Speculative Segmented Sum for Sparse Matrix-Vector Multiplication on Heterogeneous Processors

Sparse matrix-vector multiplication (SpMV) is a central building block for scientific software and graph applications. Recently, heterogeneous processors composed of different types of cores attracted much attention because of their flexible core configuration and high energy efficiency. In this paper, we propose a compressed sparse row (CSR) format based SpMV algorithm utilizing both types of cores in a CPU-GPU heterogeneous processor. We first speculatively execute segmented sum operations on the GPU part of a heterogeneous processor and generate a possibly incorrect results. Then the CPU part of the same chip is triggered to re-arrange the predicted partial sums for a correct resulting vector. On three heterogeneous processors from Intel, AMD and nVidia, using 20 sparse matrices as a benchmark suite, the experimental results show that our method obtains significant performance improvement over the best existing CSR-based SpMV algorithms. The source code of this work is downloadable at https://github.com/bhSPARSE/Benchmark_SpMV_using_CSRComment: 22 pages, 8 figures, Published at Parallel Computing (PARCO

Solving Lattice QCD systems of equations using mixed precision solvers on GPUs

Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodyamics (lattice QCD), where the main computational challenge is to efficiently solve the discretized Dirac equation in the presence of an SU(3) gauge field. Using NVIDIA's CUDA platform we have implemented a Wilson-Dirac sparse matrix-vector product that performs at up to 40 Gflops, 135 Gflops and 212 Gflops for double, single and half precision respectively on NVIDIA's GeForce GTX 280 GPU. We have developed a new mixed precision approach for Krylov solvers using reliable updates which allows for full double precision accuracy while using only single or half precision arithmetic for the bulk of the computation. The resulting BiCGstab and CG solvers run in excess of 100 Gflops and, in terms of iterations until convergence, perform better than the usual defect-correction approach for mixed precision.Comment: 30 pages, 7 figure

PyCUDA and PyOpenCL: A Scripting-Based Approach to GPU Run-Time Code Generation

High-performance computing has recently seen a surge of interest in heterogeneous systems, with an emphasis on modern Graphics Processing Units (GPUs). These devices offer tremendous potential for performance and efficiency in important large-scale applications of computational science. However, exploiting this potential can be challenging, as one must adapt to the specialized and rapidly evolving computing environment currently exhibited by GPUs. One way of addressing this challenge is to embrace better techniques and develop tools tailored to their needs. This article presents one simple technique, GPU run-time code generation (RTCG), along with PyCUDA and PyOpenCL, two open-source toolkits that support this technique. In introducing PyCUDA and PyOpenCL, this article proposes the combination of a dynamic, high-level scripting language with the massive performance of a GPU as a compelling two-tiered computing platform, potentially offering significant performance and productivity advantages over conventional single-tier, static systems. The concept of RTCG is simple and easily implemented using existing, robust infrastructure. Nonetheless it is powerful enough to support (and encourage) the creation of custom application-specific tools by its users. The premise of the paper is illustrated by a wide range of examples where the technique has been applied with considerable success.Comment: Submitted to Parallel Computing, Elsevie