Verification of Loop and Arithmetic Transformations of Array-Intensive Behaviors

Loop transformation techniques along with arithmetic transformations are applied extensively on array and loop intensive behaviors in design of area/energy efficient systems in the domain of multimedia and signal processing applications. Ensuring correctness of such transformations is crucial for the reliability of the designed systems. In this paper, array data dependence graphs (ADDGs) are used to represent both the input and the transformed behaviors and the correctness of the transformations is ensured by proving equivalence of the two ADDGs. A slice-based equivalence checking method of ADDGs is proposed for this purpose. The method relies on the normalization of arithmetic expressions and some simplification rules to handle arithmetic transformations. Unlike many other reported techniques, our method is strong enough to handle several arithmetic transformations along with all kinds of loop transformations. Correctness and complexity of the method have been dealt with. Experimental results on several test cases demonstrate the effectiveness of the method.