> On Wed, 17 Oct 2001, Popa, Frank D. asked
>
>> I'm curious as to who would need 128 bits of precision?
>
> I often need more than 64 bits. A typical example is with
> expressions like (1.D0 - A). If A = 0.99999999912D0 (14 significant
> figures), 1 - A is 8.8D-10, with only 2 significant figures.
> Small differences of two large numbers occur frequently,
> especially if the numbers are squares (calculations of
> variance) or in the resolution of ill-determined systems of
> equations. As a matter of fact, I am a bit surprised to see
> such a question asked by somebody who "did iterative solutions of large
> matrices".
>
There are situations, such as in number theory, in which the data values
are known precisely or to a very high degree of precision. However, very
few physical measurements have more than 7 significant figures. In any
particular application it is important to consider whether the errors in
computed results are dominated by lack of precision in the computation, or
lack of precision in the data.
David Hitchin
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