Interprocedural Constant Propagation

Transcription

1 RETROSPECTIVE: Interprocedural Constant Propagation David Callahan Keith D. Cooper Ken Kennedy Linda Torczon Cray Research, Inc. Department of Computer Department of Computer Department of Computer 411 First Avenue South Science Science Science Suite 600 Rice University Rice University Rice University Seattle, WA Houston, TX Houston, TX Houston, TX INTRODUCTION The notion that the compiler could discover constant-valued variables and use that knowledge to improve programs goes back to the earliest days of compilation. Early work focused on propagating constant values in expressions [14] and, later, in single procedures [17, 25, 20, 26]. Constant propagation was well studied in the literature on data-flow analysis because it is fundamentally harder than most of the classic single-procedure data-flow problems [16]. This paper presents the first standalone algorithm for approximate solution of the interprocedural constant propagation problem. It abstracts the solver into an interprocedural propagation framework and a set of functions that model the intraprocedural propagation of values. We called these latter models jump functions, after an idea that John Cocke had proposed in a different context. As part of her thesis work, Linda Torczon developed the algorithms for interprocedural constant propagation that appear in this paper [24]. David Callahan did the first implementation of these ideas in the PFC (Parallel Fortran Converter) project at Rice. This paper presents one of the first practical solutions for approximating the answers to a flow-sensitive interprocedural problem. 2. BACKGROUND This work has its origins in the R n Programming Environment project at Rice. One of its goals was to attack the problems associated with performing interprocedural analysis and optimization in a compiler. The environment supported Fortran 77. At that time, few compilers employed interprocedural techniques because of the conflict between the programmer s need for separate compilation and the compiler s need for information about the internals of every procedure in the program. Collecting this information required, at least, a linear pass over the entire program a much higher price than one would incur with separate compilation. One of the central ideas in R n was that the environment could perform per-procedure analysis when the programmer saved code from the environment s editor. This avoids the cost of re-analyzing the code on each compilation. It also creates a situation where recompilation analysis can limit the amount of compilation required in response to an editing change [12, 8]. Two major factors influenced our decision to tackle interprocedural constant propagation. First, several recent papers had focused on improvements due to procedure integration. Scheifler studied procedure integration in CLU [23]. Ball showed a simple method for predicting the improvement possible with inline substitution, 20 Years of the ACM/SIGPLAN Conference on Programming Language Design and Implementation ( ): A Selection, Copyright 2003 ACM $5.00. based on knowledge of the constant-valued parameters at a call site [4]. Allen, et al. showed the potential for interprocedural improvement in their influential Experimental Compiling System [2]. Second, a growing body of evidence suggested that many call sites pass constant values as actual parameters, particularly to library routines [2, 13]. Interprocedural constant propagation was an obvious next step after computing flow-insensitive summary sets [11]. The formulation in the paper uses an optimistic, worklist-driven, iterative data-flow algorithm to compute sets of constants that hold on entry to each procedure. Our goal was an algorithm that captured the style and insights of the single-procedure algorithm operating on def-use chains, without paying the full cost of abstract interpretation each time it examined a procedure. The final algorithm uses an iterative solver to model the flow of values between procedures. It uses abstract jump function to model the flow of values through a procedure. These jump functions play the role of complex instructions that summarize the behavior of an entire procedure, capturing the flow of values into and out of the procedure. The precision of the jump functions can vary with the amount of effort spent computing them. We proposed several ways to implement jump functions; in the R n framework, the editor would produce them. The iterative interprocedural solver would call on jump functions as needed to propagate values drawn from the usual constant propagation lattice. The set of constants that the algorithm discovered depended on the precision of the computed jump functions. 3. INFLUENCE The first papers to explicitly discuss interprocedural constant propagation were our paper and the companion paper in the same session by Burke and Cytron [7]. Earlier systems had addressed the issue through a combination of inline substitution and global constant propagation [2, 26]. Interprocedural constant propagation has become an important analysis tool in aggressive optimizing compilers, particularly systems that try to automatically discover parallelism [6]. The algorithms described in this paper were implemented in the PFC system [3] and the Convex Applications Compiler [18]. The PTRAN system used an algorithm that propagated literal constant arguments along parameter binding chains in the program [1]. The ParaScope system used an early version of the FIAT analyzer to perform interprocedural constant propagation [10]. A later version of FIAT was used in the SUIF system; today, SUIF performs constant propagation as part of a general interprocedural symbolic analysis [19]. Since this paper appeared, many papers on interprocedural constant propagation have appeared. Allen, et al. described the flowinsensitive algorithm used in PTRAN [1]. Wegman and Zadeck ACM SIGPLAN 155 Best of PLDI

2 showed how to combine their intraprocedural algorithm with inline substitution to capture interprocedural constants [27]. Grove and Torczon published a study of the effectiveness of different jumpfunction implementations [15]. Binkley proposed an algorithm that performs interprocedural analysis over a variant on the programdependence graph [5]. Carini and Hind developed an algorithm that performs flow-sensitive constant propagation, with support for general recursion, while using only one flow-sensitive analysis of each procedure [9]. Sagiv, Reps, and Horwitz describe contextsensitive algorithms for two important subsets of interprocedural constant propagation [22, 21]. 4. ACKNOWLEDGMENTS The research described in the paper was supported by both the National Science Foundation and by IBM Corporation. Our many colleagues who worked on the R n environment created a software system and a climate in which we could tackle problems like this one. To all these people, we owe a debt of thanks. REFERENCES [1] F. Allen, M. Burke, P. Charles, R. Cytron, and J. Ferrante. An overview of the PTRAN analysis systems for multiprocessing. Journal of Parallel and Distributed Computation, 5(5): , [2] F. Allen, J. Carter, J. Fabri, J. Ferrante, W. Harrison, P. Loewner, and L. Trevillyan. The experimental compiling system. IBM Journal of Research and Development, 24(6): , Nov [3] J. Allen and K. Kennedy. PFC: a program to convert FORTRAN to parallel form. In K. Hwang, editor, Supercomputers: Design and Applications. IEEE Computer Society Press, [4] J. E. Ball. Predicting the effects of optimization on a procedure body. SIGPLAN Notices, 14(8): , Aug Proceedings of the ACM SIGPLAN 79 Symposium on Compiler Construction. [5] D. Binkley. Interprocedural constant propagation using dependence graphs and a data-flow model. In Proceedings of the 5 th International Conference on Compiler Construction, pages , Springer Verlag LNCS 786. [6] W. Blume and R. Eigenmann. An overview of symbolic analysis techniques needed for the effective parallelization of the Perfect benchmarks. In Proceedings of the 23 rd International Conference on Parallel Processing, Volume 2: Software, pages CRC Press, Aug [7] M. Burke and R. Cytron. Interprocedural dependence analysis and parallelization. SIGPLAN Notices, 21(7): , July Proceedings of the ACM SIGPLAN 86 Symposium on Compiler Construction. [8] M. Burke and L. Torczon. Interprocedural optimization: Eliminating unnecessary recompilation. ACMTransactions on Programming Languages and Systems, 15(3): , July [9] P. R. Carini and M. Hind. Flow-sensitive interprocedural constant propagation. SIGPLAN Notices, 30(6):23 31, June Proceedings of the ACM SIGPLAN 95 Conference on Programming Language Design and Implementation. [10] A. Carle, M. Hall, J. Mellor-Crummey, and R. Rodriguez. FIAT: A framework for interprocedural analysis and transformation. In Proceedings of the Sixth Workshop on Langauges and Compilers for Parallel Computing, pages , Aug [11] K. D. Cooper and K. Kennedy. Interprocedural side-effect analysis in linear time. SIGPLAN Notices, 23(7):57 66, July Proceedings of the ACM SIGPLAN 88 Conference on Programming Language Design and Implementation. [12] K. D. Cooper, K. Kennedy, and L. Torczon. Interprocedural optimization: Eliminating unnecessary recompilation. SIGPLAN Notices, 21(7):58 67, July Proceedings of the ACM SIGPLAN 86 Symposium on Compiler Construction. [13] J. Dongarra. LINPACK working note #3: FORTRAN BLAS timing. Technical Report ANL-80-24, Argonne National Laboratory, Feb [14] R. Floyd. An algorithm for coding efficient arithmetic expressions. Communications of the ACM, 22(5):42 51, Jan [15] D. Grove and L. Torczon. Interprocedural constant propagation: A study of jump function implementations. SIGPLAN Notices, 28(6):90 99, June Proceedings of the ACM SIGPLAN 93 Conference on Programming Language Design and Implementation. [16] J. B. Kam and J. D. Ullman. Monotone data flow analysis frameworks. Acta Inf., 7: , [17] G. A. Kildall. A unified approach to global program optimization. In Conference Record of the ACM Symposium on Principles of Programming Languages, pages , Boston, MA, USA, Oct [18] R. Metzger and P. Smith. The CONVEX application compiler. Fortran Journal, 3(1):8 10, [19] B. R. Murphy. Frameworks for Precise Program Analysis. PhD thesis, Department of Computer Science, Stanford University, Dec [20] J. H. Reif and H. R. Lewis. Symbolic evaluation and the global value graph. In Conference Record of the Fourth ACM Symposium on Principles of Programming Languages, pages , Los Angeles, CA, USA, Jan [21] T. Reps, S. Horwitz, and M. Sagiv. Precise interprocedural dataflow analysis via graph reachability. In Conference Record of POPL 95: 22nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 49 61, San Francisco, CA, USA, Jan [22] M. Sagiv, T. Reps, and S. Horwitz. Precise interprocedural dataflow analysis with application to constant propagation. In Proceedings of the 6 th International Conference on Theory and Practice of Software Development (TAPSOFT), pages , [23] R. W. Scheifler. An analysis of inline substitution for a structured programming language. Communications of the ACM, 20(9): , [24] L. Torczon. Compilation Dependences in an Ambitious Optimizing Compiler. PhD thesis, Department of Computer Science, Rice University, May [25] B. Wegbreit. Property extraction in well-founded sets. IEEE Transactions on Software Engineering, 1(3), Sept [26] M. N. Wegman and F. K. Zadeck. Constant propagation with conditional branches. In Conference Record of the Twelfth Annual ACM Symposium on Principles of Programming Languages, pages , New Orleans, LA, USA, Jan [27] M. N. Wegman and F. K. Zadeck. Constant propagation with conditional branches. ACM Transactions on Programming Languages and Systems, 13(2): , Apr ACM SIGPLAN 156 Best of PLDI

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