// Helper functions for complex/real numbers
// to clean up #ifdef LIBMESH_USE_COMPLEX_NUMBERS elsewhere
template<typename T> LIBMESH_DEVICE_INLINE T libmesh_real(T a) { return a; }
template<typename T> LIBMESH_DEVICE_INLINE T libmesh_imag(T /*a*/) { return 0; }
template<typename T> LIBMESH_DEVICE_INLINE T libmesh_conj(T a) { return a; }

template<typename T>
LIBMESH_DEVICE_INLINE T libmesh_real(std::complex<T> a) { return std::real(a); }

template<typename T>
LIBMESH_DEVICE_INLINE T libmesh_imag(std::complex<T> a) { return std::imag(a); }

// std::isnan() is in <cmath> as of C++11.
template <typename T>
LIBMESH_DEVICE_INLINE bool libmesh_isnan(T x) { return std::isnan(x); }

template <typename T>
LIBMESH_DEVICE_INLINE bool libmesh_isnan(std::complex<T> a)

// std::isinf() is in <cmath> as of C++11.
template <typename T>
LIBMESH_DEVICE_INLINE bool libmesh_isinf(T x) { return std::isinf(x); }

template <typename T>
LIBMESH_DEVICE_INLINE bool libmesh_isinf(std::complex<T> a)

template<typename T>
LIBMESH_DEVICE_INLINE
auto norm_sq(const T & a)
{ return a * libmesh_conj(a); }

template<typename T>
LIBMESH_DEVICE_INLINE

                      sender_could_become_owner)
                    {
                      if (it != repartitioned_node_pids.end() &&
                          pid < it->second)
                        it->second = pid;
                      else
                        repartitioned_node_pids[n] = pid;
                    }
                  else
                    if (it == repartitioned_node_pids.end())
                      repartitioned_node_pids[n] =
                        DofObject::invalid_processor_id;

                  repartitioned_node_sets_to_push[pid].insert(n);