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| HAL : hal-00259950, version 2 |
| arXiv : 0803.1975 |
| Fiche détaillée |  Récupérer au format |
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| MICA'2008 : Milestones in Computer Algebra, Tobago : Trinité-et-Tobago (2008) |
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| Versions disponibles : | v1 (29-02-2008) | v2 (13-03-2008) |
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| Compressed Modular Matrix Multiplication |
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Jean-Guillaume Dumas 1Laurent Fousse 1 |
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| (05/2008) |
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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. |
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| 1 : | Laboratoire Jean Kuntzmann (LJK) |
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CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre Mendès-France - Grenoble II – Institut Polytechnique de Grenoble |
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| 2 : | ALGORITHMS (INRIA Rocquencourt) |
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INRIA |
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| Domaine | : | Informatique/Calcul formel |
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| matrix format – small prime field – exact matrix multiplication – polynomial multiplication – dot product |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00259950, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00259950 | |
| oai:hal.archives-ouvertes.fr:hal-00259950 | |
| Contributeur : Jean-Guillaume Dumas | |
| Soumis le : Jeudi 13 Mars 2008, 17:56:32 | |
| Dernière modification le : Jeudi 4 Septembre 2008, 11:11:05 | |
