Use of C99 extra long double math functions after r236148

[Peter Jeremy]

On 2012-Jul-22 17:07:29 -0500, Stephen Montgomery-Smith <stephen at missouri.edu> wrote:
>I tested out the casinh program.  After a small tweek, the worst case 
>ULP is about 2.5 or 3.  Edge cases close to I do very well, with a ULP 
>of about 0.5.  I am very pleased with how well it performs.

That's excellent.  I think the exception handling in clog() needs some
work - in particular, input NaNs should be returned, rather than
returning new default NaNs.

>I looked at Peter Jeremy's code for catanh, and I notice that he hasn't 
>yet worked to get optimal ULP, since he has concentrated on the handling 
>of the edge cases.

As I've previously mentioned, I believe handling the exception cases
can be done completely independently of handling the "normal" cases
and I was focussing on the former since it is just a (simple) matter
of implementing the text in n1256 G.6.2.3.

>If Peter is OK with me butting in, I'll could try to work on getting 
>optimal ULP for catanh.  I think it will be easier to analyze than 
>casinh, since no csqrts need to be involved.  I anticipate that the hard 
>case will be when z is close to the imaginary axis, and moderately large 
>(like 1e-5 + 10*I).

The "normal" cases are (algorithmetically with '^' as exponentiation):

catanh(z) = clog((1+z)/(1-z))/2
          = (clog(1+z) - clog(1-z))/2
catanh(x+I*y) = log((y^2 + (1+x)^2)/(y^2 + (1-x)^2))/4 + I*atan2(y^2, 1-x^2-y^2)/2

None of these approaches behave cleanly when |z| is close to 1.  If
you have some insights, feel free to work on it.

-- 
Peter Jeremy
-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: application/pgp-signature
Size: 196 bytes
Desc: not available
Url : http://lists.freebsd.org/pipermail/freebsd-numerics/attachments/20120812/2b4eecd0/attachment-0001.pgp