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.

The ability to predict at compile time the likelihood of a particular branch being taken provides valuable information for several optimizations, including global instruction scheduling, code layout, function inlining, interprocedural register allocation and many high level optimizations. Previous attempts at static branch prediction have either used simple heuristics, which can be quite inaccurate, or put the burden onto the programmer by using execution profiling data or source code hints. This paper presents a new approach to static branch prediction called value range propagation. This method tracks the weighted value ranges of variables through a program, much like constant propagation. These value ranges may be either numeric or symbolic in nature. Branch prediction is then performed by simply consulting the value range of the appropriate variable. Heuristics are used as a fallback for cases where the value range of the variable cannot be determined statically. In the process, va...

The topic of intermediate languages for optimizing and parallelizing compilers has received much attention lately. In this paper, we argue that any good representation of a program must have two crucial properties: first, it must be a data structure that can be rapidly traversed to determine dependence information, and second this representation must be a program in its own right, with a parallel, local model of execution. In this paper, we illustrate the importance of these points by examining algorithms for a standard optimization --- global constant propagation. We discuss the problems in working with current representations. Then, we propose a novel representation called the dependence flow graph which has each of the properties mentioned above. We show that this representation leads to a simple algorithm, based on abstract interpretation, for solving the constant propagation problem. Our algorithm is simpler than, and as efficient as, the best known algorithms for this problem. An...

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A program flow analysis framework is proposed for parallelizing compilers. Within this framework, symbolic analysis is used as an abstract interpretation technique to solve many of the flow analysis problems in a unified way. Some of these problems are constant propagation, global forward substitution, detection of loop invariant computations, and induction variable substitution. The solution space of the above problems is much larger than that handled by existing compiler technology. It covers many of the cases in benchmark codes that other parallelizing compilers can not handle. Employing finite difference methods, the symbolic analyzer derives a functional representation of programs, which is used in dependence analysis. A systematic method for generalized strength reduction based on this representation is also presented. This results in an effective scheme for exploitation of parallelism and optimization of the code. Symbolic analysis also serves as a basis for other code generatio...

When analyzing programs for value recomputation, one faces the problem of naming the value that flows between equivalent computations with different lexical names. This paper presents a data-flow analysis framework that overcomes this problem by synthesizing a name space tailored for tracing the values whose flow is of interest to a given data-flow problem. Furthermore, to exploit recomputation of a value with multiple, synonymous names, path-sensitive value numbering on the synthetic name space is developed. Optimizations that rely on value flow to detect redundant computations, such as partial redundancy elimination and constant propagation, become more powerful when phrased in our framework. The framework is built on a new program representation called Value Name Graph (VNG) which gains its power from integrating three orthogonal techniques: symbolic back-substitution, value numbering, and data-flow analysis. Our experiments with the implementation show that analysis on the VNG is p...

Abstract. Constant propagation aims at identifying expressions that always yield a unique constant value at run-time. It is well-known that constant propagation is undecidable for programs working on integers even if guards are ignored as in non-deterministic flow graphs. We show that polynomial constants are decidable in non-deterministic flow graphs. In polynomial constant propagation, assignment statements that use the operators +, −, ∗ are interpreted exactly but all assignments that use other operators are conservatively interpreted as non-deterministic assignments. We present a generic algorithm for constant propagation via a symbolic weakest precondition computation and show how this generic algorithm can be instantiated for polynomial constant propagation by exploiting techniques from computable ring theory. 1

. Data flow analysis expresses the solution of an information gathering problem as the fixed point of a system of monotone equations. This paper presents a technique to improve the performance of data flow analysis by systematically reducing the size of the equation system in any monotone data flow problem. Reductions result from partitioning the equations in the system according to congruence relations. We present a fast O(n log n) partitioning algorithm, where n is the size of the program, that exploits known algebraic properties in equation systems. From the resulting partition a reduced equation system is constructed that is minimized with respect to the computed congruence relation while still providing the data flow solution at all program points. 1 Introduction Along with the growing importance of static data flow analysis in current optimizing and parallelizing compilers comes an increased concern about the high time and space requirements of solving data flow problems. Experi...

This paper explores the concept of loops and loop nesting forests of control-flow graphs, using the problem of constructing the dominator tree of a graph and the problem of computing the iterated dominance frontier of a set of vertices in a graph as guiding applications. The contributions of this paper include: (1) An axiomatic characterization, as well as a constructive characterization, of a family of loop nesting forests that includes various specific loop nesting forests that have been previously defined. (2) The definition of a new loop nesting forest, as well as an e#cient, almost linear time, algorithm for constructing this forest. (3) An illustration of how loop nesting forests can be used to transform arbitrary (potentially irreducible) problem instances into equivalent acylic graph problem instances in the case of the two problems of (a) constructing the dominator tree of a graph, and (b) computing the iterated dominance frontier of a set of vertices in a graph, leading to new, almost linear time, algorithms for these problems

. We present several new compiler techniques employed by our interprocedural parallelizing research compiler, Panorama, to improve loop parallelization and the efficiency of memory references. We first present an overview of the compiler and its associated memory architecture simulation environments. We then present an interprocedural array dataflow analysis, using guarded array regions, for automatic array privatization, an interprocedural static profile analysis, and a graph reduction algorithm for parallel task assignment and data allocation which aims at reducing remote memory references while maintaining loop parallelism. 1 Introduction In recent years, researchers see a growing interest in shared-memory multiprocessors with multi-level memories which provide private caches and/or non-uniform memory accesses (NUMA) [14, 15, 28]. In order to deliver the power of such machines to ordinary programs written by a wide range of programmers, it is important for the compilers to improve ...