// $Id: tan_op.hpp 3757 2015-11-30 12:03:07Z bradbell $
# ifndef CPPAD_TAN_OP_HPP
# define CPPAD_TAN_OP_HPP

/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the
                    GNU General Public License Version 3.

A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */


namespace CppAD { // BEGIN_CPPAD_NAMESPACE
/*!
\file tan_op.hpp
Forward and reverse mode calculations for z = tan(x).
*/


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

The C++ source code corresponding to this operation is
\verbatim
	z = tan(x)
\endverbatim
The auxillary result is
\verbatim
	y = tan(x)^2
\endverbatim
The value of y, and its derivatives, are computed along with the value
and derivatives of z.

\copydetails forward_unary2_op
*/
template <class Base>
inline void forward_tan_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(TanOp) == 1 );
	CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 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* y = z      -       cap_order;

	size_t k;
	if( p == 0 )
	{	z[0] = tan( x[0] );
		y[0] = z[0] * z[0];
		p++;
	}
	for(size_t j = p; j <= q; j++)
	{	Base base_j = static_cast<Base>(j);

		z[j] = x[j];
		for(k = 1; k <= j; k++)
			z[j] += Base(k) * x[k] * y[j-k] / base_j;

		y[j] = z[0] * z[j];
		for(k = 1; k <= j; k++)
			y[j] += z[k] * z[j-k];
	}
}

/*!
Multiple directions forward mode Taylor coefficient for op = TanOp.

The C++ source code corresponding to this operation is
\verbatim
	z = tan(x)
\endverbatim
The auxillary result is
\verbatim
	y = tan(x)^2
\endverbatim
The value of y, and its derivatives, are computed along with the value
and derivatives of z.

\copydetails forward_unary2_op_dir
*/
template <class Base>
inline void forward_tan_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(TanOp) == 1 );
	CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 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* y = z      -       num_taylor_per_var;

	size_t k;
	size_t m = (q-1) * r + 1;
	for(size_t ell = 0; ell < r; ell++)
	{	z[m+ell] = Base(q) * ( x[m+ell] + x[m+ell] * y[0]);
		for(k = 1; k < q; k++)
			z[m+ell] +=  Base(k) * x[(k-1)*r+1+ell] * y[(q-k-1)*r+1+ell];
		z[m+ell] /= Base(q);
		//
		y[m+ell] = Base(2) * z[m+ell] * z[0];
		for(k = 1; k < q; k++)
			y[m+ell] += z[(k-1)*r+1+ell] * z[(q-k-1)*r+1+ell];
	}
}


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

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

\copydetails forward_unary2_op_0
*/
template <class Base>
inline void forward_tan_op_0(
	size_t i_z         ,
	size_t i_x         ,
	size_t cap_order   ,
	Base*  taylor      )
{
	// check assumptions
	CPPAD_ASSERT_UNKNOWN( NumArg(TanOp) == 1 );
	CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 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;  // called z in documentation
	Base* y = z      -       cap_order;  // called y in documentation

	z[0] = tan( x[0] );
	y[0] = z[0] * z[0];
}

/*!
Compute reverse mode partial derivatives for result of op = TanOp.

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

\copydetails reverse_unary2_op
*/

template <class Base>
inline void reverse_tan_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(TanOp) == 1 );
	CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 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; // called z in doc
	Base* pz       = partial + i_z * nc_partial;

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


	size_t j = d;
	size_t k;
	Base base_two(2);
	while(j)
	{
		px[j]   += pz[j];
		pz[j]   /= Base(j);
		for(k = 1; k <= j; k++)
		{	px[k]   += azmul(pz[j], y[j-k]) * Base(k);
			py[j-k] += azmul(pz[j], x[k]) * Base(k);
		}
		for(k = 0; k < j; k++)
			pz[k] += azmul(py[j-1], z[j-k-1]) * base_two;

		--j;
	}
	px[0] += azmul(pz[0], Base(1) + y[0]);
}

} // END_CPPAD_NAMESPACE
# endif
