Mixed-language Automatic Differentiation

As AD usage is spreading to larger and more sophisticated applications, problems arise for codes that use several programming languages. Many AD tools have been designed with one application language in mind. Only a few use an internal representation that promotes language-independence, at least conceptually. When faced with the problem of building (with AD) the derivative code of a mixed-language application, end-users may consider using several AD tools, one per language. However, this leads to several problems: • Different AD tools may implemented very different AD models such as overloading-based versus source-transformation based or association-by-address versus association-by-name. These models are often not compatible. • When selecting the source-transformation model (for efficiency of the differentiated code), performance of the differentiated code strongly depends on the quality of data-flow analysis, which must be global on the code. A global analysis with separate AD tools would require inter-tool communication at the level of data-flow analysis, which does not exist at present. In any case, interoperable data-flow analysis between tools imply that the tools share their analysis strategy, which is almost never the case. Consequently, we think the only viable approach is to use a single tool, with a single internal representation and data-flow analysis strategy, therefore converting each source file to this unique representation regardless of its original language. It turns out that Tapenade [1] provides such an internal representation, accessible at present from C or Fortran sources. Other AD tools provide a language-independent internal representation. OpenAD provides such a representation based on the XAIF formalism. However, this gives birth to two separate tools, OpenAD/F for Fortran, and ADIC2 for C. Still, it seems that their is no deep reason to prevent OpenAD application to mixed-language codes. We are lacking information about common architecture between TAF and TAC++ that would allow such mixed-language AD. Rapsodia [2] was the first AD tool to support algorithmic differentiation in tangent mode of mixed-language components, specifically C++ and Fortran. As Rapsodia uses operator overloading, it performs no global analysis of the code. To our knowledge the extension of mixed-language differentiation with Rapsodia to adjoint mode is not yet provided.