Influence of loop transformations on performance and energy consumption of the multithreded WZ factorization

High-level loop transformations are a key instrument to effectively exploit the resource in modern architectures. Energy consumption on multi-core architectures is one of the major issues connected with high-performance computing. We examine the impact of four loop transformation strategies on performance and energy consumption. The investigated strategies include: loop fission, loop interchange (permutation), strip-mining, and loop tiling. Additionally, a column-wise and row-wise store formats for dense matrices are considered. Parallelization and vectorization are implemented using OpenMP directives. As a test, the WZ factorization algorithm is used. The comparison of selected strategies of the loop transformation is done for Intel architecture, namely Cascade Lake. It has been shown that for WZ factorization, which is an example of an application in which we can use the loop transformation, optimization towards high-performance can also be an effective strategy for improving energy efficiency. Our results show also that block size selection in loop tilling has a significant impact on energy consumption.