cppdraft_translate/cppdraft/mdspan/layout/leftpad.md

[mdspan.layout.leftpad]

23 Containers library [containers]

23.7 Views [views]

23.7.3 Multidimensional access [views.multidim]

23.7.3.4 Layout mapping [mdspan.layout]

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

23.7.3.4.8.1 Overview [mdspan.layout.leftpad.overview]

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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).

namespace std {template<size_t PaddingValue>templateclass layout_left_padded::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; private:static constexpr size_t rank_ = extents_type::rank(); // exposition onlystatic constexpr size_t first-static-extent = // exposition only extents_type::static_extent(0); // [mdspan.layout.leftpad.expo], exposition-only membersstatic constexpr size_t static-padding-stride = see below; // exposition onlypublic:// [mdspan.layout.leftpad.cons], constructorsconstexpr mapping() noexcept : mapping(extents_type{}) {}constexpr mapping(const mapping&) noexcept = default; constexpr mapping(const extents_type&); templateconstexpr mapping(const extents_type&, OtherIndexType); templateconstexpr explicit(!is_convertible_v<OtherExtents, extents_type>) mapping(const layout_left::mapping&); templateconstexpr explicit(extents_type::rank() > 0) mapping(const layout_stride::mapping&); templateconstexpr explicit(see below) mapping(const LayoutLeftPaddedMapping&); templateconstexpr explicit(see below) mapping(const LayoutRightPaddedMapping&) noexcept; constexpr mapping& operator=(const mapping&) noexcept = default; // [mdspan.layout.leftpad.obs], 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; templatefriend constexpr bool operator==(const mapping&, const LayoutLeftPaddedMapping&) noexcept; private:// [mdspan.layout.leftpad.expo], exposition-only members index_type stride-1 = static-padding-stride; // exposition only extents_type extents_{}; // exposition only// [mdspan.sub.map], 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...); }};}

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If Extents is not a specialization of extents, then the program is ill-formed.

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layout_left_padded​::​mapping is a trivially copyable type that models regular for each E.

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Throughout [mdspan.layout.leftpad], let P_rank be the following size rank_ parameter pack of size_t values:

• (4.1)

the empty parameter pack, if rank_ equals zero;

• (4.2)

otherwise, 0zu, if rank_ equals one;

• (4.3)

otherwise, the parameter pack 0zu, 1zu, …, rank_- 1.

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Mandates:

• (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.

• (5.2)

  padding_value is representable as a value of type index_type.

• (5.3)

  If

  • (5.3.1)

rank_ is greater than one,

• (5.3.2)

padding_value does not equal dynamic_extent, and

• (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.

• (5.4)

  If

  • (5.4.1)

rank_ is greater than one,

• (5.4.2)

padding_value does not equal dynamic_extent, and

• (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 ofLEAST-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.

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

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

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The value is

• (1.1)

0, if rank_ equals zero or one;

• (1.2)

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

• (1.3)

otherwise, the size_t value which isLEAST-MULTIPLE-AT-LEAST(padding_value, first-static-extent).

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index_type stride-1 = static-padding-stride;

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Recommended practice: Implementations should not store this value if static-padding-stride is not dynamic_extent.

[Note 1:

Using extents<index_type, static-padding-stride> instead ofindex_type as the type of stride-1 would achieve this.

— end note]

23.7.3.4.8.3 Constructors [mdspan.layout.leftpad.cons]

🔗

constexpr mapping(const extents_type& ext);

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Preconditions:

• (1.1)

  The size of the multidimensional index space ext is representable as a value of type index_type.

• (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.

• (1.3)

  If rank_ is greater than one andpadding_value does not equal dynamic_extent, then the product ofLEAST-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.

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Effects:

• (2.1)

Direct-non-list-initializes extents_ with ext; and

• (2.2)

if rank_ is greater than one, direct-non-list-initializes stride-1

• (2.2.1)

with ext.extent(0) if padding_value is dynamic_extent,

• (2.2.2)

otherwise withLEAST-MULTIPLE-AT-LEAST(padding_value, ext.extent(0)).

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template<class OtherIndexType> constexpr mapping(const extents_type& ext, OtherIndexType pad);

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Constraints:

• (3.1)

  is_convertible_v<OtherIndexType, index_type> is true.

• (3.2)

  is_nothrow_constructible_v<index_type, OtherIndexType> is true.

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Preconditions:

• (4.1)

  pad is representable as a value of type index_type.

• (4.2)

  extents_type​::​index-cast(pad) is greater than zero.

• (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)

  If rank_ is greater than one, then the product ofLEAST-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.

• (4.5)

  If padding_value is not equal to dynamic_extent,padding_value equals extents_type​::​index-cast(pad).

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Effects: Direct-non-list-initializes extents_ with ext, and if rank_ is greater than one, direct-non-list-initializes stride-1 withLEAST-MULTIPLE-AT-LEAST(pad, ext.extent(0)).

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

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Constraints: is_constructible_v<extents_type, OtherExtents> is true.

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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.

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Preconditions:

• (8.1)

If extents_type​::​rank() > 1 is true andpadding_value == dynamic_extent is false, then other.stride(1) equalsLEAST-MULTIPLE-AT-LEAST(padding_value, extents_type::index-cast(other.extents().extent(0))) and

• (8.2)

other.required_span_size() is representable as a value of type index_type.

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Effects: Equivalent to mapping(other.extents()).

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

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Constraints: is_constructible_v<extents_type, OtherExtents> is true.

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Preconditions:

• (11.1)

  If rank_ is greater than 1 andpadding_value does not equal dynamic_extent, then other.stride(1) equalsLEAST-MULTIPLE-AT-LEAST(padding_value, extents_type::index-cast(other.extents().extent(0)))

• (11.2)

  If rank_ is greater than 0, then other.stride(0) equals 1.

• (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)

  other.required_span_size() is representable as a value of type index_type.

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Effects:

• (12.1)

Direct-non-list-initializes extents_ with other.extents() and

• (12.2)

if rank_ is greater than one, direct-non-list-initializes stride-1 withother.stride(1).

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template<class LayoutLeftPaddedMapping> constexpr explicit(see below) mapping(const LayoutLeftPaddedMapping& other);

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Constraints:

• (13.1)

  is-layout-left-padded-mapping-of is true.

• (13.2)

  is_constructible_v<extents_type, typename LayoutLeftPaddedMapping​::​extents_type>
  is true.

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Mandates: If rank_ is greater than 1, thenpadding_value == dynamic_extent || LayoutLeftPaddedMapping::padding_value == dynamic_extent || padding_value == LayoutLeftPaddedMapping::padding_value is true.

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Preconditions:

• (15.1)

If rank_ is greater than 1 andpadding_value does not equal dynamic_extent, then other.stride(1) equalsLEAST-MULTIPLE-AT-LEAST(padding_value, extents_type::index-cast(other.extent(0)))

• (15.2)

other.required_span_size() is representable as a value of type index_type.

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Effects:

• (16.1)

Direct-non-list-initializes extents_ with other.extents() and

• (16.2)

if rank_ is greater than one, direct-non-list-initializes stride-1 with other.stride(1).

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Remarks: The expression inside explicit is equivalent to:rank_> 1 &&(padding_value != dynamic_extent || LayoutLeftPaddedMapping::padding_value == dynamic_extent)

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

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Constraints:

• (18.1)

  is-layout-right-padded-mapping-of is true or
  is-mapping-of<layout_right, LayoutRightPaddedMapping> is true.

• (18.2)

  rank_ equals zero or one.

• (18.3)

  is_constructible_v<extents_type, typename LayoutRightPaddedMapping​::​extents_-
  type> is true.

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Preconditions: other.required_span_size() is representable as a value of type index_type.

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Effects: Direct-non-list-initializes extents_ with other.extents().

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Remarks: The expression inside explicit is equivalent to:!is_convertible_v<typename LayoutRightPaddedMapping::extents_type, extents_type>

[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.

— end note]

23.7.3.4.8.4 Observers [mdspan.layout.leftpad.obs]

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constexpr array<index_type, rank_> strides() const noexcept;

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Returns: array<index_type, rank_>({stride(P_rank)...}).

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constexpr index_type required_span_size() const noexcept;

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Returns:

• (2.1)

0 if the multidimensional index space extents_ is empty,

• (2.2)

otherwise, *this(((extents_(P_rank) - index_type(1))...)) + 1.

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template<class... Indices> constexpr size_t operator()(Indices... idxs) const noexcept;

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Constraints:

• (3.1)

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

• (3.2)

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

• (3.3)

  (is_nothrow_constructible_v<index_type, Indices> && ...) is true.

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Preconditions: extents_type​::​index-cast(idxs) is a multidimensional index in extents() ([mdspan.overview]).

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Returns: ((static_cast<index_type>(idxs) * stride(P_rank)) + ... + 0).

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static constexpr bool is_always_exhaustive() noexcept;

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Returns:

• (6.1)

If rank_ equals zero or one, then true;

• (6.2)

otherwise, if neither static-padding-stride nor first-static-extent equal dynamic_extent, then static-padding-stride == first-static-extent;

• (6.3)

otherwise, false.

🔗

constexpr bool is_exhaustive() const noexcept;

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Returns: true if rank_ equals zero or one; otherwise, extents_.extent(0) == stride(1).

🔗

constexpr index_type stride(rank_type r) const noexcept;

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Preconditions: r is smaller than rank_.

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Returns:

• (9.1)

If r equals zero: 1;

• (9.2)

otherwise, if r equals one: stride-1;

• (9.3)

otherwise, the product of stride-1 and all values extents_.extent(k) with k in the range [1, r).

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

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Constraints:

• (10.1)

  is-layout-left-padded-mapping-of is true.

• (10.2)

  LayoutLeftPaddedMapping​::​extents_type​::​rank() == rank_ is true.

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Returns: true if x.extents() == y.extents() is true andrank_ < 2 || x.stride(1) == y.
stride(1) is true.

Otherwise, false.