Reliable Computing

, Volume 7, Issue 4, pp 321–340 | Cite as

Automatic Forward Error Analysis for Floating Point Algorithms

  • Walter Krämer
  • Armin Bantle


We investigate absolute and relative error bounds for floating point calculations determined by means of sequences of instructions (as, for example, given by a computer program). We get rigorous error bounds on the round-off or generated error due to the actual machine floating point operations, as well as the propagated error from one sequence to the next in a very convenient way by the computer itself. The results stated in the theorems can be used to implement software tools for the automatic computation of a priori worst case error bounds for floating point computations. These automatically computed bounds are valid simultaneously for all data vectors varying in the domain specified and their corresponding machine vectors fulfilling a maximum prescribed error bound.

With great success we have used our method in the past to implement a fast interval library for elementary functions called FI_LIB [12]. Further numerical examples often show a high quality of the computed a priori bounds.


Software Tool Elementary Function Error Bound Great Success Case Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Walter Krämer
    • 1
  • Armin Bantle
    • 1
  1. 1.Wessenschaftliches Rechnen / Softwaretechnologie, Bergische Universität GH WuppertalWuppertalGermany

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