Fast low energy RNS comparators for 4-moduli sets {2n±1, 2n, m} with m∈{2n+1±1, 2n−1−1}

Abstract

Comparison is a difficult operation in residue number systems (RNS). Besides the straightforward comparison of binary equivalents of RNS numbers, shortcut methods for moduli-set τ={2n−1, 2n, 2n+1} have been proposed that only slightly improve the corresponding figures of merit. On the other hand, we have encountered only one hardware realization of 4-moduli RNS comparison, where the corresponding moduli-set does not include any power-of-two modulo. In this paper, we examine and provide shortcut RNS comparators for three moduli-sets with four modulus, all containing τ as a subset. Evaluation results show 15–136% speed-up and 39–366% less energy in comparison to the straightforward reverse-and-compare comparators.