/usr/include/cppad/local/sin_op.hpp is in cppad 2014.00.00.3-1.
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_SIN_OP_INCLUDED
# define CPPAD_SIN_OP_INCLUDED
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-13 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
/*!
\defgroup sin_op_hpp sin_op.hpp
\{
\file sin_op.hpp
Forward and reverse mode calculations for z = sin(x).
*/
/*!
Compute forward mode Taylor coefficient for result of op = SinOp.
The C++ source code corresponding to this operation is
\verbatim
z = sin(x)
\endverbatim
The auxillary result is
\verbatim
y = cos(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_sin_op(
size_t q ,
size_t p ,
size_t i_z ,
size_t i_x ,
size_t nc_taylor ,
Base* taylor )
{
// check assumptions
CPPAD_ASSERT_UNKNOWN( NumArg(SinOp) == 1 );
CPPAD_ASSERT_UNKNOWN( NumRes(SinOp) == 2 );
CPPAD_ASSERT_UNKNOWN( i_x + 1 < i_z );
CPPAD_ASSERT_UNKNOWN( p < nc_taylor );
CPPAD_ASSERT_UNKNOWN( q <= p );
// Taylor coefficients corresponding to argument and result
Base* x = taylor + i_x * nc_taylor;
Base* s = taylor + i_z * nc_taylor;
Base* c = s - nc_taylor;
// rest of this routine is identical for the following cases:
// forward_sin_op, forward_cos_op, forward_sinh_op, forward_cosh_op.
size_t k;
if( q == 0 )
{ s[0] = sin( x[0] );
c[0] = cos( x[0] );
q++;
}
for(size_t j = q; j <= p; 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 zero order forward mode Taylor coefficient for result of op = SinOp.
The C++ source code corresponding to this operation is
\verbatim
z = sin(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_sin_op_0(
size_t i_z ,
size_t i_x ,
size_t nc_taylor ,
Base* taylor )
{
// check assumptions
CPPAD_ASSERT_UNKNOWN( NumArg(SinOp) == 1 );
CPPAD_ASSERT_UNKNOWN( NumRes(SinOp) == 2 );
CPPAD_ASSERT_UNKNOWN( i_x + 1 < i_z );
CPPAD_ASSERT_UNKNOWN( 0 < nc_taylor );
// Taylor coefficients corresponding to argument and result
Base* x = taylor + i_x * nc_taylor;
Base* s = taylor + i_z * nc_taylor; // called z in documentation
Base* c = s - nc_taylor; // called y in documentation
s[0] = sin( x[0] );
c[0] = cos( x[0] );
}
/*!
Compute reverse mode partial derivatives for result of op = SinOp.
The C++ source code corresponding to this operation is
\verbatim
z = sin(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_sin_op(
size_t d ,
size_t i_z ,
size_t i_x ,
size_t nc_taylor ,
const Base* taylor ,
size_t nc_partial ,
Base* partial )
{
// check assumptions
CPPAD_ASSERT_UNKNOWN( NumArg(SinOp) == 1 );
CPPAD_ASSERT_UNKNOWN( NumRes(SinOp) == 2 );
CPPAD_ASSERT_UNKNOWN( i_x + 1 < i_z );
CPPAD_ASSERT_UNKNOWN( d < nc_taylor );
CPPAD_ASSERT_UNKNOWN( d < nc_partial );
// Taylor coefficients and partials corresponding to argument
const Base* x = taylor + i_x * nc_taylor;
Base* px = partial + i_x * nc_partial;
// Taylor coefficients and partials corresponding to first result
const Base* s = taylor + i_z * nc_taylor; // called z in doc
Base* ps = partial + i_z * nc_partial;
// Taylor coefficients and partials corresponding to auxillary result
const Base* c = s - nc_taylor; // called y in documentation
Base* pc = ps - 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] += ps[j] * Base(k) * c[j-k];
px[k] -= pc[j] * Base(k) * s[j-k];
ps[j-k] -= pc[j] * Base(k) * x[k];
pc[j-k] += ps[j] * Base(k) * x[k];
}
--j;
}
px[0] += ps[0] * c[0];
px[0] -= pc[0] * s[0];
}
/*! \} */
} // END_CPPAD_NAMESPACE
# endif
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