Differentiation transforming system

The differentiation transforming (DFT) system is developed to produce the tangent linear codes, which is used to calculate the Jacobian- and the Hessian-vector products with no truncation errors. This paper first gives the introduction of the functionality and features of the DFT system, and then discusses several techniques for the implementation of automatic differentiation tools, including data dependence analysis, singular differentiation and code optimization. Finally, the codes generated with DFT used in several applications have been demonstrated.