I have been watching various floating point threads for a while.  Having some
experience with precision instruments with floating point displays, I point
out that I have never, in fact, found it necessary to actually do the
calculations in floating point.  I usually scale until I can do a fixed point
operation, or operate with a scale factor.

I did a acoustic bearing indicator, for instance, which did a four quadrant
arctangent, but instead of operating in radians and converting, I did it with
an integer Chebyshev polynomial which produced the answer in integer tenths
of a degree.  Then displayed the number with a standard binary integer to
decimal routine.  Hardwired the decimal point.  This was done with 12 bit
arithmetic (3600<4096)  leaving lots of CYA room if I needed.  For instance,
I could improve to hundredths of a degree using 16 bit arithmetic
(36000<65k).

In contrast, the constants given in Doug Manzer's tangent calculation are 9
decimal digits.  If this were used to measure angles in a navigation system,
one could measure one's longitude anywhere on the earth to to a precision of
less than 2 inches.   For most problems, this level of precision is overkill.
 (No criticism of Mr. Manzer here, by the way -- he was accurately describing
an algorithm.)

Even problems which require a small difference between two large numbers can
often be restated to eliminate such pathological behavior.

I don't mean to be dogmatic; there _ARE_ valid reasons for FP and high
precision operations.  However, I would suggest strongly that, if you really
need such things, you might consider a more powerful processor (or, more
accurately, one with more powerful tools).  Part of being a good engineer is
choosing the right tools for the task.  The PIC is a good tool, but not the
only tool.


Mike Mullen