🚀 go-pugleaf

        Henry Spencer writes:
Unfortunately, numerical computing is too useful and too widespread to
remain the plaything of the small number of people who "know what they
are doing" in all respects.  The fact is, almost nobody who is using
computers to get real work done has time for an in-depth study of all
the fine points of numerical mathematics.  The notion that such people
shouldn't try to do numerical computing at all is hopelessly unrealistic,
not to mention obnoxiously elitist.

        Well many users apparently feel they don't have time for a
superficial review of the basics of numerical mathematics either.
Even willingness to use a little common sense would avoid a lot of
problems.  I believe it is the notion that such people are offered
any significant protection by the IEEE standard that is hopelessly
unrealistic.
        Henry Spencer also writes:
Without lengthy analysis by experts, it is not possible to say *for sure*
that the answers are right.  However, well-designed tools like IEEE FP
improve the odds a lot.  In particular, they make it much more likely that
problems will be obvious and predictable rather than subtle and mysterious.

        Well to repeat myself I don't believe IEEE floating point (part-
icularly its more esoteric aspects) improves the odds a lot because I
don't believe it addresses the main sources of error.  I also don't
believe that IEEE FP is well-designed.  Exactly why do you believe nu-
merical problems using IEEE FP are more likely to be obvious and pre-
dictable than numerical problems using IBM hex (for example)?  As long
as we are on this subject using IBM hex; 0*x is always 0, x.le.y is the
same test as .not.(x.gt.y), and (x.ne.x) is always false.  None of the
preceding properties hold with IEEE FP.  Which behavior would you call
"obvious and predictable" as opposed to "subtle and mysterious"?  Have
you considered the problems this sort of thing causes compiler writers?
        Henry Spencer also writes:
This is very important in the real world, where experts are expensive and
in short supply, and a great deal of numerical computing simply has to be
done without them.

        Expert hardware designers and expert compiler writers are also
expensive and in short supply.  Why allow compromises in the area which
is the major source of problems, while demanding perfection in an area
which is a minor source of problems?
                          James B. Shearer