High-Performance Computation in Residue Number System Using Floating-Point Arithmetic

Residue number system (RNS) is known for its parallel arithmetic and has been used in recent decades various important applications, from digital signal processing deep neural networks to cryptography high-precision computation. However, comparison, sign identification, overflow detection, division are still hard implement RNS. For such operations, most of the methods proposed literature only support small dynamic ranges (up several tens bits), so they suitable low-precision applications. We recently a method that supports arbitrary moduli sets with cryptographically sized ranges, up thousands bits. The practical interest our compared existing it relies on very fast standard floating-point multiple-precision applications can be efficiently implemented many general-purpose platforms IEEE 754 arithmetic. In this paper, we make further improvements demonstrate successfully applied efficient data-parallel primitives operating RNS domain, namely finding maximum element an array numbers graphics units. Our experimental results NVIDIA RTX 2080 GPU show random residues 128-moduli set 2048-bit range, implementation reduces running time by factor 39 memory consumption 13 based mixed-radix conversion.