FA-17083 / Floating-point arithmetic / Member archive

Closeness excludes values exactly at tolerance · case 03

Closeness excludes values exactly at tolerance.

Member previewVariant 3 · 3 implementations · 11 checks per implementation

Case contract

Symmetric binary64 closeness: equal values including like-signed infinities are close; remaining nonfinite pairs are not. For finite a,b require abs(a-b)<=max(abs_tol,rel_tol*max(abs(a),abs(b))). Negative tolerances return invalid.

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
absolute zero	`false`	`true`	Failed

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