RE: Constructors motion
Dear Nate,
The very fact that you have to explain shows that most of us are not that familiar with the semantics of Kaucher intervals (level 1). While for normal intervals, it is very clear what we want (a range and if exact range is not possible, an enclosure for the range) this is much less clear for Kaucher intervals. Before we start talking about level 2 implementations, we need to understand level 1. I know of several semantics, I am not sure they all lead to exactly the same roundings.
For example, if we add two normal intervals [a,b] and [c,d], the lower endpoint of the sum a+c is rounded down. What you are saying is that if we inverse them and add [b,a] and [d,c], then the same sum a+c becomes an upper endpoint and thus, according to your formula, is rounded up not down.
This may be true, but without a clear understanding of why this is not a good idea to add it to the standard.
My understanding is that we are somewhat behind with normal intervals, so unless this issue can be resolved quickly, I do not think it is a good idea to add Kaucher intervals to the proposed standard at this point.
What is necessary -- and I agree with you on that -- is to make sure that we do not block the way for future extensions to Kaucher intervals.
________________________________________
From: stds-1788@xxxxxxxx [stds-1788@xxxxxxxx] On Behalf Of Nate Hayes [nh@xxxxxxxxxxxxxxxxx]
Sent: Thursday, December 29, 2011 2:11 PM
To: Nate Hayes; Jürgen Wolff von Gudenberg; Dan Zuras Intervals
Cc: stds-1788@xxxxxxxxxxxxxxxxx
Subject: Re: Constructors motion
Nate Hayes wrote:
> A valid computer implementation of Kaucher addition is:
> [a,b] + [c,d] = [roundDown(a+b),roundUp(c+d)]
Dang type-o.
Of course I meant:
[a,b] + [c,d] = [roundDown(a+c),roundUp(b+d)]
Nate