Re: Draft: P1788.1 Standard for Interval Arithmetic (Simplified)
On 8 Sep 2015, at 16:16, Vincent Lefevre <vincent@xxxxxxxxxx> wrote:
> On 2015-09-08 06:24:01 -0500, Ralph Baker Kearfott wrote:
>> I agree. A major purpose of the standard is to
>> unambiguously define a particular behavior, especially
>> in cases in which different behaviors seem reasonable
>> for different reasons. That enables predictability
>> and portability across platforms.
>>
>> Giving such an example
>> would not change the normative part of the standard,
>> but would definitely clarify it, and thus make
>> it more valuable.
>
> There was an example in Draft 8.1:
>
> E.g., the common inputs for (the interval extension of) floor(x)
> are all nonempty intervals that are disjoint from Z. Thus
> floor([1, 1.9]) = [1, 1] is not common, because floor() is not
> continuous at 1, despite its restriction to [1, 1.9] being
> everywhere continuous. If it were required to be common, cset
> arithmetic could not be a flavor.
>
> but it disappeared in Draft 9.3.
Vincent, thank you for reminding us of this.
There is a nod towards an example on p27 of the standard:
"Outside domain: The implementation finds phi is not defined and continuous everywhere on x. Examples: sqrt([−4,4]), sign([0, 2])."
But it is (a) pretty obscure and (b) doesn't make the important distinction made in the example Vincent cites. I'm sorry this disappeared in Draft 9.3 and don't remember a good reason why.
John Pryce