HOTL: A Higher Order Theory of Locality
The locality metrics are many, for example, miss ratio to test performance, data footprint to manage cache sharing, and reuse distance to analyze and optimize a program. It is unclear how different metrics are related, whether one subsumes another, and what combination may represent locality completely. This paper first derives a set of formulas to convert between five locality metrics and gives the condition for correctness. The transformation is analogous to differentiation and integration. As a result, these metrics can be assigned an order and organized into a hierarchy. Using the new theory, the paper then develops two techniques: one measures the locality in real time without special hardware support, and the other predicts multicore cache interference without parallel testing. The paper evaluates them using sequential and parallel programs as well as for a parallel mix of sequential programs.
locality metrics locality modeling