Integrating loop and data transformations for global optimisation

This paper is concerned with integrating global data transformations and local loop transformations in order to minimise overhead on distributed shared memory machines such as the SGi Origin 2000. By first developing an extended algebraic transformation framework, a new technique to allow the static application of global data transformations, such as partitioning, to reshaped arrays is presented, eliminating the need for expensive temporary copies and hence eliminating any communication and synchronisation. In addition, by integrating loop and data transformations, any introduced poor spatial locality and expensive array subscripts can be eliminated. A specific optimisation algorithm is derived and applied to well-known benchmarks, where it is shown to give a significant improvement in execution time over existing approaches.