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You seem somewhat obsessed with the idea that reverse-mode autodiff is not the same technique as forward-mode autodiff. It makes you,,, angry? Seems like such a trivial thing to act a complete fool over.
What's up with that?
Anyway, here's a forward differentiation package with a file that might interest you
https://github.com/JuliaDiff/ForwardDiff.jl/blob/master/src/...
I can't reply to the guy saying julia is the only one. But there are others.
Ceres uses dual numbers
https://github.com/ceres-solver/ceres-solver/blob/master/inc...
This library from google is used everywhere in robotics, so it's hardly some backwater little side project.
So does c++ autodiff
Sure, right here: https://github.com/pytorch/pytorch/blob/main/torch/autograd/...
Here's the documentation: https://pytorch.org/tutorials/intermediate/forward_ad_usage....
> When an input, which we call “primal”, is associated with a “direction” tensor, which we call “tangent”, the resultant new tensor object is called a “dual tensor” for its connection to dual numbers[0].
The dual numbers exist just as surely as the real numbers and have been used well over 100 years
https://en.m.wikipedia.org/wiki/Dual_number
Pytorch has had them for many years.
https://pytorch.org/docs/stable/generated/torch.autograd.for...
JAX implements them and uses them exactly as stated in this thread.
https://github.com/google/jax/discussions/10157#discussionco...
As you so eloquently stated, "you shouldn't be proclaiming things you don't actually know on a public forum," and doubly so when your claimed "corrections" are so demonstrably and totally incorrect.