Parallelizing the QUDA Library for Multi-GPU Calculations in Lattice Quantum Chromodynamics

Graphics Processing Units (GPUs) are having a transformational effect on numerical lattice quantum chromodynamics (LQCD) calculations of importance in nuclear and particle physics. The QUDA library provides a package of mixed precision sparse matrix linear solvers for LQCD applications, supporting single GPUs based on NVIDIA's Compute Unified Device Architecture (CUDA). This library, interfaced to the QDP++/Chroma framework for LQCD calculations, is currently in production use on the "9g" cluster at the Jefferson Laboratory, enabling unprecedented price/performance for a range of problems in LQCD. Nevertheless, memory constraints on current GPU devices limit the problem sizes that can be tackled. In this contribution we describe the parallelization of the QUDA library onto multiple GPUs using MPI, including strategies for the overlapping of communication and computation. We report on both weak and strong scaling for up to 32 GPUs interconnected by InfiniBand, on which we sustain in excess of 4 Tflops.Comment: 11 pages, 7 figures, to appear in the Proceedings of Supercomputing 2010 (submitted April 12, 2010

Performance Engineering for Real and Complex Tall & Skinny Matrix Multiplication Kernels on GPUs

General matrix-matrix multiplications with double-precision real and complex entries (DGEMM and ZGEMM) in vendor-supplied BLAS libraries are best optimized for square matrices but often show bad performance for tall & skinny matrices, which are much taller than wide. NVIDIA's current CUBLAS implementation delivers only a fraction of the potential performance as indicated by the roofline model in this case. We describe the challenges and key characteristics of an implementation that can achieve close to optimal performance. We further evaluate different strategies of parallelization and thread distribution, and devise a flexible, configurable mapping scheme. To ensure flexibility and allow for highly tailored implementations we use code generation combined with autotuning. For a large range of matrix sizes in the domain of interest we achieve at least 2/3 of the roofline performance and often substantially outperform state-of-the art CUBLAS results on an NVIDIA Volta GPGPU.Comment: 12 pages, 22 figures. Extended version of arXiv:1905.03136v1 for journal submissio