  Algorithmic differentiation (AD) is a set of techniques that provide partial
derivatives of computer-implemented functions. Such a function can be supplied
to state-of-the-art AD tools via its source code, or via an intermediate
representation produced while compiling its source code.
  We present the novel AD tool Derivgrind, which augments the machine code of
compiled programs with forward-mode 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. Access to the source code is required
at most for the files in which input and output variables are defined.
  Derivgrind's versatility comes at the price of scaling the run-time by a
factor between 30 and 75, measured on a benchmark based on a numerical solver
for a partial differential equation. Results of our extensive regression 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, nearly all of them are academic counterexamples or originate
from highly optimized math libraries. As long as differentiating those is
avoided, Derivgrind can be applied to an unprecedentedly wide range of
cross-language or partially closed-source software with little integration
efforts.
