Analytical modeling of cache behavior for affine programs

Optimizing compilers implement program transformation strategies aimed at reducing data movement to or from main memory by exploiting the data-cache hierarchy. However, instead of attempting to minimize the number of cache misses, very approximate cost models are used, due to the lack of precise compile-time models for misses for hierarchical caches. The current state of practice for cache miss analysis is based on accurate simulation. However, simulation requires time proportional to the dataset/problem size, as well as the number of distinct cache configurations of interest to be evaluated. This paper takes a fundamentally different approach, by focusing on polyhedral programs with static control flow. Instead of relying on costly simulation, a closed-form solution for modeling of misses in a set associative cache hierarchy is developed. This solution can enable program transformation choice at compile time to optimize cache misses. A tool implementing the approach has been developed and used for validation of the framework.