[Boost-bugs] [Boost C++ Libraries] #7291: complex atan is not the best it could be

Subject: [Boost-bugs] [Boost C++ Libraries] #7291: complex atan is not the best it could be
From: Boost C++ Libraries (noreply_at_[hidden])
Date: 2012-08-26 15:25:07

#7291: complex atan is not the best it could be
-------------------------------------------------------------+--------------
 Reporter:  Stephen Montgomery-Smith <stephen@…>             |        Type:  Bugs            
   Status:  new                                              |   Milestone:  To Be Determined
Component:  None                                             |     Version:  Boost 1.52.0    
 Severity:  Problem                                          |    Keywords:                  
-------------------------------------------------------------+--------------
 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_at_[hidden]>.  He has an unpublished
 work by Hull, himself, and Tang, very similar to the work they did on the
 complex arcsine.

-- 
Ticket URL: <https://svn.boost.org/trac/boost/ticket/7291>
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