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Van et al, I still don't understand why we need two conversions from floats to intervals. As several have pointed out, we have no way of knowing how the float originated, so we cannot prescribe rigorous bounds on the accuracy. "Widening" a float hence still will not give a rigorous enclosure in general. We simply need to clearly specify how the standard converts the float, so users will have a reliable tool upon which to design procedures that are mathematically rigorous. Baker Van Snyder wrote:
On Mon, 2008-11-10 at 02:48 -0800, Arnold Neumaier wrote:intval(0.1) -> (NEAREST(0.1,-1.0):NEAREST(0.1,+1.0))So you suggest to use inflation 2ulp wide for conversion of floats? What then about intval(0.5) or intval(0.5e1)?It is desirable to have two conversions from FP numbers to intervals. In general, FP numbers already represent 2ulp intervals, but sometimes one knows they are exact.intval('0.1') should become something sharper than intval(0.1).1ulp wide?Hopefully. intval('0.5') could be a point interval. If the underlying IEEE FPA is decimal, however, one might be tempted that intval('0.3333333') ought to be a point interval. So again it may be desirable to have two conversions from text to intervals.
-- --------------------------------------------------------------- R. Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax) (337) 482-5270 (work) (337) 993-1827 (home) URL: http://interval.louisiana.edu/kearfott.html Department of Mathematics, University of Louisiana at Lafayette (Room 217 Maxim D. Doucet Hall, 1403 Johnston Street) Box 4-1010, Lafayette, LA 70504-1010, USA ---------------------------------------------------------------