Round to Nearest at Binade

Liste des GroupesRevenir à c arch 
Sujet : Round to Nearest at Binade
De : mitchalsup (at) *nospam* aol.com (MitchAlsup1)
Groupes : comp.arch
Date : 22. Apr 2025, 01:50:39
Autres entêtes
Organisation : Rocksolid Light
Message-ID : <c6be4fc7a7de8a8a83e0c0b5b874644b@www.novabbs.org>
User-Agent : Rocksolid Light
In a message over on Unum NG, there was a statement which got
me thinking about whether Round to Nearest is properly defined
in IEEE 754 (all the way back to 1985) in a theoretic sense
not in a practical sense.
Consider a calculation which produces in a result prior to
rounding with a fraction:: 1.1111111...11111 and 1 as the
½ ULP bit--properly ½ way between nearest representable
points except for the binade switching points. (ignore sticky}
Since rounding up increments the exponent, the closest number
above the result is 2 units of ½ ULP above while the closest
number below is only 1 unit of ½ ULP below. A span of 3 units
of ½ ULP. The midpoint of a span of 3×½ is 3/4 not 1/2.
Would not the Round to Nearest rule want the rounding point to
be 3/4 instead of 1/2 ?? as this is the point closest to both
representable IEEE 754 numbers ??
I know this ship sailed <gosh> 40 years ago, and I am not trying
to alter it, I am trying to wrap my head around the numerics of
it only.
I also know that the gain in accuracy is triflingly small
0.5 ULP - 1/2^53 better, that it might not be noticed in
practice.
Comments anyone ??

Date Sujet#  Auteur
22 Apr 25 * Round to Nearest at Binade2MitchAlsup1
22 Apr 25 `- Re: Round to Nearest at Binade1Anton Ertl

Haut de la page

Les messages affichés proviennent d'usenet.

NewsPortal