From: Larry Paulson
Subject: Re: arbitrary-precision real arithmetic (SUMMARY)
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From: ···@cl.cam.ac.uk (Larry Paulson)
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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