On Wednesday 02 February 2005 03:52, Lourens Veen wrote: > On Tuesday 01 February 2005 19:33, Daniel Phillips wrote: > > Anyway, if interpolation doesn't work out for some reason there's > > always Newton-Raphson, which is tried and true. I seem to recall > > that Newton-Raphson needs two multipliers for the single iteration > > step required, so if linear interpolation can do the job with one > > then I guess it's better. > > I've been thinking about this for a bit. How about the following. > Instead of just storing 16 bits of the reciprocal, how about storing > both the reciprocal and its derivative in those 18 bits? Then we > would essentially have a quantised approximation to a piecewise > linear approximation to 1/x, rather than a quantised approximation to > 1/x. The numbers would have to be adjusted slightly because we > truncate rather than round to get the table index, but that's doable. > The question is how we divide those 18 bits over the two numbers. > > Calculating the final number would then be something like > Read 1 18-bit word using lines 15:6 of the input for the address > Take bits 5:0 of the result, multiply by bits 5:0 of the input, and > add to bits 17:6 of the result > > That would fit the RAM gate constraints for a two-pixel pipeline, and > require only a single multiplier. The question is how accurate it is > and whether it's worth it. > > What is the input range for this? 16 bits, but what does it map to? > And how should the output be represented? If I can find the time I > might just write a test program and see if I can figure out what the > best split is and how good it is.
Are there savings calculating two dividends at a time using this strategy? Also, when it iterates the preceding derivative can be latched so derivatives at both the beginning and end of the interval are available, which might be good for something. Regards, Daniel _______________________________________________ Open-graphics mailing list [email protected] http://lists.duskglow.com/mailman/listinfo/open-graphics List service provided by Duskglow Consulting, LLC (www.duskglow.com)
