This article examines dynamic energy consumption caused by data during software execution on deeply embedded microprocessors, which can be significant on some devices. In worst-case energy consumption analysis, energy models are used to find the most costly execution path. Taking each instruction’s worst-case energy produces a safe but overly pessimistic upper bound. Algorithms for safe and tight bounds would be desirable. We show that finding exact worst-case energy is NP-hard, and that tight bounds cannot be approximated with guaranteed safety. We conclude that any energy model targeting tightness must either sacrifice safety or accept overapproximation proportional to data-dependent energy.
The first publication to provide a technique for computing the WCEC of software was by @cite_7 , where upper bounds on the energy consumption of several programs were inferred using energy models of software basic blocks and an ILP solver to find a maximal path through the program. The authors additionally debunk the suggestion that the execution path consuming the most time is always the path that also consumes the most energy. With regards to dynamic power, the authors assume maximal circuit switching on every clock cycle but model power management techniques within the processor such as clock gating to create a realistic energy model. The dynamic power of switching due to operand values is not specifically considered, and indeed the authors show that that its contribution of dynamic power to overall energy is low, thus their approximation does not introduce significant imprecision. We address the contribution of operand values to dynamic power in sec:xcoresw .
@cite_7
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The fact that energy is a scarce resource in many embedded real-time systems creates the need for energy-aware task schedulers, which not only guarantee timing constraints but also consider energy consumption. Unfortunately, existing approaches to analyze the worst-case execution time (WCET) of a task usually cannot be directly applied to determine its worst-case energy consumption (WCEC) due to execution time and energy consumption not being closely correlated on many state-of-the-art processors. Instead, a WCEC analyzer must take into account the particular energy characteristics of a target platform. In this paper, we present 0g, a comprehensive approach to WCEC analysis that combines different techniques to speed up the analysis and to improve results. If detailed knowledge about the energy costs of instructions on the target platform is available, our tool is able to compute upper bounds for the WCEC by statically analyzing the program code. Otherwise, a novel approach allows 0g to determine the WCEC by measurement after having identified a set of suitable program inputs based on an auxiliary energy model, which specifies the energy consumption of instructions in relation to each other. Our experiments for three target platforms show that 0g provides precise WCEC estimates.