Compressed Modular Matrix Multiplication

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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.
Published in: MICA'2008 : Milestones in Computer Algebra, Tobago : Trinité-et-Tobago (2008)

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Symbolic Computation

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http://salesiana.dossiersoluciones.com/handle/123456789/212146

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0803.1975
 http://arxiv.org/abs/0803.1975

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arXiv