Re: On behalf of Jim Demmel -- Re: back to the roots
On 2013-07-02 16:08:01 +0200, Ulrich Kulisch wrote:
> Am 01.07.2013 21:10, schrieb Vincent Lefevre:
> >On 2013-07-01 13:39:02 -0500, Ralph Baker Kearfott wrote:
> >>Please see the following communication from Jim.
> >My point is that the precision needs to be controlled by the user.
> >Sometimes small precision datums are sufficient, sometimes one needs
> >more accuracy. P1788 doesn't specify how precision is controlled
> >(and I think it shouldn't, because there are many possibilities each
> >one with its own advantages), but it doesn't forbid that. Ensuring
> >exactness is in general not possible (even if you have EDP with
> >fixed-precision inputs, as the result can't be reused as an input).
> >
> But the rouned result of the EDP is of high accuaracy. It does not suffer
> from cancellation.
So, what you need is not exact dot product, but accurate dot product
(possibly with a result in a type with a larger precision than the
inputs).
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)