Towards energy efficient scaling of scientific codes

Energy consumption is becoming a crucial concern within the high performance computing community as computers expand to the peta-scale and beyond. Although the peak execution rates on tuned dense matrix operations in supercomputers have consistently increased to approach the peta-scale regime, the linear scaling of peak execution rates has been achieved at the expense of cubic growth in power with systems already appearing in the megawatt range. In this paper, we extend the ideas of algorithm scalability and performance iso-efficiency to characterize the system-wide energy consumption. The latter includes dynamic and leakage energy for CPUs, memories and network interconnects. We propose analytical models for evaluating energy scalability and energy efficiency. These models are important for understanding the power consumption trends of data intensive applications executing on a large number of processors. We apply the models to two scientific applications to explore opportunities when using voltage/ frequency scaling for energy savings without degrading performance. Our results indicate that such models are critical for energy-aware high-performance computing in the tera- to peta-scale regime.