FA-16863 / Floating-point arithmetic / Member archive

Atan2 fails to complement its steep-slope ratio · case 03

Atan2 fails to complement its steep-slope ratio.

Member previewVariant 3 · 3 implementations · 16 checks per implementation

Case contract

Evaluate atan2(y,x) including signed zero and infinite directions; NaN produces nan. Finite nonzero coordinates use ratio of smaller magnitude and quadrant reconstruction. 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
steep slope	`"0.033320995878"`	`"1.5374753309"`	Failed

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