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 ??