Re: Table 4 proposal version 0.2...
On Thu, Mar 22, 2012 at 8:54 AM, Vincent Lefevre <vincent@xxxxxxxxxx> wrote:
> I think that operations on numbers should be out of the scope of
> P1788. Remember that P1788 specifies a behavior, but doesn't define an
> implementation, and I don't think we need (+inf)-(-inf) = +inf here.
> IMHO, the only thing we need is a well-specified order (mostly to
> define -inf and +inf), where -inf < any real number < +inf.
But we know that under any vintage of 754 the mechanisms that produce
the 754 values called "infinities" do not produce true mathematical
infinity, but are artifacts of the finite-ness of the internal
representation. All of the 754 mechanisms for producing a 754
"infinity" are really overflows. That includes division by "signed
"zero", which is not a true mathematical zero, but is really an
underflow.
So here is no 754-style representation for a true mathematical
infinity. Nor is there any 754-representation for a value greater
than any real number. All we have is a value that is produced when
the true mathematical results of a 754-based calculation bumps into
the limitations of the internal representation. And if the overflow
value is an input to a calculation rather than an output appearance of
a overflow in the output doesn't even mean that much. Instead it
means that the calculation trajectory visited an unrepresentable
number at least once, but the true mathematical result might be
perfectly representable in the internal format.
Lee Winter
Nashua, New Hampshire
United States of America