Program Performance Michelle

Many scienti c applications require sparse matrix computations. For example, Finite Element modeling and N-body simulations. It is di cult to write these codes in a portable way which also achieves high performance because of the sparsity of the matrices and because current architectures have deep memory hierarchies and multiple levels of parallelism. Therefore the implementation of such computations become obfuscated because of the hand tuning necessary to get performance on a speci c architecture. Three performance aspects which must be dealt with are the matrix sparsity, data locality, and parallelism. Typically less than 1% of the entries in the matrix are non-zero [PS98], therefore it is necessary to use sparse data structures which only store the non-zeros. There are many di erent sparse data formats which save space and computation time for matrices with certain characteristics. Deep memory hierarchies and large relative memory latencies suggest the need for data locality optimizations which take advantage of data reuse. Parallelism allows for bigger problems to be solved. Current work in this problem domain has either looked at separating the algorithm speci cation for the sparse data structure speci cation, or looked at locality and parallelism transformations for sparse computations which use speci c sparse data structures. We would like to propose having locality and parallelism transformations be able to deal with any possible combination of sparse matrix computation and sparse data structure.