From: Maximilian Bergbauer Date: Wed, 18 Jan 2023 11:55:42 +0000 (+0100) Subject: Enable vectorization over quadrature points in whole FEPointEvaluation X-Git-Tag: v9.5.0-rc1~312^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F15013%2Fhead;p=dealii.git Enable vectorization over quadrature points in whole FEPointEvaluation --- diff --git a/include/deal.II/base/signaling_nan.h b/include/deal.II/base/signaling_nan.h index bbd8d827f2..d2e001ebb2 100644 --- a/include/deal.II/base/signaling_nan.h +++ b/include/deal.II/base/signaling_nan.h @@ -82,6 +82,18 @@ namespace numbers }; + template + struct NaNInitializer> + { + static VectorizedArray + invalid_element() + { + return VectorizedArray( + NaNInitializer::invalid_element()); + } + }; + + /** * A specialization of the general NaNInitializer class that provides a * function that returns a Tensor<1,dim> value whose components are diff --git a/include/deal.II/matrix_free/fe_point_evaluation.h b/include/deal.II/matrix_free/fe_point_evaluation.h index 3b87de8f09..4e07a9a447 100644 --- a/include/deal.II/matrix_free/fe_point_evaluation.h +++ b/include/deal.II/matrix_free/fe_point_evaluation.h @@ -40,6 +40,21 @@ namespace internal { namespace FEPointEvaluation { + template + struct VectorizedPointsTypeTraits + { + using value_type = VectorizedArray; + static constexpr std::size_t stride = value_type::size(); + }; + + template + struct VectorizedPointsTypeTraits> + { + using value_type = VectorizedArray; + static constexpr std::size_t stride = 1; + }; + + /** * Struct to distinguish between the value and gradient types of different * numbers of components used by the FlexibleEvaluator class. @@ -47,8 +62,22 @@ namespace internal template struct EvaluatorTypeTraits { - using value_type = Tensor<1, n_components, Number>; + using ScalarNumber = + typename internal::VectorizedArrayTrait::value_type; + using VectorizedArrayType = + typename internal::FEPointEvaluation::VectorizedPointsTypeTraits< + Number>::value_type; + using value_type = Tensor<1, n_components, Number>; + using scalar_value_type = Tensor<1, n_components, ScalarNumber>; + using vectorized_value_type = + Tensor<1, n_components, VectorizedArrayType>; using gradient_type = Tensor<1, n_components, Tensor<1, dim, Number>>; + using scalar_gradient_type = + Tensor<1, n_components, Tensor<1, dim, ScalarNumber>>; + using vectorized_gradient_type = + Tensor<1, n_components, Tensor<1, dim, VectorizedArrayType>>; + using interface_vectorized_gradient_type = + Tensor<1, dim, Tensor<1, n_components, VectorizedArrayType>>; static void read_value(const Number vector_entry, @@ -69,11 +98,9 @@ namespace internal } static void - set_gradient( - const Tensor<1, dim, Tensor<1, n_components, VectorizedArray>> - & value, - const unsigned int vector_lane, - gradient_type & result) + set_gradient(const interface_vectorized_gradient_type &value, + const unsigned int vector_lane, + scalar_gradient_type & result) { for (unsigned int i = 0; i < n_components; ++i) for (unsigned int d = 0; d < dim; ++d) @@ -81,10 +108,19 @@ namespace internal } static void - get_gradient( - Tensor<1, dim, Tensor<1, n_components, VectorizedArray>> &value, - const unsigned int vector_lane, - const gradient_type &result) + set_gradient(const interface_vectorized_gradient_type &value, + const unsigned int, + vectorized_gradient_type &result) + { + for (unsigned int i = 0; i < n_components; ++i) + for (unsigned int d = 0; d < dim; ++d) + result[i][d] = value[d][i]; + } + + static void + get_gradient(interface_vectorized_gradient_type &value, + const unsigned int vector_lane, + const scalar_gradient_type & result) { for (unsigned int i = 0; i < n_components; ++i) for (unsigned int d = 0; d < dim; ++d) @@ -92,45 +128,125 @@ namespace internal } static void - set_value(const Tensor<1, n_components, VectorizedArray> &value, - const unsigned int vector_lane, - value_type & result) + get_gradient(interface_vectorized_gradient_type &value, + const unsigned int, + const vectorized_gradient_type &result) + { + for (unsigned int i = 0; i < n_components; ++i) + for (unsigned int d = 0; d < dim; ++d) + value[d][i] = result[i][d]; + } + + static void + set_zero_gradient(gradient_type &value, const unsigned int vector_lane) + { + for (unsigned int i = 0; i < n_components; ++i) + for (unsigned int d = 0; d < dim; ++d) + internal::VectorizedArrayTrait::get(value[i][d], + vector_lane) = 0.; + } + + static void + set_value(const vectorized_value_type &value, + const unsigned int vector_lane, + scalar_value_type & result) { for (unsigned int i = 0; i < n_components; ++i) result[i] = value[i][vector_lane]; } static void - get_value(Tensor<1, n_components, VectorizedArray> &value, - const unsigned int vector_lane, - const value_type & result) + set_value(const vectorized_value_type &value, + const unsigned int, + vectorized_value_type &result) + { + result = value; + } + + static void + get_value(vectorized_value_type & value, + const unsigned int vector_lane, + const scalar_value_type &result) { for (unsigned int i = 0; i < n_components; ++i) value[i][vector_lane] = result[i]; } - template - static Number2 & - access(Tensor<1, n_components, Number2> &value, - const unsigned int component) + static void + get_value(vectorized_value_type &value, + const unsigned int, + const vectorized_value_type &result) + { + value = result; + } + + static void + set_zero_value(value_type &value, const unsigned int vector_lane) { - return value[component]; + for (unsigned int i = 0; i < n_components; ++i) + internal::VectorizedArrayTrait::get(value[i], vector_lane) = + 0.; } - template - static const Number2 & - access(const Tensor<1, n_components, Number2> &value, - const unsigned int component) + static void + access(value_type & value, + const unsigned int vector_lane, + const unsigned int component, + const ScalarNumber &shape_value) { - return value[component]; + internal::VectorizedArrayTrait::get(value[component], + vector_lane) += shape_value; + } + + static ScalarNumber + access(const value_type & value, + const unsigned int vector_lane, + const unsigned int component) + { + return internal::VectorizedArrayTrait::get(value[component], + vector_lane); + } + + static void + access(gradient_type & value, + const unsigned int vector_lane, + const unsigned int component, + const Tensor<1, dim, ScalarNumber> &shape_gradient) + { + for (unsigned int d = 0; d < dim; ++d) + internal::VectorizedArrayTrait::get(value[component][d], + vector_lane) += + shape_gradient[d]; + } + + static Tensor<1, dim, ScalarNumber> + access(const gradient_type &value, + const unsigned int vector_lane, + const unsigned int component) + { + Tensor<1, dim, ScalarNumber> result; + for (unsigned int d = 0; d < dim; ++d) + result[d] = + internal::VectorizedArrayTrait::get(value[component][d], + vector_lane); + return result; } }; template struct EvaluatorTypeTraits { - using value_type = Number; - using gradient_type = Tensor<1, dim, Number>; + using ScalarNumber = + typename internal::VectorizedArrayTrait::value_type; + using VectorizedArrayType = + typename internal::FEPointEvaluation::VectorizedPointsTypeTraits< + Number>::value_type; + using value_type = Number; + using scalar_value_type = ScalarNumber; + using vectorized_value_type = VectorizedArrayType; + using gradient_type = Tensor<1, dim, Number>; + using scalar_gradient_type = Tensor<1, dim, ScalarNumber>; + using vectorized_gradient_type = Tensor<1, dim, VectorizedArrayType>; static void read_value(const Number vector_entry, @@ -149,59 +265,143 @@ namespace internal } static void - set_gradient(const Tensor<1, dim, VectorizedArray> &value, - const unsigned int vector_lane, - gradient_type & result) + set_gradient(const vectorized_gradient_type &value, + const unsigned int vector_lane, + scalar_gradient_type & result) { for (unsigned int d = 0; d < dim; ++d) result[d] = value[d][vector_lane]; } static void - get_gradient(Tensor<1, dim, VectorizedArray> &value, - const unsigned int vector_lane, - const gradient_type & result) + set_gradient(const vectorized_gradient_type &value, + const unsigned int, + vectorized_gradient_type &result) + { + result = value; + } + + static void + get_gradient(vectorized_gradient_type & value, + const unsigned int vector_lane, + const scalar_gradient_type &result) { for (unsigned int d = 0; d < dim; ++d) value[d][vector_lane] = result[d]; } static void - set_value(const VectorizedArray &value, - const unsigned int vector_lane, - value_type & result) + get_gradient(vectorized_gradient_type &value, + const unsigned int, + const vectorized_gradient_type &result) + { + value = result; + } + + static void + set_zero_gradient(gradient_type &value, const unsigned int vector_lane) + { + for (unsigned int d = 0; d < dim; ++d) + internal::VectorizedArrayTrait::get(value[d], vector_lane) = + 0.; + } + + static void + set_value(const vectorized_value_type &value, + const unsigned int vector_lane, + scalar_value_type & result) { result = value[vector_lane]; } static void - get_value(VectorizedArray &value, + set_value(const vectorized_value_type &value, + const unsigned int, + vectorized_value_type &result) + { + result = value; + } + + static void + get_value(vectorized_value_type & value, const unsigned int vector_lane, - const value_type & result) + const scalar_value_type &result) { value[vector_lane] = result; } - template - static Number2 & - access(Number2 &value, const unsigned int) + static void + get_value(vectorized_value_type &value, + const unsigned int, + const vectorized_value_type &result) + { + value = result; + } + + static void + set_zero_value(value_type &value, const unsigned int vector_lane) + { + internal::VectorizedArrayTrait::get(value, vector_lane) = 0.; + } + + static void + access(value_type & value, + const unsigned int vector_lane, + const unsigned int, + const ScalarNumber &shape_value) + { + internal::VectorizedArrayTrait::get(value, vector_lane) += + shape_value; + } + + static ScalarNumber + access(const value_type & value, + const unsigned int vector_lane, + const unsigned int) { - return value; + return internal::VectorizedArrayTrait::get(value, vector_lane); } - template - static const Number2 & - access(const Number2 &value, const unsigned int) + static void + access(gradient_type & value, + const unsigned int vector_lane, + const unsigned int, + const scalar_gradient_type &shape_gradient) { - return value; + for (unsigned int d = 0; d < dim; ++d) + internal::VectorizedArrayTrait::get(value[d], vector_lane) += + shape_gradient[d]; + } + + static scalar_gradient_type + access(const gradient_type &value, + const unsigned int vector_lane, + const unsigned int) + { + scalar_gradient_type result; + for (unsigned int d = 0; d < dim; ++d) + result[d] = + internal::VectorizedArrayTrait::get(value[d], vector_lane); + return result; } }; template struct EvaluatorTypeTraits { - using value_type = Tensor<1, dim, Number>; - using gradient_type = Tensor<2, dim, Number>; + using ScalarNumber = + typename internal::VectorizedArrayTrait::value_type; + using VectorizedArrayType = + typename internal::FEPointEvaluation::VectorizedPointsTypeTraits< + Number>::value_type; + using value_type = Tensor<1, dim, Number>; + using scalar_value_type = Tensor<1, dim, ScalarNumber>; + using vectorized_value_type = Tensor<1, dim, VectorizedArrayType>; + using gradient_type = Tensor<2, dim, Number>; + using scalar_gradient_type = Tensor<2, dim, ScalarNumber>; + using vectorized_gradient_type = Tensor<2, dim, VectorizedArrayType>; + using interface_vectorized_gradient_type = + Tensor<1, dim, Tensor<1, dim, VectorizedArrayType>>; static void read_value(const Number vector_entry, @@ -220,10 +420,9 @@ namespace internal } static void - set_gradient( - const Tensor<1, dim, Tensor<1, dim, VectorizedArray>> &value, - const unsigned int vector_lane, - gradient_type & result) + set_gradient(const interface_vectorized_gradient_type &value, + const unsigned int vector_lane, + scalar_gradient_type & result) { for (unsigned int i = 0; i < dim; ++i) for (unsigned int d = 0; d < dim; ++d) @@ -231,10 +430,19 @@ namespace internal } static void - get_gradient( - Tensor<1, dim, Tensor<1, dim, VectorizedArray>> &value, - const unsigned int vector_lane, - const gradient_type & result) + set_gradient(const interface_vectorized_gradient_type &value, + const unsigned int, + vectorized_gradient_type &result) + { + for (unsigned int i = 0; i < dim; ++i) + for (unsigned int d = 0; d < dim; ++d) + result[i][d] = value[d][i]; + } + + static void + get_gradient(interface_vectorized_gradient_type &value, + const unsigned int vector_lane, + const scalar_gradient_type & result) { for (unsigned int i = 0; i < dim; ++i) for (unsigned int d = 0; d < dim; ++d) @@ -242,53 +450,125 @@ namespace internal } static void - set_value(const Tensor<1, dim, VectorizedArray> &value, - const unsigned int vector_lane, - value_type & result) + get_gradient(interface_vectorized_gradient_type &value, + const unsigned int, + const vectorized_gradient_type &result) + { + for (unsigned int i = 0; i < dim; ++i) + for (unsigned int d = 0; d < dim; ++d) + value[d][i] = result[i][d]; + } + + static void + set_zero_gradient(gradient_type &value, const unsigned int vector_lane) + { + for (unsigned int i = 0; i < dim; ++i) + for (unsigned int d = 0; d < dim; ++d) + internal::VectorizedArrayTrait::get(value[i][d], + vector_lane) = 0.; + } + + static void + set_value(const vectorized_value_type &value, + const unsigned int vector_lane, + scalar_value_type & result) { for (unsigned int i = 0; i < dim; ++i) result[i] = value[i][vector_lane]; } static void - get_value(Tensor<1, dim, VectorizedArray> &value, - const unsigned int vector_lane, - const value_type & result) + set_value(const vectorized_value_type &value, + const unsigned int, + vectorized_value_type &result) + { + result = value; + } + + static void + get_value(vectorized_value_type & value, + const unsigned int vector_lane, + const scalar_value_type &result) { for (unsigned int i = 0; i < dim; ++i) value[i][vector_lane] = result[i]; } - static Number & - access(value_type &value, const unsigned int component) + static void + get_value(vectorized_value_type &value, + const unsigned int, + const vectorized_value_type &result) { - return value[component]; + value = result; } - static const Number & - access(const value_type &value, const unsigned int component) + static void + set_zero_value(value_type &value, const unsigned int vector_lane) { - return value[component]; + for (unsigned int i = 0; i < dim; ++i) + internal::VectorizedArrayTrait::get(value[i], vector_lane) = + 0.; } - static Tensor<1, dim, Number> & - access(gradient_type &value, const unsigned int component) + static void + access(value_type & value, + const unsigned int vector_lane, + const unsigned int component, + const ScalarNumber &shape_value) { - return value[component]; + internal::VectorizedArrayTrait::get(value[component], + vector_lane) += shape_value; } - static const Tensor<1, dim, Number> & - access(const gradient_type &value, const unsigned int component) + static ScalarNumber + access(const value_type & value, + const unsigned int vector_lane, + const unsigned int component) { - return value[component]; + return internal::VectorizedArrayTrait::get(value[component], + vector_lane); + } + + static void + access(gradient_type & value, + const unsigned int vector_lane, + const unsigned int component, + const Tensor<1, dim, ScalarNumber> &shape_gradient) + { + for (unsigned int d = 0; d < dim; ++d) + internal::VectorizedArrayTrait::get(value[component][d], + vector_lane) += + shape_gradient[d]; + } + + static Tensor<1, dim, ScalarNumber> + access(const gradient_type &value, + const unsigned int vector_lane, + const unsigned int component) + { + Tensor<1, dim, ScalarNumber> result; + for (unsigned int d = 0; d < dim; ++d) + result[d] = + internal::VectorizedArrayTrait::get(value[component][d], + vector_lane); + return result; } }; template struct EvaluatorTypeTraits<1, 1, Number> { - using value_type = Number; - using gradient_type = Tensor<1, 1, Number>; + using ScalarNumber = + typename internal::VectorizedArrayTrait::value_type; + using VectorizedArrayType = + typename internal::FEPointEvaluation::VectorizedPointsTypeTraits< + Number>::value_type; + using value_type = Number; + using scalar_value_type = ScalarNumber; + using vectorized_value_type = VectorizedArrayType; + using gradient_type = Tensor<1, 1, Number>; + using scalar_gradient_type = Tensor<1, 1, ScalarNumber>; + using vectorized_gradient_type = Tensor<1, 1, VectorizedArrayType>; static void read_value(const Number vector_entry, @@ -307,49 +587,118 @@ namespace internal } static void - set_gradient(const Tensor<1, 1, VectorizedArray> &value, - const unsigned int vector_lane, - gradient_type & result) + set_gradient(const vectorized_gradient_type &value, + const unsigned int vector_lane, + scalar_gradient_type & result) { result[0] = value[0][vector_lane]; } static void - get_gradient(Tensor<1, 1, VectorizedArray> &value, - const unsigned int vector_lane, - const gradient_type & result) + set_gradient(const vectorized_gradient_type &value, + const unsigned int, + vectorized_gradient_type &result) + { + result = value; + } + + static void + get_gradient(vectorized_gradient_type & value, + const unsigned int vector_lane, + const scalar_gradient_type &result) { value[0][vector_lane] = result[0]; } static void - set_value(const VectorizedArray &value, - const unsigned int vector_lane, - value_type & result) + get_gradient(vectorized_gradient_type &value, + const unsigned int, + const vectorized_gradient_type &result) + { + value = result; + } + + static void + set_zero_gradient(gradient_type &value, const unsigned int vector_lane) + { + internal::VectorizedArrayTrait::get(value[0], vector_lane) = 0.; + } + + static void + set_value(const vectorized_value_type &value, + const unsigned int vector_lane, + scalar_value_type & result) { result = value[vector_lane]; } static void - get_value(VectorizedArray &value, + set_value(const vectorized_value_type &value, + const unsigned int, + vectorized_value_type &result) + { + result = value; + } + + static void + get_value(vectorized_value_type & value, const unsigned int vector_lane, - const value_type & result) + const scalar_value_type &result) { value[vector_lane] = result; } - template - static Number2 & - access(Number2 &value, const unsigned int) + static void + get_value(vectorized_value_type &value, + const unsigned int, + const vectorized_value_type &result) + { + value = result; + } + + static void + set_zero_value(value_type &value, const unsigned int vector_lane) + { + internal::VectorizedArrayTrait::get(value, vector_lane) = 0.; + } + + static void + access(value_type & value, + const unsigned int vector_lane, + const unsigned int, + const ScalarNumber &shape_value) + { + internal::VectorizedArrayTrait::get(value, vector_lane) += + shape_value; + } + + static ScalarNumber + access(const value_type & value, + const unsigned int vector_lane, + const unsigned int) { - return value; + return internal::VectorizedArrayTrait::get(value, vector_lane); } - template - static const Number2 & - access(const Number2 &value, const unsigned int) + static void + access(gradient_type & value, + const unsigned int vector_lane, + const unsigned int, + const scalar_gradient_type &shape_gradient) { - return value; + internal::VectorizedArrayTrait::get(value[0], vector_lane) += + shape_gradient[0]; + } + + static scalar_gradient_type + access(const gradient_type &value, + const unsigned int vector_lane, + const unsigned int) + { + scalar_gradient_type result; + result[0] = + internal::VectorizedArrayTrait::get(value[0], vector_lane); + return result; } }; @@ -412,10 +761,17 @@ public: using number_type = Number; - using value_type = typename internal::FEPointEvaluation:: - EvaluatorTypeTraits::value_type; - using gradient_type = typename internal::FEPointEvaluation:: - EvaluatorTypeTraits::gradient_type; + using ScalarNumber = + typename internal::VectorizedArrayTrait::value_type; + using VectorizedArrayType = + typename internal::FEPointEvaluation::VectorizedPointsTypeTraits< + Number>::value_type; + using ETT = typename internal::FEPointEvaluation:: + EvaluatorTypeTraits; + using value_type = typename ETT::value_type; + using scalar_value_type = typename ETT::scalar_value_type; + using vectorized_value_type = typename ETT::vectorized_value_type; + using gradient_type = typename ETT::gradient_type; /** * Constructor. @@ -523,7 +879,7 @@ public: * evaluated at the points. */ void - evaluate(const ArrayView & solution_values, + evaluate(const ArrayView & solution_values, const EvaluationFlags::EvaluationFlags &evaluation_flags); /** @@ -550,7 +906,7 @@ public: * */ void - integrate(const ArrayView & solution_values, + integrate(const ArrayView & solution_values, const EvaluationFlags::EvaluationFlags &integration_flags); /** @@ -614,7 +970,7 @@ public: * given point index. Prerequisite: This class needs to be constructed with * UpdateFlags containing `update_jacobian`. */ - DerivativeForm<1, dim, spacedim> + DerivativeForm<1, dim, spacedim, Number> jacobian(const unsigned int point_index) const; /** @@ -623,7 +979,7 @@ public: * constructed with UpdateFlags containing `update_inverse_jacobian` or * `update_gradients`. */ - DerivativeForm<1, spacedim, dim> + DerivativeForm<1, spacedim, dim, Number> inverse_jacobian(const unsigned int point_index) const; /** @@ -639,21 +995,21 @@ public: * this function needs to be constructed with UpdateFlags containing * `update_normal_vectors`. */ - Tensor<1, spacedim> + Tensor<1, spacedim, Number> normal_vector(const unsigned int point_index) const; /** * Return the position in real coordinates of the given point index among * the points passed to reinit(). */ - Point + Point real_point(const unsigned int point_index) const; /** * Return the position in unit/reference coordinates of the given point * index, i.e., the respective point passed to the reinit() function. */ - Point + Point unit_point(const unsigned int point_index) const; /** @@ -684,11 +1040,44 @@ private: void do_reinit(); + /** + * Fast path of the evaluate function. + */ + void + evaluate_fast(const ArrayView & solution_values, + const EvaluationFlags::EvaluationFlags &evaluation_flags); + + /** + * Slow path of the evaluate function using FEValues. + */ + void + evaluate_slow(const ArrayView & solution_values, + const EvaluationFlags::EvaluationFlags &evaluation_flags); + + /** + * Fast path of the integrate function. + */ + void + integrate_fast(const ArrayView & solution_values, + const EvaluationFlags::EvaluationFlags &integration_flags); + + /** + * Slow path of the integrate function using FEValues. + */ + void + integrate_slow(const ArrayView & solution_values, + const EvaluationFlags::EvaluationFlags &integration_flags); + /** * Number of quadrature points of the current cell/face. */ const unsigned int n_q_points; + /** + * Number of active quadrature points of the last quadrature point batch. + */ + const unsigned int n_filled_lanes_last_batch; + /** * Pointer to the Mapping object passed to the constructor. */ @@ -719,22 +1108,19 @@ private: /** * Temporary array to store the `solution_values` passed to the evaluate() * function in a format compatible with the tensor product evaluators. For - * vector-valued setups, this array uses a `Tensor<1, n_components>` type to - * collect the unknowns for a particular basis function. + * vector-valued setups, this array uses a `Tensor<1, n_components, + * ScalarNumber>` type to collect the unknowns for a particular basis + * function. */ - std::vector solution_renumbered; + std::vector solution_renumbered; /** * Temporary array to store a vectorized version of the `solution_values` * computed during `integrate()` in a format compatible with the tensor * product evaluators. For vector-valued setups, this array uses a - * `Tensor<1, n_components, VectorizedArray>` format. + * `Tensor<1, n_components, VectorizedArrayType>` format. */ - AlignedVector>::value_type> - solution_renumbered_vectorized; + AlignedVector solution_renumbered_vectorized; /** * Temporary array to store the values at the points. @@ -821,7 +1207,7 @@ private: * Vector containing tensor product shape functions evaluated (during * reinit()) at the vectorized unit points. */ - AlignedVector, 2, dim>> shapes; + AlignedVector> shapes; }; // ----------------------- template and inline function ---------------------- @@ -834,6 +1220,7 @@ FEPointEvaluation::FEPointEvaluation( const UpdateFlags update_flags, const unsigned int first_selected_component) : n_q_points(numbers::invalid_unsigned_int) + , n_filled_lanes_last_batch(numbers::invalid_unsigned_int) , mapping(&mapping) , fe(&fe) , update_flags(update_flags) @@ -856,6 +1243,7 @@ FEPointEvaluation::FEPointEvaluation( const FiniteElement & fe, const unsigned int first_selected_component) : n_q_points(numbers::invalid_unsigned_int) + , n_filled_lanes_last_batch(numbers::invalid_unsigned_int) , mapping(&mapping_info.get_mapping()) , fe(&fe) , update_flags(mapping_info.get_update_flags()) @@ -875,6 +1263,7 @@ template FEPointEvaluation::FEPointEvaluation( FEPointEvaluation &other) noexcept : n_q_points(other.n_q_points) + , n_filled_lanes_last_batch(numbers::invalid_unsigned_int) , mapping(other.mapping) , fe(other.fe) , poly(other.poly) @@ -913,6 +1302,7 @@ template FEPointEvaluation::FEPointEvaluation( FEPointEvaluation &&other) noexcept : n_q_points(other.n_q_points) + , n_filled_lanes_last_batch(numbers::invalid_unsigned_int) , mapping(other.mapping) , fe(other.fe) , poly(other.poly) @@ -1095,7 +1485,23 @@ FEPointEvaluation::do_reinit() const auto unit_points = mapping_info->get_unit_points(current_cell_index, current_face_number); - const_cast(n_q_points) = unit_points.size(); + const unsigned int n_q_points_unvectorized = unit_points.size(); + + if (std::is_same::value) + { + const_cast(n_q_points) = unit_points.size(); + } + else + { + const unsigned int n_lanes = + internal::VectorizedArrayTrait::width; + const_cast(n_filled_lanes_last_batch) = + n_q_points_unvectorized % n_lanes; + const_cast(n_q_points) = + n_q_points_unvectorized / n_lanes; + if (n_filled_lanes_last_batch > 0) + ++const_cast(n_q_points); + } if (update_flags & update_values) values.resize(n_q_points, numbers::signaling_nan()); @@ -1105,7 +1511,7 @@ FEPointEvaluation::do_reinit() if (!polynomials_are_hat_functions) { const std::size_t n_points = unit_points.size(); - const std::size_t n_lanes = VectorizedArray::size(); + const std::size_t n_lanes = VectorizedArrayType::size(); const std::size_t n_batches = n_points / n_lanes + (n_points % n_lanes > 0 ? 1 : 0); const std::size_t n_shapes = poly.size(); @@ -1113,7 +1519,7 @@ FEPointEvaluation::do_reinit() for (unsigned int i = 0, qb = 0; i < n_points; i += n_lanes, ++qb) { // convert to vectorized format - Point> vectorized_points; + Point vectorized_points; for (unsigned int j = 0; j < n_lanes && i + j < n_points; ++j) for (unsigned int d = 0; d < dim; ++d) vectorized_points[d][j] = unit_points[i + j][d]; @@ -1131,11 +1537,215 @@ FEPointEvaluation::do_reinit() +template +inline void +FEPointEvaluation::evaluate_fast( + const ArrayView & solution_values, + const EvaluationFlags::EvaluationFlags &evaluation_flags) +{ + // fast path with tensor product evaluation + if (solution_renumbered.size() != dofs_per_component) + solution_renumbered.resize(dofs_per_component); + for (unsigned int comp = 0; comp < n_components; ++comp) + for (unsigned int i = 0; i < dofs_per_component; ++i) + internal::FEPointEvaluation:: + EvaluatorTypeTraits::read_value( + solution_values[renumber[(component_in_base_element + comp) * + dofs_per_component + + i]], + comp, + solution_renumbered[i]); + + // unit gradients are currently only implemented with the fast tensor + // path + unit_gradients.resize(n_q_points, numbers::signaling_nan()); + + const auto unit_points = + mapping_info->get_unit_points(current_cell_index, current_face_number); + const auto &mapping_data = + mapping_info->get_mapping_data(current_cell_index, current_face_number); + + const std::size_t n_points = unit_points.size(); + const std::size_t n_lanes = + internal::VectorizedArrayTrait::width; + const std::size_t stride = + internal::FEPointEvaluation::VectorizedPointsTypeTraits::stride; + + // loop over quadrature batches qb / points q + for (unsigned int qb = 0, q = 0; q < n_points; ++qb, q += n_lanes) + { + // compute + const unsigned int n_shapes = poly.size(); + const auto val_and_grad = [&]() { + if (polynomials_are_hat_functions) + { + // convert quadrature points to vectorized format + Point vectorized_points; + for (unsigned int v = 0; v < n_lanes && q + v < n_points; ++v) + for (unsigned int d = 0; d < dim; ++d) + vectorized_points[d][v] = unit_points[q + v][d]; + + return internal::evaluate_tensor_product_value_and_gradient_linear( + poly, solution_renumbered, vectorized_points); + } + else + return internal::evaluate_tensor_product_value_and_gradient_shapes< + dim, + scalar_value_type, + VectorizedArrayType>(make_array_view(shapes.begin() + qb * n_shapes, + shapes.begin() + + (qb * n_shapes + n_shapes)), + poly.size(), + solution_renumbered); + }(); + + if (evaluation_flags & EvaluationFlags::values) + { + for (unsigned int v = 0; v < stride && q + v < n_points; ++v) + internal::FEPointEvaluation:: + EvaluatorTypeTraits::set_value( + val_and_grad.first, v, values[qb * stride + v]); + } + if (evaluation_flags & EvaluationFlags::gradients) + { + Assert(update_flags & update_gradients || + update_flags & update_inverse_jacobians, + ExcNotInitialized()); + if (std::is_same::value) + { + // convert back to standard format + for (unsigned int v = 0; v < n_lanes && q + v < n_points; ++v) + { + internal::FEPointEvaluation::EvaluatorTypeTraits< + dim, + n_components, + Number>::set_gradient(val_and_grad.second, + v, + unit_gradients[q + v]); + gradients[q + v] = apply_transformation( + mapping_data.inverse_jacobians[q + v].transpose(), + unit_gradients[q + v]); + } + } + else + { + // convert to vectorized format + DerivativeForm<1, spacedim, dim, Number> + vectorized_inverse_transposed_jacobians; + for (unsigned int v = 0; v < n_lanes && q + v < n_points; ++v) + for (unsigned int d = 0; d < dim; ++d) + for (unsigned int s = 0; s < spacedim; ++s) + internal::VectorizedArrayTrait::get( + vectorized_inverse_transposed_jacobians[s][d], v) = + mapping_data.inverse_jacobians[q + v].transpose()[s][d]; + + internal::FEPointEvaluation:: + EvaluatorTypeTraits::set_gradient( + val_and_grad.second, 0, unit_gradients[qb]); + gradients[qb] = + apply_transformation(vectorized_inverse_transposed_jacobians, + unit_gradients[qb]); + } + } + } +} + + + +template +inline void +FEPointEvaluation::evaluate_slow( + const ArrayView & solution_values, + const EvaluationFlags::EvaluationFlags &evaluation_flags) +{ + // slow path with FEValues + Assert(fe_values.get() != nullptr, + ExcMessage( + "Not initialized. Please call FEPointEvaluation::reinit()!")); + + const std::size_t n_points = fe_values->get_quadrature().size(); + const std::size_t n_lanes = internal::VectorizedArrayTrait::width; + + if (evaluation_flags & EvaluationFlags::values) + { + values.resize(n_q_points); + std::fill(values.begin(), values.end(), value_type()); + for (unsigned int i = 0; i < fe->n_dofs_per_cell(); ++i) + { + const ScalarNumber value = solution_values[i]; + for (unsigned int d = 0; d < n_components; ++d) + if (nonzero_shape_function_component[i][d] && + (fe->is_primitive(i) || fe->is_primitive())) + for (unsigned int qb = 0, q = 0; q < n_points; ++qb, q += n_lanes) + for (unsigned int v = 0; + v < (q + n_lanes > n_points ? n_filled_lanes_last_batch : + n_lanes); + ++v) + internal::FEPointEvaluation:: + EvaluatorTypeTraits::access( + values[qb], + v, + d, + fe_values->shape_value(i, q + v) * value); + else if (nonzero_shape_function_component[i][d]) + for (unsigned int qb = 0, q = 0; q < n_points; ++qb, q += n_lanes) + for (unsigned int v = 0; + v < (q + n_lanes > n_points ? n_filled_lanes_last_batch : + n_lanes); + ++v) + internal::FEPointEvaluation:: + EvaluatorTypeTraits::access( + values[qb], + v, + d, + fe_values->shape_value_component(i, q + v, d) * value); + } + } + + if (evaluation_flags & EvaluationFlags::gradients) + { + gradients.resize(n_q_points); + std::fill(gradients.begin(), gradients.end(), gradient_type()); + for (unsigned int i = 0; i < fe->n_dofs_per_cell(); ++i) + { + const ScalarNumber value = solution_values[i]; + for (unsigned int d = 0; d < n_components; ++d) + if (nonzero_shape_function_component[i][d] && + (fe->is_primitive(i) || fe->is_primitive())) + for (unsigned int qb = 0, q = 0; q < n_points; ++qb, q += n_lanes) + for (unsigned int v = 0; + v < (q + n_lanes > n_points ? n_filled_lanes_last_batch : + n_lanes); + ++v) + internal::FEPointEvaluation:: + EvaluatorTypeTraits::access( + gradients[qb], + v, + d, + fe_values->shape_grad(i, q + v) * value); + else if (nonzero_shape_function_component[i][d]) + for (unsigned int qb = 0, q = 0; q < n_points; ++qb, q += n_lanes) + for (unsigned int v = 0; + v < (q + n_lanes > n_points ? n_filled_lanes_last_batch : + n_lanes); + ++v) + internal::FEPointEvaluation:: + EvaluatorTypeTraits::access( + gradients[qb], + v, + d, + fe_values->shape_grad_component(i, q + v, d) * value); + } + } +} + + + template void FEPointEvaluation::evaluate( - const ArrayView & solution_values, - const EvaluationFlags::EvaluationFlags &evaluation_flag) + const ArrayView & solution_values, + const EvaluationFlags::EvaluationFlags &evaluation_flags) { if (!is_reinitialized) reinit(); @@ -1143,143 +1753,254 @@ FEPointEvaluation::evaluate( if (n_q_points == 0) return; + Assert(!(evaluation_flags & EvaluationFlags::hessians), ExcNotImplemented()); + + if (!((evaluation_flags & EvaluationFlags::values) || + (evaluation_flags & EvaluationFlags::gradients))) // no evaluation flags + return; + AssertDimension(solution_values.size(), fe->dofs_per_cell); - if (((evaluation_flag & EvaluationFlags::values) || - (evaluation_flag & EvaluationFlags::gradients)) && - fast_path) + if (fast_path) + evaluate_fast(solution_values, evaluation_flags); + else + evaluate_slow(solution_values, evaluation_flags); +} + + + +template +inline void +FEPointEvaluation::integrate_fast( + const ArrayView & solution_values, + const EvaluationFlags::EvaluationFlags &integration_flags) + +{ + // fast path with tensor product integration + if (solution_renumbered_vectorized.size() != dofs_per_component) + solution_renumbered_vectorized.resize(dofs_per_component); + // zero content + solution_renumbered_vectorized.fill( + typename internal::FEPointEvaluation::EvaluatorTypeTraits< + dim, + n_components, + VectorizedArrayType>::value_type()); + + const auto unit_points = + mapping_info->get_unit_points(current_cell_index, current_face_number); + const auto &mapping_data = + mapping_info->get_mapping_data(current_cell_index, current_face_number); + + const std::size_t n_points = unit_points.size(); + const std::size_t n_lanes = + internal::VectorizedArrayTrait::width; + const std::size_t stride = + internal::FEPointEvaluation::VectorizedPointsTypeTraits::stride; + + // loop over quadrature batches qb / points q + for (unsigned int qb = 0, q = 0; q < n_points; ++qb, q += n_lanes) { - // fast path with tensor product evaluation - if (solution_renumbered.size() != dofs_per_component) - solution_renumbered.resize(dofs_per_component); - for (unsigned int comp = 0; comp < n_components; ++comp) - for (unsigned int i = 0; i < dofs_per_component; ++i) - internal::FEPointEvaluation:: - EvaluatorTypeTraits::read_value( - solution_values[renumber[(component_in_base_element + comp) * - dofs_per_component + - i]], - comp, - solution_renumbered[i]); - - // unit gradients are currently only implemented with the fast tensor - // path - unit_gradients.resize(n_q_points, - numbers::signaling_nan()); - - const auto unit_points = - mapping_info->get_unit_points(current_cell_index, current_face_number); - const auto &mapping_data = - mapping_info->get_mapping_data(current_cell_index, current_face_number); + const bool incomplete_last_batch = + (qb == (n_q_points - 1)) && (n_filled_lanes_last_batch > 0); + + typename internal::ProductTypeNoPoint::type value = + {}; + Tensor<1, + dim, + typename internal::ProductTypeNoPoint::type> + gradient; - const std::size_t n_points = unit_points.size(); - const std::size_t n_lanes = VectorizedArray::size(); - for (unsigned int i = 0, qb = 0; i < n_points; i += n_lanes, ++qb) + if (integration_flags & EvaluationFlags::values) { - // compute - const unsigned int n_shapes = poly.size(); - const auto val_and_grad = [&]() { - if (polynomials_are_hat_functions) - { - // convert to vectorized format - Point> vectorized_points; - for (unsigned int j = 0; j < n_lanes && i + j < n_points; ++j) - for (unsigned int d = 0; d < dim; ++d) - vectorized_points[d][j] = unit_points[i + j][d]; - - return internal:: - evaluate_tensor_product_value_and_gradient_linear( - poly, solution_renumbered, vectorized_points); - } - else - return internal:: - evaluate_tensor_product_value_and_gradient_shapes< + // zero out lanes of incomplete last quadrature point batch + if (incomplete_last_batch) + { + for (unsigned int v = n_filled_lanes_last_batch; v < n_lanes; ++v) + internal::FEPointEvaluation::EvaluatorTypeTraits< dim, - value_type, - VectorizedArray>( - make_array_view(shapes.begin() + qb * n_shapes, - shapes.begin() + (qb * n_shapes + n_shapes)), - poly.size(), - solution_renumbered); - }(); - - // convert back to standard format - if (evaluation_flag & EvaluationFlags::values) - for (unsigned int j = 0; j < n_lanes && i + j < n_points; ++j) - internal::FEPointEvaluation:: - EvaluatorTypeTraits::set_value( - val_and_grad.first, j, values[i + j]); - if (evaluation_flag & EvaluationFlags::gradients) + n_components, + Number>::set_zero_value(values[qb], v); + } + for (unsigned int v = 0; v < stride && q + v < n_points; ++v) + internal::FEPointEvaluation:: + EvaluatorTypeTraits::get_value( + value, v, values[qb * stride + v]); + } + if (integration_flags & EvaluationFlags::gradients) + { + if (std::is_same::value) { - Assert(update_flags & update_gradients || - update_flags & update_inverse_jacobians, - ExcNotInitialized()); - for (unsigned int j = 0; j < n_lanes && i + j < n_points; ++j) + for (unsigned int v = 0; v < n_lanes && q + v < n_points; ++v) { + gradients[q + v] = + apply_transformation(mapping_data.inverse_jacobians[q + v], + gradients[q + v]); internal::FEPointEvaluation::EvaluatorTypeTraits< dim, n_components, - Number>::set_gradient(val_and_grad.second, - j, - unit_gradients[i + j]); - gradients[i + j] = apply_transformation( - mapping_data.inverse_jacobians[i + j].transpose(), - unit_gradients[i + j]); + Number>::get_gradient(gradient, v, gradients[q + v]); + } + } + else + { + // convert to vectorized format + DerivativeForm<1, spacedim, dim, Number> + vectorized_inverse_jacobians; + for (unsigned int v = 0; v < n_lanes && q + v < n_points; ++v) + for (unsigned int d = 0; d < dim; ++d) + for (unsigned int s = 0; s < spacedim; ++s) + internal::VectorizedArrayTrait::get( + vectorized_inverse_jacobians[s][d], v) = + mapping_data.inverse_jacobians[q + v][s][d]; + + // zero out lanes of incomplete last quadrature point batch + if (incomplete_last_batch) + { + for (unsigned int v = n_filled_lanes_last_batch; v < n_lanes; + ++v) + internal::FEPointEvaluation::EvaluatorTypeTraits< + dim, + n_components, + Number>::set_zero_gradient(gradients[qb], v); } + + gradients[qb] = apply_transformation(vectorized_inverse_jacobians, + gradients[qb]); + internal::FEPointEvaluation:: + EvaluatorTypeTraits::get_gradient( + gradient, 0, gradients[qb]); } } + + // compute + const unsigned int n_shapes = poly.size(); + if (polynomials_are_hat_functions) + { + // convert to vectorized format + Point vectorized_points; + for (unsigned int j = 0; j < n_lanes && q + j < n_points; ++j) + for (unsigned int d = 0; d < dim; ++d) + vectorized_points[d][j] = unit_points[q + j][d]; + + internal::integrate_add_tensor_product_value_and_gradient_linear( + poly, + value, + gradient, + solution_renumbered_vectorized, + vectorized_points); + } + else + internal::integrate_add_tensor_product_value_and_gradient_shapes< + dim, + VectorizedArrayType, + typename internal::ProductTypeNoPoint::type>( + make_array_view(shapes.begin() + qb * n_shapes, + shapes.begin() + (qb * n_shapes + n_shapes)), + n_shapes, + value, + gradient, + solution_renumbered_vectorized); } - else if ((evaluation_flag & EvaluationFlags::values) || - (evaluation_flag & EvaluationFlags::gradients)) - { - // slow path with FEValues - Assert(fe_values.get() != nullptr, - ExcMessage( - "Not initialized. Please call FEPointEvaluation::reinit()!")); - if (evaluation_flag & EvaluationFlags::values) + // add between the lanes and write into the result + std::fill(solution_values.begin(), solution_values.end(), ScalarNumber()); + for (unsigned int comp = 0; comp < n_components; ++comp) + for (unsigned int i = 0; i < dofs_per_component; ++i) + { + VectorizedArrayType result; + internal::FEPointEvaluation::EvaluatorTypeTraits< + dim, + n_components, + VectorizedArrayType>::write_value(result, + comp, + solution_renumbered_vectorized[i]); + for (unsigned int lane = n_lanes / 2; lane > 0; lane /= 2) + for (unsigned int j = 0; j < lane; ++j) + result[j] += result[lane + j]; + solution_values[renumber[comp * dofs_per_component + i]] = result[0]; + } +} + + + +template +inline void +FEPointEvaluation::integrate_slow( + const ArrayView & solution_values, + const EvaluationFlags::EvaluationFlags &integration_flags) +{ + // slow path with FEValues + Assert(fe_values.get() != nullptr, + ExcMessage( + "Not initialized. Please call FEPointEvaluation::reinit()!")); + std::fill(solution_values.begin(), solution_values.end(), 0.0); + + const std::size_t n_points = fe_values->get_quadrature().size(); + const std::size_t n_lanes = internal::VectorizedArrayTrait::width; + + if (integration_flags & EvaluationFlags::values) + { + AssertIndexRange(n_q_points, values.size() + 1); + for (unsigned int i = 0; i < fe->n_dofs_per_cell(); ++i) { - values.resize(n_q_points); - std::fill(values.begin(), values.end(), value_type()); - for (unsigned int i = 0; i < fe->n_dofs_per_cell(); ++i) - { - const Number value = solution_values[i]; - for (unsigned int d = 0; d < n_components; ++d) - if (nonzero_shape_function_component[i][d] && - (fe->is_primitive(i) || fe->is_primitive())) - for (unsigned int q = 0; q < n_q_points; ++q) + for (unsigned int d = 0; d < n_components; ++d) + if (nonzero_shape_function_component[i][d] && + (fe->is_primitive(i) || fe->is_primitive())) + for (unsigned int qb = 0, q = 0; q < n_points; ++qb, q += n_lanes) + for (unsigned int v = 0; + v < (q + n_lanes > n_points ? n_filled_lanes_last_batch : + n_lanes); + ++v) + solution_values[i] += + fe_values->shape_value(i, q + v) * internal::FEPointEvaluation:: EvaluatorTypeTraits::access( - values[q], d) += fe_values->shape_value(i, q) * value; - else if (nonzero_shape_function_component[i][d]) - for (unsigned int q = 0; q < n_q_points; ++q) + values[qb], v, d); + else if (nonzero_shape_function_component[i][d]) + for (unsigned int qb = 0, q = 0; q < n_points; ++qb, q += n_lanes) + for (unsigned int v = 0; + v < (q + n_lanes > n_points ? n_filled_lanes_last_batch : + n_lanes); + ++v) + solution_values[i] += + fe_values->shape_value_component(i, q + v, d) * internal::FEPointEvaluation:: EvaluatorTypeTraits::access( - values[q], d) += - fe_values->shape_value_component(i, q, d) * value; - } + values[qb], v, d); } + } - if (evaluation_flag & EvaluationFlags::gradients) + if (integration_flags & EvaluationFlags::gradients) + { + AssertIndexRange(n_q_points, gradients.size() + 1); + for (unsigned int i = 0; i < fe->n_dofs_per_cell(); ++i) { - gradients.resize(n_q_points); - std::fill(gradients.begin(), gradients.end(), gradient_type()); - for (unsigned int i = 0; i < fe->n_dofs_per_cell(); ++i) - { - const Number value = solution_values[i]; - for (unsigned int d = 0; d < n_components; ++d) - if (nonzero_shape_function_component[i][d] && - (fe->is_primitive(i) || fe->is_primitive())) - for (unsigned int q = 0; q < n_q_points; ++q) + for (unsigned int d = 0; d < n_components; ++d) + if (nonzero_shape_function_component[i][d] && + (fe->is_primitive(i) || fe->is_primitive())) + for (unsigned int qb = 0, q = 0; q < n_points; ++qb, q += n_lanes) + for (unsigned int v = 0; + v < (q + n_lanes > n_points ? n_filled_lanes_last_batch : + n_lanes); + ++v) + solution_values[i] += + fe_values->shape_grad(i, q + v) * internal::FEPointEvaluation:: EvaluatorTypeTraits::access( - gradients[q], d) += fe_values->shape_grad(i, q) * value; - else if (nonzero_shape_function_component[i][d]) - for (unsigned int q = 0; q < n_q_points; ++q) + gradients[qb], v, d); + else if (nonzero_shape_function_component[i][d]) + for (unsigned int qb = 0, q = 0; q < n_points; ++qb, q += n_lanes) + for (unsigned int v = 0; + v < (q + n_lanes > n_points ? n_filled_lanes_last_batch : + n_lanes); + ++v) + solution_values[i] += + fe_values->shape_grad_component(i, q + v, d) * internal::FEPointEvaluation:: EvaluatorTypeTraits::access( - gradients[q], d) += - fe_values->shape_grad_component(i, q, d) * value; - } + gradients[qb], v, d); } } } @@ -1289,7 +2010,7 @@ FEPointEvaluation::evaluate( template void FEPointEvaluation::integrate( - const ArrayView & solution_values, + const ArrayView & solution_values, const EvaluationFlags::EvaluationFlags &integration_flags) { if (!is_reinitialized) @@ -1301,167 +2022,21 @@ FEPointEvaluation::integrate( return; } - AssertDimension(solution_values.size(), fe->dofs_per_cell); - if (((integration_flags & EvaluationFlags::values) || - (integration_flags & EvaluationFlags::gradients)) && - fast_path) - { - // fast path with tensor product integration + Assert(!(integration_flags & EvaluationFlags::hessians), ExcNotImplemented()); - if (integration_flags & EvaluationFlags::values) - AssertIndexRange(n_q_points, values.size() + 1); - if (integration_flags & EvaluationFlags::gradients) - AssertIndexRange(n_q_points, gradients.size() + 1); - - if (solution_renumbered_vectorized.size() != dofs_per_component) - solution_renumbered_vectorized.resize(dofs_per_component); - // zero content - solution_renumbered_vectorized.fill( - typename internal::FEPointEvaluation::EvaluatorTypeTraits< - dim, - n_components, - VectorizedArray>::value_type()); - - const auto unit_points = - mapping_info->get_unit_points(current_cell_index, current_face_number); - const auto &mapping_data = - mapping_info->get_mapping_data(current_cell_index, current_face_number); - - const std::size_t n_points = unit_points.size(); - const std::size_t n_lanes = VectorizedArray::size(); - for (unsigned int i = 0, qb = 0; i < n_points; i += n_lanes, ++qb) - { - typename internal::ProductTypeNoPoint>::type - value = {}; - Tensor<1, - dim, - typename internal::ProductTypeNoPoint< - value_type, - VectorizedArray>::type> - gradient; - - if (integration_flags & EvaluationFlags::values) - for (unsigned int j = 0; j < n_lanes && i + j < n_points; ++j) - internal::FEPointEvaluation:: - EvaluatorTypeTraits::get_value( - value, j, values[i + j]); - if (integration_flags & EvaluationFlags::gradients) - for (unsigned int j = 0; j < n_lanes && i + j < n_points; ++j) - { - gradients[i + j] = - apply_transformation(mapping_data.inverse_jacobians[i + j], - gradients[i + j]); - internal::FEPointEvaluation:: - EvaluatorTypeTraits::get_gradient( - gradient, j, gradients[i + j]); - } - - // compute - const unsigned int n_shapes = poly.size(); - if (polynomials_are_hat_functions) - { - // convert to vectorized format - Point> vectorized_points; - for (unsigned int j = 0; j < n_lanes && i + j < n_points; ++j) - for (unsigned int d = 0; d < dim; ++d) - vectorized_points[d][j] = unit_points[i + j][d]; - - internal::integrate_add_tensor_product_value_and_gradient_linear( - poly, - value, - gradient, - solution_renumbered_vectorized, - vectorized_points); - } - else - internal::integrate_add_tensor_product_value_and_gradient_shapes< - dim, - VectorizedArray, - typename internal:: - ProductTypeNoPoint>::type>( - make_array_view(shapes.begin() + qb * n_shapes, - shapes.begin() + (qb * n_shapes + n_shapes)), - n_shapes, - value, - gradient, - solution_renumbered_vectorized); - } - - // add between the lanes and write into the result - std::fill(solution_values.begin(), solution_values.end(), Number()); - for (unsigned int comp = 0; comp < n_components; ++comp) - for (unsigned int i = 0; i < dofs_per_component; ++i) - { - VectorizedArray result; - internal::FEPointEvaluation:: - EvaluatorTypeTraits>:: - write_value(result, comp, solution_renumbered_vectorized[i]); - for (unsigned int lane = n_lanes / 2; lane > 0; lane /= 2) - for (unsigned int j = 0; j < lane; ++j) - result[j] += result[lane + j]; - solution_values[renumber[comp * dofs_per_component + i]] = - result[0]; - } - } - else if ((integration_flags & EvaluationFlags::values) || - (integration_flags & EvaluationFlags::gradients)) + if (!((integration_flags & EvaluationFlags::values) || + (integration_flags & + EvaluationFlags::gradients))) // no integration flags { - // slow path with FEValues - - Assert(fe_values.get() != nullptr, - ExcMessage( - "Not initialized. Please call FEPointEvaluation::reinit()!")); std::fill(solution_values.begin(), solution_values.end(), 0.0); - - if (integration_flags & EvaluationFlags::values) - { - AssertIndexRange(n_q_points, values.size() + 1); - for (unsigned int i = 0; i < fe->n_dofs_per_cell(); ++i) - { - for (unsigned int d = 0; d < n_components; ++d) - if (nonzero_shape_function_component[i][d] && - (fe->is_primitive(i) || fe->is_primitive())) - for (unsigned int q = 0; q < n_q_points; ++q) - solution_values[i] += - fe_values->shape_value(i, q) * - internal::FEPointEvaluation:: - EvaluatorTypeTraits::access( - values[q], d); - else if (nonzero_shape_function_component[i][d]) - for (unsigned int q = 0; q < n_q_points; ++q) - solution_values[i] += - fe_values->shape_value_component(i, q, d) * - internal::FEPointEvaluation:: - EvaluatorTypeTraits::access( - values[q], d); - } - } - - if (integration_flags & EvaluationFlags::gradients) - { - AssertIndexRange(n_q_points, gradients.size() + 1); - for (unsigned int i = 0; i < fe->n_dofs_per_cell(); ++i) - { - for (unsigned int d = 0; d < n_components; ++d) - if (nonzero_shape_function_component[i][d] && - (fe->is_primitive(i) || fe->is_primitive())) - for (unsigned int q = 0; q < n_q_points; ++q) - solution_values[i] += - fe_values->shape_grad(i, q) * - internal::FEPointEvaluation:: - EvaluatorTypeTraits::access( - gradients[q], d); - else if (nonzero_shape_function_component[i][d]) - for (unsigned int q = 0; q < n_q_points; ++q) - solution_values[i] += - fe_values->shape_grad_component(i, q, d) * - internal::FEPointEvaluation:: - EvaluatorTypeTraits::access( - gradients[q], d); - } - } + return; } + + AssertDimension(solution_values.size(), fe->dofs_per_cell); + if (fast_path) + integrate_fast(solution_values, integration_flags); + else + integrate_slow(solution_values, integration_flags); } @@ -1531,27 +2106,48 @@ FEPointEvaluation::submit_gradient( template -inline DerivativeForm<1, dim, spacedim> +inline DerivativeForm<1, dim, spacedim, Number> FEPointEvaluation::jacobian( const unsigned int point_index) const { const auto &mapping_data = mapping_info->get_mapping_data(current_cell_index, current_face_number); - AssertIndexRange(point_index, mapping_data.jacobians.size()); - return mapping_data.jacobians[point_index]; + + const unsigned int n_lanes = internal::VectorizedArrayTrait::width; + DerivativeForm<1, dim, spacedim, Number> vectorized_jacobian; + for (unsigned int v = 0; + v < n_lanes && point_index * n_lanes + v < mapping_data.jacobians.size(); + ++v) + for (unsigned int d = 0; d < dim; ++d) + for (unsigned int s = 0; s < spacedim; ++s) + internal::VectorizedArrayTrait::get(vectorized_jacobian[d][s], + v) = + mapping_data.jacobians[point_index * n_lanes + v][d][s]; + return vectorized_jacobian; } template -inline DerivativeForm<1, spacedim, dim> +inline DerivativeForm<1, spacedim, dim, Number> FEPointEvaluation::inverse_jacobian( const unsigned int point_index) const { const auto &mapping_data = mapping_info->get_mapping_data(current_cell_index, current_face_number); - AssertIndexRange(point_index, mapping_data.inverse_jacobians.size()); - return mapping_data.inverse_jacobians[point_index]; + + const unsigned int n_lanes = internal::VectorizedArrayTrait::width; + DerivativeForm<1, dim, spacedim, Number> vectorized_inverse_jacobian; + for (unsigned int v = 0; + v < n_lanes && + point_index * n_lanes + v < mapping_data.inverse_jacobians.size(); + ++v) + for (unsigned int d = 0; d < dim; ++d) + for (unsigned int s = 0; s < spacedim; ++s) + internal::VectorizedArrayTrait::get( + vectorized_inverse_jacobian[d][s], v) = + mapping_data.inverse_jacobians[point_index * n_lanes + v][d][s]; + return vectorized_inverse_jacobian; } @@ -1563,46 +2159,78 @@ FEPointEvaluation::JxW( { const auto &mapping_data = mapping_info->get_mapping_data(current_cell_index, current_face_number); - AssertIndexRange(point_index, mapping_data.JxW_values.size()); - return mapping_data.JxW_values[point_index]; + + const unsigned int n_lanes = internal::VectorizedArrayTrait::width; + Number vectorized_JxW = 0; + for (unsigned int v = 0; v < n_lanes && point_index * n_lanes + v < + mapping_data.JxW_values.size(); + ++v) + internal::VectorizedArrayTrait::get(vectorized_JxW, v) = + mapping_data.JxW_values[point_index * n_lanes + v]; + return vectorized_JxW; } template -inline Tensor<1, spacedim> +inline Tensor<1, spacedim, Number> FEPointEvaluation::normal_vector( const unsigned int point_index) const { const auto &mapping_data = mapping_info->get_mapping_data(current_cell_index, current_face_number); - AssertIndexRange(point_index, mapping_data.normal_vectors.size()); - return mapping_data.normal_vectors[point_index]; + + const unsigned int n_lanes = internal::VectorizedArrayTrait::width; + Tensor<1, spacedim, Number> vectorized_normal_vectors; + for (unsigned int v = 0; v < n_lanes && point_index * n_lanes + v < + mapping_data.normal_vectors.size(); + ++v) + for (unsigned int s = 0; s < spacedim; ++s) + internal::VectorizedArrayTrait::get(vectorized_normal_vectors[s], + v) = + mapping_data.normal_vectors[point_index * n_lanes + v][s]; + return vectorized_normal_vectors; } template -inline Point +inline Point FEPointEvaluation::real_point( const unsigned int point_index) const { const auto &mapping_data = mapping_info->get_mapping_data(current_cell_index, current_face_number); - AssertIndexRange(point_index, mapping_data.quadrature_points.size()); - return mapping_data.quadrature_points[point_index]; + + const unsigned int n_lanes = internal::VectorizedArrayTrait::width; + Point vectorized_real_point; + for (unsigned int v = 0; + v < n_lanes && + point_index * n_lanes + v < mapping_data.quadrature_points.size(); + ++v) + for (unsigned int s = 0; s < spacedim; ++s) + internal::VectorizedArrayTrait::get(vectorized_real_point[s], v) = + mapping_data.quadrature_points[point_index * n_lanes + v][s]; + return vectorized_real_point; } template -inline Point +inline Point FEPointEvaluation::unit_point( const unsigned int point_index) const { - AssertIndexRange(point_index, n_q_points); const auto unit_points = mapping_info->get_unit_points(current_cell_index, current_face_number); - return unit_points[point_index]; + const unsigned int n_lanes = internal::VectorizedArrayTrait::width; + Point vectorized_unit_point; + for (unsigned int v = 0; + v < n_lanes && point_index * n_lanes + v < unit_points.size(); + ++v) + for (unsigned int d = 0; d < dim; ++d) + internal::VectorizedArrayTrait::get(vectorized_unit_point[d], v) = + unit_points[point_index * n_lanes + v][d]; + return vectorized_unit_point; } diff --git a/tests/matrix_free/point_evaluation_22.cc b/tests/matrix_free/point_evaluation_22.cc new file mode 100644 index 0000000000..816e7c16ce --- /dev/null +++ b/tests/matrix_free/point_evaluation_22.cc @@ -0,0 +1,177 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2020 - 2022 by the deal.II authors +// +// This file is part of the deal.II library. +// +// The deal.II library is free software; you can use it, 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 2.1 of the License, or (at your option) any later version. +// The full text of the license can be found in the file LICENSE.md at +// the top level directory of deal.II. +// +// --------------------------------------------------------------------- + + +// check vectorized FEPointEvaluation for scalar FE_Q and MappingQ by comparing +// to the output of FEValues with the same settings + +#include +#include + +#include + +#include +#include +#include +#include + +#include +#include + +#include + +#include + +#include + +#include + +#include "../tests.h" + +using namespace dealii; + +template > +void +test(const unsigned int degree, const bool is_mapping_q = true) +{ + Triangulation tria; + + if (dim > 1) + GridGenerator::hyper_shell(tria, Point(), 0.5, 1, 6); + else + GridGenerator::subdivided_hyper_cube(tria, 2, 0, 1); + + std::unique_ptr> mapping; + if (is_mapping_q) + mapping = std::make_unique>(degree); + else + mapping = std::make_unique>(FE_Q(degree)); + + deallog << "Mapping of degree " << degree << std::endl; + + std::vector> unit_points; + for (unsigned int i = 0; i < 13; ++i) + { + Point p; + for (unsigned int d = 0; d < dim; ++d) + p[d] = static_cast(i) / 17. + 0.015625 * d; + unit_points.push_back(p); + } + + FE_Q fe(degree); + FEValues fe_values(*mapping, + fe, + Quadrature(unit_points), + update_values | update_gradients); + + DoFHandler dof_handler(tria); + dof_handler.distribute_dofs(fe); + Vector vector(dof_handler.n_dofs()); + + FEPointEvaluation<1, dim, dim, VectorizedArrayType> evaluator( + *mapping, fe, update_values | update_gradients); + + Tensor<1, dim, Number> exponents; + exponents[0] = 1.; + VectorTools::interpolate(*mapping, + dof_handler, + Functions::Monomial(exponents), + vector); + + std::vector solution_values(fe.dofs_per_cell); + std::vector function_values(unit_points.size()); + std::vector> function_gradients(unit_points.size()); + + // For float numbers that are sensitive to roundoff in the numdiff + // tolerances (absolute 1e-8), we multiply by 1e-3 to ensure that the test + // remains robust + const double factor_float = std::is_same::value ? 0.001 : 1.; + + for (const auto &cell : dof_handler.active_cell_iterators()) + { + fe_values.reinit(cell); + fe_values.get_function_values(vector, function_values); + fe_values.get_function_gradients(vector, function_gradients); + + cell->get_dof_values(vector, + solution_values.begin(), + solution_values.end()); + + evaluator.reinit(cell, unit_points); + evaluator.evaluate(solution_values, + EvaluationFlags::values | EvaluationFlags::gradients); + + deallog << "Cell with center " << cell->center(true) << std::endl; + + const unsigned int n_points = unit_points.size(); + const unsigned int n_lanes = VectorizedArrayType::size(); + for (unsigned int qb = 0, q = 0; q < n_points; q += n_lanes, ++qb) + for (unsigned int v = 0; v < n_lanes && q + v < n_points; ++v) + { + const auto gradient = evaluator.get_gradient(q / n_lanes); + + Tensor<1, dim, Number> gradient_current_lane; + for (unsigned int d = 0; d < dim; ++d) + gradient_current_lane[d] = gradient[d][v]; + + deallog + << mapping->transform_unit_to_real_cell(cell, unit_points[q + v]) + << ": " << factor_float * evaluator.get_value(q / n_lanes)[v] + << " error value " + << factor_float * (function_values[q + v] - + evaluator.get_value(q / n_lanes)[v]) + << " error grad " + << factor_float * + (gradient_current_lane - function_gradients[q + v]).norm() + << std::endl; + } + deallog << std::endl; + + for (const unsigned int i : evaluator.quadrature_point_indices()) + { + evaluator.submit_value(evaluator.get_value(i), i); + evaluator.submit_gradient(evaluator.get_gradient(i), i); + } + + evaluator.integrate(solution_values, + EvaluationFlags::values | EvaluationFlags::gradients); + + for (const auto i : solution_values) + deallog << factor_float * i << ' '; + deallog << std::endl; + } +} + + + +int +main() +{ + initlog(); + deallog << std::setprecision(10); + + test<1>(3); + test<2>(1); + test<2>(2); + test<2>(6); + test<3>(1); + test<3, double, VectorizedArray>(5); + + test<3, float, VectorizedArray>(5); + + test<3>(1, false); +} diff --git a/tests/matrix_free/point_evaluation_22.output b/tests/matrix_free/point_evaluation_22.output new file mode 100644 index 0000000000..605e73e5c5 --- /dev/null +++ b/tests/matrix_free/point_evaluation_22.output @@ -0,0 +1,713 @@ + +DEAL::Mapping of degree 3 +DEAL::Cell with center 0.2500000000 +DEAL::0.000000000: 0.000000000 error value 0.000000000 error grad 4.440892099e-16 +DEAL::0.02941176471: 0.02941176471 error value 0.000000000 error grad 0.000000000 +DEAL::0.05882352941: 0.05882352941 error value -6.938893904e-18 error grad 2.220446049e-16 +DEAL::0.08823529412: 0.08823529412 error value 0.000000000 error grad 0.000000000 +DEAL::0.1176470588: 0.1176470588 error value 1.387778781e-17 error grad 2.220446049e-16 +DEAL::0.1470588235: 0.1470588235 error value 2.775557562e-17 error grad 3.330669074e-16 +DEAL::0.1764705882: 0.1764705882 error value 0.000000000 error grad 0.000000000 +DEAL::0.2058823529: 0.2058823529 error value -2.775557562e-17 error grad 1.110223025e-16 +DEAL::0.2352941176: 0.2352941176 error value 0.000000000 error grad 1.110223025e-16 +DEAL::0.2647058824: 0.2647058824 error value 0.000000000 error grad 2.220446049e-16 +DEAL::0.2941176471: 0.2941176471 error value 0.000000000 error grad 0.000000000 +DEAL::0.3235294118: 0.3235294118 error value 0.000000000 error grad 0.000000000 +DEAL::0.3529411765: 0.3529411765 error value 0.000000000 error grad 0.000000000 +DEAL:: +DEAL::-40.02339531 1.555249578 8.779994658 31.98226872 +DEAL::Cell with center 0.7500000000 +DEAL::0.5000000000: 0.5000000000 error value 0.000000000 error grad 5.551115123e-16 +DEAL::0.5294117647: 0.5294117647 error value 0.000000000 error grad 1.332267630e-15 +DEAL::0.5588235294: 0.5588235294 error value 0.000000000 error grad 0.000000000 +DEAL::0.5882352941: 0.5882352941 error value 0.000000000 error grad 2.220446049e-16 +DEAL::0.6176470588: 0.6176470588 error value -1.110223025e-16 error grad 4.440892099e-16 +DEAL::0.6470588235: 0.6470588235 error value -1.110223025e-16 error grad 2.220446049e-16 +DEAL::0.6764705882: 0.6764705882 error value 0.000000000 error grad 6.661338148e-16 +DEAL::0.7058823529: 0.7058823529 error value 0.000000000 error grad 2.220446049e-16 +DEAL::0.7352941176: 0.7352941176 error value 1.110223025e-16 error grad 7.771561172e-16 +DEAL::0.7647058824: 0.7647058824 error value 0.000000000 error grad 2.220446049e-16 +DEAL::0.7941176471: 0.7941176471 error value 1.110223025e-16 error grad 2.220446049e-16 +DEAL::0.8235294118: 0.8235294118 error value -1.110223025e-16 error grad 1.110223025e-16 +DEAL::0.8529411765: 0.8529411765 error value 0.000000000 error grad 0.000000000 +DEAL:: +DEAL::-39.13829456 1.322397960 12.59137926 34.01863499 +DEAL::Mapping of degree 1 +DEAL::Cell with center 0.6495190528 0.3750000000 +DEAL::0.9921875000 0.000000000: 0.9921875000 error value 0.000000000 error grad 1.717520996e-17 +DEAL::0.9344588019 0.04904636735: 0.9344588019 error value -2.220446049e-16 error grad 1.353018556e-16 +DEAL::0.8784602076 0.09509610700: 0.8784602076 error value -2.220446049e-16 error grad 4.646340395e-17 +DEAL::0.8241917171 0.1381492190: 0.8241917171 error value 0.000000000 error grad 2.524396413e-16 +DEAL::0.7716533304 0.1782057032: 0.7716533304 error value 1.110223025e-16 error grad 1.268808499e-16 +DEAL::0.7208450476 0.2152655598: 0.7208450476 error value 0.000000000 error grad 2.228698022e-16 +DEAL::0.6717668685 0.2493287887: 0.6717668685 error value 0.000000000 error grad 9.136482042e-17 +DEAL::0.6244187933 0.2803953898: 0.6244187933 error value 0.000000000 error grad 2.224027437e-16 +DEAL::0.5788008218 0.3084653633: 0.5788008218 error value -1.110223025e-16 error grad 1.514135915e-16 +DEAL::0.5349129542 0.3335387091: 0.5349129542 error value 0.000000000 error grad 4.909117292e-16 +DEAL::0.4927551903 0.3556154272: 0.4927551903 error value 0.000000000 error grad 2.868544468e-16 +DEAL::0.4523275303 0.3746955176: 0.4523275303 error value -5.551115123e-17 error grad 1.828252816e-16 +DEAL::0.4136299740 0.3907789803: 0.4136299740 error value 0.000000000 error grad 1.136953923e-16 +DEAL:: +DEAL::24.50913568 7.620733168 -12.02051095 -11.21894916 +DEAL::Cell with center 4.592425497e-17 0.7500000000 +DEAL::0.4960937500 0.8592595803: 0.4960937500 error value 0.000000000 error grad 5.349979303e-17 +DEAL::0.4247540009 0.8337882449: 0.4247540009 error value 0.000000000 error grad 1.155532360e-16 +DEAL::0.3568744593 0.8083169095: 0.3568744593 error value -5.551115123e-17 error grad 2.522293534e-16 +DEAL::0.2924551254 0.7828455741: 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17.30198640 -2.830400908 0.9058098551 -0.5650421119 -4.201512452 -4.509222471 0.1370572452 0.04839099042 2.108053768 0.3115725668 2.735381661 0.07496381392 -1.208991139 -0.1568192129 -0.2323061327 0.1843281464 1.478547563 0.05153285769 -0.03194755144 0.1246431170 0.07065993788 -2.606330583 -0.3051322559 -0.06603054076 0.2754997011 -0.3969445648 4.421675458 1.008068298 0.04247230613 -0.1606294254 0.2924683086 0.3337487039 -2.102293438 -1.672255490 0.5987288246 -0.3071796863 1.421574505 2.502007288 0.1670361760 -0.0002987835468 0.08616706985 -1.259079243 -0.5267360105 0.1249683592 0.02924947536 0.2319990438 0.3462067012 0.1447239424 -0.6928124131 -0.4960303481 0.1923404856 0.01913093793 0.2895884896 1.526830582 0.4322414014 -0.3189424887 0.1271144868 -1.000649388 -0.7297664401 0.2550569874 0.1264178755 -0.05291912112 1.106790134 0.3460740495 7.776755330 8.183977319 -2.928852756 1.533415823 -21.07145448 -7.814151326 -0.8388402882 0.2047939047 6.829083703 3.191700696 2.052606000 -0.6486725233 -4.118212476 -0.2554605543 -1.257117152 -0.2462872959 14.50972996 24.34759181 -4.632342276 2.439505378 -13.78829768 7.079250599 9.587691336 -4.016361613 2.537224108 -23.48223092 -5.306366838 1.569839045 -0.1686496940 7.667049122 2.165030173 0.6601073338 -3.381370020 -3.550873763 -7.038985492 0.1066845109 -0.4177534768 14.92432929 23.35076255 -3.163428374 2.101907402 -10.48002558 -1.187912727 2.421120246 -0.2038630493 1.620111021 -17.23744021 -1.795292249 1.901717829 1.484047685 -0.7761969095 -0.1681766792 -0.6624100960 -4.749963039 -0.9999384764 1.178948091 -0.4704363388 3.170073846 2.186512282 -0.9958982126 -0.5127916521 0.4492138976 -4.833434518 -1.534625793 +DEAL::Cell with center -2.814297100e-18 -4.163336342e-17 0.7500000000 +DEAL::-0.5879922187 -0.5412602679 0.5879922187: -0.5879922187 error value -1.110223025e-16 error grad 1.565567202e-15 +DEAL::-0.5359927398 -0.4904247681 0.6317656581: -0.5359927398 error value -1.110223025e-16 error grad 4.194685275e-15 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0.6784217227: 0.09750269006 error value -6.938893904e-17 error grad 4.781480618e-16 +DEAL::0.1518546010 0.1850850191 0.6243263560: 0.1518546010 error value 0.000000000 error grad 1.968311041e-16 +DEAL::0.1963417794 0.2277818661 0.5640861853: 0.1963417794 error value -2.775557562e-17 error grad 8.938311917e-16 +DEAL:: +DEAL::-14.22773572 0.2758248216 0.3233470251 0.002258593743 -0.4923898836 0.006479233947 0.007673405413 -0.004048900302 9.627170437 -2.691702424 1.498489731 -0.8773595554 0.1279656761 0.04225023655 0.07356622361 -0.005097731633 5.585744538 -2.164581526 1.253407572 -0.7433196577 0.1099531797 -0.01260379215 0.009252680767 -0.002884075630 0.2806678375 -0.03219643212 0.08013073348 -0.02068043400 0.005503508274 0.02306514214 0.1436682909 0.01418965267 0.1365397921 -0.06721769009 0.04142148978 -0.01326449452 0.006057540723 -0.01734942542 -0.06045758872 0.02150105957 -15.47866474 4.190338797 -2.247249335 1.336820956 0.1129724940 -0.06340047602 0.07707712475 -0.01389673634 0.1419159969 -0.08253947144 0.04544141577 -0.01902274661 0.005634069144 0.008671599223 0.06230320762 0.01872658377 3.802955058 -1.849696393 0.6332900561 -0.3887317906 -1.842055969 1.784561423 -0.2503857485 0.2210503091 1.226546978 -0.04101568182 -1.133754819 -0.1190044533 -0.7601564400 0.08751686184 -0.2793227493 0.05139340024 -0.1329003274 -0.3121519009 -0.1517036742 -0.01853214606 0.03981662170 0.6990778365 0.4622234695 -0.02355309033 -0.1192407217 0.4685421110 -2.207587028 -0.2071636127 -0.02477211090 -0.04626220360 -0.5921080046 -0.06458486085 -1.652952512 -0.5230285630 0.5694196475 -0.3687699911 -1.094754457 0.9620048241 -0.4472056934 0.1970382183 0.4464572425 -0.05759202805 1.131391592 -0.08513594443 -0.3066813743 0.1682769060 -0.2719086895 0.01808774896 -0.5435242256 0.08994829075 0.002598091303 -0.02097245176 -0.1145270174 0.09827575762 -0.2322489459 0.06448699937 0.02506076423 0.1543179337 1.755390911 0.2961776627 -0.02442773032 -0.01318002344 -0.2872705281 -0.09701074323 4.853511142 -1.261011127 0.5260121926 -0.3492584502 -1.510834566 -1.223475195 0.5106149470 -0.1256819254 0.4868871761 -0.04233145412 0.4008790018 -0.2891612909 -0.3015205279 0.03534862660 0.02896239803 0.001282034478 0.6151091397 -0.003672394594 -0.02060557343 -0.02652030389 -0.1900803421 -0.7395428375 0.3518920381 -0.04743018813 -0.09060655346 0.02608927292 0.4230800862 -0.6149689195 -0.01712199095 0.05250632458 0.3326755048 -0.07802505127 2.121697905 2.337378351 -0.4897435341 0.3746937019 8.149470066 6.289570330 -2.500186463 0.8941103156 -2.613844429 -0.6445190287 -0.9252424465 0.6674415072 1.505458734 0.3175839743 -0.2207670026 0.08565176834 -10.30178622 -2.326324795 -0.4906404539 -0.1022773676 -4.553509572 4.248087367 6.557429751 -2.070032519 0.1038855571 0.4292290765 3.613145172 -1.828609903 -0.2400124607 -0.2564040324 -0.1848736157 0.01722662098 3.248342622 0.4700541441 -2.876006785 0.5101437737 -1.098704675 -5.770074992 8.370279607 -1.740240309 4.006911615 -11.71563463 5.895269164 8.368195559 -0.02757708959 0.7988932722 -6.864812671 0.9900422846 -1.706444378 -0.04059703142 -0.01223465841 0.1212060495 0.5110737577 2.232782288 -0.9087920291 0.04007400433 0.4185159752 -0.2844351676 -1.422126838 2.547418087 0.05804302262 -0.1888393693 -1.540541812 0.3479107112 +DEAL::Cell with center -0.7500000000 -1.407148550e-18 0.000000000 +DEAL::-0.6012515503 -0.5766780283 -0.5531118850: -0.6012515503 error value 3.330669074e-16 error grad 9.751458571e-15 +DEAL::-0.6458946236 -0.5236491363 -0.5006487306: -0.6458946236 error value 3.330669074e-16 error grad 4.307640683e-15 +DEAL::-0.6898189280 -0.4638689601 -0.4413495827: -0.6898189280 error value -1.110223025e-16 error grad 4.043277104e-15 +DEAL::-0.7296048967 -0.3975220470 -0.3754490693: -0.7296048967 error value -4.440892099e-16 error grad 6.162035182e-16 +DEAL::-0.7617762381 -0.3254496235 -0.3038288032: -0.7617762381 error value 1.110223025e-16 error grad 1.047361113e-15 +DEAL::-0.7832188522 -0.2491480826 -0.2280163559: -0.7832188522 error value -1.110223025e-16 error grad 2.841590741e-15 +DEAL::-0.7915521155 -0.1706669598 -0.1500833118: -0.7915521155 error value -1.110223025e-16 error grad 4.543816489e-16 +DEAL::-0.7854001879 -0.09242877894 -0.07246518026: -0.7854001879 error value 0.000000000 error grad 1.389903243e-15 +DEAL::-0.7645345314 -0.01700078778 0.002266559507: -0.7645345314 error value 1.110223025e-16 error grad 7.287970480e-16 +DEAL::-0.7298790026 0.05314854421 0.07164727507: -0.7298790026 error value -3.330669074e-16 error grad 1.125132447e-15 +DEAL::-0.6833856700 0.1158765656 0.1335451305: -0.6833856700 error value 0.000000000 error grad 1.638629705e-15 +DEAL::-0.6278029298 0.1695497377 0.1863429372: -0.6278029298 error value 3.330669074e-16 error grad 1.877438005e-15 +DEAL::-0.5663675440 0.2131627953 0.2290556314: -0.5663675440 error value -1.110223025e-16 error grad 3.145326536e-15 +DEAL:: +DEAL::1.260272240 0.5641641783 -0.2820300017 0.002626149270 -0.2663730559 0.01134315828 -0.02182110665 -0.02018298984 -7.204005728 2.419783550 -1.261455823 0.7688360647 0.3535045379 0.01324722157 0.1324997913 0.003613291559 12.07119005 -4.432329479 2.590243215 -1.519812347 0.1640500833 -0.08860092584 0.1027229793 0.003625832158 -0.3151390449 0.1202293698 -0.007735894631 0.07082662590 0.04791361271 0.01913724455 0.2365169957 0.08705464331 0.3617859743 -0.1625753209 0.1493080084 -0.01895318589 0.006011719606 -0.1034087052 0.09562004711 0.08882807594 -10.48211045 2.364047133 -1.233799172 0.7308306939 0.5965968776 -0.09856651452 0.1475701024 -0.01745853693 -0.4993051769 0.08011872901 -0.04991347470 0.07254082725 0.03707436327 -0.001281132784 0.1581489620 0.09166901158 -26.77162863 4.361666770 -2.375917508 1.344286547 2.950864149 4.371961991 0.4655325188 -0.1893822334 -1.465139086 0.6248171799 -2.799064020 0.08373479639 0.8403727290 -0.3026270286 -0.08659427811 -0.2476503183 -1.133332463 -0.4927064371 -0.1726454660 -0.1309230727 -0.5200871384 2.493409849 0.7518109220 0.05501755503 -0.04697376955 0.7773864675 -3.841807342 -0.6572720144 -0.1685307951 0.008733944014 -1.007801339 -0.3915674010 16.17585205 -1.863849035 1.568704687 -0.9866071926 -5.897593206 -1.416101617 -1.187149061 0.4944256071 2.581286604 0.2796363015 1.177261996 -0.4569585425 -1.629776330 0.2522540387 -0.5228319785 -0.006541737064 0.8906854195 0.5976761155 -0.1154782085 -0.05192552744 -0.2446109210 -1.431594326 -0.7785347204 0.3855762568 -0.09185595454 0.7760822175 0.8549278768 -0.3669817993 -0.1312622405 0.04426656507 -0.7198716244 -0.4007579844 8.590972719 -4.045403772 1.498350404 -0.9747198397 -0.6291621853 -1.781652888 0.8676054250 -0.05588936063 0.6082991179 -0.6307174704 0.8571033086 -0.5083770516 -0.4475801888 0.2856461396 -0.3198923035 -0.05654933955 0.8577738272 -0.3732625727 -0.06233271615 -0.1639173157 0.3882612332 -1.476848134 1.010243974 -0.01109724433 -0.2370295998 -0.4334730867 0.7510997381 -1.026205059 -0.04747535093 0.3745305597 -0.3511633107 -0.3808441064 6.513922434 15.82317808 -5.124200144 3.157250895 -11.33580635 11.09433375 -4.884635903 1.423340918 4.621637753 -0.4843938470 -1.600010209 0.8919354132 -2.426310526 0.5417062796 0.3699139425 0.4880308371 -13.68873798 14.21897826 -4.835167964 1.487905739 -28.00938484 -0.5847358857 20.72097703 -7.271012538 3.017079860 -10.54402724 7.413526010 -3.022710534 -1.761172308 4.377375077 -2.455800121 -0.3527527829 4.414393180 -0.5133763812 -1.775299382 0.4771027979 2.117610059 -12.90157252 10.16016491 -3.017918066 7.051630185 -25.89194907 5.871874774 14.27529875 0.4566225273 2.239732759 -2.539177906 2.973899776 -2.342549416 0.8785855421 0.3179931406 0.6111677780 -1.175442434 4.596782210 -3.224328729 -0.2510240512 0.9492546414 0.9558893948 -2.124757022 4.376267132 0.2800747478 -1.420136473 1.408090662 1.705090670 +DEAL::Cell with center -1.407148550e-18 -0.7500000000 -4.163336342e-17 +DEAL::-0.5879922187 -0.5879922187 -0.5412602679: -0.5879922187 error value -1.110223025e-16 error grad 5.187116706e-15 +DEAL::-0.5359927398 -0.6317656581 -0.4904247681: -0.5359927398 error value -2.220446049e-16 error grad 3.123498067e-15 +DEAL::-0.4774156808 -0.6752050943 -0.4328300536: -0.4774156808 error value -5.551115123e-17 error grad 9.161293067e-16 +DEAL::-0.4123477836 -0.7149693757 -0.3686646352: -0.4123477836 error value 1.110223025e-16 error grad 2.061426650e-15 +DEAL::-0.3415220448 -0.7476112822 -0.2987437738: -0.3415220448 error value -2.775557562e-16 error grad 1.030757159e-15 +DEAL::-0.2663289165 -0.7699931685 -0.2245218407: -0.2663289165 error value -1.665334537e-16 error grad 1.372451088e-15 +DEAL::-0.1887262238 -0.7796633598 -0.1480024603: -0.1887262238 error value -5.551115123e-17 error grad 1.356803731e-15 +DEAL::-0.1110685560 -0.7751382896 -0.07156802410: -0.1110685560 error value -6.938893904e-17 error grad 3.478467253e-16 +DEAL::-0.03588516627 -0.7560592058 0.002241853775: -0.03588516627 error value -1.387778781e-17 error grad 5.713192527e-16 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error grad 3.347621259e-09 +DEAL::-0.6278029298 0.1695497377 0.1863429372: -0.0006278027892 error value -1.192092896e-10 error grad 9.746139540e-10 +DEAL::-0.5663675440 0.2131627953 0.2290556314: -0.0005663675666 error value 0.000000000 error grad 1.501763109e-09 +DEAL:: +DEAL::0.001260282874 0.0005641639233 -0.0002820300162 2.626157366e-06 -0.0002663728893 1.134316344e-05 -2.182109840e-05 -2.018296905e-05 -0.007204005718 0.002419783354 -0.001261455774 0.0007688360810 0.0003535044491 1.324730739e-05 0.0001324997991 3.613269888e-06 0.01207118607 -0.004432328701 0.002590242386 -0.001519811988 0.0001640499234 -8.860087395e-05 0.0001027229950 3.625804093e-06 -0.0003151390254 0.0001202294379 -7.735868916e-06 7.082659751e-05 4.791358113e-05 1.913732477e-05 0.0002365168929 8.705458045e-05 0.0003617857993 -0.0001625752598 0.0001493080109 -1.895320602e-05 6.011678837e-06 -0.0001034086347 9.562003613e-05 8.882801980e-05 -0.01048210621 0.002364046335 -0.001233798385 0.0007308303714 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