Align and Distribute-based Linear Loop Transformations

In this paper we generalize the framework of linear loop transformations in the sense that loop alignment is considered as a new component in the transformation process. The aim is to match the structure of loop nests with the data distribution and alignment in order to eliminate non-local references whenever possible when compiling a sequential program for a distributed memory machine. The alignment and distribution functions are assumed to be user specified or automatically generated by the compiler. The transformation process is modelled with nonsingular matrices and we use the ideas recently proposed in this field to find part of the transformation matrix and generate an efficient transformed code. However, additional aspects have to be studied when the alignment and distribution functions are considered, both in the obtaining of the transformation matrix and in the generation of code.