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cppdraft_translate/cppdraft/mdspan/layout/leftpad.md
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[mdspan.layout.leftpad]
# 23 Containers library [[containers]](./#containers)
## 23.7 Views [[views]](views#mdspan.layout.leftpad)
### 23.7.3 Multidimensional access [[views.multidim]](views.multidim#mdspan.layout.leftpad)
#### 23.7.3.4 Layout mapping [[mdspan.layout]](mdspan.layout#leftpad)
#### 23.7.3.4.8 Class template layout_left_padded​::​mapping [mdspan.layout.leftpad]
#### [23.7.3.4.8.1](#overview) Overview [[mdspan.layout.leftpad.overview]](mdspan.layout.leftpad.overview)
[1](#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)[.](#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]](#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]](#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]](#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]](#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](#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[.](#overview-2.sentence-1)
[3](#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[.](#overview-3.sentence-1)
[4](#overview-4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23043)
Throughout [mdspan.layout.leftpad],
let P_rank be the following
size *rank_* parameter pack of size_t values:
- [(4.1)](#overview-4.1)
the empty parameter pack, if *rank_* equals zero;
- [(4.2)](#overview-4.2)
otherwise, 0zu, if *rank_* equals one;
- [(4.3)](#overview-4.3)
otherwise, the parameter pack 0zu, 1zu, …, *rank_*- 1[.](#overview-4.sentence-1)
[5](#overview-5)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23056)
*Mandates*:
- [(5.1)](#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[.](#overview-5.1.sentence-1)
- [(5.2)](#overview-5.2)
padding_value is representable as a value of type index_type[.](#overview-5.2.sentence-1)
- [(5.3)](#overview-5.3)
If
* [(5.3.1)](#overview-5.3.1)
*rank_* is greater than one,
* [(5.3.2)](#overview-5.3.2)
padding_value does not equal dynamic_extent, and
* [(5.3.3)](#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[.](#overview-5.3.sentence-1)
- [(5.4)](#overview-5.4)
If
* [(5.4.1)](#overview-5.4.1)
*rank_* is greater than one,
* [(5.4.2)](#overview-5.4.2)
padding_value does not equal dynamic_extent, and
* [(5.4.3)](#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[.](#overview-5.4.sentence-1)
#### [23.7.3.4.8.2](#expo) Exposition-only members [[mdspan.layout.leftpad.expo]](mdspan.layout.leftpad.expo)
[🔗](#expo-itemdecl:1)
`static constexpr size_t static-padding-stride = see below;
`
[1](#expo-1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23104)
The value is
- [(1.1)](#expo-1.1)
0, if *rank_* equals zero or one;
- [(1.2)](#expo-1.2)
otherwise, dynamic_extent,
if padding_value or *first-static-extent* equalsdynamic_extent;
- [(1.3)](#expo-1.3)
otherwise, the size_t value which is*LEAST-MULTIPLE-AT-LEAST*(padding_value, *first-static-extent*)[.](#expo-1.sentence-1)
[🔗](#expo-itemdecl:2)
`index_type stride-1 = static-padding-stride;
`
[2](#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[.](#expo-2.sentence-1)
[*Note [1](#expo-note-1)*:
Using extents<index_type, *static-padding-stride*> instead ofindex_type as the type of *stride-1* would achieve this[.](#expo-2.sentence-2)
— *end note*]
#### [23.7.3.4.8.3](#cons) Constructors [[mdspan.layout.leftpad.cons]](mdspan.layout.leftpad.cons)
[🔗](#lib:layout_left_padded::mapping,constructor)
`constexpr mapping(const extents_type& ext);
`
[1](#cons-1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23142)
*Preconditions*:
- [(1.1)](#cons-1.1)
The size of the multidimensional index space ext is representable as
a value of type index_type[.](#cons-1.1.sentence-1)
- [(1.2)](#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*[.](#cons-1.2.sentence-1)
- [(1.3)](#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[.](#cons-1.3.sentence-1)
[2](#cons-2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23163)
*Effects*:
- [(2.1)](#cons-2.1)
Direct-non-list-initializes *extents_* with ext; and
- [(2.2)](#cons-2.2)
if *rank_* is greater than one,
direct-non-list-initializes *stride-1*
* [(2.2.1)](#cons-2.2.1)
with ext.extent(0) if padding_value is dynamic_extent,
* [(2.2.2)](#cons-2.2.2)
otherwise with*LEAST-MULTIPLE-AT-LEAST*(padding_value, ext.extent(0))[.](#cons-2.sentence-1)
[🔗](#lib:layout_left_padded::mapping,constructor_)
`template<class OtherIndexType>
constexpr mapping(const extents_type& ext, OtherIndexType pad);
`
[3](#cons-3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23188)
*Constraints*:
- [(3.1)](#cons-3.1)
is_convertible_v<OtherIndexType, index_type> is true[.](#cons-3.1.sentence-1)
- [(3.2)](#cons-3.2)
is_nothrow_constructible_v<index_type, OtherIndexType> is true[.](#cons-3.2.sentence-1)
[4](#cons-4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23197)
*Preconditions*:
- [(4.1)](#cons-4.1)
pad is representable as a value of type index_type[.](#cons-4.1.sentence-1)
- [(4.2)](#cons-4.2)
extents_type​::​index-cast(pad) is greater than zero[.](#cons-4.2.sentence-1)
- [(4.3)](#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)](#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[.](#cons-4.4.sentence-1)
- [(4.5)](#cons-4.5)
If padding_value is not equal to dynamic_extent,padding_value equals extents_type​::​*index-cast*(pad)[.](#cons-4.5.sentence-1)
[5](#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))[.](#cons-5.sentence-1)
[🔗](#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](#cons-6)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23236)
*Constraints*: is_constructible_v<extents_type, OtherExtents> is true[.](#cons-6.sentence-1)
[7](#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[.](#cons-7.sentence-1)
[8](#cons-8)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23250)
*Preconditions*:
- [(8.1)](#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)](#cons-8.2)
other.required_span_size() is representable as
a value of type index_type[.](#cons-8.sentence-1)
[9](#cons-9)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23267)
*Effects*: Equivalent to mapping(other.extents())[.](#cons-9.sentence-1)
[🔗](#lib:layout_left_padded::mapping,constructor___)
`template<class OtherExtents>
constexpr explicit(rank_ > 0)
mapping(const layout_stride::mapping<OtherExtents>& other);
`
[10](#cons-10)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23280)
*Constraints*: is_constructible_v<extents_type, OtherExtents> is true[.](#cons-10.sentence-1)
[11](#cons-11)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23284)
*Preconditions*:
- [(11.1)](#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)](#cons-11.2)
If *rank_* is greater than 0,
then other.stride(0) equals 1[.](#cons-11.2.sentence-1)
- [(11.3)](#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)](#cons-11.4)
other.required_span_size() is representable as
a value of type *index_type*[.](#cons-11.4.sentence-1)
[12](#cons-12)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23310)
*Effects*:
- [(12.1)](#cons-12.1)
Direct-non-list-initializes *extents_* with other.extents() and
- [(12.2)](#cons-12.2)
if *rank_* is greater than one,
direct-non-list-initializes *stride-1* withother.stride(1)[.](#cons-12.sentence-1)
[🔗](#lib:layout_left_padded::mapping,constructor____)
`template<class LayoutLeftPaddedMapping>
constexpr explicit(see below)
mapping(const LayoutLeftPaddedMapping& other);
`
[13](#cons-13)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23330)
*Constraints*:
- [(13.1)](#cons-13.1)
*is-layout-left-padded-mapping-of*<LayoutLeftPaddedMapping> is true[.](#cons-13.1.sentence-1)
- [(13.2)](#cons-13.2)
is_constructible_v<extents_type, typename LayoutLeftPaddedMapping​::​extents_type>
is true[.](#cons-13.2.sentence-1)
[14](#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[.](#cons-14.sentence-1)
[15](#cons-15)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23352)
*Preconditions*:
- [(15.1)](#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)](#cons-15.2)
other.required_span_size() is representable as
a value of type index_type[.](#cons-15.sentence-1)
[16](#cons-16)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23368)
*Effects*:
- [(16.1)](#cons-16.1)
Direct-non-list-initializes *extents_* with other.extents() and
- [(16.2)](#cons-16.2)
if *rank_* is greater than one,
direct-non-list-initializes *stride-1* with other.stride(1)[.](#cons-16.sentence-1)
[17](#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)
[🔗](#lib:layout_left_padded::mapping,constructor_____)
`template<class LayoutRightPaddedMapping>
constexpr explicit(see below)
mapping(const LayoutRightPaddedMapping& other) noexcept;
`
[18](#cons-18)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23396)
*Constraints*:
- [(18.1)](#cons-18.1)
*is-layout-right-padded-mapping-of*<LayoutRightPaddedMapping> is true or
*is-mapping-of*<layout_right, LayoutRightPaddedMapping> is true[.](#cons-18.1.sentence-1)
- [(18.2)](#cons-18.2)
*rank_* equals zero or one[.](#cons-18.2.sentence-1)
- [(18.3)](#cons-18.3)
is_constructible_v<extents_type, typename LayoutRightPaddedMapping​::​extents_-
type> is true[.](#cons-18.3.sentence-1)
[19](#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[.](#cons-19.sentence-1)
[20](#cons-20)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23416)
*Effects*: Direct-non-list-initializes *extents_* with other.extents()[.](#cons-20.sentence-1)
[21](#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](#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[.](#cons-21.sentence-2)
— *end note*]
#### [23.7.3.4.8.4](#obs) Observers [[mdspan.layout.leftpad.obs]](mdspan.layout.leftpad.obs)
[🔗](#obs-itemdecl:1)
`constexpr array<index_type, rank_> strides() const noexcept;
`
[1](#obs-1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23442)
*Returns*: array<index_type, *rank_*>({stride(P_rank)...})[.](#obs-1.sentence-1)
[🔗](#obs-itemdecl:2)
`constexpr index_type required_span_size() const noexcept;
`
[2](#obs-2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23452)
*Returns*:
- [(2.1)](#obs-2.1)
0 if the multidimensional index space *extents_* is empty,
- [(2.2)](#obs-2.2)
otherwise, *this(((*extents_*(P_rank) - index_type(1))...)) + 1[.](#obs-2.sentence-1)
[🔗](#obs-itemdecl:3)
`template<class... Indices>
constexpr size_t operator()(Indices... idxs) const noexcept;
`
[3](#obs-3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23468)
*Constraints*:
- [(3.1)](#obs-3.1)
sizeof...(Indices) == *rank_* is true[.](#obs-3.1.sentence-1)
- [(3.2)](#obs-3.2)
(is_convertible_v<Indices, index_type> && ...) is true[.](#obs-3.2.sentence-1)
- [(3.3)](#obs-3.3)
(is_nothrow_constructible_v<index_type, Indices> && ...) is true[.](#obs-3.3.sentence-1)
[4](#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"))[.](#obs-4.sentence-1)
[5](#obs-5)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23484)
*Returns*: ((static_cast<index_type>(idxs) * stride(P_rank)) + ... + 0)[.](#obs-5.sentence-1)
[🔗](#obs-itemdecl:4)
`static constexpr bool is_always_exhaustive() noexcept;
`
[6](#obs-6)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23494)
*Returns*:
- [(6.1)](#obs-6.1)
If *rank_* equals zero or one, then true;
- [(6.2)](#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)](#obs-6.3)
otherwise, false[.](#obs-6.sentence-1)
[🔗](#obs-itemdecl:5)
`constexpr bool is_exhaustive() const noexcept;
`
[7](#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)[.](#obs-7.sentence-1)
[🔗](#obs-itemdecl:6)
`constexpr index_type stride(rank_type r) const noexcept;
`
[8](#obs-8)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23525)
*Preconditions*: r is smaller than *rank_*[.](#obs-8.sentence-1)
[9](#obs-9)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23529)
*Returns*:
- [(9.1)](#obs-9.1)
If r equals zero: 1;
- [(9.2)](#obs-9.2)
otherwise, if r equals one: *stride-1*;
- [(9.3)](#obs-9.3)
otherwise, the product of *stride-1* and
all values extents_.extent(k) with k in the range [1, r)[.](#obs-9.sentence-1)
[🔗](#obs-itemdecl:7)
`template<class LayoutLeftPaddedMapping>
friend constexpr bool operator==(const mapping& x, const LayoutLeftPaddedMapping& y) noexcept;
`
[10](#obs-10)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L23548)
*Constraints*:
- [(10.1)](#obs-10.1)
*is-layout-left-padded-mapping-of*<LayoutLeftPaddedMapping> is true[.](#obs-10.1.sentence-1)
- [(10.2)](#obs-10.2)
LayoutLeftPaddedMapping​::​extents_type​::​rank() == rank_ is true[.](#obs-10.2.sentence-1)
[11](#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[.](#obs-11.sentence-1)
Otherwise, false[.](#obs-11.sentence-2)
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