Additivity: A Selection Criterion for Performance Events for Reliable Energy Predictive Modeling

Abstract

Performance events or performance monitoring counters (PMCs) are now the dominant predictor variables for modeling energy consumption. Modern hardware processors provide a large set of PMCs. Determination of the best subset of PMCs for energy predictive modeling is a non-trivial task given the fact that all the PMCs can not be determined using a single application run. Several techniques have been devised to address this challenge. While some techniques are based on a statistical methodology, some use expert advice to pick a subset (that may not necessarily be obtained in one application run) that, in experts' opinion, are significant contributors to energy consumption. However, the existing techniques have not considered a fundamental property of predictor variables that should have been applied in the first place to remove PMCs unfit for modeling energy. We address this oversight in this paper. We propose a novel selection criterion for PMCs called additivity, which can be used to determine the subset of PMCs that can potentially be used for reliable energy predictive modeling. It is based on the experimental observation that the energy consumption of a serial execution of two applications is the sum of energy consumptions observed for the individual execution of each application. A linear predictive energy model is consistent if and only if its predictor variables are additive in the sense that the vector of predictor variables for a serial execution of two applications is the sum of vectors for the individual execution of each application. The criterion, therefore, is based on a simple and intuitive rule that the value of a PMC for a serial execution of two applications is equal to the sum of its values obtained for the individual execution of each application. The PMC is branded as non-additive on a platform if there exists an application for which the calculated value differs significantly from the value observed for the application execution on the platform. The use of non-additive PMCs in a model renders it inconsistent. We study the additivity of PMCs offered by the popular state-of-the-art tools, Likwid and PAPI, by employing a detailed experimental methodology on a modern Intel Haswell multicore server CPU. We show that many PMCs in Likwid and PAPI that are widely used in models as key predictor variables are non-additive. This brings into question the reliability and the reported prediction accuracy of these models.