Multiple-Precision Summation on Hybrid CPU-GPU Platforms Using RNS-based Floating-Point Representation

Abstract

We consider the summation of large sets of floating-point numbers on hybrid CPU-GPU platforms using MPRES, a new software library for multiple-precision computations on CPUs and CUDA compatible GPUs. This library uses an RNSbased floating-point representation, in accordance with which the multiple-precision significands are represented in a residue number system (RNS). This representation allows the computation of digits (residues) of significands in a parallel way and without carry propagation delay. We present the addition algorithm for RNS-based representations, as well as three multiple-precision summation algorithms: recursive summation, pairwise summation, and block-parallel hybrid summation. The hybrid algorithm demonstrates better performance, as it allows the full utilization of the GPU's resources.