ADIFOR: Fortran source translation for efficient derivatives

The numerical methods employed in the solution of many scientific computing problems require the computation of derivatives of a function f: R{sup n} {yields} R{sup m}. Both the accuracy and the computational requirements of the derivative computation are usually of critical importance for the robustness and speed of the numerical method. ADIFOR (Automatic Differentiation In FORtran) is a source translation tool implemented using the data abstractions and program analysis capabilities of the ParaScope Parallel Programming Environment. ADIFOR accepts arbitrary Fortran-77 code defining the computation of a function and writes portable Fortran-77 code for the computation of its derivatives. In contrast to previous approaches, ADIFOR views automatic differentiation as a process of source translation that exploits computational context to reduce the cost of derivative computations. Experimental results show that ADIFOR can handle real-life codes, providing exact derivatives with a running time that is competitive with the standard divided-difference approximations of derivatives and which may perform orders of magnitude faster than divided-differences in cases. The computational scientist using ADIFOR is freed from worrying about the accurate and efficient computation of derivatives, even for complicated functions,'' and hence, is able to concentrate on the more important issues of algorithm design or system modeling. 35 refs