# ifndef CPPAD_LOCAL_OP_ASIN_OP_HPP
# define CPPAD_LOCAL_OP_ASIN_OP_HPP
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-21 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


// See dev documentation: forward_unary_op
template <class Base>
void forward_asin_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(AsinOp) == 1 );
    CPPAD_ASSERT_UNKNOWN( NumRes(AsinOp) == 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] = asin( 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_asin_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_asin_op_0(
    size_t i_z         ,
    size_t i_x         ,
    size_t cap_order   ,
    Base*  taylor      )
{
    // check assumptions
    CPPAD_ASSERT_UNKNOWN( NumArg(AsinOp) == 1 );
    CPPAD_ASSERT_UNKNOWN( NumRes(AsinOp) == 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] = asin( x[0] );
    b[0] = sqrt( Base(1.0) - x[0] * x[0] );
}

// See dev documentation: reverse_unary_op
template <class Base>
void reverse_asin_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(AsinOp) == 1 );
    CPPAD_ASSERT_UNKNOWN( NumRes(AsinOp) == 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
