/usr/include/cppad/local/cos_op.hpp is in cppad 2017.00.00.4-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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# ifndef CPPAD_LOCAL_COS_OP_HPP
# define CPPAD_LOCAL_COS_OP_HPP
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 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 { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE
/*!
\file cos_op.hpp
Forward and reverse mode calculations for z = cos(x).
*/
/*!
Compute forward mode Taylor coefficient for result of op = CosOp.
The C++ source code corresponding to this operation is
\verbatim
z = cos(x)
\endverbatim
The auxillary result is
\verbatim
y = sin(x)
\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_cos_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(CosOp) == 1 );
CPPAD_ASSERT_UNKNOWN( NumRes(CosOp) == 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* c = taylor + i_z * cap_order;
Base* s = c - cap_order;
// rest of this routine is identical for the following cases:
// forward_sin_op, forward_cos_op, forward_sinh_op, forward_cosh_op.
// (except that there is a sign difference for the hyperbolic case).
size_t k;
if( p == 0 )
{ s[0] = sin( x[0] );
c[0] = cos( x[0] );
p++;
}
for(size_t j = p; j <= q; j++)
{
s[j] = Base(0);
c[j] = Base(0);
for(k = 1; k <= j; k++)
{ s[j] += Base(k) * x[k] * c[j-k];
c[j] -= Base(k) * x[k] * s[j-k];
}
s[j] /= Base(j);
c[j] /= Base(j);
}
}
/*!
Compute forward mode Taylor coefficient for result of op = CosOp.
The C++ source code corresponding to this operation is
\verbatim
z = cos(x)
\endverbatim
The auxillary result is
\verbatim
y = sin(x)
\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_cos_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(CosOp) == 1 );
CPPAD_ASSERT_UNKNOWN( NumRes(CosOp) == 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* c = taylor + i_z * num_taylor_per_var;
Base* s = c - num_taylor_per_var;
// rest of this routine is identical for the following cases:
// forward_sin_op, forward_cos_op, forward_sinh_op, forward_cosh_op
// (except that there is a sign difference for the hyperbolic case).
size_t m = (q-1) * r + 1;
for(size_t ell = 0; ell < r; ell++)
{ s[m+ell] = Base(q) * x[m + ell] * c[0];
c[m+ell] = - Base(q) * x[m + ell] * s[0];
for(size_t k = 1; k < q; k++)
{ s[m+ell] += Base(k) * x[(k-1)*r+1+ell] * c[(q-k-1)*r+1+ell];
c[m+ell] -= Base(k) * x[(k-1)*r+1+ell] * s[(q-k-1)*r+1+ell];
}
s[m+ell] /= Base(q);
c[m+ell] /= Base(q);
}
}
/*!
Compute zero order forward mode Taylor coefficient for result of op = CosOp.
The C++ source code corresponding to this operation is
\verbatim
z = cos(x)
\endverbatim
The auxillary result is
\verbatim
y = sin(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_cos_op_0(
size_t i_z ,
size_t i_x ,
size_t cap_order ,
Base* taylor )
{
// check assumptions
CPPAD_ASSERT_UNKNOWN( NumArg(CosOp) == 1 );
CPPAD_ASSERT_UNKNOWN( NumRes(CosOp) == 2 );
CPPAD_ASSERT_UNKNOWN( 0 < cap_order );
// Taylor coefficients corresponding to argument and result
Base* x = taylor + i_x * cap_order;
Base* c = taylor + i_z * cap_order; // called z in documentation
Base* s = c - cap_order; // called y in documentation
c[0] = cos( x[0] );
s[0] = sin( x[0] );
}
/*!
Compute reverse mode partial derivatives for result of op = CosOp.
The C++ source code corresponding to this operation is
\verbatim
z = cos(x)
\endverbatim
The auxillary result is
\verbatim
y = sin(x)
\endverbatim
The value of y is computed along with the value of z.
\copydetails reverse_unary2_op
*/
template <class Base>
inline void reverse_cos_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(CosOp) == 1 );
CPPAD_ASSERT_UNKNOWN( NumRes(CosOp) == 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* c = taylor + i_z * cap_order; // called z in doc
Base* pc = partial + i_z * nc_partial;
// Taylor coefficients and partials corresponding to auxillary result
const Base* s = c - cap_order; // called y in documentation
Base* ps = pc - nc_partial;
// rest of this routine is identical for the following cases:
// reverse_sin_op, reverse_cos_op, reverse_sinh_op, reverse_cosh_op.
size_t j = d;
size_t k;
while(j)
{
ps[j] /= Base(j);
pc[j] /= Base(j);
for(k = 1; k <= j; k++)
{
px[k] += Base(k) * azmul(ps[j], c[j-k]);
px[k] -= Base(k) * azmul(pc[j], s[j-k]);
ps[j-k] -= Base(k) * azmul(pc[j], x[k]);
pc[j-k] += Base(k) * azmul(ps[j], x[k]);
}
--j;
}
px[0] += azmul(ps[0], c[0]);
px[0] -= azmul(pc[0], s[0]);
}
} } // END_CPPAD_LOCAL_NAMESPACE
# endif
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