Efficient GPU implementation of multiple-precision addition based on residue arithmetic

Abstract

In this work, the residue number system (RNS) is applied for efficient addition of multiple-precision integers using graphics processing units (GPUs) that support the Compute Unified Device Architecture (CUDA) platform. The RNS allows calculations with the digits of a multiple-precision number to be performed in an element-wise fashion, without the overhead of communication between them, which is especially useful for massively parallel architectures such as the GPU architecture. The paper discusses two multiple-precision integer algorithms. The first algorithm relies on if-else statements to test the signs of the operands. In turn, the second algorithm uses radix complement RNS arithmetic to handle negative numbers. While the first algorithm is more straightforward, the second one avoids branch divergence among threads that concurrently compute different elements of a multiple-precision array. As a result, the second algorithm shows significantly better performance compared to the first algorithm. Both algorithms running on an NVIDIA RTX 2080 Ti GPU are faster than the multi-core GNU MP implementation running on an Intel Xeon 4100 processor.