> "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.)
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.)