FA-16722 / Floating-point arithmetic / Member archive

Quadratic roots choose a fixed square-root sign · case 02

Quadratic roots choose a fixed square-root sign.

Member previewVariant 2 · 3 implementations · 9 checks per implementation

Case contract

Real roots of a*x*x+b*x+c=0 for finite coefficients with bounded discriminant products. Use sign-aware q to avoid subtractive cancellation and c/q for the complementary root. Return sorted rendered roots, repeated root once, or explicit degenerate/no-real markers. Finite results are rendered to eleven significant decimal digits; modeled domain violations and arithmetic errors are explicit strings.

Why this case matters

An offline floating representation model isolates a reproducible arithmetic fault.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
large negative b	`"arithmetic-error"`	`["5e-17", "2e+16"]`	Failed

MEMBER ARCHIVE

The complete case is available to members.

This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

Member access is invitation-based. Sign in with your invited account to inspect the sources.