Computational Alignment: a New, Uniied Program Transformation for Local and Global Optimization

Computational Alignment is a new class of program transformations suitable for both local and global optimization. Computational Alignment transforms all of the computations of a portion of the loop body in order to align them to other computations either in the same loop or in another loop. It extends along a new dimension and is signiicantly more powerful than linear transformations because i) it can transform subsets of dependences and references; ii) it is sensitive to the location of data in that it can move the computation relative to data; iii) it applies to imperfect loop nests; and iv) it is the rst loop transformation that can change access vectors. Linear transformations are just a special case of Computational Alignment. Computational Alignment is highly suitable for global optimization because it can transform given loops to access data in similar ways. Two important subclasses of Computational Alignment are presented as well, namely, Freeing and Isomerizing Computational Alignment.