[Types] Add float16 (Half) support

[Nucs]

Overview

Add support for float16 (C# System.Half) type to NumSharp. This is a high-priority missing type critical for modern ML workloads.

Problem

NumSharp is missing float16 (half-precision floating point):

>>> import numpy as np
>>> np.array([1.0, 2.0, 3.0], dtype=np.float16)
array([1., 2., 3.], dtype=float16)
>>> np.finfo(np.float16)
finfo(resolution=0.001, min=-6.55040e+04, max=6.55040e+04, dtype=float16)

Critical use cases:

• ML inference — Transformers, LLMs, diffusion models use fp16
• GPU interop — CUDA, DirectML, Metal all use fp16
• Memory efficiency — 50% savings vs float32, 75% vs float64
• Model loading — Many .npy model weights are fp16

Proposal

Task List

• Add NPTypeCode.Float16 = 16 to NPTypeCode.cs
• Add np.float16 type alias in np.cs
• Update NPTypeCodeExtensions.GetTypeCode() to handle typeof(Half)
• Update InfoOf<T> for Half
• Update UnmanagedStorage type switches
• Update ArraySlice allocation for Half
• Update _typemap_arr_arr and _typemap_arr_scalar in np.find_common_type.cs
• Update all type switch patterns in DefaultEngine operations
• Add tests for float16 operations
• Test with real fp16 .npy files from ML models

C# Type Mapping

NumPy	C#	Size	Range	Available Since
float16	System.Half	2 bytes	[-65504, 65504]	.NET 5+

.NET Half Support

Half h1 = (Half)1.5f;
Half h2 = (Half)2.5f;
Half sum = h1 + h2;  // All arithmetic built-in
Half sqrt = Half.Sqrt(h2);  // Math functions available

.NET System.Half has full arithmetic and math function support built-in.

Implementation Effort

LOW — System.Half is a built-in .NET type since .NET 5 with full arithmetic support.

Estimated: ~50-100 lines of changes across multiple files.

Related

• Part of NumPy 2.x alignment: [NEP50 Core] Type promotion diverges from NumPy 2.x NEP 50 for unsigned int array + signed int scalar #529
• Will benefit from DynamicMethod IL emission: [Core] Replace ~636K lines of generated math code with DynamicMethod IL emission #544
• Will benefit from SIMD optimization: [Core] SIMD-Optimized IL Emission #545 (Vector256 available)

References

• NumPy float16 docs: https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float16
• .NET Half struct: https://docs.microsoft.com/en-us/dotnet/api/system.half