[mdspan.sub.map.sliceable]

Let:

(1.1)
M denote a layout mapping class;
(1.2)
IT denote M::extent_type::index_type;
(1.3)
m denote a value of type (possibly const) M;
(1.4)
M_rank be equal to M::extent_type::rank();
(1.5)
valid_slices denote a pack of (possibly const) objects for which sizeof.(valid_slices) == M_rank is true and, for each rank index i of m.extents(), valid_slices..[i] is a valid submdspan slice for the ${i th extent of m . extents ();}^{th extent of m . extents ();}$
(1.6)
invalid_slices denote a pack of objects for which sizeof.(invalid_slices) == M_rank is true and there exists an integer k such that the cv-unqualified type of invalid_slices..[k] is none of the following:
- (1.6.1)
  IT,
- (1.6.2)
  full_extent_t,
- (1.6.3)
  a specialization of constant_wrapper, or
- (1.6.4)
  a specialization of strided_slice.

For the purpose of this section, the meaning of submdspan_mapping is established as if by performing argument-dependent lookup only ([basic.lookup.argdep]).

A type M meets the sliceable layout mapping requirements if

(3.1)
M meets the layout mapping requirements ([mdspan.layout.policy.reqmts]),
(3.2)
the expression submdspan_mapping(m, invalid_slices..) is ill-formed, and
(3.3)
the following expression is well-formed and has the specified semantics: submdspan_mapping(m, valid_slices..)

Result: A type SMR that is a specialization of type submdspan_mapping_result<SM> for some type SM such that

(4.1)
SM meets the layout mapping requirements ([mdspan.layout.policy.reqmts]),
(4.2)
SM::extents_type is a specialization of extents,
(4.3)
SM::extents_type::rank() equals MAP_RANK(valid_slices, M_rank), and
(4.4)
SM::extents_type::index_type denotes IT.

Returns: An object smr of type SMR such that

(5.1)
smr.mapping.extents() == submdspan_extents(m.extents(), valid_slices..) is true;
and
(5.2)
for each integer pack i which is a multidimensional index in smr.mapping.extents(),
smr.mapping(i..) + smr.offset == m(j) is true, where j is an integer pack such that
- (5.2.1)
  sizeof.(j) is equal to M_rank; and
- (5.2.2)
  for each rank index ρ of m.extents(), j..[ρ] is equal to the sum of
  - (5.2.2.1)
    the lower bound of the submdspan slice range of valid_slices..[ρ] for extent ρ of m.extents(), and
  - (5.2.2.2)
    zero if the type of valid_slices..[ρ] is a collapsing slice type, i..[MAP_RANK(valid_slices,ρ)] otherwise.

🔗

template<class LayoutMapping>
  concept sliceable-mapping = see below;

Let lm be an object of type LayoutMapping and let fe denote a pack of objects of type full_extent_t for which sizeof.(fe) == LayoutMapping::extents_type::rank() is true.

A type LayoutMapping satisfies sliceable-mapping if

(6.1)
the expression submdspan_mapping(m, fe..) is well-formed when treated as an unevaluated operand, and
(6.2)
the type of that expression is a specialization of submdspan_mapping_result.

A type LayoutMapping models sliceable-mapping if LayoutMapping meets the sliceable layout mapping requirements.