Characterizing the Relation Between Apex-Map Synthetic Probes and Reuse Distance Distributions

Characterizing a memory reference stream using reuse distance distribution can enable predicting the performance on a given architecture. Benchmarks can subject an architecture to a limited set of reuse distance distributions, but it cannot exhaustively test it. In contrast, Apex-Map, a synthetic memory probe with parameterized locality, can provide a better coverage of the machine use scenarios. Unfortunately, it requires a lot of expertise to relate an application memory behavior to an Apex-Map parameter set. In this work we present a mathematical formulation that describes the relation between Apex-Map and reuse distance distributions. We also introduce a process through which we can automate the estimation of Apex-Map locality parameters for a given application. This process finds the best parameters for Apex-Map probes that generate a reuse distance distribution similar to that of the original application. We tested this scheme on benchmarks from Scalable Synthetic Compact Applications and Unbalanced Tree Search, and we show that this scheme provides an accurate Apex-Map parameterization with a small percentage of mismatch in reuse distance distributions, about 3% in average and less than 8% in the worst case, on the tested applications.