Data dependent energy modelling for worst case energy consumption analysis

This paper examines the impact of operand values upon instruction level energy models of embedded processors, to explore whether the requirements for safe worst case energy consumption (WCEC) analysis can be met. WCEC is similar to worst case execution time (WCET) analysis, but seeks to determine whether a task can be completed within an energy budget rather than within a deadline. Existing energy models that underpin such analysis typically use energy measurements from random input data, providing average or otherwise unbounded estimates not necessarily suitable for worst case analysis. We examine energy consumption distributions of two benchmarks under a range of input data on two cache-less embedded architectures, AVR and XS1-L. We find that the worst case can be predicted with a distribution created from random data. We propose a model to obtain energy distributions for instruction sequences that can be composed, enabling WCEC analysis on program basic blocks. Data dependency between instructions is also examined, giving a case where dependencies create a bimodal energy distribution. The worst case energy prediction remains safe. We conclude that worst-case energy models based on a probabilistic approach are suitable for safe WCEC analysis.