Equivalence Checking of Static Affine Programs Using Widening to Handle Recurrences

Designers often apply manual or semi-automatic loop and data transformations on array and loop intensive programs to improve performance. The transformations should preserve the functionality however, and this paper presents an automatic method for constructing equivalence proofs for the class of static affine programs. The equivalence checking is performed on a dependence graph abstraction and uses a new approach based oil widening to handle recurrences. Unlike transitive closure based approaches, this widening approach can also handle non-uniform recurrences. The implementation is publicly available and is the first of its kind to fully support commutative operations.