A General Approach for Tight Timing Predictions of Non-Rectangular Loops

Static timing analyzers need to know the number of iterations associated with each loop in a real-time program so accurate timing predictions can be obtained. The number of iterations of non-rectangular loops vary due to dependencies on counter variables of outer loops. These loops have long presented a problem for timing analyzers since the resulting timing predictions are typically quite loose. This paper presents a general and efficient method for obtaining tight timing predictions of such loops. The total number of iterations executed by an inner loop inside a loop nest can be expressed in terms of summations. Equations representing such loops can be efficiently solved given that certain restrictions are met. We outline an approach for formulating the summations representing the total number of iterations of a loop, a method for solving the equation containing the summations, and a technique for integrating this method into an existing timing analyzer.