À propos de mathématiques
When a logarithm is a misspelled algorithm
Joldes, Mioara1
1 Laboratoire de l’Informatique du Parallélisme, École Normale Supérieure de Lyon 46, Allée d’Italie 69364 Lyon Cedex 07
Femmes & math, Forum 9 des Jeunes Mathématiciennes, Tome 9 (2010), pp. 43-47.

The high-quality floating-point implementation of elementary functions is a complex process. A variety of techniques ranging from numerical polynomial approximation algorithms to rigorous computation for bounding the approximation error are used. Firstly, we present a brief overview of this process. Then we show how rigorous computation methods based on multiprecision interval arithmetic and Taylor models are used for certified computation of tight bounds for supremum norms of approximation errors.

Publié le :
Joldes, Mioara 1

1 Laboratoire de l’Informatique du Parallélisme, École Normale Supérieure de Lyon 46, Allée d’Italie 69364 Lyon Cedex 07 
@article{RFM_2010__9__43_0,
     author = {Joldes, Mioara},
     title = {When a logarithm is a misspelled algorithm},
     journal = {Femmes & math},
     pages = {43--47},
     publisher = {Association femmes et math\'ematiques},
     volume = {9},
     year = {2010},
     language = {en},
     url = {http://www.numdam.org/item/RFM_2010__9__43_0/}
}
TY  - JOUR
AU  - Joldes, Mioara
TI  - When a logarithm is a misspelled algorithm
JO  - Femmes & math
PY  - 2010
SP  - 43
EP  - 47
VL  - 9
PB  - Association femmes et mathématiques
UR  - http://www.numdam.org/item/RFM_2010__9__43_0/
LA  - en
ID  - RFM_2010__9__43_0
ER  - 
%0 Journal Article
%A Joldes, Mioara
%T When a logarithm is a misspelled algorithm
%J Femmes & math
%D 2010
%P 43-47
%V 9
%I Association femmes et mathématiques
%U http://www.numdam.org/item/RFM_2010__9__43_0/
%G en
%F RFM_2010__9__43_0
Joldes, Mioara. When a logarithm is a misspelled algorithm. Femmes & math, Forum 9 des Jeunes Mathématiciennes, Tome 9 (2010), pp. 43-47. http://www.numdam.org/item/RFM_2010__9__43_0/

[1] A. Ziv, Fast evaluation of elementary mathematical functions with correctly rounded last bit, ACM Transactions on Mathematical Software, 17(3):410-423, 1991. | Zbl

[2] V. Lefevre, J.-M. Muller, Worst cases for correct rounding of the elementary functions in double precision, 15th IEEE Symposium on Computer Arithmetic, Colorado, June 2001.

[3] CRLibm, a library of correctly rounded elementary functions in double-precision, http://lipforge.ens-lyon.fr/www/crlibm/.

[4] S. Chevillard, Évaluation efficace de fonctions numériques. Outils et exemples, École Normale Supérieure de Lyon, Lyon, France, 2009.

[5] S. Chevillard, M. Joldes, C. Lauter Certified and fast computation of supremum norms of approximation errors, 19th IEEE SYMPOSIUM on Computer Arithmetic, Los Alamitos, CA, Portland, OR,169–176, 2009

[6] MPFI, Multiple Precision Floating-Point Interval Library, http://gforge.inria.fr/projects/mpfi/.

[7] K. Makino and M. Berz, Taylor Models and Other Validated Functional Inclusion Methods, International Journal of Pure and Applied Mathematics, Vol. 4, 379–456, 2003. | MR | Zbl