Automatic memory layout transformations to optimize spatial locality in parameterized loop nests

One of the most efficient ways to improve program performances onto nowadays computers is to optimize the way cache memories are used. In particular, many scientific applications contain loop nests that operate on large multi-dimensional arrays whose sizes are often parameterized. No special attention is paid to cache memory performance when such loops are written. In this work, we focus on spatial locality optimization such that all the data that are loaded as a block in the cache will be used successively by the program. Our method consists in providing a new array reference evaluation function to the compiler, such that the data layout corresponds exactly to the utilization order of these data. The computation of this function concerns the field of parameterized polyhedra and Ehrhart polynomials.