In-place accumulation of fast multiplication formulae - Archive ouverte HAL Accéder directement au contenu
Rapport Année : 2024

In-place accumulation of fast multiplication formulae

Résumé

This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples include the in-place accumulated multiplication of polynomials or matrices, C+=AB. The difficulty is to combine in-place computations with fast algorithms: those usually come at the expense of (potentially large) extra temporary space, but with accumulation the output variables are not even available to store intermediate values. We first propose a novel automatic design of fast and in-place accumulating algorithms for any bilinear formulae (and thus for polynomial and matrix multiplication) and then extend it to any linear accumulation of a collection of functions. For this, we relax the in-place model to any algorithm allowed to modify its inputs, provided that those are restored to their initial state afterwards. This allows us, in fine, to derive unprecedented in-place accumulating algorithms for fast polynomial multiplications and for Strassen-like matrix multiplications.
Fichier principal
Vignette du fichier
bilinear.pdf (347.33 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04167499 , version 1 (20-07-2023)
hal-04167499 , version 2 (24-10-2023)
hal-04167499 , version 3 (12-01-2024)

Identifiants

Citer

Jean-Guillaume Dumas, Bruno Grenet. In-place accumulation of fast multiplication formulae. Univ. Grenoble Alpes. 2024. ⟨hal-04167499v3⟩
149 Consultations
29 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More