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Re: Avoiding roundoff errors in calculations?

• To: "Roger L. Costello" <costello@m...>
• Subject: Re: Avoiding roundoff errors in calculations?
• From: Rick Marshall <rjm@z...>
• Date: 30 Aug 2003 12:30:32 +1000
• Cc: xml-dev@l...
• In-reply-to: <3F4FBBFD.7CBA3BBD@m...>
• Organization: Zenucom Pty Limited
• References: <3F4FA206.5E2367A2@m...> <3F4FAFFF.1060900@t...> <3F4FBBFD.7CBA3BBD@m...>
• Reply-to: rjm@z...

there are techniques to manage error if it really matters. i used them
to keep the error in the solution of differential equations to a small,
and maximum amount over time. can't take credit for the technique - Dr
Phil Mcrea among others has that privilege.

paraphrased you can always eliminate the calculation error if you
calculate to a higher precision such that the error is not in the
significant digits and then store the significant digits only.

so eg if you need 15 significant digits (enough for most financial
calculations) calculate to at least 17, but round off the intermediate
results to 15 so that each intermediate result is accurate.

there are always accuracy issues, but the fact that nonrepeating real
numbers in one base are repeating ones in another is a real nuisance and
another reason why i use all character data, not floats, doubles, not
even integers for storage.

hope this helps

rick

On Sat, 2003-08-30 at 06:47, Roger L. Costello wrote:
> Hi Tim,
>  
> > I'm curious; what applications require more precision than IEEE double? -Tim
> 
> Good point.  Probably none that I need to be concerned about.
> 
> I think that the problem comes when the result of one calculation gets
> fed into another computation, which gets fed into another computation,
> etc.  Each computation introduces a roundoff error.  Soon there is far
> less than IEEE double precision.  /Roger
> 
> 
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