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Extra info for Optimizing compilers for modern architectures; a dependence based approach
No execution constraint between S1 and S2 is required because the execution order S2, S1, S3 will produce exactly the same value for PI as the execution order S1, S2, S3. The other constraint that gives rise to dependences is control flow. NE. 0) GOTO S3 A = A / T CONTINUE statement S2 cannot be executed before S1 in a correctly transformed program, because the execution of S2 is conditional upon the execution of the branch in S1. Executing S2 before S1 could cause a divide-by-zero exception that would be impossible in the original version.
A. Patterson. Computer Architecture A Quantitative Approach, Second Edition. Morgan Kauffman, San Francisco, CA, 1996.  L. Lamport. The parallel execution of DO loops. Communications of the ACM, 17(2):83–93, February 1974.  L. Lamport. The coordinate method for the parallel execution of iterative DO loops. Technical Report CA-7608-0221, SRI, Menlo Park, CA, August 1976, revised October 1981.  D. Loveman. Program improvement by source-to-source transformations. Journal of the ACM, 17(2):121–145, January 1977.
In order to illustrate the concepts of program transformations, it is necessary to have a language in which examples can be presented. Since Fortran is by far and away the most heavily used language on parallel and vector computers today, the most logical choice of language is a version of Fortran extended with vector and parallel operations. For this purpose, we will use Fortran 90 with the addition of a parallel loop statement. Appendix A on page 831 contains a simple introduction to the features of Fortran 90.
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