Revised version of Level 1 text (draft)

[John Pryce <j.d.pryce@xxxxxxxxxxxx>]

P1788

Things have been relatively quiet in the P1788 forum, but much has been going on behind the scenes. I attach a revised draft of the Level 1 text of the standard, resulting from extensive work by Arnold Neumaier, Nate Hayes, myself and others. I commend it to your careful consideration.

In one respect this version represents a MAJOR advance: the Decoration System (exception handling system) is no longer just a set of mechanisms, but is now solidly specified at Level 1. There are some theoretical glitches to iron out, but I am fairly confident they are not show-stoppers. If my confidence is justified, then we have for the first time an interval system where the kind of "exception" of interest to interval algorithms -- events such as division by zero, that affect whether a function is everywhere defined, everywhere continuous, etc. -- is specified at the mathematical level, and in a way that I believe will be convenient to work with.

In particular Moore's fundamental theorem has a generalization, the "Fundamental Theorem of Decorated Interval Arithmetic", which can be stated very concisely.

Writers of interval algorithms will be able to include decorations at the level of mathematical specification, knowing that these algorithms are not only well-defined and therefore portable, but also implementable on any P1788-conforming system. Work by Hayes and Neumaier has gone a long way towards removing the efficiency problem of 17-byte decorated intervals being slow to access and wasteful to store.

I see a possible danger, however. Many ideas about decorations have been around for a while, but the details of this scheme are NEW, and represent non-trivial research. The upper levels of the IEEE may take exception (sorry!) to including such "untried" material in a standard. This will need careful exception handling... anyone who helps negotiate this minefield deserves a decoration... Someone who understands these issues, give your views, please?

I do not expect this scheme to receive universal acclaim. For one thing, it is not child's play to grasp the specifications. For another, I have followed the Neumaier approach to the mathematics. I found this easier to follow than the Hayes approach which disagrees with it in various ways. I hope, at the implementation level it does the most important things that Nate requires.

Best wishes

John Pryce

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