Flow-Sensitive Sub-Zero Control-Flow Analysis in Linear-Log Time

Traditional control-flow analysis (CFA) for higher-order languages is too expensive to be used as an every-day analysis in an otherwise fast compiler that is often called upon to compile large programs. It is even more expensive when flow sensitivity is added to handle optimizations like type recovery. In particular, the fastest known algorithms for 0CFA, the least expensive of the popular kCFA family of analyses, run in cubic time and are not flow-sensitive. A less precise form of control-flow analysis, sub-0CFA, runs in linear time, but is also not flow-sensitive. This paper presents a flow-sensitive sub-0CFA algorithm that runs in linear-log time. The algorithm has been used to perform a type recovery analysis that justifies the removal of over half of the run-time checks that would otherwise be necessary to ensure type safety in the latently typed language Scheme.