RNS Reverse Converters for Moduli Sets With Dynamic Ranges up to $(8n+1)$ -bit

In the last years, investigation on residue number systems (RNS) has targeted parallelism and larger dynamic ranges. In this paper, we start from the moduli set ${2^{n},2^{n}-1,2^{n}+1,2^{n}-2^{(n+1)/2}+1,2^{n}+2^{(n+1)/2}+1}$ , with an equivalent $5n$ -bit dynamic range, and propose horizontal and vertical extensions in order to improve the parallelism and increase the dynamic range. The vertical extensions increase the value of the power-of-2 modulus in the five-moduli set. With the horizontal extensions, new six channel sets are allowed by introducing the $2^{n+1}+1$ or $2^{n-1}+1$ moduli. This paper proposes methods to design memoryless reverse converters for the proposed moduli sets with large dynamic ranges, up to $(8n+1)$ -bit. Due to the complexity of the reverse conversion, both the Chinese Remainder Theorem and the Mixed Radix Conversion are applied in the proposed methods to derive efficient reverse converters. Experimental results suggest that the proposed vertical extensions allow to reduce the area-delay-product up to 1.34 times in comparison with the related state-of-the-art. The horizontal extensions allow larger and more balanced moduli sets, resulting in an improvement of the RNS arithmetic computation, at the cost of lower reverse conversion performance.