/* $Id$ */
# ifndef CPPAD_MUL_OP_INCLUDED
# define CPPAD_MUL_OP_INCLUDED

/* --------------------------------------------------------------------------
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 mul_op.hpp
Forward and reverse mode calculations for z = x * y.
*/

// --------------------------- Mulvv -----------------------------------------
/*!
Compute forward mode Taylor coefficients for result of op = MulvvOp.

The C++ source code corresponding to this operation is
\verbatim
	z = x * y
\endverbatim
In the documentation below,
this operations is for the case where both x and y are variables
and the argument \a parameter is not used.

\copydetails forward_binary_op
*/

template <class Base>
inline void forward_mulvv_op(
	size_t        p           ,
	size_t        q           ,
	size_t        i_z         ,
	const addr_t* arg         ,
	const Base*   parameter   ,
	size_t        cap_order   ,
	Base*         taylor      )
{
	// check assumptions
	CPPAD_ASSERT_UNKNOWN( NumArg(MulvvOp) == 2 );
	CPPAD_ASSERT_UNKNOWN( NumRes(MulvvOp) == 1 );
	CPPAD_ASSERT_UNKNOWN( q < cap_order );
	CPPAD_ASSERT_UNKNOWN( p <= q );

	// Taylor coefficients corresponding to arguments and result
	Base* x = taylor + arg[0] * cap_order;
	Base* y = taylor + arg[1] * cap_order;
	Base* z = taylor + i_z    * cap_order;

	size_t k;
	for(size_t d = p; d <= q; d++)
	{	z[d] = Base(0);
		for(k = 0; k <= d; k++)
			z[d] += x[d-k] * y[k];
	}
}
/*!
Multiple directions forward mode Taylor coefficients for op = MulvvOp.

The C++ source code corresponding to this operation is
\verbatim
	z = x * y
\endverbatim
In the documentation below,
this operations is for the case where both x and y are variables
and the argument \a parameter is not used.

\copydetails forward_binary_op_dir
*/

template <class Base>
inline void forward_mulvv_op_dir(
	size_t        q           ,
	size_t        r           ,
	size_t        i_z         ,
	const addr_t* arg         ,
	const Base*   parameter   ,
	size_t        cap_order   ,
	Base*         taylor      )
{
	// check assumptions
	CPPAD_ASSERT_UNKNOWN( NumArg(MulvvOp) == 2 );
	CPPAD_ASSERT_UNKNOWN( NumRes(MulvvOp) == 1 );
	CPPAD_ASSERT_UNKNOWN( 0 < q );
	CPPAD_ASSERT_UNKNOWN( q < cap_order );

	// Taylor coefficients corresponding to arguments and result
	size_t num_taylor_per_var = (cap_order-1) * r + 1;
	Base* x = taylor + arg[0] * num_taylor_per_var;
	Base* y = taylor + arg[1] * num_taylor_per_var;
	Base* z = taylor +    i_z * num_taylor_per_var;

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

/*!
Compute zero order forward mode Taylor coefficients for result of op = MulvvOp.

The C++ source code corresponding to this operation is
\verbatim
	z = x * y
\endverbatim
In the documentation below,
this operations is for the case where both x and y are variables
and the argument \a parameter is not used.

\copydetails forward_binary_op_0
*/

template <class Base>
inline void forward_mulvv_op_0(
	size_t        i_z         ,
	const addr_t* arg         ,
	const Base*   parameter   ,
	size_t        cap_order   ,
	Base*         taylor      )
{
	// check assumptions
	CPPAD_ASSERT_UNKNOWN( NumArg(MulvvOp) == 2 );
	CPPAD_ASSERT_UNKNOWN( NumRes(MulvvOp) == 1 );

	// Taylor coefficients corresponding to arguments and result
	Base* x = taylor + arg[0] * cap_order;
	Base* y = taylor + arg[1] * cap_order;
	Base* z = taylor + i_z    * cap_order;

	z[0] = x[0] * y[0];
}

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

The C++ source code corresponding to this operation is
\verbatim
	z = x * y
\endverbatim
In the documentation below,
this operations is for the case where both x and y are variables
and the argument \a parameter is not used.

\copydetails reverse_binary_op
*/

template <class Base>
inline void reverse_mulvv_op(
	size_t        d           ,
	size_t        i_z         ,
	const addr_t* arg         ,
	const Base*   parameter   ,
	size_t        cap_order   ,
	const Base*   taylor      ,
	size_t        nc_partial  ,
	Base*         partial     )
{
	// check assumptions
	CPPAD_ASSERT_UNKNOWN( NumArg(MulvvOp) == 2 );
	CPPAD_ASSERT_UNKNOWN( NumRes(MulvvOp) == 1 );
	CPPAD_ASSERT_UNKNOWN( d < cap_order );
	CPPAD_ASSERT_UNKNOWN( d < nc_partial );

	// Arguments
	const Base* x  = taylor + arg[0] * cap_order;
	const Base* y  = taylor + arg[1] * cap_order;

	// Partial derivatives corresponding to arguments and result
	Base* px = partial + arg[0] * nc_partial;
	Base* py = partial + arg[1] * nc_partial;
	Base* pz = partial + i_z    * nc_partial;

	// If pz is zero, make sure this operation has no effect
	// (zero times infinity or nan would be non-zero).
	bool skip(true);
	for(size_t i_d = 0; i_d <= d; i_d++)
		skip &= IdenticalZero(pz[i_d]);
	if( skip )
		return;

	// number of indices to access
	size_t j = d + 1;
	size_t k;
	while(j)
	{	--j;
		for(k = 0; k <= j; k++)
		{
			px[j-k] += pz[j] * y[k];
			py[k]   += pz[j] * x[j-k];
		}
	}
}
// --------------------------- Mulpv -----------------------------------------
/*!
Compute forward mode Taylor coefficients for result of op = MulpvOp.

The C++ source code corresponding to this operation is
\verbatim
	z = x * y
\endverbatim
In the documentation below,
this operations is for the case where x is a parameter and y is a variable.

\copydetails forward_binary_op
*/

template <class Base>
inline void forward_mulpv_op(
	size_t        p           ,
	size_t        q           ,
	size_t        i_z         ,
	const addr_t* arg         ,
	const Base*   parameter   ,
	size_t        cap_order   ,
	Base*         taylor      )
{
	// check assumptions
	CPPAD_ASSERT_UNKNOWN( NumArg(MulpvOp) == 2 );
	CPPAD_ASSERT_UNKNOWN( NumRes(MulpvOp) == 1 );
	CPPAD_ASSERT_UNKNOWN( q < cap_order );
	CPPAD_ASSERT_UNKNOWN( p <= q );

	// Taylor coefficients corresponding to arguments and result
	Base* y = taylor + arg[1] * cap_order;
	Base* z = taylor + i_z    * cap_order;

	// Paraemter value
	Base x = parameter[ arg[0] ];

	for(size_t d = p; d <= q; d++)
		z[d] = x * y[d];
}
/*!
Multiple directions forward mode Taylor coefficients for op = MulpvOp.

The C++ source code corresponding to this operation is
\verbatim
	z = x * y
\endverbatim
In the documentation below,
this operations is for the case where x is a parameter and y is a variable.

\copydetails forward_binary_op_dir
*/

template <class Base>
inline void forward_mulpv_op_dir(
	size_t        q           ,
	size_t        r           ,
	size_t        i_z         ,
	const addr_t* arg         ,
	const Base*   parameter   ,
	size_t        cap_order   ,
	Base*         taylor      )
{
	// check assumptions
	CPPAD_ASSERT_UNKNOWN( NumArg(MulpvOp) == 2 );
	CPPAD_ASSERT_UNKNOWN( NumRes(MulpvOp) == 1 );
	CPPAD_ASSERT_UNKNOWN( 0 < q );
	CPPAD_ASSERT_UNKNOWN( q < cap_order );

	// Taylor coefficients corresponding to arguments and result
	size_t num_taylor_per_var = (cap_order-1) * r + 1;
	size_t m                  = (q-1) * r + 1;
	Base* y = taylor + arg[1] * num_taylor_per_var + m;
	Base* z = taylor + i_z    * num_taylor_per_var + m;

	// Paraemter value
	Base x = parameter[ arg[0] ];

	for(size_t ell = 0; ell < r; ell++)
		z[ell] = x * y[ell];
}
/*!
Compute zero order forward mode Taylor coefficient for result of op = MulpvOp.

The C++ source code corresponding to this operation is
\verbatim
	z = x * y
\endverbatim
In the documentation below,
this operations is for the case where x is a parameter and y is a variable.

\copydetails forward_binary_op_0
*/

template <class Base>
inline void forward_mulpv_op_0(
	size_t        i_z         ,
	const addr_t* arg         ,
	const Base*   parameter   ,
	size_t        cap_order   ,
	Base*         taylor      )
{
	// check assumptions
	CPPAD_ASSERT_UNKNOWN( NumArg(MulpvOp) == 2 );
	CPPAD_ASSERT_UNKNOWN( NumRes(MulpvOp) == 1 );

	// Paraemter value
	Base x = parameter[ arg[0] ];

	// Taylor coefficients corresponding to arguments and result
	Base* y = taylor + arg[1] * cap_order;
	Base* z = taylor + i_z    * cap_order;

	z[0] = x * y[0];
}

/*!
Compute reverse mode partial derivative for result of op = MulpvOp.

The C++ source code corresponding to this operation is
\verbatim
	z = x * y
\endverbatim
In the documentation below,
this operations is for the case where x is a parameter and y is a variable.

\copydetails reverse_binary_op
*/

template <class Base>
inline void reverse_mulpv_op(
	size_t        d           ,
	size_t        i_z         ,
	const addr_t* arg         ,
	const Base*   parameter   ,
	size_t        cap_order   ,
	const Base*   taylor      ,
	size_t        nc_partial  ,
	Base*         partial     )
{
	// check assumptions
	CPPAD_ASSERT_UNKNOWN( NumArg(MulpvOp) == 2 );
	CPPAD_ASSERT_UNKNOWN( NumRes(MulpvOp) == 1 );
	CPPAD_ASSERT_UNKNOWN( d < cap_order );
	CPPAD_ASSERT_UNKNOWN( d < nc_partial );

	// Arguments
	Base x  = parameter[ arg[0] ];

	// Partial derivatives corresponding to arguments and result
	Base* py = partial + arg[1] * nc_partial;
	Base* pz = partial + i_z    * nc_partial;

	// number of indices to access
	size_t j = d + 1;
	while(j)
	{	--j;
		py[j] += pz[j] * x;
	}
}


} // END_CPPAD_NAMESPACE
# endif
