Extending compile-time reverse mode and exploiting partial separability

Abstract. The numerical methods employed in the solution of many scientic computing problems require the computation of the gradient of a function f: R n! 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 dierentiation: the ecient 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.