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From: Walter Roberson <roberson@hushmail.com>
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Subject: Re: Bug when doing simple subraction/multiplication
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Date: Wed, 24 Nov 2010 00:18:43 -0600
Xref: news.mathworks.com comp.soft-sys.matlab:689560

On 23/11/10 10:06 PM, Roger Stafford wrote:

> The basic reason there are errors in the decimal arithmetic you show,
> Lisett, is that the digital computers we all use have a base of two for
> their storage and computations. That is, they use binary numbers. If
> they had used base ten numbers as with many hand calculators, the
> computations you show would have been done without error but there would
> be errors when fractions such as 1/3 or 1/7 occurred.

Roger, it might amuse you to know that IBM has maintained decimal 
arithmetic capabilities since the 1960's, primarily for financial 
applications. Their current offerings that support decimal arithmetic 
are under their Zeos operating system, but I do not recall at the moment 
if the current model with the decimal CPU is the Z90 or Z900 (when I 
last looked at the documentation, it implied the Z90 is still supported 
but has been superceded by the Z900, but I could find very little 
information about the Z900.)

IEEE is either in the process, or already has, approved a decimal 
arithmetic extension to IEEE 754; apparently there is some interest from 
some other manufacturers as well.

 >> If you want infinite precision you need to use an analog computer.

Stan, how do you propose to implement that infinite precision in an 
analog computer? What kind of physical or electrical measurement is 
robust down past the scale of brownian motion and yet is not quantized? 
If you measure at the quantum level, how will your infinite precision 
proceed once you get into Planck Scale measurements, down around 1E-74, 
where it is suspected that space itself is quantized? I do not recall at 
the moment whether it was last month's Scientific American, or last 
month's American Scientist, but one of the two had an article that had 
as an implication that measurements below 1E-70 are effectively 
impossible: at those scales, the mass-equivalent of energy twists space 
enough (gravitational "frame dragging") that you cannot measure more 
accurately.