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From: dik@cwi.nl (Dik T. Winter)
Newsgroups: comp.arch
Subject: Re: errors and error bounds in floating-point arithmetic
Message-ID: <3613@charon.cwi.nl>
Date: 31 May 91 00:27:55 GMT
References: <391@validgh.com>
Sender: news@cwi.nl
Organization: CWI, Amsterdam
Lines: 39

A minor quible:

In article <391@validgh.com> dgh@validgh.com (David G. Hough on validgh) writes:
...
 > "Accuracy benchmark" programs which attempt to measure the quality of computer
 > arithmetic by comparing computed results to the known correct answers are
 > common but not very interesting because they don't correspond to the much
 > more typical situation in which the correct answer is not known.
 > Not many people routinely spend most of their time solving problems whose
 > answers they already know.
 > 
Although you mention later down versions of Kahan's paranoia (in that it
fails to recognize and analyze extended precision intermediate results),
I would like to mention that the program still has many virtues.  Similar
for the Floating Point Validation suit from NAG.  As long as architects
do not understand the basics of floating point arithmetic we will have
such anomalies as:
1.	If a equals b it is not necessarily true that b equals a.
2.	For some value v close to 1.0, 1.0/v = 0.0 (luckily the instruction
	where that comes from is not used on that machine).
paranoia and FPV are able to detect such basic design flaws.  Of course you
should be aware that such programs can give you false alarms.  And also of
course, those programs are dependent on both hardware and compiler.

I have some experience.  Compiler writers are also in general completely
unaware of the properties of floating point arithmetic.  In Ada each
floating point type has some attributes associated with it that tell you
the properties of the arithmetic (e.g. what is tha machine radix, does
overflow trap and so on).  I have written a program that verifies those
attributes (it will be published in a forthcoming issue of Ada Letters).
Some time ago I observed that:
1.	For every attribute there was a compiler that got it wrong.
2.	For every compiler there was a wrong attribute.
True at that time.  Luckily things are improving.

You can draw your own conclusion.
--
dik t. winter, cwi, amsterdam, nederland
dik@cwi.nl