Fast Memory Footprint Estimation based on Maximal Dependency Vector Calculation

Abstract

In data dominated applications, loop transformations have a huge impact on the lifetime of array data and therefore on memory footprint. Since a locally optimal loop transformation may have a detrimental effect somewhere else, many alternative loop transformations need to be explored. Therefore, estimation of the memory footprint is essential, and this estimation has to be fast. This paper presents a fast array based memory footprint estimation technique based on counting of iteration nodes in an iteration domain constrained by a maximal lifetime. The maximal lifetime is defined by the maximal dependency vector (MDV) of the array for a given execution ordering. We further present for the first time two approaches for calculation of the MDV: a general approach based on an ILP formulation and a novel vertexes approach when iteration domains are approximated by bounding boxes. Experiments on practical test vehicles demonstrate that the estimation based on our vertexes approach is extremely fast, on average two orders of magnitude faster than the compared approaches, while still keeping the accuracy high. This enables system-level data memory footprint exploration of many different alternative transformed program codes, within interactive time limits, and on realistic complex applications