Conditions for the existence of broadcast and spatial locality in computation threads

Abstract

Graphics Processing Units (GPUs) are considered as the target computer for implementing parallel algorithms. The set of algorithm operations to be implemented on the GPU must be split into computation threads; the threads should be grouped into computation blocks that are performed atomically on stream processors. Threads of a single block are executed on a stream processor in parts-pools called warp; warp threads are executed simultaneously. The efficiency of the parallel algorithm depends on the way the data is stored in the GPU memory. If all warp threads request the same datum when executing the current operator, then it is desirable to place it in a shared or constant GPU memory; in this case, its distribution across the cores of the multiprocessor is actually realized by means of broadcast. If warp threads request data located close to the memory, then in this case there is a spatial locality of data, which makes it advisable to place this data in the GPU’s memory. The implementation of broadcast or spatial locality by placing data in a memory of the appropriate type allows one to significantly reduce traffic when exchanging data between the memory levels of the GPU. This paper formulates and proves the necessary and sufficient conditions under which it is possible to perform a broadcast or there is a spatial locality of data. The conditions are formulated in terms of functions that determine the use of array elements at occurrences in the algorithm operators and functions that define the information dependencies of the algorithm. The results of the work can be used to optimize parallel algorithms when they are implemented on the GPU.