Optimal Small-Bitwidth Moduli Set for Residue Number Systems

Abstract

This technical note presents a algorithmic approach for generating optimal sets of co-prime moduli within specified integer ranges. The proposed method addresses the challenge of balancing moduli bit-lengths while maximizing the dynamic range in Residue Number System (RNS) implementations. Experimental results demonstrate that the generated moduli sets achieve optimal dynamic range coverage while maintaining balanced bit-length distribution, making them particularly suitable for parallel hardware implementations based on RNS.

Figures (1)

• Figure 1: Schematic representation of RNS, where $\circ \in \{+, -, \times\}$.