Implementation and measurements of an efficient Fixed Point Adjoint

Efficient Algorithmic Differentiation of Fixed-Point loops requires a specific strategy to avoid explosion of memory requirements. Among the strategies documented in literature, we have selected the one introduced by B. Christianson. This method features original mechanisms such as repeated access to the trajectory stack or duplicated differentiation of the loop body with respect to different independent variables. We describe in this paper how the method must be further specified to take into account the particularities of real codes, and how data flow information can be used to automate detection of relevant sets of variables. We describe the way we implement this method inside an AD tool. Experiments on a medium-size application demonstrate a minor, but non negligible improvement of the accuracy of the result, and more importantly a major reduction of the memory needed to store the trajectories