Cache Probabilistic Modeling for Basic Sparse Algebra Kernels involving Matrices with a Non Uniform Distribution

A probabilistic model to estimate the number of misses on a set associative cache with an LRU replacement algorithm is introduced. Such type of modeling has been done by our group in previous works for sparse matrices with an uniform distribution of the non zero elements. In this paper we present new results focusing in different types of distributions that usually appear in some well-known real matrices suites, such as Harwell-Boeing or NEP. 1. Introduction A large number of scientific applications work with sparse matrices, this is to say, matrices with a very low percentage of non zero elements or entries. These matrices are stored in compressed formats [2] in order to reduce the operations and memory needed. These formats generate irregular patterns of references to memory due to the indirect addressing, thus reducing the performance of the memory hierarchy and making hard to analyze the cache behaviour. In this paper a general model to study cache behaviour under such kind of wor..