floating point underflow
(or "floating point underflow", "floating underflow", after "overflow") A condition that can occur when the result of a floating-point operation would be smaller in magnitude (closer to zero, either positive or negative) than the smallest quantity representable. Underflow is actually (negative) overflow of the exponent of the floating point quantity. For example, an eight-bit twos complement exponent can represent multipliers of 2^-128 to 2^127. A result less than 2^-128 would cause underflow.
Depending on the processor, the programming language and the run-time system, underflow may set a status bit, raise an exception or generate a hardware interrupt or some combination of these effects. Alternatively, it may just be ignored and zero substituted for the unrepresentable value, though this might lead to a later divide by zero error which cannot be so easily ignored.