Computing the R of the QR factorization of tall and skinny matrices using MPI_Reduce

A QR factorization of a tall and skinny matrix with n columns can be represented as a reduction. The operation used along the reduction tree has in input two n-by-n upper triangular matrices and in output an n-by-n upper triangular matrix which is defined as the R factor of the two input matrices stacked the one on top of the other. This operation is binary, associative, and commutative. We can therefore leverage the MPI library capabilities by using user-defined MPI operations and MPI_Reduce to perform this reduction. The resulting code is compact and portable. In this context, the user relies on the MPI library to select a reduction tree appropriate for the underlying architecture

CellSs : Scheduling techniques to better exploit memory hierarchy

ABSTRACT: Cell Superscalar’s (CellSs) main goal is to provide a simple, flexible and easy programming approach for the Cell Broadband Engine (Cell/B.E.) that automatically exploits the inherent concurrency of the applications at a task level. The CellSs environment is based on a source-to-source compiler that translates annotated C or Fortran code and a runtime library tailored for the Cell/B.E. that takes care of the concurrent execution of the application. The first efforts for task scheduling in CellSs derived from very simple heuristics. This paper presents new scheduling techniques that have been developed for CellSs for the purpose of improving an application’s performance. Additionally, the design of a new scheduling algorithm is detailed and the algorithm evaluated. The CellSs scheduler takes an extension of the memory hierarchy for Cell/B.E. into account, with a cache memory shared between the SPEs. All new scheduling practices have been evaluated showing better behavior of our system

Self-adaptive OmpSs tasks in heterogeneous environments

As new heterogeneous systems and hardware accelerators appear, high performance computers can reach a higher level of computational power. Nevertheless, this does not come for free: the more heterogeneity the system presents, the more complex becomes the programming task in terms of resource management. OmpSs is a task-based programming model and framework focused on the runtime exploitation of parallelism from annotated sequential applications. This paper presents a set of extensions to this framework: we show how the application programmer can expose different specialized versions of tasks (i.e. pieces of specific code targeted and optimized for a particular architecture) and how the system can choose between these versions at runtime to obtain the best performance achievable for the given application. From the results obtained in a multi-GPU system, we prove that our proposal gives flexibility to application's source code and can potentially increase application's performance.This work has been supported by the European Commission through the ENCORE project (FP7-248647), the TERAFLUX project (FP7-249013), the TEXT project (FP7-261580), the HiPEAC-3 Network of Excellence (FP7-ICT 287759), the Intel-BSC Exascale Lab collaboration project, the support of the Spanish Ministry of Education (CSD2007- 00050 and FPU program), the projects of Computación de Altas Prestaciones V and VI (TIN2007-60625, TIN2012-34557) and the Generalitat de Catalunya (2009-SGR-980).Peer ReviewedPostprint (author’s final draft

Selection of Task Implementations in the Nanos++ Runtime

New heterogeneous systems and hardware accelerators can give higher levels of computational power to high performance computers. However, this does not come for free, since the more heterogeneity the system presents, the more complex becomes the programming task in terms of resource utilization. OmpSs is a task-based programming model and framework focused on the automatic parallelization of sequential applications. We present a set of extensions to this framework: we show how the application programmer can expose different specialized versions of tasks (i.e. pieces of specific code targeted and optimized for a particular architecture) and how the framework will choose between these versions at runtime to obtain the best performance achievable for the given application. From our results, obtained in a multi-GPU system, we can prove that our project gives flexibility to application's source code and can potentially increase application’s performance

Dynamic Task Execution on Shared and Distributed Memory Architectures

Multicore architectures with high core counts have come to dominate the world of high performance computing, from shared memory machines to the largest distributed memory clusters. The multicore route to increased performance has a simpler design and better power efficiency than the traditional approach of increasing processor frequencies. But, standard programming techniques are not well adapted to this change in computer architecture design. In this work, we study the use of dynamic runtime environments executing data driven applications as a solution to programming multicore architectures. The goals of our runtime environments are productivity, scalability and performance. We demonstrate productivity by defining a simple programming interface to express code. Our runtime environments are experimentally shown to be scalable and give competitive performance on large multicore and distributed memory machines. This work is driven by linear algebra algorithms, where state-of-the-art libraries (e.g., LAPACK and ScaLAPACK) using a fork-join or block-synchronous execution style do not use the available resources in the most efficient manner. Research work in linear algebra has reformulated these algorithms as tasks acting on tiles of data, with data dependency relationships between the tasks. This results in a task-based DAG for the reformulated algorithms, which can be executed via asynchronous data-driven execution paths analogous to dataflow execution. We study an API and runtime environment for shared memory architectures that efficiently executes serially presented tile based algorithms. This runtime is used to enable linear algebra applications and is shown to deliver performance competitive with state-of- the-art commercial and research libraries. We develop a runtime environment for distributed memory multicore architectures extended from our shared memory implementation. The runtime takes serially presented algorithms designed for the shared memory environment, and schedules and executes them on distributed memory architectures in a scalable and high performance manner. We design a distributed data coherency protocol and a distributed task scheduling mechanism which avoid global coordination. Experimental results with linear algebra applications show the scalability and performance of our runtime environment