Compressed Modular Matrix Multiplication

Jean-Guillaume Dumas 1, * Laurent Fousse 1 Bruno Salvy 2
* Corresponding author
2 ALGORITHMS - Algorithms
Inria Paris-Rocquencourt
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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  • HAL Id : hal-00259950, version 2
  • ARXIV : 0803.1975

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Jean-Guillaume Dumas, Laurent Fousse, Bruno Salvy. Compressed Modular Matrix Multiplication. MICA'2008 - Milestones in Computer Algebra, May 2008, Tobago, Trinidad and Tobago. pp.133-140. ⟨hal-00259950v2⟩

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