Exact Sparse Matrix-Vector Multiplication on GPU's and Multicore Architectures

We propose different implementations of the sparse matrix--dense vector multiplication (\spmv{}) for finite fields and rings \Zb/m\Zb. We take advantage of graphic card processors (GPU) and multi-core architectures. Our aim is to improve the speed of \spmv{} in the \linbox library, and henceforth the speed of its black box algorithms. Besides, we use this and a new parallelization of the sigma-basis algorithm in a parallel block Wiedemann rank implementation over finite fields

Geometry-Oblivious FMM for Compressing Dense SPD Matrices

We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, "compression," of an arbitrary dense symmetric positive definite (SPD) matrix. For many applications, GOFMM enables an approximate matrix-vector multiplication in $N \log N$ or even $N$ time, where $N$ is the matrix size. Compression requires $N \log N$ storage and work. In general, our scheme belongs to the family of hierarchical matrix approximation methods. In particular, it generalizes the fast multipole method (FMM) to a purely algebraic setting by only requiring the ability to sample matrix entries. Neither geometric information (i.e., point coordinates) nor knowledge of how the matrix entries have been generated is required, thus the term "geometry-oblivious." Also, we introduce a shared-memory parallel scheme for hierarchical matrix computations that reduces synchronization barriers. We present results on the Intel Knights Landing and Haswell architectures, and on the NVIDIA Pascal architecture for a variety of matrices.Comment: 13 pages, accepted by SC'1

Portable performance on heterogeneous architectures

Trends in both consumer and high performance computing are bringing not only more cores, but also increased heterogeneity among the computational resources within a single machine. In many machines, one of the greatest computational resources is now their graphics coprocessors (GPUs), not just their primary CPUs. But GPU programming and memory models differ dramatically from conventional CPUs, and the relative performance characteristics of the different processors vary widely between machines. Different processors within a system often perform best with different algorithms and memory usage patterns, and achieving the best overall performance may require mapping portions of programs across all types of resources in the machine. To address the problem of efficiently programming machines with increasingly heterogeneous computational resources, we propose a programming model in which the best mapping of programs to processors and memories is determined empirically. Programs define choices in how their individual algorithms may work, and the compiler generates further choices in how they can map to CPU and GPU processors and memory systems. These choices are given to an empirical autotuning framework that allows the space of possible implementations to be searched at installation time. The rich choice space allows the autotuner to construct poly-algorithms that combine many different algorithmic techniques, using both the CPU and the GPU, to obtain better performance than any one technique alone. Experimental results show that algorithmic changes, and the varied use of both CPUs and GPUs, are necessary to obtain up to a 16.5x speedup over using a single program configuration for all architectures.United States. Dept. of Energy (Award DE-SC0005288)United States. Defense Advanced Research Projects Agency (Award HR0011-10-9-0009)National Science Foundation (U.S.) (Award CCF-0632997

Optimization Techniques for Mapping Algorithms and Applications onto CUDA GPU Platforms and CPU-GPU Heterogeneous Platforms

An emerging trend in processor architecture seems to indicate the doubling of the number of cores per chip every two years with same or decreased clock speed. Of particular interest to this thesis is the class of many-core processors, which are becoming more attractive due to their high performance, low cost, and low power consumption. The main goal of this dissertation is to develop optimization techniques for mapping algorithms and applications onto CUDA GPUs and CPU-GPU heterogeneous platforms. The Fast Fourier transform (FFT) constitutes a fundamental tool in computational science and engineering, and hence a GPU-optimized implementation is of paramount importance. We first study the mapping of the 3D FFT onto the recent, CUDA GPUs and develop a new approach that minimizes the number of global memory accesses and overlaps the computations along the different dimensions. We obtain some of the fastest known implementations for the computation of multi-dimensional FFT. We then present a highly multithreaded FFT-based direct Poisson solver that is optimized for the recent NVIDIA GPUs. In addition to the massive multithreading, our algorithm carefully manages the multiple layers of the memory hierarchy so that all global memory accesses are coalesced into 128-bytes device memory transactions. As a result, we have achieved up to 375GFLOPS with a bandwidth of 120GB/s on the GTX 480. We further extend our methodology to deal with CPU-GPU based heterogeneous platforms for the case when the input is too large to fit on the GPU global memory. We develop optimization techniques for memory-bound, and computation-bound application. The main challenge here is to minimize data transfer between the CPU memory and the device memory and to overlap as much as possible these transfers with kernel execution. For memory-bounded applications, we achieve a near-peak effective PCIe bus bandwidth, 9-10GB/s and performance as high as 145 GFLOPS for multi-dimensional FFT computations and for solving the Poisson equation. We extend our CPU-GPU based software pipeline to a computation-bound application-DGEMM, and achieve the illusion of a memory of the CPU memory size and a computation throughput similar to a pure GPU

General‐purpose computation on GPUs for high performance cloud computing

This is the peer reviewed version of the following article: Expósito, R. R., Taboada, G. L., Ramos, S., Touriño, J., & Doallo, R. (2013). General‐purpose computation on GPUs for high performance cloud computing. Concurrency and Computation: Practice and Experience, 25(12), 1628-1642., which has been published in final form at https://doi.org/10.1002/cpe.2845. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.[Abstract] Cloud computing is offering new approaches for High Performance Computing (HPC) as it provides dynamically scalable resources as a service over the Internet. In addition, General‐Purpose computation on Graphical Processing Units (GPGPU) has gained much attention from scientific computing in multiple domains, thus becoming an important programming model in HPC. Compute Unified Device Architecture (CUDA) has been established as a popular programming model for GPGPUs, removing the need for using the graphics APIs for computing applications. Open Computing Language (OpenCL) is an emerging alternative not only for GPGPU but also for any parallel architecture. GPU clusters, usually programmed with a hybrid parallel paradigm mixing Message Passing Interface (MPI) with CUDA/OpenCL, are currently gaining high popularity. Therefore, cloud providers are deploying clusters with multiple GPUs per node and high‐speed network interconnects in order to make them a feasible option for HPC as a Service (HPCaaS). This paper evaluates GPGPU for high performance cloud computing on a public cloud computing infrastructure, Amazon EC2 Cluster GPU Instances (CGI), equipped with NVIDIA Tesla GPUs and a 10 Gigabit Ethernet network. The analysis of the results, obtained using up to 64 GPUs and 256‐processor cores, has shown that GPGPU is a viable option for high performance cloud computing despite the significant impact that virtualized environments still have on network overhead, which still hampers the adoption of GPGPU communication‐intensive applications. CopyrightMinisterio de Ciencia e Innovación; TIN2010-1673

Body of Knowledge for Graphics Processing Units (GPUs)

Graphics Processing Units (GPU) have emerged as a proven technology that enables high performance computing and parallel processing in a small form factor. GPUs enhance the traditional computer paradigm by permitting acceleration of complex mathematics and providing the capability to perform weighted calculations, such as those in artificial intelligence systems. Despite the performance enhancements provided by this type of microprocessor, there exist tradeoffs in regards to reliability and radiation susceptibility, which may impact mission success. This report provides an insight into GPU architecture and its potential applications in space and other similar markets. It also discusses reliability, qualification, and radiation considerations for testing GPUs

Plasma Physics Computations on Emerging Hardware Architectures

This thesis explores the potential of emerging hardware architectures to increase the impact of high performance computing in fusion plasma physics research. For next generation tokamaks like ITER, realistic simulations and data-processing tasks will become significantly more demanding of computational resources than current facilities. It is therefore essential to investigate how emerging hardware such as the graphics processing unit (GPU) and field-programmable gate array (FPGA) can provide the required computing power for large data-processing tasks and large scale simulations in plasma physics specific computations. The use of emerging technology is investigated in three areas relevant to nuclear fusion: (i) a GPU is used to process the large amount of raw data produced by the synthetic aperture microwave imaging (SAMI) plasma diagnostic, (ii) the use of a GPU to accelerate the solution of the Bateman equations which model the evolution of nuclide number densities when subjected to neutron irradiation in tokamaks, and (iii) an FPGA-based dataflow engine is applied to compute massive matrix multiplications, a feature of many computational problems in fusion and more generally in scientific computing. The GPU data processing code for SAMI provides a 60x acceleration over the previous IDL-based code, enabling inter-shot analysis in future campaigns and the data-mining (and therefore analysis) of stored raw data from previous MAST campaigns. The feasibility of porting the whole Bateman solver to a GPU system is demonstrated and verified against the industry standard FISPACT code. Finally a dataflow approach to matrix multiplication is shown to provide a substantial acceleration compared to CPU-based approaches and, whilst not performing as well as a GPU for this particular problem, is shown to be much more energy efficient. Emerging hardware technologies will no doubt continue to provide a positive contribution in terms of performance to many areas of fusion research and several exciting new developments are on the horizon with tighter integration of GPUs and FPGAs with their host central processor units. This should not only improve performance and reduce data transfer bottlenecks, but also allow more user-friendly programming tools to be developed. All of this has implications for ITER and beyond where emerging hardware technologies will no doubt provide the key to delivering the computing power required to handle the large amounts of data and more realistic simulations demanded by these complex systems

Batched Linear Algebra Problems on GPU Accelerators

The emergence of multicore and heterogeneous architectures requires many linear algebra algorithms to be redesigned to take advantage of the accelerators, such as GPUs. A particularly challenging class of problems, arising in numerous applications, involves the use of linear algebra operations on many small-sized matrices. The size of these matrices is usually the same, up to a few hundred. The number of them can be thousands, even millions. Compared to large matrix problems with more data parallel computation that are well suited on GPUs, the challenges of small matrix problems lie in the low computing intensity, the large sequential operation fractions, and the big PCI-E overhead. These challenges entail redesigning the algorithms instead of merely porting the current LAPACK algorithms. We consider two classes of problems. The first is linear systems with one-sided factorizations (LU, QR, and Cholesky) and their solver, forward and backward substitution. The second is a two-sided Householder bi-diagonalization. They are challenging to develop and are highly demanded in applications. Our main efforts focus on the same-sized problems. Variable-sized problems are also considered, though to a lesser extent. Our contributions can be summarized as follows. First, we formulated a batched linear algebra framework to solve many data-parallel, small-sized problems/tasks. Second, we redesigned a set of fundamental linear algebra algorithms for high- performance, batched execution on GPU accelerators. Third, we designed batched BLAS (Basic Linear Algebra Subprograms) and proposed innovative optimization techniques for high-performance computation. Fourth, we illustrated the batched methodology on real-world applications as in the case of scaling a CFD application up to 4096 nodes on the Titan supercomputer at Oak Ridge National Laboratory (ORNL). Finally, we demonstrated the power, energy and time efficiency of using accelerators as compared to CPUs. Our solutions achieved large speedups and high energy efficiency compared to related routines in CUBLAS on NVIDIA GPUs and MKL on Intel Sandy-Bridge multicore CPUs. The modern accelerators are all Single-Instruction Multiple-Thread (SIMT) architectures. Our solutions and methods are based on NVIDIA GPUs and can be extended to other accelerators, such as the Intel Xeon Phi and AMD GPUs based on OpenCL