Re: On Arnold's challenge & Paul's Observation...
Dan and P1788
On 27 Nov 2008, at 23:35, Dan Zuras Intervals wrote:
I was unaware of this work which implements an interval
as an ordered pair of floats, (lower,-upper), in which
all arithmetic is done in round-to-minus-infinity.
My recent two re-implementations of the bottom level of Profil/BIAS, which I have reported to this list, use this
method. Actually (-lower,upper) and rounding to +oo.
One version uses a cset model, the other uses the model I think Neumaier and Rump support. There is only about
5% speed difference between them, on a test suite from Nedialkov. But the change from (lower,upper) to (-
lower,upper) representation gave an immediate speed-up factor of about 3.5.
Disclaimer: only on one platform so far.
... This suggests to me that we may as well go ahead & define
an interval inter = (lower,upper) as conceptually (or
semantically) consisting of its lower & upper bounds with
operations performed in the direction of those bounds.
But we should NOT require that the memory encoding appear
that way. (In fact, we should point out Lambov's approach
as a practical example of another way.)
Yes!
In the terminology of P754 table 3.1, memory encoding is a Level 3 and 4 issue. Or specifications should stay at
Levels 1 and 2 as far as possible.
The most we should say is that there exists a constructor
interval(lower,upper) & extractors lowerbound(inter) &
upperbound(inter) that operate without floating-point
errors of any kind including inexact.
Yes.
John Pryce
j.d.pryce@xxxxxxxxxxxx
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