A taxonomy of automatic differentiation tools

Many of the current automatic differentiation (AD) tools have similar characteristics. Unfortunately, the similarities between these various AD tools often cannot be easily ascertained by reading the corresponding documentation. To clarify this situation, a taxonomy of AD tools is presented. The taxonomy places AD tools into the Elemental, Extensional, Integral, Operational, and Symbolic classes. This taxonomy is used to classify twenty-nine AD tools. Each tool is examined individually with respect to the mode of differentiation used and the degree of derivatives computed. A list detailing the availability of the surveyed AD tools is provided in the Appendix. 54 refs., 3 figs., 1 tab