# include <cppad/vector.hpp>
# include <cppad/poly.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <FADBAD++/tadiff.h>

bool link_poly(
	size_t                     size     , 
	size_t                     repeat   , 
	CppAD::vector<double>     &a        ,  // coefficients of polynomial
	CppAD::vector<double>     &z        ,  // polynomial argument value
	CppAD::vector<double>     &ddp      )  // second derivative w.r.t z  
{
	// -----------------------------------------------------
	// setup
	size_t i;             // temporary index     
	fadbad::T<double>  Z; // domain space AD value
	fadbad::T<double>  P; // range space AD value

	// choose the polynomial coefficients
	CppAD::uniform_01(size, a);

	// AD copy of the polynomial coefficients
	CppAD::vector< fadbad::T<double> > A(size);
	for(i = 0; i < size; i++)
		A[i] = a[i];

	// ------------------------------------------------------
	while(repeat--)
	{	// get the next argument value
		CppAD::uniform_01(1, z);

		// independent variable value
		Z    = z[0]; // argument value
		Z[1] = 1;    // argument first order Taylor coefficient

		// AD computation of the dependent variable
		P = CppAD::Poly(0, A, Z);

		// Taylor-expand P to degree one
		P.eval(2);

		// second derivative is twice second order Taylor coefficient
		ddp[0] = 2. * P[2];

		// Free DAG corresponding to P does not seem to improve speed.
		// Probably because it gets freed the next time P is assigned.
		// P.reset();
	}
	// ------------------------------------------------------
	return true;
}