Re: Motion P1788.1/M004.01
On 2016-05-17 11:35:49 -0400, Michel Hack wrote:
> On Tue, 17 May 2016 15:25:01 +0200, Vincent Lefèvre wrote, replying to me:
> (regarding exact zero vs inexact zero, i.e. underflow)
> > > Unfortunately 754 has no easy way to track the distinction.
> > This is not possible: the problem is undecidable (this is basically
> > the TMD on an exact case).
>
> Richardson's theorem does not apply to IEEE 754 (my context), since
> only finite sets of rational numbers are involved -- no Pi, log 2, or
> (to mention the one reamining requirement after some of the original
> ones were found to be inessential) an exact sin() function.
The log and atan functions are part of IEEE 754. So, math expressions
as those involved in Richardson's theorem can be written with IEEE 754
constants and operations.
> To what extent it applies to 1788 (Intervals, where irrationals are
> genuine members), I don't know.
>
> > The best that one can do is to track exactness.
>
> That's in fact all I was talking about.
But that's useless if the goal is to know whether 1/x where the
variable x is 0 corresponds to a division by 0 or a valid operation
that would overflow.
Anyway, this wouldn't handle the cases where x is not 0 but the
mathematically correct value is 0.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <https://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)