Add Complex<T> generic struct mirroring Complex API surface

[Copilot]

Implements a generic Complex<T> where T : IFloatingPointIeee754<T>, IMinMaxValue<T> that mirrors the full public API of the existing Complex struct, as scoped by @tannergooding. The IComplexNumber<TSelf, T> interface and new members on non-generic Complex are deferred to a follow-up PR.

Description

New type: Complex<T>

Direct generic port of Complex in a new Complex.Generic.cs source file:

• Arithmetic operators: all Complex<T>×Complex<T>, T×Complex<T>, and Complex<T>×T overloads for +, -, *, /, unary -/+, ++, --
• Static properties: Zero, One, ImaginaryOne, NaN, Infinity (exposed as static properties per the approved API surface; INumberBase.One and INumberBase.Zero bind implicitly to the matching public properties)
• Properties: Real, Imaginary
• Instance methods: GetMagnitude(), GetPhase() (per approved API surface — exposed as named methods rather than properties)
• Math: Abs, Conjugate, Reciprocal, Log/Log10, Exp, Sqrt, Pow, Sin/Cos/Tan, Sinh/Cosh/Tanh, Asin/Acos/Atan, FromPolarCoordinates
• Predicates: full Is* set matching INumberBase<T>
• Generic math: implements INumberBase<Complex<T>>, ISignedNumber<Complex<T>>, IAdditiveIdentity, IMultiplicativeIdentity, IEquality/Comparison operators
• Parsing / formatting: full IParsable, ISpanParsable, IUtf8SpanParsable, ISpanFormattable, IUtf8SpanFormattable
• Conversions: CreateChecked/CreateSaturating/CreateTruncating use internal TryConvertFrom*Core and TryConvertTo*Core helpers that correctly chain same-type, cross-type (Complex ↔ Complex<T>), BigInteger, and general numeric type special cases per mode

Constraint rationale

IMinMaxValue<T> is added alongside IFloatingPointIeee754<T> because the ported Sqrt and Asin_Internal algorithms compute per-instantiation overflow thresholds from T.MaxValue (e.g., s_sqrtRescaleThreshold, s_asinOverflowThreshold). Every practical floating-point type (float, double, Half, BFloat16, NFloat) implements both interfaces.

Shared constants

Complex.DefaultNumberStyle and Complex.InvalidNumberStyles are promoted from private to internal in Complex.cs so that Complex<T> can reference them directly rather than maintaining duplicate definitions.

Code sharing between Complex and Complex<T>

To ensure the non-generic Complex and Complex<T> stay in sync, all Complex methods with more than 4 lines of implementation now delegate to the corresponding Complex<double> method. This covers:

• Mixed-type operators: operator *(Complex, double), operator *(double, Complex), and all three / overloads
• Trig/math functions: Asin, Acos, Tan, Sqrt, Pow(Complex, Complex)
• Magnitude comparisons: MaxMagnitude, MinMagnitude
• Formatting: ToString(string?, IFormatProvider?)
• Explicit interface implementations MaxMagnitudeNumber, MinMagnitudeNumber, MultiplyAddEstimate: each has an internal static implementation on Complex<T>; Complex<T>'s explicit interface implementation delegates to it, and Complex's explicit interface implementation calls through Complex<double>
• Conversion helpers TryConvertFrom*: Complex<T> exposes internal static TryConvertFromCheckedCore, TryConvertFromSaturatingCore, TryConvertFromTruncatingCore that implement the full conversion logic (same-type, Complex→Complex<T>, signed types via T.TryConvertFrom*, unsigned/decimal types via TOther.TryConvertTo*<T>); Complex.TryConvertFrom replaces its long explicit type chain with a Complex<double> special case followed by delegation to Complex<double>.TryConvertFromCheckedCore
• Conversion helpers TryConvertTo*: Complex<T> exposes internal static TryConvertToCheckedCore, TryConvertToSaturatingCore, TryConvertToTruncatingCore that implement the full conversion logic (same-type fast path returning real/NaN, Complex output via double.Create*, BigInteger output with appropriate imaginary-part handling, general types via T.TryConvertTo* with fallback to TOther.TryConvertFrom*<T>); Complex's three long TryConvertTo* chains are replaced with a Complex<double> output special case followed by delegation to Complex<double>.TryConvertTo*Core

As a result, the now-unused private fields (s_sqrtRescaleThreshold, s_asinOverflowThreshold, s_log2) and helpers (Log1P, Asin_Internal) are removed from Complex.cs.

Cross-type conversion support

Both types now correctly support bi-directional conversion:

• Complex.CreateChecked(new Complex<double>(1, 2)) — Complex accepts Complex<double> input
• Complex<float>.CreateChecked(new Complex(1, 2)) — Complex<T> accepts Complex (non-generic) input, with mode-appropriate component conversion
• int.CreateChecked(new Complex<double>(5, 0)) — real types can be extracted from Complex<T> via TryConvertToCheckedCore
• int.CreateChecked(new Complex(5, 0)) — real types can be extracted from Complex via delegation to Complex<double>.TryConvertToCheckedCore

Example usage

Complex<float> z = Complex<float>.FromPolarCoordinates(2.0f, MathF.PI / 4);
float mag   = z.GetMagnitude();
float phase = z.GetPhase();
Complex<float> w = z * 3.0f + new Complex<float>(1.0f, -1.0f);
var product = Complex<float>.Sin(z) * Complex<double>.Exp(new Complex<double>(0, Math.PI));

// Cross-type conversions work in both directions:
Complex        c  = Complex.CreateChecked(new Complex<double>(3, 4));
Complex<float> cf = Complex<float>.CreateChecked(new Complex(3, 4));
int            n  = int.CreateChecked(new Complex<double>(5, 0));

// Static properties:
var zero = Complex<float>.Zero;
var one  = Complex<double>.One;

Files changed

File	Change
src/System/Numerics/Complex.cs	Promote DefaultNumberStyle and InvalidNumberStyles to internal; delegate long methods to Complex<double>; replace TryConvertFrom/TryConvertTo* chains with Complex<double>.*Core delegation
src/System/Numerics/Complex.Generic.cs	New — full Complex<T> implementation with static properties for Zero/One/ImaginaryOne/NaN/Infinity; GetMagnitude()/GetPhase() methods; internal static shared implementations for MaxMagnitudeNumber, MinMagnitudeNumber, MultiplyAddEstimate, TryConvertFrom*Core, and TryConvertTo*Core
src/System.Runtime.Numerics.csproj	Add new file to build
ref/System.Runtime.Numerics.cs	Add Complex<T> public surface to ref assembly
tests/ComplexTests.cs	Add ComplexTests_Generic with 37 tests

Note

This PR description was authored by GitHub Copilot.

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