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

namespace {
     double ArgumentValue[] = {
          .0 ,
          .2 ,
          .4 ,
          .8 ,
          1.
     };
     double FunctionValue[] = {
          std::sin( ArgumentValue[0] ) ,
          std::sin( ArgumentValue[1] ) ,
          std::sin( ArgumentValue[2] ) ,
          std::sin( ArgumentValue[3] ) ,
          std::sin( ArgumentValue[4] )
     };
     size_t TableLength = 5;

     size_t Index(const CppAD::AD<double> &x)
     {     // determine the index j such that x is between
          // ArgumentValue[j] and ArgumentValue[j+1]
          static size_t j = 0;
          while ( x < ArgumentValue[j] && j > 0 )
               j--;
          while ( x > ArgumentValue[j+1] && j < TableLength - 2)
               j++;
          // assert conditions that must be true given logic above
          assert( j >= 0 && j < TableLength - 1 );
          return j;
     }
     double Argument(const CppAD::AD<double> &x)
     {     size_t j = Index(x);
          return ArgumentValue[j];
     }
     double Function(const CppAD::AD<double> &x)
     {     size_t j = Index(x);
          return FunctionValue[j];
     }
     double Slope(const CppAD::AD<double> &x)
     {     size_t j  = Index(x);
          double dx = ArgumentValue[j+1] - ArgumentValue[j];
          double dy = FunctionValue[j+1] - FunctionValue[j];
          return dy / dx;
     }
}

bool interp_retape(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;
     CPPAD_TESTVECTOR(AD<double>) X(n);

     // loop over argument values
     size_t k;
     for(k = 0; k < TableLength - 1; k++)
     {
          X[0] = .4 * ArgumentValue[k] + .6 * ArgumentValue[k+1];

          // declare independent variables and start tape recording
          // (use a different tape for each argument value)
          CppAD::Independent(X);

          // evaluate piecewise linear interpolant at X[0]
          AD<double> A = Argument(X[0]);
          AD<double> F = Function(X[0]);
          AD<double> S = Slope(X[0]);
          AD<double> I = F + (X[0] - A) * S;

          // range space vector
          size_t m = 1;
          CPPAD_TESTVECTOR(AD<double>) Y(m);
          Y[0] = I;

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

          // vectors for arguments to the function object f
          CPPAD_TESTVECTOR(double) x(n);   // argument values
          CPPAD_TESTVECTOR(double) y(m);   // function values
          CPPAD_TESTVECTOR(double) dx(n);  // differentials in x space
          CPPAD_TESTVECTOR(double) dy(m);  // differentials in y space

          // to check function value we use the fact that X[0] is between
          // ArgumentValue[k] and ArgumentValue[k+1]
          double delta, check;
          x[0]   = Value(X[0]);
          delta  = ArgumentValue[k+1] - ArgumentValue[k];
          check  = FunctionValue[k+1] * (x[0]-ArgumentValue[k]) / delta
                    + FunctionValue[k] * (ArgumentValue[k+1]-x[0]) / delta;
          ok    &= NearEqual(Y[0], check, eps99, eps99);

          // evaluate partials w.r.t. x[0]
          dx[0] = 1.;
          dy    = f.Forward(1, dx);

          // check that the derivative is the slope
          check = (FunctionValue[k+1] - FunctionValue[k])
                / (ArgumentValue[k+1] - ArgumentValue[k]);
          ok   &= NearEqual(dy[0], check, eps99, eps99);
     }
     return ok;
}