Issue No. 01 - January (1994 vol. 43)

ISSN: 0018-9340

pp: 78-86

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.250611

ABSTRACT

<p>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.</p>

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.

CITATION

D. Reaume, G.A. Jullien, N.M. Wigley, "Large Dynamic Range Computations Over Small Finite Rings",

*IEEE Transactions on Computers*, vol. 43, no. , pp. 78-86, January 1994, doi:10.1109/12.250611