sunnypilot/external/cppad/include/cppad/local/expm1_op.hpp

# ifndef CPPAD_LOCAL_EXPM1_OP_HPP
# define CPPAD_LOCAL_EXPM1_OP_HPP
# if CPPAD_USE_CPLUSPLUS_2011

/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the
                    Eclipse Public License Version 1.0.

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 { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE
/*!
\file expm1_op.hpp
Forward and reverse mode calculations for z = expm1(x).
*/


/*!
Forward mode Taylor coefficient for result of op = Expm1Op.

The C++ source code corresponding to this operation is
\verbatim
	z = expm1(x)
\endverbatim

\copydetails CppAD::local::forward_unary1_op
*/
template <class Base>
inline void forward_expm1_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(Expm1Op) == 1 );
	CPPAD_ASSERT_UNKNOWN( NumRes(Expm1Op) == 1 );
	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;

	size_t k;
	if( p == 0 )
	{	z[0] = expm1( x[0] );
		p++;
	}
	for(size_t j = p; j <= q; j++)
	{
		z[j] = x[1] * z[j-1];
		for(k = 2; k <= j; k++)
			z[j] += Base(double(k)) * x[k] * z[j-k];
		z[j] /= Base(double(j));
		z[j] += x[j];
	}
}


/*!
Multiple direction forward mode Taylor coefficient for op = Expm1Op.

The C++ source code corresponding to this operation is
\verbatim
	z = expm1(x)
\endverbatim

\copydetails CppAD::local::forward_unary1_op_dir
*/
template <class Base>
inline void forward_expm1_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(Expm1Op) == 1 );
	CPPAD_ASSERT_UNKNOWN( NumRes(Expm1Op) == 1 );
	CPPAD_ASSERT_UNKNOWN( q < cap_order );
	CPPAD_ASSERT_UNKNOWN( 0 < q );

	// 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;

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

/*!
Zero order forward mode Taylor coefficient for result of op = Expm1Op.

The C++ source code corresponding to this operation is
\verbatim
	z = expm1(x)
\endverbatim

\copydetails CppAD::local::forward_unary1_op_0
*/
template <class Base>
inline void forward_expm1_op_0(
	size_t i_z         ,
	size_t i_x         ,
	size_t cap_order   ,
	Base*  taylor      )
{
	// check assumptions
	CPPAD_ASSERT_UNKNOWN( NumArg(Expm1Op) == 1 );
	CPPAD_ASSERT_UNKNOWN( NumRes(Expm1Op) == 1 );
	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;

	z[0] = expm1( x[0] );
}
/*!
Reverse mode partial derivatives for result of op = Expm1Op.

The C++ source code corresponding to this operation is
\verbatim
	z = expm1(x)
\endverbatim

\copydetails CppAD::local::reverse_unary1_op
*/

template <class Base>
inline void reverse_expm1_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(Expm1Op) == 1 );
	CPPAD_ASSERT_UNKNOWN( NumRes(Expm1Op) == 1 );
	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 result
	const Base* z  = taylor  + i_z * cap_order;
	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;

	// loop through orders in reverse
	size_t j, k;
	j = d;
	while(j)
	{	px[j] += pz[j];

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

		for(k = 1; k <= j; k++)
		{	px[k]   += Base(double(k)) * azmul(pz[j], z[j-k]);
			pz[j-k] += Base(double(k)) * azmul(pz[j], x[k]);
		}
		--j;
	}
	px[0] += pz[0] + azmul(pz[0], z[0]);
}

} } // END_CPPAD_LOCAL_NAMESPACE
# endif
# endif