Fast polynomial evaluation and composition - Archive ouverte HAL
Rapport Année : 2013

Fast polynomial evaluation and composition

Résumé

The library \emph{fast\_polynomial} for Sage compiles multivariate polynomials for subsequent fast evaluation. Several evaluation schemes are handled, such as Hörner, divide and conquer and new ones can be added easily. Notably, a new scheme is introduced that improves the classical divide and conquer scheme when the number of terms is not a pure power of two. Natively, the library handles polynomials over gmp big integers, boost intervals, python numeric types. And any type that supports addition and multiplication can extend the library thanks to the template design. Finally, the code is parallelized for the divide and conquer schemes, and memory allocation is localized and optimized for the different evaluation schemes. This extended abstract presents the concepts behind the \emph{fast\_polynomial} library. The sage package can be downloaded at \url{http://trac.sagemath.org/sage_trac/ticket/13358}.
Fichier principal
Vignette du fichier
fast_polynomial.pdf (125.42 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00846961 , version 1 (22-07-2013)
hal-00846961 , version 2 (26-07-2013)
hal-00846961 , version 3 (20-01-2015)

Identifiants

Citer

Guillaume Moroz. Fast polynomial evaluation and composition. 2013. ⟨hal-00846961v1⟩
502 Consultations
2298 Téléchargements

Altmetric

Partager

More