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Experimental Mathematics Seminar

Effectively multiplication- and division-free residue number systems

Eugene Zima, Wilfrid Laurier University

Location:  https://rutgers.zoom.us/j/94346444480 [password: The 20th Catalan number, alias (40)!/(20!*21!)
Date & time: Thursday, 25 April 2024 at 5:00AM - 6:00PM

Several methods of selection of moduli in modular arithmetic are considered. With the proposed choice of moduli both modular reduction of an integer and reconstruction from modular images are accelerated. Special attention is paid to the moduli of the forms 2n ± 1 and 2n ± 2k ± 1. Different schemes of choice of these types of moduli and algorithms for conversion of arbitrary precision integers into the modular representation and back are considered. Results of experimental implementation of a two-layer modular arithmetic in GMP system are discussed.

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