[Cfp-interest 2854] Re: CFP review of TS-4 and TS-5 revisions

[Damian McGuckin]

On Thu, 24 Aug 2023, David Hough CFP wrote:

> Exactly what the representable set of and bit encoding of double-double are
> unstandardized and I suppose most implementations are "whatever works
> fastest".    If speed if no concern, then just use software quad.
>
> The short algorithms I listed do have the property that {max:max} is
> not a possible result, and indeed the final result {x.h;x.t} will always
> have |x.h| > |x.t|.    Whether the signs agree might indeed depend on the
> rounding mode.   754r however says that the augmented operations compute
> x.h using roundTiesTowardZero.   So the signs should always agree.

Yes. That is the first line of 2nd paragraph.

I was reading that as round-to-nearest with Ties towards Zero. It says

the floating-point number nearest to the infinitely precise result shall 
be delivered; if the two nearest floating-point numbers bracketing an 
unrepresentable infinitely precise result are equally near, the one with 
smaller magnitude shall be delivered.

Doesn't that mean that if the infinitely precise is of an unrepresentable
result is close to its neighbor when is larger than it in magnitude, that
this

 	roundTiesTowardsZero

result will exceed the actual result and the difference (which is x.t) 
will then have a different sign.

Or have I missed something.

Thanks - Damian

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