In this paper we present an intermediate program representation, called the program dependence graph (PDG), that makes explicit both the data and control dependence5 for each operation in a program. Data dependences have been used to represent only the relevant data flow relationships of a program. Control dependence5 are introduced to analogously represent only the essential control flow relationships of a program. Control dependences are derived from the usual control flow graph. Many traditional optimizations operate more efficiently on the PDG. Since dependences in the PDG connect computationally related parts of the program, a single walk of these dependences is sufficient to perform many optimizations. The PDG allows transformations such as vectorization, that previ-ously required special treatment of control dependence, to be performed in a manner that is uniform for both control and data dependences. Program transformations that require interaction of the two dependence types can also be easily handled with our representation. As an example, an incremental approach to modifying data dependences resulting from branch deletion or loop unrolling is intro-duced. The PDG supports incremental optimization, permitting transformations to be triggered by one another and applied only to affected dependences.

Program analysis and optimization can be speeded up through the use of the dependence flow graph (DFG), a representation of program dependences which generalizes def-use chains and static single assignment (SSA) form. In this paper, we give a simple graph-theoretic description of the DFG and show how the DFG for a program can be constructed in O(EV ) time. We then show how forward and backward dataflow analyses can be performed efficiently on the DFG, using constant propagation and elimination of partial redundancies as examples. These analyses can be framed as solutions of dataflow equations in the DFG. Our construction algorithm is of independent interest because it can be used to construct a program's control dependence graph in O(E) time and its SSA representation in O(EV ) time, which are improvements over existing algorithms. 1 Introduction Anumber of recent papers have focused attention on the problem of speeding up program optimization [FOW87, BMO90, CCF91, PBJ + 91, CFR +...

In this paper, we describe the program structure tree (PST), a hierarchical representation of program structure based on single entry single exit (SESE) regions of the control flow graph. We give a linear-time algorithm for finding SESE regions and for building the PST of arbitrary control flow graphs (including irreducible ones). Next, we establish a connection between SESE regions and control dependence equivalence classes, and show how to use the algorithm to find control regions in linear time. Finally, we discuss some applications of the PST. Many control-flow algorithms, such as construction of Static Single Assignment form, can be speeded up by applying the algorithms in a divide-and-conquer style to each SESE region on its own. The PST is also used to speed up data flow analysis by exploiting `sparsity'. Experimental results from the Perfect Club and SPEC89 benchmarks confirm that the PST approach finds and exploits program structure.

We introduce the tree cross-product problem, which abstracts a data structure common to applications in graph visualization, string matching, and software analysis. We design solutions with a variety of tradeoffs, yielding improvements and new results for these applications.

Many compilation problems require computing the control dependence equivalence relation which divides nodes in a control flow graph into equivalence classes such that nodes are in the same class if and only if they have the same set of control dependences. In this paper, we show that this relation can be computed in O(E) time by reducing it to a naturally stated graph problem: in a strongly connected component, divide nodes into equivalence classes such that every cycle passes through all or none of the nodes in an equivalence class. Our algorithm does not require the computation of the control dependence relation or of the postdominator relation --- in fact, it runs faster in practice than the best algorithms for either of these problems. We also show that our algorithm can be used to determine the single entry single exit regions of a control flow graph in O(E) time. 1 Introduction The notion of control dependence plays an important role in optimization and parallelization. Intuitiv...

Abstract—Advanced computer architectures rely mainly on compiler optimizations for parallelization, vectorization, and pipelining. Efficient code generation is based on a control dependence analysis to find the basic blocks and to determine the regions of control. However, unstructured branch statements, such as jumps and goto’s, render the control flow analysis difficult, time-consuming, and result in poor code generation. Branches are part of many programming languages and occur in legacy and maintenance code as well as in assembler, intermediate languages, and byte code. A simple and effective technique is presented to convert unstructured branches into hammock graph control structures. Using three basic transformations, an equivalent program is obtained in which all control statements have a well-defined scope. In the interest of predication and branch prediction, the number of control variables has been minimized, thereby allowing a limited code replication. The correctness of the transformations has been proven using an axiomatic proof rule system. With respect to previous work, the algorithm is simpler and the branch conditions are less complex, making the program more readable and the code generation more efficient. Additionally, hammock graphs define single entry single exit regions and therefore allow localized optimizations. The restructuring method has been implemented into the parallelizing compiler FPT and allows to extract parallelism in unstructured programs. The use of hammock graph transformations in other application areas such as vectorization, decompilation, and assembly program restructuring is also demonstrated.