Data dependent energy modelling: A worst case perspective

Energy consumption of the software running on a device has become increasingly important as a growing number of devices rely on batteries or other limited sources of power. Of particular interest is constructing a bounded measure of the energy consumption - the maximum energy a program could consume for any input given to it. We explore the effect of different data on the energy consumption of individual instructions, instruction sequences and full programs. The whole program energy consumption of two benchmarks is analysed over random and hand-crafted data, and maximized with genetic algorithms for two embedded processors. We find that the worst case can be predicted from the distribution created by the random data, however, hand-crafted data can often achieve lower energy consumption. A model is constructed that allows the worst case energy for a sequence of instructions to be predicted. This is based on the observation that the transition between instructions is important and thus is not a single energy cost - it is a distribution dependent on the input and output values of the two consecutive instructions. We characterise the transition distributions for several instructions in the AVR instruction set, and show that this gives a useful upper bound on the energy consumption. We explore the effect that the transfer function of the instruction has on the data, and give an example which leads to a bimodal energy distribution. Finally, we conclude that a probabilistic approach is appropriate for estimating the energy consumption of programs.