Analytical Approach for Numerical Accuracy Estimation of Fixed-Point Systems Based on Smooth Operations

Romuald Rocher 1 Daniel Ménard 1 Olivier Sentieys 1 Pascal Scalart 1
1 CAIRN - Energy Efficient Computing ArchItectures with Embedded Reconfigurable Resources
Inria Rennes – Bretagne Atlantique , IRISA-D3 - ARCHITECTURE
Abstract : In embedded systems using fixed-point arithmetic, convert- ing applications into fixed-point representations requires a fast and efficient accuracy evaluation. This paper presents a new analytical approach to determine an estimation of the numerical accuracy of a fixed-point system, which is accurate and valid for all systems formulated with smooth operations (e.g. additions, subtractions, multiplications and divisions). The mathematical expression of the system output noise power is determined using matrices to obtain more compact expressions. The proposed approach is based on the determination of the time- varying impulse-response of the system. To speedup computation of the expressions, the impulse response is modelled using a linear prediction approach. The approach is illustrated in the general case of time-varying recursive systems by the Least Mean Square (LMS) algorithm example. Experiments on various and representative applications show the fixed- point accuracy estimation quality of the proposed approach. Moreover, the approach using the linear-prediction approximation is very fast even for recursive systems. A significant speed-up compared to the best known accuracy evaluation approaches is measured even for the most complex benchmarks.
Type de document :
Article dans une revue
IEEE Transactions on Circuits and Systems Part 1 Fundamental Theory and Applications, Institute of Electrical and Electronics Engineers (IEEE), 2012, 59 (10), pp.2326 - 2339. 〈10.1109/TCSI.2012.2188938〉
Liste complète des métadonnées

Littérature citée [36 références]  Voir  Masquer  Télécharger
https://hal.inria.fr/hal-00741741
Contributeur : Romuald Rocher <>
Soumis le : lundi 15 octobre 2012 - 11:18:13
Dernière modification le : mercredi 16 mai 2018 - 11:23:26
Document(s) archivé(s) le : mercredi 16 janvier 2013 - 03:38:03

Fichier

ArticleVersionFinale.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

INRIA | IRISA | IETR-INSA | IETR | IRISA-D3 | UR1-UFR-ISTIC | UNIV-RENNES

Citation

Romuald Rocher, Daniel Ménard, Olivier Sentieys, Pascal Scalart. Analytical Approach for Numerical Accuracy Estimation of Fixed-Point Systems Based on Smooth Operations. IEEE Transactions on Circuits and Systems Part 1 Fundamental Theory and Applications, Institute of Electrical and Electronics Engineers (IEEE), 2012, 59 (10), pp.2326 - 2339. 〈10.1109/TCSI.2012.2188938〉. 〈hal-00741741〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

2229

Téléchargements de fichiers

242

Contact


archive-ouverte@inria.fr