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With the memory bandwidth of current computer architectures being significantly slower than the (floating point) arithmetic performance, many scientific computations only leverage a fraction of the computational power in today's high-performance architectures. At the same time, memory operations are the primary energy consumer of modern architectures, heavily impacting the resource cost of large-scale applications and the battery life of mobile devices. This article tackles this mismatch between floating point arithmetic throughput and memory bandwidth by advocating a disruptive paradigm change with respect to how data are stored and processed in scientific applications. Concretely, the goal is to radically decouple the data storage format from the processing format and, ultimately, design a "modular precision ecosystem" that allows for more flexibility in terms of customized data access. For memory-bounded scientific applications, dynamically adapting the memory precision to the numerical requirements allows for attractive resource savings. In this article, we demonstrate the potential of employing a modular precision ecosystem for the block-Jacobi preconditioner and the PageRank algorithm—two applications that are popular in the communities and at the same characteristic representatives for the field of numerical linear algebra and data analytics, respectively. [ABSTRACT FROM AUTHOR]

We propose a reproducible variant of the unblocked LU factorization for graphics processor units (GPUs). For this purpose, we build upon Level-1/2 BLAS kernels that deliver correctly-rounded and reproducible results for the dot (inner) product, vector scaling, and the matrix-vector product. In addition, we draw a strategy to enhance the accuracy of the triangular solve via iterative refinement. Following a bottom-up approach, we finally construct a reproducible unblocked implementation of the LU factorization for GPUs, which accommodates partial pivoting for stability and can be eventually integrated in a high performance and stable algorithm for the (blocked) LU factorization. [ABSTRACT FROM AUTHOR]

We address the solution of large-scale eigenvalue problems that appear in the motion simulation of complex macromolecules on multithreaded platforms, consisting of multicore processors and possibly a graphics processor (graphics processing unit). In particular, we compare specialized implementations of several high-performance eigensolvers that, by relying on disk storage and out-of-core techniques, can in principle tackle the large memory requirements of these biological problems, which in general do not fit into the main memory of current desktop machines. All these out-of-core eigensolvers, except for one, are composed of compute-bound (i.e., arithmetically intensive) operations, which we accelerate by exploiting the performance of current multicore processors and, in some cases, by additionally off-loading certain parts of the computation to a graphics processing unit accelerator. One of the eigensolvers is a memory-bound algorithm, which strongly constrains its performance when the data is on disk. However, this method exhibits a much lower arithmetic cost compared with its compute-bound alternatives for this particular application. Experimental results on a desktop platform, representative of current server technology, illustrate the potential of these methods to address the simulation of biological activity. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We address the numerical solution of Lyapunov, algebraic and differential Riccati equations, via the matrix sign function, on platforms equipped with general-purpose multicore processors and, optionally, one or more graphics processing units (GPUs). In particular, we review the solvers for these equations, as well as the underlying methods, analyze their concurrency and scalability and provide details on their parallel implementation. Our experimental results show that this class of hardware provides sufficient computational power to tackle large-scale problems, which only a few years ago would have required a cluster of computers. [ABSTRACT FROM AUTHOR]

We introduce a version of the epistasis test in FaST-LMM for clusters of multithreaded processors. This new software maintains the sensitivity of the original FaST-LMM while delivering acceleration that is close to linear on 12–16 nodes of two recent platforms, with respect to improved implementation of FaST-LMM presented in an earlier work. This efficiency is attained through several enhancements on the original single-node version of FaST-LMM, together with the development of a message passing interface (MPI)-based version that ensures a balanced distribution of the workload as well as a multigraphics processing unit (GPU) module that can exploit the presence of multiple GPUs per node. [ABSTRACT FROM AUTHOR]