mdspan of All Dynamic Extents

Published Proposal,

Issue Tracking:
ISO/IEC 14882 Programming Languages — C++, ISO/IEC JTC1/SC22/WG21

1. Introduction

[P0009R12] proposes adding non-owning multidimensional span abstractions to the C++ Standard Library; basic_mdspan, which is fully generic and can represent any kind of multidimensional data, and mdspan, a convenience template alias for simpler use cases.

template <class ElementType, class Extents, class LayoutPolicy = layout_right,
          class AccessorPolicy = accessor_basic<ElementType>>
struct basic_mdspan;

template <class ElementType, size_t... Extents>
using mdspan = basic_mdspan<ElementType, extents<Extents...>>;

In the basic_mdspan/span interface, extents can be either static, e.g. expressed at compile time:

mdspan<double, 64, 64> a(data);

or dynamic, e.g. expressed at run time:

mdspan<double, dynamic_extent, dynamic_extent> a(data, 64, 64);

You can also use a mix of the two styles:

mdspan<double, 64, dynamic_extent> a(data, 64);

While basic_mdspan and mdspan are powerful, the spelling of instantiations can be verbose, especially for the common case where all extents are dynamic.

2. Class Template Argument Deduction for All Dynamic Extents

Using class template argument deduction (introduced in C++17) and alias template argument deduction (introduced in C++20), we can make it a easier to use mdspan with all dynamic extents:

Before After
mdspan<double, dynamic_extent, dynamic_extent> a(data, 64, 64); mdspan a(data, 64, 64);

To make this work, we need to add a deduction guide for basic_mdspan. Through the power of alias template argument deduction, mdspan will be able to use said deduction guide as well.

Here’s an example implementation of such a deduction guide for basic_mdspan.

In earlier versions of this paper, it was unclear whether such a deduction guide would work for the alias template mdspan, as attempts to construct one that functioned as intended had failed. However, we have since learned that the this is due to bugs in the two implementations that currently support alias template deduction, MSVC and GCC. Those bugs have been reported to the respective compilers and hopefully will be fixed soon.

Here’s an example of the current implementation bugs that prevent the deduction guide from working for mdspan.

3. Template Aliases for All Dynamic Extents

The root of the interface challenge here is the heterogeneous nature of extents in mdspan. When you need to express static extents or a mix of static and dynamic extents, we must state the kind of every extent, similar to how we state the type of every element of a tuple. This heterogenity gives us flexibility at the cost of verbosity.

However, in the case of all dynamic extents, we do not need that flexibility; the kind of every extent is the same. Instead of a tuple-like interface, we likely want an array-like interface, where we can simple state the number of extents, instead of listing every one.

We can provide this simplified interface easily by adding a template alias for extents that takes the number of extents as a parameter and expands to an extents of that many dynamic_extents. Here’s an example implementation.

tuple-like array-like
tuple<T, T, T> array<T, 3>
extents<dynamic_extent, dynamic_extent, dynamic_extent> dextents<3> (proposed)

If you are working with an array-like representation of extents, working with mdspan can become quite awkward:

template <size_t>
constexpr auto make_dynamic_extent() {
  return dynamic_extent;

template <typename T, size_t Rank>
struct tensor {
  T* data;
  array<size_t, Rank> extents;

  auto get_mdspan() {
    return get_mdspan_impl(make_index_sequence<Rank>());

  template <size_t... Pack>
  auto get_mdspan_impl(index_sequence<Pack...>) {
    return mdspan<T, make_dynamic_extent<Pack>()...>(data, extents);

With dextents, this becomes a lot simpler:

template <typename T, size_t Rank>
struct tensor {
  T* data;
  array<size_t, Rank> extents;

  auto get_mdspan() {
    return mdspan(data, dextents<Rank>(extents));

4. Remove mdspan Convenience Alias

dextents will have to be used with the unfortunately named basic_mdspan. I considered proposing something along the lines of dynamic_mdspan<T, Rank>. However, this would potentially lead to confusion, as a size_t non-type template parameter in mdspan would mean "static extent of this size" while a size_t non-type template parameter in dynamic_mdspan would mean "number of extents".

Syntax Semantics
span<T, N> span with a static size ofN.
mdspan<T, N> mdspan with a single static extent of size N.
dynamic_mdspan<T, N> (not proposed) mdspan with N dynamic extents.

Instead, I think we should:

The purpose of the mdspan alias was to provide a simple and easy to use interface for those with less complex and advanced use cases. When the mdspan/basic_mdspan dichotomy was introduced when the proposal was first under consideration, before the existence of Class Template Argument Deduction and the proposed dextents. With the combination of these two forces, I believe that a separate mdspan alias and basic_mdspan class are unnecessary to achieve a simple and easy to use interface.

Before mdspan<T> m(data, 16, 64, 64);
After mdspan<T> m(data, 16, 64, 64);
Before mdspan<T, dynamic_extent, dynamic_extent, dynamic_extent> f();
After mdspan<T, dextents<3>> f();
Before mdspan<T, 3, 3> m;
After mdspan<T, extents<3, 3>> m;
Before mdspan<T, 3, 3> f();
After mdspan<T, extents<3, 3>> f();
Before mdspan<T, 16, dynamic_extent, 64> m;
After mdspan<T, extents<16, dynamic_extent, 64>> m;
Before mdspan<T, 16, dynamic_extent, 64> f();
After mdspan<T, extents<16, dynamic_extent, 64>> f();

5. Wording

The following changes are relative to the mdspan proposal ([P0009R12]).

The � character is used to denote a placeholder number which shall be selected by the editor.

Modify the header synopsis for <mdspan> in [mdspan.syn] as follows:

22.7.� Header <mdspan> synopsis [mdspan.syn]
namespace std {
  // [mdspan.extents], class template extents
    class extents;

template<size_t Rank> using dextents = decltype([] <size_t... Pack> (index_sequence<Pack...>) constexpr { return extents<[] (auto) constexpr { return dynamic_extent; } (integral_constant<size_t, Pack>{})...>{}; }(make_index_sequence<Rank>{}));
// [mdspan.layout], Layout mapping policies class layout_left; class layout_right; class layout_stride; // [mdspan.accessor.basic] template<class ElementType> class default_accessor; // [mdspan.basic], class template mdspan template<class ElementType, class Extents, class LayoutPolicy = layout_right, class AccessorPolicy = default_accessor<ElementType>> class basic_mdspan;
template <class ElementType, class... Integrals> explicit basic_mdspan(ElementType*, Integrals...) -> basic_mdspan<ElementType, dextents<sizeof...(Integrals)>
template<class T, size_t... Extents> using mdspan = basic_mdspan<T, extents<Extents...>>;
// [mdspan.submdspan] template<class ElementType, class Extents, class LayoutPolicy, class AccessorPolicy, class... SliceSpecifiers> constexpr basic_mdspan<see below> submdspan(const basic_mdspan<ElementType, Extents, LayoutPolicy, AccessorPolicy>& m, SliceSpecifiers... specs) noexcept; // tag supporting submdspan struct full_extent_t { explicit full_extent_t() = default; }; inline constexpr full_extent_t full_extent = full_extent_t{}; }

Replace all occurences of basic_mdspan with mdspan.


Informative References

Christian Trott, D.S. Hollman, Damien Lebrun-Grandie, Mark Hoemmen, Daniel Sunderland, H. Carter Edwards, Bryce Adelstein Lelbach, Mauro Bianco, Ben Sander, Athanasios Iliopoulos, John Michopoulos, Nevin Liber. MDSPAN. 21 May 2021. URL: https://wg21.link/p0009r12