Arithmetic underflow

The term arithmetic underflow or simply underflow has the following meanings.

1. In a digital computer, the condition that occurs when a calculation produces a result that is less than a given register or storage location can store or represent.

For floating point arithmetic, and underflow occurs when the magnitude of intermediate result (i.e., before rounding) is strictly between the smallest normal floating point number in the format and zero. As specified in IEEE 754 the underflow condition is only signalled if there is also a loss of accuracy. Typically this is determined as the final result being inexact. However if the user is trapping on underflow, this happens regardless of consideration for loss of precision.