fix: overloaded_input_type for one-element vector input

[ErikQQY]

overloaded_input_type doesn't work for jacobian with one-element vector:

julia> backend = AutoForwardDiff()
AutoForwardDiff()

julia> DI.overloaded_input_type(prepare_jacobian(copy, backend, [1.0]))
ERROR: BoundsError: attempt to access 1-element Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(copy), Float64}, Float64, 1}} at index [2]

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.19%. Comparing base (cd515b3) to head (44d8e95).
⚠️ Report is 2 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #954   +/-   ##
=======================================
  Coverage   98.19%   98.19%           
=======================================
  Files         133      133           
  Lines        7982     7983    +1     
=======================================
+ Hits         7838     7839    +1     
  Misses        144      144           

Flag	Coverage Δ
DI	98.96% <100.00%> (+<0.01%)	⬆️
DIT	96.19% <ø> (ø)

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[gdalle]

Hi @ErikQQY, thanks for the suggested bug fix!
However, it turns out the issue runs deeper than that, and actually goes back to our first PR introducing this mechanism in #672. We neglected several aspects back then:

• from DerivativeConfig in the two-argument case (in-place), we used to retrieve the type of ydual but we actually want the type of xdual.
• from JacobianConfig in the one-argument case (out-of-place), we tried to retrieve the type of xduals based on this definition but we ended up pulling xduals[2] because of that definition.
• some of the tests were wrong too

I tried to fix all of that, would you mind giving it a second, closer look, comparing it with https://github.com/JuliaDiff/ForwardDiff.jl/blob/master/src/config.jl#L159?

Thanks

[ErikQQY]

I think the current fix looks good now. The previous implementation mess up different cases😅

[ErikQQY]

Can we get a new release with this patch? I need this fix for some new functionalities.

[gdalle]

I tried to register a new version but Registrator didn't notice