FA-16800 / Floating-point arithmetic / Member archive

Cosine-pi derives half-integer zero by a rounded cosine · case 05

Cosine-pi derives half-integer zero by a rounded cosine.

Member previewVariant 5 · 3 implementations · 11 checks per implementation

Case contract

Evaluate cos(pi*x) for finite x after modulo-two reduction. Half integers return positive zero; integers are exact; near half integers use a sine of the distance to the half integer. 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
half integer	`"6.1232339957e-17"`	`"0"`	Failed

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