This work presents an implementation of a linear least squares solver for distributed-memory machines with GPU accelerators, developed as part of the Software for Linear Algebra Targeting Exascale (SLATE) package. From the algorithmic standpoint, the work leverages recent advances in dense linear algebra, specifically the communication-avoiding QR factorization. From the implementation standpoint, the work represents a sharp departure from the traditional conventions established by legacy packages, such as LAPACK and ScaLAPACK. It is based on representing the matrix as a collection of individual tiles, and using batch operations for offloading work to accelerators. The article lays out the principles of the new approach, discusses the implementation details and presents the performance results.

The SLATE (Software for Linear Algebra Targeting Exascale) library is being developed to provide fundamental dense linear algebra capabilities for current and upcoming distributed high-performance systems, both accelerated CPU-GPU based and CPU based. SLATE will provide coverage of existing ScaLAPACK functionality, including the parallel BLAS; linear systems using LU and Cholesky; least squares problems using QR; and eigenvalue and singular value problems. In this respect, it will serve as a replacement for ScaLAPACK, which after two decades of operation, cannot adequately be retrofitted for modern accelerated architectures. SLATE uses modern techniques such as communication-avoiding algorithms, lookahead panels to overlap communication and computation, and task-based scheduling, along with a modern C++ framework. Here we present the design of SLATE and initial reports of several of its components.

Summary The emergence of power efficiency as a primary constraint in processor and system design poses new challenges concerning power and energy awareness for numerical libraries and scientific applications. Power consumption also plays a major role in the design of data centers, which may house petascale or exascale‐level computing systems. At these extreme scales, understanding and improving the energy efficiency of numerical libraries and their related applications becomes a crucial part of the successful implementation and operation of the computing system. In this paper, we study and investigate the practice of controlling a compute system's power usage, and we explore how different power caps affect the performance of numerical algorithms with different computational intensities. Further, we determine the impact, in terms of performance and energy usage, that these caps have on a system running scientific applications. This analysis will enable us to characterize the types of algorithms that benefit most from these power management schemes. Our experiments are performed using a set of representative kernels and several popular scientific benchmarks. We quantify a number of power and performance measurements and draw observations and conclusions that can be viewed as a roadmap to achieving energy efficiency in the design and execution of scientific algorithms.

The recent version of the Parallel Linear Algebra Software for Multicore Architectures (PLASMA) library is based on tasks with dependencies from the OpenMP standard. The main functionality of the library is presented. Extensive benchmarks are targeted on three recent multicore and manycore architectures, namely, an Intel Xeon, Intel Xeon Phi, and IBM POWER 8 processors.

Computers have been moving toward a multicore paradigm for the last several years. As a result of the recent multicore paradigm shift, software developers must design applications that exploit the inherent parallelism of modern computing architectures. One of the areas of research to simplify this shift is the development of dynamic scheduling utilities that allow the developer to specify serial code that can be parallelized using a library or compiler technology. While these tools certainly increase the developer's productivity, they can obfuscate performance bottlenecks. For this reason, it is important to evaluate algorithm performance in order to ensure that the performance of a given algorithm is being realized using dynamic scheduling utilities. This paper presents the methodology and results of a new performance analysis tool that aims to accurately simulate the performance of various superscalar schedulers, including OmpSs, StarPU, and QUARK. The process begins with careful timing of each of the computational routines that make up the algorithm. The simulation tool then uses the timing of the computational kernels in conjunction with the dependency management provided by the superscalar scheduler in order to simulate the execution time of the algorithm. This tool demonstrates that simulation results of various algorithms can accurately predict the performance of a complex dynamic scheduling system.

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 resource-specific 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.

SUMMARY The objective of this paper is to analyze the dynamic scheduling of dense linear algebra algorithms on shared‐memory, multicore architectures. Current numerical libraries (e.g., linear algebra package) show clear limitations on such emerging systems mainly because of their coarse granularity tasks. Thus, many numerical algorithms need to be redesigned to better fit the architectural design of the multicore platform. The parallel linear algebra for scalable multicore architectures library developed at the University of Tennessee tackles this challenge by using tile algorithms to achieve a finer task granularity. These tile algorithms can then be represented by directed acyclic graphs, where nodes are the tasks and edges are the dependencies between the tasks. The paramount key to achieve high performance is to implement a runtime environment to efficiently schedule the execution of the directed acyclic graph across the multicore platform. This paper studies the impact on the overall performance of some parameters, both at the level of the scheduler (e.g., window size and locality) and the algorithms (e.g., left‐looking and right‐looking variants). We conclude that some commonly accepted rules for dense linear algebra algorithms may need to be revisited. Copyright © 2011 John Wiley & Sons, Ltd.

Today's scientific workflows use distributed heterogeneous resources through diverse grid and cloud interfaces that are often hard to program. In addition, especially for time-sensitive critical applications, predictable quality of service is necessary across these distributed resources. VGrADS' virtual grid execution system (vgES) provides an uniform qualitative resource abstraction over grid and cloud systems. We apply vgES for scheduling a set of deadline sensitive weather forecasting workflows. Specifically, this paper reports on our experiences with (1) virtualized reservations for batchqueue systems, (2) coordinated usage of TeraGrid (batch queue), Amazon EC2 (cloud), our own clusters (batch queue) and Eucalyptus (cloud) resources, and (3) fault tolerance through automated task replication. The combined effect of these techniques was to enable a new workflow planning method to balance performance, reliability and cost considerations. The results point toward improved resource selection and execution management support for a variety of e-Science applications over grids and cloud systems.

This paper presents a dynamic task scheduling approach to executing dense linear algebra algorithms on multicore systems (either shared-memory or distributed-memory). We use a task-based library to replace the existing linear algebra subroutines such as PBLAS to transparently provide the same interface and computational function as the ScaLAPACK library. Linear algebra programs are written with the task-based library and executed by a dynamic runtime system. We mainly focus our runtime system design on the metric of performance scalability. We propose a distributed algorithm to solve data dependences without process cooperation. We have implemented the runtime system and applied it to three linear algebra algorithms: Cholesky, LU, and QR factorizations. Our experiments on both shared-memory machines (16, 32 cores) and distributed-memory machines (1024 cores) demonstrate that our runtime system is able to achieve good scalability. Furthermore, we provide analytical analysis to show why the tiled algorithms are scalable and the expected execution time.