Algorithms + Data Structures + Transformations = Portable Program Performance

Many scientiic applications require sparse matrix computations. For example, Finite Element model-ing and N-body simulations. It is diicult 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 speciic 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 diierent 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 speciication for the sparse data structure speciication, or looked at locality and parallelism transformations for sparse computations which use speciic 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.