Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++
ACM Transactions on Mathematical Software (TOMS)
Algorithms and design for a second-order automatic differentiation module
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Automatic differentiation and numerical software design
Proceedings of the IFIP TC2/WG2.5 working conference on Quality of numerical software: assessment and enhancement
ADIC: an extensible automatic differentiation tool for ANSI-C
Software—Practice & Experience
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Adifor 2.0: Automatic Differentiation of Fortran 77 Programs
IEEE Computational Science & Engineering
Semantics of roundoff error propagation in finite precision calculations
Higher-Order and Symbolic Computation
Program transformation for numerical precision
Proceedings of the 2009 ACM SIGPLAN workshop on Partial evaluation and program manipulation
Direct computation of critical points based on Crout's elimination and diagonal subset test function
Computers and Structures
Interval slopes as a numerical abstract domain for floating-point variables
SAS'10 Proceedings of the 17th international conference on Static analysis
An overview of semantics for the validation of numerical programs
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
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Automatic differentiation is a semantic transformation that applies the rules of differential calculus to source code. It thus transforms a computer program that computes a mathematical function into a program that computes the function and its derivatives. Derivatives play an important role in a wide variety of scientific computing applications, including optimization, solution of nonlinear equations, sensitivity analysis, and nonlinear inverse problems. We describe a simple component architecture for developing tools for automatic differentiation and other mathematically oriented semantic transformations of scientific software. This architecture consists of a compiler-based, language-specific front-end for source transformation, loosely coupled with one or more language-independent "plug-in" transformation modules. The coupling mechanism between the front-end and transformation modules is provided by the XML Abstract Interface Form (XAIF). XAIF provides an abstract, language-independent representation of language constructs common in imperative languages, such as C and Fortran. We describe the use of this architecture in constructing tools for automatic differentiation of Fortran 77 and ANSI C, and we discuss how access to compiler optimization techniques can enable more efficient derivative augmentation.