[Rafael-SOWNet]

A compiled binomial(n, k) with a whole k is a product of k factors while k fits a long, and past that it went through the gamma function.

compiled, all three compilers	master	this PR	mpmath
binomial(-5/2, 10^20)	1	7.5225277806367e29	7.5225277806367504928e29
binomial(277.7, 36!)	1	0	2.0e-11027
binomial(5, 10^20)	1	0	0
binomial(-1/2, 10^12)	does not return	5.6418958354769e-7	5.6418958354768576325e-7

• Past the longs: the logarithms of Γ(k + 1) and Γ(n - k + 1), both near k ln k, cancelled to their rounding error.
• Within the longs: an n whose factors never take the product to 0 ran k steps.

From an order of a million, with |n| at most half of it and n not a whole number at least 0, the binomial is now (-1)^k Γ(k - n)/(Γ(k + 1) Γ(-n)).

• ln Γ(k - n) - ln Γ(k + 1) comes from Stirling's series written as differences, so nothing near k ln k is subtracted.
• ln(1 + z) is taken by its series where z is small.
• Every double past 2^53 is even, which gives the sign.
• A whole n at least 0 below such a k is 0, and so is a negative k, as within the longs.

2.6.0 did not compile the binomial, so there is no BREAKING entry. Found by compilesweep at seed 13. No issue was filed.

Tests: seven of the ten rows in ACompiledBinomialOfALargeWholeOrderTest fail on master, two of them by the 30 s cap. The suite (18753), the five test projects and the eight harnesses pass, with 0 warnings.

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Codecov Report

❌ Patch coverage is 85.71429% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.76%. Comparing base (493b7ef) to head (90768f5).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
...ces/AngouriMath/Numerics/CombinatorialFunctions.cs	85.71%	1 Missing and 2 partials ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #2340   +/-   ##
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  Coverage   86.76%   86.76%           
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  Files         312      312           
  Lines       68598    68620   +22     
  Branches    19962    19971    +9     
=======================================
+ Hits        59519    59539   +20     
  Misses       4914     4914           
- Partials     4165     4167    +2     

Flag	Coverage Δ
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csharp	87.31% <85.71%> (+<0.01%)	⬆️
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interactive	40.72% <ø> (ø)

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Files with missing lines	Coverage Δ
...ces/AngouriMath/Numerics/CombinatorialFunctions.cs	92.56% <85.71%> (-1.19%)	⬇️

... and 4 files with indirect coverage changes

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