Re: Motion 4: P1788 on non-754?
Vincent LefÛvre wrote:
> Not necessarily. IMHO, an arithmetic (not necessarily floating-point)
> with exceptions and directed rounding (possibly not correct rounding,
> but an implementation should provide error bounds, so that the user
> can know how tight his intervals will be) should be sufficient to
> define an interval arithmetic.
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.
> Let's take an example: the double-double arithmetic,
That's usually a software implementation, 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.
In any case, when earlier I mentioned some other undesirable constraints
of mandating 754-conformance, I was reminded that this motion does not
actually address what the standard will say in the end, but how we should
allocate our efforts while definining the standard. This observation
applies here as well.
Michel.
---Sent: 2009-04-13 13:37:18 UTC