Jose Marin wrote:
>
> On Thu, 18 Mar 1999, Pierre Hugonnet wrote:
>
> I know that this is not the main point in the discussion, but anyway: if
> all you want is to be able to sum a very large number fp numbers and
> preserve accuracy as much as possible, there's a clever "trick" due to
> Kahan, and described in the paper:
>
> "What Every Computer Scientist Should Know about Floating-Point
> Arithmetic", by David Goldberg (including Doug Priest's supplement)
>
> And it's dead easy to implement. No need for accumulators of higher
> precision than the numbers being added. Which is not to say that sometimes
> they come in handy, as Kahan himself has written somewhere else. BTW,
> this reminds me of this related problem: why don't we have compilers which
> provide access to the "extended" fp formats of FPUs that have them (Intel,
> Motorola) -- something like 10-byte reals for Intel FPUs, for instance?
>
> Anyway, here's a good URL to the paper, available freely:
>
> http://www.validgh.com/
>
I took the summation problem as an example to illustrate
some real kind problems when needing higher precision
variables in libraries. FFT algorithms also requires
higher precision for some internal variables, when
the vector to be transformed is very long.
The point here is therefore not to find the best summation
algorithm.
Thanks anyway,
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