I should clarify. If we are stuck with XCV1000's we are going with
two chips, which will free up some CLB resources, but the memory is
more than accounted for still. The large areas in the prototype
floorplan are buffers made out of CLB resources because of the lack of
memory. We do have quite a bit more processing to do than the
prototype had, and my current estimates have us fairly well utilized,
70+%. I am very much hoping that we can get the XC2V3000's (these are
actually the mil rad *es, I just don't remember the number)
through qual early enough to be able to use them.
SO you can see I am in a bit of a pickle here. Not much room for an
added function that the systems guys thought was something easy to
do. Hence my search for simple ways to do it. The square root thing
is an approximation in the first place, so personally I don't see why
we couldn't fit a polynomial instead. Anyway, I just need to convice
the systems guys that it would be a good thing. Your input, as well
as others I have gotten helps to bolster my argument, as well as
provide me additional ideas should I not be allowed the polynomial
route. Thanks again.
> It is a space application, so depending on the results and timing
> of qual testing we are either in an XCV1000 or an XC2V3000. This
> is actually a pretty small portion of the entire algorithm. The
> prototype, which did not have this part of the algorithm fit into
> an XCV1000, but requires all of the memory for a 4k point
> FFT/IFFT. If, in the likely event that we are stuck with the
> XCV1000, then we don't have much room to work with . The floorplan
> of the prototype is on my website gallery
> (http://www.veryComputer.com/). If we are fortunate enough to
> be able to use the XC2V3000, then using memory becomes a viable
> option, and then things like successive approximation or newton's
> method become possibilities. We're talking 15-17 bits precision
> here with matching accuracy.
> I have looked at using some of the division routines, but have not
> come up with a simple extension to this yet. I'm hoping that the
> systems guys will let us go with fitting a polynomial to the curve
> instead so that I can get away with a set of cascaded
> accumulators. So far, though, they haven't been to open to
> > > My turn to ask for help. My library is still packed up in
> > > boxes (just moved), so I can't really paw through my books
> > > at the moment. Does anyone happen to know if there is an
> > > incremental solution for r(x) given x=0,1,2,3,4.... and a,
> > > b, and c are static parameters? I'm looking for a solution
> > > that maps nicely into hardware that hopefully isn't much
> > > more than some adds and perhaps a multiply. The variable x
> > > starts at 0 and increments, so an iterative solution that
> > > uses the previous result and some delta function is
> > > sufficient.
> > > r(x) = a/ (b + c*sqrt(x)).
> > > r(x+1) = a/(b + c*sqrt(x+1)) = r(x)+f(x,dx) or r(x)*f(x,dx)
> > > is what I am looking for.
> > My first thought on reading this was to wonder if it
> > could be a homework problem. Then I saw who posted it.
> > You don't say how many bits of precision and/or accuracy
> > you require. Fixed or floating point?
> > If you are doing this with an FPGA with block RAM there
> > could be lots of possibilities using that RAM. A successive
> > approximation algorithm, pipelined so that one result can
> > come out each cycle, even if it takes more than one cycle
> > to compute each should be possible.
> > > This is for hardware that has to produce a new point every
> > > clock at 120+ MHz, so the algorithm can't be very complex.
> > > The solution seems like it shouldn't be difficult, but my
> > > algebra is failing me miserably.
> > > My standby is to approximate the function with a quadratic
> > > and use a cascaded of four accumulators, but the problem is
> > > in fitting the quadratic to the parameters reasonably
> > > quickly.
> > Or a higher order polynomial. I would start by considering
> > the iterative algorithms used to do divide on pipelined
> > processors, which are well described in some of the pipelined
> > computer architecture books from some years ago. The IBM
> > 360/91 and Cray-1 are the two favorite examples. Those
> > algorithms converge quadratically (twice the digits each
> > cycle) so they might answer this problem pretty well.
> > Do you have a reasonable sized FPGA available to do this?
> > -- glen
> --Ray Andraka, P.E.
> President, the Andraka Consulting Group, Inc.
> 401/884-7930 Fax 401/884-7950
> "They that give up essential liberty to obtain a little
> temporary safety deserve neither liberty nor safety."
> -Benjamin Franklin, 1759
--Ray Andraka, P.E.
President, the Andraka Consulting Group, Inc.
401/884-7930 Fax 401/884-7950
"They that give up essential liberty to obtain a little
temporary safety deserve neither liberty nor safety."
-Benjamin Franklin, 1759