Add NaNMath extension for Unitful quantities

[Ickaser]

The current version of NaNMath.jl doesn't work on Unitful quantities; e.g.

NaNMath.sqrt(-4u"m^2")

should return NaN*u"m" but currently errors. (The point of NaNMath is that it should return NaN rather than error, which is helpful when e.g. adaptive solvers get outside of feasible space.)

This was discussed on the NaNMath side at JuliaMath/NaNMath.jl#86 but that seems to have stalled out. The extension to Unitful of the sqrt and pow methods is easy enough; NaNMath has other functions (e.g. for functions like sin that take dimensionless input, or aggregators like sum) but I think those are not as necessary.

[codecov]

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[Ickaser]

@sostock, @giordano , @gustaphe : any thoughts on this?

[sostock]

I wonder whether it makes sense to define these functions on dimensions and units as well, not just quantities? Of course, they are not different from the regular sqrt and ^ functions in that case, but it might help with writing generic code.

[Ickaser]

I wonder whether it makes sense to define these functions on dimensions and units as well, not just quantities? Of course, they are not different from the regular sqrt and ^ functions in that case, but it might help with writing generic code.

That seems unnecessary to me, I think, although I am open to discussion on that point. The current state of affairs in NaNMath is that Base.sqrt and Base.pow are used as fallbacks already (which is what necessitated this extension), so even without adding any dispatches on this end,

NaNMath.sqrt(u"m") === sqrt(u"m")

holds. I think the only reason to add more dispatches here would just be as a safeguard in case that fallback gets removed from NaNMath, and even for that, I would be a little surprised to see someone calling NaNMath.sqrt on units or dimensions without a quantity (since NaNMath.sqrt is a separate function from Base.sqrt).

[Ickaser]

That said, it's easy enough to add a test that ensures we will know if NaNMath.sqrt(u"m") === Base.sqrt(u"m") ever does stop working. I've added that now.

[sostock]

Ah, I didn’t realize that NaNMath has generic fallback methods. This looks good to me then.