Augmenting the Roofline Model via Lower Bounds on Data Movement

The roofline model is a popular approach to bottleneck-bounds performance analysis. It models upper bounds on performance as a function of operational intensity, ratio of arithmetic operations per byte of data moved from/to memory. While operational intensity can be measured for a given implementation, it is of interest to characterize the upper limits of operational intensity for different algorithms. Currently there is no systematic systematic methodology to do so. In this paper, we address the problem of developing upper bounds on the operational intensity of computations as a function of cache capacity. We demonstrate the utility of the approach in comparative analysis of algorithms, as well as in assessing fundamental performance limits for different algorithms as architectural parameters are varied.