# include <cppad/cppad.hpp>
bool Mul(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 = .5;
CPPAD_TESTVECTOR(AD<double>) x(n);
x[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(x);
// some binary multiplication 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] = x[0] * d; // AD<double> * AD<double>
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(x, y);
// check value
ok &= NearEqual(y[0] , x0*(4.*3.*2.*1.)*x0, 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], (4.*3.*2.*1.)*2.*x0, 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], (4.*3.*2.*1.)*2.*x0, eps99 , eps99);
// use a VecAD<Base>::reference object with multiplication
CppAD::VecAD<double> v(1);
AD<double> zero(0);
v[zero] = c;
AD<double> result = 4 * v[zero];
ok &= (result == d);
return ok;
}