Seasons's Greetings by AD
<|reference_start|>Seasons's Greetings by AD: We use Algorithmic Differentiation (AD) to implement type-generic tangent and adjoint versions of $$ y=\sum_{i=0}^{n-1} x_{2 i} \cdot x_{2 i+1} $$ 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 2024'' at $(72~97~112~112~121~32~50~48~50~52)^T.$ 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.<|reference_end|>
@article{naumann2023seasons's,
    title={Seasons's Greetings by AD},
    author={Uwe Naumann},
    journal={arXiv preprint arXiv:2402.09409},
    year={2023},
    archivePrefix={arXiv},
    eprint={2402.09409},
    primaryClass={cs.CE}
}