Make AbstractTracer a subtype of Real, not Number

[gdalle]

Increases compatibility with existing code

[gdalle]

Would solve control-toolbox/CTDirect.jl#88 (comment)

[jbcaillau]

@gdalle thank you for feedback. well, if this indeed solves the issue, this is most welcome. given the current type hierarchy, this seems to be no problem provided that no complex numbers are involved 👀.

[adrhill]

Sounds reasonable. We won't touch differentiation of complex numbers anyway, so this would only have been relevant for connectivity_pattern on complex functions, which isn't our priority.

I'll tag a last patch release and add this breaking change.

[adrhill]

Some weirdness resulting from this: our local tracer type Dual can contain a Complex primal value but is Real.
Maybe the most sane fix is to constrain the primal to Real as well.

[gdalle]

I agree, and we'll be forever banning complex autodiff (but so did ForwardDiff)

[gdalle]

Based on the way tracers are constructed, if the function signature is f(::Vector{<:Real}), the primal values will never be anything but Real anyway

[gdalle]

Reopening until #95 is merged

[jbcaillau]

I agree, and we'll be forever banning complex autodiff (but so did ForwardDiff)

Indeed, replacing $i^2=-1$ by $\varepsilon^2=0$ is all about ForwardDiff.jl 🤭