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  <title>P2929R0: Proposal to add simd_invoke to 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,
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 *        .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)
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 *   - .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.
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 *   - js-added ToC jump links (see fixup.js)
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 ******************************************************************************/

/* color variables included separately for reliability */

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

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

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

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

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

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

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/******************************************************************************/
/*                            Paragraphs and Lists                            */
/******************************************************************************/

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	/* Put nice boxes around each algorithm. */
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/** Terminology Markup ********************************************************/


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

/** Terminology Markup ********************************************************/
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	a > i { /* Instance of term */
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	dt dfn code, code.idl {
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	dfn var {
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/** Change Marking ************************************************************/

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		background: transparent;
		background: var(--del-bg);
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		color: #006100;
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	/* for amendments (candidate/proposed changes) */

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/** Miscellaneous improvements to inline formatting ***************************/

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/******************************************************************************/
/*                                    Code                                    */
/******************************************************************************/

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	pre {
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/** Inline Code fragments *****************************************************/

	/* Do something nice. */

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

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

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/******************************************************************************/
/*                                    Images                                  */
/******************************************************************************/

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

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

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	.note::before, .note > .marker,
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	details.note[open] > summary {
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/** Assertion Box *************************************************************/
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		background: #EEE;
		background: var(--assertion-bg);
		color: black;
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/** Advisement Box ************************************************************/
	/*  for attention-grabbing normative statements */

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		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;
    }
    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 */
    blockquote c-[f] { color: inherit; } /* Name.Tag */
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    blockquote c-[m] { color: inherit; } /* Literal.Number */
    blockquote c-[n] { color: inherit; } /* Name */
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    blockquote c-[s] { color: inherit; } /* Literal.String */
    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 */
    blockquote c-[ne] { color: inherit; } /* Name.Exception */
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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/P2929R0" 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">P2929R0<br>Proposal to add simd_invoke to 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="2023-07-14">2023-07-14</time></span></h2>
   <div data-fill-with="spec-metadata">
    <dl>
     <dt>This version:
     <dd><a class="u-url" href="http://wg21.link/P2929R0">http://wg21.link/P2929R0</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 JTC1/SC22/WG21 14882: Programming Language — C++
    </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>Proposal to extend <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> with a method of allowing a lambda to be invoked on smaller pieces of a SIMD value in order to make interaction with intrinsics easier.</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>
    <li>
     <a href="#simd_invoke_description"><span class="secno">3</span> <span class="content"><code class="highlight"><c- n>simd_invoke</c-></code> description</span></a>
     <ol class="toc">
      <li>
       <a href="#simd_indexing"><span class="secno">3.1</span> <span class="content">Using indexed Callable invocations</span></a>
       <ol class="toc">
        <li><a href="#probe_index"><span class="secno">3.1.1</span> <span class="content">Design option - probing the index capabilities</span></a>
       </ol>
      <li><a href="#simd_invoke_rules"><span class="secno">3.2</span> <span class="content">Considerations in using <code class="highlight"><c- n>simd_invoke</c-></code></span></a>
     </ol>
    <li>
     <a href="#wording"><span class="secno">4</span> <span class="content">Wording</span></a>
     <ol class="toc">
      <li><a href="#wording_simd_invoke"><span class="secno">4.1</span> <span class="content">Add new section [<strong>simd.invoke</strong>]</span></a>
     </ol>
    <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 introduced data-parallel types to the C++ Extensions for
Parallelism TS <a data-link-type="biblio" href="#biblio-p1928r3" title="Merge data-parallel types from the Parallelism TS 2">[P1928R3]</a>. That paper, and several ancillary papers, do an
excellent job of setting out the main features of an extension to C++ which
allows generic data parallel programming on arbitrary targets. However, it is
inevitable that the programmer will want to make some use of target-specific
intrinsics in order to unlock some of the more unusual features of those
specific platforms. This requires that the programmer is able to allow a SIMD
value to be used in a call to a target intrinsic, and that the result of the
intrinsic call can be used to generate a new SIMD value. This is already
permitted in <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> for SIMD values which fit into a native
register, but it is harder to achieve when the SIMD value spans multiple registers.</p>
   <p>In this paper we will propose a function called <code class="highlight"><c- n>simd_invoke</c-></code> which makes it
easy to repeatedly apply a target specific intrinsic  to native-sized pieces of
large SIMD value arguments, and to marshall their individual results back into a
SIMD result.</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>Although <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> has been carefully crafted to include APIs which access all
of the common or desirable features of SIMD instruction sets, it is inevitable
that the user will sometimes want to take advantage of instructions which are
specific to a particular platform. For example, a DSP target may have a special
type of accumulator instruction, or algorithm specific instruction (e.g., AES
crypto). Clearly, calling these intrinsics  results in non-portable code, but the
increase in hardware-accelerated performance on a given target could be a worthwhile
trade-off.</p>
   <p><code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> already includes some provision for interacting with target-specific
data types by providing the following (<a data-link-type="biblio" href="#biblio-p1928r4" title="std::simd - Merge data-parallel types from the Parallelism TS 2">[P1928R4]</a> 28.9.6.1-4):</p>
<pre class="language-cpp highlight"><c- k>constexpr</c-> <c- k>explicit</c-> <c- k>operator</c-> <c- n>implementation</c-><c- o>-</c-><c- n>defined</c-><c- p>()</c-> <c- k>const</c-><c- p>;</c->
<c- k>constexpr</c-> <c- k>explicit</c-> <c- n>basic_simd</c-><c- p>(</c-><c- k>const</c-> <c- n>implementation</c-><c- o>-</c-><c- n>defined</c-><c- o>&amp;</c-> <c- n>init</c-><c- p>);</c-></pre>
   <p>These allow a SIMD value to be converted into a target specific type which is
used to call a compiler-intrinsic. The result is then converted back into the
equivalent SIMD type:</p>
<pre class="language-cpp highlight"><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c->
<c- n>addsub</c-><c- p>(</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-> <c- n>a</c-><c- p>,</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-> <c- n>b</c-><c- p>)</c-> <c- p>{</c->
  <c- k>return</c-> <c- k>static_cast</c-><c- o>&lt;</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>>></c-><c- p>(</c-><c- n>_mm256_addsub_ps</c-><c- p>(</c-><c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>a</c-><c- p>),</c-> <c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>b</c-><c- p>)));</c->
<c- p>}</c-></pre>
   <p>In this example the inputs, which are native register-sized SIMD values, are
explicitly converted into their target-specific typed values. Those target
specific types are used to call the intrinsics, and then the target specific
return value is converted back into the closest SIMD representation.</p>
   <p>This example is straightforward, since the SIMD values are explicitly the
correct native size. For targets which supported several different register
sizes (e.g., some variants of AVX support 128-, 256- and 512-bit registers) the
code can use a <code class="highlight"><c- k>constexpr</c-></code> conditional to select which size to use:</p>
<pre class="language-cpp highlight"><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c->
<c- n>addsub</c-><c- p>(</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-> <c- n>a</c-><c- p>,</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-> <c- n>b</c-><c- p>)</c-> <c- p>{</c->
  <c- k>if</c-> <c- k>constexpr</c-> <c- p>(</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>>::</c-><c- n>size</c-><c- p>()</c-> <c- o>==</c-> <c- mi>4</c-><c- p>)</c->
    <c- k>return</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-><c- p>(</c-><c- n>_mm_addsub_ps</c-><c- p>(</c-><c- k>static_cast</c-><c- o>&lt;</c-><c- kr>__m128</c-><c- o>></c-><c- p>(</c-><c- n>a</c-><c- p>),</c-> <c- k>static_cast</c-><c- o>&lt;</c-><c- kr>__m128</c-><c- o>></c-><c- p>(</c-><c- n>b</c-><c- p>)));</c->
  <c- k>else</c-> <c- k>if</c-> <c- k>constexpr</c-> <c- p>(</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>>::</c-><c- n>size</c-><c- p>()</c-> <c- o>==</c-> <c- mi>8</c-><c- p>)</c->
    <c- k>return</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-><c- p>(</c-><c- n>_mm256_addsub_ps</c-><c- p>(</c-><c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>a</c-><c- p>),</c-> <c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>b</c-><c- p>)));</c->
  <c- k>else</c->
    <c- n>error</c-><c- p>();</c-> <c- c1>// Invalid native register</c->
<c- p>}</c-></pre>
   <p>Things become more tricky when dealing with SIMD values which are larger than
their intrinsic types. Such types cannot be converted into a type which can be
used to call an intrinsic. Instead, the big SIMD must be broken down into small
pieces which may be used to call the intrinsic, and then the results of that
glued back together. Here is one way to do that for a SIMD value which is twice
as big as a native register:</p>
<pre class="language-cpp highlight"><c- c1>// Assumes AVX is in use, and that each native register is therefore 8xfloat</c->
<c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>16</c-><c- o>></c->
<c- n>addsub</c-><c- p>(</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>16</c-><c- o>></c-> <c- n>a</c-><c- p>,</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>16</c-><c- o>></c-> <c- n>b</c-><c- p>)</c-> <c- p>{</c->

  <c- c1>// Get register-sized pieces</c->
  <c- k>auto</c-> <c- p>[</c-><c- n>lowA</c-><c- p>,</c-> <c- n>highA</c-><c- p>]</c-> <c- o>=</c-> <c- n>simd_split</c-><c- o>&lt;</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>>></c-><c- p>(</c-><c- n>a</c-><c- p>);</c->
  <c- k>auto</c-> <c- p>[</c-><c- n>lowB</c-><c- p>,</c-> <c- n>highB</c-><c- p>]</c-> <c- o>=</c-> <c- n>simd_split</c-><c- o>&lt;</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>>></c-><c- p>(</c-><c- n>b</c-><c- p>);</c->

  <c- c1>// Call the intrinsic on each pair of pieces.</c->
  <c- k>auto</c-> <c- n>resultLow</c-> <c- o>=</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-><c- p>(</c-><c- n>_mm256_addsub_ps</c-><c- p>(</c-><c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>lowA</c-><c- p>),</c->
                                                <c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>lowB</c-><c- p>)));</c->
  <c- k>auto</c-> <c- n>resultHigh</c-> <c- o>=</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-><c- p>(</c-><c- n>_mm256_addsub_ps</c-><c- p>(</c-><c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>highA</c-><c- p>),</c->
                                                 <c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>highB</c-><c- p>)));</c->

  <c- c1>// Glue the individual results back together.</c->
  <c- k>return</c-> <c- n>simd_concat</c-><c- p>(</c-><c- n>resultLow</c-><c- p>,</c-> <c- n>resultHigh</c-><c- p>);</c->
<c- p>}</c-></pre>
   <p>This is now getting verbose, and it only handles SIMD value inputs which are
twice the size of a register value. To use the intrinsic with larger SIMD
values, or SIMD value which don’t map into native register-sized pieces, more
work is needed (e.g., if <code class="highlight"><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>20</c-><c- o>></c-></code> was used then the pieces would be
of size 8, 8, and 4 respectively, and this would require a suitable call to the
intrinsic of the appropriate size).</p>
   <p>The boiler-plate code needed to handle this is technical straight-forward, but
verbose. A completely generic solution which could handle arbitrary SIMD value
size would also requires additional mechanisms like immediately invoked lambdas
or index sequences to be used too. Rather than requiring every user of <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>simd</c-></code> to have to write their own intrinsic call handlers, we can abstract
the general mechanism into something that is easily reused. In particular we
want to break a set of SIMD value arguments into smaller pieces, call an
intrinsic on each, and then glue the results of those intrinsic calls back
together. We achieve this though a proposed function called <code class="highlight"><c- n>simd_invoke</c-></code> which
we will describe in the remainder of this paper.</p>
   <h2 class="heading settled" data-level="3" id="simd_invoke_description"><span class="secno">3. </span><span class="content"><code class="highlight"><c- n>simd_invoke</c-></code> description</span><a class="self-link" href="#simd_invoke_description"></a></h2>
   <p>The <code class="highlight"><c- n>simd_invoke</c-></code> function is rather like <code class="highlight"><c- n>std</c-><c- o>::</c-><c- n>invoke</c-></code> in that it takes a
callable object and a set of arguments. It’s basic signature is as follows:</p>
<pre class="language-cpp highlight"><c- k>template</c-><c- o>&lt;</c-><c- k>typename</c-> <c- nc>Fn</c-><c- p>,</c-> <c- k>typename</c-><c- p>...</c-> <c- n>Args</c-><c- o>></c->
<c- k>auto</c-> <c- n>simd_invoke</c-><c- p>(</c-><c- n>Fn</c-><c- o>&amp;&amp;</c-> <c- n>fn</c-><c- p>,</c-> <c- n>Args</c-><c- o>&amp;&amp;</c-><c- p>...);</c-></pre>
   <p>The <code class="highlight"><c- n>fn</c-></code> parameter should be a callable that accepts some arguments which can be
used to invoke an intrinsic from a native register. For example, to continue our example from above,
we could create a utility function which calls the <code class="highlight"><c- n>_mm256_addsub_ps</c-></code> intrinsic from native-sized SIMD values:</p>
<pre class="language-cpp highlight"><c- kr>inline</c-> <c- k>auto</c-> <c- n>native_addsub</c-><c- p>(</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-> <c- n>lhs</c-><c- p>,</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-> <c- n>rhs</c-><c- p>)</c-> <c- p>{</c->
    <c- k>auto</c-> <c- n>nativeLhs</c-> <c- o>=</c-> <c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>lhs</c-><c- p>);</c->
    <c- k>auto</c-> <c- n>nativeRhs</c-> <c- o>=</c-> <c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>rhs</c-><c- p>);</c->

    <c- k>return</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-><c- p>(</c-><c- n>_mm256_addsub_ps</c-><c- p>(</c-><c- n>nativeLhs</c-><c- p>,</c-> <c- n>nativeRhs</c-><c- p>));</c->
<c- p>}</c-></pre>
   <p>Given this wrapper for native-sized intrinsic calls, we can now use <code class="highlight"><c- n>simd_invoke</c-></code> to break down a large SIMD value into individual register-sized
calls:</p>
<pre class="language-cpp highlight"><c- k>auto</c-> <c- n>addsub</c-><c- p>(</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>32</c-><c- o>></c-> <c- n>x</c-><c- p>,</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>32</c-><c- o>></c-> <c- n>y</c-><c- p>)</c->
<c- p>{</c->
    <c- k>return</c-> <c- n>simd_invoke</c-><c- p>(</c-><c- n>native_addsub</c-><c- p>,</c-> <c- n>x</c-><c- p>,</c-> <c- n>y</c-><c- p>);</c->
<c- p>}</c-></pre>
   <p>The <code class="highlight"><c- n>simd_invoke</c-></code> function accepts any number of arguments and will break each
one down into native-sized pieces which are used to invoke the supplied
function, and then glue the results back together again on completion.</p>
   <p>Let’s look how the example from <a href="#background">§ 2 Background</a> looks like with <code class="highlight"><c- n>simd_invoke</c-></code> applied
using before-after table:</p>
   <table>
    <tbody>
     <tr>
      <th>Before
      <th>After
     <tr>
      <td>
<pre class="highlight"><c- k>auto</c-> <c- n>addsub</c-><c- p>(</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>16</c-><c- o>></c-> <c- n>a</c-><c- p>,</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>16</c-><c- o>></c-> <c- n>b</c-><c- p>)</c-> <c- p>{</c->

    <c- k>auto</c-> <c- p>[</c-><c- n>lowA</c-><c- p>,</c-> <c- n>highA</c-><c- p>]</c-> <c- o>=</c-> <c- n>simd_split</c-><c- o>&lt;</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>>></c-><c- p>(</c-><c- n>a</c-><c- p>);</c->
    <c- k>auto</c-> <c- p>[</c-><c- n>lowB</c-><c- p>,</c-> <c- n>highB</c-><c- p>]</c-> <c- o>=</c-> <c- n>simd_split</c-><c- o>&lt;</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>>></c-><c- p>(</c-><c- n>b</c-><c- p>);</c->

    <c- k>auto</c-> <c- n>resultLow</c-> <c- o>=</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-><c- p>(</c-><c- n>_mm256_addsub_ps</c-><c- p>(</c->
            <c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>lowA</c-><c- p>),</c->
            <c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>lowB</c-><c- p>)));</c->
    <c- k>auto</c-> <c- n>resultHigh</c-> <c- o>=</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-><c- p>(</c-><c- n>_mm256_addsub_ps</c-><c- p>(</c->
            <c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>highA</c-><c- p>),</c-> 
            <c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>highB</c-><c- p>)));</c->

    <c- k>return</c-> <c- n>simd_concat</c-><c- p>(</c-><c- n>resultLow</c-><c- p>,</c-> <c- n>resultHigh</c-><c- p>);</c->
<c- p>}</c-></pre>
      <td>
<pre class="highlight"><c- k>auto</c-> <c- n>addsub</c-><c- p>(</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>16</c-><c- o>></c-> <c- n>a</c-><c- p>,</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>16</c-><c- o>></c-> <c- n>b</c-><c- p>)</c->
<c- p>{</c->
    <c- k>auto</c-> <c- n>do_native</c-> <c- o>=</c-> <c- p>[](</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-> <c- n>lhs</c-><c- p>,</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-> <c- n>rhs</c-><c- p>)</c-> <c- p>{</c->
        <c- k>return</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- o>></c-><c- p>(</c-><c- n>_mm256_addsub_ps</c-><c- p>(</c->
            <c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>lhs</c-><c- p>),</c->
            <c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>rhs</c-><c- p>)));</c->
    <c- p>};</c->

    <c- k>return</c-> <c- n>simd_invoke</c-><c- p>(</c-><c- n>do_native</c-><c- p>,</c-> <c- n>x</c-><c- p>,</c-> <c- n>y</c-><c- p>);</c->
<c- p>}</c-></pre>
   </table>
   <p>By default the function will use the native size for the element type, with the
aim of calling the intrinsic with the largest permitted builtin type. However, <code class="highlight"><c- n>simd_invoke</c-></code> can also be explicitly given the size of block to use. For
example, the following code breaks down into pieces of size 4 instead (and also
supplies the callable as a local lambda, to make the function self-contained):</p>
<pre class="language-cpp highlight"><c- k>auto</c-> <c- n>addsub</c-><c- p>(</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>32</c-><c- o>></c-> <c- n>x</c-><c- p>,</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>32</c-><c- o>></c-> <c- n>y</c-><c- p>)</c->
<c- p>{</c->
    <c- k>auto</c-> <c- n>do_native</c-> <c- o>=</c-> <c- p>[](</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>4</c-><c- o>></c-> <c- n>lhs</c-><c- p>,</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>4</c-><c- o>></c-> <c- n>rhs</c-><c- p>)</c-> <c- p>{</c->
        <c- k>return</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>4</c-><c- o>></c-><c- p>(</c-><c- n>_mm_addsub_ps</c-><c- p>(</c-><c- k>static_cast</c-><c- o>&lt;</c-><c- kr>__m128</c-><c- o>></c-><c- p>(</c-><c- n>lhs</c-><c- p>),</c-> <c- k>static_cast</c-><c- o>&lt;</c-><c- kr>__m128</c-><c- o>></c-><c- p>(</c-><c- n>rhs</c-><c- p>)));</c->
    <c- p>};</c->

    <c- k>return</c-> <c- n>simd_invoke</c-><c- o>&lt;</c-><c- mi>4</c-><c- o>></c-><c- p>(</c-><c- n>do_native</c-><c- p>,</c-> <c- n>x</c-><c- p>,</c-> <c- n>y</c-><c- p>);</c->
<c- p>}</c-></pre>
   <p>Being able to define a different size is useful for two reasons:</p>
   <ol>
    <li data-md>
     <p>We may wish to process data in smaller input sizes than native size. For
 example, if the data needs to be upcast to a large element size for the
 operation, then it can be useful to choose a smaller block size to begin with
 so that the upcast data fills a native register. This could be more
 efficient than accepting native register sized data and then upcasting to
 several registers.</p>
    <li data-md>
     <p>If the element type of the arguments are different then the <code class="highlight"><c- n>simd_invoke</c-></code> function cannot determine the appropriate native size for itself. For
 example, the first argument might be a SIMD value containing float
 elements, and the second argument have <code class="highlight"><c- b>uint8_t</c-></code> elements. The number of
 native elements in each argument cannot be inferred, and the <code class="highlight"><c- n>simd_invoke</c-></code> must be told how many elements to use in each block.</p>
   </ol>
   <p>So far we have only considered what happens when <code class="highlight"><c- n>simd_invoke</c-></code> is given SIMD
value arguments which are multiples of some native register size, but as we saw
in our introduction, it might be useful to be able to call invoke on SIMD values
of arbitrary size. For example, suppose that the add/sub is being called on a
SIMD value with 19 elements. In that case on a target with a native size of 8
elements <code class="highlight"><c- n>simd_invoke</c-></code> would need to break the calls down into pieces of sizes
8, 8, and 3 respectively, and the callable would need to be able to handle SIMD
values of arbitrary size. The following example shows how this might work:</p>
<pre class="language-cpp highlight"><c- k>auto</c-> <c- n>addsub</c-><c- p>(</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>19</c-><c- o>></c-> <c- n>x</c-><c- p>,</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>19</c-><c- o>></c-> <c- n>y</c-><c- p>)</c->
<c- p>{</c->
    <c- c1>// Invoke the most appropriate intrinsic for the given simd types.</c->
    <c- k>auto</c-> <c- n>do_native</c-> <c- o>=</c-> 
      <c- p>[]</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- o>></c-><c- p>(</c-><c- n>basic_simd</c-><c- o>&lt;</c-><c- n>T</c-><c- p>,</c-> <c- n>ABI</c-><c- o>></c-> <c- n>lhs</c-><c- p>,</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>T</c-><c- p>,</c-> <c- n>ABI</c-><c- o>></c-> <c- n>rhs</c-><c- p>)</c-> <c- p>{</c->
        <c- k>constexpr</c-> <c- k>auto</c-> <c- n>size</c-> <c- o>=</c-> <c- n>basic_simd</c-><c- o>&lt;</c-><c- n>T</c-><c- p>,</c-> <c- n>ABI</c-><c- o>>::</c-><c- n>size</c-><c- p>;</c->
        <c- k>if</c-> <c- k>constexpr</c-> <c- p>(</c-><c- n>size</c-> <c- o>&lt;=</c-> <c- mi>4</c-><c- p>)</c->
            <c- k>return</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- n>size</c-><c- o>></c-><c- p>(</c-><c- n>_mm_addsub_ps</c-><c- p>(</c-><c- k>static_cast</c-><c- o>&lt;</c-><c- kr>__m128</c-><c- o>></c-><c- p>(</c-><c- n>lhs</c-><c- p>),</c->
                                                   <c- k>static_cast</c-><c- o>&lt;</c-><c- kr>__m128</c-><c- o>></c-><c- p>(</c-><c- n>rhs</c-><c- p>)));</c->
        <c- k>else</c->
            <c- k>return</c-> <c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- n>size</c-><c- o>></c-><c- p>(</c-><c- n>_mm256_addsub_ps</c-><c- p>(</c-><c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>lhs</c-><c- p>),</c->
                                                   <c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>rhs</c-><c- p>)));</c->
    <c- p>};</c->

    <c- k>return</c-> <c- n>simd_invoke</c-><c- p>(</c-><c- n>do_native</c-><c- p>,</c-> <c- n>x</c-><c- p>,</c-> <c- n>y</c-><c- p>);</c->
<c- p>}</c-></pre>
   <p>In this example the local lambda function can accept SIMD inputs of any size,
and will choose the most appropriate intrinsic to use. For example, given the
block of 3 tail elements the lambda utility will convert the 3 elements to an <code class="highlight"><c- kr>__m128</c-></code> register and call <code class="highlight"><c- n>_mm_addsub_ps</c-></code>. This lambda function can then be
called by <code class="highlight"><c- n>simd_invoke</c-></code> to enable a completely arbitrarily sized set of SIMD
arguments to be mapped onto their underlying intrinsics. For the example above,
the following code was generated:</p>
<pre class="language-asm highlight"><c- nf>vmovups</c-> <c- no>ymm0</c-><c- p>,</c-> <c- no>ymmword</c-> <c- no>ptr</c-> <c- p>[</c-><c- no>rsi</c-><c- p>]</c->
<c- nf>vmovups</c-> <c- no>ymm1</c-><c- p>,</c-> <c- no>ymmword</c-> <c- no>ptr</c-> <c- p>[</c-><c- no>rsi</c-> + <c- mi>32</c-><c- p>]</c->
<c- nf>vmovups</c-> <c- no>xmm2</c-><c- p>,</c-> <c- no>xmmword</c-> <c- no>ptr</c-> <c- p>[</c-><c- no>rsi</c-> + <c- mi>64</c-><c- p>]</c->
<c- nf>mov</c->     <c- no>rax</c-><c- p>,</c-> <c- no>rdi</c->
<c- nf>vaddsubps</c->       <c- no>ymm0</c-><c- p>,</c-> <c- no>ymm0</c-><c- p>,</c-> <c- no>ymmword</c-> <c- no>ptr</c-> <c- p>[</c-><c- no>rdx</c-><c- p>]</c->
<c- nf>vaddsubps</c->       <c- no>ymm1</c-><c- p>,</c-> <c- no>ymm1</c-><c- p>,</c-> <c- no>ymmword</c-> <c- no>ptr</c-> <c- p>[</c-><c- no>rdx</c-> + <c- mi>32</c-><c- p>]</c->
<c- nf>vaddsubps</c->       <c- no>xmm2</c-><c- p>,</c-> <c- no>xmm2</c-><c- p>,</c-> <c- no>xmmword</c-> <c- no>ptr</c-> <c- p>[</c-><c- no>rdx</c-> + <c- mi>64</c-><c- p>]</c->
<c- nf>vmovups</c-> <c- no>ymmword</c-> <c- no>ptr</c-> <c- p>[</c-><c- no>rdi</c-><c- p>],</c-> <c- no>ymm0</c->
<c- nf>vmovups</c-> <c- no>ymmword</c-> <c- no>ptr</c-> <c- p>[</c-><c- no>rdi</c-> + <c- mi>32</c-><c- p>],</c-> <c- no>ymm1</c->
<c- nf>vmovups</c-> <c- no>xmmword</c-> <c- no>ptr</c-> <c- p>[</c-><c- no>rdi</c-> + <c- mi>64</c-><c- p>],</c-> <c- no>xmm2</c-> </pre>
   <p>Notice how the the load, addsub and store instructions work respectively in <code class="highlight"><c- n>ymm</c-></code>, <code class="highlight"><c- n>ymm</c-></code> and <code class="highlight"><c- n>xmm</c-></code> registers to cope with the different sizes.</p>
   <p>Having now described the basic operation of <code class="highlight"><c- n>simd_invoke</c-></code> we can consider some
of the rules for using it, and a useful extension to it which makes certain
scenarios easier to deal with.</p>
   <h3 class="heading settled" data-level="3.1" id="simd_indexing"><span class="secno">3.1. </span><span class="content">Using indexed Callable invocations</span><a class="self-link" href="#simd_indexing"></a></h3>
   <p>When a large SIMD value is broken down into pieces to invoke the Callable
function, the size of that piece can be obtained from the Callable function
invocation’s parameter type but it can also be useful to pass in the index of
that piece too. For example, suppose a function is invoking an intrinsic to
perform a special type of memory store operation. Each register-sized sub-piece
of the incoming SIMD needs to know it offset so that it can be written to the
correct pointer offset. The following example code illustrates how this could
happen:</p>
<pre class="language-cpp highlight"><c- k>auto</c-> <c- n>special_memory_store</c-><c- p>(</c-><c- n>simd</c-><c- o>&lt;</c-><c- b>float</c-><c- p>,</c-> <c- mi>32</c-><c- o>></c-> <c- n>x</c-><c- p>,</c-> <c- b>float</c-><c- o>*</c-> <c- n>ptr</c-><c- p>)</c->
<c- p>{</c->
    <c- c1>// Invoke the most appropriate intrinsic for the given simd types.</c->
    <c- k>auto</c-> <c- n>do_native</c-> <c- o>=</c-> 
      <c- p>[</c-><c- o>=</c-><c- p>]</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- o>></c-><c- p>(</c-><c- n>basic_simd</c-><c- o>&lt;</c-><c- n>T</c-><c- p>,</c-> <c- n>ABI</c-><c- o>></c-> <c- n>data</c-><c- p>,</c-> <c- k>auto</c-> <c- n>idx</c-><c- p>)</c-> <c- p>{</c->
        <c- p>(</c-><c- n>_mm256_special_store_ps</c-><c- p>(</c-><c- n>ptr</c-> <c- o>+</c-> <c- n>idx</c-><c- p>,</c-> <c- k>static_cast</c-><c- o>&lt;</c-><c- n>__m256</c-><c- o>></c-><c- p>(</c-><c- n>data</c-><c- p>)));</c->
    <c- p>};</c->

    <c- n>simd_invoke_indexed</c-><c- p>(</c-><c- n>do_native</c-><c- p>,</c-> <c- n>x</c-><c- p>);</c->
<c- p>}</c-></pre>
   <p>The <code class="highlight"><c- n>simd_invoke_indexed</c-></code> function is now used instead, and this expects that
the Callable will take an extra parameter giving the compile-time offset of the
first index of the sub-SIMD value (i.e., 0, 8, 16 and 24 in this example).</p>
   <p>Note in this example that the Callable does not return a value itself, nor does the call to <code class="highlight"><c- n>simd_invoke_indexed</c-></code>.</p>
   <h4 class="heading settled" data-level="3.1.1" id="probe_index"><span class="secno">3.1.1. </span><span class="content">Design option - probing the index capabilities</span><a class="self-link" href="#probe_index"></a></h4>
   <p>Rather than requiring the user to invoke an indexed callable using <code class="highlight"><c- n>simd_invoke_indexed</c-></code> an alternative would be to allow <code class="highlight"><c- n>simd_invoke</c-></code> to probe
the Callable to see if it accepts one extra index parameter, and if it does to
pass in that index to each Callable invocation. The advantage of doing this is
to have a single function which can use the index or not depending on the
Callable being used. The disadvantage is that the mechanism of probing the
Callable may be fragile and lead to obscure errors.</p>
   <h3 class="heading settled" data-level="3.2" id="simd_invoke_rules"><span class="secno">3.2. </span><span class="content">Considerations in using <code class="highlight"><c- n>simd_invoke</c-></code></span><a class="self-link" href="#simd_invoke_rules"></a></h3>
   <p>These are a set of considerations for using <code class="highlight"><c- n>simd_invoke</c-></code>. In the following,
SIMD-like will be taken to be a type that is either a <code class="highlight"><c- n>basic_simd</c-></code>, or a <code class="highlight"><c- n>basic_simd_mask</c-></code>, and whose native size can be queried.</p>
   <p>All the arguments that are passed to the callable function must be <code class="highlight"><c- n>simd</c-></code> or <code class="highlight"><c- n>simd_mask</c-></code> values.</p>
   <p>When more than one SIMD-like object is used as an argument, all of the SIMD-like
objects must have the same size (i.e., you can’t call <code class="highlight"><c- n>simd_invoke</c-></code> with SIMD values
which don’t break down into pieces whose respective sizes are the same).</p>
   <p>For the native block size to be deduced, all the SIMD-like values must have the same
native size. This is to ensure that when the SIMD-like arguments are broken into
piecees they will always map to the same respective sizes. If the size cannot be
deduced like this then the user must explicitly supply the block size.</p>
   <p>The order of invoking the Callable function for each sub-block is undefined.</p>
   <p>When the Callable returns a value, it must return a SIMD-like object. This is
because there is no way to take non-SIMD results from the Callable and merge
them together, except by using <code class="highlight"><c- n>simd_concat</c-></code>.</p>
   <p>When the Callable returns a SIMD-like object, it need not have the same size as
its input arguments. For example, the Callable function could perform an
operation like extracting multiples of some index, where the results have to be
concatenated back together.</p>
   <p>When the Callable returns a SIMD-like object, every invocation of the callable
must return a SIMD-like object with the same element type. This is to ensure
that the results can be glued together.</p>
   <h2 class="heading settled" data-level="4" id="wording"><span class="secno">4. </span><span class="content">Wording</span><a class="self-link" href="#wording"></a></h2>
   <h3 class="heading settled" data-level="4.1" id="wording_simd_invoke"><span class="secno">4.1. </span><span class="content">Add new section [<strong>simd.invoke</strong>]</span><a class="self-link" href="#wording_simd_invoke"></a></h3>
   <ins>
    <blockquote>
      <span><b>� <code class="highlight"><c- n>simd_invoke</c-></code> function calling utility        [simd.simd_invoke]</b></span> 
<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>BlockSize</c-> <c- o>=</c-> <c- mi>0</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>Fn</c-><c- p>,</c-> <c- k>typename</c-><c- p>...</c-> <c- n>Args</c-><c- o>></c->
<c- k>constexpr</c-> <c- k>auto</c-> <c- n>simd_invoke</c-><c- p>(</c-><c- n>Fn</c-><c- o>&amp;&amp;</c-> <c- n>fn</c-><c- p>,</c-> <c- n>Args</c-><c- o>&amp;&amp;</c-><c- p>...</c-> <c- n>args</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>BlockSize</c-> <c- o>=</c-> <c- mi>0</c-><c- p>,</c-> <c- k>typename</c-> <c- nc>Fn</c-><c- p>,</c-> <c- k>typename</c-><c- p>...</c-> <c- n>Args</c-><c- o>></c->
<c- k>constexpr</c-> <c- k>auto</c-> <c- n>simd_invoke_indexed</c-><c- p>(</c-><c- n>Fn</c-><c- o>&amp;&amp;</c-> <c- n>fn</c-><c- p>,</c-> <c- n>Args</c-><c- o>&amp;&amp;</c-><c- p>...</c-> <c- n>args</c-><c- p>);</c-></pre>
     <p><i>Constraints</i>:</p>
     <ul>
      <li data-md>
       <p><code class="highlight"><c- k>sizeof</c-><c- p>...(</c-><c- n>Args</c-><c- p>)</c-> <c- o>></c-> <c- mi>0</c-></code>.</p>
      <li data-md>
       <p>Each argument in <code class="highlight"><c- n>Args</c-><c- p>...</c-></code> is either <code class="highlight"><c- n>basic_simd</c-></code> or <code class="highlight"><c- n>basic_simd_mask</c-></code>.</p>
      <li data-md>
       <p>For every argument in <code class="highlight"><c- n>Args</c-><c- p>...</c-></code>, <code class="highlight"><c- n>Args</c-><c- o>::</c-><c- n>size</c-></code>’s must be identical.</p>
      <li data-md>
       <p><code class="highlight"><c- n>BlockSize</c-></code> is either non-zero, or every argument in <code class="highlight"><c- n>Args</c-><c- p>...</c-></code> must have the same native size.</p>
      <li data-md>
       <p>The <code class="highlight"><c- n>Fn</c-></code> return type is either <code class="highlight"><c- b>void</c-></code>, or <code class="highlight"><c- n>basic_simd</c-></code>, or <code class="highlight"><c- n>basic_simd_mask</c-></code>.</p>
     </ul>
     <p><i>Effects</i>:</p>
     <p>Let <code class="highlight"><c- n>split</c-><c- o>-</c-><c- n>size</c-></code> be a <code class="highlight"><c- n>BlockSize</c-></code> if that is non-zero, or native size, otherwise.</p>
     <ul>
      <li data-md>
       <p>Invokes <code class="highlight"><c- n>Fn</c-></code> with <code class="highlight"><c- n>args</c-></code> split by <code class="highlight"><c- n>split</c-><c- o>-</c-><c- n>size</c-></code>.
The number of invocations is <code class="highlight"><c- n>Args</c-><c- o>::</c-><c- n>size</c-> <c- o>/</c-> <c- n>split</c-><c- o>-</c-><c- n>size</c-> <c- o>+</c-> <c- p>(</c-><c- n>Args</c-><c- o>::</c-><c- n>size</c-> <c- o>%</c-> <c- n>split</c-><c- o>-</c-><c- n>size</c-> <c- o>==</c-> <c- mi>0</c-> <c- o>?</c-> <c- mi>0</c-> <c- o>:</c-> <c- mi>1</c-><c- p>)</c-></code>.
The invocation order of <code class="highlight"><c- n>Fn</c-></code> over split args is unspecified.</p>
      <li data-md>
       <p>If <code class="highlight"><c- n>Fn</c-></code> returns non-<code class="highlight"><c- b>void</c-></code> type, collects the all <code class="highlight"><c- n>Fn</c-></code> invocation results and returns it as a single value.</p>
     </ul>
     <p><i>Returns</i>:</p>
     <p>If the <code class="highlight"><c- n>Fn</c-></code> returns non-<code class="highlight"><c- b>void</c-></code>, concatenate every <code class="highlight"><c- n>Fn</c-></code> call result using <code class="highlight"><c- n>simd_concat</c-></code> and returns that value.
Otherwise, returns <code class="highlight"><c- b>void</c-></code>.</p>
    </blockquote>
   </ins>
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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-p1928r3">[P1928R3]
   <dd>Matthias Kretz. <a href="https://wg21.link/p1928r3"><cite>Merge data-parallel types from the Parallelism TS 2</cite></a>. 3 February 2023. URL: <a href="https://wg21.link/p1928r3">https://wg21.link/p1928r3</a>
   <dt id="biblio-p1928r4">[P1928R4]
   <dd>Matthias Kretz. <a href="https://wg21.link/p1928r4"><cite>std::simd - Merge data-parallel types from the Parallelism TS 2</cite></a>. 19 May 2023. URL: <a href="https://wg21.link/p1928r4">https://wg21.link/p1928r4</a>
  </dl>