I want to thank all the people who sent responses to my request for
solving the Steinhart-Hart equation.  There certainly is a consensus
out there for the lookup table idea.  After reading all the suggestions,
I would be foolish to do it any other way.  I've been thinking more
about my application, and for what I want to do, it seems that I can
implement this loop with only the knowledge of what the voltage is on
the bridge.  This voltage is read by the AD7714 (A/D converter, the
output of which is converted to a serial word) and if it is not zero
(a balanced bridge), then I can create a correction signal according
to the size of the error (proportional plus integral controller), and
apply or reduce the heat until the thermistor bridge is again balanced.
During all this, I don't really need to know the number of degrees that
the thermistor is off from the setpoint, I just need to know the bridge
voltage and take the necessary action to bring it back into balance.

   We want the number of degrees of error for design/development/diagnostic
purposes as we characterize the oven, the controller hardware, and the
software algorithm.  We are still able to do this in the lab using table
top computers running BASIC.  But for the PIC implementation, all we want
is for that bridge to balance and for the loop dynamic characteristics to
be what we specify.  So using a lookup table and simpler integer arithmetic
is certainly the way to go.

   Thanks again for the help and the good ideas and pointers to the
various utilities and methods that all you bright designers have already
thought about in great detail!

   Jim Johnson
   jjohnson@hpl.hp.com