Towards an auto-tuned and task-based SpMV (LASs Library)

We present a novel approach to parallelize the SpMV kernel included in LASs (Linear Algebra routines on OmpSs) library, after a deep review and analysis of several well-known approaches. LASs is based on OmpSs, a task-based runtime that extends OpenMP directives, providing more flexibility to apply new strategies. Based on tasking and nesting, with the aim of improving the workload imbalance inherent to the SpMV operation, we present a strategy especially useful for highly imbalanced input matrices. In this approach, the number of created tasks is dynamically decided in order to maximize the use of the resources of the platform. Throughout this paper, SpMV behavior depending on the selected strategy (state of the art and proposed strategies) is deeply analyzed, setting in this way the base for a future auto-tunable code that is able to select the most suitable approach depending on the input matrix. The experiments of this work were carried out for a set of 12 matrices from the Suite Sparse Matrix Collection, all of them with different characteristics regarding their sparsity. The experiments of this work were performed on a node of Marenostrum 4 supercomputer (with two sockets Intel Xeon, 24 cores each) and on a node of Dibona cluster (using one ARM ThunderX2 socket with 32 cores). Our tests show that, for Intel Xeon, the best parallelization strategy reduces the execution time of the reference MKL multi-threaded version up to 67%. On ARM ThunderX2, the reduction is up to 56% with respect to the OmpSs parallel reference.This project has received funding from the Spanish Ministry of Economy and Competitiveness under the project Computación de Altas Prestaciones VII (TIN2015- 65316-P), the Departament d’Innovació, Universitats i Empresa de la Generalitat de Catalunya, under project MPEXPAR: Models de Programació i Entorns d’Execució Parallels (2014-SGR-1051), and the Juan de la Cierva Grant Agreement No IJCI-2017- 33511, and the Spanish Ministry of Science and Innovation under the project Heterogeneidad y especialización en la era post-Moore (RTI2018-093684-BI00). We also acknowledge the funding provided by Fujitsu under the BSC-Fujitsu joint project: Math Libraries Migration and OptimizationPeer ReviewedPostprint (author's final draft

sLASs: a fully automatic auto-tuned linear algebra library based on OpenMP extensions implemented in OmpSs (LASs Library)

© 2019 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this work we have implemented a novel Linear Algebra Library on top of the task-based runtime OmpSs-2. We have used some of the most advanced OmpSs-2 features; weak dependencies and regions, together with the final clause for the implementation of auto-tunable code for the BLAS-3 trsm routine and the LAPACK routines npgetrf and npgesv. All these implementations are part of the first prototype of sLASs library, a novel library for auto-tunable codes for linear algebra operations based on LASs library. In all these cases, the use of the OmpSs-2 features presents an improvement in terms of execution time against other reference libraries such as, the original LASs library, PLASMA, ATLAS and Intel MKL. These codes are able to reduce the execution time in about 18% on big matrices, by increasing the IPC on gemm and reducing the time of task instantiation. For a few medium matrices, benefits are also seen. For small matrices and a subset of medium matrices, specific optimizations that allow to increase the degree of parallelism in both, gemm and trsm tasks, are applied. This strategy achieves an increment in performance of up to 40%.This project has received funding from the Spanish Ministry of Economy and Competitiveness, Spain under the project Computación de Altas Prestaciones VII (TIN2015- 65316-P), the Departament d’Innovació, Universitats i Empresa de la Generalitat de Catalunya, Spain, under project MPEXPAR: Models de Programació i Entorns d’Execució Parallels (2014-SGR-1051), and the Juan de la Cierva Grant Agreement No IJCI-2017- 33511. We also acknowledge the funding provided by Fujitsu, Japan under the BSC-Fujitsu joint project: Math Libraries Migration and Optimization.Peer ReviewedPostprint (author's final draft