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:
  • IndexType is a signed or unsigned integer type, and
  • 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 be the element of Extents.
is a dynamic extent if it is equal to dynamic_extent, otherwise is a static extent.
Let be the value of dynamic-extents[dynamic-index(r)] if is a dynamic extent, otherwise .
The interval of the multidimensional index space represented by an extents object is .

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 with for which is a dynamic extent.
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.
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.
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.
template<class OtherIndexType> static constexpr auto index-cast(OtherIndexType&& i) noexcept;
Effects:
  • If OtherIndexType is an integral type other than bool, then equivalent to return i;,
  • 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]

template<class OtherIndexType, size_t... OtherExtents> constexpr explicit(see below) extents(const extents<OtherIndexType, OtherExtents...>& other) noexcept;
Constraints:
  • sizeof...(OtherExtents) == rank() is true.
  • ((OtherExtents == dynamic_extent || Extents == dynamic_extent || OtherExtents ==
    Extents) && ...)
    is true.
Preconditions:
  • other.extent(r) equals for each r for which is a static extent, and
  • either
    • sizeof...(OtherExtents) is zero, or
    • 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())
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:
  • (is_convertible_v<OtherIndexTypes, index_type> && ...) is true,
  • (is_nothrow_constructible_v<index_type, OtherIndexTypes> && ...) is true, and
  • 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:
  • If N != rank_dynamic() is true, exts_arr[r] equals for each r for which is a static extent, and
  • either
    • sizeof...(exts) == 0 is true, or
    • each element of exts is representable as a nonnegative value of type index_type.
Postconditions: *this == extents(exts_arr) is true.
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:
  • is_convertible_v<const OtherIndexType&, index_type> is true,
  • is_nothrow_constructible_v<index_type, const OtherIndexType&> is true, and
  • N == rank_dynamic() || N == rank() is true.
Preconditions:
  • If N != rank_dynamic() is true, exts[r] equals for each r for which is a static extent, and
  • either
    • N is zero, or
    • exts[r] is representable as a nonnegative value of type index_type for every rank index r.
Effects:
  • 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]).
  • 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)]).
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]

static constexpr size_t static_extent(rank_type i) noexcept;
Preconditions: i < rank() is true.
Returns: .
constexpr index_type extent(rank_type i) const noexcept;
Preconditions: i < rank() is true.
Returns: .

23.7.3.3.5 Comparison operators [mdspan.extents.cmp]

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]

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]

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.