Re: Motion P1788/M0009.01_ExactDotProduct: NO
On Wed, November 18, 2009 14:33, Jean-Michel Muller wrote:
> Dear Walter,
>
>
> Yes, I mean that.
> I am perfectly aware that in some "extreme" cases, getting a correctly
> rounded dot product will be almost as complex as getting an exact one.
>
> And yet, in most cases, it will be much easier: one can for instance
> imagine a two-step method: the first step almost always returns a
> correctly-rounded result, and warns when it fails, so that an accurate
> second step can be used (this is the mechanism we use for correctly
> rounded elementary functions), so that we would always have correct
> results, and almost always have them quickly.
>
This suggests that in cases where the optimally rounded answer might be
expensive, the standard should require two operations, one optimally
rounded and perhaps slow, the other with at most one float in between the
result and the exact answer.
This would not apply only here but also for some elementary functions such
as the trigonometrics.
Arnold Neumaier