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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}} }@)@
AD Binary Addition: Example and Test
# include <cppad/cppad.hpp>

bool Add(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 1;
     double x0 = 0.5;
     CPPAD_TESTVECTOR(AD<double>) x(n);
     x[0]      = x0;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // some binary addition operations
     AD<double> a = x[0] + 1.; // AD<double> + double
     AD<double> b = a    + 2;  // AD<double> + int
     AD<double> c = 3.   + b;  // double     + AD<double>
     AD<double> d = 4    + c;  // int        + AD<double>

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0] = d + x[0];          // AD<double> + AD<double>

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

     // check value
     ok &= NearEqual(y[0] , 2. * x0 + 10, eps99, eps99);

     // forward computation of partials w.r.t. x[0]
     CPPAD_TESTVECTOR(double) dx(n);
     CPPAD_TESTVECTOR(double) dy(m);
     dx[0] = 1.;
     dy    = f.Forward(1, dx);
     ok   &= NearEqual(dy[0], 2., eps99, eps99);

     // reverse computation of derivative of y[0]
     CPPAD_TESTVECTOR(double)  w(m);
     CPPAD_TESTVECTOR(double) dw(n);
     w[0]  = 1.;
     dw    = f.Reverse(1, w);
     ok   &= NearEqual(dw[0], 2., eps99, eps99);

     // use a VecAD<Base>::reference object with addition
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero] = a;
     AD<double> result = v[zero] + 2;
     ok     &= (result == b);

     return ok;
}
Input File: example/general/add.cpp