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

bool pow(void)
{     bool ok = true;

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

     // domain space vector
     size_t n  = 2;
     double x = 0.5;
     double y = 2.;
     CPPAD_TESTVECTOR(AD<double>) axy(n);
     axy[0]      = x;
     axy[1]      = y;

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

     // range space vector
     size_t m = 3;
     CPPAD_TESTVECTOR(AD<double>) az(m);
     az[0] = CppAD::pow(axy[0], axy[1]); // pow(variable, variable)
     az[1] = CppAD::pow(axy[0], y);      // pow(variable, parameter)
     az[2] = CppAD::pow(x,     axy[1]);  // pow(parameter, variable)

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

     // check value
     double check = std::pow(x, y);
     size_t i;
     for(i = 0; i < m; i++)
          ok &= NearEqual(az[i] , check,  eps, eps);

     // forward computation of first partial w.r.t. x
     CPPAD_TESTVECTOR(double) dxy(n);
     CPPAD_TESTVECTOR(double) dz(m);
     dxy[0] = 1.;
     dxy[1] = 0.;
     dz    = f.Forward(1, dxy);
     check = y * std::pow(x, y-1.);
     ok   &= NearEqual(dz[0], check, eps, eps);
     ok   &= NearEqual(dz[1], check, eps, eps);
     ok   &= NearEqual(dz[2],    0., eps, eps);

     // forward computation of first partial w.r.t. y
     dxy[0] = 0.;
     dxy[1] = 1.;
     dz    = f.Forward(1, dxy);
     check = std::log(x) * std::pow(x, y);
     ok   &= NearEqual(dz[0], check, eps, eps);
     ok   &= NearEqual(dz[1],    0., eps, eps);
     ok   &= NearEqual(dz[2], check, eps, eps);

     // reverse computation of derivative of z[0] + z[1] + z[2]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     w[1]  = 1.;
     w[2]  = 1.;
     dw    = f.Reverse(1, w);
     check = y * std::pow(x, y-1.);
     ok   &= NearEqual(dw[0], 2. * check, eps, eps);
     check = std::log(x) * std::pow(x, y);
     ok   &= NearEqual(dw[1], 2. * check, eps, eps);

     // use a VecAD<Base>::reference object with pow
     CppAD::VecAD<double> v(2);
     AD<double> zero(0);
     AD<double> one(1);
     v[zero]           = axy[0];
     v[one]            = axy[1];
     AD<double> result = CppAD::pow(v[zero], v[one]);
     ok               &= NearEqual(result, az[0], eps, eps);

     return ok;
}