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Computing predecessor and successor in rounding to nearest

Siegfried Rump 1, 2 Paul Zimmermann 3 Sylvie Boldo 4 Guillaume Melquiond 5
1 IRC - Institute for Reliable Computing [Hamburg]
2 Faculty of Science and Engineering [Waseda]
3 CACAO - Curves, Algebra, Computer Arithmetic, and so On
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
4 PROVAL - Proof of Programs
UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR
5 MSR - INRIA - Microsoft Research - Inria Joint Centre
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.
Keywords : Floating-point arithmetic rounding to nearest predecessor successor directed rounding
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https://hal.inria.fr/inria-00337537
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Submitted on : Friday, November 7, 2008 - 12:05:24 PM
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Siegfried Rump, Paul Zimmermann, Sylvie Boldo, Guillaume Melquiond. Computing predecessor and successor in rounding to nearest. BIT Numerical Mathematics, Springer Verlag, 2009, 49 (2), pp.419-431. ⟨10.1007/s10543-009-0218-z⟩. ⟨inria-00337537⟩

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