# include <cppad/cppad.hpp>
# include <cmath>

bool azmul(void)
{     bool ok = true;

     using CppAD::AD;
     using CppAD::NearEqual;
     double inf = std::numeric_limits<double>::infinity();
     double eps = 10. * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 2;
     double x = 0.5;
     double y = 2.0;
     CPPAD_TESTVECTOR(AD<double>) axy(n);
     axy[0]      = x;
     axy[1]      = y;

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

     // range space vector
     size_t m = 5;
     CPPAD_TESTVECTOR(AD<double>) az(m);
     az[0] = CppAD::azmul(axy[0], axy[1]); // azmul(variable, variable)
     az[1] = CppAD::azmul(axy[0], inf);    // azmul(variable, parameter=inf)
     az[2] = CppAD::azmul(axy[0], 3.0);    // azmul(variable, parameter=3.0)
     az[3] = CppAD::azmul(0.0, axy[1]);    // azmul(parameter=0.0, variable)
     az[4] = CppAD::azmul(4.0, axy[1]);    // azmul(parameter=4.0, variable)

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

     // check value when x is not zero
     ok &= NearEqual(az[0] , x * y,  eps, eps);
     ok &= az[1] == inf;
     ok &= NearEqual(az[2] , x * 3.0,  eps, eps);
     ok &= az[3] == 0.0;
     ok &= NearEqual(az[4] , 4.0 * y,  eps, eps);


     // check value x is zero and y is infinity
     CPPAD_TESTVECTOR(double) xy(n), z(m);
     xy[0] = 0.0;
     xy[1] = inf;
     z     = f.Forward(0, xy);
     ok &= z[0] == 0.0;
     ok &= z[1] == 0.0;
     ok &= z[2] == 0.0;
     ok &= z[3] == 0.0;
     ok &= z[4] == inf;

     return ok;
}