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Re: Motion 11



> Date: Tue, 16 Feb 2010 08:16:13 +0100
> From: =?ISO-8859-1?Q?Fr=E9d=E9ric_Goualard?=
>  <Frederic.Goualard@xxxxxxxxxxxxxx>
> To: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>, 
>  "Corliss, George" <george.corliss@xxxxxxxxxxxxx>
> CC: stds-1788@xxxxxxxxxxxxxxxxx
> Subject: Motion 11
> 
> 
> Dear George, Dan, and intervallers,
> 
> . . .
> 
> In addition, as I have already pointed out twice, Motion
> 11's wrong Corollary 1 gives the impression that n+1-ary reverse
> operators can be expressed in terms of n-ary reverse operators, which
> they cannot without unreasonably enlarging the computed intervals.
> 
> . . .
> Reverse operators are an important tool, and there is more, much more to
> it than extended division.
> 
> Can reverse operators be implemented from operations already in the
> standard? No, they cannot. At least not without sacrificing performances
> beyond the reasonable.

	Frederic,

	I believe your observation about Corollary 1 & arguments
	for the need for reverse operations both contribute to an
	approach along the lines George has suggested.

	For example, Nate has pointed out the the lack of inverse
	operators within ordinary intervals can be repaired by the
	use of the Dual() operator.  Where

		Dual([a,b]) = [b,a].

	Thus, you can solve for yy in xx + yy = zz by

		             xx + yy = zz
		(xx - Dual(xx)) + yy = zz - Dual(xx)
		          [0,0] + yy = zz - Dual(xx)
		                  yy = zz - Dual(xx)

	All 4 basic operations may be inverted in this way.  (I
	will leave it to Nate to discuss the details on grounds
	of incompetence on my part. :-)

	Further, it is my understanding that inverse operations
	(for example, in Newton steps) can lead to tighter
	intervals than those defined in Motion 11.  Of course,
	one must intersect it with the original guess interval
	just as in Motion 11.

	So I guess I'm suggesting the addition of the Dual()
	operator as something out of which the needed operators
	can be constructed.

	Does this work?
	Would this be a simpler approach along the lines George
	has mentioned?
	Is anything else needed?
	In particular, are the 3-op forms needed given that we
	can just intersect the 2-op form with the original guess?

	Anyone?  - Dan

> 
> I believe with George Corliss that we should keep the standard as simple
> as possible. I voiced my dissent on some previous motions with that same
> argument. However, supporting reverse operators adds operators to the
> standard, not complexity. Supporting decorated intervals, that is
> something that added complexity.
> 
> What now? I believe that the absence of debate over Motion 11 so far
> reflects an absence of interested parties on the list. I am therefore in
> favor of having Marco Nehmeier withdraw his motion for the time being,
> and resubmit a new extended motion that presents all reverse operators,
> together with a document presenting convincing rationales in favor of
> their introduction into the standard. Let all people on the list
> understand the possible benefits of having reverse operators before
> voting on their adoption.
> 
> F.
> - --
> Frédéric Goualard                          LINA - UMR CNRS 6241