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Re: your mail



> Date: Thu, 1 Mar 2012 17:09:54 +0100
> From: Vincent Lefevre <vincent@xxxxxxxxxx>
> To: stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
> Subject: Re: your mail
> 
> On 2012-02-29 11:43:45 -0500, Michel Hack wrote:
> > Vincent Lef?vre wrote, in reply to Dan Zuras:
> > > >       Coercion: mid_F(X) = if (abs_F(round2Nearest_F(mid(X))) = +inf)
> > > >                        then roundToZero_F(mid(X))
> > > >                     else round2Nearest_F(mid(X))
> > >
> > > For X = [0,+inf], this would give:
> > >   * mid(X) = +inf
> > >   * abs_F(round2Nearest_F(mid(X))) = +inf
> > >   * roundToZero_F(mid(X)) = roundToZero_F(+inf) = +inf
> > >
> > > while I think you wanted Fmax_F. I don't think you can avoid it,
> > > except artificially, e.g. with nextDown(+inf).
> > 
> > The "roundToZero" applies to the entire operation, in the spirit of 754,
> > where there is only one rounding after a conceptually-exact computation.
> > So there is nothing artificial about ending up with Fmax_F.
> 
> No, roundToZero does not apply to entire operations (this makes no
> sense), but to unrounded results. Here the unrounded result mid(X)
> is +inf, because at Level 1:
> 
>   (inf(X) + sup(X)) / 2 = (0 + (+inf)) / 2 = (+inf) / 2 = +inf
> 
> Then the rounded result is roundToZero_F(+inf) = +inf.
> 
> -- 
> Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>


	Whether the rounding applies to the entire expression
	or not is not important.  What IS important is that
	Michel has correctly devined my intent.  Namely that
	mid always returns a finite value even when an infinity
	comes up for one reason or another.

	If I have incorrectly formulated that intent, it is not
	his fault but mine.

	The current formulation was my attempt to embody that
	intent without reference to the underlying arithmetic.
	If you have a better one, I'll use it.

	I'd still like to avoid references to Fmax_F or anything
	similar.  But if that is required to get the idea across,
	so be it.

	A finite value for the purpose of splitting is more
	important than the simplicity of the formula.

	Someone once said, "An equation should be as simple as
	possible, but no simpler."

	Now I wonder who said that...? :-)


				Dan