Cache Calculus: Modeling Caches through Differential Equations

Abstract

Caches are critical to performance, yet their behavior is hard to understand and model. In particular, prior work does not provide closed-form solutions of cache performance, i.e. simple expressions for the miss rate of a specific access pattern. Existing cache models instead use numerical methods that, unlike closed-form solutions, are computationally expensive and yield limited insight. We present cache calculus, a technique that models cache behavior as a system of ordinary differential equations, letting standard calculus techniques find simple and accurate solutions of cache performance for common access patterns.