An Improved Differential Fixpoint Iteration Method for Program Analysis

We present a differential fixpoint iteration method to be used in static program analyses. The differential method consists of two phases: first we transform the program analysis equations into differential ones, and then we apply a differential fixpoint iteration to the equations computing with the differences from the previous iterations. We implemented the method for the exception analysis of ML programs and also for the constant propagation and alias analysis of C and Fortran programs. For the exception analysis, our differential method saves about 20-50% computations. For the constant propagation and alias analysis, our method has a linear asymptotic performance: its cost remains linear to the height of the lattice structures. Our algorithm is not yet formally proven correct, but for the experiments the analysis results are confirmed identical to those from a non-differential fixpoint algorithm. Both analyses are for realistic ML/C/Fortran programs.