Seasons's Greetings by AD

arXiv (Cornell University)

Abstract

We use Algorithmic Differentiation (AD) to implement type-generic tangent and adjoint versions of $$ y=\sum_{i=0}^{n-1} x_{2 i} \cdot x_{2 i+1} $$ in C++. We run an instantiation for char-arithmetic and we print the gradient at $(101~77~114~114~32~121~109~88~115~97)^T$ to std::cout, yielding the output ``Merry Xmas''. Similar instantiations of type-generic second-order tangent and second-order adjoint versions of $$ y=\frac{1}{6} \cdot \sum_{i=0}^{n-1} x^3_{i} $$ yield ``Happy 2026'' at $(72~97~112~112~121~32~50~48~50~54)^T.$ Prepend a sufficiently large number of zeros to the input vector to explore the varying run times of the different derivative codes. The entire source code can be found on https://github.com/un110076/SeasonsGreetings.

Authors 1

1. Uwe Naumann corresponding Aachen Software and Tools for Computational Engineering

   RWTH Aachen University

   Affiliation as printed

   Software and Tools for Computational Engineering , RWTH Aachen University , Germany