BIT Numerical Mathematics

, Volume 49, Issue 2, pp 419–431 | Cite as

Computing predecessor and successor in rounding to nearest

  • Siegfried M. RumpEmail author
  • Paul Zimmermann
  • Sylvie Boldo
  • Guillaume Melquiond


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.


Floating-point arithmetic Rounding to nearest Predecessor Successor Directed rounding 

Mathematics Subject Classification (2000)

68-04 68N30 


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Copyright information

© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  • Siegfried M. Rump
    • 1
    • 2
    Email author
  • Paul Zimmermann
    • 3
  • Sylvie Boldo
    • 4
  • Guillaume Melquiond
    • 5
  1. 1.Institute for Reliable ComputingHamburg University of TechnologyHamburgGermany
  2. 2.Faculty of Science and EngineeringWaseda UniversityTokyoJapan
  3. 3.Centre de Recherche INRIA Nancy–Grand EstÉquipe-projet CACAO, Bâtiment AVillers-lès-NancyFrance
  4. 4.INRIA Saclay–Île-de-FranceParc Orsay Université–ZAC des VignesOrsay CedexFrance
  5. 5.Centre de recherche commun INRIA–Microsoft ResearchOrsay CedexFrance

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