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data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-SWAR_architectures" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#SWAR_architectures"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>SWAR architectures</span> </div> </a> <ul id="toc-SWAR_architectures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-History_of_the_SWAR_programming_model" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History_of_the_SWAR_programming_model"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>History of the SWAR programming model</span> </div> </a> <ul id="toc-History_of_the_SWAR_programming_model-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Some_applications_of_SWAR" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Some_applications_of_SWAR"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Some applications of SWAR</span> </div> </a> <ul id="toc-Some_applications_of_SWAR-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Examples" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Examples</span> </div> </a> <button aria-controls="toc-Examples-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Examples subsection</span> </button> <ul id="toc-Examples-sublist" class="vector-toc-list"> <li id="toc-Counting_bits_set" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Counting_bits_set"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Counting bits set</span> </div> </a> <ul id="toc-Counting_bits_set-sublist" class="vector-toc-list"> <li id="toc-Further_refinements" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Further_refinements"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.1</span> <span>Further refinements</span> </div> </a> <ul id="toc-Further_refinements-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Finding_zero_bytes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Finding_zero_bytes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Finding zero bytes</span> </div> </a> <ul id="toc-Finding_zero_bytes-sublist" class="vector-toc-list"> <li id="toc-Further_refinements_2" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Further_refinements_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1</span> <span>Further refinements</span> </div> </a> <ul id="toc-Further_refinements_2-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Small_table_lookups" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Small_table_lookups"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Small table lookups</span> </div> </a> <ul id="toc-Small_table_lookups-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main 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data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For musical notes, see <a href="/wiki/Swara" class="mw-redirect" title="Swara">swara</a>.</div> <p><b>SIMD within a register</b> (<b>SWAR</b>), also known by the name "packed SIMD"<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> is a technique for performing parallel operations on data contained in a <a href="/wiki/Processor_register" title="Processor register">processor register</a>. <a href="/wiki/SIMD" class="mw-redirect" title="SIMD">SIMD</a> stands for <i>single instruction, multiple data</i>. Flynn's 1972 taxonomy categorises SWAR as <a href="/wiki/Flynn%27s_taxonomy#Pipelined_processor" title="Flynn's taxonomy">"pipelined processing"</a>. </p> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist 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.sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar nomobile nowraplinks hlist"><tbody><tr><th class="sidebar-title"><a href="/wiki/Flynn%27s_taxonomy" title="Flynn's taxonomy">Flynn's taxonomy</a></th></tr><tr><th class="sidebar-heading"> Single data stream</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Single_instruction,_single_data" title="Single instruction, single data">SISD</a></li> <li><a href="/wiki/Multiple_instruction,_single_data" title="Multiple instruction, single data">MISD</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Multiple data streams</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Single_instruction,_multiple_data" title="Single instruction, multiple data">SIMD</a></li> <li><a href="/wiki/Multiple_instruction,_multiple_data" title="Multiple instruction, multiple data">MIMD</a></li></ul></td> </tr><tr><th class="sidebar-heading"> SIMD subcategories<sup id="cite_ref-flynn-1972_2-0" class="reference"><a href="#cite_note-flynn-1972-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Flynn%27s_taxonomy#Array_processor" title="Flynn's taxonomy">Array processing (SIMT)</a></li> <li><a href="/wiki/Flynn%27s_taxonomy#Pipelined_processor" title="Flynn's taxonomy">Pipelined processing (packed SIMD)</a></li> <li><a href="/wiki/Flynn%27s_taxonomy#Associative_processor" title="Flynn's taxonomy">Associative processing (predicated/masked SIMD)</a></li></ul></td> </tr><tr><th class="sidebar-heading"> See also</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Single_program,_multiple_data" title="Single program, multiple data">SPMD</a></li> <li><a href="/wiki/MPMD" class="mw-redirect" title="MPMD">MPMD</a></li></ul></td> </tr></tbody></table> <p>Many modern general-purpose computer processors have some provisions for <a href="/wiki/SIMD" class="mw-redirect" title="SIMD">SIMD</a>, in the form of a group of registers and instructions to make use of them. SWAR refers to the use of those registers and instructions, as opposed to using specialized processing engines designed to be better at SIMD operations. It also refers to the use of SIMD with general-purpose registers and instructions that were not meant to do it at the time, by way of various novel software tricks.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="SWAR_architectures">SWAR architectures</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SWAR&action=edit&section=1" title="Edit section: SWAR architectures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A SWAR architecture is one that includes instructions explicitly intended to perform parallel operations across data that is stored in the independent subwords or fields of a register. A SWAR-capable architecture is one that includes a set of instructions that is sufficient to allow data stored in these fields to be treated independently even though the architecture does not include instructions that are explicitly intended for that purpose. </p><p>An early example of a SWAR architecture was the <a href="/wiki/P5_(microarchitecture)#MMX" class="mw-redirect" title="P5 (microarchitecture)">Intel Pentium with MMX</a>, which implemented the <a href="/wiki/MMX_(instruction_set)" title="MMX (instruction set)">MMX extension set</a>. The <a href="/wiki/P5_(microarchitecture)" class="mw-redirect" title="P5 (microarchitecture)">Intel Pentium</a>, by contrast, did not include such instructions, but could still act as a SWAR architecture through careful hand-coding or compiler techniques. </p><p>Early SWAR architectures include <a href="/wiki/DEC_Alpha" title="DEC Alpha">DEC Alpha</a> <abbr title="Motion Video Instructions">MVI</abbr>, Hewlett-Packard's <a href="/wiki/PA-RISC" title="PA-RISC">PA-RISC</a> <a href="/wiki/Multimedia_Acceleration_eXtensions" title="Multimedia Acceleration eXtensions">MAX</a>, Silicon Graphics Incorporated's <a href="/wiki/MIPS_architecture" title="MIPS architecture">MIPS</a> <a href="/wiki/MDMX" title="MDMX">MDMX</a>, and Sun's <a href="/wiki/SPARC" title="SPARC">SPARC</a> V9 <a href="/wiki/Visual_Instruction_Set" title="Visual Instruction Set">VIS</a>. Like MMX, many of the SWAR instruction sets are intended for faster video coding.<sup id="cite_ref-LCPC98_4-0" class="reference"><a href="#cite_note-LCPC98-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="History_of_the_SWAR_programming_model">History of the SWAR programming model</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SWAR&action=edit&section=2" title="Edit section: History of the SWAR programming model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Wesley_A._Clark" title="Wesley A. Clark">Wesley A. Clark</a> introduced partitioned subword data operations in the 1950s<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="absolutely genuinely fascinating, but which machines? (June 2021)">citation needed</span></a></i>]</sup>. This can be seen as a very early predecessor to SWAR. <a href="/wiki/Leslie_Lamport" title="Leslie Lamport">Leslie Lamport</a> presented SWAR techniques in his paper titled "Multiple byte processing with full-word instructions"<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> in 1975. </p><p>With the introduction of Intel's MMX multimedia instruction set extensions in 1996, desktop processors with SIMD parallel processing capabilities became common. Early on, these instructions could only be used via hand-written assembly code. </p><p>In the fall of 1996, Professor Hank Dietz was the instructor for the undergraduate Compiler Construction course at Purdue University's School of Electrical and Computer Engineering. For this course, he assigned a series of projects in which the students would build a simple compiler targeting MMX. The input language was a subset dialect of <a href="/wiki/MasPar" title="MasPar">MasPar</a>'s MPL called NEMPL (Not Exactly MPL). </p><p>During the course of the semester, it became clear to the course teaching assistant, Randall (Randy) Fisher, that there were a number of issues with MMX that would make it difficult to build the back-end of the NEMPL compiler. For example, MMX has an instruction for multiplying 16-bit data but not multiplying 8-bit data. The NEMPL language did not account for this problem, allowing the programmer to write programs that required 8-bit multiplies. </p><p>Intel's x86 architecture was not the only architecture to include SIMD-like parallel instructions. Sun's <a href="/wiki/Visual_Instruction_Set" title="Visual Instruction Set">VIS</a>, SGI's <a href="/wiki/MDMX" title="MDMX">MDMX</a>, and other multimedia instruction sets had been added to other manufacturers' existing instruction set architectures to support so-called <i>new media</i> applications. These extensions had significant differences in the precision of data and types of instructions supported. </p><p>Dietz and Fisher began developing the idea of a well-defined parallel programming model that would allow the programming to target the model without knowing the specifics of the target architecture. This model would become the basis of Fisher's dissertation. The acronym "SWAR" was coined by Dietz and Fisher one day in Hank's office in the MSEE building at Purdue University.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> It refers to this form of parallel processing, architectures that are designed to natively perform this type of processing, and the general-purpose programming model that is Fisher's dissertation. </p><p>The problem of compiling for these widely varying architectures was discussed in a paper presented at LCPC98.<sup id="cite_ref-LCPC98_4-1" class="reference"><a href="#cite_note-LCPC98-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Some_applications_of_SWAR">Some applications of SWAR</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SWAR&action=edit&section=3" title="Edit section: Some applications of SWAR"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>SWAR processing has been used in image processing,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> cryptographic pairings,<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> raster processing,<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> computational fluid dynamics,<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> and communications.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SWAR&action=edit&section=4" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>SWAR techniques can be used even on systems without special hardware support. <a href="/wiki/Logical_operation" class="mw-redirect" title="Logical operation">Logical operations</a> act bitwise, so act on each bit of a register independently. Using addition and subtraction is more difficult, but can be useful if care is taken to avoid unwanted <a href="/wiki/Carry_propagation" class="mw-redirect" title="Carry propagation">carry propagation</a> between lanes. Except for this carry propagation, one 64-bit addition or subtraction is the same as performing eight 8-bit additions or subtractions. </p> <div class="mw-heading mw-heading3"><h3 id="Counting_bits_set">Counting bits set</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SWAR&action=edit&section=5" title="Edit section: Counting bits set"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Probably the archetypical example of SWAR techniques is finding the <a href="/wiki/Hamming_weight" title="Hamming weight">population count</a> of (number of bits set in) a register. The register is treated successively as a series of 1-bit, 2-bit, 4-bit, etc. fields. </p><p>To begin with, note that the population count of a 1-bit field is simply the field itself. To find the population count of a 2-bit field, sum the population counts of its two constituent 1-bit fields. This can be done in parallel for 32 2-bit fields in a 64-bit value <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">x</code>: </p> <pre>x2 := (x & 0x5555555555555555) + (x >> 1 & 0x5555555555555555); </pre> <p>The <a href="/wiki/Hexadecimal" title="Hexadecimal">hexadecimal</a> constant <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">0x5</code> is binary 0101<sub>2</sub>, which isolates even-numbered bits. The addition cannot overflow each 2-bit field, as the maximum possible sum is 2. </p><p>This can be repeated to combine 2-bit fields into 4-bit fields. Here, we use a mask of binary 0011<sub>2</sub>, or hexadecimal <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">0x3</code>, to isolate pairs of bits: </p> <pre>x4 := (x2 & 0x3333333333333333) + (x2 >> 2 & 0x3333333333333333); </pre> <p>Now each 4-bit field contains a count from 0 to 4. Because a 4-bit field can contain a value up to 15, no overflow is possible when adding two 4-bit population counts, allowing the masking to be done <i>after</i> the addition, rather than once per addend: </p> <pre>x8 := x4 + (x4 >> 4) & 0x0f0f0f0f0f0f0f0f; </pre> <p>At this point, the 8-bit fields can hold values up to 255, so there is no need for further masking until the very end: </p> <pre>x16 = x8 + (x8 >> 8); x32 = x16 + (x16 >> 16); x64 = x32 + (x32 >> 32); population_count = x64 & 0xff; </pre> <div class="mw-heading mw-heading4"><h4 id="Further_refinements">Further refinements</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SWAR&action=edit&section=6" title="Edit section: Further refinements"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are several well-known variants on this. In particular, the last three shift-and-add steps can be combined into </p> <pre> population_count = x8 * 0x0101010101010101 >> 56; </pre> <p>Three stages of shifting and adding require 6 instructions, each with a <a href="/wiki/Data_dependency" title="Data dependency">data dependency</a> on the previous one, so take at least 6 clock cycles. A multiplication can usually be performed faster. When operating on 32-bit words, it's less clear, as a 3-cycle multiply is common. </p><p>A second variant is a change to the first step. Rather than combining the two bits <i>b</i><sub>1</sub> and <i>b</i><sub>0</sub> in each 2-bit field by adding them, consider the initial value of the 2-bit field as 2<i>b</i><sub>1</sub> + <i>b</i><sub>0</sub>. Subtracting <i>b</i><sub>1</sub> from this will produce the desired sum, with only one masking operation: </p> <pre>x2 := x − (x >> 1 & 0x5555555555555555); </pre> <div class="mw-heading mw-heading3"><h3 id="Finding_zero_bytes">Finding zero bytes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SWAR&action=edit&section=7" title="Edit section: Finding zero bytes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It is common to search a <a href="/wiki/Character_string" class="mw-redirect" title="Character string">character string</a> for a <a href="/wiki/Null-terminated_string" title="Null-terminated string">null terminator</a>. Doing this one byte at a time is inefficient when a 64-bit processor can operate on 8 bytes at a time. </p><p>The same technique can be used to search for <a href="/wiki/Path_(computing)" title="Path (computing)">pathname separators</a> or other delimiters, by <a href="/wiki/Exclusive-or" class="mw-redirect" title="Exclusive-or">exclusive-oring</a> with the target byte value first. </p><p>Some architectures include special instructions for performing 8 byte comparisons at once. For example, the <a href="/wiki/DEC_Alpha" title="DEC Alpha">DEC Alpha</a> included a <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">CMPBGE</code> instruction for performing 8 byte compares at once. However, searching for a zero byte can be done without any special support. </p><p>One way would be to <a href="/wiki/Logical_or" class="mw-redirect" title="Logical or">OR</a> together 8 bits in a manner much like the bit-counting example above: </p> <pre>x2 = x | x<<1; x4 = x2 | x2<<2; x8 = x4 | x4<<4; byte_map = ~x8 & 0x8080808080808080; </pre> <p>This results in a <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">byte_map</code> with a 1 bit in the most significant bit of any byte that was originally zero. </p><p>However, this can be done more quickly by taking advantage of carry propagation using arithmetic operations. Adding <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">0x7f</code> (binary 01111111<sub>2</sub>) to each byte causes a carry into bit 7 if the low 7 bits are non-zero. The challenge is ensure the carry propagation <i>stops</i> at bit 7 and does not affect other bytes. This can be done by working on the low 7 bits and high bit of each byte separately. First, extract the low 7 bits of each byte by <a href="/wiki/Logical_and" class="mw-redirect" title="Logical and">ANDing</a> with <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">0x7f</code> before adding <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">0x7f</code>: </p> <pre>x7 = (x & 0x7f7f7f7f7f7f7f7f) + 0x7f7f7f7f7f7f7f7f; </pre> <p>Then combine with the most-significant bits: </p> <pre>x8 = x7 | x; </pre> <p>This value will have the msbit of each 8-bit field set to 1 if that byte is non-zero. Finally: </p> <pre>byte_map = ~(x8 | 0x7f7f7f7f7f7f7f7f); </pre> <p>will set all the unwanted low bits in each byte, then complement everything, leaving only 1 bits anywhere the corresponding input byte <i>is</i> zero. (This is equivalent to <code>~x8 & 0x80...80</code>, but uses the same constant value.) If there are no 1 bits, the search can continue with the following word. If there are any 1 bits, the length of the string can be computed from their positions. </p> <div class="mw-heading mw-heading4"><h4 id="Further_refinements_2">Further refinements</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SWAR&action=edit&section=8" title="Edit section: Further refinements"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If the goal is limited to finding the <i>first</i> zero byte on a <a href="/wiki/Little-endian" class="mw-redirect" title="Little-endian">little-endian</a> processor, it is possible to find the <i>least significant</i> zero byte in fewer operations, using two different constants:<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <pre>x7 = x − 0x0101010101010101; byte_map = x7 & ~x & 0x8080808080808080; </pre> <p>For each byte <i>b</i>, this sets its msbit in <code>byte_map</code> if the msbit of <i>b</i> − 1 is set and the msbit of <i>b</i> is clear, something that only happens if <i>b</i> = 0. </p><p>The preceding statement is only true <i>if there is no borrow in</i>; if there <i>is</i> a borrow, the condition will also be true if <i>b</i> = 1. However, such a borrow can only be generated by a less significant zero byte, so the <i>least significant</i> zero byte will be correctly identified, as desired. </p><p>Not only does this save one binary operation, but they are not all sequentially dependent, so it can be performed in two cycles assuming the existence of an "and not" (bit clear) instruction </p> <div class="mw-heading mw-heading3"><h3 id="Small_table_lookups">Small table lookups</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SWAR&action=edit&section=9" title="Edit section: Small table lookups"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As a generalization of a <a href="/wiki/Bitmap" title="Bitmap">bitmap</a>, it is possible to store very small <a href="/wiki/Lookup_table" title="Lookup table">lookup tables</a> in a single register. For example, the number of days in a month varies from 28 to 31, a range of 4 values. This can be stored in 12×2 = 24 bits: </p> <pre>days_table = 0xeefbb3 + (is_leap_year << 2); days_in_month = 28 + (days_table >> 2*month & 3); </pre> <p>(This is assuming a <a href="/wiki/Zero-based_numbering" title="Zero-based numbering">0-based</a> month number. A 1-based month number can be accommodated by shifting the <code class="mw-highlight mw-highlight-lang-text mw-content-ltr" style="" dir="ltr">days_table</code>.) </p><p>The fact that the table fits neatly into one register makes it easy to modify for <a href="/wiki/Leap_year" title="Leap year">leap years</a>. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SWAR&action=edit&section=10" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>SIMD engines: <a href="/wiki/Vector_processor" title="Vector processor">vector processor</a>, <a href="/wiki/Array_processor" class="mw-redirect" title="Array processor">array processor</a>, <a href="/wiki/Digital_signal_processor" title="Digital signal processor">digital signal processor</a>, <a href="/wiki/Stream_processing" title="Stream processing">stream processor</a>.</li> <li>SWAR on <a href="/wiki/X86" title="X86">x86</a> processors: <a href="/wiki/MMX_(instruction_set)" title="MMX (instruction set)">MMX</a>, <a href="/wiki/3DNow!" title="3DNow!">3DNow!</a>, <a href="/wiki/Streaming_SIMD_Extensions" title="Streaming SIMD Extensions">SSE</a>, <a href="/wiki/SSE2" title="SSE2">SSE2</a>, <a href="/wiki/SSE3" title="SSE3">SSE3</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SWAR&action=edit&section=11" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFMiyaokaChoiTogawaYanagisawa2002" class="citation conference cs1">Miyaoka, Y.; Choi, J.; Togawa, N.; Yanagisawa, M.; Ohtsuki, T. 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Retrieved <span class="nowrap">2024-12-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Quickly+checking+for+a+zero+byte+in+C+using+bitwise+operations&rft.date=2017-01-24&rft.aulast=Fisher&rft.aufirst=James&rft_id=https%3A%2F%2Fjameshfisher.com%2F2017%2F01%2F24%2Fbitwise-check-for-zero-byte%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASWAR" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=SWAR&action=edit&section=12" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.aggregate.org/SWAR/">The Aggregate - SWAR: SIMD Within A Register</a></li></ul>    </div><noscript><img src="https://auth.wikimedia.org/loginwiki/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=SWAR&oldid=1276491101">https://en.wikipedia.org/w/index.php?title=SWAR&oldid=1276491101</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Parallel_computing" title="Category:Parallel computing">Parallel computing</a></li><li><a href="/wiki/Category:SIMD_computing" title="Category:SIMD computing">SIMD computing</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_June_2021" title="Category:Articles with unsourced statements from June 2021">Articles with unsourced statements from June 2021</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 19 February 2025, at 04:22<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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