Scheduling data flow program in xkaapi: A new affinity based Algorithm for Heterogeneous Architectures

Efficient implementations of parallel applications on heterogeneous hybrid architectures require a careful balance between computations and communications with accelerator devices. Even if most of the communication time can be overlapped by computations, it is essential to reduce the total volume of communicated data. The literature therefore abounds with ad-hoc methods to reach that balance, but that are architecture and application dependent. We propose here a generic mechanism to automatically optimize the scheduling between CPUs and GPUs, and compare two strategies within this mechanism: the classical Heterogeneous Earliest Finish Time (HEFT) algorithm and our new, parametrized, Distributed Affinity Dual Approximation algorithm (DADA), which consists in grouping the tasks by affinity before running a fast dual approximation. We ran experiments on a heterogeneous parallel machine with six CPU cores and eight NVIDIA Fermi GPUs. Three standard dense linear algebra kernels from the PLASMA library have been ported on top of the Xkaapi runtime. We report their performances. It results that HEFT and DADA perform well for various experimental conditions, but that DADA performs better for larger systems and number of GPUs, and, in most cases, generates much lower data transfers than HEFT to achieve the same performance

Batched Linear Algebra Problems on GPU Accelerators

The emergence of multicore and heterogeneous architectures requires many linear algebra algorithms to be redesigned to take advantage of the accelerators, such as GPUs. A particularly challenging class of problems, arising in numerous applications, involves the use of linear algebra operations on many small-sized matrices. The size of these matrices is usually the same, up to a few hundred. The number of them can be thousands, even millions. Compared to large matrix problems with more data parallel computation that are well suited on GPUs, the challenges of small matrix problems lie in the low computing intensity, the large sequential operation fractions, and the big PCI-E overhead. These challenges entail redesigning the algorithms instead of merely porting the current LAPACK algorithms. We consider two classes of problems. The first is linear systems with one-sided factorizations (LU, QR, and Cholesky) and their solver, forward and backward substitution. The second is a two-sided Householder bi-diagonalization. They are challenging to develop and are highly demanded in applications. Our main efforts focus on the same-sized problems. Variable-sized problems are also considered, though to a lesser extent. Our contributions can be summarized as follows. First, we formulated a batched linear algebra framework to solve many data-parallel, small-sized problems/tasks. Second, we redesigned a set of fundamental linear algebra algorithms for high- performance, batched execution on GPU accelerators. Third, we designed batched BLAS (Basic Linear Algebra Subprograms) and proposed innovative optimization techniques for high-performance computation. Fourth, we illustrated the batched methodology on real-world applications as in the case of scaling a CFD application up to 4096 nodes on the Titan supercomputer at Oak Ridge National Laboratory (ORNL). Finally, we demonstrated the power, energy and time efficiency of using accelerators as compared to CPUs. Our solutions achieved large speedups and high energy efficiency compared to related routines in CUBLAS on NVIDIA GPUs and MKL on Intel Sandy-Bridge multicore CPUs. The modern accelerators are all Single-Instruction Multiple-Thread (SIMT) architectures. Our solutions and methods are based on NVIDIA GPUs and can be extended to other accelerators, such as the Intel Xeon Phi and AMD GPUs based on OpenCL

Extensions of Task-based Runtime for High Performance Dense Linear Algebra Applications

On the road to exascale computing, the gap between hardware peak performance and application performance is increasing as system scale, chip density and inherent complexity of modern supercomputers are expanding. Even if we put aside the difficulty to express algorithmic parallelism and to efficiently execute applications at large scale, other open questions remain. The ever-growing scale of modern supercomputers induces a fast decline of the Mean Time To Failure. A generic, low-overhead, resilient extension becomes a desired aptitude for any programming paradigm. This dissertation addresses these two critical issues, designing an efficient unified linear algebra development environment using a task-based runtime, and extending a task-based runtime with fault tolerant capabilities to build a generic framework providing both soft and hard error resilience to task-based programming paradigm. To bridge the gap between hardware peak performance and application perfor- mance, a unified programming model is designed to take advantage of a lightweight task-based runtime to manage the resource-specific workload, and to control the data ow and parallel execution of tasks. Under this unified development, linear algebra tasks are abstracted across different underlying heterogeneous resources, including multicore CPUs, GPUs and Intel Xeon Phi coprocessors. Performance portability is guaranteed and this programming model is adapted to a wide range of accelerators, supporting both shared and distributed-memory environments. To solve the resilient challenges on large scale systems, fault tolerant mechanisms are designed for a task-based runtime to protect applications against both soft and hard errors. For soft errors, three additions to a task-based runtime are explored. The first recovers the application by re-executing minimum number of tasks, the second logs intermediary data between tasks to minimize the necessary re-execution, while the last one takes advantage of algorithmic properties to recover the data without re- execution. For hard errors, we propose two generic approaches, which augment the data logging mechanism for soft errors. The first utilizes non-volatile storage device to save logged data, while the second saves local logged data on a remote node to protect against node failure. Experimental results have confirmed that our soft and hard error fault tolerant mechanisms exhibit the expected correctness and efficiency

Hierarchical DAG Scheduling for Hybrid Distributed Systems

International audienceAccelerator-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

Task-based multifrontal QR solver for heterogeneous architectures

Afin de s'adapter aux architectures multicoeurs et aux machines de plus en plus complexes, les modèles de programmations basés sur un parallélisme de tâche ont gagné en popularité dans la communauté du calcul scientifique haute performance. Les moteurs d'exécution fournissent une interface de programmation qui correspond à ce paradigme ainsi que des outils pour l'ordonnancement des tâches qui définissent l'application. Dans cette étude, nous explorons la conception de solveurs directes creux à base de tâches, qui représentent une charge de travail extrêmement irrégulière, avec des tâches de granularités et de caractéristiques différentes ainsi qu'une consommation mémoire variable, au-dessus d'un moteur d'exécution. Dans le cadre du solveur qr mumps, nous montrons dans un premier temps la viabilité et l'efficacité de notre approche avec l'implémentation d'une méthode multifrontale pour la factorisation de matrices creuses, en se basant sur le modèle de programmation parallèle appelé "flux de tâches séquentielles" (Sequential Task Flow). Cette approche, nous a ensuite permis de développer des fonctionnalités telles que l'intégration de noyaux dense de factorisation de type "minimisation de cAfin de s'adapter aux architectures multicoeurs et aux machines de plus en plus complexes, les modèles de programmations basés sur un parallélisme de tâche ont gagné en popularité dans la communauté du calcul scientifique haute performance. Les moteurs d'exécution fournissent une interface de programmation qui correspond à ce paradigme ainsi que des outils pour l'ordonnancement des tâches qui définissent l'application. Dans cette étude, nous explorons la conception de solveurs directes creux à base de tâches, qui représentent une charge de travail extrêmement irrégulière, avec des tâches de granularités et de caractéristiques différentes ainsi qu'une consommation mémoire variable, au-dessus d'un moteur d'exécution. Dans le cadre du solveur qr mumps, nous montrons dans un premier temps la viabilité et l'efficacité de notre approche avec l'implémentation d'une méthode multifrontale pour la factorisation de matrices creuses, en se basant sur le modèle de programmation parallèle appelé "flux de tâches séquentielles" (Sequential Task Flow). Cette approche, nous a ensuite permis de développer des fonctionnalités telles que l'intégration de noyaux dense de factorisation de type "minimisation de cAfin de s'adapter aux architectures multicoeurs et aux machines de plus en plus complexes, les modèles de programmations basés sur un parallélisme de tâche ont gagné en popularité dans la communauté du calcul scientifique haute performance. Les moteurs d'exécution fournissent une interface de programmation qui correspond à ce paradigme ainsi que des outils pour l'ordonnancement des tâches qui définissent l'application. !!br0ken!!ommunications" (Communication Avoiding) dans la méthode multifrontale, permettant d'améliorer considérablement la scalabilité du solveur par rapport a l'approche original utilisée dans qr mumps. Nous introduisons également un algorithme d'ordonnancement sous contraintes mémoire au sein de notre solveur, exploitable dans le cas des architectures multicoeur, réduisant largement la consommation mémoire de la méthode multifrontale QR avec un impacte négligeable sur les performances. En utilisant le modèle présenté ci-dessus, nous visons ensuite l'exploitation des architectures hétérogènes pour lesquelles la granularité des tâches ainsi les stratégies l'ordonnancement sont cruciales pour profiter de la puissance de ces architectures. Nous proposons, dans le cadre de la méthode multifrontale, un partitionnement hiérarchique des données ainsi qu'un algorithme d'ordonnancement capable d'exploiter l'hétérogénéité des ressources. Enfin, nous présentons une étude sur la reproductibilité de l'exécution parallèle de notre problème et nous montrons également l'utilisation d'un modèle de programmation alternatif pour l'implémentation de la méthode multifrontale. L'ensemble des résultats expérimentaux présentés dans cette étude sont évalués avec une analyse détaillée des performance que nous proposons au début de cette étude. Cette analyse de performance permet de mesurer l'impacte de plusieurs effets identifiés sur la scalabilité et la performance de nos algorithmes et nous aide ainsi à comprendre pleinement les résultats obtenu lors des tests effectués avec notre solveur.To face the advent of multicore processors and the ever increasing complexity of hardware architectures, programming models based on DAG parallelism regained popularity in the high performance, scientific computing community. Modern runtime systems offer a programming interface that complies with this paradigm and powerful engines for scheduling the tasks into which the application is decomposed. These tools have already proved their effectiveness on a number of dense linear algebra applications. In this study we investigate the design of task-based sparse direct solvers which constitute extremely irregular workloads, with tasks of different granularities and characteristics with variable memory consumption on top of runtime systems. In the context of the qr mumps solver, we prove the usability and effectiveness of our approach with the implementation of a sparse matrix multifrontal factorization based on a Sequential Task Flow parallel programming model. Using this programming model, we developed features such as the integration of dense 2D Communication Avoiding algorithms in the multifrontal method allowing for better scalability compared to the original approach used in qr mumps. In addition we introduced a memory-aware algorithm to control the memory behaviour of our solver and show, in the context of multicore architectures, an important reduction of the memory footprint for the multifrontal QR factorization with a small impact on performance. Following this approach, we move to heterogeneous architectures where task granularity and scheduling strategies are critical to achieve performance. We present, for the multifrontal method, a hierarchical strategy for data partitioning and a scheduling algorithm capable of handling the heterogeneity of resources. Finally we present a study on the reproducibility of executions and the use of alternative programming models for the implementation of the multifrontal method. All the experimental results presented in this study are evaluated with a detailed performance analysis measuring the impact of several identified effects on the performance and scalability. Thanks to this original analysis, presented in the first part of this study, we are capable of fully understanding the results obtained with our solver

Solveur multifrontal QR à base de tâches pour architectures hétérogènes

To face the advent of multicore processors and the ever increasing complexity of hardware architectures, programming models based on DAG parallelism regained popularity in the high performance, scientific computing community. Modern runtime systems offer a programming interface that complies with this paradigm and powerful engines for scheduling the tasks into which the application is decomposed. These tools have already proved their effectiveness on a number of dense linear algebra applications. In this study we investigate the design of task-based sparse direct solvers which constitute extremely irregular workloads, with tasks of different granularities and characteristics with variable memory consumption on top of runtime systems. In the context of the qr mumps solver, we prove the usability and effectiveness of our approach with the implementation of a sparse matrix multifrontal factorization based on a Sequential Task Flow parallel programming model. Using this programming model, we developed features such as the integration of dense 2D Communication Avoiding algorithms in the multifrontal method allowing for better scalability compared to the original approach used in qr mumps. In addition we introduced a memory-aware algorithm to control the memory behaviour of our solver and show, in the context of multicore architectures, an important reduction of the memory footprint for the multifrontal QR factorization with a small impact on performance. Following this approach, we move to heterogeneous architectures where task granularity and scheduling strategies are critical to achieve performance. We present, for the multifrontal method, a hierarchical strategy for data partitioning and a scheduling algorithm capable of handling the heterogeneity of resources. Finally we present a study on the reproducibility of executions and the use of alternative programming models for the implementation of the multifrontal method. All the experimental results presented in this study are evaluated with a detailed performance analysis measuring the impact of several identified effects on the performance and scalability. Thanks to this original analysis, presented in the first part of this study, we are capable of fully understanding the results obtained with our solver.Afin de s'adapter aux architectures multicoeurs et aux machines de plus en plus complexes, les modèles de programmations basés sur un parallélisme de tâche ont gagné en popularité dans la communauté du calcul scientifique haute performance. Les moteurs d'exécution fournissent une interface de programmation qui correspond à ce paradigme ainsi que des outils pour l'ordonnancement des tâches qui définissent l'application. Dans cette étude, nous explorons la conception de solveurs directes creux à base de tâches, qui représentent une charge de travail extrêmement irrégulière, avec des tâches de granularités et de caractéristiques différentes ainsi qu'une consommation mémoire variable, au-dessus d'un moteur d'exécution. Dans le cadre du solveur qr mumps, nous montrons dans un premier temps la viabilité et l'efficacité de notre approche avec l'implémentation d'une méthode multifrontale pour la factorisation de matrices creuses, en se basant sur le modèle de programmation parallèle appelé "flux de tâches séquentielles" (Sequential Task Flow). Cette approche, nous a ensuite permis de développer des fonctionnalités telles que l'intégration de noyaux dense de factorisation de type "minimisation de cAfin de s'adapter aux architectures multicoeurs et aux machines de plus en plus complexes, les modèles de programmations basés sur un parallélisme de tâche ont gagné en popularité dans la communauté du calcul scientifique haute performance. Les moteurs d'exécution fournissent une interface de programmation qui correspond à ce paradigme ainsi que des outils pour l'ordonnancement des tâches qui définissent l'application. Dans cette étude, nous explorons la conception de solveurs directes creux à base de tâches, qui représentent une charge de travail extrêmement irrégulière, avec des tâches de granularités et de caractéristiques différentes ainsi qu'une consommation mémoire variable, au-dessus d'un moteur d'exécution. Dans le cadre du solveur qr mumps, nous montrons dans un premier temps la viabilité et l'efficacité de notre approche avec l'implémentation d'une méthode multifrontale pour la factorisation de matrices creuses, en se basant sur le modèle de programmation parallèle appelé "flux de tâches séquentielles" (Sequential Task Flow). Cette approche, nous a ensuite permis de développer des fonctionnalités telles que l'intégration de noyaux dense de factorisation de type "minimisation de cAfin de s'adapter aux architectures multicoeurs et aux machines de plus en plus complexes, les modèles de programmations basés sur un parallélisme de tâche ont gagné en popularité dans la communauté du calcul scientifique haute performance. Les moteurs d'exécution fournissent une interface de programmation qui correspond à ce paradigme ainsi que des outils pour l'ordonnancement des tâches qui définissent l'application

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