# include <limits>
# include <cppad/cppad.hpp>
namespace { // --------------------------------------------------------
// define the template function ForwardCases<Vector> in empty namespace
template <class Vector>
bool ForwardCases(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;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.;
     ax[1] = 1.;

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

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

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

     // initially, the variable values during taping are stored in f
     ok &= f.size_order() == 1;

     // zero order forward mode using notation in forward_zero
     // use the template parameter Vector for the vector type
     Vector x0(n), y0(m);
     x0[0] = 3.;
     x0[1] = 4.;
     y0    = f.Forward(0, x0);
     ok  &= NearEqual(y0[0] , x0[0]*x0[0]*x0[1], eps, eps);
     ok  &= f.size_order() == 1;

     // first order forward mode using notation in forward_one
     // X(t)           = x0 + x1 * t
     // Y(t) = F[X(t)] = y0 + y1 * t + o(t)
     Vector x1(n), y1(m);
     x1[0] = 1.;
     x1[1] = 0.;
     y1    = f.Forward(1, x1); // partial F w.r.t. x_0
     ok   &= NearEqual(y1[0] , 2.*x0[0]*x0[1], eps, eps);
     ok   &= f.size_order() == 2;

     // second order forward mode using notation in forward_order
     // X(t) =           x0 + x1 * t + x2 * t^2
     // Y(t) = F[X(t)] = y0 + y1 * t + y2 * t^2 + o(t^3)
     Vector x2(n), y2(m);
     x2[0]      = 0.;
     x2[1]      = 0.;
     y2         = f.Forward(2, x2);
     double F_00 = 2. * y2[0]; // second partial F w.r.t. x_0, x_0
     ok         &= NearEqual(F_00, 2.*x0[1], eps, eps);
     ok         &= f.size_order() == 3;

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool Forward(void)
{     bool ok = true;
     // Run with Vector equal to three different cases
     // all of which are Simple Vectors with elements of type double.
     ok &= ForwardCases< CppAD::vector  <double> >();
     ok &= ForwardCases< std::vector    <double> >();
     ok &= ForwardCases< std::valarray  <double> >();
     return ok;
}