Re: Multi-precision (was...Please give me advice)
Paul
On 14 Oct 2010, at 13:30, Paul Zimmermann wrote:
>> * would a multiple-precision implementation that only implements mid-rad be
>> compliant? (With a multiple-precision 'mid' and a fixed precision 'rad'.)
>>
>> * would a multiple-precision implementation that only implements the triple
>> representation (x, inf_err, sup_err) mentioned in P1788_MAIN.pdf, paragraph
>> 6.1, be compliant? (With multiple-precision x and fixed precision inf_err
>> and sup_err.)
> you didn't answer those questions.
Well, I sort of asked questions back; sorry if I was too vague. No, iRRAM would not be conforming as it stands.
> But on the other side, if the standard requires to implement *at least* one
> inf-sup datatype then my understanding is that a package implementing only
> mid-rad or (x, inf_err, sup_err) would be not conforming.
Being an inf-sup type is a level 2, not level 3 concept: Does the set of nonempty intervals supported comprise exactly all [xlo,xhi] where xlo,xhi belong to some given set F?
As Arnold says, a package that implements only an (x, inf_err, sup_err) representation could ensure this was an inf-sup idatatype. (Rather, a sequence of these, indexed by precision.) Then it would be conforming.
John