# 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 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 double &x)
     {     size_t j = Index(x);
          return ArgumentValue[j];
     }
     double Function(const double &x)
     {     size_t j = Index(x);
          return FunctionValue[j];
     }

     double Slope(const double &x)
     {     size_t j  = Index(x);
          double dx = ArgumentValue[j+1] - ArgumentValue[j];
          double dy = FunctionValue[j+1] - FunctionValue[j];
          return dy / dx;
     }
     CPPAD_DISCRETE_FUNCTION(double, Argument)
     CPPAD_DISCRETE_FUNCTION(double, Function)
     CPPAD_DISCRETE_FUNCTION(double, Slope)
}


bool interp_onetape(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);
     X[0] = .4 * ArgumentValue[1] + .6 * ArgumentValue[2];

     // declare independent variables and start tape recording
     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[1] and ArgumentValue[2]
     x[0]          = Value(X[0]);
     double delta  = ArgumentValue[2] - ArgumentValue[1];
     double check  = FunctionValue[2] * (x[0] - ArgumentValue[1]) / delta
                   + FunctionValue[1] * (ArgumentValue[2] - x[0]) / delta;
     ok  &= NearEqual(Y[0], check, eps99, eps99);

     // evaluate f where x has different value
     x[0]   = .7 * ArgumentValue[2] + .3 * ArgumentValue[3];
     y      = f.Forward(0, x);

     // check function value
     delta  = ArgumentValue[3] - ArgumentValue[2];
     check  = FunctionValue[3] * (x[0] - ArgumentValue[2]) / delta
                   + FunctionValue[2] * (ArgumentValue[3] - 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[3] - FunctionValue[2])
           / (ArgumentValue[3] - ArgumentValue[2]);
     ok   &= NearEqual(dy[0], check, eps99, eps99);

     return ok;
}