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> 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], exposition-only members static constexpr size_t static-padding-stride = see below; // exposition only public: // [mdspan.layout.leftpad.cons], constructors constexpr 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], observers constexpr 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], exposition-only members index_type stride-1 = static-padding-stride; // exposition only extents_type extents_{}; // exposition only // [mdspan.sub.map], submdspan mapping specialization template<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<E> 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 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.

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 equals dynamic_extent;
  • (1.3)
    otherwise, the size_t value which is LEAST-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 of index_type as the type of stride-1 would achieve this.
— end note]

23.7.3.4.8.3 Constructors [mdspan.layout.leftpad.cons]

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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 and padding_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 and padding_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.
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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 with LEAST-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 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.
  • (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 with LEAST-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 and padding_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)
    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 and padding_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)
    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 with other.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<LayoutLeftPaddedMapping> 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, then padding_value == dynamic_extent || LayoutLeftPaddedMapping::padding_value == dynamic_extent || padding_value == LayoutLeftPaddedMapping::padding_value is true.
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  • (15.1)
    If rank_ is greater than 1 and padding_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)
    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<LayoutRightPaddedMapping> 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)...}).
🔗
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.
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constexpr bool is_exhaustive() const noexcept;
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Returns: true if rank_ equals zero or one; otherwise, extents_.extent(0) == stride(1).
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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).
🔗
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<LayoutLeftPaddedMapping> is true.
  • (10.2)
    LayoutLeftPaddedMapping​::​extents_type​::​rank() == rank_ is true.
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Returns: true if x.extents() == y.extents() is true and rank_ < 2 || x.stride(1) == y.
stride(1) is true.
Otherwise, false.