[Rafael-SOWNet]

This answers the question left on #2286. A function compiled to return double or float computes every intermediate value as a real number. So sin(arcsin(x)) at 2, whose value is 2, comes out as NaN, just as 1/x does at 0, where there is no value at all. That behaviour stays as it is, and it is now documented on every Compile overload.

MathS.Settings.RefuseNonRealCompilation, off by default, refuses such an expression instead. With it on, an expression that can't be shown to be real wherever it is defined throws UncompilableNodeException, so a NaN from the compiled function means only that there is no value. The check is TreeAnalyzer.IsRealValued, with every argument written as one fresh variable. It is conservative: sqrt(x) and ln(x) are refused too. The compilers over Complex, and statements, are unaffected.

Console.WriteLine("sin(arcsin(x))".Compile<double, double>("x")(2));   // NaN
using var _ = MathS.Settings.RefuseNonRealCompilation.Set(true);
"x / (1 + x^2)".Compile<double, double>("x");                          // compiles
"sin(arcsin(x))".Compile<double, double>("x");                         // throws UncompilableNodeException

IsRealValued now also reads floor, ceil, round, min and max of real arguments as real. Without that, the setting would refuse floor(x). The change also gives answers where the derivative of a modulus or a sign needs to know its argument is real:

Input	2.6.0 and master	Now
derivative(abs(floor(x)), x)	unevaluated	0 provided not floor(x) = 0 and not x in ZZ
derivative(abs(min(x, 1)), x)	unevaluated	sgn(min(x, 1)) * (1 - sgn(x - 1)) / 2 provided ...
limit(sin(floor(x)) / x, x, +oo)	0 in 2.6.0, unevaluated on master since #2284	0

RefuseNonRealCompilationTest covers:

• the default NaN
• the refusals over double and float
• real expressions still compiling
• division by zero still giving NaN
• the Complex compiler and a statement left alone

PublicApi.txt gains the setting. The setting's documented example runs under DocumentationExamplesRunTest. The suite (18,460), the trio, F#, AOT and the eight harnesses pass locally.

Fixes #2286.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 84.61538% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.72%. Comparing base (17cd9da) to head (7fdea1a).

Files with missing lines	Patch %	Lines
...s/AngouriMath/Functions/TreeAnalyzer/RealValued.cs	33.33%	1 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2297      +/-   ##
==========================================
- Coverage   86.73%   86.72%   -0.01%     
==========================================
  Files         310      310              
  Lines       67960    67973      +13     
  Branches    19740    19744       +4     
==========================================
+ Hits        58944    58952       +8     
- Misses       4884     4887       +3     
- Partials     4132     4134       +2     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.27% <84.61%> (-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
...s/AngouriMath/Convenience/CompilationExtensions.cs	100.00% <ø> (ø)
Sources/AngouriMath/Convenience/MathS.cs	90.51% <100.00%> (+0.02%)	⬆️
...h/Functions/Compilation/Compile.Linq.Definition.cs	47.05% <ø> (ø)
...Functions/Compilation/IntoLinq/IntoLinqCompiler.cs	97.40% <100.00%> (+0.34%)	⬆️
...s/AngouriMath/Functions/TreeAnalyzer/RealValued.cs	80.00% <33.33%> (-1.53%)	⬇️

... and 5 files with indirect coverage changes

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