FA-16364 / Floating-point arithmetic / Member archive

Cosine decrement forgets half-angle reduction · case 04

Cosine decrement forgets half-angle reduction.

Member previewVariant 4 · 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	`"-2.7755575616e-17"`	`"-6.9388939039e-18"`	Failed

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