Sparse Data-Flow Analysis for DAG Parallel Programs

We contrast abstract ow of control in a sequential program environment which uses a control ow graph (CFG) to the abstraction of execution order within DAG parallelism using a simple precedence graph (PG). We note that often the analogous concepts are duals of each other with regard to universal and existential quantiiers. We are studying sparse data-ow analysis techniques, which include methods of placing operators at connuence points to merge the ow of information. While the placement of merge operators is well-known for CFGs (at the iterated dominance frontier of nodes with non-identity transfer functions), we determine and prove correct placement points for merge operators within a PG in the case of reaching deenitions. We also show how to conservatively implement the placement of parallel merge operators in an eecient manner with respect to the reaching deenitions problem. To describe control ow of sequential programs, the abstraction of the Control Flow Graph (CFG) is used. The CFG summarizes potential paths of control through the program. Formally, the CFG is a graph G = , where V is a set of nodes representing basic blocks in the program, E is a set of edges representing sequential control ow in the program, and Entry and Exit are nodes representing the unique entry point into the program and the unique exit point from the program. The CFG has been the most common intermediate representation for program ow analysis for a number of years 1, 9]. Data-ow analysis is a method of collecting information about a program, such as reaching deenitions, dominance, or live variables 1, 10]. The rst two examples of data-ow analysis,