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Rafael-SOWNet merged 1 commit into from
Oct 29, 2026
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The combinatorial functions compile #2213

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14 changes: 14 additions & 0 deletions BREAKING-CHANGES.md
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Expand Up @@ -323,6 +323,20 @@ negative even integer or off the integers, since the extension through the gamma
| `"n!!".ToEntity()` | throws `UnhandledParseException` | `n!!` |
| `"n!!!".ToEntity()` | throws `UnhandledParseException` | throws `UnrecognizedFunctionParseException` |

### The binomial coefficient, the factorial powers and the double factorial compile

**Not silent: what was refused is compiled.** `binomial` was refused by both compilers with
`UncompilableNodeException`, and `fallingfactorial`, `risingfactorial` and `n!!`, new since 2.6.0, compile from the
start. Each compiles in double precision and on the interpreter's terms: a whole order is a product, and any other goes
through the gamma function, with `NaN` at a pole of the numerator and `0` at one of the denominator. The double
factorial has no value off the whole numbers or at a negative even one
([#2195](https://github.com/asc-community/AngouriMath/issues/2195)).

| Input | Was (2.6.0) | Now |
|---|---|---|
| `"binomial(x, 2)".ToEntity().Compile("x").Call(5)` | `UncompilableNodeException` | `(10, 0)` |
| `"binomial(x, 1/2)".ToEntity().Compile<double, double>("x")(3)` | `UncompilableNodeException` | `2.037183271576257` |

### `mod` compiles over `Complex`

**Not silent: what was refused is compiled.** `Compile<Complex, ...>` refused `mod` with `UncompilableNodeException`,
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6 changes: 6 additions & 0 deletions Sources/.editorconfig
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Expand Up @@ -357,6 +357,12 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed
[Tests/UnitTests/Common/FastExpressionStatementTest.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/CombinatorialCompilationTest.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

[AngouriMath/Numerics/CombinatorialFunctions.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/CompileMatrixTest.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

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49 changes: 49 additions & 0 deletions Sources/AngouriMath/Functions/Compilation/IntoFE/Compiler.cs
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Expand Up @@ -555,6 +555,55 @@ private protected override void CompileNode(Compiler compiler)
}
}

// The binomial coefficient, the factorial powers and the double factorial, on the
// interpreter's terms. https://github.com/asc-community/AngouriMath/issues/2195
public partial record DoubleFactorialf
{
private protected override bool CompilesItself => true;

private protected override void CompileNode(Compiler compiler)
{
Argument.InnerCompile(compiler);
compiler.Instructions.Add(new(InstructionType.CALL_DOUBLE_FACTORIAL));
}
}

public partial record Binomialf
{
private protected override bool CompilesItself => true;

private protected override void CompileNode(Compiler compiler)
{
Lower.InnerCompile(compiler);
Upper.InnerCompile(compiler);
compiler.Instructions.Add(new(InstructionType.CALL_BINOMIAL));
}
}

public partial record FallingFactorialf
{
private protected override bool CompilesItself => true;

private protected override void CompileNode(Compiler compiler)
{
Order.InnerCompile(compiler);
Argument.InnerCompile(compiler);
compiler.Instructions.Add(new(InstructionType.CALL_FALLING_FACTORIAL));
}
}

public partial record RisingFactorialf
{
private protected override bool CompilesItself => true;

private protected override void CompileNode(Compiler compiler)
{
Order.InnerCompile(compiler);
Argument.InnerCompile(compiler);
compiler.Instructions.Add(new(InstructionType.CALL_RISING_FACTORIAL));
}
}

public partial record Maxf
{
private protected override bool CompilesItself => true;
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18 changes: 18 additions & 0 deletions Sources/AngouriMath/Functions/Compilation/IntoFE/FastExpression.cs
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Expand Up @@ -55,6 +55,7 @@ internal enum InstructionType
CALL_RE,
CALL_IM,
CALL_NOT,
CALL_DOUBLE_FACTORIAL,

// 2-arg functions
CALL_SUM = 100,
Expand All @@ -77,6 +78,9 @@ internal enum InstructionType
CALL_IMPLIES,
// A value where its predicate holds, and NaN elsewhere.
CALL_PROVIDED,
CALL_BINOMIAL,
CALL_FALLING_FACTORIAL,
CALL_RISING_FACTORIAL,

// 3-arg: a value where its predicate holds, and the one below it elsewhere.
CALL_SELECT = 150,
Expand Down Expand Up @@ -340,6 +344,20 @@ public System.Numerics.Complex Substitute(params System.Numerics.Complex[] value
stack.Push(Truth(stack.Pop()) == true ? value : double.NaN);
break;
}
// The binomial coefficient, the factorial powers and the double factorial.
// https://github.com/asc-community/AngouriMath/issues/2195
case InstructionType.CALL_BINOMIAL:
stack.Push(AngouriMath.Numerics.CombinatorialFunctions.Binomial(stack.Pop(), stack.Pop()));
break;
case InstructionType.CALL_FALLING_FACTORIAL:
stack.Push(AngouriMath.Numerics.CombinatorialFunctions.FallingFactorial(stack.Pop(), stack.Pop()));
break;
case InstructionType.CALL_RISING_FACTORIAL:
stack.Push(AngouriMath.Numerics.CombinatorialFunctions.RisingFactorial(stack.Pop(), stack.Pop()));
break;
case InstructionType.CALL_DOUBLE_FACTORIAL:
stack.Push(AngouriMath.Numerics.CombinatorialFunctions.DoubleFactorial(stack.Pop()));
break;
case InstructionType.CALL_SELECT:
{
var value = stack.Pop();
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9 changes: 9 additions & 0 deletions Sources/AngouriMath/Functions/Compilation/IntoLinq/CompilationProtocol.cs
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Expand Up @@ -156,6 +156,7 @@ Cif when ShouldBeAtLeastDouble(e) is var newE => Expression.Call(GetDef("Ci",
Shif when ShouldBeAtLeastDouble(e) is var newE => Expression.Call(GetDef("Shi", 1, newE.Type), newE),
Chif when ShouldBeAtLeastDouble(e) is var newE => Expression.Call(GetDef("Chi", 1, newE.Type), newE),
Factorialf when ShouldBeAtLeastDouble(e) is var newE => Expression.Call(GetDef("Factorial", 1, newE.Type), newE),
DoubleFactorialf when ShouldBeAtLeastDouble(e) is var newE => Expression.Call(GetDef("DoubleFactorial", 1, newE.Type), newE),
Phif => Expression.Call(GetDef("Phi", 1, e.Type), e),

// The conjugate, the argument and the parts, widened to double as the special
Expand Down Expand Up @@ -233,6 +234,14 @@ Logf when
ShouldBeAtLeastDouble(left) is var newLeft
&& ShouldBeAtLeastDouble(right) is var newRight
=> Expression.Call(GetDef("Log", 2, newRight.Type), newLeft, newRight),
// The binomial coefficient and the factorial powers, widened to double first as the
// special functions are. https://github.com/asc-community/AngouriMath/issues/2195
Binomialf when ShouldBeAtLeastDouble(left) is var newLeft && ShouldBeAtLeastDouble(right) is var newRight
=> Expression.Call(GetDef("Binomial", 2, newLeft.Type), newLeft, newRight),
FallingFactorialf when ShouldBeAtLeastDouble(left) is var newLeft && ShouldBeAtLeastDouble(right) is var newRight
=> Expression.Call(GetDef("FallingFactorial", 2, newLeft.Type), newLeft, newRight),
RisingFactorialf when ShouldBeAtLeastDouble(left) is var newLeft && ShouldBeAtLeastDouble(right) is var newRight
=> Expression.Call(GetDef("RisingFactorial", 2, newLeft.Type), newLeft, newRight),
Maxf => Expression.Call(GetDef("Max", 2, left.Type), left, right),
Minf => Expression.Call(GetDef("Min", 2, left.Type), left, right),

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19 changes: 19 additions & 0 deletions Sources/AngouriMath/Functions/Compilation/IntoLinq/MathAllMethods.cs
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Expand Up @@ -331,6 +331,17 @@ public static System.Numerics.Complex Round(System.Numerics.Complex a)
public static System.Numerics.Complex Im(System.Numerics.Complex a) => AngouriMath.Numerics.ComplexParts.Im(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
// terms. https://github.com/asc-community/AngouriMath/issues/2195
public static System.Numerics.Complex DoubleFactorial(System.Numerics.Complex a) => AngouriMath.Numerics.CombinatorialFunctions.DoubleFactorial(a);
public static double DoubleFactorial(double a) => AngouriMath.Numerics.CombinatorialFunctions.DoubleFactorial(a);
public static System.Numerics.Complex Binomial(System.Numerics.Complex a, System.Numerics.Complex b) => AngouriMath.Numerics.CombinatorialFunctions.Binomial(a, b);
public static double Binomial(double a, double b) => AngouriMath.Numerics.CombinatorialFunctions.Binomial(a, b);
public static System.Numerics.Complex FallingFactorial(System.Numerics.Complex a, System.Numerics.Complex b) => AngouriMath.Numerics.CombinatorialFunctions.FallingFactorial(a, b);
public static double FallingFactorial(double a, double b) => AngouriMath.Numerics.CombinatorialFunctions.FallingFactorial(a, b);
public static System.Numerics.Complex RisingFactorial(System.Numerics.Complex a, System.Numerics.Complex b) => AngouriMath.Numerics.CombinatorialFunctions.RisingFactorial(a, b);
public static double RisingFactorial(double a, double b) => AngouriMath.Numerics.CombinatorialFunctions.RisingFactorial(a, b);

/// <summary>
/// True where <c>System.Numerics.Complex.IsNaN</c> is, spelled out because that overload is
/// .NET 7 and later and this assembly also targets netstandard2.0. A complex number is NaN
Expand Down Expand Up @@ -515,6 +526,14 @@ public static bool IsNaN(System.Numerics.Complex a)
{ ("Re", 1, typeof(double)), Def<double>(a => Re(a)) },
{ ("Im", 1, typeof(System.Numerics.Complex)), Def<System.Numerics.Complex>(a => Im(a)) },
{ ("Im", 1, typeof(double)), Def<double>(a => Im(a)) },
{ ("DoubleFactorial", 1, typeof(System.Numerics.Complex)), Def<System.Numerics.Complex>(a => DoubleFactorial(a)) },
{ ("DoubleFactorial", 1, typeof(double)), Def<double>(a => DoubleFactorial(a)) },
{ ("Binomial", 2, typeof(System.Numerics.Complex)), Def<System.Numerics.Complex>((a, b) => Binomial(a, b)) },
{ ("Binomial", 2, typeof(double)), Def<double>((a, b) => Binomial(a, b)) },
{ ("FallingFactorial", 2, typeof(System.Numerics.Complex)), Def<System.Numerics.Complex>((a, b) => FallingFactorial(a, b)) },
{ ("FallingFactorial", 2, typeof(double)), Def<double>((a, b) => FallingFactorial(a, b)) },
{ ("RisingFactorial", 2, typeof(System.Numerics.Complex)), Def<System.Numerics.Complex>((a, b) => RisingFactorial(a, b)) },
{ ("RisingFactorial", 2, typeof(double)), Def<double>((a, b) => RisingFactorial(a, b)) },
};

// An expression tree is how C# spells "the MethodInfo of this method" without a string:
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25 changes: 25 additions & 0 deletions Sources/AngouriMath/Functions/Compilation/IntoLinq/MathAllMethods.tt
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Expand Up @@ -15,6 +15,10 @@
// The conjugate, the argument and the parts, for Complex and double alone in the same way.
// https://github.com/asc-community/AngouriMath/issues/2195
var parts = new[]{ "Conj", "Arg", "Re", "Im" };
// The combinatorial functions, for Complex and double alone in the same way: one argument, and two.
// https://github.com/asc-community/AngouriMath/issues/2195
var combinatorial = new[]{ "DoubleFactorial" };
var combinatorialBinary = new[]{ "Binomial", "FallingFactorial", "RisingFactorial" };
var types = new[]{ "System.Numerics.Complex", "double", "float", "long", "int", "BigInteger" };
#>
//
Expand Down Expand Up @@ -217,6 +221,17 @@ namespace AngouriMath.Core.Compilation.IntoLinq
public static double <#= name #>(double a) => AngouriMath.Numerics.ComplexParts.<#= name #>(a);
<# } #>

// The binomial coefficient, the factorial powers and the double factorial, on the interpreter's
// terms. https://github.com/asc-community/AngouriMath/issues/2195
<# foreach (var name in combinatorial) { #>
public static System.Numerics.Complex <#= name #>(System.Numerics.Complex a) => AngouriMath.Numerics.CombinatorialFunctions.<#= name #>(a);
public static double <#= name #>(double a) => AngouriMath.Numerics.CombinatorialFunctions.<#= name #>(a);
<# } #>
<# foreach (var name in combinatorialBinary) { #>
public static System.Numerics.Complex <#= name #>(System.Numerics.Complex a, System.Numerics.Complex b) => AngouriMath.Numerics.CombinatorialFunctions.<#= name #>(a, b);
public static double <#= name #>(double a, double b) => AngouriMath.Numerics.CombinatorialFunctions.<#= name #>(a, b);
<# } #>

/// <summary>
/// True where <c>System.Numerics.Complex.IsNaN</c> is, spelled out because that overload is
/// .NET 7 and later and this assembly also targets netstandard2.0. A complex number is NaN
Expand Down Expand Up @@ -260,6 +275,16 @@ namespace AngouriMath.Core.Compilation.IntoLinq
<# foreach (var type in new[]{ "System.Numerics.Complex", "double" }) { #>
{ ("<#= name #>", 1, typeof(<#= type #>)), Def<<#= type #>>(a => <#= name #>(a)) },
<# } #>
<# } #>
<# foreach (var name in combinatorial) { #>
<# foreach (var type in new[]{ "System.Numerics.Complex", "double" }) { #>
{ ("<#= name #>", 1, typeof(<#= type #>)), Def<<#= type #>>(a => <#= name #>(a)) },
<# } #>
<# } #>
<# foreach (var name in combinatorialBinary) { #>
<# foreach (var type in new[]{ "System.Numerics.Complex", "double" }) { #>
{ ("<#= name #>", 2, typeof(<#= type #>)), Def<<#= type #>>((a, b) => <#= name #>(a, b)) },
<# } #>
<# } #>
};

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