Finding the limits of power-constrained application performance

As we approach exascale systems, power is turning from an optimization goal to a critical operating constraint. With power bounds imposed by both stakeholders and the limitations of existing infrastructure, we need to develop new techniques that work with limited power to extract maximum performance. In this paper, we explore this area and provide an approach to find the theoretical upper bound of computational performance on a per-application basis in hybrid MPI + OpenMP applications. We use a linear programming (LP) formulation to optimize application schedules under various power constraints, where a schedule consists of a DVFS state and number of OpenMP threads for each section of computation between consecutive MPI calls. We also provide a more flexible mixed integer-linear (ILP) formulation and show that the resulting schedules closely match schedules from the LP formulation. Across four applications, we use our LP-derived upper bounds to show that current approaches trail optimal, power-constrained performance by up to 41.1%. This demonstrates the untapped potential of current systems, and our LP formulation provides future optimization approaches with a quantitative optimization target.