Re: A proposal for motion 5 "Arithmetic operations for intervals"

[Ulrich Kulisch <Ulrich.Kulisch@xxxxxxxxxxx>]

John Pryce schrieb:
> P1788
>
> I agree with Jürgen. He suggests the level 3 part of the standard 
> could contain the Kulisch tables, and say something like "any 
> implementation functionally equivalent to these conforms to the level 
> 2 definitions".
>
> Ulrich: since 754 section 5.4.1 collects together
>   addition, subtraction, multiplication, division, squareRoot, 
> fusedMultiplyAdd
> as basic arithmetic operations, would it be appropriate for you to add 
> the last two of these to your set of tables?
John, thank you for the hint. I am thinking to add the exact dot product 
for floating-point numbers and intervals. This would include an exact 
fusedMultiplyAdd.
Considering the sqare root together with the arithmetic operations goes 
already back to K. Zuse. But I think the square root is an elementary 
function and should be considered with these.
> On 2 Jun 2009, at 21:11, Jürgen Wolff v Gudenberg wrote:
> > I think the standard should include both forms the definition and a 
> > level 3 implementation
> > Juergen
> >
> > Vincent Lefevre schrieb:
> > > On 2009-05-22 10:55:40 +0200, Arnold Neumaier wrote:
> > > > Compare the complexity of Kulisch's definition with the simplicity
> > > > of that of the Vienna Proposal, which handles all that needs to be
> > > > said about the forward mode of all unary and binary operations in
> > > > two simple formulas taking less than half a page:
> > > [...]
> > > Well, as I understand it, the Vienna Proposal proposes a definition,
> > > while Kulisch's paper proposes a high-level implementation. But
> > > that's not the goal of a standard to propose an implementation.
>
> Regards
>
> John Pryce