Optimal Worst Case Formulas Comparing Cache Memory Associativity

ct Consider an arbitrary program P which is to be executed on a computer with two alternative cache memories. The rst cache has k sets and u blocks in each set, this is denoted a (k;u)-cache. The other is a fully associative cache with q blocks; a (1;q)-cache. We present optimal formulascomparing the performance of a (k;u)-cache compared to a (1;q)-cache for worst case scenarios. Optimal mappings of the program variables to the cache blocks are assumed. Let h(P;k;u) denote the number of cache hits for the program P using a (k;u)-cache and an optimal mapping. We establish an explicit formula for the function r(n;k;u;q) and prove that infP h(P;k;u) h(P;1;q) = 1 r(n;k;u;q); where the inmum is taken over all programs P which contain n variables. We also deduce a formula for the inmum taken over all programs of any number of variables: infP h(P;k;u) h(P;1;q) = 1 R(k;u;q): Further we prove that programs which are extremal for this minimum may have any hit ratio, i.e. any ratio h(P;1;q)=m(...

• Type: Journal
• Year: 2000
• Where: SIAMCOMP
• Authors: Håkan Lennerstad, Lars Lundberg
• Keywords: Alternative Cache Memories, Cache, Optimal Mapping, SIAMCOMP 2000