Evaluating extremes in a closed interval



Stavros Macrakis wrote:
> It is interesting that you are using the same formulas regardless of the 
> precision; I would have thought that the coefficients would have to be 
> scaled for each precision to avoid overflow.
> 
> In any case, I don't think you'll be able to get very far using the 
> exact formulae involving rounding, since very few algebraic operations 
> (simplifications) are possible.  Just as in floating-point, you should 
> probably work with an error term for each operation; of course with 
> fixed-point, it is an absolute, not a relative, error.

You are right: I should not use the same formula, but compute the 
subterms - like a compiler - and balance precision.

Using float error terms might be a vehicle to get a good error 
estimation.

I'll try it.