Add 1/e constant

[alyst]

Adds inve = 1/e constant (cherry-picked from #12). Required by JuliaMath/SpecialFunctions.jl/issues/371

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[devmotion]

Required by JuliaMath/SpecialFunctions.jl/issues/371

It seems it's only used in the tests but not required by the implementation in the PR?

[alyst]

It seems it's only used in the tests but not required by the implementation in the PR?

I can make it required from the code too, because there it is used several times implicitly (as in the original version).
What I want to avoid is another round of discussions of whether "inve" required or not.
Just tell me whether you hesitate adding it.

[devmotion]

I am not hesitant per se, I just want to understand the motivation for this PR so I can review it properly.

You provided one argument for adding it but at first glance it does not seem completely convincing since the constant is not used in the package but only in the tests. Maybe you can update the SpecialFunctions PR and show how it is useful for the actual implementation as well?

I would guess that often one could also just use eg. x / e instead of inve * x. I am away from a computer but maybe you can benchmark both approaches? And provide some other examples where the constant would be useful?

[alyst]

-1/e is a branching point of Lambert's W, so inve appears there "as is" several times, you can check my PR for lambertw. I think your suggestion to use x/e instead of x * inve, although it does not apply for lambertw, would lead to degraded performance. Especially for broadcasting (x .* inve). In general, I have thought that if invpi made it here, inve also deserves that.