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From: ···@cl.cam.ac.uk (Larry Paulson)
Newsgroups: sci.math.symbolic,comp.lang.functional,comp.lang.lisp,comp.lang.ml
Subject: Re: arbitrary-precision real arithmetic (SUMMARY)
Date: 29 Aug 1995 14:57:54 GMT
Organization: Computer Laboratory, University of Cambridge
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I have been asked to post a summary of the responses to my query. There is no
way I could summarise all the ensuing discussion, but here is a list of
references that appear to be relevant.
This thesis (in French) by Valrie Mnissier-Morain was recommended as
representing the state of the art.
@PHDTHESIS{menisse-thesis,
author = "Val{\'e}rie M{\'e}nissier-Morain",
title = "Arithm{\'e}tique exacte, conception, algorithmique
et performances d'une impl{\'e}mentation
informatique en pr{\'e}cision arbitraire",
school = "Universit{\'e} Paris 7",
type = "Th{\`e}se",
year = 1994,
month = "December"}
Many people said that the continued fraction approach was simply too slow to
be usable. David Lester describes an implementation;
@InProceedings{lester91,
author = {David Lester},
title = {Vuillemin's Exact Real Arithmetic},
pages = {225--238},
booktitle = {Glasgow Workshop on Functional Programming},
year = 1991,
editor = {R. Heldal and C. Holst and P. Wadler},
publisher = {Springer}}
A survey of methods including continued fractions is
@InCollection{boehm-cartwright,
author = {Hans Boehm and Robert Cartwright},
title = {Exact Real Arithmetic: Formulating Real Numbers as
Functions},
pages = {43--64},
editor = {David Turner},
booktitle = {Research Topics in Functional Programming},
year = 1990,
publisher = {Addison-Wesley}}
Boehm has added "There is an ftp'able package containing a real arithmetic
package in the same spirit as Jean Vuillemin's in
ftp://parcftp/xerox.com/pub/russell/C_calc.tar.Z "
The following package uses more conventional methods, so the precision must be
fixed in advance. But it claims to offer high performance.
@TechReport{bailey-mpfun,
author = {David H. Bailey},
title = {{MPFUN}:A Portable High Performance Multiprecision Package},
institution = {NASA Ames Research Center},
year = 1990,
type = {RNR Technical Report},
number = {RNR-90-022},
address = {Moffett Field,CA}}
I should like to thank everybody who replied to my posting.
--
Lawrence C Paulson, University Lecturer
Computer Laboratory, University of Cambridge,
Pembroke Street, Cambridge CB2 3QG, England
Tel: +44(0)1223 334623 Fax: +44(0)1223 334678