Three-dimensional memory vectorization for high bandwidth media memory systems

Vector processors have good performance, cost and adaptability when targeting multimedia applications. However, for a significant number of media programs, conventional memory configurations fail to deliver enough memory references per cycle to feed the SIMD functional units. This paper addresses the problem of the memory bandwidth. We propose a novel mechanism suitable for 2-dimensional vector architectures and targeted at providing high effective bandwidth for SIMD memory instructions. The basis of this mechanism is the extension of the scope of vectorization at the memory level, so that 3-dimensional memory patterns can be fetched into a second-level register file. By fetching long blocks of data and by reusing 2-dimensional memory streams at this second-level register file, we obtain a significant increase in the effective memory bandwidth. As side benefits, the new 3-dimensional load instructions provide a high robustness to memory latency and a significant reduction of the cache activity, thus reducing power and energy requirements. At the investment of a 50% more area than a regular SIMD register file, we have measured and average speed-up of 13% and the potential for power savings in the L2 cache of a 30%.Peer ReviewedPostprint (published version

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

Implementing the conjugate gradient algorithm on multi-core systems

In linear solvers, like the conjugate gradient algorithm, sparse-matrix vector multiplication is an important kernel. Due to the sparseness of the matrices, the solver runs relatively slow. For digital optical tomography (DOT), a large set of linear equations have to be solved which currently takes in the order of hours on desktop computers. Our goal was to speed up the conjugate gradient solver. In this paper we present the results of applying multiple optimization techniques and exploiting multi-core solutions offered by two recently introduced architectures: Intel’s Woodcrest\ud general purpose processor and NVIDIA’s G80 graphical processing unit. Using these techniques for these architectures, a speedup of a factor three\ud has been achieved

Lattice QCD on PCs?

Current PC processors are equipped with vector processing units and have other advanced features that can be used to accelerate lattice QCD programs. Clusters of PCs with a high-bandwidth network thus become powerful and cost-effective machines for numerical simulations.Comment: Lattice2001(plenary), LaTeX source, 8 pages, figures include

Parallel structurally-symmetric sparse matrix-vector products on multi-core processors

We consider the problem of developing an efficient multi-threaded implementation of the matrix-vector multiplication algorithm for sparse matrices with structural symmetry. Matrices are stored using the compressed sparse row-column format (CSRC), designed for profiting from the symmetric non-zero pattern observed in global finite element matrices. Unlike classical compressed storage formats, performing the sparse matrix-vector product using the CSRC requires thread-safe access to the destination vector. To avoid race conditions, we have implemented two partitioning strategies. In the first one, each thread allocates an array for storing its contributions, which are later combined in an accumulation step. We analyze how to perform this accumulation in four different ways. The second strategy employs a coloring algorithm for grouping rows that can be concurrently processed by threads. Our results indicate that, although incurring an increase in the working set size, the former approach leads to the best performance improvements for most matrices.Comment: 17 pages, 17 figures, reviewed related work section, fixed typo