[views.multidim]

# 23 Containers library [[containers]](./#containers)

## 23.7 Views [[views]](views#multidim)

### 23.7.3 Multidimensional access [views.multidim]

#### [23.7.3.1](#mdspan.overview) Overview [[mdspan.overview]](mdspan.overview)

[1](#mdspan.overview-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L20993)

A [*multidimensional index space*](#def:index_space,multidimensional "23.7.3.1 Overview [mdspan.overview]") is
a Cartesian product of integer intervals[.](#mdspan.overview-1.sentence-1)

Each interval can be represented by a half-open range [Li,Ui),
where Li and Ui are the lower and upper bounds of
the ith dimension[.](#mdspan.overview-1.sentence-2)

The [*rank*](#def:rank "23.7.3.1 Overview [mdspan.overview]") of a multidimensional index space is
the number of intervals it represents[.](#mdspan.overview-1.sentence-3)

The [*size of a multidimensional index space*](#def:size_of_a_multidimensional_index_space "23.7.3.1 Overview [mdspan.overview]") is
the product of UiâLi for each dimension i if its rank is greater than 0, and 1 otherwise[.](#mdspan.overview-1.sentence-4)

[2](#mdspan.overview-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21005)

An integer r is a [*rank index*](#def:rank_index "23.7.3.1 Overview [mdspan.overview]") of an index space S if r is in the range [0,rank ofÂ S)[.](#mdspan.overview-2.sentence-1)

[3](#mdspan.overview-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21009)

A pack of integers idx is
a [*multidimensional index*](#def:index,multidimensional "23.7.3.1 Overview [mdspan.overview]") in a multidimensional index space S (or representation thereof) if both of the following are true:

- [(3.1)](#mdspan.overview-3.1)

sizeof...(idx) is equal to the rank of S, and

- [(3.2)](#mdspan.overview-3.2)

for every rank index i of S,
the ith value of idx is an integer
in the interval [Li,Ui) of S[.](#mdspan.overview-3.sentence-1)

#### [23.7.3.2](#mdspan.syn) Header <mdspan> synopsis [[mdspan.syn]](mdspan.syn)

[ð](#header:%3cmdspan%3e)

// mostly freestandingnamespace std {// [[mdspan.extents]](#mdspan.extents "23.7.3.3 Class template extents"), class template extentstemplate<class IndexType, size_t... Extents>class extents; // [[mdspan.extents.dextents]](#mdspan.extents.dextents "23.7.3.3.6 Alias template dextents"), alias template dextentstemplate<class IndexType, size_t Rank>using dextents = *see below*; // [[mdspan.extents.dims]](#mdspan.extents.dims "23.7.3.3.7 Alias template dims"), alias template dimstemplate<size_t Rank, class IndexType = size_t>using dims = *see below*; // [[mdspan.layout]](#mdspan.layout "23.7.3.4 Layout mapping"), layout mappingstruct layout_left; struct layout_right; struct layout_stride; template<size_t PaddingValue = dynamic_extent>struct layout_left_padded; template<size_t PaddingValue = dynamic_extent>struct layout_right_padded; // [[mdspan.accessor.default]](#mdspan.accessor.default "23.7.3.5.3 Class template default_­accessor"), class template default_accessortemplate<class ElementType>class default_accessor; // [[mdspan.accessor.aligned]](#mdspan.accessor.aligned "23.7.3.5.4 Class template aligned_­accessor"), class template aligned_accessortemplate<class ElementType, size_t ByteAlignment>class aligned_accessor; // [[mdspan.mdspan]](#mdspan.mdspan "23.7.3.6 Class template mdspan"), class template mdspantemplate<class ElementType, class Extents, class LayoutPolicy = layout_right, class AccessorPolicy = default_accessor<ElementType>>class mdspan; // partially freestanding// [[mdspan.sub]](#mdspan.sub "23.7.3.7 submdspan"), submdspan creationtemplate<class OffsetType, class LengthType, class StrideType>struct strided_slice; template<class LayoutMapping>struct submdspan_mapping_result; struct full_extent_t { explicit full_extent_t() = default; }; inline constexpr full_extent_t full_extent{}; template<class IndexType, size_t... Extents, class... SliceSpecifiers>constexpr auto submdspan_extents(const extents<IndexType, Extents...>&, SliceSpecifiers...); // [[mdspan.sub.sub]](#mdspan.sub.sub "23.7.3.7.7 submdspan function template"), submdspan function templatetemplate<class ElementType, class Extents, class LayoutPolicy, class AccessorPolicy, class... SliceSpecifiers>constexpr auto submdspan(const mdspan<ElementType, Extents, LayoutPolicy, AccessorPolicy>& src,
 SliceSpecifiers... slices) -> *see below*; template<class T, class IndexType>concept [*index-pair-like*](#concept:index-pair-like "23.7.3.2 Header <mdspan> synopsis [mdspan.syn]") = // *exposition only*[*pair-like*](tuple.syn#concept:pair-like "22.4.2 Header <tuple> synopsis [tuple.syn]")<T> &&[convertible_to](concept.convertible#concept:convertible_to "18.4.4 Concept convertible_­to [concept.convertible]")<tuple_element_t<0, T>, IndexType> &&[convertible_to](concept.convertible#concept:convertible_to "18.4.4 Concept convertible_­to [concept.convertible]")<tuple_element_t<1, T>, IndexType>;}

#### [23.7.3.3](#mdspan.extents) Class template extents [[mdspan.extents]](mdspan.extents)

#### [23.7.3.3.1](#mdspan.extents.overview) Overview [[mdspan.extents.overview]](mdspan.extents.overview)

The class template extents represents
a multidimensional index space of rank equal to sizeof...(Extents)[.](#mdspan.extents.overview-sentence-1)

In [[views]](views "23.7 Views"),extents is used synonymously with multidimensional index space[.](#mdspan.extents.overview-sentence-2)

namespace std {template<class IndexType, size_t... Extents>class [extents](#lib:extents "23.7.3.3.1 Overview [mdspan.extents.overview]") {public:using index_type = IndexType; using size_type = make_unsigned_t<index_type>; using rank_type = size_t; // [[mdspan.extents.obs]](#mdspan.extents.obs "23.7.3.3.4 Observers of the multidimensional index space"), observers of the multidimensional index spacestatic constexpr rank_type rank() noexcept { return sizeof...(Extents); }static constexpr rank_type rank_dynamic() noexcept { return *dynamic-index*(rank()); }static constexpr size_t static_extent(rank_type) noexcept; constexpr index_type extent(rank_type) const noexcept; // [[mdspan.extents.cons]](#mdspan.extents.cons "23.7.3.3.3 Constructors"), constructorsconstexpr extents() noexcept = default; template<class OtherIndexType, size_t... OtherExtents>constexpr explicit(*see below*) extents(const extents<OtherIndexType, OtherExtents...>&) noexcept; template<class... OtherIndexTypes>constexpr explicit extents(OtherIndexTypes...) noexcept; template<class OtherIndexType, size_t N>constexpr explicit(N != rank_dynamic()) extents(span<OtherIndexType, N>) noexcept; template<class OtherIndexType, size_t N>constexpr explicit(N != rank_dynamic()) extents(const array<OtherIndexType, N>&) noexcept; // [[mdspan.extents.cmp]](#mdspan.extents.cmp "23.7.3.3.5 Comparison operators"), comparison operatorstemplate<class OtherIndexType, size_t... OtherExtents>friend constexpr bool operator==(const extents&, const extents<OtherIndexType, OtherExtents...>&) noexcept; // [[mdspan.extents.expo]](#mdspan.extents.expo "23.7.3.3.2 Exposition-only helpers"), exposition-only helpersconstexpr size_t *fwd-prod-of-extents*(rank_type) const noexcept; // *exposition only*constexpr size_t *rev-prod-of-extents*(rank_type) const noexcept; // *exposition only*template<class OtherIndexType>static constexpr auto *index-cast*(OtherIndexType&&) noexcept; // *exposition only*private:static constexpr rank_type *dynamic-index*(rank_type) noexcept; // *exposition only*static constexpr rank_type *dynamic-index-inv*(rank_type) noexcept; // *exposition only* array<index_type, rank_dynamic()> *dynamic-extents*{}; // *exposition only*}; template<class... Integrals>explicit extents(Integrals...)-> *see below*;}

[1](#mdspan.extents.overview-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21152)

*Mandates*: 

- [(1.1)](#mdspan.extents.overview-1.1)

IndexType is a signed or unsigned integer type, and

- [(1.2)](#mdspan.extents.overview-1.2)

each element of Extents is either equal to dynamic_extent, or
is representable as a value of type IndexType[.](#mdspan.extents.overview-1.sentence-1)

[2](#mdspan.extents.overview-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21162)

Each specialization of extents models [regular](concepts.object#concept:regular "18.6 Object concepts [concepts.object]") and
is trivially copyable[.](#mdspan.extents.overview-2.sentence-1)

[3](#mdspan.extents.overview-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21166)

Let Er be the rth element of Extents[.](#mdspan.extents.overview-3.sentence-1)

Er is a [*dynamic extent*](#def:extent,dynamic "23.7.3.3.1 Overview [mdspan.extents.overview]") if it is equal to dynamic_extent,
otherwise Er is a [*static extent*](#def:extent,static "23.7.3.3.1 Overview [mdspan.extents.overview]")[.](#mdspan.extents.overview-3.sentence-2)

Let Dr be the value of *dynamic-extents*[*dynamic-index*(r)] if Er is a dynamic extent,
otherwise Er[.](#mdspan.extents.overview-3.sentence-3)

[4](#mdspan.extents.overview-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21174)

The rth interval of the multidimensional index space
represented by an extents object is [0,Dr)[.](#mdspan.extents.overview-4.sentence-1)

#### [23.7.3.3.2](#mdspan.extents.expo) Exposition-only helpers [[mdspan.extents.expo]](mdspan.extents.expo)

[ð](#mdspan.extents.expo-itemdecl:1)

`static constexpr rank_type dynamic-index(rank_type i) noexcept;
`

[1](#mdspan.extents.expo-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21185)

*Preconditions*: i <= rank() is true[.](#mdspan.extents.expo-1.sentence-1)

[2](#mdspan.extents.expo-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21189)

*Returns*: The number of Er with r<i for which Er is a dynamic extent[.](#mdspan.extents.expo-2.sentence-1)

[ð](#mdspan.extents.expo-itemdecl:2)

`static constexpr rank_type dynamic-index-inv(rank_type i) noexcept;
`

[3](#mdspan.extents.expo-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21199)

*Preconditions*: i < rank_dynamic() is true[.](#mdspan.extents.expo-3.sentence-1)

[4](#mdspan.extents.expo-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21203)

*Returns*: The minimum value of r such that *dynamic-index*(r + 1) == i + 1 is true[.](#mdspan.extents.expo-4.sentence-1)

[ð](#mdspan.extents.expo-itemdecl:3)

`constexpr size_t fwd-prod-of-extents(rank_type i) const noexcept;
`

[5](#mdspan.extents.expo-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21214)

*Preconditions*: i <= rank() is true[.](#mdspan.extents.expo-5.sentence-1)

[6](#mdspan.extents.expo-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21218)

*Returns*: If i > 0 is true,
the product of extent(k) for all k in the range [0, i),
otherwise 1[.](#mdspan.extents.expo-6.sentence-1)

[ð](#mdspan.extents.expo-itemdecl:4)

`constexpr size_t rev-prod-of-extents(rank_type i) const noexcept;
`

[7](#mdspan.extents.expo-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21230)

*Preconditions*: i < rank() is true[.](#mdspan.extents.expo-7.sentence-1)

[8](#mdspan.extents.expo-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21234)

*Returns*: If i + 1 < rank() is true,
the product of extent(k) for all k in the range [i + 1, rank()),
otherwise 1[.](#mdspan.extents.expo-8.sentence-1)

[ð](#mdspan.extents.expo-itemdecl:5)

`template<class OtherIndexType>
  static constexpr auto index-cast(OtherIndexType&& i) noexcept;
`

[9](#mdspan.extents.expo-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21248)

*Effects*: 

- [(9.1)](#mdspan.extents.expo-9.1)

If OtherIndexType is an integral type other than bool,
then equivalent to return i;,

- [(9.2)](#mdspan.extents.expo-9.2)

otherwise, equivalent to return static_cast<index_type>(i);[.](#mdspan.extents.expo-9.sentence-1)

[*Note [1](#mdspan.extents.expo-note-1)*:

This function will always return an integral type other than bool[.](#mdspan.extents.expo-9.sentence-2)

Since this function's call sites are constrained on
convertibility of OtherIndexType to index_type,
integer-class types can use the static_cast branch
without loss of precision[.](#mdspan.extents.expo-9.sentence-3)

â *end note*]

#### [23.7.3.3.3](#mdspan.extents.cons) Constructors [[mdspan.extents.cons]](mdspan.extents.cons)

[ð](#lib:extents,constructor)

`template<class OtherIndexType, size_t... OtherExtents>
  constexpr explicit(see below)
    extents(const extents<OtherIndexType, OtherExtents...>& other) noexcept;
`

[1](#mdspan.extents.cons-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21276)

*Constraints*: 

- [(1.1)](#mdspan.extents.cons-1.1)

  sizeof...(OtherExtents) == rank() is true[.](#mdspan.extents.cons-1.1.sentence-1)

- [(1.2)](#mdspan.extents.cons-1.2)

  ((OtherExtents == dynamic_extent || Extents == dynamic_extent || OtherExtents ==  
Extents) && ...) is true[.](#mdspan.extents.cons-1.2.sentence-1)

[2](#mdspan.extents.cons-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21285)

*Preconditions*: 

- [(2.1)](#mdspan.extents.cons-2.1)

other.extent(r) equals Er for each r for which Er is a static extent, and

- [(2.2)](#mdspan.extents.cons-2.2)

either
  * [(2.2.1)](#mdspan.extents.cons-2.2.1)

sizeof...(OtherExtents) is zero, or

  * [(2.2.2)](#mdspan.extents.cons-2.2.2)

other.extent(r) is representable as
a value of type index_type for every rank index r of other[.](#mdspan.extents.cons-2.sentence-1)

[3](#mdspan.extents.cons-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21302)

*Postconditions*: *this == other is true[.](#mdspan.extents.cons-3.sentence-1)

[4](#mdspan.extents.cons-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21306)

*Remarks*: The expression inside explicit is equivalent to:(((Extents != dynamic_extent) && (OtherExtents == dynamic_extent)) || ... ) ||(numeric_limits<index_type>::max() < numeric_limits<OtherIndexType>::max())

[ð](#lib:extents,constructor_)

`template<class... OtherIndexTypes>
  constexpr explicit extents(OtherIndexTypes... exts) noexcept;
`

[5](#mdspan.extents.cons-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21322)

Let N be sizeof...(OtherIndexTypes),
and let exts_arr bearray<index_type, N>{static_cast<  
index_type>(std​::​move(exts))...}[.](#mdspan.extents.cons-5.sentence-1)

[6](#mdspan.extents.cons-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21327)

*Constraints*: 

- [(6.1)](#mdspan.extents.cons-6.1)

(is_convertible_v<OtherIndexTypes, index_type> && ...) is true,

- [(6.2)](#mdspan.extents.cons-6.2)

(is_nothrow_constructible_v<index_type, OtherIndexTypes> && ...) is true, and

- [(6.3)](#mdspan.extents.cons-6.3)

N == rank_dynamic() || N == rank() is true[.](#mdspan.extents.cons-6.sentence-1)
  [*Note [1](#mdspan.extents.cons-note-1)*:
  One can construct extents from just dynamic extents,
which are all the values getting stored, or
from all the extents with a precondition[.](#mdspan.extents.cons-6.3.sentence-2)
 â *end note*]

[7](#mdspan.extents.cons-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21343)

*Preconditions*: 

- [(7.1)](#mdspan.extents.cons-7.1)

If N != rank_dynamic() is true,exts_arr[r] equals Er for each r for which Er is a static extent, and

- [(7.2)](#mdspan.extents.cons-7.2)

either
  * [(7.2.1)](#mdspan.extents.cons-7.2.1)

sizeof...(exts) == 0 is true, or

  * [(7.2.2)](#mdspan.extents.cons-7.2.2)

each element of exts is representable
as a nonnegative value of type index_type[.](#mdspan.extents.cons-7.sentence-1)

[8](#mdspan.extents.cons-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21361)

*Postconditions*: *this == extents(exts_arr) is true[.](#mdspan.extents.cons-8.sentence-1)

[ð](#lib:extents,constructor__)

`template<class OtherIndexType, size_t N>
  constexpr explicit(N != rank_dynamic())
    extents(span<OtherIndexType, N> exts) noexcept;
template<class OtherIndexType, size_t N>
  constexpr explicit(N != rank_dynamic())
    extents(const array<OtherIndexType, N>& exts) noexcept;
`

[9](#mdspan.extents.cons-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21377)

*Constraints*: 

- [(9.1)](#mdspan.extents.cons-9.1)

is_convertible_v<const OtherIndexType&, index_type> is true,

- [(9.2)](#mdspan.extents.cons-9.2)

is_nothrow_constructible_v<index_type, const OtherIndexType&> is true, and

- [(9.3)](#mdspan.extents.cons-9.3)

N == rank_dynamic() || N == rank() is true[.](#mdspan.extents.cons-9.sentence-1)

[10](#mdspan.extents.cons-10)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21388)

*Preconditions*: 

- [(10.1)](#mdspan.extents.cons-10.1)

If N != rank_dynamic() is true,exts[r] equals Er for each r for which Er is a static extent, and

- [(10.2)](#mdspan.extents.cons-10.2)

either
  * [(10.2.1)](#mdspan.extents.cons-10.2.1)

N is zero, or

  * [(10.2.2)](#mdspan.extents.cons-10.2.2)

exts[r] is representable
as a nonnegative value of type index_type for every rank index r[.](#mdspan.extents.cons-10.sentence-1)

[11](#mdspan.extents.cons-11)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21405)

*Effects*: 

- [(11.1)](#mdspan.extents.cons-11.1)

  If N equals rank_dynamic(),
for all d in the range [0, rank_dynamic()),
direct-non-list-initializes *dynamic-extents*[d] with as_const(exts[d])[.](#mdspan.extents.cons-11.1.sentence-1)

- [(11.2)](#mdspan.extents.cons-11.2)

  Otherwise, for all d in the range [0, rank_dynamic()),
direct-non-list-initializes *dynamic-extents*[d] with as_const(exts[*dynamic-index-inv*(d)])[.](#mdspan.extents.cons-11.2.sentence-1)

[ð](#lib:extents,constructor___)

`template<class... Integrals>
  explicit extents(Integrals...) -> see below;
`

[12](#mdspan.extents.cons-12)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21427)

*Constraints*: (is_convertible_v<Integrals, size_t> && ...) is true[.](#mdspan.extents.cons-12.sentence-1)

[13](#mdspan.extents.cons-13)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21431)

*Remarks*: The deduced type is extents<size_t, [*maybe-static-ext*](span.syn#concept:maybe-static-ext "23.7.2.1 Header <span> synopsis [span.syn]")<Integrals>...>[.](#mdspan.extents.cons-13.sentence-1)

#### [23.7.3.3.4](#mdspan.extents.obs) Observers of the multidimensional index space [[mdspan.extents.obs]](mdspan.extents.obs)

[ð](#lib:static_extent,extents)

`static constexpr size_t static_extent(rank_type i) noexcept;
`

[1](#mdspan.extents.obs-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21444)

*Preconditions*: i < rank() is true[.](#mdspan.extents.obs-1.sentence-1)

[2](#mdspan.extents.obs-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21448)

*Returns*: Ei[.](#mdspan.extents.obs-2.sentence-1)

[ð](#lib:extent,extents)

`constexpr index_type extent(rank_type i) const noexcept;
`

[3](#mdspan.extents.obs-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21459)

*Preconditions*: i < rank() is true[.](#mdspan.extents.obs-3.sentence-1)

[4](#mdspan.extents.obs-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21463)

*Returns*: Di[.](#mdspan.extents.obs-4.sentence-1)

#### [23.7.3.3.5](#mdspan.extents.cmp) Comparison operators [[mdspan.extents.cmp]](mdspan.extents.cmp)

[ð](#lib:operator==,extents)

`template<class OtherIndexType, size_t... OtherExtents>
  friend constexpr bool operator==(const extents& lhs,
                                   const extents<OtherIndexType, OtherExtents...>& rhs) noexcept;
`

[1](#mdspan.extents.cmp-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21478)

*Returns*: true if lhs.rank() equals rhs.rank() and
if lhs.extent(r) equals rhs.extent(r) for every rank index r of rhs,
otherwise false[.](#mdspan.extents.cmp-1.sentence-1)

#### [23.7.3.3.6](#mdspan.extents.dextents) Alias template dextents [[mdspan.extents.dextents]](mdspan.extents.dextents)

[ð](#lib:dextents)

`template<class IndexType, size_t Rank>
  using dextents = see below;
`

[1](#mdspan.extents.dextents-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21495)

*Result*: A type E that is a specialization of extents such that E​::​rank() == Rank && E​::​rank() == E​::​rank_dynamic() is true, andE​::​index_type denotes IndexType[.](#mdspan.extents.dextents-1.sentence-1)

#### [23.7.3.3.7](#mdspan.extents.dims) Alias template dims [[mdspan.extents.dims]](mdspan.extents.dims)

[ð](#lib:dims)

`template<size_t Rank, class IndexType = size_t>
  using dims = see below;
`

[1](#mdspan.extents.dims-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21511)

*Result*: A type E that is a specialization of extents such that E​::​rank() == Rank && E​::​rank() == E​::​rank_dynamic() is true, andE​::​index_type denotes IndexType[.](#mdspan.extents.dims-1.sentence-1)

#### [23.7.3.4](#mdspan.layout) Layout mapping [[mdspan.layout]](mdspan.layout)

#### [23.7.3.4.1](#mdspan.layout.general) General [[mdspan.layout.general]](mdspan.layout.general)

[1](#mdspan.layout.general-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21522)

In [[mdspan.layout.reqmts]](#mdspan.layout.reqmts "23.7.3.4.2 Requirements") and [[mdspan.layout.policy.reqmts]](#mdspan.layout.policy.reqmts "23.7.3.4.3 Layout mapping policy requirements"):

- [(1.1)](#mdspan.layout.general-1.1)

  M denotes a layout mapping class[.](#mdspan.layout.general-1.1.sentence-1)

- [(1.2)](#mdspan.layout.general-1.2)

  m denotes a (possibly const) value of type M[.](#mdspan.layout.general-1.2.sentence-1)

- [(1.3)](#mdspan.layout.general-1.3)

  i and j are packs of (possibly const) integers
that are multidimensional indices in m.extents() ([[mdspan.overview]](#mdspan.overview "23.7.3.1 Overview"))[.](#mdspan.layout.general-1.3.sentence-1)
  [*Note [1](#mdspan.layout.general-note-1)*:
  The type of each element of the packs can be a different integer type[.](#mdspan.layout.general-1.3.sentence-2)
 â *end note*]

- [(1.4)](#mdspan.layout.general-1.4)

  r is a (possibly const) rank index of typename M​::​extents_type[.](#mdspan.layout.general-1.4.sentence-1)

- [(1.5)](#mdspan.layout.general-1.5)

  dr is a pack of (possibly const) integers
for which sizeof...(dr) == M​::​extents_type​::​rank() is true,
the rth element is equal to 1, and
all other elements are equal to 0[.](#mdspan.layout.general-1.5.sentence-1)

[2](#mdspan.layout.general-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21549)

In [[mdspan.layout.reqmts]](#mdspan.layout.reqmts "23.7.3.4.2 Requirements") through [[mdspan.layout.stride]](#mdspan.layout.stride "23.7.3.4.7 Class template layout_­stride​::​mapping"):

- [(2.1)](#mdspan.layout.general-2.1)

Let *is-mapping-of* be the exposition-only variable template defined as follows:template<class Layout, class Mapping>constexpr bool *is-mapping-of* = // *exposition only* is_same_v<typename Layout::template mapping<typename Mapping::extents_type>, Mapping>;

- [(2.2)](#mdspan.layout.general-2.2)

Let *is-layout-left-padded-mapping-of* be
the exposition-only variable template defined as follows:template<class Mapping>constexpr bool *is-layout-left-padded-mapping-of* = *see below*; // *exposition only* where *is-layout-left-padded-mapping-of*<Mapping> is true if and only if Mapping denotes
a specialization of layout_left_padded<S>​::​mapping for some value S of type size_t.

- [(2.3)](#mdspan.layout.general-2.3)

Let *is-layout-right-padded-mapping-of* be
the exposition-only variable template defined as follows:template<class Mapping>constexpr bool *is-layout-right-padded-mapping-of* = *see below*; // *exposition only* where *is-layout-right-padded-mapping-of*<Mapping> is true if and only if Mapping denotes
a specialization of layout_right_padded<S>​::​mapping for some value S of type size_t.

- [(2.4)](#mdspan.layout.general-2.4)

For nonnegative integers x and y,
let LEAST-MULTIPLE-AT-LEAST(x,y) denote
  * [(2.4.1)](#mdspan.layout.general-2.4.1)

y if x is zero,

  * [(2.4.2)](#mdspan.layout.general-2.4.2)

otherwise, the least multiple of x that is greater than or equal to y.

#### [23.7.3.4.2](#mdspan.layout.reqmts) Requirements [[mdspan.layout.reqmts]](mdspan.layout.reqmts)

[1](#mdspan.layout.reqmts-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21594)

A type M meets the [*layout mapping*](#def:layout_mapping "23.7.3.4.2 Requirements [mdspan.layout.reqmts]") requirements if

- [(1.1)](#mdspan.layout.reqmts-1.1)

M models [copyable](concepts.object#concept:copyable "18.6 Object concepts [concepts.object]") and [equality_comparable](concept.equalitycomparable#concept:equality_comparable "18.5.4 Concept equality_­comparable [concept.equalitycomparable]"),

- [(1.2)](#mdspan.layout.reqmts-1.2)

is_nothrow_move_constructible_v<M> is true,

- [(1.3)](#mdspan.layout.reqmts-1.3)

is_nothrow_move_assignable_v<M> is true,

- [(1.4)](#mdspan.layout.reqmts-1.4)

is_nothrow_swappable_v<M> is true, and

- [(1.5)](#mdspan.layout.reqmts-1.5)

the following types and expressions are well-formed and
have the specified semantics.

[ð](#mdspan.layout.reqmts-itemdecl:1)

`typename M::extents_type
`

[2](#mdspan.layout.reqmts-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21616)

*Result*: A type that is a specialization of extents[.](#mdspan.layout.reqmts-2.sentence-1)

[ð](#mdspan.layout.reqmts-itemdecl:2)

`typename M::index_type
`

[3](#mdspan.layout.reqmts-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21626)

*Result*: typename M​::​extents_type​::​index_type[.](#mdspan.layout.reqmts-3.sentence-1)

[ð](#mdspan.layout.reqmts-itemdecl:3)

`typename M::rank_type
`

[4](#mdspan.layout.reqmts-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21636)

*Result*: typename M​::​extents_type​::​rank_type[.](#mdspan.layout.reqmts-4.sentence-1)

[ð](#mdspan.layout.reqmts-itemdecl:4)

`typename M::layout_type
`

[5](#mdspan.layout.reqmts-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21646)

*Result*: A type MP that meets
the layout mapping policy requirements ([[mdspan.layout.policy.reqmts]](#mdspan.layout.policy.reqmts "23.7.3.4.3 Layout mapping policy requirements")) and
for which *is-mapping-of*<MP, M> is true[.](#mdspan.layout.reqmts-5.sentence-1)

[ð](#mdspan.layout.reqmts-itemdecl:5)

`m.extents()
`

[6](#mdspan.layout.reqmts-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21658)

*Result*: const typename M​::​extents_type&

[ð](#mdspan.layout.reqmts-itemdecl:6)

`m(i...)
`

[7](#mdspan.layout.reqmts-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21668)

*Result*: typename M​::​index_type

[8](#mdspan.layout.reqmts-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21672)

*Returns*: A nonnegative integer
less than numeric_limits<typename M​::​index_type>​::​max() and
less than or equal to numeric_limits<size_t>​::​max()[.](#mdspan.layout.reqmts-8.sentence-1)

[ð](#mdspan.layout.reqmts-itemdecl:7)

`m(i...) == m(static_cast<typename M::index_type>(i)...)
`

[9](#mdspan.layout.reqmts-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21684)

*Result*: bool

[10](#mdspan.layout.reqmts-10)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21688)

*Returns*: true

[ð](#mdspan.layout.reqmts-itemdecl:8)

`m.required_span_size()
`

[11](#mdspan.layout.reqmts-11)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21698)

*Result*: typename M​::​index_type

[12](#mdspan.layout.reqmts-12)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21702)

*Returns*: If the size of the multidimensional index space m.extents() is 0,
then 0,
else 1 plus the maximum value of m(i...) for all i[.](#mdspan.layout.reqmts-12.sentence-1)

[ð](#mdspan.layout.reqmts-itemdecl:9)

`m.is_unique()
`

[13](#mdspan.layout.reqmts-13)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21714)

*Result*: bool

[14](#mdspan.layout.reqmts-14)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21718)

*Returns*: true only if
for every i and j where (i != j || ...) is true,m(i...) != m(j...) is true[.](#mdspan.layout.reqmts-14.sentence-1)

[*Note [1](#mdspan.layout.reqmts-note-1)*:

A mapping can return false even if the condition is met[.](#mdspan.layout.reqmts-14.sentence-2)

For certain layouts, it is possibly not feasible to determine efficiently
whether the layout is unique[.](#mdspan.layout.reqmts-14.sentence-3)

â *end note*]

[ð](#mdspan.layout.reqmts-itemdecl:10)

`m.is_exhaustive()
`

[15](#mdspan.layout.reqmts-15)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21735)

*Result*: bool

[16](#mdspan.layout.reqmts-16)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21739)

*Returns*: true only if
for all k in the range [0, m.required_span_size()) there exists an i such that m(i...) equals k[.](#mdspan.layout.reqmts-16.sentence-1)

[*Note [2](#mdspan.layout.reqmts-note-2)*:

A mapping can return false even if the condition is met[.](#mdspan.layout.reqmts-16.sentence-2)

For certain layouts, it is possibly not feasible to determine efficiently
whether the layout is exhaustive[.](#mdspan.layout.reqmts-16.sentence-3)

â *end note*]

[ð](#mdspan.layout.reqmts-itemdecl:11)

`m.is_strided()
`

[17](#mdspan.layout.reqmts-17)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21756)

*Result*: bool

[18](#mdspan.layout.reqmts-18)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21760)

*Returns*: true only if
for every rank index r of m.extents() there exists an integer sr such that,
for all i where (i+dr) is
a multidimensional index in m.extents() ([[mdspan.overview]](#mdspan.overview "23.7.3.1 Overview")),m((i + dr)...) - m(i...) equals sr[.](#mdspan.layout.reqmts-18.sentence-1)

[*Note [3](#mdspan.layout.reqmts-note-3)*:

This implies that for a strided layoutm(i0,â¦,ik)=m(0,â¦,0)+i0Ãs0+â¯+ikÃsk[.](#mdspan.layout.reqmts-18.sentence-2)

â *end note*]

[*Note [4](#mdspan.layout.reqmts-note-4)*:

A mapping can return false even if the condition is met[.](#mdspan.layout.reqmts-18.sentence-3)

For certain layouts, it is possibly not feasible to determine efficiently
whether the layout is strided[.](#mdspan.layout.reqmts-18.sentence-4)

â *end note*]

[ð](#mdspan.layout.reqmts-itemdecl:12)

`m.stride(r)
`

[19](#mdspan.layout.reqmts-19)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21784)

*Preconditions*: m.is_strided() is true[.](#mdspan.layout.reqmts-19.sentence-1)

[20](#mdspan.layout.reqmts-20)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21788)

*Result*: typename M​::​index_type

[21](#mdspan.layout.reqmts-21)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21792)

*Returns*: sr as defined in m.is_strided() above[.](#mdspan.layout.reqmts-21.sentence-1)

[22](#mdspan.layout.reqmts-22)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21796)

[*Note [5](#mdspan.layout.reqmts-note-5)*:

It is not required for m.stride(r) to be well-formed
if m.extents().rank() is zero,
even if m.is_always_strided() is true[.](#mdspan.layout.reqmts-22.sentence-1)

â *end note*]

[ð](#mdspan.layout.reqmts-itemdecl:13)

`M::is_always_unique()
`

[23](#mdspan.layout.reqmts-23)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21809)

*Result*: A constant expression ([[expr.const]](expr.const "7.7 Constant expressions")) of type bool[.](#mdspan.layout.reqmts-23.sentence-1)

[24](#mdspan.layout.reqmts-24)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21813)

*Returns*: true only if m.is_unique() is true for all possible objects m of type M[.](#mdspan.layout.reqmts-24.sentence-1)

[*Note [6](#mdspan.layout.reqmts-note-6)*:

A mapping can return false even if the above condition is met[.](#mdspan.layout.reqmts-24.sentence-2)

For certain layout mappings, it is possibly not feasible to determine
whether every instance is unique[.](#mdspan.layout.reqmts-24.sentence-3)

â *end note*]

[ð](#mdspan.layout.reqmts-itemdecl:14)

`M::is_always_exhaustive()
`

[25](#mdspan.layout.reqmts-25)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21829)

*Result*: A constant expression ([[expr.const]](expr.const "7.7 Constant expressions")) of type bool[.](#mdspan.layout.reqmts-25.sentence-1)

[26](#mdspan.layout.reqmts-26)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21833)

*Returns*: true only if m.is_exhaustive() is true for all possible objects m of type M[.](#mdspan.layout.reqmts-26.sentence-1)

[*Note [7](#mdspan.layout.reqmts-note-7)*:

A mapping can return false even if the above condition is met[.](#mdspan.layout.reqmts-26.sentence-2)

For certain layout mappings, it is possibly not feasible to determine
whether every instance is exhaustive[.](#mdspan.layout.reqmts-26.sentence-3)

â *end note*]

[ð](#mdspan.layout.reqmts-itemdecl:15)

`M::is_always_strided()
`

[27](#mdspan.layout.reqmts-27)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21849)

*Result*: A constant expression ([[expr.const]](expr.const "7.7 Constant expressions")) of type bool[.](#mdspan.layout.reqmts-27.sentence-1)

[28](#mdspan.layout.reqmts-28)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21853)

*Returns*: true only if m.is_strided() is true for all possible objects m of type M[.](#mdspan.layout.reqmts-28.sentence-1)

[*Note [8](#mdspan.layout.reqmts-note-8)*:

A mapping can return false even if the above condition is met[.](#mdspan.layout.reqmts-28.sentence-2)

For certain layout mappings, it is possibly not feasible to determine
whether every instance is strided[.](#mdspan.layout.reqmts-28.sentence-3)

â *end note*]

#### [23.7.3.4.3](#mdspan.layout.policy.reqmts) Layout mapping policy requirements [[mdspan.layout.policy.reqmts]](mdspan.layout.policy.reqmts)

[1](#mdspan.layout.policy.reqmts-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21866)

A type MP meets the [*layout mapping policy*](#def:layout_mapping_policy "23.7.3.4.3 Layout mapping policy requirements [mdspan.layout.policy.reqmts]") requirements
if for a type E that is a specialization of extents,MP​::​mapping<E> is valid and denotes a type X that meets the layout mapping requirements ([[mdspan.layout.reqmts]](#mdspan.layout.reqmts "23.7.3.4.2 Requirements")), and
for which the [*qualified-id*](expr.prim.id.qual#nt:qualified-id "7.5.5.3 Qualified names [expr.prim.id.qual]") X​::​layout_type is valid and
denotes the type MP and
the [*qualified-id*](expr.prim.id.qual#nt:qualified-id "7.5.5.3 Qualified names [expr.prim.id.qual]") X​::​extents_type denotes E[.](#mdspan.layout.policy.reqmts-1.sentence-1)

#### [23.7.3.4.4](#mdspan.layout.policy.overview) Layout mapping policies [[mdspan.layout.policy.overview]](mdspan.layout.policy.overview)

namespace std {struct layout_left {template<class Extents>class mapping; }; struct layout_right {template<class Extents>class mapping; }; struct layout_stride {template<class Extents>class mapping; }; template<size_t PaddingValue>struct layout_left_padded {template<class Extents> class mapping; }; template<size_t PaddingValue>struct layout_right_padded {template<class Extents> class mapping; };}

[1](#mdspan.layout.policy.overview-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21903)

Each of layout_left, layout_right, and layout_stride,
as well as each specialization oflayout_left_padded and layout_right_padded,
meets the layout mapping policy requirements and is a trivially copyable type[.](#mdspan.layout.policy.overview-1.sentence-1)

Furthermore,is_trivially_default_constructible_v<T> is true for any such type T[.](#mdspan.layout.policy.overview-1.sentence-2)

#### [23.7.3.4.5](#mdspan.layout.left) Class template layout_left​::​mapping [[mdspan.layout.left]](mdspan.layout.left)

#### [23.7.3.4.5.1](#mdspan.layout.left.overview) Overview [[mdspan.layout.left.overview]](mdspan.layout.left.overview)

[1](#mdspan.layout.left.overview-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21916)

layout_left provides a layout mapping
where the leftmost extent has stride 1, and
strides increase left-to-right as the product of extents[.](#mdspan.layout.left.overview-1.sentence-1)

namespace std {template<class 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; // [[mdspan.layout.left.cons]](#mdspan.layout.left.cons "23.7.3.4.5.2 Constructors"), constructorsconstexpr mapping() noexcept = default; constexpr mapping(const mapping&) noexcept = default; constexpr mapping(const extents_type&) noexcept; template<class OtherExtents>constexpr explicit(!is_convertible_v<OtherExtents, extents_type>) mapping(const mapping<OtherExtents>&) noexcept; template<class OtherExtents>constexpr explicit(!is_convertible_v<OtherExtents, extents_type>) mapping(const layout_right::mapping<OtherExtents>&) noexcept; template<class LayoutLeftPaddedMapping>constexpr explicit(!is_convertible_v<typename LayoutLeftPaddedMapping::extents_type,
 extents_type>) mapping(const LayoutLeftPaddedMapping&) noexcept; template<class OtherExtents>constexpr explicit(extents_type::rank() > 0) mapping(const layout_stride::mapping<OtherExtents>&); constexpr mapping& operator=(const mapping&) noexcept = default; // [[mdspan.layout.left.obs]](#mdspan.layout.left.obs "23.7.3.4.5.3 Observers"), observersconstexpr const extents_type& extents() const noexcept { return *extents_*; }constexpr index_type required_span_size() const noexcept; template<class... Indices>constexpr index_type operator()(Indices...) const noexcept; 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) const noexcept; template<class OtherExtents>friend constexpr bool operator==(const mapping&, const mapping<OtherExtents>&) noexcept; private: extents_type *extents_*{}; // *exposition only*// [[mdspan.sub.map]](#mdspan.sub.map "23.7.3.7.6 Specializations of submdspan_­mapping"), submdspan mapping specializationtemplate<class... SliceSpecifiers>constexpr auto *submdspan-mapping-impl*(SliceSpecifiers...) const // *exposition only*-> *see below*; template<class... SliceSpecifiers>friend constexpr auto submdspan_mapping(const mapping& src, SliceSpecifiers... slices) {return src.*submdspan-mapping-impl*(slices...); }};}

[2](#mdspan.layout.left.overview-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21990)

If Extents is not a specialization of extents,
then the program is ill-formed[.](#mdspan.layout.left.overview-2.sentence-1)

[3](#mdspan.layout.left.overview-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21994)

layout_left​::​mapping<E> is a trivially copyable type
that models [regular](concepts.object#concept:regular "18.6 Object concepts [concepts.object]") for each E[.](#mdspan.layout.left.overview-3.sentence-1)

[4](#mdspan.layout.left.overview-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21998)

*Mandates*: If Extents​::​rank_dynamic() == 0 is true,
then the size of the multidimensional index space Extents() is representable as a value of type typename Extents​::​index_type[.](#mdspan.layout.left.overview-4.sentence-1)

#### [23.7.3.4.5.2](#mdspan.layout.left.cons) Constructors [[mdspan.layout.left.cons]](mdspan.layout.left.cons)

[ð](#lib:layout_left::mapping,constructor)

`constexpr mapping(const extents_type& e) noexcept;
`

[1](#mdspan.layout.left.cons-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22012)

*Preconditions*: The size of the multidimensional index space e is representable as a value of type index_type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#mdspan.layout.left.cons-1.sentence-1)

[2](#mdspan.layout.left.cons-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22017)

*Effects*: Direct-non-list-initializes *extents_* with e[.](#mdspan.layout.left.cons-2.sentence-1)

[ð](#lib:layout_left::mapping,constructor_)

`template<class OtherExtents>
  constexpr explicit(!is_convertible_v<OtherExtents, extents_type>)
    mapping(const mapping<OtherExtents>& other) noexcept;
`

[3](#mdspan.layout.left.cons-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22030)

*Constraints*: is_constructible_v<extents_type, OtherExtents> is true[.](#mdspan.layout.left.cons-3.sentence-1)

[4](#mdspan.layout.left.cons-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22034)

*Preconditions*: other.required_span_size() is representable as
a value of type index_type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#mdspan.layout.left.cons-4.sentence-1)

[5](#mdspan.layout.left.cons-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22039)

*Effects*: Direct-non-list-initializes *extents_* with other.extents()[.](#mdspan.layout.left.cons-5.sentence-1)

[ð](#lib:layout_left::mapping,constructor__)

`template<class OtherExtents>
  constexpr explicit(!is_convertible_v<OtherExtents, extents_type>)
    mapping(const layout_right::mapping<OtherExtents>& other) noexcept;
`

[6](#mdspan.layout.left.cons-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22052)

*Constraints*: 

- [(6.1)](#mdspan.layout.left.cons-6.1)

extents_type​::​rank() <= 1 is true, and

- [(6.2)](#mdspan.layout.left.cons-6.2)

is_constructible_v<extents_type, OtherExtents> is true[.](#mdspan.layout.left.cons-6.sentence-1)

[7](#mdspan.layout.left.cons-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22061)

*Preconditions*: other.required_span_size() is representable as
a value of type index_type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#mdspan.layout.left.cons-7.sentence-1)

[8](#mdspan.layout.left.cons-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22066)

*Effects*: Direct-non-list-initializes *extents_* with other.extents()[.](#mdspan.layout.left.cons-8.sentence-1)

[ð](#lib:layout_left::mapping,constructor___)

`template<class LayoutLeftPaddedMapping>
  constexpr explicit(!is_convertible_v<typename LayoutLeftPaddedMapping::extents_type,
                                       extents_type>)
    mapping(const LayoutLeftPaddedMapping&) noexcept;
`

[9](#mdspan.layout.left.cons-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22080)

*Constraints*: 

- [(9.1)](#mdspan.layout.left.cons-9.1)

  *is-layout-left-padded-mapping-of*<LayoutLeftPaddedMapping> is true[.](#mdspan.layout.left.cons-9.1.sentence-1)

- [(9.2)](#mdspan.layout.left.cons-9.2)

  is_constructible_v<extents_type, typename LayoutLeftPaddedMapping​::​extents_type>  
is true[.](#mdspan.layout.left.cons-9.2.sentence-1)

[10](#mdspan.layout.left.cons-10)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22089)

*Mandates*: If

- [(10.1)](#mdspan.layout.left.cons-10.1)

Extents​::​rank() is greater than one,

- [(10.2)](#mdspan.layout.left.cons-10.2)

Extents​::​static_extent(0) does not equal dynamic_extent, and

- [(10.3)](#mdspan.layout.left.cons-10.3)

LayoutLeftPaddedMapping​::​*static-padding-stride* does not equal dynamic_extent,

then Extents​::​static_extent(0) equalsLayoutLeftPaddedMapping​::​*static-padding-stride*[.](#mdspan.layout.left.cons-10.sentence-1)

[11](#mdspan.layout.left.cons-11)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22104)

*Preconditions*: 

- [(11.1)](#mdspan.layout.left.cons-11.1)

  If extents_type​::​rank() > 1 is true,
then other.stride(1) equals other.extents(0)[.](#mdspan.layout.left.cons-11.1.sentence-1)

- [(11.2)](#mdspan.layout.left.cons-11.2)

  other.required_span_size() is representable as
a value of type index_type[.](#mdspan.layout.left.cons-11.2.sentence-1)

[12](#mdspan.layout.left.cons-12)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22115)

*Effects*: Direct-non-list-initializes extents_ with other.extents()[.](#mdspan.layout.left.cons-12.sentence-1)

[ð](#lib:layout_left::mapping,constructor____)

`template<class OtherExtents>
  constexpr explicit(extents_type::rank() > 0)
    mapping(const layout_stride::mapping<OtherExtents>& other);
`

[13](#mdspan.layout.left.cons-13)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22128)

*Constraints*: is_constructible_v<extents_type, OtherExtents> is true[.](#mdspan.layout.left.cons-13.sentence-1)

[14](#mdspan.layout.left.cons-14)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22132)

*Preconditions*: 

- [(14.1)](#mdspan.layout.left.cons-14.1)

If extents_type​::​rank() > 0 is true,
then for all r in the range [0, extents_type​::​rank()),other.stride(r) equalsother.extents().*fwd-prod-of-extents*(r), and

- [(14.2)](#mdspan.layout.left.cons-14.2)

other.required_span_size() is representable as
a value of type index_type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#mdspan.layout.left.cons-14.sentence-1)

[15](#mdspan.layout.left.cons-15)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22145)

*Effects*: Direct-non-list-initializes *extents_* with other.extents()[.](#mdspan.layout.left.cons-15.sentence-1)

#### [23.7.3.4.5.3](#mdspan.layout.left.obs) Observers [[mdspan.layout.left.obs]](mdspan.layout.left.obs)

[ð](#lib:required_span_size,layout_left::mapping)

`constexpr index_type required_span_size() const noexcept;
`

[1](#mdspan.layout.left.obs-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22158)

*Returns*: extents().*fwd-prod-of-extents*(extents_type​::​rank())[.](#mdspan.layout.left.obs-1.sentence-1)

[ð](#lib:operator(),layout_left::mapping)

`template<class... Indices>
  constexpr index_type operator()(Indices... i) const noexcept;
`

[2](#mdspan.layout.left.obs-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22170)

*Constraints*: 

- [(2.1)](#mdspan.layout.left.obs-2.1)

sizeof...(Indices) == extents_type​::​rank() is true,

- [(2.2)](#mdspan.layout.left.obs-2.2)

(is_convertible_v<Indices, index_type> && ...) is true, and

- [(2.3)](#mdspan.layout.left.obs-2.3)

(is_nothrow_constructible_v<index_type, Indices> && ...) is true[.](#mdspan.layout.left.obs-2.sentence-1)

[3](#mdspan.layout.left.obs-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22181)

*Preconditions*: extents_type​::​*index-cast*(i) is
a multidimensional index in *extents_* ([[mdspan.overview]](#mdspan.overview "23.7.3.1 Overview"))[.](#mdspan.layout.left.obs-3.sentence-1)

[4](#mdspan.layout.left.obs-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22186)

*Effects*: Let P be a parameter pack such thatis_same_v<index_sequence_for<Indices...>, index_sequence<P...>> is true[.](#mdspan.layout.left.obs-4.sentence-1)

Equivalent to:return ((static_cast<index_type>(i) * stride(P)) + ... + 0);

[ð](#lib:stride,layout_left::mapping)

`constexpr index_type stride(rank_type i) const noexcept;
`

[5](#mdspan.layout.left.obs-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22205)

*Constraints*: extents_type​::​rank() > 0 is true[.](#mdspan.layout.left.obs-5.sentence-1)

[6](#mdspan.layout.left.obs-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22209)

*Preconditions*: i < extents_type​::​rank() is true[.](#mdspan.layout.left.obs-6.sentence-1)

[7](#mdspan.layout.left.obs-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22213)

*Returns*: extents().*fwd-prod-of-extents*(i)[.](#mdspan.layout.left.obs-7.sentence-1)

[ð](#lib:operator==,layout_left::mapping)

`template<class OtherExtents>
  friend constexpr bool operator==(const mapping& x, const mapping<OtherExtents>& y) noexcept;
`

[8](#mdspan.layout.left.obs-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22225)

*Constraints*: extents_type​::​rank() == OtherExtents​::​rank() is true[.](#mdspan.layout.left.obs-8.sentence-1)

[9](#mdspan.layout.left.obs-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22229)

*Effects*: Equivalent to: return x.extents() == y.extents();

#### [23.7.3.4.6](#mdspan.layout.right) Class template layout_right​::​mapping [[mdspan.layout.right]](mdspan.layout.right)

#### [23.7.3.4.6.1](#mdspan.layout.right.overview) Overview [[mdspan.layout.right.overview]](mdspan.layout.right.overview)

[1](#mdspan.layout.right.overview-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22238)

layout_right provides a layout mapping
where the rightmost extent is stride 1, and
strides increase right-to-left as the product of extents[.](#mdspan.layout.right.overview-1.sentence-1)

namespace std {template<class 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; // [[mdspan.layout.right.cons]](#mdspan.layout.right.cons "23.7.3.4.6.2 Constructors"), constructorsconstexpr mapping() noexcept = default; constexpr mapping(const mapping&) noexcept = default; constexpr mapping(const extents_type&) noexcept; template<class OtherExtents>constexpr explicit(!is_convertible_v<OtherExtents, extents_type>) mapping(const mapping<OtherExtents>&) noexcept; template<class OtherExtents>constexpr explicit(!is_convertible_v<OtherExtents, extents_type>) mapping(const layout_left::mapping<OtherExtents>&) noexcept; template<class LayoutRightPaddedMapping>constexpr explicit(!is_convertible_v<typename LayoutRightPaddedMapping::extents_type,
 extents_type>) mapping(const LayoutRightPaddedMapping&) noexcept; template<class OtherExtents>constexpr explicit(extents_type::rank() > 0) mapping(const layout_stride::mapping<OtherExtents>&) noexcept; constexpr mapping& operator=(const mapping&) noexcept = default; // [[mdspan.layout.right.obs]](#mdspan.layout.right.obs "23.7.3.4.6.3 Observers"), observersconstexpr const extents_type& extents() const noexcept { return *extents_*; }constexpr index_type required_span_size() const noexcept; template<class... Indices>constexpr index_type operator()(Indices...) const noexcept; 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) const noexcept; template<class OtherExtents>friend constexpr bool operator==(const mapping&, const mapping<OtherExtents>&) noexcept; private: extents_type *extents_*{}; // *exposition only*// [[mdspan.sub.map]](#mdspan.sub.map "23.7.3.7.6 Specializations of submdspan_­mapping"), submdspan mapping specializationtemplate<class... SliceSpecifiers>constexpr auto *submdspan-mapping-impl*(SliceSpecifiers...) const // *exposition only*-> *see below*; template<class... SliceSpecifiers>friend constexpr auto submdspan_mapping(const mapping& src, SliceSpecifiers... slices) {return src.*submdspan-mapping-impl*(slices...); }};}

[2](#mdspan.layout.right.overview-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22312)

If Extents is not a specialization of extents,
then the program is ill-formed[.](#mdspan.layout.right.overview-2.sentence-1)

[3](#mdspan.layout.right.overview-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22316)

layout_right​::​mapping<E> is a trivially copyable type
that models [regular](concepts.object#concept:regular "18.6 Object concepts [concepts.object]") for each E[.](#mdspan.layout.right.overview-3.sentence-1)

[4](#mdspan.layout.right.overview-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22320)

*Mandates*: If Extents​::​rank_dynamic() == 0 is true,
then the size of the multidimensional index space Extents() is representable as a value of type typename Extents​::​index_type[.](#mdspan.layout.right.overview-4.sentence-1)

#### [23.7.3.4.6.2](#mdspan.layout.right.cons) Constructors [[mdspan.layout.right.cons]](mdspan.layout.right.cons)

[ð](#lib:layout_right::mapping,constructor)

`constexpr mapping(const extents_type& e) noexcept;
`

[1](#mdspan.layout.right.cons-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22334)

*Preconditions*: The size of the multidimensional index space e is representable as
a value of type index_type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#mdspan.layout.right.cons-1.sentence-1)

[2](#mdspan.layout.right.cons-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22339)

*Effects*: Direct-non-list-initializes *extents_* with e[.](#mdspan.layout.right.cons-2.sentence-1)

[ð](#lib:layout_right::mapping,constructor_)

`template<class OtherExtents>
  constexpr explicit(!is_convertible_v<OtherExtents, extents_type>)
    mapping(const mapping<OtherExtents>& other) noexcept;
`

[3](#mdspan.layout.right.cons-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22352)

*Constraints*: is_constructible_v<extents_type, OtherExtents> is true[.](#mdspan.layout.right.cons-3.sentence-1)

[4](#mdspan.layout.right.cons-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22356)

*Preconditions*: other.required_span_size() is representable as
a value of type index_type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#mdspan.layout.right.cons-4.sentence-1)

[5](#mdspan.layout.right.cons-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22361)

*Effects*: Direct-non-list-initializes *extents_* with other.extents()[.](#mdspan.layout.right.cons-5.sentence-1)

[ð](#lib:layout_right::mapping,constructor__)

`template<class OtherExtents>
  constexpr explicit(!is_convertible_v<OtherExtents, extents_type>)
    mapping(const layout_left::mapping<OtherExtents>& other) noexcept;
`

[6](#mdspan.layout.right.cons-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22374)

*Constraints*: 

- [(6.1)](#mdspan.layout.right.cons-6.1)

extents_type​::​rank() <= 1 is true, and

- [(6.2)](#mdspan.layout.right.cons-6.2)

is_constructible_v<extents_type, OtherExtents> is true[.](#mdspan.layout.right.cons-6.sentence-1)

[7](#mdspan.layout.right.cons-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22383)

*Preconditions*: other.required_span_size() is representable as
a value of type index_type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#mdspan.layout.right.cons-7.sentence-1)

[8](#mdspan.layout.right.cons-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22388)

*Effects*: Direct-non-list-initializes *extents_* with other.extents()[.](#mdspan.layout.right.cons-8.sentence-1)

[ð](#lib:layout_right::mapping,constructor___)

`template<class LayoutRightPaddedMapping>
  constexpr explicit(!is_convertible_v<typename LayoutRightPaddedMapping::extents_type,
                                       extents_type>)
    mapping(const LayoutRightPaddedMapping&) noexcept;
`

[9](#mdspan.layout.right.cons-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22402)

*Constraints*: 

- [(9.1)](#mdspan.layout.right.cons-9.1)

  *is-layout-right-padded-mapping-of*<LayoutRightPaddedMapping> is true[.](#mdspan.layout.right.cons-9.1.sentence-1)

- [(9.2)](#mdspan.layout.right.cons-9.2)

  is_constructible_v<extents_type, typename LayoutRightPaddedMapping​::​extents_-  
type> is true[.](#mdspan.layout.right.cons-9.2.sentence-1)

[10](#mdspan.layout.right.cons-10)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22413)

*Mandates*: If

- [(10.1)](#mdspan.layout.right.cons-10.1)

Extents​::​rank() is greater than one,

- [(10.2)](#mdspan.layout.right.cons-10.2)

Extents​::​static_extent(Extents​::​rank() - 1) does not equal dynamic_extent, and

- [(10.3)](#mdspan.layout.right.cons-10.3)

LayoutRightPaddedMapping​::​*static-padding-stride* does not equal dynamic_extent,

then Extents​::​static_extent(Extents​::​rank() - 1) equalsLayoutRightPaddedMapping​::​*static-padding-stride*[.](#mdspan.layout.right.cons-10.sentence-1)

[11](#mdspan.layout.right.cons-11)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22429)

*Preconditions*: 

- [(11.1)](#mdspan.layout.right.cons-11.1)

  If extents_type​::​rank() > 1 is true,
then other.stride(extents_type​::​rank() - 2)  
equalsother.extents().extent(extents_type​::​rank() - 1)[.](#mdspan.layout.right.cons-11.1.sentence-1)

- [(11.2)](#mdspan.layout.right.cons-11.2)

  other.required_span_size() is representable as
a value of type index_type[.](#mdspan.layout.right.cons-11.2.sentence-1)

[12](#mdspan.layout.right.cons-12)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22441)

*Effects*: Direct-non-list-initializes extents_ with other.extents()[.](#mdspan.layout.right.cons-12.sentence-1)

[ð](#lib:layout_right::mapping,constructor____)

`template<class OtherExtents>
 constexpr explicit(extents_type::rank() > 0)
    mapping(const layout_stride::mapping<OtherExtents>& other) noexcept;
`

[13](#mdspan.layout.right.cons-13)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22454)

*Constraints*: is_constructible_v<extents_type, OtherExtents> is true[.](#mdspan.layout.right.cons-13.sentence-1)

[14](#mdspan.layout.right.cons-14)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22458)

*Preconditions*: 

- [(14.1)](#mdspan.layout.right.cons-14.1)

  If extents_type​::​rank() > 0 is true,
then for all r in the range [0, extents_type​::​rank()),other.stride(r) equalsother.extents().*rev-prod-of-extents*(r)[.](#mdspan.layout.right.cons-14.1.sentence-1)

- [(14.2)](#mdspan.layout.right.cons-14.2)

  other.required_span_size() is representable as
a value of type index_type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#mdspan.layout.right.cons-14.2.sentence-1)

[15](#mdspan.layout.right.cons-15)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22471)

*Effects*: Direct-non-list-initializes *extents_* with other.extents()[.](#mdspan.layout.right.cons-15.sentence-1)

#### [23.7.3.4.6.3](#mdspan.layout.right.obs) Observers [[mdspan.layout.right.obs]](mdspan.layout.right.obs)

[ð](#lib:required_span_size,layout_right::mapping)

`constexpr index_type required_span_size() const noexcept;
`

[1](#mdspan.layout.right.obs-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22484)

*Returns*: extents().*fwd-prod-of-extents*(extents_type​::​rank())[.](#mdspan.layout.right.obs-1.sentence-1)

[ð](#lib:operator(),layout_right::mapping)

`template<class... Indices>
  constexpr index_type operator()(Indices... i) const noexcept;
`

[2](#mdspan.layout.right.obs-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22496)

*Constraints*: 

- [(2.1)](#mdspan.layout.right.obs-2.1)

sizeof...(Indices) == extents_type​::​rank() is true,

- [(2.2)](#mdspan.layout.right.obs-2.2)

(is_convertible_v<Indices, index_type> && ...) is true, and

- [(2.3)](#mdspan.layout.right.obs-2.3)

(is_nothrow_constructible_v<index_type, Indices> && ...) istrue[.](#mdspan.layout.right.obs-2.sentence-1)

[3](#mdspan.layout.right.obs-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22508)

*Preconditions*: extents_type​::​*index-cast*(i) is
a multidimensional index in *extents_* ([[mdspan.overview]](#mdspan.overview "23.7.3.1 Overview"))[.](#mdspan.layout.right.obs-3.sentence-1)

[4](#mdspan.layout.right.obs-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22513)

*Effects*: Let P be a parameter pack such thatis_same_v<index_sequence_for<Indices...>, index_sequence<P...>> is true[.](#mdspan.layout.right.obs-4.sentence-1)

Equivalent to:return ((static_cast<index_type>(i) * stride(P)) + ... + 0);

[ð](#lib:stride,layout_right::mapping)

`constexpr index_type stride(rank_type i) const noexcept;
`

[5](#mdspan.layout.right.obs-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22531)

*Constraints*: extents_type​::​rank() > 0 is true[.](#mdspan.layout.right.obs-5.sentence-1)

[6](#mdspan.layout.right.obs-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22535)

*Preconditions*: i < extents_type​::​rank() is true[.](#mdspan.layout.right.obs-6.sentence-1)

[7](#mdspan.layout.right.obs-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22539)

*Returns*: extents().*rev-prod-of-extents*(i)[.](#mdspan.layout.right.obs-7.sentence-1)

[ð](#lib:operator==,layout_right::mapping)

`template<class OtherExtents>
  friend constexpr bool operator==(const mapping& x, const mapping<OtherExtents>& y) noexcept;
`

[8](#mdspan.layout.right.obs-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22551)

*Constraints*: extents_type​::​rank() == OtherExtents​::​rank() is true[.](#mdspan.layout.right.obs-8.sentence-1)

[9](#mdspan.layout.right.obs-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22555)

*Effects*: Equivalent to: return x.extents() == y.extents();

#### [23.7.3.4.7](#mdspan.layout.stride) Class template layout_stride​::​mapping [[mdspan.layout.stride]](mdspan.layout.stride)

#### [23.7.3.4.7.1](#mdspan.layout.stride.overview) Overview [[mdspan.layout.stride.overview]](mdspan.layout.stride.overview)

[1](#mdspan.layout.stride.overview-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22564)

layout_stride provides a layout mapping
where the strides are user-defined[.](#mdspan.layout.stride.overview-1.sentence-1)

namespace std {template<class 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; private:static constexpr rank_type *rank_* = extents_type::rank(); // *exposition only*public:// [[mdspan.layout.stride.cons]](#mdspan.layout.stride.cons "23.7.3.4.7.3 Constructors"), constructorsconstexpr mapping() noexcept; constexpr mapping(const mapping&) noexcept = default; template<class OtherIndexType>constexpr mapping(const extents_type&, span<OtherIndexType, *rank_*>) noexcept; template<class OtherIndexType>constexpr mapping(const extents_type&, const array<OtherIndexType, *rank_*>&) noexcept; template<class StridedLayoutMapping>constexpr explicit(*see below*) mapping(const StridedLayoutMapping&) noexcept; constexpr mapping& operator=(const mapping&) noexcept = default; // [[mdspan.layout.stride.obs]](#mdspan.layout.stride.obs "23.7.3.4.7.4 Observers"), observersconstexpr const extents_type& extents() const noexcept { return *extents_*; }constexpr array<index_type, *rank_*> strides() const noexcept { return *strides_*; }constexpr index_type required_span_size() const noexcept; template<class... Indices>constexpr index_type operator()(Indices...) const noexcept; static constexpr bool is_always_unique() noexcept { return true; }static constexpr bool is_always_exhaustive() noexcept { return false; }static constexpr bool is_always_strided() noexcept { return true; }static constexpr bool is_unique() noexcept { return true; }constexpr bool is_exhaustive() const noexcept; static constexpr bool is_strided() noexcept { return true; }constexpr index_type stride(rank_type i) const noexcept { return *strides_*[i]; }template<class OtherMapping>friend constexpr bool operator==(const mapping&, const OtherMapping&) noexcept; private: extents_type *extents_*{}; // *exposition only* array<index_type, *rank_*> *strides_*{}; // *exposition only*// [[mdspan.sub.map]](#mdspan.sub.map "23.7.3.7.6 Specializations of submdspan_­mapping"), submdspan mapping specializationtemplate<class... SliceSpecifiers>constexpr auto *submdspan-mapping-impl*(SliceSpecifiers...) const // *exposition only*-> *see below*; template<class... SliceSpecifiers>friend constexpr auto submdspan_mapping(const mapping& src, SliceSpecifiers... slices) {return src.*submdspan-mapping-impl*(slices...); }};}

[2](#mdspan.layout.stride.overview-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22636)

If Extents is not a specialization of extents,
then the program is ill-formed[.](#mdspan.layout.stride.overview-2.sentence-1)

[3](#mdspan.layout.stride.overview-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22640)

layout_stride​::​mapping<E> is a trivially copyable type
that models [regular](concepts.object#concept:regular "18.6 Object concepts [concepts.object]") for each E[.](#mdspan.layout.stride.overview-3.sentence-1)

[4](#mdspan.layout.stride.overview-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22644)

*Mandates*: If Extents​::​rank_dynamic() == 0 is true,
then the size of the multidimensional index space Extents() is representable as a value of type typename Extents​::​index_type[.](#mdspan.layout.stride.overview-4.sentence-1)

#### [23.7.3.4.7.2](#mdspan.layout.stride.expo) Exposition-only helpers [[mdspan.layout.stride.expo]](mdspan.layout.stride.expo)

[1](#mdspan.layout.stride.expo-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22652)

Let *REQUIRED-SPAN-SIZE*(e, strides) be:

- [(1.1)](#mdspan.layout.stride.expo-1.1)

1, if e.rank() == 0 is true,

- [(1.2)](#mdspan.layout.stride.expo-1.2)

otherwise 0, if the size of the multidimensional index space e is 0,

- [(1.3)](#mdspan.layout.stride.expo-1.3)

otherwise 1 plus the sum of products of(e.extent(r) - 1) andextents_type::*index-cast*(strides[r]) for all r in the range [0, e.rank())[.](#mdspan.layout.stride.expo-1.sentence-1)

[2](#mdspan.layout.stride.expo-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22668)

Let *OFFSET*(m) be:

- [(2.1)](#mdspan.layout.stride.expo-2.1)

m(), if e.rank() == 0 is true,

- [(2.2)](#mdspan.layout.stride.expo-2.2)

otherwise 0, if the size of the multidimensional index space e is 0,

- [(2.3)](#mdspan.layout.stride.expo-2.3)

otherwise m(z...) for a pack of integers z that is a multidimensional index in m.extents() and
each element of z equals 0[.](#mdspan.layout.stride.expo-2.sentence-1)

[3](#mdspan.layout.stride.expo-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22681)

Let *is-extents* be the exposition-only variable template
defined as follows:template<class T>constexpr bool *is-extents* = false; // *exposition only*template<class IndexType, size_t... Args>constexpr bool *is-extents*<extents<IndexType, Args...>> = true; // *exposition only*

[4](#mdspan.layout.stride.expo-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22691)

Let [*layout-mapping-alike*](#concept:layout-mapping-alike "23.7.3.4.7.2 Exposition-only helpers [mdspan.layout.stride.expo]") be the exposition-only concept
defined as follows:template<class M>concept [*layout-mapping-alike*](#concept:layout-mapping-alike "23.7.3.4.7.2 Exposition-only helpers [mdspan.layout.stride.expo]") = requires { // *exposition only*requires *is-extents*<typename M::extents_type>; { M::is_always_strided() } -> [same_as](concept.same#concept:same_as "18.4.2 Concept same_­as [concept.same]")<bool>; { M::is_always_exhaustive() } -> [same_as](concept.same#concept:same_as "18.4.2 Concept same_­as [concept.same]")<bool>; { M::is_always_unique() } -> [same_as](concept.same#concept:same_as "18.4.2 Concept same_­as [concept.same]")<bool>;
 bool_constant<M::is_always_strided()>::value;
 bool_constant<M::is_always_exhaustive()>::value;
 bool_constant<M::is_always_unique()>::value;};

[*Note [1](#mdspan.layout.stride.expo-note-1)*:

This concept checks that the functionsM​::​is_always_strided(),M​::​is_always_exhaustive(), andM​::​is_always_unique() exist,
are constant expressions, and
have a return type of bool[.](#mdspan.layout.stride.expo-4.sentence-1)

â *end note*]

#### [23.7.3.4.7.3](#mdspan.layout.stride.cons) Constructors [[mdspan.layout.stride.cons]](mdspan.layout.stride.cons)

[ð](#lib:layout_stride::mapping,constructor)

`constexpr mapping() noexcept;
`

[1](#mdspan.layout.stride.cons-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22723)

*Preconditions*: layout_right​::​mapping<extents_type>().required_span_size() is representable as a value of type index_type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#mdspan.layout.stride.cons-1.sentence-1)

[2](#mdspan.layout.stride.cons-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22728)

*Effects*: Direct-non-list-initializes *extents_* with extents_type(), and
for all d in the range [0, *rank_*),
direct-non-list-initializes *strides_*[d] withlayout_right​::​mapping<extents_type>().stride(d)[.](#mdspan.layout.stride.cons-2.sentence-1)

[ð](#lib:layout_stride::mapping,constructor_)

`template<class OtherIndexType>
  constexpr mapping(const extents_type& e, span<OtherIndexType, rank_> s) noexcept;
template<class OtherIndexType>
  constexpr mapping(const extents_type& e, const array<OtherIndexType, rank_>& s) noexcept;
`

[3](#mdspan.layout.stride.cons-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22745)

*Constraints*: 

- [(3.1)](#mdspan.layout.stride.cons-3.1)

is_convertible_v<const OtherIndexType&, index_type> is true, and

- [(3.2)](#mdspan.layout.stride.cons-3.2)

is_nothrow_constructible_v<index_type, const OtherIndexType&> is true[.](#mdspan.layout.stride.cons-3.sentence-1)

[4](#mdspan.layout.stride.cons-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22754)

*Preconditions*: 

- [(4.1)](#mdspan.layout.stride.cons-4.1)

  The result of converting s[i] to index_type is greater than 0 for all i in the range [0, *rank_*)[.](#mdspan.layout.stride.cons-4.1.sentence-1)

- [(4.2)](#mdspan.layout.stride.cons-4.2)

  *REQUIRED-SPAN-SIZE*(e, s) is representable
as a value of type index_type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#mdspan.layout.stride.cons-4.2.sentence-1)

- [(4.3)](#mdspan.layout.stride.cons-4.3)

  If *rank_* is greater than 0,
then there exists a permutation P of the integers
in the range [0, *rank_*),
such that s[pi] >= s[piâ1] * e.extent(piâ1) is true for all i in the range [1, *rank_*),
where pi is the ith element of P[.](#mdspan.layout.stride.cons-4.3.sentence-1)
  [*Note [1](#mdspan.layout.stride.cons-note-1)*:
  For layout_stride,
this condition is necessary and sufficient
for is_unique() to be true[.](#mdspan.layout.stride.cons-4.3.sentence-2)
 â *end note*]

[5](#mdspan.layout.stride.cons-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22778)

*Effects*: Direct-non-list-initializes *extents_* with e, and
for all d in the range [0, *rank_*),
direct-non-list-initializes strides_[d] with as_const(s[d])[.](#mdspan.layout.stride.cons-5.sentence-1)

[ð](#lib:layout_stride::mapping,constructor__)

`template<class StridedLayoutMapping>
  constexpr explicit(see below)
    mapping(const StridedLayoutMapping& other) noexcept;
`

[6](#mdspan.layout.stride.cons-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22793)

*Constraints*: 

- [(6.1)](#mdspan.layout.stride.cons-6.1)

  [*layout-mapping-alike*](#concept:layout-mapping-alike "23.7.3.4.7.2 Exposition-only helpers [mdspan.layout.stride.expo]")<StridedLayoutMapping> is satisfied[.](#mdspan.layout.stride.cons-6.1.sentence-1)

- [(6.2)](#mdspan.layout.stride.cons-6.2)

  is_constructible_v<extents_type, typename StridedLayoutMapping​::​extents_type> is  
  true[.](#mdspan.layout.stride.cons-6.2.sentence-2)

- [(6.3)](#mdspan.layout.stride.cons-6.3)

  StridedLayoutMapping​::​is_always_unique() is true[.](#mdspan.layout.stride.cons-6.3.sentence-1)

- [(6.4)](#mdspan.layout.stride.cons-6.4)

  StridedLayoutMapping​::​is_always_strided() is true[.](#mdspan.layout.stride.cons-6.4.sentence-1)

[7](#mdspan.layout.stride.cons-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22806)

*Preconditions*: 

- [(7.1)](#mdspan.layout.stride.cons-7.1)

StridedLayoutMapping meets the layout mapping requirements ([[mdspan.layout.reqmts]](#mdspan.layout.reqmts "23.7.3.4.2 Requirements")),

- [(7.2)](#mdspan.layout.stride.cons-7.2)

other.stride(r) > 0 is true for every rank index r of extents(),

- [(7.3)](#mdspan.layout.stride.cons-7.3)

other.required_span_size() is representable as
a value of type index_type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types")), and

- [(7.4)](#mdspan.layout.stride.cons-7.4)

*OFFSET*(other) == 0 is true[.](#mdspan.layout.stride.cons-7.sentence-1)

[8](#mdspan.layout.stride.cons-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22821)

*Effects*: Direct-non-list-initializes *extents_* with other.extents(), and
for all d in the range [0, *rank_*),
direct-non-list-initializes *strides_*[d] with other.stride(d)[.](#mdspan.layout.stride.cons-8.sentence-1)

[9](#mdspan.layout.stride.cons-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22828)

Remarks: The expression inside explicit is equivalent to:!(is_convertible_v<typename StridedLayoutMapping::extents_type, extents_type> &&(*is-mapping-of*<layout_left, StridedLayoutMapping> ||*is-mapping-of*<layout_right, StridedLayoutMapping> ||*is-layout-left-padded-mapping-of*<StridedLayoutMapping> ||*is-layout-right-padded-mapping-of*<StridedLayoutMapping> ||*is-mapping-of*<layout_stride, StridedLayoutMapping>))

#### [23.7.3.4.7.4](#mdspan.layout.stride.obs) Observers [[mdspan.layout.stride.obs]](mdspan.layout.stride.obs)

[ð](#lib:required_span_size,layout_stride::mapping)

`constexpr index_type required_span_size() const noexcept;
`

[1](#mdspan.layout.stride.obs-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22848)

*Returns*: *REQUIRED-SPAN-SIZE*(extents(), *strides_*)[.](#mdspan.layout.stride.obs-1.sentence-1)

[ð](#lib:operator(),layout_stride::mapping)

`template<class... Indices>
  constexpr index_type operator()(Indices... i) const noexcept;
`

[2](#mdspan.layout.stride.obs-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22860)

*Constraints*: 

- [(2.1)](#mdspan.layout.stride.obs-2.1)

sizeof...(Indices) == *rank_* is true,

- [(2.2)](#mdspan.layout.stride.obs-2.2)

(is_convertible_v<Indices, index_type> && ...) is true, and

- [(2.3)](#mdspan.layout.stride.obs-2.3)

(is_nothrow_constructible_v<index_type, Indices> && ...) is true[.](#mdspan.layout.stride.obs-2.sentence-1)

[3](#mdspan.layout.stride.obs-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22871)

*Preconditions*: extents_type​::​*index-cast*(i) is
a multidimensional index in *extents_* ([[mdspan.overview]](#mdspan.overview "23.7.3.1 Overview"))[.](#mdspan.layout.stride.obs-3.sentence-1)

[4](#mdspan.layout.stride.obs-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22876)

*Effects*: Let P be a parameter pack such thatis_same_v<index_sequence_for<Indices...>, index_sequence<P...>> is true[.](#mdspan.layout.stride.obs-4.sentence-1)

Equivalent to:return ((static_cast<index_type>(i) * stride(P)) + ... + 0);

[ð](#lib:is_exhaustive,layout_stride::mapping)

`constexpr bool is_exhaustive() const noexcept;
`

[5](#mdspan.layout.stride.obs-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22895)

*Returns*: 

- [(5.1)](#mdspan.layout.stride.obs-5.1)

  true if *rank_* is 0[.](#mdspan.layout.stride.obs-5.1.sentence-1)

- [(5.2)](#mdspan.layout.stride.obs-5.2)

  Otherwise, true if there is
a permutation P of the integers in the range [0, *rank_*) such that stride(p0) equals 1, andstride(pi) equals stride(piâ1) * extents().extent(piâ1) for i in the range [1, *rank_*),
where pi is the ith element of P[.](#mdspan.layout.stride.obs-5.2.sentence-1)

- [(5.3)](#mdspan.layout.stride.obs-5.3)

  Otherwise, false[.](#mdspan.layout.stride.obs-5.3.sentence-1)

[ð](#lib:operator==,layout_stride::mapping)

`template<class OtherMapping>
  friend constexpr bool operator==(const mapping& x, const OtherMapping& y) noexcept;
`

[6](#mdspan.layout.stride.obs-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22919)

*Constraints*: 

- [(6.1)](#mdspan.layout.stride.obs-6.1)

  [*layout-mapping-alike*](#concept:layout-mapping-alike "23.7.3.4.7.2 Exposition-only helpers [mdspan.layout.stride.expo]")<OtherMapping> is satisfied[.](#mdspan.layout.stride.obs-6.1.sentence-1)

- [(6.2)](#mdspan.layout.stride.obs-6.2)

  *rank_* == OtherMapping​::​extents_type​::​rank() is true[.](#mdspan.layout.stride.obs-6.2.sentence-1)

- [(6.3)](#mdspan.layout.stride.obs-6.3)

  OtherMapping​::​is_always_strided() is true[.](#mdspan.layout.stride.obs-6.3.sentence-1)

[7](#mdspan.layout.stride.obs-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22930)

*Preconditions*: OtherMapping meets the layout mapping requirements ([[mdspan.layout.policy.reqmts]](#mdspan.layout.policy.reqmts "23.7.3.4.3 Layout mapping policy requirements"))[.](#mdspan.layout.stride.obs-7.sentence-1)

[8](#mdspan.layout.stride.obs-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22934)

*Returns*: true if x.extents() == y.extents() is true,*OFFSET*(y) == 0 is true, and
each of x.stride(r) == y.stride(r) is true for r in the range [0, x.extents().rank())[.](#mdspan.layout.stride.obs-8.sentence-1)

Otherwise, false[.](#mdspan.layout.stride.obs-8.sentence-2)

#### [23.7.3.4.8](#mdspan.layout.leftpad) Class template layout_left_padded​::​mapping [[mdspan.layout.leftpad]](mdspan.layout.leftpad)

#### [23.7.3.4.8.1](#mdspan.layout.leftpad.overview) Overview [[mdspan.layout.leftpad.overview]](mdspan.layout.leftpad.overview)

[1](#mdspan.layout.leftpad.overview-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L22947)

layout_left_padded provides a layout mapping
that behaves like layout_left​::​mapping,
except that the padding stride stride(1) can be greater than or equal to extent(0)[.](#mdspan.layout.leftpad.overview-1.sentence-1)

namespace std {template<size_t PaddingValue>template<class 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<PaddingValue>; private:static constexpr size_t *rank_* = extents_type::rank(); // *exposition only*static constexpr size_t *first-static-extent* = // *exposition only* extents_type::static_extent(0); // [[mdspan.layout.leftpad.expo]](#mdspan.layout.leftpad.expo "23.7.3.4.8.2 Exposition-only members"), exposition-only membersstatic constexpr size_t *static-padding-stride* = *see below*; // *exposition only*public:// [[mdspan.layout.leftpad.cons]](#mdspan.layout.leftpad.cons "23.7.3.4.8.3 Constructors"), constructorsconstexpr mapping() noexcept : mapping(extents_type{}) {}constexpr mapping(const mapping&) noexcept = default; constexpr mapping(const extents_type&); template<class OtherIndexType>constexpr mapping(const extents_type&, OtherIndexType); template<class OtherExtents>constexpr explicit(!is_convertible_v<OtherExtents, extents_type>) mapping(const layout_left::mapping<OtherExtents>&); template<class OtherExtents>constexpr explicit(extents_type::rank() > 0) mapping(const layout_stride::mapping<OtherExtents>&); template<class LayoutLeftPaddedMapping>constexpr explicit(*see below*) mapping(const LayoutLeftPaddedMapping&); template<class LayoutRightPaddedMapping>constexpr explicit(*see below*) mapping(const LayoutRightPaddedMapping&) noexcept; constexpr mapping& operator=(const mapping&) noexcept = default; // [[mdspan.layout.leftpad.obs]](#mdspan.layout.leftpad.obs "23.7.3.4.8.4 Observers"), observersconstexpr const extents_type& extents() const noexcept { return *extents_*; }constexpr array<index_type, rank_> strides() const noexcept; constexpr index_type required_span_size() const noexcept; template<class... Indices>constexpr index_type operator()(Indices...) const noexcept; static constexpr bool is_always_unique() noexcept { return true; }static constexpr bool is_always_exhaustive() noexcept; static constexpr bool is_always_strided() noexcept { return true; }static constexpr bool is_unique() noexcept { return true; }constexpr bool is_exhaustive() const noexcept; static constexpr bool is_strided() noexcept { return true; }constexpr index_type stride(rank_type) const noexcept; template<class LayoutLeftPaddedMapping>friend constexpr bool operator==(const mapping&, const LayoutLeftPaddedMapping&) noexcept; private:// [[mdspan.layout.leftpad.expo]](#mdspan.layout.leftpad.expo "23.7.3.4.8.2 Exposition-only members"), exposition-only members index_type *stride-1* = *static-padding-stride*; // *exposition only* extents_type *extents_*{}; // *exposition only*// [[mdspan.sub.map]](#mdspan.sub.map "23.7.3.7.6 Specializations of submdspan_­mapping"), submdspan mapping specializationtemplate<class... SliceSpecifiers>constexpr auto *submdspan-mapping-impl*(SliceSpecifiers...) const // *exposition only*-> *see below*; template<class... SliceSpecifiers>friend constexpr auto submdspan_mapping(const mapping& src, SliceSpecifiers... slices) {return src.*submdspan-mapping-impl*(slices...); }};}

[2](#mdspan.layout.leftpad.overview-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23035)

If Extents is not a specialization of extents,
then the program is ill-formed[.](#mdspan.layout.leftpad.overview-2.sentence-1)

[3](#mdspan.layout.leftpad.overview-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23039)

layout_left_padded​::​mapping<E> is a trivially copyable type
that models [regular](concepts.object#concept:regular "18.6 Object concepts [concepts.object]") for each E[.](#mdspan.layout.leftpad.overview-3.sentence-1)

[4](#mdspan.layout.leftpad.overview-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23043)

Throughout [[mdspan.layout.leftpad]](#mdspan.layout.leftpad "23.7.3.4.8 Class template layout_­left_­padded​::​mapping"),
let P_rank be the following
size *rank_* parameter pack of size_t values:

- [(4.1)](#mdspan.layout.leftpad.overview-4.1)

the empty parameter pack, if *rank_* equals zero;

- [(4.2)](#mdspan.layout.leftpad.overview-4.2)

otherwise, 0zu, if *rank_* equals one;

- [(4.3)](#mdspan.layout.leftpad.overview-4.3)

otherwise, the parameter pack 0zu, 1zu, …, *rank_*- 1[.](#mdspan.layout.leftpad.overview-4.sentence-1)

[5](#mdspan.layout.leftpad.overview-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23056)

*Mandates*: 

- [(5.1)](#mdspan.layout.leftpad.overview-5.1)

  If rank_dynamic() == 0 is true,
then the size of the multidimensional index space Extents() is representable as a value of type index_type[.](#mdspan.layout.leftpad.overview-5.1.sentence-1)

- [(5.2)](#mdspan.layout.leftpad.overview-5.2)

  padding_value is representable as a value of type index_type[.](#mdspan.layout.leftpad.overview-5.2.sentence-1)

- [(5.3)](#mdspan.layout.leftpad.overview-5.3)

  If
  * [(5.3.1)](#mdspan.layout.leftpad.overview-5.3.1)

*rank_* is greater than one,

  * [(5.3.2)](#mdspan.layout.leftpad.overview-5.3.2)

padding_value does not equal dynamic_extent, and

  * [(5.3.3)](#mdspan.layout.leftpad.overview-5.3.3)

*first-static-extent* does not equal dynamic_extent,

then *LEAST-MULTIPLE-AT-LEAST*(padding_value, *first-static-extent*) is representable as a value of type size_t, and
is representable as a value of type index_type[.](#mdspan.layout.leftpad.overview-5.3.sentence-1)

- [(5.4)](#mdspan.layout.leftpad.overview-5.4)

  If
  * [(5.4.1)](#mdspan.layout.leftpad.overview-5.4.1)

*rank_* is greater than one,

  * [(5.4.2)](#mdspan.layout.leftpad.overview-5.4.2)

padding_value does not equal dynamic_extent, and

  * [(5.4.3)](#mdspan.layout.leftpad.overview-5.4.3)

extents_type​::​static_extent(k) does not equal dynamic_extent for all k in the range [0, extents_type​::​rank()),

then the product of*LEAST-MULTIPLE-AT-LEAST*(padding_value, ext.static_extent(0)) and
all values ext.static_extent(k) with k in the range of [1, *rank_*)
is representable as a value of type size_t, and
is representable as a value of type index_type[.](#mdspan.layout.leftpad.overview-5.4.sentence-1)

#### [23.7.3.4.8.2](#mdspan.layout.leftpad.expo) Exposition-only members [[mdspan.layout.leftpad.expo]](mdspan.layout.leftpad.expo)

[ð](#mdspan.layout.leftpad.expo-itemdecl:1)

`static constexpr size_t static-padding-stride = see below;
`

[1](#mdspan.layout.leftpad.expo-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23104)

The value is

- [(1.1)](#mdspan.layout.leftpad.expo-1.1)

0, if *rank_* equals zero or one;

- [(1.2)](#mdspan.layout.leftpad.expo-1.2)

otherwise, dynamic_extent,
if padding_value or *first-static-extent* equalsdynamic_extent;

- [(1.3)](#mdspan.layout.leftpad.expo-1.3)

otherwise, the size_t value which is*LEAST-MULTIPLE-AT-LEAST*(padding_value, *first-static-extent*)[.](#mdspan.layout.leftpad.expo-1.sentence-1)

[ð](#mdspan.layout.leftpad.expo-itemdecl:2)

`index_type stride-1 = static-padding-stride;
`

[2](#mdspan.layout.leftpad.expo-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23124)

*Recommended practice*: Implementations should not store this value
if *static-padding-stride* is not dynamic_extent[.](#mdspan.layout.leftpad.expo-2.sentence-1)

[*Note [1](#mdspan.layout.leftpad.expo-note-1)*:

Using extents<index_type, *static-padding-stride*> instead ofindex_type as the type of *stride-1* would achieve this[.](#mdspan.layout.leftpad.expo-2.sentence-2)

â *end note*]

#### [23.7.3.4.8.3](#mdspan.layout.leftpad.cons) Constructors [[mdspan.layout.leftpad.cons]](mdspan.layout.leftpad.cons)

[ð](#lib:layout_left_padded::mapping,constructor)

`constexpr mapping(const extents_type& ext);
`

[1](#mdspan.layout.leftpad.cons-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23142)

*Preconditions*: 

- [(1.1)](#mdspan.layout.leftpad.cons-1.1)

  The size of the multidimensional index space ext is representable as
a value of type index_type[.](#mdspan.layout.leftpad.cons-1.1.sentence-1)

- [(1.2)](#mdspan.layout.leftpad.cons-1.2)

  If *rank_* is greater than one andpadding_value does not equal dynamic_extent,
then *LEAST-MULTIPLE-AT-LEAST*(padding_value, ext.extent(0)) is representable as a value of type *index_type*[.](#mdspan.layout.leftpad.cons-1.2.sentence-1)

- [(1.3)](#mdspan.layout.leftpad.cons-1.3)

  If *rank_* is greater than one andpadding_value does not equal dynamic_extent,
then the product of*LEAST-MULTIPLE-AT-LEAST*(padding_value, ext.extent(0)) and
all values ext.extent(k) with k in the range of [1, *rank_*)
is representable as a value of type index_type[.](#mdspan.layout.leftpad.cons-1.3.sentence-1)

[2](#mdspan.layout.leftpad.cons-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23163)

*Effects*: 

- [(2.1)](#mdspan.layout.leftpad.cons-2.1)

Direct-non-list-initializes *extents_* with ext; and

- [(2.2)](#mdspan.layout.leftpad.cons-2.2)

if *rank_* is greater than one,
direct-non-list-initializes *stride-1*
  * [(2.2.1)](#mdspan.layout.leftpad.cons-2.2.1)

with ext.extent(0) if padding_value is dynamic_extent,

  * [(2.2.2)](#mdspan.layout.leftpad.cons-2.2.2)

otherwise with*LEAST-MULTIPLE-AT-LEAST*(padding_value, ext.extent(0))[.](#mdspan.layout.leftpad.cons-2.sentence-1)

[ð](#lib:layout_left_padded::mapping,constructor_)

`template<class OtherIndexType>
constexpr mapping(const extents_type& ext, OtherIndexType pad);
`

[3](#mdspan.layout.leftpad.cons-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23188)

*Constraints*: 

- [(3.1)](#mdspan.layout.leftpad.cons-3.1)

  is_convertible_v<OtherIndexType, index_type> is true[.](#mdspan.layout.leftpad.cons-3.1.sentence-1)

- [(3.2)](#mdspan.layout.leftpad.cons-3.2)

  is_nothrow_constructible_v<index_type, OtherIndexType> is true[.](#mdspan.layout.leftpad.cons-3.2.sentence-1)

[4](#mdspan.layout.leftpad.cons-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23197)

*Preconditions*: 

- [(4.1)](#mdspan.layout.leftpad.cons-4.1)

  pad is representable as a value of type index_type[.](#mdspan.layout.leftpad.cons-4.1.sentence-1)

- [(4.2)](#mdspan.layout.leftpad.cons-4.2)

  extents_type​::​index-cast(pad) is greater than zero[.](#mdspan.layout.leftpad.cons-4.2.sentence-1)

- [(4.3)](#mdspan.layout.leftpad.cons-4.3)

  If *rank_* is greater than one,
then *LEAST-MULTIPLE-AT-LEAST*(pad, ext.extent(0)) is representable as a value of type index_type.

- [(4.4)](#mdspan.layout.leftpad.cons-4.4)

  If *rank_* is greater than one,
then the product of*LEAST-MULTIPLE-AT-LEAST*(pad, ext.extent(0)) and
all values ext.extent(k) with k in the range of [1, *rank_*)
is representable as a value of type index_type[.](#mdspan.layout.leftpad.cons-4.4.sentence-1)

- [(4.5)](#mdspan.layout.leftpad.cons-4.5)

  If padding_value is not equal to dynamic_extent,padding_value equals extents_type​::​*index-cast*(pad)[.](#mdspan.layout.leftpad.cons-4.5.sentence-1)

[5](#mdspan.layout.leftpad.cons-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23220)

*Effects*: Direct-non-list-initializes *extents_* with ext, and
if *rank_* is greater than one,
direct-non-list-initializes *stride-1* with*LEAST-MULTIPLE-AT-LEAST*(pad, ext.extent(0))[.](#mdspan.layout.leftpad.cons-5.sentence-1)

[ð](#lib:layout_left_padded::mapping,constructor__)

`template<class OtherExtents>
  constexpr explicit(!is_convertible_v<OtherExtents, extents_type>)
    mapping(const layout_left::mapping<OtherExtents>& other);
`

[6](#mdspan.layout.leftpad.cons-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23236)

*Constraints*: is_constructible_v<extents_type, OtherExtents> is true[.](#mdspan.layout.leftpad.cons-6.sentence-1)

[7](#mdspan.layout.leftpad.cons-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23240)

*Mandates*: If OtherExtents​::​rank() is greater than 1, then(*static-padding-stride* == dynamic_extent) ||(OtherExtents::static_extent(0) == dynamic_extent) ||(*static-padding-stride* == OtherExtents::static_extent(0)) is true[.](#mdspan.layout.leftpad.cons-7.sentence-1)

[8](#mdspan.layout.leftpad.cons-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23250)

*Preconditions*: 

- [(8.1)](#mdspan.layout.leftpad.cons-8.1)

If extents_type​::​rank() > 1 is true andpadding_value == dynamic_extent is false,
then other.stride(1) equals*LEAST-MULTIPLE-AT-LEAST*(padding_value,
 extents_type::*index-cast*(other.extents().extent(0))) and

- [(8.2)](#mdspan.layout.leftpad.cons-8.2)

other.required_span_size() is representable as
a value of type index_type[.](#mdspan.layout.leftpad.cons-8.sentence-1)

[9](#mdspan.layout.leftpad.cons-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23267)

*Effects*: Equivalent to mapping(other.extents())[.](#mdspan.layout.leftpad.cons-9.sentence-1)

[ð](#lib:layout_left_padded::mapping,constructor___)

`template<class OtherExtents>
  constexpr explicit(rank_ > 0)
    mapping(const layout_stride::mapping<OtherExtents>& other);
`

[10](#mdspan.layout.leftpad.cons-10)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23280)

*Constraints*: is_constructible_v<extents_type, OtherExtents> is true[.](#mdspan.layout.leftpad.cons-10.sentence-1)

[11](#mdspan.layout.leftpad.cons-11)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23284)

*Preconditions*: 

- [(11.1)](#mdspan.layout.leftpad.cons-11.1)

  If *rank_* is greater than 1 andpadding_value does not equal dynamic_extent,
then other.stride(1) equals*LEAST-MULTIPLE-AT-LEAST*(padding_value,
 extents_type::*index-cast*(other.extents().extent(0)))

- [(11.2)](#mdspan.layout.leftpad.cons-11.2)

  If *rank_* is greater than 0,
then other.stride(0) equals 1[.](#mdspan.layout.leftpad.cons-11.2.sentence-1)

- [(11.3)](#mdspan.layout.leftpad.cons-11.3)

  If *rank_* is greater than 2,
then for all r in the range [2, *rank_*),other.stride(r) equals(other.extents().*fwd-prod-of-extents*(r) / other.extents().extent(0)) * other.stride(1)

- [(11.4)](#mdspan.layout.leftpad.cons-11.4)

  other.required_span_size() is representable as
a value of type *index_type*[.](#mdspan.layout.leftpad.cons-11.4.sentence-1)

[12](#mdspan.layout.leftpad.cons-12)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23310)

*Effects*: 

- [(12.1)](#mdspan.layout.leftpad.cons-12.1)

Direct-non-list-initializes *extents_* with other.extents() and

- [(12.2)](#mdspan.layout.leftpad.cons-12.2)

if *rank_* is greater than one,
direct-non-list-initializes *stride-1* withother.stride(1)[.](#mdspan.layout.leftpad.cons-12.sentence-1)

[ð](#lib:layout_left_padded::mapping,constructor____)

`template<class LayoutLeftPaddedMapping>
  constexpr explicit(see below)
    mapping(const LayoutLeftPaddedMapping& other);
`

[13](#mdspan.layout.leftpad.cons-13)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23330)

*Constraints*: 

- [(13.1)](#mdspan.layout.leftpad.cons-13.1)

  *is-layout-left-padded-mapping-of*<LayoutLeftPaddedMapping> is true[.](#mdspan.layout.leftpad.cons-13.1.sentence-1)

- [(13.2)](#mdspan.layout.leftpad.cons-13.2)

  is_constructible_v<extents_type, typename LayoutLeftPaddedMapping​::​extents_type>  
is true[.](#mdspan.layout.leftpad.cons-13.2.sentence-1)

[14](#mdspan.layout.leftpad.cons-14)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23341)

*Mandates*: If *rank_* is greater than 1,
thenpadding_value == dynamic_extent || LayoutLeftPaddedMapping::padding_value == dynamic_extent || padding_value == LayoutLeftPaddedMapping::padding_value is true[.](#mdspan.layout.leftpad.cons-14.sentence-1)

[15](#mdspan.layout.leftpad.cons-15)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23352)

*Preconditions*: 

- [(15.1)](#mdspan.layout.leftpad.cons-15.1)

If *rank_* is greater than 1 andpadding_value does not equal dynamic_extent,
then other.stride(1) equals*LEAST-MULTIPLE-AT-LEAST*(padding_value,
 extents_type::*index-cast*(other.extent(0)))

- [(15.2)](#mdspan.layout.leftpad.cons-15.2)

other.required_span_size() is representable as
a value of type index_type[.](#mdspan.layout.leftpad.cons-15.sentence-1)

[16](#mdspan.layout.leftpad.cons-16)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23368)

*Effects*: 

- [(16.1)](#mdspan.layout.leftpad.cons-16.1)

Direct-non-list-initializes *extents_* with other.extents() and

- [(16.2)](#mdspan.layout.leftpad.cons-16.2)

if *rank_* is greater than one,
direct-non-list-initializes *stride-1* with other.stride(1)[.](#mdspan.layout.leftpad.cons-16.sentence-1)

[17](#mdspan.layout.leftpad.cons-17)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23378)

*Remarks*: The expression inside explicit is equivalent to:rank_> 1 &&(padding_value != dynamic_extent || LayoutLeftPaddedMapping::padding_value == dynamic_extent)

[ð](#lib:layout_left_padded::mapping,constructor_____)

`template<class LayoutRightPaddedMapping>
  constexpr explicit(see below)
    mapping(const LayoutRightPaddedMapping& other) noexcept;
`

[18](#mdspan.layout.leftpad.cons-18)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23396)

*Constraints*: 

- [(18.1)](#mdspan.layout.leftpad.cons-18.1)

  *is-layout-right-padded-mapping-of*<LayoutRightPaddedMapping> is true or  
*is-mapping-of*<layout_right, LayoutRightPaddedMapping> is true[.](#mdspan.layout.leftpad.cons-18.1.sentence-1)

- [(18.2)](#mdspan.layout.leftpad.cons-18.2)

  *rank_* equals zero or one[.](#mdspan.layout.leftpad.cons-18.2.sentence-1)

- [(18.3)](#mdspan.layout.leftpad.cons-18.3)

  is_constructible_v<extents_type, typename LayoutRightPaddedMapping​::​extents_-  
type> is true[.](#mdspan.layout.leftpad.cons-18.3.sentence-1)

[19](#mdspan.layout.leftpad.cons-19)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23411)

*Preconditions*: other.required_span_size() is representable as
a value of type index_type[.](#mdspan.layout.leftpad.cons-19.sentence-1)

[20](#mdspan.layout.leftpad.cons-20)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23416)

*Effects*: Direct-non-list-initializes *extents_* with other.extents()[.](#mdspan.layout.leftpad.cons-20.sentence-1)

[21](#mdspan.layout.leftpad.cons-21)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23420)

*Remarks*: The expression inside explicit is equivalent to:!is_convertible_v<typename LayoutRightPaddedMapping::extents_type, extents_type>

[*Note [1](#mdspan.layout.leftpad.cons-note-1)*:

Neither the input mapping nor the mapping to be constructed
uses the padding stride in the rank-0 or rank-1 case,
so the padding stride does not affect
either the constraints or the preconditions[.](#mdspan.layout.leftpad.cons-21.sentence-2)

â *end note*]

#### [23.7.3.4.8.4](#mdspan.layout.leftpad.obs) Observers [[mdspan.layout.leftpad.obs]](mdspan.layout.leftpad.obs)

[ð](#mdspan.layout.leftpad.obs-itemdecl:1)

`constexpr array<index_type, rank_> strides() const noexcept;
`

[1](#mdspan.layout.leftpad.obs-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23442)

*Returns*: array<index_type, *rank_*>({stride(P_rank)...})[.](#mdspan.layout.leftpad.obs-1.sentence-1)

[ð](#mdspan.layout.leftpad.obs-itemdecl:2)

`constexpr index_type required_span_size() const noexcept;
`

[2](#mdspan.layout.leftpad.obs-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23452)

*Returns*: 

- [(2.1)](#mdspan.layout.leftpad.obs-2.1)

0 if the multidimensional index space *extents_* is empty,

- [(2.2)](#mdspan.layout.leftpad.obs-2.2)

otherwise, *this(((*extents_*(P_rank) - index_type(1))...)) + 1[.](#mdspan.layout.leftpad.obs-2.sentence-1)

[ð](#mdspan.layout.leftpad.obs-itemdecl:3)

`template<class... Indices>
constexpr size_t operator()(Indices... idxs) const noexcept;
`

[3](#mdspan.layout.leftpad.obs-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23468)

*Constraints*: 

- [(3.1)](#mdspan.layout.leftpad.obs-3.1)

  sizeof...(Indices) == *rank_* is true[.](#mdspan.layout.leftpad.obs-3.1.sentence-1)

- [(3.2)](#mdspan.layout.leftpad.obs-3.2)

  (is_convertible_v<Indices, index_type> && ...) is true[.](#mdspan.layout.leftpad.obs-3.2.sentence-1)

- [(3.3)](#mdspan.layout.leftpad.obs-3.3)

  (is_nothrow_constructible_v<index_type, Indices> && ...) is true[.](#mdspan.layout.leftpad.obs-3.3.sentence-1)

[4](#mdspan.layout.leftpad.obs-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23479)

*Preconditions*: extents_type​::​*index-cast*(idxs) is
a multidimensional index in extents() ([[mdspan.overview]](#mdspan.overview "23.7.3.1 Overview"))[.](#mdspan.layout.leftpad.obs-4.sentence-1)

[5](#mdspan.layout.leftpad.obs-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23484)

*Returns*: ((static_cast<index_type>(idxs) * stride(P_rank)) + ... + 0)[.](#mdspan.layout.leftpad.obs-5.sentence-1)

[ð](#mdspan.layout.leftpad.obs-itemdecl:4)

`static constexpr bool is_always_exhaustive() noexcept;
`

[6](#mdspan.layout.leftpad.obs-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23494)

*Returns*: 

- [(6.1)](#mdspan.layout.leftpad.obs-6.1)

If *rank_* equals zero or one, then true;

- [(6.2)](#mdspan.layout.leftpad.obs-6.2)

otherwise, if
neither *static-padding-stride* nor *first-static-extent* equal dynamic_extent,
then *static-padding-stride* == *first-static-extent*;

- [(6.3)](#mdspan.layout.leftpad.obs-6.3)

otherwise, false[.](#mdspan.layout.leftpad.obs-6.sentence-1)

[ð](#mdspan.layout.leftpad.obs-itemdecl:5)

`constexpr bool is_exhaustive() const noexcept;
`

[7](#mdspan.layout.leftpad.obs-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23514)

*Returns*: true if *rank_* equals zero or one;
otherwise, extents_.extent(0) == stride(1)[.](#mdspan.layout.leftpad.obs-7.sentence-1)

[ð](#mdspan.layout.leftpad.obs-itemdecl:6)

`constexpr index_type stride(rank_type r) const noexcept;
`

[8](#mdspan.layout.leftpad.obs-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23525)

*Preconditions*: r is smaller than *rank_*[.](#mdspan.layout.leftpad.obs-8.sentence-1)

[9](#mdspan.layout.leftpad.obs-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23529)

*Returns*: 

- [(9.1)](#mdspan.layout.leftpad.obs-9.1)

If r equals zero: 1;

- [(9.2)](#mdspan.layout.leftpad.obs-9.2)

otherwise, if r equals one: *stride-1*;

- [(9.3)](#mdspan.layout.leftpad.obs-9.3)

otherwise, the product of *stride-1* and
all values extents_.extent(k) with k in the range [1, r)[.](#mdspan.layout.leftpad.obs-9.sentence-1)

[ð](#mdspan.layout.leftpad.obs-itemdecl:7)

`template<class LayoutLeftPaddedMapping>
  friend constexpr bool operator==(const mapping& x, const LayoutLeftPaddedMapping& y) noexcept;
`

[10](#mdspan.layout.leftpad.obs-10)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23548)

*Constraints*: 

- [(10.1)](#mdspan.layout.leftpad.obs-10.1)

  *is-layout-left-padded-mapping-of*<LayoutLeftPaddedMapping> is true[.](#mdspan.layout.leftpad.obs-10.1.sentence-1)

- [(10.2)](#mdspan.layout.leftpad.obs-10.2)

  LayoutLeftPaddedMapping​::​extents_type​::​rank() == rank_ is true[.](#mdspan.layout.leftpad.obs-10.2.sentence-1)

[11](#mdspan.layout.leftpad.obs-11)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23558)

*Returns*: true if x.extents() == y.extents() is true and*rank_* < 2 || x.stride(1) == y.  
stride(1) is true[.](#mdspan.layout.leftpad.obs-11.sentence-1)

Otherwise, false[.](#mdspan.layout.leftpad.obs-11.sentence-2)

#### [23.7.3.4.9](#mdspan.layout.rightpad) Class template layout_right_padded​::​mapping [[mdspan.layout.rightpad]](mdspan.layout.rightpad)

#### [23.7.3.4.9.1](#mdspan.layout.rightpad.overview) Overview [[mdspan.layout.rightpad.overview]](mdspan.layout.rightpad.overview)

[1](#mdspan.layout.rightpad.overview-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23569)

layout_right_padded provides a layout mapping
that behaves like layout_right​::​mapping,
except that the padding stride stride(extents_type​::​rank() - 2) can be greater than or equal toextents_type​::​extent(extents_type​::​rank() - 1)[.](#mdspan.layout.rightpad.overview-1.sentence-1)

namespace std {template<size_t PaddingValue>template<class 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 *rank_* = extents_type::rank(); // *exposition only*static constexpr size_t *last-static-extent* = // *exposition only* extents_type::static_extent(*rank_* - 1); // [[mdspan.layout.rightpad.expo]](#mdspan.layout.rightpad.expo "23.7.3.4.9.2 Exposition-only members"), exposition-only membersstatic constexpr size_t *static-padding-stride* = *see below*; // *exposition only*public:// [[mdspan.layout.rightpad.cons]](#mdspan.layout.rightpad.cons "23.7.3.4.9.3 Constructors"), constructorsconstexpr mapping() noexcept : mapping(extents_type{}) {}constexpr mapping(const mapping&) noexcept = default; constexpr mapping(const extents_type&); template<class OtherIndexType>constexpr mapping(const extents_type&, OtherIndexType); template<class OtherExtents>constexpr explicit(!is_convertible_v<OtherExtents, extents_type>) mapping(const layout_right::mapping<OtherExtents>&); template<class OtherExtents>constexpr explicit(rank_ > 0) mapping(const layout_stride::mapping<OtherExtents>&); template<class LayoutRightPaddedMapping>constexpr explicit(*see below*) mapping(const LayoutRightPaddedMapping&); template<class LayoutLeftPaddedMapping>constexpr explicit(*see below*) mapping(const LayoutLeftPaddedMapping&) noexcept; constexpr mapping& operator=(const mapping&) noexcept = default; // [[mdspan.layout.rightpad.obs]](#mdspan.layout.rightpad.obs "23.7.3.4.9.4 Observers"), observersconstexpr const extents_type& extents() const noexcept { return extents_; }constexpr array<index_type, rank_> strides() const noexcept; constexpr index_type required_span_size() const noexcept; template<class... Indices>constexpr index_type operator()(Indices...) const noexcept; static constexpr bool is_always_unique() noexcept { return true; }static constexpr bool is_always_exhaustive() noexcept; static constexpr bool is_always_strided() noexcept { return true; }static constexpr bool is_unique() noexcept { return true; }constexpr bool is_exhaustive() const noexcept; static constexpr bool is_strided() noexcept { return true; }constexpr index_type stride(rank_type) const noexcept; template<class LayoutRightPaddedMapping>friend constexpr bool operator==(const mapping&, const LayoutRightPaddedMapping&) noexcept; private:// [[mdspan.layout.rightpad.expo]](#mdspan.layout.rightpad.expo "23.7.3.4.9.2 Exposition-only members"), exposition-only members index_type *stride-rm2* = *static-padding-stride*; // *exposition only* extents_type *extents_*{}; // *exposition only*// [[mdspan.sub.map]](#mdspan.sub.map "23.7.3.7.6 Specializations of submdspan_­mapping"), submdspan mapping specializationtemplate<class... SliceSpecifiers>constexpr auto *submdspan-mapping-impl*(SliceSpecifiers...) const // *exposition only*-> *see below*; template<class... SliceSpecifiers>friend constexpr auto submdspan_mapping(const mapping& src, SliceSpecifiers... slices) {return src.*submdspan-mapping-impl*(slices...); }};}

[2](#mdspan.layout.rightpad.overview-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23661)

If Extents is not a specialization of extents,
then the program is ill-formed[.](#mdspan.layout.rightpad.overview-2.sentence-1)

[3](#mdspan.layout.rightpad.overview-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23665)

layout_right_padded​::​mapping<E> is a trivially copyable type
that models [regular](concepts.object#concept:regular "18.6 Object concepts [concepts.object]") for each E[.](#mdspan.layout.rightpad.overview-3.sentence-1)

[4](#mdspan.layout.rightpad.overview-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23669)

Throughout [[mdspan.layout.rightpad]](#mdspan.layout.rightpad "23.7.3.4.9 Class template layout_­right_­padded​::​mapping"),
let P_rank be the following
size *rank_* parameter pack of size_t values:

- [(4.1)](#mdspan.layout.rightpad.overview-4.1)

the empty parameter pack, if *rank_* equals zero;

- [(4.2)](#mdspan.layout.rightpad.overview-4.2)

otherwise, 0zu, if *rank_* equals one;

- [(4.3)](#mdspan.layout.rightpad.overview-4.3)

otherwise, the parameter pack 0zu, 1zu, …, *rank_*- 1[.](#mdspan.layout.rightpad.overview-4.sentence-1)

[5](#mdspan.layout.rightpad.overview-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23682)

*Mandates*: 

- [(5.1)](#mdspan.layout.rightpad.overview-5.1)

  If rank_dynamic() == 0 is true,
then the size of the multidimensional index space Extents() is representable as a value of type index_type[.](#mdspan.layout.rightpad.overview-5.1.sentence-1)

- [(5.2)](#mdspan.layout.rightpad.overview-5.2)

  padding_value is representable as a value of type index_type[.](#mdspan.layout.rightpad.overview-5.2.sentence-1)

- [(5.3)](#mdspan.layout.rightpad.overview-5.3)

  If
  * [(5.3.1)](#mdspan.layout.rightpad.overview-5.3.1)

*rank_* is greater than one,

  * [(5.3.2)](#mdspan.layout.rightpad.overview-5.3.2)

padding_value does not equal dynamic_extent, and

  * [(5.3.3)](#mdspan.layout.rightpad.overview-5.3.3)

*last-static-extent* does not equal dynamic_extent,

then *LEAST-MULTIPLE-AT-LEAST*(padding_value, *last-static-extent*) is representable as a value of type size_t, and
is representable as a value of type index_type[.](#mdspan.layout.rightpad.overview-5.3.sentence-1)

- [(5.4)](#mdspan.layout.rightpad.overview-5.4)

  If
  * [(5.4.1)](#mdspan.layout.rightpad.overview-5.4.1)

*rank_* is greater than one,

  * [(5.4.2)](#mdspan.layout.rightpad.overview-5.4.2)

padding_value does not equal dynamic_extent, and

  * [(5.4.3)](#mdspan.layout.rightpad.overview-5.4.3)

extents_type​::​static_extent(k) does not equal dynamic_extent for all k in the range [0, *rank_*),

then the product of*LEAST-MULTIPLE-AT-LEAST*(padding_value, ext.static_extent(*rank_* - 1)) and
all values ext.static_extent(k) with k in the range of [0, *rank_* - 1)
is representable as a value of type size_t, and
is representable as a value of type index_type[.](#mdspan.layout.rightpad.overview-5.4.sentence-1)

#### [23.7.3.4.9.2](#mdspan.layout.rightpad.expo) Exposition-only members [[mdspan.layout.rightpad.expo]](mdspan.layout.rightpad.expo)

[ð](#mdspan.layout.rightpad.expo-itemdecl:1)

`static constexpr size_t static-padding-stride = see below;
`

[1](#mdspan.layout.rightpad.expo-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23730)

The value is

- [(1.1)](#mdspan.layout.rightpad.expo-1.1)

0, if *rank_* equals zero or one;

- [(1.2)](#mdspan.layout.rightpad.expo-1.2)

otherwise, dynamic_extent,
if padding_value or *last-static-extent* equalsdynamic_extent;

- [(1.3)](#mdspan.layout.rightpad.expo-1.3)

otherwise, the size_t value which is*LEAST-MULTIPLE-AT-LEAST*(padding_value, *last-static-extent*)[.](#mdspan.layout.rightpad.expo-1.sentence-1)

[ð](#mdspan.layout.rightpad.expo-itemdecl:2)

`index_type stride-rm2 = static-padding-stride;
`

[2](#mdspan.layout.rightpad.expo-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23750)

*Recommended practice*: Implementations should not store this value
if *static-padding-stride* is not dynamic_extent[.](#mdspan.layout.rightpad.expo-2.sentence-1)

[*Note [1](#mdspan.layout.rightpad.expo-note-1)*:

Using extents<index_type, *static-padding-stride*> instead of index_type as the type of *stride-rm2* would achieve this[.](#mdspan.layout.rightpad.expo-2.sentence-2)

â *end note*]

#### [23.7.3.4.9.3](#mdspan.layout.rightpad.cons) Constructors [[mdspan.layout.rightpad.cons]](mdspan.layout.rightpad.cons)

[ð](#lib:layout_right_padded::mapping,constructor)

`constexpr mapping(const extents_type& ext);
`

[1](#mdspan.layout.rightpad.cons-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23769)

*Preconditions*: 

- [(1.1)](#mdspan.layout.rightpad.cons-1.1)

  The size of the multidimensional index space ext is representable as a value of type index_type[.](#mdspan.layout.rightpad.cons-1.1.sentence-1)

- [(1.2)](#mdspan.layout.rightpad.cons-1.2)

  If *rank_* is greater than one andpadding_value does not equal dynamic_extent,
then *LEAST-MULTIPLE-AT-LEAST*(padding_value, ext.extent(*rank_* - 1)) is representable as a value of type *index_type*[.](#mdspan.layout.rightpad.cons-1.2.sentence-1)

- [(1.3)](#mdspan.layout.rightpad.cons-1.3)

  If *rank_* is greater than one andpadding_value does not equal dynamic_extent,
then the product of*LEAST-MULTIPLE-AT-LEAST*(padding_value, ext.extent(*rank_* - 1)) and
all values ext.extent(k) with k in the range of [0, *rank_* - 1)
is representable as a value of type index_type[.](#mdspan.layout.rightpad.cons-1.3.sentence-1)

[2](#mdspan.layout.rightpad.cons-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23790)

*Effects*: 

- [(2.1)](#mdspan.layout.rightpad.cons-2.1)

Direct-non-list-initializes *extents_* with ext; and

- [(2.2)](#mdspan.layout.rightpad.cons-2.2)

if *rank_* is greater than one,
direct-non-list-initializes *stride-rm2*
  * [(2.2.1)](#mdspan.layout.rightpad.cons-2.2.1)

with ext.extent(*rank_* - 1) if padding_value is dynamic_extent,

  * [(2.2.2)](#mdspan.layout.rightpad.cons-2.2.2)

otherwise with*LEAST-MULTIPLE-AT-LEAST*(padding_value, ext.extent(*rank_* - 1))[.](#mdspan.layout.rightpad.cons-2.sentence-1)

[ð](#lib:layout_right_padded::mapping,constructor_)

`template<class OtherIndexType>
constexpr mapping(const extents_type& ext, OtherIndexType pad);
`

[3](#mdspan.layout.rightpad.cons-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23816)

*Constraints*: 

- [(3.1)](#mdspan.layout.rightpad.cons-3.1)

  is_convertible_v<OtherIndexType, index_type> is true[.](#mdspan.layout.rightpad.cons-3.1.sentence-1)

- [(3.2)](#mdspan.layout.rightpad.cons-3.2)

  is_nothrow_constructible_v<index_type, OtherIndexType> is true[.](#mdspan.layout.rightpad.cons-3.2.sentence-1)

[4](#mdspan.layout.rightpad.cons-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23825)

*Preconditions*: 

- [(4.1)](#mdspan.layout.rightpad.cons-4.1)

  pad is representable as a value of type index_type[.](#mdspan.layout.rightpad.cons-4.1.sentence-1)

- [(4.2)](#mdspan.layout.rightpad.cons-4.2)

  extents_type​::​*index-cast*(pad) is greater than zero[.](#mdspan.layout.rightpad.cons-4.2.sentence-1)

- [(4.3)](#mdspan.layout.rightpad.cons-4.3)

  If *rank_* is greater than one,
then *LEAST-MULTIPLE-AT-LEAST*(pad, ext.extent(*rank_* - 1)) is representable as a value of type index_type[.](#mdspan.layout.rightpad.cons-4.3.sentence-1)

- [(4.4)](#mdspan.layout.rightpad.cons-4.4)

  If *rank_* is greater than one,
then the product of*LEAST-MULTIPLE-AT-LEAST*(pad, ext.extent(*rank_* - 1)) and
all values ext.extent(k) with k in the range of [0, *rank_* - 1)
is representable as a value of type index_type[.](#mdspan.layout.rightpad.cons-4.4.sentence-1)

- [(4.5)](#mdspan.layout.rightpad.cons-4.5)

  If padding_value is not equal to dynamic_extent,padding_value equals extents_type​::​*index-cast*(pad)[.](#mdspan.layout.rightpad.cons-4.5.sentence-1)

[5](#mdspan.layout.rightpad.cons-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23848)

*Effects*: Direct-non-list-initializes *extents_* with ext, and
if *rank_* is greater than one,
direct-non-list-initializes *stride-rm2* with*LEAST-MULTIPLE-AT-LEAST*(pad, ext.extent(*rank_* - 1))[.](#mdspan.layout.rightpad.cons-5.sentence-1)

[ð](#lib:layout_right_padded::mapping,constructor__)

`template<class OtherExtents>
  constexpr explicit(!is_convertible_v<OtherExtents, extents_type>)
    mapping(const layout_right::mapping<OtherExtents>& other);
`

[6](#mdspan.layout.rightpad.cons-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23864)

*Constraints*: is_constructible_v<extents_type, OtherExtents> is true[.](#mdspan.layout.rightpad.cons-6.sentence-1)

[7](#mdspan.layout.rightpad.cons-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23868)

*Mandates*: If OtherExtents​::​rank() is greater than 1, then(*static-padding-stride* == dynamic_extent) ||(OtherExtents::static_extent(*rank_* - 1) == dynamic_extent) ||(*static-padding-stride* == OtherExtents::static_extent(*rank_* - 1)) is true[.](#mdspan.layout.rightpad.cons-7.sentence-1)

[8](#mdspan.layout.rightpad.cons-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23878)

*Preconditions*: 

- [(8.1)](#mdspan.layout.rightpad.cons-8.1)

If *rank_* > 1 is true andpadding_value == dynamic_extent is false, thenother.stride(  
*rank_* - 2) equals*LEAST-MULTIPLE-AT-LEAST*(padding_value,
 extents_type::*index-cast*(other.extents().extent(rank_ - 1))) and

- [(8.2)](#mdspan.layout.rightpad.cons-8.2)

other.required_span_size() is representable as
a value of type index_type[.](#mdspan.layout.rightpad.cons-8.sentence-1)

[9](#mdspan.layout.rightpad.cons-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23895)

*Effects*: Equivalent to mapping(other.extents())[.](#mdspan.layout.rightpad.cons-9.sentence-1)

[ð](#lib:layout_right_padded::mapping,constructor___)

`template<class OtherExtents>
  constexpr explicit(rank_ > 0)
    mapping(const layout_stride::mapping<OtherExtents>& other);
`

[10](#mdspan.layout.rightpad.cons-10)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23908)

*Constraints*: is_constructible_v<extents_type, OtherExtents> is true[.](#mdspan.layout.rightpad.cons-10.sentence-1)

[11](#mdspan.layout.rightpad.cons-11)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23912)

*Preconditions*: 

- [(11.1)](#mdspan.layout.rightpad.cons-11.1)

  If *rank_* is greater than 1 andpadding_value does not equal dynamic_extent,
then other.stride(*rank_* - 2) equals*LEAST-MULTIPLE-AT-LEAST*(padding_value,
 extents_type::*index-cast*(other.extents().extent(*rank_* - 1)))

- [(11.2)](#mdspan.layout.rightpad.cons-11.2)

  If *rank_* is greater than 0,
then other.stride(*rank_* - 1) equals 1[.](#mdspan.layout.rightpad.cons-11.2.sentence-1)

- [(11.3)](#mdspan.layout.rightpad.cons-11.3)

  If *rank_* is greater than 2,
then for all r in the range [0, *rank_* - 2),other.stride(r) equals(other.extents().*rev-prod-of-extents*(r) / other.extents().extent(*rank_* - 1)) * other.stride(*rank_* - 2)

- [(11.4)](#mdspan.layout.rightpad.cons-11.4)

  other.required_span_size() is representable as
a value of type index_type[.](#mdspan.layout.rightpad.cons-11.4.sentence-1)

[12](#mdspan.layout.rightpad.cons-12)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23939)

*Effects*: 

- [(12.1)](#mdspan.layout.rightpad.cons-12.1)

Direct-non-list-initializes *extents_* with other.extents(); and

- [(12.2)](#mdspan.layout.rightpad.cons-12.2)

if *rank_* is greater than one,
direct-non-list-initializes *stride-rm2* with other.stride(*rank_* - 2)[.](#mdspan.layout.rightpad.cons-12.sentence-1)

[ð](#lib:layout_right_padded::mapping,constructor____)

`template<class LayoutRightPaddedMapping>
  constexpr explicit(see below)
    mapping(const LayoutRightPaddedMapping& other);
`

[13](#mdspan.layout.rightpad.cons-13)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23959)

*Constraints*: 

- [(13.1)](#mdspan.layout.rightpad.cons-13.1)

  *is-layout-right-padded-mapping-of*<LayoutRightPaddedMapping> is true[.](#mdspan.layout.rightpad.cons-13.1.sentence-1)

- [(13.2)](#mdspan.layout.rightpad.cons-13.2)

  is_constructible_v<extents_type, typename LayoutRightPaddedMapping​::​extents_-  
type> is true[.](#mdspan.layout.rightpad.cons-13.2.sentence-1)

[14](#mdspan.layout.rightpad.cons-14)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23970)

*Mandates*: If *rank_* is greater than 1, thenpadding_value == dynamic_extent || LayoutRightPaddedMapping::padding_value == dynamic_extent || padding_value == LayoutRightPaddedMapping::padding_value is true[.](#mdspan.layout.rightpad.cons-14.sentence-1)

[15](#mdspan.layout.rightpad.cons-15)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23980)

*Preconditions*: 

- [(15.1)](#mdspan.layout.rightpad.cons-15.1)

If *rank_* is greater than 1 andpadding_value does not equal dynamic_extent,
then other.stride(*rank_* - 2) equals*LEAST-MULTIPLE-AT-LEAST*(padding_value,
 extents_type::*index-cast*(other.extent(*rank_* - 1)))

- [(15.2)](#mdspan.layout.rightpad.cons-15.2)

other.required_span_size() is representable as
a value of type index_type[.](#mdspan.layout.rightpad.cons-15.sentence-1)

[16](#mdspan.layout.rightpad.cons-16)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23996)

*Effects*: 

- [(16.1)](#mdspan.layout.rightpad.cons-16.1)

Direct-non-list-initializes *extents_* with other.extents(); and

- [(16.2)](#mdspan.layout.rightpad.cons-16.2)

if *rank_* is greater than one,
direct-non-list-initializes *stride-rm2* with other.stride(rank_ - 2)[.](#mdspan.layout.rightpad.cons-16.sentence-1)

[17](#mdspan.layout.rightpad.cons-17)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24007)

*Remarks*: The expression inside explicit is equivalent to:*rank_* > 1 &&(padding_value != dynamic_extent || LayoutRightPaddedMapping::padding_value == dynamic_extent)

[ð](#lib:layout_right_padded::mapping,constructor_____)

`template<class LayoutLeftPaddedMapping>
  constexpr explicit(see below)
    mapping(const LayoutLeftPaddedMapping& other) noexcept;
`

[18](#mdspan.layout.rightpad.cons-18)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24025)

*Constraints*: 

- [(18.1)](#mdspan.layout.rightpad.cons-18.1)

  *is-layout-left-padded-mapping-of*<LayoutLeftPaddedMapping> is true or  
*is-mapping-of*<layout_left, LayoutLeftPaddedMapping> is true[.](#mdspan.layout.rightpad.cons-18.1.sentence-1)

- [(18.2)](#mdspan.layout.rightpad.cons-18.2)

  *rank_* equals zero or one[.](#mdspan.layout.rightpad.cons-18.2.sentence-1)

- [(18.3)](#mdspan.layout.rightpad.cons-18.3)

  is_constructible_v<extents_type, typename LayoutLeftPaddedMapping​::​extents_type>  
is true[.](#mdspan.layout.rightpad.cons-18.3.sentence-1)

[19](#mdspan.layout.rightpad.cons-19)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24040)

*Preconditions*: other.required_span_size() is representable as
a value of type index_type[.](#mdspan.layout.rightpad.cons-19.sentence-1)

[20](#mdspan.layout.rightpad.cons-20)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24045)

*Effects*: Direct-non-list-initializes *extents_* with other.extents()[.](#mdspan.layout.rightpad.cons-20.sentence-1)

[21](#mdspan.layout.rightpad.cons-21)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24049)

*Remarks*: The expression inside explicit is equivalent to:!is_convertible_v<typename LayoutLeftPaddedMapping::extents_type, extents_type>

[*Note [1](#mdspan.layout.rightpad.cons-note-1)*:

Neither the input mapping nor the mapping to be constructed
uses the padding stride in the rank-0 or rank-1 case,
so the padding stride affects neither the constraints nor the preconditions[.](#mdspan.layout.rightpad.cons-21.sentence-1)

â *end note*]

#### [23.7.3.4.9.4](#mdspan.layout.rightpad.obs) Observers [[mdspan.layout.rightpad.obs]](mdspan.layout.rightpad.obs)

[ð](#lib:layout_right_padded::mapping,strides)

`constexpr array<index_type, rank_> strides() const noexcept;
`

[1](#mdspan.layout.rightpad.obs-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24070)

*Returns*: array<index_type, *rank_*>(stride(P_rank)...)[.](#mdspan.layout.rightpad.obs-1.sentence-1)

[ð](#lib:layout_right_padded::mapping,required_span_size)

`constexpr index_type required_span_size() const noexcept;
`

[2](#mdspan.layout.rightpad.obs-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24081)

*Returns*: 0 if the multidimensional index space *extents_* is empty,
otherwise *this(((*extents_*(P_rank) - index_type(1))...)) + 1[.](#mdspan.layout.rightpad.obs-2.sentence-1)

[ð](#lib:layout_right_padded::mapping,operator())

`template<class... Indices>
constexpr size_t operator()(Indices... idxs) const noexcept;
`

[3](#mdspan.layout.rightpad.obs-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24094)

*Constraints*: 

- [(3.1)](#mdspan.layout.rightpad.obs-3.1)

  sizeof...(Indices) == *rank_* is true[.](#mdspan.layout.rightpad.obs-3.1.sentence-1)

- [(3.2)](#mdspan.layout.rightpad.obs-3.2)

  (is_convertible_v<Indices, index_type> && ...) is true[.](#mdspan.layout.rightpad.obs-3.2.sentence-1)

- [(3.3)](#mdspan.layout.rightpad.obs-3.3)

  (is_nothrow_constructible_v<index_type, Indices> && ...) is true[.](#mdspan.layout.rightpad.obs-3.3.sentence-1)

[4](#mdspan.layout.rightpad.obs-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24105)

*Preconditions*: extents_type​::​*index-cast*(idxs) is
a multidimensional index in extents() ([[mdspan.overview]](#mdspan.overview "23.7.3.1 Overview"))[.](#mdspan.layout.rightpad.obs-4.sentence-1)

[5](#mdspan.layout.rightpad.obs-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24110)

*Returns*: ((static_cast<index_type>(idxs) * stride(P_rank)) + ... + 0)[.](#mdspan.layout.rightpad.obs-5.sentence-1)

[ð](#lib:layout_right_padded::mapping,is_always_exhaustive)

`static constexpr bool is_always_exhaustive() noexcept;
`

[6](#mdspan.layout.rightpad.obs-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24121)

*Returns*: 

- [(6.1)](#mdspan.layout.rightpad.obs-6.1)

If *rank_* equals zero or one, then true;

- [(6.2)](#mdspan.layout.rightpad.obs-6.2)

otherwise,
if neither *static-padding-stride* nor *last-static-extent* equal dynamic_extent,
then *static-padding-stride* == *last-static-extent*;

- [(6.3)](#mdspan.layout.rightpad.obs-6.3)

otherwise, false[.](#mdspan.layout.rightpad.obs-6.sentence-1)

[ð](#lib:layout_right_padded::mapping,is_exhaustive)

`constexpr bool is_exhaustive() const noexcept;
`

[7](#mdspan.layout.rightpad.obs-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24142)

*Returns*: true if *rank_* equals zero or one;
otherwise,*extents_*.extent(*rank_* - 1) == stride(*rank_* - 2)

[ð](#mdspan.layout.rightpad.obs-itemdecl:6)

`constexpr index_type stride(rank_type r) const noexcept;
`

[8](#mdspan.layout.rightpad.obs-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24156)

*Preconditions*: r is smaller than *rank_*[.](#mdspan.layout.rightpad.obs-8.sentence-1)

[9](#mdspan.layout.rightpad.obs-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24160)

*Returns*: 

- [(9.1)](#mdspan.layout.rightpad.obs-9.1)

If r equals *rank_* - 1: 1;

- [(9.2)](#mdspan.layout.rightpad.obs-9.2)

otherwise, if r equals *rank_* - 2: *stride-rm2*;

- [(9.3)](#mdspan.layout.rightpad.obs-9.3)

otherwise,
the product of *stride-rm2* and
all values extents_.extent(k) with k in the range of [r + 1, *rank_* - 1)[.](#mdspan.layout.rightpad.obs-9.sentence-1)

[ð](#lib:layout_right_padded::mapping,operator==)

`template<class LayoutRightPaddedMapping>
  friend constexpr bool operator==(const mapping& x, const LayoutRightPaddedMapping& y) noexcept;
`

[10](#mdspan.layout.rightpad.obs-10)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24182)

*Constraints*: 

- [(10.1)](#mdspan.layout.rightpad.obs-10.1)

  *is-layout-right-padded-mapping-of*<LayoutRightPaddedMapping> is true[.](#mdspan.layout.rightpad.obs-10.1.sentence-1)

- [(10.2)](#mdspan.layout.rightpad.obs-10.2)

  LayoutRightPaddedMapping​::​extents_type​::​rank() == *rank_* is true[.](#mdspan.layout.rightpad.obs-10.2.sentence-1)

[11](#mdspan.layout.rightpad.obs-11)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24193)

*Returns*: true if x.extents() == y.extents() is true and*rank_* < 2 || x.stride(*rank_* - 2) == y.stride(*rank_* - 2) is true[.](#mdspan.layout.rightpad.obs-11.sentence-1)

Otherwise, false[.](#mdspan.layout.rightpad.obs-11.sentence-2)

#### [23.7.3.5](#mdspan.accessor) Accessor policy [[mdspan.accessor]](mdspan.accessor)

#### [23.7.3.5.1](#mdspan.accessor.general) General [[mdspan.accessor.general]](mdspan.accessor.general)

[1](#mdspan.accessor.general-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24204)

An [*accessor policy*](#def:accessor_policy "23.7.3.5.1 General [mdspan.accessor.general]") defines types and operations by which
a reference to a single object is created
from an abstract data handle to a number of such objects and an index[.](#mdspan.accessor.general-1.sentence-1)

[2](#mdspan.accessor.general-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24209)

A range of indices [0,N) is an [*accessible range*](#def:range,accessible "23.7.3.5.1 General [mdspan.accessor.general]") of
a given data handle and an accessor
if, for each i in the range,
the accessor policy's access function produces a valid reference to an object[.](#mdspan.accessor.general-2.sentence-1)

[3](#mdspan.accessor.general-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24215)

In [[mdspan.accessor.reqmts]](#mdspan.accessor.reqmts "23.7.3.5.2 Requirements"),

- [(3.1)](#mdspan.accessor.general-3.1)

  A denotes an accessor policy[.](#mdspan.accessor.general-3.1.sentence-1)

- [(3.2)](#mdspan.accessor.general-3.2)

  a denotes a value of type A or const A[.](#mdspan.accessor.general-3.2.sentence-1)

- [(3.3)](#mdspan.accessor.general-3.3)

  p denotes a value of type A​::​data_handle_type or const A​::​data_handle_type[.](#mdspan.accessor.general-3.3.sentence-1)
  [*Note [1](#mdspan.accessor.general-note-1)*:
  The type A​::​data_handle_type need not be dereferenceable[.](#mdspan.accessor.general-3.3.sentence-2)
 â *end note*]

- [(3.4)](#mdspan.accessor.general-3.4)

  n, i, and j each denote values of type size_t[.](#mdspan.accessor.general-3.4.sentence-1)

#### [23.7.3.5.2](#mdspan.accessor.reqmts) Requirements [[mdspan.accessor.reqmts]](mdspan.accessor.reqmts)

[1](#mdspan.accessor.reqmts-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24234)

A type A meets the accessor policy requirements if

- [(1.1)](#mdspan.accessor.reqmts-1.1)

A models [copyable](concepts.object#concept:copyable "18.6 Object concepts [concepts.object]"),

- [(1.2)](#mdspan.accessor.reqmts-1.2)

is_nothrow_move_constructible_v<A> is true,

- [(1.3)](#mdspan.accessor.reqmts-1.3)

is_nothrow_move_assignable_v<A> is true,

- [(1.4)](#mdspan.accessor.reqmts-1.4)

is_nothrow_swappable_v<A> is true, and

- [(1.5)](#mdspan.accessor.reqmts-1.5)

the following types and expressions
are well-formed and have the specified semantics[.](#mdspan.accessor.reqmts-1.sentence-1)

[ð](#mdspan.accessor.reqmts-itemdecl:1)

`typename A::element_type
`

[2](#mdspan.accessor.reqmts-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24255)

*Result*: A complete object type that is not an abstract class type[.](#mdspan.accessor.reqmts-2.sentence-1)

[ð](#mdspan.accessor.reqmts-itemdecl:2)

`typename A::data_handle_type
`

[3](#mdspan.accessor.reqmts-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24265)

*Result*: A type that models [copyable](concepts.object#concept:copyable "18.6 Object concepts [concepts.object]"), and
for which is_nothrow_move_constructible_v<A​::​data_handle_type> is true,is_nothrow_move_assignable_v<A​::​data_handle_type> is true, andis_nothrow_swappable_v<A​::​data_handle_type> is true[.](#mdspan.accessor.reqmts-3.sentence-1)

[*Note [1](#mdspan.accessor.reqmts-note-1)*:

The type of data_handle_type need not be element_type*[.](#mdspan.accessor.reqmts-3.sentence-2)

â *end note*]

[ð](#mdspan.accessor.reqmts-itemdecl:3)

`typename A::reference
`

[4](#mdspan.accessor.reqmts-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24281)

*Result*: A type that models[common_reference_with](concept.commonref#concept:common_reference_with "18.4.5 Concept common_­reference_­with [concept.commonref]")<A​::​reference&&, A​::​element_type&>[.](#mdspan.accessor.reqmts-4.sentence-1)

[*Note [2](#mdspan.accessor.reqmts-note-2)*:

The type of reference need not be element_type&[.](#mdspan.accessor.reqmts-4.sentence-2)

â *end note*]

[ð](#mdspan.accessor.reqmts-itemdecl:4)

`typename A::offset_policy
`

[5](#mdspan.accessor.reqmts-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24295)

*Result*: A type OP such that:

- [(5.1)](#mdspan.accessor.reqmts-5.1)

OP meets the accessor policy requirements,

- [(5.2)](#mdspan.accessor.reqmts-5.2)

[constructible_from](concept.constructible#concept:constructible_from "18.4.11 Concept constructible_­from [concept.constructible]")<OP, const A&> is modeled, and

- [(5.3)](#mdspan.accessor.reqmts-5.3)

is_same_v<typename OP​::​element_type, typename A​::​element_type> is true[.](#mdspan.accessor.reqmts-5.sentence-1)

[ð](#mdspan.accessor.reqmts-itemdecl:5)

`a.access(p, i)
`

[6](#mdspan.accessor.reqmts-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24313)

*Result*: A​::​reference

[7](#mdspan.accessor.reqmts-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24317)

*Remarks*: The expression is equality preserving[.](#mdspan.accessor.reqmts-7.sentence-1)

[8](#mdspan.accessor.reqmts-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24321)

[*Note [3](#mdspan.accessor.reqmts-note-3)*:

Concrete accessor policies can impose preconditions for their access function[.](#mdspan.accessor.reqmts-8.sentence-1)

However, they might not[.](#mdspan.accessor.reqmts-8.sentence-2)

For example, an accessor wherep is span<A​::​element_type, dynamic_extent> andaccess(p, i) returns p[i % p.size()] does not need to impose a precondition on i[.](#mdspan.accessor.reqmts-8.sentence-3)

â *end note*]

[ð](#mdspan.accessor.reqmts-itemdecl:6)

`a.offset(p, i)
`

[9](#mdspan.accessor.reqmts-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24337)

*Result*: A​::​offset_policy​::​data_handle_type

[10](#mdspan.accessor.reqmts-10)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24341)

*Returns*: q such that for b being A​::​offset_policy(a), and
any integer n for which [0, n) is
an accessible range of p and a:

- [(10.1)](#mdspan.accessor.reqmts-10.1)

[0,nâi) is an accessible range of q and b; and

- [(10.2)](#mdspan.accessor.reqmts-10.2)

b.access(q, j) provides access to
the same element as a.access(p, i + j),
for every j in the range [0,nâi)[.](#mdspan.accessor.reqmts-10.sentence-1)

[11](#mdspan.accessor.reqmts-11)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24355)

*Remarks*: The expression is equality-preserving[.](#mdspan.accessor.reqmts-11.sentence-1)

#### [23.7.3.5.3](#mdspan.accessor.default) Class template default_accessor [[mdspan.accessor.default]](mdspan.accessor.default)

#### [23.7.3.5.3.1](#mdspan.accessor.default.overview) Overview [[mdspan.accessor.default.overview]](mdspan.accessor.default.overview)

namespace std {template<class ElementType>struct default_accessor {using offset_policy = default_accessor; using element_type = ElementType; using reference = ElementType&; using data_handle_type = ElementType*; constexpr default_accessor() noexcept = default; template<class OtherElementType>constexpr default_accessor(default_accessor<OtherElementType>) noexcept; constexpr reference access(data_handle_type p, size_t i) const noexcept; constexpr data_handle_type offset(data_handle_type p, size_t i) const noexcept; };}

[1](#mdspan.accessor.default.overview-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24382)

default_accessor meets the accessor policy requirements[.](#mdspan.accessor.default.overview-1.sentence-1)

[2](#mdspan.accessor.default.overview-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24385)

ElementType is required to be a complete object type
that is neither an abstract class type nor an array type[.](#mdspan.accessor.default.overview-2.sentence-1)

[3](#mdspan.accessor.default.overview-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24389)

Each specialization of default_accessor is
a trivially copyable type that models [semiregular](concepts.object#concept:semiregular "18.6 Object concepts [concepts.object]")[.](#mdspan.accessor.default.overview-3.sentence-1)

[4](#mdspan.accessor.default.overview-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24393)

[0,n) is an accessible range for
an object p of type data_handle_type and
an object of type default_accessor if and only if [p, p + n) is a valid range[.](#mdspan.accessor.default.overview-4.sentence-1)

#### [23.7.3.5.3.2](#mdspan.accessor.default.members) Members [[mdspan.accessor.default.members]](mdspan.accessor.default.members)

[ð](#lib:default_accessor,constructor)

`template<class OtherElementType>
  constexpr default_accessor(default_accessor<OtherElementType>) noexcept {}
`

[1](#mdspan.accessor.default.members-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24408)

*Constraints*: is_convertible_v<OtherElementType(*)[], element_type(*)[]> is true[.](#mdspan.accessor.default.members-1.sentence-1)

[ð](#lib:access,default_accessor)

`constexpr reference access(data_handle_type p, size_t i) const noexcept;
`

[2](#mdspan.accessor.default.members-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24420)

*Effects*: Equivalent to: return p[i];

[ð](#lib:offset,default_accessor)

`constexpr data_handle_type offset(data_handle_type p, size_t i) const noexcept;
`

[3](#mdspan.accessor.default.members-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24431)

*Effects*: Equivalent to: return p + i;

#### [23.7.3.5.4](#mdspan.accessor.aligned) Class template aligned_accessor [[mdspan.accessor.aligned]](mdspan.accessor.aligned)

#### [23.7.3.5.4.1](#mdspan.accessor.aligned.overview) Overview [[mdspan.accessor.aligned.overview]](mdspan.accessor.aligned.overview)

namespace std {template<class ElementType, size_t ByteAlignment>struct [aligned_accessor](#lib:aligned_accessor "23.7.3.5.4.1 Overview [mdspan.accessor.aligned.overview]") {using offset_policy = default_accessor<ElementType>; using element_type = ElementType; using reference = ElementType&; using data_handle_type = ElementType*; static constexpr size_t byte_alignment = ByteAlignment; constexpr aligned_accessor() noexcept = default; template<class OtherElementType, size_t OtherByteAlignment>constexpr aligned_accessor( aligned_accessor<OtherElementType, OtherByteAlignment>) noexcept; template<class OtherElementType>constexpr explicit aligned_accessor(default_accessor<OtherElementType>) noexcept; template<class OtherElementType>constexpr operator default_accessor<OtherElementType>() const noexcept; constexpr reference access(data_handle_type p, size_t i) const noexcept; constexpr typename offset_policy::data_handle_type offset( data_handle_type p, size_t i) const noexcept; };}

[1](#mdspan.accessor.aligned.overview-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24469)

*Mandates*: 

- [(1.1)](#mdspan.accessor.aligned.overview-1.1)

byte_alignment is a power of two, and

- [(1.2)](#mdspan.accessor.aligned.overview-1.2)

byte_alignment >= alignof(ElementType) is true[.](#mdspan.accessor.aligned.overview-1.sentence-1)

[2](#mdspan.accessor.aligned.overview-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24476)

aligned_accessor meets the accessor policy requirements[.](#mdspan.accessor.aligned.overview-2.sentence-1)

[3](#mdspan.accessor.aligned.overview-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24479)

ElementType is required to be a complete object type
that is neither an abstract class type nor an array type[.](#mdspan.accessor.aligned.overview-3.sentence-1)

[4](#mdspan.accessor.aligned.overview-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24483)

Each specialization of aligned_accessor is
a trivially copyable type that models [semiregular](concepts.object#concept:semiregular "18.6 Object concepts [concepts.object]")[.](#mdspan.accessor.aligned.overview-4.sentence-1)

[5](#mdspan.accessor.aligned.overview-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24487)

[0, n) is an accessible range
for an object p of type data_handle_type and
an object of type aligned_accessor if and only if

- [(5.1)](#mdspan.accessor.aligned.overview-5.1)

[p, p + n) is a valid range, and,

- [(5.2)](#mdspan.accessor.aligned.overview-5.2)

if n is greater than zero,
then is_sufficiently_aligned<byte_alignment>(p) is true[.](#mdspan.accessor.aligned.overview-5.sentence-1)

[6](#mdspan.accessor.aligned.overview-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24499)

[*Example [1](#mdspan.accessor.aligned.overview-example-1)*:

The following function compute uses is_sufficiently_aligned to check
whether a given mdspan with default_accessor has
a data handle with sufficient alignment
to be used with aligned_accessor<float, 4 * sizeof(float)>[.](#mdspan.accessor.aligned.overview-6.sentence-1)

If so, the function dispatches to
a function compute_using_fourfold_overalignment that requires fourfold over-alignment of arrays,
but can therefore use hardware-specific instructions,
such as four-wide SIMD (Single Instruction Multiple Data) instructions[.](#mdspan.accessor.aligned.overview-6.sentence-2)

Otherwise, compute dispatches to a
possibly less optimized function compute_without_requiring_overalignment that has no over-alignment requirement[.](#mdspan.accessor.aligned.overview-6.sentence-3)

void compute_using_fourfold_overalignment( std::mdspan<float, std::dims<1>, std::layout_right,
 std::aligned_accessor<float, 4 * alignof(float)>> x);

void compute_without_requiring_overalignment( std::mdspan<float, std::dims<1>, std::layout_right> x);

void compute(std::mdspan<float, std::dims<1>> x) {constexpr auto byte_alignment = 4 * sizeof(float); auto accessor = std::aligned_accessor<float, byte_alignment>{}; auto x_handle = x.data_handle(); if (std::is_sufficiently_aligned<byte_alignment>(x_handle)) { compute_using_fourfold_overalignment(std::mdspan{x_handle, x.mapping(), accessor}); } else { compute_without_requiring_overalignment(x); }} â *end example*]

#### [23.7.3.5.4.2](#mdspan.accessor.aligned.members) Members [[mdspan.accessor.aligned.members]](mdspan.accessor.aligned.members)

[ð](#lib:aligned_accessor,constructor)

`template<class OtherElementType, size_t OtherByteAlignment>
  constexpr aligned_accessor(aligned_accessor<OtherElementType, OtherByteAlignment>) noexcept;
`

[1](#mdspan.accessor.aligned.members-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24545)

*Constraints*: 

- [(1.1)](#mdspan.accessor.aligned.members-1.1)

  is_convertible_v<OtherElementType(*)[], element_type(*)[]> is true[.](#mdspan.accessor.aligned.members-1.1.sentence-1)

- [(1.2)](#mdspan.accessor.aligned.members-1.2)

  OtherByteAlignment >= byte_alignment is true[.](#mdspan.accessor.aligned.members-1.2.sentence-1)

[2](#mdspan.accessor.aligned.members-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24555)

*Effects*: None[.](#mdspan.accessor.aligned.members-2.sentence-1)

[ð](#lib:aligned_accessor,constructor_)

`template<class OtherElementType>
  constexpr explicit aligned_accessor(default_accessor<OtherElementType>) noexcept;
`

[3](#mdspan.accessor.aligned.members-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24567)

*Constraints*: is_convertible_v<OtherElementType(*)[], element_type(*)[]> is true[.](#mdspan.accessor.aligned.members-3.sentence-1)

[4](#mdspan.accessor.aligned.members-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24572)

*Effects*: None[.](#mdspan.accessor.aligned.members-4.sentence-1)

[ð](#lib:access,aligned_accessor)

`constexpr reference access(data_handle_type p, size_t i) const noexcept;
`

[5](#mdspan.accessor.aligned.members-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24583)

*Preconditions*: [0, i + 1) is an accessible range for p and *this[.](#mdspan.accessor.aligned.members-5.sentence-1)

[6](#mdspan.accessor.aligned.members-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24587)

*Effects*: Equivalent to: return assume_aligned<byte_alignment>(p)[i];

[ð](#lib:operator_default_accessor,aligned_accessor)

`template<class OtherElementType>
  constexpr operator default_accessor<OtherElementType>() const noexcept;
`

[7](#mdspan.accessor.aligned.members-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24599)

*Constraints*: is_convertible_v<element_type(*)[], OtherElementType(*)[]> is true[.](#mdspan.accessor.aligned.members-7.sentence-1)

[8](#mdspan.accessor.aligned.members-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24604)

*Effects*: Equivalent to: return {};

[ð](#lib:offset,aligned_accessor)

`constexpr typename offset_policy::data_handle_type
  offset(data_handle_type p, size_t i) const noexcept;
`

[9](#mdspan.accessor.aligned.members-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24616)

*Preconditions*: [0, i + 1) is an accessible range for p and *this[.](#mdspan.accessor.aligned.members-9.sentence-1)

[10](#mdspan.accessor.aligned.members-10)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24620)

*Effects*: Equivalent to: return assume_aligned<byte_alignment>(p) + i;

#### [23.7.3.6](#mdspan.mdspan) Class template mdspan [[mdspan.mdspan]](mdspan.mdspan)

#### [23.7.3.6.1](#mdspan.mdspan.overview) Overview [[mdspan.mdspan.overview]](mdspan.mdspan.overview)

[1](#mdspan.mdspan.overview-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24629)

mdspan is a view of a multidimensional array of elements[.](#mdspan.mdspan.overview-1.sentence-1)

namespace std {template<class ElementType, class Extents, class LayoutPolicy = layout_right, class AccessorPolicy = default_accessor<ElementType>>class mdspan {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); }// [[mdspan.mdspan.cons]](#mdspan.mdspan.cons "23.7.3.6.2 Constructors"), constructorsconstexpr mdspan(); constexpr mdspan(const mdspan& rhs) = default; constexpr mdspan(mdspan&& rhs) = default; template<class... OtherIndexTypes>constexpr explicit mdspan(data_handle_type ptr, OtherIndexTypes... exts); template<class OtherIndexType, size_t N>constexpr explicit(N != rank_dynamic()) mdspan(data_handle_type p, span<OtherIndexType, N> exts); template<class OtherIndexType, size_t N>constexpr explicit(N != rank_dynamic()) mdspan(data_handle_type p, const array<OtherIndexType, N>& exts); constexpr mdspan(data_handle_type p, const extents_type& ext); constexpr mdspan(data_handle_type p, const mapping_type& m); constexpr mdspan(data_handle_type p, const mapping_type& m, const accessor_type& a); template<class OtherElementType, class OtherExtents, class OtherLayoutPolicy, class OtherAccessorPolicy>constexpr explicit(*see below*) mdspan(const mdspan<OtherElementType, OtherExtents,
 OtherLayoutPolicy, OtherAccessorPolicy>& other); constexpr mdspan& operator=(const mdspan& rhs) = default; constexpr mdspan& operator=(mdspan&& rhs) = default; // [[mdspan.mdspan.members]](#mdspan.mdspan.members "23.7.3.6.3 Members"), memberstemplate<class... OtherIndexTypes>constexpr reference operator[](OtherIndexTypes... indices) const; template<class OtherIndexType>constexpr reference operator[](span<OtherIndexType, rank()> indices) const; template<class OtherIndexType>constexpr reference operator[](const array<OtherIndexType, rank()>& indices) const; template<class... OtherIndexTypes>constexpr reference
 at(OtherIndexTypes... indices) const; // freestanding-deletedtemplate<class OtherIndexType>constexpr reference
 at(span<OtherIndexType, rank()> indices) const; // freestanding-deletedtemplate<class OtherIndexType>constexpr reference
 at(const array<OtherIndexType, rank()>& indices) const; // freestanding-deletedconstexpr size_type size() const noexcept; constexpr bool empty() const noexcept; friend constexpr void swap(mdspan& x, mdspan& y) noexcept; constexpr const extents_type& extents() const noexcept { return *map_*.extents(); }constexpr const data_handle_type& data_handle() const noexcept { return *ptr_*; }constexpr const mapping_type& mapping() const noexcept { return *map_*; }constexpr const accessor_type& accessor() const noexcept { return *acc_*; }static constexpr bool is_always_unique(){ return mapping_type::is_always_unique(); }static constexpr bool is_always_exhaustive(){ return mapping_type::is_always_exhaustive(); }static constexpr bool is_always_strided(){ return mapping_type::is_always_strided(); }constexpr bool is_unique() const{ return *map_*.is_unique(); }constexpr bool is_exhaustive() const{ return *map_*.is_exhaustive(); }constexpr bool is_strided() const{ return *map_*.is_strided(); }constexpr index_type stride(rank_type r) const{ return *map_*.stride(r); }private: accessor_type *acc_*; // *exposition only* mapping_type *map_*; // *exposition only* data_handle_type *ptr_*; // *exposition only*}; template<class 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<class Pointer>requires (is_pointer_v<remove_reference_t<Pointer>>) mdspan(Pointer&&)-> mdspan<remove_pointer_t<remove_reference_t<Pointer>>, extents<size_t>>; template<class ElementType, class... Integrals>requires ((is_convertible_v<Integrals, size_t> && ...) && sizeof...(Integrals) > 0)explicit mdspan(ElementType*, Integrals...)-> mdspan<ElementType, extents<size_t, [*maybe-static-ext*](span.syn#concept:maybe-static-ext "23.7.2.1 Header <span> synopsis [span.syn]")<Integrals>...>>; template<class ElementType, class OtherIndexType, size_t N> mdspan(ElementType*, span<OtherIndexType, N>)-> mdspan<ElementType, dextents<size_t, N>>; template<class ElementType, class OtherIndexType, size_t N> mdspan(ElementType*, const array<OtherIndexType, N>&)-> mdspan<ElementType, dextents<size_t, N>>; template<class ElementType, class IndexType, size_t... ExtentsPack> mdspan(ElementType*, const extents<IndexType, ExtentsPack...>&)-> mdspan<ElementType, extents<IndexType, ExtentsPack...>>; template<class ElementType, class MappingType> mdspan(ElementType*, const MappingType&)-> mdspan<ElementType, typename MappingType::extents_type, typename MappingType::layout_type>; template<class MappingType, class 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>;}

[2](#mdspan.mdspan.overview-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24772)

*Mandates*: 

- [(2.1)](#mdspan.mdspan.overview-2.1)

ElementType is a complete object type
that is neither an abstract class type nor an array type,

- [(2.2)](#mdspan.mdspan.overview-2.2)

Extents is a specialization of extents, and

- [(2.3)](#mdspan.mdspan.overview-2.3)

is_same_v<ElementType, typename AccessorPolicy​::​element_type> is true[.](#mdspan.mdspan.overview-2.sentence-1)

[3](#mdspan.mdspan.overview-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24785)

LayoutPolicy shall meet
the layout mapping policy requirements ([[mdspan.layout.policy.reqmts]](#mdspan.layout.policy.reqmts "23.7.3.4.3 Layout mapping policy requirements")), andAccessorPolicy shall meet
the accessor policy requirements ([[mdspan.accessor.reqmts]](#mdspan.accessor.reqmts "23.7.3.5.2 Requirements"))[.](#mdspan.mdspan.overview-3.sentence-1)

[4](#mdspan.mdspan.overview-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24791)

Each specialization MDS of mdspan models [copyable](concepts.object#concept:copyable "18.6 Object concepts [concepts.object]") and

- [(4.1)](#mdspan.mdspan.overview-4.1)

is_nothrow_move_constructible_v<MDS> is true,

- [(4.2)](#mdspan.mdspan.overview-4.2)

is_nothrow_move_assignable_v<MDS> is true, and

- [(4.3)](#mdspan.mdspan.overview-4.3)

is_nothrow_swappable_v<MDS> is true[.](#mdspan.mdspan.overview-4.sentence-1)

[5](#mdspan.mdspan.overview-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24802)

A specialization of mdspan is a trivially copyable type if
its accessor_type, mapping_type, and data_handle_type are trivially copyable types[.](#mdspan.mdspan.overview-5.sentence-1)

#### [23.7.3.6.2](#mdspan.mdspan.cons) Constructors [[mdspan.mdspan.cons]](mdspan.mdspan.cons)

[ð](#lib:mdspan,constructor)

`constexpr mdspan();
`

[1](#mdspan.mdspan.cons-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24815)

*Constraints*: 

- [(1.1)](#mdspan.mdspan.cons-1.1)

  rank_dynamic() > 0 is true[.](#mdspan.mdspan.cons-1.1.sentence-1)

- [(1.2)](#mdspan.mdspan.cons-1.2)

  is_default_constructible_v<data_handle_type> is true[.](#mdspan.mdspan.cons-1.2.sentence-1)

- [(1.3)](#mdspan.mdspan.cons-1.3)

  is_default_constructible_v<mapping_type> is true[.](#mdspan.mdspan.cons-1.3.sentence-1)

- [(1.4)](#mdspan.mdspan.cons-1.4)

  is_default_constructible_v<accessor_type> is true[.](#mdspan.mdspan.cons-1.4.sentence-1)

[2](#mdspan.mdspan.cons-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24828)

*Preconditions*: [0, *map_*.required_span_size()) is
an accessible range of *ptr_* and *acc_* for the values of *map_* and *acc_* after the invocation of this constructor[.](#mdspan.mdspan.cons-2.sentence-1)

[3](#mdspan.mdspan.cons-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24835)

*Effects*: Value-initializes *ptr_*, *map_*, and *acc_*[.](#mdspan.mdspan.cons-3.sentence-1)

[ð](#lib:mdspan,constructor_)

`template<class... OtherIndexTypes>
  constexpr explicit mdspan(data_handle_type p, OtherIndexTypes... exts);
`

[4](#mdspan.mdspan.cons-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24847)

Let N be sizeof...(OtherIndexTypes)[.](#mdspan.mdspan.cons-4.sentence-1)

[5](#mdspan.mdspan.cons-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24850)

*Constraints*: 

- [(5.1)](#mdspan.mdspan.cons-5.1)

(is_convertible_v<OtherIndexTypes, index_type> && ...) is true,

- [(5.2)](#mdspan.mdspan.cons-5.2)

(is_nothrow_constructible<index_type, OtherIndexTypes> && ...) is true,

- [(5.3)](#mdspan.mdspan.cons-5.3)

N == rank() || N == rank_dynamic() is true,

- [(5.4)](#mdspan.mdspan.cons-5.4)

is_constructible_v<mapping_type, extents_type> is true, and

- [(5.5)](#mdspan.mdspan.cons-5.5)

is_default_constructible_v<accessor_type> is true[.](#mdspan.mdspan.cons-5.sentence-1)

[6](#mdspan.mdspan.cons-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24865)

*Preconditions*: [0, *map_*.required_span_size()) is
an accessible range of p and *acc_* for the values of *map_* and *acc_* after the invocation of this constructor[.](#mdspan.mdspan.cons-6.sentence-1)

[7](#mdspan.mdspan.cons-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24872)

*Effects*: 

- [(7.1)](#mdspan.mdspan.cons-7.1)

Direct-non-list-initializes *ptr_* with std​::​move(p),

- [(7.2)](#mdspan.mdspan.cons-7.2)

direct-non-list-initializes *map_* withextents_type(static_cast<index_type>(std​::​move(exts​))...), and

- [(7.3)](#mdspan.mdspan.cons-7.3)

value-initializes *acc_*[.](#mdspan.mdspan.cons-7.sentence-1)

[ð](#lib:mdspan,constructor__)

`template<class OtherIndexType, size_t N>
  constexpr explicit(N != rank_dynamic())
    mdspan(data_handle_type p, span<OtherIndexType, N> exts);
template<class OtherIndexType, size_t N>
  constexpr explicit(N != rank_dynamic())
    mdspan(data_handle_type p, const array<OtherIndexType, N>& exts);
`

[8](#mdspan.mdspan.cons-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24896)

*Constraints*: 

- [(8.1)](#mdspan.mdspan.cons-8.1)

is_convertible_v<const OtherIndexType&, index_type> is true,

- [(8.2)](#mdspan.mdspan.cons-8.2)

is_nothrow_constructible_v<index_type, const OtherIndexType&> is true,

- [(8.3)](#mdspan.mdspan.cons-8.3)

N == rank() || N == rank_dynamic() is true,

- [(8.4)](#mdspan.mdspan.cons-8.4)

is_constructible_v<mapping_type, extents_type> is true, and

- [(8.5)](#mdspan.mdspan.cons-8.5)

is_default_constructible_v<accessor_type> is true[.](#mdspan.mdspan.cons-8.sentence-1)

[9](#mdspan.mdspan.cons-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24911)

*Preconditions*: [0, *map_*.required_span_size()) is
an accessible range of p and *acc_* for the values of *map_* and *acc_* after the invocation of this constructor[.](#mdspan.mdspan.cons-9.sentence-1)

[10](#mdspan.mdspan.cons-10)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24918)

*Effects*: 

- [(10.1)](#mdspan.mdspan.cons-10.1)

Direct-non-list-initializes *ptr_* with std​::​move(p),

- [(10.2)](#mdspan.mdspan.cons-10.2)

direct-non-list-initializes *map_* with extents_type(exts), and

- [(10.3)](#mdspan.mdspan.cons-10.3)

value-initializes *acc_*[.](#mdspan.mdspan.cons-10.sentence-1)

[ð](#lib:mdspan,constructor___)

`constexpr mdspan(data_handle_type p, const extents_type& ext);
`

[11](#mdspan.mdspan.cons-11)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24936)

*Constraints*: 

- [(11.1)](#mdspan.mdspan.cons-11.1)

is_constructible_v<mapping_type, const extents_type&> is true, and

- [(11.2)](#mdspan.mdspan.cons-11.2)

is_default_constructible_v<accessor_type> is true[.](#mdspan.mdspan.cons-11.sentence-1)

[12](#mdspan.mdspan.cons-12)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24945)

*Preconditions*: [0, *map_*.required_span_size()) is
an accessible range of p and *acc_* for the values of *map_* and *acc_* after the invocation of this constructor[.](#mdspan.mdspan.cons-12.sentence-1)

[13](#mdspan.mdspan.cons-13)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24952)

*Effects*: 

- [(13.1)](#mdspan.mdspan.cons-13.1)

Direct-non-list-initializes *ptr_* with std​::​move(p),

- [(13.2)](#mdspan.mdspan.cons-13.2)

direct-non-list-initializes *map_* with ext, and

- [(13.3)](#mdspan.mdspan.cons-13.3)

value-initializes *acc_*[.](#mdspan.mdspan.cons-13.sentence-1)

[ð](#lib:mdspan,constructor____)

`constexpr mdspan(data_handle_type p, const mapping_type& m);
`

[14](#mdspan.mdspan.cons-14)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24970)

*Constraints*: is_default_constructible_v<accessor_type> is true[.](#mdspan.mdspan.cons-14.sentence-1)

[15](#mdspan.mdspan.cons-15)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24974)

*Preconditions*: [0, m.required_span_size()) is
an accessible range of p and *acc_* for the value of *acc_* after the invocation of this constructor[.](#mdspan.mdspan.cons-15.sentence-1)

[16](#mdspan.mdspan.cons-16)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24980)

*Effects*: 

- [(16.1)](#mdspan.mdspan.cons-16.1)

Direct-non-list-initializes *ptr_* with std​::​move(p),

- [(16.2)](#mdspan.mdspan.cons-16.2)

direct-non-list-initializes *map_* with m, and

- [(16.3)](#mdspan.mdspan.cons-16.3)

value-initializes *acc_*[.](#mdspan.mdspan.cons-16.sentence-1)

[ð](#lib:mdspan,constructor_____)

`constexpr mdspan(data_handle_type p, const mapping_type& m, const accessor_type& a);
`

[17](#mdspan.mdspan.cons-17)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L24998)

*Preconditions*: [0, m.required_span_size()) is
an accessible range of p and a[.](#mdspan.mdspan.cons-17.sentence-1)

[18](#mdspan.mdspan.cons-18)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25003)

*Effects*: 

- [(18.1)](#mdspan.mdspan.cons-18.1)

Direct-non-list-initializes *ptr_* with std​::​move(p),

- [(18.2)](#mdspan.mdspan.cons-18.2)

direct-non-list-initializes *map_* with m, and

- [(18.3)](#mdspan.mdspan.cons-18.3)

direct-non-list-initializes *acc_* with a[.](#mdspan.mdspan.cons-18.sentence-1)

[ð](#lib:mdspan,constructor______)

`template<class OtherElementType, class OtherExtents,
         class OtherLayoutPolicy, class OtherAccessor>
  constexpr explicit(see below)
    mdspan(const mdspan<OtherElementType, OtherExtents,
                        OtherLayoutPolicy, OtherAccessor>& other);
`

[19](#mdspan.mdspan.cons-19)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25025)

*Constraints*: 

- [(19.1)](#mdspan.mdspan.cons-19.1)

is_constructible_v<mapping_type, const OtherLayoutPolicy​::​template mapping<Oth-  
erExtents>&> is true, and

- [(19.2)](#mdspan.mdspan.cons-19.2)

is_constructible_v<accessor_type, const OtherAccessor&> is true[.](#mdspan.mdspan.cons-19.sentence-1)

[20](#mdspan.mdspan.cons-20)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25035)

*Mandates*: 

- [(20.1)](#mdspan.mdspan.cons-20.1)

is_constructible_v<data_handle_type, const OtherAccessor​::​data_handle_type&> is  
true, and

- [(20.2)](#mdspan.mdspan.cons-20.2)

is_constructible_v<extents_type, OtherExtents> is true[.](#mdspan.mdspan.cons-20.sentence-1)

[21](#mdspan.mdspan.cons-21)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25044)

*Preconditions*: [0, *map_*.required_span_size()) is
an accessible range of *ptr_* and *acc_* for values of *ptr_*, *map_*, and *acc_* after the invocation of this constructor[.](#mdspan.mdspan.cons-21.sentence-1)

[22](#mdspan.mdspan.cons-22)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25051)

*Hardened preconditions*: For each rank index r of extents_type,static_extent(r) == dynamic_extent || static_extent(r) == other.extent(r) is true[.](#mdspan.mdspan.cons-22.sentence-1)

[23](#mdspan.mdspan.cons-23)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25057)

*Effects*: 

- [(23.1)](#mdspan.mdspan.cons-23.1)

Direct-non-list-initializes *ptr_* with other.*ptr_*,

- [(23.2)](#mdspan.mdspan.cons-23.2)

direct-non-list-initializes *map_* with other.*map_*, and

- [(23.3)](#mdspan.mdspan.cons-23.3)

direct-non-list-initializes *acc_* with other.*acc_*[.](#mdspan.mdspan.cons-23.sentence-1)

[24](#mdspan.mdspan.cons-24)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25068)

*Remarks*: The expression inside explicit is equivalent to:!is_convertible_v<const OtherLayoutPolicy::template mapping<OtherExtents>&, mapping_type>|| !is_convertible_v<const OtherAccessor&, accessor_type>

#### [23.7.3.6.3](#mdspan.mdspan.members) Members [[mdspan.mdspan.members]](mdspan.mdspan.members)

[ð](#lib:operator%5b%5d,mdspan)

`template<class... OtherIndexTypes>
  constexpr reference operator[](OtherIndexTypes... indices) const;
`

[1](#mdspan.mdspan.members-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25086)

*Constraints*: 

- [(1.1)](#mdspan.mdspan.members-1.1)

(is_convertible_v<OtherIndexTypes, index_type> && ...) is true,

- [(1.2)](#mdspan.mdspan.members-1.2)

(is_nothrow_constructible_v<index_type, OtherIndexTypes> && ...) is true, and

- [(1.3)](#mdspan.mdspan.members-1.3)

sizeof...(OtherIndexTypes) == rank() is true[.](#mdspan.mdspan.members-1.sentence-1)

[2](#mdspan.mdspan.members-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25097)

Let I be extents_type​::​*index-cast*(std​::​move(indices))[.](#mdspan.mdspan.members-2.sentence-1)

[3](#mdspan.mdspan.members-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25100)

*Hardened preconditions*: I is a multidimensional index in extents()[.](#mdspan.mdspan.members-3.sentence-1)

[*Note [1](#mdspan.mdspan.members-note-1)*:

This implies that*map_*(I) < *map_*.required_span_size() is true[.](#mdspan.mdspan.members-3.sentence-2)

â *end note*]

[4](#mdspan.mdspan.members-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25109)

*Effects*: Equivalent to:return *acc_*.access(*ptr_*, *map_*(static_cast<index_type>(std::move(indices))...));

[ð](#lib:operator%5b%5d,mdspan_)

`template<class OtherIndexType>
  constexpr reference operator[](span<OtherIndexType, rank()> indices) const;
template<class OtherIndexType>
  constexpr reference operator[](const array<OtherIndexType, rank()>& indices) const;
`

[5](#mdspan.mdspan.members-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25126)

*Constraints*: 

- [(5.1)](#mdspan.mdspan.members-5.1)

is_convertible_v<const OtherIndexType&, index_type> is true, and

- [(5.2)](#mdspan.mdspan.members-5.2)

is_nothrow_constructible_v<index_type, const OtherIndexType&> is true[.](#mdspan.mdspan.members-5.sentence-1)

[6](#mdspan.mdspan.members-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25135)

*Effects*: Let P be a parameter pack such thatis_same_v<make_index_sequence<rank()>, index_sequence<P...>> is true[.](#mdspan.mdspan.members-6.sentence-1)

Equivalent to:return operator[](extents_type::*index-cast*(as_const(indices[P]))...);

[ð](#lib:at,mdspan)

`template<class... OtherIndexTypes>
  constexpr reference at(OtherIndexTypes... indices) const;
`

[7](#mdspan.mdspan.members-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25155)

*Constraints*: 

- [(7.1)](#mdspan.mdspan.members-7.1)

(is_convertible_v<OtherIndexTypes, index_type> && ...) is true,

- [(7.2)](#mdspan.mdspan.members-7.2)

(is_nothrow_constructible_v<index_type, OtherIndexTypes> && ...) is true, and

- [(7.3)](#mdspan.mdspan.members-7.3)

sizeof...(OtherIndexTypes) == rank() is true[.](#mdspan.mdspan.members-7.sentence-1)

[8](#mdspan.mdspan.members-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25166)

Let I be extents_type​::​*index-cast*(std​::​move(indices))[.](#mdspan.mdspan.members-8.sentence-1)

[9](#mdspan.mdspan.members-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25169)

*Returns*: (*this)[I...][.](#mdspan.mdspan.members-9.sentence-1)

[10](#mdspan.mdspan.members-10)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25173)

*Throws*: out_of_range if I is not a multidimensional index in extents()[.](#mdspan.mdspan.members-10.sentence-1)

[ð](#lib:at,mdspan_)

`template<class OtherIndexType>
  constexpr reference at(span<OtherIndexType, rank()> indices) const;
template<class OtherIndexType>
  constexpr reference at(const array<OtherIndexType, rank()>& indices) const;
`

[11](#mdspan.mdspan.members-11)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25187)

*Constraints*: 

- [(11.1)](#mdspan.mdspan.members-11.1)

is_convertible_v<const OtherIndexType&, index_type> is true, and

- [(11.2)](#mdspan.mdspan.members-11.2)

is_nothrow_constructible_v<index_type, const OtherIndexType&> is true[.](#mdspan.mdspan.members-11.sentence-1)

[12](#mdspan.mdspan.members-12)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25196)

*Effects*: Let P be a parameter pack such thatis_same_v<make_index_sequence<rank()>, index_sequence<P...>> is true[.](#mdspan.mdspan.members-12.sentence-1)

Equivalent to:return at(extents_type::*index-cast*(as_const(indices[P]))...);

[ð](#lib:size,mdspan)

`constexpr size_type size() const noexcept;
`

[13](#mdspan.mdspan.members-13)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25215)

*Preconditions*: The size of the multidimensional index space extents() is representable as a value of type size_type ([[basic.fundamental]](basic.fundamental "6.9.2 Fundamental types"))[.](#mdspan.mdspan.members-13.sentence-1)

[14](#mdspan.mdspan.members-14)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25220)

*Returns*: extents().*fwd-prod-of-extents*(rank())[.](#mdspan.mdspan.members-14.sentence-1)

[ð](#lib:empty,mdspan)

`constexpr bool empty() const noexcept;
`

[15](#mdspan.mdspan.members-15)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25231)

*Returns*: true if the size of the multidimensional index space extents() is 0,
otherwise false[.](#mdspan.mdspan.members-15.sentence-1)

[ð](#lib:swap,mdspan)

`friend constexpr void swap(mdspan& x, mdspan& y) noexcept;
`

[16](#mdspan.mdspan.members-16)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25244)

*Effects*: Equivalent to:swap(x.*ptr_*, y.*ptr_*);
swap(x.*map_*, y.*map_*);
swap(x.*acc_*, y.*acc_*);

#### [23.7.3.7](#mdspan.sub) submdspan [[mdspan.sub]](mdspan.sub)

#### [23.7.3.7.1](#mdspan.sub.overview) Overview [[mdspan.sub.overview]](mdspan.sub.overview)

[1](#mdspan.sub.overview-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25258)

The submdspan facilities create a new mdspan viewing a subset of elements of an existing input mdspan[.](#mdspan.sub.overview-1.sentence-1)

The subset viewed by the created mdspan is determined by
the SliceSpecifier arguments[.](#mdspan.sub.overview-1.sentence-2)

[2](#mdspan.sub.overview-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25264)

For each function defined in [[mdspan.sub]](#mdspan.sub "23.7.3.7 submdspan") that
takes a parameter pack named slices as an argument:

- [(2.1)](#mdspan.sub.overview-2.1)

let index_type be
  * [(2.1.1)](#mdspan.sub.overview-2.1.1)

M​::​index_type if the function is a member of a class M,

  * [(2.1.2)](#mdspan.sub.overview-2.1.2)

otherwise, remove_reference_t<decltype(src)>​::​index_type if the function has a parameter named src,

  * [(2.1.3)](#mdspan.sub.overview-2.1.3)

otherwise,
 the same type as the function's template argument IndexType;

- [(2.2)](#mdspan.sub.overview-2.2)

let rank be the number of elements in slices;

- [(2.3)](#mdspan.sub.overview-2.3)

let sk be the kth element of slices;

- [(2.4)](#mdspan.sub.overview-2.4)

let Sk be the type of sk; and

- [(2.5)](#mdspan.sub.overview-2.5)

let *map-rank* be an array<size_t, rank> such that
for each k in the range [0, rank),*map-rank*[k] equals:
  * [(2.5.1)](#mdspan.sub.overview-2.5.1)

dynamic_extent if Sk models [convertible_to](concept.convertible#concept:convertible_to "18.4.4 Concept convertible_­to [concept.convertible]")<index_type>,

  * [(2.5.2)](#mdspan.sub.overview-2.5.2)

otherwise,
 the number of types Sj with j<k that
 do not model [convertible_to](concept.convertible#concept:convertible_to "18.4.4 Concept convertible_­to [concept.convertible]")<index_type>[.](#mdspan.sub.overview-2.sentence-1)

#### [23.7.3.7.2](#mdspan.sub.strided.slice) strided_slice [[mdspan.sub.strided.slice]](mdspan.sub.strided.slice)

[1](#mdspan.sub.strided.slice-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25300)

strided_slice represents a set ofextent regularly spaced integer indices[.](#mdspan.sub.strided.slice-1.sentence-1)

The indices start at offset, and
increase by increments of stride[.](#mdspan.sub.strided.slice-1.sentence-2)

[ð](#lib:strided_slice)

namespace std {template<class OffsetType, class ExtentType, class StrideType>struct strided_slice {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{}; };}

[2](#mdspan.sub.strided.slice-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25322)

strided_slice has the data members and special members specified above[.](#mdspan.sub.strided.slice-2.sentence-1)

It has no base classes or members other than those specified[.](#mdspan.sub.strided.slice-2.sentence-2)

[3](#mdspan.sub.strided.slice-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25326)

*Mandates*: OffsetType, ExtentType, and StrideType are signed or unsigned integer types, or
model [*integral-constant-like*](span.syn#concept:integral-constant-like "23.7.2.1 Header <span> synopsis [span.syn]")[.](#mdspan.sub.strided.slice-3.sentence-1)

[*Note [1](#mdspan.sub.strided.slice-note-1)*:

strided_slice{.offset = 1, .extent = 10, .stride = 3} indicates the indices 1, 4, 7, and 10[.](#mdspan.sub.strided.slice-3.sentence-2)

Indices are selected from the half-open interval [1, 1 + 10)[.](#mdspan.sub.strided.slice-3.sentence-3)

â *end note*]

#### [23.7.3.7.3](#mdspan.sub.map.result) submdspan_mapping_result [[mdspan.sub.map.result]](mdspan.sub.map.result)

[1](#mdspan.sub.map.result-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25339)

Specializations of submdspan_mapping_result are returned by overloads of submdspan_mapping[.](#mdspan.sub.map.result-1.sentence-1)

[ð](#lib:submdspan_mapping_result)

namespace std {template<class LayoutMapping>struct submdspan_mapping_result {[[no_unique_address]] LayoutMapping mapping = LayoutMapping();
 size_t offset{}; };}

[2](#mdspan.sub.map.result-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25354)

submdspan_mapping_result has
the data members and special members specified above[.](#mdspan.sub.map.result-2.sentence-1)

It has no base classes or members other than those specified[.](#mdspan.sub.map.result-2.sentence-2)

[3](#mdspan.sub.map.result-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25359)

LayoutMapping shall meet
the layout mapping requirements ([[mdspan.layout.policy.reqmts]](#mdspan.layout.policy.reqmts "23.7.3.4.3 Layout mapping policy requirements"))[.](#mdspan.sub.map.result-3.sentence-1)

#### [23.7.3.7.4](#mdspan.sub.helpers) Exposition-only helpers [[mdspan.sub.helpers]](mdspan.sub.helpers)

[ð](#lib:de-ice)

`template<class T>
  constexpr T de-ice(T val) { return val; }
template<[integral-constant-like](span.syn#concept:integral-constant-like "23.7.2.1 Header <span> synopsis [span.syn]") T>
  constexpr auto de-ice(T) { return T::value; }

template<class IndexType, size_t k, class... SliceSpecifiers>
  constexpr IndexType first_(SliceSpecifiers... slices);
`

[1](#mdspan.sub.helpers-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25378)

*Mandates*: IndexType is a signed or unsigned integer type[.](#mdspan.sub.helpers-1.sentence-1)

[2](#mdspan.sub.helpers-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25383)

Let Ïk denote the following value:

- [(2.1)](#mdspan.sub.helpers-2.1)

sk if Sk models [convertible_to](concept.convertible#concept:convertible_to "18.4.4 Concept convertible_­to [concept.convertible]")<IndexType>;

- [(2.2)](#mdspan.sub.helpers-2.2)

otherwise,get<0>(sk) if Sk models [*index-pair-like*](#concept:index-pair-like "23.7.3.2 Header <mdspan> synopsis [mdspan.syn]")<IndexType>;

- [(2.3)](#mdspan.sub.helpers-2.3)

otherwise,*de-ice*(sk.offset) if Sk is a specialization of strided_slice;

- [(2.4)](#mdspan.sub.helpers-2.4)

otherwise,0[.](#mdspan.sub.helpers-2.sentence-1)

[3](#mdspan.sub.helpers-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25401)

*Preconditions*: Ïk is representable as a value of type IndexType[.](#mdspan.sub.helpers-3.sentence-1)

[4](#mdspan.sub.helpers-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25405)

*Returns*: extents<IndexType>​::​*index-cast*(Ïk)[.](#mdspan.sub.helpers-4.sentence-1)

[ð](#lib:last_)

`template<size_t k, class Extents, class... SliceSpecifiers>
  constexpr auto last_(const Extents& src, SliceSpecifiers... slices);
`

[5](#mdspan.sub.helpers-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25417)

*Mandates*: Extents is a specialization of extents[.](#mdspan.sub.helpers-5.sentence-1)

[6](#mdspan.sub.helpers-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25421)

Let index_type be typename Extents​::​index_type[.](#mdspan.sub.helpers-6.sentence-1)

[7](#mdspan.sub.helpers-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25425)

Let Î»k denote the following value:

- [(7.1)](#mdspan.sub.helpers-7.1)

*de-ice*(sk) + 1 if Sk models [convertible_to](concept.convertible#concept:convertible_to "18.4.4 Concept convertible_­to [concept.convertible]")<index_type>; otherwise

- [(7.2)](#mdspan.sub.helpers-7.2)

get<1>(sk) if Sk models [*index-pair-like*](#concept:index-pair-like "23.7.3.2 Header <mdspan> synopsis [mdspan.syn]")<index_type>; otherwise

- [(7.3)](#mdspan.sub.helpers-7.3)

*de-ice*(sk.offset) +*de-ice*(sk.extent) if Sk is a specialization of strided_slice; otherwise

- [(7.4)](#mdspan.sub.helpers-7.4)

src.extent(k)[.](#mdspan.sub.helpers-7.sentence-1)

[8](#mdspan.sub.helpers-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25443)

*Preconditions*: Î»k is representable as a value of type index_type[.](#mdspan.sub.helpers-8.sentence-1)

[9](#mdspan.sub.helpers-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25447)

*Returns*: Extents​::​*index-cast*(Î»k)[.](#mdspan.sub.helpers-9.sentence-1)

[ð](#lib:src-indices)

`template<class IndexType, size_t N, class... SliceSpecifiers>
  constexpr array<IndexType, sizeof...(SliceSpecifiers)>
    src-indices(const array<IndexType, N>& indices, SliceSpecifiers... slices);
`

[10](#mdspan.sub.helpers-10)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25460)

*Mandates*: IndexType is a signed or unsigned integer type[.](#mdspan.sub.helpers-10.sentence-1)

[11](#mdspan.sub.helpers-11)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25464)

*Returns*: An array<IndexType, sizeof...(SliceSpecifiers)> src_idx such that
for each k in the range [0, sizeof...(SliceSpecifiers)),src_idx[k] equals

- [(11.1)](#mdspan.sub.helpers-11.1)

*first_*<IndexType, k>(slices...) for each k where *map-rank*[k] equalsdynamic_extent,

- [(11.2)](#mdspan.sub.helpers-11.2)

otherwise,*first_*<IndexType, k>(slices...) +indices[*map-rank*[k]].

#### [23.7.3.7.5](#mdspan.sub.extents) submdspan_extents function [[mdspan.sub.extents]](mdspan.sub.extents)

[ð](#lib:submdspan_extents)

`template<class IndexType, size_t... Extents, class... SliceSpecifiers>
  constexpr auto submdspan_extents(const extents<IndexType, Extents...>& src,
                                   SliceSpecifiers... slices);
`

[1](#mdspan.sub.extents-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25496)

*Constraints*: sizeof...(slices) equals sizeof...(Extents)[.](#mdspan.sub.extents-1.sentence-1)

[2](#mdspan.sub.extents-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25500)

*Mandates*: For each rank index k of src.extents(),
exactly one of the following is true:

- [(2.1)](#mdspan.sub.extents-2.1)

Sk models [convertible_to](concept.convertible#concept:convertible_to "18.4.4 Concept convertible_­to [concept.convertible]")<IndexType>,

- [(2.2)](#mdspan.sub.extents-2.2)

Sk models [*index-pair-like*](#concept:index-pair-like "23.7.3.2 Header <mdspan> synopsis [mdspan.syn]")<IndexType>,

- [(2.3)](#mdspan.sub.extents-2.3)

is_convertible_v<Sk, full_extent_t> is true, or

- [(2.4)](#mdspan.sub.extents-2.4)

Sk is a specialization of strided_slice[.](#mdspan.sub.extents-2.sentence-1)

[3](#mdspan.sub.extents-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25511)

*Preconditions*: For each rank index k of src.extents(),
all of the following are true:

- [(3.1)](#mdspan.sub.extents-3.1)

if Sk is a specialization of strided_slice
  * [(3.1.1)](#mdspan.sub.extents-3.1.1)

sk.extent=0, or

  * [(3.1.2)](#mdspan.sub.extents-3.1.2)

sk.stride>0

- [(3.2)](#mdspan.sub.extents-3.2)

0 â¤ *first_*<IndexType, k>(slices...) â¤ *last_*<k>(src, slices...) â¤ src.extent(k)

[4](#mdspan.sub.extents-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25528)

Let SubExtents be a specialization of extents such that:

- [(4.1)](#mdspan.sub.extents-4.1)

SubExtents​::​rank() equals the number of k such thatSk does not model [convertible_to](concept.convertible#concept:convertible_to "18.4.4 Concept convertible_­to [concept.convertible]")<IndexType>; and

- [(4.2)](#mdspan.sub.extents-4.2)

for each rank index k of Extents such that*map-rank*[k] != dynamic_extent is true,SubExtents​::​static_extent(*map-rank*[k]) equals:
  * [(4.2.1)](#mdspan.sub.extents-4.2.1)

Extents​::​static_extent(k) if is_convertible_v<Sk, full_extent_t> is true;
 otherwise

  * [(4.2.2)](#mdspan.sub.extents-4.2.2)

*de-ice*(tuple_element_t<1, Sk>()) -*de-ice*(tuple_element_t<0, Sk>()) if Sk models [*index-pair-like*](#concept:index-pair-like "23.7.3.2 Header <mdspan> synopsis [mdspan.syn]")<IndexType>, and
 both tuple_element_t<0, Sk> and tuple_element_t<1, Sk> model [*integral-constant-like*](span.syn#concept:integral-constant-like "23.7.2.1 Header <span> synopsis [span.syn]"); otherwise

  * [(4.2.3)](#mdspan.sub.extents-4.2.3)

0,
 if Sk is a specialization of strided_slice, whose extent_type models *integral-constant-like*,
 for which extent_type() equals zero; otherwise

  * [(4.2.4)](#mdspan.sub.extents-4.2.4)

1 + (*de-ice*(Sk​::​extent_type()) - 1) /*de-ice*(Sk​::​stride_type()),
 if Sk is a specialization of strided_slice whose extent_type and stride_type model *integral-constant-like*;

  * [(4.2.5)](#mdspan.sub.extents-4.2.5)

otherwise, dynamic_extent[.](#mdspan.sub.extents-4.sentence-1)

[5](#mdspan.sub.extents-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25573)

*Returns*: A value ext of type SubExtents such that
for each k for which *map-rank*[k] != dynamic_extent is true,ext.extent(*map-rank*[k]) equals:

- [(5.1)](#mdspan.sub.extents-5.1)

sk.extent == 0 ? 0 : 1 + (*de-ice*(sk.extent) - 1) / *de-ice*(sk.stride) if Sk is a specialization of strided_slice,

- [(5.2)](#mdspan.sub.extents-5.2)

otherwise,*last_*<k>(src, slices...) - *first_*<IndexType, k>(slices...)[.](#mdspan.sub.extents-5.sentence-1)

#### [23.7.3.7.6](#mdspan.sub.map) Specializations of submdspan_mapping [[mdspan.sub.map]](mdspan.sub.map)

#### [23.7.3.7.6.1](#mdspan.sub.map.common) Common [[mdspan.sub.map.common]](mdspan.sub.map.common)

[1](#mdspan.sub.map.common-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25594)

The following elements apply to all functions in [[mdspan.sub.map]](#mdspan.sub.map "23.7.3.7.6 Specializations of submdspan_­mapping")[.](#mdspan.sub.map.common-1.sentence-1)

[2](#mdspan.sub.map.common-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25597)

*Constraints*: sizeof...(slices) equals extents_type​::​rank()[.](#mdspan.sub.map.common-2.sentence-1)

[3](#mdspan.sub.map.common-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25601)

*Mandates*: For each rank index k of extents(),
exactly one of the following is true:

- [(3.1)](#mdspan.sub.map.common-3.1)

Sk models [convertible_to](concept.convertible#concept:convertible_to "18.4.4 Concept convertible_­to [concept.convertible]")<index_type>,

- [(3.2)](#mdspan.sub.map.common-3.2)

Sk models [*index-pair-like*](#concept:index-pair-like "23.7.3.2 Header <mdspan> synopsis [mdspan.syn]")<index_type>,

- [(3.3)](#mdspan.sub.map.common-3.3)

is_convertible_v<Sk, full_extent_t> is true, or

- [(3.4)](#mdspan.sub.map.common-3.4)

Sk is a specialization of strided_slice[.](#mdspan.sub.map.common-3.sentence-1)

[4](#mdspan.sub.map.common-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25616)

*Preconditions*: For each rank index k of extents(),
all of the following are true:

- [(4.1)](#mdspan.sub.map.common-4.1)

if Sk is a specialization of strided_slice,sk.extent is equal to zero orsk.stride is greater than zero; and

- [(4.2)](#mdspan.sub.map.common-4.2)

0 â¤ *first_*<index_type, k>(slices...)   
0  â¤ *last_*<k>(extents(), slices...)   
0  â¤ extents().extent(k)

[5](#mdspan.sub.map.common-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25631)

Let sub_ext be
the result of submdspan_extents(extents(), slices...) and
let SubExtents be decltype(sub_ext)[.](#mdspan.sub.map.common-5.sentence-1)

[6](#mdspan.sub.map.common-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25636)

Let sub_strides be
an array<SubExtents​::​index_type, SubExtents​::​rank()> such that for each rank index k of extents() for which *map-rank*[k] is not dynamic_extent,sub_strides[*map-rank*[k]] equals:

- [(6.1)](#mdspan.sub.map.common-6.1)

stride(k) * *de-ice*(sk.stride) if Sk is a specialization of strided_slice andsk.stride < sk.extent is true;

- [(6.2)](#mdspan.sub.map.common-6.2)

otherwise, stride(k)[.](#mdspan.sub.map.common-6.sentence-1)

[7](#mdspan.sub.map.common-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25651)

Let P be a parameter pack
such that is_same_v<make_index_sequence<rank()>, index_sequence<P...>> is true[.](#mdspan.sub.map.common-7.sentence-1)

[8](#mdspan.sub.map.common-8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25656)

If *first_*<index_type, k>(slices...) equals extents().extent(k) for any rank index k of extents(), then
let offset be a value of type size_t equal to(*this).required_span_size()[.](#mdspan.sub.map.common-8.sentence-1)

Otherwise,
let offset be a value of type size_t equal to(*this)(*first_*<index_type, P>(slices...)...)[.](#mdspan.sub.map.common-8.sentence-2)

[9](#mdspan.sub.map.common-9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25666)

Given a layout mapping type M, a type S is a[*unit-stride slice for M*](#def:slice,unit-stride "23.7.3.7.6.1 Common [mdspan.sub.map.common]") if

- [(9.1)](#mdspan.sub.map.common-9.1)

S is a specialization of strided_slice where S​::​stride_type models [*integral-constant-like*](span.syn#concept:integral-constant-like "23.7.2.1 Header <span> synopsis [span.syn]") and S​::​stride_type​::​value equals 1,

- [(9.2)](#mdspan.sub.map.common-9.2)

S models [*index-pair-like*](#concept:index-pair-like "23.7.3.2 Header <mdspan> synopsis [mdspan.syn]")<M​::​index_type>, or

- [(9.3)](#mdspan.sub.map.common-9.3)

is_convertible_v<S, full_extent_t> is true[.](#mdspan.sub.map.common-9.sentence-1)

#### [23.7.3.7.6.2](#mdspan.sub.map.left) layout_left specialization of submdspan_mapping [[mdspan.sub.map.left]](mdspan.sub.map.left)

[ð](#lib:layout_left::mapping,submdspan-mapping-impl)

`template<class Extents>
template<class... SliceSpecifiers>
constexpr auto layout_left::mapping<Extents>::submdspan-mapping-impl(
      SliceSpecifiers... slices) const -> see below;
`

[1](#mdspan.sub.map.left-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25688)

*Returns*: 

- [(1.1)](#mdspan.sub.map.left-1.1)

submdspan_mapping_result{*this, 0},
if Extents​::​rank() == 0 is true;

- [(1.2)](#mdspan.sub.map.left-1.2)

otherwise,submdspan_mapping_result{layout_left​::​mapping(sub_ext), offset},
if SubExtents​::​rank() == 0 is true;

- [(1.3)](#mdspan.sub.map.left-1.3)

otherwise,submdspan_mapping_result{layout_left​::​mapping(sub_ext), offset},
if
  * [(1.3.1)](#mdspan.sub.map.left-1.3.1)

for each k in the range [0, SubExtents​::​rank() - 1)), is_convertible_v<Sk, full_extent_t> is true; and

  * [(1.3.2)](#mdspan.sub.map.left-1.3.2)

for k equal to SubExtents​::​rank() - 1, Sk is a unit-stride slice for mapping;

  [*Note [1](#mdspan.sub.map.left-note-1)*:
  If the above conditions are true,
all Sk with k larger than SubExtents​::​rank() - 1 are convertible to index_type[.](#mdspan.sub.map.left-1.3.sentence-1)
 â *end note*]

- [(1.4)](#mdspan.sub.map.left-1.4)

otherwise,submdspan_mapping_result{layout_left_padded<S_static>::mapping(sub_ext, stride(u + 1)),
 offset} if for a value u for which u+1 is
the smallest value p larger than zero
for which Sp is a unit-stride slice for mapping,
the following conditions are met:
  * [(1.4.1)](#mdspan.sub.map.left-1.4.1)

S0 is a unit-stride slice for mapping; and

  * [(1.4.2)](#mdspan.sub.map.left-1.4.2)

for each k in the range [u + 1, u + SubExtents​::​rank() - 1),is_convertible_v<Sk, full_extent_t> is true; and

  * [(1.4.3)](#mdspan.sub.map.left-1.4.3)

for k equal to u + SubExtents​::​rank() - 1,Sk is a unit-stride slice for mapping;

and where S_static is:
  * [(1.4.4)](#mdspan.sub.map.left-1.4.4)

dynamic_extent,
if static_extent(k) is dynamic_extent for any k in the range [0, u + 1),

  * [(1.4.5)](#mdspan.sub.map.left-1.4.5)

otherwise, the product of all valuesstatic_extent(k) for k in the range [0, u + 1);

- [(1.5)](#mdspan.sub.map.left-1.5)

otherwise,submdspan_mapping_result{layout_stride::mapping(sub_ext, sub_strides), offset}

#### [23.7.3.7.6.3](#mdspan.sub.map.right) layout_right specialization of submdspan_mapping [[mdspan.sub.map.right]](mdspan.sub.map.right)

[ð](#lib:layout_right::mapping,submdspan-mapping-impl)

`template<class Extents>
template<class... SliceSpecifiers>
constexpr auto layout_right::mapping<Extents>::submdspan-mapping-impl(
      SliceSpecifiers... slices) const -> see below;
`

[1](#mdspan.sub.map.right-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25764)

*Returns*: 

- [(1.1)](#mdspan.sub.map.right-1.1)

submdspan_mapping_result{*this, 0},
if Extents​::​rank() == 0 is true;

- [(1.2)](#mdspan.sub.map.right-1.2)

otherwise,submdspan_mapping_result{layout_right​::​mapping(sub_ext), offset},
if SubExtents​::​rank() == 0 is true;

- [(1.3)](#mdspan.sub.map.right-1.3)

otherwise,submdspan_mapping_result{layout_left​::​mapping(sub_ext), offset},
if
  * [(1.3.1)](#mdspan.sub.map.right-1.3.1)

for each k in the range [*rank_* - SubExtents​::​rank() + 1, *rank_*), is_convertible_v<Sk, full_extent_t> is true; and

  * [(1.3.2)](#mdspan.sub.map.right-1.3.2)

for k equal to *_rank* - SubExtents​::​rank(), Sk is a unit-stride slice for mapping;

  [*Note [1](#mdspan.sub.map.right-note-1)*:
  If the above conditions are true,
all Sk with k<_rankÂ - SubExtents::rank() are convertible to index_type[.](#mdspan.sub.map.right-1.3.sentence-1)
 â *end note*]

- [(1.4)](#mdspan.sub.map.right-1.4)

otherwise,submdspan_mapping_result{layout_right_padded<S_static>::mapping(sub_ext,
 stride(*rank_* - u - 2)), offset} if for a value u for which rank_âuâ2 is
the largest value p smaller than *rank_* - 1 for which Sp is a unit-stride slice for mapping,
the following conditions are met:
  * [(1.4.1)](#mdspan.sub.map.right-1.4.1)

for k equal to *rank_* - 1,Sk is a unit-stride slice for mapping; and

  * [(1.4.2)](#mdspan.sub.map.right-1.4.2)

for each k in the range
[*rank_* - SubExtents​::​rank() - u + 1, *rank_* - u - 1),is_convertible_v<Sk, full_extent_t> is true; and

  * [(1.4.3)](#mdspan.sub.map.right-1.4.3)

for k equal to *rank_* - SubExtents​::​rank() - u,  
Sk is a unit-stride slice for mapping;

and where S_static is:
  * [(1.4.4)](#mdspan.sub.map.right-1.4.4)

dynamic_extent,
if static_extent(k) is dynamic_extent for any k in the range [*rank_* - u - 1, *rank_*),

  * [(1.4.5)](#mdspan.sub.map.right-1.4.5)

otherwise, the product of all valuesstatic_extent(k) for k in the range [*rank_* - u - 1, *rank_*);

- [(1.5)](#mdspan.sub.map.right-1.5)

otherwise,submdspan_mapping_result{layout_stride::mapping(sub_ext, sub_strides), offset}

#### [23.7.3.7.6.4](#mdspan.sub.map.stride) layout_stride specialization of submdspan_mapping [[mdspan.sub.map.stride]](mdspan.sub.map.stride)

[ð](#lib:layout_stride::mapping,submdspan-mapping-impl)

`template<class Extents>
template<class... SliceSpecifiers>
constexpr auto layout_stride::mapping<Extents>::submdspan-mapping-impl(
      SliceSpecifiers... slices) const -> see below;
`

[1](#mdspan.sub.map.stride-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25843)

*Returns*: 

- [(1.1)](#mdspan.sub.map.stride-1.1)

submdspan_mapping_result{*this, 0},
if Extents​::​rank() == 0 is true;

- [(1.2)](#mdspan.sub.map.stride-1.2)

otherwise,submdspan_mapping_result{layout_stride::mapping(sub_ext, sub_strides), offset}

#### [23.7.3.7.6.5](#mdspan.sub.map.leftpad) layout_left_padded specialization of submdspan_mapping [[mdspan.sub.map.leftpad]](mdspan.sub.map.leftpad)

[ð](#lib:layout_left_padded::mapping,submdspan-mapping-impl)

`template<class Extents>
template<class... SliceSpecifiers>
constexpr auto layout_left_padded::mapping<Extents>::submdspan-mapping-impl(
    SliceSpecifiers... slices) const -> see below;
`

[1](#mdspan.sub.map.leftpad-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25868)

*Returns*: 

- [(1.1)](#mdspan.sub.map.leftpad-1.1)

submdspan_mapping_result{*this, 0},
if Extents​::​rank() == 0 is true;

- [(1.2)](#mdspan.sub.map.leftpad-1.2)

otherwise,submdspan_mapping_result{layout_left​::​mapping(sub_ext), offset},
if *rank_* == 1 is true orSubExtents​::​rank() == 0 is true;

- [(1.3)](#mdspan.sub.map.leftpad-1.3)

otherwise,submdspan_mapping_result{layout_left​::​mapping(sub_ext), offset},
if
  * [(1.3.1)](#mdspan.sub.map.leftpad-1.3.1)

SubExtents​::​rank() == 1 is true and

  * [(1.3.2)](#mdspan.sub.map.leftpad-1.3.2)

S0 is a unit-stride slice for mapping;

- [(1.4)](#mdspan.sub.map.leftpad-1.4)

otherwise,submdspan_mapping_result{layout_left_padded<S_static>::mapping(sub_ext, stride(u + 1)),
 offset} if for a value u for which u + 1 is the smallest value p larger than zero
for which Sp is a unit-stride slice for mapping,
the following conditions are met:
  * [(1.4.1)](#mdspan.sub.map.leftpad-1.4.1)

S0 is a unit-stride slice for mapping; and

  * [(1.4.2)](#mdspan.sub.map.leftpad-1.4.2)

for each k in the range [u + 1, u + SubExtents​::​rank() - 1),is_convertible_v<Sk, full_extent_t> is true; and

  * [(1.4.3)](#mdspan.sub.map.leftpad-1.4.3)

for k equal to u + SubExtents​::​rank() - 1,Sk is a unit-stride slice for mapping;

where S_static is:
  * [(1.4.4)](#mdspan.sub.map.leftpad-1.4.4)

dynamic_extent,
if *static-padding-stride* is dynamic_extent orstatic_extent(k) is dynamic_extent for any k in the range [1, u + 1),

  * [(1.4.5)](#mdspan.sub.map.leftpad-1.4.5)

otherwise, the product of *static-padding-stride* and
all values static_extent(k) for k in the range [1, u + 1);

- [(1.5)](#mdspan.sub.map.leftpad-1.5)

otherwise,submdspan_mapping_result{layout_stride::mapping(sub_ext, sub_strides), offset}

#### [23.7.3.7.6.6](#mdspan.sub.map.rightpad) layout_right_padded specialization of submdspan_mapping [[mdspan.sub.map.rightpad]](mdspan.sub.map.rightpad)

[ð](#lib:layout_right_padded::mapping,submdspan-mapping-impl)

`template<class Extents>
template<class... SliceSpecifiers>
constexpr auto layout_right_padded::mapping<Extents>::submdspan-mapping-impl(
    SliceSpecifiers... slices) const -> see below;
`

[1](#mdspan.sub.map.rightpad-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L25939)

*Returns*: 

- [(1.1)](#mdspan.sub.map.rightpad-1.1)

submdspan_mapping_result{*this, 0},
if *rank_* == 0 is true;

- [(1.2)](#mdspan.sub.map.rightpad-1.2)

otherwise,submdspan_mapping_result{layout_right​::​mapping(sub_ext), offset},  
if *rank_* == 1 is true orSubExtents​::​rank() == 0 is true;

- [(1.3)](#mdspan.sub.map.rightpad-1.3)

otherwise,submdspan_mapping_result{layout_right​::​mapping(sub_ext), offset},
if
  * [(1.3.1)](#mdspan.sub.map.rightpad-1.3.1)

SubExtents​::​rank() == 1 is true and

  * [(1.3.2)](#mdspan.sub.map.rightpad-1.3.2)

for k equal to *rank_* - 1,Sk is a unit-stride slice for mapping;

- [(1.4)](#mdspan.sub.map.rightpad-1.4)

otherwise,submdspan_mapping_result{layout_right_padded<S_static>::mapping(sub_ext,
 stride(*rank_* - u - 2)), offset} if for a value u for which *rank_* - u - 2 is the largest value p smaller than *rank_* - 1 for which Sp is a unit-stride slice for mapping,
the following conditions are met:
  * [(1.4.1)](#mdspan.sub.map.rightpad-1.4.1)

for k equal to *rank_* - 1,Sk is a unit-stride slice for mapping; and

  * [(1.4.2)](#mdspan.sub.map.rightpad-1.4.2)

for each k in the range
[*rank_* - SubExtents​::​rank() - u + 1, *rank_* - u - 1)),is_convertible_v<Sk, full_extent_t> is true; and

  * [(1.4.3)](#mdspan.sub.map.rightpad-1.4.3)

for k equal to *rank_* - SubExtents​::​rank() - u,  
Sk is a unit-stride slice for mapping;

and where S_static is:
  * [(1.4.4)](#mdspan.sub.map.rightpad-1.4.4)

dynamic_extent if *static-padding-stride* is dynamic_extent or
for any k in the range [*rank_* - u - 1, *rank_* - 1)static_extent(k) is dynamic_extent,

  * [(1.4.5)](#mdspan.sub.map.rightpad-1.4.5)

otherwise, the product of *static-padding-stride* and
all values static_extent(k) with k in the range [*rank_* - u - 1, *rank_* - 1);

- [(1.5)](#mdspan.sub.map.rightpad-1.5)

otherwise,submdspan_mapping_result{layout_stride::mapping(sub_ext, sub_strides), offset}

#### [23.7.3.7.7](#mdspan.sub.sub) submdspan function template [[mdspan.sub.sub]](mdspan.sub.sub)

[ð](#lib:submdspan)

`template<class ElementType, class Extents, class LayoutPolicy,
         class AccessorPolicy, class... SliceSpecifiers>
  constexpr auto submdspan(
    const mdspan<ElementType, Extents, LayoutPolicy, AccessorPolicy>& src,
    SliceSpecifiers... slices) -> see below;
`

[1](#mdspan.sub.sub-1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L26016)

Let index_type be typename Extents​::​index_type[.](#mdspan.sub.sub-1.sentence-1)

[2](#mdspan.sub.sub-2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L26019)

Let sub_map_offset be the result ofsubmdspan_mapping(src.mapping(), slices...)[.](#mdspan.sub.sub-2.sentence-1)

[*Note [1](#mdspan.sub.sub-note-1)*:

This invocation of submdspan_mapping selects a function call via overload resolution
on a candidate set that includes the lookup set
found by argument-dependent lookup ([[basic.lookup.argdep]](basic.lookup.argdep "6.5.4 Argument-dependent name lookup"))[.](#mdspan.sub.sub-2.sentence-2)

â *end note*]

[3](#mdspan.sub.sub-3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L26029)

*Constraints*: 

- [(3.1)](#mdspan.sub.sub-3.1)

sizeof...(slices) equals Extents​::​rank(), and

- [(3.2)](#mdspan.sub.sub-3.2)

the expression submdspan_mapping(src.mapping(), slices...) is well-formed when treated as an unevaluated operand[.](#mdspan.sub.sub-3.sentence-1)

[4](#mdspan.sub.sub-4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L26039)

*Mandates*: 

- [(4.1)](#mdspan.sub.sub-4.1)

  decltype(submdspan_mapping(src.mapping(), slices...)) is a specialization of submdspan_mapping_result[.](#mdspan.sub.sub-4.1.sentence-1)

- [(4.2)](#mdspan.sub.sub-4.2)

  is_same_v<remove_cvref_t<decltype(sub_map_offset.mapping.extents())>,decltype(submdspan_extents(src.mapping(), slices...))> is true[.](#mdspan.sub.sub-4.2.sentence-1)

- [(4.3)](#mdspan.sub.sub-4.3)

  For each rank index k of src.extents(),
exactly one of the following is true:
  * [(4.3.1)](#mdspan.sub.sub-4.3.1)

Sk models [convertible_to](concept.convertible#concept:convertible_to "18.4.4 Concept convertible_­to [concept.convertible]")<index_type>,

  * [(4.3.2)](#mdspan.sub.sub-4.3.2)

Sk models [*index-pair-like*](#concept:index-pair-like "23.7.3.2 Header <mdspan> synopsis [mdspan.syn]")<index_type>,

  * [(4.3.3)](#mdspan.sub.sub-4.3.3)

is_convertible_v<Sk, full_extent_t> is true, or

  * [(4.3.4)](#mdspan.sub.sub-4.3.4)

Sk is a specialization of strided_slice[.](#mdspan.sub.sub-4.3.sentence-1)

[5](#mdspan.sub.sub-5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L26062)

*Preconditions*: 

- [(5.1)](#mdspan.sub.sub-5.1)

For each rank index k of src.extents(),
all of the following are true:
  * [(5.1.1)](#mdspan.sub.sub-5.1.1)

if Sk is a specialization of strided_slice
    +
          [(5.1.1.1)](#mdspan.sub.sub-5.1.1.1)
sk.extent=0, or

    +
          [(5.1.1.2)](#mdspan.sub.sub-5.1.1.2)
sk.stride>0

  * [(5.1.2)](#mdspan.sub.sub-5.1.2)

0 â¤ *first_*<index_type, k>(slices...) â¤ *last_*<k>(src.extents(), slices...) â¤ src.extent(k)

- [(5.2)](#mdspan.sub.sub-5.2)

sub_map_offset.mapping.extents() == submdspan_extents(src.mapping(), slices...) is true; and

- [(5.3)](#mdspan.sub.sub-5.3)

for each integer pack I which is a multidimensional index
in sub_map_offset.mapping.extents(),sub_map_offset.mapping(I...) + sub_map_offset.offset == src.mapping()(*src-indices*(array{I...}, slices...)) is true[.](#mdspan.sub.sub-5.sentence-1)

[*Note [2](#mdspan.sub.sub-note-2)*:

These conditions ensure that the mapping returned by submdspan_mapping matches the algorithmically expected index-mapping given the slice specifiers[.](#mdspan.sub.sub-5.sentence-2)

â *end note*]

[6](#mdspan.sub.sub-6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L26100)

*Effects*: Equivalent to:auto sub_map_result = submdspan_mapping(src.mapping(), slices...);return mdspan(src.accessor().offset(src.data_handle(), sub_map_result.offset),
 sub_map_result.mapping, typename AccessorPolicy::offset_policy(src.accessor()));

[7](#mdspan.sub.sub-7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L26111)

[*Example [1](#mdspan.sub.sub-example-1)*:

Given a rank-3 mdspan grid3d representing a three-dimensional grid
of regularly spaced points in a rectangular prism,
the function zero_surface sets all elements on
the surface of the 3-dimensional shape to zero[.](#mdspan.sub.sub-7.sentence-1)

It does so by reusing a function zero_2d that takes a rank-2 mdspan[.](#mdspan.sub.sub-7.sentence-2)

// zero out all elements in an mdspantemplate<class T, class E, class L, class A>void zero_2d(mdspan<T, E, L, A> a) {static_assert(a.rank() == 2); for (int i = 0; i < a.extent(0); i++)for (int j = 0; j < a.extent(1); j++) a[i, j] = 0;}// zero out just the surfacetemplate<class T, class E, class L, class A>void zero_surface(mdspan<T, E, L, A> grid3d) {static_assert(grid3d.rank() == 3);
 zero_2d(submdspan(grid3d, 0, full_extent, full_extent));
 zero_2d(submdspan(grid3d, full_extent, 0, full_extent));
 zero_2d(submdspan(grid3d, full_extent, full_extent, 0));
 zero_2d(submdspan(grid3d, grid3d.extent(0) - 1, full_extent, full_extent));
 zero_2d(submdspan(grid3d, full_extent, grid3d.extent(1) - 1, full_extent));
 zero_2d(submdspan(grid3d, full_extent, full_extent, grid3d.extent(2) - 1));} â *end example*]
