Efficient Computation of Minimal Weak and Strong Control Closure

Control dependency is a fundamental concept in many program analyses, transformation, parallelization, and compiler optimization techniques. An overwhelming number of denitions 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 dened 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 and SCC algorithm provided by Danicic et al. has the cubic and the quartic 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 ecient method to compute the minimal WCC and SCC which has the quadratic and cubic 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 WCC method performs a maximum of 23:8 times and on average 10:6 times faster than the state-of-the-art method to compute WCC. The performance curves of our WCC algorithm for practical applications are closer to the NlogN curve in the microsecond scale. Our SCC method performs a maximum of 226.86 times and on average 67.66 times faster than the state-of-the-art method to compute SCC. Evidently, we improve the practical performance of WCC and SCC computation by an order of magnitude.