id,summary,reporter,owner,description,type,status,milestone,component,version,severity,resolution,keywords,cc
5385,atanh.hpp returns wrong limits for atanh(1),florian@…,John Maddock,"Hej,

in boost/math/special_functions/atanh.hpp the return value for 1 in case of ignoring  overflow errors is wrong.  This error is present in Boost 1.46.1 as well in the trunk version of today.

Starting with line 59 it states:

59: else if(x < -1 + tools::epsilon<T>())
60: {
61:   // -Infinity:
62:   return -policies::raise_overflow_error<T>(function, 0, pol);
63: }
64: else if(x > 1 - tools::epsilon<T>())
65: {
66:   // Infinity:
67:   return -policies::raise_overflow_error<T>(function, 0, pol);
68: }

While the case of -Infinity works fine, the case +Infinity return the wrong sign.
Thus, if I set 
#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
I expect that boost::math::atanh(1) would return +Inf, but instead I get -Inf, which is wrong.

Removing the minus sign (-) from the return value in line 67 solves this problem and the function behaves as intended. 
 
66: // Infinity:
67: return policies::raise_overflow_error<T>(function, 0, pol);

Best regards,
/Florian",Bugs,closed,To Be Determined,math,Boost 1.46.0,Showstopper,fixed,,