23 Containers library [containers]

23.7 Views [views]

23.7.3 Multidimensional access [views.multidim]

23.7.3.3 Class template extents [mdspan.extents]

23.7.3.3.1 Overview [mdspan.extents.overview]

The class template extents represents a multidimensional index space of rank equal to sizeof...(Extents).

In ([views]), extents is used synonymously with multidimensional index space.

namespace std { template<class IndexType, size_t... Extents> class extents { public: using index_type = IndexType; using size_type = make_unsigned_t<index_type>; using rank_type = size_t; // [mdspan.extents.obs], observers of the multidimensional index space static 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], constructors constexpr 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], comparison operators template<class OtherIndexType, size_t... OtherExtents> friend constexpr bool operator==(const extents&, const extents<OtherIndexType, OtherExtents...>&) noexcept; // [mdspan.extents.expo], exposition-only helpers constexpr 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; }

Mandates:

(1.1)
IndexType is a signed or unsigned integer type, and
(1.2)
each element of Extents is either equal to dynamic_extent, or is representable as a value of type IndexType.

Each specialization of extents models regular and is trivially copyable.

Let

E_{r}

be the

r^{th}

element of Extents.

E_{r}

is a dynamic extent if it is equal to dynamic_extent, otherwise

E_{r}

is a static extent.

Let

D_{r}

be the value of dynamic-extents[dynamic-index(r)] if

E_{r}

is a dynamic extent, otherwise

E_{r}

The

r^{th}

interval of the multidimensional index space represented by an extents object is

[0, D_{r})

23.7.3.3.2 Exposition-only helpers [mdspan.extents.expo]

🔗

static constexpr rank_type dynamic-index(rank_type i) noexcept;

Preconditions: i <= rank() is true.

Returns: The number of

E_{r}

with

r < i

for which

E_{r}

is a dynamic extent.

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static constexpr rank_type dynamic-index-inv(rank_type i) noexcept;

Preconditions: i < rank_dynamic() is true.

Returns: The minimum value of r such that dynamic-index(r + 1) == i + 1 is true.

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constexpr size_t fwd-prod-of-extents(rank_type i) const noexcept;

Preconditions: i <= rank() is true.

Returns: If i > 0 is true, the product of extent(k) for all k in the range [0, i), otherwise 1.

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constexpr size_t rev-prod-of-extents(rank_type i) const noexcept;

Preconditions: i < rank() is true.

Returns: If i + 1 < rank() is true, the product of extent(k) for all k in the range [i + 1, rank()), otherwise 1.

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template<class OtherIndexType>
  static constexpr auto index-cast(OtherIndexType&& i) noexcept;

Effects:

(9.1)
If OtherIndexType is an integral type other than bool, then equivalent to return i;,
(9.2)
otherwise, equivalent to return static_cast<index_type>(i);.

[Note 1:

This function will always return an integral type other than bool.

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.

— end note]

23.7.3.3.3 Constructors [mdspan.extents.cons]

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template<class OtherIndexType, size_t... OtherExtents>
  constexpr explicit(see below)
    extents(const extents<OtherIndexType, OtherExtents...>& other) noexcept;

Constraints:

(1.1)
sizeof...(OtherExtents) == rank() is true.
(1.2)
((OtherExtents == dynamic_extent || Extents == dynamic_extent || OtherExtents ==
Extents) && ...) is true.

Preconditions:

(2.1)
other.extent(r) equals $E_{r}$ for each r for which $E_{r}$ is a static extent, and
(2.2)
either
- (2.2.1)
  sizeof...(OtherExtents) is zero, or
- (2.2.2)
  other.extent(r) is representable as a value of type index_type for every rank index r of other.

Postconditions: *this == other is true.

Remarks: The expression inside explicit is equivalent to: (((Extents != dynamic_extent) && (OtherExtents == dynamic_extent)) || ... ) || (numeric_limits<index_type>::max() < numeric_limits<OtherIndexType>::max())

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template<class... OtherIndexTypes>
  constexpr explicit extents(OtherIndexTypes... exts) noexcept;

Let N be sizeof...(OtherIndexTypes), and let exts_arr be array<index_type, N>{static_cast<
index_type>(std::move(exts))...}.

Constraints:

(6.1)
(is_convertible_v<OtherIndexTypes, index_type> && ...) is true,
(6.2)
(is_nothrow_constructible_v<index_type, OtherIndexTypes> && ...) is true, and
(6.3)
N == rank_dynamic() || N == rank() is true.
[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.
— end note]

Preconditions:

(7.1)
If N != rank_dynamic() is true, exts_arr[r] equals $E_{r}$ for each r for which $E_{r}$ is a static extent, and
(7.2)
either
- (7.2.1)
  sizeof...(exts) == 0 is true, or
- (7.2.2)
  each element of exts is representable as a nonnegative value of type index_type.

Postconditions: *this == extents(exts_arr) is true.

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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;

Constraints:

(9.1)
is_convertible_v<const OtherIndexType&, index_type> is true,
(9.2)
is_nothrow_constructible_v<index_type, const OtherIndexType&> is true, and
(9.3)
N == rank_dynamic() || N == rank() is true.

Preconditions:

(10.1)
If N != rank_dynamic() is true, exts[r] equals $E_{r}$ for each r for which $E_{r}$ is a static extent, and
(10.2)
either
- (10.2.1)
  N is zero, or
- (10.2.2)
  exts[r] is representable as a nonnegative value of type index_type for every rank index r.

Effects:

(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]).
(11.2)
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)]).

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template<class... Integrals>
  explicit extents(Integrals...) -> see below;

Constraints: (is_convertible_v<Integrals, size_t> && ...) is true.

Remarks: The deduced type is extents<size_t, maybe-static-ext<Integrals>...>.

23.7.3.3.4 Observers of the multidimensional index space [mdspan.extents.obs]

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static constexpr size_t static_extent(rank_type i) noexcept;

Preconditions: i < rank() is true.

Returns:

E_{i}

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constexpr index_type extent(rank_type i) const noexcept;

Preconditions: i < rank() is true.

Returns:

D_{i}

23.7.3.3.5 Comparison operators [mdspan.extents.cmp]

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template<class OtherIndexType, size_t... OtherExtents>
  friend constexpr bool operator==(const extents& lhs,
                                   const extents<OtherIndexType, OtherExtents...>& rhs) noexcept;

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.

23.7.3.3.6 Alias template dextents [mdspan.extents.dextents]

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template<class IndexType, size_t Rank>
  using dextents = see below;

Result: A type E that is a specialization of extents such that E::rank() == Rank && E::rank() == E::rank_dynamic() is true, and E::index_type denotes IndexType.

23.7.3.3.7 Alias template dims [mdspan.extents.dims]

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template<size_t Rank, class IndexType = size_t>
  using dims = see below;

Result: A type E that is a specialization of extents such that E::rank() == Rank && E::rank() == E::rank_dynamic() is true, and E::index_type denotes IndexType.