namespace Eigen {

/** \page TopicVectorization Vectorization

%Eigen performs \em explicit vectorization: instead of relying on the compiler to auto-vectorize scalar
loops, %Eigen's evaluators generate SIMD instructions directly through a portable wrapper layer (the
"packet math" layer). This page gives an overview of which instruction sets are supported, how
vectorization is enabled, what gets vectorized, and how to control it.

\eigenAutoToc

\section TopicVectorizationArch Supported instruction sets

On CPUs, %Eigen provides vectorized kernels for the following instruction sets:

<table class="manual">
<tr><th>Architecture</th><th>Instruction sets</th><th>Notes</th></tr>
<tr><td>x86 / x86-64</td><td>SSE2, SSE3, SSSE3, SSE4.1, SSE4.2, AVX, AVX2+FMA, AVX512 (incl. the DQ, VL, FP16, and BF16 extensions)</td>
    <td>Selected from the compiler's target flags (e.g. \c -mavx2 \c -mfma, \c /arch:AVX2)</td></tr>
<tr class="alt"><td>ARM / AArch64</td><td>NEON, SME; SVE as an opt-in backend</td>
    <td>SVE requires \c EIGEN_ARM64_USE_SVE and a fixed vector length
        (<tt>-msve-vector-bits=N</tt>). The SME backend accelerates real and complex matrix
        products as well as large real dot products, scaled vector additions and column-major
        matrix-vector products. It is selected automatically when the compiler targets SME2
        (<tt>-march=armv9.2-a+sme2</tt>, or a <tt>-mcpu</tt> that implies it) \em without
        <tt>-msve-vector-bits</tt>, since a fixed length would pin the kernels to one runtime
        streaming vector length; everything else keeps the NEON path. Define
        \c EIGEN_ARM64_NO_SME to opt out, or \c EIGEN_ARM64_USE_SME to turn a toolchain that
        cannot provide it into a build error instead of a NEON fallback. Double precision
        additionally needs the optional FEAT_SME_F64F64 extension (<tt>+sme-f64f64</tt>, or a
        <tt>-mcpu</tt> that implies it); without it \c double and \c std::complex<double> keep
        the generic kernels. Floating-point exceptions raised in the streaming SME kernels (matrix
        products, and the vector and matrix-vector kernels) are not reported: FMOPA sets no flags,
        and the caller's flags are restored on exit, discarding those of the kernels' other
        arithmetic. Products on the NEON paths report exceptions as usual</td></tr>
<tr><td>PowerPC</td><td>AltiVec, VSX, MMA</td><td></td></tr>
<tr class="alt"><td>IBM Z (s390x)</td><td>ZVector</td><td></td></tr>
<tr><td>MIPS</td><td>MSA</td><td></td></tr>
<tr class="alt"><td>LoongArch</td><td>LSX</td><td></td></tr>
<tr><td>RISC-V</td><td>RVV 1.0</td>
    <td>Requires \c EIGEN_RISCV64_USE_RVV10 and a fixed vector length
        (<tt>-mrvv-vector-bits=zvl</tt>)</td></tr>
<tr class="alt"><td>Qualcomm Hexagon</td><td>HVX</td><td></td></tr>
</table>

In addition, the same packet abstraction is used to generate efficient device code for CUDA and HIP
GPUs (see \ref TopicCUDA) and for SYCL devices.

Vectorization is enabled automatically whenever the compiler's target flags advertise one of the
supported instruction sets. You can check what a given translation unit ended up using by printing
Eigen::SimdInstructionSetsInUse():
\code
std::cout << Eigen::SimdInstructionSetsInUse() << std::endl;
\endcode

\section TopicVectorizationWhat What gets vectorized

Vectorization applies across %Eigen, most notably to:
  - assignment of coefficient-wise expressions (e.g. <tt>a = 2*b + c.cwiseProduct(d)</tt>),
    including the fused evaluation loops described in \ref TopicEigenExpressionTemplates;
  - reductions such as sum(), minCoeff(), squaredNorm(), and their partial (colwise/rowwise)
    variants;
  - matrix-matrix and matrix-vector products, and through them most decompositions;
  - many coefficient-wise math functions; the \ref CoeffwiseMathFunctions "math function catalogue"
    lists, for every function, the instruction sets and scalar types with a vectorized
    implementation.

The scalar types with SIMD support depend on the instruction set; \c float, \c double, 32- and
64-bit integers, and <tt>std::complex<float></tt>/<tt>std::complex<double></tt> are covered on the
main backends, with \c Eigen::half and \c Eigen::bfloat16 vectorized where hardware support exists
(e.g. AVX512FP16, NEON). Types without SIMD support, such as <tt>long double</tt> or custom scalar
types, simply use scalar code.

Fixed-size objects are vectorized when their size is a multiple of the packet size; this is where
the alignment rules for \ref TopicFixedSizeVectorizable "fixed-size vectorizable types" come from.
Dynamic-size objects use aligned heap allocation plus vectorized loops with scalar prologues and
epilogues where needed. Unaligned loads and stores are used where alignment cannot be established;
this is enabled by default and controlled by \c EIGEN_UNALIGNED_VECTORIZE.

\section TopicVectorizationCtrl Controlling vectorization

Vectorization is meant to be transparent, but the following macros, all documented in
\ref TopicPreprocessorDirectives, let you control it:

  - \c EIGEN_DONT_VECTORIZE disables explicit vectorization entirely.
  - \c EIGEN_MAX_ALIGN_BYTES and \c EIGEN_MAX_STATIC_ALIGN_BYTES bound the alignment %Eigen
    requests for heap and static data respectively; note that changing them affects the ABI.
  - \c EIGEN_UNALIGNED_VECTORIZE=0 restricts vectorization to expressions whose destination is
    aligned.
  - \c EIGEN_FAST_MATH selects between faster and more accurate vectorized math functions.

Disabling vectorization also drops %Eigen's alignment: outside GPU compilation,
\c EIGEN_DONT_VECTORIZE sets the ideal alignment to zero, and the defaults for
\c EIGEN_MAX_STATIC_ALIGN_BYTES and \c EIGEN_MAX_ALIGN_BYTES follow it. Fixed-size vectorizable
types then lose their over-alignment — \c alignof(Vector4f) drops from 16 to 4 on a typical x86-64
build — so translation units that disagree about \c EIGEN_DONT_VECTORIZE disagree about the ABI.
Define the alignment macros explicitly and identically everywhere if you need the boundary to stay
fixed. See \ref TopicUnalignedArrayAssert for what the alignment is there for.

When compiling CUDA sources, host-side SIMD must be disabled; see \ref TopicCUDA.

\section TopicVectorizationInternals Under the hood

Vectorized kernels are written in terms of generic packet primitives — pload(), pstore(), padd(),
pmul(), predux(), and friends — declared in Eigen/src/Core/GenericPacketMath.h and specialized for
each instruction set under <tt>Eigen/src/Core/arch/</tt>. Expression evaluators query each
expression's packet support and alignment at compile time to choose between scalar, linear,
sliced, and unrolled vectorized evaluation loops. Custom functors can participate in vectorization
by providing a \c packetOp() and advertising \c PacketAccess in their traits; see
\ref TopicCustomizing_Functors.

*/
}