Optimizing the Performance of Multi-threaded Linear Algebra Libraries Based on Task Granularity

Abstract

Linear algebra libraries play a very important role in many HPC applications. As larger datasets are created everyday, it also becomes crucial for the multi-threaded linear algebra libraries to utilize the compute resources properly. Moving toward exascale computing, the current programming models would not be able to fully take advantage of the advances in memory hierarchies, computer architectures, and networks. Asynchronous Many-Task(AMT) Runtime systems would be the solution to help the developers to manage the available parallelism. In this Dissertation we propose an adaptive solution to improve the performance of a linear algebra library based on a set of compile-time and runtime characteristics including the machine architecture, the expression being evaluated, the number of cores to run the application on, the type of the operation, and also the size of the matrices, to get as close as possible to the highest performance. Our focus is on machine learning applications, where we are potentially dealing with very large matrices, which could make creating temporaries very expensive. For this purpose we selected Blaze C++ library, a high performance template-based math library that gives us this option to access the expression tree at compile time, along with HPX, a C++ standard library for concurrency and parallelism, as our runtime system. HPX, as an AMT runtime system, offers scalibility and fine-grained parallelism through creating lightweight threads for fast context switching between the threads. Finding the optimum task granularity is a challenge in AMTs. Creating too many small tasks would result in performance degradation due to scheduling overhead of the tasks, and creating too few tasks would lead to under-utilization of the resources. Our work focuses on finding the optimum task granularity for each specific problem. We tried two different approaches to model the relationship between the performance and the grain size, in order to find a range of grain sizes that could lead us to the maximum performance. First, we used polynomial functions to model how throughput changes in terms of the grain size, and number of cores. Although this method was successful in finding the range of grain sizes for maximum throughput, it was not physical. This motivated us to go deeper and try to develop an analytical model for execution time in terms of grain size for balanced parallel for loops. Based on the analytical model we propose a method to predict the range of grain size for minimum execution time. Moreover,