handful and interval

[Don Clugston]

On 02/09/12 22:42, SomeDude wrote:
> On Sunday, 2 September 2012 at 15:09:50 UTC, deadalnix wrote:
>> Le 02/09/2012 16:51, Jacob Carlborg a écrit :
>>> I really don't like the name "handful". What would be the difference
>>> compared to a regular set container? To me it sounds like we should have
>>> a standard set container in Phobos, std.container.set.
>>>
>>
>> +1, and we are back to the allocator design.
>
> +2 on the basis of typical "real world" (if I may says so) usage. It
> calls for a set container, both mutable and immutable.
>
> For a "handful" of values (say 5 or less), I'm not even sure the O(1)
> method is faster than the O(n) one.
>
> As for the intervals, I suppose one would have to define open intervals,
> because I think they would be much more useful than closed ones when the
> intervals are contiguous (in particular with floats/doubles).
> One must be able to translate x0 <= x < x1 in intervals else they are
> practically useless for anything else than integers and other discrete
> values.

But practically everything on a computer uses discrete values. Floating 
point numbers always do, for example; they are *not* mathematical real 
numbers with infinite precision.
For floats and doubles, any non-empty interval can be expressed using 
closed intervals.

Use the nextUp() and nextDown() to convert between open and closed 
intervals.

[ x .. y ] == ( nextDown(x) .. nextUp(y) )
( x .. y ) == [ nextUp(x) .. nextDown(y) ]


In general:

Fully closed interval: cannot express an empty interval.
Fully open interval: cannot express a maximum-sized interval. Empty 
intervals can be expressed but not uniquely.
Half-open: not closed under negation.

Either of the first two are reasonable choices for arithmetic 
applications. The third is broken for anything that allows negative values.