A unifying framework for iteration reordering transformations

We present a framework for unifying iteration reordering transformations such as loop interchange, loop distribution, skewing, tiling, index set splitting and statement reordering. The framework is based on the idea that a transformation can be represented as a mapping from the original iteration space to a new iteration space. The framework is designed to provide a uniform way to represent and reason about transformations. We also provide algorithms to test the legality of mappings, and to generate optimized code for mappings