Data flow frequency analysis

Conventional dataflow analysis computes information about what facts may or will not hold during the execution of a program. Sometimes it is useful, for program optimization, to know how often or with what probability a fact holds true during program execution. In this paper, we provide a precise formulation of this problem for a large class of dataflow problems - the class of finite bi-distributive subset problems. We show how it can be reduced to a generalization of the standard dataflow analysis problem, one that requires a sum-over-all-paths quantity instead of the usual meet-overall-paths quantity. We show that Kildall's result expressing the meet-over-all-paths value as a maximal-fixed-point carries over to the generalized setting, We then outline ways to adapt the standard dataflow analysis algorithms to solve this generalized problem, both in the intraprocedural and the interprocedural case.