New multi-moduli residue and quadratic residue systems for large dynamic ranges

The residue number system (RNS) is a useful tool for digital signal processing (DSP) since it can support parallel, carry-free, high-speed arithmetic. An RNS is defined by a set of relatively prime integers called the moduli set. The most important consideration when designing RNS systems is the choice of the moduli set. In order to maintain simple arithmetic, moduli sets with numbers of forms 2/sup n1/+1, 2/sup n2/-1 and 2/sup n3/ have been given serious consideration by RNS researchers in the past. The most popular such sets are the 3-moduli set {2/sup n/-1, 2/sup n/, 2/sup n/+1} and the 4-moduli set {2/sup n-1/-1, 2/sup n/-1, 2/sup n+1/-1, 2/sup n+1/} for even n. However, if very large dynamic ranges are desirable, the number of moduli should increase so that performance degradation is avoided. New multi-moduli RNS systems are presented that are based on moduli of forms 2/sup n1/+1, 2/sup n2/-1, 2/sup n3/. For a given dynamic range, these new systems exhibit performance of 2 to 3 times better than the performance of the known 3-moduli and 4-moduli systems.