Re: Suggestions for hardware implementation

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

Paul Zimmermann schrieb:

> >        Dear Arnold,

> > I think the question amounts to whether there is an algorithm
> > that computes the product of either two complex numbers xx,yx or two 
> > intervals xx,yy, both represented by the same pair of numbers,

[formulation corrected]

> > xx = xl+i*xu = [xl,xu] at a similar complexity as only the product of
> > complex numbers. This would allow the implementation to share a
> > circuit for both kinds of operations.
> >
> > xx*yy = [xl*yl-xu*yu,xl*yu+xu*yl]                 for complex *
> > xx*yy = convexHull(xl*yl,xu*yu,xl*yu,xu*yl)       for interval *
> >
> > seems to allow for some synergy.
> >
> > Arnold Neumaier
>
> yes this was exactly my question, thanks!
>
> Paul Zimmermann


Since round to nearest is not guaranteed anyway by complex operations 
with multiple real operations, one could compute the products in the
rounding mode required for the interval operations and then do
either a hull for intervals or a sum and difference for complex.

Division is not so similar, however.


Arnold Neumaier