Constructive/recursive real arithmetic package

[Gregory V. Tarsy]

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From: boehmahoh.engr.sgi.com (Hans Boehm)
Date: Wed, 4 Aug 1999 11:31:27 -0700
To: reliable_computingainterval.usl.edu
Subject: Constructive/recursive real arithmetic package
Cc: boehmahoh.engr.sgi.com
Mime-Version: 1.0

We just made available a desk calculator utility and Java library that
implements a flavor of constructive real arithmetic.  Effectively it provides
for demand-driven evaluation of the result to guarantee accuracy to the
requested precision, evaluating intermediate results to whatever precision is
necessary to ensure that.  The calculator allows you to scroll the display
sideways to obtain whatever precision is desired.

This is of course not suitable for large scale computation, since it is several
orders of magnitude slower than either conventional floating point arithmetic
or hardware precision interval arithmetic.  But I hope it is useful for
instructional purposes and for small to medium sized computations that require
guaranteed accuracy with a minimum of effort.  Performance is easily adequate
for a calculator.

The package does not use interval arithmetic per se, though iterated variable
precision interval arithmetic would probably lead to a faster, though larger,
implementation.

The calculator, library, source code, and further description is available at

http://oss.sgi.com/projects/crcalc/CRCalc.html

This will attempt to start up the calculator if you are running a recent
Java-enabled browser.  We're still trying to deal with various browser
idiosyncracies, so this may not be successful.  So far, it usually appears to
work with Netscape 4.05 or later, or Internet Explorer 4 or later on reasonably
modern hardware.  In either case, you should get access to the description of
the package as well as the code itself.

This is the initial release of this package.  Bug reports are welcome, as are
anecdotes of browser/hardware/OS combinations that do or don't work.

The underlying algorithms are largely similar to a package that Vernon Lee and
I wrote many years ago at Rice University.  However, the emphasis in this
version tended to be on simplicity, small size, and reasonable algorithms
rather than using the world's asymptotically fastest algorithms.

-- 
Hans-J. Boehm
boehmasgi.com

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