[Rafael-SOWNet]

A two-sided limit at a finite point compares the limits from each side. When a side's descent comes back NaN, the comparison asks each side outright. Outside a real codomain, it does that only if the expression is real on both sides of the point, which is decided by reading its structure. That reading knew the sine, the cosine, the arctangent, the arcsine and the arccosine. Anything else counted as not real, so the two-sided limit was NaN even where both sides agree.

This adds the tangent, the arccotangent, erf, erfc, erfi, floor, ceil, round and sgn, each real when its argument is real.

Input, at 0, two-sided	2.6.0	master	this branch
(pi^2 + (1/2) / x) * erf(x)	unevaluated	NaN	1 / sqrt(pi)
(1 + 1/x) * erf(x)	unevaluated	NaN	2 * 1 / sqrt(pi)
(abs(x)^(x/pi))^sgn(x)	unevaluated	NaN	1
floor(x)	unevaluated	NaN	NaN
sgn(x)	unevaluated	NaN	NaN
erfc(x) / x	NaN	NaN	NaN
x * sgn(x)	0	0	0
tan(x) / x	1	1	1
sgn(x) / x	unevaluated	+oo	+oo

The first three rows are in BREAKING-CHANGES.md. The new test pins them by value, and pins floor(x), sgn(x) and erfc(x) / x as NaN, since their sides differ.

Not in this PR: x * floor(2/x) at 0 two-sided is NaN on master and on this branch, while each side is 2. The sides there are undecided, not different, and that is a separate change.

Checked on this branch:

• Tests: UnitTests 19320 passed (the seed-43 case was added to the test after that run and passes alone), plus the MCP, Terminal, InteractiveWrapper and F# wrapper suites, and the AOT smoke test.
• Harnesses: BoundCheck, RootCheck, CasBench, PropCheck, SimpSweep, RuleCheck, CanonCheck and Confluence all pass.
• limitcheck at DEPTH=3, COUNT=600, on 42 seeds against master: one row changed, the (abs(x)^(x/pi))^sgn(x) row above (seed 43). Seed 45's tanh(log(x, -1) - tan(x)) from the left also moved into "did not finish in 5 s", but that limit takes 5.7 s on master as well as on this branch, so the 5 s cap decides it. That limit is unevaluated on both. Seed 237 of a wider sweep found the case.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 63.63636% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.81%. Comparing base (f17be26) to head (d690f70).

Files with missing lines	Patch %	Lines
...ns/Continuous/Limits/Solvers/Solvers.Definition.cs	63.63%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2418      +/-   ##
==========================================
+ Coverage   86.80%   86.81%   +0.01%     
==========================================
  Files         312      312              
  Lines       69503    69514      +11     
  Branches    20300    20300              
==========================================
+ Hits        60329    60347      +18     
+ Misses       4940     4934       -6     
+ Partials     4234     4233       -1     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.35% <63.63%> (+0.01%)	⬆️
fsharp	32.97% <ø> (ø)
interactive	39.81% <ø> (ø)

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Files with missing lines	Coverage Δ
...ns/Continuous/Limits/Solvers/Solvers.Definition.cs	91.69% <63.63%> (-1.12%)	⬇️

... and 6 files with indirect coverage changes

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