Locality Principle Revisited: A Probability-Based Quantitative Approach

Abstract

This paper revisits the fundamental concept of the locality of references and proposes to quantify it as a conditional probability: in an address stream, given the condition that an address is accessed, how likely the same address (temporal locality) or an address within its neighborhood (spatial locality) will be accessed in the near future. Based on this definition, spatial locality is a function of two parameters, the neighborhood size and the scope of near future, and can be visualized with a 3D mesh. Temporal locality becomes a special case of spatial locality with the neighborhood size being zero byte. Previous works on locality analysis use stack/reuse distances to compute distance histograms as a measure of temporal locality. For spatial locality, some ad-hoc metrics have been proposed as a quantitative measure. In contrast, our conditional probability-based locality measure has a clear mathematical meaning, offers justification for distance histograms, and provides a theoretically sound and unified way to quantify both temporal and spatial locality. The proposed locality measure clearly exhibits the inherent application characteristics, from which we can easily derive information such as the sizes of the working data sets and how locality can be exploited. We showcase that our quantified locality visualized in 3D-meshes can be used to evaluate compiler optimizations, to analyze the locality at different levels of memory hierarchy, to optimize the cache architecture to effectively leverage the locality, and to examine the effect of data prefetching mechanisms. A GPU-based parallel algorithm is also presented to accelerate the locality computation for large address traces.