feat(vector): add overflow-safe Euclidean norms

[acgetchell]

• Add allocation-free Vector::norm2 with scaled accumulation for large and subnormal finite coordinates.
• Resolve upper-range rounding with exact stack-based square sums, preventing false or hidden overflow without the exact feature.
• Report VectorNorm-tagged NonFinite errors only when the exact norm rounds to infinity; preserve norm2_sq's distinct range contract.
• Avoid redundant first-coordinate arithmetic and share binary64 rounding primitives across vector and interval operations.
• Document approximation limits and add peer-crate norm benchmarks plus scenario comparisons with hypot and Delaunay reference kernels.

Resolves #217

Summary by CodeRabbit

• New Features

  • Added overflow- and underflow-safe Euclidean norm handling, including correctly rounded results near floating-point limits.
  • Added clear errors when a vector norm cannot be represented.
  • Renamed vector APIs from norm2() to norm() and norm2_sq() to norm_squared().
  • Renamed the matrix infinity-norm API from inf_norm() to norm_inf().

• Documentation

  • Updated API, mathematical, migration, and benchmarking documentation with the new names and numerical behavior.

• Tests

  • Expanded coverage for extreme magnitudes, subnormals, rounding boundaries, dimensionality, and cross-library agreement.

[coderabbitai]

📝 Walkthrough

Walkthrough

Changes

The pull request renames vector and matrix norm APIs, adds exact near-overflow vector norm handling, centralizes rounding helpers, and expands tests, benchmarks, and numerical documentation.

Norm implementation and API updates

Layer / File(s)	Summary
Certified arithmetic and overflow fallback src/rounding.rs, src/norm.rs, src/interval.rs, src/lib.rs	Shared binary64 helpers support exact comparisons, interval arithmetic, and correctly rounded near-overflow norms.
Vector norm API and validation src/vector.rs, src/error.rs, tests/proptest_vector.rs, tests/proptest_exact.rs, tests/regressions.rs	The vector methods use norm and norm_squared. Tests cover dimensions 0–8, dynamic range, subnormals, overflow, and exact rounding.
Matrix norm rename and integration src/matrix.rs, tests/proptest_matrix.rs, benches/common/vs_linalg.rs, tests/vs_linalg_inputs.rs	The matrix infinity-norm method uses norm_inf. Overflow handling, symmetry calculations, adapters, and tests use the renamed API.
Benchmark and documentation updates benches/vs_linalg.rs, docs/BENCHMARKING.md, README.md, REFERENCES.md, docs/mathematical_basis.md, AGENTS.md	Benchmarks compare norm implementations across dynamic-range scenarios. Documentation describes the renamed APIs and numerical behavior.

Estimated code review effort: 4 (Complex) | ~60 minutes

Merge Risk: 🟡 Moderate · up to ab483

The renamed matrix norm API leaves a benchmark caller using the removed name, so benchmark builds can fail until that caller is updated to norm_inf().

Sequence Diagram(s)

sequenceDiagram
  participant Caller
  participant Vector_norm
  participant Norm_fallback
  participant Rounding_helpers
  Caller->>Vector_norm: call norm()
  Vector_norm->>Norm_fallback: handle near-overflow input
  Norm_fallback->>Rounding_helpers: compare exact sums and midpoints
  Rounding_helpers-->>Norm_fallback: return binary64 ordering
  Norm_fallback-->>Vector_norm: return finite norm or VectorNorm error
  Vector_norm-->>Caller: return Result<f64, LaError>

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🚥 Pre-merge checks | ✅ 2 | ❌ 2

❌ Failed checks (2 warnings)

Check name	Status	Explanation	Resolution
Linked Issues check	⚠️ Warning	The implementation satisfies the numerical, allocation, feature, documentation, test, and benchmark objectives in issue [#217]. However, it renames norm2_sq() to norm_squared() without a compatibi…	Preserve Vector::norm2_sq() as the public API, or provide a compatibility alias while retaining norm_squared() if the breaking rename is required.
Out of Scope Changes check	⚠️ Warning	Most changes support issue [#217], including norm implementation, rounding helpers, documentation, tests, and benchmarks. The unrelated src/exact.rs comment change and the separate `Matrix::inf_norm…	Remove the unrelated src/exact.rs comment change and move the matrix API rename and its associated documentation and tests to a separate pull request, unless the linked issue is expanded to include that work.

✅ Passed checks (2 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title clearly identifies the primary change: adding overflow-safe Euclidean norms for vectors.

Full details: Linked Issues check

Explanation

The implementation satisfies the numerical, allocation, feature, documentation, test, and benchmark objectives in issue [#217]. However, it renames norm2_sq() to norm_squared() without a compatibility alias, despite the issue requiring norm2_sq() to remain unchanged for existing callers.

Full details: Out of Scope Changes check

Explanation

Most changes support issue [#217], including norm implementation, rounding helpers, documentation, tests, and benchmarks. The unrelated src/exact.rs comment change and the separate Matrix::inf_norm() to Matrix::norm_inf() rename are outside the linked issue's vector-norm scope.

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.93%. Comparing base (0d947ac) to head (ab483d4).
⚠️ Report is 3 commits behind head on main.
✅ All tests successful. No failed tests found.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #235      +/-   ##
==========================================
+ Coverage   97.85%   97.93%   +0.07%     
==========================================
  Files          10       12       +2     
  Lines        6440     6574     +134     
==========================================
+ Hits         6302     6438     +136     
+ Misses        138      136       -2     

Flag	Coverage Δ
unittests	97.93% <100.00%> (+0.07%)	⬆️

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Actionable comments posted: 1

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Inline comments:
In `@src/matrix.rs`:
- Line 527: Update the benchmark caller in the comparison code to replace the
removed inf_norm() call with norm_inf(), preserving the existing result handling
and benchmark behavior.

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📥 Commits

Reviewing files that changed from the base of the PR and between f1f7b11 and ab483d4.

📒 Files selected for processing (16)

• AGENTS.md
• README.md
• REFERENCES.md
• benches/common/vs_linalg.rs
• benches/vs_linalg.rs
• docs/BENCHMARKING.md
• docs/mathematical_basis.md
• src/lib.rs
• src/matrix.rs
• src/rounding.rs
• src/vector.rs
• tests/proptest_exact.rs
• tests/proptest_matrix.rs
• tests/proptest_vector.rs
• tests/regressions.rs
• tests/vs_linalg_inputs.rs

🚧 Files skipped from review as they are similar to previous changes (2)

• REFERENCES.md
• docs/mathematical_basis.md

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[acgetchell]

@coderabbitai approve

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✅ Action performed

Comments resolved and changes approved.