The Tapenade automatic differentiation tool

TLDR

Tapenade is an automatic differentiation tool that transforms Fortran or C code into tangent or adjoint derivative code, emphasizing low‑cost adjoint differentiation. This article outlines Tapenade’s principles, formally specifies its AD model, discusses its architectural design, and presents planned extensions to support future research. The authors formalize the AD model with data‑flow equations and operational‑semantics rules, describing code structure and efficiency strategies for both tangent and adjoint modes. Benchmarking on industrial‑size applications shows that Tapenade delivers competitive performance.

Abstract

Tapenade is an Automatic Differentiation (AD) tool which, given a Fortran or C code that computes a function, creates a new code that computes its tangent or adjoint derivatives. Tapenade puts particular emphasis on adjoint differentiation, which computes gradients at a remarkably low cost. This article describes the principles of Tapenade, a subset of the general principles of AD. We motivate and illustrate with examples the AD model of Tapenade, that is, the structure of differentiated codes and the strategies used to make them more efficient. Along with this informal description, we formally specify this model by means of data-flow equations and rules of Operational Semantics, making this the reference specification of the tangent and adjoint modes of Tapenade. One benefit we expect from this formal specification is the capacity to formally study the AD model itself, especially for the adjoint mode and its sophisticated strategies. This article also describes the architectural choices of the implementation of Tapenade. We describe the current performance of Tapenade on a set of codes that include industrial-size applications. We present the extensions of the tool that are planned in a foreseeable future, deriving from our ongoing research on AD.