Conclusion and Perspectives Muller, Jean-Michel; Brisebarre, Nicolas; de Dinechin, Florent ...
Handbook of Floating-Point Arithmetic
Book Chapter
With the recent IEEE standard update resulting in IEEE 754-2008, computer arithmetic will soon see important changes: the fused multiply-add (FMA) instruction will probably be available on most ...processors, and correctly rounded functions (at least in some domains) and decimal arithmetic will be provided on most systems. Also, it should be easier to specify whether one wishes the implicit intermediate variables of an arithmetic expression to be computed and stored in the largest available format (to improve the accuracy of the calculations) or in a format clearly specified in the program (to enhance software portability and provability).
Introduction Muller, Jean-Michel; Brisebarre, Nicolas; de Dinechin, Florent ...
Handbook of Floating-Point Arithmetic
Book Chapter
Representing and manipulating real numbers efficiently is required in many fields of science, engineering, finance, and more. Since the early years of electronic computing, many different ways of ...approximating real numbers on computers have been introduced. One can cite (this list is far from being exhaustive): fixed-point arithmetic, logarithmic 220, 400 and semi-logarithmic 294 number systems, continued fractions 228, 424, rational numbers 227 and possibly infinite strings of rational numbers 275, level-index number systems 71, 318, fixed-slash and floating-slash number systems 273, and 2-adic numbers 425.
