# include <cppad/cppad.hpp>

bool atanh(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;

     // 10 times machine epsilon
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // a temporary value
     AD<double> tanh_of_x0 = CppAD::tanh(x[0]);

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = CppAD::atanh(tanh_of_x0);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(x, y);

     // check value
     ok &= NearEqual(y[0] , x0,  eps, eps);

     // forward computation of first partial w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 1., eps, eps);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 1., eps, eps);

     // use a VecAD<Base>::reference object with atanh
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = tanh_of_x0;
     AD<double> result = CppAD::atanh(v[zero]);
     ok     &= NearEqual(result, x0, eps, eps);

     return ok;
}