Optimal Small-Bitwidth Moduli Set for Residue Number Systems

TL;DR

This paper introduces an algorithm for generating optimal co-prime moduli sets in Residue Number Systems, balancing bit-lengths and maximizing dynamic range for efficient hardware implementation.

Contribution

It presents a novel algorithmic approach to produce optimal moduli sets that improve RNS performance by balancing bit-lengths and maximizing dynamic range.

Findings

Generated moduli sets achieve optimal dynamic range coverage

Sets maintain balanced bit-length distribution

Suitable for parallel hardware RNS implementations

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.