[PATCH v4 1/5] libstdc++: Implement submdspan and submdspan_mapping for layout_left. [PR110352]

Luc Grosheintz luc.grosheintz@gmail.com
Fri Dec 5 15:28:36 GMT 2025



On 12/5/25 11:04, Tomasz Kaminski wrote:
> On Thu, Dec 4, 2025 at 10:34 PM Luc Grosheintz <luc.grosheintz@gmail.com>
> wrote:
> 
>> Implements `submdspan` and `submdspan_mapping` for layout_left as
>> described in P3663 (Future proofing mdspan).
>>
>> When computing the offset of the submdspan, one must check that the
>> lower bound of the slice range isn't out-of-range. There's a few
>> cases when the lower bound is never out-of-range:
>>
>>    - full_extent and exts.extent(k) != 0,
>>    - collapsing slice types.
>>
>> If those conditions are known to hold, no checks are generated.
>>
>> Similarly, if all slices are full_extent, there's no need to call
>> mapping(0,...,0) for standardized mappings.
>>
>> The implementation prepares to use the symmetry between layout_left and
>> layout_right and introduces concepts like a "layout side", i.e. left,
>> right or unknown/strided.
>>
>> The tests use an iterator to replace nested for-loops. Which also makes
>> it easier to write the core test logic in a rank-independent manner.
>>
>>          PR libstdc++/110352
>>
>> libstdc++-v3/ChangeLog:
>>
>>          * include/std/mdspan (layout_left::mapping::submdspan_mapping):
>>          New friend function.
>>          (submdspan): New function.
>>          * src/c++23/std.cc.in: Add submdspan.
>>          * testsuite/23_containers/mdspan/submdspan/submdspan.cc: New test.
>>          * testsuite/23_containers/mdspan/submdspan/submdspan_mapping.cc:
>> New test.
>>          * testsuite/23_containers/mdspan/submdspan/submdspan_neg.cc: New
>> test.
>>
>> Signed-off-by: Luc Grosheintz <luc.grosheintz@gmail.com>
>>
> This really looks solid to me now, thank you for the update. I will go over
> the remaining ones in the afternoon.
> Comments below:
>   - slice-mapping is not SFINEAing correctly (body inside lambda inside
> concept is not checked),
>     left some suggestions
> - we can eliminate few <size_t Size> parameters, and make it normal
> function parameters now
> - some comment about extracting span declaration
> - submdspan.cc test needs to be parallelized, already is timeint out, left
> some suggestion bellow,
>    this apply to remaining patches also
> 
>> ---
>>   libstdc++-v3/include/std/mdspan               | 557 ++++++++++++++++--
>>   libstdc++-v3/src/c++23/std.cc.in              |   2 +-
>>   .../mdspan/submdspan/submdspan.cc             | 369 ++++++++++++
>>   .../mdspan/submdspan/submdspan_mapping.cc     | 136 +++++
>>   .../mdspan/submdspan/submdspan_neg.cc         | 161 +++++
>>   5 files changed, 1163 insertions(+), 62 deletions(-)
>>   create mode 100644
>> libstdc++-v3/testsuite/23_containers/mdspan/submdspan/submdspan.cc
>>   create mode 100644
>> libstdc++-v3/testsuite/23_containers/mdspan/submdspan/submdspan_mapping.cc
>>   create mode 100644
>> libstdc++-v3/testsuite/23_containers/mdspan/submdspan/submdspan_neg.cc
>>
>> diff --git a/libstdc++-v3/include/std/mdspan
>> b/libstdc++-v3/include/std/mdspan
>> index bfec288aded..54739c0008d 100644
>> --- a/libstdc++-v3/include/std/mdspan
>> +++ b/libstdc++-v3/include/std/mdspan
>> @@ -357,40 +357,50 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
>>         static_assert(__is_standard_integer<_ExtentType>::value
>>          || __detail::__integral_constant_like<_ExtentType>);
>>         static_assert(__is_standard_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_standard_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;
>>
>> @@ -572,40 +582,50 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
>>
>>       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);
>>            }
>>         }
>>
>> @@ -849,64 +869,503 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
>>          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)>)
>> +                 __ret[__krev] = __stride * __slice.stride;
>>
> We seem to be missing the check that __slice.stride <  __slice.extent.
> 
>> +               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>()...};
>> +      }
>> +
>> +    //                   _BlockSize - 1
>> +    // [full, ..., full, unit_slice    , *]
>> +    template<size_t _BlockSize>
>>
> Make this a normal function parameter, i.e. size_t _BlockSioe.
> 
>> +      consteval bool
>> +      __is_block(span<const _SliceKind> __slice_kinds)
>> +      {
>> +       if (_BlockSize == 0)
>> +         return false;
>> +
>> +       if (_BlockSize > __slice_kinds.size())
>> +         return false;
>> +
>> +       for (size_t __i = 0; __i < _BlockSize - 1; ++__i)
>> +         if (__slice_kinds[__i] != _SliceKind::__full)
>> +           return false;
>> +
>> +       auto __last = __slice_kinds[_BlockSize - 1];
>> +       return __last == _SliceKind::__full
>> +           || __last == _SliceKind::__unit_strided_slice;
>> +      }
>> +
>> +    //                         __u              __u + _SubRank-2
>> +    // [unit_slice, i, ..., k, full, ..., full, unit_slice, *]
>> +    template<size_t _SubRank>
>>
> // Same here for _SubRank
> 
>> +      static consteval size_t
>> +      __padded_block_begin_generic(span<const _SliceKind> __slice_kinds)
>> +      {
>> +       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
>> +         {
>> +           static_assert(_SubRank != dynamic_extent,
>> +             "The implementation can't handle submdspans with rank ==
>> size_t(-1)");
>> +
>> +           size_t __u = 1;
>> +           while(__u < __slice_kinds.size()
>> +                 && __slice_kinds[__u] == _SliceKind::__collapsing)
>> +             ++__u;
>> +
>> +           if
>> (__mdspan::__is_block<_SubRank-1>(__slice_kinds.subspan(__u)))
>> +             return __u;
>> +           return dynamic_extent;
>>
> That looks really nice.
> 
>> +         }
>> +      }
>> +
>> +    template<_LayoutSide _Side, size_t _SubRank, size_t _Nm>
>>
> Again, make _SubRank a template parameter.
> 
>> +      static consteval size_t
>> +      __padded_block_begin(span<const _SliceKind, _Nm> __slice_kinds)
>> +      {
>> +       if constexpr (_Side == _LayoutSide::__left)
>> +         return
>> __mdspan::__padded_block_begin_generic<_SubRank>(__slice_kinds);
>> +       else
>> +         {
>> +           std::array<_SliceKind, _Nm> __rev_slice_kinds;
>>
> I would name it __rev_slice_array
> 
>> +           for(size_t __i = 0; __i < _Nm; ++__i)
>> +             __rev_slice_kinds[__i] = __slice_kinds[_Nm - 1 - __i];
>>
> And declare below.
>                  std::span<const _SliceKind, _Nm>
> __rev_slick_kinds(__rev_slice_array);
> 
>> +
>> +           auto __u = __mdspan::__padded_block_begin_generic<_SubRank>(
>> +               std::span<const _SliceKind>(__rev_slice_kinds));
>> +           return __u == dynamic_extent ? dynamic_extent : _Nm - 1 - __u;
>> +         }
>> +      }
>> +
>> +    template<_LayoutSide _Side>
>> +      struct _SubMdspanMapping;
>> +
>> +    template<>
>> +      struct _SubMdspanMapping<_LayoutSide::__left>
>> +      {
>> +       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 _SubRank, size_t _Nm>
>> +         static consteval bool
>> +         _S_is_unpadded_submdspan(span<const _SliceKind, _Nm>
>> __slice_kinds)
>> +         { return __mdspan::__is_block<_SubRank>(__slice_kinds); }
>> +      };
>> +
>> +    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)
>> +      {
>> +       constexpr auto __side = __mdspan::__mapping_side<_Mapping>();
>> +       using _Trait = _SubMdspanMapping<__side>;
>> +
>> +       constexpr auto __slice_kinds =
>> __mdspan::__make_slice_kind_array<_Slices...>();
>>
> Again here, declaring __slice_kinds_array and __slice_kind as span below
> it, we are creating
> the span 3 times below.
> 

I might be doing it wrong, but the compiler is adamant that this isn't
permitted. Essentially, it says that __slice_kinds_span isn't a constant
expression. Clang expands: it's because the pointer in __slice_kinds_array
can be different on different invocations.

Godbolt: https://godbolt.org/z/vPPhPxva6

Easy fix: pass the array by value (just this once). We anyway need to know
the size, passing as an array, ensures that the size isn't `size_t(-1)`,
accidentally. Since we never need subspans of the array (at this point)
it should be fine. (There's no copying because it's always passed to
consteval functions).

>> +       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::template _S_is_unpadded_submdspan<__sub_rank>(
>> +             std::span<const _SliceKind,
>> __slice_kinds.size()>(__slice_kinds)))
>> +         return submdspan_mapping_result{
>> +           typename _Trait::_Layout::mapping(__sub_exts), __offset};
>> +       else if constexpr (
>> +           constexpr auto __u = __padded_block_begin<__side, __sub_rank>(
>> +             span<const _SliceKind, __slice_kinds.size()>(__slice_kinds));
>> +           __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};
>> +         }
>> +      }
>> +
>> +    // Enables ADL-only calls from submdspan.
>> +    void submdspan_mapping() = delete;
>>
> Please put it before the concept __sliceable_mapping definition.
> 
>>   #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
>> @@ -1014,40 +1473,48 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
>>         }
>>
>>         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<__mdspan::__acceptable_slice_type<index_type>... _Slices>
>>
> Make this a static assert inside submdspan_impl, we do not need a concept
> check here.
> 
>> +       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],
>> @@ -2673,118 +3140,86 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
>>          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 _IndexType, size_t _Extent, typename _Slice>
>> -      consteval size_t
>> -      __static_slice_extent()
>>
> 
> 
>> +    template<typename _Mapping>
>> +      concept __sliceable_mapping = requires(_Mapping __m)
>>         {
>> -       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>(index_sequence<_Indices...>)
>>          {
>> -         using _SubExtents = extents<_IndexType,
>> -             (__mdspan::__static_slice_extent<_IndexType,
>> -                _Extents...[__inv_map[_Indices]],
>> -                _Slices...[__inv_map[_Indices]]>())...>;
>> -         if constexpr (_SubExtents::rank_dynamic() == 0)
>> -           return _SubExtents{};
>> -         else
>> -           {
>> -             using _StaticSubExtents = __mdspan::_StaticExtents<
>> -               __mdspan::__static_extents<_SubExtents>()>;
>> -             auto __create = [&]<size_t... _Is>(index_sequence<_Is...>)
>> -             {
>> -               constexpr auto __slice_idx = [__inv_map](size_t __i)
>> consteval
>> -               {
>> -                 return
>> __inv_map[_StaticSubExtents::_S_dynamic_index_inv(__i)];
>> -               };
>> -
>> -               return _SubExtents{
>> -                 (__mdspan::__dynamic_slice_extent<__slice_idx(_Is)>(
>> -                    __exts, __slices...[__slice_idx(_Is)]))...};
>> -             };
>> -             constexpr auto __dyn_subrank = _SubExtents::rank_dynamic();
>> -             return __create(make_index_sequence<__dyn_subrank>());
>> -           }
>> -       };
>> -
>> -       return __impl(make_index_sequence<__inv_map.size()>());
>> -      }
>> +         [__m]<size_t... _Is>(index_sequence<_Is...>)
>> +         {
>> +           return submdspan_mapping(__m, ((void) _Is, full_extent)...);
>> +         }(make_index_sequence<_Mapping::extents_type::rank()>())
>>
> This is not doing the check correctly, as the lambda body is not considered
> part of SFINAE.
> (Please add a test that on mdspan with custom mapping without submapping,
> doing
>    require { submdspan(m, slices....); }
> returns false.
> 
> To bring this as part of SFINAE, we should put the call inside the return
> type of lamba:
>           [__m]<size_t... _Is>(index_sequence<_Is...>)
>           -> decltype(submdspan_mapping(__m, ((void) _Is, full_extent)...))
>           {  return submdspan_mapping(__m, ((void) _Is, full_extent)...); }
> 
>    template<typename _Mapping, typename... Slices>
>      concept __sliceable_mapping = requires(_Mapping __m, Slices... slices)
>     {
>         { submdspan_mapping(__m, slices...); } -> __submdspan_mapping_result;
>     }
> 
> And then checking __mdspan::__sliceable_mapping<typename
> _Layout::mapping<_Extents>, __mdspan::__full_extent_t<Slices>...>.
> This will give much more readable error message.
> 
>> +       } -> __submdspan_mapping_result;
>> +      };
>>     }
>>
>>     template<typename _IndexType, size_t... _Extents, typename...
>> _RawSlices>
>>       requires (sizeof...(_RawSlices) == sizeof...(_Extents))
>>       constexpr auto
>>       submdspan_extents(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
>>       submdspan_canonicalize_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::mapping<_Extents>>)
>> +    constexpr auto
>> +    submdspan(
>> +       const mdspan<_ElementType, _Extents, _Layout, _Accessor>& __md,
>> +       _RawSlices... __raw_slices)
>> +    {
>> +      using _IndexType = typename _Extents::index_type;
>> +      auto __impl = [&__md](auto... __slices)
>> +      {
>> +       using __mdspan::submdspan_mapping;
>>
> I would define the __subbmapping function inside __mdspan below the concet
> that will return submdspan_mapping_result.
> This will avoid the need for this using:
> template<typename _Mapping, typename... Slices>
> constexpr auto __submapping(const _Mapping& __map, _Slices... slices)
>   {
>       __mdspan::__check_valid_slices(__md.extents(), __slices...);
>      return __result = submdspan_mapping(__md.mapping(), __slices...);
> }
> 
> 
> 
>> +       __mdspan::__check_valid_slices(__md.extents(), __slices...);
>> +       auto __result = submdspan_mapping(__md.mapping(), __slices...);
>>
> I would use auto [__mapping, __offset] = submdspan_mapping(__md.mapping(),
> __slices...) here.
> 
>> +       return std::mdspan(__md.accessor().offset(__md.data_handle(),
>> __result.offset),
>> +           __result.mapping, typename
>> _Accessor::offset_policy(__md.accessor()));
>>
> I would move mapping here, the user defined one may have more efficient
> moves.
> 
>> +      };
>> +      return __impl(__mdspan::__slice_cast<_IndexType>(__raw_slices)...);
>> +    }
>>   #endif // __glibcxx_submdspan
>>
>>   _GLIBCXX_END_NAMESPACE_VERSION
>>   }
>>   #endif
>>   #endif
>> diff --git a/libstdc++-v3/src/c++23/std.cc.in b/libstdc++-v3/src/c++23/
>> std.cc.in
>> index c2a9293b05a..2dac6a6d887 100644
>> --- a/libstdc++-v3/src/c++23/std.cc.in
>> +++ b/libstdc++-v3/src/c++23/std.cc.in
>> @@ -1868,42 +1868,42 @@ export namespace std
>>   #endif
>>     using std::layout_left;
>>     using std::layout_right;
>>     using std::layout_stride;
>>     using std::default_accessor;
>>   #if __glibcxx_aligned_accessor
>>     using std::aligned_accessor;
>>   #endif
>>     using std::mdspan;
>>   #if __glibcxx_padded_layouts
>>     using std::layout_left_padded;
>>     using std::layout_right_padded;
>>   #endif
>>   #if __glibcxx_submdspan
>>     using std::strided_slice;
>>     using std::full_extent_t;
>>     using std::full_extent;
>>     using std::submdspan_mapping_result;
>>     using std::submdspan_canonicalize_slices;
>>     using std::submdspan_extents;
>> +  using std::submdspan;
>>   #endif
>> -  // FIXME mdsubspan
>>   }
>>   #endif
>>
>>   // 20.2 <memory>
>>   export namespace std
>>   {
>>     using std::align;
>>     using std::allocator;
>>     using std::allocator_arg;
>>     using std::allocator_arg_t;
>>     using std::allocator_traits;
>>     using std::assume_aligned;
>>   #if __glibcxx_is_sufficiently_aligned
>>     using std::is_sufficiently_aligned;
>>   #endif
>>     using std::make_obj_using_allocator;
>>     using std::pointer_traits;
>>     using std::to_address;
>>     using std::uninitialized_construct_using_allocator;
>>     using std::uses_allocator;
>> diff --git
>> a/libstdc++-v3/testsuite/23_containers/mdspan/submdspan/submdspan.cc
>> b/libstdc++-v3/testsuite/23_containers/mdspan/submdspan/submdspan.cc
>> new file mode 100644
>> index 00000000000..53e91407a9c
>> --- /dev/null
>> +++ b/libstdc++-v3/testsuite/23_containers/mdspan/submdspan/submdspan.cc
>> @@ -0,0 +1,369 @@
>> +// { dg-do run { target c++26 } }
>>
> This test is already timeout out in the debug mode, my suggestion would be,
> create and mdspan dir, where you will have the test machinery in header,
> and then inside files for instantiating for each layout, with separation
> for
> cheap and expensive tests. I will later in separate commit.
> We should also add, to the test.
> // { dg-timeout-factor 2.0 }
> 
> I will then increase value as needed.
> 
> +#include <mdspan>
>> +
>> +#include <iostream> // TODO remove
>> +#include <vector>
>> +#include <numeric>
>> +#include "../layout_traits.h"
>> +#include <testsuite_hooks.h>
>> +
>> +constexpr size_t dyn = std::dynamic_extent;
>> +constexpr auto all = std::full_extent;
>> +
>> +template<typename T>
>> +  constexpr bool is_strided_slice = false;
>> +
>> +template<typename O, typename E, typename S>
>> +  constexpr bool is_strided_slice<std::strided_slice<O, E, S>> = true;
>> +
>> +template<typename MDSpan>
>> +  constexpr void
>> +  fill(const MDSpan& md)
>> +  {
>> +    using IndexType = typename MDSpan::index_type;
>> +    auto exts = md.extents();
>> +    if constexpr (exts.rank() == 3)
>> +      for(IndexType i = 0; i < exts.extent(0); ++i)
>> +       for(IndexType j = 0; j < exts.extent(1); ++j)
>> +         for(IndexType k = 0; k < exts.extent(2); ++k)
>> +           md[i, j, k] = 100 * i + 10 * j + k;
>> +  }
>> +
>> +template<typename Int, size_t Rank>
>> +  class multi_index_generator
>> +  {
>> +    class EndIt
>>
> These are usually named sentinel.
> I would just name it struct sentinel
> 
>> +    { };
>> +
>> +    class BeginIt
>>
> // And this, just name the iterator.
> 
>> +    {
>> +    public:
>> +      constexpr
>> +      BeginIt(const std::array<Int, Rank>& shape)
>> +       : M_shape(shape)
>> +      { }
>> +
>> +      constexpr BeginIt&
>> +      operator++()
>> +      {
>> +       if constexpr (Rank > 0)
>> +         {
>> +           ++M_indices[Rank-1];
>> +           for(size_t i = Rank; i > 1; --i)
>> +             if (M_indices[i-1] == M_shape[i-1])
>> +               {
>> +                 M_indices[i-1] = 0;
>> +                 ++M_indices[i-2];
>> +               }
>> +         }
>> +       return *this;
>> +      }
>> +
>> +      constexpr auto
>> +      operator*()
>> +      { return M_indices; }
>> +
>> +      constexpr bool
>> +      operator==(EndIt)
>>
> Making this hidden friend:
> constexpr friend bool operator==(const BeginIt&, _EndIt) {}
> 
>> +      {
>> +       if constexpr (Rank > 0)
>> +         return M_indices[0] == M_shape[0];
>> +       else
>> +         return true;
>> +      }
>> +
>> +    private:
>> +      std::array<Int, Rank> M_indices{};
>> +      std::array<Int, Rank> M_shape;
>> +    };
>> +
>> +  public:
>> +    constexpr
>> +    multi_index_generator(std::array<Int, Rank> shape)
>> +      : M_shape(shape)
>> +    { }
>> +
>> +    constexpr BeginIt
>> +    begin() const
>> +    { return BeginIt(M_shape); }
>> +
>> +    constexpr EndIt
>> +    end() const
>> +    { return EndIt{}; }
>> +
>> +  private:
>> +    std::array<Int, Rank> M_shape;
>> +  };
>>
> 
> 
>> +
>> +constexpr bool
>> +test_multi_index()
>> +{
>> +  auto shape = std::array{3, 5, 7, 1};
>> +
>> +  std::vector<std::array<int, 4>> expected;
>> +  for (int i = 0; i < shape[0]; ++i)
>> +    for (int j = 0; j < shape[1]; ++j)
>> +      for (int k = 0; k <shape[2]; ++k)
>> +       for (int l = 0; l <shape[3]; ++l)
> 
> Instead of creating vector of array, I would do:
> multi_index_generator gen(shape);
> auto it = gen.begin();
> auto end = gen.end();
> 
> And then inside loop:
>       {
>          VERIFY(it != end);
>          VERIFY(*it == std::array{i, j, k, l});
>         ++it;
>      }
> 
> 
>> +         expected.push_back(std::array{i, j, k, l});
>> +
>> +  size_t i = 0;
>> +  for (auto actual : multi_index_generator(shape))
>> +    VERIFY(expected[i++] == actual);
>> +  return true;
>> +}
>> +
>> +static_assert(test_multi_index());
>> +
>> +struct
>> +collapse
>> +{ };
>> +
>> +template<typename... Slices>
>> +  consteval auto
>> +  inv_collapsed_index_map()
>> +  {
>> +    constexpr size_t rank = sizeof...(Slices);
>> +    auto is_collapsing = std::array{std::same_as<Slices, collapse>...};
>> +    constexpr auto collapsed_rank = ((!std::same_as<Slices, collapse>) +
>> ... + 0);
>> +
>> +    std::array<size_t, collapsed_rank> ret;
>> +    if constexpr (collapsed_rank > 0)
>> +      for(size_t k = 0, i = 0; i < rank; ++i)
>> +       if (!is_collapsing[i])
>> +         ret[k++] = i;
>> +    return ret;
>> +  }
>> +
>> +static_assert(inv_collapsed_index_map<collapse, collapse, collapse>()
>> +             == std::array<size_t, 0>{});
>> +
>> +static_assert(inv_collapsed_index_map<collapse, decltype(all), collapse>()
>> +             == std::array<size_t, 1>{1});
>> +
>> +template<typename IndexType, typename Slice>
>> +  constexpr std::vector<IndexType>
>> +  make_selection(IndexType extent, const Slice& slice)
>> +  {
>> +    if constexpr (std::convertible_to<Slice, IndexType>)
>> +      return {static_cast<IndexType>(slice)};
>> +    else if constexpr (std::same_as<Slice, std::full_extent_t>)
>> +      {
>> +       auto ret = std::vector<IndexType>(static_cast<size_t>(extent));
>> +       std::ranges::iota(ret, 0);
>> +       return ret;
>> +      }
>> +    else if constexpr (is_strided_slice<Slice>)
>> +      {
>> +       auto ret = std::vector<IndexType>{};
>> +       size_t n = static_cast<size_t>(slice.extent);
>> +       for(size_t i = 0; i < n; i += slice.stride)
>> +         ret.push_back(slice.offset + i);
>> +       return ret;
>> +      }
>> +    else
>> +      {
>> +       auto [begin, end] = slice;
>> +       auto ret = std::vector<IndexType>(static_cast<size_t>(end -
>> begin));
>> +       std::ranges::iota(ret, begin);
>> +       return ret;
>> +      }
>> +  }
>> +
>> +template<typename Layout, size_t... I, typename... Slices>
>> +  constexpr bool
>> +  check_selection(std::index_sequence<I...>, auto md, Slices... slices)
>> +  {
>> +    auto exts = md.extents();
>> +    auto outer_shape = std::array{exts.extent(0), exts.extent(1),
>> exts.extent(2)};
>> +
>> +    constexpr auto full_index = inv_collapsed_index_map<Slices...>();
>> +    auto make_slice = [](size_t i, auto slice)
>> +    {
>> +      if constexpr (std::same_as<decltype(slice), collapse>)
>> +       return i;
>> +      else
>> +       return slice;
>> +    };
>> +
>> +    auto loop_body = [&]<size_t... J>(std::index_sequence<J...>, auto ijk,
>> +                                     auto... slices)
>> +    {
>> +      auto submd = submdspan(md, slices...[I]...);
>> +      auto selection = std::tuple{make_selection(exts.extent(I),
>> slices...[I])...};
>> +      auto inner_shape = std::array<size_t, full_index.size()>{
>> +       std::get<full_index[J]>(selection).size()...
>> +      };
>> +
>> +      for (auto ij : multi_index_generator(inner_shape))
>> +      {
>> +       ((ijk[full_index[J]] = get<full_index[J]>(selection)[ij[J]]),...);
>> +       VERIFY(submd[ij] == md[ijk]);
>> +      }
>> +    };
>> +
>> +    for (auto ijk : multi_index_generator(outer_shape))
>> +      loop_body(std::make_index_sequence<full_index.size()>(), ijk,
>> +               make_slice(ijk[I], slices...[I])...);
>> +    return true;
>> +  }
>> +
>> +template<typename Layout, typename...MD, typename... Slices>
>> +  constexpr bool
>> +  check_selection(std::mdspan<MD...> md, Slices... slices)
>> +  {
>> +    auto indices = std::make_index_sequence<sizeof...(slices)>();
>> +    return check_selection<Layout>(indices, md, slices...);
>> +  }
>> +
>> +template<typename Layout, typename IndexType, size_t... Extents,
>> +        typename... Slices>
>> +  constexpr bool
>> +  check_selection(std::extents<IndexType, Extents...>exts, Slices...
>> slices)
>> +  {
>> +    auto run = [&](auto m)
>> +    {
>> +      auto storage = std::vector<double>(m.required_span_size());
>> +      auto md = std::mdspan(storage.data(), m);
>> +      fill(md);
>> +      return check_selection<Layout>(md, slices...);
>> +    };
>> +
>> +    if constexpr (std::same_as<Layout, std::layout_stride>)
>> +      {
>> +       auto m = typename Layout::mapping(exts, std::array{15, 2, 50});
>> +       return run(m);
>> +      }
>> +    else
>> +      {
>> +       auto m = typename Layout::mapping(exts);
>> +       return run(m);
>> +      }
>> +  }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_scalar_selection(auto exts)
>> +  {
>> +    check_selection<Layout>(exts, collapse{}, collapse{}, collapse{});
>> +    return true;
>> +  }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_full_lines(auto exts)
>> +  {
>> +    check_selection<Layout>(exts, all, collapse{}, collapse{});
>> +    check_selection<Layout>(exts, collapse{}, all, collapse{});
>> +    check_selection<Layout>(exts, collapse{}, collapse{}, all);
>> +    return true;
>> +  }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_full_blocks(auto exts)
>> +  {
>> +    check_selection<Layout>(exts, all, all, collapse{});
>> +    check_selection<Layout>(exts, all, collapse{}, all);
>> +    check_selection<Layout>(exts, collapse{}, all, all);
>> +    return true;
>> +  }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_cubes(auto exts)
>> +  {
>> +    auto s0 = std::pair{0, 2};
>> +    auto s1 = std::pair{1, 4};
>> +    auto s2 = std::pair{3, 7};
>> +
>> +    check_selection<Layout>(exts, all, all, all);
>> +    check_selection<Layout>(exts, all, all, s2);
>> +    check_selection<Layout>(exts, s0, all, all);
>> +    check_selection<Layout>(exts, s0, all, s2);
>> +    check_selection<Layout>(exts, s0, s1, s2);
>> +    return true;
>> +  }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_strided_line_selection(auto exts)
>> +  {
>> +    auto check = [&](auto s)
>> +    {
>> +      check_selection<Layout>(exts, collapse{}, s, collapse{});
>> +    };
>> +
>> +    check(std::strided_slice(0, 2, 2));
>> +    check(std::strided_slice(0, 3, 2));
>> +    check(std::strided_slice(1, 3, 2));
>> +    check(std::strided_slice(1, std::cw<3>, std::cw<2>));
>> +    return true;
>> +  }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_strided_box_selection(auto exts)
>> +  {
>> +    auto s0 = std::strided_slice(0, 3, 2);
>> +    auto s1 = std::strided_slice(1, 4, 2);
>> +    auto s2 = std::strided_slice(0, 7, 3);
>> +
>> +    check_selection<Layout>(exts, s0, s1, s2);
>> +    return true;
>> +  }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_all_cheap()
>> +  {
>> +    constexpr auto dyn_exts = std::extents(3, 5, 7);
>> +    constexpr auto sta_exts = std::extents<int, 3, 5, 7>{};
>> +
>> +    test_scalar_selection<Layout>(dyn_exts);
>> +    test_scalar_selection<Layout>(sta_exts);
>> +    static_assert(test_scalar_selection<Layout>(dyn_exts));
>> +    static_assert(test_scalar_selection<Layout>(sta_exts));
>> +
>> +    test_full_lines<Layout>(dyn_exts);
>> +    test_full_lines<Layout>(sta_exts);
>> +    static_assert(test_full_lines<Layout>(dyn_exts));
>> +    static_assert(test_full_lines<Layout>(sta_exts));
>> +
>> +    test_strided_box_selection<Layout>(dyn_exts);
>> +    test_strided_box_selection<Layout>(sta_exts);
>> +    static_assert(test_strided_box_selection<Layout>(dyn_exts));
>> +    static_assert(test_strided_box_selection<Layout>(sta_exts));
>> +    return true;
>> +  }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_all_expensive()
>> +  {
>> +    auto run = [](auto exts)
>> +    {
>> +      test_full_blocks<Layout>(exts);
>> +      test_cubes<Layout>(exts);
>> +    };
>> +
>> +    run(std::extents(3, 5, 7));
>> +    run(std::extents<int, 3, 5, 7>{});
>> +    return true;
>> +  }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_all()
>> +  {
>> +    test_all_cheap<Layout>();
>> +    test_all_expensive<Layout>();
>> +    return true;
>> +  }
>> +
>> +int
>> +main()
>> +{
>> +  test_all<std::layout_left>();
>> +  return 0;
>> +}
>> diff --git
>> a/libstdc++-v3/testsuite/23_containers/mdspan/submdspan/submdspan_mapping.cc
>> b/libstdc++-v3/testsuite/23_containers/mdspan/submdspan/submdspan_mapping.cc
>> new file mode 100644
>> index 00000000000..a37d3cd588f
>> --- /dev/null
>> +++
>> b/libstdc++-v3/testsuite/23_containers/mdspan/submdspan/submdspan_mapping.cc
>> @@ -0,0 +1,136 @@
>> +// { dg-do run { target c++26 } }
>> +#include <mdspan>
>> +
>> +#include <iostream> // TODO remove
>> +#include "../layout_traits.h"
>> +#include <testsuite_hooks.h>
>> +
>> +constexpr size_t dyn = std::dynamic_extent;
>> +
>> +template<typename Mapping, typename... Slices>
>> +  constexpr auto
>> +  call_submdspan_mapping(const Mapping& m, std::tuple<Slices...> slices)
>> +  {
>> +    auto impl = [&]<size_t... I>(std::index_sequence<I...>)
>> +    { return submdspan_mapping(m, get<I>(slices)...); };
>> +    return impl(std::make_index_sequence<sizeof...(Slices)>());
>> +  }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_layout_unpadded_return_types()
>> +  {
>> +    constexpr auto padding_side =
>> DeducePaddingSide::from_typename<Layout>();
>> +    using Traits = LayoutTraits<padding_side>;
>> +
>> +    {
>> +      auto m0 = typename Layout::mapping(std::extents());
>> +      auto result = submdspan_mapping(m0);
>> +      using layout_type = typename decltype(result.mapping)::layout_type;
>> +      static_assert(std::same_as<layout_type, Layout>);
>> +    }
>> +
>> +    auto exts = Traits::make_extents(std::dims<5, int>(3, 5, 7, 11, 13));
>> +    auto m = typename Layout::mapping(exts);
>> +    auto all = std::full_extent;
>> +    auto s251 = std::strided_slice{2, 5, std::cw<1>};
>> +
>> +    {
>> +      auto slices = std::tuple{0, 0, 0, 0, 0};
>> +      auto result = call_submdspan_mapping(m, Traits::make_tuple(slices));
>> +      using layout_type = typename decltype(result.mapping)::layout_type;
>> +      static_assert(std::same_as<layout_type, Layout>);
>> +    }
>> +
>> +    {
>> +      auto slices = std::tuple{all, all, all, s251, 0};
>> +      auto result = call_submdspan_mapping(m, Traits::make_tuple(slices));
>> +      using layout_type = typename decltype(result.mapping)::layout_type;
>> +      static_assert(std::same_as<layout_type, Layout>);
>> +    }
>> +
>> +    {
>> +      auto s0 = std::strided_slice{1, 1, std::cw<1>};
>> +      auto slices = std::tuple{s0, all, all, s251, 0};
>> +      auto result = call_submdspan_mapping(m, Traits::make_tuple(slices));
>> +      using layout_type = typename decltype(result.mapping)::layout_type;
>> +      static_assert(is_same_padded<padding_side, layout_type>);
>> +    }
>> +
>> +    {
>> +      auto s0 = std::strided_slice{1, 2, std::cw<1>};
>> +      auto slices = std::tuple{s0, all, all, s251, 0};
>> +      auto result = call_submdspan_mapping(m, Traits::make_tuple(slices));
>> +      using layout_type = typename decltype(result.mapping)::layout_type;
>> +      static_assert(is_same_padded<padding_side, layout_type>);
>> +    }
>> +
>> +    {
>> +      auto s0 = std::strided_slice{1, 2, std::cw<1>};
>> +      auto slices = std::tuple{s0, 0, all, s251, 0};
>> +      auto result = call_submdspan_mapping(m, Traits::make_tuple(slices));
>> +      using layout_type = typename decltype(result.mapping)::layout_type;
>> +      static_assert(is_same_padded<padding_side, layout_type>);
>> +    }
>> +
>> +    {
>> +      auto s0 = std::strided_slice{1, 2, 1};
>> +      auto slices = std::tuple{s0, all, all, s251, 0};
>> +      auto result = call_submdspan_mapping(m, Traits::make_tuple(slices));
>> +      using layout_type = decltype(result.mapping)::layout_type;
>> +      static_assert(std::same_as<layout_type, std::layout_stride>);
>> +    }
>> +
>> +    {
>> +      auto slices = std::tuple{1, all, all, s251, 0};
>> +      auto result = call_submdspan_mapping(m, Traits::make_tuple(slices));
>> +      using layout_type = decltype(result.mapping)::layout_type;
>> +      static_assert(std::same_as<layout_type, std::layout_stride>);
>> +    }
>> +
>> +    {
>> +      auto s3 = std::strided_slice{2, std::cw<7>, std::cw<2>};
>> +      auto slices = std::tuple{all, all, all, s3, 0};
>> +      auto result = call_submdspan_mapping(m, Traits::make_tuple(slices));
>> +      using layout_type = decltype(result.mapping)::layout_type;
>> +      static_assert(std::same_as<layout_type, std::layout_stride>);
>> +    }
>> +    return true;
>> +  }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_layout_unpadded_padding_value()
>> +  {
>> +    using Traits =
>> LayoutTraits<DeducePaddingSide::from_typename<Layout>()>;
>> +    auto s0 = std::strided_slice{size_t(1), size_t(2),
>> std::cw<size_t(1)>};
>> +    auto s3 = std::strided_slice{size_t(2), size_t(5),
>> std::cw<size_t(1)>};
>> +    auto all = std::full_extent;
>> +
>> +    auto check = [&](auto exts, size_t expected)
>> +    {
>> +      auto m = typename Layout::mapping(Traits::make_extents(exts));
>> +      auto slices = std::tuple{s0, size_t(0), all, s3, size_t(0)};
>> +      auto result = call_submdspan_mapping(m, Traits::make_tuple(slices));
>> +      auto padding_value = decltype(result.mapping)::padding_value;
>> +      VERIFY(padding_value == expected);
>> +    };
>> +
>> +    check(std::extents(std::cw<3>, std::cw<5>, std::cw<7>, 11, 13), 3*5);
>> +    check(std::extents(std::cw<3>, std::cw<5>, 7, 11, 13), 3*5);
>> +    check(std::extents(std::cw<3>, 5, 7, 11, 13), dyn);
>> +    check(std::extents(3, 5, 7, 11, 13), dyn);
>> +    return true;
>> +  }
>> +
>> +int
>> +main()
>> +{
>> +  test_layout_unpadded_return_types<std::layout_left>();
>> +  static_assert(test_layout_unpadded_return_types<std::layout_left>());
>> +
>> +  test_layout_unpadded_padding_value<std::layout_left>();
>> +  static_assert(test_layout_unpadded_padding_value<std::layout_left>());
>> +  return 0;
>> +}
>> +
>> diff --git
>> a/libstdc++-v3/testsuite/23_containers/mdspan/submdspan/submdspan_neg.cc
>> b/libstdc++-v3/testsuite/23_containers/mdspan/submdspan/submdspan_neg.cc
>> new file mode 100644
>> index 00000000000..cdc8a2b7e23
>> --- /dev/null
>> +++
>> b/libstdc++-v3/testsuite/23_containers/mdspan/submdspan/submdspan_neg.cc
>> @@ -0,0 +1,161 @@
>> +// { dg-do compile { target c++26 } }
>> +#include <mdspan>
>> +
>> +#include <vector>
>> +
>> +template<typename Layout, typename... Slices>
>> +  constexpr bool
>> +  check_slice_range(Slices... slices)
>> +  {
>> +    auto m = typename Layout::mapping<std::extents<int, 3, 5, 7>>{};
>> +    auto storage = std::vector<double>(m.required_span_size());
>> +    auto md = std::mdspan(storage.data(), m);
>> +
>> +    auto submd = submdspan(md, slices...);           // { dg-error
>> "expansion of" }
>> +    (void) submd;
>> +    return true;
>> +  }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_int_under()
>> +  {
>> +    check_slice_range<Layout>(1, -1, 2);             // { dg-error
>> "expansion of" }
>> +    return true;
>> +  }
>> +static_assert(test_int_under<std::layout_left>());   // { dg-error
>> "expansion of" }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_int_over()
>> +  {
>> +    check_slice_range<Layout>(1, 5, 2);              // { dg-error
>> "expansion of" }
>> +    return true;
>> +  }
>> +static_assert(test_int_over<std::layout_left>());    // { dg-error
>> "expansion of" }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_tuple_under()
>> +  {
>> +    check_slice_range<Layout>(1, std::tuple{-1, 2}, 2);  // { dg-error
>> "expansion of" }
>> +    return true;
>> +  }
>> +static_assert(test_tuple_under<std::layout_left>());     // { dg-error
>> "expansion of" }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_tuple_reversed()
>> +  {
>> +    check_slice_range<Layout>(1, std::tuple{3, 2}, 2);   // { dg-error
>> "expansion of" }
>> +    return true;
>> +  }
>> +static_assert(test_tuple_reversed<std::layout_left>());   // { dg-error
>> "expansion of" }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_tuple_over()
>> +  {
>> +    check_slice_range<Layout>(1, std::tuple{0, 6}, 2); // { dg-error
>> "expansion of" }
>> +    return true;
>> +  }
>> +static_assert(test_tuple_over<std::layout_left>());   // { dg-error
>> "expansion of" }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_strided_slice_zero()
>> +  {
>> +    check_slice_range<Layout>(1, std::strided_slice{1, 1, 0}, 2);  // {
>> dg-error "expansion of" }
>> +    return true;
>> +  }
>> +static_assert(test_strided_slice_zero<std::layout_left>());   // {
>> dg-error "expansion of" }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_strided_slice_offset_under()
>> +  {
>> +    check_slice_range<Layout>(1, std::strided_slice{-1, 1, 1}, 2);   // {
>> dg-error "expansion of" }
>> +    return true;
>> +  }
>> +static_assert(test_strided_slice_offset_under<std::layout_left>());   //
>> { dg-error "expansion of" }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_strided_slice_offset_over()
>> +  {
>> +    check_slice_range<Layout>(1, std::strided_slice{6, 0, 1}, 2);    // {
>> dg-error "expansion of" }
>> +    return true;
>> +  }
>> +static_assert(test_strided_slice_offset_over<std::layout_left>());   // {
>> dg-error "expansion of" }
>> +
>> +template<typename Layout>
>> +  constexpr bool
>> +  test_strided_slice_extent_over()
>> +  {
>> +    check_slice_range<Layout>(1, std::strided_slice{1, 5, 1}, 2);    // {
>> dg-error "expansion of" }
>> +    return true;
>> +  }
>> +static_assert(test_strided_slice_extent_over<std::layout_left>());   // {
>> dg-error "expansion of" }
>> +
>> +namespace adl
>> +{
>> +  struct NoFull
>>
> Add test with no submdpsan_mapping at all,
> it should then be checkable with requires { submdspan(mapping, slice,
> slice); }
> Test will only one dimension should be fine.
> 
>> +  {
>> +    template<typename Extents>
>> +      class mapping
>> +      {
>> +      public:
>> +       using extents_type = Extents;
>> +       using index_type = typename extents_type::index_type;
>> +
>> +      private:
>> +       friend constexpr auto
>> +       submdspan_mapping(mapping, int)
>> +       { return std::submdspan_mapping_result{mapping{}, 0}; }
>> +      };
>> +  };
>> +
>> +  struct WrongReturnValue
>> +  {
>> +    template<typename Extents>
>> +      class mapping
>> +      {
>> +      public:
>> +       using extents_type = Extents;
>> +       using index_type = typename extents_type::index_type;
>> +
>> +      private:
>> +       friend constexpr int
>> +       submdspan_mapping(mapping, std::full_extent_t)
>> +       { return 42; }
>> +      };
>> +  };
>> +}
>> +
>> +constexpr bool
>> +test_invalid_mapping1()
>> +{
>> +  using Extents = std::extents<int, 3>;
>> +  auto map = adl::NoFull::mapping<Extents>{};
>> +  std::mdspan<double, Extents, adl::NoFull> m(nullptr, map);
>> +  std::submdspan(m, 1); // { dg-error "no matching function" }
>> +  return true;
>> +}
>> +static_assert(test_invalid_mapping1());
>> +
>> +constexpr bool
>> +test_invalid_mapping2()
>> +{
>> +  using Extents = std::extents<int, 3>;
>> +  auto map = adl::WrongReturnValue::mapping<Extents>{};
>> +  std::mdspan<double, Extents, adl::WrongReturnValue>  m(nullptr, map);
>> +  std::submdspan(m, std::full_extent); // { dg-error "no matching
>> function" }
>> +  return true;
>> +}
>> +static_assert(test_invalid_mapping2());
>> +
>> +// { dg-prune-output "static assertion failed" }
>> +// { dg-prune-output "__glibcxx_assert_fail" }
>> +// { dg-prune-output "non-constant condition" }
>> +// { dg-prune-output "no matching function" }
>> +// { dg-prune-output "does not satisfy placeholder constraints" }
>> --
>> 2.52.0
>>
>>
> 



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