Investigating the Dirac operator evaluation with FPGAs

In recent years the computational capacity of single Field Programmable Gate Arrays (FPGA) devices as well as their versatility has increased significantly. Adding to that the High Level Synthesis frameworks allowing to program such processors in a high level language like C++, makes modern FPGA devices a serious candidate as building blocks of a general purpose High Performance Computing solution. In this contribution we describe benchmarks which we performed using a Lattice QCD code, a highly compute-demanding HPC academic code for elementary particle simulations. We benchmark the performance of a single FPGA device running in two modes: using the external or embedded memory. We discuss both approaches in detail using the Xilinx U250 device and provide estimates for the necessary memory throughput and the minimal amount of resources needed to deliver optimal performance depending on the available hardware platform.Comment: 8 pages, 5 figure

Software Transactional Memory, OpenMP and Pthread implementations of the Conjugate Gradients Method - a Preliminary Evaluation

This paper shows the runtime and cache-efficiency of parallel implementations of the Conjugate Gradients Method based on the three paradigms Software Transactional Memory (STM), OpenMP and Pthreads. While the two last named concepts are used to manage parallelization as well as synchronization, STM was designed to handle only the latter. In our work we disclose that an improved cache efficiency does not necessarily lead to a better execution time because the execution time is dominated by the thread wait time at the barriers

Predict-and-recompute conjugate gradient variants

The standard implementation of the conjugate gradient algorithm suffers from communication bottlenecks on parallel architectures, due primarily to the two global reductions required every iteration. In this paper, we introduce several predict-and-recompute type conjugate gradient variants, which decrease the runtime per iteration by overlapping global synchronizations, and in the case of our pipelined variants, matrix vector products. Through the use of a predict-and-recompute scheme, whereby recursively updated quantities are first used as a predictor for their true values and then recomputed exactly at a later point in the iteration, our variants are observed to have convergence properties nearly as good as the standard conjugate gradient problem implementation on every problem we tested. It is also verified experimentally that our variants do indeed reduce runtime per iteration in practice, and that they scale similarly to previously studied communication hiding variants. Finally, because our variants achieve good convergence without the use of any additional input parameters, they have the potential to be used in place of the standard conjugate gradient implementation in a range of applications.Comment: This material is based upon work supported by the NSF GRFP. Code for reproducing all figures and tables in the this paper can be found here: https://github.com/tchen01/new_cg_variant