Editing Computable number (section)

==Implementations of exact arithmetic==

Computer packages representing real numbers as programs computing approximations have been proposed as early as 1985, under the name "exact arithmetic".<ref>{{cite book |last1=Boehm |first1=Hans-J. |last2=Cartwright |first2=Robert |last3=Riggle |first3=Mark |last4=O'Donnell |first4=Michael J. |title=Proceedings of the 1986 ACM conference on LISP and functional programming - LFP '86 |chapter=Exact real arithmetic: A case study in higher order programming |date=8 August 1986 |pages=162–173 |doi=10.1145/319838.319860 |isbn=0897912004 |s2cid=12934546 |chapter-url=http://fricas-wiki.math.uni.wroc.pl/public/refs/exact-real-p162-boehm.pdf |archive-url=https://web.archive.org/web/20200924021221/http://fricas-wiki.math.uni.wroc.pl/public/refs/exact-real-p162-boehm.pdf |archive-date=2020-09-24 |url-status=live}}</ref> Modern examples include the CoRN library (Coq),<ref>{{cite book |last1=O’Connor |first1=Russell |title=Theorem Proving in Higher Order Logics |chapter=Certified Exact Transcendental Real Number Computation in Coq |series=Lecture Notes in Computer Science |date=2008 |volume=5170 |pages=246–261 |doi=10.1007/978-3-540-71067-7_21 |arxiv=0805.2438 |isbn=978-3-540-71065-3 |s2cid=17959745 }}</ref> and the RealLib package (C++).{{sfnp|Lambov|2015}} A related line of work is based on taking a [[real RAM]] program and running it with rational or floating-point numbers of sufficient precision, such as the {{proper name|iRRAM}} package.<ref>{{cite book |last1=Gowland |first1=Paul |last2=Lester |first2=David |title=Computability and Complexity in Analysis |chapter=A Survey of Exact Arithmetic Implementations |series=Lecture Notes in Computer Science |date=2001 |volume=2064 |pages=30–47 |doi=10.1007/3-540-45335-0_3 |chapter-url=https://link.springer.com/content/pdf/10.1007%2F3-540-45335-0_3.pdf |archive-url=https://web.archive.org/web/20220324193302/https://link.springer.com/content/pdf/10.1007%2F3-540-45335-0_3.pdf |archive-date=2022-03-24 |url-status=live |publisher=Springer |isbn=978-3-540-42197-9 |language=en}}</ref>