NAG Library Manual, Mark 27.2
```/* D02PT_A1W_F C++ Header Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.2, 2021.
*/

#include <dco.hpp>
#include <iostream>
#include <math.h>
#include <nag.h>
#include <stdio.h>
using namespace std;

#ifdef __cplusplus
extern "C"
{
#endif
static void NAG_CALL f(void *&                  ad_handle,
const Integer &          n,
Integer                  iuser[],
#ifdef __cplusplus
}
#endif

int main(void)
{
const Integer n      = 2;
const Integer liwsav = 130;
const Integer lrwsav = 350 + 32 * n;

Integer exit_status = 0;

nagad_a1w_w_rtype *rwsav = 0, *thresh = 0, *ynow = 0, *yinit = 0;
nagad_a1w_w_rtype *ypnow = 0, *y = 0, ruser[2];
Integer *          iwsav = 0, iuser[1];

cout << "D02PT_A1W_F C++ Header Example Program Results\n\n";

iwsav  = new Integer[liwsav];

// Set initial conditions for ODE and parameters for the integrator.
Integer           method = 2;
tstart    = 0.0;
tol       = 1.0e-4;
tend      = 2.0 * nag_math_pi;
yinit[0]  = 0.0;
yinit[1]  = 1.0;
hstart    = 0.0;
thresh[0] = 1.0e-8;
thresh[1] = 1.0e-8;
ruser[0]  = 1.0;
ruser[1]  = 1.0;

{
double tolr = dco::value(tol);
cout << "\n  Calculation with tol = " << tolr << endl;
}
cout.setf(ios::fixed);
cout.setf(ios::right);
cout.precision(3);
{
double t = dco::value(tstart);
cout << "\n    t         y1        y2" << endl;
cout.width(6);
cout << t;
}
for (int k = 0; k < n; k++)
{
double yr = dco::value(yinit[k]);
cout.width(10);
cout << yr;
}
cout << endl;

dco::ga1s<double>::global_tape = dco::ga1s<double>::tape_t::create();

// Create AD configuration data object
Integer ifail     = 0;

dco::ga1s<double>::global_tape->register_variable(ruser[0]);
dco::ga1s<double>::global_tape->register_variable(ruser[1]);

y[0] = yinit[0];
y[1] = yinit[1];

// Initialize Runge-Kutta method for integrating ODE
ifail = 0;
iwsav, rwsav, ifail);

tnow = tstart;
do
{
ifail = 0;
iwsav, rwsav, ifail);
cout.width(6);
cout << dco::value(tnow);
for (int k = 0; k < n; ++k)
{
cout.width(10);
cout << dco::value(ynow[k]);
}
cout << endl;
}
while (tnow < tend);

Integer           fevals, stepcost, stepsok;
ifail = 0;
rwsav, ifail);
cout << "\n Cost of the integration in evaluations of f is " << fevals;
cout << endl;

// Setup evaluation of derivatives via adjoints.
double inc = 1.0;
dco::derivative(ynow[0]) += inc;
ifail                                              = 0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;

cout << "\n Derivatives calculated: First order adjoints\n";
cout << " Computational mode    : algorithmic\n";

// Get derivatives
cout << "\n Derivatives: (solution w.r.t. function parameter)\n";

cout.setf(ios::scientific, ios::floatfield);
cout.precision(5);
double dr;
dr = dco::derivative(ruser[0]);
cout << " dy(t)/druser[0] = ";
cout.width(12);
cout << dr << endl;
dr = dco::derivative(ruser[1]);
cout << " dy(t)/druser[1] = ";
cout.width(12);
cout << dr << endl;

dco::ga1s<double>::tape_t::remove(dco::ga1s<double>::global_tape);

delete[] thresh;
delete[] ynow;
delete[] y;
delete[] yinit;
delete[] ypnow;
delete[] iwsav;
delete[] rwsav;
return exit_status;
}

static void NAG_CALL f(void *&                  ad_handle,