Simple and Efficient Computation of Minimal Weak Control Closure

Control dependency is a fundamental concept in many program analyses, transformation, parallelization, and compiler optimization techniques. An overwhelming number of definitions of control dependency relations are found in the literature that capture various kinds of program control flow structures. Weak and strong control closure (WCC and SCC) relations capture nontermination insensitive and sensitive control dependencies and subsume all previously defined control dependency relations. In this paper, we have shown that static dependency-based program slicing requires the repeated computation of WCC and SCC. The state-of-the-art WCC algorithm provided by Danicic et al. has the cubic worst-case complexity in terms of the size of the control flow graph and is a major obstacle to be used in static program slicing. We have provided a simple yet efficient method to compute the minimal WCC which has the quadratic worst-case complexity and proved the correctness of our algorithms. We implemented ours and the state-of-the-art algorithms in the Clang/LLVM compiler framework and run experiments on a number of SPEC CPU 2017 benchmarks. Our method performs a maximum of 23.8 times and on average 11.1 times faster than the state-of-the-art method. The performance curves of our WCC algorithm for practical applications are closer to the NlogN curve in the microsecond scale. Evidently, we improve the practical performance of WCC computation by an order of magnitude.