Maria Francesca Cascone
Implementation of the comparison in the Residue Numeral System.
Rel. Guido Masera. Politecnico di Torino, Corso di laurea magistrale in Ingegneria Elettronica (Electronic Engineering), 2022
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Abstract
Residue Number Systems, RNSs, have been considered a potential tool to parallelize the arithmetic breaking the long carry-propagation chain by bounding the RNS inside smaller modulo channels that work in parallel with each other. This parallelism is quite profitable for addition and multiplication and has made possible the usage of RNS in a range of application from embedded and digital signal processing systems to cryptography. However, some operations are difficult to perform using RNS: its non-positional representation makes hard to implement the comparison, indeed the existing comparison methods compare the RNS numbers by converting them in positional numeral system. The Positional Attribute Non-positional Code, PANC, method is a mathematical algorithm that allows the comparison in RNS without converting the numbers under consideration.
It associates the RNS number to an index that identifies the interval in which the number falls and then performs the comparison between the two indexes associated to both inputs
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