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. Previous works use reuse 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 and provides a theoretically sound and unified way to quantify both temporal and spatial locality. We showcase that our quantified locality measure 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.