FA-16372 / Floating-point arithmetic / Member archive

Cosine decrement returns a positive half-angle square · case 02

Cosine decrement returns a positive half-angle square.

Member previewVariant 2 · 3 implementations · 7 checks per implementation

Case contract

Evaluate cos(x)-1 for finite x without cancellation using the half-angle identity. 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
tiny	`"1.734723476e-18"`	`"-1.734723476e-18"`	Failed

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