Contributions to the Design of Residue Number System Architectures

Abstract

Residue Number System (RNS) is nowadays considered as a real alternative to other hardware architectures for handling large-number computations. In this paper we propose algorithmic answers to some of the questions that may face a designer when implementing such solution. More precisely, we investigated the following three problems. First, we propose an efficient method for constructing maximal bases noticing that this problem can be seen as a max-clique problem. Second we consider the logical gates count reduction when two different bases share the same hardware modules. Again it is linked to graph theory since it corresponds to finding a maximum weighted matching. Eventually we detail how the presence of DSP blocks in FPGAs can be leveraged to reach higher design frequencies by implementing full computation units inside.