Towards an abstract mathematical theory of floating-point arithmetic

Abstract

The representation of integers by a place value sequence of digits taken from a radix polynomial is one of the profound mathematical developments of all times. It provides an elegant foundation for mathematical questions where algorithmic procedures are needed, such as how to computationally effect the operations of addition, subtraction, multiplication, division and comparison. Nevertheless, as invaluable as the place value representation system is to computational mathematics, most questions regarding the mathematical structure of the integers are usually answered with proofs which make no reference to any representational form of the integers, but are based solely on an abstract characterization of the integers.