Now *there's* a man who knows his maths!

  Ray Gardiner wrote:

> I stand corrected, to use the simplified version you need to
> keep the remainders of each division so that you can round
> the result correctly. If I re-write as follows....

>     X/3 = (X*256/4 + X*256/16 + X*256/64 + X*256/256 +128 )/256

> which becomes...

>     X/3 = (X*64 + X*16 + X*4 + X + 128)/256

> I think the rounding errors become minimal. (not proven)

  But I can see why they *do*.  Common sense.  We've been through this
*all* before in the thread on basic digital filtering.  Remember?

> The interesting point (which I missed completely!) was that
> with your method the rounding errors tend to cancel.

  Sheer accident as it happens!

  The rule is you only *ever*, *ever* drop the precision (by right-
shifting to free space) when you don't want it, usually at the point of
output (display).  Accumulators *must* hold all intermediate precision.
I just read (killed) a posting on another list talking of 16-bit DSP
processors with 32-bit intermediate tally processing.

  Cheers,
        Paul B.