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MathGroup Archive 2000

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Re: RE:Working Precision

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24054] Re: [mg23928] RE:Working Precision
  • From: mend0070 at garnet.tc.umn.edu (Philip C Mendelsohn)
  • Date: Thu, 22 Jun 2000 01:01:47 -0400 (EDT)
  • Organization: University of Minnesota, Twin Cities Campus
  • References: <8ihv28$led@smc.vnet.net> <8in7e4$4kc@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Richard Fateman (fateman at cs.berkeley.edu) wrote:

: Here's an easily defended rule:  Do all arithmetic exactly. When
: you must store the result into a finite sized memory location, 
: round it to the nearest representable number exactly representable
: in that memory location. In case of a tie, round to even.

Numeric math is not my expertise, but is your error not limited by
the intervals between exactly representable numbers?  And, if performing
calculations on numbers that have been stored, is not the propagation
(and acculmulation) of error still present?

Pardon my ignorance, but I fail to see how this rule improves anything.
The best thing would be to do exact arithmetic all along, and only convert
to the required precision at the very end, but I doubt it would be
the fastest or most economical approach.



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