[Types] Add complex64 support

Overview

Add support for complex64 (two float32 components) to NumSharp. Currently NumSharp only supports complex128 (two float64 components).

Problem

NumSharp has Complex (complex128) but not complex64:

>>> import numpy as np
>>> np.array([1+2j, 3+4j], dtype=np.complex64)
array([1.+2.j, 3.+4.j], dtype=complex64)
>>> np.dtype(np.complex64).itemsize
8  # 2 x 4 bytes (float32)

>>> np.dtype(np.complex128).itemsize
16  # 2 x 8 bytes (float64)

Use cases:

• FFT/Signal processing — Many FFT implementations use complex64
• Memory efficiency — 50% savings vs complex128
• Scientific computing — Matches hardware complex types
• NumPy file interop — Some .npy files use complex64

Proposal

Task List

• Create Complex64 struct in Utilities/Complex64.cs:

  [StructLayout(LayoutKind.Sequential)]
  public readonly struct Complex64 : IEquatable<Complex64>
  {
      public readonly float Real;
      public readonly float Imaginary;
      // Arithmetic operators, math functions
  }
  

• Add NPTypeCode.Complex64 = 64 to NPTypeCode.cs
• Add np.complex64 type alias
• Update NPTypeCodeExtensions.GetTypeCode() for Complex64
• Update InfoOf<T> for Complex64
• Update UnmanagedStorage type switches
• Update ArraySlice allocation
• Update type promotion tables
• Implement arithmetic operations (+, -, *, /)
• Implement math functions (abs, sqrt, exp, etc.)
• Add tests

C# Type Implementation

[StructLayout(LayoutKind.Sequential)]
public readonly struct Complex64
{
    public readonly float Real;
    public readonly float Imaginary;
    
    public Complex64(float real, float imaginary) => (Real, Imaginary) = (real, imaginary);
    
    public static Complex64 operator +(Complex64 a, Complex64 b) 
        => new(a.Real + b.Real, a.Imaginary + b.Imaginary);
    
    public float Magnitude => MathF.Sqrt(Real * Real + Imaginary * Imaginary);
    // ... etc
}

Implementation Effort

MEDIUM — Requires custom struct with arithmetic and math operations.

Estimated: ~200-300 lines for the struct + type switch updates.

Related

• Part of NumPy 2.x alignment: #529
• Will benefit from DynamicMethod IL emission: #544
• Will benefit from SIMD optimization: #545

References

• NumPy complex64 docs: https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.complex64