High-Precision Computing based on the CUDA Architecture in Residual Number Systems

Residual Number Systems (RNS) are recognized for their parallel arithmetic capabilities. In recent years, they have been employed in various demanding applications, including digital signal processing, high-precision computing, cryptography, and large neural networks. With the advancement of multiprocessor systems on general-purpose platforms, the utilization of RNS for the effective parallelization of arithmetic computational operations with a large dynamic range of up to several tens of bits becomes a crucial aspect. To this end, modern Graphics Processing Units (GPUs) with several thousands of computational cores are ideal platforms. This study evaluates the efficacy of using RNS for implementing multiple precision arithmetic on NVIDIA GPUs using the CUDA hardware and software parallel computing architecture. The results of the experiments demonstrate the high efficiency of RNS for the multiplication operation. A configuration of 256 modules providing a 6400-bit dynamic range results in a computation time that is 7.92 times faster compared to the implementation on the standard GMP MP variant.