Functionally Arranged Data for Algorithms with Space-Time Wavefront

Abstract

AbstractAlgorithms with space-time tiling increase the performance of numerical simulations by increasing data reuse and arithmetic intensity; they also improve parallel scaling by making process synchronization less frequent. The theory of Locally Recursive non-Locally Asynchronous (LRnLA) algorithms provides the performance model with account for data localization at all levels of the memory hierarchy. However, effective implementation is difficult since modern optimizing compilers do not support the required traversal methods and data structures by default. The data exchange is typically implemented by writing the updated values to the main data array. Here, we suggest a new data structure that contains the partially updated state of the simulation domain. Data is arranged within this structure for coalesced access and seamless exchange between subtasks. We demonstrate the preliminary results of its superiority over previously used methods by localizing the processed data in the L2 GPU cache for the Lattice Boltzmann Method (LBM) simulation so that the performance is not limited by the GDDR throughput but is determined by the L2 cache access rate. If we estimate the ideal stepwise code performance to be memory-bound with a read/write ratio equal to 1 and assume it is localized in the GPU memory and performs at 100% of the theoretical memory bandwidth, then the results of our benchmarks exceed that peak by a factor of the order of 1.2.KeywordsLRnLA algorithmsTemporal blockingLoop skewingParallel algorithmsData structure