Ticket #7291 (closed Bugs: fixed)
complex atan is not the best it could be
|Reported by:||Stephen Montgomery-Smith <stephen@…>||Owned by:||johnmaddock|
|Milestone:||To Be Determined||Component:||math|
For complex atan, when x and y are non-negative, the following formula is rather foolproof:
atanh(z) = 0.25 * log1p(4*x / pow(|z-1|,2)) + 0.5 * I * atan2(2y, (1-x*x-y*y))
where z = x+I*y. Just handle the few special cases when you get overflow or underflow.
I have implemented a C version at http://people.freebsd.org/~stephen/catrig.c.
Also, email Tom Fairgrieve <tff@…>. He has an unpublished work by Hull, himself, and Tang, very similar to the work they did on the complex arcsine.
- Owner set to johnmaddock
- Component changed from None to math