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Re: Putting features in vs. leaving them out, especially functions



On 05/25/2011 02:51 PM, Arnold Neumaier wrote:
On Wed, May 25, 2011 13:35, John Pryce wrote:
Arnold
Thanks, that modifies my opinion. But what's the justification for
including these particular ones? What about something like
   (log(1-x) - x)/x^2  or  (atan(x) - x)/x^3  or  ...?
When you need THOSE, do you code them yourself?

The functions dividing the difference to a Taylor expansion by x and x^2
are needed for _every_ basic elementary function to get sharp first and
2nd order slopes.

Currently, we code them all ourselves, but this is slow. Using continued
fractions or lookup tables would be better, but we weren't patient enough
to do it.


I agree with Arnold. The only difference is that we are using symbolic software do the job for us: possibly leading to a non optimal enclosure (compared to a form that has been tuned by hand) but less work and error-free..