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Compressed modular matrix multiplication

By Jean-Guillaume Dumas, Laurent Fousse and Bruno Salvy

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

Year: 2008
OAI identifier: oai:CiteSeerX.psu:10.1.1.313.7429
Provided by: CiteSeerX
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