Re: Suggestions for hardware implementation
Chenyi Hu schrieb:
Paul Zimmermann <Paul.Zimmermann@xxxxxxxx> 11/25/2008 8:59 AM >>>
a random (maybe dummy) thought about hardware implementation: is it
possible to have hardware instructions that would be helpful both for
interval arithmetic (for the [lo, hi] representation) and for complex
floating-point arithmetic (for the cartesian representation)? If so,
this would increase the impact of such instructions, and maybe help to
convince the hardware vendors.
> I am not sure if I understand your question correctly or not.
> The midpoint-radius representation of an interval can be considered
as > Cartisian representation. If we use x- and y-axis to represent
> midpoint and radius, respectfully, then a point in the upper-half
> plane specifies an interval. But, I am not sure if this can be
> helpful to the hardware vendors or not.
I think the question amounts to whether there is an algorithm
that computes either the product of two complex numbers xx,yx and two
intervals xx,yy, both represented by the same pair of numbers,
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 kind 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