inline void reverse_tan_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(TanOp) == 1 );
CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 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* z = taylor + i_z * cap_order; // called z in doc
Base* pz = partial + i_z * nc_partial;
// Taylor coefficients and partials corresponding to auxillary result
const Base* y = z - cap_order; // called y in documentation
Base* py = pz - 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;
size_t j = d;
size_t k;
Base base_two(2);
while(j)
{
px[j] += pz[j];
pz[j] /= Base(j);
for(k = 1; k <= j; k++)
{ px[k] += pz[j] * y[j-k] * Base(k);
py[j-k] += pz[j] * x[k] * Base(k);
}
for(k = 0; k < j; k++)
pz[k] += py[j-1] * z[j-k-1] * base_two;
--j;
}
px[0] += pz[0] * (Base(1) + y[0]);
}
inline void reverse_tanh_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(TanOp) == 1 );
CPPAD_ASSERT_UNKNOWN( NumRes(TanOp) == 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* z = taylor + i_z * nc_taylor; // called z in doc
Base* pz = partial + i_z * nc_partial;
// Taylor coefficients and partials corresponding to auxillary result
const Base* y = z - nc_taylor; // called y in documentation
Base* py = pz - nc_partial;
size_t j = d;
size_t k;
Base base_two(2);
while(j)
{
px[j] += pz[j];
pz[j] /= Base(j);
for(k = 1; k <= j; k++)
{ px[k] -= pz[j] * y[j-k] * Base(k);
py[j-k] -= pz[j] * x[k] * Base(k);
}
for(k = 0; k < j; k++)
pz[k] += py[j-1] * z[j-k-1] * base_two;
--j;
}
px[0] += pz[0] * (Base(1) - y[0]);
}
