perf: improve exact arithmetic benchmark coverage with diverse inputs

[acgetchell]

Dependencies

• perf: integer-only forward elimination for gauss_solve (BigInt hybrid) #72

Summary

The current benches/exact.rs benchmarks use a single fixed well-conditioned matrix per dimension. This measures typical-case performance but misses important input classes where exact arithmetic performance varies significantly.

Current State

Each dimension (D=2–5) benchmarks one diagonally dominant matrix with small entries (matrix_entry produces values near D+1 on the diagonal, small off-diagonal). The only exception is near_singular_3x3, which benchmarks det_sign_exact and det_exact but not solve_exact.

This is methodologically sound for reproducibility but leaves gaps:

• No near-singular solve benchmarks (the primary use case for exact solve)
• No inputs that stress BigInt intermediate value growth
• No variance measurement across different input structures

Proposed Changes

1. Near-singular solve benchmarks

Add solve_exact and solve_exact_f64 benchmarks for near-singular matrices (at least D=3). These are the inputs where exact solve matters most and where intermediate values grow largest.

2. Adversarial BigInt growth inputs

Add a matrix with large entries (e.g. entries near f64::MAX / 2) that maximizes intermediate BigInt bit-lengths during Bareiss/Gauss elimination. This stress-tests the allocator and big-integer multiply.

3. Random-input percentile benchmarks (optional)

Consider adding a benchmark group that runs N random matrices per dimension and reports median/p95/p99. This captures variance from branch misprediction, allocation patterns, and intermediate value sizes that a single fixed input misses.

4. Ill-conditioned matrix benchmarks

Add a Hilbert-like or Vandermonde matrix where entries span many orders of magnitude. This exercises different exponent-scaling behavior in the f64_decompose → BigInt path.

Benefits

• More representative performance characterization for the exact arithmetic use case (geometric predicates on near-degenerate configurations)
• Better detection of performance regressions on adversarial inputs
• Stronger empirical evidence for docs/PERFORMANCE.md

Implementation Notes

• Related: perf: integer-only forward elimination for gauss_solve (BigInt hybrid) #72 (once the Bareiss hybrid solve lands, these benchmarks will measure its improvement)
• The near-singular solve_exact benchmark can reuse or adapt near_singular_3x3()
• Criterion supports custom measurement and iteration counts for random-input benchmarks

[acgetchell]

Blocked by #72 (benchmark the improved Bareiss hybrid solve, not the old BigRational path).