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AD Binary Multiplication: Example and Test
 
# include <cppad/cppad.hpp>

bool Mul(void)
{	bool ok = true;
	using CppAD::AD;
	using CppAD::NearEqual;

	// domain space vector
	size_t n  = 1;
	double x0 = .5;
	CPPAD_TEST_VECTOR< 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_TEST_VECTOR< 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,  1e-10 , 1e-10);

	// forward computation of partials w.r.t. x[0]
	CPPAD_TEST_VECTOR<double> dx(n);
	CPPAD_TEST_VECTOR<double> dy(m);
	dx[0] = 1.;
	dy    = f.Forward(1, dx);
	ok   &= NearEqual(dy[0], (4.*3.*2.*1.)*2.*x0, 1e-10 , 1e-10); 

	// reverse computation of derivative of y[0]
	CPPAD_TEST_VECTOR<double>  w(m);
	CPPAD_TEST_VECTOR<double> dw(n); 
	w[0]  = 1.;
	dw    = f.Reverse(1, w);
	ok   &= NearEqual(dw[0], (4.*3.*2.*1.)*2.*x0, 1e-10 , 1e-10); 

	// 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;
}


Input File: example/mul.cpp