# include <cstddef>  // used to defined size_t
# include <cppad/utility/check_simple_vector.hpp>

namespace CppAD {    // BEGIN CppAD namespace

template <class Type, class Vector>
Type Poly(size_t k, const Vector &a, const Type &z)
{     size_t i;
     size_t d = a.size() - 1;

     Type tmp;

     // check Vector is Simple Vector class with Type elements
     CheckSimpleVector<Type, Vector>();

     // case where derivative order greater than degree of polynomial
     if( k > d )
     {     tmp = 0;
          return tmp;
     }
     // case where we are evaluating a derivative
     if( k > 0 )
     {     // initialize factor as (k-1) !
          size_t factor = 1;
          for(i = 2; i < k; i++)
               factor *= i;

          // set b to coefficient vector corresponding to derivative
          Vector b(d - k + 1);
          for(i = k; i <= d; i++)
          {     factor   *= i;
               tmp       = double( factor );
               b[i - k]  = a[i] * tmp;
               factor   /= (i - k + 1);
          }
          // value of derivative polynomial
          return Poly(0, b, z);
     }
     // case where we are evaluating the original polynomial
     Type sum = a[d];
     i        = d;
     while(i > 0)
     {     sum *= z;
          sum += a[--i];
     }
     return sum;
}
} // END CppAD namespace