Precise Interprocedural Dataflow Analysis with Applications to Constant Propagation

This paper concerns inter-procedural dataflow-analysis problems in which the dataflow information at a program point is represented by an environment (i.e., a mapping from symbols to values), and the effect of a program operation is represented by a distributive environment transformer. We present two efficient algorithms that produce precise solutions: an exhaustive algorithm that finds values for all symbols at all program points, and a demand algorithm that finds the value for an individual symbol at a particular program point. Two interesting problems that can be handled by our algorithms are (decidable) variants of the interprocedural constant-propagation problem: copy-constant propagation and linear-constant propagation. The former interprets program statements of the form x := 7 and x := y. The latter also interprets statements of the form x := 5 * y + 17. Experimental results on C programs have shown that Although solving constant-propagation problems precisely (i.e., finding the meet-over-allvalid-paths solution, rather than the meet-over-all-paths solution) resulted in a slowdown by a factor ranging from 2.2 to 4.5, the precise algorithm found additional constants in 7 of 38 test programs. In contrast to previous results for numeric Fortran programs, linear-constant propagation found more constants than copy-constant propagation in 6 of 38 test programs. The demand algorithm, when used to demand values for all uses of scalar integer variables, was faster than the exhaustive algorithm by a factor ranging from 1.14 to about 6. * Corresponding author. ’ This work was supported in part by a David and Lucile Packard Fellowship for Science and Engineering, by the National Science Foundation under granta CCR-8958530 and CCR-9100424, by the Defense Advanced Research Projects Agency under ARPA Order No. 8856 (monitored by the Office of Naval Research under contract N00014-92-J-1937), and by a grant from Xerox Corporate Research. Part of this work was done while the authors were visiting the University of Copenhagen. A preliminary version of this paper appeared in Proc. of FASE 95: Colloquium on Formal Approaches in Software Engineering, (Aarhus, Denmark, May 22-26, 1995) [27]. z Current address: Department of Computer Science, The University of Chicago, 1100 East 58th Street, Chicago, IL 60637, USA. 0304-3975/96/$15.00 @ 1996-Elsevier Science B.V. All rights reserved PZI SO304-3975(96)00072-2 132 M. Sagiv et al. I Theoretical Computer Science 167 (1996) 131-170