libcomposition/build-config/cppad/include/cppad/local/exp_op.hpp

# ifndef CPPAD_LOCAL_EXP_OP_HPP
# define CPPAD_LOCAL_EXP_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 exp_op.hpp
Forward and reverse mode calculations for z = exp(x).
*/


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

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

\copydetails CppAD::local::forward_unary1_op
*/
template <class Base>
void forward_exp_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(ExpOp) == 1 );
    CPPAD_ASSERT_UNKNOWN( NumRes(ExpOp) == 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] = exp( 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));
    }
}


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

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

\copydetails CppAD::local::forward_unary1_op_dir
*/
template <class Base>
void forward_exp_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(ExpOp) == 1 );
    CPPAD_ASSERT_UNKNOWN( NumRes(ExpOp) == 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));
    }
}

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

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

\copydetails CppAD::local::forward_unary1_op_0
*/
template <class Base>
void forward_exp_op_0(
    size_t i_z         ,
    size_t i_x         ,
    size_t cap_order   ,
    Base*  taylor      )
{
    // check assumptions
    CPPAD_ASSERT_UNKNOWN( NumArg(ExpOp) == 1 );
    CPPAD_ASSERT_UNKNOWN( NumRes(ExpOp) == 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] = exp( x[0] );
}
/*!
Reverse mode partial derivatives for result of op = ExpOp.

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

\copydetails CppAD::local::reverse_unary1_op
*/

template <class Base>
void reverse_exp_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(ExpOp) == 1 );
    CPPAD_ASSERT_UNKNOWN( NumRes(ExpOp) == 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)
    {   // 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] += azmul(pz[0], z[0]);
}

} } // END_CPPAD_LOCAL_NAMESPACE
# endif