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The moduli set {$2^{n}-1$ , $2^{n}$ , $2^{n}+1$ } has been widely used in residue number system (RNS)-based computations. Its sign extraction problem, albeit fundamentally important in magnitude comparison and other difficult algorithms in RNS, has received considerably less attention than its scaling and reverse conversion problems. This brief presents a new algorithm for the design of a fast...
Comparison of residue representations in signed Residue Number System (RNS) involves sign detection and magnitude comparison. Both are difficult operations in RNS. This paper proposes a new signed magnitude comparator for the three-moduli set RNS {2n-1, 2n, 2n+1-1}. Two subrange identifiers are computed to simplify sign detection and accelerate the magnitude comparison without requiring full reverse...
Sign detection and magnitude comparison are two difficult operations in Residue Number System (RNS). Existing residue comparators tackle only unsigned integer for magnitude comparison. In this paper, a new algorithm for signed integer comparison in the four-moduli supersets, {2n, 2n −1, 2n +1, 2n+1-1} with even n, is proposed. The dynamic range is quantized into equal subranges to facilitate fast...
This paper presents an efficient RNS scaling algorithm for the balanced special moduli set {2n−1, 2n, 2n+1}. By exploiting the relationship between the scaling constant and the residues of the three-moduli set using the New Chinese Remainder Theorem I (New CRT-I), the complicated modulo reduction operations for large integer scaling in RNS can be greatly simplified. The scaling constant has been chosen...
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