Conditions for privatizing the elements of arrays by computing threads

The set of operations of the parallel algorithm for implementation on the GPU must be split into computation threads. The threads must be grouped into computation units that run atomically on stream processors, also called multiprocessors. For good GPU performance, it is important that as much data as possible can fit into fast register and shared memory, otherwise slow global and local memory are used. The degree of memory usage with fast access reflects the computational property of the algorithm, called locality. When implementing algorithms on multiprocessor computing devices, the use of locality plays a crucial role in achieving high performance. In this paper, necessary conditions and sufficient conditions have been formulated and proved, the use of which allows receiving threads with privatized data, i. e. it allows to receive such computation threads that the array element is used only by one thread and therefore it is advisable to place it in the register