Updated Lambert W function implementation

[alyst]

This is a fork of #84. I did:

• rebased PR #84 against the current master
• synced with the current master of LambertW.jl
• implemented suggestions from #84
• made some code simplifications that utilize compile-time dispatch
• updated tests to check for compile-time type inference and improved approximation testing
• ~~moved Omega and 1/e constants to IrrationalConstants.jl (PR https://github.com/JuliaMath/IrrationalConstants.jl/issues/12), so this PR requires that Omega constant PR is merged~~uses inve = 1/e constant from https://github.com/JuliaMath/IrrationalConstants.jl/issues/13
• Omega constant is exported as LambertW.Omega or LambertW.Ω

[codecov[bot]]

Codecov Report

Patch coverage: 96.74% and project coverage change: -0.07 :warning:

Comparison is base (07a890c) 94.25% compared to head (ed3c825) 94.19%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #371      +/-   ##
==========================================
- Coverage   94.25%   94.19%   -0.07%     
==========================================
  Files          14       15       +1     
  Lines        2908     3031     +123     
==========================================
+ Hits         2741     2855     +114     
- Misses        167      176       +9     

Flag	Coverage Δ
unittests	94.19% <96.74%> (-0.07%)	:arrow_down:

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files	Coverage Δ
src/SpecialFunctions.jl	100.00% <ø> (ø)
src/lambertw.jl	96.74% <96.74%> (ø)
src/beta_inc.jl	91.46% <0.00%> (-0.75%)	:arrow_down:

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[ViralBShah]

cc @jlapeyre

[CarloLucibello]

Can this be merged? Seems well tested and well documented

[devmotion]

No, I don't think it should be merged. My impression from the discussion in https://github.com/JuliaMath/SpecialFunctions.jl/pull/84 was that there was a tendency/agreement to keep the function in a separate package.

[alyst]

At this point I wonder if you are interested to improve the implementation of this function at all.

[devmotion]

There's a package with this function, and the general opinion (not just my personal one) was to keep the function there. So if it can be improved, I guess you should open a PR in that repo.

[alyst]

The "general opinion" is a bit of a stretch. But thank you for your efforts to guard the quality of Julia ecosystem.

As for me, I think trying to put this code elsewhere would be a waste of my resources, given that nobody have reviewed it here (I have noted "if it can be improved").

[ViralBShah]

@alyst thanks for putting it together. It is generally true that it has been hard to get reviews here.

[devmotion]

I'm sorry for you that the PR is not reviewed, but I guess many people, including myself, are not eager to review a PR in detail if there's already a longer discussion that indicates that there is no general agreement that the Lambert W function should be added to SpecialFunctions but instead shows that people seem to be in favour of keeping it in LambertW.jl. Therefore my suggestion was to make a PR to LambertW.jl instead if you would like to improve its implementation. I think you will receive more reviews and comments there.

[ViralBShah]

It did seem that the original author @jlapeyre (IIRC, and if I have my facts straight) expressed interest in keeping it separate - and thus I feel that we should respect that opinion.

[ViralBShah]

Since I was the one who triggered the original thought of getting this in - I would like to apologize for causing wasted effort here. :-(

[jlapeyre]

I'm also sorry if I caused wasted effort. Like many people, I'm over-extended and this is not the highest priority. I was also reluctant to put effort into a PR because I made one (for the same question) a few years ago, and it sat around till it bitrotted. I'm not blaming anyone: Most of us are not paid for this and have other obligations. But, my best estimation was that the best first step is to put LambertW under the JuliaMath org. I asked how to do that in the appropriate (I think) channel in slack a few weeks ago. But, I never got a response.

[ViralBShah]

@jlapeyre I can help with moving LambertW.jl to the JuliaMath org. I'm inviting you as an owner of JuliaMath, and you should be able to then transfer the package.

[jlapeyre]

The separate package has been moved here https://github.com/JuliaMath/LambertW.jl