[tspiteri]

Imagine you get the result correct with infinite precision, and then round to the required precision in the specified way (round up, round down, round towards zero, round to nearest with ties to even, etc.). Correct rounding is equivalent to this. It is also reproducible, as there is only one possible correct result.

There is a similar concept which is supported experimentally by MPFR, which is faithful rounding. With faithful rounding, a number is rounded either to the closest value up or to the closest value down, but it is not necessarily the nearest of them. That is, if a and b are representable and no value between them is representable, and if a < x < b, then with faithful rounding x will be rounded to any of a or b. This can sometimes be faster, but is not reproducible any more.