Time- and Space-Efficient Evaluation of Some Hypergeometric Constants

Howard Cheng 1 Guillaume Hanrot 2 Emmanuel Thomé 2, * Eugene Zima 3 Paul Zimmermann 2
* Auteur correspondant
1 Department of Mathematics and Computer Science
2 CACAO - Curves, Algebra, Computer Arithmetic, and so On
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
3 Department of physics and computer science
Abstract : The currently best known algorithms for the numerical evaluation of hypergeometric constants such as $\zeta(3)$ to $d$ decimal digits have time complexity $O(M(d) \log^2 d)$ and space complexity of $O(d \log d)$ or $O(d)$. Following work from Cheng, Gergel, Kim and Zima, we present a new algorithm with the same asymptotic complexity, but more efficient in practice. Our implementation of this algorithm improves slightly over existing programs for the computation of $\pi$, and we announce a new record of 2 billion digits for $\zeta(3)$.
Keywords : high-precision evaluation hypergeometric constants
Type de document :
Communication dans un congrès
International Symposium on Symbolic and Algebraic Computation - ISSAC'07, Jul 2007, Waterloo, Canada. ACM, pp.85-91, 2007, Proceedings of the 2007 international symposium on Symbolic and algebraic computation. 〈10.1145/1277548.1277561〉
Liste complète des métadonnées

Littérature citée [20 références]  Voir  Masquer  Télécharger
https://hal.inria.fr/inria-00177850
Contributeur : Emmanuel Thomé <>
Soumis le : mardi 9 octobre 2007 - 14:04:48
Dernière modification le : mercredi 13 février 2019 - 14:58:21
Document(s) archivé(s) le : dimanche 11 avril 2010 - 22:34:15

Fichier

zeta3.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

Collections

INRIA | LORIA | UNIV-LORRAINE

Citation

Howard Cheng, Guillaume Hanrot, Emmanuel Thomé, Eugene Zima, Paul Zimmermann. Time- and Space-Efficient Evaluation of Some Hypergeometric Constants. International Symposium on Symbolic and Algebraic Computation - ISSAC'07, Jul 2007, Waterloo, Canada. ACM, pp.85-91, 2007, Proceedings of the 2007 international symposium on Symbolic and algebraic computation. 〈10.1145/1277548.1277561〉. 〈inria-00177850〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

490

Téléchargements de fichiers

130

Contact


archive-ouverte@inria.fr