Solving the Phase Ordering Problem $\ne$ Generating the Globally Optimal Code

Phase ordering problem has been a long-standing challenge in compiler optimizations. Over the past four decades, a significant amount of effort has been devoted, and indeed, substantial progress has been made. However, in this paper, we raise questions about the overall significance of solving the phase ordering problem in the first place, as pursuing a solution to this problem may not align with the fundamental goal of compiler optimizations, \ie, generating the globally optimal code among all programs that compilers deem semantically equivalent to an input program. Our findings, supported by both theoretical and empirical evidence, show that solving the phase ordering problem is not equivalent to generating such globally optimal code. The fundamental reason that applying the optimal phase ordering may still result in suboptimal code is the exclusion of programs of less efficiency during the optimization process. Motivated by this insight, we propose a theoretical approach, called \textit{infinitive iterative bi-directional optimizations} (\textit{IIBO}), which is guaranteed to converge to the globally optimal code for any input program. We realize IIBO into a practical algorithm and apply it to optimize real-world programs. Results show that IIBO frequently generates more efficient code than GCC/LLVM, two state-of-the-art industry compilers, as well as exhaustive search, which can be deemed the solution to the phasing ordering problem.% input programs. Given the significance and impact of our results, we are currently in active discussions with LLVM engineers on the possible incorporation of our findings into their next release. In general, we expect our work to inspire new design principles for compiler development in the pursuit of generating the globally optimal code.