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From: dseal (David Seal)
Newsgroups: comp.arch
Subject: Re: IEEE arithmetic (Goldberg paper)
Message-ID: <196@armltd.uucp>
Date: 13 Jun 91 16:22:09 GMT
References: <1991Jun11.175639.22558@zoo.toronto.edu>
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In article <1991Jun11.175639.22558@zoo.toronto.edu> henry@zoo.toronto.edu
(Henry Spencer) writes:

>In article <192@armltd.uucp> dseal (David Seal) writes:
>>>Who knows whether IEEE infinity is a "mathematically defined result"? If you
>>
>>I would think it isn't: it doesn't correspond to a single mathematical real
>>number in the way that ordinary IEEE numbers do.
>
>Why do you insist that the standard real numbers be the mathematical system
>used?  Number systems which include infinities are neither novel nor somehow
>illegitimate.  The real question about FORTRAN vs IEEE is how precise the
>FORTRAN standard is about the nature of the number system it is running on.
>Given that FP systems containing infinities are *not* new -- IEEE did not
>invent this idea -- I would be surprised if a careful reading of the
>standard mandated pure mathematical reals.
>
>(The real answer, of course, is that the FORTRAN standard was too early
>to even consider IEEE FP, and attempts to determine the interaction of the
>two by reading between the lines are a bit silly.)

A fair point, and I agree it's open to interpretation. I would favour (*not*
"insist on") the 'subset of the unextended real numbers' interpretation
because (a) the unextended real numbers are a mathematical system which is
*comparatively* easy to work with; (b) in the absence of any clues to the
contrary, I would expect the Fortran standard to mean either 'using whatever
number system is most appropriate on your machine' or 'using a system based
on the unextended real numbers'. There seems to be a reasonable chance of
writing reasonably portable Fortran code for the latter, despite the
problems in establishing e.g. how big rounding errors can be and what the
limits of the exponent range are. There are more major portability problems
with using whatever number system you like - in particular, this whole
thread was started by such problems with NaNs and infinities! As a major
reason for having language standards is to promote portability, allowing a
completely free choice of number system seems a bit awkward.

In any case, the main point of my previous posting is that *if* you
interpret the Fortran standard as insisting on the 'subset of the unextended
real numbers' interpretation, you can achieve the required effect inside an
IEEE system. Furthermore, statements like "0.0 * X = 0.0" are
unconditionally true in such a system, so they can be used safely by
optimisers.

You are of course free to interpret the Fortran standard in other ways. (I
should probably have been a bit less dogmatic in talking about "strict"
compliance with the standard.) But if you use the full IEEE model, you then
have to solve quite a few problems: e.g. how does the programmer detect the
use of an infinity/NaN; how do you achieve a reasonable level of
optimisation without breaking the IEEE standard; how do you make code
written for your system portable to systems without IEEE arithmetic, etc.?

To sum up: I suggested a way to have your Fortran adhere to the Fortran
standard and your arithmetic to the IEEE standard, in a portable fashion. As
a result, I don't see any evidence that the IEEE committee ignored existing
language standards. There may well be other ways of achieving the same
effect which additionally give you more complete access to the facilities of
an IEEE arithmetic system, but IMHO they are all likely to be more complex
and to require more understanding by the programmer.

David Seal
Sorry about the bad "From" line. This is on a list of things to be fixed
here. Correct email address is "dseal@armltd.co.uk".

All opinions are mine only...