# include <limits>
# include <cppad/cppad.hpp>
bool forward_order(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;

     // Compute three forward orders at one
     size_t q = 2, q1 = q+1;
     CPPAD_TESTVECTOR(double) xq(n*q1), yq;
     xq[q1*0 + 0] = 3.;    xq[q1*1 + 0] = 4.; // x^0 (order zero)
     xq[q1*0 + 1] = 1.;    xq[q1*1 + 1] = 0.; // x^1 (order one)
     xq[q1*0 + 2] = 0.;    xq[q1*1 + 2] = 0.; // x^2 (order two)
     // X(t) =   x^0 + x^1 * t + x^2 * t^2
     //      = [ 3 + t, 4 ]
     yq  = f.Forward(q, xq);
     ok &= size_t( yq.size() ) == m*q1;
     // Y(t) = F[X(t)]
     //      = (3 + t) * (3 + t) * 4
     //      = y^0 + y^1 * t + y^2 * t^2 + o(t^3)
     //
     // check y^0 (order zero)
     CPPAD_TESTVECTOR(double) x0(n);
     x0[0] = xq[q1*0 + 0];
     x0[1] = xq[q1*1 + 0];
     ok  &= NearEqual(yq[q1*0 + 0] , x0[0]*x0[0]*x0[1], eps, eps);
     //
     // check y^1 (order one)
     ok  &= NearEqual(yq[q1*0 + 1] , 2.*x0[0]*x0[1], eps, eps);
     //
     // check y^2 (order two)
     double F_00 = 2. * yq[q1*0 + 2]; // second partial F w.r.t. x_0, x_0
     ok   &= NearEqual(F_00, 2.*x0[1], eps, eps);

     // check number of orders per variable
     ok   &= f.size_order() == 3;

     return ok;
}