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@(@\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@ This is cppad-20221105 documentation. Here is a link to its current documentation .
Forward Mode: Example and Test of Multiple Directions
# 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