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Re: Draft C bindings for IEEE 754-2008 part 4 now available
- From: Vincent Lefevre <vincent+gcc at vinc17 dot org>
- To: "Joseph S. Myers" <joseph at codesourcery dot com>, Andrew Haley <aph at redhat dot com>
- Cc: Florian Weimer <fweimer at redhat dot com>, gcc at gcc dot gnu dot org, libc-alpha at sourceware dot org
- Date: Tue, 7 Jan 2014 17:07:16 +0100
- Subject: Re: Draft C bindings for IEEE 754-2008 part 4 now available
- Authentication-results: sourceware.org; auth=none
On 2014-01-07 14:36:58 +0000, Joseph S. Myers wrote:
> (As far as I know, the state of the art on exhaustive searches for
> worst cases for correct rounding - as needed to implement correctly
> rounded transcendental functions with bounded resource use - does
> not make such searches feasible for IEEE binary128, which is a clear
> reason not to require such functions to be provided.)
Well, an implementation can still provide very accurate versions
(say, with a guaranteed 512 bits accuracy), and the functions will
be correctly rounded with a very high probability. In practice, the
proof of correct rounding can be obtained only with an exhaustive
search (well there is some hope to obtain a proof if the maximum
precision of the implementation is around several thousands bits).
The exhaustive search also allows one to optimize code even more.
On 2014-01-07 14:55:31 +0000, Andrew Haley wrote:
> On 01/07/2014 02:48 PM, Joseph S. Myers wrote:
> > On Tue, 7 Jan 2014, Joseph S. Myers wrote:
> >
> >> The IEEE 754 operations are corrected rounded. However, the C bindings
> >
> > (Except that the IEEE 754 reduction operations - subclause 9.4 - return
> > "an implementation-defined approximation". But 9.2 is "Recommended
> > correctly rounded functions", e.g. exp and sin, for which the strictly
> > corresponding C functions are crexp and crsin.)
>
> Has anyone found a way to do it? Even crlibm only provides routines
> that are probably correctly rounded. Although I'll grant you that the
> probability of incorrect rounding is very low.
For some of them, this is proved. Here's a summary of the current
status:
http://tamadiwiki.ens-lyon.fr/tamadiwiki/images/c/c1/Lefevre2013.pdf
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Vincent Lefèvre <vincent@vinc17.net> - Web: <http://www.vinc17.net/>
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