Supporting Timing Analysis by Automatic Bounding of LoopIterations

Abstract

Static timing analyzers, which are used to analyze real-time systems, need to know the minimum and maximum number of iterations associated with each loop in a real-time program so accurate timing predictions can be obtained. This paper describes three complementary methods to support timing analysis by bounding the number of loop iterations. First, an algorithm is presented that determines the minimum and maximum number of iterations of loops with multiple exits. Even when the number of iterations cannot be exactly determined, it is desirable to know the lower and upper iteration bounds. Second, when the number of iterations is dependent on unknown values of variables, the user is asked to provide bounds for these variables. These bounds are used to determine the minimum and maximum number of iterations. Specifying the values of variables is less error prone than specifying the number of loop iterations directly. Finally, a method is given to tightly predict the execution time of inner loops whose number of iterations is dependent on counter variables of outer level loops. This is accomplished by formulating the total number of iterations of a loop in terms of summations and solving the resulting equation. These three methods have been successfully integrated in an existing timing analyzer that predicts the performance for optimized code on a machine that exploits caching and pipelining. The result is tighter timing analysis predictions and less work for the user.