Speed up leaving-variable test with a linear argmin ratio scan

[adelaett]

Summary

Speeds up the leaving-variable (minimum-ratio) test, which runs on every pivot regardless of pricing rule.

choose_leaving only ever needs the argmin of the candidate ratios, but the old code:

1. built a list of Q.make b pv ratios — a GCD per candidate,
2. List.fast_sorted it on (Q.compare, index) — cross-multiplying GCD-reduced fractions,
3. then read only the head.

Profiling the hot rand_25x60 solve showed Q.compare as the 3rd hottest symbol, rivalling the core fraction-free Z.sub/Z.divexact.

Change

Replace the build-list-and-sort with a single linear argmin scan. Candidates are compared by ratio_compare, a direct cross-multiplication:

sign(b1/p1 − b2/p2) = sign(b1·p2 − b2·p1) · sign(p1) · sign(p2)

Only exact Z.mul/Z.sub/Z.sign on the shared-denominator integers — no GCD, no reduced-rational allocation, no sort. The sign correction makes it valid on the ignore_neg transition path too (negative pivots), so both paths share it.

Correctness

Bit-identical selection. Scanning rows upward and replacing only on a strict ratio decrease reproduces the old stable (ratio, index) ascending order, so the same leaving variable is chosen every time.

• All golden cram tests pass unchanged (they diff full -v per-pivot tableaux).
• Pivot geomean ratio 1.0000× and rational objectives match on every held-out instance.
• Benchmark correctness: matches the GLPK + Gurobi oracle consensus on all 19 instances.

Performance

bench/evaluate.py --baseline main --candidate alain/simplex-leaving-argmin --rule bland --trials 60:

Metric	Result
Time geomean speedup	1.127× (+12.68%)
95% bootstrap CI	[1.089, 1.177] — entirely above 1.0
Pivot ratio	1.0000× (no behavioral change)
Correctness	passed (GLPK + Gurobi)

Every instance is faster or equal (worst +4.7%). Verdict: ACCEPTED.

Note on trials: at --trials 30 laptop noise (CI ≈ [0.90, 1.04]) can flip this borderline ~12% win to REJECTED; --trials 60 gives a clean, stable verdict, as AGENTS.md advises for small speedups.

🤖 Generated with Claude Code