Analysis of a Memory Bandwidth Limited Scenario for NUMA and GPU Systems

The processing power and parallelism in hardware is expected to increase rapidly over the next years, whereas memory bandwidth per flop and the amount of main memory per flop will be falling behind. These trends will result in both more algorithms to become limited by memory bandwidth, and overall memory requirements to become an important factor for algorithm design. In this paper we study the Gauß-Seidel stencil as an example of a memory bandwidth limited algorithm. We consider GPUs and NUMA systems, which are both designed to provide high memory bandwidth at the cost of making algorithm design more complex. The mapping of the non-linear memory access pattern of the Gauß-Seidel stencil to the different hardware is important to achieve high performance. We show that there is a trade-off between overall performance and memory requirements when optimizing for optimal memory access pattern. Vectorizing on the NUMA system and optimizing to utilize all processors on the GPU does not pay off in terms of performance per memory used, which we consider an important measurement regarding the trends named before.