xassign.hpp

/***************************************************************************
 * Copyright (c) Johan Mabille, Sylvain Corlay and Wolf Vollprecht          *
 * Copyright (c) QuantStack                                                 *
 *                                                                          *
 * Distributed under the terms of the BSD 3-Clause License.                 *
 *                                                                          *
 * The full license is in the file LICENSE, distributed with this software. *
 ****************************************************************************/
 
#ifndef XTENSOR_ASSIGN_HPP
#define XTENSOR_ASSIGN_HPP
 
#include <algorithm>
#include <functional>
#include <type_traits>
#include <utility>
 
#include <xtl/xcomplex.hpp>
#include <xtl/xsequence.hpp>
 
#include "xexpression.hpp"
#include "xfunction.hpp"
#include "xiterator.hpp"
#include "xstrides.hpp"
#include "xtensor_config.hpp"
#include "xtensor_forward.hpp"
#include "xutils.hpp"
 
#if defined(XTENSOR_USE_TBB)
#include <tbb/tbb.h>
#endif
 
namespace xt
{
 
    /********************
     * Assign functions *
     ********************/
 
    template <class E1, class E2>
    void assign_data(xexpression<E1>& e1, const xexpression<E2>& e2, bool trivial);
 
    template <class E1, class E2>
    void assign_xexpression(xexpression<E1>& e1, const xexpression<E2>& e2);
 
    template <class E1, class E2>
    void computed_assign(xexpression<E1>& e1, const xexpression<E2>& e2);
 
    template <class E1, class E2, class F>
    void scalar_computed_assign(xexpression<E1>& e1, const E2& e2, F&& f);
 
    template <class E1, class E2>
    void assert_compatible_shape(const xexpression<E1>& e1, const xexpression<E2>& e2);
 
    template <class E1, class E2>
    void strided_assign(E1& e1, const E2& e2, std::false_type /*disable*/);
 
    template <class E1, class E2>
    void strided_assign(E1& e1, const E2& e2, std::true_type /*enable*/);
 
    /************************
     * xexpression_assigner *
     ************************/
 
    template <class Tag>
    class xexpression_assigner_base;
 
    template <>
    class xexpression_assigner_base<xtensor_expression_tag>
    {
    public:
 
        template <class E1, class E2>
        static void assign_data(xexpression<E1>& e1, const xexpression<E2>& e2, bool trivial);
    };
 
    template <class Tag>
    class xexpression_assigner : public xexpression_assigner_base<Tag>
    {
    public:
 
        using base_type = xexpression_assigner_base<Tag>;
 
        template <class E1, class E2>
        static void assign_xexpression(E1& e1, const E2& e2);
 
        template <class E1, class E2>
        static void computed_assign(xexpression<E1>& e1, const xexpression<E2>& e2);
 
        template <class E1, class E2, class F>
        static void scalar_computed_assign(xexpression<E1>& e1, const E2& e2, F&& f);
 
        template <class E1, class E2>
        static void assert_compatible_shape(const xexpression<E1>& e1, const xexpression<E2>& e2);
 
    private:
 
        template <class E1, class E2>
        static bool resize(E1& e1, const E2& e2);
 
        template <class E1, class F, class... CT>
        static bool resize(E1& e1, const xfunction<F, CT...>& e2);
    };
 
    /********************
     * stepper_assigner *
     ********************/
 
    template <class E1, class E2, layout_type L>
    class stepper_assigner
    {
    public:
 
        using lhs_iterator = typename E1::stepper;
        using rhs_iterator = typename E2::const_stepper;
        using shape_type = typename E1::shape_type;
        using index_type = xindex_type_t<shape_type>;
        using size_type = typename lhs_iterator::size_type;
        using difference_type = typename lhs_iterator::difference_type;
 
        stepper_assigner(E1& e1, const E2& e2);
 
        void run();
 
        void step(size_type i);
        void step(size_type i, size_type n);
        void reset(size_type i);
 
        void to_end(layout_type);
 
    private:
 
        E1& m_e1;
 
        lhs_iterator m_lhs;
        rhs_iterator m_rhs;
 
        index_type m_index;
    };
 
    /*******************
     * linear_assigner *
     *******************/
 
    template <bool simd_assign>
    class linear_assigner
    {
    public:
 
        template <class E1, class E2>
        static void run(E1& e1, const E2& e2);
    };
 
    template <>
    class linear_assigner<false>
    {
    public:
 
        template <class E1, class E2>
        static void run(E1& e1, const E2& e2);
 
    private:
 
        template <class E1, class E2>
        static void run_impl(E1& e1, const E2& e2, std::true_type);
 
        template <class E1, class E2>
        static void run_impl(E1& e1, const E2& e2, std::false_type);
    };
 
    /*************************
     * strided_loop_assigner *
     *************************/
 
    namespace strided_assign_detail
    {
        struct loop_sizes_t
        {
            bool can_do_strided_assign;
            bool is_row_major;
            std::size_t inner_loop_size;
            std::size_t outer_loop_size;
            std::size_t cut;
            std::size_t dimension;
        };
    }
 
    template <bool simd>
    class strided_loop_assigner
    {
    public:
 
        using loop_sizes_t = strided_assign_detail::loop_sizes_t;
        // is_row_major, inner_loop_size, outer_loop_size, cut
        template <class E1, class E2>
        static void run(E1& e1, const E2& e2, const loop_sizes_t& loop_sizes);
        template <class E1, class E2>
        static loop_sizes_t get_loop_sizes(E1& e1, const E2& e2);
        template <class E1, class E2>
        static void run(E1& e1, const E2& e2);
    };
 
    /***********************************
     * Assign functions implementation *
     ***********************************/
 
    template <class E1, class E2>
    inline void assign_data(xexpression<E1>& e1, const xexpression<E2>& e2, bool trivial)
    {
        using tag = xexpression_tag_t<E1, E2>;
        xexpression_assigner<tag>::assign_data(e1, e2, trivial);
    }
 
    template <class E1, class E2>
    inline void assign_xexpression(xexpression<E1>& e1, const xexpression<E2>& e2)
    {
        xtl::mpl::static_if<has_assign_to<E1, E2>::value>(
            [&](auto self)
            {
                self(e2).derived_cast().assign_to(e1);
            },
            /*else*/
            [&](auto /*self*/)
            {
                using tag = xexpression_tag_t<E1, E2>;
                xexpression_assigner<tag>::assign_xexpression(e1, e2);
            }
        );
    }
 
    template <class E1, class E2>
    inline void computed_assign(xexpression<E1>& e1, const xexpression<E2>& e2)
    {
        using tag = xexpression_tag_t<E1, E2>;
        xexpression_assigner<tag>::computed_assign(e1, e2);
    }
 
    template <class E1, class E2, class F>
    inline void scalar_computed_assign(xexpression<E1>& e1, const E2& e2, F&& f)
    {
        using tag = xexpression_tag_t<E1, E2>;
        xexpression_assigner<tag>::scalar_computed_assign(e1, e2, std::forward<F>(f));
    }
 
    template <class E1, class E2>
    inline void assert_compatible_shape(const xexpression<E1>& e1, const xexpression<E2>& e2)
    {
        using tag = xexpression_tag_t<E1, E2>;
        xexpression_assigner<tag>::assert_compatible_shape(e1, e2);
    }
 
    /***************************************
     * xexpression_assigner implementation *
     ***************************************/
 
    namespace detail
    {
        template <class E1, class E2>
        constexpr bool linear_static_layout()
        {
            // A row_major or column_major container with a dimension <= 1 is computed as
            // layout any, leading to some performance improvements, for example when
            // assigning a col-major vector to a row-major vector etc
            return compute_layout(
                       select_layout<E1::static_layout, typename E1::shape_type>::value,
                       select_layout<E2::static_layout, typename E2::shape_type>::value
                   )
                   != layout_type::dynamic;
        }
 
        template <class E1, class E2>
        inline auto is_linear_assign(const E1& e1, const E2& e2)
            -> std::enable_if_t<has_strides<E1>::value, bool>
        {
            return (E1::contiguous_layout && E2::contiguous_layout && linear_static_layout<E1, E2>())
                   || (e1.is_contiguous() && e2.has_linear_assign(e1.strides()));
        }
 
        template <class E1, class E2>
        inline auto is_linear_assign(const E1&, const E2&) -> std::enable_if_t<!has_strides<E1>::value, bool>
        {
            return false;
        }
 
        template <class E1, class E2>
        inline bool linear_dynamic_layout(const E1& e1, const E2& e2)
        {
            return e1.is_contiguous() && e2.is_contiguous()
                   && compute_layout(e1.layout(), e2.layout()) != layout_type::dynamic;
        }
 
        template <class E, class = void>
        struct has_step_leading : std::false_type
        {
        };
 
        template <class E>
        struct has_step_leading<E, void_t<decltype(std::declval<E>().step_leading())>> : std::true_type
        {
        };
 
        template <class T>
        struct use_strided_loop
        {
            static constexpr bool stepper_deref()
            {
                return std::is_reference<typename T::stepper::reference>::value;
            }
 
            static constexpr bool value = has_strides<T>::value
                                          && has_step_leading<typename T::stepper>::value && stepper_deref();
        };
 
        template <class T>
        struct use_strided_loop<xscalar<T>>
        {
            static constexpr bool value = true;
        };
 
        template <class F, class... CT>
        struct use_strided_loop<xfunction<F, CT...>>
        {
            static constexpr bool value = xtl::conjunction<use_strided_loop<std::decay_t<CT>>...>::value;
        };
 
        template <class T1, class T2>
        struct conditional_promote_to_complex
        {
            static constexpr bool cond = xtl::is_gen_complex<T1>::value && !xtl::is_gen_complex<T2>::value;
            // Alternative: use std::complex<T2> or xcomplex<T2, T2, bool> depending on T1
            using type = std::conditional_t<cond, T1, T2>;
        };
 
        template <class T1, class T2>
        using conditional_promote_to_complex_t = typename conditional_promote_to_complex<T1, T2>::type;
    }
 
    template <class E1, class E2>
    class xassign_traits
    {
    private:
 
        using e1_value_type = typename E1::value_type;
        using e2_value_type = typename E2::value_type;
 
        template <class T>
        using is_bool = std::is_same<T, bool>;
 
        static constexpr bool is_bool_conversion()
        {
            return is_bool<e2_value_type>::value && !is_bool<e1_value_type>::value;
        }
 
        static constexpr bool contiguous_layout()
        {
            return E1::contiguous_layout && E2::contiguous_layout;
        }
 
        static constexpr bool convertible_types()
        {
            return std::is_convertible<e2_value_type, e1_value_type>::value && !is_bool_conversion();
        }
 
        static constexpr bool use_xsimd()
        {
            return xt_simd::simd_traits<int8_t>::size > 1;
        }
 
        template <class T>
        static constexpr bool simd_size_impl()
        {
            return xt_simd::simd_traits<T>::size > 1 || (is_bool<T>::value && use_xsimd());
        }
 
        static constexpr bool simd_size()
        {
            return simd_size_impl<e1_value_type>() && simd_size_impl<e2_value_type>();
        }
 
        static constexpr bool simd_interface()
        {
            return has_simd_interface<E1, requested_value_type>()
                   && has_simd_interface<E2, requested_value_type>();
        }
 
    public:
 
        // constexpr methods instead of constexpr data members avoid the need of definitions at namespace
        // scope of these data members (since they are odr-used).
 
        static constexpr bool simd_assign()
        {
            return convertible_types() && simd_size() && simd_interface();
        }
 
        static constexpr bool linear_assign(const E1& e1, const E2& e2, bool trivial)
        {
            return trivial && detail::is_linear_assign(e1, e2);
        }
 
        static constexpr bool strided_assign()
        {
            return detail::use_strided_loop<E1>::value && detail::use_strided_loop<E2>::value;
        }
 
        static constexpr bool simd_linear_assign()
        {
            return contiguous_layout() && simd_assign();
        }
 
        static constexpr bool simd_strided_assign()
        {
            return strided_assign() && simd_assign();
        }
 
        static constexpr bool simd_linear_assign(const E1& e1, const E2& e2)
        {
            return simd_assign() && detail::linear_dynamic_layout(e1, e2);
        }
 
        using e2_requested_value_type = std::
            conditional_t<is_bool<e2_value_type>::value, typename E2::bool_load_type, e2_value_type>;
        using requested_value_type = detail::conditional_promote_to_complex_t<e1_value_type, e2_requested_value_type>;
    };
 
    template <class E1, class E2>
    inline void xexpression_assigner_base<xtensor_expression_tag>::assign_data(
        xexpression<E1>& e1,
        const xexpression<E2>& e2,
        bool trivial
    )
    {
        E1& de1 = e1.derived_cast();
        const E2& de2 = e2.derived_cast();
        using traits = xassign_traits<E1, E2>;
 
        bool linear_assign = traits::linear_assign(de1, de2, trivial);
        constexpr bool simd_assign = traits::simd_assign();
        constexpr bool simd_linear_assign = traits::simd_linear_assign();
        constexpr bool simd_strided_assign = traits::simd_strided_assign();
        if (linear_assign)
        {
            if (simd_linear_assign || traits::simd_linear_assign(de1, de2))
            {
                // Do not use linear_assigner<true> here since it will make the compiler
                // instantiate this branch even if the runtime condition is false, resulting
                // in compilation error for expressions that do not provide a SIMD interface.
                // simd_assign is true if simd_linear_assign() or simd_linear_assign(de1, de2)
                // is true.
                linear_assigner<simd_assign>::run(de1, de2);
            }
            else
            {
                linear_assigner<false>::run(de1, de2);
            }
        }
        else if (simd_strided_assign)
        {
            strided_loop_assigner<simd_strided_assign>::run(de1, de2);
        }
        else
        {
            stepper_assigner<E1, E2, default_assignable_layout(E1::static_layout)>(de1, de2).run();
        }
    }
 
    template <class Tag>
    template <class E1, class E2>
    inline void xexpression_assigner<Tag>::assign_xexpression(E1& e1, const E2& e2)
    {
        bool trivial_broadcast = resize(e1.derived_cast(), e2.derived_cast());
        base_type::assign_data(e1, e2, trivial_broadcast);
    }
 
    template <class Tag>
    template <class E1, class E2>
    inline void xexpression_assigner<Tag>::computed_assign(xexpression<E1>& e1, const xexpression<E2>& e2)
    {
        using shape_type = typename E1::shape_type;
        using comperator_type = std::greater<typename shape_type::value_type>;
 
        using size_type = typename E1::size_type;
 
        E1& de1 = e1.derived_cast();
        const E2& de2 = e2.derived_cast();
 
        size_type dim2 = de2.dimension();
        shape_type shape = uninitialized_shape<shape_type>(dim2);
 
        bool trivial_broadcast = de2.broadcast_shape(shape, true);
 
        auto&& de1_shape = de1.shape();
        if (dim2 > de1.dimension()
            || std::lexicographical_compare(
                shape.begin(),
                shape.end(),
                de1_shape.begin(),
                de1_shape.end(),
                comperator_type()
            ))
        {
            typename E1::temporary_type tmp(shape);
            base_type::assign_data(tmp, e2, trivial_broadcast);
            de1.assign_temporary(std::move(tmp));
        }
        else
        {
            base_type::assign_data(e1, e2, trivial_broadcast);
        }
    }
 
    template <class Tag>
    template <class E1, class E2, class F>
    inline void xexpression_assigner<Tag>::scalar_computed_assign(xexpression<E1>& e1, const E2& e2, F&& f)
    {
        E1& d = e1.derived_cast();
        using size_type = typename E1::size_type;
        auto dst = d.storage().begin();
        for (size_type i = d.size(); i > 0; --i)
        {
            *dst = f(*dst, e2);
            ++dst;
        }
    }
 
    template <class Tag>
    template <class E1, class E2>
    inline void
    xexpression_assigner<Tag>::assert_compatible_shape(const xexpression<E1>& e1, const xexpression<E2>& e2)
    {
        const E1& de1 = e1.derived_cast();
        const E2& de2 = e2.derived_cast();
        if (!broadcastable(de2.shape(), de1.shape()))
        {
            throw_broadcast_error(de2.shape(), de1.shape());
        }
    }
 
    namespace detail
    {
        template <bool B, class... CT>
        struct static_trivial_broadcast;
 
        template <class... CT>
        struct static_trivial_broadcast<true, CT...>
        {
            static constexpr bool value = detail::promote_index<typename std::decay_t<CT>::shape_type...>::value;
        };
 
        template <class... CT>
        struct static_trivial_broadcast<false, CT...>
        {
            static constexpr bool value = false;
        };
    }
 
    template <class Tag>
    template <class E1, class E2>
    inline bool xexpression_assigner<Tag>::resize(E1& e1, const E2& e2)
    {
        // If our RHS is not a xfunction, we know that the RHS is at least potentially trivial
        // We check the strides of the RHS in detail::is_trivial_broadcast to see if they match up!
        // So we can skip a shape copy and a call to broadcast_shape(...)
        e1.resize(e2.shape());
        return true;
    }
 
    template <class Tag>
    template <class E1, class F, class... CT>
    inline bool xexpression_assigner<Tag>::resize(E1& e1, const xfunction<F, CT...>& e2)
    {
        return xtl::mpl::static_if<detail::is_fixed<typename xfunction<F, CT...>::shape_type>::value>(
            [&](auto /*self*/)
            {
                /*
                 * If the shape of the xfunction is statically known, we can compute the broadcast triviality
                 * at compile time plus we can resize right away.
                 */
                // resize in case LHS is not a fixed size container. If it is, this is a NOP
                e1.resize(typename xfunction<F, CT...>::shape_type{});
                return detail::static_trivial_broadcast<
                    detail::is_fixed<typename xfunction<F, CT...>::shape_type>::value,
                    CT...>::value;
            },
            /* else */
            [&](auto /*self*/)
            {
                using index_type = xindex_type_t<typename E1::shape_type>;
                using size_type = typename E1::size_type;
                size_type size = e2.dimension();
                index_type shape = uninitialized_shape<index_type>(size);
                bool trivial_broadcast = e2.broadcast_shape(shape, true);
                e1.resize(std::move(shape));
                return trivial_broadcast;
            }
        );
    }
 
    /***********************************
     * stepper_assigner implementation *
     ***********************************/
 
    template <class FROM, class TO>
    struct is_narrowing_conversion
    {
        using argument_type = std::decay_t<FROM>;
        using result_type = std::decay_t<TO>;
 
        static const bool value = xtl::is_arithmetic<result_type>::value
                                  && (sizeof(result_type) < sizeof(argument_type)
                                      || (xtl::is_integral<result_type>::value
                                          && std::is_floating_point<argument_type>::value));
    };
 
    template <class FROM, class TO>
    struct has_sign_conversion
    {
        using argument_type = std::decay_t<FROM>;
        using result_type = std::decay_t<TO>;
 
        static const bool value = xtl::is_signed<argument_type>::value != xtl::is_signed<result_type>::value;
    };
 
    template <class FROM, class TO>
    struct has_assign_conversion
    {
        using argument_type = std::decay_t<FROM>;
        using result_type = std::decay_t<TO>;
 
        static const bool value = is_narrowing_conversion<argument_type, result_type>::value
                                  || has_sign_conversion<argument_type, result_type>::value;
    };
 
    template <class E1, class E2, layout_type L>
    inline stepper_assigner<E1, E2, L>::stepper_assigner(E1& e1, const E2& e2)
        : m_e1(e1)
        , m_lhs(e1.stepper_begin(e1.shape()))
        , m_rhs(e2.stepper_begin(e1.shape()))
        , m_index(xtl::make_sequence<index_type>(e1.shape().size(), size_type(0)))
    {
    }
 
    template <class E1, class E2, layout_type L>
    inline void stepper_assigner<E1, E2, L>::run()
    {
        using tmp_size_type = typename E1::size_type;
        using argument_type = std::decay_t<decltype(*m_rhs)>;
        using result_type = std::decay_t<decltype(*m_lhs)>;
        constexpr bool needs_cast = has_assign_conversion<argument_type, result_type>::value;
 
        tmp_size_type s = m_e1.size();
        for (tmp_size_type i = 0; i < s; ++i)
        {
            *m_lhs = conditional_cast<needs_cast, result_type>(*m_rhs);
            stepper_tools<L>::increment_stepper(*this, m_index, m_e1.shape());
        }
    }
 
    template <class E1, class E2, layout_type L>
    inline void stepper_assigner<E1, E2, L>::step(size_type i)
    {
        m_lhs.step(i);
        m_rhs.step(i);
    }
 
    template <class E1, class E2, layout_type L>
    inline void stepper_assigner<E1, E2, L>::step(size_type i, size_type n)
    {
        m_lhs.step(i, n);
        m_rhs.step(i, n);
    }
 
    template <class E1, class E2, layout_type L>
    inline void stepper_assigner<E1, E2, L>::reset(size_type i)
    {
        m_lhs.reset(i);
        m_rhs.reset(i);
    }
 
    template <class E1, class E2, layout_type L>
    inline void stepper_assigner<E1, E2, L>::to_end(layout_type l)
    {
        m_lhs.to_end(l);
        m_rhs.to_end(l);
    }
 
    /**********************************
     * linear_assigner implementation *
     **********************************/
 
    template <bool simd_assign>
    template <class E1, class E2>
    inline void linear_assigner<simd_assign>::run(E1& e1, const E2& e2)
    {
        using lhs_align_mode = xt_simd::container_alignment_t<E1>;
        constexpr bool is_aligned = std::is_same<lhs_align_mode, aligned_mode>::value;
        using rhs_align_mode = std::conditional_t<is_aligned, inner_aligned_mode, unaligned_mode>;
        using e1_value_type = typename E1::value_type;
        using e2_value_type = typename E2::value_type;
        using value_type = typename xassign_traits<E1, E2>::requested_value_type;
        using simd_type = xt_simd::simd_type<value_type>;
        using size_type = typename E1::size_type;
        size_type size = e1.size();
        constexpr size_type simd_size = simd_type::size;
        constexpr bool needs_cast = has_assign_conversion<e1_value_type, e2_value_type>::value;
 
        size_type align_begin = is_aligned ? 0 : xt_simd::get_alignment_offset(e1.data(), size, simd_size);
        size_type align_end = align_begin + ((size - align_begin) & ~(simd_size - 1));
 
        for (size_type i = 0; i < align_begin; ++i)
        {
            e1.data_element(i) = conditional_cast<needs_cast, e1_value_type>(e2.data_element(i));
        }
 
#if defined(XTENSOR_USE_TBB)
        if (size >= XTENSOR_TBB_THRESHOLD)
        {
            tbb::static_partitioner ap;
            tbb::parallel_for(
                align_begin,
                align_end,
                simd_size,
                [&e1, &e2](size_t i)
                {
                    e1.template store_simd<lhs_align_mode>(
                        i,
                        e2.template load_simd<rhs_align_mode, value_type>(i)
                    );
                },
                ap
            );
        }
        else
        {
            for (size_type i = align_begin; i < align_end; i += simd_size)
            {
                e1.template store_simd<lhs_align_mode>(i, e2.template load_simd<rhs_align_mode, value_type>(i));
            }
        }
#elif defined(XTENSOR_USE_OPENMP)
        if (size >= size_type(XTENSOR_OPENMP_TRESHOLD))
        {
#pragma omp parallel for default(none) shared(align_begin, align_end, e1, e2)
#ifndef _WIN32
            for (size_type i = align_begin; i < align_end; i += simd_size)
            {
                e1.template store_simd<lhs_align_mode>(i, e2.template load_simd<rhs_align_mode, value_type>(i));
            }
#else
            for (auto i = static_cast<std::ptrdiff_t>(align_begin); i < static_cast<std::ptrdiff_t>(align_end);
                 i += static_cast<std::ptrdiff_t>(simd_size))
            {
                size_type ui = static_cast<size_type>(i);
                e1.template store_simd<lhs_align_mode>(ui, e2.template load_simd<rhs_align_mode, value_type>(ui));
            }
#endif
        }
        else
        {
            for (size_type i = align_begin; i < align_end; i += simd_size)
            {
                e1.template store_simd<lhs_align_mode>(i, e2.template load_simd<rhs_align_mode, value_type>(i));
            }
        }
#else
        for (size_type i = align_begin; i < align_end; i += simd_size)
        {
            e1.template store_simd<lhs_align_mode>(i, e2.template load_simd<rhs_align_mode, value_type>(i));
        }
#endif
        for (size_type i = align_end; i < size; ++i)
        {
            e1.data_element(i) = conditional_cast<needs_cast, e1_value_type>(e2.data_element(i));
        }
    }
 
    template <class E1, class E2>
    inline void linear_assigner<false>::run(E1& e1, const E2& e2)
    {
        using is_convertible = std::
            is_convertible<typename std::decay_t<E2>::value_type, typename std::decay_t<E1>::value_type>;
        // If the types are not compatible, this function is still instantiated but never called.
        // To avoid compilation problems in effectively unused code trivial_assigner_run_impl is
        // empty in this case.
        run_impl(e1, e2, is_convertible());
    }
 
    template <class E1, class E2>
    inline void linear_assigner<false>::run_impl(E1& e1, const E2& e2, std::true_type /*is_convertible*/)
    {
        using value_type = typename E1::value_type;
        using size_type = typename E1::size_type;
        auto src = linear_begin(e2);
        auto dst = linear_begin(e1);
        size_type n = e1.size();
#if defined(XTENSOR_USE_TBB)
        tbb::static_partitioner sp;
        tbb::parallel_for(
            std::ptrdiff_t(0),
            static_cast<std::ptrdiff_t>(n),
            [&](std::ptrdiff_t i)
            {
                *(dst + i) = static_cast<value_type>(*(src + i));
            },
            sp
        );
#elif defined(XTENSOR_USE_OPENMP)
        if (n >= XTENSOR_OPENMP_TRESHOLD)
        {
#pragma omp parallel for default(none) shared(src, dst, n)
            for (std::ptrdiff_t i = std::ptrdiff_t(0); i < static_cast<std::ptrdiff_t>(n); i++)
            {
                *(dst + i) = static_cast<value_type>(*(src + i));
            }
        }
        else
        {
            for (; n > size_type(0); --n)
            {
                *dst = static_cast<value_type>(*src);
                ++src;
                ++dst;
            }
        }
#else
        for (; n > size_type(0); --n)
        {
            *dst = static_cast<value_type>(*src);
            ++src;
            ++dst;
        }
#endif
    }
 
    template <class E1, class E2>
    inline void linear_assigner<false>::run_impl(E1&, const E2&, std::false_type /*is_convertible*/)
    {
        XTENSOR_PRECONDITION(false, "Internal error: linear_assigner called with unrelated types.");
    }
 
    /****************************************
     * strided_loop_assigner implementation *
     ****************************************/
 
    namespace strided_assign_detail
    {
        template <layout_type layout>
        struct idx_tools;
 
        template <>
        struct idx_tools<layout_type::row_major>
        {
            template <class T>
            static void next_idx(T& outer_index, T& outer_shape)
            {
                auto i = outer_index.size();
                for (; i > 0; --i)
                {
                    if (outer_index[i - 1] + 1 >= outer_shape[i - 1])
                    {
                        outer_index[i - 1] = 0;
                    }
                    else
                    {
                        outer_index[i - 1]++;
                        break;
                    }
                }
            }
 
            template <class T>
            static void nth_idx(size_t n, T& outer_index, const T& outer_shape)
            {
                dynamic_shape<std::size_t> stride_sizes;
                xt::resize_container(stride_sizes, outer_shape.size());
                // compute strides
                using size_type = typename T::size_type;
                for (size_type i = outer_shape.size(); i > 0; i--)
                {
                    stride_sizes[i - 1] = (i == outer_shape.size()) ? 1 : stride_sizes[i] * outer_shape[i];
                }
 
                // compute index
                for (size_type i = 0; i < outer_shape.size(); i++)
                {
                    auto d_idx = n / stride_sizes[i];
                    outer_index[i] = d_idx;
                    n -= d_idx * stride_sizes[i];
                }
            }
        };
 
        template <>
        struct idx_tools<layout_type::column_major>
        {
            template <class T>
            static void next_idx(T& outer_index, T& outer_shape)
            {
                using size_type = typename T::size_type;
                size_type i = 0;
                auto sz = outer_index.size();
                for (; i < sz; ++i)
                {
                    if (outer_index[i] + 1 >= outer_shape[i])
                    {
                        outer_index[i] = 0;
                    }
                    else
                    {
                        outer_index[i]++;
                        break;
                    }
                }
            }
 
            template <class T>
            static void nth_idx(size_t n, T& outer_index, const T& outer_shape)
            {
                dynamic_shape<std::size_t> stride_sizes;
                xt::resize_container(stride_sizes, outer_shape.size());
 
                using size_type = typename T::size_type;
 
                // compute required strides
                for (size_type i = 0; i < outer_shape.size(); i++)
                {
                    stride_sizes[i] = (i == 0) ? 1 : stride_sizes[i - 1] * outer_shape[i - 1];
                }
 
                // compute index
                for (size_type i = outer_shape.size(); i > 0;)
                {
                    i--;
                    auto d_idx = n / stride_sizes[i];
                    outer_index[i] = d_idx;
                    n -= d_idx * stride_sizes[i];
                }
            }
        };
 
        template <layout_type L, class S>
        struct check_strides_functor
        {
            using strides_type = S;
 
            check_strides_functor(const S& strides)
                : m_cut(L == layout_type::row_major ? 0 : strides.size())
                , m_strides(strides)
            {
            }
 
            template <class T, layout_type LE = L>
            std::enable_if_t<LE == layout_type::row_major, std::size_t> operator()(const T& el)
            {
                // All dimenions less than var have differing strides
                auto var = check_strides_overlap<layout_type::row_major>::get(m_strides, el.strides());
                if (var > m_cut)
                {
                    m_cut = var;
                }
                return m_cut;
            }
 
            template <class T, layout_type LE = L>
            std::enable_if_t<LE == layout_type::column_major, std::size_t> operator()(const T& el)
            {
                auto var = check_strides_overlap<layout_type::column_major>::get(m_strides, el.strides());
                // All dimensions >= var have differing strides
                if (var < m_cut)
                {
                    m_cut = var;
                }
                return m_cut;
            }
 
            template <class T>
            std::size_t operator()(const xt::xscalar<T>& /*el*/)
            {
                return m_cut;
            }
 
            template <class F, class... CT>
            std::size_t operator()(const xt::xfunction<F, CT...>& xf)
            {
                xt::for_each(*this, xf.arguments());
                return m_cut;
            }
 
        private:
 
            std::size_t m_cut;
            const strides_type& m_strides;
        };
 
        template <bool possible = true, class E1, class E2, std::enable_if_t<!has_strides<E1>::value || !possible, bool> = true>
        loop_sizes_t get_loop_sizes(const E1& e1, const E2&)
        {
            return {false, true, 1, e1.size(), e1.dimension(), e1.dimension()};
        }
 
        template <bool possible = true, class E1, class E2, std::enable_if_t<has_strides<E1>::value && possible, bool> = true>
        loop_sizes_t get_loop_sizes(const E1& e1, const E2& e2)
        {
            using shape_value_type = typename E1::shape_type::value_type;
            bool is_row_major = true;
 
            // Try to find a row-major scheme first, where the outer loop is on the first N = `cut`
            // dimensions, and the inner loop is
            is_row_major = true;
            auto is_zero = [](auto i)
            {
                return i == 0;
            };
            auto&& strides = e1.strides();
            auto it_bwd = std::find_if_not(strides.rbegin(), strides.rend(), is_zero);
            bool de1_row_contiguous = it_bwd != strides.rend() && *it_bwd == 1;
            auto it_fwd = std::find_if_not(strides.begin(), strides.end(), is_zero);
            bool de1_col_contiguous = it_fwd != strides.end() && *it_fwd == 1;
            if (de1_row_contiguous)
            {
                is_row_major = true;
            }
            else if (de1_col_contiguous)
            {
                is_row_major = false;
            }
            else
            {
                // No strided loop possible.
                return {false, true, 1, e1.size(), e1.dimension(), e1.dimension()};
            }
 
            // Cut is the number of dimensions in the outer loop
            std::size_t cut = 0;
 
            if (is_row_major)
            {
                auto csf = check_strides_functor<layout_type::row_major, decltype(e1.strides())>(e1.strides());
                cut = csf(e2);
                // This makes that only one dimension will be treated in the inner loop.
                if (cut < e1.strides().size() - 1)
                {
                    // Only make the inner loop go over one dimension by default for now
                    cut = e1.strides().size() - 1;
                }
            }
            else if (!is_row_major)
            {
                auto csf = check_strides_functor<layout_type::column_major, decltype(e1.strides())>(e1.strides()
                );
                cut = csf(e2);
                if (cut > 1)
                {
                    // Only make the inner loop go over one dimension by default for now
                    cut = 1;
                }
            }  // can't reach here because this would have already triggered the fallback
 
            std::size_t outer_loop_size = static_cast<std::size_t>(std::accumulate(
                e1.shape().begin(),
                e1.shape().begin() + static_cast<std::ptrdiff_t>(cut),
                shape_value_type(1),
                std::multiplies<shape_value_type>{}
            ));
            std::size_t inner_loop_size = static_cast<std::size_t>(std::accumulate(
                e1.shape().begin() + static_cast<std::ptrdiff_t>(cut),
                e1.shape().end(),
                shape_value_type(1),
                std::multiplies<shape_value_type>{}
            ));
 
            if (!is_row_major)
            {
                std::swap(outer_loop_size, inner_loop_size);
            }
 
            return {inner_loop_size > 1, is_row_major, inner_loop_size, outer_loop_size, cut, e1.dimension()};
        }
    }
 
    template <bool simd>
    template <class E1, class E2>
    inline strided_assign_detail::loop_sizes_t strided_loop_assigner<simd>::get_loop_sizes(E1& e1, const E2& e2)
    {
        return strided_assign_detail::get_loop_sizes<simd>(e1, e2);
    }
 
#define strided_parallel_assign
 
    template <bool simd>
    template <class E1, class E2>
    inline void strided_loop_assigner<simd>::run(E1& e1, const E2& e2, const loop_sizes_t& loop_sizes)
    {
        bool is_row_major = loop_sizes.is_row_major;
        std::size_t inner_loop_size = loop_sizes.inner_loop_size;
        std::size_t outer_loop_size = loop_sizes.outer_loop_size;
        std::size_t cut = loop_sizes.cut;
 
 
        // TODO can we get rid of this and use `shape_type`?
        dynamic_shape<std::size_t> idx, max_shape;
 
        if (is_row_major)
        {
            xt::resize_container(idx, cut);
            max_shape.assign(e1.shape().begin(), e1.shape().begin() + static_cast<std::ptrdiff_t>(cut));
        }
        else
        {
            xt::resize_container(idx, e1.shape().size() - cut);
            max_shape.assign(e1.shape().begin() + static_cast<std::ptrdiff_t>(cut), e1.shape().end());
        }
 
        // add this when we have std::array index!
        // std::fill(idx.begin(), idx.end(), 0);
        using e1_value_type = typename E1::value_type;
        using e2_value_type = typename E2::value_type;
        constexpr bool needs_cast = has_assign_conversion<e1_value_type, e2_value_type>::value;
        using value_type = typename xassign_traits<E1, E2>::requested_value_type;
        using simd_type = std::conditional_t<
            std::is_same<e1_value_type, bool>::value,
            xt_simd::simd_bool_type<value_type>,
            xt_simd::simd_type<value_type>>;
 
        std::size_t simd_size = inner_loop_size / simd_type::size;
        std::size_t simd_rest = inner_loop_size % simd_type::size;
 
        auto fct_stepper = e2.stepper_begin(e1.shape());
        auto res_stepper = e1.stepper_begin(e1.shape());
 
        // TODO in 1D case this is ambiguous -- could be RM or CM.
        //      Use default layout to make decision
        std::size_t step_dim = 0;
        if (!is_row_major)  // row major case
        {
            step_dim = cut;
        }
#if defined(XTENSOR_USE_OPENMP) && defined(strided_parallel_assign)
        if (outer_loop_size >= XTENSOR_OPENMP_TRESHOLD / inner_loop_size)
        {
            std::size_t first_step = true;
#pragma omp parallel for schedule(static) firstprivate(first_step, fct_stepper, res_stepper, idx)
            for (std::size_t ox = 0; ox < outer_loop_size; ++ox)
            {
                if (first_step)
                {
                    is_row_major
                        ? strided_assign_detail::idx_tools<layout_type::row_major>::nth_idx(ox, idx, max_shape)
                        : strided_assign_detail::idx_tools<layout_type::column_major>::nth_idx(ox, idx, max_shape);
 
                    for (std::size_t i = 0; i < idx.size(); ++i)
                    {
                        fct_stepper.step(i + step_dim, idx[i]);
                        res_stepper.step(i + step_dim, idx[i]);
                    }
                    first_step = false;
                }
 
                for (std::size_t i = 0; i < simd_size; ++i)
                {
                    res_stepper.template store_simd(fct_stepper.template step_simd<value_type>());
                }
                for (std::size_t i = 0; i < simd_rest; ++i)
                {
                    *(res_stepper) = conditional_cast<needs_cast, e1_value_type>(*(fct_stepper));
                    res_stepper.step_leading();
                    fct_stepper.step_leading();
                }
 
                // next unaligned index
                is_row_major
                    ? strided_assign_detail::idx_tools<layout_type::row_major>::next_idx(idx, max_shape)
                    : strided_assign_detail::idx_tools<layout_type::column_major>::next_idx(idx, max_shape);
 
                fct_stepper.to_begin();
 
                // need to step E1 as well if not contigous assign (e.g. view)
                if (!E1::contiguous_layout)
                {
                    res_stepper.to_begin();
                    for (std::size_t i = 0; i < idx.size(); ++i)
                    {
                        fct_stepper.step(i + step_dim, idx[i]);
                        res_stepper.step(i + step_dim, idx[i]);
                    }
                }
                else
                {
                    for (std::size_t i = 0; i < idx.size(); ++i)
                    {
                        fct_stepper.step(i + step_dim, idx[i]);
                    }
                }
            }
        }
        else
        {
#elif defined(strided_parallel_assign) && defined(XTENSOR_USE_TBB)
        if (outer_loop_size > XTENSOR_TBB_THRESHOLD / inner_loop_size)
        {
            tbb::static_partitioner sp;
            tbb::parallel_for(
                tbb::blocked_range<size_t>(0ul, outer_loop_size),
                [&e1, &e2, is_row_major, step_dim, simd_size, simd_rest, &max_shape, &idx_ = idx](
                    const tbb::blocked_range<size_t>& r
                )
                {
                    auto idx = idx_;
                    auto fct_stepper = e2.stepper_begin(e1.shape());
                    auto res_stepper = e1.stepper_begin(e1.shape());
                    std::size_t first_step = true;
                    // #pragma omp parallel for schedule(static) firstprivate(first_step, fct_stepper,
                    // res_stepper, idx)
                    for (std::size_t ox = r.begin(); ox < r.end(); ++ox)
                    {
                        if (first_step)
                        {
                            is_row_major
                                ? strided_assign_detail::idx_tools<layout_type::row_major>::nth_idx(ox, idx, max_shape)
                                : strided_assign_detail::idx_tools<layout_type::column_major>::nth_idx(
                                    ox,
                                    idx,
                                    max_shape
                                );
 
                            for (std::size_t i = 0; i < idx.size(); ++i)
                            {
                                fct_stepper.step(i + step_dim, idx[i]);
                                res_stepper.step(i + step_dim, idx[i]);
                            }
                            first_step = false;
                        }
 
                        for (std::size_t i = 0; i < simd_size; ++i)
                        {
                            res_stepper.template store_simd(fct_stepper.template step_simd<value_type>());
                        }
                        for (std::size_t i = 0; i < simd_rest; ++i)
                        {
                            *(res_stepper) = conditional_cast<needs_cast, e1_value_type>(*(fct_stepper));
                            res_stepper.step_leading();
                            fct_stepper.step_leading();
                        }
 
                        // next unaligned index
                        is_row_major
                            ? strided_assign_detail::idx_tools<layout_type::row_major>::next_idx(idx, max_shape)
                            : strided_assign_detail::idx_tools<layout_type::column_major>::next_idx(idx, max_shape);
 
                        fct_stepper.to_begin();
 
                        // need to step E1 as well if not contigous assign (e.g. view)
                        if (!E1::contiguous_layout)
                        {
                            res_stepper.to_begin();
                            for (std::size_t i = 0; i < idx.size(); ++i)
                            {
                                fct_stepper.step(i + step_dim, idx[i]);
                                res_stepper.step(i + step_dim, idx[i]);
                            }
                        }
                        else
                        {
                            for (std::size_t i = 0; i < idx.size(); ++i)
                            {
                                fct_stepper.step(i + step_dim, idx[i]);
                            }
                        }
                    }
                },
                sp
            );
        }
        else
        {
 
#endif
            for (std::size_t ox = 0; ox < outer_loop_size; ++ox)
            {
                for (std::size_t i = 0; i < simd_size; ++i)
                {
                    res_stepper.store_simd(fct_stepper.template step_simd<value_type>());
                }
                for (std::size_t i = 0; i < simd_rest; ++i)
                {
                    *(res_stepper) = conditional_cast<needs_cast, e1_value_type>(*(fct_stepper));
                    res_stepper.step_leading();
                    fct_stepper.step_leading();
                }
 
                is_row_major
                    ? strided_assign_detail::idx_tools<layout_type::row_major>::next_idx(idx, max_shape)
                    : strided_assign_detail::idx_tools<layout_type::column_major>::next_idx(idx, max_shape);
 
                fct_stepper.to_begin();
 
                // need to step E1 as well if not contigous assign (e.g. view)
                if (!E1::contiguous_layout)
                {
                    res_stepper.to_begin();
                    for (std::size_t i = 0; i < idx.size(); ++i)
                    {
                        fct_stepper.step(i + step_dim, idx[i]);
                        res_stepper.step(i + step_dim, idx[i]);
                    }
                }
                else
                {
                    for (std::size_t i = 0; i < idx.size(); ++i)
                    {
                        fct_stepper.step(i + step_dim, idx[i]);
                    }
                }
            }
#if (defined(XTENSOR_USE_OPENMP) || defined(XTENSOR_USE_TBB)) && defined(strided_parallel_assign)
        }
#endif
    }
 
    template <>
    template <class E1, class E2>
    inline void strided_loop_assigner<true>::run(E1& e1, const E2& e2)
    {
        strided_assign_detail::loop_sizes_t loop_sizes = strided_loop_assigner<true>::get_loop_sizes(e1, e2);
        if (loop_sizes.can_do_strided_assign)
        {
            run(e1, e2, loop_sizes);
        }
        else
        {
            // trigger the fallback assigner
            stepper_assigner<E1, E2, default_assignable_layout(E1::static_layout)>(e1, e2).run();
        }
    }
 
    template <>
    template <class E1, class E2>
    inline void strided_loop_assigner<false>::run(E1& /*e1*/, const E2& /*e2*/, const loop_sizes_t&)
    {
    }
 
    template <>
    template <class E1, class E2>
    inline void strided_loop_assigner<false>::run(E1& e1, const E2& e2)
    {
        // trigger the fallback assigner
        stepper_assigner<E1, E2, default_assignable_layout(E1::static_layout)>(e1, e2).run();
    }
}
 
#endif