Algorithmic Differentiation for Domain-Specific Languages in C++ with Expression Templates

The application of operator overloading algorithmic differentiation (AD) to computer programs to compute derivatives is quite common. However, the replacement of the underlying computational floating-point type with the specialized type of an AD tool has two problems. First, the memory structure of the program is changed and floating-point data is interleaved with identifiers from AD. This property prevents the compiler from performing optimizations such as SIMD optimizations. Second, the AD tool does not recognize any domainspecific operations, e. g. linear algebra operations, which are executed by the program. This characteristic prevents the AD tool from using specialized algorithms in such places. We propose a new AD tool that is tailored to such situations. The memory structure of the primal data is retained by associating an identifier with each entity, e. g. a matrix, and not with each floating-point value, e. g. an element of a matrix. Operations on such entities can then be annotated and a generator is used to create the AD overloads. We demonstrate that this approach provides performance comparable to that of other specializations. In addition, the run-time overhead factor of reverse AD is quite low for programs that are written purely with linear algebra entities and operations.