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aka_common.hh
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			/**
			* @file aka_common.hh
			*
			* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			*
			* @date creation: Mon Jun 14 2010
			* @date last modification: Mon Feb 12 2018
			*
			* @brief common type descriptions for akantu
			*
			*
			* Copyright (©) 2010-2018 EPFL (Ecole Polytechnique Fédérale de Lausanne)
			* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
			*
			* Akantu is free software: you can redistribute it and/or modify it under the
			* terms of the GNU Lesser General Public License as published by the Free
			* Software Foundation, either version 3 of the License, or (at your option) any
			* later version.
			*
			* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
			* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
			* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
			* details.
			*
			* You should have received a copy of the GNU Lesser General Public License
			* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
			*
			*/

			/* -------------------------------------------------------------------------- */

			#ifndef AKANTU_COMMON_HH_
			#define AKANTU_COMMON_HH_

			#include "aka_compatibilty_with_cpp_standard.hh"

			/* -------------------------------------------------------------------------- */
			#if defined(WIN32)
			#define __attribute__(x)
			#endif

			/* -------------------------------------------------------------------------- */
			#include "aka_config.hh"
			#include "aka_error.hh"
			#include "aka_safe_enum.hh"
			/* -------------------------------------------------------------------------- */
			#include <boost/preprocessor.hpp>
			#include <limits>
			#include <list>
			#include <memory>
			#include <string>
			#include <type_traits>
			#include <unordered_map>
			/* -------------------------------------------------------------------------- */

			namespace akantu {

			/* -------------------------------------------------------------------------- */
			/* Constants */
			/* -------------------------------------------------------------------------- */
			namespace {
			[[gnu::unused]] constexpr UInt _all_dimensions{
			std::numeric_limits<UInt>::max()};
			#ifdef AKANTU_NDEBUG
			[[gnu::unused]] constexpr Real REAL_INIT_VALUE{0.};
			#else
			[[gnu::unused]] constexpr Real REAL_INIT_VALUE{
			std::numeric_limits<Real>::quiet_NaN()};
			#endif
			} // namespace

			/* -------------------------------------------------------------------------- */
			/* Common types */
			/* -------------------------------------------------------------------------- */
			using ID = std::string;
			} // namespace akantu

			/* -------------------------------------------------------------------------- */
			#include "aka_enum_macros.hh"
			/* -------------------------------------------------------------------------- */
			#include "aka_element_classes_info.hh"
			/* -------------------------------------------------------------------------- */

			namespace akantu {
			/* -------------------------------------------------------------------------- */
			/* Mesh/FEM/Model types */
			/* -------------------------------------------------------------------------- */

			/// small help to use names for directions
			enum SpatialDirection { _x = 0, _y = 1, _z = 2 };

			/// enum MeshIOType type of mesh reader/writer
			enum MeshIOType {
			_miot_auto, ///< Auto guess of the reader to use based on the extension
			_miot_gmsh, ///< Gmsh files
			_miot_gmsh_struct, ///< Gsmh reader with reintpretation of elements has
			/// structures elements
			_miot_diana, ///< TNO Diana mesh format
			_miot_abaqus ///< Abaqus mesh format
			};

			/// enum MeshEventHandlerPriority defines relative order of execution of
			/// events
			enum EventHandlerPriority {
			_ehp_highest = 0,
			_ehp_mesh = 5,
			_ehp_fe_engine = 9,
			_ehp_synchronizer = 10,
			_ehp_dof_manager = 20,
			_ehp_model = 94,
			_ehp_non_local_manager = 100,
			_ehp_lowest = 100
			};

			#if !defined(DOXYGEN)
			// clang-format off
			#define AKANTU_MODEL_TYPES \
			(model) \
			(solid_mechanics_model) \
			(solid_mechanics_model_cohesive) \
			(heat_transfer_model) \
			(structural_mechanics_model) \
			(embedded_model)
			// clang-format on

			/// enum ModelType defines which type of physics is solved
			AKANTU_CLASS_ENUM_DECLARE(ModelType, AKANTU_MODEL_TYPES)
			AKANTU_CLASS_ENUM_OUTPUT_STREAM(ModelType, AKANTU_MODEL_TYPES)
			AKANTU_CLASS_ENUM_INPUT_STREAM(ModelType, AKANTU_MODEL_TYPES)
			#else
			enum class ModelType {
			model,
			solid_mechanics_model,
			solid_mechanics_model_cohesive,
			heat_transfer_model,
			structural_mechanics_model,
			embedded_model,
			};
			#endif
			/// enum AnalysisMethod type of solving method used to solve the equation of
			/// motion
			enum AnalysisMethod {
			_static = 0,
			_implicit_dynamic = 1,
			_explicit_lumped_mass = 2,
			_explicit_lumped_capacity = 2,
			_explicit_consistent_mass = 3
			};

			/// enum DOFSupportType defines which kind of dof that can exists
			enum DOFSupportType { _dst_nodal, _dst_generic };

			#if !defined(DOXYGEN)
			// clang-format off
			#define AKANTU_NON_LINEAR_SOLVER_TYPES \
			(linear) \
			(newton_raphson) \
			(newton_raphson_modified) \
			(lumped) \
			(gmres) \
			(bfgs) \
			(cg) \
			(auto)
			// clang-format on
			AKANTU_CLASS_ENUM_DECLARE(NonLinearSolverType, AKANTU_NON_LINEAR_SOLVER_TYPES)
			AKANTU_CLASS_ENUM_OUTPUT_STREAM(NonLinearSolverType,
			AKANTU_NON_LINEAR_SOLVER_TYPES)
			AKANTU_CLASS_ENUM_INPUT_STREAM(NonLinearSolverType,
			AKANTU_NON_LINEAR_SOLVER_TYPES)
			#else
			/// Type of non linear resolution available in akantu
			enum class NonLinearSolverType {
			_linear, ///< No non linear convergence loop
			_newton_raphson, ///< Regular Newton-Raphson
			_newton_raphson_modified, ///< Newton-Raphson with initial tangent
			_lumped, ///< Case of lumped mass or equivalent matrix
			_gmres,
			_bfgs,
			_cg,
			_auto ///< This will take a default value that make sense in case of
			/// model::getNewSolver
			};
			#endif

			#if !defined(DOXYGEN)
			// clang-format off
			#define AKANTU_TIME_STEP_SOLVER_TYPE \
			(static) \
			(dynamic) \
			(dynamic_lumped) \
			(not_defined)
			// clang-format on
			AKANTU_CLASS_ENUM_DECLARE(TimeStepSolverType, AKANTU_TIME_STEP_SOLVER_TYPE)
			AKANTU_CLASS_ENUM_OUTPUT_STREAM(TimeStepSolverType,
			AKANTU_TIME_STEP_SOLVER_TYPE)
			AKANTU_CLASS_ENUM_INPUT_STREAM(TimeStepSolverType, AKANTU_TIME_STEP_SOLVER_TYPE)
			#else
			/// Type of time stepping solver
			enum class TimeStepSolverType {
			_static, ///< Static solution
			_dynamic, ///< Dynamic solver
			_dynamic_lumped, ///< Dynamic solver with lumped mass
			_not_defined, ///< For not defined cases
			};
			#endif

			#if !defined(DOXYGEN)
			// clang-format off
			#define AKANTU_INTEGRATION_SCHEME_TYPE \
			(pseudo_time) \
			(forward_euler) \
			(trapezoidal_rule_1) \
			(backward_euler) \
			(central_difference) \
			(fox_goodwin) \
			(trapezoidal_rule_2) \
			(linear_acceleration) \
			(newmark_beta) \
			(generalized_trapezoidal)
			// clang-format on
			AKANTU_CLASS_ENUM_DECLARE(IntegrationSchemeType, AKANTU_INTEGRATION_SCHEME_TYPE)
			AKANTU_CLASS_ENUM_OUTPUT_STREAM(IntegrationSchemeType,
			AKANTU_INTEGRATION_SCHEME_TYPE)
			AKANTU_CLASS_ENUM_INPUT_STREAM(IntegrationSchemeType,
			AKANTU_INTEGRATION_SCHEME_TYPE)
			#else
			/// Type of integration scheme
			enum class IntegrationSchemeType {
			_pseudo_time, ///< Pseudo Time
			_forward_euler, ///< GeneralizedTrapezoidal(0)
			_trapezoidal_rule_1, ///< GeneralizedTrapezoidal(1/2)
			_backward_euler, ///< GeneralizedTrapezoidal(1)
			_central_difference, ///< NewmarkBeta(0, 1/2)
			_fox_goodwin, ///< NewmarkBeta(1/6, 1/2)
			_trapezoidal_rule_2, ///< NewmarkBeta(1/2, 1/2)
			_linear_acceleration, ///< NewmarkBeta(1/3, 1/2)
			_newmark_beta, ///< generic NewmarkBeta with user defined
			/// alpha and beta
			_generalized_trapezoidal ///< generic GeneralizedTrapezoidal with user
			/// defined alpha
			};
			#endif

			#if !defined(DOXYGEN)
			// clang-format off
			#define AKANTU_SOLVE_CONVERGENCE_CRITERIA \
			(residual) \
			(solution) \
			(residual_mass_wgh)
			// clang-format on
			AKANTU_CLASS_ENUM_DECLARE(SolveConvergenceCriteria,
			AKANTU_SOLVE_CONVERGENCE_CRITERIA)
			AKANTU_CLASS_ENUM_OUTPUT_STREAM(SolveConvergenceCriteria,
			AKANTU_SOLVE_CONVERGENCE_CRITERIA)
			AKANTU_CLASS_ENUM_INPUT_STREAM(SolveConvergenceCriteria,
			AKANTU_SOLVE_CONVERGENCE_CRITERIA)
			#else
			/// enum SolveConvergenceCriteria different convergence criteria
			enum class SolveConvergenceCriteria {
			_residual, ///< Use residual to test the convergence
			_solution, ///< Use solution to test the convergence
			_residual_mass_wgh ///< Use residual weighted by inv. nodal mass to
			///< testb
			};
			#endif

			/// enum CohesiveMethod type of insertion of cohesive elements
			enum CohesiveMethod { _intrinsic, _extrinsic };

			/// @enum MatrixType type of sparse matrix used
			enum MatrixType { _unsymmetric, _symmetric, _mt_not_defined };

			/* -------------------------------------------------------------------------- */
			/* Ghosts handling */
			/* -------------------------------------------------------------------------- */
			/// @enum CommunicatorType type of communication method to use
			enum CommunicatorType { _communicator_mpi, _communicator_dummy };

			#if !defined(DOXYGEN)
			// clang-format off
			#define AKANTU_SYNCHRONIZATION_TAG \
			(whatever) \
			(update) \
			(ask_nodes) \
			(size) \
			(smm_mass) \
			(smm_for_gradu) \
			(smm_boundary) \
			(smm_uv) \
			(smm_res) \
			(smm_init_mat) \
			(smm_stress) \
			(smmc_facets) \
			(smmc_facets_conn) \
			(smmc_facets_stress) \
			(smmc_damage) \
			(giu_global_conn) \
			(ce_groups) \
			(ce_insertion_order) \
			(gm_clusters) \
			(htm_temperature) \
			(htm_gradient_temperature) \
			(htm_phi) \
			(htm_gradient_phi) \
			(mnl_for_average) \
			(mnl_weight) \
			(nh_criterion) \
			(test) \
			(user_1) \
			(user_2) \
			(material_id) \
			(for_dump) \
			(cf_nodal) \
			(cf_incr) \
			(solver_solution)
			// clang-format on
			AKANTU_CLASS_ENUM_DECLARE(SynchronizationTag, AKANTU_SYNCHRONIZATION_TAG)
			AKANTU_CLASS_ENUM_OUTPUT_STREAM(SynchronizationTag, AKANTU_SYNCHRONIZATION_TAG)
			#else
			/// @enum SynchronizationTag type of synchronizations
			enum class SynchronizationTag {
			//--- Generic tags ---
			_whatever,
			_update,
			_ask_nodes,
			_size,

			//--- SolidMechanicsModel tags ---
			_smm_mass, ///< synchronization of the SolidMechanicsModel.mass
			_smm_for_gradu, ///< synchronization of the
			/// SolidMechanicsModel.displacement
			_smm_boundary, ///< synchronization of the boundary, forces, velocities
			/// and displacement
			_smm_uv, ///< synchronization of the nodal velocities and displacement
			_smm_res, ///< synchronization of the nodal residual
			_smm_init_mat, ///< synchronization of the data to initialize materials
			_smm_stress, ///< synchronization of the stresses to compute the
			///< internal
			/// forces
			_smmc_facets, ///< synchronization of facet data to setup facet synch
			_smmc_facets_conn, ///< synchronization of facet global connectivity
			_smmc_facets_stress, ///< synchronization of facets' stress to setup
			///< facet
			/// synch
			_smmc_damage, ///< synchronization of damage

			// --- GlobalIdsUpdater tags ---
			_giu_global_conn, ///< synchronization of global connectivities

			// --- CohesiveElementInserter tags ---
			_ce_groups, ///< synchronization of cohesive element insertion depending
			/// on facet groups
			_ce_insertion_order, ///< synchronization of the order of insertion of
			///cohesive elements

			// --- GroupManager tags ---
			_gm_clusters, ///< synchronization of clusters

			// --- HeatTransfer tags ---
			_htm_temperature, ///< synchronization of the nodal temperature
			_htm_gradient_temperature, ///< synchronization of the element gradient
			/// temperature
			// --- LevelSet tags ---
			_htm_phi, ///< synchronization of the nodal level set value phi
			_htm_gradient_phi, ///< synchronization of the element gradient phi

			//--- Material non local ---
			_mnl_for_average, ///< synchronization of data to average in non local
			/// material
			_mnl_weight, ///< synchronization of data for the weight computations

			// --- NeighborhoodSynchronization tags ---
			_nh_criterion,

			// --- General tags ---
			_test, ///< Test tag
			_user_1, ///< tag for user simulations
			_user_2, ///< tag for user simulations
			_material_id, ///< synchronization of the material ids
			_for_dump, ///< everything that needs to be synch before dump

			// --- Contact & Friction ---
			_cf_nodal, ///< synchronization of disp, velo, and current position
			_cf_incr, ///< synchronization of increment

			// --- Solver tags ---
			_solver_solution ///< synchronization of the solution obained with the
			/// PETSc solver
			};
			#endif

			/// @enum GhostType type of ghost
			enum GhostType {
			_not_ghost = 0,
			_ghost = 1,
			_casper // not used but a real cute ghost
			};

			/// Define the flag that can be set to a node
			enum class NodeFlag : std::uint8_t {
			_normal = 0x00,
			_distributed = 0x01,
			_master = 0x03,
			_slave = 0x05,
			_pure_ghost = 0x09,
			_shared_mask = 0x0F,
			_periodic = 0x10,
			_periodic_master = 0x30,
			_periodic_slave = 0x50,
			_periodic_mask = 0xF0,
			_local_master_mask = 0xCC, // ~(_master & _periodic_mask)
			};

			inline NodeFlag operator&(const NodeFlag & a, const NodeFlag & b) {
			using under = std::underlying_type_t<NodeFlag>;
			return NodeFlag(under(a) & under(b));
			}

			inline NodeFlag operator\|(const NodeFlag & a, const NodeFlag & b) {
			using under = std::underlying_type_t<NodeFlag>;
			return NodeFlag(under(a) \| under(b));
			}

			inline NodeFlag & operator\|=(NodeFlag & a, const NodeFlag & b) {
			a = a \| b;
			return a;
			}

			inline NodeFlag & operator&=(NodeFlag & a, const NodeFlag & b) {
			a = a & b;
			return a;
			}

			inline NodeFlag operator~(const NodeFlag & a) {
			using under = std::underlying_type_t<NodeFlag>;
			return NodeFlag(~under(a));
			}

			std::ostream & operator<<(std::ostream & stream, NodeFlag flag);

			} // namespace akantu

			AKANTU_ENUM_HASH(GhostType)

			namespace akantu {
			/* -------------------------------------------------------------------------- */
			struct GhostType_def {
			using type = GhostType;
			static const type _begin_ = _not_ghost;
			static const type _end_ = _casper;
			};

			using ghost_type_t = safe_enum<GhostType_def>;
			namespace {
			constexpr ghost_type_t ghost_types{_casper};
			}

			/// standard output stream operator for GhostType
			// inline std::ostream & operator<<(std::ostream & stream, GhostType type);

			/* -------------------------------------------------------------------------- */
			/* Global defines */
			/* -------------------------------------------------------------------------- */
			#define AKANTU_MIN_ALLOCATION 2000

			#define AKANTU_INDENT ' '
			#define AKANTU_INCLUDE_INLINE_IMPL

			/* -------------------------------------------------------------------------- */
			#define AKANTU_SET_MACRO(name, variable, type) \
			inline void set##name(type variable) { this->variable = variable; }

			#define AKANTU_GET_MACRO(name, variable, type) \
			inline type get##name() const { return variable; }

			#define AKANTU_GET_MACRO_NOT_CONST(name, variable, type) \
			inline type get##name() { return variable; }

			#define AKANTU_GET_MACRO_DEREF_PTR(name, ptr) \
			inline const auto & get##name() const { \
			if (not(ptr)) { \
			AKANTU_EXCEPTION("The member " << #ptr << " is not initialized"); \
			} \
			return (*(ptr)); \
			}

			#define AKANTU_GET_MACRO_DEREF_PTR_NOT_CONST(name, ptr) \
			inline auto & get##name() { \
			if (not(ptr)) { \
			AKANTU_EXCEPTION("The member " << #ptr << " is not initialized"); \
			} \
			return (*(ptr)); \
			}

			#define AKANTU_GET_MACRO_BY_SUPPORT_TYPE(name, variable, type, support, con) \
			inline con Array<type> & get##name(const support & el_type, \
			GhostType ghost_type = _not_ghost) \
			con { /* NOLINT */ \
			return variable(el_type, ghost_type); \
			} // NOLINT

			#define AKANTU_GET_MACRO_BY_ELEMENT_TYPE(name, variable, type) \
			AKANTU_GET_MACRO_BY_SUPPORT_TYPE(name, variable, type, ElementType, )
			#define AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(name, variable, type) \
			AKANTU_GET_MACRO_BY_SUPPORT_TYPE(name, variable, type, ElementType, const)

			#define AKANTU_GET_MACRO_BY_GEOMETRIE_TYPE(name, variable, type) \
			AKANTU_GET_MACRO_BY_SUPPORT_TYPE(name, variable, type, GeometricalType, )
			#define AKANTU_GET_MACRO_BY_GEOMETRIE_TYPE_CONST(name, variable, type) \
			AKANTU_GET_MACRO_BY_SUPPORT_TYPE(name, variable, type, GeometricalType, const)

			/* -------------------------------------------------------------------------- */
			/// initialize the static part of akantu
			void initialize(int & argc, char **& argv);
			/// initialize the static part of akantu and read the global input_file
			void initialize(const std::string & input_file, int & argc, char **& argv);
			/* -------------------------------------------------------------------------- */
			/// finilize correctly akantu and clean the memory
			void finalize();
			/* -------------------------------------------------------------------------- */
			/// Read an new input file
			void readInputFile(const std::string & input_file);
			/* -------------------------------------------------------------------------- */

			/* -------------------------------------------------------------------------- */
			/* string manipulation */
			/* -------------------------------------------------------------------------- */
			inline std::string to_lower(const std::string & str);
			/* -------------------------------------------------------------------------- */
			inline std::string trim(const std::string & to_trim);
			inline std::string trim(const std::string & to_trim, char c);
			/* -------------------------------------------------------------------------- */

			/* -------------------------------------------------------------------------- */
			/// give a string representation of the a human readable size in bit
			template <typename T> std::string printMemorySize(UInt size);
			/* -------------------------------------------------------------------------- */

			struct TensorTrait {};
			struct TensorProxyTrait {};

			} // namespace akantu

			/* -------------------------------------------------------------------------- */
			/* Type traits */
			/* -------------------------------------------------------------------------- */
			namespace aka {

			/* ------------------------------------------------------------------------ */
			template <typename T> using is_tensor = std::is_base_of<akantu::TensorTrait, T>;
			template <typename T>
			using is_tensor_proxy = std::is_base_of<akantu::TensorProxyTrait, T>;
			/* ------------------------------------------------------------------------ */
			template <typename T> using is_scalar = std::is_arithmetic<T>;
			/* ------------------------------------------------------------------------ */
			template <typename R, typename T,
			std::enable_if_t<std::is_reference<T>::value> * = nullptr>
			bool is_of_type(T && t) {
			return (
			dynamic_cast<std::add_pointer_t<
			std::conditional_t<std::is_const<std::remove_reference_t<T>>::value,
			std::add_const_t<R>, R>>>(&t) != nullptr);
			}

			/* -------------------------------------------------------------------------- */
			template <typename R, typename T> bool is_of_type(std::unique_ptr<T> & t) {
			return (
			dynamic_cast<std::add_pointer_t<
			std::conditional_t<std::is_const<T>::value, std::add_const_t<R>, R>>>(
			t.get()) != nullptr);
			}

			/* ------------------------------------------------------------------------ */
			template <typename R, typename T,
			std::enable_if_t<std::is_reference<T>::value> * = nullptr>
			decltype(auto) as_type(T && t) {
			static_assert(
			disjunction<
			std::is_base_of<std::decay_t<T>, std::decay_t<R>>, // down-cast
			std::is_base_of<std::decay_t<R>, std::decay_t<T>> // up-cast
			>::value,
			"Type T and R are not valid for a as_type conversion");
			return dynamic_cast<std::add_lvalue_reference_t<
			std::conditional_t<std::is_const<std::remove_reference_t<T>>::value,
			std::add_const_t<R>, R>>>(t);
			}

			/* -------------------------------------------------------------------------- */
			template <typename R, typename T,
			std::enable_if_t<std::is_pointer<T>::value> * = nullptr>
			decltype(auto) as_type(T && t) {
			return &as_type<R>(*t);
			}

			/* -------------------------------------------------------------------------- */
			template <typename R, typename T>
			decltype(auto) as_type(const std::shared_ptr<T> & t) {
			return std::dynamic_pointer_cast<R>(t);
			}

			} // namespace aka

			#include "aka_common_inline_impl.hh"

			#include "aka_fwd.hh"

			namespace akantu {
			/// get access to the internal argument parser
			cppargparse::ArgumentParser & getStaticArgumentParser();

			/// get access to the internal input file parser
			Parser & getStaticParser();

			/// get access to the user part of the internal input file parser
			const ParserSection & getUserParser();

			#define AKANTU_CURRENT_FUNCTION \
			(std::string(__func__) + "():" + std::to_string(__LINE__))

			} // namespace akantu

			/* -------------------------------------------------------------------------- */
			#if AKANTU_INTEGER_SIZE == 4
			#define AKANTU_HASH_COMBINE_MAGIC_NUMBER 0x9e3779b9
			#elif AKANTU_INTEGER_SIZE == 8
			#define AKANTU_HASH_COMBINE_MAGIC_NUMBER 0x9e3779b97f4a7c13LL
			#endif

			namespace std {
			/**
			* Hashing function for pairs based on hash_combine from boost The magic
			* number is coming from the golden number @f[\phi = \frac{1 + \sqrt5}{2}@f]
			* @f[\frac{2^32}{\phi} = 0x9e3779b9@f]
			* http://stackoverflow.com/questions/4948780/magic-number-in-boosthash-combine
			* http://burtleburtle.net/bob/hash/doobs.html
			*/
			template <typename a, typename b> struct hash<std::pair<a, b>> {
			hash() = default;
			size_t operator()(const std::pair<a, b> & p) const {
			size_t seed = ah(p.first);
			return bh(p.second) + AKANTU_HASH_COMBINE_MAGIC_NUMBER + (seed << 6) +
			(seed >> 2);
			}

			private:
			const hash<a> ah{};
			const hash<b> bh{};
			};

			} // namespace std

			#endif // AKANTU_COMMON_HH_

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aka_common.hh
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