Re: Portable syntax of interval literals
Dima, replying to me:
> > it is not much more trouble to compute an enclosure with an
> > error bound of somewhere between half an ulp and one ulp
>
> This is true for rounding to nearest. For directed rounding it is easy
> to compute enclosure with an error bound say 1.001*ulp as 754-2008 does.
Dima is right. Anything other than "tightest" will require tolerating
an error strictly larger than 1 ulp for directed rounding. So perhaps
we should require "faithful" rounding, which allows directed rounding
to return one of two nearest representable values on the correct side
of the true result. That would allow an error of up to two ulp. We
should encourage implementations to document when tighter bounds are
achieved, to allow programs to take advantage thereof when warranted.
Note that one can get faithful directed rounding from round-to-nearest
with an error strictly less than 0.5 ulp, e.g. the 0.47 ulp that was
required by 754-1985 for excessive exponents or precision.
Michel.
---Sent: 2013-09-29 21:23:04 UTC