A Method for Improving the Caching Strategy for Computing Systems with Shared Memory

Abstract

This paper considers the problem of increasing the software efficiency in terms of reducing the costs of their development and operation in the process of solving production and research tasks. We have analysed the existing approaches to solving this problem by example of parameterized algorithms for implementing mVm (matrix—vector multiplication) and MMM (matrix—matrix multiplication)) BLAS (Basic Linear Algebra Subroutines) operations. To achieve the goal of increasing the software efficiency, we proposed a new design method, designed to improve data caching algorithms in the software development for computing systems with a hierarchical memory structure. Using the proposed design procedure, we developed an analytical approach to evaluating the software effectiveness from the point of view of using a memory subsystem with a hierarchical structure is implemented. We applied the proposed method to the two-sided Householder transformation for the task of reducing the general form matrix to the Hessenberg form. Then we presented new algorithms for solving the problem, which are optimized variants of the Householder classical transformation: Row-Oriented Householder and Single-Pass Householder. The use of these algorithms can significantly reduce the software execution time. Computational experiments were carried out on a parallel computing system with shared memory, which is one of the nodes of the computing cluster of the Volgograd State Technical University. We made a comparison of the software execution time that reduce general-form matrices to Hessenberg form, written using the proposed algorithms and using the LAPACKE_dgehrd() function of the Intel MKL library. The conclusions made in the work are confirmed by the results of the conducted computational experiments.