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<div class="title">Fixed-size vectorizable Eigen objects<div class="ingroups"><a class="el" href="group__DenseMatrixManipulation__Alignement.html">Alignment issues</a></div></div> </div>
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<p>The goal of this page is to explain what we mean by "fixed-size vectorizable".</p>
<h1><a class="anchor" id="summary"></a>
Executive Summary</h1>
<p>An <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library. ">Eigen</a> object is called "fixed-size vectorizable" if it has fixed size and that size is a multiple of 16 bytes.</p>
<p>Examples include: </p>
<ul>
<li><a class="el" href="group__matrixtypedefs.html#ga685d563d586f4820b4a2df9a07d98c23">Eigen::Vector2d</a> </li>
<li><a class="el" href="group__matrixtypedefs.html#ga9bdb6b1010218b700f4bc0d23c7d2ee8">Eigen::Vector4d</a> </li>
<li><a class="el" href="group__matrixtypedefs.html#ga96452a1b0400ea4ef7935e06914a56b1">Eigen::Vector4f</a> </li>
<li><a class="el" href="group__matrixtypedefs.html#ga5521d9f6a8d61d3f04a819b799ad9a65">Eigen::Matrix2d</a> </li>
<li><a class="el" href="group__matrixtypedefs.html#ga535a919504bb3bc463b8995c196c1eed">Eigen::Matrix2f</a> </li>
<li><a class="el" href="group__matrixtypedefs.html#gacd860ff07358f6a703c2c0d4a174e920">Eigen::Matrix4d</a> </li>
<li><a class="el" href="group__matrixtypedefs.html#ga548963d9c2934037af5f8e5b3df87e45">Eigen::Matrix4f</a> </li>
<li><a class="el" href="group__Geometry__Module.html#ga1cee3e45cad60050d3c94cf603e2ff45">Eigen::Affine3d</a> </li>
<li><a class="el" href="group__Geometry__Module.html#gaca1e57a15de08fe20c934c5600f19314">Eigen::Affine3f</a> </li>
<li><a class="el" href="group__Geometry__Module.html#ga0d2bd45f1215359f8e7c0d7ab53c4acb">Eigen::Quaterniond</a> </li>
<li><a class="el" href="group__Geometry__Module.html#gaf65cf6f803890e57488d7de750bef682">Eigen::Quaternionf</a></li>
</ul>
<h1><a class="anchor" id="explanation"></a>
General explanation of this assertion</h1>
<p>First, "fixed-size" should be clear: an <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library. ">Eigen</a> object has fixed size if its number of rows and its number of columns are fixed at compile-time. So for example Matrix3f has fixed size, but MatrixXf doesn't (the opposite of fixed-size is dynamic-size).</p>
<p>The array of coefficients of a fixed-size <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library. ">Eigen</a> object is a plain "static array", it is not dynamically allocated. For example, the data behind a Matrix4f is just a "float array[16]".</p>
<p>Fixed-size objects are typically very small, which means that we want to handle them with zero runtime overhead – both in terms of memory usage and of speed.</p>
<p>Now, vectorization (both SSE and AltiVec) works with 128-bit packets. Moreover, for performance reasons, these packets need to be have 128-bit alignment.</p>
<p>So it turns out that the only way that fixed-size <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library. ">Eigen</a> objects can be vectorized, is if their size is a multiple of 128 bits, or 16 bytes. <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library. ">Eigen</a> will then request 16-byte alignment for these objects, and henceforth rely on these objects being aligned so no runtime check for alignment is performed. </p>
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