(SC22WG14.1750) Complex bakeoff - example 1

[Doug Gwyn (ACISD/MCSB)]

> Now if the expression was 1/0, then the true value is infinity.

But there is no "true value" for 1/0.  Like many other young
mathematicians, I tried working out arithmetic involving "infinite
values" when I was in high school, and it turns out that it is not
possible to make such a system consistent with the usual axioms
for real numbers which we have to maintain.  Infinite quantities
would have to be given special rules, which is in effect what IEEE
f.p. do, and once that is done and a computation enters into the
domain of the special rules (i.e. has an "infinite value" as an
intermediate value within an expression), essential guarantees
that apply for pure-real arithmetic get lost.

Maybe I should propose built-in support for "surreal numbers" in
C9x.  Surreal numbers are much more useful than complex numbers;
for example, they directly provide an entirely consistent
normal-looking arithmetic over not only real numbers, but also
weird numbers that are ideal for representing various shades of
0 (not the IEEE signed zero, but more like different magnitudes
of infinitesimals).  Modern game-theory algorithms are best
implemented using surreal numbers.