[Rafael-SOWNet]

A limit of floor, ceil or sgn whose argument arrives on a jump was left unevaluated, even where the side is plain: limitleft(floor(x), x, 0), limitright(sgn(x), x, 0). The side the argument arrives from is not always the side x comes from: floor(2 - x^2) comes to 2 from below as x comes to 0 from the right. It is the sign that the argument minus the jump keeps near the destination. SignNear already reads that from the limit, or from the first derivative that does not vanish. floor gives the jump from above and one less from below; ceil gives one more from above and the jump from below; sgn gives the side itself. A two-sided limit asks each side, and when they differ, as at a jump, it is NaN.

Input	2.6.0 and master	Now
limitleft(floor(x), x, 0)	unevaluated	-1
limitright(floor(2 - x^2), x, 0)	unevaluated	1
limitright(sgn(x^3 - x), x, 0)	unevaluated	-1
limit(floor(x), x, 1)	unevaluated	NaN
limit(sgn(x), x, 0)	unevaluated	NaN

StepFunctionAtAJumpTest: 15 of its 16 cases fail on master. FloorCeilTest and SignumLimitTest pinned the old declines. They now pin the values: NaN for the two-sided limits, which do not exist, and the side's sign for the one-sided ones. Each is still bounded in time, which is what those tests are for. The suite (18,272), the trio, F#, AOT and the eight harnesses pass locally.

This complements #2268. That PR stops substitution from evaluating straight through a jump, and this one gives the step's own limit. Built together, the composed expressions are answered correctly: limitleft(floor(x) - 1, x, 0) is -2, limitleft(arcsin(floor(x)), x, 0) is -pi/2, and limit(floor(x) + x, x, 1) is NaN. Each of the two is measured alone, and they touch different files.

Part of #2266.

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[codecov]

Codecov Report

❌ Patch coverage is 90.00000% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 86.71%. Comparing base (47ea3b3) to head (cd84d98).
⚠️ Report is 2 commits behind head on master.

Files with missing lines	Patch %	Lines
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs	90.00%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #2283   +/-   ##
=======================================
  Coverage   86.71%   86.71%           
=======================================
  Files         310      310           
  Lines       67845    67852    +7     
  Branches    19689    19694    +5     
=======================================
+ Hits        58830    58839    +9     
+ Misses       4895     4891    -4     
- Partials     4120     4122    +2     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.26% <90.00%> (+<0.01%)	⬆️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
...ath/Functions/Continuous/Limits/Transformations.cs	87.78% <ø> (+0.18%)	⬆️
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs	70.64% <90.00%> (+0.35%)	⬆️

... and 7 files with indirect coverage changes

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