life speed wrote:
> The application is a microwave
> synthesizer operating at frequencies up to 24 X 10^9
> Hz, with sub-Herz resolution, a 40-bit number.

How are you going to measure or synthesize these frequencies to that
accuracy unless you've got your own atomic clock?  The latest cesmium clocks
are good to about 47 bits, so I guess this is at least theoretically
possible.

> All the inputs to that last equation must be exact.

Exact?  Really?  That will be tough as it requires an inifinte number bits
to represent arbitrary values exactly.

> You
> may be sure if there were a mathematically more simple
> approach I would have used it.

But that's the point, I'm not sure.  It may be that high precision is
required for the solution approach you present, but I'm questioning whether
there may not be other solution approaches at a higher level.

> Now that I have taken the time to explain that I need
> precision math, will you, if you can, answer my
> question?

You've hardly said anything about your application other than it's a
"microwave synthesizer".  I don't know what that is nor why you think it
needs to synthesize frequencies to atomic clock accuracies.

In any case, wide multiplies can be done by stringing together numerous 8
bit multiplies.  This works just like doing long multiplication by hand with
decimal digits.  The basic multiplier in your head only works on two 0-9
digits at a time but you can use that basic operation multiple times to
multiply large numbers.  For example, suppose each upper case letter below
is a digit in a decimal number:

  ABC * DE = E*C + E*B*10 + E*A*100 + D*C*10 + D*B*100 + D*A*1000

The same mechanism can be used to harness the 8x8 multiplier inside the 18F
by using bytes instead of decimal digits.  The equation above still works if
the letters represented bytes and fixed multipliers were powers of 256
instead of 10.


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