Static Estimation of Reuse Profiles for Arrays in Nested Loops

Abstract: Efficient memory access patterns play a crucial role in determining the overall performance of applications by exploiting temporal and spatial locality, thus maximizing cache locality. The Reuse Distance Histogram (RDH) is a widely used metric to quantify temporal locality, measuring the distance between consecutive accesses to the same memory location. Traditionally, calculating RDH requires program execution and memory trace collection to obtain dynamic memory access behavior. This trace collection is often time-consuming, resource-intensive, and unsuitable for early-stage optimization or large-scale applications. Static prediction, on the other hand, offers a significant speedup in estimating RDH and cache hit rates. However, these approaches lack accuracy, since the predictions come without running the program and knowing the complete memory access pattern, more specifically when arrays are used inside nested loops. This paper presents a novel static analysis framework for predicting the reuse profiles of array references in programs with nested loop structures, without requiring any runtime information. By analyzing loop bounds, access patterns in smaller problem sizes, and predictive equations, our method predicts access patterns of arrays and estimates reuse distances and cache hit rate at compile time. This paper extends our previous study by incorporating more analysis and improving prediction by addressing previously unhandled reuse patterns. We evaluate our technique against a widely accepted traditional trace-driven profiling tool, Parallel Reuse Distance Analysis (PARDA). The results demonstrate that our static predictor achieves comparable accuracy while offering orders-of-magnitude improvement in the analysis speed. This work offers a practical alternative to dynamic reuse profiling and paves the way for integration into compilers and static performance modeling tools.