void producer(void)
{
int i;
unsigned long long start, end, sum = 0, avg, dev = 0;
for (i = 0 ; i < RB_ITER ; i++) {
rdtscll(start);
__p();
rdtscll(end);
meas[i] = end - start;
sum += meas[i];
}
avg = sum/RB_ITER;
for (i = 0 ; i < RB_ITER ; i++) {
unsigned long long diff = (meas[i] > avg) ?
meas[i] - avg :
avg - meas[i];
dev += (diff*diff);
}
dev /= RB_ITER;
printf("round trip deviation^2 = %llu\n", dev);
printf("RPC pipe: Producer: %llu\n", avg);
}
strstreambuf::pos_type
strstreambuf::seekpos(pos_type __sp, ios_base::openmode __which)
{
off_type __p(-1);
bool pos_in = (__which & ios::in) != 0;
bool pos_out = (__which & ios::out) != 0;
if (pos_in || pos_out)
{
if (!((pos_in && gptr() == nullptr) || (pos_out && pptr() == nullptr)))
{
off_type newoff = __sp;
char* seekhigh = epptr() ? epptr() : egptr();
if (0 <= newoff && newoff <= seekhigh - eback())
{
char* newpos = eback() + newoff;
if (pos_in)
setg(eback(), newpos, _VSTD::max(newpos, egptr()));
if (pos_out)
{
// min(pbase, newpos), newpos, epptr()
off_type temp = epptr() - newpos;
setp(min(pbase(), newpos), epptr());
pbump(static_cast<int>((epptr() - pbase()) - temp));
}
__p = newoff;
}
}
}
return pos_type(__p);
}
strstreambuf::pos_type
strstreambuf::seekoff(off_type __off, ios_base::seekdir __way, ios_base::openmode __which)
{
off_type __p(-1);
bool pos_in = (__which & ios::in) != 0;
bool pos_out = (__which & ios::out) != 0;
bool legal = false;
switch (__way)
{
case ios::beg:
case ios::end:
if (pos_in || pos_out)
legal = true;
break;
case ios::cur:
if (pos_in != pos_out)
legal = true;
break;
}
if (pos_in && gptr() == nullptr)
legal = false;
if (pos_out && pptr() == nullptr)
legal = false;
if (legal)
{
off_type newoff;
char* seekhigh = epptr() ? epptr() : egptr();
switch (__way)
{
case ios::beg:
newoff = 0;
break;
case ios::cur:
newoff = (pos_in ? gptr() : pptr()) - eback();
break;
case ios::end:
newoff = seekhigh - eback();
break;
default:
return pos_type(off_type(-1));
}
newoff += __off;
if (0 <= newoff && newoff <= seekhigh - eback())
{
char* newpos = eback() + newoff;
if (pos_in)
setg(eback(), newpos, _VSTD::max(newpos, egptr()));
if (pos_out)
{
// min(pbase, newpos), newpos, epptr()
__off = epptr() - newpos;
setp(min(pbase(), newpos), epptr());
pbump(static_cast<int>((epptr() - pbase()) - __off));
}
__p = newoff;
}
}
return pos_type(__p);
}
PTile pf_synth(bool negative, bool inverted, long long epoch, unsigned long long lattice){
//check for overflow condition.
if (epoch > ((1 << (PENV->epochbits - 1)) - 1)){
if (negative){
return (inverted ? __nfew : __nmany);
} else {
return (inverted ? __few : __many);
}
}
PTile temp = __p(((epoch << PENV->latticebits | lattice) * (PENV->increment)) | __one);
if (inverted) {temp = tile_multiplicativeinverse(temp);};
if (negative) {temp = tile_additiveinverse(temp);};
return temp;
}
typename Evaluator<iDim, Iterator, Pset, ExprT>::eval_element_type
Evaluator<iDim, Iterator, Pset, ExprT>::operator()( mpl::size_t<MESH_FACES> ) const
{
boost::timer __timer;
VLOG(2) << "evaluator(MESH_FACES) " << "\n";
//
// a few typedefs
//
// mesh element
typedef typename mesh_element_type::entity_type geoelement_type;
//typedef typename geoelement_type::face_type face_type;
typedef mesh_element_type face_type;
// geometric mapping context
typedef typename geoelement_type::gm_type gm_type;
typedef boost::shared_ptr<gm_type> gm_ptrtype;
typedef typename geoelement_type::gm1_type gm1_type;
typedef boost::shared_ptr<gm1_type> gm1_ptrtype;
typedef typename gm_type::template Context<context, geoelement_type> gmc_type;
typedef boost::shared_ptr<gmc_type> gmc_ptrtype;
typedef fusion::map<fusion::pair<vf::detail::gmc<0>, gmc_ptrtype> > map_gmc_type;
typedef typename gm1_type::template Context<context, geoelement_type> gmc1_type;
typedef boost::shared_ptr<gmc1_type> gmc1_ptrtype;
typedef fusion::map<fusion::pair<vf::detail::gmc<0>, gmc1_ptrtype> > map_gmc1_type;
// expression
//typedef typename expression_type::template tensor<map_gmc_type,fecontext_type> t_expr_type;
//typedef decltype( basis_type::isomorphism( M_expr ) ) the_expression_type;
typedef expression_type the_expression_type;
typedef typename boost::remove_reference<typename boost::remove_const<the_expression_type>::type >::type iso_expression_type;
typedef typename iso_expression_type::template tensor<map_gmc_type> t_expr_type;
typedef typename iso_expression_type::template tensor<map_gmc1_type> t_expr1_type;
typedef typename t_expr_type::shape shape;
//
// start
//
iterator_type __face_it, __face_en;
boost::tie( boost::tuples::ignore, __face_it, __face_en ) = M_range;
int npoints = M_pset.fpoints(0,1).size2();
element_type __v( M_pset.fpoints(0,1).size2()*std::distance( __face_it, __face_en )*shape::M );
node_type __p( mesh_element_type::nRealDim, M_pset.fpoints(0,1).size2()*std::distance( __face_it, __face_en ) );
__v.setZero();
__p.setZero();
VLOG(2) << "pset: " << M_pset.fpoints(0,1);
VLOG(2) << "Checking trivial result...";
if ( __face_it == __face_en )
return boost::make_tuple( __v, __p );
gm_ptrtype __gm( new gm_type );
gm1_ptrtype __gm1( new gm1_type );
//
// Precompute some data in the reference element for
// geometric mapping and reference finite element
//
typedef typename geoelement_type::permutation_type permutation_type;
typedef typename gm_type::precompute_ptrtype geopc_ptrtype;
typedef typename gm_type::precompute_type geopc_type;
typedef typename gm1_type::precompute_ptrtype geopc1_ptrtype;
typedef typename gm1_type::precompute_type geopc1_type;
std::vector<std::map<permutation_type, geopc_ptrtype> > __geopc( M_pset.nFaces() );
std::vector<std::map<permutation_type, geopc1_ptrtype> > __geopc1( M_pset.nFaces() );
VLOG(2) << "computing geopc...";
for ( uint16_type __f = 0; __f < M_pset.nFaces(); ++__f )
{
for ( permutation_type __p( permutation_type::IDENTITY );
__p < permutation_type( permutation_type::N_PERMUTATIONS ); ++__p )
{
__geopc[__f][__p] = geopc_ptrtype( new geopc_type( __gm, M_pset.fpoints(__f, __p.value() ) ) );
__geopc1[__f][__p] = geopc1_ptrtype( new geopc1_type( __gm1, M_pset.fpoints(__f, __p.value() ) ) );
DVLOG(2) << "pset " << __f << " : " << M_pset.fpoints(__f, __p.value() );
CHECK( __geopc[__f][__p]->nPoints() ) << "invalid number of points for geopc";
CHECK( __geopc1[__f][__p]->nPoints() ) << "invalid number of points for geopc1";
}
}
uint16_type __face_id = __face_it->pos_first();
gmc_ptrtype __c( new gmc_type( __gm, __face_it->element( 0 ), __geopc, __face_id ) );
gmc1_ptrtype __c1( new gmc1_type( __gm1, __face_it->element( 0 ), __geopc1, __face_id ) );
map_gmc_type mapgmc( fusion::make_pair<vf::detail::gmc<0> >( __c ) );
t_expr_type expr( M_expr, mapgmc );
map_gmc1_type mapgmc1( fusion::make_pair<vf::detail::gmc<0> >( __c1 ) );
t_expr1_type expr1( M_expr, mapgmc1 );
size_type nbFaceDof = invalid_size_type_value;
for ( int e = 0; __face_it != __face_en; ++__face_it, ++e )
{
FEELPP_ASSERT( __face_it->isOnBoundary() && !__face_it->isConnectedTo1() )
( __face_it->marker() )
( __face_it->isOnBoundary() )
( __face_it->ad_first() )
( __face_it->pos_first() )
( __face_it->ad_second() )
( __face_it->pos_second() )
( __face_it->id() ).warn( "inconsistent data face" );
DVLOG(2) << "[evaluator] FACE_ID = " << __face_it->id()
<< " element id= " << __face_it->ad_first()
<< " pos in elt= " << __face_it->pos_first()
<< " marker: " << __face_it->marker() << "\n";
DVLOG(2) << "[evaluator] FACE_ID = " << __face_it->id() << " real pts=" << __face_it->G() << "\n";
uint16_type __face_id = __face_it->pos_first();
switch ( M_geomap_strategy )
{
default:
case GeomapStrategyType::GEOMAP_OPT:
case GeomapStrategyType::GEOMAP_HO:
{
__c->update( __face_it->element( 0 ), __face_id );
DVLOG(2) << "[evaluator::GEOMAP_HO|GEOMAP_OPT] FACE_ID = " << __face_it->id() << " ref pts=" << __c->xRefs() << "\n";
DVLOG(2) << "[evaluator::GEOMAP_HO|GEOMAP_OPT] FACE_ID = " << __face_it->id() << " real pts=" << __c->xReal() << "\n";
map_gmc_type mapgmc( fusion::make_pair<vf::detail::gmc<0> >( __c ) );
expr.update( mapgmc );
for ( uint16_type p = 0; p < npoints; ++p )
{
for ( uint16_type c1 = 0; c1 < mesh_element_type::nRealDim; ++c1 )
{
__p(c1, e*npoints+p) = __c->xReal(p)[c1];
}
for ( uint16_type c1 = 0; c1 < shape::M; ++c1 )
{
__v( e*npoints*shape::M+shape::M*p+c1) = expr.evalq( c1, 0, p );
}
}
}
break;
case GeomapStrategyType::GEOMAP_O1:
{
__c1->update( __face_it->element( 0 ), __face_id );
DVLOG(2) << "[evaluator::GEOMAP_O1] FACE_ID = " << __face_it->id() << " ref pts=" << __c1->xRefs() << "\n";
DVLOG(2) << "[evaluator::GEOMAP_O1] FACE_ID = " << __face_it->id() << " real pts=" << __c1->xReal() << "\n";
map_gmc1_type mapgmc1( fusion::make_pair<vf::detail::gmc<0> >( __c1 ) );
expr1.update( mapgmc1 );
for ( uint16_type p = 0; p < npoints; ++p )
{
for ( uint16_type c1 = 0; c1 < mesh_element_type::nRealDim; ++c1 )
{
__p(c1, e*npoints+p) = __c1->xReal(p)[c1];
}
for ( uint16_type c1 = 0; c1 < shape::M; ++c1 )
{
__v( e*npoints*shape::M+shape::M*p+c1) = expr1.evalq( c1, 0, p );
}
}
}
break;
}
} // face_it
return boost::make_tuple( __v, __p );
}
typename Evaluator<iDim, Iterator, Pset, ExprT>::eval_element_type
Evaluator<iDim, Iterator, Pset, ExprT>::operator()( mpl::size_t<MESH_ELEMENTS> ) const
{
boost::timer __timer;
typedef typename mesh_element_type::gm_type gm_type;
typedef typename gm_type::template Context<context, mesh_element_type> gm_context_type;
typedef typename mesh_element_type::gm1_type gm1_type;
typedef typename gm1_type::template Context<context, mesh_element_type> gm1_context_type;
typedef boost::shared_ptr<gm_context_type> gm_context_ptrtype;
typedef boost::shared_ptr<gm1_context_type> gm1_context_ptrtype;
typedef fusion::map<fusion::pair<vf::detail::gmc<0>, gm_context_ptrtype> > map_gmc_type;
typedef fusion::map<fusion::pair<vf::detail::gmc<0>, gm1_context_ptrtype> > map_gmc1_type;
//typedef typename expression_type::template tensor<map_gmc_type,fusion::map<fusion::pair<vf::detail::gmc<0>,boost::shared_ptr<fecontext_type> > > > t_expr_type;
//typedef decltype( basis_type::isomorphism( M_expr ) ) the_expression_type;
typedef expression_type the_expression_type;
typedef typename boost::remove_reference<typename boost::remove_const<the_expression_type>::type >::type iso_expression_type;
typedef typename iso_expression_type::template tensor<map_gmc_type> t_expr_type;
typedef typename iso_expression_type::template tensor<map_gmc1_type> t_expr1_type;
typedef typename t_expr_type::value_type value_type;
// we should manipulate the same type of functions on the left and
// on the right
//BOOST_STATIC_ASSERT(( boost::is_same<return_value_type, typename functionspace_type::return_value_type>::value ));
typedef typename t_expr_type::shape shape;
iterator_type it, en;
boost::tie( boost::tuples::ignore, it, en ) = M_range;
int npoints = M_pset.points().size2();
element_type __v( M_pset.points().size2()*std::distance( it, en )*shape::M );
node_type __p( mesh_element_type::nDim, M_pset.points().size2()*std::distance( it, en ) );
__v.setZero();
__p.setZero();
// return if no elements
if ( it == en )
return boost::make_tuple( __v, __p );
//
// Precompute some data in the reference element for
// geometric mapping and reference finite element
//
typename gm_type::precompute_ptrtype __geopc( new typename gm_type::precompute_type( it->gm(),
M_pset.points() ) );
typename gm1_type::precompute_ptrtype __geopc1( new typename gm1_type::precompute_type( it->gm1(),
M_pset.points() ) );
gm_context_ptrtype __c( new gm_context_type( it->gm(),*it,__geopc ) );
gm1_context_ptrtype __c1( new gm1_context_type( it->gm1(),*it,__geopc1 ) );
map_gmc_type mapgmc( fusion::make_pair<vf::detail::gmc<0> >( __c ) );
t_expr_type tensor_expr( M_expr, mapgmc );
map_gmc1_type mapgmc1( fusion::make_pair<vf::detail::gmc<0> >( __c1 ) );
t_expr1_type tensor_expr1( M_expr, mapgmc1 );
for ( int e = 0; it!=en ; ++it, ++e )
{
switch ( M_geomap_strategy )
{
case GeomapStrategyType::GEOMAP_HO:
{
__c->update( *it );
map_gmc_type mapgmc( fusion::make_pair<vf::detail::gmc<0> >( __c ) );
tensor_expr.update( mapgmc );
for ( uint16_type p = 0; p < npoints; ++p )
{
for ( uint16_type c1 = 0; c1 < mesh_element_type::nDim; ++c1 )
{
__p(c1, e*npoints+p) = __c->xReal(p)[c1];
}
for ( uint16_type c1 = 0; c1 < shape::M; ++c1 )
{
__v( e*npoints*shape::M+shape::M*p+c1) = tensor_expr.evalq( c1, 0, p );
}
}
}
break;
case GeomapStrategyType::GEOMAP_O1:
{
__c1->update( *it );
map_gmc1_type mapgmc1( fusion::make_pair<vf::detail::gmc<0> >( __c1 ) );
tensor_expr1.update( mapgmc1 );
for ( uint16_type p = 0; p < npoints; ++p )
{
for ( uint16_type c1 = 0; c1 < mesh_element_type::nDim; ++c1 )
{
__p(c1, e*npoints+p) = __c1->xReal(p)[c1];
}
for ( uint16_type c1 = 0; c1 < shape::M; ++c1 )
{
__v( e*npoints*shape::M+shape::M*p+c1) = tensor_expr1.evalq( c1, 0, p );
}
}
}
break;
case GeomapStrategyType::GEOMAP_OPT:
{
if ( it->isOnBoundary() )
{
// HO if on boundary
__c->update( *it );
map_gmc_type mapgmc( fusion::make_pair<vf::detail::gmc<0> >( __c ) );
tensor_expr.update( mapgmc );
for ( uint16_type p = 0; p < npoints; ++p )
{
for ( uint16_type c1 = 0; c1 < mesh_element_type::nDim; ++c1 )
{
__p(c1, e*npoints+p) = __c->xReal(p)[c1];
}
for ( uint16_type c1 = 0; c1 < shape::M; ++c1 )
{
__v( e*npoints*shape::M+shape::M*p+c1) = tensor_expr.evalq( c1, 0, p );
}
}
}
else
{
__c1->update( *it );
map_gmc1_type mapgmc1( fusion::make_pair<vf::detail::gmc<0> >( __c1 ) );
tensor_expr1.update( mapgmc1 );
for ( uint16_type p = 0; p < npoints; ++p )
{
for ( uint16_type c1 = 0; c1 < mesh_element_type::nDim; ++c1 )
{
__p(c1, e*npoints+p) = __c1->xReal(p)[c1];
}
for ( uint16_type c1 = 0; c1 < shape::M; ++c1 )
{
__v( e*npoints*shape::M+shape::M*p+c1) = tensor_expr1.evalq( c1, 0, p );
}
}
}
}
break;
}
}
return boost::make_tuple( __v, __p );
}
void
modifVec(std::list<ElementRange> const& __r, eltType const& u,vectorType & UnVec,ExprType const& expr,
size_type rowstart, int ComponentShiftFactor,
mpl::int_<MESH_FACES> /**/ )
{
//using namespace Feel::vf;
typedef typename eltType::functionspace_type::mesh_type mesh_type;
typedef typename mesh_type::face_iterator face_iterator;
typedef typename mesh_type::face_const_iterator face_const_iterator;
typedef typename mesh_type::element_type geoelement_type;
typedef typename geoelement_type::face_type face_type;
// basis
typedef typename eltType::functionspace_type::fe_type fe_type;
typedef typename eltType::functionspace_type::dof_type dof_type;
const size_type context = ExprType::context|vm::POINT;
// geometric mapping context
typedef typename mesh_type::gm_type gm_type;
typedef boost::shared_ptr<gm_type> gm_ptrtype;
typedef typename gm_type::template Context<context, geoelement_type> gmc_type;
typedef boost::shared_ptr<gmc_type> gmc_ptrtype;
typedef fusion::map<fusion::pair<vf::detail::gmc<0>, gmc_ptrtype> > map_gmc_type;
typedef typename ExprType::template tensor<map_gmc_type> t_expr_type;
if ( __r.size() == 0 ) return;
auto __face_it = __r.begin()->template get<1>();
auto __face_en = __r.begin()->template get<2>();
//if ( __face_it == __face_en ) return;
bool findAFace = false;
for( auto lit = __r.begin(), len = __r.end(); lit != len; ++lit )
{
__face_it = lit->template get<1>();
__face_en = lit->template get<2>();
if ( __face_it != __face_en )
{
findAFace=true;
break;
}
}
if ( !findAFace ) return;
// get the first face properly connected
bool findAFaceToInit=false;
for( auto lit = __r.begin(), len = __r.end(); lit != len; ++lit )
{
__face_it = lit->template get<1>();
__face_en = lit->template get<2>();
for( ; __face_it != __face_en; ++__face_it )
{
if ( boost::unwrap_ref(*__face_it).isConnectedTo0() )
{
findAFaceToInit=true;
break;
}
}
if ( findAFaceToInit ) break;
}
CHECK( findAFaceToInit ) << "not find a face to init\n";
size_type nbFaceDof = invalid_size_type_value;
if ( !fe_type::is_modal )
nbFaceDof = ( face_type::numVertices * fe_type::nDofPerVertex +
face_type::numEdges * fe_type::nDofPerEdge +
face_type::numFaces * fe_type::nDofPerFace );
else
nbFaceDof = face_type::numVertices * fe_type::nDofPerVertex;
//dof_type const* __dof = u.functionSpace()->dof().get();
fe_type const* __fe = u.functionSpace()->fe().get();
gm_ptrtype __gm( new gm_type );
//
// Precompute some data in the reference element for
// geometric mapping and reference finite element
//
typedef typename geoelement_type::permutation_type permutation_type;
typedef typename gm_type::precompute_ptrtype geopc_ptrtype;
typedef typename gm_type::precompute_type geopc_type;
std::vector<std::map<permutation_type, geopc_ptrtype> > __geopc( geoelement_type::numTopologicalFaces );
for ( uint16_type __f = 0; __f < geoelement_type::numTopologicalFaces; ++__f )
{
permutation_type __p( permutation_type::IDENTITY );
__geopc[__f][__p] = geopc_ptrtype( new geopc_type( __gm, __fe->points( __f ) ) );
}
uint16_type __face_id = __face_it->pos_first();
gmc_ptrtype __c( new gmc_type( __gm, __face_it->element(0), __geopc, __face_id ) );
map_gmc_type mapgmc( fusion::make_pair<vf::detail::gmc<0> >( __c ) );
t_expr_type LExpr( expr, mapgmc );
std::vector<bool> dofdone( u.functionSpace()->dof()->nLocalDofWithGhost(), false );
//face_const_iterator __face_it, __face_en;
for( auto lit = __r.begin(), len = __r.end(); lit != len; ++lit )
{
__face_it = lit->template get<1>();
__face_en = lit->template get<2>();
for ( ; __face_it != __face_en; ++__face_it )
{
uint16_type __face_id = __face_it->pos_first();
__c->update( __face_it->element(0), __face_id );
map_gmc_type mapgmc( fusion::make_pair<vf::detail::gmc<0> >( __c ) );
LExpr.update( mapgmc );
for (uint c1=0;c1<eltType::nComponents1;c1++)
for (uint c2=0;c2<eltType::nComponents2;c2++)
{
for ( uint16_type l = 0; l < nbFaceDof; ++l )
{
size_type index = boost::get<0>(u.functionSpace()->dof()->faceLocalToGlobal( __face_it->id(), l, c1 ));
if ( dofdone[index] ) continue;
size_type thedof = u.start() + ComponentShiftFactor*index;
double __value=LExpr.evalq( c1, c2, l );
//u( thedof ) = __value;
UnVec->set(rowstart+thedof,__value);
dofdone[index] = true;
}
}
}
}
//UnVec->close();
} // modifVec
void
lanczos()
{
std::cout.precision(std::numeric_limits<_Tp>::digits10);
// From Pugh..
int __n_old = 0;
int __n = -2 - 0.3 * std::log(std::numeric_limits<_Tp>::epsilon());
std::cout << "n = " << __n << '\n';
auto __g = __n - _Tp{0.5L};
std::cout << "g = " << __g << '\n';
while (__n != __n_old)
{
std::cout << '\n';
std::vector<_Tp> __a;
for (unsigned int k = 1; k <= __n; ++k)
{
for (unsigned int j = 1; j <= k; ++j)
std::cout << " C(" << std::setw(2) << k
<< ", " << std::setw(2) << j
<< ") = " << std::setw(4) << __c(k, j);
std::cout << '\n';
}
std::cout << '\n';
auto __prev = std::numeric_limits<_Tp>::max();
for (unsigned int __k = 0; __k <= __n + 5; ++__k)
{
auto __curr = __p(__k, __g);
if (std::abs(__curr) > std::abs(__prev))
{
__n_old = __n;
__n = __k;
__g = __n - _Tp{0.5L};
break;
}
__prev = __curr;
std::cout << " p(" << __k << ", " << __g << ") = " << __curr << '\n';
}
std::cout << "n = " << __n << '\n';
}
constexpr auto _S_log_sqrt_2pi = 9.189385332046727417803297364056176398620e-1L;
auto
__log_gamma_lanczos = [=](_Tp __z) -> _Tp
{
auto __fact = _Tp{1};
auto __sum = _Tp{0.5L} * __p(0, __g);
for (unsigned int __k = 1; __k < __n; ++__k)
{
__fact *= (__z - __k + 1) / (__z + __k);
__sum += __fact * __p(__k, __g);
}
return _S_log_sqrt_2pi + std::log(__sum)
+ (__z + 0.5L) * std::log(__z + __g + 0.5L)
- (__z + __g + 0.5L) - std::log(__z);
};
std::cout << '\n';
for (int i = 0; i <= 500; ++i)
{
auto z = _Tp{0.01Q} * i;
std::cout << ' ' << z
<< ' ' << __log_gamma_lanczos(z)
<< ' ' << std::lgamma(z)
<< ' ' << __log_gamma_lanczos(z) - std::lgamma(z) << '\n';
}
}
void
hankel_transition()
{
auto sign = [](int s, int r){return (s + r) % 2 == 1 ? -1 : +1; };
using rational = _Tp;
std::cout.precision(std::numeric_limits<_Tp>::digits10);
auto width = std::cout.precision() + 6;
__gnu_cxx::_Polynomial<int> poo({0, -2});
std::vector<__gnu_cxx::_Polynomial<int>> phi;
std::vector<__gnu_cxx::_Polynomial<int>> psi;
phi.push_back(__gnu_cxx::_Polynomial<int>(1));
phi.push_back(__gnu_cxx::_Polynomial<int>(0));
phi.push_back(__gnu_cxx::_Polynomial<int>({0, -2}));
psi.push_back(__gnu_cxx::_Polynomial<int>(0));
psi.push_back(__gnu_cxx::_Polynomial<int>(-1));
psi.push_back(__gnu_cxx::_Polynomial<int>(0));
for (int s = 3; s <= 18; ++s)
{
phi.push_back(poo * phi[s - 2] -2 * (s - 2) * phi[s - 3]);
psi.push_back(poo * psi[s - 2] -2 * (s - 2) * psi[s - 3]);
}
std::cout << "\nphi polynomial\n";
for (const auto& p : phi)
std::cout << p << '\n';
std::cout << "\npsi polynomial\n";
for (const auto& p : psi)
std::cout << p << '\n';
std::vector<__gnu_cxx::_Polynomial<rational>> A(6);
std::vector<__gnu_cxx::_Polynomial<rational>> B(6);
for (int s = 0; s < 6; ++s)
{
for (int r = 0; r <= s; ++r)
A[s] += phi[2 * s + r] * __gnu_cxx::_Polynomial<rational>(sign(r, s), r);
std::cout << "A_" << s << ": " << A[s] << '\n';
for (int r = 0; r <= s; ++r)
B[s] += psi[2 * s + r] * __gnu_cxx::_Polynomial<rational>(sign(r, s), r);
std::cout << "B_" << s << ": " << B[s] << '\n';
}
std::vector<__gnu_cxx::_Polynomial<__gnu_cxx::_Rational<long long>>>
P
{
{{1, 1}},
{{}, {-1, 5}},
{{}, {}, {3, 35}, {}, {}, {-9, 100}},
{{-1, 225}, {}, {}, {-173, 3150}, {}, {}, {957, 7000}},
{{}, {947, 346500}, {}, {}, {5903, 138600}, {}, {}, {-23573, 147000}, {}, {}, {27, 20000}}
};
std::vector<__gnu_cxx::_Polynomial<__gnu_cxx::_Rational<long long>>>
Q
{
{{}, {}, {3, 10}},
{{1, 70}, {}, {}, {-17, 70}},
{{}, {-37, 3150}, {}, {}, {611, 3150}, {}, {}, {-9, 1000}},
{{}, {}, {79, 12375}, {}, {}, {-110767, 693000}, {}, {}, {549, 28000}}
};
std::vector<__gnu_cxx::_Polynomial<__gnu_cxx::_Rational<long long>>>
R
{
{{1, 1}},
{{}, {-4, 5}},
{{}, {}, {57, 70}, {}, {}, {-9, 100}},
{{23, 3150}, {}, {}, {-2617, 3150}, {}, {}, {699, 3500}},
{{}, {-1159, 115500}, {}, {}, {3889, 4620}, {}, {}, {-46631, 147000}, {}, {}, {27, 20000}}
};
std::vector<__gnu_cxx::_Polynomial<__gnu_cxx::_Rational<long long>>>
S
{
{{-1, 5}, {}, {}, {3, 5}},
{{}, {1, 5}, {}, {}, {-131, 140}},
{{}, {}, {-593, 3150}, {}, {}, {5437, 4500}, {}, {}, {-9, 500}},
{{947, 346500}, {}, {}, {31727, 173250}, {}, {}, {-999443, 693000}, {}, {}, {369, 7000}}
};
std::cout << "\nP polynomial\n";
for (const auto& p : P)
std::cout << p << '\n';
std::cout << "\nP values\n";
for (int i = -100; i <= +100; ++i)
{
auto z = _Tp{0.01Q} * i;
std::cout << std::setw(width) << z;
for (const auto& p : P)
std::cout << std::setw(width) << p(z);
std::cout << '\n';
}
std::cout << "\nQ polynomial\n";
for (const auto& q : Q)
std::cout << q << '\n';
std::cout << "\nQ values\n";
for (int i = -100; i <= +100; ++i)
{
auto z = _Tp{0.01Q} * i;
std::cout << std::setw(width) << z;
for (const auto& q : Q)
std::cout << std::setw(width) << q(z);
std::cout << '\n';
}
std::cout << "\nR polynomial\n";
for (const auto& r : R)
std::cout << r << '\n';
std::cout << "\nR values\n";
for (int i = -100; i <= +100; ++i)
{
auto z = _Tp{0.01Q} * i;
std::cout << std::setw(width) << z;
for (const auto& r : R)
std::cout << std::setw(width) << r(z);
std::cout << '\n';
}
std::cout << "\nS polynomial\n";
for (const auto& s : S)
std::cout << s << '\n';
std::cout << "\nS values\n";
for (int i = -100; i <= +100; ++i)
{
auto z = _Tp{0.01Q} * i;
std::cout << std::setw(width) << z;
for (const auto& s : S)
std::cout << std::setw(width) << s(z);
std::cout << '\n';
}
auto __nu = _Tp{20};
const auto _S_2p13 = _Tp{1.259921049894873164767210607278228350570Q};
const auto _S_2p23 = _Tp{1.587401051968199474751705639272308260393Q};
const auto _S_2p43 = _Tp{2.519842099789746329534421214556456701140Q};
const auto _S_2p53 = _Tp{3.174802103936398949503411278544616520785Q};
const auto _S_pi = _Tp{3.141592653589793238462643383279502884195Q};
const auto __nu13 = std::pow(__nu, _Tp{1} / _Tp{3});
const auto __nu23 = __nu13 * __nu13;
const auto __nu43 = __nu23 * __nu23;
std::cout << "\n\nTransition region Bessel functions: J_\\nu(\\nu + a\\nu^{1/3})\n";
std::cout << "\nnu = " << __nu << "\n"
<< std::setw(width) << "a"
<< std::setw(width) << "J_\\nu"
<< std::setw(width) << "N_\\nu"
<< std::setw(width) << "J'_\\nu"
<< std::setw(width) << "N'_\\nu"
<< '\n';
for (int __i = -100; __i <= +100; ++__i)
{
auto __a = _Tp{0.005Q} * __i;
const auto __airy_arg = -_S_2p13 * __a;
_Tp _Ai, _Bi, _Aip, _Bip;
std::__detail::__airy(__airy_arg, _Ai, _Bi, _Aip, _Bip);
auto __num2k3 = _Tp{1};
auto _Jsum1 = _Tp{0};
auto _Nsum1 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __p : P)
{
_Jsum1 += __p(__a) * __num2k3;
_Nsum1 += __p(__a) * __num2k3;
__num2k3 /= __nu23;
}
auto _Jsum2 = _Tp{0};
auto _Nsum2 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __q : Q)
{
_Jsum2 += __q(__a) * __num2k3;
_Nsum2 += __q(__a) * __num2k3;
__num2k3 /= __nu23;
}
const auto _Jt = _S_2p13 * _Ai * _Jsum1 / __nu13
+ _S_2p23 * _Aip * _Jsum2 / __nu;
const auto _Nt = -_S_2p13 * _Bi * _Nsum1 / __nu13
- _S_2p23 * _Bip * _Nsum2 / __nu;
auto _Jpsum1 = _Tp{0};
auto _Npsum1 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __r : R)
{
_Jpsum1 += __r(__a) * __num2k3;
_Npsum1 += __r(__a) * __num2k3;
__num2k3 /= __nu23;
}
auto _Jpsum2 = _Tp{0};
auto _Npsum2 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __s : S)
{
_Jpsum2 += __s(__a) * __num2k3;
_Npsum2 += __s(__a) * __num2k3;
__num2k3 /= __nu23;
}
const auto _Jtp = -_S_2p23 * _Aip * _Jpsum1 / __nu23
+ _S_2p13 * _Ai * _Jpsum2 / __nu43;
const auto _Ntp = _S_2p23 * _Bip * _Npsum1 / __nu23
- _S_2p13 * _Bi * _Npsum2 / __nu43;
std::cout << std::setw(width) << __a
<< std::setw(width) << _Jt
<< std::setw(width) << _Nt
<< std::setw(width) << _Jtp
<< std::setw(width) << _Ntp
<< std::setw(width) << '\n';
}
const auto __mipi3 = std::polar(-_S_pi / _Tp{3});
const auto __pipi3 = std::polar(+_S_pi / _Tp{3});
std::cout << "\n\nTransition region Bessel functions: J_\\nu(\\nu + a\\nu^{1/3})\n";
std::cout << "\nnu = " << __nu << "\n"
<< std::setw(2*width) << "a"
<< std::setw(2*width) << "J_\\nu"
<< std::setw(2*width) << "N_\\nu"
<< std::setw(2*width) << "J'_\\nu"
<< std::setw(2*width) << "N'_\\nu"
<< '\n';
const auto __eps = std::numeric_limits<_Tp>::epsilon();
for (int __i = -100; __i <= +100; ++__i)
{
auto __a = _Tp{0.005Q} * __i;
const std::complex<_Tp> __airy_argm = _S_2p13 * __a * __mipi3;
std::complex<_Tp> _Ami, _Bmi, _Amip, _Bmip;
std::__detail::__airy(__airy_argm, __eps, _Ami, _Bmi, _Amip, _Bmip);
const std::complex<_Tp> __airy_argp = _S_2p13 * __a * __pipi3;
std::complex<_Tp> _Api, _Bpi, _Apip, _Bpip;
std::__detail::__airy(__airy_argp, __eps, _Api, _Bpi, _Apip, _Bpip);
auto __num2k3 = _Tp{1};
auto _H1sum1 = _Tp{0};
auto _H2sum1 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __p : P)
{
_H1sum1 += __p(__a) * __num2k3;
_H2sum1 += __p(__a) * __num2k3;
__num2k3 /= __nu23;
}
auto _H1sum2 = _Tp{0};
auto _H2sum2 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __q : Q)
{
_H1sum2 += __q(__a) * __num2k3;
_H2sum2 += __q(__a) * __num2k3;
__num2k3 /= __nu23;
}
const auto _H1t = _S_2p43 * __mipi3 * _Ami * _H1sum1 / __nu13
+ _S_2p53 * __mipi3 * _Amip * _H1sum2 / __nu;
const auto _H2t = _S_2p43 * __pipi3 * _Api * _H2sum1 / __nu13
+ _S_2p53 * __pipi3 * _Apip * _H2sum2 / __nu;
auto _H1psum1 = _Tp{0};
auto _H2psum1 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __r : R)
{
_H1psum1 += __r(__a) * __num2k3;
_H2psum1 += __r(__a) * __num2k3;
__num2k3 /= __nu23;
}
auto _H1psum2 = _Tp{0};
auto _H2psum2 = _Tp{0};
__num2k3 = _Tp{1};
for (const auto& __s : S)
{
_H1psum2 += __s(__a) * __num2k3;
_H2psum2 += __s(__a) * __num2k3;
__num2k3 /= __nu23;
}
const auto _H1pt = -_S_2p53 * __mipi3 * _Amip * _H1psum1 / __nu23
+ _S_2p43 * __mipi3 * _Ami * _H1psum2 / __nu43;
const auto _H2pt = -_S_2p53 * __pipi3 * _Apip * _H2psum1 / __nu23
+ _S_2p43 * __pipi3 * _Api * _H2psum2 / __nu43;
std::cout << std::setw(2*width) << __a
<< std::setw(2*width) << _H1t
<< std::setw(2*width) << _H2t
<< std::setw(2*width) << _H1pt
<< std::setw(2*width) << _H2pt
<< std::setw(2*width) << '\n';
}
}
double X = lua_tonumber(L, 1); \
double Y = lua_tonumber(L, 2); \
double Z = lua_tonumber(L, 3); \
\
double s[3]; \
for(int j=0; j<3; j++) \
{ \
lua_pushinteger(L, 1+j); \
lua_gettable(L, 4); \
s[j] = lua_tonumber(L, -1); \
lua_pop(L, 1); \
} \
lua_pushnumber(L, F(X, Y, Z, s)); \
return 1; \
static int l_pxx(lua_State* L){ __p(magnetostatic_Pxx) }
static int l_pxy(lua_State* L){ __p(magnetostatic_Pxy) }
static int l_pxz(lua_State* L){ __p(magnetostatic_Pxz) }
static int l_pyx(lua_State* L){ __p(magnetostatic_Pyx) }
static int l_pyy(lua_State* L){ __p(magnetostatic_Pyy) }
static int l_pyz(lua_State* L){ __p(magnetostatic_Pyz) }
static int l_pzx(lua_State* L){ __p(magnetostatic_Pzx) }
static int l_pzy(lua_State* L){ __p(magnetostatic_Pzy) }
static int l_pzz(lua_State* L){ __p(magnetostatic_Pzz) }
MAGNETOSTATICS2D_API int lib_register(lua_State* L)
{
luaT_register<Magnetostatics2D>(L);