Density results on floating-point invertible numbers

Abstract : Let $F_k$ denote the $k$-bit mantissa floating-point (FP) numbers. We prove a conjecture of J.-M. Muller according to which the proportion of numbers in $F_k$ with no FP-reciprocal (for rounding to the nearest element) approaches $\frac{1}{2}-\frac{3}{2}\log\frac43\approx 0.068476\ 89$ as $k\to\infty$. We investigate a similar question for the inverse square root.
Type de document :
Article dans une revue
Theoretical Computer Science, Elsevier, 2003, 291 (2), pp.135-141
Liste complète des métadonnées

https://hal.inria.fr/inria-00099510
Contributeur : Publications Loria <>
Soumis le : mardi 26 septembre 2006 - 09:37:58
Dernière modification le : jeudi 17 mai 2018 - 12:52:03

Identifiants

  • HAL Id : inria-00099510, version 1

Collections

Citation

Guillaume Hanrot, Joel Rivat, Gérald Tenenbaum, Paul Zimmermann. Density results on floating-point invertible numbers. Theoretical Computer Science, Elsevier, 2003, 291 (2), pp.135-141. 〈inria-00099510〉

Partager

Métriques

Consultations de la notice

311