<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml" lang xml:lang>
<head>
  <meta charset="utf-8" />
  <meta name="generator" content="mpark/wg21" />
  <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes" />
  <meta name="dcterms.date" content="2024-10-29" />
  <title>Fix submdspan for C++26</title>
  <style>
code{white-space: pre-wrap;}
span.smallcaps{font-variant: small-caps;}
span.underline{text-decoration: underline;}
div.column{display: inline-block; vertical-align: top; width: 50%;}
</style>
  <style>
pre > code.sourceCode { white-space: pre; position: relative; }
pre > code.sourceCode > span { line-height: 1.25; }
pre > code.sourceCode > span:empty { height: 1.2em; }
.sourceCode { overflow: visible; }
code.sourceCode > span { color: inherit; text-decoration: inherit; }
div.sourceCode { margin: 1em 0; }
pre.sourceCode { margin: 0; }
@media screen {
div.sourceCode { overflow: auto; }
}
@media print {
pre > code.sourceCode { white-space: pre-wrap; }
pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
}
pre.numberSource code
{ counter-reset: source-line 0; }
pre.numberSource code > span
{ position: relative; left: -4em; counter-increment: source-line; }
pre.numberSource code > span > a:first-child::before
{ content: counter(source-line);
position: relative; left: -1em; text-align: right; vertical-align: baseline;
border: none; display: inline-block;
-webkit-touch-callout: none; -webkit-user-select: none;
-khtml-user-select: none; -moz-user-select: none;
-ms-user-select: none; user-select: none;
padding: 0 4px; width: 4em;
color: #aaaaaa;
}
pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa; padding-left: 4px; }
div.sourceCode
{ background-color: #f6f8fa; }
@media screen {
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
}
code span { } 
code span.al { color: #ff0000; } 
code span.an { } 
code span.at { } 
code span.bn { color: #9f6807; } 
code span.bu { color: #9f6807; } 
code span.cf { color: #00607c; } 
code span.ch { color: #9f6807; } 
code span.cn { } 
code span.co { color: #008000; font-style: italic; } 
code span.cv { color: #008000; font-style: italic; } 
code span.do { color: #008000; } 
code span.dt { color: #00607c; } 
code span.dv { color: #9f6807; } 
code span.er { color: #ff0000; font-weight: bold; } 
code span.ex { } 
code span.fl { color: #9f6807; } 
code span.fu { } 
code span.im { } 
code span.in { color: #008000; } 
code span.kw { color: #00607c; } 
code span.op { color: #af1915; } 
code span.ot { } 
code span.pp { color: #6f4e37; } 
code span.re { } 
code span.sc { color: #9f6807; } 
code span.ss { color: #9f6807; } 
code span.st { color: #9f6807; } 
code span.va { } 
code span.vs { color: #9f6807; } 
code span.wa { color: #008000; font-weight: bold; } 
code.diff {color: #898887}
code.diff span.va {color: #00AA00}
code.diff span.st {color: #bf0303}
</style>
  <style type="text/css">
body {
margin: 5em;
font-family: serif;

hyphens: auto;
line-height: 1.35;
}
div.wrapper {
max-width: 60em;
margin: auto;
}
ul {
list-style-type: none;
padding-left: 2em;
margin-top: -0.2em;
margin-bottom: -0.2em;
}
a {
text-decoration: none;
color: #4183C4;
}
a.hidden_link {
text-decoration: none;
color: inherit;
}
li {
margin-top: 0.6em;
margin-bottom: 0.6em;
}
h1, h2, h3, h4 {
position: relative;
line-height: 1;
}
a.self-link {
position: absolute;
top: 0;
left: calc(-1 * (3.5rem - 26px));
width: calc(3.5rem - 26px);
height: 2em;
text-align: center;
border: none;
transition: opacity .2s;
opacity: .5;
font-family: sans-serif;
font-weight: normal;
font-size: 83%;
}
a.self-link:hover { opacity: 1; }
a.self-link::before { content: "§"; }
ul > li:before {
content: "\2014";
position: absolute;
margin-left: -1.5em;
}
:target { background-color: #C9FBC9; }
:target .codeblock { background-color: #C9FBC9; }
:target ul { background-color: #C9FBC9; }
.abbr_ref { float: right; }
.folded_abbr_ref { float: right; }
:target .folded_abbr_ref { display: none; }
:target .unfolded_abbr_ref { float: right; display: inherit; }
.unfolded_abbr_ref { display: none; }
.secnum { display: inline-block; min-width: 35pt; }
.header-section-number { display: inline-block; min-width: 35pt; }
.annexnum { display: block; }
div.sourceLinkParent {
float: right;
}
a.sourceLink {
position: absolute;
opacity: 0;
margin-left: 10pt;
}
a.sourceLink:hover {
opacity: 1;
}
a.itemDeclLink {
position: absolute;
font-size: 75%;
text-align: right;
width: 5em;
opacity: 0;
}
a.itemDeclLink:hover { opacity: 1; }
span.marginalizedparent {
position: relative;
left: -5em;
}
li span.marginalizedparent { left: -7em; }
li ul > li span.marginalizedparent { left: -9em; }
li ul > li ul > li span.marginalizedparent { left: -11em; }
li ul > li ul > li ul > li span.marginalizedparent { left: -13em; }
div.footnoteNumberParent {
position: relative;
left: -4.7em;
}
a.marginalized {
position: absolute;
font-size: 75%;
text-align: right;
width: 5em;
}
a.enumerated_item_num {
position: relative;
left: -3.5em;
display: inline-block;
margin-right: -3em;
text-align: right;
width: 3em;
}
div.para { margin-bottom: 0.6em; margin-top: 0.6em; text-align: justify; }
div.section { text-align: justify; }
div.sentence { display: inline; }
span.indexparent {
display: inline;
position: relative;
float: right;
right: -1em;
}
a.index {
position: absolute;
display: none;
}
a.index:before { content: "⟵"; }

a.index:target {
display: inline;
}
.indexitems {
margin-left: 2em;
text-indent: -2em;
}
div.itemdescr {
margin-left: 3em;
}
.bnf {
font-family: serif;
margin-left: 40pt;
margin-top: 0.5em;
margin-bottom: 0.5em;
}
.ncbnf {
font-family: serif;
margin-top: 0.5em;
margin-bottom: 0.5em;
margin-left: 40pt;
}
.ncsimplebnf {
font-family: serif;
font-style: italic;
margin-top: 0.5em;
margin-bottom: 0.5em;
margin-left: 40pt;
background: inherit; 
}
span.textnormal {
font-style: normal;
font-family: serif;
white-space: normal;
display: inline-block;
}
span.rlap {
display: inline-block;
width: 0px;
}
span.descr { font-style: normal; font-family: serif; }
span.grammarterm { font-style: italic; }
span.term { font-style: italic; }
span.terminal { font-family: monospace; font-style: normal; }
span.nonterminal { font-style: italic; }
span.tcode { font-family: monospace; font-style: normal; }
span.textbf { font-weight: bold; }
span.textsc { font-variant: small-caps; }
a.nontermdef { font-style: italic; font-family: serif; }
span.emph { font-style: italic; }
span.techterm { font-style: italic; }
span.mathit { font-style: italic; }
span.mathsf { font-family: sans-serif; }
span.mathrm { font-family: serif; font-style: normal; }
span.textrm { font-family: serif; }
span.textsl { font-style: italic; }
span.mathtt { font-family: monospace; font-style: normal; }
span.mbox { font-family: serif; font-style: normal; }
span.ungap { display: inline-block; width: 2pt; }
span.textit { font-style: italic; }
span.texttt { font-family: monospace; }
span.tcode_in_codeblock { font-family: monospace; font-style: normal; }
span.phantom { color: white; }

span.math { font-style: normal; }
span.mathblock {
display: block;
margin-left: auto;
margin-right: auto;
margin-top: 1.2em;
margin-bottom: 1.2em;
text-align: center;
}
span.mathalpha {
font-style: italic;
}
span.synopsis {
font-weight: bold;
margin-top: 0.5em;
display: block;
}
span.definition {
font-weight: bold;
display: block;
}
.codeblock {
margin-left: 1.2em;
line-height: 127%;
}
.outputblock {
margin-left: 1.2em;
line-height: 127%;
}
div.itemdecl {
margin-top: 2ex;
}
code.itemdeclcode {
white-space: pre;
display: block;
}
span.textsuperscript {
vertical-align: super;
font-size: smaller;
line-height: 0;
}
.footnotenum { vertical-align: super; font-size: smaller; line-height: 0; }
.footnote {
font-size: small;
margin-left: 2em;
margin-right: 2em;
margin-top: 0.6em;
margin-bottom: 0.6em;
}
div.minipage {
display: inline-block;
margin-right: 3em;
}
div.numberedTable {
text-align: center;
margin: 2em;
}
div.figure {
text-align: center;
margin: 2em;
}
table {
border: 1px solid black;
border-collapse: collapse;
margin-left: auto;
margin-right: auto;
margin-top: 0.8em;
text-align: left;
hyphens: none; 
}
td, th {
padding-left: 1em;
padding-right: 1em;
vertical-align: top;
}
td.empty {
padding: 0px;
padding-left: 1px;
}
td.left {
text-align: left;
}
td.right {
text-align: right;
}
td.center {
text-align: center;
}
td.justify {
text-align: justify;
}
td.border {
border-left: 1px solid black;
}
tr.rowsep, td.cline {
border-top: 1px solid black;
}
tr.even, tr.odd {
border-bottom: 1px solid black;
}
tr.capsep {
border-top: 3px solid black;
border-top-style: double;
}
tr.header {
border-bottom: 3px solid black;
border-bottom-style: double;
}
th {
border-bottom: 1px solid black;
}
span.centry {
font-weight: bold;
}
div.table {
display: block;
margin-left: auto;
margin-right: auto;
text-align: center;
width: 90%;
}
span.indented {
display: block;
margin-left: 2em;
margin-bottom: 1em;
margin-top: 1em;
}
ol.enumeratea { list-style-type: none; background: inherit; }
ol.enumerate { list-style-type: none; background: inherit; }

code.sourceCode > span { display: inline; }

div#refs p { padding-left: 32px; text-indent: -32px; }
</style>
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<h1 class="title" style="text-align:center">Fix submdspan for C++26</h1>

<table style="border:none;float:right">
  <tr>
    <td>Document #: </td>
    <td>P3355R2</td>
  </tr>
  <tr>
    <td>Date: </td>
    <td>2024-10-29</td>
  </tr>
  <tr>
    <td style="vertical-align:top">Project: </td>
    <td>Programming Language C++<br>
      Library Evolution<br>
    </td>
  </tr>
  <tr>
    <td style="vertical-align:top">Reply-to: </td>
    <td>
      Mark Hoemmen<br>&lt;<a href="mailto:mhoemmen@nvidia.com" class="email">mhoemmen@nvidia.com</a>&gt;<br>
    </td>
  </tr>
</table>

</header>
<div style="clear:both">
<div id="TOC" role="doc-toc">
<h1 id="toctitle">Contents</h1>
<ul>
<li><a href="#revision-history" id="toc-revision-history"><span class="toc-section-number">1</span> Revision History</a></li>
<li><a href="#abstract" id="toc-abstract"><span class="toc-section-number">2</span> Abstract</a></li>
<li><a href="#motivation-and-design-discussion" id="toc-motivation-and-design-discussion"><span class="toc-section-number">3</span> Motivation and design discussion</a>
<ul>
<li><a href="#vectorization-example" id="toc-vectorization-example"><span class="toc-section-number">3.1</span> Vectorization example</a></li>
<li><a href="#issues-with-c-working-draft" id="toc-issues-with-c-working-draft"><span class="toc-section-number">3.2</span> Issues with C++ Working
Draft</a></li>
<li><a href="#what-this-proposal-does-and-doesnt-change" id="toc-what-this-proposal-does-and-doesnt-change"><span class="toc-section-number">3.3</span> What this proposal does and
doesn’t change</a></li>
<li><a href="#why-we-dont-try-to-fix-aligned_accessoroffset" id="toc-why-we-dont-try-to-fix-aligned_accessoroffset"><span class="toc-section-number">3.4</span> Why we don’t try to fix
<code>aligned_accessor::offset</code></a></li>
</ul></li>
<li><a href="#implementation-experience" id="toc-implementation-experience"><span class="toc-section-number">4</span> Implementation experience</a></li>
<li><a href="#desired-ship-vehicle" id="toc-desired-ship-vehicle"><span class="toc-section-number">5</span> Desired ship vehicle</a></li>
<li><a href="#wording" id="toc-wording"><span class="toc-section-number">6</span> Wording</a>
<ul>
<li><a href="#increment-__cpp_lib_submdspan-feature-test-macro" id="toc-increment-__cpp_lib_submdspan-feature-test-macro"><span class="toc-section-number">6.1</span> Increment
<code>__cpp_lib_submdspan</code> feature test macro</a></li>
<li><a href="#change-existing-layout-mappings-submdspan_mapping-results" id="toc-change-existing-layout-mappings-submdspan_mapping-results"><span class="toc-section-number">6.2</span> Change existing layout mappings’
<code>submdspan_mapping</code> results</a></li>
</ul></li>
</ul>
</div>
<h1 data-number="1" id="revision-history"><span class="header-section-number">1</span> Revision History<a href="#revision-history" class="self-link"></a></h1>
<ul>
<li><p>Revision 0 submitted 2024-07-14</p>
<ul>
<li>LEWG reviewed this version 2024-10-15, and voted to forward the
[mdspan.sub] changes (with the [mdspan.syn], i.e., the “accept
user-defined pair types” part, removed) to LWG. LEWG also asked that we
increment the <code>submdspan</code> feature test macro
<code>__cpp_lib_submdspan</code> from its current value
(<code>202403L</code>, set by adoption of P2642R6 (“Padded mdspan
layouts”) into the Working Draft for C++26).</li>
</ul></li>
<li><p>Revision 1 to be submitted for the 2024-10-16 mailing</p>
<ul>
<li><p>Remove “user-defined pair types as slices” feature. We will make
this a separate paper.</p></li>
<li><p>Increment <code>__cpp_lib_submdspan</code> from its current value
(<code>202403L</code>).</p></li>
<li><p>Implement suggestion during LEWG wording review to define a
“wording macro” for all the slice specifier types that have unit stride.
We call it <em>unit-stride slice for <code>M</code></em>, where
<code>M</code> is a layout mapping type. (The definition only depends on
an <code>index_type</code>, but the wording is most natural when it
depends on the layout mapping type for which
<em><code>submdspan-mapping-impl</code></em> is a private member
function.)</p></li>
</ul></li>
<li><p>Revision 2 to be submitted for the next mailing</p>
<ul>
<li><p>Use green and red text in Wording to make changes more
clear.</p></li>
<li><p>Per pre-LWG feedback, change “unit-stride slice for
<code>decltype(*this)</code>” to “unit-stride slice for
<code>mapping</code>.”</p></li>
</ul></li>
</ul>
<h1 data-number="2" id="abstract"><span class="header-section-number">2</span> Abstract<a href="#abstract" class="self-link"></a></h1>
<p>We propose to change <code>submdspan_mapping</code> for the following
layouts’ layout mappings:</p>
<ul>
<li><code>layout_left</code>,</li>
<li><code>layout_right</code>,</li>
<li><code>layout_left_padded</code>, and</li>
<li><code>layout_right_padded</code>,</li>
</ul>
<p>so that a <code>strided_slice</code> slice with compile-time unit
stride results in the returned mapping having the same layout as if the
slice were a pair of integers. This preserves compile-time optimization
information for common layouts.</p>
<p>This change needs to be merged into the Working Draft before C++26.
Otherwise, it would be a breaking change.</p>
<h1 data-number="3" id="motivation-and-design-discussion"><span class="header-section-number">3</span> Motivation and design
discussion<a href="#motivation-and-design-discussion" class="self-link"></a></h1>
<h2 data-number="3.1" id="vectorization-example"><span class="header-section-number">3.1</span> Vectorization example<a href="#vectorization-example" class="self-link"></a></h2>
<p>Suppose that one wants to vectorize a 1-D array copy operation using
<code>mdspan</code> and <code>aligned_accessor</code> (P2897). One has a
<code>copy_8_floats</code> function that optimizes the special case of
copying a contiguous array of 8 <code>float</code>s, where the start of
the array is aligned to <code>8 * sizeof(float)</code> (32) bytes. In
practice, plenty of libraries exist to optimize 1-D array copy. This is
just an example that simplifies the use cases for explicit 8-wide SIMD
enough to show in a brief proposal.</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span><span class="op">&lt;</span><span class="kw">class</span> ElementType, <span class="dt">size_t</span> ext, <span class="dt">size_t</span> byte_alignment<span class="op">&gt;</span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> aligned_array_view <span class="op">=</span> mdspan<span class="op">&lt;</span>ElementType,</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a>  extents<span class="op">&lt;</span><span class="dt">int</span>, ext<span class="op">&gt;</span>, layout_right,</span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a>  aligned_accessor<span class="op">&lt;</span>ElementType, byte_alignment<span class="op">&gt;&gt;</span>;</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="dt">void</span></span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a>copy_8_floats<span class="op">(</span>aligned_array_view<span class="op">&lt;</span><span class="kw">const</span> <span class="dt">float</span>, <span class="dv">8</span>, <span class="dv">32</span><span class="op">&gt;</span> src,</span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a>  aligned_array_view<span class="op">&lt;</span><span class="dt">float</span>, <span class="dv">8</span>, <span class="dv">32</span><span class="op">&gt;</span> dst<span class="op">)</span></span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a><span class="op">{</span></span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a>  <span class="co">// One would instead use a hardware instruction for aligned copy,</span></span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a>  <span class="co">// or a &quot;simd&quot; or &quot;unroll&quot; pragma.</span></span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a>  <span class="cf">for</span> <span class="op">(</span><span class="dt">int</span> k <span class="op">=</span> <span class="dv">0</span>; k <span class="op">&lt;</span> <span class="dv">8</span>; <span class="op">++</span>k<span class="op">)</span> <span class="op">{</span></span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a>    dst<span class="op">[</span>k<span class="op">]</span> <span class="op">=</span> src<span class="op">[</span>k<span class="op">]</span>;</span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a>  <span class="op">}</span></span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span></code></pre></div>
<p>The natural next step would be to use <code>copy_8_floats</code> to
implement copying 1-D <code>float</code> arrays by the usual
“strip-mining” approach.</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span><span class="op">&lt;</span><span class="kw">class</span> ElementType<span class="op">&gt;</span></span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> array_view <span class="op">=</span> mdspan<span class="op">&lt;</span>ElementType, dims<span class="op">&lt;</span><span class="dv">1</span>, <span class="dt">int</span><span class="op">&gt;&gt;</span>;</span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="dt">void</span> slow_copy<span class="op">(</span>array_view<span class="op">&lt;</span><span class="kw">const</span> <span class="dt">float</span><span class="op">&gt;</span> src, array_view<span class="op">&lt;</span><span class="dt">float</span><span class="op">&gt;</span> dst<span class="op">)</span></span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a><span class="op">{</span></span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a>  <span class="ot">assert</span><span class="op">(</span>src<span class="op">.</span>extent<span class="op">(</span><span class="dv">0</span><span class="op">)</span> <span class="op">==</span> dst<span class="op">.</span>extent<span class="op">(</span><span class="dv">0</span><span class="op">))</span>;</span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a>  <span class="cf">for</span> <span class="op">(</span><span class="dt">int</span> k <span class="op">=</span> <span class="dv">0</span>; k <span class="op">&lt;</span> src<span class="op">.</span>extent<span class="op">(</span><span class="dv">0</span><span class="op">)</span>; <span class="op">++</span>k<span class="op">)</span> <span class="op">{</span></span>
<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a>    dst<span class="op">[</span>k<span class="op">]</span> <span class="op">=</span> src<span class="op">[</span>k<span class="op">]</span>;</span>
<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a>  <span class="op">}</span></span>
<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span>
<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span><span class="op">&lt;</span><span class="dt">size_t</span> vector_length<span class="op">&gt;</span></span>
<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a><span class="dt">void</span> strip_mined_copy<span class="op">(</span></span>
<span id="cb2-14"><a href="#cb2-14" aria-hidden="true" tabindex="-1"></a>  aligned_array_view<span class="op">&lt;</span><span class="kw">const</span> <span class="dt">float</span>, dynamic_extent,</span>
<span id="cb2-15"><a href="#cb2-15" aria-hidden="true" tabindex="-1"></a>    vector_length <span class="op">*</span> <span class="kw">sizeof</span><span class="op">(</span><span class="dt">float</span><span class="op">)&gt;</span> src,</span>
<span id="cb2-16"><a href="#cb2-16" aria-hidden="true" tabindex="-1"></a>  aligned_array_view<span class="op">&lt;</span>      <span class="dt">float</span>, dynamic_extent,</span>
<span id="cb2-17"><a href="#cb2-17" aria-hidden="true" tabindex="-1"></a>    vector_length <span class="op">*</span> <span class="kw">sizeof</span><span class="op">(</span><span class="dt">float</span><span class="op">)&gt;</span> dst<span class="op">)</span></span>
<span id="cb2-18"><a href="#cb2-18" aria-hidden="true" tabindex="-1"></a><span class="op">{</span></span>
<span id="cb2-19"><a href="#cb2-19" aria-hidden="true" tabindex="-1"></a>  <span class="ot">assert</span><span class="op">(</span>src<span class="op">.</span>extent<span class="op">(</span><span class="dv">0</span><span class="op">)</span> <span class="op">==</span> dst<span class="op">.</span>extent<span class="op">(</span><span class="dv">0</span><span class="op">))</span>;</span>
<span id="cb2-20"><a href="#cb2-20" aria-hidden="true" tabindex="-1"></a>  <span class="ot">assert</span><span class="op">(</span>src<span class="op">.</span>extent<span class="op">(</span><span class="dv">0</span><span class="op">)</span> <span class="op">%</span> vector_length <span class="op">==</span> <span class="dv">0</span><span class="op">)</span>;</span>
<span id="cb2-21"><a href="#cb2-21" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-22"><a href="#cb2-22" aria-hidden="true" tabindex="-1"></a>  <span class="cf">for</span> <span class="op">(</span><span class="dt">int</span> beg <span class="op">=</span> <span class="dv">0</span>; beg <span class="op">&lt;</span> src<span class="op">.</span>extent<span class="op">(</span><span class="dv">0</span><span class="op">)</span>; beg <span class="op">+=</span> vector_length<span class="op">)</span> <span class="op">{</span></span>
<span id="cb2-23"><a href="#cb2-23" aria-hidden="true" tabindex="-1"></a>    <span class="kw">constexpr</span> <span class="kw">auto</span> one <span class="op">=</span> std<span class="op">::</span>integral_constant<span class="op">&lt;</span><span class="dt">int</span>, <span class="dv">1</span><span class="op">&gt;{}</span>;</span>
<span id="cb2-24"><a href="#cb2-24" aria-hidden="true" tabindex="-1"></a>    <span class="kw">constexpr</span> <span class="kw">auto</span> vec_len <span class="op">=</span> std<span class="op">::</span>integral_constant<span class="op">&lt;</span><span class="dt">int</span>, vector_length<span class="op">&gt;{}</span>;</span>
<span id="cb2-25"><a href="#cb2-25" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-26"><a href="#cb2-26" aria-hidden="true" tabindex="-1"></a>    <span class="co">// Using strided_slice lets the extent be a compile-time constant.</span></span>
<span id="cb2-27"><a href="#cb2-27" aria-hidden="true" tabindex="-1"></a>    <span class="co">// tuple{beg, beg + vector_length} would result in dynamic_extent.</span></span>
<span id="cb2-28"><a href="#cb2-28" aria-hidden="true" tabindex="-1"></a>    <span class="kw">constexpr</span> <span class="kw">auto</span> vector_slice <span class="op">=</span></span>
<span id="cb2-29"><a href="#cb2-29" aria-hidden="true" tabindex="-1"></a>      strided_slice<span class="op">{.</span>offset<span class="op">=</span>dst_lower, <span class="op">.</span>extent<span class="op">=</span>vector_length, <span class="op">.</span>stride<span class="op">=</span>one<span class="op">}</span>;</span>
<span id="cb2-30"><a href="#cb2-30" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-31"><a href="#cb2-31" aria-hidden="true" tabindex="-1"></a>    <span class="co">// PROBLEM: Current wording makes this always layout_stride,</span></span>
<span id="cb2-32"><a href="#cb2-32" aria-hidden="true" tabindex="-1"></a>    <span class="co">// but we know that it could be layout_right.</span></span>
<span id="cb2-33"><a href="#cb2-33" aria-hidden="true" tabindex="-1"></a>    <span class="kw">auto</span> src_slice <span class="op">=</span> submdspan<span class="op">(</span>src, vector_slice<span class="op">)</span>;</span>
<span id="cb2-34"><a href="#cb2-34" aria-hidden="true" tabindex="-1"></a>    <span class="kw">auto</span> dst_slice <span class="op">=</span> submdspan<span class="op">(</span>dst, vector_slice<span class="op">)</span>;</span>
<span id="cb2-35"><a href="#cb2-35" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-36"><a href="#cb2-36" aria-hidden="true" tabindex="-1"></a>    copy_8_floats<span class="op">(</span>src_slice, dst_slice<span class="op">)</span>;</span>
<span id="cb2-37"><a href="#cb2-37" aria-hidden="true" tabindex="-1"></a>  <span class="op">}</span></span>
<span id="cb2-38"><a href="#cb2-38" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span>
<span id="cb2-39"><a href="#cb2-39" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-40"><a href="#cb2-40" aria-hidden="true" tabindex="-1"></a><span class="dt">void</span> copy<span class="op">(</span>array_view<span class="op">&lt;</span><span class="kw">const</span> <span class="dt">float</span><span class="op">&gt;</span> src, array_view<span class="op">&lt;</span><span class="dt">float</span><span class="op">&gt;</span> dst<span class="op">)</span></span>
<span id="cb2-41"><a href="#cb2-41" aria-hidden="true" tabindex="-1"></a><span class="op">{</span></span>
<span id="cb2-42"><a href="#cb2-42" aria-hidden="true" tabindex="-1"></a>  <span class="ot">assert</span><span class="op">(</span>src<span class="op">.</span>extent<span class="op">(</span><span class="dv">0</span><span class="op">)</span> <span class="op">==</span> dst<span class="op">.</span>extent<span class="op">(</span><span class="dv">0</span><span class="op">))</span>;</span>
<span id="cb2-43"><a href="#cb2-43" aria-hidden="true" tabindex="-1"></a>  <span class="kw">constexpr</span> <span class="dt">int</span> vector_length <span class="op">=</span> <span class="dv">8</span>;</span>
<span id="cb2-44"><a href="#cb2-44" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-45"><a href="#cb2-45" aria-hidden="true" tabindex="-1"></a>  <span class="co">// Handle possibly unaligned prefix of less than vector_length elements. </span></span>
<span id="cb2-46"><a href="#cb2-46" aria-hidden="true" tabindex="-1"></a>  <span class="kw">auto</span> aligned_starting_index <span class="op">=</span> <span class="op">[](</span><span class="kw">auto</span><span class="op">*</span> ptr<span class="op">)</span> <span class="op">{</span></span>
<span id="cb2-47"><a href="#cb2-47" aria-hidden="true" tabindex="-1"></a>    <span class="kw">constexpr</span> <span class="kw">auto</span> v <span class="op">=</span> <span class="kw">static_cast</span><span class="op">&lt;</span><span class="dt">unsigned</span><span class="op">&gt;(</span>vector_length<span class="op">)</span>;</span>
<span id="cb2-48"><a href="#cb2-48" aria-hidden="true" tabindex="-1"></a>    <span class="kw">auto</span> ptr_value <span class="op">=</span> <span class="kw">reinterpret_cast</span><span class="op">&lt;</span><span class="dt">uintptr_t</span><span class="op">&gt;(</span>ptr_value<span class="op">)</span>;</span>
<span id="cb2-49"><a href="#cb2-49" aria-hidden="true" tabindex="-1"></a>    <span class="kw">auto</span> remainder <span class="op">=</span> ptr_value <span class="op">%</span> v;</span>
<span id="cb2-50"><a href="#cb2-50" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> <span class="kw">static_cast</span><span class="op">&lt;</span><span class="dt">int</span><span class="op">&gt;(</span>ptr_value <span class="op">+</span> <span class="op">(</span>v <span class="op">-</span> remainder<span class="op">)</span> <span class="op">%</span> v<span class="op">)</span>;</span>
<span id="cb2-51"><a href="#cb2-51" aria-hidden="true" tabindex="-1"></a>  <span class="op">}</span>;</span>
<span id="cb2-52"><a href="#cb2-52" aria-hidden="true" tabindex="-1"></a>  <span class="dt">int</span> src_beg <span class="op">=</span> aligned_starting_index<span class="op">(</span>src<span class="op">.</span>data<span class="op">())</span>;</span>
<span id="cb2-53"><a href="#cb2-53" aria-hidden="true" tabindex="-1"></a>  <span class="dt">int</span> dst_beg <span class="op">=</span> aligned_starting_index<span class="op">(</span>dst<span class="op">.</span>data<span class="op">())</span>;</span>
<span id="cb2-54"><a href="#cb2-54" aria-hidden="true" tabindex="-1"></a>  <span class="cf">if</span> <span class="op">(</span>src_beg <span class="op">!=</span> dst_beg<span class="op">)</span> <span class="op">{</span></span>
<span id="cb2-55"><a href="#cb2-55" aria-hidden="true" tabindex="-1"></a>    slow_copy<span class="op">(</span>src, dst<span class="op">)</span>;</span>
<span id="cb2-56"><a href="#cb2-56" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span>;</span>
<span id="cb2-57"><a href="#cb2-57" aria-hidden="true" tabindex="-1"></a>  <span class="op">}</span></span>
<span id="cb2-58"><a href="#cb2-58" aria-hidden="true" tabindex="-1"></a>  slow_copy<span class="op">(</span>submdspan<span class="op">(</span>src, tuple<span class="op">{</span><span class="dv">0</span>, src_beg<span class="op">})</span>,</span>
<span id="cb2-59"><a href="#cb2-59" aria-hidden="true" tabindex="-1"></a>    submdspan<span class="op">(</span>dst, tuple<span class="op">{</span><span class="dv">0</span>, dst_beg<span class="op">}))</span>;</span>
<span id="cb2-60"><a href="#cb2-60" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-61"><a href="#cb2-61" aria-hidden="true" tabindex="-1"></a>  <span class="co">// Strip-mine the aligned vector_length segments of the array.</span></span>
<span id="cb2-62"><a href="#cb2-62" aria-hidden="true" tabindex="-1"></a>  <span class="dt">int</span> src_end <span class="op">=</span> <span class="op">(</span>src<span class="op">.</span>size<span class="op">()</span> <span class="op">/</span> vector_length<span class="op">)</span> <span class="op">*</span> vector_length;</span>
<span id="cb2-63"><a href="#cb2-63" aria-hidden="true" tabindex="-1"></a>  <span class="dt">int</span> dst_end <span class="op">=</span> <span class="op">(</span>dst<span class="op">.</span>size<span class="op">()</span> <span class="op">/</span> vector_length<span class="op">)</span> <span class="op">*</span> vector_length;</span>
<span id="cb2-64"><a href="#cb2-64" aria-hidden="true" tabindex="-1"></a>  strip_mined_copy<span class="op">&lt;</span><span class="dv">8</span><span class="op">&gt;(</span>submdspan<span class="op">(</span>src, tuple<span class="op">{</span>src_beg, src_end<span class="op">})</span>,</span>
<span id="cb2-65"><a href="#cb2-65" aria-hidden="true" tabindex="-1"></a>    submdspan<span class="op">(</span>dst, tuple<span class="op">{</span>dst_beg, dst_end<span class="op">}))</span>;</span>
<span id="cb2-66"><a href="#cb2-66" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-67"><a href="#cb2-67" aria-hidden="true" tabindex="-1"></a>  <span class="co">// Handle suffix of less than vector_length elements.</span></span>
<span id="cb2-68"><a href="#cb2-68" aria-hidden="true" tabindex="-1"></a>  slow_copy<span class="op">(</span>submdspan<span class="op">(</span>src, tuple<span class="op">{</span>src_end, src<span class="op">.</span>extent<span class="op">(</span><span class="dv">0</span><span class="op">)})</span>,</span>
<span id="cb2-69"><a href="#cb2-69" aria-hidden="true" tabindex="-1"></a>    submdspan<span class="op">(</span>dst, tuple<span class="op">{</span>dst_end, dst<span class="op">.</span>extent<span class="op">(</span><span class="dv">0</span><span class="op">)}))</span>;</span>
<span id="cb2-70"><a href="#cb2-70" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span></code></pre></div>
<p>The <code>strip_mined_copy</code> function must use
<code>strided_slice</code> to get slices of 8 elements at a time, rather
than <code>tuple</code>. This ensures that the resulting extent is a
compile-time constant 8, even though the slice starts at a run-time
index <code>beg</code>.</p>
<h2 data-number="3.2" id="issues-with-c-working-draft"><span class="header-section-number">3.2</span> Issues with C++ Working Draft<a href="#issues-with-c-working-draft" class="self-link"></a></h2>
<p>The current C++ Working Draft has two issues that hinder optimization
of the above code.</p>
<ol type="1">
<li><p>The above <code>submdspan</code> results always have
<code>layout_stride</code>, even though we know that they are contiguous
and thus should have <code>layout_right</code>.</p></li>
<li><p>The <code>submdspan</code> operations in
<code>strip_mined_copy</code> should result in
<code>aligned_accessor</code> with 32-byte alignment, but instead give
<code>default_accessor</code>. This is because
<code>aligned_accessor</code>’s <code>offset</code> member function
takes the offset as a <code>size_t</code>. This discards compile-time
information, namely that the offset can be expressed as the product of
some integer and the overalignment factor, where the overalignment
factor is known at compile time.</p></li>
</ol>
<h2 data-number="3.3" id="what-this-proposal-does-and-doesnt-change"><span class="header-section-number">3.3</span> What this proposal does and
doesn’t change<a href="#what-this-proposal-does-and-doesnt-change" class="self-link"></a></h2>
<p>This proposal fixes (1) for all layouts currently in the Working
Draft that have a <code>submdspan_mapping</code> customization:
<code>layout_left</code>, <code>layout_right</code>,
<code>layout_left_padded</code>, and <code>layout_right_padded</code>.
We can do that without breaking changes, as long as this proposal is
merged before C++26 is finalized. After that, merging the proposal would
be a breaking change.</p>
<p>This proposal does <em>not</em> fix (2), because that would require a
breaking change to both the layout mapping requirements and the accessor
requirements, and because it would complicate both of them quite a
bit.</p>
<h2 data-number="3.4" id="why-we-dont-try-to-fix-aligned_accessoroffset"><span class="header-section-number">3.4</span> Why we don’t try to fix
<code>aligned_accessor::offset</code><a href="#why-we-dont-try-to-fix-aligned_accessoroffset" class="self-link"></a></h2>
<p>Regarding (2),
<a href="https://eel.is/c++draft/views.multidim#mdspan.submdspan.submdspan-6"><strong>[mdspan.submdspan.submdspan]</strong>
6</a> says that <code>submdspan(src, slices...)</code> has effects
equivalent to the following.</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="kw">auto</span> sub_map_offset <span class="op">=</span> submdspan_mapping<span class="op">(</span>src<span class="op">.</span>mapping<span class="op">()</span>, slices<span class="op">...)</span>;</span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a><span class="cf">return</span> mdspan<span class="op">(</span>src<span class="op">.</span>accessor<span class="op">().</span>offset<span class="op">(</span>src<span class="op">.</span>data<span class="op">()</span>, sub_map_offset<span class="op">.</span>offset<span class="op">)</span>,</span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a>              sub_map_offset<span class="op">.</span>mapping,</span>
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a>              AccessorPolicy<span class="op">::</span>offset_policy<span class="op">(</span>src<span class="op">.</span>accessor<span class="op">()))</span>;</span></code></pre></div>
<p>The problem is
<code>AccessorPolicy::offset_policy(src.accessor())</code>. The type
<code>offset_policy</code> is the wrong type in this case,
<code>default_accessor&lt;const float&gt;</code> instead of
<code>aligned_accessor&lt;const float, 32&gt;</code>. If we want an
offset with suitable compile-time alignment to have a different accessor
type, then we would need at least the following changes.</p>
<ol type="1">
<li><p>The Standard Library would need a new type that represents the
product of a compile-time integer (that is, an
<em><code>integral-constant-like</code></em> type) and a “run-time”
integer (an <code>integral</code>-not-<code>bool</code> type). It would
need overloaded arithmetic operators that preserve this product form as
much as possible. For example, <span class="math inline">8<em>x</em> + 4</span> for a run-time integer <span class="math inline"><em>x</em></span> should result in <span class="math inline">4<em>y</em></span> where <span class="math inline"><em>y</em> = 2<em>x</em> + 1</span> is a run-time
integer.</p></li>
<li><p>At least the Standard layout mappings’ <code>operator()</code>
would need to compute with these types and return them if possible. The
layout mapping requirements would thus need to change, as currently
<code>operator()</code> must return <code>index_type</code> (see
<a href="https://eel.is/c++draft/mdspan.layout.reqmts#7"><strong>[[mdspan.layout.reqmts]]</strong>
7</a>).</p></li>
<li><p><code>aligned_accessor::offset</code> would need an overload
taking a type that expresses the product of a compile-time integer (of
suitable alignment) and a run-time integer. The accessor requirements
<a href="https://eel.is/c++draft/mdspan.accessor.reqmts"><strong>[[mdspan.accessor.reqmts]]</strong></a>
may also need to change to permit this.</p></li>
<li><p>The definition of <code>submdspan</code> would need some way to
get the accessor type corresponding to the new <code>offset</code>
overload, instead of <code>aligned_accessor::offset_policy</code> (which
in this case is <code>default_accessor</code>).</p></li>
</ol>
<p>The work-around is to convert the result of <code>submdspan</code> by
hand to use the desired accessor. In the above <code>copy</code>
example, one would replace the line</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>    copy_8_floats<span class="op">(</span>src_slice, dst_slice<span class="op">)</span>;</span></code></pre></div>
<p>with the following, that depends on <code>aligned_accessor</code>’s
<code>explicit</code> constructor from
<code>default_accessor</code>.</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>    copy_8_floats<span class="op">(</span>aligned_array_view<span class="op">&lt;</span><span class="kw">const</span> <span class="dt">float</span>, <span class="dv">8</span>, <span class="dv">32</span><span class="op">&gt;{</span>src<span class="op">}</span>,</span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>      aligned_array_view<span class="op">&lt;</span><span class="dt">float</span>, <span class="dv">8</span>, <span class="dv">32</span><span class="op">&gt;{</span>dst<span class="op">})</span>;</span></code></pre></div>
<p>Given that this work-around is easy to do, should only be needed for
a few special cases, and avoids a big design change to the accessor
policy requirements, we don’t propose trying to fix this issue in the
C++ Working Draft.</p>
<h1 data-number="4" id="implementation-experience"><span class="header-section-number">4</span> Implementation experience<a href="#implementation-experience" class="self-link"></a></h1>
<p>Daisy Hollman’s original implementation of <code>submdspan</code>
implemented strided slices in this way.</p>
<h1 data-number="5" id="desired-ship-vehicle"><span class="header-section-number">5</span> Desired ship vehicle<a href="#desired-ship-vehicle" class="self-link"></a></h1>
<p>C++26 / IS.</p>
<h1 data-number="6" id="wording"><span class="header-section-number">6</span> Wording<a href="#wording" class="self-link"></a></h1>
<blockquote>
<p>Text in blockquotes is not proposed wording, but rather instructions
for generating proposed wording.</p>
</blockquote>
<h2 data-number="6.1" id="increment-__cpp_lib_submdspan-feature-test-macro"><span class="header-section-number">6.1</span> Increment
<code>__cpp_lib_submdspan</code> feature test macro<a href="#increment-__cpp_lib_submdspan-feature-test-macro" class="self-link"></a></h2>
<blockquote>
<p>In <strong>[version.syn]</strong>, increase the value of the
<code>__cpp_lib_submdspan</code> macro by replacing YYYMML below with
the integer literal encoding the appropriate year (YYYY) and month
(MM).</p>
</blockquote>
<div class="sourceCode" id="cb6"><pre class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="pp">#define __cpp_lib_submdspan </span>YYYYMML<span class="pp"> </span><span class="co">// also in &lt;mdspan&gt;</span></span></code></pre></div>
<h2 data-number="6.2" id="change-existing-layout-mappings-submdspan_mapping-results"><span class="header-section-number">6.2</span> Change existing layout
mappings’ <code>submdspan_mapping</code> results<a href="#change-existing-layout-mappings-submdspan_mapping-results" class="self-link"></a></h2>
<blockquote>
<p>Append the following to the end of
<strong>[mdspan.sub.map.common]</strong>. Additions are shown in green
text.</p>
</blockquote>
<div class="add" style="color: #00AA00">
<p><span class="marginalizedparent"><a class="marginalized">9</a></span>
Given a layout mapping type <code>M</code>, a type <code>S</code> is a
<em>unit-stride slice for <code>M</code></em> if</p>
<ul>
<li><p><span class="marginalizedparent"><a class="marginalized">(9.1)</a></span>
<code>S</code> is a specialization of <code>strided_slice</code> where
<code>S::stride_type</code> models
<em><code>integral-constant-like</code></em> and
<code>S::stride_type::value</code> equals 1,</p></li>
<li><p><span class="marginalizedparent"><a class="marginalized">(9.2)</a></span>
<code>S</code> models
<em><code>index-pair-like</code></em><code>&lt;M::index_type&gt;</code>,
or</p></li>
<li><p><span class="marginalizedparent"><a class="marginalized">(9.3)</a></span>
<code>is_convertible_v&lt;S, full_extent_t&gt;</code> is
<code>true</code>.</p></li>
</ul>

</div>
<blockquote>
<p>Throughout <strong>[mdspan.sub]</strong>, wherever the text says</p>
</blockquote>
<div class="rm" style="color: #bf0303">
<p><span class="math inline"><em>S</em><sub><em>k</em></sub></span>
models
<em><code>index-pair-like</code></em><code>&lt;index_type&gt;</code> or
<code>is_convertible_v&lt;</code><span class="math inline"><em>S</em><sub><em>k</em></sub></span><code>, full_extent_t&gt;</code>
is <code>true</code>,</p>
</div>
<blockquote>
<p>replace it with</p>
</blockquote>
<div class="add" style="color: #00AA00">
<p><span class="math inline"><em>S</em><sub><em>k</em></sub></span> is a
unit-stride slice for <code>mapping</code>.</p>
</div>
<blockquote>
<p>Additions are shown in green text and removals in red text. Apply the
analogous transformation if the text says <span class="math inline"><em>S</em><sub><em>p</em></sub></span> or <span class="math inline"><em>S</em><sub>0</sub></span>, but is otherwise the
same. Make this set of changes in the following places.</p>
<ul>
<li><p><strong>[mdspan.sub.map.left]</strong> (1.3.2), (1.4), (1.4.1),
and (1.4.3);</p></li>
<li><p><strong>[mdspan.sub.map.right]</strong> (1.3.2), (1.4), (1.4.1),
and (1.4.3);</p></li>
<li><p><strong>[mdspan.sub.map.leftpad]</strong> (1.3.2), (1.4),
(1.4.1), and (1.4.3); and</p></li>
<li><p><strong>[mdspan.sub.map.rightpad]</strong> (1.3.2), (1.4),
(1.4.1), and (1.4.3).</p></li>
</ul>
</blockquote>
<blockquote>
<p>For example, here are the changes to
<strong>[mdspan.sub.map.left]</strong>. The other sections have
analogous changes.</p>
</blockquote>
<p><em>Returns</em>:</p>
<ul>
<li><p><span class="marginalizedparent"><a class="marginalized">(1.1)</a></span>
<code>submdspan_mapping_result{*this, 0}</code>, if
<code>Extents​::​rank() == 0</code> is <code>true</code>;</p></li>
<li><p><span class="marginalizedparent"><a class="marginalized">(1.2)</a></span>
otherwise,
<code>submdspan_mapping_result{layout_left​::​mapping(sub_ext), offset}</code>,
if <code>SubExtents​::​rank() == 0</code> is <code>true</code>;</p></li>
<li><p><span class="marginalizedparent"><a class="marginalized">(1.3)</a></span>
otherwise,
<code>submdspan_mapping_result{layout_left​::​mapping(sub_ext), offset}</code>,
if</p>
<ul>
<li><p><span class="marginalizedparent"><a class="marginalized">(1.3.1)</a></span>
for each <code>k</code> in the range <span class="math inline">[</span>
<code>0</code>, <code>SubExtents​::​rank() - 1</code> <span class="math inline">)</span>, <code>is_convertible_v&lt;</code> <span class="math inline"><em>S</em><sub><em>k</em></sub></span>
<code>, full_extent_t&gt;</code> is <code>true</code>; and</p></li>
<li><p><span class="marginalizedparent"><a class="marginalized">(1.3.2)</a></span>
for <code>k</code> equal to <code>SubExtents​::​rank() - 1</code>, <span class="math inline"><em>S</em><sub><em>k</em></sub></span> <span class="rm" style="color: #bf0303"><del>models
<em><span><code>index-pair-like&lt;index_type&gt;</code></span></em> or
<span><code>is_convertible_v&lt;</code></span> <span class="math inline"><em>S</em><sub><em>k</em></sub></span>
<span><code>, full_extent_t&gt;</code></span> is
<span><code>true</code></span></del></span><span class="add" style="color: #00AA00"><ins>is a unit-stride slice for
<span><code>mapping</code></span></ins></span>;</p></li>
</ul>
<p><i>[Note 1: </i> If the above conditions are true, all <span class="math inline"><em>S</em><sub><em>k</em></sub></span> with <span class="math inline"><em>k</em></span> larger than
<code>SubExtents​::​rank() - 1</code> are convertible to
<code>index_type</code>. <i>- end note]</i></p></li>
<li><p><span class="marginalizedparent"><a class="marginalized">(1.4)</a></span>
otherwise,
<code>submdspan_mapping_result{layout_left_padded&lt;S_static&gt;::mapping(sub_ext, stride(u + 1)), offset}</code>
if for a value <span class="math inline"><em>u</em></span> for which
<span class="math inline"><em>u</em> + 1</span> is the smallest value
<span class="math inline"><em>p</em></span> larger than zero for which
<span class="math inline"><em>S</em><sub><em>p</em></sub></span> <span class="rm" style="color: #bf0303"><del>models
<em><span><code>index-pair-like&lt;index_type&gt;</code></span></em> or
<span><code>is_convertible_v&lt;</code></span> <span class="math inline"><em>S</em><sub><em>p</em></sub></span>
<span><code>, full_extent_t&gt;</code></span> is
<span><code>true</code></span></del></span><span class="add" style="color: #00AA00"><ins>is a unit-stride slice for
<span><code>mapping</code></span></ins></span>, the following conditions
are met:</p>
<ul>
<li><p><span class="marginalizedparent"><a class="marginalized">(1.4.1)</a></span>
<span class="math inline"><em>S</em><sub>0</sub></span> <span class="rm" style="color: #bf0303"><del>models
<em><span><code>index-pair-like&lt;index_type&gt;</code></span></em> or
<span><code>is_convertible_v&lt;</code></span> <span class="math inline"><em>S</em><sub>0</sub></span>
<span><code>, full_extent_t&gt;</code></span> is
<span><code>true</code></span></del></span><span class="add" style="color: #00AA00"><ins>is a unit-stride slice for
<span><code>mapping</code></span></ins></span>; <span class="rm" style="color: #bf0303"><del>and</del></span></p></li>
<li><p><span class="marginalizedparent"><a class="marginalized">(1.4.2)</a></span>
for each <span class="math inline"><em>k</em></span> in the range <span class="math inline">[<em>u</em> + 1</span>, <span class="math inline"><em>u</em></span> + <code>SubExtents​::​rank()</code>
- 1 <span class="math inline">)</span>,
<code>is_convertible_v&lt;</code> <span class="math inline"><em>S</em><sub><em>k</em></sub></span>
<code>, full_extent_t&gt;</code> is <code>true</code>; and</p></li>
<li><p><span class="marginalizedparent"><a class="marginalized">(1.4.3)</a></span>
for <span class="math inline"><em>k</em></span> equal to <span class="math inline"><em>u</em></span> + <code>SubExtents​::​rank()</code>
- 1, <span class="math inline"><em>S</em><sub><em>k</em></sub></span>
<span class="rm" style="color: #bf0303"><del>models
<em><span><code>index-pair-like&lt;index_type&gt;</code></span></em> or
<span><code>is_convertible_v&lt;</code></span> <span class="math inline"><em>S</em><sub><em>k</em></sub></span>
<span><code>, full_extent_t&gt;</code></span> is
<span><code>true</code></span></del></span><span class="add" style="color: #00AA00"><ins>is a unit-stride slice for
<span><code>mapping</code></span></ins></span>;</p></li>
</ul>
<p>and where <code>S_static</code> is:</p></li>
</ul>
</div>
</div>
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</html>
