Variable batched DGEMM

Many scientific applications are in need to solve a high number of small-size independent problems. These individual problems do not provide enough parallelism and then, these must be computed as a batch. Today, vendors such as Intel and NVIDIA are developing their own suite of batch routines. Although most of the works focus on computing batches of fixed size, in real applications we can not assume a uniform size for all set of problems. We explore and analyze different strategies based on parallel for, task and taskloop OpenMP pragmas. Although these strategies are straightforward from a programmer's point of view, they have a different impact on performance. We also analyze a new prototype provided by Intel (MKL), which deals with batch operations (cblas dgemm batch). We propose a new approach called grouping. It basically groups a set of problems until filling a limit in terms of memory occupancy or number of operations. In this way, groups composed by different number of problems are distributed on cores, achieving a more balanced distribution in terms of computational cost. This strategy is able to be up to 6× faster than the Intel (MKL) batch routineThis project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 720270 (HBP SGA1), from the Spanish Ministry of Economy and Competitiveness under the project Computacion de Altas Prestaciones VII (TIN2015-65316-P) and the Departament d’Innovacio, Universitats i Empresa de la Generalitat de Catalunya, under project MPEXPAR: Models de Programacio i Entorns d’Execucio Paral·lels (2014-SGR-1051).Peer ReviewedPostprint (author's final draft

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

Lecture 11: The Road to Exascale and Legacy Software for Dense Linear Algebra

In this talk, we will look at the current state of high performance computing and look at the next stage of extreme computing. With extreme computing, there will be fundamental changes in the character of floating point arithmetic and data movement. In this talk, we will look at how extreme-scale computing has caused algorithm and software developers to change their way of thinking on implementing and program-specific applications

The ESCAPE project : Energy-efficient Scalable Algorithms for Weather Prediction at Exascale

In the simulation of complex multi-scale flows arising in weather and climate modelling, one of the biggest challenges is to satisfy strict service requirements in terms of time to solution and to satisfy budgetary constraints in terms of energy to solution, without compromising the accuracy and stability of the application. These simulations require algorithms that minimise the energy footprint along with the time required to produce a solution, maintain the physically required level of accuracy, are numerically stable, and are resilient in case of hardware failure. The European Centre for Medium-Range Weather Forecasts (ECMWF) led the ESCAPE (Energy-efficient Scalable Algorithms for Weather Prediction at Exascale) project, funded by Horizon 2020 (H2020) under the FET-HPC (Future and Emerging Technologies in High Performance Computing) initiative. The goal of ESCAPE was to develop a sustainable strategy to evolve weather and climate prediction models to next-generation computing technologies. The project partners incorporate the expertise of leading European regional forecasting consortia, university research, experienced high-performance computing centres, and hardware vendors. This paper presents an overview of the ESCAPE strategy: (i) identify domain-specific key algorithmic motifs in weather prediction and climate models (which we term Weather & Climate Dwarfs), (ii) categorise them in terms of computational and communication patterns while (iii) adapting them to different hardware architectures with alternative programming models, (iv) analyse the challenges in optimising, and (v) find alternative algorithms for the same scheme. The participating weather prediction models are the following: IFS (Integrated Forecasting System); ALARO, a combination of AROME (Application de la Recherche a l'Operationnel a Meso-Echelle) and ALADIN (Aire Limitee Adaptation Dynamique Developpement International); and COSMO-EULAG, a combination of COSMO (Consortium for Small-scale Modeling) and EULAG (Eulerian and semi-Lagrangian fluid solver). For many of the weather and climate dwarfs ESCAPE provides prototype implementations on different hardware architectures (mainly Intel Skylake CPUs, NVIDIA GPUs, Intel Xeon Phi, Optalysys optical processor) with different programming models. The spectral transform dwarf represents a detailed example of the co-design cycle of an ESCAPE dwarf. The dwarf concept has proven to be extremely useful for the rapid prototyping of alternative algorithms and their interaction with hardware; e.g. the use of a domain-specific language (DSL). Manual adaptations have led to substantial accelerations of key algorithms in numerical weather prediction (NWP) but are not a general recipe for the performance portability of complex NWP models. Existing DSLs are found to require further evolution but are promising tools for achieving the latter. Measurements of energy and time to solution suggest that a future focus needs to be on exploiting the simultaneous use of all available resources in hybrid CPU-GPU arrangements

Tasking in accelerators: performance evaluation

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this work, we analyze the implications and results of implementing dynamic parallelism, concurrent kernels and CUDA Graphs to solve task-oriented problems. As a benchmark we propose three different methods for solving DGEMM operation on tiled-matrices; which might be the most popular benchmark for performance analysis. For the algorithms that we study, we present significant differences in terms of data dependencies, synchronization and granularity. The main contribution of this work is determining which of the previous approaches work better for having multiple task running concurrently in a single GPU, as well as stating the main limitations and benefits of every technique. Using dynamic parallelism and CUDA Streams we were able to achieve up to 30% speedups and for CUDA Graph API up to 25x acceleration outperforming state of the art results.This project has received funding from the EPEEC project from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 801051, from the Spanish Ministry of Economy and Competitiveness under the project Computación de Altas Prestaciones VII ( TIN2015-65316-P ) and the Departament d’Innovació, Universitats i Empresa de la Generalitat de Catalunya, under project MPEXPAR: Models de Pro-gramació i Entorns d’Execució Paral·lels (2014-SGR-1051 ). Finally, this project also received funding from the Spanish Ministry of Economy and Competitiveness under the Juan de la Cierva Grant Agreement No IJCI-2017-33511 , and from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska Curie grant agreement No. 749516 .Peer ReviewedPostprint (author's final draft

Accelerating Correlated Quantum Chemistry Calculations Using Graphical Processing Units and a Mixed Precision Matrix Multiplication Library

Two new tools for the acceleration of computational chemistry codes using graphical processing units (GPUs) are presented. First, we propose a general black-box approach for the efficient GPU acceleration of matrix−matrix multiplications where the matrix size is too large for the whole computation to be held in the GPU’s onboard memory. Second, we show how to improve the accuracy of matrix multiplications when using only single-precision GPU devices by proposing a heterogeneous computing model, whereby single- and double-precision operations are evaluated in a mixed fashion on the GPU and central processing unit, respectively. The utility of the library is illustrated for quantum chemistry with application to the acceleration of resolution-of-the-identity second-order Møller−Plesset perturbation theory calculations for molecules, which we were previously unable to treat. In particular, for the 168-atom valinomycin molecule in a cc-pVDZ basis set, we observed speedups of 13.8, 7.8, and 10.1 times for single-, double- and mixed-precision general matrix multiply (SGEMM, DGEMM, and MGEMM), respectively. The corresponding errors in the correlation energy were reduced from −10.0 to −1.2 kcal mol$^{-1}$ for SGEMM and MGEMM, respectively, while higher accuracy can be easily achieved with a different choice of cutoff parameter.Chemistry and Chemical Biolog

Fine-Grained Scheduling for Containerized HPC Workloads in Kubernetes Clusters

Containerization technology offers lightweight OS-level virtualization, and enables portability, reproducibility, and flexibility by packing applications with low performance overhead and low effort to maintain and scale them. Moreover, container orchestrators (e.g., Kubernetes) are widely used in the Cloud to manage large clusters running many containerized applications. However, scheduling policies that consider the performance nuances of containerized High Performance Computing (HPC) workloads have not been well-explored yet. This paper conducts fine-grained scheduling policies for containerized HPC workloads in Kubernetes clusters, focusing especially on partitioning each job into a suitable multi-container deployment according to the application profile. We implement our scheduling schemes on different layers of management (application and infrastructure), so that each component has its own focus and algorithms but still collaborates with others. Our results show that our fine-grained scheduling policies outperform baseline and baseline with CPU/memory affinity enabled policies, reducing the overall response time by 35% and 19%, respectively, and also improving the makespan by 34% and 11%, respectively. They also provide better usability and flexibility to specify HPC workloads than other comparable HPC Cloud frameworks, while providing better scheduling efficiency thanks to their multi-layered approach.Comment: HPCC202

The ESCAPE project: Energy-efficient Scalable Algorithms for Weather Prediction at Exascale

Abstract. In the simulation of complex multi-scale flows arising in weather and climate modelling, one of the biggest challenges is to satisfy strict service requirements in terms of time to solution and to satisfy budgetary constraints in terms of energy to solution, without compromising the accuracy and stability of the application. These simulations require algorithms that minimise the energy footprint along with the time required to produce a solution, maintain the physically required level of accuracy, are numerically stable, and are resilient in case of hardware failure. The European Centre for Medium-Range Weather Forecasts (ECMWF) led the ESCAPE (Energy-efficient Scalable Algorithms for Weather Prediction at Exascale) project, funded by Horizon 2020 (H2020) under the FET-HPC (Future and Emerging Technologies in High Performance Computing) initiative. The goal of ESCAPE was to develop a sustainable strategy to evolve weather and climate prediction models to next-generation computing technologies. The project partners incorporate the expertise of leading European regional forecasting consortia, university research, experienced high-performance computing centres, and hardware vendors. This paper presents an overview of the ESCAPE strategy: (i) identify domain-specific key algorithmic motifs in weather prediction and climate models (which we term Weather & Climate Dwarfs), (ii) categorise them in terms of computational and communication patterns while (iii) adapting them to different hardware architectures with alternative programming models, (iv) analyse the challenges in optimising, and (v) find alternative algorithms for the same scheme. The participating weather prediction models are the following: IFS (Integrated Forecasting System); ALARO, a combination of AROME (Application de la Recherche à l'Opérationnel à Meso-Echelle) and ALADIN (Aire Limitée Adaptation Dynamique Développement International); and COSMO–EULAG, a combination of COSMO (Consortium for Small-scale Modeling) and EULAG (Eulerian and semi-Lagrangian fluid solver). For many of the weather and climate dwarfs ESCAPE provides prototype implementations on different hardware architectures (mainly Intel Skylake CPUs, NVIDIA GPUs, Intel Xeon Phi, Optalysys optical processor) with different programming models. The spectral transform dwarf represents a detailed example of the co-design cycle of an ESCAPE dwarf. The dwarf concept has proven to be extremely useful for the rapid prototyping of alternative algorithms and their interaction with hardware; e.g. the use of a domain-specific language (DSL). Manual adaptations have led to substantial accelerations of key algorithms in numerical weather prediction (NWP) but are not a general recipe for the performance portability of complex NWP models. Existing DSLs are found to require further evolution but are promising tools for achieving the latter. Measurements of energy and time to solution suggest that a future focus needs to be on exploiting the simultaneous use of all available resources in hybrid CPU–GPU arrangements

Evaluation of two topology-aware heuristics on level-3 BLAS library for multi-GPU platforms

International audienceNowadays GPUs have dominated the market considering the computing/power metric and numerous research works have provided Basic Linear Algebra Subprograms implementations accelerated on GPUs. Several software libraries have been developed for exploiting performance of systems with accelerators, but the real performance may be far from the platform peak performance with multiple GPUs. This paper presents two runtime heuristics to gain in performance when task based programs are performed on heterogeneous architecture such as multi-GPU systems. The first is a topology-aware policy to takes into account the heterogeneity of the high speed links that interconnect GPUs. The second is an optimistic heuristic that favor communication between devices. These have been implemented in the XKBLAS library BLAS-3 library. We made experiments on a NVIDIA DGX-1 with up to 8 GPUs V100 on a set of Basic Linear Algebra Subroutines. Experimental results on kernels showed that XKBlas outperformed most implementations including the overhead of creation and scheduling of dynamic tasks