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<center><b><big><big>Example Differentiating a Stack Machine Interpreter</big></big></b></center>
<code><font color="blue"><pre style='display:inline'> 

# include &lt;cstring&gt;
# include &lt;cstddef&gt;
# include &lt;cstdlib&gt;
# include &lt;cctype&gt;
# include &lt;cassert&gt;
# include &lt;stack&gt;

# include &lt;cppad/cppad.hpp&gt;

namespace { 
// Begin empty namespace ------------------------------------------------

bool is_number( const std::string &amp;s )
{	char ch = s[0];
	bool number = (std::strchr(&quot;0123456789.&quot;, ch) != 0);
	return number;
}
bool is_binary( const std::string &amp;s )
{	char ch = s[0];
	bool binary = (strchr(&quot;+-*/.&quot;, ch) != 0);
	return binary;
}
bool is_variable( const std::string &amp;s )
{	char ch = s[0];
	bool variable = ('a' &lt;= ch) &amp; (ch &lt;= 'z');
	return variable;
}

void StackMachine( 
	std::stack&lt; std::string &gt;          &amp;token_stack  ,
	CppAD::vector&lt; CppAD::<a href="ad.xml" target="_top">AD</a>&lt;double&gt; &gt; &amp;variable     )
{	using std::string;
	using std::stack;

	using CppAD::AD;

	stack&lt; <a href="ad.xml" target="_top">AD</a>&lt;double&gt; &gt; value_stack;
	string              token;
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt;          value_one;
	<a href="ad.xml" target="_top">AD</a>&lt;double&gt;          value_two;

	while( ! token_stack.empty() )
	{	string s = token_stack.top();
		token_stack.pop();

		if( is_number(s) )
		{	value_one = std::atof( s.c_str() );
			value_stack.push( value_one );
		}
		else if( is_variable(s) )
		{	value_one = variable[ size_t(s[0]) - size_t('a') ];
			value_stack.push( value_one );
		}
		else if( is_binary(s) ) 
		{	assert( value_stack.size() &gt;= 2 );
			value_one = value_stack.top();
			value_stack.pop();
			value_two = value_stack.top();
			value_stack.pop();

			switch( s[0] )
			{
				case '+':
				value_stack.push(value_one + value_two);
				break;

				case '-':
				value_stack.push(value_one - value_two);
				break;

				case '*':
				value_stack.push(value_one * value_two);
				break;

				case '/':
				value_stack.push(value_one / value_two);
				break;

				default:
				assert(0);
			}
		}
		else if( s[0] == '=' )
		{	assert( value_stack.size() &gt;= 1 ); 	
			assert( token_stack.size() &gt;= 1 );
			//
			s = token_stack.top();
			token_stack.pop();
			//
			assert( is_variable( s ) );
			value_one = value_stack.top();
			value_stack.pop();
			//
			variable[ size_t(s[0]) - size_t('a') ] = value_one;
		}
		else assert(0);
	}
	return;
}

// End empty namespace -------------------------------------------------------
}

bool StackMachine(void)
{	bool ok = true;

	using std::string;
	using std::stack;

	using CppAD::AD;
	using CppAD::NearEqual;
	using CppAD::vector;

	// The users program in that stack machine language
	const char *program[] = {
		&quot;1.0&quot;, &quot;a&quot;, &quot;+&quot;, &quot;=&quot;, &quot;b&quot;,  // b = a + 1
		&quot;2.0&quot;, &quot;b&quot;, &quot;*&quot;, &quot;=&quot;, &quot;c&quot;,  // c = b * 2
		&quot;3.0&quot;, &quot;c&quot;, &quot;-&quot;, &quot;=&quot;, &quot;d&quot;,  // d = c - 3
		&quot;4.0&quot;, &quot;d&quot;, &quot;/&quot;, &quot;=&quot;, &quot;e&quot;   // e = d / 4
	};
	size_t n_program = sizeof( program ) / sizeof( program[0] );

	// put the program in the token stack
	stack&lt; string &gt; token_stack;
	size_t i = n_program;
	while(i--)
		token_stack.push( program[i] );

	// domain space vector
	size_t n = 1;
	vector&lt; <a href="ad.xml" target="_top">AD</a>&lt;double&gt; &gt; X(n);
	X[0] = 0.;

	// declare independent variables and start tape recording
	CppAD::<a href="independent.xml" target="_top">Independent</a>(X);
		
	// x[0] corresponds to a in the stack machine
	vector&lt; <a href="ad.xml" target="_top">AD</a>&lt;double&gt; &gt; variable(26);
	variable[0] = X[0];

	// calculate the resutls of the program
	StackMachine( token_stack , variable);

	// range space vector
	size_t m = 4;
	vector&lt; <a href="ad.xml" target="_top">AD</a>&lt;double&gt; &gt; Y(m);
	Y[0] = variable[1];   // b = a + 1
	Y[1] = variable[2];   // c = (a + 1) * 2
	Y[2] = variable[3];   // d = (a + 1) * 2 - 3
	Y[3] = variable[4];   // e = ( (a + 1) * 2 - 3 ) / 4 
	
	// create f : X -&gt; Y and stop tape recording
	CppAD::<a href="funconstruct.xml" target="_top">ADFun</a>&lt;double&gt; f(X, Y);

	// use forward mode to evaluate function at different argument value
	size_t p = 0;
	vector&lt;double&gt; x(n);
	vector&lt;double&gt; y(m);
	x[0] = 1.;
	y    = f.<a href="forward.xml" target="_top">Forward</a>(p, x);

	// check function values
	ok &amp;= (y[0] == x[0] + 1.);
	ok &amp;= (y[1] == (x[0] + 1.) * 2.);
	ok &amp;= (y[2] == (x[0] + 1.) * 2. - 3.);
	ok &amp;= (y[3] == ( (x[0] + 1.) * 2. - 3.) / 4.);

	// Use forward mode (because x is shorter than y) to calculate Jacobian
	p = 1;
	vector&lt;double&gt; dx(n);
	vector&lt;double&gt; dy(m);
	dx[0] = 1.;
	dy    = f.<a href="forward.xml" target="_top">Forward</a>(p, dx);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dy[0], 1., 1e-10, 1e-10);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dy[1], 2., 1e-10, 1e-10);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dy[2], 2., 1e-10, 1e-10);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dy[3], .5, 1e-10, 1e-10);

	// Use Jacobian routine (which automatically decides which mode to use)
	dy = f.<a href="jacobian.xml" target="_top">Jacobian</a>(x);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dy[0], 1., 1e-10, 1e-10);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dy[1], 2., 1e-10, 1e-10);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dy[2], 2., 1e-10, 1e-10);
	ok   &amp;= <a href="nearequal.xml" target="_top">NearEqual</a>(dy[3], .5, 1e-10, 1e-10);

	return ok;
}
</pre>

</font></code>


<hr/>Input File: example/stack_machine.cpp

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