Re: Table 4 proposal version 0.2...
> Date: Thu, 22 Mar 2012 11:28:46 -0500
> Subject: Re: Table 4 proposal version 0.2...
> From: Lee Winter <lee.j.i.winter@xxxxxxxxx>
> To: stds-1788@xxxxxxxxxxxxxxxxx
>
> . . .
>
> 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.
>
> . . .
>
> Lee Winter
> Nashua, New Hampshire
> United States of America
I'm sorry Lee, this is just not so.
From 754-2008, Clause 7.3 "The divideByZero exception shall be
signaled if and only if an exact infinite result is defined for
an operation on finite operands."
And from Clause 7.4 "The overflow exception shall be signaled
if and only if the destination format's largest finite number
is exceeded in magnitude by what would have been the rounded
floating-point result were the exponent range unbounded.
. . . and the inexact exception shall be signaled."
Whether you want to call it a "true mathematical infinity"
(whatever that means) or not is up to you. But there are 2
ways of getting there.
However, zero really IS a "true mathematical zero" if there
ever was one. And there are both exact & inexact (underflow)
ways of getting there too.
Dan