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From: "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>
Newsgroups: comp.lang.ada
Subject: Re: REAL
Date: Wed, 14 Mar 2012 22:52:42 +0100
Organization: cbb software GmbH
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Date: 2012-03-14T22:52:42+01:00
List-Id: <comp.lang.ada>

On Wed, 14 Mar 2012 20:37:28 +0000 (UTC), Brian Drummond wrote:

> On Wed, 14 Mar 2012 14:51:59 +0100, Dmitry A. Kazakov wrote:
> 
>> Comparing to analytical methods of error estimation. Intervals give a
>> pessimistic one. 
> 
> Indeed. As has been pointed out frequently on comp.arch by (I think) Nick 
> Maclaren, any sufficiently complex calculation in interval arithmetic 
> will return the interval (-inf, +inf).

That depends on the nature of computations. Complex direct numerically
instable computation which evaluate garbage are no better. Normally
computations are iterative, actually narrowing the interval rather than
widening it.

>> A manual analysis based on additional knowledge
>> (especially if variables are dependant) may sufficiently improve the
>> estimation. 
> 
> But surely the same analysis can be performed on float arithmetic - 
> admittedly this time, to widen the estimated range.

Not necessarily. Example: x + x. When replaced by 2*x, it would have no
effect on the accuracy of floating-point computation, while may narrow the
interval.

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de