Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++
ACM Transactions on Mathematical Software (TOMS)
Bisimilarity in term graph rewriting
Information and Computation - Special issue on EXPRESS 1997
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Optimal accumulation of Jacobian matrices by elimination methods on the dual computational graph
Mathematical Programming: Series A and B
Representation-independent program analysis
PASTE '05 Proceedings of the 6th ACM SIGPLAN-SIGSOFT workshop on Program analysis for software tools and engineering
On the implementation of automatic differentiation tools
Higher-Order and Symbolic Computation
Hybrid static/dynamic activity analysis
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
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Automatic differentiation is a technique for the rule-based transformation of a subprogram that computes some mathematical function into a subprogram that computes the derivatives of that function. Automatic differentiation algorithms are typically expressed as operating on a weighted term graph called a linearized computational graph. Constructing this weighted term graph for imperative programming languages such as C/C++ and Fortran introduces several challenges. Alias and definition-use information is needed to construct term graphs for individual statements and then combine them into one graph for a collection of statements. Furthermore, the resulting weighted term graph must be represented in a language-independent fashion to enable the use of AD algorithms in tools for various languages. We describe the construction and representation of weighted term graphs for C/C++ and Fortran, as implemented in the ADIC 2.0 and OpenAD/F tools for automatic differentiation.