> "If f is a (possibly multivariate) function on the set of floats to the reals, the IEEE-compliant approximation of f must give the closest float for all float values of its arguments."

It should be noted that this is not exactly true for some IEEE functions, due to the table-maker's dilemma: computing the "closest float approximation" to an arbitrary function can be computationally infeasible if the true result is close to being halfway in-between two consecutive floats. (This applies to the default rounding mode, but can be extended by analogy to other rounding modes.)