RE: That other flavour...

[Nathan Hayes <nh@xxxxxxxxxxxxxxxxx>]

I apologize for being out of the loop. I've been very busy and for some time now am no longer a member of the Working Group. I do not know where P1788 currently stands, but in response to Michel's CC to me I will share my perspective with anyone that may be interested.

I'm working on a multi-core RISC processor with support for the modal interval arithmetic operations for about a year. Attached is a draft of a Level 1 definition based on that work. In all aspects possible, efforts have been made to reconcile with the P1788 view of things. Most notably:

- Intervals are closed connected sets of real numbers

- The seven comparison relations are included

- The Fundamental Theorem of Interval Arithmetic appears as a special case of the more generalized Semantic Theorems of modal interval analysis

- As a consequence, the interval operations of Motion 5 are a special case of the extended modal interval arithmetic

The attached document is a work in progress, but my conclusion based thus far on that effort is this: the notion of "flavors" is unnecessary, perhaps even detrimental.

However, I believe P1788 has also missed the opportunity to define a standard that reconciles classical set-theoretic interval arithmetic with the also very important algebraic structures of Kaucher. The modal interval analysis is the unique framework that unites these two aspects of interval analysis into a single system.

In its current form (or at least last I checked), I don't see how the P1788 document could be amended to be capable of this without breaking what may become "standard" implementations. It is one reason we decided to start a second document of our own. We plan to publish the document on our website as we make progress and invite comments and feedback from anyone interested.

Practical application of modal arithmetic, such as computing narrow bounds on polynomials with non-degenerate interval inputs, solves fundamental problems in technical fields such as computer graphics, CAD, aerospace and financial modeling. All things being equal, a modal interval processor will ALWAYS perform these calculations more efficiently than an interval processor which uses only the intervals and operations defined in the current P1788 document. That much is not opinion, it is a fact. The question for debate is: as intervals find their way into a competitive marketplace, will users pay money for a less efficient interval processor only because it is designated as "P1788" conforming? Time will tell. But I'm personally betting the answer will be "NO."

So we try to reconcile to P1778 as much as possible. But as it stands, we feel a strong need to keep our future customers in mind.

Sincerely,

Nate

-----Original Message-----
From: Michel Hack [mailto:mhack@xxxxxxx] 
Sent: Friday, September 20, 2013 2:39 PM
To: stds-1788
Cc: Nathan Hayes
Subject: That other flavour...

As time progresses inexorably, I'm beginning to wonder what will happen to Chapter 3.  Do we really expect this to undergo the same level of discussions and refinements that we have been doing to Chapter 2?  At this point it seems that the most likely way to describe another flavour will be relative to the set-based flavour, pointing out first the conceptual differences, and then the detailed differences with respect to decorations and non-common evaluations, so as to take advantage of all the work we have done on Chapter 2.

I also have a more specific question:  Does clause 13.7 on Dot Product and Complete Arithmetic belong in Chapter 2?  It seems to me that it is flavour-independent since it does not involve any actual intervals.  I suppose that whether a Correctly-Rounded Dot Product is required or not might be flavour-dependent -- but Motion M0045.02 said nothing about flavours at all.

Perhaps we need a separate chapter on non-interval operations, or move clause 13.7 to the end of Chapter 1.  We also had Motion M0024.03 which required availability of explicit directed-rounding for the basic point arithmetic operations (which comes for free with 754-2008, but could be an additional requirement for non-754 implementations).  This belongs in the same place.

Michel.

---Sent: 2013-09-20 19:39:43 UTC

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