The residue number system, complex residue number systems, and digital signal processing
M.F. Griffin, Fred J. Taylor · University of Florida Digital Collections (University of Florida) · 1989
To achieve high speed signal processing, the Residue Number System (RNS) is receiving growing attention because of its ability to support high-speed integer arithmetic. However, the RNS is not without its shortcomings, one of which is the scaling. In this dissertation two new scaling policies, based on the Chinese Remainder Theorem, are given which circumvent the hardware complexity normally required for scaling of systems with large dynamic ranges. It will be shown that the error properties of this scaling method are modest and can be predicted precisely. Therefore, with these two scaling algorithms, the RNS can expect a marked improvement in throughput when the dynamic range is large. The fundamental problem with complex integer arithmetic is the four products and two add/subtracts required for each complex multiplication. A new result, the index quadratic RNS, has reduced the complex product complexity to two adds. The significance of this result is the reduction in memory table address space, by a factor of two, over the existing extension field index calculus method. Finally, an RNS array processor design is presented, primarily to investigate the impact that the RNS has on the design of a high speed programmable array processor. It is shown that a programmable RNS array processor is feasible when based on a systolic architecture. The computational throughput, on a 15 element linear array, is estimated to be 1 Gops.