Re: Motion 46: finalise interval literals, amendments
Baker, Michel
On 26 Jun 2013, at 18:27, Ralph Baker Kearfott wrote:
> That's a good point. That makes me think it is not
> as easy to dismiss the text2interval function.
> However, what about this argument: If Ned's
> function gives, say, as a lower bound,
> the largest floating point number less than
> or equal to the value represented by the text
> corresponding to the lower bound, won't the
> lower bound of the interval hull (what you
> called "union") also be the best floating
> point lower bound (with a corresponding argument
> for the upper bound)?
That assumes an inf-sup type, for which it is true, I believe. It won't necessarily give an optimal bound for other types, e.g. mid-rad.
John P
> Baker
>
> Michel Hack wrote:
> Ned Nedialkov wrote:
>>> I meant take a string that represents one decimal number, e.g. "0.1".
>>> Then text2interval("0.1") will return the binary interval containing 0.1.
>>>
>>> Then leave to the user to convert left and right bounds. This will make
>>> it simpler for the standard and more flexible for the user.
>
> Baker Kearfott replied:
>> The user would then rely on the P-1788 floating-point-to-interval
>> constructor "nums2interval".
>
> No -- Ned's text2interval() returns an interval enclosing the singleton.
> The next step would therefore be the Union operator.
>
> Ned's approach could also be used for midrad input, by first constructing
> two intervals imid and irad, and then taking Union(imid-irad,imid+irad).
>
> This approach guarantees enclosure. We should check if there are cases
> where the enclosure is not tightest, assuming the primitives do return
> a tightest enclosure in the target format.