Taking advantage of hybrid systems for sparse direct solvers via task-based runtimes

The ongoing hardware evolution exhibits an escalation in the number, as well as in the heterogeneity, of computing resources. The pressure to maintain reasonable levels of performance and portability forces 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 manycore architectures. In this paper, we study the benefits and limits of replacing the highly specialized internal scheduler of the PaStiX solver with two generic runtime systems: PaRSEC and StarPU. The tasks graph of the factorization step is made available to the two runtimes, providing them the opportunity to process and optimize its traversal in order to maximize the algorithm efficiency for the targeted hardware platform. A comparative study of the performance of the PaStiX solver on top of its native internal scheduler, PaRSEC, and StarPU frameworks, on different execution environments, is performed. The analysis highlights that these generic task-based runtimes achieve comparable results to the application-optimized embedded scheduler on homogeneous platforms. Furthermore, they are able to significantly speed up the solver on heterogeneous environments by taking advantage of the accelerators while hiding the complexity of their efficient manipulation from the programmer.Comment: Heterogeneity in Computing Workshop (2014

Towards seismic wave modeling on heterogeneous many-core architectures using task-based runtime system

International audienceUnderstanding three-dimensional seismic wave propagation in complex media remains one of the main challenges of quantitative seismology. Because of its simplicity and numerical efficiency, the finite-differences method is one of the standard techniques implemented to consider the elastodynamics equation. Additionally, this class of modelling heavily relies on parallel architectures in order to tackle large scale geometries including a detailed description of the physics. Last decade, significant efforts have been devoted towards efficient implementation of the finite-differences methods on emerging architectures. These contributions have demonstrated their efficiency leading to robust industrial applications. The growing representation of heterogeneous architectures combining general purpose multicore platforms and accelerators leads to redesign current parallel application. In this paper, we consider StarPU task-based runtime system in order to harness the power of heterogeneous CPU+GPU computing nodes. We detail our implementation and compare the performance obtained with the classical CPU or GPU only versions. Preliminary results demonstrate significant speedups in comparison with the best implementation suitable for homogeneous cores

Task-based programming for Seismic Imaging: Preliminary Results

International audienceThe 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 an homogenous multicore node and can exploit much more efficiently complex hardware such as a cache coherent Non Uniform Memory Access (ccNUMA) node or an Intel Xeon Phi accelerator

Dataflow Programming Paradigms for Computational Chemistry Methods

The transition to multicore and heterogeneous architectures has shaped the High Performance Computing (HPC) landscape over the past decades. With the increase in scale, complexity, and heterogeneity of modern HPC platforms, one of the grim challenges for traditional programming models is to sustain the expected performance at scale. By contrast, dataflow programming models have been growing in popularity as a means to deliver a good balance between performance and portability in the post-petascale era. This work introduces dataflow programming models for computational chemistry methods, and compares different dataflow executions in terms of programmability, resource utilization, and scalability. This effort is driven by computational chemistry applications, considering that they comprise one of the driving forces of HPC. In particular, many-body methods, such as Coupled Cluster methods (CC), which are the gold standard to compute energies in quantum chemistry, are of particular interest for the applied chemistry community. On that account, the latest development for CC methods is used as the primary vehicle for this research, but our effort is not limited to CC and can be applied across other application domains. Two programming paradigms for expressing CC methods into a dataflow form, in order to make them capable of utilizing task scheduling systems, are presented. Explicit dataflow, is the programming model where the dataflow is explicitly specified by the developer, is contrasted with implicit dataflow, where a task scheduling runtime derives the dataflow. An abstract model is derived to explore the limits of the different dataflow programming paradigms

Reordering Strategy for Blocking Optimization in Sparse Linear Solvers

International audienceSolving sparse linear systems is a problem that arises in many scientific applications, and sparse direct solvers are a time-consuming and key kernel for those applications and for more advanced solvers such as hybrid direct-iterative solvers. For this reason, optimizing their performance on modern architectures is critical. The preprocessing steps of sparse direct solvers—ordering and block-symbolic factorization—are two major steps that lead to a reduced amount of computation and memory and to a better task granularity to reach a good level of performance when using BLAS kernels. With the advent of GPUs, the granularity of the block computation has become more important than ever. In this paper, we present a reordering strategy that increases this block granularity. This strategy relies on block-symbolic factorization to refine the ordering produced by tools such as Metis or Scotch, but it does not impact the number of operations required to solve the problem. We integrate this algorithm in the PaStiX solver and show an important reduction of the number of off-diagonal blocks on a large spectrum of matrices. This improvement leads to an increase in efficiency of up to 20% on GPUs. 1. Introduction. Many scientific applications, such as electromagnetism, astrophysics , and computational fluid dynamics, use numerical models that require solving linear systems of the form Ax = b. In those problems, the matrix A can be considered as either dense (almost no zero entries) or sparse (mostly zero entries). Due to multiple structural and numerical differences that appear in those problems, many different solutions exist to solve them. In this paper, we focus on problems leading to sparse systems with a symmetric pattern and, more specifically, on direct methods which factorize the matrix A in LL t , LDL t , or LU , with L, D, and U, respectively, unit lower triangular, diagonal, and upper triangular according to the problem numerical properties. Those sparse matrices appear mostly when discretizing partial differential equations (PDEs) on two-(2D) and three-(3D) dimensional finite element or finite volume meshes. The main issue with such factorizations is the fill-in—zero entries becoming nonzero—that appears in the factorized form of A during the execution of the algorithm. If not correctly considered, the fill-in can transform the sparse matrix into a dense one which might not fit in memory. In this context, sparse direct solvers rely on two important preprocessing steps to reduce this fill-in and control where it appears. The first one finds a suitable ordering of the unknowns that aims at minimizing the fill-in to limit the memory overhead and floating point operations (Flops) required to complete the factorization. The problem is then transformed into (P AP t)(P x) = P b

Task-based FMM for heterogeneous architectures

International audienceHigh performance fast multipole method is crucial for the numerical simulation of many physical problems. In a previous study, we have shown that task-based fast multipole method provides the flexibility required to process a wide spectrum of particle distributions efficiently on multicore architectures. In this paper, we now show how such an approach can be extended to fully exploit heterogeneous platforms. For that, we design highly tuned graphics processing unit (GPU) versions of the two dominant operators P2P and M2L) as well as a scheduling strategy that dynamically decides which proportion of subsequent tasks is processed on regular CPU cores and on GPU accelerators. We assess our method with the StarPU runtime system for executing the resulting task flow on an Intel X5650 Nehalem multicore processor possibly enhanced with one, two, or three Nvidia Fermi M2070 or M2090 GPUs (Santa Clara, CA, USA). A detailed experimental study on two 30 million particle distributions (a cube and an ellipsoid) shows that the resulting software consistently achieves high performance across architectures

Stratégie de renumérotation pour optimiser la granularité des calculs dans la résolution des systèmes linéaires creux

Solving sparse linear systems is a problem that arises in many scientific applications, and sparse direct solvers are a time consuming and key kernel for those applications and for more advanced solvers such as hybrid direct-iterative solvers. For this reason, optimizing their performance on modern architectures is critical. The preprocessing steps of sparse direct solvers, ordering and block-symbolic factorization, are two major steps that lead to a reduced amount of computation and memory and to a better task granularity to reach a good level of performance when using BLAS kernels. With the advent of GPUs, the granularity of the block computation became more important than ever. In this paper, we present a reordering strategy that increases this block granularity. This strategy relies on the block-symbolic factorization to refine the ordering produced by tools such as Metis or Scotch, but it does not impact the number of operations required to solve the problem. We integrate this algorithm in the PaStiX solver and show an important reduction of the number of off-diagonal blocks on a large spectrum of matrices. This improvement leads to an increase in efficiency of up to 20% on GPUs.De nombreuses applications scientifiques recquièrent La résolution de large systèmes linéaires creux qui est généralement l'étape la plus comnsommatrice de ressources, que ce soit en temps de calculs ou mémoire. Il est donc primordial d'optimiser les bibliothèques de résolution de ces problèmes sur les architectures modernes. Nous présentons dans ce documents une technique de renumérotation des inconnues qui permet d'élargir la granularité des calculs afin de mieux exploiter les accélérateurs, comme les GPUs, dans ces bibliothèques. Cet algorithme s'appuie sur les renumérotations calculées par des outils comme Metis ou Scotch sans changer le nombre d'opérations de la factorisation numérique. Nous présentons les résultats de l'intégration de cette stratégie dans la bibliothèque architectures hétérogènes

Task-based FMM for heterogeneous architectures

High performance \FMM is crucial for the numerical simulation of many physical problems. In a previous study~\cite{Agullo2013}, we have shown that task-based \FMM provides the flexibility required to process a wide spectrum of particle distributions efficiently on multicore architectures. In this paper, we now show how such an approach can be extended to fully exploit heterogeneous platforms. For that, we design highly tuned GPU versions of the two dominant operators (P2P and M2L) as well as a scheduling strategy that dynamically decides which proportion of subsequent tasks are processed on regular CPU cores and on GPU accelerators. We assess our method with the StarPU runtime system for executing the resulting task flow on an Intel X5650 Nehalem multicore processor possibly enhanced with one, two or three Nvidia Fermi M2070 or M2090 GPUs. A detailed experimental study on two 30 million particle distributions (a cube and an ellipsoid) shows that the resulting software consistently achieves high performance across architectures.Développer une méthode des Multipôles Rapide (FMM) à haute performance est cruciale pour des simulations numériques dans beaucoup de problèmes physiques. Dans une étude précédente~\cite{Agullo2013}, nous avons montré que l'utilisation d'un paradigme à base de tâches fournit la flexibilité nécessaire pour traiter efficacement un large spectre de distributions de particules sur des architectures homogènes. Dans ce document, nous montrons maintenant comment une telle approche peut être étendue pour exploiter toutes les unités de calculs (CPU et GPU) des machines hétérogènes. Pour cela, nous présentons une version optimisée pour GPU des deux opérateurs dominants (P2P et M2L) de la FMM ainsi qu'une stratégie d'ordonnancement qui décide dynamiquement quelle proportion de tâches est traitée par les cœurs CPU et par des accélérateurs GPU. Nous évaluons notre méthode avec le moteur d'exécution StarPU pour exécuter le flot de tâches résultant sur un processeur Intel X5650 Nehalem augmenté avec un, deux ou trois Nvidia Fermi M2070 ou M2090. Une étude expérimentale détaillée sur deux distributions de 30 millions de particules (un cube et un ellipsoïde) montre que nous obtenons des résultats performants sur cette architecture

A Visual Performance Analysis Framework for Task-based Parallel Applications running on Hybrid Clusters

International audienceProgramming paradigms in High-Performance Computing have been shifting towards task-based models which are capable of adapting readily to heterogeneous and scalable supercomputers. The performance of task-based application heavily depends on the runtime scheduling heuristics and on its ability to exploit computing and communication resources. Unfortunately, the traditional performance analysis strategies are unfit to fully understand task-based runtime systems and applications: they expect a regular behavior with communication and computation phases, while task-based applications demonstrate no clear phases. Moreover, the finer granularity of task-based applications typically induces a stochastic behavior that leads to irregular structures that are difficult to analyze. Furthermore, the combination of application structure, scheduler, and hardware information is generally essential to understand performance issues. This paper presents a flexible framework that enables one to combine several sources of information and to create custom visualization panels allowing to understand and pinpoint performance problems incurred by bad scheduling decisions in task-based applications. Three case-studies using StarPU-MPI, a task-based multi-node runtime system, are detailed to show how our framework can be used to study the performance of the well-known Cholesky factorization. Performance improvements include a better task partitioning among the multi-(GPU,core) to get closer to theoretical lower bounds, improved MPI pipelining in multi-(node,core,GPU) to reduce the slow start, and changes in the runtime system to increase MPI bandwidth, with gains of up to 13% in the total makespan