FA-16658 / Floating-point arithmetic / Member archive

Stochastic rounding replaces the remainder probability with a fair coin · case 03

Stochastic rounding replaces the remainder probability with a fair coin.

Member previewVariant 3 · 3 implementations · 10 checks per implementation

Case contract

Stipulated stochastic rounding of nonnegative significand with exact dyadic remainder rem/2**k. Draw is uniform integer in [0,2**k); increment magnitude iff draw<rem, then apply sign. Exact results never increment. Return rounded value and whether magnitude incremented.

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
draw equality	`[4, true]`	`[3, false]`	Failed

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