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

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

Pipelining the Fast Multipole Method over a Runtime System

Fast Multipole Methods (FMM) are a fundamental operation for the simulation of many physical problems. The high performance design of such methods usually requires to carefully tune the algorithm for both the targeted physics and the hardware. In this paper, we propose a new approach that achieves high performance across architectures. Our method consists of expressing the FMM algorithm as a task flow and employing a state-of-the-art runtime system, StarPU, in order to process the tasks on the different processing units. We carefully design the task flow, the mathematical operators, their Central Processing Unit (CPU) and Graphics Processing Unit (GPU) implementations, as well as scheduling schemes. We compute potentials and forces of 200 million particles in 48.7 seconds on a homogeneous 160 cores SGI Altix UV 100 and of 38 million particles in 13.34 seconds on a heterogeneous 12 cores Intel Nehalem processor enhanced with 3 Nvidia M2090 Fermi GPUs.Comment: No. RR-7981 (2012

COLAB:A Collaborative Multi-factor Scheduler for Asymmetric Multicore Processors

Funding: Partially funded by the UK EPSRC grants Discovery: Pattern Discovery and Program Shaping for Many-core Systems (EP/P020631/1) and ABC: Adaptive Brokerage for Cloud (EP/R010528/1); Royal Academy of Engineering under the Research Fellowship scheme.Increasingly prevalent asymmetric multicore processors (AMP) are necessary for delivering performance in the era of limited power budget and dark silicon. However, the software fails to use them efficiently. OS schedulers, in particular, handle asymmetry only under restricted scenarios. We have efficient symmetric schedulers, efficient asymmetric schedulers for single-threaded workloads, and efficient asymmetric schedulers for single program workloads. What we do not have is a scheduler that can handle all runtime factors affecting AMP for multi-threaded multi-programmed workloads. This paper introduces the first general purpose asymmetry-aware scheduler for multi-threaded multi-programmed workloads. It estimates the performance of each thread on each type of core and identifies communication patterns and bottleneck threads. The scheduler then makes coordinated core assignment and thread selection decisions that still provide each application its fair share of the processor's time. We evaluate our approach using the GEM5 simulator on four distinct big.LITTLE configurations and 26 mixed workloads composed of PARSEC and SPLASH2 benchmarks. Compared to the state-of-the art Linux CFS and AMP-aware schedulers, we demonstrate performance gains of up to 25% and 5% to 15% on average depending on the hardware setup.Postprin

Geometry-Oblivious FMM for Compressing Dense SPD Matrices

We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, "compression," of an arbitrary dense symmetric positive definite (SPD) matrix. For many applications, GOFMM enables an approximate matrix-vector multiplication in $N \log N$ or even $N$ time, where $N$ is the matrix size. Compression requires $N \log N$ storage and work. In general, our scheme belongs to the family of hierarchical matrix approximation methods. In particular, it generalizes the fast multipole method (FMM) to a purely algebraic setting by only requiring the ability to sample matrix entries. Neither geometric information (i.e., point coordinates) nor knowledge of how the matrix entries have been generated is required, thus the term "geometry-oblivious." Also, we introduce a shared-memory parallel scheme for hierarchical matrix computations that reduces synchronization barriers. We present results on the Intel Knights Landing and Haswell architectures, and on the NVIDIA Pascal architecture for a variety of matrices.Comment: 13 pages, accepted by SC'1