Add Complex<T> and IComplexNumber<TSelf, T> (WIP — scoping question)

[Copilot]

Implement the approved API surface from #117451 for a generic Complex<T> where T : IFloatingPointIeee754<T> plus a corresponding IComplexNumber<TSelf, T> interface, and expand the non-generic Complex to implement the new interface.

Status: no code committed yet — need scoping direction before proceeding

After analyzing the approved surface against the existing implementation, the scope is substantially larger than a single surgical change and I want to confirm direction before committing code. Specifically, landing this requires:

• A new IComplexNumber<TSelf, T> interface (generic-math family).
• A new Complex<T> struct with ~100+ members: operators, Create/CreateFromPolarCoordinates, GetMagnitude/GetPhase, Conjugate/Reciprocal/Abs, full transcendental suite (Sqrt, Exp/ExpM1/Exp2/Exp10/…, Log/LogP1/Log2/Log10/…, Sin/Cos/Tan + *h + *Pi, Asin/Acos/Atan + *h + *Pi), Hypot, Pow, RootN, DegreesToRadians/RadiansToDegrees, MultiplyAddEstimate (5 overloads), MaxMagnitude/MinMagnitude(+Number) overloads, Is* predicates, parsing/formatting for char/byte/string, and the full INumberBase/ISignedNumber/IFloatingPointConstants/IAdditiveIdentity/IMultiplicativeIdentity explicit impls.
• Generalizing ~2,300 lines of double-specific algorithms in Complex.cs to arbitrary T : IFloatingPointIeee754<T>, including several precomputed magic constants (s_sqrtRescaleThreshold, s_asinOverflowThreshold, s_log2, InverseOfLog10, …) and IEEE‑754 edge-case handling (NaN/±∞/signed‑zero propagation) that today rely on double‑specific values.
• Adding the new members on non-generic Complex (Acosh/Asinh/Atanh, CosPi/SinPi/TanPi, Cbrt, DegreesToRadians/RadiansToDegrees, ExpM1/Exp2/Exp2M1/Exp10/Exp10M1, Hypot, LogP1/Log2/Log2P1/Log10P1, new Log/MaxMagnitude/MinMagnitude/*Number/Pow overloads, MultiplyAddEstimate, RootN) and the IComplexNumber<Complex, double> explicit impls.
• Corresponding ref/System.Runtime.Numerics.cs updates and test coverage in ComplexTests / ComplexTests.GenericMath.cs.

Per repo policy any commit must compile and pass tests, so I'd rather not push a large approximation of the math.

Description

Proposed approaches (please pick one):

• Phased — API shape first (recommended). Land IComplexNumber<TSelf, T>, the Complex<T> skeleton (layout, ctor, Real/Imaginary, arithmetic operators, Conjugate, Abs, Create/CreateFromPolarCoordinates, GetMagnitude/GetPhase, Is*, Equals/GetHashCode/ToString, generic-math explicit impls that port cleanly to T), the full ref assembly surface, and the non-generic Complex interface wiring. Defer transcendental math (Sqrt, Log*, Exp*, Asin/Acos/Atan + variants, Pow, Sinh/Cosh/Tanh, Hypot, RootN) to follow-up PRs so each port of a double-tuned algorithm to generic T can be reviewed and tested on its own.
• Scope down. Ship only IComplexNumber<TSelf, T> + the new methods on non-generic Complex (which can reuse existing double algorithms), and leave Complex<T> for a separate PR.
• All-in, multi-commit. Implement the full surface in one PR across many commits; expect iterative questions on algorithmic choices (e.g. how to derive T-generic equivalents of the double rescale thresholds for types like Half/float).

Example of the target shape once landed:

Complex<float> z = Complex<float>.CreateFromPolarCoordinates(2.0f, MathF.PI / 4);
float mag   = Complex<float>.GetMagnitude(z);
float phase = Complex<float>.GetPhase(z);
Complex<float> w = z * 3.0f + Complex<float>.Create(1.0f, -1.0f);

No files are modified in this PR yet — awaiting direction on scope.

Note

This PR description was authored by GitHub Copilot.

[tannergooding]

@copilot, lets go with a third different approach instead where we expose Complex<T> only mirroring the API surface that Complex already exposes. We can then have a follow up PR which exposes the IComplex<T> interface with the new members that require more complex implementation work on both the existing non-generic and new generic Complex types.

[Copilot]

@tannergooding I've opened a new pull request, #127333, to work on those changes. Once the pull request is ready, I'll request review from you.

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