Automatic differentiation and numerical software design

Automatic diierentiation (AD) tools can generate accurate and eecient derivative code for computer programs of arbitrary length. In some cases, however, the developer of the code to be diierentiated may be required to provide additional information to an AD tool to ensure the desired solution. We illustrate these issues with nondiierentiable language intrinsics such as max() in the context of computing the Euclidean norm and numerical integrators. In both cases, very little additional information is required to ensure that AD computes the \do-what-I-mean" derivatives. In addition, the provision of such information makes it easy to derive \derivative-enhanced" versions of these codes.