id	summary	reporter	owner	description	type	status	milestone	component	version	severity	resolution	keywords	cc
7290	complex acos is occasionally wrong	Stephen Montgomery-Smith <stephen@…>	John Maddock	"I am finding that the acos function is getting some of them wrong. For example, your program evaluates
acos(1.00000002785941 + I*5.72464869028403e-200)
as
0 - I*0.000236048349018331
whereas it should be
2.42520172707401e-196 - I*0.000236048349018331.

Looking at http://www.boost.org/doc/libs/1_51_0/boost/math/complex/acos.hpp, I am somewhat sure that the mistake is in the last line of this code fragment:

         //
         // This is the Hull et al exception handling code from Fig 6 of their paper:
         //
         if(y <= (std::numeric_limits<T>::epsilon() * std::fabs(xm1)))
         {
            if(x < one)
            {
               real = std::acos(x);
               imag = y / std::sqrt(xp1*(one-x));
            }
            else
            {
               real = 0;

For asin, setting real = half_pi does just fine.  But for acos, real should be something extremely small, but definitely not 0."	Bugs	closed	To Be Determined	math	Boost 1.52.0	Problem	fixed