Worst Cases and Lattice Reduction

@inproceedings{Stehl2003WorstCA,
  title={Worst Cases and Lattice Reduction},
  author={Damien Stehl{\'e} and Vincent Lef{\`e}vre and Paul Zimmermann},
  booktitle={IEEE Symposium on Computer Arithmetic},
  year={2003}
}
We propose a new algorithm to find worst cases for correct rounding of an analytic function. We first reduce this problem to the real small value problem — i.e. for polynomials with real coefficients. Then we show that this second problem can be solved efficiently, by extending Coppersmith’s work on the integer small value problem — for polynomials with integer coefficients — using lattice reduction [4, 5, 6]. For floating-point numbers with a mantissa less than , and a polynomial approximation… CONTINUE READING
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A note on finding difficult values to evaluate numerically

  • G. Gonnet
  • http://www.inf.ethz.ch/personal/ gonnet…
  • 2002
Highly Influential
4 Excerpts

Moyens arithmétiques pour un calcul fiable

  • V. Lefèvre
  • Thèse de doctorat, École Normale Supérieure de…
  • 2000
Highly Influential
13 Excerpts

Proposals for a specification of the elementary functions

  • J.-M. Muller
  • In Abstracts of SCAN’2002,
  • 2002
1 Excerpt

Software carry-save for fast multiple-precision algorithms. Research Report 2002-08

  • D. Defour, F. de Dinechin
  • Laboratoire de l’Informatique du Parallélisme,
  • 2002
1 Excerpt

Correctly rounded exponential function in double precision arithmetic

  • D. Defour, F. de Dinechin, J.-M. Muller
  • Research Report 2001-26, Laboratoire de l…
  • 2001
1 Excerpt

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