Worst Cases and Lattice Reduction

  title={Worst Cases and Lattice Reduction},
  author={Damien Stehl{\'e} and Vincent Lef{\`e}vre and Paul Zimmermann},
  booktitle={IEEE Symposium on Computer Arithmetic},
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
Highly Cited
This paper has 23 citations. REVIEW CITATIONS
16 Extracted Citations
23 Extracted References
Similar Papers

Citing Papers

Publications influenced by this paper.

Referenced Papers

Publications referenced by this paper.
Showing 1-10 of 23 references

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

Similar Papers

Loading similar papers…