FA-16718 / Floating-point arithmetic / Member archive

Quadratic roots compute the small root by subtraction · case 03

Quadratic roots compute the small root by subtraction.

Member previewVariant 3 · 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 positive b	`["-3e+16", "0"]`	`["-3e+16", "-3.3333333333e-17"]`	Failed

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