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INDEPENDENT NUMERICAL AUDIT3 September 2026

A one-line contradiction in Swift Numerics' tie-to-zero documentation

Permanent archive: Zenodo · 10.5281/zenodo.22729048.

An exact arithmetic check found that one Swift Numerics example reported 3 where its stated rounding rule and its own explanation require 2.

Xamit Kadirbekov
Xamit KadirbekovIndependent verification · GERO Research
Numerical auditSwiftRounding
STATUS · VERIFIED DOCUMENTATION DEFECTThe arithmetic, source line and proposed correction were checked. This finding concerns documentation, not a demonstrated runtime or security defect.
UPSTREAM RECORD · APPLE SWIFT NUMERICS Pull request #348 ↗

Finding

At source commit 899af71c0256d0ad181e3b7eb3453c1065d928a5, the documentation for RoundingRule.toNearestOrZero stated that 5.shifted(rightBy: 1, rounding: .toNearestOrZero) is 3. The next sentence says that 5/2 = 2.5 is equally close to 2 and 3 and that 2 is closer to zero. The example and its explanation therefore contradicted one another.

Exact certificate

  1. The exact quotient is 5/2 = 2.5.
  2. The two nearest integers are 2 and 3.
  3. Both are exactly 0.5 from 2.5.
  4. The documented tie-break is toward zero.
  5. Therefore the result is 2.
5 ÷ 2 = 2.5tie → 2

Correction submitted upstream

- is `3`,
+ is `2`,

The one-character correction was submitted to the official repository as apple/swift-numerics#348. The reviewed source is preserved at the exact commit and line range; the repository remains the authoritative upstream record.

Validation

  • Recomputed the result with exact rational arithmetic.
  • Checked the example against the enum's stated tie-breaking contract.
  • Applied the minimal one-line documentation patch.
  • Ran swift build successfully.
  • Ran git diff --check successfully.