Hubert Holin wrote:

Paris (U.E.), le 08/08/2008

Bonjour

This not only looks just plain wrong, it *IS* just plain wrong... or at the very least badly suboptimal. Sorry! To fix it (as it is correctly in asinh.hpp), one has to add:

static T const upper_taylor_n_bound = one/ taylor_n_bound;

and replace "else if (x >= taylor_n_bound)" by "else if (x >= upper_taylor_n_bound)" at the line you point out.

Hmm, isn't the final else clause for x near 1? So the check would be else if(x - 1 > taylor_n_bound)

The reason this has not been detected by the unit tests is rather unfortunate: due to a very poor QOI of GCC on 64 bits ppc (my platform of choice at the time), the unit tests are rather lenient, and only compare the functions to test with (user platform) library provided functions, instead of also comparing with hand-computed special values. Perhaps is it now time to change this?

Nod, how about adding some tests along the lines of the newer special functions where we test both random values (with results computed at high precision), and a few specific sanity-check values generated by functions.wolfram.com ? That way we can get a much better handle on the accuracy, and any potential problem area of these older functions. I can try and work up some tests in week or so if that would help, or can you handle this? Cheers, John.