1*bf2c3715SXin Linamespace Eigen { 2*bf2c3715SXin Li 3*bf2c3715SXin Li/** \eigenManualPage TopicFixedSizeVectorizable Fixed-size vectorizable %Eigen objects 4*bf2c3715SXin Li 5*bf2c3715SXin LiThe goal of this page is to explain what we mean by "fixed-size vectorizable". 6*bf2c3715SXin Li 7*bf2c3715SXin Li\section FixedSizeVectorizable_summary Executive Summary 8*bf2c3715SXin Li 9*bf2c3715SXin LiAn Eigen object is called "fixed-size vectorizable" if it has fixed size and that size is a multiple of 16 bytes. 10*bf2c3715SXin Li 11*bf2c3715SXin LiExamples include: 12*bf2c3715SXin Li\li Eigen::Vector2d 13*bf2c3715SXin Li\li Eigen::Vector4d 14*bf2c3715SXin Li\li Eigen::Vector4f 15*bf2c3715SXin Li\li Eigen::Matrix2d 16*bf2c3715SXin Li\li Eigen::Matrix2f 17*bf2c3715SXin Li\li Eigen::Matrix4d 18*bf2c3715SXin Li\li Eigen::Matrix4f 19*bf2c3715SXin Li\li Eigen::Affine3d 20*bf2c3715SXin Li\li Eigen::Affine3f 21*bf2c3715SXin Li\li Eigen::Quaterniond 22*bf2c3715SXin Li\li Eigen::Quaternionf 23*bf2c3715SXin Li 24*bf2c3715SXin Li\section FixedSizeVectorizable_explanation Explanation 25*bf2c3715SXin Li 26*bf2c3715SXin LiFirst, "fixed-size" should be clear: an %Eigen object has fixed size if its number of rows and its number of columns are fixed at compile-time. So for example \ref Matrix3f has fixed size, but \ref MatrixXf doesn't (the opposite of fixed-size is dynamic-size). 27*bf2c3715SXin Li 28*bf2c3715SXin LiThe array of coefficients of a fixed-size %Eigen object is a plain "static array", it is not dynamically allocated. For example, the data behind a \ref Matrix4f is just a "float array[16]". 29*bf2c3715SXin Li 30*bf2c3715SXin LiFixed-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. 31*bf2c3715SXin Li 32*bf2c3715SXin LiNow, vectorization works with 128-bit packets (e.g., SSE, AltiVec, NEON), 256-bit packets (e.g., AVX), or 512-bit packets (e.g., AVX512). Moreover, for performance reasons, these packets are most efficiently read and written if they have the same alignment as the packet size, that is 16 bytes, 32 bytes, and 64 bytes respectively. 33*bf2c3715SXin Li 34*bf2c3715SXin LiSo it turns out that the best way that fixed-size %Eigen objects can be vectorized, is if their size is a multiple of 16 bytes (or more). %Eigen will then request 16-byte alignment (or more) for these objects, and henceforth rely on these objects being aligned to achieve maximal efficiency. 35*bf2c3715SXin Li 36*bf2c3715SXin Li*/ 37*bf2c3715SXin Li 38*bf2c3715SXin Li} 39