# ifndef CPPAD_LOCAL_ACOS_OP_HPP
# define CPPAD_LOCAL_ACOS_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 acos_op.hpp
Forward and reverse mode calculations for z = acos(x).
*/


/*!
Compute forward mode Taylor coefficient for result of op = AcosOp.

The C++ source code corresponding to this operation is
\verbatim
    z = acos(x)
\endverbatim
The auxillary result is
\verbatim
    y = sqrt(1 - x * x)
\endverbatim
The value of y, and its derivatives, are computed along with the value
and derivatives of z.

\copydetails CppAD::local::forward_unary2_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];
    }
}
/*!
Multiple directions forward mode Taylor coefficient for op = AcosOp.

The C++ source code corresponding to this operation is
\verbatim
    z = acos(x)
\endverbatim
The auxillary result is
\verbatim
    y = sqrt(1 - x * x)
\endverbatim
The value of y, and its derivatives, are computed along with the value
and derivatives of z.

\copydetails CppAD::local::forward_unary2_op_dir
*/
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];
    }
}

/*!
Compute zero order forward mode Taylor coefficient for result of op = AcosOp.

The C++ source code corresponding to this operation is
\verbatim
    z = acos(x)
\endverbatim
The auxillary result is
\verbatim
    y = sqrt( 1 - x * x )
\endverbatim
The value of y is computed along with the value of z.

\copydetails CppAD::local::forward_unary2_op_0
*/
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] );
}
/*!
Compute reverse mode partial derivatives for result of op = AcosOp.

The C++ source code corresponding to this operation is
\verbatim
    z = acos(x)
\endverbatim
The auxillary result is
\verbatim
    y = sqrt( 1 - x * x )
\endverbatim
The value of y is computed along with the value of z.

\copydetails CppAD::local::reverse_unary2_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
