Evaluating extremes in a closed interval



Daniel Lakeland wrote:
> Fixed point extrapolation is probably relatively easy to put an error
> bound on though when compared with discrete logarithm approximations
> and soforth.

It seems, that storing log with 8 bit precision is enough, to 
compute dew point with a resolution of 0.1K - the problem is very 
good-natured. (The formula itself is an approximation of a series 
of physical measurement and not a theoretical result.)

Dew point is only a vehicle for me, to get more clearity about 
fixedpoint computations on ?Cs.

It seems to me, that there are two general strategies to solve 
the problem:

- Lookup tables and optional interpolation, if not enough
   memory is available to store the full table.
- Using an integer formula and implement it in a way, that
   balances subexpressions to minimize distortions.

The first is more general, but more expensive to realize, while 
the second can be done quite easy, if it is possible - simply 
manipulate an integer expression.

If the error estimation can be done in some generalized way, I 
would prefer the second strategy. For known sensor resolutions, 
it can be done using the brute force method.

On the other hand, the lookup table approach might be a good 
candidate to build a generator, that eats a formula and generates 
the table and a (C-) function to query it - maxima is a good 
vehicle to implement such a generator.