Conversion

BFloat16

Conversion to and from Microfloat uses BFloat16 as an intermediate type, since BFloat16 has 1 sign bit, 8 exponent bits, and 7 significand (mantissa) bits, and is therefore able to represent all Microfloat types.

Rounding

Converting from larger types will round to the nearest even value, i.e. the value whose bit representation ends in 0.

Overflow policies

When converting from a wider type to a Microfloat, one may want certain behaviors in regard to Inf and NaN handling.

Source Value	Destination Value
	Has Inf+NaN		Has NaN		Finite
	SAT	OVF	SAT	OVF	SAT	OVF
NaN	NaN	NaN	NaN	NaN	Error	Error
±Inf	±floatmax	±Inf	±floatmax	NaN	±floatmax	Error
>\|floatmax\|	±floatmax	±Inf	±floatmax	NaN	±floatmax	Error

Microfloats.OVF — Type

OVF

source

Microfloats.SAT — Type

SAT

source