# include <limits>
# include <cppad/cppad.hpp>
bool forward_dir(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps = 10. * std::numeric_limits<double>::epsilon();
     size_t j;

     // domain space vector
     size_t n = 3;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.;
     ax[1] = 1.;
     ax[2] = 2.;

     // 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[1] * ax[2];

     // 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 Taylor coefficients
     CPPAD_TESTVECTOR(double) x0(n), y0;
     for(j = 0; j < n; j++)
          x0[j] = double(j+1);
     y0          = f.Forward(0, x0);
     ok         &= size_t( y0.size() ) == m;
     double y_0  = 1.*2.*3.;
     ok         &= NearEqual(y0[0], y_0, eps, eps);

     // first order Taylor coefficients
     size_t r = 2, ell;
     CPPAD_TESTVECTOR(double) x1(r*n), y1;
     for(ell = 0; ell < r; ell++)
     {     for(j = 0; j < n; j++)
               x1[ r * j + ell ] = double(j + 1 + ell);
     }
     y1  = f.Forward(1, r, x1);
     ok &= size_t( y1.size() ) == r*m;

     // secondorder Taylor coefficients
     CPPAD_TESTVECTOR(double) x2(r*n), y2;
     for(ell = 0; ell < r; ell++)
     {     for(j = 0; j < n; j++)
               x2[ r * j + ell ] = 0.0;
     }
     y2  = f.Forward(2, r, x2);
     ok &= size_t( y2.size() ) == r*m;
     //
     // Y_0 (t)     = F[X_0(t)]
     //             =  (1 + 1t)(2 + 2t)(3 + 3t)
     double y_1_0   = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.;
     double y_2_0   = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.;
     //
     // Y_1 (t)     = F[X_1(t)]
     //             =  (1 + 2t)(2 + 3t)(3 + 4t)
     double y_1_1   = 2.*2.*3. + 3.*1.*3. + 4.*1.*2.;
     double y_2_1   = 1.*3.*4. + 2.*2.*4. + 3.*2.*3.;
     //
     ok  &= NearEqual(y1[0] , y_1_0, eps, eps);
     ok  &= NearEqual(y1[1] , y_1_1, eps, eps);
     ok  &= NearEqual(y2[0] , y_2_0, eps, eps);
     ok  &= NearEqual(y2[1] , y_2_1, eps, eps);
     //
     // check number of orders
     ok   &= f.size_order() == 3;
     //
     // check number of directions
     ok   &= f.size_direction() == 2;
     //
     return ok;
}