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> On Sep 19, 2016, at 09:44, Vincent Lefevre <vincent@xxxxxxxxxx> wrote:
>
> On 2016-09-19 09:43:38 -0300, Walter Mascarenhas wrote:
>> Dear colleagues,
>>
>> I am implementing the function cancel_minus
>> and I do not understand the rational behind
>> its definition in the standard. In the "normal case"
>> (ie. non empty and bounded intervals) section
>> 10.5.6 of the standard states that
>>
>> Definition I: cancel_minus(sum, parcel) = tightest interval c
>> such that parcel + c contains sum.
>>
>> In my opinion, the definition should be
>>
>> Definition II: cancel_minus(sum, parcel) =
>> (the convex hull of) the union of all intervals c
>> such that parcel + c is contained in sum.
>
> IIRC, I was wondering something like that, said otherwise:
>
> * At Level 1, one wants to have: parcel + c = sum.
I would say so.
>
> * At Level 2, one normally rounds outwards. But here, since this
> is a reverse operation, I was wondering whether one should round
> inwards (which should probably be specified as your Definition II).
I think the rounding should be inwards.
Ned
>
> But as I am not a user of this function, I didn't think further
> about it. So, I understand your point, but I don't have any
> opinion on the subject concerning what users expect.
>
> --
> Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <https://www.vinc17.net/>
> 100% accessible validated (X)HTML - Blog: <https://www.vinc17.net/blog/>
> Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)