Definitions and Basic Notions

Abstract

As said in the Introduction, roughly speaking, a radix-β floating-point number x is a number of the form m · β e , where β is the radix of the floating-point system, m such that |m| < β is the significand of x, and e is its exponent. And yet, portability, accuracy, and the ability to prove interesting and useful properties as well as to design smart algorithms require more rigorous definitions, and much care in the specifications. This is the first purpose of this chapter. The second one is to deal with basic problems: rounding, exceptions, properties of real arithmetic that become wrong in floating-point arithmetic, best choices for the radix, and radix conversions.