zimmermann
3. Sylvie Boldo
4. Guillaume Melquiond

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Correspondence toSiegfried M. Rump.

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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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• Received: 12 September 2008
• Accepted: 05 February 2009
• Published: 24 February 2009
• Issue date: June 2009
• DOI: https://doi.org/10.1007/s10543-009-0218-z

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Mathematics Subject Classification (2000)