// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-22 Bradley M. Bell
// ----------------------------------------------------------------------------

/*
Old example and test now just used for validation testing.
*/

# include <cppad/cppad.hpp>
# include <cmath>

namespace { // begin empty namespace

bool ad_ad(void)
{  bool ok = true;
   using CppAD::AD;
   using CppAD::NearEqual;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

   AD< AD<double> > x(2.), y(2.);
   AD< AD<double> > z = atan2(y, x);
   NearEqual( Value( Value(z) ), atan(1.), eps99, eps99);

   return ok;
}

bool general(void)
{  bool ok = true;

   using CppAD::atan;
   using CppAD::sin;
   using CppAD::cos;
   using namespace CppAD;
   using CppAD::NearEqual;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

   // independent variable vector
   CPPAD_TESTVECTOR(AD<double>) U(1);
   U[0]     = 1.;
   Independent(U);

   // a temporary values
   AD<double> x = cos(U[0]);
   AD<double> y = sin(U[0]);

   // dependent variable vector
   CPPAD_TESTVECTOR(AD<double>) Z(1);
   Z[0] = atan2(y, x);

   // create f: U -> Z and vectors used for derivative calculations
   ADFun<double> f(U, Z);
   CPPAD_TESTVECTOR(double) v(1);
   CPPAD_TESTVECTOR(double) w(1);

   // check original value (u in first quadrant)
   ok &= NearEqual(U[0] , Z[0], eps99, eps99);

   // check case where u is in second quadrant
   v[0] = 3.;
   w    = f.Forward(0, v);
   ok  &= NearEqual(w[0] , v[0], eps99, eps99);

   // check case where u is in third quadrant
   v[0] = -3.;
   w    = f.Forward(0, v);
   ok  &= NearEqual(w[0] , v[0], eps99, eps99);

   // check case where u is in fourth quadrant
   v[0] = -1.;
   w    = f.Forward(0, v);
   ok  &= NearEqual(w[0] , v[0], eps99, eps99);

   // forward computation of partials w.r.t. u
   size_t j;
   size_t p     = 5;
   double jfac  = 1.;
   double value = 1.;
   v[0]         = 1.;
   for(j = 1; j < p; j++)
   {  jfac *= double(j);
      w     = f.Forward(j, v);
      ok &= NearEqual(w[0], value/jfac, eps99, eps99); // d^jz/du^j
      v[0]  = 0.;
      value = 0.;
   }

   // reverse computation of partials of Taylor coefficients
   CPPAD_TESTVECTOR(double) r(p);
   w[0]  = 1.;
   r     = f.Reverse(p, w);
   jfac  = 1.;
   value = 1.;
   for(j = 0; j < p; j++)
   {  ok &= NearEqual(r[j], value/jfac, eps99, eps99); // d^jz/du^j
      jfac *= double(j + 1);
      value = 0.;
   }

   return ok;
}

} // end empty namespace

bool atan2(void)
{  bool ok = true;
   ok     &= ad_ad();
   ok     &= general();

   return ok;
}
