Compressed Modular Matrix Multiplication
Abstract
We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo. Modular Multiplication is not directly accessible but modular dot product can be performed by an integer multiplication by the reverse integer. Modular multiplication by a word containing a single residue is a also possible. Therefore matrix multiplication can be performed on such a compressed storage. We here give bounds on the sizes of primes and matrices for which such a compression is possible. We also explicit the details of the required compressed arithmetic routines.
Cite
@article{arxiv.0803.1975,
title = {Compressed Modular Matrix Multiplication},
author = {Jean-Guillaume Dumas and Laurent Fousse and Bruno Salvy},
journal= {arXiv preprint arXiv:0803.1975},
year = {2008}
}
Comments
Published in: MICA'2008 : Milestones in Computer Algebra, Tobago : Trinit\'e-et-Tobago (2008)