complex_test.cpp

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   check_complex(ct(half_pi), result, 2);
   
   result = boost::math::acos(ct(mzero));
   check_complex(ct(half_pi), result, 2);
   
   result = boost::math::acos(ct(zero, mzero));
   check_complex(ct(half_pi), result, 2);
   
   result = boost::math::acos(ct(mzero, mzero));
   check_complex(ct(half_pi), result, 2);
   
   if(test_nan)
   {
      result = boost::math::acos(ct(zero,nan));
      BOOST_CHECK_CLOSE(result.real(), half_pi, eps*200);
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));
   
      result = boost::math::acos(ct(mzero,nan));
      BOOST_CHECK_CLOSE(result.real(), half_pi, eps*200);
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));
   }
   if(test_infinity)
   {
      result = boost::math::acos(ct(zero, infinity));
      BOOST_CHECK_CLOSE(result.real(), half_pi, eps*200);
      BOOST_CHECK(result.imag() == -infinity);

      result = boost::math::acos(ct(zero, -infinity));
      BOOST_CHECK_CLOSE(result.real(), half_pi, eps*200);
      BOOST_CHECK(result.imag() == infinity);
   }

   if(test_nan)
   {
      result = boost::math::acos(ct(one, nan));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));
   }
   if(test_infinity)
   {
      result = boost::math::acos(ct(-infinity, one));
      BOOST_CHECK_CLOSE(result.real(), pi, eps*200);
      BOOST_CHECK(result.imag() == -infinity);

      result = boost::math::acos(ct(infinity, one));
      BOOST_CHECK(result.real() == 0);
      BOOST_CHECK(result.imag() == -infinity);

      result = boost::math::acos(ct(-infinity, -one));
      BOOST_CHECK_CLOSE(result.real(), pi, eps*200);
      BOOST_CHECK(result.imag() == infinity);

      result = boost::math::acos(ct(infinity, -one));
      BOOST_CHECK(result.real() == 0);
      BOOST_CHECK(result.imag() == infinity);

      result = boost::math::acos(ct(-infinity, infinity));
      BOOST_CHECK_CLOSE(result.real(), three_quarter_pi, eps*200);
      BOOST_CHECK(result.imag() == -infinity);

      result = boost::math::acos(ct(infinity, infinity));
      BOOST_CHECK_CLOSE(result.real(), quarter_pi, eps*200);
      BOOST_CHECK(result.imag() == -infinity);

      result = boost::math::acos(ct(-infinity, -infinity));
      BOOST_CHECK_CLOSE(result.real(), three_quarter_pi, eps*200);
      BOOST_CHECK(result.imag() == infinity);

      result = boost::math::acos(ct(infinity, -infinity));
      BOOST_CHECK_CLOSE(result.real(), quarter_pi, eps*200);
      BOOST_CHECK(result.imag() == infinity);
   }
   if(test_nan)
   {
      result = boost::math::acos(ct(infinity, nan));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(std::fabs(result.imag()) == infinity);

      result = boost::math::acos(ct(-infinity, nan));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(std::fabs(result.imag()) == infinity);

      result = boost::math::acos(ct(nan, zero));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));

      result = boost::math::acos(ct(nan, -zero));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));

      result = boost::math::acos(ct(nan, one));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));

      result = boost::math::acos(ct(nan, -one));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));

      result = boost::math::acos(ct(nan, nan));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));

      result = boost::math::acos(ct(nan, infinity));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(result.imag() == -infinity);
      
      result = boost::math::acos(ct(nan, -infinity));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(result.imag() == infinity);
   }

   //
   // C99 spot tests for acosh:
   //
   result = boost::math::acosh(ct(zero, zero));
   BOOST_CHECK(result.real() == 0);
   BOOST_CHECK_CLOSE(result.imag(), half_pi, eps*200);

   result = boost::math::acosh(ct(zero, mzero));
   BOOST_CHECK(result.real() == 0);
   BOOST_CHECK_CLOSE(result.imag(), half_pi, eps*200);

   result = boost::math::acosh(ct(mzero, zero));
   BOOST_CHECK(result.real() == 0);
   BOOST_CHECK_CLOSE(result.imag(), half_pi, eps*200);
   
   result = boost::math::acosh(ct(mzero, mzero));
   BOOST_CHECK(result.real() == 0);
   BOOST_CHECK_CLOSE(result.imag(), half_pi, eps*200);
   
   if(test_infinity)
   {
      result = boost::math::acosh(ct(one, infinity));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK_CLOSE(result.imag(), half_pi, eps*200);

      result = boost::math::acosh(ct(one, -infinity));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK_CLOSE(result.imag(), -half_pi, eps*200);
   }

   if(test_nan)
   {
      result = boost::math::acosh(ct(one, nan));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));
   }
   if(test_infinity)
   {
      result = boost::math::acosh(ct(-infinity, one));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK_CLOSE(result.imag(), pi, eps*200);
      
      result = boost::math::acosh(ct(infinity, one));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK(result.imag() == 0);
      
      result = boost::math::acosh(ct(-infinity, -one));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK_CLOSE(result.imag(), -pi, eps*200);
      
      result = boost::math::acosh(ct(infinity, -one));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK(result.imag() == 0);
      
      result = boost::math::acosh(ct(-infinity, infinity));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK_CLOSE(result.imag(), three_quarter_pi, eps*200);
      
      result = boost::math::acosh(ct(infinity, infinity));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK_CLOSE(result.imag(), quarter_pi, eps*200);
      
      result = boost::math::acosh(ct(-infinity, -infinity));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK_CLOSE(result.imag(), -three_quarter_pi, eps*200);
      
      result = boost::math::acosh(ct(infinity, -infinity));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK_CLOSE(result.imag(), -quarter_pi, eps*200);
   }
   
   if(test_nan)
   {
      result = boost::math::acosh(ct(infinity, nan));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));
      
      result = boost::math::acosh(ct(-infinity, nan));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));
      
      result = boost::math::acosh(ct(nan, one));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));
      
      result = boost::math::acosh(ct(nan, infinity));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));
      
      result = boost::math::acosh(ct(nan, -one));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));
      
      result = boost::math::acosh(ct(nan, -infinity));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));
      
      result = boost::math::acosh(ct(nan, nan));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));
   }
   //
   // C99 spot checks for asinh:
   //
   result = boost::math::asinh(ct(zero, zero));
   BOOST_CHECK(result.real() == 0);
   BOOST_CHECK(result.imag() == 0);

   result = boost::math::asinh(ct(mzero, zero));
   BOOST_CHECK(result.real() == 0);
   BOOST_CHECK(result.imag() == 0);

   result = boost::math::asinh(ct(zero, mzero));
   BOOST_CHECK(result.real() == 0);
   BOOST_CHECK(result.imag() == 0);

   result = boost::math::asinh(ct(mzero, mzero));
   BOOST_CHECK(result.real() == 0);
   BOOST_CHECK(result.imag() == 0);

   if(test_infinity)
   {
      result = boost::math::asinh(ct(one, infinity));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK_CLOSE(result.imag(), half_pi, eps*200);
      
      result = boost::math::asinh(ct(one, -infinity));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK_CLOSE(result.imag(), -half_pi, eps*200);
      
      result = boost::math::asinh(ct(-one, -infinity));
      BOOST_CHECK(result.real() == -infinity);
      BOOST_CHECK_CLOSE(result.imag(), -half_pi, eps*200);
      
      result = boost::math::asinh(ct(-one, infinity));
      BOOST_CHECK(result.real() == -infinity);
      BOOST_CHECK_CLOSE(result.imag(), half_pi, eps*200);
   }

   if(test_nan)
   {
      result = boost::math::asinh(ct(one, nan));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));

      result = boost::math::asinh(ct(-one, nan));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));

      result = boost::math::asinh(ct(zero, nan));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.real()));
      BOOST_CHECK(boost::math::detail::test_is_nan(result.imag()));
   }

   if(test_infinity)
   {
      result = boost::math::asinh(ct(infinity, one));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK(result.imag() == 0);
      
      result = boost::math::asinh(ct(infinity, -one));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK(result.imag() == 0);
      
      result = boost::math::asinh(ct(-infinity, -one));
      BOOST_CHECK(result.real() == -infinity);
      BOOST_CHECK(result.imag() == 0);
      
      result = boost::math::asinh(ct(-infinity, one));
      BOOST_CHECK(result.real() == -infinity);
      BOOST_CHECK(result.imag() == 0);
      
      result = boost::math::asinh(ct(infinity, infinity));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK_CLOSE(result.imag(), quarter_pi, eps*200);
      
      result = boost::math::asinh(ct(infinity, -infinity));
      BOOST_CHECK(result.real() == infinity);
      BOOST_CHECK_CLOSE(result.imag(), -quarter_pi, eps*200);