# include <cppad/cppad.hpp>
# include <cmath>
# include <limits>

bool Erf(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

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

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

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = CppAD::erf(ax[0]);

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

     // check relative erorr
     double erf_x0 = 0.5204998778130465;
     ok &= NearEqual(ay[0] , erf_x0,  0.,    4e-4);
# if CPPAD_USE_CPLUSPLUS_2011
     double tmp = std::max(1e-15, eps);
     ok &= NearEqual(ay[0] , erf_x0,  0.,    tmp);
# endif

     // value of derivative of erf at x0
     double pi     = 4. * std::atan(1.);
     double factor = 2. / sqrt(pi);
     double check  = factor * std::exp(-x0 * x0);

     // 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], check,  0.,  1e-3);
# if CPPAD_USE_CPLUSPLUS_2011
     ok   &= NearEqual(dy[0], check,  0.,  eps);
# endif

     // 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], check,  0., 1e-1);
# if CPPAD_USE_CPLUSPLUS_2011
     ok   &= NearEqual(dw[0], check,  0., eps);
# endif

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

     // use a double with erf
     ok   &= NearEqual(CppAD::erf(x0), ay[0], eps, eps);

     return ok;
}