On Formally Correct Implementation of IEEE Computer Arithmetic

IEEE oating-point arithmetic standards 754 and 854 re ect the present state of the art in designing and implementing oating-point arithmetic units. A formalism applied to a standard non-trapping mode oating-point system shows incorrectness of some numeric and non-numeric results. A software emulation of decimal oating-point computer arithmetic supporting an enhanced set of exception symbols is reported. Some implementation details, discussion of some open questions about utility and consistency of the implemented arithmetic with the IEEE Standards are provided. The potential bene t for computations with in nite symbolic elements is outlined.