The gap between processor and main memory performance increases every year. In order to overcome this problem, cache memories are widely used. However, they are only effective when programs exhibit sufficient data locality. Compile-time program transformations can significantly improve the performance of the cache. To apply most of these transformations, the compiler requires a precise knowledge of the locality of the different sections of the code, both before and after being transformed.Cache miss equations (CMEs) allow us to obtain an analytical and precise description of the cache memory behavior for loop-oriented codes. Unfortunately, a direct solution of the CMEs is computationally intractable due to its NP-complete nature.This article proposes a fast and accurate approach to estimate the solution of the CMEs. We use sampling techniques to approximate the absolute miss ratio of each reference by analyzing a small subset of the iteration space. The size of the subset, and therefore the analysis time, is determined by the accuracy selected by the user. In order to reduce the complexity of the algorithm to solve CMEs, effective mathematical techniques have been developed to analyze the subset of the iteration space that is being considered. These techniques exploit some properties of the particular polyhedra represented by CMEs.

Cache Miss Equations (CME) (S. Ghosh et al., 1997) is a method that accurately describes the cache behavior by means of polyhedra. Even though the computation cost of generating CME is a linear function of the number of references, solving them is a very time consuming task and thus trying to study a whole program may be infeasible. The paper presents effective techniques that exploit some properties of the particular polyhedra generated by CME. Such techniques reduce the complexity of the algorithm to solve CME, which results in a significant speedup when compared with traditional methods. In particular, the proposed approach does not require the computation of the vertices of each polyhedron, which has an exponential complexity.