[Rafael-SOWNet]

Fixes #2236. Fixes #2239. Both were found by work/compilesweep.

The branch cuts (#2236). System.Numerics.Complex computes -0 as a part of many real values: cos(2) is (cos 2, -sin 2 · sinh 0), which is (-0.416, -0), and conj(-2) is (-2, -0). Complex.Log, Complex.Sqrt and the inverse functions read a -0 as the lower side of the negative real axis. The library has no signed zero, so a real number is on the upper side. So in both compilers ln(cos(x)) at 2 was -0.8767 - pi i, where evaluation gives -0.8767 + pi i, and sqrt(conj(x)) at -4 was -2i.

ComplexBranches.Unsigned reads each zero part as +0, by adding +0.0, which turns -0 into +0 and changes no other number. It is taken at the entry of every compiled function with a cut, in FastExpression and in MathAllMethods:

• the logarithm;
• a power that is not whole, in RealProducts.Power;
• arcsin, arccos, arctan, arccotan, arcsec and arccosec;
• arg;
• the exponential and logarithmic integrals;
• lambertw.

ComplexBranches.Arcsin already conjugated on its cut. It now does so from the +0 side, which is the case it was written for.

The logarithm's base (#2239). FastExpression's logarithm was Complex.Log(value, base.Real), whose base parameter is a double, so a complex base lost its imaginary part: log(x, 2) at 1 + i was NaN. It is now ComplexBranches.Log, ln(value) / ln(base), which is how the LINQ compiler already took it.

	2.6.0 and master	now
"ln(cos(x))".ToEntity().Compile("x").Call(2)	(-0.8767, -3.1416)	(-0.8767, 3.1416)
"log(x, 2)".ToEntity().Compile("x").Call(new Complex(1, 1))	(NaN, NaN)	(0.3260, -0.7387)

Tests. BranchCutCompilationTest takes each of the 19 functions at 11 real points, with its argument written three ways that land on a cut: conj(x), cos(x) and i * x. It compares both compilers with evaluation, and adds three logarithms to complex bases. 9 of its 22 cases fail on master. Two kinds of point are left out:

• a pole, where the infinity has a NaN part, which is not what this test is about;
• an exponent with an odd denominator, where evaluation takes the real root, which a double exponent cannot show.

Full suite 18135/0, interactive trio, AOT smoke 73/0, all frameworks build.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.70%. Comparing base (b8a6a6f) to head (c64e0a0).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2240      +/-   ##
==========================================
+ Coverage   86.68%   86.70%   +0.02%     
==========================================
  Files         310      310              
  Lines       67766    67773       +7     
  Branches    19660    19660              
==========================================
+ Hits        58744    58764      +20     
+ Misses       4909     4896      -13     
  Partials     4113     4113              

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.25% <100.00%> (+0.02%)	⬆️
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
...gouriMath/Functions/Compilation/ComplexBranches.cs	100.00% <100.00%> (ø)
...ath/Functions/Compilation/IntoFE/FastExpression.cs	96.77% <100.00%> (+0.01%)	⬆️
...h/Functions/Compilation/IntoLinq/MathAllMethods.cs	73.97% <100.00%> (+0.25%)	⬆️
.../AngouriMath/Functions/Compilation/RealProducts.cs	100.00% <100.00%> (ø)

... and 9 files with indirect coverage changes

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.