Tuning linear algebra for energy efficiency on multicore machines by adapting the ATLAS library

Abstract

While automated tuning is an established method for minimising the execution time of scientific applications, it has rarely been used for an automated minimisation of the energy consumption. This article presents a study on how to adapt the auto-tuned linear algebra library ATLAS to consider the energy consumption of the execution in its tuning decision. For different tuning parameters of ATLAS, it investigates which differences occur in the tuning results when ATLAS is tuned for a minimal execution time or for a minimal energy consumption. The tuning parameters include the matrix size for the low-level matrix multiplication, loop unrolling factors, crossover points for different matrix-multiplication implementations, the minimum size for matrices to be transposed, or blocking sizes for the last-level cache. Also, parameters for multithreaded execution, such as the number of threads and thread affinity are investigated. The emphasis of this article is on a method proposed with which it is possible to replace a tuning process for execution time by a tuning for energy consumption, especially in the parallel case. ATLAS serves as a prominent example for a tuned library. Furthermore, the article draws conclusions on how to design an energy-optimising autotuning package and how to choose tuning parameters. The article also discusses why the matrix-matrix multiplication has a potential for increasing the energy efficiency while the time efficiency remains constant, whereas other routines have shown to improve their energy efficiency by reducing the execution time.