# include <cppad/cppad.hpp>

bool fabs(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]     = 0.;

     // declare independent variables and start tape recording
     CppAD::Independent(x);

     // range space vector
     size_t m = 6;
     CPPAD_TESTVECTOR(AD<double>) y(m);
     y[0]     = fabs(x[0] - 1.);
     y[1]     = fabs(x[0]);
     y[2]     = fabs(x[0] + 1.);
     //
     y[3]     = fabs(x[0] - 1.);
     y[4]     = fabs(x[0]);
     y[5]     = fabs(x[0] + 1.);

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

     // check values
     ok &= (y[0] == 1.);
     ok &= (y[1] == 0.);
     ok &= (y[2] == 1.);
     //
     ok &= (y[3] == 1.);
     ok &= (y[4] == 0.);
     ok &= (y[5] == 1.);

     // forward computation of partials w.r.t. a positive x[0] direction
     size_t p = 1;
     CPPAD_TESTVECTOR(double) dx(n), dy(m);
     dx[0] = 1.;
     dy    = f.Forward(p, dx);
     ok  &= (dy[0] == - dx[0]);
     ok  &= (dy[1] ==   0.   ); // used to be (dy[1] == + dx[0]);
     ok  &= (dy[2] == + dx[0]);
     //
     ok  &= (dy[3] == - dx[0]);
     ok  &= (dy[4] ==   0.   ); // used to be (dy[1] == + dx[0]);
     ok  &= (dy[5] == + dx[0]);

     // forward computation of partials w.r.t. a negative x[0] direction
     dx[0] = -1.;
     dy    = f.Forward(p, dx);
     ok  &= (dy[0] == - dx[0]);
     ok  &= (dy[1] ==   0.   ); // used to be (dy[1] == - dx[0]);
     ok  &= (dy[2] == + dx[0]);
     //
     ok  &= (dy[3] == - dx[0]);
     ok  &= (dy[4] ==   0.   ); // used to be (dy[1] == - dx[0]);
     ok  &= (dy[5] == + dx[0]);

     // reverse computation of derivative of y[0]
     p    = 1;
     CPPAD_TESTVECTOR(double)  w(m), dw(n);
     w[0] = 1.; w[1] = 0.; w[2] = 0.; w[3] = 0.; w[4] = 0.; w[5] = 0.;
     dw   = f.Reverse(p, w);
     ok  &= (dw[0] == -1.);

     // reverse computation of derivative of y[1]
     w[0] = 0.; w[1] = 1.;
     dw   = f.Reverse(p, w);
     ok  &= (dw[0] == 0.);

     // reverse computation of derivative of y[5]
     w[1] = 0.; w[5] = 1.;
     dw   = f.Reverse(p, w);
     ok  &= (dw[0] == 1.);

     // use a VecAD<Base>::reference object with abs and fabs
     CppAD::VecAD<double> v(1);
     AD<double> zero(0);
     v[zero]           = -1;
     AD<double> result = fabs(v[zero]);
     ok    &= NearEqual(result, 1., eps99, eps99);
     result = fabs(v[zero]);
     ok    &= NearEqual(result, 1., eps99, eps99);

     return ok;
}