feat(numerics): add branchless 2D/3D Hilbert curve Radix sort

[Sambit003]

Pull Request

Description

Introduces a 4-pass 16-bit LSD Radix sort backend for sorting complex coordinates along a continuous Hilbert space-filling curve.

This PR addresses the need for a highly optimized, locality-preserving multidimensional sorting mechanism without recursive overhead. By leveraging branchless bit-parallel Gray code transformations for Hilbert encoding and mapping the coordinates to an $O(N)$ contiguous auxiliary buffer, we ensure strictly monotonic ordering across both single and double precision floats while avoiding branch mispredictions and dynamic allocations during the scatter passes.

Fixes #33

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Type of Change

• feat: New algorithm, heuristic, or capability
• fix: Bug fix
• perf: Performance optimization
• refactor: Code refactoring without behavioral change
• docs: Documentation addition or update
• enhance: Incremental enhancement to existing feature
• test: New or updated tests
• chore: Build system, CI, dependencies, or tooling

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Implementation Details

• Time Complexity:
  • Best / Average / Worst: $O(N)$ (4 passes over 16-bit buckets for a 64-bit key)
• Space Complexity:
  • Auxiliary: $O(N)$ (One single contiguous Payload buffer allocated once)
• Stability / In-place guarantees:
  • Stable LSD Radix sort backend.
  • Out-of-place (requires auxiliary buffer), gracefully falling back to IntroSort for segments under 256 elements to prevent buffer allocation overhead on small inputs.

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Benchmarks & Performance Metrics (if applicable)

N/A - Formal benchmark regression analysis pending in follow-up profiling.

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Dependencies

None

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Testing & Verification

• C++ Unit Tests (ctest --preset debug or ctest --test-dir build --output-on-failure)
• Python Tests (pytest tests/python/ -v)
• Memory & UB Sanitizers (cmake --preset asan)
• Custom / Manual test script: RapidCheck Property-Based Tests (HilbertSortPBT)

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Developer Checklist

• My PR title follows <Type>(<scope>): <Precise PR deliverable>.
• My branch was created from main using an approved prefix (feat/, fix/, perf/, etc.).
• I have formatted my C++ code using clang-format.
• My code produces no new compiler warnings or static analysis issues (clang-tidy).
• I have added unit tests covering the new functionality or regression fix.
• I have updated documentation / docstrings where appropriate.
• My changes do not break existing functionality.

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Impact Assessment

• Isolated: Changes are localized and do not affect existing algorithm dispatch or public APIs.
• Breaking / Affects Others: Changes modify public APIs or dispatcher heuristics (explain below).

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Future Improvements

Potential integration with simd vectorized routines to parallelize the 24-state $SO(3)$ table lookups for 3D coordinates.

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Additional Notes

None

[github-actions]

🎉 Welcome, @Sambit003!

Thank you for contributing to **Algoat**! 🚀 Your pull request has been automatically assigned to you.

### 📋 Next Steps
- ✅ Ensure all tests pass:
  - C++ GoogleTest: `ctest --preset debug`
  - Python suite: `pytest tests/python/`
  - Sanitizers: `cmake --preset asan`
- ✅ Verify formatting: `clang-format -i ...`
- ✅ Include benchmark numbers if introducing or modifying algorithms
- ✅ Address any reviewer comments or suggestions

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