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The numerical methods employed in the solution of many scientific computing problems require the computation of the gradient of a function f: R[sup n] [yields] R. ADIFOR is a source translator that, given a collection of subroutines to compute f, generates Fortran 77 code for computing the derivative of this function. Using the so-called torsion problem from the MINPACK-2 test collection as an example, this paper explores two issues in automatic differentiation: the efficient computation of derivatives for partial separable functions and the use of the compile-time reverse mode for the generation of derivatives. We show that orders of magnitudes of improvement are possible when exploiting partial separability and maximizing use of the reverse mode.

Extending compile-time reverse mode and exploiting partial separability in ADIFOR