[std-interval] Interval comparison operators
Fernando Cacciola
fernando_cacciola at datafull.com
Mon May 29 20:45:47 PDT 2006
Hello Lee,
For now just a question and a quick comment:
Can you justify your claim that:
given a non-degenerate interval X, the expression ceq(X,X) will return false
Maybe I'm just totally missing a point but your Prinicpal Model doesn't look
to me like a usefull model of interval numbers. Aren't "bounds" the central
notion of anything called an "interval"?? This models looks to me like the
"arithmetic expansions" described by Priest here:
http://citeseer.ist.psu.edu/priest91algorithms.html
In such an expansion, roughly, a "result" is given explicitely as a
"principal value" and a sequence of error terms.
The comparison semantics that you suggest are in line with those concepts,
but not so much IMO with interval artihmetic.
IOW, the comparison semantics that take into account the "accumulated
roundoff" (those you cite from Knuth) are well suited for a model which is
centered around the fact that a result is always a real-point-value but
which is represented as machine-point-value which differs from the actual
value by some error. That's why these comparisons are essentiually
point-based.
But IIUC the very purpose of interval arithmetic when applied to certified
computations in the presence of roundoff is precisely to provide an
alternative view centered not on the "principal" value but the error
bounds...
If you want a number conceptually centered around an "actual value" which
can't be exactly represented due to roundoff, OK, but I woudn't call that an
interval.
Fernando Cacciola
SciSoft
http://fcacciola.50webs.com/
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