Using the Gelfond -- Schneider theorem and Lindemann -- Weierstrass theorem many of the standard elementary functions can be proved to return transcendental results when given rational non-zero arguments ; therefore it is always possible to correctly round such functions .
Using the Gelfond -- Schneider theorem and Lindemann -- Weierstrass theorem , many of the standard elementary functions can be proved to return transcendental results when given rational non-zero arguments ; therefore it is always possible to correctly round such functions .