Many scientific applications, ranging from national security to medical advances, require solving a number of relatively small-size independent problems. As the size of each individual problem does not provide sufficient parallelism for the underlying hardware, especially accelerators, these problems must be solved concurrently as a batch in order to saturate the hardware with enough work, hence the name batched computation. A possible simplification is to assume a uniform size for all problems. However, real applications do not necessarily satisfy such assumption. Consequently, an efficient solution for variable-size batched computations is required.

This paper proposes a foundation for high performance variable-size batched matrix computation based on Graphics Processing Units (GPUs). Being throughput-oriented processors, GPUs favor regular computation and less divergence among threads, in order to achieve high performance. Therefore, the development of high performance numerical software for this kind of problems is challenging. As a case study, we developed efficient batched Cholesky factorization algorithms for relatively small matrices of different sizes. However, most of the strategies and the software developed, and in particular a set of variable size batched BLAS kernels, can be used in many other dense matrix factorizations, large scale sparse direct multifrontal solvers, and applications. We propose new interfaces and mechanisms to handle the irregular computation pattern on the GPU. According to the authors’ knowledge, this is the first attempt to develop high performance software for this class of problems. Using a K40c GPU, our performance tests show speedups of up to 2:5 against two Sandy Bridge CPUs (8-core each) running Intel MKL library.

%B The 17th IEEE International Workshop on Parallel and Distributed Scientific and Engineering Computing (PDSEC 2016), IPDPS 2016 %I IEEE %C Chicago, IL %8 05-2016 %G eng %0 Conference Proceedings %B Software for Exascale Computing - SPPEXA %D 2016 %T Domain Overlap for Iterative Sparse Triangular Solves on GPUs %A Hartwig Anzt %A Edmond Chow %A Daniel Szyld %A Jack Dongarra %E Hans-Joachim Bungartz %E Philipp Neumann %E Wolfgang E. Nagel %X Iterative methods for solving sparse triangular systems are an attractive alternative to exact forward and backward substitution if an approximation of the solution is acceptable. On modern hardware, performance benefits are available as iterative methods allow for better parallelization. In this paper, we investigate how block-iterative triangular solves can benefit from using overlap. Because the matrices are triangular, we use “directed” overlap, depending on whether the matrix is upper or lower triangular. We enhance a GPU implementation of the block-asynchronous Jacobi method with directed overlap. For GPUs and other cases where the problem must be overdecomposed, i.e., more subdomains and threads than cores, there is a preference in processing or scheduling the subdomains in a specific order, following the dependencies specified by the sparse triangular matrix. For sparse triangular factors from incomplete factorizations, we demonstrate that moderate directed overlap with subdomain scheduling can improve convergence and time-to-solution. %B Software for Exascale Computing - SPPEXA %S Lecture Notes in Computer Science and Engineering %I Springer International Publishing %V 113 %P 527–545 %8 09-2016 %G eng %R 10.1007/978-3-319-40528-5_24 %0 Conference Paper %B The Sixth International Workshop on Accelerators and Hybrid Exascale Systems (AsHES) %D 2016 %T Efficiency of General Krylov Methods on GPUs – An Experimental Study %A Hartwig Anzt %A Jack Dongarra %A Moritz Kreutzer %A Gerhard Wellein %A Martin Kohler %K algorithmic bombardment %K BiCGSTAB %K CGS %K gpu %K IDR(s) %K Krylov solver %K QMR %X This paper compares different Krylov methods based on short recurrences with respect to their efficiency when implemented on GPUs. The comparison includes BiCGSTAB, CGS, QMR, and IDR using different shadow space dimensions. These methods are known for their good convergence characteristics. For a large set of test matrices taken from the University of Florida Matrix Collection, we evaluate the methods’ performance against different target metrics: convergence, number of sparse matrix-vector multiplications, and execution time. We also analyze whether the methods are “orthogonal” in terms of problem suitability. We propose best practices for choosing methods in a “black box” scenario, where no information about the optimal solver is available. %B The Sixth International Workshop on Accelerators and Hybrid Exascale Systems (AsHES) %I IEEE %C Chicago, IL %8 05-2016 %G eng %R 10.1109/IPDPSW.2016.45 %0 Conference Proceedings %B 2016 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW) %D 2016 %T Efficiency of General Krylov Methods on GPUs – An Experimental Study %A Hartwig Anzt %A Jack Dongarra %A Moritz Kreutzer %A Gerhard Wellein %A Martin Kohler %K algorithmic bombardment %K BiCGSTAB %K CGS %K Convergence %K Electric breakdown %K gpu %K graphics processing units %K Hardware %K IDR(s) %K Krylov solver %K Libraries %K linear systems %K QMR %K Sparse matrices %X This paper compares different Krylov methods based on short recurrences with respect to their efficiency whenimplemented on GPUs. The comparison includes BiCGSTAB, CGS, QMR, and IDR using different shadow space dimensions. These methods are known for their good convergencecharacteristics. For a large set of test matrices taken from theUniversity of Florida Matrix Collection, we evaluate the methods'performance against different target metrics: convergence, number of sparse matrix-vector multiplications, and executiontime. We also analyze whether the methods are "orthogonal"in terms of problem suitability. We propose best practicesfor choosing methods in a "black box" scenario, where noinformation about the optimal solver is available. %B 2016 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW) %P 683-691 %8 05-2016 %G eng %R 10.1109/IPDPSW.2016.45 %0 Conference Proceedings %B Proceedings of the The International Conference for High Performance Computing, Networking, Storage and Analysis (SC'16) %D 2016 %T Failure Detection and Propagation in HPC Systems %A George Bosilca %A Aurelien Bouteiller %A Amina Guermouche %A Thomas Herault %A Yves Robert %A Pierre Sens %A Jack Dongarra %K failure detection %K fault-tolerance %K MPI %B Proceedings of the The International Conference for High Performance Computing, Networking, Storage and Analysis (SC'16) %I IEEE Press %C Salt Lake City, Utah %P 27:1-27:11 %8 11-2016 %@ 978-1-4673-8815-3 %G eng %U http://dl.acm.org/citation.cfm?id=3014904.3014941 %0 Journal Article %J Journal of Computational Science %D 2016 %T Fine-grained Bit-Flip Protection for Relaxation Methods %A Hartwig Anzt %A Jack %A Enrique S. Quintana-Ortí %K Bit flips %K Fault tolerance %K High Performance Computing %K iterative solvers %K Jacobi method %K sparse linear systems %X Resilience is considered a challenging under-addressed issue that the high performance computing community (HPC) will have to face in order to produce reliable Exascale systems by the beginning of the next decade. As part of a push toward a resilient HPC ecosystem, in this paper we propose an error-resilient iterative solver for sparse linear systems based on stationary component-wise relaxation methods. Starting from a plain implementation of the Jacobi iteration, our approach introduces a low-cost component-wise technique that detects bit-flips, rejecting some component updates, and turning the initial synchronized solver into an asynchronous iteration. Our experimental study with sparse incomplete factorizations from a collection of real-world applications, and a practical GPU implementation, exposes the convergence delay incurred by the fault-tolerant implementation and its practical performance. %B Journal of Computational Science %8 11-2016 %G eng %R 10.1016/j.jocs.2016.11.013 %0 Conference Paper %B 25th International Symposium on High-Performance Parallel and Distributed Computing (HPDC'16) %D 2016 %T GPU-Aware Non-contiguous Data Movement In Open MPI %A Wei Wu %A George Bosilca %A Rolf vandeVaart %A Sylvain Jeaugey %A Jack Dongarra %K datatype %K gpu %K hybrid architecture %K MPI %K non-contiguous data %XDue to better parallel density and power efficiency, GPUs have become more popular for use in scientific applications. Many of these applications are based on the ubiquitous Message Passing Interface (MPI) programming paradigm, and take advantage of non-contiguous memory layouts to exchange data between processes. However, support for efficient non-contiguous data movements for GPU-resident data is still in its infancy, imposing a negative impact on the overall application performance.

To address this shortcoming, we present a solution where we take advantage of the inherent parallelism in the datatype packing and unpacking operations. We developed a close integration between Open MPI's stack-based datatype engine, NVIDIA's Unied Memory Architecture and GPUDirect capabilities. In this design the datatype packing and unpacking operations are offloaded onto the GPU and handled by specialized GPU kernels, while the CPU remains the driver for data movements between nodes. By incorporating our design into the Open MPI library we have shown significantly better performance for non-contiguous GPU-resident data transfers on both shared and distributed memory machines.

%B 25th International Symposium on High-Performance Parallel and Distributed Computing (HPDC'16) %I ACM %C Kyoto, Japan %8 06-2016 %G eng %R http://dx.doi.org/10.1145/2907294.2907317 %0 Conference Paper %B 30th IEEE International Parallel & Distributed Processing Symposium (IPDPS) %D 2016 %T Hessenberg Reduction with Transient Error Resilience on GPU-Based Hybrid Architectures %A Yulu Jia %A Piotr Luszczek %A Jack Dongarra %X Graphics Processing Units (GPUs) have been seeing widespread adoption in the field of scientific computing, owing to the performance gains provided on computation-intensive applications. In this paper, we present the design and implementation of a Hessenberg reduction algorithm immune to simultaneous soft-errors, capable of taking advantage of hybrid GPU-CPU platforms. These soft-errors are detected and corrected on the fly, preventing the propagation of the error to the rest of the data. Our design is at the intersection between several fault tolerant techniques and employs the algorithm-based fault tolerance technique, diskless checkpointing, and reverse computation to achieve its goal. By utilizing the idle time of the CPUs, and by overlapping both host-side and GPU-side workloads, we minimize the resilience overhead. Experimental results have validated our design decisions as our algorithm introduced less than 2% performance overhead compared to the optimized, but fault-prone, hybrid Hessenberg reduction. %B 30th IEEE International Parallel & Distributed Processing Symposium (IPDPS) %I IEEE %C Chicago, IL %8 05-2016 %G eng %0 Conference Paper %B The Sixth International Workshop on Accelerators and Hybrid Exascale Systems (AsHES), IPDPS 2016 %D 2016 %T Heterogeneous Streaming %A Chris J. Newburn %A Gaurav Bansal %A Michael Wood %A Luis Crivelli %A Judit Planas %A Alejandro Duran %A Paulo Souza %A Leonardo Borges %A Piotr Luszczek %A Stanimire Tomov %A Jack Dongarra %A Hartwig Anzt %A Mark Gates %A Azzam Haidar %A Yulu Jia %A Khairul Kabir %A Ichitaro Yamazaki %A Jesus Labarta %X This paper introduces a new heterogeneous streaming library called hetero Streams (hStreams). We show how a simple FIFO streaming model can be applied to heterogeneous systems that include manycore coprocessors and multicore CPUs. This model supports concurrency across nodes, among tasks within a node, and between data transfers and computation. We give examples for different approaches, show how the implementation can be layered, analyze overheads among layers, and apply those models to parallelize applications using simple, intuitive interfaces. We compare the features and versatility of hStreams, OpenMP, CUDA Streams1 and OmpSs. We show how the use of hStreams makes it easier for scientists to identify tasks and easily expose concurrency among them, and how it enables tuning experts and runtime systems to tailor execution for different heterogeneous targets. Practical application examples are taken from the field of numerical linear algebra, commercial structural simulation software, and a seismic processing application. %B The Sixth International Workshop on Accelerators and Hybrid Exascale Systems (AsHES), IPDPS 2016 %I IEEE %C Chicago, IL %8 05-2016 %G eng %0 Journal Article %J International Journal of High Performance Computing Applications %D 2016 %T High Performance Conjugate Gradient Benchmark: A new Metric for Ranking High Performance Computing Systems %A Jack Dongarra %A Michael Heroux %A Piotr Luszczek %B International Journal of High Performance Computing Applications %V 30 %P 3 - 10 %8 02-2016 %G eng %U http://hpc.sagepub.com/cgi/doi/10.1177/1094342015593158 %N 1 %! International Journal of High Performance Computing Applications %R 10.1177/1094342015593158 %0 Generic %D 2016 %T High Performance Realtime Convex Solver for Embedded Systems %A Ichitaro Yamazaki %A Saeid Nooshabadi %A Stanimire Tomov %A Jack Dongarra %K KKT %K Realtime embedded convex optimization solver %X Convex optimization solvers for embedded systems find widespread use. This letter presents a novel technique to reduce the run-time of decomposition of KKT matrix for the convex optimization solver for an embedded system, by two orders of magnitude. We use the property that although the KKT matrix changes, some of its block sub-matrices are fixed during the solution iterations and the associated solving instances. %B University of Tennessee Computer Science Technical Report %8 10-2016 %G eng %0 Conference Paper %B 22nd International European Conference on Parallel and Distributed Computing (Euro-Par'16) %D 2016 %T High-performance Matrix-matrix Multiplications of Very Small Matrices %A Ian Masliah %A Ahmad Abdelfattah %A Azzam Haidar %A Stanimire Tomov %A Joël Falcou %A Jack Dongarra %X The use of the general dense matrix-matrix multiplication (GEMM) is fundamental for obtaining high performance in many scientific computing applications. GEMMs for small matrices (of sizes less than 32) however, are not sufficiently optimized in existing libraries. In this paper we consider the case of many small GEMMs on either CPU or GPU architectures. This is a case that often occurs in applications like big data analytics, machine learning, high-order FEM, and others. The GEMMs are grouped together in a single batched routine. We present specialized for these cases algorithms and optimization techniques to obtain performance that is within 90% of the optimal. We show that these results outperform currently available state-of-the-art implementations and vendor-tuned math libraries. %B 22nd International European Conference on Parallel and Distributed Computing (Euro-Par'16) %I Springer International Publishing %C Grenoble, France %8 08-2016 %G eng %0 Conference Paper %B International Conference on Computational Science (ICCS'16) %D 2016 %T High-Performance Tensor Contractions for GPUs %A Ahmad Abdelfattah %A Marc Baboulin %A Veselin Dobrev %A Jack Dongarra %A Christopher Earl %A Joël Falcou %A Azzam Haidar %A Ian Karlin %A Tzanio Kolev %A Ian Masliah %A Stanimire Tomov %K Applications %K Batched linear algebra %K FEM %K gpu %K Tensor contractions %K Tensor HPC %X We present a computational framework for high-performance tensor contractions on GPUs. High-performance is difficult to obtain using existing libraries, especially for many independent contractions where each contraction is very small, e.g., sub-vector/warp in size. However, using our framework to batch contractions plus application-specifics, we demonstrate close to peak performance results. In particular, to accelerate large scale tensor-formulated high-order finite element method (FEM) simulations, which is the main focus and motivation for this work, we represent contractions as tensor index reordering plus matrix-matrix multiplications (GEMMs). This is a key factor to achieve algorithmically many-fold acceleration (vs. not using it) due to possible reuse of data loaded in fast memory. In addition to using this context knowledge, we design tensor data-structures, tensor algebra interfaces, and new tensor contraction algorithms and implementations to achieve 90+% of a theoretically derived peak on GPUs. On a K40c GPU for contractions resulting in GEMMs on square matrices of size 8 for example, we are 2.8× faster than CUBLAS, and 8.5× faster than MKL on 16 cores of Intel Xeon E5-2670 (Sandy Bridge) 2.60GHz CPUs. Finally, we apply autotuning and code generation techniques to simplify tuning and provide an architecture-aware, user-friendly interface. %B International Conference on Computational Science (ICCS'16) %C San Diego, CA %8 06-2016 %G eng %0 Generic %D 2016 %T High-Performance Tensor Contractions for GPUs %A Ahmad Abdelfattah %A Marc Baboulin %A Veselin Dobrev %A Jack Dongarra %A Christopher Earl %A Joël Falcou %A Azzam Haidar %A Ian Karlin %A Tzanio Kolev %A Ian Masliah %A Stanimire Tomov %X We present a computational framework for high-performance tensor contractions on GPUs. High-performance is difficult to obtain using existing libraries, especially for many independent contractions where each contraction is very small, e.g., sub-vector/warp in size. However, using our framework to batch contractions plus application-specifics, we demonstrate close to peak performance results. In particular, to accelerate large scale tensor-formulated high-order finite element method (FEM) simulations, which is the main focus and motivation for this work, we represent contractions as tensor index reordering plus matrix-matrix multiplications (GEMMs). This is a key factor to achieve algorithmically many-fold acceleration (vs. not using it) due to possible reuse of data loaded in fast memory. In addition to using this context knowledge, we design tensor data-structures, tensor algebra interfaces, and new tensor contraction algorithms and implementations to achieve 90+% of a theoretically derived peak on GPUs. On a K40c GPU for contractions resulting in GEMMs on square matrices of size 8 for example, we are 2.8× faster than CUBLAS, and 8.5× faster than MKL on 16 cores of Intel Xeon ES-2670 (Sandy Bridge) 2.60GHz CPUs. Finally, we apply autotuning and code generation techniques to simplify tuning and provide an architecture-aware, user-friendly interface. %B University of Tennessee Computer Science Technical Report %I University of Tennessee %8 01-2016 %G eng %0 Generic %D 2016 %T The HPL Benchmark: Past, Present & Future %A Jack Dongarra %C ISC High Performance, Frankfurt, Germany %8 07-2016 %G eng %9 Conference Presentation %0 Conference Paper %B IEEE High Performance Extreme Computing Conference (HPEC'16) %D 2016 %T LU, QR, and Cholesky Factorizations: Programming Model, Performance Analysis and Optimization Techniques for the Intel Knights Landing Xeon Phi %A Azzam Haidar %A Stanimire Tomov %A Konstantin Arturov %A Murat Guney %A Shane Story %A Jack Dongarra %X A wide variety of heterogeneous compute resources, ranging from multicore CPUs to GPUs and coprocessors, are available to modern computers, making it challenging to design unified numerical libraries that efficiently and productively use all these varied resources. For example, in order to efficiently use Intel’s Knights Langing (KNL) processor, the next-generation of Xeon Phi architectures, one must design and schedule an application in multiple degrees of parallelism and task grain sizes in order to obtain efficient performance. We propose a productive and portable programming model that allows us to write a serial-looking code, which, however, achieves parallelism and scalability by using a lightweight runtime environment to manage the resource-specific workload, and to control the dataflow and the parallel execution. This is done through multiple techniques ranging from multi-level data partitioning to adaptive task grain sizes, and dynamic task scheduling. In addition, our task abstractions enable unified algorithmic development across all the heterogeneous resources. Finally, we outline the strengths and the effectiveness of this approach – especially in regards to hardware trends and ease of programming high-performance numerical software that current applications need – in order to motivate current work and future directions for the next generation of parallel programming models for high-performance linear algebra libraries on heterogeneous systems. %B IEEE High Performance Extreme Computing Conference (HPEC'16) %I IEEE %C Waltham, MA %8 09-2016 %G eng %0 Journal Article %J Concurrency and Computation: Practice and Experience %D 2016 %T Non-GPU-resident Dense Symmetric Indefinite Factorization %A Ichitaro Yamazaki %A Stanimire Tomov %A Jack Dongarra %X We study various algorithms to factorize a symmetric indefinite matrix that does not fit in the core memory of a computer. There are two sources of the data movement into the memory: one needed for selecting and applying pivots and the other needed to update each column of the matrix for the factorization. It is a challenge to obtain high performance of such an algorithm when the pivoting is required to ensure the numerical stability of the factorization. For example, when factorizing each column of the matrix, a diagonal entry, which ensures the stability, may need to be selected as a pivot among the remaining diagonals, and moved to the leading diagonal by swapping both the corresponding rows and columns of the matrix. If the pivot is not in the core memory, then it must be loaded into the core memory. For updating the matrix, the data locality may be improved by partitioning the matrix. For example, a right-looking partitioned algorithm first factorizes the leading columns, called panel, and then uses the factorized panel to update the trailing submatrix. This algorithm only accesses the trailing submatrix after each panel factorization (instead of after each column factorization) and performs most of its floating-point operations (flops) using BLAS-3, which can take advantage of the memory hierarchy. However, because the pivots cannot be predetermined, the whole trailing submatrix must be updated before the next panel factorization can start. When the whole submatrix does not fit in the core memory all at once, loading the block columns into the memory can become the performance bottleneck. Similarly, the left-looking variant of the algorithm would require to update each panel with all of the previously factorized columns. This makes it a much greater challenge to implement an efficient out-of-core symmetric indefinite factorization compared with an out-of-core nonsymmetric LU factorization with partial pivoting, which only requires to swap the rows of the matrix and accesses the trailing submatrix after each in-core factorization (instead of after each panel factorization by the symmetric factorization). To reduce the amount of the data transfer, in this paper we uses the recently proposed left-looking communication-avoiding variant of the symmetric factorization algorithm to factorize the columns in the core memory, and then perform the partitioned right-looking out-of-core trailing submatrix updates. This combination may still require to load the pivots into the core memory, but it only updates the trailing submatrix after each in-core factorization, while the previous algorithm updates it after each panel factorization.Although these in-core and out-of-core algorithms can be applied at any level of the memory hierarchy, we apply our designs to the GPU and CPU memory, respectively. We call this specific implementation of the algorithm a non–GPU-resident implementation. Our performance results on the current hybrid CPU/GPU architecture demonstrate that when the matrix is much larger than the GPU memory, the proposed algorithm can obtain significant speedups over the communication-hiding implementations of the previous algorithms. %B Concurrency and Computation: Practice and Experience %8 11-2016 %G eng %R 10.1002/cpe.4012 %0 Conference Paper %B 2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS) %D 2016 %T Optimal Resilience Patterns to Cope with Fail-stop and Silent Errors %A Anne Benoit %A Aurelien Cavelan %A Yves Robert %A Hongyang Sun %K fail-stop errors %K multilevel checkpoint %K optimal pattern %K resilience %K silent errors %K verification %X This work focuses on resilience techniques at extreme scale. Many papers deal with fail-stop errors. Many others deal with silent errors (or silent data corruptions). But very few papers deal with fail-stop and silent errors simultaneously. However, HPC applications will obviously have to cope with both error sources. This paper presents a unified framework and optimal algorithmic solutions to this double challenge. Silent errors are handled via verification mechanisms (either partially or fully accurate) and in-memory checkpoints. Fail-stop errors are processed via disk checkpoints. All verification and checkpoint types are combined into computational patterns. We provide a unified model, and a full characterization of the optimal pattern. Our results nicely extend several published solutions and demonstrate how to make use of different techniques to solve the double threat of fail-stop and silent errors. Extensive simulations based on real data confirm the accuracy of the model, and show that patterns that combine all resilience mechanisms are required to provide acceptable overheads. %B 2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS) %I IEEE %C Chicago, IL %8 05-2016 %G eng %R 10.1109/IPDPS.2016.39 %0 Conference Paper %B 2016 IEEE High Performance Extreme Computing Conference (HPEC ‘16) %D 2016 %T Performance Analysis and Acceleration of Explicit Integration for Large Kinetic Networks using Batched GPU Computations %A Azzam Haidar %A Benjamin Brock %A Stanimire Tomov %A Michael Guidry %A Jay Jay Billings %A Daniel Shyles %A Jack Dongarra %X We demonstrate the systematic implementation of recently-developed fast explicit kinetic integration algorithms that solve efficiently N coupled ordinary differential equations (subject to initial conditions) on modern GPUs. We take representative test cases (Type Ia supernova explosions) and demonstrate two or more orders of magnitude increase in efficiency for solving such systems (of realistic thermonuclear networks coupled to fluid dynamics). This implies that important coupled, multiphysics problems in various scientific and technical disciplines that were intractable, or could be simulated only with highly schematic kinetic networks, are now computationally feasible. As examples of such applications we present the computational techniques developed for our ongoing deployment of these new methods on modern GPU accelerators. We show that similarly to many other scientific applications, ranging from national security to medical advances, the computation can be split into many independent computational tasks, each of relatively small-size. As the size of each individual task does not provide sufficient parallelism for the underlying hardware, especially for accelerators, these tasks must be computed concurrently as a single routine, that we call batched routine, in order to saturate the hardware with enough work. %B 2016 IEEE High Performance Extreme Computing Conference (HPEC ‘16) %I IEEE %C Waltham, MA %8 09-2016 %G eng %0 Thesis %B Department of Electrical Engineering and Computer Science %D 2016 %T Performance Analysis and Modeling of Task-Based Runtimes %A Blake Haugen %X The shift toward multicore processors has transformed the software and hardware landscape in the last decade. As a result, software developers must adopt parallelism in order to efficiently make use of multicore CPUs. Task-based scheduling has emerged as one method to reduce the complexity of parallel computing. Although task-based scheduling has been around for many years, the inclusion of task dependencies in OpenMP 4.0 suggests the paradigm will be around for the foreseeable future. While task-based schedulers simplify the process of parallel software development, they can obfuscate the performance characteristics of the execution of an algorithm. Additionally, they can create a challenge for users to analyze the performance of their software and tune algorithmic parameters accordingly.We will present the basic principles of task-based runtimes as well as two new tools developed to assist engineers developing these runtimes and users employing them to parallelize their workloads. The first is a tool allowing users to simulate the execution of their algorithm. The second is an extension to the common execution trace which includes information about task dependencies. %B Department of Electrical Engineering and Computer Science %I University of Tennessee %C Knoxville %V PhD %8 05-2016 %G eng %0 Journal Article %J International Journal of High Performance Computing Applications %D 2016 %T On the performance and energy efficiency of sparse linear algebra on GPUs %A Hartwig Anzt %A Stanimire Tomov %A Jack Dongarra %X In this paper we unveil some performance and energy efficiency frontiers for sparse computations on GPU-based supercomputers. We compare the resource efficiency of different sparse matrix–vector products (SpMV) taken from libraries such as cuSPARSE and MAGMA for GPU and Intel’s MKL for multicore CPUs, and develop a GPU sparse matrix–matrix product (SpMM) implementation that handles the simultaneous multiplication of a sparse matrix with a set of vectors in block-wise fashion. While a typical sparse computation such as the SpMV reaches only a fraction of the peak of current GPUs, we show that the SpMM succeeds in exceeding the memory-bound limitations of the SpMV. We integrate this kernel into a GPU-accelerated Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) eigensolver. LOBPCG is chosen as a benchmark algorithm for this study as it combines an interesting mix of sparse and dense linear algebra operations that is typical for complex simulation applications, and allows for hardware-aware optimizations. In a detailed analysis we compare the performance and energy efficiency against a multi-threaded CPU counterpart. The reported performance and energy efficiency results are indicative of sparse computations on supercomputers. %B International Journal of High Performance Computing Applications %8 10-2016 %G eng %U http://hpc.sagepub.com/content/early/2016/10/05/1094342016672081.abstract %R 10.1177/1094342016672081 %0 Conference Paper %B The International Supercomputing Conference (ISC High Performance 2016) %D 2016 %T Performance, Design, and Autotuning of Batched GEMM for GPUs %A Ahmad Abdelfattah %A Azzam Haidar %A Stanimire Tomov %A Jack Dongarra %K Autotuning %K Batched GEMM %K GEMM %K GPU computing %K HPC %X The general matrix-matrix multiplication (GEMM) is the most important numerical kernel in dense linear algebra, and is the key component for obtaining high performance in most LAPACK routines. As batched computations on relatively small problems continue to gain interest in many scientific applications, a need arises for a high performance GEMM kernel for batches of small matrices. Such a kernel should be well designed and tuned to handle small sizes, and to maintain high performance for realistic test cases found in the higher level LAPACK routines, and scientific computing applications in general. This paper presents a high performance batched GEMM kernel on Graphics Processing Units (GPUs). We address batched problems with both fixed and variable sizes, and show that specialized GEMM designs and a comprehensive autotuning process are needed to handle problems of small sizes. For most performance tests reported in this paper, the proposed kernels outperform state-of-the-art approaches using a K40c GPU. %B The International Supercomputing Conference (ISC High Performance 2016) %C Frankfurt, Germany %8 06-2016 %G eng %0 Book Section %B High Performance Computing: 31st International Conference, ISC High Performance 2016, Frankfurt, Germany, June 19-23, 2016, Proceedings %D 2016 %T Performance, Design, and Autotuning of Batched GEMM for GPUs %A Ahmad Abdelfattah %A Azzam Haidar %A Stanimire Tomov %A Jack Dongarra %E Julian M. Kunkel %E Pavan Balaji %E Jack Dongarra %X The general matrix-matrix multiplication (GEMM) is the most important numerical kernel in dense linear algebra, and is the key component for obtaining high performance in most LAPACK routines. As batched computations on relatively small problems continue to gain interest in many scientific applications, a need arises for a high performance GEMM kernel for batches of small matrices. Such a kernel should be well designed and tuned to handle small sizes, and to maintain high performance for realistic test cases found in the higher level LAPACK routines, and scientific computing applications in general. This paper presents a high performance batched GEMM kernel on Graphics Processing Units (GPUs). We address batched problems with both fixed and variable sizes, and show that specialized GEMM designs and a comprehensive autotuning process are needed to handle problems of small sizes. For most performance tests reported in this paper, the proposed kernels outperform state-of-the-art approaches using a K40c GPU. %B High Performance Computing: 31st International Conference, ISC High Performance 2016, Frankfurt, Germany, June 19-23, 2016, Proceedings %I Springer International Publishing %P 21–38 %@ 978-3-319-41321-1 %G eng %U http://dx.doi.org/10.1007/978-3-319-41321-1_2 %R 10.1007/978-3-319-41321-1_2 %0 Generic %D 2016 %T Performance, Design, and Autotuning of Batched GEMM for GPUs %A Ahmad Abdelfattah %A Azzam Haidar %A Stanimire Tomov %A Jack Dongarra %K Autotuning %K Batched GEMM %K GEMM %K GPU computing %K HPC %X Abstract. The general matrix-matrix multiplication (GEMM) is the most important numerical kernel in dense linear algebra. It is the key component for obtaining high performance in most LAPACK routines. As batched computations on relatively small problems continue to gain interest in many scientific applications, there becomes a need to have a high performance GEMM kernel for a batch of small matrices. Such kernel should be well designed and tuned to handle small sizes, and to maintain high performance for realistic test cases found in the higher level LAPACK routines, and scientific computing applications in general. This paper presents a high performance batched GEMM kernel on Graphics Processing Units (GPUs). We address batched problems with both xed and variable sizes, and show that specialized GEMM designs and a comprehensive autotuning process are needed to handle problems of small sizes. For most performance test reported in this paper, the proposed kernels outperform state-of-the-art approaches using a K40c GPU. %B University of Tennessee Computer Science Technical Report %I University of Tennessee %8 02-2016 %G eng %0 Journal Article %J Concurrency and Computation: Practice and Experience %D 2016 %T Performance optimization of Sparse Matrix-Vector Multiplication for multi-component PDE-based applications using GPUs %A Ahmad Abdelfattah %A Hatem Ltaeif %A David Keyes %A Jack Dongarra %X Simulations of many multi-component PDE-based applications, such as petroleum reservoirs or reacting flows, are dominated by the solution, on each time step and within each Newton step, of large sparse linear systems. The standard solver is a preconditioned Krylov method. Along with application of the preconditioner, memory-bound Sparse Matrix-Vector Multiplication (SpMV) is the most time-consuming operation in such solvers. Multi-species models produce Jacobians with a dense block structure, where the block size can be as large as a few dozen. Failing to exploit this dense block structure vastly underutilizes hardware capable of delivering high performance on dense BLAS operations. This paper presents a GPU-accelerated SpMV kernel for block-sparse matrices. Dense matrix-vector multiplications within the sparse-block structure leverage optimization techniques from the KBLAS library, a high performance library for dense BLAS kernels. The design ideas of KBLAS can be applied to block-sparse matrices. Furthermore, a technique is proposed to balance the workload among thread blocks when there are large variations in the lengths of nonzero rows. Multi-GPU performance is highlighted. The proposed SpMV kernel outperforms existing state-of-the-art implementations using matrices with real structures from different applications. %B Concurrency and Computation: Practice and Experience %V 28 %P 3447 - 3465 %8 05-2016 %G eng %U http://onlinelibrary.wiley.com/doi/10.1002/cpe.3874/full %N 12 %! Concurrency Computat.: Pract. Exper. %R 10.1002/cpe.v28.1210.1002/cpe.3874 %0 Conference Paper %B International Conference on Computational Science (ICCS'16) %D 2016 %T Performance Tuning and Optimization Techniques of Fixed and Variable Size Batched Cholesky Factorization on GPUs %A Ahmad Abdelfattah %A Azzam Haidar %A Stanimire Tomov %A Jack Dongarra %K batched computation %K Cholesky Factorization %K GPUs %K Tuning %X

Solving a large number of relatively small linear systems has recently drawn more attention in the HPC community, due to the importance of such computational workloads in many scientific applications, including sparse multifrontal solvers. Modern hardware accelerators and their architecture require a set of optimization techniques that are very different from the ones used in solving one relatively large matrix. In order to impose concurrency on such throughput-oriented architectures, a common practice is to batch the solution of these matrices as one task offloaded to the underlying hardware, rather than solving them individually.

This paper presents a high performance batched Cholesky factorization on large sets of relatively small matrices using Graphics Processing Units (GPUs), and addresses both fixed and variable size batched problems. We investigate various algorithm designs and optimization techniques, and show that it is essential to combine kernel design with performance tuning in order to achieve the best possible performance. We compare our approaches against state-of-the-art CPU solutions as well as GPU-based solutions using existing libraries, and show that, on a K40c GPU for example, our kernels are more than 2 faster.

%B International Conference on Computational Science (ICCS'16) %C San Diego, CA %8 06-2016 %G eng %0 Journal Article %J International Journal of Parallel Programming %D 2016 %T Porting the PLASMA Numerical Library to the OpenMP Standard %A Asim YarKhan %A Jakub Kurzak %A Piotr Luszczek %A Jack Dongarra %X PLASMA is a numerical library intended as a successor to LAPACK for solving problems in dense linear algebra on multicore processors. PLASMA relies on the QUARK scheduler for efficient multithreading of algorithms expressed in a serial fashion. QUARK is a superscalar scheduler and implements automatic parallelization by tracking data dependencies and resolving data hazards at runtime. Recently, this type of scheduling has been incorporated in the OpenMP standard, which allows to transition PLASMA from the proprietary solution offered by QUARK to the standard solution offered by OpenMP. This article studies the feasibility of such transition. %B International Journal of Parallel Programming %8 06-2016 %G eng %U http://link.springer.com/10.1007/s10766-016-0441-6http://link.springer.com/content/pdf/10.1007/s10766-016-0441-6http://link.springer.com/content/pdf/10.1007/s10766-016-0441-6.pdfhttp://link.springer.com/article/10.1007/s10766-016-0441-6/fulltext.html %! Int J Parallel Prog %R 10.1007/s10766-016-0441-6 %0 Conference Proceedings %B Tools for High Performance Computing 2015: Proceedings of the 9th International Workshop on Parallel Tools for High Performance Computing, September 2015, Dresden, Germany %D 2016 %T Power Management and Event Verification in PAPI %A Heike Jagode %A Asim YarKhan %A Anthony Danalis %A Jack Dongarra %X For more than a decade, the PAPI performance monitoring library has helped to implement the familiar maxim attributed to Lord Kelvin: “If you cannot measure it, you cannot improve it.” Widely deployed and widely used, PAPI provides a generic, portable interface for the hardware performance counters available on all modern CPUs and some other components of interest that are scattered across the chip and system. Recent and radical changes in processor and system design—systems that combine multicore CPUs and accelerators, shared and distributed memory, PCI- express and other interconnects—as well as the emergence of power efficiency as a primary design constraint, and reduced data movement as a primary programming goal, pose new challenges and bring new opportunities to PAPI. We discuss new developments of PAPI that allow for multiple sources of performance data to be measured simultaneously via a common software interface. Specifically, a new PAPI component that controls power is discussed. We explore the challenges of shared hardware counters that include system-wide measurements in existing multicore architectures. We conclude with an exploration of future directions for the PAPI interface. %B Tools for High Performance Computing 2015: Proceedings of the 9th International Workshop on Parallel Tools for High Performance Computing, September 2015, Dresden, Germany %I Springer International Publishing %C Dresden, Germany %P pp. 41-51 %@ 978-3-319-39589-0 %G eng %0 Generic %D 2016 %T Report on the Sunway TaihuLight System %A Jack Dongarra %B University of Tennessee Computer Science Technical Report %I University of Tennessee %8 06-2016 %G eng %U http://www.netlib.org/utk/people/JackDongarra/PAPERS/sunway-report-2016.pdf %0 Journal Article %J International Journal of Networking and Computing %D 2016 %T Scheduling Computational Workflows on Failure-prone Platforms %A Guillaume Aupy %A Anne Benoit %A Henri Casanova %A Yves Robert %K checkpointing %K fault-tolerance %K reliability %K scheduling %K workflow %X We study the scheduling of computational workflows on compute resources that experience exponentially distributed failures. When a failure occurs, rollback and recovery is used to resume the execution from the last checkpointed state. The scheduling problem is to minimize the expected execution time by deciding in which order to execute the tasks in the workflow and deciding for each task whether to checkpoint it or not after it completes. We give a polynomialtime optimal algorithm for fork DAGs (Directed Acyclic Graphs) and show that the problem is NP-complete with join DAGs. We also investigate the complexity of the simple case in which no task is checkpointed. Our main result is a polynomial-time algorithm to compute the expected execution time of a workflow, with a given task execution order and specified to-be-checkpointed tasks. Using this algorithm as a basis, we propose several heuristics for solving the scheduling problem. We evaluate these heuristics for representative workflow configurations. %B International Journal of Networking and Computing %V 6 %P 2-26 %G eng %0 Conference Paper %B 30th IEEE International Parallel & Distributed Processing Symposium (IPDPS) %D 2016 %T Search Space Generation and Pruning System for Autotuners %A Piotr Luszczek %A Mark Gates %A Jakub Kurzak %A Anthony Danalis %A Jack Dongarra %X This work tackles two simultaneous challenges faced by autotuners: the ease of describing a complex, multidimensional search space, and the speed of evaluating that space, while applying a multitude of pruning constraints. This article presents a declarative notation for describing a search space and a translation system for conversion to a standard C code for fast and multithreaded, as necessary, evaluation. The notation is Python-based and thus simple in syntax and easy to assimilate by the user interested in tuning rather than learning a new programming language. A large number of dimensions and a large number of pruning constraints may be expressed with little effort. The system is discussed in the context of autotuning the canonical matrix multiplication kernel for NVIDIA GPUs, where the search space has 15 dimensions and involves application of 10 complex pruning constrains. The speed of evaluation is compared against generators created using imperative programming style in various scripting and compiled languages. %B 30th IEEE International Parallel & Distributed Processing Symposium (IPDPS) %I IEEE %C Chicago, IL %8 05-2016 %G eng %0 Journal Article %J ACM Transactions on Mathematical Software (TOMS) %D 2016 %T Stability and Performance of Various Singular Value QR Implementations on Multicore CPU with a GPU %A Ichitaro Yamazaki %A Stanimire Tomov %A Jack Dongarra %X To orthonormalize a set of dense vectors, Singular Value QR (SVQR) requires only one global reduction between the parallel processing units, and uses BLAS-3 kernels to perform most of its local computation. As a result, compared to other orthogonalization schemes, SVQR obtains superior performance on many of the current computers. In this paper, we study the stability and performance of various SVQR implementations on multicore CPUs with a GPU, focusing on the dense triangular solve, which performs half of the total floating-point operations in SVQR. As a part of this study, we examine its adaptive mixed-precision variant that decides if a lower-precision arithmetic can be used for the triangular solution at runtime without increasing the order of its orthogonality error. Since the backward error of this adaptive mixed-precision variant is significantly greater than that of the standard SVQR, we study its effects on the solution convergence of several subspace projection methods for solving a linear system of equations and for computing singular values or eigenvalues of a sparse matrix. Our experimental results indicate that in some cases, the convergence rate of the solver may not be affected by the larger backward errors, while reducing the time to solution. %B ACM Transactions on Mathematical Software (TOMS) %V 43 %8 10-2016 %G eng %N 2 %0 Conference Paper %B The International Conference for High Performance Computing, Networking, Storage and Analysis (SC'16), Third Workshop on Accelerator Programming Using Directives (WACCPD) %D 2016 %T Towards Achieving Performance Portability Using Directives for Accelerators %A Lopez, M %A Larrea, V %A Joubert, W %A Hernandez, O %A Azzam Haidar %A Stanimire Tomov %A Jack Dongarra %X In this paper we explore the performance portability of directives provided by OpenMP 4 and OpenACC to program various types of node architectures with attached accelerators, both self-hosted multicore and offload multicore/GPU. Our goal is to examine how successful OpenACC and the newer of- fload features of OpenMP 4.5 are for moving codes between architectures, how much tuning might be required and what lessons we can learn from this experience. To do this, we use examples of algorithms with varying computational intensities for our evaluation, as both compute and data access efficiency are important considerations for overall application performance. We implement these kernels using various methods provided by newer OpenACC and OpenMP implementations, and we evaluate their performance on various platforms including both X86 64 with attached NVIDIA GPUs, self-hosted Intel Xeon Phi KNL, as well as an X86 64 host system with Intel Xeon Phi coprocessors. In this paper, we explain what factors affected the performance portability such as how to pick the right programming model, its programming style, its availability on different platforms, and how well compilers can optimize and target to multiple platforms. %B The International Conference for High Performance Computing, Networking, Storage and Analysis (SC'16), Third Workshop on Accelerator Programming Using Directives (WACCPD) %I Innovative Computing Laboratory, University of Tennessee %C Salt Lake City, Utah %8 11-2016 %G eng %0 Journal Article %J Numerical Algorithms %D 2016 %T Updating Incomplete Factorization Preconditioners for Model Order Reduction %A Hartwig Anzt %A Edmond Chow %A Jens Saak %A Jack Dongarra %K key publication %X When solving a sequence of related linear systems by iterative methods, it is common to reuse the preconditioner for several systems, and then to recompute the preconditioner when the matrix has changed significantly. Rather than recomputing the preconditioner from scratch, it is potentially more efficient to update the previous preconditioner. Unfortunately, it is not always known how to update a preconditioner, for example, when the preconditioner is an incomplete factorization. A recently proposed iterative algorithm for computing incomplete factorizations, however, is able to exploit an initial guess, unlike existing algorithms for incomplete factorizations. By treating a previous factorization as an initial guess to this algorithm, an incomplete factorization may thus be updated. We use a sequence of problems from model order reduction. Experimental results using an optimized GPU implementation show that updating a previous factorization can be inexpensive and effective, making solving sequences of linear systems a potential niche problem for the iterative incomplete factorization algorithm. %B Numerical Algorithms %V 73 %P 611–630 %8 02-2016 %G eng %N 3 %R 10.1007/s11075-016-0110-2 %0 Conference Paper %B 2015 IEEE International Conference on Big Data (IEEE BigData 2015) %D 2015 %T Accelerating Collaborative Filtering for Implicit Feedback Datasets using GPUs %A Mark Gates %A Hartwig Anzt %A Jakub Kurzak %A Jack Dongarra %X In this paper we accelerate the Alternating Least Squares (ALS) algorithm used for generating product recommendations on the basis of implicit feedback datasets. We approach the algorithm with concepts proven to be successful in High Performance Computing. This includes the formulation of the algorithm as a mix of cache-optimized algorithm-specific kernels and standard BLAS routines, acceleration via graphics processing units (GPUs), use of parallel batched kernels, and autotuning to identify performance winners. For benchmark datasets, the multi-threaded CPU implementation we propose achieves more than a 10 times speedup over the implementations available in the GraphLab and Spark MLlib software packages. For the GPU implementation, the parameters of an algorithm-specific kernel were optimized using a comprehensive autotuning sweep. This results in an additional 2 times speedup over our CPU implementation. %B 2015 IEEE International Conference on Big Data (IEEE BigData 2015) %I IEEE %C Santa Clara, CA %8 11-2015 %G eng %0 Conference Paper %B 11th International Conference on Parallel Processing and Applied Mathematics (PPAM 2015) %D 2015 %T Accelerating NWChem Coupled Cluster through dataflow-based Execution %A Heike Jagode %A Anthony Danalis %A George Bosilca %A Jack Dongarra %K CCSD %K dag %K dataflow %K NWChem %K parsec %K ptg %K tasks %X Numerical techniques used for describing many-body systems, such as the Coupled Cluster methods (CC) of the quantum chemistry package NWChem, are of extreme interest to the computational chemistry community in fields such as catalytic reactions, solar energy, and bio-mass conversion. In spite of their importance, many of these computationally intensive algorithms have traditionally been thought of in a fairly linear fashion, or are parallelised in coarse chunks. In this paper, we present our effort of converting the NWChem’s CC code into a dataflow-based form that is capable of utilizing the task scheduling system PaRSEC (Parallel Runtime Scheduling and Execution Controller) – a software package designed to enable high performance computing at scale. We discuss the modularity of our approach and explain how the PaRSEC-enabled dataflow version of the subroutines seamlessly integrate into the NWChem codebase. Furthermore, we argue how the CC algorithms can be easily decomposed into finer grained tasks (compared to the original version of NWChem); and how data distribution and load balancing are decoupled and can be tuned independently. We demonstrate performance acceleration by more than a factor of two in the execution of the entire CC component of NWChem, concluding that the utilization of dataflow-based execution for CC methods enables more efficient and scalable computation. %B 11th International Conference on Parallel Processing and Applied Mathematics (PPAM 2015) %I Springer International Publishing %C Krakow, Poland %8 09-2015 %G eng %0 Conference Paper %B Spring Simulation Multi-Conference 2015 (SpringSim'15) %D 2015 %T Accelerating the LOBPCG method on GPUs using a blocked Sparse Matrix Vector Product %A Hartwig Anzt %A Stanimire Tomov %A Jack Dongarra %X This paper presents a heterogeneous CPU-GPU implementation for a sparse iterative eigensolver the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG). For the key routine generating the Krylov search spaces via the product of a sparse matrix and a block of vectors, we propose a GPU kernel based on a modied sliced ELLPACK format. Blocking a set of vectors and processing them simultaneously accelerates the computation of a set of consecutive SpMVs significantly. Comparing the performance against similar routines from Intel's MKL and NVIDIA's cuSPARSE library we identify appealing performance improvements. We integrate it into the highly optimized LOBPCG implementation. Compared to the BLOBEX CPU implementation running on two eight-core Intel Xeon E5-2690s, we accelerate the computation of a small set of eigenvectors using NVIDIA's K40 GPU by typically more than an order of magnitude. %B Spring Simulation Multi-Conference 2015 (SpringSim'15) %I SCS %C Alexandria, VA %8 04-2015 %G eng %0 Journal Article %J International Journal of High Performance Computing Applications %D 2015 %T Acceleration of GPU-based Krylov solvers via Data Transfer Reduction %A Hartwig Anzt %A William Sawyer %A Stanimire Tomov %A Piotr Luszczek %A Jack Dongarra %B International Journal of High Performance Computing Applications %G eng %0 Conference Paper %B 3rd International Workshop on Energy Efficient Supercomputing (E2SC '15) %D 2015 %T Adaptive Precision Solvers for Sparse Linear Systems %A Hartwig Anzt %A Jack Dongarra %A Enrique S. Quintana-Ortí %B 3rd International Workshop on Energy Efficient Supercomputing (E2SC '15) %I ACM %C Austin, TX %8 11-2015 %G eng %0 Journal Article %J ACM Transactions on Parallel Computing %D 2015 %T Algorithm-based Fault Tolerance for Dense Matrix Factorizations, Multiple Failures, and Accuracy %A Aurelien Bouteiller %A Thomas Herault %A George Bosilca %A Peng Du %A Jack Dongarra %E Phillip B. Gibbons %K ABFT %K algorithms %K fault-tolerance %K High Performance Computing %K linear algebra %X Dense matrix factorizations, such as LU, Cholesky and QR, are widely used for scientific applications that require solving systems of linear equations, eigenvalues and linear least squares problems. Such computations are normally carried out on supercomputers, whose ever-growing scale induces a fast decline of the Mean Time To Failure (MTTF). This paper proposes a new hybrid approach, based on Algorithm-Based Fault Tolerance (ABFT), to help matrix factorizations algorithms survive fail-stop failures. We consider extreme conditions, such as the absence of any reliable node and the possibility of losing both data and checksum from a single failure. We will present a generic solution for protecting the right factor, where the updates are applied, of all above mentioned factorizations. For the left factor, where the panel has been applied, we propose a scalable checkpointing algorithm. This algorithm features high degree of checkpointing parallelism and cooperatively utilizes the checksum storage leftover from the right factor protection. The fault-tolerant algorithms derived from this hybrid solution is applicable to a wide range of dense matrix factorizations, with minor modifications. Theoretical analysis shows that the fault tolerance overhead decreases inversely to the scaling in the number of computing units and the problem size. Experimental results of LU and QR factorization on the Kraken (Cray XT5) supercomputer validate the theoretical evaluation and confirm negligible overhead, with- and without-errors. Applicability to tolerate multiple failures and accuracy after multiple recovery is also considered. %B ACM Transactions on Parallel Computing %V 1 %P 10:1-10:28 %8 01-2015 %G eng %N 2 %R 10.1145/2686892 %0 Conference Paper %B International Supercomputing Conference (ISC 2015) %D 2015 %T Asynchronous Iterative Algorithm for Computing Incomplete Factorizations on GPUs %A Edmond Chow %A Hartwig Anzt %A Jack Dongarra %B International Supercomputing Conference (ISC 2015) %C Frankfurt, Germany %8 07-2015 %G eng %0 Conference Paper %B EuroMPI/Asia 2015 Workshop %D 2015 %T Batched Matrix Computations on Hardware Accelerators %A Azzam Haidar %A Piotr Luszczek %A Stanimire Tomov %A Jack Dongarra %X Scientific applications require solvers that work on many small size problems that are independent from each other. At the same time, the high-end hardware evolves rapidly and becomes ever more throughput-oriented and thus there is an increasing need for effective approach to develop energy efficient, high-performance codes for these small matrix problems that we call batched factorizations. The many applications that need this functionality could especially benefit from the use of GPUs, which currently are four to five times more energy efficient than multicore CPUs on important scientific workloads. This paper, consequently, describes the development of the most common, one-sided factorizations: Cholesky, LU, and QR for a set of small dense matrices. The algorithms we present together with their implementations are, by design, inherently parallel. In particular, our approach is based on representing the process as a sequence of batched BLAS routines that are executed entirely on a GPU. Importantly, this is unlike the LAPACK and the hybridMAGMAfactorization algorithms that work under drastically different assumptions of hardware design and efficiency of execution of the various computational kernels involved in the implementation. Thus, our approach is more efficient than what works for a combination of multicore CPUs and GPUs for the problems sizes of interest of the application use cases. The paradigm where upon a single chip (a GPU or a CPU) factorizes a single problem at a time is not at all efficient for in our applications’ context. We illustrate all these claims through a detailed performance analysis. With the help of profiling and tracing tools, we guide our development of batched factorizations to achieve up to two-fold speedup and three-fold better energy efficiency as compared against our highly optimized batched CPU implementations based on MKL library. The tested system featured two sockets of Intel Sandy Bridge CPUs and we compared to a batched LU factorizations featured in the CUBLAS library for GPUs, we achieve as high as 2.5x speedup on the NVIDIA K40 GPU. %B EuroMPI/Asia 2015 Workshop %C Bordeaux, France %8 09-2015 %G eng %0 Conference Paper %B 2015 SIAM Conference on Applied Linear Algebra (SIAM LA) %D 2015 %T Batched Matrix Computations on Hardware Accelerators Based on GPUs %A Azzam Haidar %A Ahmad Abdelfattah %A Stanimire Tomov %A Jack Dongarra %X We will present techniques for small matrix computations on GPUs and their use for energy efficient, high-performance solvers. Work on small problems delivers high performance through improved data reuse. Many numerical libraries and applications need this functionality further developed. We describe the main factorizations LU, QR, and Cholesky for a set of small dense matrices in parallel. We achieve significant acceleration and reduced energy consumption against other solutions. Our techniques are of interest to GPU application developers in general. %B 2015 SIAM Conference on Applied Linear Algebra (SIAM LA) %I SIAM %C Atlanta, GA %8 10-2015 %G eng %0 Journal Article %J International Journal of High Performance Computing Applications %D 2015 %T Batched matrix computations on hardware accelerators based on GPUs %A Azzam Haidar %A Tingxing Dong %A Piotr Luszczek %A Stanimire Tomov %A Jack Dongarra %K batched factorization %K hardware accelerators %K numerical linear algebra %K numerical software libraries %K one-sided factorization algorithms %X Scientific applications require solvers that work on many small size problems that are independent from each other. At the same time, the high-end hardware evolves rapidly and becomes ever more throughput-oriented and thus there is an increasing need for an effective approach to develop energy-efficient, high-performance codes for these small matrix problems that we call batched factorizations. The many applications that need this functionality could especially benefit from the use of GPUs, which currently are four to five times more energy efficient than multicore CPUs on important scientific workloads. This paper, consequently, describes the development of the most common, one-sided factorizations, Cholesky, LU, and QR, for a set of small dense matrices. The algorithms we present together with their implementations are, by design, inherently parallel. In particular, our approach is based on representing the process as a sequence of batched BLAS routines that are executed entirely on a GPU. Importantly, this is unlike the LAPACK and the hybrid MAGMA factorization algorithms that work under drastically different assumptions of hardware design and efficiency of execution of the various computational kernels involved in the implementation. Thus, our approach is more efficient than what works for a combination of multicore CPUs and GPUs for the problems sizes of interest of the application use cases. The paradigm where upon a single chip (a GPU or a CPU) factorizes a single problem at a time is not at all efficient in our applications’ context. We illustrate all of these claims through a detailed performance analysis. With the help of profiling and tracing tools, we guide our development of batched factorizations to achieve up to two-fold speedup and three-fold better energy efficiency as compared against our highly optimized batched CPU implementations based on MKL library. The tested system featured two sockets of Intel Sandy Bridge CPUs and we compared with a batched LU factorizations featured in the CUBLAS library for GPUs, we achieve as high as 2.5× speedup on the NVIDIA K40 GPU. %B International Journal of High Performance Computing Applications %8 02-2015 %G eng %R 10.1177/1094342014567546 %0 Conference Paper %B 17th IEEE International Conference on High Performance Computing and Communications (HPCC 2015) %D 2015 %T Cholesky Across Accelerators %A Asim YarKhan %A Azzam Haidar %A Chongxiao Cao %A Piotr Luszczek %A Stanimire Tomov %A Jack Dongarra %B 17th IEEE International Conference on High Performance Computing and Communications (HPCC 2015) %I IEEE %C Elizabeth, NJ %8 08-2015 %G eng %0 Conference Paper %B 2015 SIAM Conference on Applied Linear Algebra %D 2015 %T Comparing Hybrid CPU-GPU and Native GPU-only Acceleration for Linear Algebra %A Mark Gates %A Stanimire Tomov %A Azzam Haidar %X Accelerating dense linear algebra using GPUs admits two models: hybrid CPU-GPU and GPU-only. The hybrid model factors the panel on the CPU while updating the trailing matrix on the GPU, concentrating the GPU on high-performance matrix multiplies. The GPU-only model performs the entire computation on the GPU, avoiding costly data transfers to the CPU. We compare these two approaches for three QR-based algorithms: QR factorization, rank revealing QR, and reduction to Hessenberg. %B 2015 SIAM Conference on Applied Linear Algebra %I SIAM %C Atlanta, GA %8 10-2015 %G eng %0 Journal Article %J International Journal of Networking and Computing %D 2015 %T Composing Resilience Techniques: ABFT, Periodic, and Incremental Checkpointing %A George Bosilca %A Aurelien Bouteiller %A Thomas Herault %A Yves Robert %A Jack Dongarra %K ABFT %K checkpoint %K fault-tolerance %K High-performance computing %K model %K performance evaluation %K resilience %X Algorithm Based Fault Tolerant (ABFT) approaches promise unparalleled scalability and performance in failure-prone environments. Thanks to recent advances in the understanding of the involved mechanisms, a growing number of important algorithms (including all widely used factorizations) have been proven ABFT-capable. In the context of larger applications, these algorithms provide a temporal section of the execution, where the data is protected by its own intrinsic properties, and can therefore be algorithmically recomputed without the need of checkpoints. However, while typical scientific applications spend a significant fraction of their execution time in library calls that can be ABFT-protected, they interleave sections that are difficult or even impossible to protect with ABFT. As a consequence, the only practical fault-tolerance approach for these applications is checkpoint/restart. In this paper we propose a model to investigate the efficiency of a composite protocol, that alternates between ABFT and checkpoint/restart for the effective protection of an iterative application composed of ABFT- aware and ABFT-unaware sections. We also consider an incremental checkpointing composite approach in which the algorithmic knowledge is leveraged by a novel optimal dynamic program- ming to compute checkpoint dates. We validate these models using a simulator. The model and simulator show that the composite approach drastically increases the performance delivered by an execution platform, especially at scale, by providing the means to increase the interval between checkpoints while simultaneously decreasing the volume of each checkpoint. %B International Journal of Networking and Computing %V 5 %P 2-15 %8 01-2015 %G eng %0 Journal Article %J Scientific Programming %D 2015 %T Computing Low-rank Approximation of a Dense Matrix on Multicore CPUs with a GPU and its Application to Solving a Hierarchically Semiseparable Linear System of Equations %A Ichitaro Yamazaki %A Stanimire Tomov %A Jack Dongarra %X Low-rank matrices arise in many scientific and engineering computation. Both computational and storage costs of manipulating such matrices may be reduced by taking advantages of their low-rank properties. To compute a low-rank approximation of a dense matrix, in this paper, we study the performance of QR factorization with column pivoting or with restricted pivoting on multicore CPUs with a GPU. We first propose several techniques to reduce the postprocessing time, which is required for restricted pivoting, on a modern CPU. We then examine the potential of using a GPU to accelerate the factorization process with both column and restricted pivoting. Our performance results on two eight-core Intel Sandy Bridge CPUs with one NVIDIA Kepler GPU demonstrate that using the GPU, the factorization time can be reduced by a factor of more than two. In addition, to study the performance of our implementations in practice, we integrate them into a recently-developed software StruMF which algebraically exploits such low-rank structures for solving a general sparse linear system of equations. Our performance results for solving Poisson's equations demonstrate that the proposed techniques can significantly reduce the preconditioner construction time of StruMF on the CPUs, and the construction time can be further reduced by 10%-50% using the GPU. %B Scientific Programming %G eng %0 Conference Paper %B 29th IEEE International Parallel & Distributed Processing Symposium (IPDPS) %D 2015 %T A Data Flow Divide and Conquer Algorithm for Multicore Architecture %A Azzam Haidar %A Jakub Kurzak %A Gregoire Pichon %A Mathieu Faverge %K Eigensolver %K lapack %K Multicore %K plasma %K task-based programming %X Computing eigenpairs of a symmetric matrix is a problem arising in many industrial applications, including quantum physics and finite-elements computation for automobiles. A classical approach is to reduce the matrix to tridiagonal form before computing eigenpairs of the tridiagonal matrix. Then, a back-transformation allows one to obtain the final solution. Parallelism issues of the reduction stage have already been tackled in different shared-memory libraries. In this article, we focus on solving the tridiagonal eigenproblem, and we describe a novel implementation of the Divide and Conquer algorithm. The algorithm is expressed as a sequential task-flow, scheduled in an out-of-order fashion by a dynamic runtime which allows the programmer to play with tasks granularity. The resulting implementation is between two and five times faster than the equivalent routine from the Intel MKL library, and outperforms the best MRRR implementation for many matrices. %B 29th IEEE International Parallel & Distributed Processing Symposium (IPDPS) %I IEEE %C Hyderabad, India %8 05-2015 %G eng %0 Conference Paper %B ISC High Performance 2015 %D 2015 %T On the Design, Development, and Analysis of Optimized Matrix-Vector Multiplication Routines for Coprocessors %A Khairul Kabir %A Azzam Haidar %A Stanimire Tomov %A Jack Dongarra %X The dramatic change in computer architecture due to the manycore paradigm shift, made the development of numerical routines that are optimal extremely challenging. In this work, we target the development of numerical algorithms and implementations for Xeon Phi coprocessor architecture designs. In particular, we examine and optimize the general and symmetric matrix-vector multiplication routines (gemv/symv), which are some of the most heavily used linear algebra kernels in many important engineering and physics applications. We describe a successful approach on how to address the challenges for this problem, starting from our algorithm design, performance analysis and programing model, to kernel optimization. Our goal, by targeting low-level, easy to understand fundamental kernels, is to develop new optimization strategies that can be effective elsewhere for the use on manycore coprocessors, and to show significant performance improvements compared to the existing state-of-the-art implementations. Therefore, in addition to the new optimization strategies, analysis, and optimal performance results, we finally present the significance of using these routines/strategies to accelerate higher-level numerical algorithms for the eigenvalue problem (EVP) and the singular value decomposition (SVD) that by themselves are foundational for many important applications. %B ISC High Performance 2015 %C Frankfurt, Germany %8 07-2015 %G eng %0 Conference Paper %B 29th IEEE International Parallel & Distributed Processing Symposium (IPDPS) %D 2015 %T Design for a Soft Error Resilient Dynamic Task-based Runtime %A Chongxiao Cao %A George Bosilca %A Thomas Herault %A Jack Dongarra %X As the scale of modern computing systems grows, failures will happen more frequently. On the way to Exascale a generic, low-overhead, resilient extension becomes a desired aptitude of any programming paradigm. In this paper we explore three additions to a dynamic task-based runtime to build a generic framework providing soft error resilience to task-based programming paradigms. The first recovers the application by re-executing the minimum required sub-DAG, the second takes critical checkpoints of the data flowing between tasks to minimize the necessary re-execution, while the last one takes advantage of algorithmic properties to recover the data without re-execution. These mechanisms have been implemented in the PaRSEC task-based runtime framework. Experimental results validate our approach and quantify the overhead introduced by such mechanisms. %B 29th IEEE International Parallel & Distributed Processing Symposium (IPDPS) %I IEEE %C Hyderabad, India %8 05-2015 %G eng %0 Journal Article %J International Journal on High Performance Computing Applications %D 2015 %T Efficient Checkpoint/Verification Patterns %A Anne Benoit %A Saurabh K. Raina %A Yves Robert %K checkpointing %K Fault tolerance %K High Performance Computing %K silent data corruption %K silent error %K verification %X Errors have become a critical problem for high performance computing. Checkpointing protocols are often used for error recovery after fail-stop failures. However, silent errors cannot be ignored, and their peculiarity is that such errors are identified only when the corrupted data is activated. To cope with silent errors, we need a verification mechanism to check whether the application state is correct. Checkpoints should be supplemented with verifications to detect silent errors. When a verification is successful, only the last checkpoint needs to be kept in memory because it is known to be correct. In this paper, we analytically determine the best balance of verifications and checkpoints so as to optimize platform throughput. We introduce a balanced algorithm using a pattern with p checkpoints and q verifications, which regularly interleaves both checkpoints and verifications across same-size computational chunks. We show how to compute the waste of an arbitrary pattern, and we prove that the balanced algorithm is optimal when the platform MTBF (Mean Time Between Failures) is large in front of the other parameters (checkpointing, verification and recovery costs). We conduct several simulations to show the gain achieved by this balanced algorithm for well-chosen values of p and q, compared to the base algorithm that always perform a verification just before taking a checkpoint (p = q = 1), and we exhibit gains of up to 19%. %B International Journal on High Performance Computing Applications %8 07-2015 %G eng %R 10.1177/1094342015594531 %0 Conference Paper %B 2015 SIAM Conference on Applied Linear Algebra (SIAM LA) %D 2015 %T Efficient Eigensolver Algorithms on Accelerator Based Architectures %A Azzam Haidar %A Piotr Luszczek %A Stanimire Tomov %A Jack Dongarra %X The enormous gap between the high-performance capabilities of GPUs and the slow interconnect between them has made the development of numerical software that is scalable across multiple GPUs extremely challenging. We describe a successful methodology on how to address the challenges -starting from our algorithm design, kernel optimization and tuning, to our programming model- in the development of a scalable high-performance symmetric eigenvalue and singular value solver. %B 2015 SIAM Conference on Applied Linear Algebra (SIAM LA) %I SIAM %C Atlanta, GA %8 10-2015 %G eng %0 Conference Paper %B The International Conference for High Performance Computing, Networking, Storage and Analysis (SC15) %D 2015 %T Efficient Implementation Of Quantum Materials Simulations On Distributed CPU-GPU Systems %A Raffaele Solcà %A Anton Kozhevnikov %A Azzam Haidar %A Stanimire Tomov %A Thomas C. Schulthess %A Jack Dongarra %X We present a scalable implementation of the Linearized Augmented Plane Wave method for distributed memory systems, which relies on an efficient distributed, block-cyclic setup of the Hamiltonian and overlap matrices and allows us to turn around highly accurate 1000+ atom all-electron quantum materials simulations on clusters with a few hundred nodes. The implementation runs efficiently on standard multicore CPU nodes, as well as hybrid CPU-GPU nodes. The key for the latter is a novel algorithm to solve the generalized eigenvalue problem for dense, complex Hermitian matrices on distributed hybrid CPU-GPU systems. Performance tests for Li-intercalated CoO2 supercells containing 1501 atoms demonstrate that high-accuracy, transferable quantum simulations can now be used in throughput materials search problems. While our application can benefit and get scalable performance through CPU-only libraries like ScaLAPACK or ELPA2, our new hybrid solver enables the efficient use of GPUs and shows that a hybrid CPU-GPU architecture scales to a desired performance using substantially fewer cluster nodes, and notably, is considerably more energy efficient than the traditional multicore CPU only systems for such complex applications. %B The International Conference for High Performance Computing, Networking, Storage and Analysis (SC15) %I ACM %C Austin, TX %8 11-2015 %G eng %0 Conference Paper %B Sixth International Workshop on Programming Models and Applications for Multicores and Manycores (PMAM '15) %D 2015 %T Energy Efficiency and Performance Frontiers for Sparse Computations on GPU Supercomputers %A Hartwig Anzt %A Stanimire Tomov %A Jack Dongarra %X In this paper we unveil some energy efficiency and performance frontiers for sparse computations on GPU-based supercomputers. To do this, we consider state-of-the-art implementations of the sparse matrix-vector (SpMV) product in libraries like cuSPARSE, MKL, and MAGMA, and their use in the LOBPCG eigen-solver. LOBPCG is chosen as a benchmark for this study as it combines an interesting mix of sparse and dense linear algebra operations with potential for hardware-aware optimizations. Most notably, LOBPCG includes a blocking technique that is a common performance optimization for many applications. In particular, multiple memory-bound SpMV operations are blocked into a SpM-matrix product (SpMM), that achieves significantly higher performance than a sequence of SpMVs. We provide details about the GPU kernels we use for the SpMV, SpMM, and the LOBPCG implementation design, and study performance and energy consumption compared to CPU solutions. While a typical sparse computation like the SpMV reaches only a fraction of the peak of current GPUs, we show that the SpMM achieves up to a 6x performance improvement over the GPU's SpMV, and the GPU-accelerated LOBPCG based on this kernel is 3 to 5x faster than multicore CPUs with the same power draw, e.g., a K40 GPU vs. two Sandy Bridge CPUs (16 cores). In practice though, we show that currently available CPU implementations are much slower due to missed optimization opportunities. These performance results translate to similar improvements in energy consumption, and are indicative of today's frontiers in energy efficiency and performance for sparse computations on supercomputers. %B Sixth International Workshop on Programming Models and Applications for Multicores and Manycores (PMAM '15) %I ACM %C San Francisco, CA %8 02-2015 %@ 978-1-4503-3404-4 %G eng %R 10.1145/2712386.2712387 %0 Generic %D 2015 %T Exascale Computing and Big Data %A Dan Reed %A Jack Dongarra %X Scientific discovery and engineering innovation requires unifying traditionally separated high-performance computing and big data analytics. %B Communications of the ACM %I ACM %V 58 %P 56-68 %8 07-2015 %G eng %9 Magazine Article %R 10.1145/2699414 %0 Journal Article %J Concurrency and Computation: Practice and Experience %D 2015 %T Experiences in Autotuning Matrix Multiplication for Energy Minimization on GPUs %A Hartwig Anzt %A Blake Haugen %A Jakub Kurzak %A Piotr Luszczek %A Jack Dongarra %K Autotuning %K energy efficiency %K hardware accelerators %K matrix multiplication %K power %X In this paper, we report extensive results and analysis of autotuning the computationally intensive graphics processing units kernel for dense matrix–matrix multiplication in double precision. In contrast to traditional autotuning and/or optimization for runtime performance only, we also take the energy efficiency into account. For kernels achieving equal performance, we show significant differences in their energy balance. We also identify the memory throughput as the most influential metric that trades off performance and energy efficiency. As a result, the performance optimal case ends up not being the most efficient kernel in overall resource use. %B Concurrency and Computation: Practice and Experience %V 27 %P 5096 - 5113 %8 Oct-12-2015 %G eng %U http://doi.wiley.com/10.1002/cpe.3516https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fcpe.3516 %N 17 %! Concurrency Computat.: Pract. Exper. %R 10.1002/cpe.3516 %0 Journal Article %J Concurrency in Computation: Practice and Experience %D 2015 %T Experiences in autotuning matrix multiplication for energy minimization on GPUs %A Hartwig Anzt %A Blake Haugen %A Jakub Kurzak %A Piotr Luszczek %A Jack Dongarra %B Concurrency in Computation: Practice and Experience %V 27 %P 5096-5113 %8 12-2015 %G eng %N 17 %R 10.1002/cpe.3516 %0 Generic %D 2015 %T Fault Tolerance Techniques for High-performance Computing %A Jack Dongarra %A Thomas Herault %A Yves Robert %X This report provides an introduction to resilience methods. The emphasis is on checkpointing, the de-facto standard technique for resilience in High Performance Computing. We present the main two protocols, namely coordinated checkpointing and hierarchical checkpointing. Then we introduce performance models and use them to assess the performance of theses protocols. We cover the Young/Daly formula for the optimal period and much more! Next we explain how the efficiency of checkpointing can be improved via fault prediction or replication. Then we move to application-specific methods, such as ABFT. We conclude the report by discussing techniques to cope with silent errors (or silent data corruption). %B University of Tennessee Computer Science Technical Report (also LAWN 289) %I University of Tennessee %8 05-2015 %G eng %U http://www.netlib.org/lapack/lawnspdf/lawn289.pdf %0 Conference Paper %B 17th IEEE International Conference on High Performance Computing and Communications %D 2015 %T Flexible Linear Algebra Development and Scheduling with Cholesky Factorization %A Azzam Haidar %A Asim YarKhan %A Chongxiao Cao %A Piotr Luszczek %A Stanimire Tomov %A Jack Dongarra %X Modern high performance computing environments are composed of networks of compute nodes that often contain a variety of heterogeneous compute resources, such as multicore-CPUs, GPUs, and coprocessors. One challenge faced by domain scientists is how to efficiently use all these distributed, heterogeneous resources. In order to use the GPUs effectively, the workload parallelism needs to be much greater than the parallelism for a multicore-CPU. On the other hand, a Xeon Phi coprocessor will work most effectively with degree of parallelism between GPUs and multicore-CPUs. Additionally, effectively using distributed memory nodes brings out another level of complexity where the workload must be carefully partitioned over the nodes. In this work we are using a lightweight runtime environment to handle many of the complexities in such distributed, heterogeneous systems. The runtime environment uses task-superscalar concepts to enable the developer to write serial code while providing parallel execution. The task-programming model allows the developer to write resource-specialization code, so that each resource gets the appropriate sized workload-grain. Our task programming abstraction enables the developer to write a single algorithm that will execute efficiently across the distributed heterogeneous machine. We demonstrate the effectiveness of our approach with performance results for dense linear algebra applications, specifically the Cholesky factorization. %B 17th IEEE International Conference on High Performance Computing and Communications %C Newark, NJ %8 08-2015 %G eng %0 Conference Paper %B ISC High Performance %D 2015 %T Framework for Batched and GPU-resident Factorization Algorithms to Block Householder Transformations %A Azzam Haidar %A Tingxing Dong %A Stanimire Tomov %A Piotr Luszczek %A Jack Dongarra %B ISC High Performance %I Springer %C Frankfurt, Germany %8 07-2015 %G eng %0 Conference Paper %B 2nd International Workshop on Hardware-Software Co-Design for High Performance Computing %D 2015 %T GPU-accelerated Co-design of Induced Dimension Reduction: Algorithmic Fusion and Kernel Overlap %A Hartwig Anzt %A Eduardo Ponce %A Gregory D. Peterson %A Jack Dongarra %X In this paper we present an optimized GPU co-design of the Induced Dimension Reduction (IDR) algorithm for solving linear systems. Starting from a baseline implementation based on the generic BLAS routines from the MAGMA software library, we apply optimizations that are based on kernel fusion and kernel overlap. Runtime experiments are used to investigate the benefit of the distinct optimization techniques for different variants of the IDR algorithm. A comparison to the reference implementation reveals that the interplay between them can succeed in cutting the overall runtime by up to about one third. %B 2nd International Workshop on Hardware-Software Co-Design for High Performance Computing %I ACM %C Austin, TX %8 11-2015 %G eng %0 Conference Paper %B 29th IEEE International Parallel & Distributed Processing Symposium (IPDPS) %D 2015 %T Hierarchical DAG scheduling for Hybrid Distributed Systems %A Wei Wu %A Aurelien Bouteiller %A George Bosilca %A Mathieu Faverge %A Jack Dongarra %K dense linear algebra %K gpu %K heterogeneous architecture %K PaRSEC runtime %X Accelerator-enhanced computing platforms have drawn a lot of attention due to their massive peak com-putational capacity. Despite significant advances in the pro-gramming interfaces to such hybrid architectures, traditional programming paradigms struggle mapping the resulting multi-dimensional heterogeneity and the expression of algorithm parallelism, resulting in sub-optimal effective performance. Task-based programming paradigms have the capability to alleviate some of the programming challenges on distributed hybrid many-core architectures. In this paper we take this concept a step further by showing that the potential of task-based programming paradigms can be greatly increased with minimal modification of the underlying runtime combined with the right algorithmic changes. We propose two novel recursive algorithmic variants for one-sided factorizations and describe the changes to the PaRSEC task-scheduling runtime to build a framework where the task granularity is dynamically adjusted to adapt the degree of available parallelism and kernel effi-ciency according to runtime conditions. Based on an extensive set of results we show that, with one-sided factorizations, i.e. Cholesky and QR, a carefully written algorithm, supported by an adaptive tasks-based runtime, is capable of reaching a degree of performance and scalability never achieved before in distributed hybrid environments. %B 29th IEEE International Parallel & Distributed Processing Symposium (IPDPS) %I IEEE %C Hyderabad, India %8 05-2015 %G eng %0 Book Section %B The Princeton Companion to Applied Mathematics %D 2015 %T High-Performance Computing %A Jack Dongarra %A Nicholas J. Higham %A Mark R. Dennis %A Paul Glendinning %A Paul A. Martin %A Fadil Santosa %A Jared Tanner %B The Princeton Companion to Applied Mathematics %I Princeton University Press %C Princeton, New Jersey %P 839-842 %@ 9781400874477 %G eng %0 Journal Article %J The International Journal of High Performance Computing Applications %D 2015 %T High-Performance Conjugate-Gradient Benchmark: A New Metric for Ranking High-Performance Computing Systems %A Jack Dongarra %A Michael Heroux %A Piotr Luszczek %K Additive Schwarz %K HPC Benchmarking %K Multigrid smoothing %K Preconditioned Conjugate Gradient %K Validation and Verification %X We describe a new high-performance conjugate-gradient (HPCG) benchmark. HPCG is composed of computations and data-access patterns commonly found in scientific applications. HPCG strives for a better correlation to existing codes from the computational science domain and to be representative of their performance. HPCG is meant to help drive the computer system design and implementation in directions that will better impact future performance improvement. %B The International Journal of High Performance Computing Applications %G eng %R 10.1177/1094342015593158 %0 Journal Article %J Scientific Programming %D 2015 %T HPC Programming on Intel Many-Integrated-Core Hardware with MAGMA Port to Xeon Phi %A Azzam Haidar %A Jack Dongarra %A Khairul Kabir %A Mark Gates %A Piotr Luszczek %A Stanimire Tomov %A Yulu Jia %K communication and computation overlap %K dynamic runtime scheduling using dataflow dependences %K hardware accelerators and coprocessors %K Intel Xeon Phi processor %K Many Integrated Cores %K numerical linear algebra %X This paper presents the design and implementation of several fundamental dense linear algebra (DLA) algorithms for multicore with Intel Xeon Phi Coprocessors. In particular, we consider algorithms for solving linear systems. Further, we give an overview of the MAGMA MIC library, an open source, high performance library that incorporates the developments presented, and in general provides to heterogeneous architectures of multicore with coprocessors the DLA functionality of the popular LAPACK library. The LAPACK-compliance simplifies the use of the MAGMA MIC library in applications, while providing them with portably performant DLA. High performance is obtained through use of the high-performance BLAS, hardware-specific tuning, and a hybridization methodology where we split the algorithm into computational tasks of various granularities. Execution of those tasks is properly scheduled over the heterogeneous hardware components by minimizing data movements and mapping algorithmic requirements to the architectural strengths of the various heterogeneous hardware components. Our methodology and programming techniques are incorporated into the MAGMA MIC API, which abstracts the application developer from the specifics of the Xeon Phi architecture and is therefore applicable to algorithms beyond the scope of DLA. %B Scientific Programming %V 23 %8 01-2015 %G eng %N 1 %R 10.3233/SPR-140404 %0 Generic %D 2015 %T HPCG Benchmark: a New Metric for Ranking High Performance Computing Systems %A Jack Dongarra %A Michael Heroux %A Piotr Luszczek %K Additive Schwarz %K HPC Benchmarking %K Multigrid smoothing %K Preconditioned Conjugate Gradient %K Validation and Verification %X We describe a new high performance conjugate gradient (HPCG) benchmark. HPCG is composed of computations and data access patterns commonly found in scientific applications. HPCG strives for a better correlation to existing codes from the computational science domain and be representative of their performance. HPCG is meant to help drive the computer system design and implementation in directions that will better impact future performance improvement. %B University of Tennessee Computer Science Technical Report %I University of Tennessee %8 01-2015 %G eng %U http://www.eecs.utk.edu/resources/library/file/1047/ut-eecs-15-736.pdf %0 Journal Article %J IEEE Transactions on Parallel and Distributed Systems %D 2015 %T Implementation and Tuning of Batched Cholesky Factorization and Solve for NVIDIA GPUs %A Jakub Kurzak %A Hartwig Anzt %A Mark Gates %A Jack Dongarra %B IEEE Transactions on Parallel and Distributed Systems %8 11-2015 %G eng %0 Conference Paper %B EuroPar 2015 %D 2015 %T Iterative Sparse Triangular Solves for Preconditioning %A Hartwig Anzt %A Edmond Chow %A Jack Dongarra %X Sparse triangular solvers are typically parallelized using level scheduling techniques, but parallel eciency is poor on high-throughput architectures like GPUs. We propose using an iterative approach for solving sparse triangular systems when an approximation is suitable. This approach will not work for all problems, but can be successful for sparse triangular matrices arising from incomplete factorizations, where an approximate solution is acceptable. We demonstrate the performance gains that this approach can have on GPUs in the context of solving sparse linear systems with a preconditioned Krylov subspace method. We also illustrate the effect of using asynchronous iterations. %B EuroPar 2015 %I Springer Berlin %C Vienna, Austria %8 08-2015 %G eng %U http://dx.doi.org/10.1007/978-3-662-48096-0_50 %R 10.1007/978-3-662-48096-0_50 %0 Conference Paper %B 2015 IEEE High Performance Extreme Computing Conference (HPEC ’15), (Best Paper Award) %D 2015 %T MAGMA Embedded: Towards a Dense Linear Algebra Library for Energy Efficient Extreme Computing %A Azzam Haidar %A Stanimire Tomov %A Piotr Luszczek %A Jack Dongarra %X Embedded computing, not only in large systems like drones and hybrid vehicles, but also in small portable devices like smart phones and watches, gets more extreme to meet ever increasing demands for extended and improved functionalities. This, combined with the typical constrains for low power consumption and small sizes, makes the design of numerical libraries for embedded systems challenging. In this paper, we present the design and implementation of embedded system aware algorithms, that target these challenges in the area of dense linear algebra. We consider the fundamental problems of solving linear systems of equations and least squares problems, using the LU, QR, and Cholesky factorizations, and illustrate our results, both in terms of performance and energy efficiency, on the Jetson TK1 development kit. We developed performance optimizations for both small and large problems. In contrast to the corresponding LAPACK algorithms, the new designs target the use of many-cores, readily available now even in mobile devices like the Jetson TK1, e.g., featuring 192 CUDA cores. The implementations presented will form the core of a MAGMA Embedded library, to be released as part of the MAGMA libraries. %B 2015 IEEE High Performance Extreme Computing Conference (HPEC ’15), (Best Paper Award) %I IEEE %C Waltham, MA %8 09-2015 %G eng %0 Conference Paper %B 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems %D 2015 %T Mixed-precision Block Gram Schmidt Orthogonalization %A Ichitaro Yamazaki %A Stanimire Tomov %A Jakub Kurzak %A Jack Dongarra %A Jesse Barlow %X The mixed-precision Cholesky QR (CholQR) can orthogonalize the columns of a dense matrix with the minimum communication cost. Moreover, its orthogonality error depends only linearly to the condition number of the input matrix. However, when the desired higher-precision is not supported by the hardware, the software-emulated arithmetics are needed, which could significantly increase its computational cost. When there are a large number of columns to be orthogonalized, this computational overhead can have a significant impact on the orthogonalization time, and the mixed-precision CholQR can be much slower than the standard CholQR. In this paper, we examine several block variants of the algorithm, which reduce the computational overhead associated with the software-emulated arithmetics, while maintaining the same orthogonality error bound as the mixed-precision CholQR. Our numerical and performance results on multicore CPUs with a GPU, as well as a hybrid CPU/GPU cluster, demonstrate that compared to the mixed-precision CholQR, such a block variant can obtain speedups of up to 7:1 while maintaining about the same order of the numerical errors. %B 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems %I ACM %C Austin, TX %8 11-2015 %G eng %0 Journal Article %J SIAM Journal on Scientific Computing %D 2015 %T Mixed-Precision Cholesky QR Factorization and its Case Studies on Multicore CPU with Multiple GPUs %A Ichitaro Yamazaki %A Stanimire Tomov %A Jack Dongarra %X To orthonormalize the columns of a dense matrix, the Cholesky QR (CholQR) requires only one global reduction between the parallel processing units and performs most of its computation using BLAS-3 kernels. As a result, compared to other orthogonalization algorithms, CholQR obtains superior performance on many of the current computer architectures, where the communication is becoming increasingly expensive compared to the arithmetic operations. This is especially true when the input matrix is tall-skinny. Unfortunately, the orthogonality error of CholQR depends quadratically on the condition number of the input matrix, and it is numerically unstable when the matrix is ill-conditioned. To enhance the stability of CholQR, we recently used mixed-precision arithmetic; the input and output matrices are in the working precision, but some of its intermediate results are accumulated in the doubled precision. In this paper, we analyze the numerical properties of this mixed-precision CholQR. Our analysis shows that by selectively using the doubled precision, the orthogonality error of the mixed-precision CholQR only depends linearly on the condition number of the input matrix. We provide numerical results to demonstrate the improved numerical stability of the mixed-precision CholQR in practice. We then study its performance. When the target hardware does not support the desired higher precision, software emulation is needed. For example, using software-emulated double-double precision for the working 64-bit double precision, the mixed-precision CholQR requires about 8.5x more floating-point instructions than that required by the standard CholQR. On the other hand, the increase in the communication cost using the double-double precision is less significant, and our performance results on multicore CPU with a different graphics processing unit (GPU) demonstrate that the overhead of using the double-double arithmetic is decreasing on a newer architecture, where the computation is becoming less expensive compared to the communication. As a result, with a latest NVIDIA GPU, the mixed-precision CholQR was only 1.4x slower than the standard CholQR. Finally, we present case studies of using the mixed-precision CholQR within communication-avoiding variants of Krylov subspace projection methods for solving a nonsymmetric linear system of equations and for solving a symmetric eigenvalue problem, on a multicore CPU with multiple GPUs. These case studies demonstrate that by using the higher precision for this small but critical segment of the Krylov methods, we can improve not only the overall numerical stability of the solvers but also, in some cases, their performance. %B SIAM Journal on Scientific Computing %V 37 %P C203-C330 %8 05-2015 %G eng %R DOI:10.1137/14M0973773 %0 Conference Paper %B 2015 SIAM Conference on Applied Linear Algebra %D 2015 %T Mixed-precision orthogonalization process Performance on multicore CPUs with GPUs %A Ichitaro Yamazaki %A Jesse Barlow %A Stanimire Tomov %A Jakub Kurzak %A Jack Dongarra %X Orthogonalizing a set of dense vectors is an important computational kernel in subspace projection methods for solving large-scale problems. In this talk, we discuss our efforts to improve the performance of the kernel, while maintaining its numerical accuracy. Our experimental results demonstrate the effectiveness of our approaches. %B 2015 SIAM Conference on Applied Linear Algebra %I SIAM %C Atlanta, GA %8 10-2015 %G eng %0 Journal Article %J Journal of Parallel and Distributed Computing %D 2015 %T Mixing LU-QR Factorization Algorithms to Design High-Performance Dense Linear Algebra Solvers %A Mathieu Faverge %A Julien Herrmann %A Julien Langou %A Bradley Lowery %A Yves Robert %A Jack Dongarra %K lu factorization %K Numerical algorithms %K QR factorization %K Stability; Performance %X This paper introduces hybrid LU–QR algorithms for solving dense linear systems of the form Ax=b. Throughout a matrix factorization, these algorithms dynamically alternate LU with local pivoting and QR elimination steps based upon some robustness criterion. LU elimination steps can be very efficiently parallelized, and are twice as cheap in terms of floating-point operations, as QR steps. However, LU steps are not necessarily stable, while QR steps are always stable. The hybrid algorithms execute a QR step when a robustness criterion detects some risk for instability, and they execute an LU step otherwise. The choice between LU and QR steps must have a small computational overhead and must provide a satisfactory level of stability with as few QR steps as possible. In this paper, we introduce several robustness criteria and we establish upper bounds on the growth factor of the norm of the updated matrix incurred by each of these criteria. In addition, we describe the implementation of the hybrid algorithms through an extension of the PaRSEC software to allow for dynamic choices during execution. Finally, we analyze both stability and performance results compared to state-of-the-art linear solvers on parallel distributed multicore platforms. A comprehensive set of experiments shows that hybrid LU–QR algorithms provide a continuous range of trade-offs between stability and performances. %B Journal of Parallel and Distributed Computing %V 85 %P 32-46 %8 11-2015 %G eng %R doi:10.1016/j.jpdc.2015.06.007 %0 Conference Paper %B 8th Workshop on General Purpose Processing Using GPUs (GPGPU 8) %D 2015 %T Optimization for Performance and Energy for Batched Matrix Computations on GPUs %A Azzam Haidar %A Tingxing Dong %A Piotr Luszczek %A Stanimire Tomov %A Jack Dongarra %K batched factorization %K hardware accelerators %K numerical linear algebra %K numerical software libraries %K one-sided factorization algorithms %X As modern hardware keeps evolving, an increasingly effective approach to develop energy efficient and high-performance solvers is to design them to work on many small size independent problems. Many applications already need this functionality, especially for GPUs, which are known to be currently about four to five times more energy efficient than multicore CPUs. We describe the development of the main one-sided factorizations that work for a set of small dense matrices in parallel, and we illustrate our techniques on the LU and Cholesky factorizations. We refer to this mode of operation as a batched factorization. Our approach is based on representing the algorithms as a sequence of batched BLAS routines for GPU-only execution. The goal of avoiding multicore CPU use, e.g., as in the hybrid CPU-GPU algorithms, is to exclusively benefit from the GPU’s significantly higher energy efficiency, as well as from the removal of the costly CPU-to-GPU communications. Furthermore, we do not use a single symmetric multiprocessor (on the GPU) to factorize a single problem at a time. We illustrate how our performance analysis and the use of profiling and tracing tools guided the development and optimization of batched factorizations to achieve up to 2-fold speedup and 3-fold better energy efficiency compared to our highly optimized batched CPU implementations based on the MKL library (when using two sockets of Intel Sandy Bridge CPUs). Compared to a batched LU factorization featured in the CUBLAS library for GPUs, we achieved up to 2.5 speedup on the K40 GPU. %B 8th Workshop on General Purpose Processing Using GPUs (GPGPU 8) %I ACM %C San Francisco, CA %8 02-2015 %G eng %R 10.1145/2716282.2716288 %0 Journal Article %J Supercomputing Frontiers and Innovations %D 2015 %T Parallel Programming Models for Dense Linear Algebra on Heterogeneous Systems %A Maksims Abalenkovs %A Ahmad Abdelfattah %A Jack Dongarra %A Mark Gates %A Azzam Haidar %A Jakub Kurzak %A Piotr Luszczek %A Stanimire Tomov %A Ichitaro Yamazaki %A Asim YarKhan %K dense linear algebra %K gpu %K HPC %K Multicore %K Programming models %K runtime %X We present a review of the current best practices in parallel programming models for dense linear algebra (DLA) on heterogeneous architectures. We consider multicore CPUs, stand alone manycore coprocessors, GPUs, and combinations of these. Of interest is the evolution of the programming models for DLA libraries – in particular, the evolution from the popular LAPACK and ScaLAPACK libraries to their modernized counterparts PLASMA (for multicore CPUs) and MAGMA (for heterogeneous architectures), as well as other programming models and libraries. Besides providing insights into the programming techniques of the libraries considered, we outline our view of the current strengths and weaknesses of their programming models – especially in regards to hardware trends and ease of programming high-performance numerical software that current applications need – in order to motivate work and future directions for the next generation of parallel programming models for high-performance linear algebra libraries on heterogeneous systems. %B Supercomputing Frontiers and Innovations %V 2 %8 10-2015 %G eng %R 10.14529/jsfi1504 %0 Conference Paper %B 2015 IEEE International Conference on Cluster Computing %D 2015 %T PaRSEC in Practice: Optimizing a Legacy Chemistry Application through Distributed Task-Based Execution %A Anthony Danalis %A Heike Jagode %A George Bosilca %A Jack Dongarra %K dag %K parsec %K ptg %K tasks %X Task-based execution has been growing in popularity as a means to deliver a good balance between performance and portability in the post-petascale era. The Parallel Runtime Scheduling and Execution Control (PARSEC) framework is a task-based runtime system that we designed to achieve high performance computing at scale. PARSEC offers a programming paradigm that is different than what has been traditionally used to develop large scale parallel scientific applications. In this paper, we discuss the use of PARSEC to convert a part of the Coupled Cluster (CC) component of the Quantum Chemistry package NWCHEM into a task-based form. We explain how we organized the computation of the CC methods in individual tasks with explicitly defined data dependencies between them and re-integrated the modified code into NWCHEM. We present a thorough performance evaluation and demonstrate that the modified code outperforms the original by more than a factor of two. We also compare the performance of different variants of the modified code and explain the different behaviors that lead to the differences in performance. %B 2015 IEEE International Conference on Cluster Computing %I IEEE %C Chicago, IL %8 09-2015 %G eng %0 Conference Paper %B The Spring Simulation Multi-Conference 2015 (SpringSim'15), Best Paper Award %D 2015 %T Performance Analysis and Design of a Hessenberg Reduction using Stabilized Blocked Elementary Transformations for New Architectures %A Khairul Kabir %A Azzam Haidar %A Stanimire Tomov %A Jack Dongarra %K Eigenvalues problem %K Hessenberg reduction %K Multi/Many-core %K Stabilized Elementary Transformations %X The solution of nonsymmetric eigenvalue problems, Ax = λx, can be accelerated substantially by first reducing A to an upper Hessenberg matrix H that has the same eigenvalues as A. This can be done using Householder orthogonal transformations, which is a well established standard, or stabilized elementary transformations. The latter approach, although having half the flops of the former, has been used less in practice, e.g., on computer architectures with well developed hierarchical memories, because of its memory-bound operations and the complexity in stabilizing it. In this paper we revisit the stabilized elementary transformations approach in the context of new architectures – both multicore CPUs and Xeon Phi coprocessors. We derive for a first time a blocking version of the algorithm. The blocked version reduces the memory-bound operations and we analyze its performance. A performance model is developed that shows the limitations of both approaches. The competitiveness of using stabilized elementary transformations has been quantified, highlighting that it can be 20 to 30% faster on current high-end multicore CPUs and Xeon Phi coprocessors. %B The Spring Simulation Multi-Conference 2015 (SpringSim'15), Best Paper Award %C Alexandria, VA %8 04-2015 %G eng %0 Conference Paper %B International Conference on Computational Science (ICCS 2015) %D 2015 %T Performance Analysis and Optimization of Two-Sided Factorization Algorithms for Heterogeneous Platform %A Khairul Kabir %A Azzam Haidar %A Stanimire Tomov %A Jack Dongarra %B International Conference on Computational Science (ICCS 2015) %C Reykjavík, Iceland %8 06-2015 %G eng %0 Conference Paper %B The International Conference for High Performance Computing, Networking, Storage and Analysis (SC15) %D 2015 %T Performance of Random Sampling for Computing Low-rank Approximations of a Dense Matrix on GPUs %A Theo Mary %A Ichitaro Yamazaki %A Jakub Kurzak %A Piotr Luszczek %A Stanimire Tomov %A Jack Dongarra %B The International Conference for High Performance Computing, Networking, Storage and Analysis (SC15) %I ACM %C Austin, TX %8 11-2015 %G eng %0 Conference Paper %B 22nd European MPI Users' Group Meeting %D 2015 %T Plan B: Interruption of Ongoing MPI Operations to Support Failure Recovery %A Aurelien Bouteiller %A George Bosilca %A Jack Dongarra %X Advanced failure recovery strategies in HPC system benefit tremendously from in-place failure recovery, in which the MPI infrastructure can survive process crashes and resume communication services. In this paper we present the rationale behind the specification, and an effective implementation of the Revoke MPI operation. The purpose of the Revoke operation is the propagation of failure knowledge, and the interruption of ongoing, pending communication, under the control of the user. We explain that the Revoke operation can be implemented with a reliable broadcast over the scalable and failure resilient Binomial Graph (BMG) overlay network. Evaluation at scale, on a Cray XC30 supercomputer, demonstrates that the Revoke operation has a small latency, and does not introduce system noise outside of failure recovery periods. %B 22nd European MPI Users' Group Meeting %I ACM %C Bordeaux, France %8 09-2015 %G eng %R 10.1145/2802658.2802668 %0 Generic %D 2015 %T Practical Scalable Consensus for Pseudo-Synchronous Distributed Systems: Formal Proof %A Thomas Herault %A Aurelien Bouteiller %A George Bosilca %A Marc Gamell %A Keita Teranishi %A Manish Parashar %A Jack Dongarra %B Innovative Computing Laboratory Technical Report %8 04-2015 %G eng %0 Conference Paper %B The International Conference for High Performance Computing, Networking, Storage and Analysis (SC15) %D 2015 %T Practical Scalable Consensus for Pseudo-Synchronous Distributed Systems %A Thomas Herault %A Aurelien Bouteiller %A George Bosilca %A Marc Gamell %A Keita Teranishi %A Manish Parashar %A Jack Dongarra %X The ability to consistently handle faults in a distributed environment requires, among a small set of basic routines, an agreement algorithm allowing surviving entities to reach a consensual decision between a bounded set of volatile resources. This paper presents an algorithm that implements an Early Returning Agreement (ERA) in pseudo-synchronous systems, which optimistically allows a process to resume its activity while guaranteeing strong progress. We prove the correctness of our ERA algorithm, and expose its logarithmic behavior, which is an extremely desirable property for any algorithm which targets future exascale platforms. We detail a practical implementation of this consensus algorithm in the context of an MPI library, and evaluate both its efficiency and scalability through a set of benchmarks and two fault tolerant scientific applications. %B The International Conference for High Performance Computing, Networking, Storage and Analysis (SC15) %I ACM %C Austin, TX %8 11-2015 %G eng %0 Conference Paper %B The International Conference for High Performance Computing, Networking, Storage and Analysis (SC15) %D 2015 %T Randomized Algorithms to Update Partial Singular Value Decomposition on a Hybrid CPU/GPU Cluster %A Ichitaro Yamazaki %A Jakub Kurzak %A Piotr Luszczek %A Jack Dongarra %B The International Conference for High Performance Computing, Networking, Storage and Analysis (SC15) %I ACM %C Austin, TX %8 11-2015 %G eng %0 Conference Paper %B 2015 SIAM Conference on Applied Linear Algebra (SIAM LA) %D 2015 %T Random-Order Alternating Schwarz for Sparse Triangular Solves %A Hartwig Anzt %A Edmond Chow %A Daniel Szyld %A Jack Dongarra %X Block-asynchronous Jacobi is an iteration method where a locally synchronous iteration is embedded in an asynchronous global iteration. The unknowns are partitioned into small subsets, and while the components within the same subset are iterated in Jacobi fashion, no update order in-between the subsets is enforced. The values of the non-local entries remain constant during the local iterations, which can result in slow inter-subset information propagation and slow convergence. Interpreting of the subsets as subdomains allows to transfer the concept of domain overlap typically enhancing the information propagation to block-asynchronous solvers. In this talk we explore the impact of overlapping domains to convergence and performance of block-asynchronous Jacobi iterations, and present results obtained by running this solver class on state-of-the-art HPC systems. %B 2015 SIAM Conference on Applied Linear Algebra (SIAM LA) %I SIAM %C Atlanta, GA %8 10-2015 %G eng %0 Journal Article %J Concurrency and Computation: Practice and Experience %D 2015 %T A Scalable Approach to Solving Dense Linear Algebra Problems on Hybrid CPU-GPU Systems %A Fengguang Song %A Jack Dongarra %K dense linear algebra %K distributed dataﬂow scheduling %K heterogeneous HPC systems %K runtime systems %X Aiming to fully exploit the computing power of all CPUs and all graphics processing units (GPUs) on hybrid CPU-GPU systems to solve dense linear algebra problems, we design a class of heterogeneous tile algorithms to maximize the degree of parallelism, to minimize the communication volume, and to accommodate the heterogeneity between CPUs and GPUs. The new heterogeneous tile algorithms are executed upon our decentralized dynamic scheduling runtime system, which schedules a task graph dynamically and transfers data between compute nodes automatically. The runtime system uses a new distributed task assignment protocol to solve data dependencies between tasks without any coordination between processing units. By overlapping computation and communication through dynamic scheduling, we are able to attain scalable performance for the double-precision Cholesky factorization and QR factorization. Our approach demonstrates a performance comparable to Intel MKL on shared-memory multicore systems and better performance than both vendor (e.g., Intel MKL) and open source libraries (e.g., StarPU) in the following three environments: heterogeneous clusters with GPUs, conventional clusters without GPUs, and shared-memory systems with multiple GPUs. %B Concurrency and Computation: Practice and Experience %V 27 %P 3702-3723 %8 09-2015 %G eng %N 14 %R 10.1002/cpe.3403 %0 Generic %D 2015 %T Scheduling for fault-tolerance: an introduction %A Guillaume Aupy %A Yves Robert %B Innovative Computing Laboratory Technical Report %I University of Tennessee %8 01-2015 %G eng %0 Journal Article %J Concurrency and Computation: Practice and Experience %D 2015 %T A Survey of Recent Developments in Parallel Implementations of Gaussian Elimination %A Simplice Donfack %A Jack Dongarra %A Mathieu Faverge %A Mark Gates %A Jakub Kurzak %A Piotr Luszczek %A Ichitaro Yamazaki %K Gaussian elimination %K lu factorization %K Multicore %K parallel %K shared memory %X Gaussian elimination is a canonical linear algebra procedure for solving linear systems of equations. In the last few years, the algorithm has received a lot of attention in an attempt to improve its parallel performance. This article surveys recent developments in parallel implementations of Gaussian elimination for shared memory architecture. Five different flavors are investigated. Three of them are based on different strategies for pivoting: partial pivoting, incremental pivoting, and tournament pivoting. The fourth one replaces pivoting with the Partial Random Butterfly Transformation, and finally, an implementation without pivoting is used as a performance baseline. The technique of iterative refinement is applied to recover numerical accuracy when necessary. All parallel implementations are produced using dynamic, superscalar, runtime scheduling and tile matrix layout. Results on two multisocket multicore systems are presented. Performance and numerical accuracy is analyzed. %B Concurrency and Computation: Practice and Experience %V 27 %P 1292-1309 %8 04-2015 %G eng %N 5 %R 10.1002/cpe.3306 %0 Journal Article %J IEEE Computer %D 2015 %T The TOP500 List and Progress in High-Performance Computing %A Erich Strohmaier %A Hans Meuer %A Jack Dongarra %A Horst D. Simon %K application performance %K Benchmark testing %K benchmarks %K Computer architecture %K High Performance Computing %K High-performance computing %K Linpack %K Market research %K Parallel computing %K Program processors %K Scientific computing %K Supercomputers %K top500 %X For more than two decades, the TOP500 list has enjoyed incredible success as a metric for supercomputing performance and as a source of data for identifying technological trends. The project's editors reflect on its usefulness and limitations for guiding large-scale scientific computing into the exascale era. %B IEEE Computer %V 48 %P 42-49 %8 11-2015 %G eng %N 11 %R doi:10.1109/MC.2015.338 %0 Conference Paper %B 8th Workshop on General Purpose Processing Using GPUs (GPGPU 8) co-located with PPOPP 2015 %D 2015 %T Towards Batched Linear Solvers on Accelerated Hardware Platforms %A Azzam Haidar %A Piotr Luszczek %A Stanimire Tomov %A Jack Dongarra %K batched factorization %K hardware accelerators %K numerical linear algebra %K numerical software libraries %K one-sided factorization algorithms %X As hardware evolves, an increasingly effective approach to develop energy efficient, high-performance solvers, is to design them to work on many small and independent problems. Indeed, many applications already need this functionality, especially for GPUs, which are known to be currently about four to five times more energy efficient than multicore CPUs for every floating-point operation. In this paper, we describe the development of the main one-sided factorizations: LU, QR, and Cholesky; that are needed for a set of small dense matrices to work in parallel. We refer to such algorithms as batched factorizations. Our approach is based on representing the algorithms as a sequence of batched BLAS routines for GPU-contained execution. Note that this is similar in functionality to the LAPACK and the hybrid MAGMA algorithms for large-matrix factorizations. But it is different from a straightforward approach, whereby each of GPU’s symmetric multiprocessors factorizes a single problem at a time.We illustrate how our performance analysis together with the profiling and tracing tools guided the development of batched factorizations to achieve up to 2-fold speedup and 3-fold better energy efficiency compared to our highly optimized batched CPU implementations based on the MKL library on a two-sockets, Intel Sandy Bridge server. Compared to a batched LU factorization featured in the NVIDIA’s CUBLAS library for GPUs, we achieves up to 2.5-fold speedup on the K40 GPU. %B 8th Workshop on General Purpose Processing Using GPUs (GPGPU 8) co-located with PPOPP 2015 %I ACM %C San Francisco, CA %8 02-2015 %G eng %0 Conference Paper %B 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA15) %D 2015 %T Tuning Stationary Iterative Solvers for Fault Resilience %A Hartwig Anzt %A Jack Dongarra %A Enrique S. Quintana-Ortí %X As the transistor’s feature size decreases following Moore’s Law, hardware will become more prone to permanent, intermittent, and transient errors, increasing the number of failures experienced by applications, and diminishing the confidence of users. As a result, resilience is considered the most difficult under addressed issue faced by the High Performance Computing community. In this paper, we address the design of error resilient iterative solvers for sparse linear systems. Contrary to most previous approaches, based on Krylov subspace methods, for this purpose we analyze stationary component-wise relaxation. Concretely, starting from a plain implementation of the Jacobi iteration, we design a low-cost component-wise technique that elegantly handles bit-flips, turning the initial synchronized solver into an asynchronous iteration. Our experimental study employs sparse incomplete factorizations from several practical applications to expose the convergence delay incurred by the fault-tolerant implementation. %B 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA15) %I ACM %C Austin, TX %8 11-2015 %G eng %0 Conference Paper %B 2nd Workshop on Visual Performance Analysis (VPA '15) %D 2015 %T Visualizing Execution Traces with Task Dependencies %A Blake Haugen %A Stephen Richmond %A Jakub Kurzak %A Chad A. Steed %A Jack Dongarra %X Task-based scheduling has emerged as one method to reduce the complexity of parallel computing. When using task-based schedulers, developers must frame their computation as a series of tasks with various data dependencies. The scheduler can take these tasks, along with their input and output dependencies, and schedule the task in parallel across a node or cluster. While these schedulers simplify the process of parallel software development, they can obfuscate the performance characteristics of the execution of an algorithm. The execution trace has been used for many years to give developers a visual representation of how their computations are performed. These methods can be employed to visualize when and where each of the tasks in a task-based algorithm is scheduled. In addition, the task dependencies can be used to create a directed acyclic graph (DAG) that can also be visualized to demonstrate the dependencies of the various tasks that make up a workload. The work presented here aims to combine these two data sets and extend execution trace visualization to better suit task-based workloads. This paper presents a brief description of task-based schedulers and the performance data they produce. It will then describe an interactive extension to the current trace visualization methods that combines the trace and DAG data sets. This new tool allows users to gain a greater understanding of how their tasks are scheduled. It also provides a simplified way for developers to evaluate and debug the performance of their scheduler. %B 2nd Workshop on Visual Performance Analysis (VPA '15) %I ACM %C Austin, TX %8 11-2015 %G eng %0 Conference Proceedings %B Proceedings of the 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA'15) %D 2015 %T Weighted Dynamic Scheduling with Many Parallelism Grains for Offloading of Numerical Workloads to Multiple Varied Accelerators %A Azzam Haidar %A Yulu Jia %A Piotr Luszczek %A Stanimire Tomov %A Asim YarKhan %A Jack Dongarra %K dataflow scheduling %K hardware accelerators %K multi-grain parallelism %X A wide variety of heterogeneous compute resources are available to modern computers, including multiple sockets containing multicore CPUs, one-or-more GPUs of varying power, and coprocessors such as the Intel Xeon Phi. The challenge faced by domain scientists is how to efficiently and productively use these varied resources. For example, in order to use GPUs effectively, the workload must have a greater degree of parallelism than a workload designed for a multicore-CPU. The domain scientist would have to design and schedule an application in multiple degrees of parallelism and task grain sizes in order to obtain efficient performance from the resources. We propose a productive programming model starting from serial code, which achieves parallelism and scalability by using a task-superscalar runtime environment to adapt the computation to the available resources. The adaptation is done at multiple points, including multi-level data partitioning, adaptive task grain sizes, and dynamic task scheduling. The effectiveness of this approach for utilizing multi-way heterogeneous hardware resources is demonstrated by implementing dense linear algebra applications. %B Proceedings of the 6th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA'15) %I ACM %C Austin, TX %V No. 5 %8 11-2015 %G eng %0 Conference Paper %B VECPAR 2014 %D 2014 %T Accelerating Eigenvector Computation in the Nonsymmetric Eigenvalue Problem %A Mark Gates %A Azzam Haidar %A Jack Dongarra %X In the nonsymmetric eigenvalue problem, work has focused on the Hessenberg reduction and QR iteration, using efficient algorithms and fast, Level 3 BLAS routines. Comparatively, computation of eigenvectors performs poorly, limited to slow, Level 2 BLAS performance with little speedup on multi-core systems. It has thus become a dominant cost in the eigenvalue problem. To address this, we present improvements for the eigenvector computation to use Level 3 BLAS where applicable and parallelize the remaining triangular solves, achieving good parallel scaling and accelerating the overall eigenvalue problem more than three-fold. %B VECPAR 2014 %C Eugene, OR %8 06-2014 %G eng %0 Book Section %B Numerical Computations with GPUs %D 2014 %T Accelerating Numerical Dense Linear Algebra Calculations with GPUs %A Jack Dongarra %A Mark Gates %A Azzam Haidar %A Jakub Kurzak %A Piotr Luszczek %A Stanimire Tomov %A Ichitaro Yamazaki %B Numerical Computations with GPUs %I Springer International Publishing %P 3-28 %@ 978-3-319-06547-2 %G eng %& 1 %R 10.1007/978-3-319-06548-9_1 %0 Generic %D 2014 %T Accelerating the LOBPCG method on GPUs using a blocked Sparse Matrix Vector Product %A Hartwig Anzt %A Stanimire Tomov %A Jack Dongarra %X This paper presents a heterogeneous CPU-GPU algorithm design and optimized implementation for an entire sparse iterative eigensolver – the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) – starting from low-level GPU data structures and kernels to the higher-level algorithmic choices and overall heterogeneous design. Most notably, the eigensolver leverages the high-performance of a new GPU kernel developed for the simultaneous multiplication of a sparse matrix and a set of vectors (SpMM). This is a building block that serves as a backbone for not only block-Krylov, but also for other methods relying on blocking for acceleration in general. The heterogeneous LOBPCG developed here reveals the potential of this type of eigensolver by highly optimizing all of its components, and can be viewed as a benchmark for other SpMM-dependent applications. Compared to non-blocked algorithms, we show that the performance speedup factor of SpMM vs. SpMV-based algorithms is up to six on GPUs like NVIDIA’s K40. In particular, a typical SpMV performance range in double precision is 20 to 25 GFlop/s, while the SpMM is in the range of 100 to 120 GFlop/s. Compared to highly-optimized CPU implementations, e.g., the SpMM from MKL on two eight-core Intel Xeon E5-2690s, our kernel is 3 to 5x. faster on a K40 GPU. For comparison to other computational loads, the same GPU to CPU performance acceleration is observed for the SpMV product, as well as dense linear algebra, e.g., matrix-matrix multiplication and factorizations like LU, QR, and Cholesky. Thus, the modeled GPU (vs. CPU) acceleration for the entire solver is also 3 to 5x. In practice though, currently available CPU implementations are much slower due to missed optimization opportunities, as we show. %B University of Tennessee Computer Science Technical Report %I University of Tennessee %8 10-2014 %G eng %0 Conference Paper %B First International Workshop on High Performance Big Graph Data Management, Analysis, and Mining %D 2014 %T Access-averse Framework for Computing Low-rank Matrix Approximations %A Ichitaro Yamazaki %A Theo Mary %A Jakub Kurzak %A Stanimire Tomov %A Jack Dongarra %B First International Workshop on High Performance Big Graph Data Management, Analysis, and Mining %C Washington, DC %8 10-2014 %G eng %0 Journal Article %J Concurrency and Computation: Practice and Experience %D 2014 %T Achieving numerical accuracy and high performance using recursive tile LU factorization with partial pivoting %A Jack Dongarra %A Mathieu Faverge %A Hatem Ltaeif %A Piotr Luszczek %K factorization %K parallel linear algebra %K recursion %K shared memory synchronization %K threaded parallelism %X The LU factorization is an important numerical algorithm for solving systems of linear equations in science and engineering and is a characteristic of many dense linear algebra computations. For example, it has become the de facto numerical algorithm implemented within the LINPACK benchmark to rank the most powerful supercomputers in the world, collected by the TOP500 website. Multicore processors continue to present challenges to the development of fast and robust numerical software due to the increasing levels of hardware parallelism and widening gap between core and memory speeds. In this context, the difficulty in developing new algorithms for the scientific community resides in the combination of two goals: achieving high performance while maintaining the accuracy of the numerical algorithm. This paper proposes a new approach for computing the LU factorization in parallel on multicore architectures, which not only improves the overall performance but also sustains the numerical quality of the standard LU factorization algorithm with partial pivoting. While the update of the trailing submatrix is computationally intensive and highly parallel, the inherently problematic portion of the LU factorization is the panel factorization due to its memory-bound characteristic as well as the atomicity of selecting the appropriate pivots. Our approach uses a parallel fine-grained recursive formulation of the panel factorization step and implements the update of the trailing submatrix with the tile algorithm. Based on conflict-free partitioning of the data and lockless synchronization mechanisms, our implementation lets the overall computation flow naturally without contention. The dynamic runtime system called QUARK is then able to schedule tasks with heterogeneous granularities and to transparently introduce algorithmic lookahead. The performance results of our implementation are competitive compared to the currently available software packages and libraries. For example, it is up to 40% faster when compared to the equivalent Intel MKL routine and up to threefold faster than LAPACK with multithreaded Intel MKL BLAS. %B Concurrency and Computation: Practice and Experience %V 26 %P 1408-1431 %8 05-2014 %G eng %U http://doi.wiley.com/10.1002/cpe.3110 %N 7 %! Concurrency Computat.: Pract. Exper. %& 1408 %R 10.1002/cpe.3110 %0 Journal Article %J VMWare Technical Journal %D 2014 %T Analyzing PAPI Performance on Virtual Machines %A John Nelson %X Performance Application Programming Interface (PAPI) aims to provide a consistent interface for measuring performance events using the performance counter hardware available on the CPU as well as available software performance events and off-chip hardware. Without PAPI, a user may be forced to search through specific processor documentation to discover the name of processor performance events. These names can change from model to model and vendor to vendor. PAPI simplifies this process by providing a consistent interface and a set of processor-agnostic preset events. Software engineers can use data collected through source-code instrumentation using the PAPI interface to examine the relation between software performance and performance events. PAPI can also be used within many high-level performance-monitoring utilities such as TAU, Vampir, and Score-P. VMware® ESXiTM and KVM have both added support within the last year for virtualizing performance counters. This article compares results measuring the performance of five real-world applications included in the Mantevo Benchmarking Suite in a VMware virtual machine, a KVM virtual machine, and on bare metal. By examining these results, it will be shown that PAPI provides accurate performance counts in a virtual machine environment. %B VMWare Technical Journal %V Winter 2013 %8 01-2014 %G eng %U https://labs.vmware.com/vmtj/analyzing-papi-performance-on-virtual-machines %0 Conference Paper %B Euro-Par 2014 %D 2014 %T Assembly Operations for Multicore Architectures using Task-Based Runtime Systems %A Damien Genet %A Abdou Guermouche %A George Bosilca %X Traditionally, numerical simulations based on finite element methods consider the algorithm as being divided in three major steps: the generation of a set of blocks and vectors, the assembly of these blocks in a matrix and a big vector, and the inversion of the matrix. In this paper we tackle the second step, the block assembly, where no parallel algorithm is widely available. Several strategies are proposed to decompose the assembly problem while relying on a scheduling middle-ware to maximize the overlap between stages and increase the parallelism and thus the performance. These strategies are quantified using examples covering two extremes in the field, large number of non-overlapping small blocks for CFD-like problems, and a smaller number of larger blocks with significant overlap which can be met in sparse linear algebra solvers. %B Euro-Par 2014 %I Springer International Publishing %C Porto, Portugal %8 08-2014 %G eng %0 Conference Paper %B 16th Workshop on Advances in Parallel and Distributed Computational Models, IPDPS 2014 %D 2014 %T Assessing the Impact of ABFT and Checkpoint Composite Strategies %A George Bosilca %A Aurelien Bouteiller %A Thomas Herault %A Yves Robert %A Jack Dongarra %K ABFT %K checkpoint %K fault-tolerance %K High-performance computing %K resilience %X Algorithm-specific fault tolerant approaches promise unparalleled scalability and performance in failure-prone environments. With the advances in the theoretical and practical understanding of algorithmic traits enabling such approaches, a growing number of frequently used algorithms (including all widely used factorization kernels) have been proven capable of such properties. These algorithms provide a temporal section of the execution when the data is protected by it’s own intrinsic properties, and can be algorithmically recomputed without the need of checkpoints. However, while typical scientific applications spend a significant fraction of their execution time in library calls that can be ABFT-protected, they interleave sections that are difficult or even impossible to protect with ABFT. As a consequence, the only fault-tolerance approach that is currently used for these applications is checkpoint/restart. In this paper we propose a model and a simulator to investigate the behavior of a composite protocol, that alternates between ABFT and checkpoint/restart protection for effective protection of each phase of an iterative application composed of ABFT-aware and ABFTunaware sections. We highlight this approach drastically increases the performance delivered by the system, especially at scale, by providing means to rarefy the checkpoints while simultaneously decreasing the volume of data needed to be checkpointed. %B 16th Workshop on Advances in Parallel and Distributed Computational Models, IPDPS 2014 %I IEEE %C Phoenix, AZ %8 05-2014 %G eng %0 Conference Paper %B International Workshop on OpenCL %D 2014 %T clMAGMA: High Performance Dense Linear Algebra with OpenCL %A Chongxiao Cao %A Jack Dongarra %A Peng Du %A Mark Gates %A Piotr Luszczek %A Stanimire Tomov %X This paper presents the design and implementation of several fundamental dense linear algebra (DLA) algorithms in OpenCL. In particular, these are linear system solvers and eigenvalue problem solvers. Further, we give an overview of the clMAGMA library, an open source, high performance OpenCL library that incorporates the developments presented, and in general provides to heterogeneous architectures the DLA functionality of the popular LAPACK library. The LAPACK-compliance and use of OpenCL simplify the use of clMAGMA in applications, while providing them with portably performant DLA. High performance is obtained through use of the high-performance OpenCL BLAS, hardware and OpenCL-specific tuning, and a hybridization methodology where we split the algorithm into computational tasks of various granularities. Execution of those tasks is properly scheduled over the heterogeneous hardware components by minimizing data movements and mapping algorithmic requirements to the architectural strengths of the various heterogeneous hardware components. %B International Workshop on OpenCL %C Bristol University, England %8 05-2014 %G eng %0 Journal Article %J SIAM Journal on Matrix Analysis and Application %D 2014 %T Communication-Avoiding Symmetric-Indefinite Factorization %A Grey Ballard %A Dulceneia Becker %A James Demmel %A Jack Dongarra %A Alex Druinsky %A I Peled %A Oded Schwartz %A Sivan Toledo %A Ichitaro Yamazaki %X We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen’s triangular tridiagonalization. It factors a dense symmetric matrix A as the product A = P LT L T P T where P is a permutation matrix, L is lower triangular, and T is block tridiagonal and banded. The algorithm is the first symmetric-indefinite communication-avoiding factorization: it performs an asymptotically optimal amount of communication in a two-level memory hierarchy for almost any cache-line size. Adaptations of the algorithm to parallel computers are likely to be communication efficient as well; one such adaptation has been recently published. The current paper describes the algorithm, proves that it is numerically stable, and proves that it is communication optimal. %B SIAM Journal on Matrix Analysis and Application %V 35 %P 1364-1406 %8 07-2014 %G eng %N 4 %0 Conference Paper %B International Interdisciplinary Conference on Applied Mathematics, Modeling and Computational Science (AMMCS) %D 2014 %T Computing Least Squares Condition Numbers on Hybrid Multicore/GPU Systems %A Marc Baboulin %A Jack Dongarra %A Remi Lacroix %X This paper presents an efficient computation for least squares conditioning or estimates of it. We propose performance results using new routines on top of the multicore-GPU library MAGMA. This set of routines is based on an efficient computation of the variance-covariance matrix for which, to our knowledge, there is no implementation in current public domain libraries LAPACK and ScaLAPACK. %B International Interdisciplinary Conference on Applied Mathematics, Modeling and Computational Science (AMMCS) %C Waterloo, Ontario, CA %8 08-2014 %G eng %0 Conference Paper %B 5th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems %D 2014 %T Deflation Strategies to Improve the Convergence of Communication-Avoiding GMRES %A Ichitaro Yamazaki %A Stanimire Tomov %A Jack Dongarra %B 5th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems %C New Orleans, LA %8 11-2014 %G eng %0 Conference Paper %B Workshop on Large-Scale Parallel Processing, IPDPS 2014 %D 2014 %T Design and Implementation of a Large Scale Tree-Based QR Decomposition Using a 3D Virtual Systolic Array and a Lightweight Runtime %A Ichitaro Yamazaki %A Jakub Kurzak %A Piotr Luszczek %A Jack Dongarra %K dataflow %K message-passing %K multithreading %K QR decomposition %K runtime %K systolic array %X A systolic array provides an alternative computing paradigm to the von Neuman architecture. Though its hardware implementation has failed as a paradigm to design integrated circuits in the past, we are now discovering that the systolic array as a software virtualization layer can lead to an extremely scalable execution paradigm. To demonstrate this scalability, in this paper, we design and implement a 3D virtual systolic array to compute a tile QR decomposition of a tall-and-skinny dense matrix. Our implementation is based on a state-of-the-art algorithm that factorizes a panel based on a tree-reduction. Using a runtime developed as a part of the Parallel Ultra Light Systolic Array Runtime (PULSAR) project, we demonstrate on a Cray-XT5 machine how our virtual systolic array can be mapped to a large-scale machine and obtain excellent parallel performance. This is an important contribution since such a QR decomposition is used, for example, to compute a least squares solution of an overdetermined system, which arises in many scientific and engineering problems. %B Workshop on Large-Scale Parallel Processing, IPDPS 2014 %I IEEE %C Phoenix, AZ %8 05-2014 %G eng %0 Generic %D 2014 %T Design for a Soft Error Resilient Dynamic Task-based Runtime %A Chongxiao Cao %A Thomas Herault %A George Bosilca %A Jack Dongarra %X Abstract—As the scale of modern computing systems grows, failures will happen more frequently. On the way to Exascale a generic, low-overhead, resilient extension becomes a desired aptitude of any programming paradigm. In this paper we explore three additions to a dynamic task-based runtime to build a generic framework providing soft error resilience to task-based programming paradigms. The first recovers the application by re-executing the minimum required sub-DAG, the second takes critical checkpoints of the data flowing between tasks to minimize the necessary re-execution, while the last one takes advantage of algorithmic properties to recover the data without re-execution. These mechanisms have been implemented in the PaRSEC task-based runtime framework. Experimental results validate our approach and quantify the overhead introduced by such mechanisms. %B ICL Technical Report %I University of Tennessee %8 11-2014 %G eng %0 Conference Paper %B IPDPS 2014 %D 2014 %T Designing LU-QR Hybrid Solvers for Performance and Stability %A Mathieu Faverge %A Julien Herrmann %A Julien Langou %A Bradley Lowery %A Yves Robert %A Jack Dongarra %X This paper introduces hybrid LU-QR algorithms for solving dense linear systems of the form Ax = b. Throughout a matrix factorization, these algorithms dynamically alternate LU with local pivoting and QR elimination steps, based upon some robustness criterion. LU elimination steps can be very efficiently parallelized, and are twice as cheap in terms of operations, as QR steps. However, LU steps are not necessarily stable, while QR steps are always stable. The hybrid algorithms execute a QR step when a robustness criterion detects some risk for instability, and they execute an LU step otherwise. Ideally, the choice between LU and QR steps must have a small computational overhead and must provide a satisfactory level of stability with as few QR steps as possible. In this paper, we introduce several robustness criteria and we establish upper bounds on the growth factor of the norm of the updated matrix incurred by each of these criteria. In addition, we describe the implementation of the hybrid algorithms through an extension of the Parsec software to allow for dynamic choices during execution. Finally, we analyze both stability and performance results compared to state-of-the-art linear solvers on parallel distributed multicore platforms. %B IPDPS 2014 %I IEEE %C Phoenix, AZ %8 05-2014 %@ 978-1-4799-3800-1 %G eng %R 10.1109/IPDPS.2014.108 %0 Conference Paper %B The International Conference for High Performance Computing, Networking, Storage and Analysis (SC 14) %D 2014 %T Domain Decomposition Preconditioners for Communication-Avoiding Krylov Methods on a Hybrid CPU/GPU Cluster %A Ichitaro Yamazaki %A Sivasankaran Rajamanickam %A Eric G. Boman %A Mark Hoemmen %A Michael Heroux %A Stanimire Tomov %B The International Conference for High Performance Computing, Networking, Storage and Analysis (SC 14) %I IEEE %C New Orleans, LA %8 11-2014 %G eng %0 Conference Paper %B Fourth International Workshop on Accelerators and Hybrid Exascale Systems (AsHES), IPDPS 2014 %D 2014 %T Dynamically balanced synchronization-avoiding LU factorization with multicore and GPUs %A Simplice Donfack %A Stanimire Tomov %A Jack Dongarra %X Graphics processing units (GPUs) brought huge performance improvements in the scientific and numerical fields. We present an efficient hybrid CPU/GPU approach that is portable, dynamically and efficiently balances the workload between the CPUs and the GPUs, and avoids data transfer bottlenecks that are frequently present in numerical algorithms. Our approach determines the amount of initial work to assign to the CPUs before the execution, and then dynamically balances workloads during the execution. Then, we present a theoretical model to guide the choice of the initial amount of work for the CPUs. The validation of our model allows our approach to self-adapt on any architecture using the manufacturer’s characteristics of the underlying machine. We illustrate our method for the LU factorization. For this case, we show that the use of our approach combined with a communication avoiding LU algorithm is efficient. For example, our experiments on a 24 cores AMD Opteron 6172 show that by adding one GPU (Tesla S2050) we accelerate LU up to 2.4x compared to the corresponding routine in MKL using 24 cores. The comparisons with MAGMA also show significant improvements. %B Fourth International Workshop on Accelerators and Hybrid Exascale Systems (AsHES), IPDPS 2014 %8 05-2014 %G eng %0 Generic %D 2014 %T Efficient checkpoint/verification patterns for silent error detection %A Anne Benoit %A Yves Robert %A Saurabh K. Raina %X Resilience has become a critical problem for high performance computing. Checkpointing protocols are often used for error recovery after fail-stop failures. However, silent errors cannot be ignored, and their particularities is that such errors are identified only when the corrupted data is activated. To cope with silent errors, we need a verification mechanism to check whether the application state is correct. Checkpoints should be supplemented with verifications to detect silent errors. When a verification is successful, only the last checkpoint needs to be kept in memory because it is known to be correct. In this paper, we analytically determine the best balance of verifications and checkpoints so as to optimize platform throughput. We introduce a balanced algorithm using a pattern with p checkpoints and q verifications, which regularly interleaves both checkpoints and verifications across same-size computational chunks. We show how to compute the waste of an arbitrary pattern, and we prove that the balanced algorithm is optimal when the platform MTBF (Mean Time Between Failures) is large in front of the other parameters (checkpointing, verification and recovery costs). We conduct several simulations to show the gain achieved by this balanced algorithm for well-chosen values of p and q, compared to the base algorithm that always perform a verification just before taking a checkpoint (p = q = 1), and we exhibit gains of up to 19%. %B Innovative Computing Laboratory Technical Report %I University of Tennessee %8 05-2014 %G eng %9 LAWN 287 %0 Journal Article %J Parallel Computing %D 2014 %T An Efficient Distributed Randomized Algorithm for Solving Large Dense Symmetric Indefinite Linear Systems %A Marc Baboulin %A Du Becker %A George Bosilca %A Anthony Danalis %A Jack Dongarra %K Distributed linear algebra solvers %K LDLT factorization %K PaRSEC runtime %K Randomized algorithms %K Symmetric indefinite systems %X Randomized algorithms are gaining ground in high-performance computing applications as they have the potential to outperform deterministic methods, while still providing accurate results. We propose a randomized solver for distributed multicore architectures to efficiently solve large dense symmetric indefinite linear systems that are encountered, for instance, in parameter estimation problems or electromagnetism simulations. The contribution of this paper is to propose efficient kernels for applying random butterfly transformations and a new distributed implementation combined with a runtime (PaRSEC) that automatically adjusts data structures, data mappings, and the scheduling as systems scale up. Both the parallel distributed solver and the supporting runtime environment are innovative. To our knowledge, the randomization approach associated with this solver has never been used in public domain software for symmetric indefinite systems. The underlying runtime framework allows seamless data mapping and task scheduling, mapping its capabilities to the underlying hardware features of heterogeneous distributed architectures. The performance of our software is similar to that obtained for symmetric positive definite systems, but requires only half the execution time and half the amount of data storage of a general dense solver. %B Parallel Computing %V 40 %P 213-223 %8 07-2014 %G eng %N 7 %R 10.1016/j.parco.2013.12.003 %0 Conference Paper %B International Conference on Parallel Processing (ICPP-2014) %D 2014 %T A Fast Batched Cholesky Factorization on a GPU %A Tingxing Dong %A Azzam Haidar %A Stanimire Tomov %A Jack Dongarra %X Currently, state of the art libraries, like MAGMA, focus on very large linear algebra problems, while solving many small independent problems, which is usually referred to as batched problems, is not given adequate attention. In this paper, we proposed a batched Cholesky factorization on a GPU. Three algorithms – nonblocked, blocked, and recursive blocked – were examined. The left-looking version of the Cholesky factorization is used to factorize the panel, and the right-looking Cholesky version is used to update the trailing matrix in the recursive blocked algorithm. Our batched Cholesky achieves up to 1:8 speedup compared to the optimized parallel implementation in the MKL library on two sockets of Intel Sandy Bridge CPUs. Further, we use the new routines to develop a single Cholesky factorization solver which targets large matrix sizes. Our approach differs from MAGMA by having an entirely GPU implementation where both the panel factorization and the trailing matrix updates are on the GPU. Such an implementation does not depend on the speed of the CPU. Compared to the MAGMA library, our full GPU solution achieves 85% of the hybrid MAGMA performance which uses 16 Sandy Bridge cores, in addition to a K40 Nvidia GPU. Moreover, we achieve 80% of the practical dgemm peak of the machine, while MAGMA achieves only 75%, and finally, in terms of energy consumption, we outperform MAGMA by 1.5 in performance-per-watt for large matrices. %B International Conference on Parallel Processing (ICPP-2014) %C Minneapolis, MN %8 09-2014 %G eng %0 Conference Paper %B VECPAR 2014 %D 2014 %T Heterogeneous Acceleration for Linear Algebra in Mulit-Coprocessor Environments %A Azzam Haidar %A Piotr Luszczek %A Stanimire Tomov %A Jack Dongarra %K Computer science %K factorization %K Heterogeneous systems %K Intel Xeon Phi %K linear algebra %X We present an efficient and scalable programming model for the development of linear algebra in heterogeneous multi-coprocessor environments. The model incorporates some of the current best design and implementation practices for the heterogeneous acceleration of dense linear algebra (DLA). Examples are given as the basis for solving linear systems’ algorithms – the LU, QR, and Cholesky factorizations. To generate the extreme level of parallelism needed for the efficient use of coprocessors, algorithms of interest are redesigned and then split into well-chosen computational tasks. The tasks execution is scheduled over the computational components of a hybrid system of multi-core CPUs and coprocessors using a light-weight runtime system. The use of light-weight runtime systems keeps scheduling overhead low, while enabling the expression of parallelism through otherwise sequential code. This simplifies the development efforts and allows the exploration of the unique strengths of the various hardware components. %B VECPAR 2014 %C Eugene, OR %8 06-2014 %G eng %0 Conference Paper %B International Heterogeneity in Computing Workshop (HCW), IPDPS 2014 %D 2014 %T Hybrid Multi-Elimination ILU Preconditioners on GPUs %A Dimitar Lukarski %A Hartwig Anzt %A Stanimire Tomov %A Jack Dongarra %X Abstract—Iterative solvers for sparse linear systems often benefit from using preconditioners. While there are implementations for many iterative methods that leverage the computing power of accelerators, porting the latest developments in preconditioners to accelerators has been challenging. In this paper we develop a selfadaptive multi-elimination preconditioner for graphics processing units (GPUs). The preconditioner is based on a multi-level incomplete LU factorization and uses a direct dense solver for the bottom-level system. For test matrices from the University of Florida matrix collection, we investigate the influence of handling the triangular solvers in the distinct iteration steps in either single or double precision arithmetic. Integrated into a Conjugate Gradient method, we show that our multi-elimination algorithm is highly competitive against popular preconditioners, including multi-colored symmetric Gauss-Seidel relaxation preconditioners, and (multi-colored symmetric) ILU for numerous problems. %B International Heterogeneity in Computing Workshop (HCW), IPDPS 2014 %I IEEE %C Phoenix, AZ %8 05-2014 %G eng %0 Generic %D 2014 %T Implementing a Sparse Matrix Vector Product for the SELL-C/SELL-C-σ formats on NVIDIA GPUs %A Hartwig Anzt %A Stanimire Tomov %A Jack Dongarra %X Numerical methods in sparse linear algebra typically rely on a fast and efficient matrix vector product, as this usually is the backbone of iterative algorithms for solving eigenvalue problems or linear systems. Against the background of a large diversity in the characteristics of high performance computer architectures, it is a challenge to derive a cross-platform efficient storage format along with fast matrix vector kernels. Recently, attention focused on the SELL-C- format, a sliced ELLPACK format enhanced by row-sorting to reduce the fill in when padding rows with zeros. In this paper we propose an additional modification resulting in the padded sliced ELLPACK (SELLP) format, for which we develop a sparse matrix vector CUDA kernel that is able to efficiently exploit the computing power of NVIDIA GPUs. We show that the kernel we developed outperforms straight-forward implementations for the widespread CSR and ELLPACK formats, and is highly competitive to the implementations in the highly optimized CUSPARSE library. %B University of Tennessee Computer Science Technical Report %I University of Tennessee %8 04-2014 %G eng %0 Journal Article %J Philosophical Transactions of the Royal Society A -- Mathematical, Physical and Engineering Sciences %D 2014 %T Improving the Energy Efficiency of Sparse Linear System Solvers on Multicore and Manycore Systems %A Hartwig Anzt %A Enrique S. Quintana-Ortí %K energy efficiency %K graphics processing units %K High Performance Computing %K iterative solvers %K multicore processors %K sparse linear systems %X While most recent breakthroughs in scientific research rely on complex simulations carried out in large-scale supercomputers, the power draft and energy spent for this purpose is increasingly becoming a limiting factor to this trend. In this paper, we provide an overview of the current status in energy-efficient scientific computing by reviewing different technologies used to monitor power draft as well as power- and energy-saving mechanisms available in commodity hardware. For the particular domain of sparse linear algebra, we analyze the energy efficiency of a broad collection of hardware architectures and investigate how algorithmic and implementation modifications can improve the energy performance of sparse linear system solvers, without negatively impacting their performance. %B Philosophical Transactions of the Royal Society A -- Mathematical, Physical and Engineering Sciences %V 372 %8 07-2014 %G eng %N 2018 %R 10.1098/rsta.2013.0279 %0 Conference Paper %B IPDPS 2014 %D 2014 %T Improving the performance of CA-GMRES on multicores with multiple GPUs %A Ichitaro Yamazaki %A Hartwig Anzt %A Stanimire Tomov %A Mark Hoemmen %A Jack Dongarra %X Abstract—The Generalized Minimum Residual (GMRES) method is one of the most widely-used iterative methods for solving nonsymmetric linear systems of equations. In recent years, techniques to avoid communication in GMRES have gained attention because in comparison to floating-point operations, communication is becoming increasingly expensive on modern computers. Since graphics processing units (GPUs) are now becoming crucial component in computing, we investigate the effectiveness of these techniques on multicore CPUs with multiple GPUs. While we present the detailed performance studies of a matrix powers kernel on multiple GPUs, we particularly focus on orthogonalization strategies that have a great impact on both the numerical stability and performance of GMRES, especially as the matrix becomes sparser or ill-conditioned. We present the experimental results on two eight-core Intel Sandy Bridge CPUs with three NDIVIA Fermi GPUs and demonstrate that significant speedups can be obtained by avoiding communication, either on a GPU or between the GPUs. As part of our study, we investigate several optimization techniques for the GPU kernels that can also be used in other iterative solvers besides GMRES. Hence, our studies not only emphasize the importance of avoiding communication on GPUs, but they also provide insight about the effects of these optimization techniques on the performance of the sparse solvers, and may have greater impact beyond GMRES. %B IPDPS 2014 %I IEEE %C Phoenix, AZ %8 05-2014 %G eng %0 Journal Article %J Journal of Parallel and Distributed Computing %D 2014 %T Looking Back at Dense Linear Algebra Software %A Piotr Luszczek %A Jakub Kurzak %A Jack Dongarra %K decompositional approach %K dense linear algebra %K parallel algorithms %X Over the years, computational physics and chemistry served as an ongoing source of problems that demanded the ever increasing performance from hardware as well as the software that ran on top of it. Most of these problems could be translated into solutions for systems of linear equations: the very topic of numerical linear algebra. Seemingly then, a set of efficient linear solvers could be solving important scientific problems for years to come. We argue that dramatic changes in hardware designs precipitated by the shifting nature of the marketplace of computer hardware had a continuous effect on the software for numerical linear algebra. The extraction of high percentages of peak performance continues to require adaptation of software. If the past history of this adaptive nature of linear algebra software is any guide then the future theme will feature changes as well–changes aimed at harnessing the incredible advances of the evolving hardware infrastructure. %B Journal of Parallel and Distributed Computing %V 74 %P 2548–2560 %8 07-2014 %G eng %N 7 %& 2548 %R 10.1016/j.jpdc.2013.10.005 %0 Conference Paper %B 16th IEEE International Conference on High Performance Computing and Communications (HPCC) %D 2014 %T LU Factorization of Small Matrices: Accelerating Batched DGETRF on the GPU %A Tingxing Dong %A Azzam Haidar %A Piotr Luszczek %A James Harris %A Stanimire Tomov %A Jack Dongarra %X Gaussian Elimination is commonly used to solve dense linear systems in scientific models. In a large number of applications, a need arises to solve many small size problems, instead of few large linear systems. The size of each of these small linear systems depends, for example, on the number of the ordinary differential equations (ODEs) used in the model, and can be on the order of hundreds of unknowns. To efficiently exploit the computing power of modern accelerator hardware, these linear systems are processed in batches. To improve the numerical stability of the Gaussian Elimination, at least partial pivoting is required, most often accomplished with row pivoting. However, row pivoting can result in a severe performance penalty on GPUs because it brings in thread divergence and non-coalesced memory accesses. The state-of-the-art libraries for linear algebra that target GPUs, such as MAGMA, focus on large matrix sizes. They change the data layout by transposing the matrix to avoid these divergence and non-coalescing penalties. However, the data movement associated with transposition is very expensive for small matrices. In this paper, we propose a batched LU factorization for GPUs by using a multi-level blocked right looking algorithm that preserves the data layout but minimizes the penalty of partial pivoting. Our batched LU achieves up to 2:5-fold speedup when compared to the alternative CUBLAS solutions on a K40c GPU and 3:6-fold speedup over MKL on a node of the Titan supercomputer at ORNL in a nuclear reaction network simulation. %B 16th IEEE International Conference on High Performance Computing and Communications (HPCC) %I IEEE %C Paris, France %8 08-2014 %G eng %0 Conference Paper %B IPASS-2014 %D 2014 %T MIAMI: A Framework for Application Performance Diagnosis %A Gabriel Marin %A Jack Dongarra %A Dan Terpstra %X A typical application tuning cycle repeats the following three steps in a loop: performance measurement, analysis of results, and code refactoring. While performance measurement is well covered by existing tools, analysis of results to understand the main sources of inefficiency and to identify opportunities for optimization is generally left to the user. Today's state of the art performance analysis tools use instrumentation or hardware counter sampling to measure the performance of interactions between code and the target architecture during execution. Such measurements are useful to identify hotspots in applications, places where execution time is spent or where cache misses are incurred. However, explanatory understanding of tuning opportunities requires a more detailed, mechanistic modeling approach. This paper presents MIAMI (Machine Independent Application Models for performance Insight), a set of tools for automatic performance diagnosis. MIAMI uses application characterization and models of target architectures to reason about an application's performance. MIAMI uses a modeling approach based on first-order principles to identify performance bottlenecks, pinpoint optimization opportunities, and compute bounds on the potential for improvement. %B IPASS-2014 %I IEEE %C Monterey, CA %8 03-2014 %@ 978-1-4799-3604-5 %G eng %R 10.1109/ISPASS.2014.6844480 %0 Conference Paper %B VECPAR 2014 (Best Paper) %D 2014 %T Mixed-precision orthogonalization scheme and adaptive step size for CA-GMRES on GPUs %A Ichitaro Yamazaki %A Stanimire Tomov %A Tingxing Dong %A Jack Dongarra %X We propose a mixed-precision orthogonalization scheme that takes the input matrix in a standard 32 or 64-bit floating-point precision, but uses higher-precision arithmetics to accumulate its intermediate results. For the 64-bit precision, our scheme uses software emulation for the higher-precision arithmetics, and requires about 20x more computation but about the same amount of communication as the standard orthogonalization scheme. Since the computation is becoming less expensive compared to the communication on new and emerging architectures, the relative cost of our mixed-precision scheme is decreasing. Our case studies with CA-GMRES on a GPU demonstrate that using mixed-precision for this small but critical segment of CA-GMRES can improve not only its overall numerical stability but also, in some cases, its performance. %B VECPAR 2014 (Best Paper) %C Eugene, OR %8 06-2014 %G eng %0 Journal Article %J Supercomputing Frontiers and Innovations %D 2014 %T Model-Driven One-Sided Factorizations on Multicore, Accelerated Systems %A Jack Dongarra %A Azzam Haidar %A Jakub Kurzak %A Piotr Luszczek %A Stanimire Tomov %A Asim YarKhan %K dense linear algebra %K hardware accelerators %K task superscalar scheduling %X Hardware heterogeneity of the HPC platforms is no longer considered unusual but instead have become the most viable way forward towards Exascale. In fact, the multitude of the heterogeneous resources available to modern computers are designed for different workloads and their efficient use is closely aligned with the specialized role envisaged by their design. Commonly in order to efficiently use such GPU resources, the workload in question must have a much greater degree of parallelism than workloads often associated with multicore processors (CPUs). Available GPU variants differ in their internal architecture and, as a result, are capable of handling workloads of varying degrees of complexity and a range of computational patterns. This vast array of applicable workloads will likely lead to an ever accelerated mixing of multicore-CPUs and GPUs in multi-user environments with the ultimate goal of offering adequate computing facilities for a wide range of scientific and technical workloads. In the following paper, we present a research prototype that uses a lightweight runtime environment to manage the resource-specific workloads, and to control the dataflow and parallel execution in hybrid systems. Our lightweight runtime environment uses task superscalar concepts to enable the developer to write serial code while providing parallel execution. This concept is reminiscent of dataflow and systolic architectures in its conceptualization of a workload as a set of side-effect-free tasks that pass data items whenever the associated work assignment have been completed. Additionally, our task abstractions and their parametrization enable uniformity in the algorithmic development across all the heterogeneous resources without sacrificing precious compute cycles. We include performance results for dense linear algebra functions which demonstrate the practicality and effectiveness of our approach that is aptly capable of full utilization of a wide range of accelerator hardware. %B Supercomputing Frontiers and Innovations %V 1 %G eng %N 1 %R http://dx.doi.org/10.14529/jsfi1401 %0 Conference Paper %B 8th International Conference on Partitioned Global Address Space Programming Models (PGAS) %D 2014 %T A Multithreaded Communication Substrate for OpenSHMEM %A Aurelien Bouteiller %A Thomas Herault %A George Bosilca %X OpenSHMEM scalability is strongly dependent on the capa- bility of its communication layer to efficiently handle multi- ple threads. In this paper, we present an early evaluation of the thread safety specification in the Unified Common Com- munication Substrate (UCCS) employed in OpenSHMEM. Results demonstrate that thread safety can be provided at an acceptable cost and can improve efficiency for some op- erations, compared to serializing communication. %B 8th International Conference on Partitioned Global Address Space Programming Models (PGAS) %C Eugene, OR %8 10-2014 %G eng %0 Conference Paper %B Workshop on Parallel and Distributed Scientific and Engineering Computing, IPDPS 2014 (Best Paper) %D 2014 %T New Algorithm for Computing Eigenvectors of the Symmetric Eigenvalue Problem %A Azzam Haidar %A Piotr Luszczek %A Jack Dongarra %X We describe a design and implementation of a multi-stage algorithm for computing eigenvectors of a dense symmetric matrix. We show that reformulating the existing algorithms is beneficial in terms of performance even if that doubles the computational complexity. Through detailed analysis, we show that the effect of the increase in the asymptotic operation count may be compensated by a much improved performance rate. Our performance results indicate that using our approach achieves very good speedup and scalability even when directly compared with the existing state-of-the-art software. %B Workshop on Parallel and Distributed Scientific and Engineering Computing, IPDPS 2014 (Best Paper) %I IEEE %C Phoenix, AZ %8 05-2014 %G eng %R 10.1109/IPDPSW.2014.130 %0 Journal Article %J International Journal of High Performance Computing Applications %D 2014 %T A Novel Hybrid CPU-GPU Generalized Eigensolver for Electronic Structure Calculations Based on Fine Grained Memory Aware Tasks %A Azzam Haidar %A Raffaele Solcà %A Mark Gates %A Stanimire Tomov %A Thomas C. Schulthess %A Jack Dongarra %K Eigensolver %K electronic structure calculations %K generalized eigensolver %K gpu %K high performance %K hybrid %K Multicore %K two-stage %X The adoption of hybrid CPU–GPU nodes in traditional supercomputing platforms such as the Cray-XK6 opens acceleration opportunities for electronic structure calculations in materials science and chemistry applications, where medium-sized generalized eigenvalue problems must be solved many times. These eigenvalue problems are too small to effectively solve on distributed systems, but can benefit from the massive computing power concentrated on a single-node, hybrid CPU–GPU system. However, hybrid systems call for the development of new algorithms that efficiently exploit heterogeneity and massive parallelism of not just GPUs, but of multicore/manycore CPUs as well. Addressing these demands, we developed a generalized eigensolver featuring novel algorithms of increased computational intensity (compared with the standard algorithms), decomposition of the computation into fine-grained memory aware tasks, and their hybrid execution. The resulting eigensolvers are state-of-the-art in high-performance computing, significantly outperforming existing libraries. We describe the algorithm and analyze its performance impact on applications of interest when different fractions of eigenvectors are needed by the host electronic structure code. %B International Journal of High Performance Computing Applications %V 28 %P 196-209 %8 05-2014 %G eng %N 2 %& 196 %R 10.1177/1094342013502097 %0 Conference Paper %B Fourth International Workshop on Accelerators and Hybrid Exascale Systems (AsHES), IPDPS 2014 %D 2014 %T Optimizing Krylov Subspace Solvers on Graphics Processing Units %A Stanimire Tomov %A Piotr Luszczek %A Ichitaro Yamazaki %A Jack Dongarra %A Hartwig Anzt %A William Sawyer %X Krylov subspace solvers are often the method of choice when solving sparse linear systems iteratively. At the same time, hardware accelerators such as graphics processing units (GPUs) continue to offer significant floating point performance gains for matrix and vector computations through easy-to-use libraries of computational kernels. However, as these libraries are usually composed of a well optimized but limited set of linear algebra operations, applications that use them often fail to leverage the full potential of the accelerator. In this paper we target the acceleration of the BiCGSTAB solver for GPUs, showing that significant improvement can be achieved by reformulating the method and developing application-specific kernels instead of using the generic CUBLAS library provided by NVIDIA. We propose an implementation that benefits from a significantly reduced number of kernel launches and GPUhost communication events, by means of increased data locality and a simultaneous reduction of multiple scalar products. Using experimental data, we show that, depending on the dominance of the untouched sparse matrix vector products, significant performance improvements can be achieved compared to a reference implementation based on the CUBLAS library. We feel that such optimizations are crucial for the subsequent development of highlevel sparse linear algebra libraries. %B Fourth International Workshop on Accelerators and Hybrid Exascale Systems (AsHES), IPDPS 2014 %I IEEE %C Phoenix, AZ %8 05-2014 %G eng %0 Generic %D 2014 %T Performance Analysis of the MPAS-Ocean Code using HPCToolkit and MIAMI %A Gabriel Marin %K MIAMI %B ICL Technical Report %I University of Tennessee %8 02-2014 %G eng %0 Conference Paper %B 5th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA '14) %D 2014 %T Performance and Portability with OpenCL for Throughput-Oriented HPC Workloads Across Accelerators, Coprocessors, and Multicore Processors %A Azzam Haidar %A Chongxiao Cao %A Ichitaro Yamazaki %A Jack Dongarra %A Mark Gates %A Piotr Luszczek %A Stanimire Tomov %X Ever since accelerators and coprocessors became the mainstream hardware for throughput-oriented HPC workloads, various programming techniques have been proposed to increase productivity in terms of both the performance and ease-of-use. We evaluate these aspects of OpenCL on a number of hardware platforms for an important subset of dense linear algebra operations that are relevant to a wide range of scientific applications. Our findings indicate that OpenCL portability has improved since our previous publication and many new and surprising usage scenarios are possible that rival those available after decades of software development on the CPUs. The combined performance-portability metric, even though not promised by the OpenCL standard, reflects the need for tuning performance-critical operations during the porting process and we show how a large portion of the available efficiency is lost if the tuning is not done correctly. %B 5th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA '14) %I IEEE %C New Orleans, LA %8 11-2014 %G eng %R 10.1109/ScalA.2014.8 %0 Journal Article %J International Journal of Networking and Computing %D 2014 %T Performance and Reliability Trade-offs for the Double Checkpointing Algorithm %A Jack Dongarra %A Thomas Herault %A Yves Robert %K communication contention %K in-memory checkpoint %K performance %K resilience %K risk %X Fast checkpointing algorithms require distributed access to stable storage. This paper revisits the approach based upon double checkpointing, and compares the blocking algorithm of Zheng, Shi and Kalé [23], with the non-blocking algorithm of Ni, Meneses and Kalé [15] in terms of both performance and risk. We also extend the model proposedcan provide a better efficiency in [23, 15] to assess the impact of the overhead associated to non-blocking communications. In addition, we deal with arbitrary failure distributions (as opposed to uniform distributions in [23]). We then provide a new peer-to-peer checkpointing algorithm, called the triple checkpointing algorithm, that can work without additional memory, and achieves both higher efficiency and better risk handling than the double checkpointing algorithm. We provide performance and risk models for all the evaluated protocols, and compare them through comprehensive simulations. %B International Journal of Networking and Computing %V 4 %P 32-41 %8 2014 %G eng %& 32 %0 Generic %D 2014 %T Performance of Various Computers Using Standard Linear Equations Software, (Linpack Benchmark Report) %A Jack Dongarra %X This report compares the performance of different computer systems in solving dense systems of linear equations. The comparison involves approximately a hundred computers, ranging from the Earth Simulator to personal computers. %B University of Tennessee Computer Science Technical Report %I University of Tennessee %8 06-2014 %G eng %0 Conference Paper %B 2014 IEEE International Conference on Cluster Computing %D 2014 %T Power Monitoring with PAPI for Extreme Scale Architectures and Dataflow-based Programming Models %A Heike McCraw %A James Ralph %A Anthony Danalis %A Jack Dongarra %X For more than a decade, the PAPI performance-monitoring library has provided a clear, portable interface to the hardware performance counters available on all modern CPUs and other components of interest (e.g., GPUs, network, and I/O systems). Most major end-user tools that application developers use to analyze the performance of their applications rely on PAPI to gain access to these performance counters. One of the critical road-blockers on the way to larger, more complex high performance systems, has been widely identified as being the energy efficiency constraints. With modern extreme scale machines having hundreds of thousands of cores, the ability to reduce power consumption for each CPU at the software level becomes critically important, both for economic and environmental reasons. In order for PAPI to continue playing its well established role in HPC, it is pressing to provide valuable performance data that not only originates from within the processing cores but also delivers insight into the power consumption of the system as a whole. An extensive effort has been made to extend the Performance API to support power monitoring capabilities for various platforms. This paper provides detailed information about three components that allow power monitoring on the Intel Xeon Phi and Blue Gene/Q. Furthermore, we discuss the integration of PAPI in PARSEC – a taskbased dataflow-driven execution engine – enabling hardware performance counter and power monitoring at true task granularity. %B 2014 IEEE International Conference on Cluster Computing %I IEEE %C Madrid, Spain %8 09-2014 %G eng %0 Conference Paper %B International Workshop on Domain-Specific Languages and High-Level Frameworks for High Performance Computing (WOLFHPC) %D 2014 %T PTG: An Abstraction for Unhindered Parallelism %A Anthony Danalis %A George Bosilca %A Aurelien Bouteiller %A Thomas Herault %A Jack Dongarra %XIncreased parallelism and use of heterogeneous computing resources is now an established trend in High Performance Computing (HPC), a trend that, looking forward to Exascale, seems bound to intensify. Despite the evolution of hardware over the past decade, the programming paradigm of choice was invariably derived from Coarse Grain Parallelism with explicit data movements. We argue that message passing has remained the de facto standard in HPC because, until now, the ever increasing challenges that application developers had to address to create efficient portable applications remained manageable for expert programmers.

Data-flow based programming is an alternative approach with significant potential. In this paper, we discuss the Parameterized Task Graph (PTG) abstraction and present the specialized input language that we use to specify PTGs in our data-flow task-based runtime system, PaRSEC. This language and the corresponding execution model are in contrast with the execution model of explicit message passing as well as the model of alternative task based runtime systems. The Parameterized Task Graph language decouples the expression of the parallelism in the algorithm from the control-flow ordering, load balance, and data distribution. Thus, programs are more adaptable and map more efficiently on challenging hardware, as well as maintain portability across diverse architectures. To support these claims, we discuss the different challenges of HPC programming and how PaRSEC can address them, and we demonstrate that in today’s large scale supercomputers, PaRSEC can significantly outperform state-of-the-art MPI applications and libraries, a trend that will increase with future architectural evolution.

%B International Workshop on Domain-Specific Languages and High-Level Frameworks for High Performance Computing (WOLFHPC) %I IEEE Press %C New Orleans, LA %8 11-2014 %G eng %0 Generic %D 2014 %T PULSAR Users’ Guide, Parallel Ultra-Light Systolic Array Runtime %A Jack Dongarra %A Jakub Kurzak %A Piotr Luszczek %A Ichitaro Yamazaki %X PULSAR version 2.0, released in November 2014, is a complete programming platform for large-scale distributed memory systems with multicore processors and hardware accelerators. PULSAR provides a simple abstraction layer over multithreading, message passing, and multi-GPU, multi-stream programming. PULSAR offers a general-purpose programming model, suitable for a wide range of scientific and engineering applications. PULSAR was inspired by systolic arrays, popularized by Hsiang-Tsung Kung and Charles E. Leiserson. %B University of Tennessee EECS Technical Report %I University of Tennessee %8 11-2014 %G eng %0 Conference Proceedings %B International conference on Supercomputing %D 2014 %T Scaling Up Matrix Computations on Shared-Memory Manycore Systems with 1000 CPU Cores %A Fengguang Song %A Jack Dongarra %X While the growing number of cores per chip allows researchers to solve larger scientific and engineering problems, the parallel efficiency of the deployed parallel software starts to decrease. This unscalability problem happens to both vendor-provided and open-source software and wastes CPU cycles and energy. By expecting CPUs with hundreds of cores to be imminent, we have designed a new framework to perform matrix computations for massively many cores. Our performance analysis on manycore systems shows that the unscalability bottleneck is related to Non-Uniform Memory Access (NUMA): memory bus contention and remote memory access latency. To overcome the bottleneck, we have designed NUMA-aware tile algorithms with the help of a dynamic scheduling runtime system to minimize NUMA memory accesses. The main idea is to identify the data that is, either read a number of times or written once by a thread resident on a remote NUMA node, then utilize the runtime system to conduct data caching and movement between different NUMA nodes. Based on the experiments with QR factorizations, we demonstrate that our framework is able to achieve great scalability on a 48-core AMD Opteron system (e.g., parallel efficiency drops only 3% from one core to 48 cores). We also deploy our framework to an extreme-scale shared-memory SGI machine which has 1024 CPU cores and runs a single Linux operating system image. Our framework continues to scale well, and can outperform the vendor-optimized Intel MKL library by up to 750%. %B International conference on Supercomputing %I ACM %C Munich, Germany %P 333-342 %8 06-2014 %@ 978-1-4503-2642-1 %G eng %R 10.1145/2597652.2597670 %0 Conference Paper %B VISSOFT'14: 2nd IEEE Working Conference on Software Visualization %D 2014 %T Search Space Pruning Constraints Visualization %A Blake Haugen %A Jakub Kurzak %X The field of software optimization, among others, is interested in finding an optimal solution in a large search space. These search spaces are often large, complex, non-linear and even non-continuous at times. The size of the search space makes a brute force solution intractable. As a result, one or more search space pruning constraints are often used to reduce the number of candidate configurations that must be evaluated in order to solve the optimization problem. If more than one pruning constraint is employed, it can be challenging to understand how the pruning constraints interact and overlap. This work presents a visualization technique based on a radial, space-filling technique that allows the user to gain a better understanding of how the pruning constraints remove candidates from the search space. The technique is then demonstrated using a search space pruning data set derived from the optimization of a matrix multiplication code for NVIDIA CUDA accelerators. %B VISSOFT'14: 2nd IEEE Working Conference on Software Visualization %I IEEE %C Victoria, BC, Canada %8 09-2014 %G eng %0 Conference Paper %B VECPAR 2014 %D 2014 %T Self-Adaptive Multiprecision Preconditioners on Multicore and Manycore Architectures %A Hartwig Anzt %A Dimitar Lukarski %A Stanimire Tomov %A Jack Dongarra %X Based on the premise that preconditioners needed for scientific computing are not only required to be robust in the numerical sense, but also scalable for up to thousands of light-weight cores, we argue that this two-fold goal is achieved for the recently developed self-adaptive multi-elimination preconditioner. For this purpose, we revise the underlying idea and analyze the performance of implementations realized in the PARALUTION and MAGMA open-source software libraries on GPU architectures (using either CUDA or OpenCL), Intel’s Many Integrated Core Architecture, and Intel’s Sandy Bridge processor. The comparison with other well-established preconditioners like multi-coloured Gauss-Seidel, ILU(0) and multi-colored ILU(0), shows that the twofold goal of a numerically stable cross-platform performant algorithm is achieved. %B VECPAR 2014 %C Eugene, OR %8 06-2014 %G eng %0 Conference Paper %B IPDPS 2014 %D 2014 %T A Step towards Energy Efficient Computing: Redesigning A Hydrodynamic Application on CPU-GPU %A Tingxing Dong %A Veselin Dobrev %A Tzanio Kolev %A Robert Rieben %A Stanimire Tomov %A Jack Dongarra %K Computer science %K CUDA %K FEM %K Finite element method %K linear algebra %K nVidia %K Tesla K20 %X Power and energy consumption are becoming an increasing concern in high performance computing. Compared to multi-core CPUs, GPUs have a much better performance per watt. In this paper we discuss efforts to redesign the most computation intensive parts of BLAST, an application that solves the equations for compressible hydrodynamics with high order finite elements, using GPUs [10, 1]. In order to exploit the hardware parallelism of GPUs and achieve high performance, we implemented custom linear algebra kernels. We intensively optimized our CUDA kernels by exploiting the memory hierarchy, which exceed the vendor’s library routines substantially in performance. We proposed an autotuning technique to adapt our CUDA kernels to the orders of the finite element method. Compared to a previous base implementation, our redesign and optimization lowered the energy consumption of the GPU in two aspects: 60% less time to solution and 10% less power required. Compared to the CPU-only solution, our GPU accelerated BLAST obtained a 2:5x overall speedup and 1:42x energy efficiency (greenup) using 4th order (Q4) finite elements, and a 1:9x speedup and 1:27x greenup using 2nd order (Q2) finite elements. %B IPDPS 2014 %I IEEE %C Phoenix, AZ %8 05-2014 %G eng %0 Conference Paper %B 23rd International Heterogeneity in Computing Workshop, IPDPS 2014 %D 2014 %T Taking Advantage of Hybrid Systems for Sparse Direct Solvers via Task-Based Runtimes %A Xavier Lacoste %A Mathieu Faverge %A Pierre Ramet %A Samuel Thibault %A George Bosilca %K DAG based runtime %K gpu %K Multicore %K Sparse linear solver %X The ongoing hardware evolution exhibits an escalation in the number, as well as in the heterogeneity, of the computing resources. The pressure to maintain reasonable levels of performance and portability, forces the application developers to leave the traditional programming paradigms and explore alternative solutions. PaStiX is a parallel sparse direct solver, based on a dynamic scheduler for modern hierarchical architectures. In this paper, we study the replacement of the highly specialized internal scheduler in PaStiX by two generic runtime frameworks: PaRSEC and StarPU. The tasks graph of the factorization step is made available to the two runtimes, providing them with the opportunity to optimize it in order to maximize the algorithm eefficiency for a predefined execution environment. A comparative study of the performance of the PaStiX solver with the three schedulers { native PaStiX, StarPU and PaRSEC schedulers { on different execution contexts is performed. The analysis highlights the similarities from a performance point of view between the different execution supports. These results demonstrate that these generic DAG-based runtimes provide a uniform and portable programming interface across heterogeneous environments, and are, therefore, a sustainable solution for hybrid environments. %B 23rd International Heterogeneity in Computing Workshop, IPDPS 2014 %I IEEE %C Phoenix, AZ %8 05-2014 %G eng %0 Conference Paper %B 2014 IEEE International Conference on High Performance Computing and Communications (HPCC) %D 2014 %T Task-Based Programming for Seismic Imaging: Preliminary Results %A Lionel Boillot %A George Bosilca %A Emmanuel Agullo %A Henri Calandra %X The level of hardware complexity of current supercomputers is forcing the High Performance Computing (HPC) community to reconsider parallel programming paradigms and standards. The high-level of hardware abstraction provided by task-based paradigms make them excellent candidates for writing portable codes that can consistently deliver high performance across a wide range of platforms. While this paradigm has proved efficient for achieving such goals for dense and sparse linear solvers, it is yet to be demonstrated that industrial parallel codes—relying on the classical Message Passing Interface (MPI) standard and that accumulate dozens of years of expertise (and countless lines of code)—may be revisited to turn them into efficient task-based programs. In this paper, we study the applicability of task-based programming in the case of a Reverse Time Migration (RTM) application for Seismic Imaging. The initial MPI-based application is turned into a task-based code executed on top of the PaRSEC runtime system. Preliminary results show that the approach is competitive with (and even potentially superior to) the original MPI code on a homogeneous multicore node, and can more efficiently exploit complex hardware such as a cache coherent Non Uniform Memory Access (ccNUMA) node or an Intel Xeon Phi accelerator. %B 2014 IEEE International Conference on High Performance Computing and Communications (HPCC) %I IEEE %C Paris, France %8 08-2014 %G eng %0 Conference Paper %B IPDPS 2014 %D 2014 %T Unified Development for Mixed Multi-GPU and Multi-Coprocessor Environments using a Lightweight Runtime Environment %A Azzam Haidar %A Chongxiao Cao %A Jack Dongarra %A Piotr Luszczek %A Stanimire Tomov %K algorithms %K Computer science %K CUDA %K Heterogeneous systems %K Intel Xeon Phi %K linear algebra %K nVidia %K Tesla K20 %K Tesla M2090 %X Many of the heterogeneous resources available to modern computers are designed for different workloads. In order to efficiently use GPU resources, the workload must have a greater degree of parallelism than a workload designed for multicore-CPUs. And conceptually, the Intel Xeon Phi coprocessors are capable of handling workloads somewhere in between the two. This multitude of applicable workloads will likely lead to mixing multicore-CPUs, GPUs, and Intel coprocessors in multi-user environments that must offer adequate computing facilities for a wide range of workloads. In this work, we are using a lightweight runtime environment to manage the resourcespecific workload, and to control the dataflow and parallel execution in two-way hybrid systems. The lightweight runtime environment uses task superscalar concepts to enable the developer to write serial code while providing parallel execution. In addition, our task abstractions enable unified algorithmic development across all the heterogeneous resources. We provide performance results for dense linear algebra applications, demonstrating the effectiveness of our approach and full utilization of a wide variety of accelerator hardware. %B IPDPS 2014 %I IEEE %C Phoenix, AZ %8 05-2014 %G eng %0 Journal Article %J Concurrency and Computation: Practice and Experience %D 2014 %T Unveiling the Performance-energy Trade-off in Iterative Linear System Solvers for Multithreaded Processors %A José I. Aliaga %A Hartwig Anzt %A Maribel Castillo %A Juan C. Fernández %A Germán León %A Joaquín Pérez %A Enrique S. Quintana-Ortí %K CG %K CPUs %K energy efficiency %K GPUs %K low-power architectures %X In this paper, we analyze the interactions occurring in the triangle performance-power-energy for the execution of a pivotal numerical algorithm, the iterative conjugate gradient (CG) method, on a diverse collection of parallel multithreaded architectures. This analysis is especially timely in a decade where the power wall has arisen as a major obstacle to build faster processors. Moreover, the CG method has recently been proposed as a complement to the LINPACK benchmark, as this iterative method is argued to be more archetypical of the performance of today's scientific and engineering applications. To gain insights about the benefits of hands-on optimizations we include runtime and energy efficiency results for both out-of-the-box usage relying exclusively on compiler optimizations, and implementations manually optimized for target architectures, that range from general-purpose and digital signal multicore processors to manycore graphics processing units, all representative of current multithreaded systems. %B Concurrency and Computation: Practice and Experience %V 27 %P 885-904 %8 09-2014 %G eng %U http://dx.doi.org/10.1002/cpe.3341 %N 4 %& 885 %R 10.1002/cpe.3341 %0 Conference Paper %B 2014 IEEE International Conference on Cluster Computing %D 2014 %T Utilizing Dataflow-based Execution for Coupled Cluster Methods %A Heike McCraw %A Anthony Danalis %A George Bosilca %A Jack Dongarra %A Karol Kowalski %A Theresa Windus %X Computational chemistry comprises one of the driving forces of High Performance Computing. In particular, many-body methods, such as Coupled Cluster (CC) methods of the quantum chemistry package NWCHEM, are of particular interest for the applied chemistry community. Harnessing large fractions of the processing power of modern large scale computing platforms has become increasingly difficult. With the increase in scale, complexity, and heterogeneity of modern platforms, traditional programming models fail to deliver the expected performance scalability. On our way to Exascale and with these extremely hybrid platforms, dataflow-based programming models may be the only viable way for achieving and maintaining computation at scale. In this paper, we discuss a dataflow-based programming model and its applicability to NWCHEM’s CC methods. Our dataflow version of the CC kernels breaks down the algorithm into fine-grained tasks with explicitly defined data dependencies. As a result, many of the traditional synchronization points can be eliminated, allowing for a dynamic reshaping of the execution based on the ongoing availability of computational resources. We build this experiment using PARSEC – a task-based dataflow-driven execution engine – that enables efficient task scheduling on distributed systems, providing a desirable portability layer for application developers. %B 2014 IEEE International Conference on Cluster Computing %I IEEE %C Madrid, Spain %8 09-2014 %G eng %0 Generic %D 2013 %T Analyzing PAPI Performance on Virtual Machines %A John Nelson %X Over the last ten years, virtualization techniques have become much more widely popular as a result of fast and cheap processors. Virtualization provides many benefits making it appealing for testing environments. Encapsulating configurations is a huge motivator for wanting to do performance testing on virtual machines. Provisioning, a technique that is used by FutureGrid, is also simplified using virtual machines. Virtual machines enable portability among heterogeneous systems while providing an identical configuration within the guest operating system. My work in ICL has focused on using PAPI inside of virtual machines. There were two main areas of focus throughout my research. The first originated because of anomalous results of the HPC Challenge Benchmark reported in a paper submitted by ICL [3] in which the order of input sizes tested impacted run time on virtual machines but not on bare metal. A discussion of this anomaly will be given in section II along with a discussion of timers used in virtual machines. The second area of focus was exploring the recently implemented support by KVM (Kernel-based Virtual Machine) and VMware for guest OS level performance counters. A discussion of application tests run to observe the behavior of event counts measured in a virtual machine as well as a discussion of information learned pertinent to event measurement will be given in section III. %B ICL Technical Report %8 08-2013 %G eng %0 Generic %D 2013 %T Assessing the impact of ABFT and Checkpoint composite strategies %A George Bosilca %A Aurelien Bouteiller %A Thomas Herault %A Yves Robert %A Jack Dongarra %K ABFT %K checkpoint %K fault-tolerance %K High-performance computing %K resilience %X Algorithm-specific fault tolerant approaches promise unparalleled scalability and performance in failure-prone environments. With the advances in the theoretical and practical understanding of algorithmic traits enabling such approaches, a growing number of frequently used algorithms (including all widely used factorization kernels) have been proven capable of such properties. These algorithms provide a temporal section of the execution when the data is protected by it’s own intrinsic properties, and can be algorithmically recomputed without the need of checkpoints. However, while typical scientific applications spend a significant fraction of their execution time in library calls that can be ABFT-protected, they interleave sections that are difficult or even impossible to protect with ABFT. As a consequence, the only fault-tolerance approach that is currently used for these applications is checkpoint/restart. In this paper we propose a model and a simulator to investigate the behavior of a composite protocol, that alternates between ABFT and checkpoint/restart protection for effective protection of each phase of an iterative application composed of ABFT-aware and ABFT-unaware sections. We highlight this approach drastically increases the performance delivered by the system, especially at scale, by providing means to rarefy the checkpoints while simultaneously decreasing the volume of data needed to be checkpointed. %B University of Tennessee Computer Science Technical Report %G eng %0 Journal Article %J The Computer Journal %D 2013 %T BlackjackBench: Portable Hardware Characterization with Automated Results Analysis %A Anthony Danalis %A Piotr Luszczek %A Gabriel Marin %A Jeffrey Vetter %A Jack Dongarra %K hardware characterization %K micro-benchmarks %K statistical analysis %X DARPA's AACE project aimed to develop Architecture Aware Compiler Environments. Such a compiler automatically characterizes the targeted hardware and optimizes the application codes accordingly. We present the BlackjackBench suite, a collection of portable micro-benchmarks that automate system characterization, plus statistical analysis techniques for interpreting the results. The BlackjackBench benchmarks discover the effective sizes and speeds of the hardware environment rather than the often unattainable peak values. We aim at hardware characteristics that can be observed by running executables generated by existing compilers from standard C codes. We characterize the memory hierarchy, including cache sharing and non-uniform memory access characteristics of the system, properties of the processing cores affecting the instruction execution speed and the length of the operating system scheduler time slot. We show how these features of modern multicores can be discovered programmatically. We also show how the features could potentially interfere with each other resulting in incorrect interpretation of the results, and how established classification and statistical analysis techniques can reduce experimental noise and aid automatic interpretation of results. We show how effective hardware metrics from our probes allow guided tuning of computational kernels that outperform an autotuning library further tuned by the hardware vendor. %B The Computer Journal %8 03-2013 %G eng %R 10.1093/comjnl/bxt057 %0 Journal Article %J Journal of Parallel and Distributed Computing %D 2013 %T A Block-Asynchronous Relaxation Method for Graphics Processing Units %A Hartwig Anzt %A Stanimire Tomov %A Jack Dongarra %A Vincent Heuveline %X In this paper, we analyze the potential of asynchronous relaxation methods on Graphics Processing Units (GPUs). We develop asynchronous iteration algorithms in CUDA and compare them with parallel implementations of synchronous relaxation methods on CPU- or GPU-based systems. For a set of test matrices from UFMC we investigate convergence behavior, performance and tolerance to hardware failure. We observe that even for our most basic asynchronous relaxation scheme, the method can efficiently leverage the GPUs computing power and is, despite its lower convergence rate compared to the Gauss–Seidel relaxation, still able to provide solution approximations of certain accuracy in considerably shorter time than Gauss–Seidel running on CPUs- or GPU-based Jacobi. Hence, it overcompensates for the slower convergence by exploiting the scalability and the good fit of the asynchronous schemes for the highly parallel GPU architectures. Further, enhancing the most basic asynchronous approach with hybrid schemes–using multiple iterations within the ‘‘subdomain’’ handled by a GPU thread block–we manage to not only recover the loss of global convergence but often accelerate convergence of up to two times, while keeping the execution time of a global iteration practically the same. The combination with the advantageous properties of asynchronous iteration methods with respect to hardware failure identifies the high potential of the asynchronous methods for Exascale computing. %B Journal of Parallel and Distributed Computing %V 73 %P 1613–1626 %8 12-2013 %G eng %N 12 %R http://dx.doi.org/10.1016/j.jpdc.2013.05.008 %0 Generic %D 2013 %T clMAGMA: High Performance Dense Linear Algebra with OpenCL %A Chongxiao Cao %A Jack Dongarra %A Peng Du %A Mark Gates %A Piotr Luszczek %A Stanimire Tomov %X This paper presents the design and implementation of sev- eral fundamental dense linear algebra (DLA) algorithms in OpenCL. In particular, these are linear system solvers and eigenvalue problem solvers. Further, we give an overview of the clMAGMA library, an open source, high performance OpenCL library that incorporates the developments pre- sented, and in general provides to heterogeneous architec- tures the DLA functionality of the popular LAPACK library. The LAPACK-compliance and use of OpenCL simplify the use of clMAGMA in applications, while providing them with portably performant DLA. High performance is ob- tained through use of the high-performance OpenCL BLAS, hardware and OpenCL-speci c tuning, and a hybridization methodology where we split the algorithm into computa- tional tasks of various granularities. Execution of those tasks is properly scheduled over the heterogeneous hardware components by minimizing data movements and mapping algorithmic requirements to the architectural strengths of the various heterogeneous hardware components. %B University of Tennessee Technical Report (Lawn 275) %I University of Tennessee %8 03-2013 %G eng %0 Generic %D 2013 %T On the Combination of Silent Error Detection and Checkpointing %A Guillaume Aupy %A Anne Benoit %A Thomas Herault %A Yves Robert %A Frederic Vivien %A Dounia Zaidouni %K checkpointing %K error recovery %K High-performance computing %K silent data corruption %K verification %X In this paper, we revisit traditional checkpointing and rollback recovery strategies, with a focus on silent data corruption errors. Contrarily to fail-stop failures, such latent errors cannot be detected immediately, and a mechanism to detect them must be provided. We consider two models: (i) errors are detected after some delays following a probability distribution (typically, an Exponential distribution); (ii) errors are detected through some verification mechanism. In both cases, we compute the optimal period in order to minimize the waste, i.e., the fraction of time where nodes do not perform useful computations. In practice, only a fixed number of checkpoints can be kept in memory, and the first model may lead to an irrecoverable failure. In this case, we compute the minimum period required for an acceptable risk. For the second model, there is no risk of irrecoverable failure, owing to the verification mechanism, but the corresponding overhead is included in the waste. Finally, both models are instantiated using realistic scenarios and application/architecture parameters. %B UT-CS-13-710 %I University of Tennessee Computer Science Technical Report %8 06-2013 %G eng %U http://www.netlib.org/lapack/lawnspdf/lawn278.pdf %0 Journal Article %J Concurrency and Computation: Practice and Experience %D 2013 %T Correlated Set Coordination in Fault Tolerant Message Logging Protocols %A Aurelien Bouteiller %A Thomas Herault %A George Bosilca %A Jack Dongarra %X With our current expectation for the exascale systems, composed of hundred of thousands of many-core nodes, the mean time between failures will become small, even under the most optimistic assumptions. One of the most scalable checkpoint restart techniques, the message logging approach, is the most challenged when the number of cores per node increases because of the high overhead of saving the message payload. Fortunately, for two processes on the same node, the failure probability is correlated, meaning that coordinated recovery is free. In this paper, we propose an intermediate approach that uses coordination between correlated processes but retains the scalability advantage of message logging between independent ones. The algorithm still belongs to the family of event logging protocols but eliminates the need for costly payload logging between coordinated processes. %B Concurrency and Computation: Practice and Experience %V 25 %P 572-585 %8 03-2013 %G eng %N 4 %R 10.1002/cpe.2859 %0 Conference Proceedings %B ScalA '13 Proceedings of the Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems %D 2013 %T CPU-GPU Hybrid Bidiagonal Reduction With Soft Error Resilience %A Yulu Jia %A Piotr Luszczek %A George Bosilca %A Jack Dongarra %X Soft errors pose a real challenge to applications running on modern hardware as the feature size becomes smaller and the integration density increases for both the modern processors and the memory chips. Soft errors manifest themselves as bit-flips that alter the user value, and numerical software is a category of software that is sensitive to such data changes. In this paper, we present a design of a bidiagonal reduction algorithm that is resilient to soft errors, and we also describe its implementation on hybrid CPU-GPU architectures. Our fault-tolerant algorithm employs Algorithm Based Fault Tolerance, combined with reverse computation, to detect, locate, and correct soft errors. The tests were performed on a Sandy Bridge CPU coupled with an NVIDIA Kepler GPU. The included experiments show that our resilient bidiagonal reduction algorithm adds very little overhead compared to the error-prone code. At matrix size 10110 x 10110, our algorithm only has a performance overhead of 1.085% when one error occurs, and 0.354% when no errors occur. %B ScalA '13 Proceedings of the Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems %C Montpellier, France %8 11-2013 %G eng %0 Journal Article %J Scalable Computing and Communications: Theory and Practice %D 2013 %T Dense Linear Algebra on Distributed Heterogeneous Hardware with a Symbolic DAG Approach %A George Bosilca %A Aurelien Bouteiller %A Anthony Danalis %A Thomas Herault %A Piotr Luszczek %A Jack Dongarra %E Samee Khan %E Lin-Wang Wang %E Albert Zomaya %B Scalable Computing and Communications: Theory and Practice %I John Wiley & Sons %P 699-735 %8 03-2013 %G eng %0 Generic %D 2013 %T Designing LU-QR hybrid solvers for performance and stability %A Mathieu Faverge %A Julien Herrmann %A Julien Langou %A Bradley Lowery %A Yves Robert %A Jack Dongarra %B University of Tennessee Computer Science Technical Report (also LAWN 282) %I University of Tennessee %8 10-2013 %G eng %0 Conference Paper %B Proceedings of the 27th ACM International Conference on Supercomputing (ICS '13) %D 2013 %T Diagnosis and Optimization of Application Prefetching Performance %A Gabriel Marin %A Colin McCurdy %A Jeffrey Vetter %E Malony, Allen %E Nemirovsky, Mario %E Midkiff, Sam %X Hardware prefetchers are effective at recognizing streaming memory access patterns and at moving data closer to the processing units to hide memory latency. However, hardware prefetchers can track only a limited number of data streams due to finite hardware resources. In this paper, we introduce the term