Add generic fallback to all scalar functions

[YingboMa]

No description provided.

[oscardssmith]

IMO this isn't quite correct. NaNMath says that functions return NaN rather than throwing so we should check if we get an error and return NaN in these fallback methods.

[oscardssmith]

This also needs tests.

[oameye]

Can this be merged?

I stumbled upon it when running:

using Symbolics
m = [cos(ψ) -sin(ψ); sin(ψ) cos(ψ)] 
jacfunc = Symbolics.build_function(m, ψ; expression=Val(false))[1]
jacfunc((0+0.1im))

[ChrisRackauckas]

No because it fails tests. But if someone fixes the ambiguities then it would be good to merge.

[codecov]

Codecov Report

Attention: Patch coverage is 85.71429% with 1 line in your changes missing coverage. Please review.

Project coverage is 96.33%. Comparing base (b351b97) to head (cf61ad0).
Report is 5 commits behind head on master.

Files with missing lines	Patch %	Lines
src/NaNMath.jl	85.71%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #71      +/-   ##
==========================================
+ Coverage   96.15%   96.33%   +0.17%     
==========================================
  Files           1        1              
  Lines         104      109       +5     
==========================================
+ Hits          100      105       +5     
  Misses          4        4              

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[oameye]

❤️

[devmotion]

IMO this isn't quite correct. NaNMath says that functions return NaN rather than throwing so we should check if we get an error and return NaN in these fallback methods.

That was not addressed? IMO the definitions in this PR are just wrong. Fallbacks require to check for errors or must be known to be safe (as was the case e.g. for the pow fallbacks before this PR).

[ChrisRackauckas]

It was addressed when the other PR was related to it though?

[devmotion]

Which other PR?

[devmotion]

For instance, this PR added

NaNMath.jl/src/NaNMath.jl

Line 39 in ca02438

pow(x, y) = ^(x, y)

to the master branch which is completely unsafe in general. What's safe, however are the fallbacks for integer exponents and complex arguments added in #83.