Analytical Derivation of Concurrent Reuse Distance Profile for Multi-Threaded Application Running on Chip Multi-Processor

Reuse distance has been shown to be a useful metric for performance analysis of caches and programs, locality analysis and compiler optimization. Concurrent reuse distance profile defined as the reuse distance profile of a thread sharing the cache with many other threads varies from its standalone reuse distance profile due to interference from other threads. Measurement of reuse distance profile through simulation, especially for multi-threaded applications, consumes lot of time. Analytical model based reuse distance prediction can reduce drastically the time taken for exploring the cache memory design space. The objective of this work is to propose an analytical model to find the concurrent reuse distance profile of a thread belonging to multi-threaded applications in a shared memory environment. Using the standalone reuse distance profile of each thread as input, we derive three other reuse distance profiles: 1) The concurrent reuse distance profile of a thread sharing the cache with other threads 2) The combined reuse distance profile of all threads sharing the cache and 3) The coherent reuse distance profile of each thread, considering the coherency effect when each thread runs with private cache. We use Markov chain besides combinatorics and basic probability theory as a main analytical tool for the model. We validate our analytical model against simulations, using the multi-core simulator Sniper for the benchmarks of the PARSEC and the SPLASH benchmark suites.