Re: Arguments for supporting Motion P1788/0023.01:NoMidRad

["Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>]

Yes, indeed.

I would further point out and remind people that in these arguments Arnold 
supports his position by performing a component-wise computation of the 
Kaucher arithmetic on two separate floating-point processors.

Although this probably makes perfect sense to a mathematician, what of 
course it does not take into consideration at all is physical reality: that 
branch conditions in the code limit pipelined designs in the hardware and on 
some platforms will even stall the floating-point processor. Hence, his 
"solution" will never be faster than a processor that uses true Kaucher 
arithmetic which can compute the results with no branching and in a deeply 
pipelined manner.

This is just one illustration, in my view, that Arnold clearly does not 
understand the connection between pure mathematics and applied hardware 
design. This is why I find his arguments so uncompelling and lacking 
credibility, both against Kaucher arithmetic as well as mid-rad.

I'm not going to make any further point of this, since I assume that I am 
just pointing out the obvious to people in the forum with backround in 
semiconductor design.

Sincerely,

Nate



----- Original Message ----- 
From: "Arnold Neumaier" <Arnold.Neumaier@xxxxxxxxxxxx>
To: "Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>
Cc: "Dan Zuras Intervals" <intervals08@xxxxxxxxxxxxxx>; 
<stds-1788@xxxxxxxxxxxxxxxxx>
Sent: Wednesday, September 15, 2010 2:29 AM
Subject: Re: Arguments for supporting Motion P1788/0023.01:NoMidRad


> Nate Hayes wrote:
>
> > Of course, I do not agree with Arnold's views and positions on mid-rad 
> > and Kaucher arithmetic. In particular, his assertion:
> >
> > "1.4. No strong case has been made that ... nonstandard arithmetic
> > is actually more efficient on a significant class of problems than what
> > can be done without it."
> >
> > Perhaps he does not care about industries such as CAD, CAM, computer 
> > graphics, etc. where fast processing of polynomial b-splines and NURBS is 
> > essential foundation of almost all computations. But these do represent 
> > global, multi-billion dollar industries and with the proper hardware 
> > support the Kaucher arithmetic will always be faster than a processor 
> > supporting only textbook intervals as he advocates. This subject has 
> > already been examined and discussed at length in this forum and also in 
> > the position papers Arnold mentions; so I will refer to those rather than 
> > taking time to repeat an elaboration of this topic again.
>
>
> Indeed, we disagree on this.
>
> Nage gave what he thinks is supporting evidence that Kaucher arithmetic is 
> more efficient for certain computer graphics applications.
>
> I gave support for my assessment that Kaucher arithmentic will not be
> more efficient for the same computer graphics applications.
>
> It is up to everyone to make their own assessment based on the two
> position papers.
>
>
> Arnold Neumaier