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[mdspan.extents.cmp]
# 23 Containers library [[containers]](./#containers)
## 23.7 Views [[views]](views#mdspan.extents.cmp)
### 23.7.3 Multidimensional access [[views.multidim]](views.multidim#mdspan.extents.cmp)
#### 23.7.3.3 Class template extents [[mdspan.extents]](mdspan.extents#cmp)
#### 23.7.3.3.5 Comparison operators [mdspan.extents.cmp]
[🔗](#lib:operator==,extents)
`template<class OtherIndexType, size_t... OtherExtents>
friend constexpr bool operator==(const extents& lhs,
const extents<OtherIndexType, OtherExtents...>& rhs) noexcept;
`
[1](#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[.](#1.sentence-1)

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[mdspan.extents.cons]
# 23 Containers library [[containers]](./#containers)
## 23.7 Views [[views]](views#mdspan.extents.cons)
### 23.7.3 Multidimensional access [[views.multidim]](views.multidim#mdspan.extents.cons)
#### 23.7.3.3 Class template extents [[mdspan.extents]](mdspan.extents#cons)
#### 23.7.3.3.3 Constructors [mdspan.extents.cons]
[🔗](#lib:extents,constructor)
`template<class OtherIndexType, size_t... OtherExtents>
constexpr explicit(see below)
extents(const extents<OtherIndexType, OtherExtents...>& other) noexcept;
`
[1](#1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21276)
*Constraints*:
- [(1.1)](#1.1)
sizeof...(OtherExtents) == rank() is true[.](#1.1.sentence-1)
- [(1.2)](#1.2)
((OtherExtents == dynamic_extent || Extents == dynamic_extent || OtherExtents ==
Extents) && ...) is true[.](#1.2.sentence-1)
[2](#2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21285)
*Preconditions*:
- [(2.1)](#2.1)
other.extent(r) equals Er for each r for which Er is a static extent, and
- [(2.2)](#2.2)
either
* [(2.2.1)](#2.2.1)
sizeof...(OtherExtents) is zero, or
* [(2.2.2)](#2.2.2)
other.extent(r) is representable as
a value of type index_type for every rank index r of other[.](#2.sentence-1)
[3](#3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21302)
*Postconditions*: *this == other is true[.](#3.sentence-1)
[4](#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())
[🔗](#lib:extents,constructor_)
`template<class... OtherIndexTypes>
constexpr explicit extents(OtherIndexTypes... exts) noexcept;
`
[5](#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))...}[.](#5.sentence-1)
[6](#6)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21327)
*Constraints*:
- [(6.1)](#6.1)
(is_convertible_v<OtherIndexTypes, index_type> && ...) is true,
- [(6.2)](#6.2)
(is_nothrow_constructible_v<index_type, OtherIndexTypes> && ...) is true, and
- [(6.3)](#6.3)
N == rank_dynamic() || N == rank() is true[.](#6.sentence-1)
[*Note [1](#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[.](#6.3.sentence-2)
— *end note*]
[7](#7)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21343)
*Preconditions*:
- [(7.1)](#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)](#7.2)
either
* [(7.2.1)](#7.2.1)
sizeof...(exts) == 0 is true, or
* [(7.2.2)](#7.2.2)
each element of exts is representable
as a nonnegative value of type index_type[.](#7.sentence-1)
[8](#8)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21361)
*Postconditions*: *this == extents(exts_arr) is true[.](#8.sentence-1)
[🔗](#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](#9)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21377)
*Constraints*:
- [(9.1)](#9.1)
is_convertible_v<const OtherIndexType&, index_type> is true,
- [(9.2)](#9.2)
is_nothrow_constructible_v<index_type, const OtherIndexType&> is true, and
- [(9.3)](#9.3)
N == rank_dynamic() || N == rank() is true[.](#9.sentence-1)
[10](#10)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21388)
*Preconditions*:
- [(10.1)](#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)](#10.2)
either
* [(10.2.1)](#10.2.1)
N is zero, or
* [(10.2.2)](#10.2.2)
exts[r] is representable
as a nonnegative value of type index_type for every rank index r[.](#10.sentence-1)
[11](#11)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21405)
*Effects*:
- [(11.1)](#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])[.](#11.1.sentence-1)
- [(11.2)](#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)])[.](#11.2.sentence-1)
[🔗](#lib:extents,constructor___)
`template<class... Integrals>
explicit extents(Integrals...) -> see below;
`
[12](#12)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21427)
*Constraints*: (is_convertible_v<Integrals, size_t> && ...) is true[.](#12.sentence-1)
[13](#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>...>[.](#13.sentence-1)

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[mdspan.extents.dextents]
# 23 Containers library [[containers]](./#containers)
## 23.7 Views [[views]](views#mdspan.extents.dextents)
### 23.7.3 Multidimensional access [[views.multidim]](views.multidim#mdspan.extents.dextents)
#### 23.7.3.3 Class template extents [[mdspan.extents]](mdspan.extents#dextents)
#### 23.7.3.3.6 Alias template dextents [mdspan.extents.dextents]
[🔗](#lib:dextents)
`template<class IndexType, size_t Rank>
using dextents = see below;
`
[1](#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[.](#1.sentence-1)

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[mdspan.extents.dims]
# 23 Containers library [[containers]](./#containers)
## 23.7 Views [[views]](views#mdspan.extents.dims)
### 23.7.3 Multidimensional access [[views.multidim]](views.multidim#mdspan.extents.dims)
#### 23.7.3.3 Class template extents [[mdspan.extents]](mdspan.extents#dims)
#### 23.7.3.3.7 Alias template dims [mdspan.extents.dims]
[🔗](#lib:dims)
`template<size_t Rank, class IndexType = size_t>
using dims = see below;
`
[1](#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[.](#1.sentence-1)

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[mdspan.extents.expo]
# 23 Containers library [[containers]](./#containers)
## 23.7 Views [[views]](views#mdspan.extents.expo)
### 23.7.3 Multidimensional access [[views.multidim]](views.multidim#mdspan.extents.expo)
#### 23.7.3.3 Class template extents [[mdspan.extents]](mdspan.extents#expo)
#### 23.7.3.3.2 Exposition-only helpers [mdspan.extents.expo]
[🔗](#itemdecl:1)
`static constexpr rank_type dynamic-index(rank_type i) noexcept;
`
[1](#1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21185)
*Preconditions*: i <= rank() is true[.](#1.sentence-1)
[2](#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[.](#2.sentence-1)
[🔗](#itemdecl:2)
`static constexpr rank_type dynamic-index-inv(rank_type i) noexcept;
`
[3](#3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21199)
*Preconditions*: i < rank_dynamic() is true[.](#3.sentence-1)
[4](#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[.](#4.sentence-1)
[🔗](#itemdecl:3)
`constexpr size_t fwd-prod-of-extents(rank_type i) const noexcept;
`
[5](#5)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21214)
*Preconditions*: i <= rank() is true[.](#5.sentence-1)
[6](#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[.](#6.sentence-1)
[🔗](#itemdecl:4)
`constexpr size_t rev-prod-of-extents(rank_type i) const noexcept;
`
[7](#7)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21230)
*Preconditions*: i < rank() is true[.](#7.sentence-1)
[8](#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[.](#8.sentence-1)
[🔗](#itemdecl:5)
`template<class OtherIndexType>
static constexpr auto index-cast(OtherIndexType&& i) noexcept;
`
[9](#9)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21248)
*Effects*:
- [(9.1)](#9.1)
If OtherIndexType is an integral type other than bool,
then equivalent to return i;,
- [(9.2)](#9.2)
otherwise, equivalent to return static_cast<index_type>(i);[.](#9.sentence-1)
[*Note [1](#note-1)*:
This function will always return an integral type other than bool[.](#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[.](#9.sentence-3)
— *end note*]

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[mdspan.extents.obs]
# 23 Containers library [[containers]](./#containers)
## 23.7 Views [[views]](views#mdspan.extents.obs)
### 23.7.3 Multidimensional access [[views.multidim]](views.multidim#mdspan.extents.obs)
#### 23.7.3.3 Class template extents [[mdspan.extents]](mdspan.extents#obs)
#### 23.7.3.3.4 Observers of the multidimensional index space [mdspan.extents.obs]
[🔗](#lib:static_extent,extents)
`static constexpr size_t static_extent(rank_type i) noexcept;
`
[1](#1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21444)
*Preconditions*: i < rank() is true[.](#1.sentence-1)
[2](#2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21448)
*Returns*: Ei[.](#2.sentence-1)
[🔗](#lib:extent,extents)
`constexpr index_type extent(rank_type i) const noexcept;
`
[3](#3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21459)
*Preconditions*: i < rank() is true[.](#3.sentence-1)
[4](#4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21463)
*Returns*: Di[.](#4.sentence-1)

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[mdspan.extents.overview]
# 23 Containers library [[containers]](./#containers)
## 23.7 Views [[views]](views#mdspan.extents.overview)
### 23.7.3 Multidimensional access [[views.multidim]](views.multidim#mdspan.extents.overview)
#### 23.7.3.3 Class template extents [[mdspan.extents]](mdspan.extents#overview)
#### 23.7.3.3.1 Overview [mdspan.extents.overview]
The class template extents represents
a multidimensional index space of rank equal to sizeof...(Extents)[.](#sentence-1)
In [[views]](views "23.7 Views"),extents is used synonymously with multidimensional index space[.](#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](#1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21152)
*Mandates*:
- [(1.1)](#1.1)
IndexType is a signed or unsigned integer type, and
- [(1.2)](#1.2)
each element of Extents is either equal to dynamic_extent, or
is representable as a value of type IndexType[.](#1.sentence-1)
[2](#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[.](#2.sentence-1)
[3](#3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21166)
Let Er be the rth element of Extents[.](#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]")[.](#3.sentence-2)
Let Dr be the value of *dynamic-extents*[*dynamic-index*(r)] if Er is a dynamic extent,
otherwise Er[.](#3.sentence-3)
[4](#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)[.](#4.sentence-1)