# include <cppad/cppad.hpp>

namespace {
     struct tape_size { size_t n_var; size_t n_op; };

     template <class Vector> void fun(
          const Vector& x, Vector& y, tape_size& before, tape_size& after
     )
     {     typedef typename Vector::value_type scalar;

          // phantom variable with index 0 and independent variables
          // begin operator, independent variable operators and end operator
          before.n_var = 1 + x.size(); before.n_op  = 2 + x.size();
          after.n_var  = 1 + x.size(); after.n_op   = 2 + x.size();

          // operators that are identical, and that will be made part of the
          // cummulative summation. Make sure do not replace second variable
          // using the first and then remove the first as part of the
          // cumulative summation.
          scalar first  = x[0] + x[1];
          scalar second = x[0] + x[1];
          before.n_var += 2; before.n_op  += 2;
          after.n_var  += 0; after.n_op   += 0;

          // test that subtractions are also included in cumulative summations
          scalar third = x[1] - 2.0;
          before.n_var += 1; before.n_op  += 1;
          after.n_var  += 0; after.n_op   += 0;

          // the finial summation is converted to a cumulative summation
          // the other is removed.
          scalar csum = first + second + third;
          before.n_var += 2; before.n_op  += 2;
          after.n_var  += 1; after.n_op   += 1;

          // results for this operation sequence
          y[0] = csum;
          before.n_var += 0; before.n_op  += 0;
          after.n_var  += 0; after.n_op   += 0;
     }
}
bool cumulative_sum(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps10 = 10.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n  = 2;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.5;
     ax[1] = 1.5;

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

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     tape_size before, after;
     fun(ax, ay, before, after);

     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(ax, ay);
     ok &= f.size_var() == before.n_var;
     ok &= f.size_op()  == before.n_op;

     // Optimize the operation sequence
     f.optimize();
     ok &= f.size_var() == after.n_var;
     ok &= f.size_op()  == after.n_op;

     // Check result for a zero order calculation for a different x,
     CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
     x[0] = 0.75;
     x[1] = 2.25;
     y    = f.Forward(0, x);
     fun(x, check, before, after);
     ok  &= CppAD::NearEqual(y[0], check[0], eps10, eps10);

     return ok;
}