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From: scorpion@titan.rice.edu (Vernon Lee)
Newsgroups: comp.lang.misc
Subject: Re: An alternative to floating point (was Re: Floating point non-exactness)
Message-ID: <1990Aug1.182901.12714@rice.edu>
Date: 1 Aug 90 18:29:01 GMT
References: <3491@goanna.cs.rmit.oz.au> <1990Jul31.130623.15963@mintaka.lcs.mit.edu> <1990Aug1.152945.12826@ux1.cso.uiuc.edu>
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Here's a brief bibliography of implementing exact reals.  These
implementations are by necessity of the _constructive reals_, that is,
those reals for which one can give an algorithm to produce arbitrarily
accurate approximations.

    Hans-J. Boehm, "Constructive real interpretation of numerical
    programs," SIGPLAN Notices, 22(7):214-221. July 1987

    Hans-J. Boehm, Robert Cartwright, Mark Riggle, and Michael J.
    O'Donnell, "Exact real arithmetic:  A case study in higher order
    programming."  In Proceedings of the 1986 Lisp and Functional
    Programming Conference, pp 162-173, 1986.

    Vernon Lee and Hans-J. Boehm, "Optimizing programs over the
    constructive reals."  In Proceedings of the ACM SIGPLAN '90 Conference
    on Programming Language Design and Implementation, pp 102-111, June
    1990.

    Jean Vuillemin, "Exact real computer arithmetic with continued
    fractions."  Research Report 760, INRIA, 1987.

    Jean Vuillemin, "Exact real computer arithmetic with continued
    fractions."  In ACM Conference on Lisp and Functional Programming, pp.
    14-27.  ACM, July 1988.

    Jerry Schwartz, "Implementing Infinite Precision Arithmetic."  9th
    Symposium on Computer Arithmetic, 1989.


These works address implementing a system that requires only that the
programmer provide a requested accuracy for real values - the packages
automatically produce the required accuracy.  Many other works have
studied an approach that puts the programmer more in charge of producing
the accuracy, by for example raising the precision of a multiple-precision
arithmetic package.

-- 
    "The Movement You Need is on Your Shoulder"
		- John Lennon's favorite line from "Hey, Jude"

-=- Vernon Lee -=- Warning: Myers-Briggs INTP -=- scorpion@rice.edu -=-