Glossary

Round to nearest, ties to even

Beginner

The rule for rounding a number that doesn’t fit: pick the closest value the format can store, and when it’s exactly halfway, pick the one ending in an even digit.

Novice

The default rounding mode for floating point. A value is rounded to the nearest representable number; exact ties go to the one whose last bit is 0. Breaking ties this way avoids a systematic upward drift.

Expert

IEEE 754’s roundTiesToEven, required by the OCP FP8 and MX specifications for conversions. Unbiased on average, but deterministic: repeated tiny updates can round away to nothing, which is why low-precision training sometimes uses stochastic rounding instead.

Explained in Number formats (Architectures).

See also: Stochastic rounding.

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