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From: David Abrahams (dave_at_[hidden])
Date: 2005-12-08 17:00:44

Guillaume Melquiond <guillaume.melquiond_at_[hidden]> writes:

> Le jeudi 08 décembre 2005 à 07:23 -0500, David Abrahams a écrit :
>> > The documentation means that empty() generates the empty subset and
>> > whole() generates the subset
>> Of what? The universe of all possible intervals?

Do you understand that talking about subsets is no good if you don't
say what the superset is?

>> This is a static function!

Do you understand why the fact that it's a static function might be
confusing? We know intervals represent sets, yet the static function
can't return a subset of an interval, because there's no interval
object to operate on.

>> > that is the whole set. Maybe the documentation should stress that
>> > something empty does not contain any element
> As I said, intervals are a subset of a given set. This set is implicitly
> described by the template arguments of the interval type. For example,
> with the default interval<double>, the set is the field of real numbers
> (and not just the set of double-precision floating-point numbers). So
> interval<double>::whole() contains all the real numbers.
>> > If you want to express these intervals as pair of bounds [l,u], for the
>> > empty subset there must be no x such that l <= x <= u (by having !(l <=
>> > u) for example), and for the whole set, any x must verify l <= x <= u
>> > (by having l = -infinity and u = +infinity for example).
>> ... okay, then you do mean the universe. So why don't you just tell
>> us that empty() includes no values of the underlying type while
>> whole() includes all non-NAN values of the underlying type?
> Because this is false. To continue with the example of interval<double>,
> there are intervals of real numbers that do not contain any value of the
> underlying type (I assume you meant the type of the bounds), yet they
> are not empty. So interval<double>::empty() is not just empty with
> respect to floating-point numbers, it is also empty with respect to the
> set of real numbers.
> This distinction is important, because we are not just looking if
> elements are in intervals, we are doing arithmetic on intervals. If
> interval<double>::empty() was simply defined as not containing any
> double-precision number, then the sum of two empty intervals would have
> to return the whole set, in order to respect the inclusion property.
> In conclusion, empty() still represents the set (properly typed for the
> sake of C++) that contains no elements. And whole() represents the whole
> set as implied by the policies of the interval type.

Okay, I understand why you've chosen to use that particular language.
Do you understand why it isn't sufficient without some additional
context, and are you planning to address that?

Dave Abrahams
Boost Consulting

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