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.

A Dynamic Precision Floating-Point Arithmetic Based on the Infinity Computer Framework / Amodio, Pierluigi; Brugnano, Luigi; Iavernaro, Felice; Mazzia, Francesca. - STAMPA. - 11974:(2020), pp. 289-297. (Intervento presentato al convegno NUMTA 2019) [10.1007/978-3-030-40616-5_22].

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

#### Abstract

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.
##### Scheda breve Scheda completa Scheda completa (DC) 2020
Numerical Computations: Theory and Algorithms Third International Conference, NUMTA 2019
NUMTA 2019
Amodio, Pierluigi; Brugnano, Luigi; Iavernaro, Felice; Mazzia, Francesca
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Utilizza questo identificatore per citare o creare un link a questa risorsa: `https://hdl.handle.net/2158/1184376`
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