Access normalization

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Abstract
In scalable parallel machines, processors can make local memory accesses much faster than they can make remote memory accesses. In addition, when a number of remote accesses must be made, it is usually more efficient to use block transfers of data rather than to use many small messages. To run well on such machines, software must exploit these features. We believe it is too onerous for a pro- grammer to do this by hand, so we have been exploring the use of restructuring compiler technology for this purpose. In this paper, we start with a language like FORTRAN-D with user-specified data distributionanddevelopa systematic loop transformation strategy called access normalization that re- structures loop nests to exploit locality and block transfers. We demonstrate the power of our techniques using routines from the BLAS (Basic Linear Algebra Subprograms) library. An important feature of our approach is that we model loop transformations using invertible matrices and integer lattice theory, thereby generalizing Banerjee's framework of uni- modular matrices (5).

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