Seasons's Greetings by AD

We use Algorithmic Differentiation (AD) to implement type-generic tangent and adjoint versions of $$y=\sum _{i=0}^{n-1}{x}_{2i}\cdot x_{2i+1}$$ in C++. We run an instantiation for char-arithmetic and we print the gradient at $(10177114114321211098811597{)}^T$ 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 $(72971121121213250485054{)}^T\mathrm{.}$ 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.