Reading even more into IEEE 754-2008, some operations can also be marked as having 6th rounding mode, called Exact. They will produce results normally as any other rounding mode (i.e. nearest), but if the result is not exact (i.e. sqrt(2) will produce result that is not exact, it will be rounded to something that is different that real result, but 2*3 or 1/2 will produce exact results), it will throw FP exception. Really cool feature, because it allows to write a fast path without carrying too much about handling all rounding, and handle the inexact results in some slow handler. It would be most useful in integer to float conversions, and float to int conversions. I.e. conversion of 2.5 to int will produce inexact value, and throw exception, but 2.0 to int will produce exact result, and continue execution.
Reply To: Floating Point Rounding Witold Baryluk