Extended vector proposal (#5734)

Closes https://github.com/shader-slang/slang/issues/5504

Co-authored-by: Yong He <yonghe@outlook.com>

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+# SP #13: Extended Length Vectors
+
+This proposal introduces support for vectors with 0 or more than 4 components in
+Slang, extending the current vector type system while maintaining compatibility
+with existing features.
+
+## Status
+
+Status: Design Review
+
+Implementation: N/A
+
+Author: Ellie Hermaszewska
+
+Reviewer: TBD
+
+## Background
+
+Currently, Slang supports vectors between 1 and 4 components (float1, float2,
+float3, float4, (etc for other element types)), following HLSL conventions.
+This limitation stems from historical GPU hardware constraints and HLSL's
+graphics-focused heritage. However, modern compute applications may require
+working with longer vectors for tasks like machine learning, scientific
+computing, and select graphics tasks.
+
+Related Work
+
+- C++: std::array provides fixed-size array containers but lacks
+  vector-specific operations. SIMD types like std::simd (C++23) support
+  hardware-specific vector lengths.
+
+- CUDA: While CUDA doesn't provide native long vectors, libraries like Thrust
+  implement vector abstractions. Built-in vector types are limited to 1-4
+  components (float1, float2, float3, float4).
+
+- OpenCL: Provides vector types up to 16 components (float2, float4, float8,
+  float16, etc.) with full arithmetic and logical operations.
+
+- Modern CPU SIMD: Hardware support for longer vectors continues to grow:
+  - Intel AVX-512: 512-bit vectors (16 float32s)
+  - ARM SVE/SVE2: Scalable vector lengths up to 2048 bits
+  - RISC-V Vector Extensions: Variable-length vector support
+
+These approaches demonstrate different strategies for handling longer vectors,
+from fixed-size containers to hardware-specific implementations.
+
+## Motivation
+
+The primary motivation for extended length vectors is to support mathematical
+operations and algorithms that naturally operate on higher-dimensional vectors.
+While Slang already supports arrays for data storage, certain computations
+specifically require vector semantics and operations that arrays don't provide.
+
+A key principle of this proposal is consistency: there is no fundamental
+mathematical reason to limit vectors to 4 components. While the current limit
+stems from graphics hardware history, modern compute applications shouldn't be
+constrained by this arbitrary boundary. Supporting any natural length N
+provides a clean, orthogonal design that follows mathematical principles rather
+than historical limitations.
+
+Some example use cases:
+
+- Geometric Algebra and Clifford Algebras:
+
+  - 6D vectors for Plücker coordinates (representing lines in 3D space)
+  - 6D vectors for screw theory in robotics (combining rotation and translation)
+  - 8D vectors for dual quaternions in their vector representation
+  - Higher-dimensional geometric products and outer products
+
+- Machine Learning:
+
+  - Neural network feature vectors where vector operations (dot products,
+    normalization) are fundamental
+  - Distance metrics in high-dimensional embedding spaces
+  - Principal Component Analysis with multiple components
+
+- Scientific Computing:
+  - Spherical harmonics: Vector operations on coefficient spaces beyond 4D
+  - Quantum computing: State vectors in higher-dimensional Hilbert spaces
+
+This extension maintains Slang's mathematical vector semantics while enabling
+computations that naturally operate in higher dimensions. The focus is not on
+data storage (which arrays already handle) but on preserving vector-specific
+operations and mathematical properties in higher dimensions and improving
+consistency in the language.
+
+## Proposed Approach
+
+We propose extending Slang's vector type system to support vectors of arbitrary
+length, supporting as many of the operations available to 4-vectors as
+possible. Hardware limitations will prohibit a complete implementation, for
+example certain atomic operations may not be possible on longer vectors.
+
+Key aspects:
+
+- Support vectors of any length that is a natural number, subject to the same
+  limits as fixed-length arrays
+- Maintain existing syntax for vectors up to length 4
+- Maintain numeric swizzling operators.
+- Support standard vector operations (add, multiply, etc.)
+
+## Detailed Explanation
+
+### Type System Integration
+
+There are no type system changes required, as the vector type constructor is
+already parameterized over arbitrary vector length.
+
+### Operations
+
+#### Component Access:
+
+```slang
+vector<float, 8> v;
+float f0 = v.x; // First component
+float f1 = v[1]; // Array-style access
+float2 f3 = v_6_7; // last two member
+vector<float, 8> = float2(1,2).xxxxxxxx; // extended swizzling example
+```
+
+#### Arithmetic Operations:
+
+Any operations currently supported and generic over restricted vector length
+will be made unrestricted.
+
+Part of the scope of this work is to generate a precise list.
+
+For example all componentwise operations will be supported, as well as
+reductions.
+
+Cross product will remain restricted to 3-vectors, and will not be overloaded
+to 0-vectors or 7-vectors; this is due to worse type inference and error
+messages should overloads be added.
+
+#### Atomic Operations:
+
+Not supported
+
+### Storage Operations:
+
+Most platforms restrict the type of data able to be stored in textures, this
+proposal does not intend to work-around these restrictions.
+
+### Implementation Details
+
+Memory Layout:
+
+- Vectors are stored in contiguous memory
+- Alignment follows platform requirements
+- Padding may be required for certain lengths, for example padding to the
+  nearest multiple of 4
+
+Performance Considerations:
+
+- No performance degredation for 1,2,3,4-vectors
+- SIMD implementation work possible, not initially required
+
+## Alternatives Considered
+
+Fixed Maximum Length:
+
+- Could limit to common sizes (8, 16, 32)
+- Simpler implementation but less flexible
+- Rejected due to limiting future use cases
+
+Do nothing:
+
+- See motivation section
+
+## Additional notes
+
+### Zero-Length Vectors
+
+This proposal includes support for zero-length vectors. While seemingly
+unusual, zero-length vectors are mathematically well-defined and provide
+important completeness properties:
+
+- They are the natural result of certain slicing operations
+- They serve as the identity element for vector concatenation
+
+### Extended Matrices
+
+While this proposal focuses on vectors, it naturally suggests a future
+extension to matrices beyond the current 4x4 limit. Extended matrices would
+follow similar principles.
+
+However, extended matrices introduce additional considerations:
+
+- Memory layout and padding strategies for large matrices
+- Optimization of common operations (multiplication, transpose)
+
+These matrix-specific concerns are best addressed in a separate proposal that
+can build upon the extended vector foundation established here.