On equivalences and fair comparisons among residue number systems with special moduli

Properties and applications of residue number systems (RNS) with special moduli of the form 2^k ± 1, with a single power-of-2 modulus often also included, have been studied extensively. We show that lack of systematic studies has led to rediscovery of “new” moduli sets that are really equivalent to previously studied ones and that certain comparisons presented to show advantages of some proposed moduli sets are rather unfair. We prove a general mathematical result that allows us to normalize the single power-of-2 modulus, thus removing some of the problematic variations from such proposed sets. We then offer an assessment strategy based on dynamic ranges of the RNS sets being compared, rather than on artificial parameters that may be different for comparable systems.