nep-0054-simd-cpp-highway.html


<!DOCTYPE html>


<html lang="en" data-content_root="./" >

  <head>
    <meta charset="utf-8" />
    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />

    <title>NEP 54 — SIMD infrastructure evolution: adopting Google Highway when moving to C++ &#8212; NumPy Enhancement Proposals</title>
  
  
  <script data-cfasync="false">
    document.documentElement.dataset.mode = localStorage.getItem("mode") || "";
    document.documentElement.dataset.theme = localStorage.getItem("theme") || "";
  </script>
  <!--
    this give us a css class that will be invisible only if js is disabled
  -->
  <noscript>
    <style>
      .pst-js-only { display: none !important; }

    </style>
  </noscript>
  
  <!-- Loaded before other Sphinx assets -->
  <link href="_static/styles/theme.css?digest=8878045cc6db502f8baf" rel="stylesheet" />
<link href="_static/styles/pydata-sphinx-theme.css?digest=8878045cc6db502f8baf" rel="stylesheet" />

    <link rel="stylesheet" type="text/css" href="_static/pygments.css?v=03e43079" />
  
  <!-- So that users can add custom icons -->
  <script src="_static/scripts/fontawesome.js?digest=8878045cc6db502f8baf"></script>
  <!-- Pre-loaded scripts that we'll load fully later -->
  <link rel="preload" as="script" href="_static/scripts/bootstrap.js?digest=8878045cc6db502f8baf" />
<link rel="preload" as="script" href="_static/scripts/pydata-sphinx-theme.js?digest=8878045cc6db502f8baf" />

    <script src="_static/documentation_options.js?v=7f41d439"></script>
    <script src="_static/doctools.js?v=888ff710"></script>
    <script src="_static/sphinx_highlight.js?v=dc90522c"></script>
    <script>DOCUMENTATION_OPTIONS.pagename = 'nep-0054-simd-cpp-highway';</script>
    <link rel="icon" href="_static/favicon.ico"/>
    <link rel="index" title="Index" href="genindex.html" />
    <link rel="search" title="Search" href="search.html" />
    <link rel="next" title="Open NEPs (under consideration)" href="open.html" />
    <link rel="prev" title="NEP 51 — Changing the representation of NumPy scalars" href="nep-0051-scalar-representation.html" />
  <meta name="viewport" content="width=device-width, initial-scale=1"/>
  <meta name="docsearch:language" content="en"/>
  <meta name="docsearch:version" content="" />
    <meta name="docbuild:last-update" content="May 06, 2025"/>
  </head>
  
  
  <body data-bs-spy="scroll" data-bs-target=".bd-toc-nav" data-offset="180" data-bs-root-margin="0px 0px -60%" data-default-mode="">

  
  <div id="pst-skip-link" class="skip-link d-print-none"><a href="#main-content">Skip to main content</a></div>
  
  <div id="pst-scroll-pixel-helper"></div>
  
  <button type="button" class="btn rounded-pill" id="pst-back-to-top">
    <i class="fa-solid fa-arrow-up"></i>Back to top</button>

  
  <dialog id="pst-search-dialog">
    
<form class="bd-search d-flex align-items-center"
      action="search.html"
      method="get">
  <i class="fa-solid fa-magnifying-glass"></i>
  <input type="search"
         class="form-control"
         name="q"
         placeholder="Search the docs ..."
         aria-label="Search the docs ..."
         autocomplete="off"
         autocorrect="off"
         autocapitalize="off"
         spellcheck="false"/>
  <span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd>K</kbd></span>
</form>
  </dialog>

  <div class="pst-async-banner-revealer d-none">
  <aside id="bd-header-version-warning" class="d-none d-print-none" aria-label="Version warning"></aside>
</div>

  
    <header class="bd-header navbar navbar-expand-lg bd-navbar d-print-none">
<div class="bd-header__inner bd-page-width">
  <button class="pst-navbar-icon sidebar-toggle primary-toggle" aria-label="Site navigation">
    <span class="fa-solid fa-bars"></span>
  </button>
  
  
  <div class="col-lg-3 navbar-header-items__start">
    
      <div class="navbar-item">

  
<a class="navbar-brand logo" href="content.html">
  
  
    <img src="_static/numpylogo.svg" class="logo__image only-light" alt="NumPy Enhancement Proposals - Home"/>
    <img src="_static/numpylogo_dark.svg" class="logo__image only-dark pst-js-only" alt="NumPy Enhancement Proposals - Home"/>
  
  
</a></div>
    
  </div>
  
  <div class="col-lg-9 navbar-header-items">
    
    <div class="me-auto navbar-header-items__center">
      
        <div class="navbar-item">
<nav>
  <ul class="bd-navbar-elements navbar-nav">
    
<li class="nav-item current active">
  <a class="nav-link nav-internal" href="index.html">
    Index
  </a>
</li>


<li class="nav-item ">
  <a class="nav-link nav-internal" href="scope.html">
    The Scope of NumPy
  </a>
</li>


<li class="nav-item ">
  <a class="nav-link nav-internal" href="roadmap.html">
    Current roadmap
  </a>
</li>


<li class="nav-item ">
  <a class="nav-link nav-external" href="https://github.com/numpy/numpy/issues?q=is%3Aopen+is%3Aissue+label%3A%2223+-+Wish+List%22">
    Wishlist
  </a>
</li>

  </ul>
</nav></div>
      
    </div>
    
    
    <div class="navbar-header-items__end">
      
        <div class="navbar-item navbar-persistent--container">
          

<button class="btn search-button-field search-button__button pst-js-only" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
 <i class="fa-solid fa-magnifying-glass"></i>
 <span class="search-button__default-text">Search</span>
 <span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd class="kbd-shortcut__modifier">K</kbd></span>
</button>
        </div>
      
      
        <div class="navbar-item">

<button class="btn btn-sm nav-link pst-navbar-icon theme-switch-button pst-js-only" aria-label="Color mode" data-bs-title="Color mode"  data-bs-placement="bottom" data-bs-toggle="tooltip">
  <i class="theme-switch fa-solid fa-sun                fa-lg" data-mode="light" title="Light"></i>
  <i class="theme-switch fa-solid fa-moon               fa-lg" data-mode="dark"  title="Dark"></i>
  <i class="theme-switch fa-solid fa-circle-half-stroke fa-lg" data-mode="auto"  title="System Settings"></i>
</button></div>
      
        <div class="navbar-item"><ul class="navbar-icon-links"
    aria-label="Icon Links">
        <li class="nav-item">
          
          
          <a href="https://github.com/numpy/numpy" title="GitHub" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-brands fa-square-github fa-lg" aria-hidden="true"></i>
            <span class="sr-only">GitHub</span></a>
        </li>
</ul></div>
      
    </div>
    
  </div>
  
  
    <div class="navbar-persistent--mobile">

<button class="btn search-button-field search-button__button pst-js-only" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
 <i class="fa-solid fa-magnifying-glass"></i>
 <span class="search-button__default-text">Search</span>
 <span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd class="kbd-shortcut__modifier">K</kbd></span>
</button>
    </div>
  

    <button class="pst-navbar-icon sidebar-toggle secondary-toggle" aria-label="On this page">
      <span class="fa-solid fa-outdent"></span>
    </button>
  
</div>

    </header>
  

  <div class="bd-container">
    <div class="bd-container__inner bd-page-width">
      
      
      <dialog id="pst-primary-sidebar-modal"></dialog>
      <div id="pst-primary-sidebar" class="bd-sidebar-primary bd-sidebar">
        

  <div class="sidebar-header-items sidebar-primary__section">
    
    
      <div class="sidebar-header-items__center">
        
          
            <div class="navbar-item">
<nav>
  <ul class="bd-navbar-elements navbar-nav">
    
<li class="nav-item current active">
  <a class="nav-link nav-internal" href="index.html">
    Index
  </a>
</li>


<li class="nav-item ">
  <a class="nav-link nav-internal" href="scope.html">
    The Scope of NumPy
  </a>
</li>


<li class="nav-item ">
  <a class="nav-link nav-internal" href="roadmap.html">
    Current roadmap
  </a>
</li>


<li class="nav-item ">
  <a class="nav-link nav-external" href="https://github.com/numpy/numpy/issues?q=is%3Aopen+is%3Aissue+label%3A%2223+-+Wish+List%22">
    Wishlist
  </a>
</li>

  </ul>
</nav></div>
          
        
      </div>
    
    
      <div class="sidebar-header-items__end">
        
          <div class="navbar-item">

<button class="btn btn-sm nav-link pst-navbar-icon theme-switch-button pst-js-only" aria-label="Color mode" data-bs-title="Color mode"  data-bs-placement="bottom" data-bs-toggle="tooltip">
  <i class="theme-switch fa-solid fa-sun                fa-lg" data-mode="light" title="Light"></i>
  <i class="theme-switch fa-solid fa-moon               fa-lg" data-mode="dark"  title="Dark"></i>
  <i class="theme-switch fa-solid fa-circle-half-stroke fa-lg" data-mode="auto"  title="System Settings"></i>
</button></div>
        
          <div class="navbar-item"><ul class="navbar-icon-links"
    aria-label="Icon Links">
        <li class="nav-item">
          
          
          <a href="https://github.com/numpy/numpy" title="GitHub" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-brands fa-square-github fa-lg" aria-hidden="true"></i>
            <span class="sr-only">GitHub</span></a>
        </li>
</ul></div>
        
      </div>
    
  </div>
  
    <div class="sidebar-primary-items__start sidebar-primary__section">
        <div class="sidebar-primary-item">
<nav class="bd-docs-nav bd-links"
     aria-label="Section Navigation">
  <p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
  <div class="bd-toc-item navbar-nav"><ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="scope.html">The Scope of NumPy</a></li>
<li class="toctree-l1"><a class="reference internal" href="roadmap.html">Current roadmap</a></li>
</ul>
<ul class="current nav bd-sidenav">
<li class="toctree-l1 has-children"><a class="reference internal" href="meta.html">Meta-NEPs (NEPs about NEPs or active Processes)</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="nep-0000.html">NEP 0 — Purpose and process</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0023-backwards-compatibility.html">NEP 23 — Backwards compatibility and deprecation policy</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0036-fair-play.html">NEP 36 — Fair play</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0045-c_style_guide.html">NEP 45 — C style guide</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0046-sponsorship-guidelines.html">NEP 46 — NumPy sponsorship guidelines</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0048-spending-project-funds.html">NEP 48 — Spending NumPy project funds</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-template.html">NEP X — Template and instructions</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="provisional.html">Provisional NEPs (provisionally accepted; interface may change)</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul class="simple">
</ul>
</details></li>
<li class="toctree-l1 current active has-children"><a class="reference internal" href="accepted.html">Accepted NEPs (implementation in progress)</a><details open="open"><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="nep-0041-improved-dtype-support.html">NEP 41 — First step towards a new datatype system</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0042-new-dtypes.html">NEP 42 — New and extensible DTypes</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0044-restructuring-numpy-docs.html">NEP 44 — Restructuring the NumPy documentation</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0051-scalar-representation.html">NEP 51 — Changing the representation of NumPy scalars</a></li>
<li class="toctree-l2 current active"><a class="current reference internal" href="#">NEP 54 — SIMD infrastructure evolution: adopting Google Highway when moving to C++</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="open.html">Open NEPs (under consideration)</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="nep-0043-extensible-ufuncs.html">NEP 43 — Enhancing the extensibility of UFuncs</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0053-c-abi-evolution.html">NEP 53 — Evolving the NumPy C-API for NumPy 2.0</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="finished.html">Finished NEPs</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="nep-0001-npy-format.html">NEP 1 — A simple file format for NumPy arrays</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0005-generalized-ufuncs.html">NEP 5 — Generalized universal functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0007-datetime-proposal.html">NEP 7 — A proposal for implementing some date/time types in NumPy</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0010-new-iterator-ufunc.html">NEP 10 — Optimizing iterator/UFunc performance</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0013-ufunc-overrides.html">NEP 13 — A mechanism for overriding Ufuncs</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0014-dropping-python2.7-proposal.html">NEP 14 — Plan for dropping Python 2.7 support</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0015-merge-multiarray-umath.html">NEP 15 — Merging multiarray and umath</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0018-array-function-protocol.html">NEP 18 — A dispatch mechanism for NumPy's high level array functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0019-rng-policy.html">NEP 19 — Random number generator policy</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0020-gufunc-signature-enhancement.html">NEP 20 — Expansion of generalized universal function signatures</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0022-ndarray-duck-typing-overview.html">NEP 22 — Duck typing for NumPy arrays – high level overview</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0027-zero-rank-arrarys.html">NEP 27 — Zero rank arrays</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0028-website-redesign.html">NEP 28 — numpy.org website redesign</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0029-deprecation_policy.html">NEP 29 — Recommend Python and NumPy version support as a community policy standard</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0032-remove-financial-functions.html">NEP 32 — Remove the financial functions from NumPy</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0034-infer-dtype-is-object.html">NEP 34 — Disallow inferring ``dtype=object`` from sequences</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0035-array-creation-dispatch-with-array-function.html">NEP 35 — Array creation dispatching with __array_function__</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0038-SIMD-optimizations.html">NEP 38 — Using SIMD optimization instructions for performance</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0040-legacy-datatype-impl.html">NEP 40 — Legacy datatype implementation in NumPy</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0049.html">NEP 49 — Data allocation strategies</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0050-scalar-promotion.html">NEP 50 — Promotion rules for Python scalars</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0052-python-api-cleanup.html">NEP 52 — Python API cleanup for NumPy 2.0</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0055-string_dtype.html">NEP 55 — Add a UTF-8 variable-width string DType to NumPy</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0056-array-api-main-namespace.html">NEP 56 — Array API standard support in NumPy's main namespace</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="deferred.html">Deferred and Superseded NEPs</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="nep-0002-warnfix.html">NEP 2 — A proposal to build numpy without warning with a big set of warning flags</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0003-math_config_clean.html">NEP 3 — Cleaning the math configuration of numpy.core</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0004-datetime-proposal3.html">NEP 4 — A (third) proposal for implementing some date/time types in NumPy</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0006-newbugtracker.html">NEP 6 — Replacing Trac with a different bug tracker</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0008-groupby_additions.html">NEP 8 — A proposal for adding groupby functionality to NumPy</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0009-structured_array_extensions.html">NEP 9 — Structured array extensions</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0011-deferred-ufunc-evaluation.html">NEP 11 — Deferred UFunc evaluation</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0012-missing-data.html">NEP 12 — Missing data functionality in NumPy</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0021-advanced-indexing.html">NEP 21 — Simplified and explicit advanced indexing</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0024-missing-data-2.html">NEP 24 — Missing data functionality - alternative 1 to NEP 12</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0025-missing-data-3.html">NEP 25 — NA support via special dtypes</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0026-missing-data-summary.html">NEP 26 — Summary of missing data NEPs and discussion</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0030-duck-array-protocol.html">NEP 30 — Duck typing for NumPy arrays - implementation</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0031-uarray.html">NEP 31 — Context-local and global overrides of the NumPy API</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0037-array-module.html">NEP 37 — A dispatch protocol for NumPy-like modules</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0047-array-api-standard.html">NEP 47 — Adopting the array API standard</a></li>
</ul>
</details></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="rejected.html">Rejected and Withdrawn NEPs</a><details><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul>
<li class="toctree-l2"><a class="reference internal" href="nep-0016-abstract-array.html">NEP 16 — An abstract base class for identifying "duck arrays"</a></li>
<li class="toctree-l2"><a class="reference internal" href="nep-0017-split-out-maskedarray.html">NEP 17 — Split out masked arrays</a></li>
</ul>
</details></li>
</ul>
</div>
</nav></div>
    </div>
  
  
  <div class="sidebar-primary-items__end sidebar-primary__section">
      <div class="sidebar-primary-item">
<div id="ethical-ad-placement"
      class="flat"
      data-ea-publisher="readthedocs"
      data-ea-type="readthedocs-sidebar"
      data-ea-manual="true">
</div></div>
  </div>


      </div>
      
      <main id="main-content" class="bd-main" role="main">
        
        
          <div class="bd-content">
            <div class="bd-article-container">
              
              <div class="bd-header-article d-print-none">
<div class="header-article-items header-article__inner">
  
    <div class="header-article-items__start">
      
        <div class="header-article-item">

<nav aria-label="Breadcrumb" class="d-print-none">
  <ul class="bd-breadcrumbs">
    
    <li class="breadcrumb-item breadcrumb-home">
      <a href="content.html" class="nav-link" aria-label="Home">
        <i class="fa-solid fa-home"></i>
      </a>
    </li>
    
    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Roadmap &amp; NumPy enhancement proposals</a></li>
    
    
    <li class="breadcrumb-item"><a href="accepted.html" class="nav-link">Accepted NEPs (implementation in progress)</a></li>
    
    <li class="breadcrumb-item active" aria-current="page"><span class="ellipsis">NEP 54 — SIMD infrastructure evolution: adopting Google Highway when moving to C++</span></li>
  </ul>
</nav>
</div>
      
    </div>
  
  
</div>
</div>
              
              
<div id="searchbox"></div>
                <article class="bd-article">
                  
  <section id="nep-54-simd-infrastructure-evolution-adopting-google-highway-when-moving-to-c">
<span id="nep54"></span><h1>NEP 54 — SIMD infrastructure evolution: adopting Google Highway when moving to C++<a class="headerlink" href="#nep-54-simd-infrastructure-evolution-adopting-google-highway-when-moving-to-c" title="Link to this heading">#</a></h1>
<dl class="field-list simple">
<dt class="field-odd">Author<span class="colon">:</span></dt>
<dd class="field-odd"><p>Sayed Adel, Jan Wassenberg, Matti Picus, Ralf Gommers, Chris Sidebottom</p>
</dd>
<dt class="field-even">Status<span class="colon">:</span></dt>
<dd class="field-even"><p>Accepted</p>
</dd>
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>Standards Track</p>
</dd>
<dt class="field-even">Created<span class="colon">:</span></dt>
<dd class="field-even"><p>2023-07-06</p>
</dd>
<dt class="field-odd">Resolution<span class="colon">:</span></dt>
<dd class="field-odd"><p>TODO</p>
</dd>
</dl>
<section id="abstract">
<h2>Abstract<a class="headerlink" href="#abstract" title="Link to this heading">#</a></h2>
<p>We are moving the SIMD intrinsic framework, Universal Intrinsics, from C to
C++. We have also moved to Meson as the build system. The Google Highway
intrinsics project is proposing we use Highway instead of our Universal
Intrinsics as described in <a class="reference internal" href="nep-0038-SIMD-optimizations.html#nep38"><span class="std std-ref">NEP 38</span></a>. This is a complex and multi-faceted
decision - this NEP is an attempt to describe the trade-offs involved and
what would need to be done.</p>
</section>
<section id="motivation-and-scope">
<h2>Motivation and Scope<a class="headerlink" href="#motivation-and-scope" title="Link to this heading">#</a></h2>
<p>We want to refactor the C-based Universal Intrinsics (see <a class="reference internal" href="nep-0038-SIMD-optimizations.html#nep38"><span class="std std-ref">NEP 38</span></a>) to C++. This work was ongoing for some time, and Google’s Highway
was suggested as an alternative, which was already written in C++ and had
support for scalable SVE and other reusable components (such as VQSort).</p>
<p>The move from C to C++ is motivated by (a) code readability and ease of
development, (b) the need to add support for sizeless SIMD instructions (e.g.,
ARM’s SVE, RISC-V’s RVV).</p>
<p>As an example of the readability improvement, here is a typical line of C code
from our current C universal intrinsics framework:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">//</span> <span class="n">The</span> <span class="nd">@name</span><span class="o">@</span> <span class="ow">is</span> <span class="n">the</span> <span class="n">numpy</span><span class="o">-</span><span class="n">specific</span> <span class="n">templating</span> <span class="ow">in</span> <span class="o">.</span><span class="n">c</span><span class="o">.</span><span class="n">src</span> <span class="n">files</span>
<span class="n">npyv_</span><span class="nd">@sfx</span><span class="o">@</span>  <span class="n">a5</span> <span class="o">=</span> <span class="n">npyv_load_</span><span class="nd">@sfx</span><span class="o">@</span><span class="p">(</span><span class="n">src1</span> <span class="o">+</span> <span class="n">npyv_nlanes_</span><span class="nd">@sfx</span><span class="o">@</span> <span class="o">*</span> <span class="mi">4</span><span class="p">);</span>
</pre></div>
</div>
<p>This will change (as implemented in PR <a class="reference external" href="https://github.com/numpy/numpy/pull/21057">gh-21057</a>) to:</p>
<div class="highlight-C++ notranslate"><div class="highlight"><pre><span></span><span class="k">auto</span><span class="w"> </span><span class="n">a5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Load</span><span class="p">(</span><span class="n">src1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nlanes</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">4</span><span class="p">);</span>
</pre></div>
</div>
<p>If the above C++ code were to use Highway under the hood it would look quite
similar, it uses similarly understandable names as <code class="docutils literal notranslate"><span class="pre">Load</span></code> for individual
portable intrinsics.</p>
<p>The <code class="docutils literal notranslate"><span class="pre">&#64;sfx</span></code> in the C version above is the template variable for type
identifiers, e.g.: <code class="docutils literal notranslate"><span class="pre">#sfx</span> <span class="pre">=</span> <span class="pre">u8,</span> <span class="pre">s8,</span> <span class="pre">u16,</span> <span class="pre">s16,</span> <span class="pre">u32,</span> <span class="pre">s32,</span> <span class="pre">u64,</span> <span class="pre">s64,</span> <span class="pre">f32,</span> <span class="pre">f64#</span></code>.
Explicit use of bitsize-encoded types like this won’t work for sizeless SIMD
instruction sets. With C++ this is easier to handle; PR <a class="reference external" href="https://github.com/numpy/numpy/pull/21057">gh-21057</a> shows how
and contains more complete examples of what the C++ code will look like.</p>
<p>The scope of this NEP includes discussing most relevant aspects of adopting
Google Highway to replace our current Universal Intrinsics framework, including
but not limited to:</p>
<ul class="simple">
<li><p>Maintainability, domain expertise availability, ease of onboarding new
contributor, and other social aspects,</p></li>
<li><p>Key technical differences and constraints that may impact NumPy’s internal
design or performance,</p></li>
<li><p>Build system related aspects,</p></li>
<li><p>Release timing related aspects.</p></li>
</ul>
<p>Out of scope (at least for now) is revisiting other aspects of our current SIMD
support strategy:</p>
<ul class="simple">
<li><p>accuracy vs. performance trade-offs when adding SIMD support to a function</p></li>
<li><p>use of SVML and x86-simd-sort (and possibly its equivalents for aarch64)</p></li>
<li><p>pulling in individual bits or algorithms of Highway (as in <a class="reference external" href="https://github.com/numpy/numpy/pull/24018">gh-24018</a>) or
SLEEF (as discussed in that same PR)</p></li>
</ul>
</section>
<section id="usage-and-impact">
<h2>Usage and Impact<a class="headerlink" href="#usage-and-impact" title="Link to this heading">#</a></h2>
<p>N/A - there will be no significant user-visible changes.</p>
</section>
<section id="backward-compatibility">
<h2>Backward compatibility<a class="headerlink" href="#backward-compatibility" title="Link to this heading">#</a></h2>
<p>There will be no changes in user-facing Python or C APIs: all the methods to
control compilation and runtime CPU feature selection should remain, although
there may be some changes due to moving to C++ without regards to the
Highway/Universal Intrinsics choice.</p>
<p>The naming of the CPU features in Highway is different from that of the
Universal Intrinsics (see “Supported features/targets” below)</p>
<p>On Windows, MSVC may have to be avoided, as a result of Highway’s use of
pragmas which are less well supported by MSVC. This means that we likely have
to build our wheels with clang-cl or Mingw-w64. Both of those should work - we
merged clang-cl support a while back (see <a class="reference external" href="https://github.com/numpy/numpy/pull/20866">gh-20866</a>), and SciPy builds with
Mingw-w64. It may however impact other redistributors or end users who build
from source on Windows.</p>
<p>In response to the earlier discussions around this NEP, Highway is now
dual-licensed as Apache 2 / BSD-3.</p>
</section>
<section id="high-level-considerations">
<h2>High-level considerations<a class="headerlink" href="#high-level-considerations" title="Link to this heading">#</a></h2>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Currently this section attempts to cover each topic separately, and
comparing the future use of a NumPy-specific C++ implementation vs. use of
Google Highway with our own numerical routines on top of that. It does not
(yet) assume a decision or proposed decision is made. Hence this NEP is not
“this is proposed” with another option in the Alternatives section, but
rather a side-by-side comparison.</p>
</div>
<section id="development-effort-and-long-term-maintainability">
<h3>Development effort and long-term maintainability<a class="headerlink" href="#development-effort-and-long-term-maintainability" title="Link to this heading">#</a></h3>
<p>Moving to Highway is likely to be a significant development effort.
Longer-term, this will hopefully be offset by Highway itself having more
maintainer bandwidth to deal with ongoing issues in compiler support and adding
new platforms.</p>
<p>Highway being used by other projects, like Chromium and <a class="reference external" href="https://github.com/libjxl/libjxl">JPEG XL</a> (see
<a class="reference external" href="https://google.github.io/highway/en/master/README.html#examples">this more complete list</a>
in the Highway documentation), does imply that there is likely to be a benefit
of a wider range of testing and bug reporting/fixing.</p>
<p>One concern is that new instructions may have to be added, and that that is
often best done as part of the process of developing the numerical kernel that
needs the instruction. This will be a little more clumsy if the instruction
lives in Highway which is a git submodule inside the NumPy repo - there will be
a need to implement a temporary/generic version first, and then update the
submodule after upstreaming the new intrinsic.</p>
<p>Documentation-wise, Highway would be a clear win. NumPy’s
<a class="reference external" href="https://numpy.org/doc/1.25/reference/simd/">CPU/SIMD Optimizations</a> docs are fairly sparse compared to
<a class="reference external" href="https://google.github.io/highway/">the Highway docs</a>.</p>
</section>
<section id="migration-strategy-can-it-be-gradual">
<h3>Migration strategy - can it be gradual?<a class="headerlink" href="#migration-strategy-can-it-be-gradual" title="Link to this heading">#</a></h3>
<p>This is a story of two halves. Moving to Highway’s statically dispatched
intrinsics could be done gradually, as already seen in PR <a class="reference external" href="https://github.com/numpy/numpy/pull/24018">gh-24018</a>. However,
adopting Highway’s way of performing runtime dispatching has to be done in one
go - we can’t (or shouldn’t) have two ways of doing that.</p>
</section>
<section id="highway-policies-for-compiler-and-platform-support">
<h3>Highway policies for compiler and platform support<a class="headerlink" href="#highway-policies-for-compiler-and-platform-support" title="Link to this heading">#</a></h3>
<p>When adding new instructions, Highway has a policy that they must be
implemented in a way that fairly balances across CPU architectures.</p>
<p>Regarding the support status and whether all currently-supported architectures
will remain supported, Jan stated that Highway can commit to the following:</p>
<ol class="arabic simple">
<li><p>If it cross-compiles with Clang and can be tested via standard QEMU, it can
go into Highway’s CI.</p></li>
<li><p>If it cross-compiles via clang/gcc and can be tested with a new QEMU
(possibly with extra flags), then it can be support via manual testing
before each Highway release.</p></li>
<li><p>Existing targets will remain supported as long as they compile/run in QEMU.</p></li>
</ol>
<p>Highway is not subject to Google’s “no longer supported” strategy (or, as
written in its README, <em>This is not an officially supported Google product</em>).
That is not a bad thing; it means that it is less likely to go unsupported due
to a Google business decision about the project. Quite a few well-known open
source projects under the <code class="docutils literal notranslate"><span class="pre">google</span></code> GitHub org state this, e.g. <a class="reference external" href="https://github.com/google/jax">JAX</a> and
<a class="reference external" href="https://github.com/google/tcmalloc">tcmalloc</a>.</p>
</section>
<section id="supported-features-targets">
<h3>Supported features/targets<a class="headerlink" href="#supported-features-targets" title="Link to this heading">#</a></h3>
<p>Both frameworks support a large set of platforms and SIMD instruction sets,
as well as generic scalar/fallback versions. The main differences right now are:</p>
<ul class="simple">
<li><p>NumPy supports IBM Z-system (s390x, VX/VXE/VXE2) while Highway supports Z14, Z15.</p></li>
<li><p>Highway supports ARM SVE/SVE2 and RISC-V RVV (sizeless instructions), while
NumPy does not.</p>
<ul>
<li><p>The groundwork for sizeless SIMD support in NumPy has been done in
<a class="reference external" href="https://github.com/numpy/numpy/pull/21057">gh-21057</a>, however SVE/SVE2 and RISC-V are not yet implemented there.</p></li>
</ul>
</li>
</ul>
<p>There is also a difference in the granularity of instruction set groups: NumPy
supports a more granular set of architectures than Highway. See the list of
targets for Highway <a class="reference external" href="https://github.com/google/highway/#targets">here</a>
(it’s roughly per CPU family) and for NumPy
<a class="reference external" href="https://numpy.org/doc/1.25/reference/simd/build-options.html#supported-features">here</a>
(roughly per SIMD instruction set). Hence with Highway we’d lose some
granularity - but that is probably fine, we don’t really need this level of
granularity, and there isn’t much evidence that users explicitly play with this
to squeeze out the last bit of performance for their own CPU.</p>
</section>
<section id="compilation-strategy-for-multiple-targets-and-runtime-dispatching">
<h3>Compilation strategy for multiple targets and runtime dispatching<a class="headerlink" href="#compilation-strategy-for-multiple-targets-and-runtime-dispatching" title="Link to this heading">#</a></h3>
<p>Highway compiles once while using preprocessing tricks to generate multiple
stanzas for each CPU feature within the same compilation unit (see the
<code class="docutils literal notranslate"><span class="pre">foreach_target.h</span></code> usage and dynamic dispatch docs for how that is done).
Universal Intrinsics generate multiple compilation units, one for each CPU
feature group, and compiles multiple times, linking them all together (with
different names) for runtime dispatch. The Highway technique may not work
reliably on MSVC, the Universal Intrinsic technique does work on MSVC.</p>
<p>Which one is more robust? The experts disagree. Jan thinks that the Highway
approach is more robust and in particular avoids the linker pulling in
functions with too-new instructions into the final binary. Sayed thinks that
the current NumPy approach (also used by OpenCV) is more robust, and in
particular is less likely to run into compiler-specific bugs or catch them
earlier. Both agree the meson build system allows specifying object link order,
which produces more consistent builds. However that does tie NumPy to meson.</p>
<p>Matti and Ralf think the current build strategy is working well for NumPy and
the advantages of changing the build and runtime dispatch, with possible
unknown instabilities outweighs the advantages that adopting Highway’s dynamic
dispatch may bring.</p>
<p>Our experience of the past four years says that bugs with “invalid instruction”
type crashes are invariably due to issues with feature detection - most often
because users are running under emulation, and sometimes because there are
actual issues with our CPU feature detection code. There is little evidence
we’re aware of of the linker pulling in a function which is compiled multiple
times for different architectures and picking the one with unsupported
instructions. To ensure to avoid the issue, it’s advisable to keep numerical
kernels inside the source code and refrain from defining non-inlined functions
within cache-able objects.</p>
</section>
<section id="c-refactoring-considerations">
<h3>C++ refactoring considerations<a class="headerlink" href="#c-refactoring-considerations" title="Link to this heading">#</a></h3>
<p>We want to move from C to C++, which will naturally involve a significant
amount of refactoring, for two main reasons:</p>
<ul class="simple">
<li><p>get rid of the NumPy-specific templating language for more expressive C++</p></li>
<li><p>this would make using sizeless intrinsics (like for SVE) easier.</p></li>
</ul>
<p>In addition, we see the following considerations:</p>
<ul class="simple">
<li><p>If we use Highway, we would need to switch the C++ wrappers from universal
intrinsics to Highway. On the other hand, the work to move to C++ is not
complete.</p></li>
<li><p>If we use Highway, we’d need to rewrite existing kernels using Highway
intrinsics. But again, moving to C++ requires touching all those kernels
anyway.</p></li>
<li><p>One concern regarding Highway was whether it is possible to obtain a function
pointer for an architecture-specific function instead of calling that
function directly. This so that we can be sure that calling 1-D inner loop
many times for a single Python API invocation does not incur the dispatching
overhead many times. This was investigated: this can be done with Highway
too.</p></li>
<li><p>A second concern was whether it’s possible with Highway to allow the user at
runtime to select or disable dispatching to certain instruction sets. This is
possible.</p></li>
<li><p>Use of tags in Highway’s C++ implementation reduces code duplication but the
added templating makes C-level testing and tracing more complicated.</p></li>
</ul>
</section>
<section id="the-simd-unit-testing-module">
<h3>The <code class="docutils literal notranslate"><span class="pre">_simd</span></code> unit testing module<a class="headerlink" href="#the-simd-unit-testing-module" title="Link to this heading">#</a></h3>
<p>Rewriting the <code class="docutils literal notranslate"><span class="pre">_simd</span> <span class="pre">testing</span></code> module to use C++ was done very recently in PR
<a class="reference external" href="https://github.com/numpy/numpy/pull/24069">gh-24069</a>. It depends on the main PR for the move to C++, <a class="reference external" href="https://github.com/numpy/numpy/pull/21057">gh-21057</a>.
It allows one to access the C++ intrinsics with almost the same signature, but
from Python. This is a great way not only for testing, but also for designing
new SIMD kernels.</p>
<p>It may be possible to add a similar testing and prototyping feature to Highway
(which uses plain <code class="docutils literal notranslate"><span class="pre">googletest</span></code>), however currently the NumPy way is quite a
bit nicer.</p>
</section>
<section id="math-routines">
<h3>Math routines<a class="headerlink" href="#math-routines" title="Link to this heading">#</a></h3>
<p>Math or numerical routines are written at a higher level of abstraction than
the universal intrinsics that are the main focus of this NEP. Highway has only
a limited number of math routines, and they are not precise enough for NumPy’s
needs. So either way, NumPy’s existing routines (which use universal
intrinsics) will stay, and if we go the Highway route they’ll simply have to
use Highway primitives internally. We could still use Highway sorting routines.
If we do accept lower-precision routines (via a user-supplied choice, i.e.
extending <code class="docutils literal notranslate"><span class="pre">errstate</span></code> to allow a precision option), we could use
Highway-native routines.</p>
<p>There may be other libraries that have numerical routines that can be reused in
NumPy (e.g., from SLEEF, or perhaps from JPEG XL or some other Highway-using
libraries). There may be a small benefit here, but likely it doesn’t matter too
much.</p>
</section>
<section id="supported-and-missing-intrinsics">
<h3>Supported and missing intrinsics<a class="headerlink" href="#supported-and-missing-intrinsics" title="Link to this heading">#</a></h3>
<p>Some specific intrinsics that NumPy needs may be missing from Highway.
Similarly, some intrinsics that NumPy needs to implement routines are already
implemented in Highway and are missing from NumPy.</p>
<p>Highway has more instructions that NumPy’s universal intrinsics, so it’s
possible that some future needs for NumPy kernels may already be met there.</p>
<p>Either way, we will always have to implement intrinsics in either solution.</p>
</section>
</section>
<section id="related-work">
<h2>Related Work<a class="headerlink" href="#related-work" title="Link to this heading">#</a></h2>
<ul class="simple">
<li><p><a class="reference external" href="https://github.com/google/highway/">Google Highway</a></p></li>
<li><p><a class="reference external" href="https://github.com/xtensor-stack/xsimd">Xsimd</a></p></li>
<li><p>OpenCV’s SIMD framework (<a class="reference external" href="https://docs.opencv.org/4.x/df/d91/group__core__hal__intrin.html">API reference</a>, <a class="reference external" href="https://github.com/opencv/opencv/wiki/CPU-optimizations-build-options">docs</a>)</p></li>
<li><p><a class="reference external" href="https://en.cppreference.com/w/cpp/experimental/simd/simd">std::experimental::simd</a></p></li>
<li><p>See the Related Work section in <a class="reference internal" href="nep-0038-SIMD-optimizations.html#nep38"><span class="std std-ref">NEP 38 — Using SIMD optimization instructions for performance</span></a> for more related work (as of 2019)</p></li>
</ul>
</section>
<section id="implementation">
<h2>Implementation<a class="headerlink" href="#implementation" title="Link to this heading">#</a></h2>
<p>TODO</p>
</section>
<section id="alternatives">
<h2>Alternatives<a class="headerlink" href="#alternatives" title="Link to this heading">#</a></h2>
<p>Use Google Highway for dynamic dispatch. Other alternatives include: do nothing and
stay with C universal intrinsics, use <a class="reference external" href="https://github.com/xtensor-stack/xsimd">Xsimd</a> as the SIMD framework (less
comprehensive than Highway - no SVE or PowerPC support for example), or
use/vendor <a class="reference external" href="https://sleef.org/">SLEEF</a> (a good library, but inconsistently maintained). Neither of
these alternatives seems appealing.</p>
</section>
<section id="discussion">
<h2>Discussion<a class="headerlink" href="#discussion" title="Link to this heading">#</a></h2>
</section>
<section id="references-and-footnotes">
<h2>References and Footnotes<a class="headerlink" href="#references-and-footnotes" title="Link to this heading">#</a></h2>
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="id1" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">1</a><span class="fn-bracket">]</span></span>
<p>Each NEP must either be explicitly labeled as placed in the public domain (see
this NEP as an example) or licensed under the <a class="reference external" href="https://www.opencontent.org/openpub/">Open Publication License</a>.</p>
</aside>
</aside>
</section>
<section id="copyright">
<h2>Copyright<a class="headerlink" href="#copyright" title="Link to this heading">#</a></h2>
<p>This document has been placed in the public domain. <a class="footnote-reference brackets" href="#id1" id="id2" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a></p>
</section>
</section>


                </article>
              
              
            </div>
            
            
                <dialog id="pst-secondary-sidebar-modal"></dialog>
                <div id="pst-secondary-sidebar" class="bd-sidebar-secondary bd-toc"><div class="sidebar-secondary-items sidebar-secondary__inner">


  <div class="sidebar-secondary-item">
<div
    id="pst-page-navigation-heading-2"
    class="page-toc tocsection onthispage">
    <i class="fa-solid fa-list"></i> On this page
  </div>
  <nav class="bd-toc-nav page-toc" aria-labelledby="pst-page-navigation-heading-2">
    <ul class="visible nav section-nav flex-column">
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#abstract">Abstract</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#motivation-and-scope">Motivation and Scope</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#usage-and-impact">Usage and Impact</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#backward-compatibility">Backward compatibility</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#high-level-considerations">High-level considerations</a><ul class="nav section-nav flex-column">
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#development-effort-and-long-term-maintainability">Development effort and long-term maintainability</a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#migration-strategy-can-it-be-gradual">Migration strategy - can it be gradual?</a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#highway-policies-for-compiler-and-platform-support">Highway policies for compiler and platform support</a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#supported-features-targets">Supported features/targets</a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#compilation-strategy-for-multiple-targets-and-runtime-dispatching">Compilation strategy for multiple targets and runtime dispatching</a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#c-refactoring-considerations">C++ refactoring considerations</a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#the-simd-unit-testing-module">The <code class="docutils literal notranslate"><span class="pre">_simd</span></code> unit testing module</a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#math-routines">Math routines</a></li>
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#supported-and-missing-intrinsics">Supported and missing intrinsics</a></li>
</ul>
</li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#related-work">Related Work</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#implementation">Implementation</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#alternatives">Alternatives</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#discussion">Discussion</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#references-and-footnotes">References and Footnotes</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#copyright">Copyright</a></li>
</ul>
  </nav></div>

</div></div>
              
            
          </div>
          <footer class="bd-footer-content">
            
          </footer>
        
      </main>
    </div>
  </div>
  
  <!-- Scripts loaded after <body> so the DOM is not blocked -->
  <script defer src="_static/scripts/bootstrap.js?digest=8878045cc6db502f8baf"></script>
<script defer src="_static/scripts/pydata-sphinx-theme.js?digest=8878045cc6db502f8baf"></script>

  <footer class="bd-footer">
<div class="bd-footer__inner bd-page-width">
  
    <div class="footer-items__start">
      
        <div class="footer-item">

  <p class="copyright">
    
      © Copyright 2017-2025, NumPy Developers.
      <br/>
    
  </p>
</div>
      
        <div class="footer-item">

  <p class="sphinx-version">
    Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.6.
    <br/>
  </p>
</div>
      
    </div>
  
  
    <div class="footer-items__end">
      
        <div class="footer-item">
<p class="theme-version">
  <!-- # L10n: Setting the PST URL as an argument as this does not need to be localized -->
  Built with the <a href="https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html">PyData Sphinx Theme</a> 0.16.1.
</p></div>
      
    </div>
  
</div>

  </footer>
  </body>
</html>