Time–Energy Correlation for Multithreaded Matrix Factorizations

Abstract

The relationship between time and energy is an important aspect related to energy savings in modern multicore architectures. In this paper, we investigated and analyzed the correlation between time and energy. We compared the execution time and energy consumption of the LU factorization algorithms (versions with and without pivoting) and Cholesky with the Math Kernel Library (MKL) on a multicore machine. To reduce the energy of these multithreaded factorizations, the Dynamic Voltage and Frequency Scaling (DVFS) technique was used. This technique allows the clock frequency to be scaled without changing the implementation. In particular, we studied the correlations between time and energy using two metrics: Energy Delay Product (EDP) and Greenup, Powerup, and Speedup (GPS-UP). An experimental evaluation was performed on an Intel Xeon Gold multicore machine as a function of the number of threads and the clock speed. Our test results showed that scalability in terms of execution time, expressed by the Speedup metric, had values close to a linear function as the number of threads increased. In contrast, the scalability in terms of energy consumption, expressed by the Greenup metric, had values close to a logarithmic function as the number of threads increased. The use of the EDP and GPS-UP metrics allowed us to evaluate the impact of the optimized code (DVFS and increase in the number of threads) on the time and energy consumption and to determine a better green category representing energy savings without losing performance.