24 Containers library [containers]

24.7 Views [views]

24.7.3 Multidimensional access [views.multidim]

24.7.3.4 Layout mapping [mdspan.layout]

24.7.3.4.7 Class template layout_stride​::​mapping [mdspan.layout.stride]

24.7.3.4.7.1 Overview [mdspan.layout.stride.overview]

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layout_stride provides a layout mapping where the strides are user-defined.
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], constructors constexpr 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], observers constexpr 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 }; }
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If Extents is not a specialization of extents, then the program is ill-formed.
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layout_stride​::​mapping<E> is a trivially copyable type that models regular for each E.
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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.

24.7.3.4.7.2 Exposition-only helpers [mdspan.layout.stride.expo]

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Let REQUIRED-SPAN-SIZE(e, strides) be:
  • (1.1)
    1, if e.rank() == 0 is true,
  • (1.2)
    otherwise 0, if the size of the multidimensional index space e is 0,
  • (1.3)
    otherwise 1 plus the sum of products of (e.extent(r) - 1) and strides[r] for all r in the range [0, e.rank()).
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Let OFFSET(m) be:
  • (2.1)
    m(), if e.rank() == 0 is true,
  • (2.2)
    otherwise 0, if the size of the multidimensional index space e is 0,
  • (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.
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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
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Let layout-mapping-alike be the exposition-only concept defined as follows: template<class M> concept layout-mapping-alike = requires { // exposition only requires is-extents<typename M::extents_type>; { M::is_always_strided() } -> same_as<bool>; { M::is_always_exhaustive() } -> same_as<bool>; { M::is_always_unique() } -> same_as<bool>; bool_constant<M::is_always_strided()>::value; bool_constant<M::is_always_exhaustive()>::value; bool_constant<M::is_always_unique()>::value; };
[Note 1: 
This concept checks that the functions M​::​is_always_strided(), M​::​is_always_exhaustive(), and M​::​is_always_unique() exist, are constant expressions, and have a return type of bool.
— end note]

24.7.3.4.7.3 Constructors [mdspan.layout.stride.cons]

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constexpr mapping() noexcept;
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Preconditions: layout_right​::​mapping<extents_type>().required_span_size() is representable as a value of type index_type ([basic.fundamental]).
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Effects: Direct-non-list-initializes extents_ with extents_type(), and for all d in the range [0, rank_), direct-non-list-initializes strides_[d] with layout_right​::​mapping<extents_type>().stride(d).
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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;
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Constraints:
  • (3.1)
    is_convertible_v<const OtherIndexType&, index_type> is true, and
  • (3.2)
    is_nothrow_constructible_v<index_type, const OtherIndexType&> is true.
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Preconditions:
  • (4.1)
    s[i] > 0 is true for all i in the range [0, rank_).
  • (4.2)
    REQUIRED-SPAN-SIZE(e, s) is representable as a value of type index_type ([basic.fundamental]).
  • (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[] >= s[] * e.extent(p) is true for all i in the range [1, rank_), where is the element of P.
    [Note 1: 
    For layout_stride, this condition is necessary and sufficient for is_unique() to be true.
    — end note]
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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]).
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template<class StridedLayoutMapping> constexpr explicit(see below) mapping(const StridedLayoutMapping& other) noexcept;
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Constraints:
  • (6.1)
    layout-mapping-alike<StridedLayoutMapping> is satisfied.
  • (6.2)
    is_constructible_v<extents_type, typename StridedLayoutMapping​::​extents_type> is
    true.
  • (6.3)
    StridedLayoutMapping​::​is_always_unique() is true.
  • (6.4)
    StridedLayoutMapping​::​is_always_strided() is true.
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Preconditions:
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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).
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Remarks: The expression inside explicit is equivalent to: !(is_convertible_v<typename StridedLayoutMapping::extents_type, extents_type> && (is-mapping-of<layout_left, LayoutStrideMapping> || is-mapping-of<layout_right, LayoutStrideMapping> || is-mapping-of<layout_stride, LayoutStrideMapping>))

24.7.3.4.7.4 Observers [mdspan.layout.stride.obs]

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constexpr index_type required_span_size() const noexcept;
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Returns: REQUIRED-SPAN-SIZE(extents(), strides_).
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template<class... Indices> constexpr index_type operator()(Indices... i) const noexcept;
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Constraints:
  • (2.1)
    sizeof...(Indices) == rank_ is true,
  • (2.2)
    (is_convertible_v<Indices, index_type> && ...) is true, and
  • (2.3)
    (is_nothrow_constructible_v<index_type, Indices> && ...) is true.
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Preconditions: extents_type​::​index-cast(i) is a multidimensional index in extents_ ([mdspan.overview]).
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Effects: Let P be a parameter pack such that is_same_v<index_sequence_for<Indices...>, index_sequence<P...>> is true.
Equivalent to: return ((static_cast<index_type>(i) * stride(P)) + ... + 0);
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constexpr bool is_exhaustive() const noexcept;
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Returns:
  • (5.1)
    true if rank_ is 0.
  • (5.2)
    Otherwise, true if there is a permutation P of the integers in the range [0, rank_) such that stride() equals 1, and stride() equals stride() * extents().extent() for i in the range [1, rank_), where is the element of P.
  • (5.3)
    Otherwise, false.
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template<class OtherMapping> friend constexpr bool operator==(const mapping& x, const OtherMapping& y) noexcept;
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Constraints:
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Preconditions: OtherMapping meets the layout mapping requirements ([mdspan.layout.policy.reqmts]).
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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()).
Otherwise, false.