ADIC | An extensible automatic dierentiation tool for ANSI-C, Software{Practice and Experience

1 Abstract. In scientic 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 dierentiation (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 Dierentiation 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 dierent languages. A component architecture called AIF (Automatic Dierentiation Intermediate Form) separates core AD concepts from their language-specic implementation and allows the development of generic AD modules that can be reused directly in other AIF-based AD tools. The language-specic ADIC front-end and back-end canonicalize C programs to make them t for semantic augmentation and manage, for example, th