The justification for this definition is to preserve the sign of the result in case of arithmetic underflow.

In a computer implementation, as the three s sums become large, we need to consider round-off error, arithmetic overflow, and arithmetic underflow.

Subnormal values fill the arithmetic underflow gap with values where the absolute distance between them are the same as for adjacent values just outside of the underflow gap.

One may obtain negative zero as the result of certain computations, for instance as the result of arithmetic underflow on a negative number, or , or simply as .

An invalid operation is also not the same as an arithmetic overflow (which might return an infinity) or an arithmetic underflow (which would return the smallest normal number, a denormal number, or zero).

The term arithmetic underflow (or "floating point underflow", or just "underflow") is a condition in a computer program where the result of a calculation is a smaller number than the computer can actually store in memory.

Arithmetic underflow can occur when the true result of a floating point operation is smaller in magnitude (that is, closer to zero) than the smallest value representable as a normal floating point number in the target datatype.