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arXiv · 0803.1975

Compressed Modular Matrix Multiplication

Jean-Guillaume Dumas·Laurent Fousse·Bruno Salvy
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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.

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Jean-Guillaume Dumas, Laurent Fousse, Bruno Salvy. 2008-03-13. Compressed Modular Matrix Multiplication. https://arxiv.org/abs/0803.1975

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