[Rafael-SOWNet]

limitcheck found this at DEPTH=3, SEED=18. No issue was filed.

	2.6.0 and master	now
limitright(floor(4^((-1)^x)), x, 1)	0, where every floor near 1 is -i	unevaluated
limitleft(ceil(4^((-1)^x)), x, 1)	1, where it is 1 + i	unevaluated
limitleft(floor(4^((-1)^x)), x, 1)	0, right	unevaluated
floor(sqrt(x)) at 4, floor(x^x) at 2, floor(ln(x)) at 1 from the left	1 / 2, 3, -1	unchanged

The limit of a floor or a ceil read its argument as real along the path, and the code said so: "an argument that is complex near the destination and real at it can still be answered here when it should not be". 4^((-1)^x) at 1 from the right tends to 1/4 from below the real line. Floor is taken part by part (floor(1/4 - 0.001i) is -i), so the limit is -i, and the floor of the limit, 0, was the answer.

• Where the limit is real, the argument is evaluated at an exact point just off the destination on each side approached. Real there, it is read as before.
• Not real there, the side its imaginary part arrives from (SignNear(Im(argument))) decides the imaginary step, and where that is not decided the limit is declined.
• TreeAnalyzer.IsRealValued is asked first, but it does not list x^x. Asked alone, it declined floor(x^x) at 1, 1/2 and 2, which the limitcheck diff showed. The sample sends a limit only to the question or to declining, never to an answer of its own.
• For 4^((-1)^x) the imaginary part's side is not decided, so the left limit, which was right, is declined with the right one. Answering it would need a sign rule for Im of a complex power; NaN or a wrong value would be worse than unevaluated.

limitcheck: at DEPTH=3, SEED=18 the two wrong limits go, and the only declined limits added are these four. At SEED=16 the declined limits are master's exactly.

Tests: AStepOfAComplexArgumentNearARealLimitTest, 9 cases. The 3 that must be declined fail on master; the 6 real ones pass on both. The full suite, AOT and the nine harnesses pass. There is a BREAKING-CHANGES entry, measured on 2.6.0.

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[codecov]

Codecov Report

❌ Patch coverage is 80.76923% with 5 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.77%. Comparing base (0116c08) to head (97aa232).

Files with missing lines	Patch %	Lines
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs	80.76%	1 Missing and 4 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2355      +/-   ##
==========================================
+ Coverage   86.75%   86.77%   +0.01%     
==========================================
  Files         312      312              
  Lines       68753    68777      +24     
  Branches    20025    20034       +9     
==========================================
+ Hits        59648    59679      +31     
+ Misses       4921     4912       -9     
- Partials     4184     4186       +2     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.31% <80.76%> (+0.01%)	⬆️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

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Files with missing lines	Coverage Δ
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs	72.90% <80.76%> (+0.66%)	⬆️

... and 8 files with indirect coverage changes

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