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Simultaneous conversions with the Residue Number System using linear algebra

Javad Doliskani 1 Pascal Giorgi 2 Romain Lebreton 2 Éric Schost 3 
2 ECO - Exact Computing
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We present an algorithm for simultaneous conversion between a given set of integers and their Residue Number System representations based on linear algebra. We provide a highly optimized implementation of the algorithm that exploits the computational features of modern processors. The main application of our algorithm is matrix multiplication over integers. Our speed-up of the conversions to and from the Residue Number System significantly improves the overall running time of matrix multiplication.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01415472
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Submitted on : Friday, February 9, 2018 - 11:51:38 AM
Last modification on : Friday, August 5, 2022 - 3:02:58 PM
Long-term archiving on: : Friday, May 4, 2018 - 12:04:30 AM

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Javad Doliskani, Pascal Giorgi, Romain Lebreton, Éric Schost. Simultaneous conversions with the Residue Number System using linear algebra. ACM Transactions on Mathematical Software, 2018, 44 (3), pp.#27. ⟨10.1145/3145573⟩. ⟨lirmm-01415472v2⟩

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