An Efficient Scalable RNS Architecture for Large Dynamic Ranges

Abstract

This paper proposes an efficient scalable Residue Number System (RNS) architecture supporting moduli sets with an arbitrary number of channels, allowing to achieve larger dynamic range and a higher level of parallelism. The proposed architecture allows the forward and reverse RNS conversion, by reusing the arithmetic channel units. The arithmetic operations supported at the channel level include addition, subtraction, and multiplication with accumulation capability. For the reverse conversion two algorithms are considered, one based on the Chinese Remainder Theorem and the other one on Mixed-Radix-Conversion, leading to implementations optimized for delay and required circuit area. With the proposed architecture a complete and compact RNS platform is achieved . Experimental results suggest gains of 17 % in the delay in the arithmetic operations, with an area reduction of 23 % regarding the RNS state of the art. When compared with a binary system the proposed architecture allows to perform the same computation 20 times faster alongside with only 10 % of the circuit area resources.