Tangent-Linear Models by Augmented LL-Parsers

We describe a novel method for the generation of tangent-linear code by augmentation of LL-parsers generated by the software tool ANTLR. The main advantage of this approach to source code augmentation is the missing requirement for an internal representation of the original program. We consider this work as the basis for further investigations into how far this technique can be extended in the context of more sophisticated transformations, for example, the automatic generation of adjoint codes. Our prototype tool AD C ANTLR currently accepts a subset of the ANSI C standard. We discuss its theoretical basis, and we present case studies to underline the elegance of the parser-based approach to source augmentation. 1 Motivation and Summary of Results What are tangent-linear models good for? Consider the elliptic partial differential equation −∆y − λe = 0 (1) on the unit square Ω where y(x1, x2) = 0 on ∂Ω. 1 The Laplacian operator is defined as ∆ ≡ ∂ ∂x 1 + ∂ ∂x 2 . It can be solved using a centered finite difference scheme by approximating the first derivative with respect to x1 and x2 at the midpoints of the discretization intervals a = ( x1i − x 1 i−1 2 , x2j ), b = ( x1i+1 − x 1 i