Re: Is infinity equal to infinity?

Henry Spencer wrote:


> Actually it does, but careful reading is needed. A good resource for
> interpretation of IEEE 754 is David Goldberg's paper "What Every Computer
> Scientist Should Know About Floating-Point Arithmetic", in the March 1991
> issue of ACM Computing Surveys.
> So, what about Inf:Inf (that is, infinity compared to infinity)? The
> paper explains this, as per the standard's terse wording, as the limit of
> f(x):g(x), as x approaches some limit that makes both f(x) and g(x) go to
> infinity. Just what is the limit of f(x):g(x)? Depending on what f(x)
> and g(x) are, it could be "less than", "equal", or "greater than". So
> there is no single limit... and that means the result of Inf:Inf must be
> "unordered".
> ...
>
> And the table on page 13 of the standard specifies that the .EQ. predicate
> (one of the first six, which according to 5.7 are the ones that map into
> the traditional six predicates of programming languages) yields false,
> and does not cause an exception, for a comparison result of "unordered".
> So (Inf==Inf) is false.
>
> Sigh, I doubt that many compiler writers or silicon builders have gotten
> this right... It's awfully subtle.


I have, since first posting this question discussed the issue with both
David Goldberg and William Kahan (known as the father of floating
point). They both agree that the comparison Inf=Inf should be true
according to the IEEE 754 standard. Goldberg wrote:


"If you have a copy of the IEEE standard, you will see that Inf == Inf.
The only time that you can get 'unordered' is if one of the operands is
NaN."


Myself, I don't find this at all obvious (I suppose this goes for many
of us...), but Kahan had more arguments:


"(...) +Infinity == +Infinity has to be true because +Infinity is the
coordinate of a point on a model of the real numbers. This means that
the logical equivalence of " x == y " and " x-y == 0 " is valid only
if at least one of x and y is a finite real number."


/Erik Runeson


----------------------------------------------------------------------
Erik Runeson
Email: erikr@iar.se (work, summer -98)
                d95err@csd.uu.se (home and education)
Cellphone: +46 708 723597
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