FA-16819 / Floating-point arithmetic / Member archive

Tangent-pi measures pole distance from an integer · case 04

Tangent-pi measures pole distance from an integer.

Member previewVariant 4 · 3 implementations · 10 checks per implementation

Case contract

Evaluate tan(pi*x) after modulo-one reduction. Exact half integers are poles; integer zeros carry the sign of x. Near poles use a reciprocal tangent of distance to the pole. 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
near positive pole	`"1.1040997906e-14"`	`"8.95962678e+13"`	Failed

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