Energy of computing is a serious environmental concern and mitigating it is an important technological challenge. Accurate measurement of energy consumption during an application execution is key to application-level energy minimization techniques. There are three popular approaches to providing it: (a) System-level physical measurements using external power meters; (b) Measurements using on-chip power sensors and (c) Energy predictive models. In this work, we present a comprehensive study comparing the accuracy of state-of-the-art on-chip power sensors and energy predictive models against system-level physical measurements using external power meters, which we consider to be the ground truth. We show that the average error of the dynamic energy profiles obtained using on-chip power sensors can be as high as 73% and the maximum reaches 300% for two scientific applications, matrix-matrix multiplication and 2D fast Fourier transform for a wide range of problem sizes. The applications are executed on three modern Intel multicore CPUs, two Nvidia GPUs and an Intel Xeon Phi accelerator. The average error of the energy predictive models employing performance monitoring counters (PMCs) as predictor variables can be as high as 32% and the maximum reaches 100% for a diverse set of seventeen benchmarks executed on two Intel multicore CPUs (one Haswell and the other Skylake). We also demonstrate that using inaccurate energy measurements provided by on-chip sensors for dynamic energy optimization can result in significant energy losses up to 84%. We show that, owing to the nature of the deviations of the energy measurements provided by on-chip sensors from the ground truth, calibration can not improve the accuracy of the on-chip sensors to an extent that can allow them to be used in optimization of applications for dynamic energy. Finally, we present the lessons learned, our recommendations for the use of on-chip sensors and energy predictive models and future directions.

Performance and energy are the two most important objectives for optimization on modern parallel platforms. In this article, we show that moving from single-objective optimization for performance or energy to their bi-objective optimization on heterogeneous processors results in a tremendous increase in the number of optimal solutions (workload distributions) even for the simple case of linear performance and energy profiles. We then study full performance and energy profiles of two real-life data-parallel applications and find that they exhibit shapes that are non-linear and complex enough to prevent good approximation of them as analytical functions for input to exact algorithms or optimization software for determining the Pareto front. We, therefore, propose a solution method solving the bi-objective optimization problem on heterogeneous processors. The method's novel component is an efficient and exact global optimization algorithm that takes as an input performance and energy profiles as arbitrary discrete functions of workload size, which accurately and realistically take into account resource contention and NUMA inherent in modern parallel platforms, and returns the Pareto-optimal solutions (generally speaking, load imbalanced). To construct the input discrete energy functions, the method employs a methodology that accurately models the energy consumption by a hybrid data-parallel application executing on a heterogeneous HPC platform containing different computing devices using system-level power measurements provided by power meters. We experimentally analyse the proposed solution method using three data-parallel applications, matrix multiplication, 2D fast Fourier transform (2D-FFT), and gene sequencing, on two connected heterogeneous servers consisting of multicore CPUs, GPUs, and Intel Xeon Phi. We show that it determines a superior Pareto front containing the best load balanced solutions and all the load imbalanced solutions that are ignored by load balancing methods.

The energy efficiency in ICT is becoming a grand technological challenge and is now a first-class design constraint in all computing settings. Energy predictive modelling based on performance monitoring counters (PMCs) is the leading method for application-level energy optimization. However, a sound theoretical framework to understand the fundamental significance of the PMCs to the energy consumption and the causes of the inaccuracy of the models is lacking. In this work, we propose a small but insightful theory of energy predictive models of computing, which formalizes both the assumptions behind the existing PMC-based energy predictive models and properties, heretofore unconsidered, that are basic implications of the universal energy conservation law. The theory's basic practical implications include selection criteria for model variables, model intercept, and model coefficients. The experiments on two modern Intel multicore servers show that applying the proposed selection criteria improves the prediction accuracy of state-of-the-art linear regression models from 31.2% to 18%. Finally, we demonstrate that employing energy models constructed using the proposed theory for energy optimization can save a significant amount of energy (up to 80% for applications used in experiments) compared to state-of-the-art energy measurement tools.

Accurate and reliable measurement of energy consumption is essential to energy optimization at an application level. Energy predictive modelling using performance monitoring counters (PMCs) emerged as a promising approach, one of the main drivers being its capacity to provide fine-grained component-level breakdown of energy consumption. In this work, we compare two types of energy predictive models constructed from the same set of experimental data and at two levels, platform and application. The first type contains linear regression (LR) models employing PMCs selected using a theoretical model of energy of computing. The second type contains sophisticated statistical learning models, random forest (RF) and neural network (NN), that are based on PMCs selected using correlation and principal component analysis. Our experimental results performed on two modern Intel multicore processors using a diverse set of applications and a wide range of application configurations, show that the average proportional prediction accuracy of platform-level LR models is 5.09× and 4.37× times better than the platform-level RF and NN models. We also present an experimental methodology to select a reliable subset of four PMCs for constructing accurate application-specific online models. Using the methodology, we demonstrate that LR models perform 1.57× and 1.74× times better than RF and NN models. The consistent accuracy of LR models stress the importance of taking into account domain-specific knowledge for model variable selection, in this case, the physical significance of the PMCs originating from the conservation of energy of computing. The results also endorse the guidelines of the theory of energy of computing, which states that any non-linear energy model (in this case, the RF and NN models) employing PMCs only, will be inconsistent and hence inherently inaccurate.

Modern high-performance computing platforms, cloud computing systems, and data centers are highly heterogeneous containing nodes where a multicore CPU is tightly integrated with accelerators. An important challenge for energy optimization of hybrid parallel applications on such platforms is how to accurately estimate the energy consumption of application components running on different compute devices of the platform. In this work, we propose a method for accurate estimation of the application component-level energy consumption employing system-level power measurements with power meters. We experimentally validate the method on a cluster of two hybrid heterogeneous computing nodes using three parallel applications – matrix-matrix multiplication, 2D fast Fourier transform and gene sequencing. The experiments demonstrate a high estimation accuracy of the proposed method, with the average estimation error ranging between 2% and 5%. The average error demonstrated by the state-of-the-art estimation methods for the same experimental setup ranges from 15% to 75%, while the maximum reaches 178%. We also show that the use of the state-of-the-art estimation methods instead of the proposed one in the energy optimization loop leads to significant energy losses (up to 45% in our case).

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.