outside the gap is called the machine epsilon, typically characterized by the largest value whose sum with the value 1 will result in the answer with value 1 in that floating point scheme. This can be written as , where is a function which converts the real value into the floating point representation. While the machine epsilon is not to be confused with the underflow level (assuming subnormal numbers), it is closely related. The machine epsilon is dependent on the number of bits which make up the significand, whereas the underflow level depends on the number of digits which make up the exponent field. In most floating point systems, the underflow level is smaller than the machine epsilon. Handling of underflow The occurrence of an underflow may set a ("sticky") status bit, raise an exception, at the hardware level generate an interrupt, or may cause some combination of these effects. As specified in IEEE 754, the underflow condition is only signaled if there is also a loss of precision. Typically this is determined as the final result being inexact. However, if the user is trapping on underflow, this may happen regardless of consideration for loss of precision. The default handling in IEEE 754 for underflow (as well as other exceptions) is to record as a floating point status that underflow has occurred. This is specified for the application-programming level, but often also interpreted as how to handle it at the hardware level. See also Denormal number Floating-point arithmetic IEEE 754 Integer overflow Logarithmic number system Machine epsilon Normal number (computing) References Computer arithmetic