LARGE DYNAMIC-RANGE COMPUTATIONS OVER SMALL FINITE RINGS

This paper presents a new multivariate mapping strategy for the recent ly introduced Modulus Replication Residue Number System (MRRNS). This mapping allows computation over a large dynamic range using replicatio ns of extremely small rings. The technique maintains the useful featur es of the MRRNS, namely: ease of input coding; absence of a Chinese Re mainder Theorem inverse mapping across the full dynamic range; replica tion of identical rings; and natural integration of complex data proce ssing. The concepts are illustrated by a specific example of complex i nner product processing associated with a radix-4 decimation in time f ast Fourier transform algorithm. A complete quantization analysis is p erformed and an efficient scaling strategy chosen based on the analysi s. The example processor uses replications of three rings: modulo-3, - 5, and -7; the effective dynamic range is in excess of 32 b. The paper also includes very-large-scale-integration implementation strategies for the processor architecture that consists of arrays of massively pa rallel linear bit-level pipelines.