perf!: optimize exact conversion and dense 4D determinants

[acgetchell]

• Avoid redundant fraction reduction in strict RationalVector conversion.
• Share minors in dense exact 4×4 determinants while preserving the sparse fast path.
• Add adversarial solve benchmarks across D=2,3,4,5,8,16,32,64 and exact-arithmetic diagnostics.
• Include Gaussian reference working-copy costs in benchmark timings.
• Document the decision to retain existing LU/LDLT solve finalization after finding no repeatable speedup.
• Align tooling with Rust 1.98.1 and refresh dependency and tool pins.

BREAKING CHANGE: la-stack now requires Rust 1.98.1.

Closes #234

Summary by CodeRabbit

• Compatibility

  • Updated the minimum supported Rust version and pinned toolchain to Rust 1.98.1.

• Improvements

  • Improved exact rational-to-binary64 conversion support and documentation, including clearer handling of rounding and overflow.
  • Optimized dense 4×4 determinant calculations while preserving sparse-case behavior.

• Benchmarks & Validation

  • Added diagnostic benchmark coverage for exact conversions, determinants, and LU solves across challenging numerical scenarios.
  • Expanded regression and allocation tests for conversion, determinant, and solve correctness.

• Documentation & Maintenance

  • Added benchmarking guidance and solve-finalization decision documentation.
  • Updated contributor tooling versions.

[coderabbitai]

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📥 Commits

Reviewing files that changed from the base of the PR and between 188c35b and 7fd6d8e.

⛔ Files ignored due to path filters (2)

• Cargo.lock is excluded by !**/*.lock
• uv.lock is excluded by !**/*.lock

📒 Files selected for processing (21)

• AGENTS.md
• CONTRIBUTING.md
• Cargo.toml
• README.md
• benches/common/exact_diagnostics.rs
• benches/common/vs_linalg.rs
• benches/exact.rs
• benches/vs_linalg.rs
• clippy.toml
• docs/BENCHMARKING.md
• docs/performance/solve-finalization.md
• justfile
• rust-toolchain.toml
• src/exact.rs
• src/lu.rs
• src/rational.rs
• tests/canonical_conversion_allocations.rs
• tests/exact_bench_config.rs
• tests/exact_conversion_boundaries.rs
• tests/solve_finalization.rs
• tests/vs_linalg_inputs.rs

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📝 Walkthrough

Walkthrough

The PR adds exact rational conversion and determinant diagnostics, validated LU benchmark scenarios, arithmetic and solve-finalization regression tests, benchmark documentation, and Rust/toolchain version updates.

Changes

Exact arithmetic and determinant diagnostics

Layer / File(s)	Summary
Exact conversion and determinant diagnostics benches/common/exact_diagnostics.rs, src/exact.rs, src/rational.rs, benches/exact.rs, tests/canonical_conversion_allocations.rs, tests/exact_bench_config.rs, tests/exact_conversion_boundaries.rs	Adds canonical rational conversion support for RationalVector, optimized dense 4×4 determinant evaluation, diagnostic fixtures, allocation checks, benchmark registration, and conversion and determinant validation.

Validated LU diagnostic benchmarks

Layer / File(s)	Summary
Validated LU diagnostic benchmarks benches/common/vs_linalg.rs, benches/vs_linalg.rs, tests/vs_linalg_inputs.rs, docs/BENCHMARKING.md	Adds pivoting and dense ill-conditioned LU scenarios. It validates la-stack, nalgebra, and faer solutions before benchmarking complete and reusable-factor solves.

Solve arithmetic and finalization regression coverage

Layer / File(s)	Summary
Solve arithmetic and finalization regression coverage src/lu.rs, tests/solve_finalization.rs, docs/performance/solve-finalization.md	Adds bit-exact LU arithmetic-order tests and LU/LDLT non-finite error tests for operation and index reporting across dimensions 2–64. Documents the retained solve finalization approach.

Toolchain and benchmark documentation

Layer / File(s)	Summary
Toolchain and benchmark documentation Cargo.toml, rust-toolchain.toml, clippy.toml, justfile, AGENTS.md, CONTRIBUTING.md, README.md, docs/BENCHMARKING.md	Updates the Rust version from 1.98.0 to 1.98.1, refreshes tool pins, and documents benchmark timing, diagnostic commands, allocation tests, and historical results.

Estimated code review effort: 4 (Complex) | ~45 minutes

Merge Risk: ⚪ Minimal · up to 7fd6d

No actionable merge-blocking risk remains in the reviewed changes.

Sequence Diagram(s)

sequenceDiagram
  participant FixtureBuilder
  participant LaStack
  participant Nalgebra
  participant Faer
  participant Criterion
  FixtureBuilder->>LaStack: build and validate LU scenarios
  FixtureBuilder->>Nalgebra: solve reference inputs
  FixtureBuilder->>Faer: solve reference inputs
  LaStack->>Criterion: benchmark complete and reusable-factor solves
  Nalgebra->>Criterion: benchmark reference solves
  Faer->>Criterion: benchmark reference solves

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🚥 Pre-merge checks | ✅ 3 | ❌ 1

❌ Failed checks (1 warning)

Check name	Status	Explanation	Resolution
Out of Scope Changes check	⚠️ Warning	The pull request includes substantial work unrelated to issue #234, including exact rational-to-f64 conversion changes, dense 4×4 determinant optimization, exact-arithmetic diagnostics, and Rust/tool …	Remove the unrelated conversion, determinant, diagnostic, and tooling changes, or link them to separate issues that define those objectives.

✅ Passed checks (3 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 two primary optimization changes: exact conversion and dense 4×4 determinant computation.
Linked Issues check	✅ Passed	The changes satisfy issue #234. They add LU solve benchmarks for the required dimensions, preserve finite-value invariants, retain typed non-finite diagnostics, avoid unsafe code, and document retaini…

Full details: Out of Scope Changes check

Explanation

The pull request includes substantial work unrelated to issue #234, including exact rational-to-f64 conversion changes, dense 4×4 determinant optimization, exact-arithmetic diagnostics, and Rust/tool version updates.

• Fix all pre-merge checks with AI

✨ Finishing Touches

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• Create stacked PR
• Commit on current branch

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• Create PR with unit tests
• Commit unit tests in branch perf/234-solve-finalization

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.04%. Comparing base (188c35b) to head (7fd6d8e).
✅ All tests successful. No failed tests found.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #238      +/-   ##
==========================================
+ Coverage   98.00%   98.04%   +0.03%     
==========================================
  Files          13       13              
  Lines        6579     6694     +115     
==========================================
+ Hits         6448     6563     +115     
  Misses        131      131              

Flag	Coverage Δ
unittests	98.04% <100.00%> (+0.03%)	⬆️

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