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Large Dynamic Range Computations Over Small Finite Rings
January 1994 (vol. 43 no. 1)
pp. 78-86

Presents a new multivariate mapping strategy for the recently introduced Modulus Replication Residue Number System (MRRNS). This mapping allows computation over a large dynamic range using replications of extremely small rings. The technique maintains the useful features of the MRRNS, namely: ease of input coding; absence of a Chinese Remainder Theorem inverse mapping across the full dynamic range; replication of identical rings; and natural integration of complex data processing. The concepts are illustrated by a specific example of complex inner product processing associated with a radix-4 decimation in time fast Fourier transform algorithm. A complete quantization analysis is performed and an efficient scaling strategy chosen based on the analysis. 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 parallel linear bit-level pipelines.

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Index Terms:
digital arithmetic; small finite rings; multivariate mapping strategy; Modulus Replication Residue Number System; Chinese Remainder Theorem; processor architecture; scaling strategy; complex arithmetic; dynamic logic; inner product computations; polynomial rings; quadratic residue rings; residue number systems; VLSI signal processors.
N.M. Wigley, G.A. Jullien, D. Reaume, "Large Dynamic Range Computations Over Small Finite Rings," IEEE Transactions on Computers, vol. 43, no. 1, pp. 78-86, Jan. 1994, doi:10.1109/12.250611
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