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Re: Avoiding roundoff errors in calculations?

• To: Chiusano Joseph <chiusano_joseph@b...>
• Subject: Re: Avoiding roundoff errors in calculations?
• From: Rick Marshall <rjm@z...>
• Date: 03 Sep 2003 09:35:53 +1000
• Cc: "Roger L. Costello" <costello@m...>, xml-dev@l...
• In-reply-to: <3F549323.CF1486C@b...>
• Organization: Zenucom Pty Limited
• References: <3F4FA206.5E2367A2@m...> <3F549323.CF1486C@b...>
• Reply-to: rjm@z...

On Tue, 2003-09-02 at 22:54, Chiusano Joseph wrote:
> <Quote>
> I am considering returning the result in numerator/denominator form, and
> leaving it up to the recipient to do the division (and decide what
> precision is suitable), i.e.,
> 
> <Length>
>     <value>
>         <numerator>33.02</numerator>
>         <denominator>600</denominator>
>     </value>
>     <unit rdf:resource="#Meter"/>
> </Length>
> </Quote>
> 
> Leaving the precision to the recipient may not be desirable,
> particularly if the calculation is an "aggregate calculation" that is
> carried out by multiple processes each on a different processor (or
> different programming language), which may lead a less-than-accurate
> precision in the final result.
> 
> So an alternative approach is to also specify the required precision for
> the calculation result in the XML request:
> 
> <Length>
>     <value precision="15">
>         <numerator>33.02</numerator>
>         <denominator>600</denominator>
>     </value>
>     <unit rdf:resource="#Meter"/>
> </Length>
> 
> where "precision" is the number of decimal places for the result.
don't you mean "significant digits"?

decimal places is only meaningful in unimportant areas like finance ;)

rick
>  If a
> process cannot honor this precision, it could throw an exception.
> 
> Kind Regards,
> Joe Chiusano
> Booz | Allen | Hamilton
> 
> "Roger L. Costello" wrote:
> > 
> > Hi Folks,
> > 
> > Suppose that I would like to convert this Length to meters (there are 6
> > picas per inch):
> > 
> > <Length>
> >     <value>13</value>
> >     <unit rdf:resource="#Pica"/>
> > </Length>
> > 
> > Doing the arithmetic:
> > 
> > 13 picas * in/6 picas * 2.54 cm/in * m/100 cm
> > 
> >     = 33.02/600 m
> > 
> >     = 0.055033333333333333333333333333 m (the "3" repeats infinitely)
> > 
> > The problem is that everyone has different precision requirements.  Some
> > people would be happy with this as the result:
> > 
> > <Length>
> >     <value>0.055</value>
> >     <unit rdf:resource="#Meter"/>
> > </Length>
> > 
> > For other people such a roundoff could be catastrophic.
> > 
> > Even if I were to return a result that is as precise as my machine can
> > produce,
> > 
> > <Length>
> >     <value>0.055033333333333333333333333333</value>
> >     <unit rdf:resource="#Meter"/>
> > </Length>
> > 
> > there is still a roundoff that may be unacceptable to some.
> > 
> > I am considering returning the result in numerator/denominator form, and
> > leaving it up to the recipient to do the division (and decide what
> > precision is suitable), i.e.,
> > 
> > <Length>
> >     <value>
> >         <numerator>33.02</numerator>
> >         <denominator>600</denominator>
> >     </value>
> >     <unit rdf:resource="#Meter"/>
> > </Length>
> > 
> > What are your thoughts on this?  What techniques do people use to avoid
> > introducing roundoff errors?  /Roger
> > 
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  • Re: Avoiding roundoff errors in calculations?
    • From: "Chiusano Joseph" <chiusano_joseph@b...>

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