Dynamically Balanced Synchronization-Avoiding LU Factorization with Multicore and GPUs

Abstract

Graphics processing units (GPUs) brought huge performance improvements in the scientific and numerical fields. We present an efficient hybrid CPU/GPU computing approach that is portable, dynamically and efficiently balances the workload between the CPUs and the GPUs, and avoids data transfer bottlenecks that are frequently present in numerical algorithms. Our approach determines the amount of initial work to assign to the CPUs before the execution, and then dynamically balances workloads during the execution. Then, we present a theoretical model to guide the choice of the initial amount of work for the CPUs. The validation of our model allows our approach to self-adapt on any architecture using the manufacturer's characteristics of the underlying machine. We illustrate our method for the LU factorization. For this case, we show that the use of our approach combined with a communication avoiding LU algorithm is efficient. For example, our experiments on high-end hybrid CPU/GPU systems show that our dynamically balanced synchronization-avoiding LU is both multicore and GPU scalable. Comparisons with state-of-the-art libraries like MKL (for multicore) and MAGMA (for hybrid systems) are provided, demonstrating significant performance improvements. The approach is applicable to other linear algebra algorithms. The scheduling mechanisms and tuning models can be incorporated into respectively dynamic runtime systems/schedulers and autotuning frameworks for hybrid CPU/MIC/GPU architectures.

Performance Framework for HPC Applications on Homogeneous Computing Platform

“…After computation of execution time, we computed performance of saxpy in GFLOPs using eq (5). The Fig.7, plots comparison of pageable and pinned memory for saxpy applications on a hybrid programming model.…”

“…Simplice Donfack et.al [5] present effective hybrid CPU/GPU approaches that is portable. It dynamically and efficiently balances the workload between the CPUs and the GPU.…”

“…Let T[Cpi+Gpi]execution time of the HPC applications on the CPU+GPU and T Gpi execution time of the HPC applications on the GPU and P [Cpi+Gpi] performance(GFLOPs) presented for target HPC applications on the CPU+GPU and P Gpi performance(GFLOPs)presented for target HPC applications on individual nodes in a cluster are computed using eq (5). Hence, the load on the CPU [L CPi ] is computed using eq(2).…”

“…In this work, we are comparing applications performance by measuring execution time and GFLOPs. The GFLOPs is computed using the eq (5) Another application of the random number is in the field of operational research. In this application, random numbers are used to provide optimal or near optimal solution to decision making problems.…”

Auto-tuning techniques for linear algebra routines on hybrid platforms

“…Another auto-tuned library for this platform is MAGMA MIC [31], which uses a hybridization methodology, where the algorithms are split into computational tasks of varying granularity and, then, they are properly scheduled over the heterogeneous hardware. In [32] an auto-tuning method for the LU factorization is described. In this proposal, the initial amount of work to assign to both the CPU and GPU is determined before execution by means of an analytical model of the execution time, and the workload is dynamically balanced during the execution.…”