// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-25 Bradley M. Bell
// SPDX-FileContributor: 2003-25 Bradley M. Bell
// ----------------------------------------------------------------------------

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

namespace { // BEGIN_EMPTY_NAMESPACE
// ----------------------------------------------------------------------------
//
// pul_323
// Test that the with_no_op has the same number of dynamic parameters
// (and variables) as without_no_op.
bool pull_232_fun(
   bool with_no_op         ,
   CppAD::ADFun<double>& f )
{  //
   // ok
   bool ok = true;
   //
   // azero, aone
   CppAD::AD<double> azero(0.0);
   CppAD::AD<double> aone(1.0);
   //
   // ap, ax, ay
   CPPAD_TESTVECTOR( CppAD::AD<double> ) ap(1), ax(1), ay(1);
   ap[0] = 2.0;
   ax[0] = 3.0;
   //
   // ax. ap
   CppAD::Independent(ax, ap);
   //
   // ay
   ay[0] = 0.0;
   if( with_no_op ) {
      ay[0] += ax[0] * ( ap[0] + azero );
      ay[0] += ax[0] * ( ap[0] - azero );
      ay[0] += ax[0] * ( ap[0] * aone );
      ay[0] += ax[0] * ( ap[0] / aone );
      ay[0] += azero;
      ay[0] -= azero;
      ay[0] *= aone;
      ay[0] /= aone;
      ay[0] += ax[0] * pow(ap[0] , azero);
      ay[0] += ax[0] + pow(azero, ap[0]);
      ay[0] += ax[0] + azmul(azero, ap[0]);
      ay[0] += ax[0] + azmul(ap[0], azero);
   } else {
      ay[0] += ax[0] * ap[0];
      ay[0] += ax[0] * ap[0];
      ay[0] += ax[0] * ap[0];
      ay[0] += ax[0] * ap[0];
      ay[0] += ax[0];
      ay[0] += ax[0];
      ay[0] += ax[0];
      ay[0] += ax[0];
   }
   //
   // f
   f.Dependent(ay);
   //
   // y, check
   CPPAD_TESTVECTOR(double) p(1), x(1), y(1);
   p[0] = 4.0;
   x[0] = 5.0;
   f.new_dynamic(p);
   y = f.Forward(0, x);
   double check = 0;
   check += x[0] * p[0];
   check += x[0] * p[0];
   check += x[0] * p[0];
   check += x[0] * p[0];
   check += x[0];
   check += x[0];
   check += x[0];
   check += x[0];
   //
   // ok
   ok &= y[0] == check;
   //
   return ok;
}
bool pull_232(void)
{  //
   // ok, no_op
   bool ok = true;
   //
   // with_no_op
   bool with_no_op;
   //
   // ok, f_without
   CppAD::ADFun<double> f_without;
   with_no_op = false;
   ok     &= pull_232_fun(with_no_op, f_without);
   //
   // ok, f_with
   CppAD::ADFun<double> f_with;
   with_no_op = true;
   ok     &= pull_232_fun(with_no_op, f_with);
   //
   // ok
   ok &= f_without.size_dyn_par() == f_with.size_dyn_par();
   ok &= f_without.size_var() == f_with.size_var();
   //
   return ok;
}
// ----------------------------------------------------------------------------
bool vecad(void)
{  bool ok = true;
   using CppAD::AD;

   // dynamic parameter vector
   size_t np = 2;
   size_t nx = 1;
   size_t ny = 2;
   CPPAD_TESTVECTOR(AD<double>) ap(np), ax(nx), ay(ny);
   ap[0] = 0.0;
   ap[1] = 1.0;
   ax[0] = 2.0;

   // declare independent variables, dynamic parameters, start recording
   CppAD::Independent(ax, ap);

   // Create a VecAD object
   size_t nv = 2;
   CppAD::VecAD<double> av(nv);
   // ap[0] is either 0 or 1
   av[ ap[0] ]       = ap[1];
   av[ 1.0 - ap[0] ] = 2.0 * ap[1];

   // create f: x -> y and stop tape recording
   CppAD::AD<double> zero(0.0), one(1.0);
   ay[0] = av[zero];
   ay[1] = av[one];
   CppAD::ADFun<double> f(ax, ay);

   // zero order forward mode with p[0] = 0
   CPPAD_TESTVECTOR(double) p(np), x(nx), y(ny);
   p[0] = 0.0;
   p[1] = 1.0;
   x[0] = 2.0;
   f.new_dynamic(p);
   y   = f.Forward(0, x);
   ok &= y[0] == p[1];
   ok &= y[1] == 2.0 * p[1];

   // zero order forward mode with p[0] = 1
   p[0] = 1.0;
   p[1] = 2.0;
   x[0] = 3.0;
   f.new_dynamic(p);
   y   = f.Forward(0, x);
   ok &= y[0] == 2.0 * p[1];
   ok &= y[1] == p[1];
   CPPAD_TESTVECTOR(double) dx(nx), dy(ny);
   dx[0] = 1.0;
   dy    = f.Forward(1, dx);
   ok   &= dy[0] == 0.0;
   ok   &= dy[1] == 0.0;

   return ok;
}
// ----------------------------------------------------------------------------
bool operator_with_variable(void)
{  bool ok = true;
   using CppAD::AD;
   using CppAD::NearEqual;
   using CppAD::azmul;
   using CppAD::CondExpLt;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   size_t n   = 11;

   // dynamic parameter vector
   CPPAD_TESTVECTOR(AD<double>) adynamic(n);
   for(size_t j = 0; j < n; ++j)
      adynamic[j] = 2.0;

   // domain space vector
   CPPAD_TESTVECTOR(AD<double>) ax(n);
   for(size_t j = 0; j < n; ++j)
      ax[j] = AD<double>(j + 1);

   // declare independent variables, dynamic parameters, starting recording
   CppAD::Independent(ax, adynamic);

   // range space vector
   CPPAD_TESTVECTOR(AD<double>) ay(n);
   size_t k = 0;
   ay[k] = -1.0*double(k+1)*(adynamic[k] + ax[k]) * (ax[k] + adynamic[k]);
   ++k;
   ay[k] = -1.0*double(k+1)*(adynamic[k] - ax[k]) * (ax[k] - adynamic[k]);
   ++k;
   ay[k] = -1.0*double(k+1)*(adynamic[k] * ax[k]) + (ax[k] * adynamic[k]);
   ++k;
   ay[k] = -1.0*double(k+1)*(adynamic[k] / ax[k]) + (ax[k] / adynamic[k]);
   ++k;
   ay[k]  = ax[k];
   ay[k] += adynamic[k];
   ++k;
   ay[k]  = adynamic[k];
   ay[k] -= ax[k];
   ++k;
   ay[k]  = ax[k];
   ay[k] *= adynamic[k];
   ++k;
   ay[k]  = adynamic[k];
   ay[k] /= ax[k];
   ++k;
   ay[k]  = pow(ax[k], adynamic[k]) + pow(adynamic[k], ax[k]);
   ++k;
   ay[k]  = azmul(ax[k], adynamic[k]) + azmul(adynamic[k], ax[k]);
   ++k;
   ay[k]  = CondExpLt(ax[k], adynamic[k], ax[k], adynamic[k]);
   ++k;
   ok &= size_t(k) == n;

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

   // zero order forward mode
   CPPAD_TESTVECTOR(double) x(n), y(n);
   for(size_t j = 0; j < n; ++j)
      x[j] = double(j + 1);
   y    = f.Forward(0, x);
   double check;
   k = 0;
   check  = ( Value(adynamic[k]) + x[k] ) * ( x[k] + Value(adynamic[k]) );
   check *= -1.0*double(k+1);
   ok    &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check  = ( Value(adynamic[k]) - x[k] ) * ( x[k] - Value(adynamic[k]) );
   check *= -1.0*double(k+1);
   ok    &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check  = -1.0*double(k+1)*( Value(adynamic[k]) * x[k] );
   check += ( x[k] * Value(adynamic[k]) );
   ok    &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check  = -1.0*double(k+1)*( Value(adynamic[k]) / x[k] );
   check += ( x[k] / Value(adynamic[k]) );
   ok    &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check  = x[k] + Value(adynamic[k]);
   ok    &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check  = Value(adynamic[k]) - x[k];
   ok    &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check  = x[k] * Value(adynamic[k]);
   ok    &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check  = Value(adynamic[k]) / x[k];
   ok    &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check  = std::pow(x[k], Value(adynamic[k]));
   check += std::pow(Value(adynamic[k]), x[k]);
   ok    &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check  = azmul(x[k], Value(adynamic[k])) + azmul(Value(adynamic[k]), x[k]);
   ok    &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check  = CondExpLt( x[k], Value(adynamic[k]), x[k], Value(adynamic[k]) );
   ok    &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   ok &= size_t(k) == n;

   // change the dynamic parameter values
   CPPAD_TESTVECTOR(double) dynamic(n);
   for(size_t j = 0; j < n; j++)
      dynamic[j] = double(2 * j + 1);
   f.new_dynamic(dynamic);
   //
   y = f.Forward(0, x);
   k     = 0;
   check = -1.0*double(k+1)*( dynamic[k] + x[k] ) * ( x[k] + dynamic[k] );
   ok   &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check = -1.0*double(k+1)*( dynamic[k] - x[k] ) * ( x[k] - dynamic[k] );
   ok   &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check = -1.0*double(k+1)*( dynamic[k] * x[k] ) + ( x[k] * dynamic[k] );
   ok   &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check = -1.0*double(k+1)*( dynamic[k] / x[k] ) + ( x[k] / dynamic[k] );
   ok   &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check = x[k] + dynamic[k];
   ok   &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check = dynamic[k] - x[k];
   ok   &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check = x[k] * dynamic[k];
   ok   &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check = dynamic[k] / x[k];
   ok   &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check  = std::pow(x[k], dynamic[k]);
   check += std::pow(dynamic[k], x[k]);
   ok    &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check  = azmul(x[k], dynamic[k]) + CppAD::azmul(dynamic[k], x[k]);
   ok    &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   check  = CondExpLt(x[k], dynamic[k], x[k], dynamic[k]);
   ok    &= NearEqual(y[k] , check, eps99, eps99);
   ++k;
   ok &= size_t(k) == n;
   //
   return ok;
}
// ----------------------------------------------------------------------------
bool dynamic_operator(void)
{  bool ok = true;
   using CppAD::AD;
   using CppAD::NearEqual;
   using CppAD::azmul;
   using CppAD::sign;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

   // independent dynamic parameter vector
   size_t nd  = 1;
   CPPAD_TESTVECTOR(AD<double>) adynamic(nd);
   adynamic[0] = 0.5;

   // domain space vector
   size_t nx = 1;
   CPPAD_TESTVECTOR(AD<double>) ax(nx);
   ax[0] = 0.25;

   // declare independent variables, dynamic parameters, starting recording
   CppAD::Independent(ax, adynamic);

   // range space vector
   size_t ny = 27;
   ny += 6;
   CPPAD_TESTVECTOR(AD<double>) ay(ny);
   size_t k = 0;
   // ----------------------------------------------------------
   // 98 standard math
   ay[k] = acos(adynamic[0]);
   ++k;
   ay[k] = asin(adynamic[0]);
   ++k;
   ay[k] = atan(adynamic[0]);
   ++k;
   ay[k] = cos(adynamic[0]);
   ++k;
   ay[k] = cosh(adynamic[0]);
   ++k;
   ay[k] = exp(adynamic[0]);
   ++k;
   ay[k] = acos(adynamic[0]);
   ++k;
   ay[k] = log(adynamic[0]);
   ++k;
   ay[k] = sin(adynamic[0]);
   ++k;
   ay[k] = sinh(adynamic[0]);
   ++k;
   ay[k] = sqrt(adynamic[0]);
   ++k;
   ay[k] = tan(adynamic[0]);
   ++k;
   ay[k] = tanh(adynamic[0]);
   ++k;
   // ----------------------------------------------------------
   // 2011 standard math
   ay[k] = asinh(adynamic[0]);
   ++k;
   ay[k] = acosh(adynamic[0] + 1.0);
   ++k;
   ay[k] = atanh(adynamic[0]);
   ++k;
   ay[k] = expm1(adynamic[0]);
   ++k;
   ay[k] = erf(adynamic[0]);
   ++k;
   ay[k] = log1p(adynamic[0]);
   ++k;
   // ----------------------------------------------------------
   // binary
   ay[k]  = 2.0 + adynamic[0];
   ++k;
   ay[k]  = 2.0;
   ay[k] += adynamic[0];  // constant += dynamic
   ++k;
   ay[k]  = adynamic[0] / 2.0;
   ++k;
   ay[k]  = adynamic[0];
   ay[k] /= 2.0;          // dynamic /= constant
   ++k;
   ay[k]  = 2.0 * adynamic[0];
   ++k;
   ay[k]  = 2.0;
   ay[k] *= adynamic[0];  // constant *= dynamic
   ++k;
   ay[k]  = adynamic[0] - 2.0;
   ++k;
   ay[k]  = adynamic[0];
   ay[k] -= 2.0;          // dynamic -= constant
   ++k;
   // ----------------------------------------------------------
   // other
   ay[k] = - adynamic[0];
   ++k;
   ay[k] = fabs(adynamic[0]);
   ++k;
   ay[k] = pow(adynamic[0], 2.0);
   ++k;
   ay[k] = sign(adynamic[0]);
   ++k;
   ay[k] = azmul(2.0, adynamic[0]);
   ++k;
   // if dynamic[0] == 0.5 then ay[k] = 1.0 else ay[k] = -1.0
   ay[k] = CppAD::CondExpEq(
      adynamic[0], AD<double>(0.5), AD<double>(1.0), AD<double>(-1.0)
   );
   ++k;
   // ----------------------------------------------------------
   ok &= size_t(k) == ny;

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

   // change the dynamic parameter values
   CPPAD_TESTVECTOR(double) dynamic(nd);
   dynamic[0] = 0.75;
   f.new_dynamic(dynamic);
   //
   CPPAD_TESTVECTOR(double) x(nx), y(ny);
   y = f.Forward(0, x);
   k = 0;
   // ----------------------------------------------------------
   // 98 standard math
   double check = std::acos(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::asin(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::atan(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::cos(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::cosh(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::exp(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::acos(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::log(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::sin(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::sinh(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::sqrt(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::tan(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::tanh(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   // ----------------------------------------------------------
   // 2011 standard math
   check = asinh(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::acosh(dynamic[0] + 1.0);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::atanh(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::expm1(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::erf(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::log1p(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   // ----------------------------------------------------------
   // binary
   check = 2.0 + dynamic[0];
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = dynamic[0] / 2.0;
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = 2.0 * dynamic[0];
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = dynamic[0] - 2.0;
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   // ----------------------------------------------------------
   // other
   check = - dynamic[0];
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::fabs(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = std::pow(dynamic[0], 2.0);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = CppAD::sign(dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   check = azmul(2.0, dynamic[0]);
   ok   &= NearEqual(y[k], check, eps99, eps99);
   ++k;
   // if dynamic[0] == 0.5 then ay[k] = 1.0 else ay[k] = -1.0
   check = CppAD::CondExpEq(dynamic[0], 0.5, 1.0, -1.0);
   ++k;
   // ----------------------------------------------------------
   ok &= k == ny;
   //
   return ok;
}
// ----------------------------------------------------------------------------
bool dynamic_compare(void)
{  bool ok = true;
   using CppAD::AD;

   // independent dynamic parameter vector
   size_t nd  = 1;
   CPPAD_TESTVECTOR(AD<double>) adynamic(nd);

   // domain space vector
   size_t nx = 1;
   CPPAD_TESTVECTOR(AD<double>) ax(nx);
   ax[0] = 0.0; // value does not matter for this example;

   // range space vector
   size_t ny = 2;
   CPPAD_TESTVECTOR(AD<double>) ay(ny);

   // not using abort_op_index, are recording compare operators
   size_t abort_op_index = 0;
   bool   record_compare = true;

   // Function object
   CppAD::ADFun<double> f;

   // vectors used for new_dynamic and Forward.
   CPPAD_TESTVECTOR(double) dynamic(nd), x(nx), y(ny);

   // ----------------------------------------------------------
   // operators: ==, !=
   adynamic[0] = 0.5;
   CppAD::Independent(ax, abort_op_index, record_compare, adynamic);
   //
   // ==
   if( adynamic[0] == 0.5 )
      ay[0] = 1.0;
   else
      ay[0] = 0.0;
   //
   // !=
   if( adynamic[0] != 0.5 )
      ay[1] = 1.0;
   else
      ay[1] = 0.0;

   // create f: x -> y and stop tape recording
   f.Dependent(ax, ay);
   //
   dynamic[0] = Value( adynamic[0] );
   f.new_dynamic(dynamic);
   y  = f.Forward(0, x);
   ok = f.compare_change_number() == 0;
   //
   dynamic[0] = 1.0;
   f.new_dynamic(dynamic);
   y  = f.Forward(0, x);
   ok = f.compare_change_number() == 2;

   // ----------------------------------------------------------
   // operators: <, <=
   adynamic[0] = 0.5;
   CppAD::Independent(ax, abort_op_index, record_compare, adynamic);
   //
   // <
   if( adynamic[0] < 0.5 )
      ay[0] = 0.0;
   else
      ay[0] = 1.0;
   //
   // <=
   if( adynamic[0] <= 0.5 )
      ay[1] = 1.0;
   else
      ay[1] = 0.0;

   // create f: x -> y and stop tape recording
   f.Dependent(ax, ay);
   //
   dynamic[0] = Value( adynamic[0] );
   f.new_dynamic(dynamic);
   y  = f.Forward(0, x);
   ok = f.compare_change_number() == 0;
   //
   dynamic[0] = 1.0;
   f.new_dynamic(dynamic);
   y  = f.Forward(0, x);
   ok = f.compare_change_number() == 1;

   // ----------------------------------------------------------
   // operators: >, >=
   adynamic[0] = 0.5;
   CppAD::Independent(ax, abort_op_index, record_compare, adynamic);
   //
   // >
   if( adynamic[0] > 0.4 )
      ay[0] = 1.0;
   else
      ay[0] = 0.0;
   //
   // >=
   if( adynamic[0] >= 0.4 )
      ay[1] = 1.0;
   else
      ay[1] = 0.0;

   // create f: x -> y and stop tape recording
   f.Dependent(ax, ay);
   //
   dynamic[0] = Value( adynamic[0] );
   f.new_dynamic(dynamic);
   y  = f.Forward(0, x);
   ok = f.compare_change_number() == 0;
   //
   dynamic[0] = 0.3;
   f.new_dynamic(dynamic);
   y  = f.Forward(0, x);
   ok = f.compare_change_number() == 2;
   //
   // ----------------------------------------------------------
   return ok;
}
// ----------------------------------------------------------------------------
bool optimize_csum(void)
{  bool ok = true;
   using CppAD::AD;
   using CppAD::NearEqual;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

   // independent dynamic parameter vector
   size_t num_dyn_ind  = 2;
   CPPAD_TESTVECTOR(AD<double>) adynamic(num_dyn_ind);

   // domain space vector
   size_t nx = 1;
   CPPAD_TESTVECTOR(AD<double>) ax(nx);
   ax[0] = 0.0; // value does not matter for this example;

   // range space vector
   size_t ny = 2;
   CPPAD_TESTVECTOR(AD<double>) ay(ny);

   // not using abort_op_index, are recording compare operators
   size_t abort_op_index = 0;
   bool   record_compare = true;

   // Function object
   CppAD::ADFun<double> f;
   // ----------------------------------------------------------
   // record f
   adynamic[0] = 1.0;
   adynamic[1] = 2.0;
   CppAD::Independent(ax, abort_op_index, record_compare, adynamic);
   //
   // create three constant parameters that are only used in a cumulative
   // summation and will be optimized to just one constant parameter
   ay[0] = 3.0 - ax[0];
   ay[0] = ay[0] - 4.0;
   ay[0] = ay[0] + 5.0;
   //
   // create a dependent dynamic parameter that is not used
   AD<double> adp1 = adynamic[0] + adynamic[1];
   //
   // create a dependent dynamic parameter that is used
   AD<double> adp2 = adynamic[1] - adynamic[0];
   ay[1] = ax[0] + adp2;
   //
   // create f: x -> y and stop tape recording
   f.Dependent(ax, ay);
   ok &= f.size_dyn_ind() == num_dyn_ind;
   ok &= f.size_dyn_par() == num_dyn_ind + 2;
   // constant parameters: nan, 3.0, 4.0, 5.0
   ok &= f.size_par()     == num_dyn_ind + 2 + 4;
   // -------------------------------------------------------------
   // vectors used for new_dynamic and Forward.
   CPPAD_TESTVECTOR(double) dynamic(num_dyn_ind), x(nx), y(ny);
   dynamic[0] = 3.0;
   dynamic[1] = 4.0;
   f.new_dynamic(dynamic);
   x[0] = 5.0;
   y    = f.Forward(0, x);
   double check = 3.0 - x[0] - 4.0 + 5.0;
   ok   &= NearEqual(y[0], check, eps99, eps99);
   check = x[0] + dynamic[1] - dynamic[0];
   ok   &= NearEqual(y[1], check, eps99, eps99);
   // -------------------------------------------------------------
   // optimize and re-test
   f.optimize(); // add the zero parameter
   ok &= f.size_dyn_ind() == num_dyn_ind;
   ok &= f.size_dyn_par() == num_dyn_ind + 1;
   // constant parameters: nan, zero, (3.0 - 4.0 + 5.0)
   ok &= f.size_par()     == num_dyn_ind + 1 + 3;
   dynamic[0] = 0.3;
   dynamic[1] = 0.4;
   f.new_dynamic(dynamic);
   x[0] = 0.5;
   y    = f.Forward(0, x);
   check = 3.0 - x[0] - 4.0 + 5.0;
   ok   &= NearEqual(y[0], check, eps99, eps99);
   check = x[0] + dynamic[1] - dynamic[0];
   ok   &= NearEqual(y[1], check, eps99, eps99);
   //
   return ok;
}

// ----------------------------------------------------------------------------
typedef CPPAD_TESTVECTOR( CppAD::AD<double> )  ADvector;
void g_algo(const ADvector& ax, ADvector& ay)
{  ay[0] = ax[0] * ax[1];
}
bool dynamic_atomic(void)
{  bool ok = true;

   // checkpoint version of g(x) = x[0] * x[1];
   ADvector ax(2), ay(1);
   ax[0] = 2.0;
   ax[1] = 3.0;
   CppAD::checkpoint<double> atom_g("g_algo", g_algo, ax, ay);

   // record the function f(x) = dynamic[0] * dynamic[1]
   // using atom_g to compute the product
   ADvector adynamic(2);
   adynamic[0] = 1.0;
   adynamic[1] = 2.0;
   size_t abort_op_index = 0;
   bool   record_compare = true;
   Independent(ax, abort_op_index, record_compare, adynamic);
   atom_g(adynamic, ay);
   CppAD::ADFun<double> f(ax, ay);

   // change the dynamic parameter values
   CPPAD_TESTVECTOR(double) x(2), y(1), dynamic(2);
   dynamic[0] = 4.0;
   dynamic[1] = 5.0;
   f.new_dynamic(dynamic);

   // check zero order forward
   x[0] = std::numeric_limits<double>::quiet_NaN();
   x[1] = std::numeric_limits<double>::quiet_NaN();
   y    = f.Forward(0, x);
   ok  &= y[0] == dynamic[0] * dynamic[1];


   return ok;
}

// ----------------------------------------------------------------------------
double n_digits(const double& x)
{  double logx = std::log10(x);
   double ret  = floor(logx) + 1.0;
   return ret;
}
CPPAD_DISCRETE_FUNCTION(double, n_digits)
//
bool dynamic_discrete(void)
{  bool ok = true;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

   // record the function f(x) = x[0] * n_digits( dynamic[0] )
   ADvector ax(1);
   ax[0] = 2.0;
   ADvector adynamic(1);
   adynamic[0] = 3.0;
   size_t abort_op_index = 0;
   bool   record_compare = true;
   Independent(ax, abort_op_index, record_compare, adynamic);
   ADvector ay(1);
   ay[0] = ax[0] * n_digits( adynamic[0] );
   CppAD::ADFun<double> f(ax, ay);

   // change the dynamic parameter value to 14
   CPPAD_TESTVECTOR(double) x(1), y(1), dynamic(1);
   dynamic[0] = 14.0;
   f.new_dynamic(dynamic);

   // check zero order forward
   x[0] = 3.0;
   y    = f.Forward(0, x);
   ok  &= CppAD::NearEqual(y[0], x[0] * 2.0, eps99, eps99);

   return ok;
}
// ----------------------------------------------------------------------------
bool dynamic_optimize(void)
{  bool ok = true;
   using CppAD::AD;
   using CppAD::NearEqual;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

   // independent dynamic parameter vector
   size_t nd  = 1;
   CPPAD_TESTVECTOR(AD<double>) adynamic(nd);

   // domain space vector
   size_t nx = 1;
   CPPAD_TESTVECTOR(AD<double>) ax(nx);
   ax[0] = 0.0; // value does not matter for this example;

   // range space vector
   size_t ny = 2;
   CPPAD_TESTVECTOR(AD<double>) ay(ny);

   // not using abort_op_index, are recording compare operators
   size_t abort_op_index = 0;
   bool   record_compare = true;

   // Function object
   CppAD::ADFun<double> f;
   // ----------------------------------------------------------
   // record f
   adynamic[0] = 1.0;
   CppAD::Independent(ax, abort_op_index, record_compare, adynamic);
   //
   // Avoid cumulative summations because it adds constant parameters.
   // Use one constant parameter, namely 3.0.
   // Create five dynamic parameters where the second, fourth, and fifth,
   // should be optimized out.
   //
   // first extra dynamic parameter (also is in optimized tape)
   AD<double> first  = 3.0 + adynamic[0];
   //
   // second that is the same as first because addition is communative
   AD<double> second = adynamic[0] + 3.0;
   //
   // third extra dynamic parameter (also in optimized tape)
   AD<double> third  = first * first;
   //
   // fourth is same as third and uses second which gets optimized out
   AD<double> fourth = second * second;
   //
   // fifth is not used and so should be optimized out
   AD<double> fifth  = first / 3.0;
   //
   ay[0] = ax[0] + third;
   ay[1] = ax[0] * fourth;
   //
   // create f: x -> y and stop tape recording
   f.Dependent(ax, ay);
   ok &= f.size_dyn_ind() == nd;
   ok &= f.size_dyn_par() == nd + 5;
   // constant parameters: nan, 3.0
   ok &= f.size_par()     == nd + 5 + 2;
   // -------------------------------------------------------------
   // vectors used for new_dynamic and Forward.
   CPPAD_TESTVECTOR(double) dynamic(nd), x(nx), y(ny);
   dynamic[0] = 4.0;
   f.new_dynamic(dynamic);
   x[0] = 5.0;
   y    = f.Forward(0, x);
   double check = x[0] + (3.0 + dynamic[0] ) * (3.0 + dynamic[0]);
   ok   &= NearEqual(y[0], check, eps99, eps99);
   check = x[0] * (3.0 + dynamic[0] ) * (3.0 + dynamic[0]);
   ok   &= NearEqual(y[1], check, eps99, eps99);
   // -------------------------------------------------------------
   // optimize and re-test
   f.optimize(); // adds the zero parameter
   ok &= f.size_dyn_ind() == nd;
   ok &= f.size_dyn_par() == nd + 2;
   // constant parameters: nan, zero, 3.0
   ok &= f.size_par()     == nd + 2 + 3;
   dynamic[0] = 6.0;
   f.new_dynamic(dynamic);
   y     = f.Forward(0, x);
   check = x[0] + (3.0 + dynamic[0]) * (3.0 + dynamic[0]);
   ok   &= NearEqual(y[0], check, eps99, eps99);
   check = x[0] * (3.0 + dynamic[0]) * (3.0 + dynamic[0]);
   ok   &= NearEqual(y[1], check, eps99, eps99);
   //
   return ok;
}


} // END_EMPTY_NAMESPACE

// ----------------------------------------------------------------------------
bool new_dynamic(void)
{  bool ok = true;
   ok     &= pull_232();
   ok     &= vecad();
   ok     &= operator_with_variable();
   ok     &= dynamic_operator();
   ok     &= dynamic_compare();
   ok     &= optimize_csum();
   ok     &= dynamic_atomic();
   ok     &= dynamic_discrete();
   ok     &= dynamic_optimize();
   //
   return ok;
}
