Re: Zero or not?

[kensmith]

On Sunday 22 July 2007 22:42, Miroslaw Kwasniak wrote:
> On Mon, Jul 23, 2007 at 01:24:03AM +0200, Francesco Potorti` wrote:
> > >Ok, that's a start. If I calculate the sum of N numbers, what is
> > > the maximum 'offset' of the numerical result to mathematically
> > > correct result?
> >
> > Not a numerical expert, but the error magnitude should be bounded
> > by eps*sum(abs(x[1:N])).
>
> I'm not a numerical expert ;)
>
> I think your expression is an average error.
> A bound should be like this:
>
>    N*eps*max(abs(x))

With "sticky bits", the error is slightly less than this because it 
breaks the tie on rounding 0.5 in favor of the direction that tends to 
reduce the error.  On the x86 machines, there is another consideration.  
So long as the numbers stay in the floating point unit, they are kept 
in an internal 80 bit format.

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