Expression-rewriting framework to generate communication sets for HPF programs with block-cyclic distribution

In this paper, we present a new framework based on expression rewritings and a calculus form called CSD calculus to generate the local enumeration set and communication set for HPF programs with Block-Cyclic distribution. Our framework is a practical software framework, and can handle the general cases so that the communication set of HPF programs of `Block-Cyclic' distributions with two-level alignments (or multiple-level alignments), multidimensional arrays, array intrinsic functions (such as Transpose operation), and affine indexes and axis exchange in the array subscript, can be calculated in a systematic way with a sound software foundation. Previously, existing work do not report a software framework to solve a problem with such general cases. In addition, our expression-rewriting framework is based on a new representative form, CSD (common-stride descriptor), to describe the regularity of the access patterns of HPF programs with `Block-Cyclic' distribution. We also demonstrate a calculus of CSD that CSD is closed under intersection and normalization, which helps the process of calculating local enumeration and communication sets of HPF programs with Block-Cyclic distributions. Experimental results show that our software scheme not only can be easily implemented in the practice, but also is with good efficiency.