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  <title>P3067R0: Named permutation functions for `std::simd`</title>
<style data-fill-with="stylesheet">/******************************************************************************
 *                   Style sheet for the W3C specifications                   *
 *
 * Special classes handled by this style sheet include:
 *
 * Indices
 *   - .toc for the Table of Contents (<ol class="toc">)
 *     + <span class="secno"> for the section numbers
 *   - #toc for the Table of Contents (<nav id="toc">)
 *   - ul.index for Indices (<a href="#ref">term</a><span>, in § N.M</span>)
 *   - table.index for Index Tables (e.g. for properties or elements)
 *
 * Structural Markup
 *   - table.data for general data tables
 *     -> use 'scope' attribute, <colgroup>, <thead>, and <tbody> for best results !
 *     -> use <table class='complex data'> for extra-complex tables
 *     -> use <td class='long'> for paragraph-length cell content
 *     -> use <td class='pre'> when manual line breaks/indentation would help readability
 *   - dl.switch for switch statements
 *   - ol.algorithm for algorithms (helps to visualize nesting)
 *   - .figure and .caption (HTML4) and figure and figcaption (HTML5)
 *     -> .sidefigure for right-floated figures
 *   - ins/del
 *     -> ins/del.c### for candidate and proposed changes (amendments)
 *
 * Code
 *   - pre and code
 *
 * Special Sections
 *   - .note       for informative notes             (div, p, span, aside, details)
 *   - .example    for informative examples          (div, p, pre, span)
 *   - .issue      for issues                        (div, p, span)
 *   - .advisement for loud normative statements     (div, p, strong)
 *   - .annoying-warning for spec obsoletion notices (div, aside, details)
 *   - .correction for "candidate corrections"       (div, aside, details, section)
 *   - .addition   for "candidate additions"         (div, aside, details, section)
 *   - .correction.proposed for "proposed corrections" (div, aside, details, section)
 *   - .addition.proposed   for "proposed additions"   (div, aside, details, section)
 *
 * Definition Boxes
 *   - pre.def   for WebIDL definitions
 *   - table.def for tables that define other entities (e.g. CSS properties)
 *   - dl.def    for definition lists that define other entitles (e.g. HTML elements)
 *
 * Numbering
 *   - .secno for section numbers in .toc and headings (<span class='secno'>3.2</span>)
 *   - .marker for source-inserted example/figure/issue numbers (<span class='marker'>Issue 4</span>)
 *   - ::before styled for CSS-generated issue/example/figure numbers:
 *     -> Documents wishing to use this only need to add
 *        figcaption::before,
 *        .caption::before { content: "Figure "  counter(figure) " ";  }
 *        .example::before { content: "Example " counter(example) " "; }
 *        .issue::before   { content: "Issue "   counter(issue) " ";   }
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 * Header Stuff (ignore, just don't conflict with these classes)
 *   - .head for the header
 *   - .copyright for the copyright
 *
 * Outdated warning for old specs
 *
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 *     on its container, depending on the effect desired.
 *     Note that this styling basically doesn't help at all when printing,
 *     since A4 paper isn't much wider than the max-width here.
 *     It's better to design things to fit into a narrower measure if possible.
 *
 *   - js-added ToC jump links (see fixup.js)
 *
 ******************************************************************************/

/* color variables included separately for reliability */

/******************************************************************************/
/*                                    Body                                    */
/******************************************************************************/

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/******************************************************************************/
/*                         Front Matter & Navigation                          */
/******************************************************************************/

/** Header ********************************************************************/

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	/* see also additional rules in Link Styling section */

/** Copyright *****************************************************************/

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/** Back to Top / ToC Toggle **************************************************/

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		/* See also Overflow section at the bottom */

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/******************************************************************************/
/*                                Sectioning                                  */
/******************************************************************************/

/** Headings ******************************************************************/

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	h6 { font-variant: small-caps; }
	dt { font-weight: bold; }

/** Subheadings ***************************************************************/

	h1 + h2,
	#profile-and-date {
		/* #profile-and-date is a subtitle in an H2 under the H1 */
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	h2 + h3,
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/** Section divider ***********************************************************/

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	:not(.head) > hr::before {
		content: "\2727\2003\2003\2727\2003\2003\2727";
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/******************************************************************************/
/*                            Paragraphs and Lists                            */
/******************************************************************************/

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	dl dd {
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	.head dd + dd { /* compact for header */
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	/* Style for algorithms */
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	/* Put nice boxes around each algorithm. */
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	 border: thin solid var(--algo-border);
	 border-radius: .5em;
	 margin: .5em calc(-0.5em - 1px);
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	[data-algorithm]:not(.heading) > :last-child {
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	/* Style for switch/case <dl>s */
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	margin-left: 0;
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	dl.switch {
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	dl.switch > dt {
	text-indent: -1.5em;
	margin-top: 1em;
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	dl.switch > dt + dt {
	margin-top: 0;
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	padding: 0 0.5em 0 0;
	display: inline-block;
	width: 1em;
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	line-height: 0.5em;
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/** Terminology Markup ********************************************************/


/******************************************************************************/
/*                                 Inline Markup                              */
/******************************************************************************/

/** Terminology Markup ********************************************************/
	dfn   { /* Defining instance */
		font-weight: bolder;
	}
	a > i { /* Instance of term */
		font-style: normal;
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	dt dfn code, code.idl {
		font-size: inherit;
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	dfn var {
		font-style: normal;
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/** Change Marking ************************************************************/

	del {
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		color: var(--del-text);
		background: transparent;
		background: var(--del-bg);
		text-decoration: line-through;
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	ins {
		color: #006100;
		color: var(--ins-text);
		background: transparent;
		background: var(--ins-bg);
		text-decoration: underline;
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	/* for amendments (candidate/proposed changes) */

	.amendment ins, .correction ins, .addition ins,
	ins[class^=c] {
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	.amendment del, .correction del, .addition del,
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	.amendment.proposed ins, .correction.proposed ins, .addition.proposed ins,
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	.amendment.proposed del, .correction.proposed del, .addition.proposed del,
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/** Miscellaneous improvements to inline formatting ***************************/

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		font-size: 80%
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/******************************************************************************/
/*                                    Code                                    */
/******************************************************************************/

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	pre {
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		overflow: auto;
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/** Inline Code fragments *****************************************************/

	/* Do something nice. */

/******************************************************************************/
/*                                    Links                                   */
/******************************************************************************/

/** General Hyperlinks ********************************************************/

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	a[href] {
		color: #034575;
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	/* Backout above styling for W3C logo */
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/******************************************************************************/
/*                                    Images                                  */
/******************************************************************************/

	img {
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	/* For autogen numbers, add
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	*/

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/******************************************************************************/
/*                             Colored Boxes                                  */
/******************************************************************************/

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	blockquote > :last-child,
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	.example::before, .example > .marker,
	.note::before, .note > .marker,
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	.amendment::before, .amendment > .marker,
	details.amendment > summary > .marker,
	.addition::before, .addition > .marker,
	addition.amendment > summary > .marker,
	.correction::before, .correction > .marker,
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		display: block;
		padding-right: 0em;
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/** Blockquotes ***************************************************************/

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		border-color: silver;
		border-color: var(--blockquote-border);
		background: transparent;
		background: var(--blockquote-bg);
		color: currentcolor;
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/** Open issue ****************************************************************/

	.issue {
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		background: #fbe9e9;
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		overflow: auto;
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		color: var(--issueheading-text);
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	/* Add .issue::before { content: "Issue " counter(issue) " "; } for autogen numbers,
	  or use class="marker" to mark up the issue number in source. */

/** Example *******************************************************************/

	.example {
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	/* Add .example::before { content: "Example " counter(example) " "; } for autogen numbers,
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/** Non-normative Note ********************************************************/

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		background: #e9fbe9;
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		color: black;
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		overflow: auto;
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	.note::before, .note > .marker,
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	/* Add .note::before { content: "Note "; } for autogen label,
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	details.note[open] > summary {
		border-bottom: 1px silver solid;
		border-bottom: 1px var(--notesummary-underline) solid;
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/** Assertion Box *************************************************************/
	/*  for assertions in algorithms */

	.assertion {
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		border-color: var(--assertion-border);
		background: #EEE;
		background: var(--assertion-bg);
		color: black;
		color: var(--assertion-text);
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/** Advisement Box ************************************************************/
	/*  for attention-grabbing normative statements */

	.advisement {
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		border-color: var(--advisement-border);
		border-style: none solid;
		background: #fec;
		background: var(--advisement-bg);
		color: black;
		color: var(--advisement-text);
	}
	strong.advisement {
		display: block;
		text-align: center;
	}
	.advisement::before, .advisement > .marker {
		color: #b35f00;
		color: var(--advisementheading-text);
	}

/** Amendment Box *************************************************************/

	.amendment, .correction, .addition {
		border-color: #330099;
		border-color: var(--amendment-border);
		background: #F5F0FF;
		background: var(--amendment-bg);
		color: black;
		color: var(--amendment-text);
	}
	.amendment.proposed, .correction.proposed, .addition.proposed {
		border-style: solid;
		border-block-width: 0.25em;
	}
	.amendment::before, .amendment > .marker,
	details.amendment > summary::before, details.amendment > summary > .marker,
	.correction::before, .correction > .marker,
	details.correction > summary::before, details.correction > summary > .marker,
	.addition::before, .addition > .marker,
	details.addition > summary::before, details.addition > summary > .marker {
		color: #220066;
		color: var(--amendmentheading-text);
	}
	.amendment.proposed::before, .amendment.proposed > .marker,
	details.amendment.proposed > summary::before, details.amendment.proposed > summary > .marker,
	.correction.proposed::before, .correction.proposed > .marker,
	details.correction.proposed > summary::before, details.correction.proposed > summary > .marker,
	.addition.proposed::before, .addition.proposed > .marker,
	details.addition.proposed > summary::before, details.addition.proposed > summary > .marker {
		font-weight: bold;
	}

/** Spec Obsoletion Notice ****************************************************/
	/* obnoxious obsoletion notice for older/abandoned specs. */

	details {
		display: block;
	}
	summary {
		font-weight: bolder;
	}

	.annoying-warning:not(details),
	details.annoying-warning:not([open]) > summary,
	details.annoying-warning[open] {
		background: hsla(40,100%,50%,0.95);
		background: var(--warning-bg);
		color: black;
		color: var(--warning-text);
		padding: .75em 1em;
		border: red;
		border: var(--warning-border);
		border-style: solid none;
		box-shadow: 0 2px 8px black;
		text-align: center;
	}
	.annoying-warning :last-child {
		margin-bottom: 0;
	}

@media not print {
	details.annoying-warning[open] {
		position: fixed;
		left: 0;
		right: 0;
		bottom: 2em;
		z-index: 1000;
	}
}

	details.annoying-warning:not([open]) > summary {
		text-align: center;
	}

/** Entity Definition Boxes ***************************************************/

	.def {
		padding: .5em 1em;
		background: #def;
		background: var(--def-bg);
		margin: 1.2em 0;
		border-left: 0.5em solid #8ccbf2;
		border-left: 0.5em solid var(--def-border);
		color: black;
		color: var(--def-text);
	}

/******************************************************************************/
/*                                    Tables                                  */
/******************************************************************************/

	th, td {
		text-align: left;
		text-align: start;
	}

/** Property/Descriptor Definition Tables *************************************/

	table.def {
		/* inherits .def box styling, see above */
		width: 100%;
		border-spacing: 0;
	}

	table.def td,
	table.def th {
		padding: 0.5em;
		vertical-align: baseline;
		border-bottom: 1px solid #bbd7e9;
		border-bottom: 1px solid var(--defrow-border);
	}

	table.def > tbody > tr:last-child th,
	table.def > tbody > tr:last-child td {
		border-bottom: 0;
	}

	table.def th {
		font-style: italic;
		font-weight: normal;
		padding-left: 1em;
		width: 3em;
	}

	/* For when values are extra-complex and need formatting for readability */
	table td.pre {
		white-space: pre-wrap;
	}

	/* A footnote at the bottom of a def table */
	table.def td.footnote {
		padding-top: 0.6em;
	}
	table.def td.footnote::before {
		content: " ";
		display: block;
		height: 0.6em;
		width: 4em;
		border-top: thin solid;
	}

/** Data tables (and properly marked-up index tables) *************************/
	/*
		<table class="data"> highlights structural relationships in a table
		when correct markup is used (e.g. thead/tbody, th vs. td, scope attribute)

		Use class="complex data" for particularly complicated tables --
		(This will draw more lines: busier, but clearer.)

		Use class="long" on table cells with paragraph-like contents
		(This will adjust text alignment accordingly.)
		Alternately use class="longlastcol" on tables, to have the last column assume "long".
	*/

	table {
		word-wrap: normal;
		overflow-wrap: normal;
		hyphens: manual;
	}

	table.data,
	table.index {
		margin: 1em auto;
		border-collapse: collapse;
		border: hidden;
		width: 100%;
	}
	table.data caption,
	table.index caption {
		max-width: 50em;
		margin: 0 auto 1em;
	}

	table.data td,  table.data th,
	table.index td, table.index th {
		padding: 0.5em 1em;
		border-width: 1px;
		border-color: silver;
		border-color: var(--datacell-border);
		border-top-style: solid;
	}

	table.data thead td:empty {
		padding: 0;
		border: 0;
	}

	table.data  thead,
	table.index thead,
	table.data  tbody,
	table.index tbody {
		border-bottom: 2px solid;
	}

	table.data colgroup,
	table.index colgroup {
		border-left: 2px solid;
	}

	table.data  tbody th:first-child,
	table.index tbody th:first-child  {
		border-right: 2px solid;
		border-top: 1px solid silver;
		border-top: 1px solid var(--datacell-border);
		padding-right: 1em;
	}

	table.data th[colspan],
	table.data td[colspan] {
		text-align: center;
	}

	table.complex.data th,
	table.complex.data td {
		border: 1px solid silver;
		border: 1px solid var(--datacell-border);
		text-align: center;
	}

	table.data.longlastcol td:last-child,
	table.data td.long {
		vertical-align: baseline;
		text-align: left;
	}

	table.data img {
		vertical-align: middle;
	}


/*
Alternate table alignment rules

	table.data,
	table.index {
		text-align: center;
	}

	table.data  thead th[scope="row"],
	table.index thead th[scope="row"] {
		text-align: right;
	}

	table.data  tbody th:first-child,
	table.index tbody th:first-child  {
		text-align: right;
	}

Possible extra rowspan handling

	table.data  tbody th[rowspan]:not([rowspan='1']),
	table.index tbody th[rowspan]:not([rowspan='1']),
	table.data  tbody td[rowspan]:not([rowspan='1']),
	table.index tbody td[rowspan]:not([rowspan='1']) {
		border-left: 1px solid silver;
	}

	table.data  tbody th[rowspan]:first-child,
	table.index tbody th[rowspan]:first-child,
	table.data  tbody td[rowspan]:first-child,
	table.index tbody td[rowspan]:first-child{
		border-left: 0;
		border-right: 1px solid silver;
	}
*/

/******************************************************************************/
/*                                  Indices                                   */
/******************************************************************************/


/** Table of Contents *********************************************************/

	.toc a {
		/* More spacing; use padding to make it part of the click target. */
		padding: 0.1rem 1px 0;
		/* Larger, more consistently-sized click target */
		display: block;
		/* Switch to using border-bottom for underlines */
		text-decoration: none;
		border-bottom: 1px solid;
		/* Reverse color scheme */
		color: black;
		color: var(--toclink-text);
		border-color: #3980b5;
		border-color: var(--toclink-underline);
	}
	.toc a:visited {
		color: black;
		color: var(--toclink-visited-text);
		border-color: #054572;
		border-color: var(--toclink-visited-underline);
	}
	.toc a:focus,
	.toc a:hover {
		background: rgba(75%, 75%, 75%, .25);
		background: var(--a-hover-bg);
		border-bottom-width: 3px;
		margin-bottom: -2px;
	}
	.toc a:not(:focus):not(:hover) {
		/* Allow colors to cascade through from link styling */
		border-bottom-color: transparent;
	}

	.toc, .toc ol, .toc ul, .toc li {
		list-style: none; /* Numbers must be inlined into source */
		/* because generated content isn't search/selectable and markers can't do multilevel yet */
		margin:  0;
		padding: 0;
	}
	.toc {
		line-height: 1.1em;
	}

	/* ToC not indented until third level, but font style & margins show hierarchy */
	.toc > li			{ font-weight: bold;   }
	.toc > li li		 { font-weight: normal; }
	.toc > li li li	  { font-size:   95%;	}
	.toc > li li li li	{ font-size:   90%;	}
	.toc > li li li li li { font-size:   85%;	}

	/* @supports not (display:grid) { */
		.toc > li			{ margin: 1.5rem 0;	}
		.toc > li li		 { margin: 0.3rem 0;	}
		.toc > li li li	  { margin-left: 2rem;   }

		/* Section numbers in a column of their own */
		.toc .secno {
			float: left;
			width: 4rem;
			white-space: nowrap;
		}
		.toc > li li li li .secno { font-size: 85%; }
		.toc > li li li li li .secno { font-size: 100%; }

		.toc li {
			clear: both;
		}

		:not(li) > .toc			 { margin-left:  5rem; }
		.toc .secno				 { margin-left: -5rem; }
		.toc > li li li .secno	  { margin-left: -7rem; }
		.toc > li li li li .secno	{ margin-left: -9rem; }
		.toc > li li li li li .secno { margin-left: -11rem; }

		/* Tighten up indentation in narrow ToCs */
		@media (max-width: 30em) {
			:not(li) > .toc			 { margin-left:  4rem; }
			.toc .secno				 { margin-left: -4rem; }
			.toc > li li li			 { margin-left:  1rem; }
			.toc > li li li .secno	  { margin-left: -5rem; }
			.toc > li li li li .secno	{ margin-left: -6rem; }
			.toc > li li li li li .secno { margin-left: -7rem; }
		}
		/* Loosen it on wide screens */
		@media screen and (min-width: 78em) {
			body:not(.toc-inline) :not(li) > .toc			 { margin-left:  4rem; }
			body:not(.toc-inline) .toc .secno				 { margin-left: -4rem; }
			body:not(.toc-inline) .toc > li li li			 { margin-left:  1rem; }
			body:not(.toc-inline) .toc > li li li .secno	  { margin-left: -5rem; }
			body:not(.toc-inline) .toc > li li li li .secno	{ margin-left: -6rem; }
			body:not(.toc-inline) .toc > li li li li li .secno { margin-left: -7rem; }
	}
	/* } */

	@supports (display:grid) and (display:contents) {
		/* Use #toc over .toc to override non-@supports rules. */
		#toc {
			display: grid;
			align-content: start;
			grid-template-columns: auto 1fr;
			grid-column-gap: 1rem;
			column-gap: 1rem;
			grid-row-gap: .6rem;
			row-gap: .6rem;
		}
		#toc h2 {
			grid-column: 1 / -1;
			margin-bottom: 0;
		}
		#toc ol,
		#toc li,
		#toc a {
			display: contents;
			/* Switch <a> to subgrid when supported */
		}
		#toc span {
			margin: 0;
		}
		#toc > .toc > li > a > span {
			/* The spans of the top-level list,
			  comprising the first items of each top-level section. */
			margin-top: 1.1rem;
		}
		#toc#toc .secno { /* Ugh, need more specificity to override base.css */
			grid-column: 1;
			width: auto;
			margin-left: 0;
		}
		#toc .content {
			grid-column: 2;
			width: auto;
			margin-right: 1rem;
			border-bottom: 3px solid transparent;
			margin-bottom: -3px;
		}
		#toc .content:hover,
		#toc .content:focus {
			background: rgba(75%, 75%, 75%, .25);
			background: var(--a-hover-bg);
			border-bottom-color: #054572;
			border-bottom-color: var(--toclink-underline);
		}
		#toc li li li .content {
			margin-left: 1rem;
		}
		#toc li li li li .content {
			margin-left: 2rem;
		}
	}


/** Index *********************************************************************/

	/* Index Lists: Layout */
	ul.index	  { margin-left: 0; columns: 15em; text-indent: 1em hanging; }
	ul.index li	{ margin-left: 0; list-style: none; break-inside: avoid; }
	ul.index li li { margin-left: 1em; }
	ul.index dl	{ margin-top: 0; }
	ul.index dt	{ margin: .2em 0 .2em 20px;}
	ul.index dd	{ margin: .2em 0 .2em 40px;}
	/* Index Lists: Typography */
	ul.index ul,
	ul.index dl { font-size: smaller; }
	@media not print {
		ul.index li a + span {
			white-space: nowrap;
			color: transparent; }
		ul.index li a:hover + span,
		ul.index li a:focus + span {
			color: #707070;
			color: var(--indexinfo-text);
		}
	}

/** Index Tables *****************************************************/
	/* See also the data table styling section, which this effectively subclasses */

	table.index {
		font-size: small;
		border-collapse: collapse;
		border-spacing: 0;
		text-align: left;
		margin: 1em 0;
	}

	table.index td,
	table.index th {
		padding: 0.4em;
	}

	table.index tr:hover td:not([rowspan]),
	table.index tr:hover th:not([rowspan]) {
		color: black;
		color: var(--indextable-hover-text);
		background: #f7f8f9;
		background: var(--indextable-hover-bg);
	}

	/* The link in the first column in the property table (formerly a TD) */
	table.index th:first-child a {
		font-weight: bold;
	}

/** Outdated warning **********************************************************/

.outdated-spec {
	color: black;
	color: var(--outdatedspec-text);
	background-color: rgba(0,0,0,0.5);
	background-color: var(--outdatedspec-bg);
}

.outdated-warning {
	position: fixed;
	bottom: 50%;
	left: 0;
	right: 0;
	margin: 0 auto;
	width: 50%;
	background: maroon;
	background: var(--outdated-bg);
	color: white;
	color: var(--outdated-text);
	border-radius: 1em;
	box-shadow: 0 0 1em red;
	box-shadow: 0 0 1em var(--outdated-shadow);
	padding: 2em;
	text-align: center;
	z-index: 2;
}

.outdated-warning a {
	color: currentcolor;
	background: transparent;
}

.edited-rec-warning {
	background: darkorange;
	background: var(--editedrec-bg);
	box-shadow: 0 0 1em;
}

.outdated-warning button {
	color: var(--outdated-text);
	border-radius: 1em;
	box-shadow: 0 0 1em red;
	box-shadow: 0 0 1em var(--outdated-shadow);
	padding: 2em;
	text-align: center;
	z-index: 2;
}

.outdated-warning a {
	color: currentcolor;
	background: transparent;
}

.edited-rec-warning {
	background: darkorange;
	background: var(--editedrec-bg);
	box-shadow: 0 0 1em;
}

.outdated-warning button {
	position: absolute;
	top: 0;
	right:0;
	margin: 0;
	border: 0;
	padding: 0.25em 0.5em;
	background: transparent;
	color: white;
	color: var(--outdated-text);
	font:1em sans-serif;
	text-align:center;
}

.outdated-warning span {
	display: block;
}

.outdated-collapsed {
	bottom: 0;
	border-radius: 0;
	width: 100%;
	padding: 0;
}

/******************************************************************************/
/*                                    Print                                   */
/******************************************************************************/

	@media print {
		/* Pages have their own margins. */
		html {
			margin: 0;
		}
		/* Serif for print. */
		body {
			font-family: serif;
		}

		.outdated-warning {
			position: absolute;
			border-style: solid;
			border-color: red;
		}

		.outdated-warning input {
			display: none;
		}
	}
	@page {
		margin: 1.5cm 1.1cm;
	}



/******************************************************************************/
/*                             Overflow Control                               */
/******************************************************************************/

	.figure .caption, .sidefigure .caption, figcaption {
		/* in case figure is overlarge, limit caption to 50em */
		max-width: 50rem;
		margin-left: auto;
		margin-right: auto;
	}
	.overlarge {
		/* Magic to create good item positioning:
		  "content column" is 50ems wide at max; less on smaller screens.
		  Extra space (after ToC + content) is empty on the right.

		  1. When item < content column, centers item in column.
		  2. When content < item < available, left-aligns.
		  3. When item > available, fills available + scroll bar.
		*/
		display: grid;
		grid-template-columns: minmax(0, 50em);
	}
	.overlarge > table {
		/* limit preferred width of table */
		max-width: 50em;
		margin-left: auto;
		margin-right: auto;
	}

	@media (min-width: 55em) {
		.overlarge {
			margin-right: calc(13px + 26.5rem - 50vw);
			max-width: none;
		}
	}
	@media screen and (min-width: 78em) {
		body:not(.toc-inline) .overlarge {
			/* 30.5em body padding 50em content area */
			margin-right: calc(40em - 50vw) !important;
		}
	}
	@media screen and (min-width: 90em) {
		body:not(.toc-inline) .overlarge {
			/* 4em html margin 30.5em body padding 50em content area */
			margin-right: calc(84.5em - 100vw) !important;
		}
	}

	@media not print {
		.overlarge {
			overflow-x: auto;
			/* See Lea Verou's explanation background-attachment:
			* http://lea.verou.me/2012/04/background-attachment-local/
			*
			background: top left  / 4em 100% linear-gradient(to right,  #ffffff, rgba(255, 255, 255, 0)) local,
						top right / 4em 100% linear-gradient(to left, #ffffff, rgba(255, 255, 255, 0)) local,
						top left  / 1em 100% linear-gradient(to right,  #c3c3c5, rgba(195, 195, 197, 0)) scroll,
						top right / 1em 100% linear-gradient(to left, #c3c3c5, rgba(195, 195, 197, 0)) scroll,
						white;
			background-repeat: no-repeat;
			*/
		}
	}
</style>
<style>
    table, th, td {
      border: 1px solid black;
      border-collapse: collapse;
      vertical-align: top;
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    th, td {
      border-left: none;
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      padding: 0px 10px;
    }
    th {
      text-align: center;
    }

    del { background: #fcc; color: #000; text-decoration: line-through; }
    ins { background: #cfc; color: #000; }
    blockquote .highlight:not(.idl) { background: initial; margin: initial; padding: 0.5em }
    blockquote ul { background: inherit; }
    blockquote code.highlight:not(.idl) { padding: initial; }
    blockquote c-[a] { color: inherit; } /* Keyword.Declaration */
    blockquote c-[b] { color: inherit; } /* Keyword.Type */
    blockquote c-[c] { color: inherit; } /* Comment */
    blockquote c-[d] { color: inherit; } /* Comment.Multiline */
    blockquote c-[e] { color: inherit; } /* Name.Attribute */
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    blockquote c-[m] { color: inherit; } /* Literal.Number */
    blockquote c-[n] { color: inherit; } /* Name */
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    blockquote c-[t] { color: inherit; } /* Literal.String.Single */
    blockquote c-[u] { color: inherit; } /* Literal.String.Double */
    blockquote c-[cp] { color: inherit; } /* Comment.Preproc */
    blockquote c-[c1] { color: inherit; } /* Comment.Single */
    blockquote c-[cs] { color: inherit; } /* Comment.Special */
    blockquote c-[kc] { color: inherit; } /* Keyword.Constant */
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    blockquote c-[kp] { color: inherit; } /* Keyword.Pseudo */
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    blockquote c-[ni] { color: inherit; } /* Name.Entity */
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    blockquote c-[py] { color: inherit; } /* Name.Property */
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    blockquote c-[mf] { color: inherit; } /* Literal.Number.Float */
    blockquote c-[mh] { color: inherit; } /* Literal.Number.Hex */
    blockquote c-[mi] { color: inherit; } /* Literal.Number.Integer */
    blockquote c-[mo] { color: inherit; } /* Literal.Number.Oct */
    blockquote c-[sb] { color: inherit; } /* Literal.String.Backtick */
    blockquote c-[sc] { color: inherit; } /* Literal.String.Char */
    blockquote c-[sd] { color: inherit; } /* Literal.String.Doc */
    blockquote c-[se] { color: inherit; } /* Literal.String.Escape */
    blockquote c-[sh] { color: inherit; } /* Literal.String.Heredoc */
    blockquote c-[si] { color: inherit; } /* Literal.String.Interpol */
    blockquote c-[sx] { color: inherit; } /* Literal.String.Other */
    blockquote c-[sr] { color: inherit; } /* Literal.String.Regex */
    blockquote c-[ss] { color: inherit; } /* Literal.String.Symbol */
    blockquote c-[vc] { color: inherit; } /* Name.Variable.Class */
    blockquote c-[vg] { color: inherit; } /* Name.Variable.Global */
    blockquote c-[vi] { color: inherit; } /* Name.Variable.Instance */
    blockquote c-[il] { color: inherit; } /* Literal.Number.Integer.Long */
  </style>
  <meta content="Bikeshed version 74068a90b, updated Wed Mar 22 17:34:51 2023 -0700" name="generator">
  <link href="http://wg21.link/P3067R0" rel="canonical">
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<style>
.ins, ins, ins * {
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 <body class="h-entry">
  <div class="head">
   <p data-fill-with="logo"></p>
   <h1 class="p-name no-ref" id="title">P3067R0<br>Named permutation functions for `std::simd`</h1>
   <h2 class="no-num no-toc no-ref heading settled" id="profile-and-date"><span class="content">Published Proposal, <time class="dt-updated" datetime="2024-05-22">2024-05-22</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>This version:
     <dd><a class="u-url" href="http://wg21.link/P3067R0">http://wg21.link/P3067R0</a>
     <dt class="editor">Authors:
     <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:daniel.towner@intel.com">Daniel Towner</a> (<span class="p-org org">Intel</span>)
     <dd class="editor p-author h-card vcard"><a class="p-name fn u-email email" href="mailto:ruslan.arutyunyan@intel.com">Ruslan Arutyunyan</a> (<span class="p-org org">Intel</span>)
     <dt>Audience:
     <dd>LEWG
     <dt>Project:
     <dd>ISO/IEC 14882 Programming Languages — C++, ISO/IEC JTC1/SC22/WG21
    </dl>
   </div>
   <div data-fill-with="warning"></div>
   <hr title="Separator for header">
  </div>
  <div class="p-summary" data-fill-with="abstract">
   <h2 class="no-num no-toc no-ref heading settled" id="abstract"><span class="content">Abstract</span></h2>
   <p>The paper proposes to provide a set of named functions for common permutation operations.</p>
  </div>
  <nav data-fill-with="table-of-contents" id="toc">
   <h2 class="no-num no-toc no-ref" id="contents">Table of Contents</h2>
   <ol class="toc" role="directory">
    <li><a href="#intro"><span class="secno">1</span> <span class="content">Motivation</span></a>
    <li>
     <a href="#background"><span class="secno">2</span> <span class="content">Background</span></a>
     <ol class="toc">
      <li><a href="#background_original"><span class="secno">2.1</span> <span class="content">Original <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> proposal</span></a>
      <li><a href="#background_named_permutes"><span class="secno">2.2</span> <span class="content">Suggestion to include selected named permute functions</span></a>
      <li><a href="#background_intel_response"><span class="secno">2.3</span> <span class="content"><code class="highlight"><c- n>insert</c-></code>, <code class="highlight"><c- n>extract</c-></code> and <code class="highlight"><c- n>resize</c-></code></span></a>
      <li><a href="#background_other_libraries"><span class="secno">2.4</span> <span class="content">Named permute functions in other data parallel libraries</span></a>
      <li><a href="#background_generic_api"><span class="secno">2.5</span> <span class="content">Powerful generic <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> API</span></a>
     </ol>
    <li>
     <a href="#add_utility_functions"><span class="secno">3</span> <span class="content">Addition of common utility functions</span></a>
     <ol class="toc">
      <li><a href="#named_functions_overview"><span class="secno">3.1</span> <span class="content">Named permute functions overview</span></a>
      <li><a href="#design_function_or_object"><span class="secno">3.2</span> <span class="content">Design option - functions or function objects</span></a>
      <li><a href="#design_function_constant_parameters"><span class="secno">3.3</span> <span class="content">Design option - constant parameters</span></a>
     </ol>
    <li><a href="#implementation_experience"><span class="secno">4</span> <span class="content">Implementation Experience</span></a>
    <li><a href="#conclusion"><span class="secno">5</span> <span class="content">Conclusion</span></a>
    <li>
     <a href="#references"><span class="secno"></span> <span class="content">References</span></a>
     <ol class="toc">
      <li><a href="#informative"><span class="secno"></span> <span class="content">Informative References</span></a>
     </ol>
   </ol>
  </nav>
  <main>
   <h2 class="heading settled" data-level="1" id="intro"><span class="secno">1. </span><span class="content">Motivation</span><a class="self-link" href="#intro"></a></h2>
   <p>ISO/IEC 19570:2018 (1) introduced data-parallel types to the C++ Extensions for
Parallelism TS. <a data-link-type="biblio" href="#biblio-p1928r8" title="std::simd - Merge data-parallel types from the Parallelism TS 2">[P1928R8]</a> is proposing to make that a part of C++ IS. Intel
supports the concept of a standard interface to SIMD instruction capabilities
and in document <a data-link-type="biblio" href="#biblio-p2638r0" title="Intel&apos;s response to P1915R0 for std::simd parallelism in TS 2">[P2638R0]</a> we made a number of suggestions for extending the
capabilities of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> to handle named permutation for common operations
like <code class="highlight"><c- n>insert</c-></code>, <code class="highlight"><c- n>extract</c-></code> and <code class="highlight"><c- n>resize</c-></code>. Intel then also proposed in <a data-link-type="biblio" href="#biblio-p2664r6" title="Proposal to extend std::simd with permutation API">[P2664R6]</a> an even
more capable generic API for handling permutes using generated static indexes,
dynamic indexes, selection by mask, and memory-based gather/scatter operations.
In this paper we will revisit the original proposals from <a data-link-type="biblio" href="#biblio-p2638r0" title="Intel&apos;s response to P1915R0 for std::simd parallelism in TS 2">[P2638R0]</a> and see
how they can be modified in the light of the generic API, and from feedback
received from the community.</p>
   <h2 class="heading settled" data-level="2" id="background"><span class="secno">2. </span><span class="content">Background</span><a class="self-link" href="#background"></a></h2>
   <p>While <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> is undoubtedly most useful for expressing parallel operations
(e.g., arithmetic) across entire sets of input arguments, many real-world
algorithms require the data to be marshalled into new positions before
operating on it. For example, modifying the order of values, concatenating or
splitting data, or pulling out specific elements for some purpose. In the
discussions around <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> there have been of number of attempts to defined
some sort of permute function, and these will be summarised below.</p>
   <p>Our aim in this paper is to accept that the generic permute API discussed in <a data-link-type="biblio" href="#biblio-p2664r6" title="Proposal to extend std::simd with permutation API">[P2664R6]</a> does everything that we could possible want in a permute API, but
that it is useful to standardise a few specific and common types of permute so
that users of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> aren’t required to keep reinventing them. In all of
the summaries of other proposals below we can learn from the them and provide something that
mimics the original intent with the new generic API.</p>
   <h3 class="heading settled" data-level="2.1" id="background_original"><span class="secno">2.1. </span><span class="content">Original <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> proposal</span><a class="self-link" href="#background_original"></a></h3>
   <p>In <a data-link-type="biblio" href="#biblio-p1928r0" title="Merge data-parallel types from the Parallelism TS 2">[P1928R0]</a> there were only a few functions which could be used to
achieve any sort of element permutation across or within <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-><c- o>&lt;></c-></code> values.
Those functions were relatively modest in scope and they built upon the ability
to split and concatenate simd values at compile-time. For example, a simd value
containing 5 elements could be split into two smaller pieces of sizes 2 and 3
respectively:</p>
<pre class="language-cpp highlight"><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>5</c-><c- o>></c-> <c- n>x</c-><c- p>;</c->
…
<c- k>const</c-> <c- k>auto</c-> <c- p>[</c-><c- n>piece0</c-><c- p>,</c-> <c- n>piece1</c-><c- p>]</c-> <c- o>=</c-> <c- n>simd_split</c-><c- o>&lt;</c-><c- mi>3</c-><c- o>></c-><c- p>(</c-><c- n>x</c-><c- p>);</c-></pre>
   <p>Those smaller pieces could be acted on using any of the <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> features, and
then later recombined using <code class="highlight"><c- n>simd_cat</c-></code>, possibly in a different order or with
duplication:</p>
   <p><code class="highlight"><c- k>const</c-> <c- k>auto</c-> <c- n>output</c-> <c- o>=</c-> <c- n>simd_cat</c-><c- p>(</c-><c- n>piece1</c-><c- p>,</c-> <c- n>piece1</c-><c- p>,</c-> <c- n>piece0</c-><c- p>);</c-></code></p>
   <p>The <code class="highlight"><c- n>simd_split</c-></code>, <code class="highlight"><c- n>simd_split_by</c-></code> and <code class="highlight"><c- n>simd_cat</c-></code> functions can be used to achieve several permutation
effects, but they are unwieldy for anything complicated, and since they
are also compile-time they preclude any dynamic runtime permutation.</p>
   <p>Since the original proposal a few changes have taken place. The original <code class="highlight"><c- n>split</c-></code> function shown above, which could accept an arbitrary set of indexes to perform
the split, was removed and the original <code class="highlight"><c- n>split_by</c-></code> function was renamed to <code class="highlight"><c- n>split</c-></code>. The new variant <code class="highlight"><c- n>split</c-></code> now breaks a <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> value into a set of
identically sized pieces, and a remainder. The concatenation function remains in
its original state.</p>
   <p>As a small aside, the <code class="highlight"><c- n>split</c-></code> operation is equivalent to what is called chunking
in the views/ranges library, and <code class="highlight"><c- n>ranges</c-><c- o>::</c-><c- n>split</c-></code> does something different. It
may be better to call simd’s function <code class="highlight"><c- n>simd_chunk</c-></code> instead to avoid confusion.</p>
   <p>One of the purposes of the original <code class="highlight"><c- n>split</c-></code> and <code class="highlight"><c- n>concat</c-></code> functions was to allow
a large <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> to be broken into pieces which had a native register size so
that builtin operations (intrinsics) could be called on individual pieces, and
the results glued back together. Such manual permutation for these purposes has
been superseded by <a data-link-type="biblio" href="#biblio-p2929r0" title="simd_invoke">[P2929R0]</a> which proposes a function called <code class="highlight"><c- n>simd_invoke</c-></code> which automates this task.</p>
   <h3 class="heading settled" data-level="2.2" id="background_named_permutes"><span class="secno">2.2. </span><span class="content">Suggestion to include selected named permute functions</span><a class="self-link" href="#background_named_permutes"></a></h3>
   <p>Two suggestions were made in <a data-link-type="biblio" href="#biblio-p0918r1" title="More simd<> Operations">[P0918R1]</a>: add an arbitrary compile-time shuffle
function, and add a specific type of permutation called an interleave. The
arbitrary shuffle has been replaced by a generated-permute function for reasons
explained in <a data-link-type="biblio" href="#biblio-p2664r6" title="Proposal to extend std::simd with permutation API">[P2664R6]</a> and will not be considered further here.</p>
   <p>The other proposal was to add a function called interleave which accepts two
SIMD values and interleaves respective elements into a new SIMD value which is
twice the size. For example, given inputs <code class="highlight"><c- p>[</c-><c- n>a0</c-> <c- n>a1</c-> <c- n>a2</c-><c- p>]</c-></code> and <code class="highlight"><c- p>[</c-><c- n>b0</c-> <c- n>b1</c-> <c- n>b2</c-><c- p>]</c-></code>,
the output would be <code class="highlight"><c- p>[</c-><c- n>a0</c-> <c- n>b0</c-> <c- n>a1</c-> <c- n>b1</c-> <c- n>a2</c-> <c- n>b2</c-><c- p>]</c-></code>. Interleaving is a common
operation and is often directly supported by processors with explicit
instructions (e.g., Intel’s <code class="highlight"><c- n>punpcklwd</c-></code>), so as in <a data-link-type="biblio" href="#biblio-p0918r1" title="More simd<> Operations">[P0918R1]</a> and also in
other SIMD libraries there will be named functions which expose that
instruction. This is a relatively common operations in certain workloads (e.g.,
signal processing) and so it was called out as a specific function to allow
programmers from having to keep defining their own versions of what is a
basic utility.</p>
   <h3 class="heading settled" data-level="2.3" id="background_intel_response"><span class="secno">2.3. </span><span class="content"><code class="highlight"><c- n>insert</c-></code>, <code class="highlight"><c- n>extract</c-></code> and <code class="highlight"><c- n>resize</c-></code></span><a class="self-link" href="#background_intel_response"></a></h3>
   <p>In <a data-link-type="biblio" href="#biblio-p2638r0" title="Intel&apos;s response to P1915R0 for std::simd parallelism in TS 2">[P2638R0]</a> Intel suggested three new functions:</p>
   <ul>
    <li data-md>
     <p><code class="highlight"><c- n>insert</c-></code> - Place a copy of the elements from one <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> within another <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code>, replacing the original elements at the given insertion position.</p>
    <li data-md>
     <p><code class="highlight"><c- n>extract</c-></code> - Create a smaller <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> value from a sub-set of the elements of another <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> value.</p>
    <li data-md>
     <p><code class="highlight"><c- n>resize</c-></code> - Grow or shrink a <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> to a new number of elements.</p>
   </ul>
   <p>These all operate purely statically, using fixed sizes and positions. There was
a discussion of whether they should work dynamically too (e.g., insert data into
some run-time specified position of another <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code>) but there was no consensus to
pursue this.</p>
   <p>There was feedback that the names should have more thought. For example, <code class="highlight"><c- n>insert</c-></code> doesn’t make the <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> value into which the insertion is taking
place any larger, but instead replaces elements. Also there was some concern
that <code class="highlight"><c- n>resize</c-></code> might silently do something unexpected, and that having functions
which explicitly truncate (and lose) elements to shrink a <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code>, or explicitly
grow a <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> by adding value-initialised elements to reach the new size  might be
clearer. However, against this is that other containers in C++ (e.g., vector)
have <code class="highlight"><c- n>resize</c-></code> methods which ambiguously (and dynamically too) grow or shrink a
container without warning.</p>
   <p>In Intel’s experience of using these functions in some of our software products
we have found that no-one is using <code class="highlight"><c- n>insert</c-></code>, but <code class="highlight"><c- n>extract</c-></code> and <code class="highlight"><c- n>resize</c-></code> are both found in real code.</p>
   <p>Those functions can be implemented using the functions proposed in <a data-link-type="biblio" href="#biblio-p2664r6" title="Proposal to extend std::simd with permutation API">[P2664R6]</a>.
For example:</p>
<pre class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- b>size_t</c-> <c- n>_NewSize</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>_Tp</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>_Abi</c-><c- o>></c->
<c- k>constexpr</c-> <c- k>auto</c-> <c- n>resize</c-><c- p>(</c-><c- k>const</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>_Tp</c-><c- p>,</c-> <c- n>_Abi</c-><c- o>>&amp;</c-> <c- n>v</c-><c- p>)</c->
<c- p>{</c->
  <c- k>constexpr</c-> <c- b>int</c-> <c- n>_OldSize</c-> <c- o>=</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>_Tp</c-><c- p>,</c-> <c- n>_Abi</c-><c- o>>::</c-><c- n>size</c-><c- p>;</c->
  <c- k>return</c-> <c- n>permute</c-><c- o>&lt;</c-><c- n>_NewSize</c-><c- o>></c-><c- p>(</c-><c- n>v</c-><c- p>,</c->
             <c- p>[](</c-><c- n>std</c-><c- o>::</c-><c- b>size_t</c-> <c- n>i</c-><c- p>)</c-> <c- p>{</c-> <c- k>return</c-> <c- p>(</c-><c- n>i</c-> <c- o>&lt;</c-> <c- n>_OldSize</c-><c- p>)</c-> <c- o>?</c-> <c- n>i</c-> <c- o>:</c-> <c- n>simd_zero_element</c-><c- p>;</c-> <c- p>});</c->
<c- p>}</c->

<c- k>template</c-><c- o>&lt;</c-><c- n>std</c-><c- o>::</c-><c- b>size_t</c-> <c- n>_Begin</c-><c- p>,</c-> <c- n>std</c-><c- o>::</c-><c- b>size_t</c-> <c- n>_End</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>_Tp</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>_Abi</c-><c- o>></c->
<c- k>constexpr</c-> <c- k>auto</c-> <c- n>extract</c-><c- p>(</c-><c- k>const</c-> <c- n>simd_impl</c-><c- o>&lt;</c-><c- n>_Tp</c-><c- p>,</c-> <c- n>_OldSize</c-><c- o>>&amp;</c-> <c- n>v</c-><c- p>)</c->
<c- p>{</c->
  <c- k>return</c-> <c- n>permute</c-><c- o>&lt;</c-><c- n>_End</c-> <c- o>-</c-> <c- n>_Begin</c-><c- o>></c-><c- p>(</c-><c- n>v</c-><c- p>,</c-> <c- p>[](</c-><c- n>std</c-><c- o>::</c-><c- b>size_t</c-> <c- n>i</c-><c- p>)</c-> <c- p>{</c-> <c- k>return</c-> <c- n>i</c-> <c- o>+</c-> <c- n>_Begin</c-><c- p>;</c-> <c- p>});</c->
<c- p>}</c-></pre>
   <h3 class="heading settled" data-level="2.4" id="background_other_libraries"><span class="secno">2.4. </span><span class="content">Named permute functions in other data parallel libraries</span><a class="self-link" href="#background_other_libraries"></a></h3>
   <p>Other data parallel libraries provide functions for common permutation
operations though often it will be to expose selected native instructions. For
example, <a data-link-type="biblio" href="#biblio-highway" title="Google Highway">[Highway]</a> provides <code class="highlight"><c- n>DupOdd</c-></code>, <code class="highlight"><c- n>DupEven</c-></code>, <code class="highlight"><c- n>ReverseBlocks</c-></code>, <code class="highlight"><c- n>Shuffle0231</c-></code>, and so on, which map efficiently to Intel instructions. In
this case the choice of which functions to expose will guide the user to use
permutes which are known to be efficient on a particular target, but this may
come at the expense of portability.</p>
   <h3 class="heading settled" data-level="2.5" id="background_generic_api"><span class="secno">2.5. </span><span class="content">Powerful generic <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> API</span><a class="self-link" href="#background_generic_api"></a></h3>
   <p>In <a data-link-type="biblio" href="#biblio-p2664r6" title="Proposal to extend std::simd with permutation API">[P2664R6]</a> Intel proposed a comprehensive permutation API which covered the most common requirements of most users:</p>
   <ul>
    <li data-md>
     <p>Static permute generator - using a callable generator (e.g., lambda) to generate a static permutation. This can allow the compiler to perform arbitrary permutes in what are often very sophisticated and efficient ways.</p>
    <li data-md>
     <p>Dynamic permute using another <code class="highlight"><c- n>simd</c-></code> value as an index.</p>
    <li data-md>
     <p>Mask-based permute where elements corresponding to the active elements of a <code class="highlight"><c- n>simd</c-></code> are compressed or expanded, and inactive elements discarded.</p>
    <li data-md>
     <p>Memory-based permute where values are gathered from or scattered to a specific memory region (i.e., safely, with no access permitted outside the specificed region).</p>
   </ul>
   <p>The subject of naming came into the discussions and at time of writing this hasn’t been completely
resolved (e.g., should there be a <code class="highlight"><c- n>simd_</c-></code> prefix or a namespace?). Fundamentally there is nothing
wrong with the set of permute functions or their behaviours.</p>
   <p>One problem with the generic API though is that although it can do anything
required, there are inevitably certain operations which are so common that every
user of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> will write their own version of it. We received feedback
that we should explore the provision of a set of common functions of this type,
which brings us to the purpose of this paper.</p>
   <h2 class="heading settled" data-level="3" id="add_utility_functions"><span class="secno">3. </span><span class="content">Addition of common utility functions</span><a class="self-link" href="#add_utility_functions"></a></h2>
   <p>In our experience, the most useful of all the generic permute functions proposed
in <a data-link-type="biblio" href="#biblio-p2664r6" title="Proposal to extend std::simd with permutation API">[P2664R6]</a> is the generated permute. Here is an example to refresh the reader:</p>
<pre class="language-cpp highlight"><c- k>const</c-> <c- k>auto</c-> <c- n>dupEvenIndex</c-> <c- o>=</c-> <c- p>[](</c-><c- k>auto</c-> <c- n>idx</c-><c- p>)</c-> <c- p>{</c-> <c- k>return</c-> <c- p>(</c-><c- n>idx</c-> <c- o>/</c-> <c- mi>2</c-><c- p>)</c-> <c- o>*</c-> <c- mi>2</c-><c- p>;</c-> <c- p>};</c->
<c- k>const</c-> <c- k>auto</c-> <c- n>de</c-> <c- o>=</c-> <c- n>permute</c-><c- p>(</c-><c- n>values</c-><c- p>,</c-> <c- n>dupEvenIndex</c-><c- p>);</c-></pre>
   <p>For every index position in the output value the generator lambda function is called with
that index to determine what the source index should be for that element. In
this particular example the generator is duplicating every even value.</p>
   <p>The generator function can take both an index parameter and also a size
parameter. This gives the ability to write a reversing permute generator:</p>
<pre class="language-cpp highlight"><c- k>auto</c-> <c- n>rev</c-> <c- o>=</c-> <c- n>permute</c-><c- p>(</c-><c- n>s</c-><c- p>,</c-> <c- p>[](</c-><c- k>auto</c-> <c- n>idx</c-><c- p>,</c-> <c- k>auto</c-> <c- n>size</c-><c- p>)</c-> <c- p>{</c-> <c- k>return</c-> <c- p>(</c-><c- n>size</c-> <c- o>-</c-> <c- mi>1</c-><c- p>)</c-> <c- o>-</c-> <c- n>idx</c-><c- p>;</c-> <c- p>});</c-></pre>
   <p>Finally, the output size of the generated simd may also be specified:</p>
<pre class="language-cpp highlight"><c- k>auto</c-> <c- n>repeat_simd</c-><c- p>(</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>3</c-><c- o>></c-> <c- n>s</c-><c- p>)</c-> <c- p>{</c->
  <c- k>return</c-> <c- n>permute</c-><c- o>&lt;</c-><c- mi>7</c-><c- o>></c-><c- p>(</c-><c- n>s</c-><c- p>,</c-> <c- p>[](</c-><c- k>auto</c-> <c- n>idx</c-><c- p>,</c-> <c- k>auto</c-> <c- n>size</c-><c- p>)</c-> <c- p>{</c-> <c- k>return</c-> <c- n>idx</c-> <c- o>%</c-> <c- n>size</c-><c- p>;</c-> <c- p>});</c->
<c- p>}</c-></pre>
   <p>In this example a simd value such as <code class="highlight"><c- p>[</c-><c- n>a</c-><c- p>,</c-> <c- n>b</c-><c- p>,</c-> <c- n>c</c-><c- p>]</c-></code> will be repeated to fill 7
elements, forming the value <code class="highlight"><c- p>[</c-><c- n>a</c-><c- p>,</c-> <c- n>b</c-><c- p>,</c-> <c- n>c</c-><c- p>,</c-> <c- n>a</c-><c- p>,</c-> <c- n>b</c-><c- p>,</c-> <c- n>c</c-><c- p>,</c-> <c- n>a</c-><c- p>]</c-></code>.</p>
   <p>If the onus is placed on the user of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> to provide the generator
functions for all types of permutes then they will inevitably duplicate
common permute generators at any level from a single translation unit, in
multiple files across a whole project, and even across unrelated projects.
Within a file or project the user can obviously create a single permute
generator which can be reused, but we don’t want entirely different projects to
have to keep duplicating common functions either.</p>
   <p>Another issue with requiring the user to provide their own generators is that it
is very easy to write something quite obscure. For example, <code class="highlight"><c- n>permute</c-><c- p>(</c-><c- n>x</c-><c- p>,</c-> <c- p>[](</c-><c- k>auto</c-> <c- n>i</c-><c- p>)</c-> <c- p>{</c-> <c- k>return</c-> <c- n>i</c-> <c- o>^</c-> <c- mi>2</c-><c- p>;</c-> <c- p>})</c-></code> does not immediately tell the reader what is happening,
but <code class="highlight"><c- n>permute</c-><c- p>(</c-><c- n>s</c-><c- p>,</c-> <c- n>swap_adjacent</c-><c- p>)</c-></code> is much clearer. With discipline the user can
make the code clear with appropriate naming, but it adds to the workload of the
user to get this right, and it would be simpler to use a standardised function
provided by <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> itself.</p>
   <p>One final issue is that inevitably bugs will creep in to generator functions, and
providing a set of known-working standard permute generators will improve
development time by reducing debug time.</p>
   <p>An initial step (and indeed, one that was suggested at the C++ committee
meeting) is to propose a set of generator functions that can be dropped in to a
generated permute. This feels initially promising, such as creating a lambda for reverse:</p>
<pre class="language-cpp highlight"><c- k>namespace</c-> <c- nn>simd_perm</c->
<c- p>{</c->
  <c- k>constexpr</c-> <c- k>auto</c-> <c- n>reverse</c-> <c- o>=</c-> <c- p>[](</c-><c- k>auto</c-> <c- n>idx</c-><c- p>,</c-> <c- k>auto</c-> <c- n>size</c-><c- p>)</c-> <c- p>{</c-> <c- k>return</c-> <c- p>(</c-><c- n>size</c-> <c- o>-</c-> <c- mi>1</c-><c- p>)</c-> <c- o>-</c-> <c- n>idx</c-><c- p>;</c-> <c- p>};</c->
<c- p>}</c->


<c- k>auto</c-> <c- n>rev</c-> <c- o>=</c-> <c- n>permute</c-><c- p>(</c-><c- n>values</c-><c- p>,</c-> <c- n>simd_perm</c-><c- o>::</c-><c- n>reverse</c-><c- p>);</c-></pre>
   <p>Note that we have assumed that the function is put into some suitable namespace.
We shall return to the question of naming these functions shortly.</p>
   <p>Unfortunately following the idea of a named permute generator as above quickly
leads to a problem; permutation often (even mostly) requires a change in size as
well as a change in index order. For example, suppose we build a generator which
reads values which are multiples of some constant - a strided read. The
generator can be defined and used as below. Note that we aren’t using a lambda
for this example because we wish to be able to template parameterise the stride
distance.</p>
<pre class="language-cpp highlight"><c- k>template</c-><c- o>&lt;</c-><c- b>int</c-> <c- n>N</c-><c- o>></c->
<c- k>struct</c-> <c- nc>stride</c-> <c- p>{</c->
    <c- k>constexpr</c-> <c- k>auto</c-> <c- k>operator</c-><c- p>()(</c-><c- k>auto</c-> <c- n>idx</c-><c- p>)</c-> <c- k>const</c-> <c- p>{</c-> <c- k>return</c-> <c- n>idx</c-> <c- o>*</c-> <c- n>N</c-><c- p>;</c-> <c- p>};</c->
<c- p>};</c->

<c- k>auto</c-> <c- n>everyThird</c-> <c- o>=</c-> <c- n>permute</c-><c- o>&lt;</c-><c- mi>3</c-><c- o>></c-><c- p>(</c-><c- n>s</c-><c- p>,</c-> <c- n>stride</c-><c- o>&lt;</c-><c- mi>3</c-><c- o>></c-><c- p>{});;</c-></pre>
   <p>In this example we have to provide how many output values we require, as well as
the generator. If we don’t provide the correct number then the permutation will
fail as it tries to read invalid indexes. Therefore, for generic common
permutation it isn’t sufficient to provide named permute generators, we may also
need to provide wrappers to make them useful.</p>
   <p>To complete this particular example we would want a <code class="highlight"><c- n>simd</c-></code> permute function for <code class="highlight"><c- n>stride</c-></code> which was implemented as something like this:</p>
<pre class="language-cpp highlight"><c- k>namespace</c-> <c- nn>__details</c-> <c- p>{</c->
  <c- k>template</c-><c- o>&lt;</c-><c- b>int</c-> <c- n>N</c-><c- o>></c->
  <c- k>struct</c-> <c- nc>stride_helper</c-> <c- p>{</c->
    <c- k>constexpr</c-> <c- k>auto</c-> <c- k>operator</c-><c- p>()(</c-><c- k>auto</c-> <c- n>idx</c-><c- p>)</c-> <c- p>{</c-> <c- k>return</c-> <c- n>idx</c-> <c- o>*</c-> <c- n>N</c-><c- p>;</c-> <c- p>};</c->
  <c- p>};</c->
<c- p>}</c->

<c- k>namespace</c-> <c- nn>simd_permute</c-> <c- p>{</c->
  <c- k>template</c-><c- o>&lt;</c-><c- b>int</c-> <c- n>N</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>_Simd</c-><c- o>></c->
  <c- k>constexpr</c-> <c- k>auto</c-> <c- n>stride</c-><c- p>(</c-><c- k>const</c-> <c- n>_Simd</c-><c- o>&amp;</c-> <c- n>s</c-><c- p>)</c-> <c- p>{</c->
    <c- k>return</c-> <c- n>permute</c-><c- o>&lt;</c-><c- n>_Simd</c-><c- o>::</c-><c- n>size</c-> <c- o>/</c-> <c- n>N</c-><c- o>></c-><c- p>(</c-><c- n>s</c-><c- p>,</c-> <c- n>__details</c-><c- o>::</c-><c- n>stride_helper</c-><c- o>&lt;</c-><c- n>N</c-><c- o>></c-><c- p>{});</c->
  <c- p>}</c->
<c- p>}</c->

<c- k>auto</c-> <c- n>everyThird</c-> <c- o>=</c-> <c- n>simd_permute</c-><c- o>::</c-><c- n>stride</c-><c- o>&lt;</c-><c- mi>3</c-><c- o>></c-><c- p>(</c-><c- n>s</c-><c- p>);</c-></pre>
   <p>We are faced with some small dilemma with how this relates to existing functions
in the C++ libraries. There is already a range adaptor object <code class="highlight"><c- k>constexpr</c-> <c- k>auto</c-> <c- n>views</c-><c- o>::</c-><c- n>stride</c-><c- p>(</c-><c- n>Range</c-><c- o>&amp;&amp;</c-> <c- n>r</c-><c- p>,</c-> <c- n>DifferenceType</c-><c- o>&amp;&amp;</c-> <c- n>n</c-><c- p>)</c-></code> which has the same behaviour
(i.e., pick out every N’th value of some input), but which works on a dynamic
range. Our <code class="highlight"><c- n>simd</c-></code>-specific version of stride differs in having to be called with a <code class="highlight"><c- n>simd</c-></code> of a static size, return a <code class="highlight"><c- n>simd</c-></code> of a different static size, and provide a
template parameter rather than a variable parameter. This does change the
function’s signature and call-site use. However, the advantage of reusing an
existing name is that it is immediately clear what the intent and behaviour are
supposed to be. We are not trying to invent a new name for an existing operation
as that would require the user to learn an alternate name for every operations
which already exists.</p>
   <p>If we used the same name, but placed it inside a suitable namespace, then we
will have to rely on either namespace qualifiers (e.g., simd_permutes::stride)
to identify the correct function to call, or overloading:</p>
<pre class="language-cpp highlight"><c- k>using</c-> <c- k>namespace</c-> <c- nn>simd_permutes</c-><c- p>;</c->

<c- k>auto</c-> <c- n>r0</c-> <c- o>=</c-> <c- n>stride</c-><c- o>&lt;</c-><c- mi>2</c-><c- o>></c-><c- p>(</c-><c- n>s</c-><c- p>);</c-> <c- c1>// Call the stride operation on a simd.</c->

<c- k>auto</c-> <c- n>r1</c-> <c- o>=</c-> <c- n>stride</c-><c- p>(</c-><c- n>c</c-><c- p>,</c-> <c- mi>2</c-><c- p>);</c-> <c- c1>// Call ranges::stride. This might even convert a simd into a range</c-></pre>
   <p>For now we will assume that the <code class="highlight"><c- n>simd</c-></code> version of such a function will be named to
match the existing C++ name, but use overloading to differentiate it. Note that
we could make the function signature more similar to what exists already if we
used a <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>integral_constant</c-></code> as a parameter, instead of using a template
parameter, but this leads to verbose call sites. We discuss this option further
later in this proposal, but for now use a template parameter to give a concise
call site.</p>
   <p>In the existing proposal we have a mixture of naming conventions. For example:</p>
<pre class="highlight"><c- n>permute</c->
<c- n>compress</c->
<c- n>expand</c->
<c- n>simd_select</c->
<c- n>simd_cat</c->
<c- n>simd_split</c-></pre>
   <p>Clearly we need to agree on a common naming convention. Most recently <a data-link-type="biblio" href="#biblio-p1928r8" title="std::simd - Merge data-parallel types from the Parallelism TS 2">[P1928R8]</a> is using <code class="highlight"> <c- n>simd_</c-></code> prefix on functions, but it may be more
appropriate to provide namespaces. This topic will be discussed further in a
separate paper. Until that is resolved, this proposal’s main intent is to
discuss the ideas of creating common functions, with their naming to be decided
later.</p>
   <h3 class="heading settled" data-level="3.1" id="named_functions_overview"><span class="secno">3.1. </span><span class="content">Named permute functions overview</span><a class="self-link" href="#named_functions_overview"></a></h3>
   <p>Next we can consider what functions should be provided as part of the standard <code class="highlight"><c- n>simd</c-></code> permute package. We should provide functions which are sufficiently common</p>
   <p>and obvious that they will get wide-spread use. However, we should also avoid
the temptation of providing functions which map onto specific native hardware
implementations, unless the functions are truly useful on all targets. It isn’t
appropriate to expose functions which force a degree of target-specifity in a
portable library. The list of suggested functions below takes as its inspiration
suggestions from <a data-link-type="biblio" href="#biblio-p2664r6" title="Proposal to extend std::simd with permutation API">[P2664R6]</a>, <a data-link-type="biblio" href="#biblio-p2638r0" title="Intel&apos;s response to P1915R0 for std::simd parallelism in TS 2">[P2638R0]</a>, existing names from <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>views</c-></code>, and the names of generator functions we use in Intel’s
software products. Note that all of these functions will apply to either <code class="highlight"><c- n>simd</c-></code> or <code class="highlight"><c- n>simd_mask</c-></code>, since they map onto the underlying <code class="highlight"><c- n>permute</c-></code> functions which
also work on either of those types.</p>
   <table>
    <thead>
     <tr>
      <th class="tg-0pky">Function
      <th class="tg-0pky">Behaviour
    <tbody>
     <tr>
      <td class="tg-0pky"><code class="highlight"><c- n>take</c-><c- o>&lt;</c-><c- b>int</c-><c- o>></c-><c- p>(</c-><c- n>simd</c-><c- p>)</c-></code>
      <td class="tg-0pky">Return a new <code class="highlight"><c- n>simd</c-></code> containing the first N values. Replaces <code class="highlight"><c- n>resize</c-></code> where the output must be smaller (i.e., a shrink). Can trap incorrect resizing (e.g., to something bigger).
     <tr>
      <td class="tg-0pky"><code class="highlight"><c- n>grow</c-><c- o>&lt;</c-><c- b>int</c-><c- o>></c-><c- p>(</c-><c- n>simd</c-><c- p>,</c-> <c- n>value</c-><c- o>=</c-><c- p>{})</c-></code>
      <td class="tg-0pky">Return a new <code class="highlight"><c- n>simd</c-></code> which is bigger than the original value by new elements with the given value, which defaults to value initialised. Replaces <code class="highlight"><c- n>resize</c-></code> where the new size is bigger than the original.
     <tr>
      <td class="tg-0pky"><code class="highlight"><c- n>stride</c-><c- o>&lt;</c-><c- b>int</c-> <c- n>N</c-><c- o>></c-><c- p>(</c-><c- n>simd</c-><c- p>)</c-></code>
      <td class="tg-0pky">Return a new <code class="highlight"><c- n>simd</c-></code> which contains every N’th element of the input.
     <tr>
      <td class="tg-0pky"><code class="highlight"><c- n>chunk</c-><c- o>&lt;</c-><c- b>int</c-><c- o>></c-><c- p>(</c-><c- n>simd</c-><c- p>)</c-></code>
      <td class="tg-0pky">Existing <code class="highlight"><c- n>simd</c-><c- o>::</c-><c- n>split</c-></code> renamed/moved.
     <tr>
      <td class="tg-0pky"><code class="highlight"><c- n>reverse</c-><c- p>(</c-><c- n>simd</c-><c- p>)</c-></code>
      <td class="tg-0pky">Return a new <code class="highlight"><c- n>simd</c-></code> of the same size with its elements in reverse order.
     <tr>
      <td class="tg-0pky"><code class="highlight"><c- n>repeat_all</c-><c- o>&lt;</c-><c- b>int</c-><c- o>></c-><c- p>(</c-><c- n>simd</c-><c- p>)</c-></code>
      <td class="tg-0pky">Create a new <code class="highlight"><c- n>simd</c-></code> which is N copies of the original (e.g., <code class="highlight"><c- n>repeat_all</c-><c- o>&lt;</c-><c- mi>3</c-><c- o>></c-><c- p>([</c-><c- n>a</c-> <c- n>b</c-><c- p>])</c-></code> is <code class="highlight"><c- p>[</c-><c- n>a</c-> <c- n>b</c-> <c- n>a</c-> <c- n>b</c-> <c- n>a</c-> <c- n>b</c-><c- p>]</c-></code>)
     <tr>
      <td class="tg-0pky"><code class="highlight"><c- n>repeat_each</c-><c- o>&lt;</c-><c- b>int</c-><c- o>></c-><c- p>(</c-><c- n>simd</c-><c- p>)</c-></code>
      <td class="tg-0pky">Create a new <code class="highlight"><c- n>simd</c-></code> in which every element repeats N times (e.g., <code class="highlight"><c- n>repeat_each</c-><c- o>&lt;</c-><c- mi>3</c-><c- o>></c-><c- p>([</c-><c- n>a</c-> <c- n>b</c-><c- p>])</c-></code> is <code class="highlight"><c- p>[</c-><c- n>a</c-> <c- n>a</c-> <c- n>a</c-> <c- n>b</c-> <c- n>b</c-> <c- n>b</c-><c- p>]</c-></code>)
     <tr>
      <td class="tg-0pky"><code class="highlight"><c- n>transpose</c-><c- o>&lt;</c-><c- n>ROWS</c-><c- p>,</c-><c- n>COLS</c-><c- o>></c-><c- p>(</c-><c- n>simd</c-><c- p>)</c-></code>
      <td class="tg-0pky">Treat the <code class="highlight"><c- n>simd</c-></code> as a row-major matrix with the given number of rows and columns and returns its transpose (i.e., in column major)
     <tr>
      <td class="tg-0pky"><code class="highlight"><c- n>zip</c-><c- p>(</c-><c- n>simd</c-><c- p>...)</c-></code>
      <td class="tg-0pky">(aka interleave?) Generate a new <code class="highlight"><c- n>simd</c-></code> which interleaves or zips corresponding element together. <code class="highlight"><c- n>zip</c-><c- p>([</c-><c- n>a</c-> <c- n>b</c-> <c- n>c</c-><c- p>],</c-> <c- p>[</c-><c- mi>0</c-> <c- mi>1</c-> <c- mi>2</c-><c- p>])</c-></code> returns <code class="highlight"><c- p>[</c-><c- n>a</c-> <c- mi>0</c-> <c- n>b</c-> <c- mi>1</c-> <c- n>c</c-> <c- mi>2</c-><c- p>]</c-></code>. Useful for working with matrix-like values (e.g., signal processing). 
     <tr>
      <td class="tg-0pky"><code class="highlight"><c- n>unzip</c-><c- o>&lt;</c-><c- n>N</c-><c- o>></c-><c- p>(</c-><c- n>simd</c-><c- p>...)</c-></code>
      <td class="tg-0pky">(aka deinterleave?) Generate a new <code class="highlight"><c- n>simd</c-></code> which deinterleaves the input. <code class="highlight"><c- n>unzip</c-><c- o>&lt;</c-><c- mi>2</c-><c- o>></c-><c- p>([</c-><c- n>a</c-> <c- mi>0</c-> <c- n>b</c-> <c- mi>1</c-> <c- n>c</c-> <c- mi>2</c-><c- p>])</c-></code> gives <code class="highlight"><c- n>make_tuple</c-><c- p>([</c-><c- n>a</c-> <c- n>b</c-> <c- n>c</c-><c- p>],</c-> <c- p>[</c-><c- mi>0</c-> <c- mi>1</c-> <c- mi>2</c-><c- p>])</c-></code>. Useful for working with matrix-like values (e.g., signal processing). 
     <tr>
      <td class="tg-0pky"><code class="highlight"><c- n>cat</c-><c- p>(</c-><c- n>simd</c-><c- p>...)</c-></code>
      <td class="tg-0pky">Renamed version of <code class="highlight"><c- n>simd_cat</c-></code>. Should it be called <code class="highlight"><c- n>join</c-></code>? Should it take a tuple of simd values instead?
     <tr>
      <td class="tg-0pky"><code class="highlight"><c- n>extract</c-><c- o>&lt;</c-><c- n>N</c-><c- p>,</c-> <c- n>M</c-><c- o>></c-><c- p>(</c-><c- n>simd</c-><c- p>)</c-></code>
      <td class="tg-0pky">Extract a <code class="highlight"><c- n>simd</c-></code> which contains the elements in the range [N..M). Equivalent to <code class="highlight"><c- n>drop</c-><c- o>&lt;</c-><c- n>N</c-><c- o>></c-> <c- o>|</c-> <c- n>take</c-><c- o>&lt;</c-><c- n>M</c-><c- o>-</c-><c- n>N</c-><c- o>></c-></code>. 
     <tr>
      <td class="tg-0pky"><code class="highlight"><c- n>rotate</c-><c- o>&lt;</c-><c- n>MIDDLE</c-><c- o>></c-><c- p>(</c-><c- n>simd</c-><c- p>)</c-></code>
      <td class="tg-0pky">Perform a left rotation on the elements of the <code class="highlight"><c- n>simd</c-></code> such that the element at the MIDDLE index becomes the first element. This matches the behaviour of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>rotate</c-></code> but not <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>rotl</c-></code>/<code class="highlight"><c- nl>std</c-><c- p>:</c-><c- n>rotr</c-></code> which also allows negative rotations or rotations larger than the container (i.e., mod container size)
     <tr>
      <td class="tg-0pky"><code class="highlight"><c- n>shift_left</c-><c- o>&lt;</c-><c- n>N</c-><c- o>></c-><c- p>(</c-><c- n>simd</c-><c- p>)</c-></code>/<code class="highlight"><c- n>shift_right</c-><c- o>&lt;</c-><c- n>N</c-><c- o>></c-><c- p>(</c-><c- n>simd</c-><c- p>)</c-></code>
      <td class="tg-0pky">return a <code class="highlight"><c- n>simd</c-></code> of the same size as the input but with the elements shifted left or right and value-initialised elements inserted. These would behave like <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>range</c-><c- o>::</c-><c- n>shift_left</c-><c- o>/</c-><c- n>right</c-></code>. The disadvantage of these is that shifting a mask using this function would be the opposite of what might be expected. A <code class="highlight"><c- n>simd_mask</c-></code> is similar to a plain set of bits, and shifting a set of bits left would move them towards the MSB. In contrast, applying <code class="highlight"><c- n>shift_left</c-></code> to a <code class="highlight"><c- n>simd_mask</c-></code> would move the bits towards the LSB. Maybe this shouldn’t matter, because a <code class="highlight"><c- n>simd_mask</c-></code> is not an integer which can be shifted, but conceptually it might be confusing. Also, should value initialised elements be shifted in, or should the new values be left valid but undefined?
     <tr>
      <td class="tg-0pky"><code class="highlight"><c- n>align</c-><c- o>&lt;</c-><c- n>N</c-><c- o>></c-><c- p>(</c-><c- n>simd</c-> <c- n>a</c-><c- p>,</c-> <c- n>simd</c-> <c- n>b</c-><c- p>)</c-></code>
      <td class="tg-0pky">Given two <code class="highlight"><c- n>simd</c-></code> objects perform an extraction of a <code class="highlight"><c- n>simd</c-></code> from <code class="highlight"><c- n>cat</c-><c- p>(</c-><c- n>a</c-><c- p>,</c-> <c- n>b</c-><c- p>)</c-></code>. Used to implement unaligned operations on targets where aligned operations are either inefficient or non-existant.
   </table>
   <h3 class="heading settled" data-level="3.2" id="design_function_or_object"><span class="secno">3.2. </span><span class="content">Design option - functions or function objects</span><a class="self-link" href="#design_function_or_object"></a></h3>
   <p>Although the paper has described a collection of "functions" to perform named permutes, we could  make these all function objects which then gives us some more freedom in how they can be used. For example, in Intel’s example implementation of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> we make them function objects which derive from a named permute base-class, which then allows us to compose them into pipelines of permute transformations:</p>
<pre class="language-cpp highlight"><c- k>auto</c-> <c- n>demo1</c-><c- p>(</c-><c- k>const</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>>&amp;</c-> <c- n>x</c-><c- p>)</c-> <c- p>{</c->
    <c- k>return</c-> <c- n>x</c-> <c- o>|</c-> <c- n>rotate</c-><c- o>&lt;</c-><c- mi>5</c-><c- o>></c-> <c- o>|</c-> <c- n>reverse</c-><c- p>;</c->
<c- p>}</c->

<c- k>auto</c-> <c- n>demo2</c-><c- p>(</c-><c- k>const</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>16</c-><c- o>>&amp;</c-> <c- n>x</c-><c- p>)</c-> <c- p>{</c->
    <c- k>return</c-> <c- n>x</c-> <c- o>|</c-> <c- n>transpose</c-><c- o>&lt;</c-><c- mi>4</c-><c- o>></c-><c- p>;</c->
<c- p>}</c->

<c- k>auto</c-> <c- n>even</c-><c- p>(</c-><c- k>const</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>>&amp;</c-> <c- n>x</c-><c- p>)</c-> <c- p>{</c->
    <c- k>return</c-> <c- n>x</c-> <c- o>|</c-> <c- n>stride</c-><c- o>&lt;</c-><c- mi>2</c-><c- o>></c-><c- p>;</c->
<c- p>}</c->

<c- k>auto</c-> <c- n>odd</c-><c- p>(</c-><c- k>const</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>>&amp;</c-> <c- n>x</c-><c- p>)</c-> <c- p>{</c->
    <c- k>return</c-> <c- n>x</c-> <c- o>|</c-> <c- n>drop</c-><c- o>&lt;</c-><c- mi>1</c-><c- o>></c-> <c- o>|</c-> <c- n>stride</c-><c- o>&lt;</c-><c- mi>2</c-><c- o>></c-><c- p>;</c->
<c- p>}</c->

<c- k>auto</c-> <c- n>dupEven</c-><c- p>(</c-><c- k>const</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>>&amp;</c-> <c- n>x</c-><c- p>)</c-> <c- p>{</c->
    <c- k>return</c-> <c- n>x</c-> <c- o>|</c-> <c- n>stride</c-><c- o>&lt;</c-><c- mi>2</c-><c- o>></c-> <c- o>|</c-> <c- n>repeat_each</c-><c- o>&lt;</c-><c- mi>2</c-><c- o>></c-><c- p>;</c->
<c- p>}</c->

<c- k>auto</c-> <c- n>dupOdd</c-><c- p>(</c-><c- k>const</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>>&amp;</c-> <c- n>x</c-><c- p>)</c-> <c- p>{</c->
    <c- k>return</c-> <c- n>x</c-> <c- o>|</c-> <c- n>drop</c-><c- o>&lt;</c-><c- mi>1</c-><c- o>></c-> <c- o>|</c-> <c- n>stride</c-><c- o>&lt;</c-><c- mi>2</c-><c- o>></c-> <c- o>|</c-> <c- n>repeat_each</c-><c- o>&lt;</c-><c- mi>2</c-><c- o>></c-><c- p>;</c->
<c- p>}</c-></pre>
   <p>We are not currently proposing that such pipelines should be formalised into the
proposal, but we do ask for direction in deciding whether the suggested named
permute functions should be functions or function objects.</p>
   <h3 class="heading settled" data-level="3.3" id="design_function_constant_parameters"><span class="secno">3.3. </span><span class="content">Design option - constant parameters</span><a class="self-link" href="#design_function_constant_parameters"></a></h3>
   <p>There is a discrepancy between the signatures of function like <code class="highlight"><c- n>views</c-><c- o>::</c-><c- n>ranges</c-><c- o>::</c-><c- n>take</c-><c- p>(</c-><c- n>e</c-><c- p>,</c-> <c- n>N</c-><c- p>)</c-></code> and <code class="highlight"><c- n>simd_permute</c-><c- o>::</c-><c- n>take</c-><c- o>&lt;</c-><c- n>N</c-><c- o>></c-><c- p>(</c-><c- n>s</c-><c- p>)</c-></code>. Most <code class="highlight"><c- n>simd</c-></code> permute
functions operate on statically sized <code class="highlight"><c- n>simd</c-></code> values with known element. It is
therefore not possible to permute with dynamic sizing. Consequently the permute
functions take constant template parameters, rather than dynamic parameters as
with the <code class="highlight"><c- n>views</c-><c- o>::</c-><c- n>ranges</c-></code> functions.</p>
   <p>In order to more closely match the function signature from functions in <code class="highlight"><c- n>views</c-><c- o>::</c-><c- n>ranges</c-></code>, we could modify the signature of <code class="highlight"><c- n>simd_permute</c-><c- o>::</c-><c- n>take</c-></code> to be
more similar:</p>
<pre class="highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>_T</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>_Abi</c-><c- p>,</c-> <c- b>int</c-> <c- n>_N</c-><c- o>></c->
<c- k>constexpr</c-> <c- k>auto</c-> <c- n>take</c-><c- p>(</c-><c- k>const</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>_T</c-><c- p>,</c-> <c- n>_Abi</c-><c- o>>&amp;</c-> <c- n>s</c-><c- p>,</c->
                    <c- n>std</c-><c- o>::</c-><c- n>integral_constant</c-><c- o>&lt;</c-><c- b>int</c-><c- p>,</c-> <c- n>_N</c-><c- o>></c-><c- p>);</c->


<c- k>auto</c-> <c- n>first3</c-> <c- o>=</c-> <c- n>take</c-><c- p>(</c-><c- n>s</c-><c- p>,</c-> <c- n>std</c-><c- o>::</c-><c- n>integral_constant</c-><c- o>&lt;</c-><c- b>int</c-><c- p>,</c-> <c- mi>3</c-><c- o>></c-><c- p>{});</c-></pre>
   <p>This gives a more familiar call site, but is rather verbose for the common case.</p>
   <h2 class="heading settled" data-level="4" id="implementation_experience"><span class="secno">4. </span><span class="content">Implementation Experience</span><a class="self-link" href="#implementation_experience"></a></h2>
   <p>One of the drivers for this paper was the observation that in software which
used Intel’s example implementation of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code>, different developers were
inventing their own versions of common permutes, often in slightly different
ways. We wanted to guide different users to use a common language in the sorts
of permutes that they should be using, and to avoid unnecessary duplication of
effort in building what are sometimes quite sophisticated features from the
underlying permute functions. We do still encounter permute functions which are
unique in their behaviour, and don’t deserve to be pulled out into a common
library, and we have disregarded those functions in this proposal.</p>
   <h2 class="heading settled" data-level="5" id="conclusion"><span class="secno">5. </span><span class="content">Conclusion</span><a class="self-link" href="#conclusion"></a></h2>
   <p>In this paper we have set out an argument for providing a set of common
permutation functions which have wide-spread use across different types of
software which will use <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code>. There are still some open questions about
naming conventions, but our main goal with this paper is to set out a proposed
direction for what sorts of functions should be commonly provide, and to get
feedback from the wider community.</p>
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  <h2 class="no-num no-ref heading settled" id="references"><span class="content">References</span><a class="self-link" href="#references"></a></h2>
  <h3 class="no-num no-ref heading settled" id="informative"><span class="content">Informative References</span><a class="self-link" href="#informative"></a></h3>
  <dl>
   <dt id="biblio-highway">[Highway]
   <dd>Google. <a href="https://github.com/google/highway/"><cite>Google Highway</cite></a>. URL: <a href="https://github.com/google/highway/">https://github.com/google/highway/</a>
   <dt id="biblio-p0918r1">[P0918R1]
   <dd>Tim Shen. <a href="https://wg21.link/p0918r1"><cite>More simd&lt;> Operations</cite></a>. 29 March 2018. URL: <a href="https://wg21.link/p0918r1">https://wg21.link/p0918r1</a>
   <dt id="biblio-p1928r0">[P1928R0]
   <dd>Matthias Kretz. <a href="https://wg21.link/p1928r0"><cite>Merge data-parallel types from the Parallelism TS 2</cite></a>. 7 October 2019. URL: <a href="https://wg21.link/p1928r0">https://wg21.link/p1928r0</a>
   <dt id="biblio-p1928r8">[P1928R8]
   <dd>Matthias Kretz. <a href="https://wg21.link/p1928r8"><cite>std::simd - Merge data-parallel types from the Parallelism TS 2</cite></a>. 9 November 2023. URL: <a href="https://wg21.link/p1928r8">https://wg21.link/p1928r8</a>
   <dt id="biblio-p2638r0">[P2638R0]
   <dd>Daniel Towner. <a href="https://wg21.link/p2638r0"><cite>Intel's response to P1915R0 for std::simd parallelism in TS 2</cite></a>. 22 September 2022. URL: <a href="https://wg21.link/p2638r0">https://wg21.link/p2638r0</a>
   <dt id="biblio-p2664r6">[P2664R6]
   <dd>Daniel Towner, Ruslan Arutyunyan. <a href="https://wg21.link/p2664r6"><cite>Proposal to extend std::simd with permutation API</cite></a>. 16 January 2024. URL: <a href="https://wg21.link/p2664r6">https://wg21.link/p2664r6</a>
   <dt id="biblio-p2929r0">[P2929R0]
   <dd>Daniel Towner, Ruslan Arutyunyan. <a href="https://wg21.link/p2929r0"><cite>simd_invoke</cite></a>. 19 July 2023. URL: <a href="https://wg21.link/p2929r0">https://wg21.link/p2929r0</a>
  </dl>