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Re: why extending numbers by zeros instead of dropping precision

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  Re: why extending numbers by zeros instead of dropping precision Daniel Lichtblau <danl@wolfram.com> - 2011-04-09 11:11 +0000

#1568 — Re: why extending numbers by zeros instead of dropping precision

Richard Fateman wrote:
> [...]
>> although appreciation of the problem goes back farther (why did the
>> ENIAC have ten digit accumulators?).
> 
> You might refer to MANIAC, which had significance arithmetic, and also 
> lost out.
>>> Oh, as for subtraction being a problem... Typically if you subtract two
>>> nearly equal items you get a small quantity.  The small quantity is not
>>> troublesome if you add it to something that is not so small.  What
>>> sometimes happens is that you do something ELSE.  Like divide by it.
>>> That is more likely to cause problems.
>> Exactly. That's a very common issue in numerical analysis. And that's
>> why your "hardly ever" assertion is silly.
> 
> I recommend you look at the Kahan paper, which would explain to you this 
> issue.

For those with an interest in the computer arithmetic of our 
predecessors (that is to say, a predilection for precise pronouncements 
about our processor's predecessors), there is a paper (scanned pdf) from 
1962 describing MANIAC III arithmetic, available from the URL below.

http://doi.ieeecomputersociety.org/10.1109/AFIPS.1962.31

Daniel Lichtblau
Wolfram Research

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