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Forward Mode Automatic Differentiation for Julia

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This PR backports the following PRs from the master branch to the release-0.10 branch such that they can be released: - #586 - #615 (backport requested in https://github.com/JuliaDiff/ForwardDiff.jl/pull/615#issuecomment-1946030042) - #631...

The following works: ```julia N = 8; t = (0:N-1)*2π/N; yt = cos.(t); fun = (yt) -> begin yf = rfft(yt); yout = real(yf); return yout; end; Dh = ForwardDiff.jacobian(fun,...

by adding the suggestion done in #720 . Closes #720

This is largely to improve printing and reduce visual noise for packages with large function types (e.g. SciML) Compare `tag = :small`: ``` ForwardDiff.Dual{ForwardDiff.SmallTag{0x39f35d61d979c3d1}, Float64, 3} ``` to `tag =...

First commit adds only those in `api.md`, but perhaps we should add more... like `Dual`? ```julia help?> ForwardDiff.Dual │ Warning │ │ The following bindings may be internal; they may...

I just learnt that since Preferences 1.4.3, `Preferences.set_preferences!` accepts package names in addition to modules and UUIDs. This PR updates the docs accordingly, I think most users would prefer not...

ForwardDiff (v1.0.1 as well as v0.10.38) fails to compute the gradient when the inputs are too large for the following function. ```julia julia> using ForwardDiff julia> foo(a) = a[1] *...

I think with v1.0 it makes sense to drop the support for earlier versions of Julia before the LTS. The benefits are: 1. We can drop StaticArrays as a dependency...