[Rafael-SOWNet]

Two defects in numerical factorial quotients. Sweep 7's compilesweep found the first on catalannumber(Ei(sinh(x))) at 6, and probing it turned up the second. No issues were filed.

	master	now	mpmath
catalannumber(449.5)	NaN	2.4958e266	2.4958e266
catalannumber(500.5)	NaN	1.0774e297	1.0774e297
catalannumber(-60.3)	NaN	-8.3875e-40	-8.3875e-40
catalannumber(2000.5)	NaN	+oo	1.66e1199, past the range
fallingfactorial(0.5, -100.5)	0	9.4020e-161	9.4020e-161
risingfactorial(100.5, -60.5)	0	2.1884e-111	2.1884e-111

• The Catalan number. 4^n Γ(n + 1/2) / (√π Γ(n + 2)) took each gamma in the context's exponent range. Both were +oo from n = 449.5, so the quotient was NaN. The gammas are now one QuotientOfFactorials, as the binomial's are since Divide a quotient of factorials before rounding it into the exponent range #2338. For a real n, 4^n times the quotient is formed in decimals with no bound on the exponent. An entity is not made from 4^(1e20) itself: its exponent is near 6e19, and the downcasting's integer check throws NotSupportedException on it, which an earlier version of this branch did.
• A quotient read as a residual. QuotientOfFactorials (from Divide a quotient of factorials before rounding it into the exponent range #2338) made its result with Real.Create. That reads a value under the downcasting tolerance, 1e-50, as what a cancellation left, and rounds it onto zero. A quotient cancels nothing, so it is now made at a zero scale, as The derivative of an answer at a large hyperbolic argument evaluates to NaN or loses its imaginary part #1944 does for every product and quotient. So is the falling factorial over k! beside it. These were wrong answers: an exact 0 for a value that is not 0.

Agreement with mpmath is to 1e-99 relative everywhere, except catalannumber(1600.25) at 1.2e-96. There, 4^n multiplies the error of ln 4 by n ln 4 ≈ 2200, as it did on the old path.

Tests: ACatalanNumberPastTheExponentRangeTest, 9 cases against mpmath at 120 digits. 8 fail on master; the control, catalannumber(10.5), passes on both. The full suite, AOT and the nine harnesses pass. None of catalannumber, fallingfactorial or risingfactorial is in 2.6.0, so there is no breaking entry.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.79%. Comparing base (0e96927) to head (0cb38fb).

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #2349   +/-   ##
=======================================
  Coverage   86.79%   86.79%           
=======================================
  Files         312      312           
  Lines       68664    68675   +11     
  Branches    19987    19988    +1     
=======================================
+ Hits        59595    59605   +10     
- Misses       4902     4903    +1     
  Partials     4167     4167           

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.33% <100.00%> (+<0.01%)	⬆️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

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Files with missing lines	Coverage Δ
...nuous/Evaluation.Continuous.Arithmetics.Classes.cs	87.69% <100.00%> (+0.14%)	⬆️

... and 2 files with indirect coverage changes

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