The IEEE 754 standard defines five exceptions that can occur during a calculation. Each corresponds to a particular sort of error, such as overflow.
When exceptions occur (when exceptions are raised, in the language of the standard), one of two things can happen. By default the exception is simply noted in the floating-point status word, and the program continues as if nothing had happened. The operation produces a default value, which depends on the exception (see the table below). Your program can check the status word to find out which exceptions happened.
Alternatively, you can enable traps for exceptions. In that case,
when an exception is raised, your program will receive the
signal. The default action for this signal is to terminate the
program. See Signal Handling, for how you can change the effect of
The exceptions defined in IEEE 754 are:
This exception is raised if the given operands are invalid for the operation to be performed. Examples are (see IEEE 754, section 7):
If the exception does not trap, the result of the operation is NaN.
This exception is raised when a finite nonzero number is divided by zero. If no trap occurs the result is either +∞ or -∞, depending on the signs of the operands.
This exception is raised whenever the result cannot be represented as a finite value in the precision format of the destination. If no trap occurs the result depends on the sign of the intermediate result and the current rounding mode (IEEE 754, section 7.3):
Whenever the overflow exception is raised, the inexact exception is also raised.
The underflow exception is raised when an intermediate result is too small to be calculated accurately, or if the operation’s result rounded to the destination precision is too small to be normalized.
When no trap is installed for the underflow exception, underflow is signaled (via the underflow flag) only when both tininess and loss of accuracy have been detected. If no trap handler is installed the operation continues with an imprecise small value, or zero if the destination precision cannot hold the small exact result.
This exception is signalled if a rounded result is not exact (such as when calculating the square root of two) or a result overflows without an overflow trap.