# ifndef CPPAD_LOCAL_OP_ACOS_OP_HPP
# define CPPAD_LOCAL_OP_ACOS_OP_HPP
// 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
// ----------------------------------------------------------------------------


namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE


// See dev documentation: forward_unary_op
template <class Base>
void forward_acos_op(
   size_t p           ,
   size_t q           ,
   size_t i_z         ,
   size_t i_x         ,
   size_t cap_order   ,
   Base*  taylor      )
{
   // check assumptions
   CPPAD_ASSERT_UNKNOWN( NumArg(AcosOp) == 1 );
   CPPAD_ASSERT_UNKNOWN( NumRes(AcosOp) == 2 );
   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;
   Base* b = z      -       cap_order;  // called y in documentation

   size_t k;
   Base uj;
   if( p == 0 )
   {  z[0] = acos( x[0] );
      uj   = Base(1.0) - x[0] * x[0];
      b[0] = sqrt( uj );
      p++;
   }
   for(size_t j = p; j <= q; j++)
   {  uj = Base(0.0);
      for(k = 0; k <= j; k++)
         uj -= x[k] * x[j-k];
      b[j] = Base(0.0);
      z[j] = Base(0.0);
      for(k = 1; k < j; k++)
      {  b[j] -= Base(double(k)) * b[k] * b[j-k];
         z[j] -= Base(double(k)) * z[k] * b[j-k];
      }
      b[j] /= Base(double(j));
      z[j] /= Base(double(j));
      //
      b[j] += uj / Base(2.0);
      z[j] -= x[j];
      //
      b[j] /= b[0];
      z[j] /= b[0];
   }
}
// See dev documentation: forward_unary_op
template <class Base>
void forward_acos_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(AcosOp) == 1 );
   CPPAD_ASSERT_UNKNOWN( NumRes(AcosOp) == 2 );
   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;
   Base* b = z - num_taylor_per_var;  // called y in documentation

   size_t k, ell;
   size_t m = (q-1) * r + 1;
   for(ell = 0; ell < r; ell ++)
   {  Base uq = - 2.0 * x[m + ell] * x[0];
      for(k = 1; k < q; k++)
         uq -= x[(k-1)*r+1+ell] * x[(q-k-1)*r+1+ell];
      b[m+ell] = Base(0.0);
      z[m+ell] = Base(0.0);
      for(k = 1; k < q; k++)
      {  b[m+ell] += Base(double(k)) * b[(k-1)*r+1+ell] * b[(q-k-1)*r+1+ell];
         z[m+ell] += Base(double(k)) * z[(k-1)*r+1+ell] * b[(q-k-1)*r+1+ell];
      }
      b[m+ell] =  ( uq / Base(2.0) - b[m+ell] / Base(double(q)) ) / b[0];
      z[m+ell] = -( x[m+ell]     + z[m+ell] / Base(double(q)) ) / b[0];
   }
}

// See dev documentation: forward_unary_op
template <class Base>
void forward_acos_op_0(
   size_t i_z         ,
   size_t i_x         ,
   size_t cap_order   ,
   Base*  taylor      )
{
   // check assumptions
   CPPAD_ASSERT_UNKNOWN( NumArg(AcosOp) == 1 );
   CPPAD_ASSERT_UNKNOWN( NumRes(AcosOp) == 2 );
   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;
   Base* b = z      -       cap_order; // called y in documentation

   z[0] = acos( x[0] );
   b[0] = sqrt( Base(1.0) - x[0] * x[0] );
}

// See dev documentation: reverse_unary_op
template <class Base>
void reverse_acos_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      )
{
   // check assumptions
   CPPAD_ASSERT_UNKNOWN( NumArg(AcosOp) == 1 );
   CPPAD_ASSERT_UNKNOWN( NumRes(AcosOp) == 2 );
   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 first result
   const Base* z  = taylor  + i_z * cap_order;
   Base* pz       = partial + i_z * nc_partial;

   // Taylor coefficients and partials corresponding to auxillary result
   const Base* b  = z  - cap_order; // called y in documentation
   Base* pb       = pz - nc_partial;

   Base inv_b0 = Base(1.0) / b[0];

   // number of indices to access
   size_t j = d;
   size_t k;
   while(j)
   {
      // scale partials w.r.t b[j] by 1 / b[0]
      pb[j]  = azmul(pb[j], inv_b0);

      // scale partials w.r.t z[j] by 1 / b[0]
      pz[j]  = azmul(pz[j], inv_b0);

      // update partials w.r.t b^0
      pb[0] -= azmul(pz[j], z[j]) + azmul(pb[j], b[j]);

      // update partial w.r.t. x^0
      px[0] -= azmul(pb[j], x[j]);

      // update partial w.r.t. x^j
      px[j] -= pz[j] + azmul(pb[j], x[0]);

      // further scale partial w.r.t. z[j] by 1 / j
      pz[j] /= Base(double(j));

      for(k = 1; k < j; k++)
      {  // update partials w.r.t b^(j-k)
         pb[j-k] -= Base(double(k)) * azmul(pz[j], z[k]) + azmul(pb[j], b[k]);

         // update partials w.r.t. x^k
         px[k]   -= azmul(pb[j], x[j-k]);

         // update partials w.r.t. z^k
         pz[k]   -= Base(double(k)) * azmul(pz[j], b[j-k]);
      }
      --j;
   }

   // j == 0 case
   px[0] -= azmul( pz[0] + azmul(pb[0], x[0]), inv_b0);
}

} } // END_CPPAD_LOCAL_NAMESPACE
# endif
