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Forward Mode: Example and Test of Multiple Directions
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    # 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;
    }

`

Input File: example/general/forward_dir.cpp