[mdspan.overview]

# 23 Containers library [[containers]](./#containers)

## 23.7 Views [[views]](views#mdspan.overview)

### 23.7.3 Multidimensional access [[views.multidim]](views.multidim#mdspan.overview)

#### 23.7.3.1 Overview [mdspan.overview]

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L20993)

A [*multidimensional index space*](#def:index_space,multidimensional "23.7.3.1 Overview [mdspan.overview]") is
a Cartesian product of integer intervals[.](#1.sentence-1)

Each interval can be represented by a half-open range [Li,Ui),
where Li and Ui are the lower and upper bounds of
the ith dimension[.](#1.sentence-2)

The [*rank*](#def:rank "23.7.3.1 Overview [mdspan.overview]") of a multidimensional index space is
the number of intervals it represents[.](#1.sentence-3)

The [*size of a multidimensional index space*](#def:size_of_a_multidimensional_index_space "23.7.3.1 Overview [mdspan.overview]") is
the product of Ui−Li for each dimension i if its rank is greater than 0, and 1 otherwise[.](#1.sentence-4)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21005)

An integer r is a [*rank index*](#def:rank_index "23.7.3.1 Overview [mdspan.overview]") of an index space S if r is in the range [0,rank of S)[.](#2.sentence-1)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/containers.tex#L21009)

A pack of integers idx is
a [*multidimensional index*](#def:index,multidimensional "23.7.3.1 Overview [mdspan.overview]") in a multidimensional index space S (or representation thereof) if both of the following are true:

- [(3.1)](#3.1)

sizeof...(idx) is equal to the rank of S, and

- [(3.2)](#3.2)

for every rank index i of S,
the ith value of idx is an integer
in the interval [Li,Ui) of S[.](#3.sentence-1)