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Rafael-SOWNet merged 2 commits into from
Oct 31, 2026
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Compiling over the reals can refuse what is not real #2297

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1fdf490
Compiling over the reals can refuse what is not real
Rafael-SOWNet Oct 31, 2026
7fdea1a
Write the Compile remark into the templates the overloads come from
Rafael-SOWNet Oct 31, 2026
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18 changes: 18 additions & 0 deletions BREAKING-CHANGES.md
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Expand Up @@ -607,6 +607,24 @@ interpreter leaves them as written ([#2195](https://github.com/asc-community/Ang
| `"valuation(x, 2)".ToEntity().Compile("x").Call(12)` | `UncompilableNodeException` | `(2, 0)` |
| `"valuation(x, 2)".ToEntity().Compile<double, double>("x")(0)` | `UncompilableNodeException` | `Infinity` |

### Compiling over the reals can refuse what is not real

**Not silent, and only where asked for: `MathS.Settings.RefuseNonRealCompilation`, off by default, refuses to compile into a
function returning `double` or `float` an expression that is not real wherever it is defined.** Over the reals every value
computed on the way is real, so `sin(arcsin(x))` at 2, which is 2, is NaN there, as `1/x` is at 0. That is now documented
on every `Compile` overload, and with the setting on, such an expression throws `UncompilableNodeException`, so that a NaN
means only that there is no value. The check is structural and conservative: `sqrt(x)` and `ln(x)` are refused too.

**Silent: `floor`, `ceil`, `round`, `min` and `max` of real arguments are known to be real**, which the derivative of a
modulus or a sign needs, so these are answered where they were left unevaluated
([#2286](https://github.com/asc-community/AngouriMath/issues/2286)).

| Input | Was (2.6.0) | Now |
|---|---|---|
| `"x^y".Compile<double, double, double>("x", "y")` under the setting | (no setting) | throws `UncompilableNodeException` |
| `"derivative(abs(floor(x)), x)".ToEntity().Simplify()` | unevaluated | `0 provided not floor(x) = 0 and not x in ZZ` |
| `"derivative(abs(min(x, 1)), x)".ToEntity().Simplify()` | unevaluated | `sgn(min(x, 1)) * (1 - sgn(x - 1)) / 2 provided not min(x, 1) = 0 and not x - 1 = 0` |

### Membership and divisibility compile

**Not silent: what was refused is compiled.** `x in S` and `a divides b` were refused by both compilers with
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3 changes: 3 additions & 0 deletions Sources/.editorconfig
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Expand Up @@ -1013,5 +1013,8 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed
[Tests/UnitTests/Common/DivisionByZeroOverDoubleTest.cs]
file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n

[Tests/UnitTests/Common/RefuseNonRealCompilationTest.cs]
file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n

[Tests/UnitTests/Common/BranchCutCompilationTest.cs]
file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
45 changes: 45 additions & 0 deletions Sources/AngouriMath/Convenience/CompilationExtensions.cs
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Expand Up @@ -53,6 +53,11 @@ public static partial class AngouriMathExtensions
/// 3
/// </code>
/// </example>
/// <remarks>
/// Into a function that returns <see cref="double"/> or <see cref="float"/>, a value that is not real is NaN, and
/// so is every value computed from one, though the expression may be real there: <c>sin(arcsin(x))</c> at 2.
/// <see cref="MathS.Settings.RefuseNonRealCompilation"/> refuses such an expression instead.
/// </remarks>
public static TDelegate Compile<TDelegate>(this string @this, CompilationProtocol protocol, Type returnType, IEnumerable<(Type type, Variable variable)> typesAndNames) where TDelegate : Delegate
=> IntoLinqCompiler.Compile<TDelegate>(@this, returnType, protocol, typesAndNames);

Expand Down Expand Up @@ -86,6 +91,11 @@ public static TDelegate Compile<TDelegate>(this string @this, CompilationProtoco
/// 10
/// </code>
/// </example>
/// <remarks>
/// Into a function that returns <see cref="double"/> or <see cref="float"/>, a value that is not real is NaN, and
/// so is every value computed from one, though the expression may be real there: <c>sin(arcsin(x))</c> at 2.
/// <see cref="MathS.Settings.RefuseNonRealCompilation"/> refuses such an expression instead.
/// </remarks>
public static Func<TIn1, TOut> Compile<TIn1, TOut>(this string @this, Variable var1)
=> IntoLinqCompiler.Compile<Func<TIn1, TOut>>(@this, typeof(TOut), new(),
new[] { (typeof(TIn1), var1) });
Expand Down Expand Up @@ -126,6 +136,11 @@ public static Func<TIn1, TOut> Compile<TIn1, TOut>(this string @this, Variable v
/// 30
/// </code>
/// </example>
/// <remarks>
/// Into a function that returns <see cref="double"/> or <see cref="float"/>, a value that is not real is NaN, and
/// so is every value computed from one, though the expression may be real there: <c>sin(arcsin(x))</c> at 2.
/// <see cref="MathS.Settings.RefuseNonRealCompilation"/> refuses such an expression instead.
/// </remarks>
public static Func<TIn1, TIn2, TOut> Compile<TIn1, TIn2, TOut>(this string @this, Variable var1, Variable var2)
=> IntoLinqCompiler.Compile<Func<TIn1, TIn2, TOut>>(@this, typeof(TOut), new(),
new[] { (typeof(TIn1), var1), (typeof(TIn2), var2) });
Expand Down Expand Up @@ -172,6 +187,11 @@ public static Func<TIn1, TIn2, TOut> Compile<TIn1, TIn2, TOut>(this string @this
/// 60
/// </code>
/// </example>
/// <remarks>
/// Into a function that returns <see cref="double"/> or <see cref="float"/>, a value that is not real is NaN, and
/// so is every value computed from one, though the expression may be real there: <c>sin(arcsin(x))</c> at 2.
/// <see cref="MathS.Settings.RefuseNonRealCompilation"/> refuses such an expression instead.
/// </remarks>
public static Func<TIn1, TIn2, TIn3, TOut> Compile<TIn1, TIn2, TIn3, TOut>(this string @this, Variable var1, Variable var2, Variable var3)
=> IntoLinqCompiler.Compile<Func<TIn1, TIn2, TIn3, TOut>>(@this, typeof(TOut), new(),
new[] { (typeof(TIn1), var1), (typeof(TIn2), var2) , (typeof(TIn3), var3) });
Expand Down Expand Up @@ -224,6 +244,11 @@ public static Func<TIn1, TIn2, TIn3, TOut> Compile<TIn1, TIn2, TIn3, TOut>(this
/// 100
/// </code>
/// </example>
/// <remarks>
/// Into a function that returns <see cref="double"/> or <see cref="float"/>, a value that is not real is NaN, and
/// so is every value computed from one, though the expression may be real there: <c>sin(arcsin(x))</c> at 2.
/// <see cref="MathS.Settings.RefuseNonRealCompilation"/> refuses such an expression instead.
/// </remarks>
public static Func<TIn1, TIn2, TIn3, TIn4, TOut> Compile<TIn1, TIn2, TIn3, TIn4, TOut>(this string @this, Variable var1, Variable var2, Variable var3, Variable var4)
=> IntoLinqCompiler.Compile<Func<TIn1, TIn2, TIn3, TIn4, TOut>>(@this, typeof(TOut), new(),
new[] { (typeof(TIn1), var1), (typeof(TIn2), var2) , (typeof(TIn3), var3) , (typeof(TIn4), var4) });
Expand Down Expand Up @@ -282,6 +307,11 @@ public static Func<TIn1, TIn2, TIn3, TIn4, TOut> Compile<TIn1, TIn2, TIn3, TIn4,
/// 150
/// </code>
/// </example>
/// <remarks>
/// Into a function that returns <see cref="double"/> or <see cref="float"/>, a value that is not real is NaN, and
/// so is every value computed from one, though the expression may be real there: <c>sin(arcsin(x))</c> at 2.
/// <see cref="MathS.Settings.RefuseNonRealCompilation"/> refuses such an expression instead.
/// </remarks>
public static Func<TIn1, TIn2, TIn3, TIn4, TIn5, TOut> Compile<TIn1, TIn2, TIn3, TIn4, TIn5, TOut>(this string @this, Variable var1, Variable var2, Variable var3, Variable var4, Variable var5)
=> IntoLinqCompiler.Compile<Func<TIn1, TIn2, TIn3, TIn4, TIn5, TOut>>(@this, typeof(TOut), new(),
new[] { (typeof(TIn1), var1), (typeof(TIn2), var2) , (typeof(TIn3), var3) , (typeof(TIn4), var4) , (typeof(TIn5), var5) });
Expand Down Expand Up @@ -346,6 +376,11 @@ public static Func<TIn1, TIn2, TIn3, TIn4, TIn5, TOut> Compile<TIn1, TIn2, TIn3,
/// 210
/// </code>
/// </example>
/// <remarks>
/// Into a function that returns <see cref="double"/> or <see cref="float"/>, a value that is not real is NaN, and
/// so is every value computed from one, though the expression may be real there: <c>sin(arcsin(x))</c> at 2.
/// <see cref="MathS.Settings.RefuseNonRealCompilation"/> refuses such an expression instead.
/// </remarks>
public static Func<TIn1, TIn2, TIn3, TIn4, TIn5, TIn6, TOut> Compile<TIn1, TIn2, TIn3, TIn4, TIn5, TIn6, TOut>(this string @this, Variable var1, Variable var2, Variable var3, Variable var4, Variable var5, Variable var6)
=> IntoLinqCompiler.Compile<Func<TIn1, TIn2, TIn3, TIn4, TIn5, TIn6, TOut>>(@this, typeof(TOut), new(),
new[] { (typeof(TIn1), var1), (typeof(TIn2), var2) , (typeof(TIn3), var3) , (typeof(TIn4), var4) , (typeof(TIn5), var5) , (typeof(TIn6), var6) });
Expand Down Expand Up @@ -416,6 +451,11 @@ public static Func<TIn1, TIn2, TIn3, TIn4, TIn5, TIn6, TOut> Compile<TIn1, TIn2,
/// 280
/// </code>
/// </example>
/// <remarks>
/// Into a function that returns <see cref="double"/> or <see cref="float"/>, a value that is not real is NaN, and
/// so is every value computed from one, though the expression may be real there: <c>sin(arcsin(x))</c> at 2.
/// <see cref="MathS.Settings.RefuseNonRealCompilation"/> refuses such an expression instead.
/// </remarks>
public static Func<TIn1, TIn2, TIn3, TIn4, TIn5, TIn6, TIn7, TOut> Compile<TIn1, TIn2, TIn3, TIn4, TIn5, TIn6, TIn7, TOut>(this string @this, Variable var1, Variable var2, Variable var3, Variable var4, Variable var5, Variable var6, Variable var7)
=> IntoLinqCompiler.Compile<Func<TIn1, TIn2, TIn3, TIn4, TIn5, TIn6, TIn7, TOut>>(@this, typeof(TOut), new(),
new[] { (typeof(TIn1), var1), (typeof(TIn2), var2) , (typeof(TIn3), var3) , (typeof(TIn4), var4) , (typeof(TIn5), var5) , (typeof(TIn6), var6) , (typeof(TIn7), var7) });
Expand Down Expand Up @@ -492,6 +532,11 @@ public static Func<TIn1, TIn2, TIn3, TIn4, TIn5, TIn6, TIn7, TOut> Compile<TIn1,
/// 360
/// </code>
/// </example>
/// <remarks>
/// Into a function that returns <see cref="double"/> or <see cref="float"/>, a value that is not real is NaN, and
/// so is every value computed from one, though the expression may be real there: <c>sin(arcsin(x))</c> at 2.
/// <see cref="MathS.Settings.RefuseNonRealCompilation"/> refuses such an expression instead.
/// </remarks>
public static Func<TIn1, TIn2, TIn3, TIn4, TIn5, TIn6, TIn7, TIn8, TOut> Compile<TIn1, TIn2, TIn3, TIn4, TIn5, TIn6, TIn7, TIn8, TOut>(this string @this, Variable var1, Variable var2, Variable var3, Variable var4, Variable var5, Variable var6, Variable var7, Variable var8)
=> IntoLinqCompiler.Compile<Func<TIn1, TIn2, TIn3, TIn4, TIn5, TIn6, TIn7, TIn8, TOut>>(@this, typeof(TOut), new(),
new[] { (typeof(TIn1), var1), (typeof(TIn2), var2) , (typeof(TIn3), var3) , (typeof(TIn4), var4) , (typeof(TIn5), var5) , (typeof(TIn6), var6) , (typeof(TIn7), var7) , (typeof(TIn8), var8) });
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10 changes: 10 additions & 0 deletions Sources/AngouriMath/Convenience/CompilationExtensions.tt
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Expand Up @@ -53,6 +53,11 @@ namespace AngouriMath.Extensions
/// 3
/// </code>
/// </example>
/// <remarks>
/// Into a function that returns <see cref="double"/> or <see cref="float"/>, a value that is not real is NaN, and
/// so is every value computed from one, though the expression may be real there: <c>sin(arcsin(x))</c> at 2.
/// <see cref="MathS.Settings.RefuseNonRealCompilation"/> refuses such an expression instead.
/// </remarks>
public static TDelegate Compile<TDelegate>(this string @this, CompilationProtocol protocol, Type returnType, IEnumerable<(Type type, Variable variable)> typesAndNames) where TDelegate : Delegate
=> IntoLinqCompiler.Compile<TDelegate>(@this, returnType, protocol, typesAndNames);

Expand Down Expand Up @@ -104,6 +109,11 @@ namespace AngouriMath.Extensions
/// <#= total #>
/// </code>
/// </example>
/// <remarks>
/// Into a function that returns <see cref="double"/> or <see cref="float"/>, a value that is not real is NaN, and
/// so is every value computed from one, though the expression may be real there: <c>sin(arcsin(x))</c> at 2.
/// <see cref="MathS.Settings.RefuseNonRealCompilation"/> refuses such an expression instead.
/// </remarks>
public static Func<<# for(var t=1;t<=i;t++){ #>TIn<#= t #>, <# } #>TOut> Compile<<# for(var t=1;t<=i;t++){ #>TIn<#= t #>, <# } #>TOut>(this string @this, Variable var1<# for(var t=2; t<=i; t++){ #>, Variable var<#= t #><# } #>)
=> IntoLinqCompiler.Compile<Func<<# for(var t=1;t<=i;t++){ #>TIn<#= t #>, <# } #>TOut>>(@this, typeof(TOut), new(),
new[] { (typeof(TIn1), var1)<# for(var t=2;t<=i;t++){ #>, (typeof(TIn<#= t #>), var<#= t #>) <# } #> });
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37 changes: 37 additions & 0 deletions Sources/AngouriMath/Convenience/MathS.cs
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Expand Up @@ -6285,6 +6285,43 @@ internal static EDecimal DowncastingTolerance
/// </example>
public static Setting<bool> AllowNewton { get; } = true;

/// <summary>
/// Whether compiling into a function that returns <see cref="double"/> or <see cref="float"/> refuses an
/// expression that is not real wherever it is defined. Off by default.
/// </summary>
/// <remarks>
/// Compiled over the reals, every value the function computes on the way is a real number. So an expression
/// whose value at a real argument is not real, or is real only by way of a value that is not -- <c>sqrt(x)</c>
/// at -4, <c>sin(arcsin(x))</c> at 2 -- evaluates to NaN there, as it does where it has no value at all, as
/// <c>1/x</c> at 0. With this off, that is how such an expression compiles, and a NaN from the compiled
/// function means that the expression has no value there or that its computation left the reals. With it on,
/// an expression that cannot be shown to be real wherever it is defined is refused with
/// <see cref="Core.Exceptions.UncompilableNodeException"/>, and a NaN means only that there is no value. The
/// showing is structural and so conservative: <c>sqrt(x)</c> and <c>ln(x)</c> are refused, though both are
/// real for positive x. Compile over <see cref="System.Numerics.Complex"/> for the value itself.
/// <a href="https://github.com/asc-community/AngouriMath/issues/2286">#2286</a>
/// </remarks>
/// <example>
/// <code>
/// using static AngouriMath.MathS;
///
/// Console.WriteLine("sin(arcsin(x))".Compile&lt;double, double&gt;("x")(2));
///
/// using var _ = Settings.RefuseNonRealCompilation.Set(true);
///
/// Console.WriteLine("x / (1 + x^2)".Compile&lt;double, double&gt;("x")(2));
/// try { "sin(arcsin(x))".Compile&lt;double, double&gt;("x"); }
/// catch (AngouriMath.Core.Exceptions.UncompilableNodeException) { Console.WriteLine("refused"); }
/// </code>
/// Prints
/// <code>
/// NaN
/// 0.4
/// refused
/// </code>
/// </example>
public static Setting<bool> RefuseNonRealCompilation { get; } = false;

/// <summary>
/// Criteria for simplifier so you could control which expressions are considered easier by you.
/// The higher the value - the more complicated an expression is.
Expand Down
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