Re: Motion 4: P1788 on non-754?
On 2009-04-13 09:19:34 -0400, Michel Hack wrote:
> If the underlying arithmetic is not correctly-rounding, it would be
> difficult to define "tightest bound" for the enclosures of primitive
> IA operations, which we are considering for the standaed. In this
> context I interpret "tightest" as saying that no narrower representable
> result would guarantee containment.
Is the "tightest bound" required or only recommended? Having it
required would be annoying if one wants interval arithmetic on
the elementary functions, as IEEE 754-2008 only recommends
correct rounding for such functions.
> > Let's take an example: the double-double arithmetic,
>
> That's usually a software implementation,
The standards don't make the difference between software and hardware
implementations.
> and it touches on what means are allowed to extend basic precision.
> It doesn't extend the exponent range, and its effective precision is
> variable (and not one of the sequence sanctioned by 754-2008. It can
> be correctly-rounding in its own domain, and support directed
> rounding properly as well. It is used with IBM's PowerPC, which does
> not support Binary128.
But it is not a floating-point format.
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Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.org/>
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Work: CR INRIA - computer arithmetic / Arenaire project (LIP, ENS-Lyon)