Worst Cases for the Exponential Function in the IEEE 754r decimal64 Format

  • Vincent Lefèvre
  • Damien Stehlé
  • Paul Zimmermann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5045)

Abstract

We searched for the worst cases for correct rounding of the exponential function in the IEEE 754r decimal64 format, and computed all the bad cases whose distance from a breakpoint (for all rounding modes) is less than 10− 15 ulp, and we give the worst ones. In particular, the worst case for |x| ≥ 3 ×10− 11 is \(\exp(9.407822313572878 \times 10^{-2}) = 1.098645682066338\,5\,0000000000000000\,278\ldots\). This work can be extended to other elementary functions in the decimal64 format and allows the design of reasonably fast routines that will evaluate these functions with correct rounding, at least in some domains.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Vincent Lefèvre
    • 1
  • Damien Stehlé
    • 2
  • Paul Zimmermann
    • 3
  1. 1.INRIA/ÉNS LyonUniversité de Lyon/LIPLyon Cedex 07France
  2. 2.CNRS/ÉNS LyonUniversité de Lyon/LIP/INRIA ArenaireLyon Cedex 07France
  3. 3.LORIA/INRIA Lorraine, Bâtiment A, Technopôle de Nancy-Brabois Villers-lès-Nancy CedexFrance

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