Automatic optimization of symbolic algol programs. I. General principles

The symbolic style of programming referred to as Symbolic Algol I [1] appears to have a number of advantages when applied to the solution of sets of nonlinear partial-differential equations. Programs written in that style are clear, elegant, and concise and their modular structure enables large parts of the programs to be used over and over again for many different problems. Such programs, however, tend to be slow because they involve a large number of nested procedure calls at execution time. Finite-difference methods in several dimensions require in general that a relatively small number of equations be solved a large number of times and much is gained if these nested procedure calls are executed only once. This is achieved by a generator or translator program, written in Algol, which processes input written in a related style named Symbolic Algol II. Usually only finite-difference equations in very compact symbolic form are input, while output is completely explicit and can be in a number of computer languages. Of greatest interest are Assembler code modules automatically produced in this way. They are competitive in speed with fully hand-optimized Fortran versions and are produced effortlessly and error free, so that complex sets of equations can readily be programmed or alterations made. For production runs these modules can be incorporated, into a Fortran control program.