A Method for Computing the Number of Iterations in Data Dependent Loops

Abstract

This paper addresses the problem of loop iteration number estimation, applied to linear loops. This is important to statically put an upper bound on the execution time of real-time systems and implement timing constraint verification. In our approach, matrix calculation is applied to derive the analytical equation that holds the number of iterations as a solution, and it is proved that such solution is related to a zero of an exponential function of the eigenvalues. So, the number of iterations turns out to be an implicit variable of the equation, which can be easily exactly calculated for loops depending on few free variables.