[mdspan.overview]

A multidimensional index space is a Cartesian product of integer intervals.

Each interval can be represented by a half-open range

[{L i, {U i), where {L i and {U i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}_{i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}}_{i and {U i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}_{i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}}}_{i), where {L i and {U i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}_{i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}}_{i and {U i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}_{i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}}}}_{i, {U i), where {L i and {U i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}_{i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}}_{i and {U i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}_{i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}}}_{i), where {L i and {U i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}_{i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}}_{i and {U i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}_{i are the lower and upper bounds of the {i th dimension .}^{th dimension .}}}}}

The rank of a multidimensional index space is the number of intervals it represents.

The size of a multidimensional index space is the product of

{U i - {L i for each dimension i if its rank is greater than 0, and 1 otherwise .}_{i for each dimension i if its rank is greater than 0, and 1 otherwise .}}_{i - {L i for each dimension i if its rank is greater than 0, and 1 otherwise .}_{i for each dimension i if its rank is greater than 0, and 1 otherwise .}}

An integer r is a rank index of an index space S if r is in the range

[0, rank of S) .

A pack of integers idx is a multidimensional index in a multidimensional index space S (or representation thereof) if both of the following are true:

(3.1)
sizeof.(idx) is equal to the rank of S, and
(3.2)
for every rank index i of S, the ${i th value of idx is an integer in the interval [{L i, {U i) of S .}_{i) of S .}}_{i, {U i) of S .}_{i) of S .}}}^{th value of idx is an integer in the interval [{L i, {U i) of S .}_{i) of S .}}_{i, {U i) of S .}_{i) of S .}}}$