Abstract

ion for Inner Loops When the algorithm finds a loop nested inside a loop body, it will recursively call itself on the inner loop. To hide the control flow of an inner loop, we introduce some abstraction and extend the previous definition from a basic block to a complete loop. We start by defining the information for one iteration of the loop. Definition 5 Let L be a loop and V AR be the variables in the program. We define the following set as summary set for body(L). 1. DEF b (L) := fv 2 V AR : v has a MRD reaching all exits node of body(L) g 2. USE b (L) := fv 2 V AR : v has an outward exposed use in body(L) g 3. KILL b (L) := DEF b (L) 4. PRI b (L) := fv 2 V AR : every use of v has a reaching MRD in body(L) g 2 The summary set is an abstraction of the effect of a loop iteration on the data flow values. Using the summary set, we can ignore the structure of the inner loops in the analysis of the outer loop. The trade-off is that we have to make a conservative approximation and ma...

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