Multi-spectral Reuse Distance: Divining Spatial Information from Temporal Data

Abstract

The problem of efficiently feeding processing elements and finding ways to reduce data movement is pervasive in computing. Efficient modeling of both temporal and spatial locality of memory references is invaluable in identifying superfluous data movement in a given application. To this end, we present a new way to infer both spatial and temporal locality using reuse distance analysis. This is accomplished by performing reuse distance analysis at different data block granularities: specifically, 64B, 4KiB, and 2MiB sizes. This process of simultaneously observing reuse distance with multiple granularities is called multi-spectral reuse distance. This approach allows for a qualitative analysis of spatial locality, through observing the shifting of mass in an application’s reuse signature at different granularities. Furthermore, the shift of mass is empirically measured by calculating the Earth Mover’s Distance between reuse signatures of an application. From the characterization, it is possible to determine how spatially dense the memory references of an application are based on the degree to which the mass has shifted (or not shifted) and how close (or far) the Earth Mover’s Distance is to zero as the data block granularity is increased. It is also possible to determine an appropriate page size from this information, and whether or not a given page is being fully utilized. From the applications profiled, it is observed that not all applications will benefit from having a larger page size. Additionally, larger data block granularities subsuming smaller ones suggest that larger pages will allow for more spatial locality exploitation, but examining the memory footprint will show whether those larger pages are fully utilized or not.