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Rafael-SOWNet merged 1 commit into from
Oct 30, 2026
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A compiled function takes the side of its branch cut evaluation takes #2240

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17 changes: 17 additions & 0 deletions BREAKING-CHANGES.md
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Expand Up @@ -445,6 +445,23 @@ then had no truth value for. A product or a quotient of two real numbers is now
| `"-x".ToEntity().Compile("x").Call(double.PositiveInfinity)` | `(-Infinity, NaN)` | `(-Infinity, 0)` |
| `"x / 2".ToEntity().Compile<Complex, Complex>("x")(double.PositiveInfinity)` | `(Infinity, NaN)` | `(Infinity, 0)` |

### A compiled function takes the side of its branch cut evaluation takes

**Silent: a compiled logarithm, root or inverse function of a number on its cut is evaluation's value, where it was
the conjugate.** `System.Numerics.Complex` computes `-0` as a part of many real values, `cos(2)` being `(-0.416, -0)`,
and reads it as the lower side of a cut. The library has no signed zero, so a real number is on the upper side. Every
compiled function with a cut now reads a zero part as `+0`: the logarithm, a power that is not whole, the inverse
trigonometric functions, `arg`, the exponential and logarithmic integrals and `lambertw`, in FastExpression and in the
LINQ compiler. A `conj` of a real number, new to compile since 2.6.0, took the same wrong side, as `ln(conj(x))` at
`-2` did ([#2236](https://github.com/asc-community/AngouriMath/issues/2236)). FastExpression's logarithm also kept only
the real part of a complex base, and takes `ln(value) / ln(base)` now
([#2239](https://github.com/asc-community/AngouriMath/issues/2239)).

| Input | Was (2.6.0) | Now |
|---|---|---|
| `"ln(cos(x))".ToEntity().Compile("x").Call(2)` | `(-0.8767171085319084, -3.141592653589793)` | `(-0.8767171085319084, 3.141592653589793)` |
| `"log(x, 2)".ToEntity().Compile("x").Call(new Complex(1, 1))` | `(NaN, NaN)` | `(0.32596797216345985, -0.7387021222729507)` |

### A compiled power of real numbers is the real power, at an infinity and at zero

**Silent: a compiled power over `Complex` is what evaluation gives where it had no value or the wrong one.** In
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3 changes: 3 additions & 0 deletions Sources/.editorconfig
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Expand Up @@ -931,3 +931,6 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed

[Tests/UnitTests/Common/RealPowerCompilationTest.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
28 changes: 27 additions & 1 deletion Sources/AngouriMath/Functions/Compilation/ComplexBranches.cs
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Expand Up @@ -39,10 +39,36 @@ internal static class ComplexBranches
/// see https://github.com/asc-community/AngouriMath/issues/115.
/// </remarks>
public static NumericsComplex Arcsin(NumericsComplex a)
=> a.Imaginary == 0 && Math.Abs(a.Real) > 1
=> (a = Unsigned(a)).Imaginary == 0 && Math.Abs(a.Real) > 1
? NumericsComplex.Conjugate(NumericsComplex.Asin(a))
: NumericsComplex.Asin(a);

/// <summary>
/// <paramref name="z"/> with each zero part read as <c>+0</c>. The library has no signed zero, so a real
/// number is on the upper side of every branch cut it lies on; <see cref="System.Numerics.Complex"/>
/// computes <c>-0</c> as a part of many real values, <c>cos(2)</c> and <c>conj(-2)</c> among them, and reads
/// it as the lower side, which made <c>ln(cos(x))</c> at 2 the conjugate of the logarithm. Adding <c>+0</c>
/// turns <c>-0</c> into <c>+0</c> and changes no other number. Taken at the entry of every function with a cut.
/// https://github.com/asc-community/AngouriMath/issues/2236
/// </summary>
public static NumericsComplex Unsigned(NumericsComplex z) => new(z.Real + 0.0, z.Imaginary + 0.0);

/// <summary>
/// The logarithm of <paramref name="value"/> to <paramref name="base"/>, <c>ln(value) / ln(base)</c> for any
/// base, where FastExpression's <c>Complex.Log(value, base.Real)</c> dropped a complex base's imaginary part.
/// https://github.com/asc-community/AngouriMath/issues/2239
/// </summary>
public static NumericsComplex Log(NumericsComplex @base, NumericsComplex value)
=> RealProducts.Quotient(NumericsComplex.Log(Unsigned(value)), NumericsComplex.Log(Unsigned(@base)));

public static NumericsComplex Arccos(NumericsComplex a) => NumericsComplex.Acos(Unsigned(a));

public static NumericsComplex Arctan(NumericsComplex a) => NumericsComplex.Atan(Unsigned(a));

public static NumericsComplex Arccotan(NumericsComplex a) => NumericsComplex.Atan(Unsigned(1 / a));

public static NumericsComplex Arcsecant(NumericsComplex a) => NumericsComplex.Acos(Unsigned(1 / a));

/// <summary>
/// The arccosecant the library evaluates to, which is <see cref="Arcsin"/> of the
/// reciprocal and so lands on the same cuts -- for arccosecant, at the real arguments
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25 changes: 14 additions & 11 deletions Sources/AngouriMath/Functions/Compilation/IntoFE/FastExpression.cs
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Expand Up @@ -250,22 +250,25 @@ public System.Numerics.Complex Substitute(params System.Numerics.Complex[] value
stack.Push(1 / System.Numerics.Complex.Tan(stack.Pop()));
break;
case InstructionType.CALL_LOG:
stack.Push(System.Numerics.Complex.Log(stack.Pop(), stack.Pop().Real));
{
var value = stack.Pop();
stack.Push(Core.Compilation.ComplexBranches.Log(stack.Pop(), value));
}
break;
case InstructionType.CALL_ARCSIN:
stack.Push(Core.Compilation.ComplexBranches.Arcsin(stack.Pop()));
break;
case InstructionType.CALL_ARCCOS:
stack.Push(System.Numerics.Complex.Acos(stack.Pop()));
stack.Push(Core.Compilation.ComplexBranches.Arccos(stack.Pop()));
break;
case InstructionType.CALL_ARCTAN:
stack.Push(System.Numerics.Complex.Atan(stack.Pop()));
stack.Push(Core.Compilation.ComplexBranches.Arctan(stack.Pop()));
break;
case InstructionType.CALL_ARCCOTAN:
stack.Push(System.Numerics.Complex.Atan(1 / stack.Pop()));
stack.Push(Core.Compilation.ComplexBranches.Arccotan(stack.Pop()));
break;
case InstructionType.CALL_ARCSECANT:
stack.Push(System.Numerics.Complex.Acos(1 / stack.Pop()));
stack.Push(Core.Compilation.ComplexBranches.Arcsecant(stack.Pop()));
break;
case InstructionType.CALL_ARCCOSECANT:
stack.Push(Core.Compilation.ComplexBranches.Arccosecant(stack.Pop()));
Expand All @@ -282,22 +285,22 @@ public System.Numerics.Complex Substitute(params System.Numerics.Complex[] value
stack.Push(AngouriMath.Numerics.SpecialFunctions.Erfi(stack.Pop()));
break;
case InstructionType.CALL_EI:
stack.Push(AngouriMath.Numerics.SpecialFunctions.Ei(stack.Pop()));
stack.Push(AngouriMath.Numerics.SpecialFunctions.Ei(Core.Compilation.ComplexBranches.Unsigned(stack.Pop())));
break;
case InstructionType.CALL_LI:
stack.Push(AngouriMath.Numerics.SpecialFunctions.Li(stack.Pop()));
stack.Push(AngouriMath.Numerics.SpecialFunctions.Li(Core.Compilation.ComplexBranches.Unsigned(stack.Pop())));
break;
case InstructionType.CALL_SI:
stack.Push(AngouriMath.Numerics.SpecialFunctions.Si(stack.Pop()));
break;
case InstructionType.CALL_CI:
stack.Push(AngouriMath.Numerics.SpecialFunctions.Ci(stack.Pop()));
stack.Push(AngouriMath.Numerics.SpecialFunctions.Ci(Core.Compilation.ComplexBranches.Unsigned(stack.Pop())));
break;
case InstructionType.CALL_SHI:
stack.Push(AngouriMath.Numerics.SpecialFunctions.Shi(stack.Pop()));
break;
case InstructionType.CALL_CHI:
stack.Push(AngouriMath.Numerics.SpecialFunctions.Chi(stack.Pop()));
stack.Push(AngouriMath.Numerics.SpecialFunctions.Chi(Core.Compilation.ComplexBranches.Unsigned(stack.Pop())));
break;
case InstructionType.CALL_FACTORIAL:
stack.Push(AngouriMath.Numerics.SpecialFunctions.Factorial(stack.Pop()));
Expand All @@ -315,7 +318,7 @@ public System.Numerics.Complex Substitute(params System.Numerics.Complex[] value
stack.Push(AngouriMath.Numerics.ComplexParts.Conj(stack.Pop()));
break;
case InstructionType.CALL_ARG:
stack.Push(AngouriMath.Numerics.ComplexParts.Arg(stack.Pop()));
stack.Push(AngouriMath.Numerics.ComplexParts.Arg(Core.Compilation.ComplexBranches.Unsigned(stack.Pop())));
break;
case InstructionType.CALL_RE:
stack.Push(AngouriMath.Numerics.ComplexParts.Re(stack.Pop()));
Expand Down Expand Up @@ -374,7 +377,7 @@ public System.Numerics.Complex Substitute(params System.Numerics.Complex[] value
stack.Push(AngouriMath.Numerics.CombinatorialFunctions.RisingFactorial(stack.Pop(), stack.Pop()));
break;
case InstructionType.CALL_LAMBERTW:
stack.Push(AngouriMath.Numerics.LambertWFunction.LambertW(stack.Pop(), stack.Pop()));
stack.Push(AngouriMath.Numerics.LambertWFunction.LambertW(stack.Pop(), Core.Compilation.ComplexBranches.Unsigned(stack.Pop())));
break;
case InstructionType.CALL_POLYGAMMA:
stack.Push(AngouriMath.Numerics.PolygammaFunction.Polygamma(stack.Pop(), stack.Pop()));
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40 changes: 20 additions & 20 deletions Sources/AngouriMath/Functions/Compilation/IntoLinq/MathAllMethods.cs
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Expand Up @@ -23,7 +23,7 @@ internal static class MathAllMethods
/* POWERS */

public static System.Numerics.Complex Log(System.Numerics.Complex a, System.Numerics.Complex b)
=> System.Numerics.Complex.Log(b) / System.Numerics.Complex.Log(a);
=> AngouriMath.Core.Compilation.ComplexBranches.Log(a, b);
public static double Log(double a, double b)
=> Math.Log(b, a);
public static float Log(float a, float b)
Expand Down Expand Up @@ -109,7 +109,7 @@ public static BigInteger Asin(BigInteger a)


public static System.Numerics.Complex Acos(System.Numerics.Complex a)
=> System.Numerics.Complex.Acos(a);
=> AngouriMath.Core.Compilation.ComplexBranches.Arccos(a);
public static double Acos(double a)
=> Math.Acos(a);
public static float Acos(float a)
Expand All @@ -123,7 +123,7 @@ public static BigInteger Acos(BigInteger a)


public static System.Numerics.Complex Atan(System.Numerics.Complex a)
=> System.Numerics.Complex.Atan(a);
=> AngouriMath.Core.Compilation.ComplexBranches.Arctan(a);
public static double Atan(double a)
=> Math.Atan(a);
public static float Atan(float a)
Expand Down Expand Up @@ -185,7 +185,7 @@ public static BigInteger Csc(BigInteger a)


public static System.Numerics.Complex Acot(System.Numerics.Complex a)
=> System.Numerics.Complex.Atan(1 / a);
=> AngouriMath.Core.Compilation.ComplexBranches.Arccotan(a);
public static double Acot(double a)
=> Math.Atan(1 / a);
public static float Acot(float a)
Expand All @@ -199,7 +199,7 @@ public static BigInteger Acot(BigInteger a)


public static System.Numerics.Complex Asec(System.Numerics.Complex a)
=> System.Numerics.Complex.Acos(1 / a);
=> AngouriMath.Core.Compilation.ComplexBranches.Arcsecant(a);
public static double Asec(double a)
=> Math.Acos(1 / a);
public static float Asec(float a)
Expand Down Expand Up @@ -299,36 +299,36 @@ public static System.Numerics.Complex Round(System.Numerics.Complex a)

// The special functions, in double precision as the kernels define them, and the factorial,
// the gamma function one along. https://github.com/asc-community/AngouriMath/issues/1607
public static System.Numerics.Complex Erf(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Erf(a);
public static System.Numerics.Complex Erf(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Erf(AngouriMath.Core.Compilation.ComplexBranches.Unsigned(a));
public static double Erf(double a) => AngouriMath.Numerics.SpecialFunctions.Erf(a);
public static System.Numerics.Complex Erfc(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Erfc(a);
public static System.Numerics.Complex Erfc(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Erfc(AngouriMath.Core.Compilation.ComplexBranches.Unsigned(a));
public static double Erfc(double a) => AngouriMath.Numerics.SpecialFunctions.Erfc(a);
public static System.Numerics.Complex Erfi(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Erfi(a);
public static System.Numerics.Complex Erfi(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Erfi(AngouriMath.Core.Compilation.ComplexBranches.Unsigned(a));
public static double Erfi(double a) => AngouriMath.Numerics.SpecialFunctions.Erfi(a);
public static System.Numerics.Complex Ei(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Ei(a);
public static System.Numerics.Complex Ei(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Ei(AngouriMath.Core.Compilation.ComplexBranches.Unsigned(a));
public static double Ei(double a) => AngouriMath.Numerics.SpecialFunctions.Ei(a);
public static System.Numerics.Complex Li(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Li(a);
public static System.Numerics.Complex Li(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Li(AngouriMath.Core.Compilation.ComplexBranches.Unsigned(a));
public static double Li(double a) => AngouriMath.Numerics.SpecialFunctions.Li(a);
public static System.Numerics.Complex Si(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Si(a);
public static System.Numerics.Complex Si(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Si(AngouriMath.Core.Compilation.ComplexBranches.Unsigned(a));
public static double Si(double a) => AngouriMath.Numerics.SpecialFunctions.Si(a);
public static System.Numerics.Complex Ci(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Ci(a);
public static System.Numerics.Complex Ci(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Ci(AngouriMath.Core.Compilation.ComplexBranches.Unsigned(a));
public static double Ci(double a) => AngouriMath.Numerics.SpecialFunctions.Ci(a);
public static System.Numerics.Complex Shi(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Shi(a);
public static System.Numerics.Complex Shi(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Shi(AngouriMath.Core.Compilation.ComplexBranches.Unsigned(a));
public static double Shi(double a) => AngouriMath.Numerics.SpecialFunctions.Shi(a);
public static System.Numerics.Complex Chi(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Chi(a);
public static System.Numerics.Complex Chi(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Chi(AngouriMath.Core.Compilation.ComplexBranches.Unsigned(a));
public static double Chi(double a) => AngouriMath.Numerics.SpecialFunctions.Chi(a);
public static System.Numerics.Complex Factorial(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Factorial(a);
public static System.Numerics.Complex Factorial(System.Numerics.Complex a) => AngouriMath.Numerics.SpecialFunctions.Factorial(AngouriMath.Core.Compilation.ComplexBranches.Unsigned(a));
public static double Factorial(double a) => AngouriMath.Numerics.SpecialFunctions.Factorial(a);

// The conjugate, the principal argument and the real and the imaginary parts.
// https://github.com/asc-community/AngouriMath/issues/2195
public static System.Numerics.Complex Conj(System.Numerics.Complex a) => AngouriMath.Numerics.ComplexParts.Conj(a);
public static System.Numerics.Complex Conj(System.Numerics.Complex a) => AngouriMath.Numerics.ComplexParts.Conj(AngouriMath.Core.Compilation.ComplexBranches.Unsigned(a));
public static double Conj(double a) => AngouriMath.Numerics.ComplexParts.Conj(a);
public static System.Numerics.Complex Arg(System.Numerics.Complex a) => AngouriMath.Numerics.ComplexParts.Arg(a);
public static System.Numerics.Complex Arg(System.Numerics.Complex a) => AngouriMath.Numerics.ComplexParts.Arg(AngouriMath.Core.Compilation.ComplexBranches.Unsigned(a));
public static double Arg(double a) => AngouriMath.Numerics.ComplexParts.Arg(a);
public static System.Numerics.Complex Re(System.Numerics.Complex a) => AngouriMath.Numerics.ComplexParts.Re(a);
public static System.Numerics.Complex Re(System.Numerics.Complex a) => AngouriMath.Numerics.ComplexParts.Re(AngouriMath.Core.Compilation.ComplexBranches.Unsigned(a));
public static double Re(double a) => AngouriMath.Numerics.ComplexParts.Re(a);
public static System.Numerics.Complex Im(System.Numerics.Complex a) => AngouriMath.Numerics.ComplexParts.Im(a);
public static System.Numerics.Complex Im(System.Numerics.Complex a) => AngouriMath.Numerics.ComplexParts.Im(AngouriMath.Core.Compilation.ComplexBranches.Unsigned(a));
public static double Im(double a) => AngouriMath.Numerics.ComplexParts.Im(a);

// The binomial coefficient, the factorial powers and the double factorial, on the interpreter's
Expand All @@ -346,7 +346,7 @@ public static System.Numerics.Complex Round(System.Numerics.Complex a)

// The Lambert W function on the branch the first argument names.
// https://github.com/asc-community/AngouriMath/issues/2195
public static System.Numerics.Complex LambertW(System.Numerics.Complex a, System.Numerics.Complex b) => AngouriMath.Numerics.LambertWFunction.LambertW(a, b);
public static System.Numerics.Complex LambertW(System.Numerics.Complex a, System.Numerics.Complex b) => AngouriMath.Numerics.LambertWFunction.LambertW(a, AngouriMath.Core.Compilation.ComplexBranches.Unsigned(b));
public static double LambertW(double a, double b) => AngouriMath.Numerics.LambertWFunction.LambertW(a, b);

// The polygamma functions of a whole order, and the harmonic numbers.
Expand Down
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