%0 Conference Paper %1 10.1007/3-540-45699-6_5 %A Edalat, Abbas %A Heckmann, Reinhold %B Applied Semantics %C Berlin, Heidelberg %D 2002 %E Barthe, Gilles %E Dybjer, Peter %E Pinto, Luís %E Saraiva, João %I Springer Berlin Heidelberg %K 2002 computational-geometry computer-science %P 193--267 %T Computing with Real Numbers %X We introduce, in Part I, a number representation suitable for exact real number computation, consisting of an exponent and a mantissa, which is an infinite stream of signed digits, based on the interval −1,1. Numerical operations are implemented in terms of linear fractional transformations (LFT's). We derive lower and upper bounds for the number of argument digits that are needed to obtain a desired number of result digits of a computation, which imply that the complexity of LFT application is that of multiplying n-bit integers. In Part II, we present an accessible account of a domain-theoretic approach to computational geometry and solid modelling which provides a data-type for designing robust geometric algorithms, illustrated here by the convex hull algorithm. %@ 978-3-540-45699-5

@inproceedings{10.1007/3-540-45699-6_5, abstract = {We introduce, in Part I, a number representation suitable for exact real number computation, consisting of an exponent and a mantissa, which is an infinite stream of signed digits, based on the interval [−1,1]. Numerical operations are implemented in terms of linear fractional transformations (LFT's). We derive lower and upper bounds for the number of argument digits that are needed to obtain a desired number of result digits of a computation, which imply that the complexity of LFT application is that of multiplying n-bit integers. In Part II, we present an accessible account of a domain-theoretic approach to computational geometry and solid modelling which provides a data-type for designing robust geometric algorithms, illustrated here by the convex hull algorithm.}, added-at = {2020-02-07T13:48:28.000+0100}, address = {Berlin, Heidelberg}, author = {Edalat, Abbas and Heckmann, Reinhold}, biburl = {https://www.bibsonomy.org/bibtex/2d4c00be2c08e1f9b4e44143083bc7795/analyst}, booktitle = {Applied Semantics}, description = {Computing with Real Numbers | SpringerLink}, editor = {Barthe, Gilles and Dybjer, Peter and Pinto, Lu{\'i}s and Saraiva, Jo{\~a}o}, interhash = {1a9843a9ed6ff52b74803e7e6495e62f}, intrahash = {d4c00be2c08e1f9b4e44143083bc7795}, isbn = {978-3-540-45699-5}, keywords = {2002 computational-geometry computer-science}, pages = {193--267}, publisher = {Springer Berlin Heidelberg}, timestamp = {2020-02-07T13:48:28.000+0100}, title = {Computing with Real Numbers}, year = 2002 }