Towards Unimodular Transformations for Non-perfectly Nested Loops

In this paper we discuss a possibility to extend unimodular transformations to non-perfectly nested loops. The main idea behind this extension is to convert a non-perfectly nested loop into a perfectly nested one by moving code into to innermost loop and properly guarding it to avoid multiple execution. This form of the loop can be viewed as an intermediate form for the transformation. Having obtained a perfectly nested loop, unimodular transformations can be applied in the usual way. The result of this transformation still contains guards. We show how to eliminate these guards. We illustrate our technique by transforming the ijk-version of LU-decomposition to the ikj-version.