text: # ifndef CPPAD_LOCAL_LOG_OP_HPP
  # define CPPAD_LOCAL_LOG_OP_HPP
  /* --------------------------------------------------------------------------
  CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell
  
  CppAD is distributed under the terms of the
               Eclipse Public License Version 2.0.
  
  This Source Code may also be made available under the following
  Secondary License when the conditions for such availability set forth
  in the Eclipse Public License, Version 2.0 are satisfied:
        GNU General Public License, Version 2.0 or later.
  ---------------------------------------------------------------------------- */
  
  namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE
  /*!
  \file log_op.hpp
  Forward and reverse mode calculations for z = log(x).
  */
  
  /*!
  Compute forward mode Taylor coefficient for result of op = LogOp.
  
  The C++ source code corresponding to this operation is
  \verbatim
      z = log(x)
  \endverbatim
  
  \copydetails CppAD::local::forward_unary1_op
  */
  template <class Base>
  void forward_log_op(
      size_t p           ,
      size_t q           ,
      size_t i_z         ,
      size_t i_x         ,
      size_t cap_order   ,
      Base*  taylor      )
  {
      size_t k;
  
      // check assumptions
      CPPAD_ASSERT_UNKNOWN( NumArg(LogOp) == 1 );
      CPPAD_ASSERT_UNKNOWN( NumRes(LogOp) == 1 );
      CPPAD_ASSERT_UNKNOWN( q < cap_order );
      CPPAD_ASSERT_UNKNOWN( p <= q );
  
      // Taylor coefficients corresponding to argument and result
      Base* x = taylor + i_x * cap_order;
      Base* z = taylor + i_z * cap_order;
  
      if( p == 0 )
      {   z[0] = log( x[0] );
          p++;
          if( q == 0 )
              return;
      }
      if ( p == 1 )
      {   z[1] = x[1] / x[0];
          p++;
      }
      for(size_t j = p; j <= q; j++)
      {
          z[j] = -z[1] * x[j-1];
          for(k = 2; k < j; k++)
              z[j] -= Base(double(k)) * z[k] * x[j-k];
          z[j] /= Base(double(j));
          z[j] += x[j];
          z[j] /= x[0];
      }
  }
  
  /*!
  Muiltiple directions Taylor coefficient for op = LogOp.
  
  The C++ source code corresponding to this operation is
  \verbatim
      z = log(x)
  \endverbatim
  
  \copydetails CppAD::local::forward_unary1_op_dir
  */
  template <class Base>
  void forward_log_op_dir(
      size_t q           ,
      size_t r           ,
      size_t i_z         ,
      size_t i_x         ,
      size_t cap_order   ,
      Base*  taylor      )
  {
  
      // check assumptions
      CPPAD_ASSERT_UNKNOWN( NumArg(LogOp) == 1 );
      CPPAD_ASSERT_UNKNOWN( NumRes(LogOp) == 1 );
      CPPAD_ASSERT_UNKNOWN( 0 < q );
      CPPAD_ASSERT_UNKNOWN( q < cap_order );
  
      // Taylor coefficients corresponding to argument and result
      size_t num_taylor_per_var = (cap_order-1) * r + 1;
      Base* x = taylor + i_x * num_taylor_per_var;
      Base* z = taylor + i_z * num_taylor_per_var;
  
      size_t m = (q-1) * r + 1;
      for(size_t ell = 0; ell < r; ell++)
      {   z[m+ell] = Base(double(q)) * x[m+ell];
          for(size_t k = 1; k < q; k++)
              z[m+ell] -= Base(double(k)) * z[(k-1)*r+1+ell] * x[(q-k-1)*r+1+ell];
          z[m+ell] /= (Base(double(q)) * x[0]);
      }
  }
  
  /*!
  Compute zero order forward mode Taylor coefficient for result of op = LogOp.
  
  The C++ source code corresponding to this operation is
  \verbatim
      z = log(x)
  \endverbatim
  
  \copydetails CppAD::local::forward_unary1_op_0
  */
  template <class Base>
  void forward_log_op_0(
      size_t i_z         ,
      size_t i_x         ,
      size_t cap_order   ,
      Base*  taylor      )
  {
  
      // check assumptions
      CPPAD_ASSERT_UNKNOWN( NumArg(LogOp) == 1 );
      CPPAD_ASSERT_UNKNOWN( NumRes(LogOp) == 1 );
      CPPAD_ASSERT_UNKNOWN( 0 < cap_order );
  
      // Taylor coefficients corresponding to argument and result
      Base* x = taylor + i_x * cap_order;
      Base* z = taylor + i_z * cap_order;
  
      z[0] = log( x[0] );
  }
  
  /*!
  Compute reverse mode partial derivatives for result of op = LogOp.
  
  The C++ source code corresponding to this operation is
  \verbatim
      z = log(x)
  \endverbatim
  
  \copydetails CppAD::local::reverse_unary1_op
  */
  
  template <class Base>
  void reverse_log_op(
      size_t      d            ,
      size_t      i_z          ,
      size_t      i_x          ,
      size_t      cap_order    ,
      const Base* taylor       ,
      size_t      nc_partial   ,
      Base*       partial      )
  {   size_t j, k;
  
      // check assumptions
      CPPAD_ASSERT_UNKNOWN( NumArg(LogOp) == 1 );
      CPPAD_ASSERT_UNKNOWN( NumRes(LogOp) == 1 );
      CPPAD_ASSERT_UNKNOWN( d < cap_order );
      CPPAD_ASSERT_UNKNOWN( d < nc_partial );
  
      // Taylor coefficients and partials corresponding to argument
      const Base* x  = taylor  + i_x * cap_order;
      Base* px       = partial + i_x * nc_partial;
  
      // Taylor coefficients and partials corresponding to result
      const Base* z  = taylor  + i_z * cap_order;
      Base* pz       = partial + i_z * nc_partial;
  
      Base inv_x0 = Base(1.0) / x[0];
  
      j = d;
      while(j)
      {   // scale partial w.r.t z[j]
          pz[j]   = azmul(pz[j]   , inv_x0);
  
          px[0]   -= azmul(pz[j], z[j]);
          px[j]   += pz[j];
  
          // further scale partial w.r.t. z[j]
          pz[j]   /= Base(double(j));
  
          for(k = 1; k < j; k++)
          {   pz[k]   -= Base(double(k)) * azmul(pz[j], x[j-k]);
              px[j-k] -= Base(double(k)) * azmul(pz[j], z[k]);
          }
          --j;
      }
      px[0] += azmul(pz[0], inv_x0);
  }
  
  } } // END_CPPAD_LOCAL_NAMESPACE
  # endif
  