phobos#10826 improved handling of beta function edge cases

[tedgin]

The implementation std.mathspecial.beta(x, y) of B(x,y) is extended to handle its edge cases that occur when using the main algorithm gamma(x) * gamma(y) / gamma(x + y) to compute B(x,y). Theses cases happen in the regions of the (x,y) plane where gamma(x), gamma(y), or gamma(x+y) is not finite. These cause beta(x, y) to return NaN in regions where B(x,y) exists. This PR extends beta to cover the following cases.

• usage of the large value algorithm involving logGamma is extended to every region where |Γ(x)|, |Γ(y)|, or |Γ(x+y)| is too large to be represented with a real
• x+y is a non-positive integer, where Γ(x+y) does not exist, but 1/Γ(x+y) = 0
• either x or y is +0 with the other value being nonnegative and finite
• x,y > 0 and x or y is infinite
• either x or y is -0 with the other value being positive
• either x or y is negative, finite, and not an integer and the other value is +∞
• either x or y is +0 and the other value is negative, finite, and not an integer
• either x or y is -0 and the other value is negative, finite, and not an integer

Extending beta in this way required the recent bug fixes to beta and sgnGamma to be in place, so these where cherry picked from the stable branch into this PR.

The resulting implementation of beta is no longer a few lines of code, so it was moved into a new eponymous function in the module std.internal.math.gammafunction. This required the implementation of sgnGamma to be moved into an new eponymous function in the same module as well. I made this a separate commit, in case I shouldn't have done this.

The larger value algorithm for compute B is used two times in the new implementation of beta, so I moved this logic out of beta and into a new function betaLarge. I made this a separate commit, in case I shouldn't have done this.

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Testing this PR locally

If you don't have a local development environment setup, you can use Digger to test this PR:

dub run digger -- build "master + phobos#10846"

[tedgin]

Is this able to be merged?

[thewilsonator]

Yes, sorry, was preoccupied with travel and Dconf.