Compiler optimizations pose many problems to source-level debugging of an optimized program due to reordering, insertion, and deletion of code. On such problem is to determine whether the value of a varible is current at a breakpoint—that is, whether its actual value is the same as its expected value. We use the notion of dynamic currency of a variable in source-level debugging and propose the use of a minimal unrolled graph to reduce the run-time overhead of dynamic currency determination. We prove that the minimal unrolled graph is an adequate basis for performing bit-vector data flow analyses at a breakpoint. This property is used to perform dynamic currency determination. It is also shown to help in recovery of a dynamically noncurrent variable.

The classical theory of data flow analysis, which has its roots in unidirectional flows, is inadequate to characterize bidirectional data flow problems. We present a generalized theory of bit vector data flow analysis which explains the known results in unidirectional and bidirectional data flows and provides a deeper insight into the process of data flow analysis. Based on the theory, we develop a worklist-based generic algorithm which is uniformly applicable to unidirectional and bidirectional data flow problems. It is simple, versatile, and easy to adapt for a specific problem. We show that the theory and the algorithm are applicable to all bounded monotone data flow problems which possess the property of the separability of solution. The theory yields valuable information about the complexity of data flow analysis. We show that the complexity of worklist-based iterative analysis is the same for unidirectional and bidirectional problems. We also define a measure of the complexity of round-robin iterative analysis. This measure, called width , is uniformly applicable to unidirectional and bidirectional problems and provides a tighter bound for unidirectional problems than the traditional measure of depth . Other applications include explanation of isolated results in efficient solution techniques and motivation of new techniques for bidirectional flows. In particular, we discuss edge splitting and edge placement and develop a feasibility criterion for decomposition of a bidirectional flow into a sequence of unidirectional flows.

The concept of an information flow path arising from the generalized theory of data flow analysis [21] is used to analyze the complexity of data flow analysis. The width (w) of a program flow graph with respect to a class of data flow problems is introduced as a measure of the complexity of round-robin iterative analysis. This provides the first known complexity result for round robin iterative analysis of bidirectional data flows commonly used in algorithms based on the suppression of partial redundancies [6, 7, 8, 9, 17, 18, 25]. We also show that width provides a better bound on the complexity of unidirectional data flows than the classical notion of depth.

Bidirectional data flow problems, useful in a wide range of optimizing transformations, are conventionally solved using the iterative approach.Thm paper shows that use of the edge placement technique makes bidirectional data flow problems amenable to effkient solution.An elimination algorithm for bidirectional data flow problems using edge placement is presented, and its complexity is shown to be ldentlcal to the complexity of elimination algorithms for unidirectional data flows.

Elimination of partial redundancies is a powerful optimization that has been implemented in at least three important production compilers and has inspired several similar optimizations. The global data flow analysis that supports this family of optimizations includes some bidirectional problems. (A bidirectional problem is one in which the global information at each basic block depends on both control flow predecessors and control flow successors.) This paper contributes two ways to simplify and expedite the analysis, especially for large programs. For each global data flow question, we examine only the places in the program where the question might have an answer different from a trivial default answer. In a large program, we may examine only a small fraction of the places conventional algorithms would examine. We reduce the relevant bidirectional problems to simpler unidirectional problems. These bidirectional problems can be solved by applying a quick correction to a unidirectional approximation.

We present some modifications to Morel and Renvoise's algorithm for global optimization by suppression of partial redundancies.The modifications are motivated by the desire to ( 1) eliminate redundant code motion, and (2) extend the scope of optimization to the movement of assignments.The complexity of the modified algorithm is compared with that of the original algorithm.