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Re: MidRad to/from InfSup

Siegfried M. Rump schrieb:
On Fri, 13 Feb 2009 11:28:35 -0100, Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx> wrote: 


Siegfried M. Rump schrieb:
On Thu, 12 Feb 2009 12:15:10 -0100, Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx> wrote: 


Shin'ichi Oishi proposed

set round up
m=0.5*(l+u)
r=m-l


I think the formula that should be in the standard is
     set round up
     m=l+0.5*(u-l);r=m-l

In binary arithmetic, or when intermediate results are kept to higher
precision, the two formulas appear to be equivalent.

 Given this last remark, I suggest to use Oishi's proposal at least
for binary arithmetic:
- it uses only 3 rather than 4 operations,
- the midpoint is always inside [l,u], see Higham: ASNA.


But in Intlab (version 5.2), you use my new proposal, not Oishi's!



I use what you call your proposal since INTLAB Version 1, that
is in 1998. 

Of course, the priority is yours.

I just used ''my'' to distinguish it from ''your'' proposal
yesterday.



For scalar intervals, the design decision may be different. Then
25 % less computing time as in Oishi's method may be important.
Only if the conversion has to be done frequently (in an innermost loop), which is very, very unlikely. 


Arnold Neumaier