ADIC: An Extensible Automatic Differentiation Tool for ANSI-C

In scienti c computing, we often require the derivatives @f=@x of a function f expressed as a program with respect to some input parameter(s) x, say. Automatic di erentiation (AD) techniques augment the program with derivative computation by applying the chain rule of calculus to elementary operations in an automated fashion. This article introduces ADIC (Automatic Di erentiation of C), a new AD tool for ANSI-C programs. ADIC is currently the only tool for ANSI-C that employs a source-to-source program transformation approach; that is, it takes a C code and produces a new C code that computes the original results as well as the derivatives. We rst present ADIC \by example" to illustrate the functionality and ease of use of ADIC and then describe in detail the architecture of ADIC. ADIC incorporates a modular design that provides a foundation for both rapid prototyping of better AD algorithms and their sharing across AD tools for di erent languages. A component architecture called AIF (Automatic Di erentiation Intermediate Form) separates core AD concepts from their language-speci c implementation and allows the development of generic AD modules that can be reused directly in other AIF-based AD tools. The language-speci c ADIC front-end and backend canonicalize C programs to make them t for semantic augmentation and manage, for example, the association of a program variable with its derivative object. We also report on applications of ADIC to a semiconductor device simulator, 3-D CFD grid generator, vehicle simulator, and neural network code.