A Dynamic Precision Floating-Point Arithmetic Based on the Infinity Computer Framework

We introduce a dynamic precision floating-point arithmetic based on the Infinity Computer. This latter is a computational platform which can handle both infinite and infinitesimal quantities epitomized by the positive and negative finite powers of the symbol GrossOne, which acts as a radix in a corresponding positional numeral system. The idea is to use the positional numeral system from the Infinity Computer to devise a variable precision representation of finite floating-point numbers and to execute arithmetical operations between them using the Infinity Computer Arithmetics. Here, numerals with negative finite powers of 1 will act as infinitesimal-like quantities whose aim is to dynamically improve the accuracy of representation only when needed during the execution of a computation. An application to the iterative refinement technique to solve linear systems is also presented.