mdspan

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// <mdspan> -*- C++ -*-
 
// Copyright The GNU Toolchain Authors.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.
 
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
 
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.
 
// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.
 
/** @file mdspan
 *  This is a Standard C++ Library header.
 */
 
#ifndef _GLIBCXX_MDSPAN
#define _GLIBCXX_MDSPAN 1
 
#ifdef _GLIBCXX_SYSHDR
#pragma GCC system_header
#endif
 
#include <span>
#include <array>
#include <type_traits>
#include <utility>
 
#define __glibcxx_want_mdspan
#define __glibcxx_want_aligned_accessor
#define __glibcxx_want_submdspan
#include <bits/version.h>
 
#if __glibcxx_aligned_accessor
#include <bits/align.h>
#endif
 
#if __glibcxx_submdspan
#include <tuple>
#endif
 
#if __cplusplus > 202302L
#include <bits/stdexcept_throw.h>
#endif
 
#ifdef __glibcxx_mdspan
 
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
  namespace __mdspan
  {
    consteval bool
    __all_static(std::span<const size_t> __extents)
    {
      for(auto __ext : __extents)
        if (__ext == dynamic_extent)
          return false;
      return true;
    }
 
    consteval bool
    __all_dynamic(std::span<const size_t> __extents)
    {
      for(auto __ext : __extents)
        if (__ext != dynamic_extent)
          return false;
      return true;
    }
 
    template<typename _IndexType, typename _OIndexType>
      constexpr _IndexType
      __index_type_cast(_OIndexType&& __other)
      {
        if constexpr (std::is_integral_v<_OIndexType>)
          {
            constexpr _IndexType __index_type_max
              = __gnu_cxx::__int_traits<_IndexType>::__max;
            constexpr _OIndexType __oindex_type_max
              = __gnu_cxx::__int_traits<_OIndexType>::__max;
 
            if constexpr (__index_type_max < __oindex_type_max)
              __glibcxx_assert(cmp_less_equal(__other, __index_type_max));
 
            if constexpr (std::is_signed_v<_OIndexType>)
              __glibcxx_assert(__other >= 0);
            return static_cast<_IndexType>(__other);
          }
        else
          {
            auto __ret = static_cast<_IndexType>(std::move(__other));
            if constexpr (std::is_signed_v<_IndexType>)
              __glibcxx_assert(__ret >= 0);
            return __ret;
          }
      }
 
    template<array _Extents>
      class _StaticExtents
      {
      public:
        static constexpr size_t _S_rank = _Extents.size();
 
        // For __r in [0, _S_rank], _S_dynamic_index(__r) is the number
        // of dynamic extents up to (and not including) __r.
        //
        // If __r is the index of a dynamic extent, then
        // _S_dynamic_index[__r] is the index of that extent in
        // _M_dyn_exts.
        static constexpr size_t
        _S_dynamic_index(size_t __r) noexcept
        { return _S_dynamic_index_data[__r]; }
 
        static constexpr auto _S_dynamic_index_data = [] consteval
        {
          array<size_t, _S_rank+1> __ret;
          size_t __dyn = 0;
          for (size_t __i = 0; __i < _S_rank; ++__i)
            {
              __ret[__i] = __dyn;
              __dyn += (_Extents[__i] == dynamic_extent);
            }
          __ret[_S_rank] = __dyn;
          return __ret;
        }();
 
        static constexpr size_t _S_rank_dynamic = _S_dynamic_index(_S_rank);
 
        // For __r in [0, _S_rank_dynamic), _S_dynamic_index_inv(__r) is the
        // index of the __r-th dynamic extent in _Extents.
        static constexpr size_t
        _S_dynamic_index_inv(size_t __r) noexcept
        { return _S_dynamic_index_inv_data[__r]; }
 
        static constexpr auto _S_dynamic_index_inv_data = [] consteval
        {
          array<size_t, _S_rank_dynamic> __ret;
          for (size_t __i = 0, __r = 0; __i < _S_rank; ++__i)
            if (_Extents[__i] == dynamic_extent)
              __ret[__r++] = __i;
          return __ret;
        }();
 
        static constexpr size_t
        _S_static_extent(size_t __r) noexcept
        { return _Extents[__r]; }
      };
 
    template<array _Extents>
      requires (__all_dynamic<_Extents>())
      class _StaticExtents<_Extents>
      {
      public:
        static constexpr size_t _S_rank = _Extents.size();
 
        static constexpr size_t
        _S_dynamic_index(size_t __r) noexcept
        { return __r; }
 
        static constexpr size_t _S_rank_dynamic = _S_rank;
 
        static constexpr size_t
        _S_dynamic_index_inv(size_t __k) noexcept
        { return __k; }
 
        static constexpr size_t
        _S_static_extent(size_t) noexcept
        { return dynamic_extent; }
      };
 
    template<typename _IndexType, array _Extents>
      class _ExtentsStorage : public _StaticExtents<_Extents>
      {
      private:
        using _Base = _StaticExtents<_Extents>;
 
      public:
        using _Base::_S_rank;
        using _Base::_S_rank_dynamic;
        using _Base::_S_dynamic_index;
        using _Base::_S_dynamic_index_inv;
        using _Base::_S_static_extent;
 
        static constexpr bool
        _S_is_dynamic(size_t __r) noexcept
        {
          if constexpr (__all_static(_Extents))
            return false;
          else if constexpr (__all_dynamic(_Extents))
            return true;
          else
            return _Extents[__r] == dynamic_extent;
        }
 
        template<typename _OIndexType>
          static constexpr _IndexType
          _S_int_cast(const _OIndexType& __other) noexcept
          { return _IndexType(__other); }
 
        constexpr _IndexType
        _M_extent(size_t __r) const noexcept
        {
          if (_S_is_dynamic(__r))
            return _M_dyn_exts[_S_dynamic_index(__r)];
          else
            return _S_static_extent(__r);
        }
 
        template<size_t _OtherRank, typename _GetOtherExtent>
          static constexpr bool
          _S_is_compatible_extents(_GetOtherExtent __get_extent) noexcept
          {
            if constexpr (_OtherRank == _S_rank)
              for (size_t __i = 0; __i < _S_rank; ++__i)
                if (!_S_is_dynamic(__i)
                    && !cmp_equal(_Extents[__i], _S_int_cast(__get_extent(__i))))
                  return false;
            return true;
          }
 
        template<size_t _OtherRank, typename _GetOtherExtent>
          constexpr void
          _M_init_dynamic_extents(_GetOtherExtent __get_extent) noexcept
          {
            __glibcxx_assert(_S_is_compatible_extents<_OtherRank>(__get_extent));
            for (size_t __i = 0; __i < _S_rank_dynamic; ++__i)
              {
                size_t __di = __i;
                if constexpr (_OtherRank != _S_rank_dynamic)
                  __di = _S_dynamic_index_inv(__i);
                _M_dyn_exts[__i] = _S_int_cast(__get_extent(__di));
              }
          }
 
        constexpr
        _ExtentsStorage() noexcept = default;
 
        template<typename _OIndexType, array _OExtents>
          constexpr
          _ExtentsStorage(const _ExtentsStorage<_OIndexType, _OExtents>&
                          __other) noexcept
          {
            _M_init_dynamic_extents<_S_rank>([&__other](size_t __i)
              { return __other._M_extent(__i); });
          }
 
        template<typename _OIndexType, size_t _Nm>
          constexpr
          _ExtentsStorage(span<const _OIndexType, _Nm> __exts) noexcept
          {
            _M_init_dynamic_extents<_Nm>(
              [&__exts](size_t __i) -> const _OIndexType&
              { return __exts[__i]; });
          }
 
        static constexpr const array<size_t, _S_rank>&
        _S_static_extents() noexcept
        { return _Extents; }
 
        constexpr span<const _IndexType>
        _M_dynamic_extents(size_t __begin, size_t __end) const noexcept
        requires (_Extents.size() > 0)
        {
          return {_M_dyn_exts + _S_dynamic_index(__begin),
                  _S_dynamic_index(__end) - _S_dynamic_index(__begin)};
        }
 
      private:
        using _Storage = __array_traits<_IndexType, _S_rank_dynamic>::_Type;
        [[no_unique_address]] _Storage _M_dyn_exts{};
      };
 
    template<typename _OIndexType, typename _SIndexType>
      concept __valid_index_type =
        is_convertible_v<_OIndexType, _SIndexType> &&
        is_nothrow_constructible_v<_SIndexType, _OIndexType>;
 
    template<size_t _Extent, typename _IndexType>
      concept
      __valid_static_extent = _Extent == dynamic_extent
        || _Extent <= __gnu_cxx::__int_traits<_IndexType>::__max;
 
    template<typename _Extents>
      constexpr const array<size_t, _Extents::rank()>&
      __static_extents() noexcept
      { return _Extents::_Storage::_S_static_extents(); }
 
    template<typename _Extents>
      constexpr span<const size_t>
      __static_extents(size_t __begin, size_t __end) noexcept
      {
        const auto& __sta_exts = __static_extents<_Extents>();
        return span<const size_t>(__sta_exts.data() + __begin, __end - __begin);
      }
 
    // Pre-compute: \prod_{i = 0}^r _Extents[i], for r = 0,..., n (exclusive)
    template<array _Extents>
      constexpr auto __fwd_partial_prods = [] consteval
        {
          constexpr size_t __rank = _Extents.size();
          std::array<size_t, __rank> __ret;
          size_t __prod = 1;
          for (size_t __r = 0; __r < __rank; ++__r)
            {
              __ret[__r] = __prod;
              if (size_t __ext = _Extents[__r]; __ext != dynamic_extent)
                __prod *= __ext;
            }
          return __ret;
        }();
 
    // Pre-compute: \prod_{i = r+1}^{n-1} _Extents[i]
    template<array _Extents>
      constexpr auto __rev_partial_prods = [] consteval
        {
          constexpr size_t __rank = _Extents.size();
          std::array<size_t, __rank> __ret;
          size_t __prod = 1;
          for (size_t __r = __rank; __r > 0; --__r)
            {
              __ret[__r - 1] = __prod;
              if (size_t __ext = _Extents[__r - 1]; __ext != dynamic_extent)
                __prod *= __ext;
            }
          return __ret;
        }();
 
    template<typename _Extents>
      constexpr span<const typename _Extents::index_type>
      __dynamic_extents(const _Extents& __exts, size_t __begin = 0,
                        size_t __end = _Extents::rank()) noexcept
      { return __exts._M_exts._M_dynamic_extents(__begin, __end); }
  }
 
#if __glibcxx_submdspan
  struct full_extent_t
  {
    explicit full_extent_t() = default;
  };
 
  inline constexpr full_extent_t full_extent{};
 
  template<typename _OffsetType, typename _ExtentType, typename _StrideType>
    struct strided_slice
    {
      static_assert(__is_signed_or_unsigned_integer<_OffsetType>::value
        || __detail::__integral_constant_like<_OffsetType>);
      static_assert(__is_signed_or_unsigned_integer<_ExtentType>::value
        || __detail::__integral_constant_like<_ExtentType>);
      static_assert(__is_signed_or_unsigned_integer<_StrideType>::value
        || __detail::__integral_constant_like<_StrideType>);
 
      using offset_type = _OffsetType;
      using extent_type = _ExtentType;
      using stride_type = _StrideType;
 
      [[no_unique_address]] offset_type offset{};
      [[no_unique_address]] extent_type extent{};
      [[no_unique_address]] stride_type stride{};
    };
 
  template<typename _Mapping>
    struct submdspan_mapping_result
    {
      [[no_unique_address]] _Mapping mapping = _Mapping();
      size_t offset{};
    };
 
  template<typename _Tp>
    constexpr bool __is_submdspan_mapping_result = false;
 
  template<typename _Mapping>
    constexpr bool __is_submdspan_mapping_result<submdspan_mapping_result<_Mapping>> = true;
 
  template<typename _Mapping>
    concept __submdspan_mapping_result = __is_submdspan_mapping_result<_Mapping>;
 
#endif // __glibcxx_submdspan
 
  template<typename _IndexType, size_t... _Extents>
    class extents
    {
      static_assert(__is_signed_or_unsigned_integer<_IndexType>::value,
                    "IndexType must be a signed or unsigned integer type");
      static_assert(
          (__mdspan::__valid_static_extent<_Extents, _IndexType> && ...),
          "Extents must either be dynamic or representable as IndexType");
 
      using _Storage = __mdspan::_ExtentsStorage<
        _IndexType, array<size_t, sizeof...(_Extents)>{_Extents...}>;
      [[no_unique_address]] _Storage _M_exts;
 
    public:
      using index_type = _IndexType;
      using size_type = make_unsigned_t<index_type>;
      using rank_type = size_t;
 
      static constexpr rank_type
      rank() noexcept { return _Storage::_S_rank; }
 
      static constexpr rank_type
      rank_dynamic() noexcept { return _Storage::_S_rank_dynamic; }
 
      static constexpr size_t
      static_extent(rank_type __r) noexcept
      {
        __glibcxx_assert(__r < rank());
        if constexpr (rank() == 0)
          __builtin_trap();
        else
          return _Storage::_S_static_extent(__r);
      }
 
      constexpr index_type
      extent(rank_type __r) const noexcept
      {
        __glibcxx_assert(__r < rank());
        if constexpr (rank() == 0)
          __builtin_trap();
        else
          return _M_exts._M_extent(__r);
      }
 
      constexpr
      extents() noexcept = default;
 
    private:
      static consteval bool
      _S_is_less_dynamic(size_t __ext, size_t __oext)
      { return (__ext != dynamic_extent) && (__oext == dynamic_extent); }
 
      template<typename _OIndexType, size_t... _OExtents>
        static consteval bool
        _S_ctor_explicit()
        {
          return (_S_is_less_dynamic(_Extents, _OExtents) || ...)
            || (__gnu_cxx::__int_traits<index_type>::__max
                < __gnu_cxx::__int_traits<_OIndexType>::__max);
        }
 
      template<size_t... _OExtents>
        static consteval bool
        _S_is_compatible_extents()
        {
          if constexpr (sizeof...(_OExtents) != rank())
            return false;
          else
            return ((_OExtents == dynamic_extent || _Extents == dynamic_extent
                     || _OExtents == _Extents) && ...);
        }
 
    public:
      template<typename _OIndexType, size_t... _OExtents>
        requires (_S_is_compatible_extents<_OExtents...>())
        constexpr explicit(_S_ctor_explicit<_OIndexType, _OExtents...>())
        extents(const extents<_OIndexType, _OExtents...>& __other) noexcept
        : _M_exts(__other._M_exts)
        { }
 
      template<__mdspan::__valid_index_type<index_type>... _OIndexTypes>
        requires (sizeof...(_OIndexTypes) == rank()
                  || sizeof...(_OIndexTypes) == rank_dynamic())
        constexpr explicit extents(_OIndexTypes... __exts) noexcept
        : _M_exts(span<const _IndexType, sizeof...(_OIndexTypes)>(
            initializer_list{static_cast<_IndexType>(std::move(__exts))...}))
        { }
 
      template<typename _OIndexType, size_t _Nm>
        requires __mdspan::__valid_index_type<const _OIndexType&, index_type>
          && (_Nm == rank() || _Nm == rank_dynamic())
        constexpr explicit(_Nm != rank_dynamic())
        extents(span<_OIndexType, _Nm> __exts) noexcept
        : _M_exts(span<const _OIndexType, _Nm>(__exts))
        { }
 
      template<typename _OIndexType, size_t _Nm>
        requires __mdspan::__valid_index_type<const _OIndexType&, index_type>
          && (_Nm == rank() || _Nm == rank_dynamic())
        constexpr explicit(_Nm != rank_dynamic())
        extents(const array<_OIndexType, _Nm>& __exts) noexcept
        : _M_exts(span<const _OIndexType, _Nm>(__exts))
        { }
 
      template<typename _OIndexType, size_t... _OExtents>
        friend constexpr bool
        operator==(const extents& __self,
                   const extents<_OIndexType, _OExtents...>& __other) noexcept
        {
          if constexpr (!_S_is_compatible_extents<_OExtents...>())
            return false;
          else
            {
              auto __impl = [&__self, &__other]<size_t... _Counts>(
                  index_sequence<_Counts...>)
                { return (cmp_equal(__self.extent(_Counts),
                                    __other.extent(_Counts)) && ...); };
              return __impl(make_index_sequence<__self.rank()>());
            }
        }
 
    private:
      friend constexpr const array<size_t, rank()>&
      __mdspan::__static_extents<extents>() noexcept;
 
      friend constexpr span<const index_type>
      __mdspan::__dynamic_extents<extents>(const extents&, size_t, size_t)
      noexcept;
 
      template<typename _OIndexType, size_t... _OExtents>
        friend class extents;
    };
 
  namespace __mdspan
  {
    template<typename _Tp, size_t _Nm>
      constexpr bool
      __contains_zero(span<_Tp, _Nm> __exts) noexcept
      {
        for (size_t __i = 0; __i < __exts.size(); ++__i)
          if (__exts[__i] == 0)
            return true;
        return false;
      }
 
    template<typename _Tp, size_t _Nm>
      consteval bool
      __contains_zero(const array<_Tp, _Nm>& __exts) noexcept
      { return __contains_zero(span<const _Tp>(__exts)); }
 
    template<typename _Extents>
      constexpr bool
      __empty(const _Extents& __exts) noexcept
      {
        if constexpr (__contains_zero(__static_extents<_Extents>()))
          return true;
        else if constexpr (_Extents::rank_dynamic() > 0)
          return __contains_zero(__dynamic_extents(__exts));
        else
          return false;
      }
 
    template<typename _Extents>
      constexpr typename _Extents::index_type
      __extents_prod(const _Extents& __exts, size_t __sta_prod, size_t __begin,
                     size_t __end) noexcept
      {
        if (__sta_prod == 0)
          return 0;
 
        size_t __ret = __sta_prod;
        if constexpr (_Extents::rank_dynamic() > 0)
          for (auto __factor : __dynamic_extents(__exts, __begin, __end))
            __ret *= size_t(__factor);
        return static_cast<typename _Extents::index_type>(__ret);
      }
 
    // Preconditions: _r < _Extents::rank()
    template<typename _Extents>
      constexpr typename _Extents::index_type
      __fwd_prod(const _Extents& __exts, size_t __begin, size_t __end) noexcept
      {
        size_t __sta_prod = [__begin, __end] {
          span<const size_t> __sta_exts
            = __static_extents<_Extents>(__begin, __end);
          size_t __ret = 1;
          for(auto __ext : __sta_exts)
            if (__ext != dynamic_extent)
              __ret *= __ext;
          return __ret;
        }();
        return __extents_prod(__exts, __sta_prod, __begin, __end);
      }
 
    template<typename _Extents>
      constexpr typename _Extents::index_type
      __fwd_prod(const _Extents& __exts, size_t __r) noexcept
      {
        constexpr size_t __rank = _Extents::rank();
        constexpr auto& __sta_exts = __static_extents<_Extents>();
        if constexpr (__rank == 1)
          return 1;
        else if constexpr (__rank == 2)
          return __r == 0 ? 1 : __exts.extent(0);
        else if constexpr (__all_dynamic(std::span(__sta_exts).first(__rank-1)))
          return __extents_prod(__exts, 1, 0, __r);
        else
          {
            size_t __sta_prod = __fwd_partial_prods<__sta_exts>[__r];
            return __extents_prod(__exts, __sta_prod, 0, __r);
          }
      }
 
    template<typename _IndexType, size_t _Nm>
      consteval _IndexType
      __fwd_prod(span<const _IndexType, _Nm> __values)
      {
        _IndexType __ret = 1;
        for(auto __value : __values)
          __ret *= __value;
        return __ret;
      }
 
    // Preconditions: _r < _Extents::rank()
    template<typename _Extents>
      constexpr typename _Extents::index_type
      __rev_prod(const _Extents& __exts, size_t __r) noexcept
      {
        constexpr size_t __rank = _Extents::rank();
        constexpr auto& __sta_exts = __static_extents<_Extents>();
        if constexpr (__rank == 1)
          return 1;
        else if constexpr (__rank == 2)
          return __r == 0 ? __exts.extent(1) : 1;
        else if constexpr (__all_dynamic(std::span(__sta_exts).last(__rank-1)))
          return __extents_prod(__exts, 1, __r + 1, __rank);
        else
          {
            size_t __sta_prod = __rev_partial_prods<__sta_exts>[__r];
            return __extents_prod(__exts, __sta_prod, __r + 1, __rank);
          }
      }
 
    template<typename _Extents>
      constexpr typename _Extents::index_type
      __size(const _Extents& __exts) noexcept
      {
        constexpr size_t __sta_prod = [] {
          span<const size_t> __sta_exts = __static_extents<_Extents>();
          size_t __ret = 1;
          for(auto __ext : __sta_exts)
            if (__ext != dynamic_extent)
              __ret *= __ext;
          return __ret;
        }();
        return __extents_prod(__exts, __sta_prod, 0, _Extents::rank());
      }
 
    template<typename _IndexType, size_t... _Counts>
      auto __build_dextents_type(integer_sequence<size_t, _Counts...>)
        -> extents<_IndexType, ((void) _Counts, dynamic_extent)...>;
  }
 
  template<typename _IndexType, size_t _Rank>
    using dextents = decltype(__mdspan::__build_dextents_type<_IndexType>(
        make_index_sequence<_Rank>()));
 
#if __glibcxx_mdspan >= 202406L
  template<size_t _Rank, typename _IndexType = size_t>
    using dims = dextents<_IndexType, _Rank>;
#endif
 
  template<typename... _Integrals>
    requires (is_convertible_v<_Integrals, size_t> && ...)
    explicit extents(_Integrals...) ->
      extents<size_t, __detail::__maybe_static_ext<_Integrals>...>;
 
  struct layout_left
  {
    template<typename _Extents>
      class mapping;
  };
 
  struct layout_right
  {
    template<typename _Extents>
      class mapping;
  };
 
  struct layout_stride
  {
    template<typename _Extents>
      class mapping;
  };
 
#ifdef __glibcxx_padded_layouts
  template<size_t _PaddingValue>
    struct layout_left_padded
    {
      template<typename _Extents>
        class mapping;
    };
 
  template<size_t _PaddingValue>
    struct layout_right_padded
    {
      template<typename _Extents>
        class mapping;
    };
#endif
 
  namespace __mdspan
  {
    template<typename _Tp>
      constexpr bool __is_extents = false;
 
    template<typename _IndexType, size_t... _Extents>
      constexpr bool __is_extents<extents<_IndexType, _Extents...>> = true;
 
    template<typename _Extents, typename... _Indices>
      constexpr typename _Extents::index_type
      __linear_index_left(const _Extents& __exts, _Indices... __indices)
      noexcept
      {
        using _IndexType = typename _Extents::index_type;
        _IndexType __res = 0;
        if constexpr (sizeof...(__indices) > 0)
          {
            _IndexType __mult = 1;
            auto __update = [&, __pos = 0u](_IndexType __idx) mutable
              {
                _GLIBCXX_DEBUG_ASSERT(cmp_less(__idx, __exts.extent(__pos)));
                __res += __idx * __mult;
                __mult *= __exts.extent(__pos);
                ++__pos;
              };
            (__update(__indices), ...);
          }
        return __res;
      }
 
    template<typename _IndexType>
      consteval _IndexType
      __static_quotient(std::span<const size_t> __sta_exts,
        _IndexType __nom = __gnu_cxx::__int_traits<_IndexType>::__max)
      {
        for (auto __factor : __sta_exts)
          {
            if (__factor != dynamic_extent)
              __nom /= _IndexType(__factor);
            if (__nom == 0)
              break;
          }
        return __nom;
      }
 
    template<typename _Extents,
             typename _IndexType = typename _Extents::index_type>
      requires __is_extents<_Extents>
      consteval _IndexType
      __static_quotient(_IndexType __nom
                          = __gnu_cxx::__int_traits<_IndexType>::__max)
      {
        std::span<const size_t> __sta_exts = __static_extents<_Extents>();
        return __static_quotient<_IndexType>(__sta_exts, __nom);
      }
 
    template<typename _Extents>
      constexpr bool
      __is_representable_extents(const _Extents& __exts) noexcept
      {
        using _IndexType = _Extents::index_type;
 
        if constexpr (__contains_zero(__static_extents<_Extents>()))
          return true;
        else
          {
            constexpr auto __sta_quo = __static_quotient<_Extents>();
            if constexpr (_Extents::rank_dynamic() == 0)
              return __sta_quo != 0;
            else
              {
                auto __dyn_exts = __dynamic_extents(__exts);
                if (__contains_zero(__dyn_exts))
                  return true;
 
                if constexpr (__sta_quo == 0)
                  return false;
                else
                  {
                    auto __dyn_quo = _IndexType(__sta_quo);
                    for (auto __factor : __dyn_exts)
                      {
                        __dyn_quo /= __factor;
                        if (__dyn_quo == 0)
                          return false;
                      }
                    return true;
                  }
              }
          }
      }
 
    template<typename _Extents, typename _IndexType>
      concept __representable_size = _Extents::rank_dynamic() != 0
        || __contains_zero(__static_extents<_Extents>())
        || (__static_quotient<_Extents, _IndexType>() != 0);
 
    template<typename _Layout, typename _Mapping>
      concept __mapping_of =
        is_same_v<typename _Layout::template mapping<
                    typename _Mapping::extents_type>,
                  _Mapping>;
 
    template<template<size_t> typename _Layout, typename _Mapping>
      concept __padded_mapping_of = __mapping_of<
        _Layout<_Mapping::padding_value>, _Mapping>;
 
#ifdef __glibcxx_padded_layouts
    template<typename _Mapping>
      constexpr bool __is_left_padded_mapping = __padded_mapping_of<
        layout_left_padded, _Mapping>;
 
    template<typename _Mapping>
      constexpr bool __is_right_padded_mapping = __padded_mapping_of<
        layout_right_padded, _Mapping>;
 
    template<typename _Mapping>
      constexpr bool __is_padded_mapping = __is_left_padded_mapping<_Mapping>
        || __is_right_padded_mapping<_Mapping>;
#endif
 
    template<typename _PaddedMapping>
      consteval size_t
      __get_static_stride()
      { return _PaddedMapping::_PaddedStorage::_S_static_stride; }
 
    template<typename _Mapping>
      concept __standardized_mapping = __mapping_of<layout_left, _Mapping>
                                       || __mapping_of<layout_right, _Mapping>
                                       || __mapping_of<layout_stride, _Mapping>
#ifdef __glibcxx_padded_layouts
                                       || __is_left_padded_mapping<_Mapping>
                                       || __is_right_padded_mapping<_Mapping>
#endif
                                       ;
 
    // A tag type to create internal ctors.
    class __internal_ctor
    { };
 
    template<typename _Mapping>
      constexpr typename _Mapping::index_type
      __offset(const _Mapping& __m) noexcept
      {
        using _IndexType = typename _Mapping::index_type;
        constexpr auto __rank = _Mapping::extents_type::rank();
 
        if constexpr (__standardized_mapping<_Mapping>)
          return 0;
        else if (__empty(__m.extents()))
          return 0;
        else
          {
            auto __impl = [&__m]<size_t... _Counts>(index_sequence<_Counts...>)
              { return __m(((void) _Counts, _IndexType(0))...); };
            return __impl(make_index_sequence<__rank>());
          }
      }
 
#ifdef __glibcxx_submdspan
    template<typename _Tp>
      constexpr bool __is_strided_slice = false;
 
    template<typename _OffsetType, typename _ExtentType, typename _StrideType>
      constexpr bool __is_strided_slice<strided_slice<_OffsetType,
          _ExtentType, _StrideType>> = true;
 
    template<typename _IndexType, typename _OIndexType>
      consteval bool
      __is_representable_integer(_OIndexType __value)
      {
        constexpr auto __min = __gnu_cxx::__int_traits<_IndexType>::__min;
        constexpr auto __max = __gnu_cxx::__int_traits<_IndexType>::__max;
        return std::cmp_less_equal(__min, __value)
            && std::cmp_less_equal(__value, __max);
      }
 
    template<typename _Tp>
      constexpr bool __is_constant_wrapper = false;
 
    template<_CwFixedValue _Xv, typename _Tp>
      constexpr bool __is_constant_wrapper<constant_wrapper<_Xv, _Tp>>
        = true;
 
    template<size_t _Index, typename _Extents>
      constexpr auto
      __extract_extent(const _Extents& __exts)
      {
        using _IndexType = typename _Extents::index_type;
        return extents<_IndexType, _Extents::static_extent(_Index)>{
          __exts.extent(_Index)};
      }
 
    template<typename _Slice, typename _IndexType>
      concept __acceptable_slice_type = same_as<_Slice, full_extent_t>
          || same_as<_Slice, _IndexType> || __is_constant_wrapper<_Slice>
          || __is_strided_slice<_Slice>;
 
    template<typename _IndexType, typename... _Slices>
      consteval auto
      __subrank()
      {
        return (static_cast<size_t>(!convertible_to<_Slices, _IndexType>)
                + ... + 0);
      }
 
    template<typename _IndexType, typename... _Slices>
      consteval auto
      __inv_map_rank()
      {
        constexpr auto __rank = sizeof...(_Slices);
        constexpr auto __sub_rank = __subrank<_IndexType, _Slices...>();
        auto __map = std::array<size_t, __sub_rank>{};
        auto __is_int_like = std::array<bool, __rank>{
          convertible_to<_Slices, _IndexType>...};
 
        size_t __i = 0;
        for (size_t __k = 0; __k < __rank; ++__k)
          if (!__is_int_like[__k])
            __map[__i++] = __k;
        return __map;
      }
 
    template<typename _Slice>
      constexpr auto
      __slice_begin(_Slice __slice)
      {
        if constexpr (same_as<_Slice, full_extent_t>)
          return 0;
        else if constexpr (__is_strided_slice<_Slice>)
          return __slice.offset;
        else
          return __slice; // collapsing slice
      }
 
    template<typename _Mapping, typename... _Slices>
      constexpr size_t
      __suboffset(const _Mapping& __mapping, const _Slices&... __slices)
      {
        using _IndexType = typename _Mapping::index_type;
        auto __any_past_the_end = [&]<size_t... _Is>(index_sequence<_Is...>)
        {
          auto __is_past_the_end = [](const auto& __slice, const auto& __ext)
          {
            using _Slice = remove_cvref_t<decltype(__slice)>;
            if constexpr (is_convertible_v<_Slice, _IndexType>)
              return false;
            else if constexpr (same_as<_Slice, full_extent_t>
                && __ext.static_extent(0) != 0
                && __ext.static_extent(0) != dynamic_extent)
              return false;
            else
              return __mdspan::__slice_begin(__slice) == __ext.extent(0);
          };
 
          const auto& __exts = __mapping.extents();
          return ((__is_past_the_end(__slices...[_Is],
                                     __mdspan::__extract_extent<_Is>(__exts))) || ...);
        };
 
        if constexpr ((same_as<_Slices, full_extent_t> && ...))
          return __mdspan::__offset(__mapping);
 
        if (__any_past_the_end(std::make_index_sequence<sizeof...(__slices)>()))
          return __mapping.required_span_size();
        return __mapping(__mdspan::__slice_begin(__slices)...);
      }
 
    template<typename _IndexType, size_t _Extent, typename _Slice>
      consteval size_t
      __static_slice_extent()
      {
        if constexpr (same_as<_Slice, full_extent_t>)
          return _Extent;
        else if constexpr (same_as<_Slice, constant_wrapper<_IndexType(0)>>)
          return 0;
        else if constexpr (__is_constant_wrapper<typename _Slice::extent_type>
                        && __is_constant_wrapper<typename _Slice::stride_type>)
          return 1 + ((typename _Slice::extent_type{}) - 1)
                   / (typename _Slice::stride_type{});
        else
          return dynamic_extent;
      }
 
    template<size_t _K, typename _Extents, typename _Slice>
      constexpr typename _Extents::index_type
      __dynamic_slice_extent(const _Extents& __exts, _Slice __slice)
      {
        if constexpr (__is_strided_slice<_Slice>)
          return __slice.extent == 0 ? 0 : 1 + (__slice.extent - 1) / __slice.stride;
        else
          return __exts.extent(_K);
      }
 
    template<typename _IndexType, size_t... _Extents, typename... _Slices>
      requires (sizeof...(_Slices) == sizeof...(_Extents))
      constexpr auto
      __subextents(const extents<_IndexType, _Extents...>& __exts,
                   _Slices... __slices)
      {
        constexpr auto __inv_map = __mdspan::__inv_map_rank<_IndexType, _Slices...>();
        auto __impl = [&]<size_t... _Indices>(std::index_sequence<_Indices...>)
        {
          using _SubExts = extents<_IndexType,
              __mdspan::__static_slice_extent<_IndexType,
                 _Extents...[__inv_map[_Indices]],
                 _Slices...[__inv_map[_Indices]]>()...>;
          if constexpr (_SubExts::rank_dynamic() == 0)
            return _SubExts{};
          else
            {
              using _StaticSubExtents = __mdspan::_StaticExtents<
                __mdspan::__static_extents<_SubExts>()>;
              auto __create = [&]<size_t... _Is>(std::index_sequence<_Is...>)
              {
                constexpr auto __slice_idx = [__inv_map](size_t __i) consteval
                {
                  return __inv_map[_StaticSubExtents::_S_dynamic_index_inv(__i)];
                };
 
                return _SubExts{__mdspan::__dynamic_slice_extent<__slice_idx(_Is)>(
                     __exts, __slices...[__slice_idx(_Is)])...};
              };
              constexpr auto __dyn_subrank = _SubExts::rank_dynamic();
              return __create(std::make_index_sequence<__dyn_subrank>());
            }
        };
 
        return __impl(std::make_index_sequence<__inv_map.size()>());
      }
 
    enum class _LayoutSide
    {
      __left,
      __right,
      __unknown
    };
 
    template<typename _Mapping>
      consteval _LayoutSide
      __mapping_side()
      {
        if constexpr (__is_left_padded_mapping<_Mapping>
            || __mapping_of<layout_left, _Mapping>)
          return _LayoutSide::__left;
        if constexpr (__is_right_padded_mapping<_Mapping>
            || __mapping_of<layout_right, _Mapping>)
          return _LayoutSide::__right;
        else
          return _LayoutSide::__unknown;
      }
 
    template<_LayoutSide _Side, size_t _Rank>
      struct _StridesTrait
      {
        static constexpr const _LayoutSide _S_side = _Side;
 
        static constexpr size_t
        _S_idx(size_t __k) noexcept
        {
          if constexpr (_Side == _LayoutSide::__left)
            return __k;
          else
            return _Rank - 1 - __k;
        }
 
        // Unifies the formulas for computing strides for padded and unpadded
        // layouts.
        template<typename _Mapping>
          static constexpr typename _Mapping::index_type
          _S_padded_extent(const _Mapping& __mapping, size_t __k)
          {
            if (__k == 0)
              return __mapping.stride(_S_idx(1));
            else
              return __mapping.extents().extent(_S_idx(__k));
          }
 
        template<typename _IndexType, typename... _Slices>
          static consteval auto
          _S_inv_map()
          {
            static_assert(_Side != _LayoutSide::__unknown);
            auto __impl = [&]<size_t... _Is>(std::index_sequence<_Is...>)
            {
              return __mdspan::__inv_map_rank<_IndexType, _Slices...[_S_idx(_Is)]...>();
            };
            return __impl(std::make_index_sequence<_Rank>());
          }
      };
 
    template<typename _SubExts, typename _Mapping, typename... _Slices>
      constexpr auto
      __substrides_generic(const _Mapping& __mapping, const _Slices&... __slices)
      {
        using _IndexType = typename _Mapping::index_type;
        if constexpr (_SubExts::rank() == 0)
          return array<_IndexType, _SubExts::rank()>{};
        else
          {
            auto __stride = [&__mapping](size_t __k, auto __slice) -> _IndexType
            {
              if constexpr (__is_strided_slice<decltype(__slice)>)
                if (__slice.stride < __slice.extent)
                  return __mapping.stride(__k) * __slice.stride;
              return __mapping.stride(__k);
            };
 
            auto __impl = [&]<size_t... _Is>(std::index_sequence<_Is...>)
            {
              constexpr auto __inv_map
                = __mdspan::__inv_map_rank<_IndexType, _Slices...>();
              return array<_IndexType, _SubExts::rank()>{
                __stride(__inv_map[_Is], __slices...[__inv_map[_Is]])...};
            };
            return __impl(std::make_index_sequence<_SubExts::rank()>());
          }
      };
 
    template<typename _SubExts, typename _Mapping, typename... _Slices>
      constexpr auto
      __substrides_standardized(const _Mapping& __mapping,
                               const _Slices&... __slices)
      {
        using _IndexType = typename _Mapping::index_type;
        using _Trait = _StridesTrait<__mapping_side<_Mapping>(),
                                     _Mapping::extents_type::rank()>;
        using _SubTrait = _StridesTrait<__mapping_side<_Mapping>(), _SubExts::rank()>;
 
        constexpr size_t __sub_rank = _SubExts::rank();
 
        std::array<_IndexType, __sub_rank> __ret;
        if constexpr (__sub_rank > 0)
          {
            constexpr auto __inv_map
              = _Trait::template _S_inv_map<_IndexType, _Slices...>();
            auto __loop = [&]<size_t... _Ks>(std::index_sequence<_Ks...>)
            {
              size_t __i0 = 0;
              size_t __stride = 1;
              auto __body = [&](size_t __k, auto __slice)
              {
                for (size_t __i = __i0; __i < __inv_map[__k]; ++__i)
                  __stride *= _Trait::_S_padded_extent(__mapping, __i);
 
                size_t __krev = _SubTrait::_S_idx(__k);
                if constexpr (__is_strided_slice<decltype(__slice)>)
                  {
                    if (__slice.stride < __slice.extent)
                      __ret[__krev] = __stride * __slice.stride;
                    else
                      __ret[__krev] = __stride;
                  }
                else
                  __ret[__krev] = __stride;
 
                __i0 = __inv_map[__k];
              };
 
              ((__body(_Ks, __slices...[_Trait::_S_idx(__inv_map[_Ks])])),...);
            };
            __loop(std::make_index_sequence<__sub_rank>());
          }
        return __ret;
      }
 
 
    template<typename _SubExts, typename _Mapping, typename... _Slices>
      constexpr auto
      __substrides(const _Mapping& __mapping, const _Slices&... __slices)
      {
        if constexpr (__mdspan::__mapping_side<_Mapping>() == _LayoutSide::__unknown)
          return __mdspan::__substrides_generic<_SubExts>(__mapping, __slices...);
        else
          return __mdspan::__substrides_standardized<_SubExts>(__mapping, __slices...);
      }
 
    template<typename _Slice>
      concept __is_unit_stride_slice = (__mdspan::__is_strided_slice<_Slice>
          && __mdspan::__is_constant_wrapper<typename _Slice::stride_type>
          && _Slice::stride_type::value == 1)
        || std::same_as<_Slice, full_extent_t>;
 
    // These are (forced) exclusive categories:
    //  - full & collapsing: obvious,
    //  - unit_strided_slice: strided_slice{a, b, cw<1>}, but not `full`,
    //  - strided_slice: strided_slice{a, b, c} with c != cw<1>.
    enum class _SliceKind
    {
      __strided_slice,
      __unit_strided_slice,
      __full,
      __collapsing
    };
 
    template<typename _Slice>
      consteval _SliceKind
      __make_slice_kind()
      {
        if constexpr (std::same_as<_Slice, full_extent_t>)
          return _SliceKind::__full;
        else if constexpr (__mdspan::__is_strided_slice<_Slice>)
          {
            if constexpr (__mdspan::__is_unit_stride_slice<_Slice>)
              return _SliceKind::__unit_strided_slice;
            else
              return _SliceKind::__strided_slice;
          }
        else
          return _SliceKind::__collapsing;
      }
 
    template<typename... _Slices>
      consteval array<_SliceKind, sizeof...(_Slices)>
      __make_slice_kind_array()
      {
        return array<_SliceKind, sizeof...(_Slices)>{
          __mdspan::__make_slice_kind<_Slices>()...};
      }
 
    //                   __block_size - 1
    // [full, ..., full, unit_slice    , *]
    consteval bool
    __is_block(span<const _SliceKind> __slice_kinds, size_t __block_size)
    {
      if (__block_size == 0)
        return false;
 
      if (__block_size > __slice_kinds.size())
        return false;
 
      for (size_t __i = 0; __i < __block_size - 1; ++__i)
        if (__slice_kinds[__i] != _SliceKind::__full)
          return false;
 
      auto __last = __slice_kinds[__block_size - 1];
      return __last == _SliceKind::__full
          || __last == _SliceKind::__unit_strided_slice;
    }
 
    //                         __u              __u + __sub_rank-2
    // [unit_slice, i, ..., k, full, ..., full, unit_slice, *]
    static consteval size_t
    __padded_block_begin_generic(span<const _SliceKind> __slice_kinds,
                                 size_t __sub_rank)
    {
      if (__slice_kinds[0] != _SliceKind::__full
          && __slice_kinds[0] != _SliceKind::__unit_strided_slice)
        return dynamic_extent;
      else if (__slice_kinds.size() == 1)
        return dynamic_extent;
      else
        {
          size_t __u = 1;
          while(__u < __slice_kinds.size()
                && __slice_kinds[__u] == _SliceKind::__collapsing)
            ++__u;
 
          if (__mdspan::__is_block(__slice_kinds.subspan(__u), __sub_rank -1))
            return __u;
          return dynamic_extent;
        }
    }
 
    template<_LayoutSide _Side, size_t _Nm>
      static consteval size_t
      __padded_block_begin(span<const _SliceKind, _Nm> __slice_kinds, size_t __sub_rank)
      {
        if constexpr (_Side == _LayoutSide::__left)
          return __mdspan::__padded_block_begin_generic(__slice_kinds, __sub_rank);
        else
          {
            std::array<_SliceKind, _Nm> __rev_slices;
            for(size_t __i = 0; __i < _Nm; ++__i)
              __rev_slices[__i] = __slice_kinds[_Nm - 1 - __i];
            auto __rev_slice_kinds = span<const _SliceKind>(__rev_slices);
 
            auto __u = __mdspan::__padded_block_begin_generic(__rev_slice_kinds,
                                                              __sub_rank);
            return __u == dynamic_extent ? dynamic_extent : _Nm - 1 - __u;
          }
      }
 
    template<_LayoutSide _Side, bool _Padded>
      struct _SubMdspanMapping;
 
    template<>
      struct _SubMdspanMapping<_LayoutSide::__left, false>
      {
        using _Layout = layout_left;
        template<size_t _Pad> using _PaddedLayout = layout_left_padded<_Pad>;
 
        template<typename _Mapping, size_t _Us>
          static consteval size_t
          _S_pad()
          {
            using _Extents = typename _Mapping::extents_type;
            constexpr auto __sta_exts = __mdspan::__static_extents<_Extents>(0, _Us);
            if constexpr (!__mdspan::__all_static(__sta_exts))
              return dynamic_extent;
            else
              return __mdspan::__fwd_prod(__sta_exts);
          }
 
        template<size_t _Nm>
          static consteval bool
          _S_is_unpadded_submdspan(span<const _SliceKind, _Nm> __slice_kinds, size_t __sub_rank)
          { return __mdspan::__is_block(__slice_kinds, __sub_rank); }
      };
 
    template<>
      struct _SubMdspanMapping<_LayoutSide::__left, true>
      {
        using _Layout = layout_left;
        template<size_t _Pad> using _PaddedLayout = layout_left_padded<_Pad>;
 
        template<typename _Mapping, size_t _Us>
          static consteval size_t
          _S_pad()
          {
            using _Extents = typename _Mapping::extents_type;
            constexpr auto __sta_exts
              = __mdspan::__static_extents<_Extents>(1, _Us);
            constexpr auto __sta_padstride
              = __mdspan::__get_static_stride<_Mapping>();
            if constexpr (__sta_padstride == dynamic_extent
                          || !__mdspan::__all_static(__sta_exts))
              return dynamic_extent;
            else
              return __sta_padstride * __mdspan::__fwd_prod(__sta_exts);
          }
 
        template<size_t _Nm>
          static consteval bool
          _S_is_unpadded_submdspan(span<const _SliceKind, _Nm> __slice_kinds,
                                   size_t __sub_rank)
          {
            if (__sub_rank == 1)
              return __slice_kinds[0] == _SliceKind::__unit_strided_slice
                || __slice_kinds[0] == _SliceKind::__full;
            else
              return false;
          }
      };
 
    template<>
      struct _SubMdspanMapping<_LayoutSide::__right, false>
      {
        using _Layout = layout_right;
        template<size_t _Pad> using _PaddedLayout = layout_right_padded<_Pad>;
 
        template<typename _Mapping, size_t _Us>
          static consteval size_t
          _S_pad()
          {
            using _Extents = typename _Mapping::extents_type;
            constexpr auto __rank = _Extents::rank();
            constexpr auto __sta_exts
              = __mdspan::__static_extents<_Extents>(_Us + 1, __rank);
            if constexpr (!__mdspan::__all_static(__sta_exts))
              return dynamic_extent;
            else
              return __fwd_prod(__sta_exts);
          }
 
        template<size_t _Nm>
          static consteval bool
          _S_is_unpadded_submdspan(span<const _SliceKind, _Nm> __slice_kinds,
                                   size_t __sub_rank)
          {
            auto __rev_slice_kinds = array<_SliceKind, _Nm>{};
            for(size_t __i = 0; __i < _Nm; ++__i)
              __rev_slice_kinds[__i] = __slice_kinds[_Nm - 1 - __i];
            return __mdspan::__is_block(span(__rev_slice_kinds), __sub_rank);
          }
      };
 
    template<>
      struct _SubMdspanMapping<_LayoutSide::__right, true>
      {
        using _Layout = layout_right;
        template<size_t _Pad> using _PaddedLayout = layout_right_padded<_Pad>;
 
        template<typename _Mapping, size_t _Us>
          static consteval size_t
          _S_pad()
          {
            using _Extents = typename _Mapping::extents_type;
            constexpr auto __rank = _Extents::rank();
            constexpr auto __sta_exts
              = __mdspan::__static_extents<_Extents>(_Us + 1, __rank - 1);
            constexpr auto __sta_padstride
              = __mdspan::__get_static_stride<_Mapping>();
            if constexpr (__sta_padstride == dynamic_extent
                          || !__mdspan::__all_static(__sta_exts))
              return dynamic_extent;
            else
              return __sta_padstride * __mdspan::__fwd_prod(__sta_exts);
          }
 
        template<size_t _Nm>
          static consteval bool
          _S_is_unpadded_submdspan(span<const _SliceKind, _Nm> __slice_kinds,
                                   size_t __sub_rank)
          {
            if (__sub_rank == 1)
              return __slice_kinds[_Nm - 1] == _SliceKind::__unit_strided_slice
                || __slice_kinds[_Nm - 1] == _SliceKind::__full;
            else
              return false;
          }
      };
 
 
    template<typename _Mapping>
      constexpr auto
      __submdspan_mapping_impl(const _Mapping& __mapping)
      { return submdspan_mapping_result{__mapping, 0}; }
 
    template<typename _Mapping, typename... _Slices>
      requires (sizeof...(_Slices) > 0)
      constexpr auto
      __submdspan_mapping_impl(const _Mapping& __mapping, _Slices... __slices)
      {
        using _IndexType = typename _Mapping::index_type;
        static_assert((__acceptable_slice_type<_Slices, _IndexType> && ...));
 
        constexpr auto __side = __mdspan::__mapping_side<_Mapping>();
        constexpr auto __rank = sizeof...(_Slices);
        using _Trait = _SubMdspanMapping<__side, __is_padded_mapping<_Mapping>>;
        using _SliceView = span<const _SliceKind, __rank>;
 
        constexpr auto __slice_kinds = __mdspan::__make_slice_kind_array<_Slices...>();
        auto __offset = __mdspan::__suboffset(__mapping, __slices...);
        auto __sub_exts = __mdspan::__subextents(__mapping.extents(), __slices...);
        using _SubExts = decltype(__sub_exts);
        constexpr auto __sub_rank = _SubExts::rank();
        if constexpr (__sub_rank == 0)
          return submdspan_mapping_result{
            typename _Trait::_Layout::mapping(__sub_exts), __offset};
        else if constexpr (_Trait::_S_is_unpadded_submdspan(
              _SliceView(__slice_kinds), __sub_rank))
          return submdspan_mapping_result{
            typename _Trait::_Layout::mapping(__sub_exts), __offset};
        else if constexpr (
            constexpr auto __u = __padded_block_begin<__side>(
                _SliceView(__slice_kinds), __sub_rank);
            __u != dynamic_extent)
          {
            constexpr auto __pad = _Trait::template _S_pad<_Mapping, __u>();
            using _Layout = typename _Trait::template _PaddedLayout<__pad>;
            return submdspan_mapping_result{
              typename _Layout::mapping(__sub_exts, __mapping.stride(__u)),
              __offset};
          }
        else
          {
            auto __sub_strides
              = __mdspan::__substrides<_SubExts>(__mapping, __slices...);
            return submdspan_mapping_result{
              layout_stride::mapping(__sub_exts, __sub_strides),  __offset};
          }
      }
#endif // __glibcxx_submdspan
  }
 
  template<typename _Extents>
    class layout_left::mapping
    {
    public:
      using extents_type = _Extents;
      using index_type = typename extents_type::index_type;
      using size_type = typename extents_type::size_type;
      using rank_type = typename extents_type::rank_type;
      using layout_type = layout_left;
 
      static_assert(__mdspan::__representable_size<extents_type, index_type>,
        "The size of extents_type must be representable as index_type");
 
      constexpr
      mapping() noexcept = default;
 
      constexpr
      mapping(const mapping&) noexcept = default;
 
      constexpr
      mapping(const extents_type& __extents) noexcept
      : _M_extents(__extents)
      { __glibcxx_assert(__mdspan::__is_representable_extents(_M_extents)); }
 
      template<typename _OExtents>
        requires is_constructible_v<extents_type, _OExtents>
        constexpr explicit(!is_convertible_v<_OExtents, extents_type>)
        mapping(const mapping<_OExtents>& __other) noexcept
        : mapping(__other.extents(), __mdspan::__internal_ctor{})
        { }
 
      template<typename _OExtents>
        requires (extents_type::rank() <= 1)
                  && is_constructible_v<extents_type, _OExtents>
        constexpr explicit(!is_convertible_v<_OExtents, extents_type>)
        mapping(const layout_right::mapping<_OExtents>& __other) noexcept
        : mapping(__other.extents(), __mdspan::__internal_ctor{})
        { }
 
      // noexcept for consistency with other layouts.
      template<typename _OExtents>
        requires is_constructible_v<extents_type, _OExtents>
        constexpr explicit(!(extents_type::rank() == 0
                             && is_convertible_v<_OExtents, extents_type>))
        mapping(const layout_stride::mapping<_OExtents>& __other) noexcept
        : mapping(__other.extents(), __mdspan::__internal_ctor{})
        { __glibcxx_assert(*this == __other); }
 
#if __glibcxx_padded_layouts
      template<typename _LeftpadMapping>
        requires __mdspan::__is_left_padded_mapping<_LeftpadMapping>
                 && is_constructible_v<extents_type,
                                       typename _LeftpadMapping::extents_type>
        constexpr
        explicit(!is_convertible_v<typename _LeftpadMapping::extents_type,
                                   extents_type>)
        mapping(const _LeftpadMapping& __other) noexcept
        : mapping(__other.extents(), __mdspan::__internal_ctor{})
        {
          constexpr size_t __ostride_sta
            = __mdspan::__get_static_stride<_LeftpadMapping>();
 
          if constexpr (extents_type::rank() > 1)
            {
              if constexpr (extents_type::static_extent(0) != dynamic_extent
                            && __ostride_sta != dynamic_extent)
                static_assert(extents_type::static_extent(0) == __ostride_sta);
              else
                __glibcxx_assert(__other.stride(1)
                    == __other.extents().extent(0));
            }
        }
#endif // __glibcxx_padded_layouts
 
      constexpr mapping&
      operator=(const mapping&) noexcept = default;
 
      constexpr const extents_type&
      extents() const noexcept { return _M_extents; }
 
      constexpr index_type
      required_span_size() const noexcept
      { return __mdspan::__size(_M_extents); }
 
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // 4314. Missing move in mdspan layout mapping::operator()
      template<__mdspan::__valid_index_type<index_type>... _Indices>
        requires (sizeof...(_Indices) == extents_type::rank())
        constexpr index_type
        operator()(_Indices... __indices) const noexcept
        {
          return __mdspan::__linear_index_left(_M_extents,
            static_cast<index_type>(std::move(__indices))...);
        }
 
      static constexpr bool
      is_always_unique() noexcept { return true; }
 
      static constexpr bool
      is_always_exhaustive() noexcept { return true; }
 
      static constexpr bool
      is_always_strided() noexcept { return true; }
 
      static constexpr bool
      is_unique() noexcept { return true; }
 
      static constexpr bool
      is_exhaustive() noexcept { return true; }
 
      static constexpr bool
      is_strided() noexcept { return true; }
 
      constexpr index_type
      stride(rank_type __i) const noexcept
      requires (extents_type::rank() > 0)
      {
        __glibcxx_assert(__i < extents_type::rank());
        return __mdspan::__fwd_prod(_M_extents, __i);
      }
 
      template<typename _OExtents>
        requires (extents_type::rank() == _OExtents::rank())
        friend constexpr bool
        operator==(const mapping& __self, const mapping<_OExtents>& __other)
        noexcept
        { return __self.extents() == __other.extents(); }
 
    private:
      template<typename _OExtents>
        constexpr explicit
        mapping(const _OExtents& __oexts, __mdspan::__internal_ctor) noexcept
        : _M_extents(__oexts)
        {
          static_assert(__mdspan::__representable_size<_OExtents, index_type>,
            "The size of OtherExtents must be representable as index_type");
          __glibcxx_assert(__mdspan::__is_representable_extents(_M_extents));
        }
 
#if __glibcxx_submdspan
      template<typename... _Slices>
        requires (extents_type::rank() == sizeof...(_Slices))
        friend constexpr auto
        submdspan_mapping(const mapping& __mapping, _Slices... __slices)
        { return __mdspan::__submdspan_mapping_impl(__mapping, __slices...); }
#endif // __glibcxx_submdspan
 
        [[no_unique_address]] extents_type _M_extents{};
    };
 
  namespace __mdspan
  {
    template<typename _Extents, typename... _Indices>
      constexpr typename _Extents::index_type
      __linear_index_right(const _Extents& __exts, _Indices... __indices)
      noexcept
      {
        using _IndexType = typename _Extents::index_type;
        array<_IndexType, sizeof...(__indices)> __ind_arr{__indices...};
        _IndexType __res = 0;
        if constexpr (sizeof...(__indices) > 0)
          {
            _IndexType __mult = 1;
            auto __update = [&, __pos = __exts.rank()](_IndexType) mutable
              {
                --__pos;
                _GLIBCXX_DEBUG_ASSERT(cmp_less(__ind_arr[__pos],
                                               __exts.extent(__pos)));
                __res += __ind_arr[__pos] * __mult;
                __mult *= __exts.extent(__pos);
              };
            (__update(__indices), ...);
          }
        return __res;
      }
  }
 
  template<typename _Extents>
    class layout_right::mapping
    {
    public:
      using extents_type = _Extents;
      using index_type = typename extents_type::index_type;
      using size_type = typename extents_type::size_type;
      using rank_type = typename extents_type::rank_type;
      using layout_type = layout_right;
 
      static_assert(__mdspan::__representable_size<extents_type, index_type>,
        "The size of extents_type must be representable as index_type");
 
      constexpr
      mapping() noexcept = default;
 
      constexpr
      mapping(const mapping&) noexcept = default;
 
      constexpr
      mapping(const extents_type& __extents) noexcept
      : _M_extents(__extents)
      { __glibcxx_assert(__mdspan::__is_representable_extents(_M_extents)); }
 
      template<typename _OExtents>
        requires is_constructible_v<extents_type, _OExtents>
        constexpr explicit(!is_convertible_v<_OExtents, extents_type>)
        mapping(const mapping<_OExtents>& __other) noexcept
        : mapping(__other.extents(), __mdspan::__internal_ctor{})
        { }
 
      template<typename _OExtents>
        requires (extents_type::rank() <= 1)
            && is_constructible_v<extents_type, _OExtents>
        constexpr explicit(!is_convertible_v<_OExtents, extents_type>)
        mapping(const layout_left::mapping<_OExtents>& __other) noexcept
        : mapping(__other.extents(), __mdspan::__internal_ctor{})
        { }
 
      template<typename _OExtents>
        requires is_constructible_v<extents_type, _OExtents>
        constexpr explicit(!(extents_type::rank() == 0
                             && is_convertible_v<_OExtents, extents_type>))
        mapping(const layout_stride::mapping<_OExtents>& __other) noexcept
        : mapping(__other.extents(), __mdspan::__internal_ctor{})
        { __glibcxx_assert(*this == __other); }
 
#if __glibcxx_padded_layouts
      template<typename _RightPaddedMapping>
        requires __mdspan::__is_right_padded_mapping<_RightPaddedMapping>
                 && is_constructible_v<extents_type,
                      typename _RightPaddedMapping::extents_type>
        constexpr
        explicit(!is_convertible_v<typename _RightPaddedMapping::extents_type,
                                   extents_type>)
        mapping(const _RightPaddedMapping& __other) noexcept
        : mapping(__other.extents(), __mdspan::__internal_ctor{})
        {
          constexpr size_t __rank = extents_type::rank();
          constexpr size_t __ostride_sta
            = __mdspan::__get_static_stride<_RightPaddedMapping>();
 
          if constexpr (__rank > 1)
            {
              if constexpr (extents_type::static_extent(__rank - 1) != dynamic_extent
                  && __ostride_sta != dynamic_extent)
                static_assert(extents_type::static_extent(__rank - 1)
                    == __ostride_sta);
              else
                __glibcxx_assert(__other.stride(__rank - 2)
                    == __other.extents().extent(__rank - 1));
            }
        }
#endif
 
      constexpr mapping&
      operator=(const mapping&) noexcept = default;
 
      constexpr const extents_type&
      extents() const noexcept { return _M_extents; }
 
      constexpr index_type
      required_span_size() const noexcept
      { return __mdspan::__size(_M_extents); }
 
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // 4314. Missing move in mdspan layout mapping::operator()
      template<__mdspan::__valid_index_type<index_type>... _Indices>
        requires (sizeof...(_Indices) == extents_type::rank())
        constexpr index_type
        operator()(_Indices... __indices) const noexcept
        {
          return __mdspan::__linear_index_right(
            _M_extents, static_cast<index_type>(std::move(__indices))...);
        }
 
      static constexpr bool
      is_always_unique() noexcept
      { return true; }
 
      static constexpr bool
      is_always_exhaustive() noexcept
      { return true; }
 
      static constexpr bool
      is_always_strided() noexcept
      { return true; }
 
      static constexpr bool
      is_unique() noexcept
      { return true; }
 
      static constexpr bool
      is_exhaustive() noexcept
      { return true; }
 
      static constexpr bool
      is_strided() noexcept
      { return true; }
 
      constexpr index_type
      stride(rank_type __i) const noexcept
      requires (extents_type::rank() > 0)
      {
        __glibcxx_assert(__i < extents_type::rank());
        return __mdspan::__rev_prod(_M_extents, __i);
      }
 
      template<typename _OExtents>
        requires (extents_type::rank() == _OExtents::rank())
        friend constexpr bool
        operator==(const mapping& __self, const mapping<_OExtents>& __other)
        noexcept
        { return __self.extents() == __other.extents(); }
 
    private:
      template<typename _OExtents>
        constexpr explicit
        mapping(const _OExtents& __oexts, __mdspan::__internal_ctor) noexcept
        : _M_extents(__oexts)
        {
          static_assert(__mdspan::__representable_size<_OExtents, index_type>,
            "The size of OtherExtents must be representable as index_type");
          __glibcxx_assert(__mdspan::__is_representable_extents(_M_extents));
        }
 
#if __glibcxx_submdspan
      template<typename... _Slices>
        requires (extents_type::rank() == sizeof...(_Slices))
        friend constexpr auto
        submdspan_mapping(const mapping& __mapping, _Slices... __slices)
        { return __mdspan::__submdspan_mapping_impl(__mapping, __slices...); }
#endif // __glibcxx_submdspan
 
        [[no_unique_address]] extents_type _M_extents{};
    };
 
  namespace __mdspan
  {
    template<typename _Mp>
      concept __mapping_alike = requires
      {
        requires __is_extents<typename _Mp::extents_type>;
        { _Mp::is_always_strided() } -> same_as<bool>;
        { _Mp::is_always_exhaustive() } -> same_as<bool>;
        { _Mp::is_always_unique() } -> same_as<bool>;
        bool_constant<_Mp::is_always_strided()>::value;
        bool_constant<_Mp::is_always_exhaustive()>::value;
        bool_constant<_Mp::is_always_unique()>::value;
      };
 
    template<typename _Mapping, typename... _Indices>
      constexpr typename _Mapping::index_type
      __linear_index_strides(const _Mapping& __m, _Indices... __indices)
      noexcept
      {
        using _IndexType = typename _Mapping::index_type;
        _IndexType __res = 0;
        if constexpr (sizeof...(__indices) > 0)
          {
            auto __update = [&, __pos = 0u](_IndexType __idx) mutable
              {
                _GLIBCXX_DEBUG_ASSERT(cmp_less(__idx,
                                               __m.extents().extent(__pos)));
                __res += __idx * __m.stride(__pos++);
              };
            (__update(__indices), ...);
          }
        return __res;
      }
  }
 
  template<typename _Extents>
    class layout_stride::mapping
    {
    public:
      using extents_type = _Extents;
      using index_type = typename extents_type::index_type;
      using size_type = typename extents_type::size_type;
      using rank_type = typename extents_type::rank_type;
      using layout_type = layout_stride;
 
      static_assert(__mdspan::__representable_size<extents_type, index_type>,
        "The size of extents_type must be representable as index_type");
 
      constexpr
      mapping() noexcept
      {
        // The precondition is either statically asserted, or automatically
        // satisfied because dynamic extents are zero-initialized.
        size_t __stride = 1;
        for (size_t __i = extents_type::rank(); __i > 0; --__i)
          {
            _M_strides[__i - 1] = index_type(__stride);
            __stride *= size_t(_M_extents.extent(__i - 1));
          }
      }
 
      constexpr
      mapping(const mapping&) noexcept = default;
 
      template<typename _OIndexType>
        requires __mdspan::__valid_index_type<const _OIndexType&, index_type>
        constexpr
        mapping(const extents_type& __exts,
                span<_OIndexType, extents_type::rank()> __strides) noexcept
        : _M_extents(__exts)
        {
          for (size_t __i = 0; __i < extents_type::rank(); ++__i)
            _M_strides[__i] = index_type(as_const(__strides[__i]));
        }
 
      template<typename _OIndexType>
        requires __mdspan::__valid_index_type<const _OIndexType&, index_type>
        constexpr
        mapping(const extents_type& __exts,
                const array<_OIndexType, extents_type::rank()>& __strides)
        noexcept
        : mapping(__exts,
                  span<const _OIndexType, extents_type::rank()>(__strides))
        { }
 
      template<__mdspan::__mapping_alike _StridedMapping>
        requires (is_constructible_v<extents_type,
                                     typename _StridedMapping::extents_type>
                  && _StridedMapping::is_always_unique()
                  && _StridedMapping::is_always_strided())
        constexpr explicit(!(
          is_convertible_v<typename _StridedMapping::extents_type, extents_type>
          && __mdspan::__standardized_mapping<_StridedMapping>))
        mapping(const _StridedMapping& __other) noexcept
        : _M_extents(__other.extents())
        {
          using _OIndexType = _StridedMapping::index_type;
          using _OExtents = _StridedMapping::extents_type;
 
          __glibcxx_assert(__mdspan::__offset(__other) == 0);
          static_assert(__mdspan::__representable_size<_OExtents, index_type>,
            "The size of StridedMapping::extents_type must be representable as"
            " index_type");
          if constexpr (cmp_greater(__gnu_cxx::__int_traits<_OIndexType>::__max,
                                    __gnu_cxx::__int_traits<index_type>::__max))
            __glibcxx_assert(!cmp_less(
                __gnu_cxx::__int_traits<index_type>::__max,
                __other.required_span_size())
              && "other.required_span_size() must be representable"
                 " as index_type");
          if constexpr (extents_type::rank() > 0)
            for (size_t __i = 0; __i < extents_type::rank(); ++__i)
              _M_strides[__i] = index_type(__other.stride(__i));
        }
 
      constexpr mapping&
      operator=(const mapping&) noexcept = default;
 
      constexpr const extents_type&
      extents() const noexcept { return _M_extents; }
 
      constexpr array<index_type, extents_type::rank()>
      strides() const noexcept
      {
        array<index_type, extents_type::rank()> __ret;
        for (size_t __i = 0; __i < extents_type::rank(); ++__i)
          __ret[__i] = _M_strides[__i];
        return __ret;
      }
 
      constexpr index_type
      required_span_size() const noexcept
      {
        if (__mdspan::__empty(_M_extents))
          return 0;
 
        index_type __ret = 1;
        for (size_t __i = 0; __i < extents_type::rank(); ++__i)
          __ret += (_M_extents.extent(__i) - 1) * _M_strides[__i];
        return __ret;
      }
 
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // 4314. Missing move in mdspan layout mapping::operator()
      template<__mdspan::__valid_index_type<index_type>... _Indices>
        requires (sizeof...(_Indices) == extents_type::rank())
        constexpr index_type
        operator()(_Indices... __indices) const noexcept
        {
          return __mdspan::__linear_index_strides(*this,
            static_cast<index_type>(std::move(__indices))...);
        }
 
      static constexpr bool
      is_always_unique() noexcept { return true; }
 
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // 4266. layout_stride::mapping should treat empty mappings as exhaustive
      static constexpr bool
      is_always_exhaustive() noexcept
      {
        return (_Extents::rank() == 0) || __mdspan::__contains_zero(
            __mdspan::__static_extents<extents_type>());
      }
 
      static constexpr bool
      is_always_strided() noexcept { return true; }
 
      static constexpr bool
      is_unique() noexcept { return true; }
 
      // _GLIBCXX_RESOLVE_LIB_DEFECTS
      // 4266. layout_stride::mapping should treat empty mappings as exhaustive
      constexpr bool
      is_exhaustive() const noexcept
      {
        if constexpr (!is_always_exhaustive())
          {
            auto __size = __mdspan::__size(_M_extents);
            if(__size > 0)
              return __size == required_span_size();
          }
        return true;
      }
 
      static constexpr bool
      is_strided() noexcept { return true; }
 
      constexpr index_type
      stride(rank_type __r) const noexcept { return _M_strides[__r]; }
 
      template<__mdspan::__mapping_alike _OMapping>
        requires ((extents_type::rank() == _OMapping::extents_type::rank())
                  && _OMapping::is_always_strided())
        friend constexpr bool
        operator==(const mapping& __self, const _OMapping& __other) noexcept
        {
          if (__self.extents() != __other.extents())
            return false;
          if constexpr (extents_type::rank() > 0)
            for (size_t __i = 0; __i < extents_type::rank(); ++__i)
              if (!cmp_equal(__self.stride(__i), __other.stride(__i)))
                return false;
          return __mdspan::__offset(__other) == 0;
        }
 
    private:
#if __glibcxx_submdspan
      template<typename... _Slices>
        requires (extents_type::rank() == sizeof...(_Slices))
        friend constexpr auto
        submdspan_mapping(const mapping& __mapping, _Slices... __slices)
        {
          if constexpr (sizeof...(_Slices) == 0)
            return submdspan_mapping_result{__mapping, 0};
          else
            {
              auto __offset = __mdspan::__suboffset(__mapping, __slices...);
              auto __sub_exts = __mdspan::__subextents(__mapping.extents(), __slices...);
              auto __sub_strides
                = __mdspan::__substrides<decltype(__sub_exts)>(__mapping, __slices...);
              return submdspan_mapping_result{
                layout_stride::mapping(__sub_exts, __sub_strides), __offset};
            }
        }
#endif
 
      using _Strides = typename __array_traits<index_type,
                                               extents_type::rank()>::_Type;
      [[no_unique_address]] extents_type _M_extents;
      [[no_unique_address]] _Strides _M_strides;
    };
 
#ifdef __glibcxx_padded_layouts
  namespace __mdspan
  {
    constexpr size_t
    __least_multiple(size_t __x, size_t __y)
    {
      if (__x <= 1)
        return __y;
      return (__y / __x + (__y % __x != 0)) * __x ;
    }
 
    template<typename _IndexType>
    constexpr bool
    __is_representable_least_multiple(size_t __x, size_t __y)
    {
      constexpr auto __y_max = __gnu_cxx::__int_traits<_IndexType>::__max;
      if(std::cmp_greater(__y, __y_max))
        return false;
 
      if(__x <= 1)
        return true;
 
      auto __max_delta = __y_max - static_cast<_IndexType>(__y);
      auto __y_mod_x = __y % __x;
      auto __delta = (__y_mod_x == 0) ? size_t(0) : (__x - __y_mod_x);
      return std::cmp_less_equal(__delta, __max_delta);
    }
 
    template<typename _Extents, size_t _PaddingValue, typename _LayoutTraits,
             size_t _Rank = _Extents::rank()>
      concept __valid_static_stride = (_Extents::rank() <= 1)
        || (_PaddingValue == dynamic_extent)
        || (_Extents::static_extent(_LayoutTraits::_S_ext_idx) == dynamic_extent)
        || (__is_representable_least_multiple<size_t>(
            _PaddingValue, _Extents::static_extent(_LayoutTraits::_S_ext_idx)));
 
    template<size_t _PaddedStride, typename _Extents,
             typename _LayoutTraits>
      consteval bool
      __is_representable_padded_size()
      {
        using _IndexType = typename _Extents::index_type;
        auto __sta_exts = __static_extents<_Extents>(
          _LayoutTraits::_S_unpad_begin, _LayoutTraits::_S_unpad_end);
        size_t __max = __gnu_cxx::__int_traits<_IndexType>::__max;
        return __static_quotient(__sta_exts, __max / _PaddedStride) != 0;
      }
 
    template<typename _Extents, size_t _PaddedStride, typename _LayoutTraits,
             size_t _Rank = _Extents::rank()>
      concept __valid_padded_size = (_Rank <= 1)
        || (_PaddedStride == dynamic_extent)
        || (!__all_static(__static_extents<_Extents>()))
        || (__contains_zero(__static_extents<_Extents>()))
        || (__is_representable_padded_size<_PaddedStride, _Extents,
                                           _LayoutTraits>());
 
    template<typename _Extents, typename _Stride, typename... _Indices>
      constexpr typename _Extents::index_type
      __linear_index_leftpad(const _Extents& __exts, _Stride __stride,
                             _Indices... __indices)
      {
        // i0 + stride*(i1 + extents.extent(1)*...)
        using _IndexType = typename _Extents::index_type;
        _IndexType __res = 0;
        if constexpr (sizeof...(__indices) > 0)
          {
            _IndexType __mult = 1;
 
            auto __update_rest = [&, __pos = 1u](_IndexType __idx) mutable
              {
                __res += __idx * __mult;
                __mult *= __exts.extent(__pos);
                ++__pos;
              };
 
            auto __update = [&](_IndexType __idx, auto... __rest)
              {
                __res += __idx;
                __mult = __stride.extent(0);
                (__update_rest(__rest), ...);
              };
            __update(__indices...);
          }
        return __res;
      }
 
    template<typename _Extents, typename _Stride, typename... _Indices>
      constexpr typename _Extents::index_type
      __linear_index_rightpad(const _Extents& __exts, _Stride __stride,
                             _Indices... __indices)
      {
        // i[n-1] + stride*(i[n-2] + extents.extent(n-2])*...)
        using _IndexType = typename _Extents::index_type;
        _IndexType __res = 0;
        if constexpr (sizeof...(__indices) > 0)
          {
            _IndexType __mult = 1;
            array<_IndexType, sizeof...(__indices)> __ind_arr{__indices...};
 
            auto __update_rest = [&, __pos = __exts.rank()-1](_IndexType) mutable
              {
                --__pos;
                __res += __ind_arr[__pos] * __mult;
                __mult *= __exts.extent(__pos);
              };
 
            auto __update = [&](_IndexType, auto... __rest)
              {
                __res += __ind_arr[__exts.rank() - 1];
                __mult = __stride.extent(0);
                (__update_rest(__rest), ...);
              };
            __update(__indices...);
          }
        return __res;
      }
 
    template<size_t _Rank>
      struct _LeftPaddedLayoutTraits
      {
        using _LayoutSame = layout_left;
        using _LayoutOther = layout_right;
 
        constexpr static const size_t _S_ext_idx = 0;
        constexpr static const size_t _S_stride_idx = 1;
        constexpr static const size_t _S_unpad_begin = 1;
        constexpr static const size_t _S_unpad_end = _Rank;
 
        template<typename _IndexType, size_t _StaticStride, size_t..._Extents>
          constexpr static auto
          _S_make_padded_extent(
            extents<_IndexType, _StaticStride> __stride,
            const extents<_IndexType, _Extents...>& __exts)
          {
            auto __impl = [&]<size_t... _Is>(integer_sequence<size_t, _Is...>)
            {
              return extents<_IndexType, _StaticStride,
                             (_Extents...[_Is + 1])...>{
                __stride.extent(0), __exts.extent(_Is + 1)...};
            };
            return __impl(make_index_sequence<sizeof...(_Extents) - 1>());
          }
      };
 
    template<size_t _Rank>
      struct _RightPaddedLayoutTraits
      {
        using _LayoutSame = layout_right;
        using _LayoutOther = layout_left;
 
        constexpr static size_t _S_ext_idx = _Rank - 1;
        constexpr static size_t _S_stride_idx = _Rank - 2;
        constexpr static size_t _S_unpad_begin = 0;
        constexpr static size_t _S_unpad_end = _Rank - 1;
 
        template<typename _IndexType, size_t _StaticStride, size_t..._Extents>
          constexpr static auto
          _S_make_padded_extent(
            extents<_IndexType, _StaticStride> __stride,
            const extents<_IndexType, _Extents...>& __exts)
          {
            auto __impl = [&]<size_t... _Is>(integer_sequence<size_t, _Is...>)
            {
              return extents<_IndexType, (_Extents...[_Is])..., _StaticStride>{
                __exts.extent(_Is)..., __stride.extent(0)};
            };
            return __impl(make_index_sequence<sizeof...(_Extents) - 1>());
          }
      };
 
    template<size_t _PaddingValue, typename _Extents, typename _LayoutTraits>
      class _PaddedStorage
      {
        using _LayoutSame = typename _LayoutTraits::_LayoutSame;
 
      public:
        using _IndexType = typename _Extents::index_type;
        constexpr static size_t _S_rank = _Extents::rank();
 
        // _GLIBCXX_RESOLVE_LIB_DEFECTS
        // 4372. Weaken Mandates: for dynamic padding values in padded layouts
        static_assert((_PaddingValue == dynamic_extent)
            || (cmp_less_equal(_PaddingValue,
                               __gnu_cxx::__int_traits<_IndexType>::__max)),
          "padding_value must be representable as index_type");
 
        static_assert(__representable_size<_Extents, _IndexType>,
          "The size of extents_type must be representable as index_type");
 
        static_assert(__valid_static_stride<_Extents, _PaddingValue,
                                            _LayoutTraits>,
          "The padded stride must be representable as size_t");
 
        static constexpr size_t _S_static_stride = [] consteval
        {
          constexpr size_t __rank = _Extents::rank();
          if constexpr (__rank <= 1)
            return 0;
          else
            {
              constexpr size_t __ext_idx = _LayoutTraits::_S_ext_idx;
              constexpr size_t __sta_ext = _Extents::static_extent(__ext_idx);
              if constexpr (__sta_ext == 0)
                return size_t(0);
              else if constexpr (_PaddingValue == dynamic_extent
                  || __sta_ext == dynamic_extent)
                return dynamic_extent;
              else
                return __least_multiple(_PaddingValue, __sta_ext);
            }
        }();
 
        static_assert(_S_static_stride == dynamic_extent
          || cmp_less_equal(_S_static_stride,
                            __gnu_cxx::__int_traits<_IndexType>::__max),
          "Padded stride must be representable as index_type");
 
        static_assert(__valid_padded_size<_Extents, _S_static_stride,
                                          _LayoutTraits>);
 
        constexpr
        _PaddedStorage() noexcept
        {
          if constexpr (_S_rank > 1)
            if constexpr (_S_static_stride == dynamic_extent
                          && _S_static_padextent() != dynamic_extent)
              _M_stride = _Stride{_S_static_padextent()};
        }
 
        constexpr explicit
        _PaddedStorage(const _Extents& __exts)
        : _M_extents(__exts)
        {
          if constexpr (!__all_static(__static_extents<_Extents>()))
            __glibcxx_assert(__is_representable_extents(_M_extents));
 
          if constexpr (_S_rank > 1)
            {
              _IndexType __stride;
              if constexpr (_PaddingValue == dynamic_extent)
                __stride = _M_padextent();
              else if constexpr (_S_static_padextent() != dynamic_extent)
                return;
              else
                {
                  __glibcxx_assert(
                      __is_representable_least_multiple<_IndexType>(
                        _PaddingValue, _M_padextent()));
 
                  __stride = static_cast<_IndexType>(
                    __least_multiple(_PaddingValue, _M_padextent()));
 
                  __glibcxx_assert(__is_representable_extents(
                      _LayoutTraits::_S_make_padded_extent(
                        std::dextents<_IndexType, 1>{__stride},
                        _M_extents)));
                }
              _M_stride = _Stride{__stride};
            }
        }
 
        constexpr explicit
        _PaddedStorage(const _Extents& __exts, _IndexType __pad)
        : _M_extents(__exts)
        {
          if constexpr (_PaddingValue != dynamic_extent)
            __glibcxx_assert(cmp_equal(_PaddingValue, __pad));
          if constexpr (_S_rank > 1 && _S_static_stride == dynamic_extent)
            {
              __glibcxx_assert(
                __is_representable_least_multiple<_IndexType>(
                  __pad, _M_padextent()));
 
              _M_stride = _Stride{static_cast<_IndexType>(
                __least_multiple(__pad, _M_padextent()))};
 
              __glibcxx_assert(__is_representable_extents(
                _LayoutTraits::_S_make_padded_extent(
                  _M_stride, _M_extents)));
            }
        }
 
        template<typename _OExtents>
          constexpr explicit
          _PaddedStorage(
              const typename _LayoutSame::template mapping<_OExtents>& __other)
          : _PaddedStorage(_Extents(__other.extents()))
          {
            constexpr size_t __stride_idx = _LayoutTraits::_S_stride_idx;
            constexpr size_t __ext_idx = _LayoutTraits::_S_ext_idx;
            if constexpr (_S_rank > 1 && _PaddingValue != dynamic_extent)
              {
                static_assert(_S_static_stride == dynamic_extent
                    || _OExtents::static_extent(__ext_idx) == dynamic_extent
                    || _S_static_stride == _OExtents::static_extent(__ext_idx),
                  "The padded stride must be compatible with other");
 
                if constexpr (_S_static_stride == dynamic_extent
                    || _OExtents::static_extent(__stride_idx) == dynamic_extent)
                  __glibcxx_assert(std::cmp_equal(_M_padstride(),
                                                  _M_padextent()));
              }
          }
 
        template<typename _OExtents>
          constexpr explicit
          _PaddedStorage(const typename layout_stride::mapping<_OExtents>&
                         __other)
          : _M_extents(__other.extents())
          {
            __glibcxx_assert(cmp_less_equal(__other.required_span_size(),
                                            __gnu_cxx::__int_traits<_IndexType>
                                                     ::__max));
 
            constexpr size_t __stride_idx = _LayoutTraits::_S_stride_idx;
            if constexpr (_S_rank > 1)
              {
                if constexpr (_PaddingValue != dynamic_extent)
                  __glibcxx_assert(cmp_equal(__other.stride(__stride_idx),
                                             _M_calc_padstride())
                    && "The padded stride must be compatible with other");
                if constexpr (_S_static_stride == dynamic_extent)
                  _M_stride = _Stride{__other.stride(__stride_idx)};
              }
          }
 
        template<typename _SamePaddedMapping>
          constexpr explicit
          _PaddedStorage(_LayoutTraits::_LayoutSame,
                         const _SamePaddedMapping& __other)
          : _M_extents(__other.extents())
          {
            if constexpr (_S_rank > 1)
              {
                static_assert(_PaddingValue == dynamic_extent
                    || _SamePaddedMapping::padding_value  == dynamic_extent
                    || _PaddingValue == _SamePaddedMapping::padding_value,
                  "If neither PaddingValue is dynamic_extent, then they must "
                  "be equal");
 
                constexpr size_t __stride_idx = _LayoutTraits::_S_stride_idx;
                if constexpr (_PaddingValue != dynamic_extent)
                  __glibcxx_assert(cmp_equal(__other.stride(__stride_idx),
                                             _M_calc_padstride())
                    && "The padded stride must be compatible with other");
                if constexpr (_S_static_stride == dynamic_extent)
                  _M_stride = _Stride{__other.stride(__stride_idx)};
              }
            __glibcxx_assert(cmp_less_equal(__other.required_span_size(),
                __gnu_cxx::__int_traits<_IndexType>::__max));
          }
 
        template<typename _OtherPaddedMapping>
          constexpr explicit
          _PaddedStorage(_LayoutTraits::_LayoutOther,
                         const _OtherPaddedMapping& __other) noexcept
          : _M_extents(__other.extents())
          {
            __glibcxx_assert(cmp_less_equal(__other.required_span_size(),
                __gnu_cxx::__int_traits<_IndexType>::__max));
          }
 
        static constexpr bool
        _M_is_always_exhaustive() noexcept
        {
          if constexpr (_S_rank <= 1)
            return true;
          else
            return _S_static_padextent() != dynamic_extent
                   && _S_static_stride != dynamic_extent
                   && _S_static_padextent() == _S_static_stride;
        }
 
        constexpr bool
        _M_is_exhaustive() const noexcept
        {
          if constexpr (_M_is_always_exhaustive())
            return true;
          else
            return cmp_equal(_M_padextent(), _M_padstride());
        }
 
        constexpr static size_t
        _S_static_padextent() noexcept
        { return _Extents::static_extent(_LayoutTraits::_S_ext_idx); }
 
        constexpr _IndexType
        _M_padextent() const noexcept
        { return _M_extents.extent(_LayoutTraits::_S_ext_idx); }
 
        constexpr _IndexType
        _M_calc_padstride() const noexcept
        {
          if constexpr (_S_static_stride != dynamic_extent)
            return _S_static_stride;
          else if constexpr (_PaddingValue != dynamic_extent)
            return __least_multiple(_PaddingValue, _M_padextent());
          else
            return _M_padextent();
        }
 
        constexpr _IndexType
        _M_padstride() const noexcept
        { return _M_stride.extent(0); }
 
        constexpr _IndexType
        _M_required_span_size() const noexcept
        {
          if constexpr (_S_rank == 0)
            return 1;
          else if (__mdspan::__empty(_M_extents))
            return 0;
          else
            {
              size_t __stride = static_cast<size_t>(_M_padstride());
              size_t __prod_rest = __mdspan::__fwd_prod(_M_extents,
                _LayoutTraits::_S_unpad_begin, _LayoutTraits::_S_unpad_end);
              size_t __delta = _M_padstride() - _M_padextent();
              return static_cast<_IndexType>(__stride * __prod_rest - __delta);
            }
        }
 
        template<typename _SamePaddedMapping>
          constexpr bool
          _M_equal(const _SamePaddedMapping& __other) const noexcept
          {
            return _M_extents == __other.extents()
              && (_S_rank < 2
                || cmp_equal(_M_stride.extent(0),
                             __other.stride(_LayoutTraits::_S_stride_idx)));
          }
 
        using _Stride = std::extents<_IndexType, _S_static_stride>;
        [[no_unique_address]] _Stride _M_stride;
        [[no_unique_address]] _Extents _M_extents;
      };
  }
 
  template<size_t _PaddingValue>
    template<typename _Extents>
      class layout_left_padded<_PaddingValue>::mapping
      {
      public:
        static constexpr size_t padding_value = _PaddingValue;
 
        using extents_type = _Extents;
        using index_type = typename extents_type::index_type;
        using size_type = typename extents_type::size_type;
        using rank_type = typename extents_type::rank_type;
        using layout_type = layout_left_padded<padding_value>;
 
      private:
        static constexpr size_t _S_rank = extents_type::rank();
        using _PaddedStorage = __mdspan::_PaddedStorage<_PaddingValue,
              _Extents, __mdspan::_LeftPaddedLayoutTraits<_S_rank>>;
        [[no_unique_address]] _PaddedStorage _M_storage;
 
        consteval friend size_t
        __mdspan::__get_static_stride<mapping>();
 
        constexpr index_type
        _M_extent(size_t __r) const noexcept
        { return _M_storage._M_extents.extent(__r); }
 
        constexpr index_type
        _M_padstride() const noexcept
        { return _M_storage._M_stride.extent(0); }
 
      public:
        constexpr
        mapping() noexcept
        { }
 
        constexpr
        mapping(const mapping&) noexcept = default;
 
        constexpr
        mapping(const extents_type& __exts)
        : _M_storage(__exts)
        { }
 
        template<__mdspan::__valid_index_type<index_type> _OIndexType>
          constexpr
          mapping(const extents_type& __exts, _OIndexType __pad)
          : _M_storage(__exts,
              __mdspan::__index_type_cast<index_type>(std::move(__pad)))
          { }
 
        template<typename _OExtents>
          requires is_constructible_v<extents_type, _OExtents>
          constexpr explicit(!is_convertible_v<_OExtents, extents_type>)
          mapping(const layout_left::mapping<_OExtents>& __other)
          : _M_storage(__other)
          { }
 
        template<typename _OExtents>
          requires is_constructible_v<_OExtents, extents_type>
          constexpr explicit(!(_OExtents::rank() == 0
                               && is_convertible_v<_OExtents, extents_type>))
          mapping(const typename layout_stride::mapping<_OExtents>& __other)
          : _M_storage(__other)
          { __glibcxx_assert(*this == __other); }
 
        template<typename _LeftPaddedMapping>
          requires __mdspan::__is_left_padded_mapping<_LeftPaddedMapping>
              && is_constructible_v<extents_type,
                                    typename _LeftPaddedMapping::extents_type>
          constexpr explicit(
           !is_convertible_v<typename _LeftPaddedMapping::extents_type,
                             extents_type>
           || _S_rank > 1 && (padding_value != dynamic_extent
                || _LeftPaddedMapping::padding_value == dynamic_extent))
          mapping(const _LeftPaddedMapping& __other)
          : _M_storage(layout_left{}, __other)
          { }
 
        template<typename _RightPaddedMapping>
          requires (__mdspan::__is_right_padded_mapping<_RightPaddedMapping>
              || __mdspan::__mapping_of<layout_right, _RightPaddedMapping>)
            && (_S_rank <= 1)
            && is_constructible_v<extents_type,
                                  typename _RightPaddedMapping::extents_type>
          constexpr explicit(!is_convertible_v<
              typename _RightPaddedMapping::extents_type, extents_type>)
          mapping(const _RightPaddedMapping& __other) noexcept
          : _M_storage(layout_right{}, __other)
          { }
 
        constexpr mapping&
        operator=(const mapping&) noexcept = default;
 
        constexpr const extents_type&
        extents() const noexcept { return _M_storage._M_extents; }
 
        constexpr array<index_type, _S_rank>
        strides() const noexcept
        {
          array<index_type, _S_rank> __ret;
          if constexpr (_S_rank > 0)
            __ret[0] = 1;
          if constexpr (_S_rank > 1)
            __ret[1] = _M_padstride();
          if constexpr (_S_rank > 2)
            for(size_t __i = 2; __i < _S_rank; ++__i)
              __ret[__i] = __ret[__i - 1] * _M_extent(__i - 1);
          return __ret;
        }
 
        constexpr index_type
        required_span_size() const noexcept
        { return _M_storage._M_required_span_size(); }
 
        // _GLIBCXX_RESOLVE_LIB_DEFECTS
        // 4314. Missing move in mdspan layout mapping::operator()
        template<__mdspan::__valid_index_type<index_type>... _Indices>
          requires (sizeof...(_Indices) == _S_rank)
          constexpr index_type
          operator()(_Indices... __indices) const noexcept
          {
            return __mdspan::__linear_index_leftpad(
              extents(), _M_storage._M_stride,
              static_cast<index_type>(std::move(__indices))...);
          }
 
        static constexpr bool
        is_always_exhaustive() noexcept
        { return _PaddedStorage::_M_is_always_exhaustive(); }
 
        constexpr bool
        is_exhaustive() noexcept
        { return _M_storage._M_is_exhaustive(); }
 
        static constexpr bool
        is_always_unique() noexcept { return true; }
 
        static constexpr bool
        is_unique() noexcept { return true; }
 
        static constexpr bool
        is_always_strided() noexcept { return true; }
 
        static constexpr bool
        is_strided() noexcept { return true; }
 
        constexpr index_type
        stride(rank_type __r) const noexcept
        {
          __glibcxx_assert(__r < _S_rank);
          if (__r == 0)
            return 1;
          else
            return static_cast<index_type>(
              static_cast<size_t>(_M_padstride()) *
              static_cast<size_t>(__mdspan::__fwd_prod(extents(), 1, __r)));
        }
 
        template<typename _LeftpadMapping>
          requires(__mdspan::__is_left_padded_mapping<_LeftpadMapping>
                   && _LeftpadMapping::extents_type::rank() == _S_rank)
          friend constexpr bool
          operator==(const mapping& __self, const _LeftpadMapping& __other)
          noexcept
          { return __self._M_storage._M_equal(__other); }
 
      private:
#if __glibcxx_submdspan
        template<typename... _Slices>
          requires (extents_type::rank() == sizeof...(_Slices))
          friend constexpr auto
          submdspan_mapping(const mapping& __mapping, _Slices... __slices)
          { return __mdspan::__submdspan_mapping_impl(__mapping, __slices...); }
#endif // __glibcxx_submdspan
      };
 
  template<size_t _PaddingValue>
    template<typename _Extents>
      class layout_right_padded<_PaddingValue>::mapping {
      public:
        static constexpr size_t padding_value = _PaddingValue;
        using extents_type = _Extents;
        using index_type = typename extents_type::index_type;
        using size_type = typename extents_type::size_type;
        using rank_type = typename extents_type::rank_type;
        using layout_type = layout_right_padded<_PaddingValue>;
 
      private:
        static constexpr size_t _S_rank = extents_type::rank();
        using _PaddedStorage = __mdspan::_PaddedStorage<_PaddingValue,
              _Extents, __mdspan::_RightPaddedLayoutTraits<_S_rank>>;
        [[no_unique_address]] _PaddedStorage _M_storage;
 
        consteval friend size_t
        __mdspan::__get_static_stride<mapping>();
 
        constexpr index_type
        _M_extent(size_t __r) const noexcept
        { return _M_storage._M_extents.extent(__r); }
 
        constexpr index_type
        _M_padstride() const noexcept
        { return _M_storage._M_stride.extent(0); }
 
      public:
        constexpr
        mapping() noexcept
        { }
 
        constexpr
        mapping(const mapping&) noexcept = default;
 
        constexpr
        mapping(const extents_type& __exts)
        : _M_storage(__exts)
        { }
 
        template<__mdspan::__valid_index_type<index_type> _OIndexType>
          constexpr
          mapping(const extents_type& __exts, _OIndexType __pad)
          : _M_storage(__exts,
              __mdspan::__index_type_cast<index_type>(std::move(__pad)))
          { }
 
        template<typename _OExtents>
          requires is_constructible_v<extents_type, _OExtents>
          constexpr explicit(!is_convertible_v<_OExtents, extents_type>)
          mapping(const layout_right::mapping<_OExtents>& __other)
          : _M_storage(__other)
          { }
 
        template<typename _OExtents>
          requires is_constructible_v<_OExtents, extents_type>
          constexpr explicit(!(_OExtents::rank() == 0
                               && is_convertible_v<_OExtents, extents_type>))
          mapping(const typename layout_stride::mapping<_OExtents>& __other)
          : _M_storage(__other)
          { __glibcxx_assert(*this == __other); }
 
        template<typename _RightPaddedMapping>
          requires __mdspan::__is_right_padded_mapping<_RightPaddedMapping>
              && is_constructible_v<extents_type,
                                    typename _RightPaddedMapping::extents_type>
          constexpr explicit(
            !is_convertible_v<typename _RightPaddedMapping::extents_type,
                              extents_type>
            || _S_rank > 1 && (padding_value != dynamic_extent
                 || _RightPaddedMapping::padding_value == dynamic_extent))
          mapping(const _RightPaddedMapping& __other)
          : _M_storage(layout_right{}, __other)
          { }
 
        template<typename _LeftPaddedMapping>
          requires (__mdspan::__is_left_padded_mapping<_LeftPaddedMapping>
              || __mdspan::__mapping_of<layout_left, _LeftPaddedMapping>)
            && (_S_rank <= 1)
            && is_constructible_v<extents_type,
                                  typename _LeftPaddedMapping::extents_type>
          constexpr explicit(!is_convertible_v<
              typename _LeftPaddedMapping::extents_type, extents_type>)
          mapping(const _LeftPaddedMapping& __other) noexcept
          : _M_storage(layout_left{}, __other)
          { }
 
        constexpr mapping& operator=(const mapping&) noexcept = default;
 
        constexpr const extents_type&
        extents() const noexcept { return _M_storage._M_extents; }
 
        constexpr array<index_type, _S_rank>
        strides() const noexcept
        {
          array<index_type, _S_rank> __ret;
          if constexpr (_S_rank > 0)
            __ret[_S_rank - 1] = 1;
          if constexpr (_S_rank > 1)
            __ret[_S_rank - 2] = _M_padstride();
          if constexpr (_S_rank > 2)
            for(size_t __i = _S_rank - 2; __i > 0; --__i)
              __ret[__i - 1] = __ret[__i] * _M_extent(__i);
          return __ret;
        }
 
        constexpr index_type
        required_span_size() const noexcept
        { return _M_storage._M_required_span_size(); }
 
        // _GLIBCXX_RESOLVE_LIB_DEFECTS
        // 4314. Missing move in mdspan layout mapping::operator()
        template<__mdspan::__valid_index_type<index_type>... _Indices>
          requires (sizeof...(_Indices) == _S_rank)
          constexpr index_type
          operator()(_Indices... __indices) const noexcept
          {
            return __mdspan::__linear_index_rightpad(
              extents(), _M_storage._M_stride,
              static_cast<index_type>(std::move(__indices))...);
          }
 
        static constexpr bool
        is_always_exhaustive() noexcept
        { return _PaddedStorage::_M_is_always_exhaustive(); }
 
        constexpr bool
        is_exhaustive() noexcept
        { return _M_storage._M_is_exhaustive(); }
 
        static constexpr bool
        is_always_unique() noexcept { return true; }
 
        static constexpr bool
        is_unique() noexcept { return true; }
 
        static constexpr bool
        is_always_strided() noexcept { return true; }
 
        static constexpr bool
        is_strided() noexcept { return true; }
 
        constexpr index_type
        stride(rank_type __r) const noexcept
        {
          __glibcxx_assert(__r < _S_rank);
          if constexpr (_S_rank <= 1)
            return 1;
          else if (__r == _S_rank - 1)
            return 1;
          else if (__r == _S_rank - 2)
            return _M_padstride();
          else
            return static_cast<index_type>(
              static_cast<size_t>(_M_padstride()) *
              static_cast<size_t>(__mdspan::__fwd_prod(
                  extents(), __r + 1, _S_rank - 1)));
        }
 
        template<typename _RightPaddedMapping>
          requires(__mdspan::__is_right_padded_mapping<_RightPaddedMapping>
                   && _RightPaddedMapping::extents_type::rank() == _S_rank)
          friend constexpr bool
          operator==(const mapping& __self, const _RightPaddedMapping& __other)
          noexcept
          { return __self._M_storage._M_equal(__other); }
 
#if __glibcxx_submdspan
      private:
        template<typename... _Slices>
          requires (extents_type::rank() == sizeof...(_Slices))
          friend constexpr auto
          submdspan_mapping(const mapping& __mapping, _Slices... __slices)
          { return __mdspan::__submdspan_mapping_impl(__mapping, __slices...); }
#endif // __glibcxx_submdspan
      };
#endif // __glibcxx_padded_layouts
 
  template<typename _ElementType>
    struct default_accessor
    {
      static_assert(!is_array_v<_ElementType>,
        "ElementType must not be an array type");
      static_assert(!is_abstract_v<_ElementType>,
        "ElementType must not be an abstract class type");
 
      using offset_policy = default_accessor;
      using element_type = _ElementType;
      using reference = element_type&;
      using data_handle_type = element_type*;
 
      constexpr
      default_accessor() noexcept = default;
 
      template<typename _OElementType>
        requires is_convertible_v<_OElementType(*)[], element_type(*)[]>
        constexpr
        default_accessor(default_accessor<_OElementType>) noexcept
        { }
 
      constexpr reference
      access(data_handle_type __p, size_t __i) const noexcept
      { return __p[__i]; }
 
      constexpr data_handle_type
      offset(data_handle_type __p, size_t __i) const noexcept
      { return __p + __i; }
    };
 
#ifdef __glibcxx_aligned_accessor
  template<typename _ElementType, size_t _ByteAlignment>
    struct aligned_accessor
    {
      static_assert(has_single_bit(_ByteAlignment),
        "ByteAlignment must be a power of two");
      static_assert(_ByteAlignment >= alignof(_ElementType));
 
      using offset_policy = default_accessor<_ElementType>;
      using element_type = _ElementType;
      using reference = element_type&;
      using data_handle_type = element_type*;
 
      static constexpr size_t byte_alignment = _ByteAlignment;
 
      constexpr
      aligned_accessor() noexcept = default;
 
      template<typename _OElementType, size_t _OByteAlignment>
        requires (_OByteAlignment >= byte_alignment)
            && is_convertible_v<_OElementType(*)[], element_type(*)[]>
        constexpr
        aligned_accessor(aligned_accessor<_OElementType, _OByteAlignment>)
        noexcept
        { }
 
      template<typename _OElementType>
        requires is_convertible_v<_OElementType(*)[], element_type(*)[]>
        constexpr explicit
        aligned_accessor(default_accessor<_OElementType>) noexcept
        { }
 
      template<typename _OElementType>
        requires is_convertible_v<element_type(*)[], _OElementType(*)[]>
        constexpr
        operator default_accessor<_OElementType>() const noexcept
        { return {}; }
 
      constexpr reference
      access(data_handle_type __p, size_t __i) const noexcept
      { return std::assume_aligned<byte_alignment>(__p)[__i]; }
 
      constexpr typename offset_policy::data_handle_type
      offset(data_handle_type __p, size_t __i) const noexcept
      { return std::assume_aligned<byte_alignment>(__p) + __i; }
    };
#endif
 
  template<typename _ElementType, typename _Extents,
           typename _LayoutPolicy = layout_right,
           typename _AccessorPolicy = default_accessor<_ElementType>>
    class mdspan
    {
      static_assert(!is_array_v<_ElementType>,
        "ElementType must not be an array type");
      static_assert(!is_abstract_v<_ElementType>,
        "ElementType must not be an abstract class type");
      static_assert(__mdspan::__is_extents<_Extents>,
        "Extents must be a specialization of std::extents");
      static_assert(is_same_v<_ElementType,
                              typename _AccessorPolicy::element_type>);
 
    public:
      using extents_type = _Extents;
      using layout_type = _LayoutPolicy;
      using accessor_type = _AccessorPolicy;
      using mapping_type = typename layout_type::template mapping<extents_type>;
      using element_type = _ElementType;
      using value_type = remove_cv_t<element_type>;
      using index_type = typename extents_type::index_type;
      using size_type = typename extents_type::size_type;
      using rank_type = typename extents_type::rank_type;
      using data_handle_type = typename accessor_type::data_handle_type;
      using reference = typename accessor_type::reference;
 
      static constexpr rank_type
      rank() noexcept { return extents_type::rank(); }
 
      static constexpr rank_type
      rank_dynamic() noexcept { return extents_type::rank_dynamic(); }
 
      static constexpr size_t
      static_extent(rank_type __r) noexcept
      { return extents_type::static_extent(__r); }
 
      constexpr index_type
      extent(rank_type __r) const noexcept { return extents().extent(__r); }
 
      constexpr
      mdspan()
      requires (rank_dynamic() > 0)
          && is_default_constructible_v<data_handle_type>
          && is_default_constructible_v<mapping_type>
          && is_default_constructible_v<accessor_type> = default;
 
      constexpr
      mdspan(const mdspan& __other) = default;
 
      constexpr
      mdspan(mdspan&& __other) = default;
 
      template<__mdspan::__valid_index_type<index_type>... _OIndexTypes>
        requires (sizeof...(_OIndexTypes) == rank()
                   || sizeof...(_OIndexTypes) == rank_dynamic())
                 && is_constructible_v<mapping_type, extents_type>
                 && is_default_constructible_v<accessor_type>
        constexpr explicit
        mdspan(data_handle_type __handle, _OIndexTypes... __exts)
        : _M_accessor(),
          _M_mapping(_Extents(static_cast<index_type>(std::move(__exts))...)),
          _M_handle(std::move(__handle))
        { }
 
      template<typename _OIndexType, size_t _Nm>
        requires __mdspan::__valid_index_type<const _OIndexType&, index_type>
                 && (_Nm == rank() || _Nm == rank_dynamic())
                 && is_constructible_v<mapping_type, extents_type>
                 && is_default_constructible_v<accessor_type>
        constexpr explicit(_Nm != rank_dynamic())
        mdspan(data_handle_type __handle, span<_OIndexType, _Nm> __exts)
        : _M_accessor(), _M_mapping(extents_type(__exts)),
          _M_handle(std::move(__handle))
        { }
 
      template<typename _OIndexType, size_t _Nm>
        requires __mdspan::__valid_index_type<const _OIndexType&, index_type>
                 && (_Nm == rank() || _Nm == rank_dynamic())
                 && is_constructible_v<mapping_type, extents_type>
                 && is_default_constructible_v<accessor_type>
        constexpr explicit(_Nm != rank_dynamic())
        mdspan(data_handle_type __handle, const array<_OIndexType, _Nm>& __exts)
        : _M_accessor(), _M_mapping(extents_type(__exts)),
          _M_handle(std::move(__handle))
        { }
 
      constexpr
      mdspan(data_handle_type __handle, const extents_type& __exts)
      requires is_constructible_v<mapping_type, const extents_type&>
               && is_default_constructible_v<accessor_type>
      : _M_accessor(), _M_mapping(__exts), _M_handle(std::move(__handle))
      { }
 
      constexpr
      mdspan(data_handle_type __handle, const mapping_type& __mapping)
      requires is_default_constructible_v<accessor_type>
      : _M_accessor(), _M_mapping(__mapping), _M_handle(std::move(__handle))
      { }
 
      constexpr
      mdspan(data_handle_type __handle, const mapping_type& __mapping,
             const accessor_type& __accessor)
      : _M_accessor(__accessor), _M_mapping(__mapping),
        _M_handle(std::move(__handle))
      { }
 
      template<typename _OElementType, typename _OExtents, typename _OLayout,
               typename _OAccessor>
        requires is_constructible_v<mapping_type,
              const typename _OLayout::template mapping<_OExtents>&>
          && is_constructible_v<accessor_type, const _OAccessor&>
        constexpr explicit(!is_convertible_v<
            const typename _OLayout::template mapping<_OExtents>&, mapping_type>
          || !is_convertible_v<const _OAccessor&, accessor_type>)
        mdspan(const mdspan<_OElementType, _OExtents, _OLayout, _OAccessor>&
                 __other)
        : _M_accessor(__other.accessor()), _M_mapping(__other.mapping()),
          _M_handle(__other.data_handle())
        {
          static_assert(is_constructible_v<data_handle_type,
              const typename _OAccessor::data_handle_type&>);
          static_assert(is_constructible_v<extents_type, _OExtents>);
        }
 
      constexpr mdspan&
      operator=(const mdspan& __other) = default;
 
      constexpr mdspan&
      operator=(mdspan&& __other) = default;
 
      template<__mdspan::__valid_index_type<index_type>... _OIndexTypes>
        requires (sizeof...(_OIndexTypes) == rank())
        constexpr reference
        operator[](_OIndexTypes... __indices) const
        {
          if constexpr (rank() == 0)
            return _M_accessor.access(_M_handle, _M_mapping());
          else if constexpr (!(is_same_v<_OIndexTypes, index_type> && ...))
            return operator[](
              __mdspan::__index_type_cast<index_type>(std::move(__indices))...);
          else
           {
             auto __is_multi_index = [&]<size_t... _Counts>(index_sequence<_Counts...>)
             { return ((__indices < extents().extent(_Counts)) && ...); };
 
             __glibcxx_assert(__is_multi_index(make_index_sequence<rank()>()));
             return _M_accessor.access(_M_handle, _M_mapping(__indices...));
           }
        }
 
      template<typename _OIndexType>
        requires __mdspan::__valid_index_type<const _OIndexType&, index_type>
        constexpr reference
        operator[](span<_OIndexType, rank()> __indices) const
        {
          auto __call = [&]<size_t... _Counts>(index_sequence<_Counts...>)
            -> reference
            {
               return operator[](
                 __mdspan::__index_type_cast<index_type>(as_const(__indices[_Counts]))...);
            };
          return __call(make_index_sequence<rank()>());
        }
 
      template<typename _OIndexType>
        requires __mdspan::__valid_index_type<const _OIndexType&, index_type>
        constexpr reference
        operator[](const array<_OIndexType, rank()>& __indices) const
        { return operator[](span<const _OIndexType, rank()>(__indices)); }
 
#if __cplusplus > 202302L
      template<__mdspan::__valid_index_type<index_type>... _OIndexTypes>
        requires (sizeof...(_OIndexTypes) == rank())
        constexpr reference
        at(_OIndexTypes... __indices) const
        {
          if constexpr (rank() == 0)
            return _M_accessor.access(_M_handle, _M_mapping());
          else if constexpr (!(is_integral_v<_OIndexTypes> && ...))
            return at(__index_int_t<_OIndexTypes>(std::move(__indices))...);
          else
           {
             auto __check_bound = [&]<typename _OIntType>(size_t __dim, _OIntType __index)
             {
               if constexpr (is_signed_v<_OIntType>)
                 if (__index < 0)
                   std::__throw_out_of_range_fmt(
                     __N("mdspan::at: %zuth index is negative"), __dim);
 
               const auto __ext = extents().extent(__dim);
               if (std::cmp_greater_equal(__index, __ext))
                 std::__throw_out_of_range_fmt(
                   __N("mdspan::at: %zuth index (which is %zu)"
                       " >= extent(%zu) (which is %zu)"),
                   __dim, size_t(__index), __dim, size_t(__ext));
             };
             auto __check_bounds = [&]<size_t... _Counts>(index_sequence<_Counts...>)
             { (__check_bound(_Counts, __indices), ...); };
 
             __check_bounds(make_index_sequence<rank()>());
             auto __index = _M_mapping(static_cast<index_type>(__indices)...);
             return _M_accessor.access(_M_handle, __index);
           }
        }
 
      template<typename _OIndexType>
        requires __mdspan::__valid_index_type<const _OIndexType&, index_type>
        constexpr reference
        at(span<_OIndexType, rank()> __indices) const
        {
          auto __call = [&]<size_t... _Counts>(index_sequence<_Counts...>)
            -> reference
            {
              return at(
                __index_int_t<_OIndexType>(as_const(__indices[_Counts]))...);
            };
          return __call(make_index_sequence<rank()>());
        }
 
      template<typename _OIndexType>
        requires __mdspan::__valid_index_type<const _OIndexType&, index_type>
        constexpr reference
        at(const array<_OIndexType, rank()>& __indices) const
        { return at(span<const _OIndexType, rank()>(__indices)); }
#endif // C++26
 
      constexpr size_type
      size() const noexcept
      {
        __glibcxx_assert(cmp_less_equal(_M_mapping.required_span_size(),
                                        __gnu_cxx::__int_traits<size_t>
                                                 ::__max));
        return size_type(__mdspan::__size(extents()));
      }
 
      [[nodiscard]]
      constexpr bool
      empty() const noexcept
      { return __mdspan::__empty(extents()); }
 
      friend constexpr void
      swap(mdspan& __x, mdspan& __y) noexcept
      {
        using std::swap;
        swap(__x._M_mapping, __y._M_mapping);
        swap(__x._M_accessor, __y._M_accessor);
        swap(__x._M_handle, __y._M_handle);
      }
 
      constexpr const extents_type&
      extents() const noexcept { return _M_mapping.extents(); }
 
      constexpr const data_handle_type&
      data_handle() const noexcept { return _M_handle; }
 
      constexpr const mapping_type&
      mapping() const noexcept { return _M_mapping; }
 
      constexpr const accessor_type&
      accessor() const noexcept { return _M_accessor; }
 
      // Strengthened noexcept for all `is_*` methods.
 
      static constexpr bool
      is_always_unique() noexcept(noexcept(mapping_type::is_always_unique()))
      { return mapping_type::is_always_unique(); }
 
      static constexpr bool
      is_always_exhaustive()
      noexcept(noexcept(mapping_type::is_always_exhaustive()))
      { return mapping_type::is_always_exhaustive(); }
 
      static constexpr bool
      is_always_strided()
      noexcept(noexcept(mapping_type::is_always_strided()))
      { return mapping_type::is_always_strided(); }
 
      constexpr bool
      is_unique() const noexcept(noexcept(_M_mapping.is_unique()))
      { return _M_mapping.is_unique(); }
 
      constexpr bool
      is_exhaustive() const noexcept(noexcept(_M_mapping.is_exhaustive()))
      { return _M_mapping.is_exhaustive(); }
 
      constexpr bool
      is_strided() const noexcept(noexcept(_M_mapping.is_strided()))
      { return _M_mapping.is_strided(); }
 
      constexpr index_type
      stride(rank_type __r) const { return _M_mapping.stride(__r); }
 
    private:
      template<typename _OIndexType>
        using __index_int_t = std::__conditional_t<
          is_integral_v<_OIndexType>, _OIndexType, index_type>;
 
      [[no_unique_address]] accessor_type _M_accessor = accessor_type();
      [[no_unique_address]] mapping_type _M_mapping = mapping_type();
      [[no_unique_address]] data_handle_type _M_handle = data_handle_type();
    };
 
  template<typename _CArray>
    requires is_array_v<_CArray> && (rank_v<_CArray> == 1)
    mdspan(_CArray&)
    -> mdspan<remove_all_extents_t<_CArray>,
              extents<size_t, extent_v<_CArray, 0>>>;
 
  template<typename _Pointer>
    requires is_pointer_v<remove_reference_t<_Pointer>>
    mdspan(_Pointer&&)
    -> mdspan<remove_pointer_t<remove_reference_t<_Pointer>>, extents<size_t>>;
 
  template<typename _ElementType, typename... _Integrals>
    requires (is_convertible_v<_Integrals, size_t> && ...)
              && (sizeof...(_Integrals) > 0)
    explicit mdspan(_ElementType*, _Integrals...)
    -> mdspan<_ElementType,
              extents<size_t, __detail::__maybe_static_ext<_Integrals>...>>;
 
  template<typename _ElementType, typename _OIndexType, size_t _Nm>
    mdspan(_ElementType*, span<_OIndexType, _Nm>)
    -> mdspan<_ElementType, dextents<size_t, _Nm>>;
 
  template<typename _ElementType, typename _OIndexType, size_t _Nm>
    mdspan(_ElementType*, const array<_OIndexType, _Nm>&)
    -> mdspan<_ElementType, dextents<size_t, _Nm>>;
 
  template<typename _ElementType, typename _IndexType, size_t... _ExtentsPack>
    mdspan(_ElementType*, const extents<_IndexType, _ExtentsPack...>&)
    -> mdspan<_ElementType, extents<_IndexType, _ExtentsPack...>>;
 
  template<typename _ElementType, typename _MappingType>
    mdspan(_ElementType*, const _MappingType&)
    -> mdspan<_ElementType, typename _MappingType::extents_type,
              typename _MappingType::layout_type>;
 
  template<typename _MappingType, typename _AccessorType>
    mdspan(const typename _AccessorType::data_handle_type&, const _MappingType&,
           const _AccessorType&)
    -> mdspan<typename _AccessorType::element_type,
              typename _MappingType::extents_type,
              typename _MappingType::layout_type, _AccessorType>;
 
#if __glibcxx_submdspan
  namespace __mdspan
  {
    template<typename _IndexType, typename _Slice>
      constexpr auto
      __canonical_index(_Slice&& __slice)
      {
        if constexpr (__detail::__integral_constant_like<_Slice>)
          {
            static_assert(__is_representable_integer<_IndexType>(_Slice::value));
            static_assert(_Slice::value >= 0);
            return std::cw<_IndexType(_Slice::value)>;
          }
        else
          return __mdspan::__index_type_cast<_IndexType>(std::move(__slice));
      }
 
    template<typename _IndexType, typename _Slice>
      constexpr auto
      __slice_cast(_Slice&& __slice)
      {
        using _SliceType = remove_cvref_t<_Slice>;
        if constexpr (is_convertible_v<_SliceType, full_extent_t>)
          return static_cast<full_extent_t>(std::move(__slice));
        else if constexpr (is_convertible_v<_SliceType, _IndexType>)
          return __mdspan::__canonical_index<_IndexType>(std::move(__slice));
        else if constexpr (__is_strided_slice<_SliceType>)
          {
            auto __extent
              = __mdspan::__canonical_index<_IndexType>(std::move(__slice.extent));
            auto __offset
              = __mdspan::__canonical_index<_IndexType>(std::move(__slice.offset));
            if constexpr (is_same_v<decltype(__extent),
                                    constant_wrapper<_IndexType(0)>>)
              return strided_slice{
                .offset = __offset,
                .extent = __extent,
                .stride = cw<_IndexType(1)>
              };
            else
              return strided_slice{
                .offset = __offset,
                .extent = __extent,
                .stride
                  = __mdspan::__canonical_index<_IndexType>(std::move(__slice.stride))
              };
          }
        else
          {
            auto [__sbegin, __send] = std::move(__slice);
            auto __offset
              = __mdspan::__canonical_index<_IndexType>(std::move(__sbegin));
            auto __end
              = __mdspan::__canonical_index<_IndexType>(std::move(__send));
            return strided_slice{
              .offset = __offset,
              .extent = __mdspan::__canonical_index<_IndexType>(__end - __offset),
              .stride = cw<_IndexType(1)>
            };
          }
      }
 
    template<typename _IndexType, size_t _Extent, typename _OIndexType>
      constexpr void
      __check_valid_index(const extents<_IndexType, _Extent>& __ext,
                           const _OIndexType& __idx)
      {
        if constexpr (__is_constant_wrapper<_OIndexType>
                      && _Extent != dynamic_extent)
          {
            static_assert(_OIndexType::value >= 0);
            static_assert(std::cmp_less_equal(_OIndexType::value, _Extent));
          }
        else
          __glibcxx_assert(__idx <= __ext.extent(0));
}
 
    template<typename _IndexType, size_t _Extent, typename _Slice>
      constexpr void
      __check_valid_slice(const extents<_IndexType, _Extent>& __ext,
                           const _Slice& __slice)
      {
        if constexpr (__is_strided_slice<_Slice>)
          {
            // DEVIATION: For empty slices, P3663r3 does not allow us to check
            // that this is less than or equal to the k-th extent (at runtime).
            // We're only allowed to check if __slice.offset, __slice.extent
            // are constant wrappers and __ext is a static extent.
            __mdspan::__check_valid_index(__ext, __slice.offset);
            __mdspan::__check_valid_index(__ext, __slice.extent);
 
            if constexpr (__is_constant_wrapper<typename _Slice::extent_type>
                          && __is_constant_wrapper<typename _Slice::stride_type>)
              static_assert(_Slice::stride_type::value > 0);
            else
              __glibcxx_assert(__slice.extent == 0 || __slice.stride > 0);
 
            if constexpr (__is_constant_wrapper<typename _Slice::offset_type>
                && __is_constant_wrapper<typename _Slice::extent_type>
                && _Extent != dynamic_extent)
              static_assert(std::cmp_greater_equal(
                  _Extent - _Slice::offset_type::value,
                  _Slice::extent_type::value));
            else
              __glibcxx_assert(__ext.extent(0) - __slice.offset
                               >= __slice.extent);
          }
        else if constexpr (__is_constant_wrapper<_Slice>
                           && _Extent != dynamic_extent)
          static_assert(std::cmp_less(_Slice::value, _Extent));
        else if constexpr (convertible_to<_Slice, _IndexType>)
          __glibcxx_assert(__slice < __ext.extent(0));
      }
 
    template<typename _Extents, typename... _Slices>
      constexpr void
      __check_valid_slices(const _Extents& __exts, const _Slices&... __slices)
      {
        constexpr auto __rank = _Extents::rank();
        auto __impl = [&]<size_t... _Is>(index_sequence<_Is...>)
        {
          ((__mdspan::__check_valid_slice(__extract_extent<_Is>(__exts),
                                          __slices...[_Is])),...);
        };
        __impl(make_index_sequence<__rank>());
      }
 
    template<typename _Slice>
      using __full_extent_t = std::full_extent_t;
 
    // Enables ADL-only calls from submdspan.
    void submdspan_mapping() = delete;
 
    template<typename _Mapping, typename... _Slices>
      concept __sliceable_mapping = requires(const _Mapping __m, _Slices... __slices)
      {
        { submdspan_mapping(__m, __slices...) } -> __submdspan_mapping_result;
      };
 
    template<typename _Mapping, typename... _Slices>
      constexpr auto
      __submapping(const _Mapping& __mapping, _Slices... __slices)
      {
        __mdspan::__check_valid_slices(__mapping.extents(), __slices...);
        return submdspan_mapping(__mapping, __slices...);
      }
  }
 
  template<typename _IndexType, size_t... _Extents, typename... _RawSlices>
    requires (sizeof...(_RawSlices) == sizeof...(_Extents))
    constexpr auto
    subextents(const extents<_IndexType, _Extents...>& __exts,
               _RawSlices... __raw_slices)
    {
      auto __impl = [&__exts](auto... __slices)
      {
        __mdspan::__check_valid_slices(__exts, __slices...);
        return __mdspan::__subextents(__exts, __slices...);
      };
      return __impl(__mdspan::__slice_cast<_IndexType>(__raw_slices)...);
    }
 
  template<typename _IndexType, size_t... _Extents, typename... _RawSlices>
    requires (sizeof...(_Extents) == sizeof...(_RawSlices))
    constexpr auto
    canonical_slices(const extents<_IndexType, _Extents...>& __exts,
                     _RawSlices... __raw_slices)
    {
      auto __impl = [&__exts](auto... __slices)
      {
        __mdspan::__check_valid_slices(__exts, __slices...);
        return std::make_tuple(__slices...);
      };
      return __impl(__mdspan::__slice_cast<_IndexType>(__raw_slices)...);
    }
 
  template<typename _ElementType, typename _Extents, typename _Layout,
           typename _Accessor, typename... _RawSlices>
    requires (sizeof...(_RawSlices) == _Extents::rank()
        && __mdspan::__sliceable_mapping<typename _Layout::template mapping<_Extents>,
                                         __mdspan::__full_extent_t<_RawSlices>...>)
    constexpr auto
    submdspan(
        const mdspan<_ElementType, _Extents, _Layout, _Accessor>& __md,
        _RawSlices... __raw_slices)
    {
      using _IndexType = typename _Extents::index_type;
      auto [__mapping, __offset] = __mdspan::__submapping(
        __md.mapping(), __mdspan::__slice_cast<_IndexType>(__raw_slices)...);
      return std::mdspan(
               __md.accessor().offset(__md.data_handle(), __offset),
               std::move(__mapping),
               typename _Accessor::offset_policy(__md.accessor()));
    }
#endif // __glibcxx_submdspan
 
_GLIBCXX_END_NAMESPACE_VERSION
}
#endif
#endif