Forward-Mode Automatic Differentiation of Compiled Programs

Algorithmic differentiation (AD) is a set of techniques to obtain accurate derivatives of a computer-implemented function in an automatic fashion. State-of-the-art AD tools rely on the source code of the implementation or internal representations of compilers building it. We present the new AD tool Derivgrind, which augments the machine code of compiled programs with forward AD logic. Derivgrind leverages the Valgrind instrumentation framework for a structured access to the machine code, and a shadow memory tool to store dot values. Depending on the application scenario, no access to the source code is required at all, or the access is restricted to the parts defining input and output variables. Derivgrind's versatility comes at the price of scaling the running time by a factor between 60 and 140, measured on a benchmark based on a PDE solver. Results of our extensive test suite indicate that Derivgrind produces correct results on GCC- and Clang-compiled programs, including a Python interpreter, with a small number of exceptions. While we provide a list of scenarios that Derivgrind does not handle correctly, most of them are academic examples or originate from highly optimized math libraries. We will therefore further study the potential of our tool in more complex software projects.