Add 5.0.1 release notes and a few unreleased features.

(cherry picked from commit 91526464aef156bb0f847db6e00f0b971f9d9ac8)

.clang-format

@@ -7,6 +7,8 @@ BasedOnStyle: Google
 ColumnLimit:  120
 StatementMacros:
   - EIGEN_STATIC_ASSERT
+  - EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
+  - EIGEN_INTERNAL_DENSE_STORAGE_CTOR_PLUGIN
 SortIncludes: false
 AttributeMacros:
 - EIGEN_STRONG_INLINE

.gitattributes

@@ -0,0 +1,3 @@
+*.sh                         eol=lf
+debug/msvc/*.dat             eol=crlf
+debug/msvc/*.natvis          eol=crlf

.gitlab-ci.yml

@@ -7,10 +7,15 @@
 # Public License v. 2.0. If a copy of the MPL was not distributed
 # with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
+default:
+# automatically cancels a job when a new pipeline for the same branch is triggered
+  interruptible: true
+
 stages:
   - checkformat
   - build
   - test
+  - deploy
 
 variables:
   # CMake build directory.
@@ -19,8 +24,9 @@ variables:
   EIGEN_CI_BUILD_TARGET: ""
   # If a test regex is specified, that will be selected.
   # Otherwise, we will try a label if specified.
-  EIGEN_CI_TEST_REGEX: ""
-  EIGEN_CI_TEST_LABEL: ""
+  EIGEN_CI_CTEST_REGEX: ""
+  EIGEN_CI_CTEST_LABEL: ""
+  EIGEN_CI_CTEST_ARGS: ""
 
 include:
   - "/ci/checkformat.gitlab-ci.yml"
@@ -29,3 +35,4 @@ include:
   - "/ci/build.windows.gitlab-ci.yml"
   - "/ci/test.linux.gitlab-ci.yml"
   - "/ci/test.windows.gitlab-ci.yml"
+  - "/ci/deploy.gitlab-ci.yml"

.hgeol

@@ -1,11 +0,0 @@
-[patterns]
-*.sh = LF
-*.MINPACK = CRLF
-scripts/*.in = LF
-debug/msvc/*.dat = CRLF
-debug/msvc/*.natvis = CRLF
-unsupported/test/mpreal/*.* = CRLF
-** = native
-
-[repository]
-native = LF

CMakeLists.txt

@@ -29,6 +29,11 @@ if (POLICY CMP0146)
   cmake_policy(SET CMP0146 OLD)
 endif ()
 
+# Normalize DESTINATION paths
+if (POLICY CMP0177)
+  cmake_policy(SET CMP0177 NEW)
+endif ()
+
 #==============================================================================
 # CMake Project.
 #==============================================================================
@@ -58,13 +63,8 @@ option(EIGEN_LEAVE_TEST_IN_ALL_TARGET "Leaves tests in the all target, needed by
 option(EIGEN_BUILD_BLAS "Toggles the building of the Eigen Blas library" ${PROJECT_IS_TOP_LEVEL})
 option(EIGEN_BUILD_LAPACK "Toggles the building of the included Eigen LAPACK library" ${PROJECT_IS_TOP_LEVEL})
 if (EIGEN_BUILD_BLAS OR EIGEN_BUILD_LAPACK)
-  # BLAS and LAPACK currently need a fortran compiler.
-  include(CMakeDetermineFortranCompiler)
-  if (NOT CMAKE_Fortran_COMPILER)
-    set(EIGEN_BUILD_BLAS OFF)
-    set(EIGEN_BUILD_LAPACK OFF)
-  else()
-    # Determine if we should build shared libraries for BLAS/LAPACK on this platform.
+  # Determine if we should build shared libraries for BLAS/LAPACK on this platform.
+  if (NOT EIGEN_BUILD_SHARED_LIBS)
     get_cmake_property(EIGEN_BUILD_SHARED_LIBS TARGET_SUPPORTS_SHARED_LIBS)
   endif()
 endif()
@@ -95,34 +95,64 @@ endif()
 # Version Info.
 #==============================================================================
 
-# Automatically parse the version number from header files.
-file(READ "${PROJECT_SOURCE_DIR}/Eigen/src/Core/util/Macros.h" _eigen_version_header)
-string(REGEX MATCH "define[ \t]+EIGEN_WORLD_VERSION[ \t]+([0-9]+)" _eigen_world_version_match "${_eigen_version_header}")
-set(EIGEN_WORLD_VERSION "${CMAKE_MATCH_1}")
-string(REGEX MATCH "define[ \t]+EIGEN_MAJOR_VERSION[ \t]+([0-9]+)" _eigen_major_version_match "${_eigen_version_header}")
-set(EIGEN_MAJOR_VERSION "${CMAKE_MATCH_1}")
-string(REGEX MATCH "define[ \t]+EIGEN_MINOR_VERSION[ \t]+([0-9]+)" _eigen_minor_version_match "${_eigen_version_header}")
-set(EIGEN_MINOR_VERSION "${CMAKE_MATCH_1}")
-set(EIGEN_VERSION_NUMBER ${EIGEN_WORLD_VERSION}.${EIGEN_MAJOR_VERSION}.${EIGEN_MINOR_VERSION})
+# If version information is not provided, automatically parse the version number
+# from header files.
+file(READ "${PROJECT_SOURCE_DIR}/Eigen/Version" _eigen_version_header)
+if (NOT DEFINED EIGEN_WORLD_VERSION)
+  string(REGEX MATCH "define[ \t]+EIGEN_WORLD_VERSION[ \t]+([0-9]+)" _eigen_world_version_match "${_eigen_version_header}")
+  set(EIGEN_WORLD_VERSION "${CMAKE_MATCH_1}")
+endif()
+if (NOT DEFINED EIGEN_MAJOR_VERSION)
+  string(REGEX MATCH "define[ \t]+EIGEN_MAJOR_VERSION[ \t]+([0-9]+)" _eigen_major_version_match "${_eigen_version_header}")
+  set(EIGEN_MAJOR_VERSION "${CMAKE_MATCH_1}")
+endif()
+if (NOT DEFINED EIGEN_MINOR_VERSION)
+  string(REGEX MATCH "define[ \t]+EIGEN_MINOR_VERSION[ \t]+([0-9]+)" _eigen_minor_version_match "${_eigen_version_header}")
+  set(EIGEN_MINOR_VERSION "${CMAKE_MATCH_1}")
+endif()
+if (NOT DEFINED EIGEN_PATCH_VERSION)
+  string(REGEX MATCH "define[ \t]+EIGEN_PATCH_VERSION[ \t]+([0-9]+)" _eigen_patch_version_match "${_eigen_version_header}")
+  set(EIGEN_PATCH_VERSION "${CMAKE_MATCH_1}")
+endif()
+if (NOT DEFINED EIGEN_PRERELEASE_VERSION)
+  set(EIGEN_PRERELEASE_VERSION "dev")
+endif()
 
 # If we are in a git repo, extract a changeset.
 if(IS_DIRECTORY ${CMAKE_SOURCE_DIR}/.git)
   # if the git program is absent or this will leave the EIGEN_GIT_REVNUM string empty,
   # but won't stop CMake.
-  execute_process(COMMAND git ls-remote --refs -q ${CMAKE_SOURCE_DIR} HEAD OUTPUT_VARIABLE EIGEN_GIT_OUTPUT)
+  execute_process(COMMAND git ls-remote -q ${CMAKE_SOURCE_DIR} HEAD OUTPUT_VARIABLE EIGEN_GIT_OUTPUT)
 endif()
+
 # extract the git rev number from the git output...
 if(EIGEN_GIT_OUTPUT)
-string(REGEX MATCH "^([0-9;a-f]+).*" EIGEN_GIT_CHANGESET_MATCH "${EIGEN_GIT_OUTPUT}")
-set(EIGEN_GIT_REVNUM "${CMAKE_MATCH_1}")
+  string(REGEX MATCH "^([0-9;a-f]+).*" EIGEN_GIT_CHANGESET_MATCH "${EIGEN_GIT_OUTPUT}")
+  set(EIGEN_GIT_REVNUM "${CMAKE_MATCH_1}")
 endif()
-#...and show it next to the version number
-if(EIGEN_GIT_REVNUM)
-  set(EIGEN_VERSION "${EIGEN_VERSION_NUMBER} (git rev ${EIGEN_GIT_REVNUM})")
+
+if (NOT DEFINED EIGEN_BUILD_VERSION AND DEFINED EIGEN_GIT_REVNUM)
+  string(SUBSTRING "${EIGEN_GIT_REVNUM}" 0 8 EIGEN_BUILD_VERSION)
 else()
-  set(EIGEN_VERSION "${EIGEN_VERSION_NUMBER}")
+  set(EIGEN_BUILD_VERSION "")
 endif()
 
+# The EIGEN_VERSION_NUMBER must be of the form <major.minor.patch>.
+# The EIGEN_VERSION_STRING can contain the preprelease/build strings.
+set(EIGEN_VERSION_NUMBER "${EIGEN_MAJOR_VERSION}.${EIGEN_MINOR_VERSION}.${EIGEN_PATCH_VERSION}")
+set(EIGEN_VERSION_STRING "${EIGEN_VERSION_NUMBER}")
+if (NOT "x${EIGEN_PRERELEASE_VERSION}" STREQUAL "x")
+  set(EIGEN_VERSION_STRING "${EIGEN_VERSION_STRING}-${EIGEN_PRERELEASE_VERSION}")
+endif()
+if (NOT "x${EIGEN_BUILD_VERSION}" STREQUAL "x")
+  set(EIGEN_VERSION_STRING "${EIGEN_VERSION_STRING}+${EIGEN_BUILD_VERSION}")
+endif()
+
+
+# Generate version file.
+configure_file("${CMAKE_CURRENT_SOURCE_DIR}/cmake/Version.in"
+               "${CMAKE_CURRENT_BINARY_DIR}/include/Eigen/Version")
+
 #==============================================================================
 # Install Path Configuration.
 #==============================================================================
@@ -170,11 +200,6 @@ endforeach()
 # Eigen Library.
 #==============================================================================
 
-set ( EIGEN_VERSION_STRING ${EIGEN_VERSION_NUMBER} )
-set ( EIGEN_VERSION_MAJOR  ${EIGEN_WORLD_VERSION} )
-set ( EIGEN_VERSION_MINOR  ${EIGEN_MAJOR_VERSION} )
-set ( EIGEN_VERSION_PATCH  ${EIGEN_MINOR_VERSION} )
-
 # Alias Eigen_*_DIR to Eigen3_*_DIR:
 set(Eigen_SOURCE_DIR ${Eigen3_SOURCE_DIR})
 set(Eigen_BINARY_DIR ${Eigen3_BINARY_DIR})
@@ -187,6 +212,9 @@ target_include_directories (eigen INTERFACE
   $<INSTALL_INTERFACE:${INCLUDE_INSTALL_DIR}>
 )
 
+# Eigen requires at least C++14
+target_compile_features (eigen INTERFACE cxx_std_14)
+
 # Export as title case Eigen
 set_target_properties (eigen PROPERTIES EXPORT_NAME Eigen)
 
@@ -206,6 +234,9 @@ if(EIGEN_BUILD_PKGCONFIG)
 endif()
 
 install(DIRECTORY Eigen DESTINATION ${INCLUDE_INSTALL_DIR} COMPONENT Devel)
+# Replace the "Version" header file with the generated one.
+install(FILES ${CMAKE_CURRENT_BINARY_DIR}/include/Eigen/Version
+    DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/ COMPONENT Devel)
 
 install(TARGETS eigen EXPORT Eigen3Targets)
 
@@ -219,25 +250,10 @@ if(EIGEN_BUILD_CMAKE_PACKAGE)
     NO_CHECK_REQUIRED_COMPONENTS_MACRO # Eigen does not provide components
   )
 
-  # NOTE Remove the first code path once the minimum required CMake version is
-  # bumped to 3.14 or above.
-  if (CMAKE_VERSION VERSION_LESS 3.14)
-    # Remove CMAKE_SIZEOF_VOID_P from Eigen3ConfigVersion.cmake since Eigen does
-    # not depend on architecture specific settings or libraries. More
-    # specifically, an Eigen3Config.cmake generated from a 64 bit target can be
-    # used for 32 bit targets as well (and vice versa).
-    set (_Eigen3_CMAKE_SIZEOF_VOID_P ${CMAKE_SIZEOF_VOID_P})
-    unset (CMAKE_SIZEOF_VOID_P)
-    write_basic_package_version_file (Eigen3ConfigVersion.cmake
-                                      VERSION ${EIGEN_VERSION_NUMBER}
-                                      COMPATIBILITY SameMajorVersion)
-    set (CMAKE_SIZEOF_VOID_P ${_Eigen3_CMAKE_SIZEOF_VOID_P})
-  else (CMAKE_VERSION VERSION_LESS 3.14)
-    write_basic_package_version_file (Eigen3ConfigVersion.cmake
-                                      VERSION ${EIGEN_VERSION_NUMBER}
-                                      COMPATIBILITY SameMajorVersion
-                                      ARCH_INDEPENDENT)
-  endif (CMAKE_VERSION VERSION_LESS 3.14)
+  set(CVF_VERSION "${EIGEN_VERSION_NUMBER}")
+  configure_file("${CMAKE_CURRENT_SOURCE_DIR}/cmake/Eigen3ConfigVersion.cmake.in"
+                 "Eigen3ConfigVersion.cmake"
+                 @ONLY)
 
   # The Eigen target will be located in the Eigen3 namespace. Other CMake
   # targets can refer to it using Eigen3::Eigen.
@@ -253,7 +269,7 @@ if(EIGEN_BUILD_CMAKE_PACKAGE)
           DESTINATION ${CMAKEPACKAGE_INSTALL_DIR})
 
   # Add uninstall target
-  if(NOT TARGET uninstall)
+  if(NOT TARGET uninstall AND PROJECT_IS_TOP_LEVEL)
     add_custom_target ( uninstall
         COMMAND ${CMAKE_COMMAND} -P ${CMAKE_CURRENT_SOURCE_DIR}/cmake/EigenUninstall.cmake)
   endif()
@@ -383,12 +399,17 @@ if (EIGEN_BUILD_TESTING)
     ei_add_cxx_compiler_flag("-Wno-psabi")
     ei_add_cxx_compiler_flag("-Wno-variadic-macros")
     ei_add_cxx_compiler_flag("-Wno-long-long")
-    ei_add_cxx_compiler_flag("-fno-check-new")
     ei_add_cxx_compiler_flag("-fno-common")
     ei_add_cxx_compiler_flag("-fstrict-aliasing")
     ei_add_cxx_compiler_flag("-wd981")                    # disable ICC's "operands are evaluated in unspecified order" remark
     ei_add_cxx_compiler_flag("-wd2304")                   # disable ICC's "warning #2304: non-explicit constructor with single argument may cause implicit type conversion" produced by -Wnon-virtual-dtor
 
+    # Clang emits warnings about unused flag.
+    if (NOT CMAKE_CXX_COMPILER_ID MATCHES "Clang")
+      ei_add_cxx_compiler_flag("-fno-check-new")
+    endif()
+
+
     if(ANDROID_NDK)
       ei_add_cxx_compiler_flag("-pie")
       ei_add_cxx_compiler_flag("-fPIE")
@@ -486,6 +507,12 @@ if (EIGEN_BUILD_TESTING)
       message(STATUS "Enabling MSA in tests/examples")
     endif()
 
+   option(EIGEN_TEST_LSX "Enable/Disable LSX in tests/examples" OFF)
+   if(EIGEN_TEST_LSX)
+     set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mlsx")
+     message(STATUS "Enabling LSX in tests/examples")
+   endif()
+
     option(EIGEN_TEST_NEON "Enable/Disable Neon in tests/examples" OFF)
     if(EIGEN_TEST_NEON)
       if(EIGEN_TEST_FMA)
@@ -738,36 +765,37 @@ if(PROJECT_IS_TOP_LEVEL)
   else()
     message(STATUS "Available targets (use: cmake --build . --target TARGET):")
   endif()
-  message(STATUS "---------+--------------------------------------------------------------")
-  message(STATUS "Target   |   Description")
-  message(STATUS "---------+--------------------------------------------------------------")
-  message(STATUS "install  | Install Eigen. Headers will be installed to:")
-  message(STATUS "         |     <CMAKE_INSTALL_PREFIX>/<INCLUDE_INSTALL_DIR>")
-  message(STATUS "         |   Using the following values:")
-  message(STATUS "         |     CMAKE_INSTALL_PREFIX: ${CMAKE_INSTALL_PREFIX}")
-  message(STATUS "         |     INCLUDE_INSTALL_DIR:  ${INCLUDE_INSTALL_DIR}")
-  message(STATUS "         |   Change the install location of Eigen headers using:")
-  message(STATUS "         |     cmake . -DCMAKE_INSTALL_PREFIX=yourprefix")
-  message(STATUS "         |   Or:")
-  message(STATUS "         |     cmake . -DINCLUDE_INSTALL_DIR=yourdir")
-  message(STATUS "uninstall| Remove files installed by the install target")
+  message(STATUS "------------+--------------------------------------------------------------")
+  message(STATUS "Target      |   Description")
+  message(STATUS "------------+--------------------------------------------------------------")
+  message(STATUS "install     | Install Eigen. Headers will be installed to:")
+  message(STATUS "            |     <CMAKE_INSTALL_PREFIX>/<INCLUDE_INSTALL_DIR>")
+  message(STATUS "            |   Using the following values:")
+  message(STATUS "            |     CMAKE_INSTALL_PREFIX: ${CMAKE_INSTALL_PREFIX}")
+  message(STATUS "            |     INCLUDE_INSTALL_DIR:  ${INCLUDE_INSTALL_DIR}")
+  message(STATUS "            |   Change the install location of Eigen headers using:")
+  message(STATUS "            |     cmake . -DCMAKE_INSTALL_PREFIX=yourprefix")
+  message(STATUS "            |   Or:")
+  message(STATUS "            |     cmake . -DINCLUDE_INSTALL_DIR=yourdir")
+  message(STATUS "uninstall   | Remove files installed by the install target")
   if (EIGEN_BUILD_DOC)
-    message(STATUS "doc      | Generate the API documentation, requires Doxygen & LaTeX")
+    message(STATUS "doc         | Generate the API documentation, requires Doxygen & LaTeX")
+    message(STATUS "install-doc | Install the API documentation")
   endif()
   if(EIGEN_BUILD_TESTING)
-    message(STATUS "check    | Build and run the unit-tests. Read this page:")
-    message(STATUS "         |   http://eigen.tuxfamily.org/index.php?title=Tests")
+    message(STATUS "check       | Build and run the unit-tests. Read this page:")
+    message(STATUS "            |   http://eigen.tuxfamily.org/index.php?title=Tests")
   endif()
   if (EIGEN_BUILD_BLAS)
-    message(STATUS "blas     | Build BLAS library (not the same thing as Eigen)")
+    message(STATUS "blas        | Build BLAS library (not the same thing as Eigen)")
   endif()
   if (EIGEN_BUILD_LAPACK)
-    message(STATUS "lapack   | Build LAPACK subset library (not the same thing as Eigen)")
+    message(STATUS "lapack      | Build LAPACK subset library (not the same thing as Eigen)")
   endif()
-  message(STATUS "---------+--------------------------------------------------------------")
+  message(STATUS "------------+--------------------------------------------------------------")
   message(STATUS "")
 endif()
 
 message(STATUS "")
-message(STATUS "Configured Eigen ${EIGEN_VERSION_NUMBER}")
+message(STATUS "Configured Eigen ${EIGEN_VERSION_STRING}")
 message(STATUS "")

Eigen/Core

@@ -11,6 +11,9 @@
 #ifndef EIGEN_CORE_MODULE_H
 #define EIGEN_CORE_MODULE_H
 
+// Eigen version information.
+#include "Version"
+
 // first thing Eigen does: stop the compiler from reporting useless warnings.
 #include "src/Core/util/DisableStupidWarnings.h"
 
@@ -92,6 +95,7 @@
 #include <algorithm>
 
 #include <array>
+#include <memory>
 #include <vector>
 
 // for std::is_nothrow_move_assignable
@@ -102,6 +106,16 @@
 #include <thread>
 #endif
 
+// for __cpp_lib feature test macros
+#if defined(__has_include) && __has_include(<version>)
+#include <version>
+#endif
+
+// for std::bit_cast()
+#if defined(__cpp_lib_bit_cast) && __cpp_lib_bit_cast >= 201806L
+#include <bit>
+#endif
+
 // for outputting debug info
 #ifdef EIGEN_DEBUG_ASSIGN
 #include <iostream>
@@ -121,7 +135,6 @@
 #undef isfinite
 #include <CL/sycl.hpp>
 #include <map>
-#include <memory>
 #include <thread>
 #include <utility>
 #ifndef EIGEN_SYCL_LOCAL_THREAD_DIM0
@@ -193,38 +206,52 @@ using std::ptrdiff_t;
 #include "src/Core/arch/Default/GenericPacketMathFunctionsFwd.h"
 
 #if defined EIGEN_VECTORIZE_AVX512
+#include "src/Core/arch/SSE/PacketMath.h"
+#include "src/Core/arch/SSE/Reductions.h"
+#include "src/Core/arch/AVX/PacketMath.h"
+#include "src/Core/arch/AVX/Reductions.h"
+#include "src/Core/arch/AVX512/PacketMath.h"
+#include "src/Core/arch/AVX512/Reductions.h"
 #if defined EIGEN_VECTORIZE_AVX512FP16
 #include "src/Core/arch/AVX512/PacketMathFP16.h"
 #endif
-#include "src/Core/arch/SSE/PacketMath.h"
 #include "src/Core/arch/SSE/TypeCasting.h"
-#include "src/Core/arch/SSE/Complex.h"
-#include "src/Core/arch/AVX/PacketMath.h"
 #include "src/Core/arch/AVX/TypeCasting.h"
-#include "src/Core/arch/AVX/Complex.h"
-#include "src/Core/arch/AVX512/PacketMath.h"
 #include "src/Core/arch/AVX512/TypeCasting.h"
+#if defined EIGEN_VECTORIZE_AVX512FP16
+#include "src/Core/arch/AVX512/TypeCastingFP16.h"
+#endif
+#include "src/Core/arch/SSE/Complex.h"
+#include "src/Core/arch/AVX/Complex.h"
 #include "src/Core/arch/AVX512/Complex.h"
 #include "src/Core/arch/SSE/MathFunctions.h"
 #include "src/Core/arch/AVX/MathFunctions.h"
 #include "src/Core/arch/AVX512/MathFunctions.h"
+#if defined EIGEN_VECTORIZE_AVX512FP16
+#include "src/Core/arch/AVX512/MathFunctionsFP16.h"
+#endif
 #include "src/Core/arch/AVX512/TrsmKernel.h"
 #elif defined EIGEN_VECTORIZE_AVX
-   // Use AVX for floats and doubles, SSE for integers
+// Use AVX for floats and doubles, SSE for integers
 #include "src/Core/arch/SSE/PacketMath.h"
+#include "src/Core/arch/SSE/Reductions.h"
 #include "src/Core/arch/SSE/TypeCasting.h"
 #include "src/Core/arch/SSE/Complex.h"
 #include "src/Core/arch/AVX/PacketMath.h"
+#include "src/Core/arch/AVX/Reductions.h"
 #include "src/Core/arch/AVX/TypeCasting.h"
 #include "src/Core/arch/AVX/Complex.h"
 #include "src/Core/arch/SSE/MathFunctions.h"
 #include "src/Core/arch/AVX/MathFunctions.h"
 #elif defined EIGEN_VECTORIZE_SSE
 #include "src/Core/arch/SSE/PacketMath.h"
+#include "src/Core/arch/SSE/Reductions.h"
 #include "src/Core/arch/SSE/TypeCasting.h"
 #include "src/Core/arch/SSE/MathFunctions.h"
 #include "src/Core/arch/SSE/Complex.h"
-#elif defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX)
+#endif
+
+#if defined(EIGEN_VECTORIZE_ALTIVEC) || defined(EIGEN_VECTORIZE_VSX)
 #include "src/Core/arch/AltiVec/PacketMath.h"
 #include "src/Core/arch/AltiVec/TypeCasting.h"
 #include "src/Core/arch/AltiVec/MathFunctions.h"
@@ -234,6 +261,11 @@ using std::ptrdiff_t;
 #include "src/Core/arch/NEON/TypeCasting.h"
 #include "src/Core/arch/NEON/MathFunctions.h"
 #include "src/Core/arch/NEON/Complex.h"
+#elif defined EIGEN_VECTORIZE_LSX
+#include "src/Core/arch/LSX/PacketMath.h"
+#include "src/Core/arch/LSX/TypeCasting.h"
+#include "src/Core/arch/LSX/MathFunctions.h"
+#include "src/Core/arch/LSX/Complex.h"
 #elif defined EIGEN_VECTORIZE_SVE
 #include "src/Core/arch/SVE/PacketMath.h"
 #include "src/Core/arch/SVE/TypeCasting.h"
@@ -300,11 +332,8 @@ using std::ptrdiff_t;
 #include "src/Core/Product.h"
 #include "src/Core/CoreEvaluators.h"
 #include "src/Core/AssignEvaluator.h"
-
-#ifndef EIGEN_PARSED_BY_DOXYGEN  // work around Doxygen bug triggered by Assign.h r814874
-                                 // at least confirmed with Doxygen 1.5.5 and 1.5.6
+#include "src/Core/RealView.h"
 #include "src/Core/Assign.h"
-#endif
 
 #include "src/Core/ArrayBase.h"
 #include "src/Core/util/BlasUtil.h"
@@ -318,6 +347,7 @@ using std::ptrdiff_t;
 #include "src/Core/PlainObjectBase.h"
 #include "src/Core/Matrix.h"
 #include "src/Core/Array.h"
+#include "src/Core/Fill.h"
 #include "src/Core/CwiseTernaryOp.h"
 #include "src/Core/CwiseBinaryOp.h"
 #include "src/Core/CwiseUnaryOp.h"
@@ -342,6 +372,7 @@ using std::ptrdiff_t;
 #include "src/Core/SkewSymmetricMatrix3.h"
 #include "src/Core/Redux.h"
 #include "src/Core/Visitor.h"
+#include "src/Core/FindCoeff.h"
 #include "src/Core/Fuzzy.h"
 #include "src/Core/Swap.h"
 #include "src/Core/CommaInitializer.h"
@@ -380,6 +411,8 @@ using std::ptrdiff_t;
 #include "src/Core/arch/AltiVec/MatrixProduct.h"
 #elif defined EIGEN_VECTORIZE_NEON
 #include "src/Core/arch/NEON/GeneralBlockPanelKernel.h"
+#elif defined EIGEN_VECTORIZE_LSX
+#include "src/Core/arch/LSX/GeneralBlockPanelKernel.h"
 #endif
 
 #if defined(EIGEN_VECTORIZE_AVX512)

Eigen/Geometry

@@ -22,13 +22,11 @@
  *  - fixed-size homogeneous transformations
  *  - translation, scaling, 2D and 3D rotations
  *  - \link Quaternion quaternions \endlink
- *  - cross products (\ref MatrixBase::cross, \ref MatrixBase::cross3)
- *  - orthogonal vector generation (\ref MatrixBase::unitOrthogonal)
- *  - some linear components: \link ParametrizedLine parametrized-lines \endlink and \link Hyperplane hyperplanes
- * \endlink
+ *  - cross products (\ref MatrixBase::cross(), \ref MatrixBase::cross3())
+ *  - orthogonal vector generation (MatrixBase::unitOrthogonal)
+ *  - some linear components: \link ParametrizedLine parametrized-lines \endlink and \link Hyperplane hyperplanes \endlink
  *  - \link AlignedBox axis aligned bounding boxes \endlink
- *  - \link umeyama least-square transformation fitting \endlink
- *
+ *  - \link umeyama() least-square transformation fitting \endlink
  * \code
  * #include <Eigen/Geometry>
  * \endcode

Eigen/ThreadPool

@@ -72,6 +72,7 @@
 #include "src/ThreadPool/Barrier.h"
 #include "src/ThreadPool/NonBlockingThreadPool.h"
 #include "src/ThreadPool/CoreThreadPoolDevice.h"
+#include "src/ThreadPool/ForkJoin.h"
 // IWYU pragma: end_exports
 
 #include "src/Core/util/ReenableStupidWarnings.h"

Eigen/Version

@@ -0,0 +1,14 @@
+#ifndef EIGEN_VERSION_H
+#define EIGEN_VERSION_H
+
+// The "WORLD" version will forever remain "3" for the "Eigen3" library.
+#define EIGEN_WORLD_VERSION 3
+// As of Eigen3 5.0.0, we have moved to Semantic Versioning (semver.org).
+#define EIGEN_MAJOR_VERSION 5
+#define EIGEN_MINOR_VERSION 0
+#define EIGEN_PATCH_VERSION 1
+#define EIGEN_PRERELEASE_VERSION ""
+#define EIGEN_BUILD_VERSION ""
+#define EIGEN_VERSION_STRING "5.0.1"
+
+#endif  // EIGEN_VERSION_H

Eigen/src/AccelerateSupport/AccelerateSupport.h

@@ -11,7 +11,7 @@ template <typename MatrixType_, int UpLo_, SparseFactorization_t Solver_, bool E
 class AccelerateImpl;
 
 /** \ingroup AccelerateSupport_Module
- * \class AccelerateLLT
+ * \typedef AccelerateLLT
  * \brief A direct Cholesky (LLT) factorization and solver based on Accelerate
  *
  * \warning Only single and double precision real scalar types are supported by Accelerate
@@ -25,7 +25,7 @@ template <typename MatrixType, int UpLo = Lower>
 using AccelerateLLT = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationCholesky, true>;
 
 /** \ingroup AccelerateSupport_Module
- * \class AccelerateLDLT
+ * \typedef AccelerateLDLT
  * \brief The default Cholesky (LDLT) factorization and solver based on Accelerate
  *
  * \warning Only single and double precision real scalar types are supported by Accelerate
@@ -39,7 +39,7 @@ template <typename MatrixType, int UpLo = Lower>
 using AccelerateLDLT = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLT, true>;
 
 /** \ingroup AccelerateSupport_Module
- * \class AccelerateLDLTUnpivoted
+ * \typedef AccelerateLDLTUnpivoted
  * \brief A direct Cholesky-like LDL^T factorization and solver based on Accelerate with only 1x1 pivots and no pivoting
  *
  * \warning Only single and double precision real scalar types are supported by Accelerate
@@ -53,7 +53,7 @@ template <typename MatrixType, int UpLo = Lower>
 using AccelerateLDLTUnpivoted = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLTUnpivoted, true>;
 
 /** \ingroup AccelerateSupport_Module
- * \class AccelerateLDLTSBK
+ * \typedef AccelerateLDLTSBK
  * \brief A direct Cholesky (LDLT) factorization and solver based on Accelerate with Supernode Bunch-Kaufman and static
  * pivoting
  *
@@ -68,7 +68,7 @@ template <typename MatrixType, int UpLo = Lower>
 using AccelerateLDLTSBK = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLTSBK, true>;
 
 /** \ingroup AccelerateSupport_Module
- * \class AccelerateLDLTTPP
+ * \typedef AccelerateLDLTTPP
  * \brief A direct Cholesky (LDLT) factorization and solver based on Accelerate with full threshold partial pivoting
  *
  * \warning Only single and double precision real scalar types are supported by Accelerate
@@ -82,7 +82,7 @@ template <typename MatrixType, int UpLo = Lower>
 using AccelerateLDLTTPP = AccelerateImpl<MatrixType, UpLo | Symmetric, SparseFactorizationLDLTTPP, true>;
 
 /** \ingroup AccelerateSupport_Module
- * \class AccelerateQR
+ * \typedef AccelerateQR
  * \brief A QR factorization and solver based on Accelerate
  *
  * \warning Only single and double precision real scalar types are supported by Accelerate
@@ -95,7 +95,7 @@ template <typename MatrixType>
 using AccelerateQR = AccelerateImpl<MatrixType, 0, SparseFactorizationQR, false>;
 
 /** \ingroup AccelerateSupport_Module
- * \class AccelerateCholeskyAtA
+ * \typedef AccelerateCholeskyAtA
  * \brief A QR factorization and solver based on Accelerate without storing Q (equivalent to A^TA = R^T R)
  *
  * \warning Only single and double precision real scalar types are supported by Accelerate

Eigen/src/Cholesky/LDLT.h

@@ -230,8 +230,8 @@ class LDLT : public SolverBase<LDLT<MatrixType_, UpLo_> > {
    */
   const LDLT& adjoint() const { return *this; }
 
-  EIGEN_DEVICE_FUNC inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
-  EIGEN_DEVICE_FUNC inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_matrix.rows(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_matrix.cols(); }
 
   /** \brief Reports whether previous computation was successful.
    *

Eigen/src/Cholesky/LLT.h

@@ -182,10 +182,10 @@ class LLT : public SolverBase<LLT<MatrixType_, UpLo_> > {
    * This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
    * \code x = decomposition.adjoint().solve(b) \endcode
    */
-  const LLT& adjoint() const EIGEN_NOEXCEPT { return *this; }
+  const LLT& adjoint() const noexcept { return *this; }
 
-  inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
-  inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
+  constexpr Index rows() const noexcept { return m_matrix.rows(); }
+  constexpr Index cols() const noexcept { return m_matrix.cols(); }
 
   template <typename VectorType>
   LLT& rankUpdate(const VectorType& vec, const RealScalar& sigma = 1);

Eigen/src/Core/Array.h

@@ -102,8 +102,13 @@ class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxR
     return Base::_set(other);
   }
 
-  /** This is a special case of the templated operator=. Its purpose is to
-   * prevent a default operator= from hiding the templated operator=.
+  /**
+   * \brief Assigns arrays to each other.
+   *
+   * \note This is a special case of the templated operator=. Its purpose is
+   * to prevent a default operator= from hiding the templated operator=.
+   *
+   * \callgraph
    */
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array& operator=(const Array& other) { return Base::_set(other); }
 
@@ -117,23 +122,27 @@ class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxR
    *
    * \sa resize(Index,Index)
    */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Array() : Base() { EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED }
-
-#ifndef EIGEN_PARSED_BY_DOXYGEN
-  // FIXME is it still needed ??
-  /** \internal */
-  EIGEN_DEVICE_FUNC Array(internal::constructor_without_unaligned_array_assert)
-      : Base(internal::constructor_without_unaligned_array_assert()){EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED}
+#ifdef EIGEN_INITIALIZE_COEFFS
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array() : Base() { EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED }
+#else
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array() = default;
 #endif
-
-        EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array(Array && other) = default;
-  EIGEN_DEVICE_FUNC Array& operator=(Array&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value) {
+  /** \brief Move constructor */
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array(Array&&) = default;
+  EIGEN_DEVICE_FUNC Array& operator=(Array&& other) noexcept(std::is_nothrow_move_assignable<Scalar>::value) {
     Base::operator=(std::move(other));
     return *this;
   }
 
-  /** \copydoc PlainObjectBase(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const
-   * ArgTypes&... args)
+  /** \brief Construct a row of column vector with fixed size from an arbitrary number of coefficients.
+   *
+   * \only_for_vectors
+   *
+   * This constructor is for 1D array or vectors with more than 4 coefficients.
+   *
+   * \warning To construct a column (resp. row) vector of fixed length, the number of values passed to this
+   * constructor must match the the fixed number of rows (resp. columns) of \c *this.
+   *
    *
    * Example: \include Array_variadic_ctor_cxx11.cpp
    * Output: \verbinclude Array_variadic_ctor_cxx11.out
@@ -230,7 +239,7 @@ class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxR
   }
 
   /** Copy constructor */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array(const Array& other) = default;
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Array(const Array&) = default;
 
  private:
   struct PrivateType {};
@@ -244,8 +253,8 @@ class Array : public PlainObjectBase<Array<Scalar_, Rows_, Cols_, Options_, MaxR
           PrivateType())
       : Base(other.derived()) {}
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const EIGEN_NOEXCEPT { return 1; }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const EIGEN_NOEXCEPT { return this->innerSize(); }
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return 1; }
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return this->innerSize(); }
 
 #ifdef EIGEN_ARRAY_PLUGIN
 #include EIGEN_ARRAY_PLUGIN

Eigen/src/Core/ArrayBase.h

@@ -81,9 +81,6 @@ class ArrayBase : public DenseBase<Derived> {
 
   typedef typename Base::CoeffReturnType CoeffReturnType;
 
-#endif  // not EIGEN_PARSED_BY_DOXYGEN
-
-#ifndef EIGEN_PARSED_BY_DOXYGEN
   typedef typename Base::PlainObject PlainObject;
 
   /** \internal Represents a matrix with all coefficients equal to one another*/
@@ -118,19 +115,57 @@ class ArrayBase : public DenseBase<Derived> {
     return derived();
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator+=(const Scalar& scalar);
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator-=(const Scalar& scalar);
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator+=(const Scalar& other) {
+    internal::call_assignment(this->derived(), PlainObject::Constant(rows(), cols(), other),
+                              internal::add_assign_op<Scalar, Scalar>());
+    return derived();
+  }
 
-  template <typename OtherDerived>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator+=(const ArrayBase<OtherDerived>& other);
-  template <typename OtherDerived>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator-=(const ArrayBase<OtherDerived>& other);
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator-=(const Scalar& other) {
+    internal::call_assignment(this->derived(), PlainObject::Constant(rows(), cols(), other),
+                              internal::sub_assign_op<Scalar, Scalar>());
+    return derived();
+  }
 
+  /** replaces \c *this by \c *this + \a other.
+   *
+   * \returns a reference to \c *this
+   */
   template <typename OtherDerived>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*=(const ArrayBase<OtherDerived>& other);
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator+=(const ArrayBase<OtherDerived>& other) {
+    call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar, typename OtherDerived::Scalar>());
+    return derived();
+  }
 
+  /** replaces \c *this by \c *this - \a other.
+   *
+   * \returns a reference to \c *this
+   */
   template <typename OtherDerived>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator/=(const ArrayBase<OtherDerived>& other);
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator-=(const ArrayBase<OtherDerived>& other) {
+    call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar, typename OtherDerived::Scalar>());
+    return derived();
+  }
+
+  /** replaces \c *this by \c *this * \a other coefficient wise.
+   *
+   * \returns a reference to \c *this
+   */
+  template <typename OtherDerived>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*=(const ArrayBase<OtherDerived>& other) {
+    call_assignment(derived(), other.derived(), internal::mul_assign_op<Scalar, typename OtherDerived::Scalar>());
+    return derived();
+  }
+
+  /** replaces \c *this by \c *this / \a other coefficient wise.
+   *
+   * \returns a reference to \c *this
+   */
+  template <typename OtherDerived>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator/=(const ArrayBase<OtherDerived>& other) {
+    call_assignment(derived(), other.derived(), internal::div_assign_op<Scalar, typename OtherDerived::Scalar>());
+    return derived();
+  }
 
  public:
   EIGEN_DEVICE_FUNC ArrayBase<Derived>& array() { return *this; }
@@ -173,50 +208,6 @@ class ArrayBase : public DenseBase<Derived> {
   }
 };
 
-/** replaces \c *this by \c *this - \a other.
- *
- * \returns a reference to \c *this
- */
-template <typename Derived>
-template <typename OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator-=(const ArrayBase<OtherDerived>& other) {
-  call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar, typename OtherDerived::Scalar>());
-  return derived();
-}
-
-/** replaces \c *this by \c *this + \a other.
- *
- * \returns a reference to \c *this
- */
-template <typename Derived>
-template <typename OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator+=(const ArrayBase<OtherDerived>& other) {
-  call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar, typename OtherDerived::Scalar>());
-  return derived();
-}
-
-/** replaces \c *this by \c *this * \a other coefficient wise.
- *
- * \returns a reference to \c *this
- */
-template <typename Derived>
-template <typename OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator*=(const ArrayBase<OtherDerived>& other) {
-  call_assignment(derived(), other.derived(), internal::mul_assign_op<Scalar, typename OtherDerived::Scalar>());
-  return derived();
-}
-
-/** replaces \c *this by \c *this / \a other coefficient wise.
- *
- * \returns a reference to \c *this
- */
-template <typename Derived>
-template <typename OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator/=(const ArrayBase<OtherDerived>& other) {
-  call_assignment(derived(), other.derived(), internal::div_assign_op<Scalar, typename OtherDerived::Scalar>());
-  return derived();
-}
-
 }  // end namespace Eigen
 
 #endif  // EIGEN_ARRAYBASE_H

Eigen/src/Core/ArrayWrapper.h

@@ -56,14 +56,10 @@ class ArrayWrapper : public ArrayBase<ArrayWrapper<ExpressionType> > {
 
   EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE ArrayWrapper(ExpressionType& matrix) : m_expression(matrix) {}
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const EIGEN_NOEXCEPT {
-    return m_expression.outerStride();
-  }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const EIGEN_NOEXCEPT {
-    return m_expression.innerStride();
-  }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_expression.rows(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_expression.cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return m_expression.outerStride(); }
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_expression.innerStride(); }
 
   EIGEN_DEVICE_FUNC constexpr ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
   EIGEN_DEVICE_FUNC constexpr const Scalar* data() const { return m_expression.data(); }
@@ -135,14 +131,10 @@ class MatrixWrapper : public MatrixBase<MatrixWrapper<ExpressionType> > {
 
   EIGEN_DEVICE_FUNC explicit inline MatrixWrapper(ExpressionType& matrix) : m_expression(matrix) {}
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const EIGEN_NOEXCEPT {
-    return m_expression.outerStride();
-  }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const EIGEN_NOEXCEPT {
-    return m_expression.innerStride();
-  }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_expression.rows(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_expression.cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return m_expression.outerStride(); }
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_expression.innerStride(); }
 
   EIGEN_DEVICE_FUNC constexpr ScalarWithConstIfNotLvalue* data() { return m_expression.data(); }
   EIGEN_DEVICE_FUNC constexpr const Scalar* data() const { return m_expression.data(); }

Eigen/src/Core/Assign_MKL.h

@@ -56,11 +56,11 @@ class vml_assign_traits {
                                                    : int(Dst::MaxRowsAtCompileTime),
     MaxSizeAtCompileTime = Dst::SizeAtCompileTime,
 
-    MightEnableVml = StorageOrdersAgree && DstHasDirectAccess && SrcHasDirectAccess &&
+    MightEnableVml = bool(StorageOrdersAgree) && bool(DstHasDirectAccess) && bool(SrcHasDirectAccess) &&
                      Src::InnerStrideAtCompileTime == 1 && Dst::InnerStrideAtCompileTime == 1,
-    MightLinearize = MightEnableVml && (int(Dst::Flags) & int(Src::Flags) & LinearAccessBit),
-    VmlSize = MightLinearize ? MaxSizeAtCompileTime : InnerMaxSize,
-    LargeEnough = VmlSize == Dynamic || VmlSize >= EIGEN_MKL_VML_THRESHOLD
+    MightLinearize = bool(MightEnableVml) && (int(Dst::Flags) & int(Src::Flags) & LinearAccessBit),
+    VmlSize = bool(MightLinearize) ? MaxSizeAtCompileTime : InnerMaxSize,
+    LargeEnough = (VmlSize == Dynamic) || VmlSize >= EIGEN_MKL_VML_THRESHOLD
   };
 
  public:
@@ -89,7 +89,7 @@ class vml_assign_traits {
     static void run(DstXprType &dst, const SrcXprType &src, const assign_op<EIGENTYPE, EIGENTYPE> &func) { \
       resize_if_allowed(dst, src, func);                                                                   \
       eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());                                  \
-      if (vml_assign_traits<DstXprType, SrcXprNested>::Traversal == LinearTraversal) {                     \
+      if (vml_assign_traits<DstXprType, SrcXprNested>::Traversal == (int)LinearTraversal) {                \
         VMLOP(dst.size(), (const VMLTYPE *)src.nestedExpression().data(),                                  \
               (VMLTYPE *)dst.data() EIGEN_PP_EXPAND(EIGEN_VMLMODE_EXPAND_x##VMLMODE));                     \
       } else {                                                                                             \

Eigen/src/Core/BandMatrix.h

@@ -200,16 +200,16 @@ class BandMatrix : public BandMatrixBase<BandMatrix<Scalar_, Rows, Cols, Supers,
       : m_coeffs(1 + supers + subs, cols), m_rows(rows), m_supers(supers), m_subs(subs) {}
 
   /** \returns the number of columns */
-  inline EIGEN_CONSTEXPR Index rows() const { return m_rows.value(); }
+  constexpr Index rows() const { return m_rows.value(); }
 
   /** \returns the number of rows */
-  inline EIGEN_CONSTEXPR Index cols() const { return m_coeffs.cols(); }
+  constexpr Index cols() const { return m_coeffs.cols(); }
 
   /** \returns the number of super diagonals */
-  inline EIGEN_CONSTEXPR Index supers() const { return m_supers.value(); }
+  constexpr Index supers() const { return m_supers.value(); }
 
   /** \returns the number of sub diagonals */
-  inline EIGEN_CONSTEXPR Index subs() const { return m_subs.value(); }
+  constexpr Index subs() const { return m_subs.value(); }
 
   inline const CoefficientsType& coeffs() const { return m_coeffs; }
   inline CoefficientsType& coeffs() { return m_coeffs; }
@@ -260,16 +260,16 @@ class BandMatrixWrapper
   }
 
   /** \returns the number of columns */
-  inline EIGEN_CONSTEXPR Index rows() const { return m_rows.value(); }
+  constexpr Index rows() const { return m_rows.value(); }
 
   /** \returns the number of rows */
-  inline EIGEN_CONSTEXPR Index cols() const { return m_coeffs.cols(); }
+  constexpr Index cols() const { return m_coeffs.cols(); }
 
   /** \returns the number of super diagonals */
-  inline EIGEN_CONSTEXPR Index supers() const { return m_supers.value(); }
+  constexpr Index supers() const { return m_supers.value(); }
 
   /** \returns the number of sub diagonals */
-  inline EIGEN_CONSTEXPR Index subs() const { return m_subs.value(); }
+  constexpr Index subs() const { return m_subs.value(); }
 
   inline const CoefficientsType& coeffs() const { return m_coeffs; }
 

Eigen/src/Core/Block.h

@@ -289,13 +289,9 @@ class BlockImpl_dense : public internal::dense_xpr_base<Block<XprType, BlockRows
 
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE XprType& nestedExpression() { return m_xpr; }
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR StorageIndex startRow() const EIGEN_NOEXCEPT {
-    return m_startRow.value();
-  }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr StorageIndex startRow() const noexcept { return m_startRow.value(); }
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR StorageIndex startCol() const EIGEN_NOEXCEPT {
-    return m_startCol.value();
-  }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr StorageIndex startCol() const noexcept { return m_startCol.value(); }
 
  protected:
   XprTypeNested m_xpr;
@@ -319,8 +315,7 @@ class BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel, true>
    * Adding an offset to nullptr is undefined behavior, so we must avoid it.
    */
   template <typename Scalar>
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE static Scalar* add_to_nullable_pointer(Scalar* base,
-                                                                                               Index offset) {
+  EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE static Scalar* add_to_nullable_pointer(Scalar* base, Index offset) {
     return base != nullptr ? base + offset : nullptr;
   }
 
@@ -378,30 +373,25 @@ class BlockImpl_dense<XprType, BlockRows, BlockCols, InnerPanel, true>
     init();
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const internal::remove_all_t<XprTypeNested>& nestedExpression() const
-      EIGEN_NOEXCEPT {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const internal::remove_all_t<XprTypeNested>& nestedExpression() const noexcept {
     return m_xpr;
   }
 
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE XprType& nestedExpression() { return m_xpr; }
 
   /** \sa MapBase::innerStride() */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index innerStride() const EIGEN_NOEXCEPT {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index innerStride() const noexcept {
     return internal::traits<BlockType>::HasSameStorageOrderAsXprType ? m_xpr.innerStride() : m_xpr.outerStride();
   }
 
   /** \sa MapBase::outerStride() */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index outerStride() const EIGEN_NOEXCEPT {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index outerStride() const noexcept {
     return internal::traits<BlockType>::HasSameStorageOrderAsXprType ? m_xpr.outerStride() : m_xpr.innerStride();
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR StorageIndex startRow() const EIGEN_NOEXCEPT {
-    return m_startRow.value();
-  }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr StorageIndex startRow() const noexcept { return m_startRow.value(); }
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR StorageIndex startCol() const EIGEN_NOEXCEPT {
-    return m_startCol.value();
-  }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr StorageIndex startCol() const noexcept { return m_startCol.value(); }
 
 #ifndef __SUNPRO_CC
   // FIXME sunstudio is not friendly with the above friend...

Eigen/src/Core/CommaInitializer.h

@@ -92,7 +92,7 @@ struct CommaInitializer {
 
   EIGEN_DEVICE_FUNC inline ~CommaInitializer()
 #if defined VERIFY_RAISES_ASSERT && (!defined EIGEN_NO_ASSERTION_CHECKING) && defined EIGEN_EXCEPTIONS
-      EIGEN_EXCEPTION_SPEC(Eigen::eigen_assert_exception)
+      noexcept(false)  // Eigen::eigen_assert_exception
 #endif
   {
     finished();

Eigen/src/Core/CwiseBinaryOp.h

@@ -108,12 +108,12 @@ class CwiseBinaryOp : public CwiseBinaryOpImpl<BinaryOp, LhsType, RhsType,
     eigen_assert(aLhs.rows() == aRhs.rows() && aLhs.cols() == aRhs.cols());
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const noexcept {
     // return the fixed size type if available to enable compile time optimizations
     return internal::traits<internal::remove_all_t<LhsNested>>::RowsAtCompileTime == Dynamic ? m_rhs.rows()
                                                                                              : m_lhs.rows();
   }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const noexcept {
     // return the fixed size type if available to enable compile time optimizations
     return internal::traits<internal::remove_all_t<LhsNested>>::ColsAtCompileTime == Dynamic ? m_rhs.cols()
                                                                                              : m_lhs.cols();

Eigen/src/Core/CwiseNullaryOp.h

@@ -71,9 +71,13 @@ class CwiseNullaryOp : public internal::dense_xpr_base<CwiseNullaryOp<NullaryOp,
     eigen_assert(rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows) && cols >= 0 &&
                  (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
   }
+  EIGEN_DEVICE_FUNC CwiseNullaryOp(Index size, const NullaryOp& func = NullaryOp())
+      : CwiseNullaryOp(RowsAtCompileTime == 1 ? 1 : size, RowsAtCompileTime == 1 ? size : 1, func) {
+    EIGEN_STATIC_ASSERT(CwiseNullaryOp::IsVectorAtCompileTime, YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX);
+  }
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index rows() const { return m_rows.value(); }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index cols() const { return m_cols.value(); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const { return m_rows.value(); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const { return m_cols.value(); }
 
   /** \returns the functor representing the nullary operation */
   EIGEN_DEVICE_FUNC const NullaryOp& functor() const { return m_functor; }
@@ -90,7 +94,7 @@ class CwiseNullaryOp : public internal::dense_xpr_base<CwiseNullaryOp<NullaryOp,
  * the returned matrix. Must be compatible with this MatrixBase type.
  *
  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
- * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
+ * it is redundant to pass \a rows and \a cols as arguments, so NullaryExpr(const CustomNullaryOp&) should be used
  * instead.
  *
  * The template parameter \a CustomNullaryOp is the type of the functor.
@@ -117,7 +121,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
  * \only_for_vectors
  *
  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
- * it is redundant to pass \a size as argument, so Zero() should be used
+ * it is redundant to pass \a size as argument, so NullaryExpr(const CustomNullaryOp&) should be used
  * instead.
  *
  * The template parameter \a CustomNullaryOp is the type of the functor.
@@ -170,7 +174,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
  * the returned matrix. Must be compatible with this DenseBase type.
  *
  * This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
- * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used
+ * it is redundant to pass \a rows and \a cols as arguments, so Constant(const Scalar&) should be used
  * instead.
  *
  * The template parameter \a CustomNullaryOp is the type of the functor.
@@ -191,7 +195,7 @@ DenseBase<Derived>::Constant(Index rows, Index cols, const Scalar& value) {
  * \only_for_vectors
  *
  * This variant is meant to be used for dynamic-size vector types. For fixed-size types,
- * it is redundant to pass \a size as argument, so Zero() should be used
+ * it is redundant to pass \a size as argument, so Constant(const Scalar&) should be used
  * instead.
  *
  * The template parameter \a CustomNullaryOp is the type of the functor.
@@ -231,8 +235,7 @@ DenseBase<Derived>::Constant(const Scalar& value) {
  * \sa LinSpaced(Index,const Scalar&, const Scalar&), setLinSpaced(Index,const Scalar&,const Scalar&)
  */
 template <typename Derived>
-EIGEN_DEPRECATED EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<
-    Derived>::RandomAccessLinSpacedReturnType
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
 DenseBase<Derived>::LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high) {
   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
   return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar>(low, high, size));
@@ -243,8 +246,7 @@ DenseBase<Derived>::LinSpaced(Sequential_t, Index size, const Scalar& low, const
  * \sa LinSpaced(const Scalar&, const Scalar&)
  */
 template <typename Derived>
-EIGEN_DEPRECATED EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<
-    Derived>::RandomAccessLinSpacedReturnType
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType
 DenseBase<Derived>::LinSpaced(Sequential_t, const Scalar& low, const Scalar& high) {
   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
   EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
@@ -283,7 +285,7 @@ DenseBase<Derived>::LinSpaced(Index size, const Scalar& low, const Scalar& high)
 }
 
 /**
- * \copydoc DenseBase::LinSpaced(Index, const Scalar&, const Scalar&)
+ * \copydoc DenseBase::LinSpaced(Index, const DenseBase::Scalar&, const DenseBase::Scalar&)
  * Special version for fixed size types which does not require the size parameter.
  */
 template <typename Derived>
@@ -343,7 +345,8 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void DenseBase<Derived>::fill(const Scalar
  */
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setConstant(const Scalar& val) {
-  return derived() = Constant(rows(), cols(), val);
+  internal::eigen_fill_impl<Derived>::run(derived(), val);
+  return derived();
 }
 
 /** Resizes to the given \a size, and sets all coefficients in this expression to the given value \a val.
@@ -479,9 +482,9 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setEqualSpace
  * \sa Zero(), Zero(Index)
  */
 template <typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType DenseBase<Derived>::Zero(
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ZeroReturnType DenseBase<Derived>::Zero(
     Index rows, Index cols) {
-  return Constant(rows, cols, Scalar(0));
+  return ZeroReturnType(rows, cols);
 }
 
 /** \returns an expression of a zero vector.
@@ -501,9 +504,9 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::Constan
  * \sa Zero(), Zero(Index,Index)
  */
 template <typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType DenseBase<Derived>::Zero(
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ZeroReturnType DenseBase<Derived>::Zero(
     Index size) {
-  return Constant(size, Scalar(0));
+  return ZeroReturnType(size);
 }
 
 /** \returns an expression of a fixed-size zero matrix or vector.
@@ -517,8 +520,8 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::Constan
  * \sa Zero(Index), Zero(Index,Index)
  */
 template <typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType DenseBase<Derived>::Zero() {
-  return Constant(Scalar(0));
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ZeroReturnType DenseBase<Derived>::Zero() {
+  return ZeroReturnType(RowsAtCompileTime, ColsAtCompileTime);
 }
 
 /** \returns true if *this is approximately equal to the zero matrix,
@@ -547,7 +550,8 @@ EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isZero(const RealScalar& prec) const
  */
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setZero() {
-  return setConstant(Scalar(0));
+  internal::eigen_zero_impl<Derived>::run(derived());
+  return derived();
 }
 
 /** Resizes to the given \a size, and sets all coefficients in this expression to zero.
@@ -562,7 +566,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setZero() {
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setZero(Index newSize) {
   resize(newSize);
-  return setConstant(Scalar(0));
+  return setZero();
 }
 
 /** Resizes to the given size, and sets all coefficients in this expression to zero.
@@ -578,7 +582,7 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setZero
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& PlainObjectBase<Derived>::setZero(Index rows, Index cols) {
   resize(rows, cols);
-  return setConstant(Scalar(0));
+  return setZero();
 }
 
 /** Resizes to the given size, changing only the number of columns, and sets all

Eigen/src/Core/CwiseUnaryOp.h

@@ -60,8 +60,8 @@ class CwiseUnaryOp : public CwiseUnaryOpImpl<UnaryOp, XprType, typename internal
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit CwiseUnaryOp(const XprType& xpr, const UnaryOp& func = UnaryOp())
       : m_xpr(xpr), m_functor(func) {}
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_xpr.rows(); }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_xpr.cols(); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const noexcept { return m_xpr.rows(); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const noexcept { return m_xpr.cols(); }
 
   /** \returns the functor representing the unary operation */
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const UnaryOp& functor() const { return m_functor; }

Eigen/src/Core/CwiseUnaryView.h

@@ -66,13 +66,13 @@ class CwiseUnaryViewImpl<ViewOp, MatrixType, StrideType, Dense, false>
 
   EIGEN_DEVICE_FUNC inline const Scalar* data() const { return &(this->coeffRef(0)); }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const {
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const {
     return StrideType::InnerStrideAtCompileTime != 0 ? int(StrideType::InnerStrideAtCompileTime)
                                                      : derived().nestedExpression().innerStride() *
                                                            sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar);
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const {
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const {
     return StrideType::OuterStrideAtCompileTime != 0 ? int(StrideType::OuterStrideAtCompileTime)
                                                      : derived().nestedExpression().outerStride() *
                                                            sizeof(typename traits<MatrixType>::Scalar) / sizeof(Scalar);
@@ -145,8 +145,8 @@ class CwiseUnaryView : public internal::CwiseUnaryViewImpl<ViewOp, MatrixType, S
 
   EIGEN_INHERIT_ASSIGNMENT_OPERATORS(CwiseUnaryView)
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const noexcept { return m_matrix.rows(); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const noexcept { return m_matrix.cols(); }
 
   /** \returns the functor representing unary operation */
   EIGEN_DEVICE_FUNC const ViewOp& functor() const { return m_functor; }

Eigen/src/Core/DenseBase.h

@@ -208,7 +208,7 @@ class DenseBase
    * \note For a vector, this returns just 1. For a matrix (non-vector), this is the major dimension
    * with respect to the \ref TopicStorageOrders "storage order", i.e., the number of columns for a
    * column-major matrix, and the number of rows for a row-major matrix. */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index outerSize() const {
+  EIGEN_DEVICE_FUNC constexpr Index outerSize() const {
     return IsVectorAtCompileTime ? 1 : int(IsRowMajor) ? this->rows() : this->cols();
   }
 
@@ -217,7 +217,7 @@ class DenseBase
    * \note For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension
    * with respect to the \ref TopicStorageOrders "storage order", i.e., the number of rows for a
    * column-major matrix, and the number of columns for a row-major matrix. */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index innerSize() const {
+  EIGEN_DEVICE_FUNC constexpr Index innerSize() const {
     return IsVectorAtCompileTime ? this->size() : int(IsRowMajor) ? this->cols() : this->rows();
   }
 
@@ -243,6 +243,8 @@ class DenseBase
 #ifndef EIGEN_PARSED_BY_DOXYGEN
   /** \internal Represents a matrix with all coefficients equal to one another*/
   typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> ConstantReturnType;
+  /** \internal Represents a matrix with all coefficients equal to zero*/
+  typedef CwiseNullaryOp<internal::scalar_zero_op<Scalar>, PlainObject> ZeroReturnType;
   /** \internal \deprecated Represents a vector with linearly spaced coefficients that allows sequential access only. */
   EIGEN_DEPRECATED typedef CwiseNullaryOp<internal::linspaced_op<Scalar>, PlainObject> SequentialLinSpacedReturnType;
   /** \internal Represents a vector with linearly spaced coefficients that allows random access. */
@@ -304,12 +306,12 @@ class DenseBase
   EIGEN_DEVICE_FUNC static const ConstantReturnType Constant(Index size, const Scalar& value);
   EIGEN_DEVICE_FUNC static const ConstantReturnType Constant(const Scalar& value);
 
-  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(Sequential_t, Index size,
-                                                                                            const Scalar& low,
-                                                                                            const Scalar& high);
-  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(Sequential_t,
-                                                                                            const Scalar& low,
-                                                                                            const Scalar& high);
+  EIGEN_DEPRECATED_WITH_REASON("The method may result in accuracy loss. Use .EqualSpaced() instead.")
+  EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(Sequential_t, Index size, const Scalar& low,
+                                                                           const Scalar& high);
+  EIGEN_DEPRECATED_WITH_REASON("The method may result in accuracy loss. Use .EqualSpaced() instead.")
+  EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(Sequential_t, const Scalar& low,
+                                                                           const Scalar& high);
 
   EIGEN_DEVICE_FUNC static const RandomAccessLinSpacedReturnType LinSpaced(Index size, const Scalar& low,
                                                                            const Scalar& high);
@@ -328,9 +330,9 @@ class DenseBase
   template <typename CustomNullaryOp>
   EIGEN_DEVICE_FUNC static const CwiseNullaryOp<CustomNullaryOp, PlainObject> NullaryExpr(const CustomNullaryOp& func);
 
-  EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(Index rows, Index cols);
-  EIGEN_DEVICE_FUNC static const ConstantReturnType Zero(Index size);
-  EIGEN_DEVICE_FUNC static const ConstantReturnType Zero();
+  EIGEN_DEVICE_FUNC static const ZeroReturnType Zero(Index rows, Index cols);
+  EIGEN_DEVICE_FUNC static const ZeroReturnType Zero(Index size);
+  EIGEN_DEVICE_FUNC static const ZeroReturnType Zero();
   EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index rows, Index cols);
   EIGEN_DEVICE_FUNC static const ConstantReturnType Ones(Index size);
   EIGEN_DEVICE_FUNC static const ConstantReturnType Ones();
@@ -365,7 +367,12 @@ class DenseBase
   EIGEN_DEVICE_FUNC inline bool allFinite() const;
 
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*=(const Scalar& other);
+  template <bool Enable = !internal::is_same<Scalar, RealScalar>::value, typename = std::enable_if_t<Enable>>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*=(const RealScalar& other);
+
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator/=(const Scalar& other);
+  template <bool Enable = !internal::is_same<Scalar, RealScalar>::value, typename = std::enable_if_t<Enable>>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator/=(const RealScalar& other);
 
   typedef internal::add_const_on_value_type_t<typename internal::eval<Derived>::type> EvalReturnType;
   /** \returns the matrix or vector obtained by evaluating this expression.
@@ -595,6 +602,13 @@ class DenseBase
   inline const_iterator end() const;
   inline const_iterator cend() const;
 
+  using RealViewReturnType = std::conditional_t<NumTraits<Scalar>::IsComplex, RealView<Derived>, Derived&>;
+  using ConstRealViewReturnType =
+      std::conditional_t<NumTraits<Scalar>::IsComplex, RealView<const Derived>, const Derived&>;
+
+  EIGEN_DEVICE_FUNC RealViewReturnType realView();
+  EIGEN_DEVICE_FUNC ConstRealViewReturnType realView() const;
+
 #define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::DenseBase
 #define EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL
 #define EIGEN_DOC_BLOCK_ADDONS_INNER_PANEL_IF(COND)
@@ -642,6 +656,18 @@ class DenseBase
   EIGEN_DEVICE_FUNC explicit DenseBase(const DenseBase<OtherDerived>&);
 };
 
+/** Free-function swap.
+ */
+template <typename DerivedA, typename DerivedB>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+    // Use forwarding references to capture all combinations of cv-qualified l+r-value cases.
+    std::enable_if_t<std::is_base_of<DenseBase<std::decay_t<DerivedA>>, std::decay_t<DerivedA>>::value &&
+                         std::is_base_of<DenseBase<std::decay_t<DerivedB>>, std::decay_t<DerivedB>>::value,
+                     void>
+    swap(DerivedA&& a, DerivedB&& b) {
+  a.swap(b);
+}
+
 }  // end namespace Eigen
 
 #endif  // EIGEN_DENSEBASE_H

Eigen/src/Core/DenseCoeffsBase.h

@@ -45,10 +45,16 @@ class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
   // - This is the return type of the coeff() method.
   // - The LvalueBit means exactly that we can offer a coeffRef() method, which means exactly that we can get references
   // to coeffs, which means exactly that we can have coeff() return a const reference (as opposed to returning a value).
+  // - The DirectAccessBit means exactly that the underlying data of coefficients can be directly accessed as a plain
+  // strided array, which means exactly that the underlying data of coefficients does exist in memory, which means
+  // exactly that the coefficients is const-referencable, which means exactly that we can have coeff() return a const
+  // reference. For example, Map<const Matrix> have DirectAccessBit but not LvalueBit, so that Map<const Matrix>.coeff()
+  // does points to a const Scalar& which exists in memory, while does not allow coeffRef() as it would not provide a
+  // lvalue. Notice that DirectAccessBit and LvalueBit are mutually orthogonal.
   // - The is_arithmetic check is required since "const int", "const double", etc. will cause warnings on some systems
   // while the declaration of "const T", where T is a non arithmetic type does not. Always returning "const Scalar&" is
   // not possible, since the underlying expressions might not offer a valid address the reference could be referring to.
-  typedef std::conditional_t<bool(internal::traits<Derived>::Flags& LvalueBit), const Scalar&,
+  typedef std::conditional_t<bool(internal::traits<Derived>::Flags&(LvalueBit | DirectAccessBit)), const Scalar&,
                              std::conditional_t<internal::is_arithmetic<Scalar>::value, Scalar, const Scalar>>
       CoeffReturnType;
 
@@ -89,13 +95,12 @@ class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
    *
    * \sa operator()(Index,Index) const, coeffRef(Index,Index), coeff(Index) const
    */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR CoeffReturnType coeff(Index row, Index col) const {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType coeff(Index row, Index col) const {
     eigen_internal_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
     return internal::evaluator<Derived>(derived()).coeff(row, col);
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR CoeffReturnType coeffByOuterInner(Index outer,
-                                                                                          Index inner) const {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType coeffByOuterInner(Index outer, Index inner) const {
     return coeff(rowIndexByOuterInner(outer, inner), colIndexByOuterInner(outer, inner));
   }
 
@@ -103,7 +108,7 @@ class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
    *
    * \sa operator()(Index,Index), operator[](Index)
    */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR CoeffReturnType operator()(Index row, Index col) const {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType operator()(Index row, Index col) const {
     eigen_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
     return coeff(row, col);
   }
@@ -123,7 +128,7 @@ class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
    * \sa operator[](Index) const, coeffRef(Index), coeff(Index,Index) const
    */
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR CoeffReturnType coeff(Index index) const {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType coeff(Index index) const {
     EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,
                         THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)
     eigen_internal_assert(index >= 0 && index < size());
@@ -138,7 +143,7 @@ class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
    * z() const, w() const
    */
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR CoeffReturnType operator[](Index index) const {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType operator[](Index index) const {
     EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
                         THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
     eigen_assert(index >= 0 && index < size());
@@ -155,32 +160,32 @@ class DenseCoeffsBase<Derived, ReadOnlyAccessors> : public EigenBase<Derived> {
    * z() const, w() const
    */
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR CoeffReturnType operator()(Index index) const {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType operator()(Index index) const {
     eigen_assert(index >= 0 && index < size());
     return coeff(index);
   }
 
   /** equivalent to operator[](0).  */
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR CoeffReturnType x() const { return (*this)[0]; }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType x() const { return (*this)[0]; }
 
   /** equivalent to operator[](1).  */
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR CoeffReturnType y() const {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType y() const {
     EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime == -1 || Derived::SizeAtCompileTime >= 2, OUT_OF_RANGE_ACCESS);
     return (*this)[1];
   }
 
   /** equivalent to operator[](2).  */
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR CoeffReturnType z() const {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType z() const {
     EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime == -1 || Derived::SizeAtCompileTime >= 3, OUT_OF_RANGE_ACCESS);
     return (*this)[2];
   }
 
   /** equivalent to operator[](3).  */
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR CoeffReturnType w() const {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType w() const {
     EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime == -1 || Derived::SizeAtCompileTime >= 4, OUT_OF_RANGE_ACCESS);
     return (*this)[3];
   }
@@ -298,7 +303,7 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
    *
    * \sa operator()(Index,Index), coeff(Index, Index) const, coeffRef(Index)
    */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col) {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& coeffRef(Index row, Index col) {
     eigen_internal_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
     return internal::evaluator<Derived>(derived()).coeffRef(row, col);
   }
@@ -312,7 +317,7 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
    * \sa operator[](Index)
    */
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator()(Index row, Index col) {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& operator()(Index row, Index col) {
     eigen_assert(row >= 0 && row < rows() && col >= 0 && col < cols());
     return coeffRef(row, col);
   }
@@ -332,7 +337,7 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
    * \sa operator[](Index), coeff(Index) const, coeffRef(Index,Index)
    */
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& coeffRef(Index index) {
     EIGEN_STATIC_ASSERT(internal::evaluator<Derived>::Flags & LinearAccessBit,
                         THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS)
     eigen_internal_assert(index >= 0 && index < size());
@@ -346,7 +351,7 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
    * \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
    */
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& operator[](Index index) {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& operator[](Index index) {
     EIGEN_STATIC_ASSERT(Derived::IsVectorAtCompileTime,
                         THE_BRACKET_OPERATOR_IS_ONLY_FOR_VECTORS__USE_THE_PARENTHESIS_OPERATOR_INSTEAD)
     eigen_assert(index >= 0 && index < size());
@@ -362,32 +367,32 @@ class DenseCoeffsBase<Derived, WriteAccessors> : public DenseCoeffsBase<Derived,
    * \sa operator[](Index) const, operator()(Index,Index), x(), y(), z(), w()
    */
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Scalar& operator()(Index index) {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& operator()(Index index) {
     eigen_assert(index >= 0 && index < size());
     return coeffRef(index);
   }
 
   /** equivalent to operator[](0).  */
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Scalar& x() { return (*this)[0]; }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& x() { return (*this)[0]; }
 
   /** equivalent to operator[](1).  */
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Scalar& y() {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& y() {
     EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime == -1 || Derived::SizeAtCompileTime >= 2, OUT_OF_RANGE_ACCESS);
     return (*this)[1];
   }
 
   /** equivalent to operator[](2).  */
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Scalar& z() {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& z() {
     EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime == -1 || Derived::SizeAtCompileTime >= 3, OUT_OF_RANGE_ACCESS);
     return (*this)[2];
   }
 
   /** equivalent to operator[](3).  */
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Scalar& w() {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& w() {
     EIGEN_STATIC_ASSERT(Derived::SizeAtCompileTime == -1 || Derived::SizeAtCompileTime >= 4, OUT_OF_RANGE_ACCESS);
     return (*this)[3];
   }
@@ -421,33 +426,29 @@ class DenseCoeffsBase<Derived, DirectAccessors> : public DenseCoeffsBase<Derived
    *
    * \sa outerStride(), rowStride(), colStride()
    */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const { return derived().innerStride(); }
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const { return derived().innerStride(); }
 
   /** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
    *          in a column-major matrix).
    *
    * \sa innerStride(), rowStride(), colStride()
    */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const { return derived().outerStride(); }
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const { return derived().outerStride(); }
 
   // FIXME shall we remove it ?
-  EIGEN_CONSTEXPR inline Index stride() const { return Derived::IsVectorAtCompileTime ? innerStride() : outerStride(); }
+  constexpr Index stride() const { return Derived::IsVectorAtCompileTime ? innerStride() : outerStride(); }
 
   /** \returns the pointer increment between two consecutive rows.
    *
    * \sa innerStride(), outerStride(), colStride()
    */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rowStride() const {
-    return Derived::IsRowMajor ? outerStride() : innerStride();
-  }
+  EIGEN_DEVICE_FUNC constexpr Index rowStride() const { return Derived::IsRowMajor ? outerStride() : innerStride(); }
 
   /** \returns the pointer increment between two consecutive columns.
    *
    * \sa innerStride(), outerStride(), rowStride()
    */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index colStride() const {
-    return Derived::IsRowMajor ? innerStride() : outerStride();
-  }
+  EIGEN_DEVICE_FUNC constexpr Index colStride() const { return Derived::IsRowMajor ? innerStride() : outerStride(); }
 };
 
 /** \brief Base class providing direct read/write coefficient access to matrices and arrays.
@@ -478,25 +479,23 @@ class DenseCoeffsBase<Derived, DirectWriteAccessors> : public DenseCoeffsBase<De
    *
    * \sa outerStride(), rowStride(), colStride()
    */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const EIGEN_NOEXCEPT { return derived().innerStride(); }
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return derived().innerStride(); }
 
   /** \returns the pointer increment between two consecutive inner slices (for example, between two consecutive columns
    *          in a column-major matrix).
    *
    * \sa innerStride(), rowStride(), colStride()
    */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const EIGEN_NOEXCEPT { return derived().outerStride(); }
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return derived().outerStride(); }
 
   // FIXME shall we remove it ?
-  EIGEN_CONSTEXPR inline Index stride() const EIGEN_NOEXCEPT {
-    return Derived::IsVectorAtCompileTime ? innerStride() : outerStride();
-  }
+  constexpr Index stride() const noexcept { return Derived::IsVectorAtCompileTime ? innerStride() : outerStride(); }
 
   /** \returns the pointer increment between two consecutive rows.
    *
    * \sa innerStride(), outerStride(), colStride()
    */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rowStride() const EIGEN_NOEXCEPT {
+  EIGEN_DEVICE_FUNC constexpr Index rowStride() const noexcept {
     return Derived::IsRowMajor ? outerStride() : innerStride();
   }
 
@@ -504,7 +503,7 @@ class DenseCoeffsBase<Derived, DirectWriteAccessors> : public DenseCoeffsBase<De
    *
    * \sa innerStride(), outerStride(), rowStride()
    */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index colStride() const EIGEN_NOEXCEPT {
+  EIGEN_DEVICE_FUNC constexpr Index colStride() const noexcept {
     return Derived::IsRowMajor ? innerStride() : outerStride();
   }
 };
@@ -513,7 +512,7 @@ namespace internal {
 
 template <int Alignment, typename Derived, bool JustReturnZero>
 struct first_aligned_impl {
-  static EIGEN_CONSTEXPR inline Index run(const Derived&) EIGEN_NOEXCEPT { return 0; }
+  static constexpr Index run(const Derived&) noexcept { return 0; }
 };
 
 template <int Alignment, typename Derived>

Eigen/src/Core/DeviceWrapper.h

@@ -66,7 +66,7 @@ struct AssignmentWithDevice<DstXprType, Product<Lhs, Rhs, Options>, Functor, Dev
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(DstXprType& dst, const SrcXprType& src, const Functor& func,
                                                         Device&) {
     Base::run(dst, src, func);
-  };
+  }
 };
 
 // specialization for coeffcient-wise assignment
@@ -87,13 +87,13 @@ template <typename Kernel, typename Device, int Traversal = Kernel::AssignmentTr
           int Unrolling = Kernel::AssignmentTraits::Unrolling>
 struct dense_assignment_loop_with_device {
   using Base = dense_assignment_loop<Kernel, Traversal, Unrolling>;
-  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void run(Kernel& kernel, Device&) { Base::run(kernel); }
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void run(Kernel& kernel, Device&) { Base::run(kernel); }
 };
 
 // entry point for a generic expression with device
 template <typename Dst, typename Src, typename Func, typename Device>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void call_assignment_no_alias(DeviceWrapper<Dst, Device> dst,
-                                                                                    const Src& src, const Func& func) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void call_assignment_no_alias(DeviceWrapper<Dst, Device> dst,
+                                                                              const Src& src, const Func& func) {
   enum {
     NeedToTranspose = ((int(Dst::RowsAtCompileTime) == 1 && int(Src::ColsAtCompileTime) == 1) ||
                        (int(Dst::ColsAtCompileTime) == 1 && int(Src::RowsAtCompileTime) == 1)) &&
@@ -115,10 +115,8 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void call_assignment_no_al
 
 // copy and pasted from AssignEvaluator except forward device to kernel
 template <typename DstXprType, typename SrcXprType, typename Functor, typename Device>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR void call_dense_assignment_loop(DstXprType& dst,
-                                                                                      const SrcXprType& src,
-                                                                                      const Functor& func,
-                                                                                      Device& device) {
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void call_dense_assignment_loop(DstXprType& dst, const SrcXprType& src,
+                                                                                const Functor& func, Device& device) {
   using DstEvaluatorType = evaluator<DstXprType>;
   using SrcEvaluatorType = evaluator<SrcXprType>;
 

Eigen/src/Core/Diagonal.h

@@ -83,13 +83,11 @@ class Diagonal : public internal::dense_xpr_base<Diagonal<MatrixType, DiagIndex_
                                : numext::mini<Index>(m_matrix.rows(), m_matrix.cols() - m_index.value());
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return 1; }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return 1; }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const EIGEN_NOEXCEPT {
-    return m_matrix.outerStride() + 1;
-  }
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_matrix.outerStride() + 1; }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const EIGEN_NOEXCEPT { return 0; }
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return 0; }
 
   typedef std::conditional_t<internal::is_lvalue<MatrixType>::value, Scalar, const Scalar> ScalarWithConstIfNotLvalue;
 
@@ -134,13 +132,13 @@ class Diagonal : public internal::dense_xpr_base<Diagonal<MatrixType, DiagIndex_
 
  private:
   // some compilers may fail to optimize std::max etc in case of compile-time constants...
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index absDiagIndex() const EIGEN_NOEXCEPT {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index absDiagIndex() const noexcept {
     return m_index.value() > 0 ? m_index.value() : -m_index.value();
   }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index rowOffset() const EIGEN_NOEXCEPT {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rowOffset() const noexcept {
     return m_index.value() > 0 ? 0 : -m_index.value();
   }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index colOffset() const EIGEN_NOEXCEPT {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index colOffset() const noexcept {
     return m_index.value() > 0 ? m_index.value() : 0;
   }
   // trigger a compile-time error if someone try to call packet

Eigen/src/Core/DiagonalMatrix.h

@@ -76,9 +76,9 @@ class DiagonalBase : public EigenBase<Derived> {
   }
 
   /** \returns the number of rows. */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const { return diagonal().size(); }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const { return diagonal().size(); }
   /** \returns the number of columns. */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const { return diagonal().size(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const { return diagonal().size(); }
 
   /** \returns the diagonal matrix product of \c *this by the dense matrix, \a matrix */
   template <typename MatrixDerived>
@@ -256,10 +256,13 @@ class DiagonalMatrix : public DiagonalBase<DiagonalMatrix<Scalar_, SizeAtCompile
   typedef DiagonalWrapper<const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, DiagonalVectorType>>
       InitializeReturnType;
 
+  typedef DiagonalWrapper<const CwiseNullaryOp<internal::scalar_zero_op<Scalar>, DiagonalVectorType>>
+      ZeroInitializeReturnType;
+
   /** Initializes a diagonal matrix of size SizeAtCompileTime with coefficients set to zero */
-  EIGEN_DEVICE_FUNC static const InitializeReturnType Zero() { return DiagonalVectorType::Zero().asDiagonal(); }
+  EIGEN_DEVICE_FUNC static const ZeroInitializeReturnType Zero() { return DiagonalVectorType::Zero().asDiagonal(); }
   /** Initializes a diagonal matrix of size dim with coefficients set to zero */
-  EIGEN_DEVICE_FUNC static const InitializeReturnType Zero(Index size) {
+  EIGEN_DEVICE_FUNC static const ZeroInitializeReturnType Zero(Index size) {
     return DiagonalVectorType::Zero(size).asDiagonal();
   }
   /** Initializes a identity matrix of size SizeAtCompileTime */
@@ -386,8 +389,9 @@ struct AssignmentKind<DenseShape, DiagonalShape> {
 // Diagonal matrix to Dense assignment
 template <typename DstXprType, typename SrcXprType, typename Functor>
 struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Dense> {
-  static void run(DstXprType& dst, const SrcXprType& src,
-                  const internal::assign_op<typename DstXprType::Scalar, typename SrcXprType::Scalar>& /*func*/) {
+  static EIGEN_DEVICE_FUNC void run(
+      DstXprType& dst, const SrcXprType& src,
+      const internal::assign_op<typename DstXprType::Scalar, typename SrcXprType::Scalar>& /*func*/) {
     Index dstRows = src.rows();
     Index dstCols = src.cols();
     if ((dst.rows() != dstRows) || (dst.cols() != dstCols)) dst.resize(dstRows, dstCols);
@@ -396,13 +400,15 @@ struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Dense> {
     dst.diagonal() = src.diagonal();
   }
 
-  static void run(DstXprType& dst, const SrcXprType& src,
-                  const internal::add_assign_op<typename DstXprType::Scalar, typename SrcXprType::Scalar>& /*func*/) {
+  static EIGEN_DEVICE_FUNC void run(
+      DstXprType& dst, const SrcXprType& src,
+      const internal::add_assign_op<typename DstXprType::Scalar, typename SrcXprType::Scalar>& /*func*/) {
     dst.diagonal() += src.diagonal();
   }
 
-  static void run(DstXprType& dst, const SrcXprType& src,
-                  const internal::sub_assign_op<typename DstXprType::Scalar, typename SrcXprType::Scalar>& /*func*/) {
+  static EIGEN_DEVICE_FUNC void run(
+      DstXprType& dst, const SrcXprType& src,
+      const internal::sub_assign_op<typename DstXprType::Scalar, typename SrcXprType::Scalar>& /*func*/) {
     dst.diagonal() -= src.diagonal();
   }
 };

Eigen/src/Core/EigenBase.h

@@ -46,22 +46,22 @@ struct EigenBase {
   typedef typename internal::traits<Derived>::StorageKind StorageKind;
 
   /** \returns a reference to the derived object */
-  EIGEN_DEVICE_FUNC Derived& derived() { return *static_cast<Derived*>(this); }
+  EIGEN_DEVICE_FUNC constexpr Derived& derived() { return *static_cast<Derived*>(this); }
   /** \returns a const reference to the derived object */
-  EIGEN_DEVICE_FUNC const Derived& derived() const { return *static_cast<const Derived*>(this); }
+  EIGEN_DEVICE_FUNC constexpr const Derived& derived() const { return *static_cast<const Derived*>(this); }
 
-  EIGEN_DEVICE_FUNC inline Derived& const_cast_derived() const {
+  EIGEN_DEVICE_FUNC inline constexpr Derived& const_cast_derived() const {
     return *static_cast<Derived*>(const_cast<EigenBase*>(this));
   }
   EIGEN_DEVICE_FUNC inline const Derived& const_derived() const { return *static_cast<const Derived*>(this); }
 
   /** \returns the number of rows. \sa cols(), RowsAtCompileTime */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return derived().rows(); }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return derived().rows(); }
   /** \returns the number of columns. \sa rows(), ColsAtCompileTime*/
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return derived().cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return derived().cols(); }
   /** \returns the number of coefficients, which is rows()*cols().
    * \sa rows(), cols(), SizeAtCompileTime. */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index size() const EIGEN_NOEXCEPT { return rows() * cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index size() const noexcept { return rows() * cols(); }
 
   /** \internal Don't use it, but do the equivalent: \code dst = *this; \endcode */
   template <typename Dest>

Eigen/src/Core/Fill.h

@@ -0,0 +1,138 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2024 Charles Schlosser <cs.schlosser@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_FILL_H
+#define EIGEN_FILL_H
+
+// IWYU pragma: private
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Xpr>
+struct eigen_fill_helper : std::false_type {};
+
+template <typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+struct eigen_fill_helper<Matrix<Scalar, Rows, Cols, Options, MaxRows, MaxCols>> : std::true_type {};
+
+template <typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+struct eigen_fill_helper<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols>> : std::true_type {};
+
+template <typename Xpr, int BlockRows, int BlockCols>
+struct eigen_fill_helper<Block<Xpr, BlockRows, BlockCols, /*InnerPanel*/ true>> : eigen_fill_helper<Xpr> {};
+
+template <typename Xpr, int BlockRows, int BlockCols>
+struct eigen_fill_helper<Block<Xpr, BlockRows, BlockCols, /*InnerPanel*/ false>>
+    : std::integral_constant<bool, eigen_fill_helper<Xpr>::value &&
+                                       (Xpr::IsRowMajor ? (BlockRows == 1) : (BlockCols == 1))> {};
+
+template <typename Xpr, int Options>
+struct eigen_fill_helper<Map<Xpr, Options, Stride<0, 0>>> : eigen_fill_helper<Xpr> {};
+
+template <typename Xpr, int Options, int OuterStride_>
+struct eigen_fill_helper<Map<Xpr, Options, Stride<OuterStride_, 0>>>
+    : std::integral_constant<bool, eigen_fill_helper<Xpr>::value &&
+                                       enum_eq_not_dynamic(OuterStride_, Xpr::InnerSizeAtCompileTime)> {};
+
+template <typename Xpr, int Options, int OuterStride_>
+struct eigen_fill_helper<Map<Xpr, Options, Stride<OuterStride_, 1>>>
+    : eigen_fill_helper<Map<Xpr, Options, Stride<OuterStride_, 0>>> {};
+
+template <typename Xpr, int Options, int InnerStride_>
+struct eigen_fill_helper<Map<Xpr, Options, InnerStride<InnerStride_>>>
+    : eigen_fill_helper<Map<Xpr, Options, Stride<0, InnerStride_>>> {};
+
+template <typename Xpr, int Options, int OuterStride_>
+struct eigen_fill_helper<Map<Xpr, Options, OuterStride<OuterStride_>>>
+    : eigen_fill_helper<Map<Xpr, Options, Stride<OuterStride_, 0>>> {};
+
+template <typename Xpr>
+struct eigen_fill_impl<Xpr, /*use_fill*/ false> {
+  using Scalar = typename Xpr::Scalar;
+  using Func = scalar_constant_op<Scalar>;
+  using PlainObject = typename Xpr::PlainObject;
+  using Constant = typename PlainObject::ConstantReturnType;
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void run(Xpr& dst, const Scalar& val) {
+    const Constant src(dst.rows(), dst.cols(), val);
+    run(dst, src);
+  }
+  template <typename SrcXpr>
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void run(Xpr& dst, const SrcXpr& src) {
+    call_dense_assignment_loop(dst, src, assign_op<Scalar, Scalar>());
+  }
+};
+
+#if EIGEN_COMP_MSVC || defined(EIGEN_GPU_COMPILE_PHASE)
+template <typename Xpr>
+struct eigen_fill_impl<Xpr, /*use_fill*/ true> : eigen_fill_impl<Xpr, /*use_fill*/ false> {};
+#else
+template <typename Xpr>
+struct eigen_fill_impl<Xpr, /*use_fill*/ true> {
+  using Scalar = typename Xpr::Scalar;
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Xpr& dst, const Scalar& val) {
+    const Scalar val_copy = val;
+    using std::fill_n;
+    fill_n(dst.data(), dst.size(), val_copy);
+  }
+  template <typename SrcXpr>
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Xpr& dst, const SrcXpr& src) {
+    resize_if_allowed(dst, src, assign_op<Scalar, Scalar>());
+    const Scalar& val = src.functor()();
+    run(dst, val);
+  }
+};
+#endif
+
+template <typename Xpr>
+struct eigen_memset_helper {
+  static constexpr bool value =
+      std::is_trivially_copyable<typename Xpr::Scalar>::value && eigen_fill_helper<Xpr>::value;
+};
+
+template <typename Xpr>
+struct eigen_zero_impl<Xpr, /*use_memset*/ false> {
+  using Scalar = typename Xpr::Scalar;
+  using PlainObject = typename Xpr::PlainObject;
+  using Zero = typename PlainObject::ZeroReturnType;
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void run(Xpr& dst) {
+    const Zero src(dst.rows(), dst.cols());
+    run(dst, src);
+  }
+  template <typename SrcXpr>
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void run(Xpr& dst, const SrcXpr& src) {
+    call_dense_assignment_loop(dst, src, assign_op<Scalar, Scalar>());
+  }
+};
+
+template <typename Xpr>
+struct eigen_zero_impl<Xpr, /*use_memset*/ true> {
+  using Scalar = typename Xpr::Scalar;
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Xpr& dst) {
+    const std::ptrdiff_t num_bytes = dst.size() * static_cast<std::ptrdiff_t>(sizeof(Scalar));
+    if (num_bytes <= 0) return;
+    void* dst_ptr = static_cast<void*>(dst.data());
+#ifndef EIGEN_NO_DEBUG
+    eigen_assert((dst_ptr != nullptr) && "null pointer dereference error!");
+#endif
+    EIGEN_USING_STD(memset);
+    memset(dst_ptr, 0, static_cast<std::size_t>(num_bytes));
+  }
+  template <typename SrcXpr>
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Xpr& dst, const SrcXpr& src) {
+    resize_if_allowed(dst, src, assign_op<Scalar, Scalar>());
+    run(dst);
+  }
+};
+
+}  // namespace internal
+}  // namespace Eigen
+
+#endif  // EIGEN_FILL_H

Eigen/src/Core/FindCoeff.h

@@ -0,0 +1,464 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2025 Charlie Schlosser <cs.schlosser@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_FIND_COEFF_H
+#define EIGEN_FIND_COEFF_H
+
+// IWYU pragma: private
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Scalar, int NaNPropagation, bool IsInteger = NumTraits<Scalar>::IsInteger>
+struct max_coeff_functor {
+  EIGEN_DEVICE_FUNC inline bool compareCoeff(const Scalar& incumbent, const Scalar& candidate) const {
+    return candidate > incumbent;
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) const {
+    return pcmp_lt(incumbent, candidate);
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
+    return predux_max(a);
+  }
+};
+
+template <typename Scalar>
+struct max_coeff_functor<Scalar, PropagateNaN, false> {
+  EIGEN_DEVICE_FUNC inline Scalar compareCoeff(const Scalar& incumbent, const Scalar& candidate) {
+    return (candidate > incumbent) || ((candidate != candidate) && (incumbent == incumbent));
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) {
+    return pandnot(pcmp_lt_or_nan(incumbent, candidate), pisnan(incumbent));
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
+    return predux_max<PropagateNaN>(a);
+  }
+};
+
+template <typename Scalar>
+struct max_coeff_functor<Scalar, PropagateNumbers, false> {
+  EIGEN_DEVICE_FUNC inline bool compareCoeff(const Scalar& incumbent, const Scalar& candidate) const {
+    return (candidate > incumbent) || ((candidate == candidate) && (incumbent != incumbent));
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) const {
+    return pandnot(pcmp_lt_or_nan(incumbent, candidate), pisnan(candidate));
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
+    return predux_max<PropagateNumbers>(a);
+  }
+};
+
+template <typename Scalar, int NaNPropagation, bool IsInteger = NumTraits<Scalar>::IsInteger>
+struct min_coeff_functor {
+  EIGEN_DEVICE_FUNC inline bool compareCoeff(const Scalar& incumbent, const Scalar& candidate) const {
+    return candidate < incumbent;
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) const {
+    return pcmp_lt(candidate, incumbent);
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
+    return predux_min(a);
+  }
+};
+
+template <typename Scalar>
+struct min_coeff_functor<Scalar, PropagateNaN, false> {
+  EIGEN_DEVICE_FUNC inline Scalar compareCoeff(const Scalar& incumbent, const Scalar& candidate) {
+    return (candidate < incumbent) || ((candidate != candidate) && (incumbent == incumbent));
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) {
+    return pandnot(pcmp_lt_or_nan(candidate, incumbent), pisnan(incumbent));
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
+    return predux_min<PropagateNaN>(a);
+  }
+};
+
+template <typename Scalar>
+struct min_coeff_functor<Scalar, PropagateNumbers, false> {
+  EIGEN_DEVICE_FUNC inline bool compareCoeff(const Scalar& incumbent, const Scalar& candidate) const {
+    return (candidate < incumbent) || ((candidate == candidate) && (incumbent != incumbent));
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline Packet comparePacket(const Packet& incumbent, const Packet& candidate) const {
+    return pandnot(pcmp_lt_or_nan(candidate, incumbent), pisnan(candidate));
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& a) const {
+    return predux_min<PropagateNumbers>(a);
+  }
+};
+
+template <typename Scalar>
+struct min_max_traits {
+  static constexpr bool PacketAccess = packet_traits<Scalar>::Vectorizable;
+};
+template <typename Scalar, int NaNPropagation>
+struct functor_traits<max_coeff_functor<Scalar, NaNPropagation>> : min_max_traits<Scalar> {};
+template <typename Scalar, int NaNPropagation>
+struct functor_traits<min_coeff_functor<Scalar, NaNPropagation>> : min_max_traits<Scalar> {};
+
+template <typename Evaluator, typename Func, bool Linear, bool Vectorize>
+struct find_coeff_loop;
+template <typename Evaluator, typename Func>
+struct find_coeff_loop<Evaluator, Func, /*Linear*/ false, /*Vectorize*/ false> {
+  using Scalar = typename Evaluator::Scalar;
+  static EIGEN_DEVICE_FUNC inline void run(const Evaluator& eval, Func& func, Scalar& res, Index& outer, Index& inner) {
+    Index outerSize = eval.outerSize();
+    Index innerSize = eval.innerSize();
+
+    /* initialization performed in calling function */
+    /* result = eval.coeff(0, 0); */
+    /* outer = 0; */
+    /* inner = 0; */
+
+    for (Index j = 0; j < outerSize; j++) {
+      for (Index i = 0; i < innerSize; i++) {
+        Scalar xprCoeff = eval.coeffByOuterInner(j, i);
+        bool newRes = func.compareCoeff(res, xprCoeff);
+        if (newRes) {
+          outer = j;
+          inner = i;
+          res = xprCoeff;
+        }
+      }
+    }
+  }
+};
+template <typename Evaluator, typename Func>
+struct find_coeff_loop<Evaluator, Func, /*Linear*/ true, /*Vectorize*/ false> {
+  using Scalar = typename Evaluator::Scalar;
+  static EIGEN_DEVICE_FUNC inline void run(const Evaluator& eval, Func& func, Scalar& res, Index& index) {
+    Index size = eval.size();
+
+    /* initialization performed in calling function */
+    /* result = eval.coeff(0); */
+    /* index = 0; */
+
+    for (Index k = 0; k < size; k++) {
+      Scalar xprCoeff = eval.coeff(k);
+      bool newRes = func.compareCoeff(res, xprCoeff);
+      if (newRes) {
+        index = k;
+        res = xprCoeff;
+      }
+    }
+  }
+};
+template <typename Evaluator, typename Func>
+struct find_coeff_loop<Evaluator, Func, /*Linear*/ false, /*Vectorize*/ true> {
+  using ScalarImpl = find_coeff_loop<Evaluator, Func, false, false>;
+  using Scalar = typename Evaluator::Scalar;
+  using Packet = typename Evaluator::Packet;
+  static constexpr int PacketSize = unpacket_traits<Packet>::size;
+  static EIGEN_DEVICE_FUNC inline void run(const Evaluator& eval, Func& func, Scalar& result, Index& outer,
+                                           Index& inner) {
+    Index outerSize = eval.outerSize();
+    Index innerSize = eval.innerSize();
+    Index packetEnd = numext::round_down(innerSize, PacketSize);
+
+    /* initialization performed in calling function */
+    /* result = eval.coeff(0, 0); */
+    /* outer = 0; */
+    /* inner = 0; */
+
+    bool checkPacket = false;
+
+    for (Index j = 0; j < outerSize; j++) {
+      Packet resultPacket = pset1<Packet>(result);
+      for (Index i = 0; i < packetEnd; i += PacketSize) {
+        Packet xprPacket = eval.template packetByOuterInner<Unaligned, Packet>(j, i);
+        if (predux_any(func.comparePacket(resultPacket, xprPacket))) {
+          outer = j;
+          inner = i;
+          result = func.predux(xprPacket);
+          resultPacket = pset1<Packet>(result);
+          checkPacket = true;
+        }
+      }
+
+      for (Index i = packetEnd; i < innerSize; i++) {
+        Scalar xprCoeff = eval.coeffByOuterInner(j, i);
+        if (func.compareCoeff(result, xprCoeff)) {
+          outer = j;
+          inner = i;
+          result = xprCoeff;
+          checkPacket = false;
+        }
+      }
+    }
+
+    if (checkPacket) {
+      result = eval.coeffByOuterInner(outer, inner);
+      Index i_end = inner + PacketSize;
+      for (Index i = inner; i < i_end; i++) {
+        Scalar xprCoeff = eval.coeffByOuterInner(outer, i);
+        if (func.compareCoeff(result, xprCoeff)) {
+          inner = i;
+          result = xprCoeff;
+        }
+      }
+    }
+  }
+};
+template <typename Evaluator, typename Func>
+struct find_coeff_loop<Evaluator, Func, /*Linear*/ true, /*Vectorize*/ true> {
+  using ScalarImpl = find_coeff_loop<Evaluator, Func, true, false>;
+  using Scalar = typename Evaluator::Scalar;
+  using Packet = typename Evaluator::Packet;
+  static constexpr int PacketSize = unpacket_traits<Packet>::size;
+  static constexpr int Alignment = Evaluator::Alignment;
+
+  static EIGEN_DEVICE_FUNC inline void run(const Evaluator& eval, Func& func, Scalar& result, Index& index) {
+    Index size = eval.size();
+    Index packetEnd = numext::round_down(size, PacketSize);
+
+    /* initialization performed in calling function */
+    /* result = eval.coeff(0); */
+    /* index = 0; */
+
+    Packet resultPacket = pset1<Packet>(result);
+    bool checkPacket = false;
+
+    for (Index k = 0; k < packetEnd; k += PacketSize) {
+      Packet xprPacket = eval.template packet<Alignment, Packet>(k);
+      if (predux_any(func.comparePacket(resultPacket, xprPacket))) {
+        index = k;
+        result = func.predux(xprPacket);
+        resultPacket = pset1<Packet>(result);
+        checkPacket = true;
+      }
+    }
+
+    for (Index k = packetEnd; k < size; k++) {
+      Scalar xprCoeff = eval.coeff(k);
+      if (func.compareCoeff(result, xprCoeff)) {
+        index = k;
+        result = xprCoeff;
+        checkPacket = false;
+      }
+    }
+
+    if (checkPacket) {
+      result = eval.coeff(index);
+      Index k_end = index + PacketSize;
+      for (Index k = index; k < k_end; k++) {
+        Scalar xprCoeff = eval.coeff(k);
+        if (func.compareCoeff(result, xprCoeff)) {
+          index = k;
+          result = xprCoeff;
+        }
+      }
+    }
+  }
+};
+
+template <typename Derived>
+struct find_coeff_evaluator : public evaluator<Derived> {
+  using Base = evaluator<Derived>;
+  using Scalar = typename Derived::Scalar;
+  using Packet = typename packet_traits<Scalar>::type;
+  static constexpr int Flags = Base::Flags;
+  static constexpr bool IsRowMajor = bool(Flags & RowMajorBit);
+  EIGEN_DEVICE_FUNC inline find_coeff_evaluator(const Derived& xpr) : Base(xpr), m_xpr(xpr) {}
+
+  EIGEN_DEVICE_FUNC inline Scalar coeffByOuterInner(Index outer, Index inner) const {
+    Index row = IsRowMajor ? outer : inner;
+    Index col = IsRowMajor ? inner : outer;
+    return Base::coeff(row, col);
+  }
+  template <int LoadMode, typename PacketType>
+  EIGEN_DEVICE_FUNC inline PacketType packetByOuterInner(Index outer, Index inner) const {
+    Index row = IsRowMajor ? outer : inner;
+    Index col = IsRowMajor ? inner : outer;
+    return Base::template packet<LoadMode, PacketType>(row, col);
+  }
+
+  EIGEN_DEVICE_FUNC inline Index innerSize() const { return m_xpr.innerSize(); }
+  EIGEN_DEVICE_FUNC inline Index outerSize() const { return m_xpr.outerSize(); }
+  EIGEN_DEVICE_FUNC inline Index size() const { return m_xpr.size(); }
+
+  const Derived& m_xpr;
+};
+
+template <typename Derived, typename Func>
+struct find_coeff_impl {
+  using Evaluator = find_coeff_evaluator<Derived>;
+  static constexpr int Flags = Evaluator::Flags;
+  static constexpr int Alignment = Evaluator::Alignment;
+  static constexpr bool IsRowMajor = Derived::IsRowMajor;
+  static constexpr int MaxInnerSizeAtCompileTime =
+      IsRowMajor ? Derived::MaxColsAtCompileTime : Derived::MaxRowsAtCompileTime;
+  static constexpr int MaxSizeAtCompileTime = Derived::MaxSizeAtCompileTime;
+
+  using Scalar = typename Derived::Scalar;
+  using Packet = typename Evaluator::Packet;
+
+  static constexpr int PacketSize = unpacket_traits<Packet>::size;
+  static constexpr bool Linearize = bool(Flags & LinearAccessBit);
+  static constexpr bool DontVectorize =
+      enum_lt_not_dynamic(Linearize ? MaxSizeAtCompileTime : MaxInnerSizeAtCompileTime, PacketSize);
+  static constexpr bool Vectorize =
+      !DontVectorize && bool(Flags & PacketAccessBit) && functor_traits<Func>::PacketAccess;
+
+  using Loop = find_coeff_loop<Evaluator, Func, Linearize, Vectorize>;
+
+  template <bool ForwardLinearAccess = Linearize, std::enable_if_t<!ForwardLinearAccess, bool> = true>
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& xpr, Func& func, Scalar& res, Index& outer,
+                                                        Index& inner) {
+    Evaluator eval(xpr);
+    Loop::run(eval, func, res, outer, inner);
+  }
+  template <bool ForwardLinearAccess = Linearize, std::enable_if_t<ForwardLinearAccess, bool> = true>
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& xpr, Func& func, Scalar& res, Index& outer,
+                                                        Index& inner) {
+    // where possible, use the linear loop and back-calculate the outer and inner indices
+    Index index = 0;
+    run(xpr, func, res, index);
+    outer = index / xpr.innerSize();
+    inner = index % xpr.innerSize();
+  }
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& xpr, Func& func, Scalar& res, Index& index) {
+    Evaluator eval(xpr);
+    Loop::run(eval, func, res, index);
+  }
+};
+
+template <typename Derived, typename IndexType, typename Func>
+EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar findCoeff(const DenseBase<Derived>& mat, Func& func,
+                                                                       IndexType* rowPtr, IndexType* colPtr) {
+  eigen_assert(mat.rows() > 0 && mat.cols() > 0 && "you are using an empty matrix");
+  using Scalar = typename DenseBase<Derived>::Scalar;
+  using FindCoeffImpl = internal::find_coeff_impl<Derived, Func>;
+  Index outer = 0;
+  Index inner = 0;
+  Scalar res = mat.coeff(0, 0);
+  FindCoeffImpl::run(mat.derived(), func, res, outer, inner);
+  *rowPtr = internal::convert_index<IndexType>(Derived::IsRowMajor ? outer : inner);
+  if (colPtr) *colPtr = internal::convert_index<IndexType>(Derived::IsRowMajor ? inner : outer);
+  return res;
+}
+
+template <typename Derived, typename IndexType, typename Func>
+EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar findCoeff(const DenseBase<Derived>& mat, Func& func,
+                                                                       IndexType* indexPtr) {
+  eigen_assert(mat.size() > 0 && "you are using an empty matrix");
+  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
+  using Scalar = typename DenseBase<Derived>::Scalar;
+  using FindCoeffImpl = internal::find_coeff_impl<Derived, Func>;
+  Index index = 0;
+  Scalar res = mat.coeff(0);
+  FindCoeffImpl::run(mat.derived(), func, res, index);
+  *indexPtr = internal::convert_index<IndexType>(index);
+  return res;
+}
+
+}  // namespace internal
+
+/** \fn DenseBase<Derived>::minCoeff(IndexType* rowId, IndexType* colId) const
+ * \returns the minimum of all coefficients of *this and puts in *row and *col its location.
+ *
+ * If there are multiple coefficients with the same extreme value, the location of the first instance is returned.
+ *
+ * In case \c *this contains NaN, NaNPropagation determines the behavior:
+ *   NaNPropagation == PropagateFast : undefined
+ *   NaNPropagation == PropagateNaN : result is NaN
+ *   NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
+ * \warning the matrix must be not empty, otherwise an assertion is triggered.
+ *
+ * \sa DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visit(), DenseBase::minCoeff()
+ */
+template <typename Derived>
+template <int NaNPropagation, typename IndexType>
+EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::minCoeff(IndexType* rowPtr,
+                                                                                          IndexType* colPtr) const {
+  using Func = internal::min_coeff_functor<Scalar, NaNPropagation>;
+  Func func;
+  return internal::findCoeff(derived(), func, rowPtr, colPtr);
+}
+
+/** \returns the minimum of all coefficients of *this and puts in *index its location.
+ *
+ * If there are multiple coefficients with the same extreme value, the location of the first instance is returned.
+ *
+ * In case \c *this contains NaN, NaNPropagation determines the behavior:
+ *   NaNPropagation == PropagateFast : undefined
+ *   NaNPropagation == PropagateNaN : result is NaN
+ *   NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
+ * \warning the matrix must be not empty, otherwise an assertion is triggered.
+ *
+ * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visit(),
+ * DenseBase::minCoeff()
+ */
+template <typename Derived>
+template <int NaNPropagation, typename IndexType>
+EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::minCoeff(IndexType* indexPtr) const {
+  using Func = internal::min_coeff_functor<Scalar, NaNPropagation>;
+  Func func;
+  return internal::findCoeff(derived(), func, indexPtr);
+}
+
+/** \fn DenseBase<Derived>::maxCoeff(IndexType* rowId, IndexType* colId) const
+ * \returns the maximum of all coefficients of *this and puts in *row and *col its location.
+ *
+ * If there are multiple coefficients with the same extreme value, the location of the first instance is returned.
+ *
+ * In case \c *this contains NaN, NaNPropagation determines the behavior:
+ *   NaNPropagation == PropagateFast : undefined
+ *   NaNPropagation == PropagateNaN : result is NaN
+ *   NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
+ * \warning the matrix must be not empty, otherwise an assertion is triggered.
+ *
+ * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visit(), DenseBase::maxCoeff()
+ */
+template <typename Derived>
+template <int NaNPropagation, typename IndexType>
+EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::maxCoeff(IndexType* rowPtr,
+                                                                                          IndexType* colPtr) const {
+  using Func = internal::max_coeff_functor<Scalar, NaNPropagation>;
+  Func func;
+  return internal::findCoeff(derived(), func, rowPtr, colPtr);
+}
+
+/** \returns the maximum of all coefficients of *this and puts in *index its location.
+ *
+ * If there are multiple coefficients with the same extreme value, the location of the first instance is returned.
+ *
+ * In case \c *this contains NaN, NaNPropagation determines the behavior:
+ *   NaNPropagation == PropagateFast : undefined
+ *   NaNPropagation == PropagateNaN : result is NaN
+ *   NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
+ * \warning the matrix must be not empty, otherwise an assertion is triggered.
+ *
+ * \sa DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(),
+ * DenseBase::maxCoeff()
+ */
+template <typename Derived>
+template <int NaNPropagation, typename IndexType>
+EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::maxCoeff(IndexType* indexPtr) const {
+  using Func = internal::max_coeff_functor<Scalar, NaNPropagation>;
+  Func func;
+  return internal::findCoeff(derived(), func, indexPtr);
+}
+
+}  // namespace Eigen
+
+#endif  // EIGEN_FIND_COEFF_H

Eigen/src/Core/ForceAlignedAccess.h

@@ -41,14 +41,10 @@ class ForceAlignedAccess : public internal::dense_xpr_base<ForceAlignedAccess<Ex
 
   EIGEN_DEVICE_FUNC explicit inline ForceAlignedAccess(const ExpressionType& matrix) : m_expression(matrix) {}
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const EIGEN_NOEXCEPT {
-    return m_expression.outerStride();
-  }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const EIGEN_NOEXCEPT {
-    return m_expression.innerStride();
-  }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_expression.rows(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_expression.cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return m_expression.outerStride(); }
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_expression.innerStride(); }
 
   EIGEN_DEVICE_FUNC inline const CoeffReturnType coeff(Index row, Index col) const {
     return m_expression.coeff(row, col);

Eigen/src/Core/GeneralProduct.h

@@ -327,6 +327,7 @@ struct gemv_dense_selector<OnTheRight, ColMajor, true> {
 
       if (!evalToDest) {
 #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+        constexpr int Size = Dest::SizeAtCompileTime;
         Index size = dest.size();
         EIGEN_DENSE_STORAGE_CTOR_PLUGIN
 #endif
@@ -391,6 +392,7 @@ struct gemv_dense_selector<OnTheRight, RowMajor, true> {
 
     if (!DirectlyUseRhs) {
 #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
+      constexpr int Size = ActualRhsTypeCleaned::SizeAtCompileTime;
       Index size = actualRhs.size();
       EIGEN_DENSE_STORAGE_CTOR_PLUGIN
 #endif

Eigen/src/Core/GenericPacketMath.h

@@ -65,13 +65,14 @@ struct default_packet_traits {
     HasAbsDiff = 0,
     HasBlend = 0,
     // This flag is used to indicate whether packet comparison is supported.
-    // pcmp_eq, pcmp_lt and pcmp_le should be defined for it to be true.
+    // pcmp_eq and pcmp_lt should be defined for it to be true.
     HasCmp = 0,
 
     HasDiv = 0,
     HasReciprocal = 0,
     HasSqrt = 0,
     HasRsqrt = 0,
+    HasCbrt = 0,
     HasExp = 0,
     HasExpm1 = 0,
     HasLog = 0,
@@ -194,7 +195,7 @@ struct is_half {
   static constexpr int Size = unpacket_traits<Packet>::size;
   using DefaultPacket = typename packet_traits<Scalar>::type;
   static constexpr int DefaultSize = unpacket_traits<DefaultPacket>::size;
-  static constexpr bool value = Size < DefaultSize;
+  static constexpr bool value = Size != 1 && Size < DefaultSize;
 };
 
 template <typename Src, typename Tgt>
@@ -252,6 +253,12 @@ struct preinterpret_generic<Packet, Packet, true> {
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet run(const Packet& a) { return a; }
 };
 
+template <typename ComplexPacket>
+struct preinterpret_generic<typename unpacket_traits<ComplexPacket>::as_real, ComplexPacket, false> {
+  using RealPacket = typename unpacket_traits<ComplexPacket>::as_real;
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE RealPacket run(const ComplexPacket& a) { return a.v; }
+};
+
 /** \internal \returns reinterpret_cast<Target>(a) */
 template <typename Target, typename Packet>
 EIGEN_DEVICE_FUNC inline Target preinterpret(const Packet& a) {
@@ -368,8 +375,13 @@ template <typename Packet>
 EIGEN_DEVICE_FUNC inline Packet pdiv(const Packet& a, const Packet& b) {
   return a / b;
 }
+// Avoid compiler warning for boolean algebra.
+template <>
+EIGEN_DEVICE_FUNC inline bool pdiv(const bool& a, const bool& b) {
+  return a && b;
+}
 
-// In the generic case, memset to all one bits.
+// In the generic packet case, memset to all one bits.
 template <typename Packet, typename EnableIf = void>
 struct ptrue_impl {
   static EIGEN_DEVICE_FUNC inline Packet run(const Packet& /*a*/) {
@@ -379,19 +391,16 @@ struct ptrue_impl {
   }
 };
 
+// Use a value of one for scalars.
+template <typename Scalar>
+struct ptrue_impl<Scalar, std::enable_if_t<is_scalar<Scalar>::value>> {
+  static EIGEN_DEVICE_FUNC inline Scalar run(const Scalar&) { return Scalar(1); }
+};
+
 // For booleans, we can only directly set a valid `bool` value to avoid UB.
 template <>
 struct ptrue_impl<bool, void> {
-  static EIGEN_DEVICE_FUNC inline bool run(const bool& /*a*/) { return true; }
-};
-
-// For non-trivial scalars, set to Scalar(1) (i.e. a non-zero value).
-// Although this is technically not a valid bitmask, the scalar path for pselect
-// uses a comparison to zero, so this should still work in most cases. We don't
-// have another option, since the scalar type requires initialization.
-template <typename T>
-struct ptrue_impl<T, std::enable_if_t<is_scalar<T>::value && NumTraits<T>::RequireInitialization>> {
-  static EIGEN_DEVICE_FUNC inline T run(const T& /*a*/) { return T(1); }
+  static EIGEN_DEVICE_FUNC inline bool run(const bool&) { return true; }
 };
 
 /** \internal \returns one bits. */
@@ -400,7 +409,7 @@ EIGEN_DEVICE_FUNC inline Packet ptrue(const Packet& a) {
   return ptrue_impl<Packet>::run(a);
 }
 
-// In the general case, memset to zero.
+// In the general packet case, memset to zero.
 template <typename Packet, typename EnableIf = void>
 struct pzero_impl {
   static EIGEN_DEVICE_FUNC inline Packet run(const Packet& /*a*/) {
@@ -423,74 +432,44 @@ EIGEN_DEVICE_FUNC inline Packet pzero(const Packet& a) {
   return pzero_impl<Packet>::run(a);
 }
 
-/** \internal \returns a <= b as a bit mask */
-template <typename Packet>
-EIGEN_DEVICE_FUNC inline Packet pcmp_le(const Packet& a, const Packet& b) {
-  return a <= b ? ptrue(a) : pzero(a);
-}
-
-/** \internal \returns a < b as a bit mask */
-template <typename Packet>
-EIGEN_DEVICE_FUNC inline Packet pcmp_lt(const Packet& a, const Packet& b) {
-  return a < b ? ptrue(a) : pzero(a);
-}
-
-/** \internal \returns a == b as a bit mask */
-template <typename Packet>
-EIGEN_DEVICE_FUNC inline Packet pcmp_eq(const Packet& a, const Packet& b) {
-  return a == b ? ptrue(a) : pzero(a);
-}
-
-/** \internal \returns a < b or a==NaN or b==NaN as a bit mask */
-template <typename Packet>
-EIGEN_DEVICE_FUNC inline Packet pcmp_lt_or_nan(const Packet& a, const Packet& b) {
-  return a >= b ? pzero(a) : ptrue(a);
-}
-
 template <typename T>
 struct bit_and {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a, const T& b) const { return a & b; }
+  EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE T operator()(const T& a, const T& b) const { return a & b; }
 };
 
 template <typename T>
 struct bit_or {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a, const T& b) const { return a | b; }
+  EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE T operator()(const T& a, const T& b) const { return a | b; }
 };
 
 template <typename T>
 struct bit_xor {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a, const T& b) const { return a ^ b; }
+  EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE T operator()(const T& a, const T& b) const { return a ^ b; }
 };
 
 template <typename T>
 struct bit_not {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a) const { return ~a; }
+  EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE T operator()(const T& a) const { return ~a; }
 };
 
 template <>
 struct bit_and<bool> {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE bool operator()(const bool& a, const bool& b) const {
-    return a && b;
-  }
+  EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE bool operator()(const bool& a, const bool& b) const { return a && b; }
 };
 
 template <>
 struct bit_or<bool> {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE bool operator()(const bool& a, const bool& b) const {
-    return a || b;
-  }
+  EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE bool operator()(const bool& a, const bool& b) const { return a || b; }
 };
 
 template <>
 struct bit_xor<bool> {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE bool operator()(const bool& a, const bool& b) const {
-    return a != b;
-  }
+  EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE bool operator()(const bool& a, const bool& b) const { return a != b; }
 };
 
 template <>
 struct bit_not<bool> {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE bool operator()(const bool& a) const { return !a; }
+  EIGEN_DEVICE_FUNC constexpr EIGEN_ALWAYS_INLINE bool operator()(const bool& a) const { return !a; }
 };
 
 // Use operators &, |, ^, ~.
@@ -579,8 +558,32 @@ EIGEN_DEVICE_FUNC inline Packet pandnot(const Packet& a, const Packet& b) {
   return pand(a, pnot(b));
 }
 
+/** \internal \returns a < b as a bit mask */
+template <typename Packet>
+EIGEN_DEVICE_FUNC inline Packet pcmp_lt(const Packet& a, const Packet& b) {
+  return a < b ? ptrue(a) : pzero(a);
+}
+
+/** \internal \returns a == b as a bit mask */
+template <typename Packet>
+EIGEN_DEVICE_FUNC inline Packet pcmp_eq(const Packet& a, const Packet& b) {
+  return a == b ? ptrue(a) : pzero(a);
+}
+
+/** \internal \returns a <= b as a bit mask */
+template <typename Packet>
+EIGEN_DEVICE_FUNC inline Packet pcmp_le(const Packet& a, const Packet& b) {
+  return por(pcmp_eq(a, b), pcmp_lt(a, b));
+}
+
+/** \internal \returns a < b or a==NaN or b==NaN as a bit mask */
+template <typename Packet>
+EIGEN_DEVICE_FUNC inline Packet pcmp_lt_or_nan(const Packet& a, const Packet& b) {
+  return a >= b ? pzero(a) : ptrue(a);
+}
+
 // In the general case, use bitwise select.
-template <typename Packet, typename EnableIf = void>
+template <typename Packet, bool is_scalar = is_scalar<Packet>::value>
 struct pselect_impl {
   static EIGEN_DEVICE_FUNC inline Packet run(const Packet& mask, const Packet& a, const Packet& b) {
     return por(pand(a, mask), pandnot(b, mask));
@@ -589,9 +592,9 @@ struct pselect_impl {
 
 // For scalars, use ternary select.
 template <typename Packet>
-struct pselect_impl<Packet, std::enable_if_t<is_scalar<Packet>::value>> {
+struct pselect_impl<Packet, true> {
   static EIGEN_DEVICE_FUNC inline Packet run(const Packet& mask, const Packet& a, const Packet& b) {
-    return numext::equal_strict(mask, Packet(0)) ? b : a;
+    return numext::select(mask, a, b);
   }
 };
 
@@ -608,7 +611,7 @@ EIGEN_DEVICE_FUNC inline bool pselect<bool>(const bool& cond, const bool& a, con
 
 /** \internal \returns the min or of \a a and \a b (coeff-wise)
     If either \a a or \a b are NaN, the result is implementation defined. */
-template <int NaNPropagation>
+template <int NaNPropagation, bool IsInteger>
 struct pminmax_impl {
   template <typename Packet, typename Op>
   static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a, const Packet& b, Op op) {
@@ -619,7 +622,7 @@ struct pminmax_impl {
 /** \internal \returns the min or max of \a a and \a b (coeff-wise)
     If either \a a or \a b are NaN, NaN is returned. */
 template <>
-struct pminmax_impl<PropagateNaN> {
+struct pminmax_impl<PropagateNaN, false> {
   template <typename Packet, typename Op>
   static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a, const Packet& b, Op op) {
     Packet not_nan_mask_a = pcmp_eq(a, a);
@@ -632,7 +635,7 @@ struct pminmax_impl<PropagateNaN> {
     If both \a a and \a b are NaN, NaN is returned.
     Equivalent to std::fmin(a, b).  */
 template <>
-struct pminmax_impl<PropagateNumbers> {
+struct pminmax_impl<PropagateNumbers, false> {
   template <typename Packet, typename Op>
   static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a, const Packet& b, Op op) {
     Packet not_nan_mask_a = pcmp_eq(a, a);
@@ -641,7 +644,7 @@ struct pminmax_impl<PropagateNumbers> {
   }
 };
 
-#define EIGEN_BINARY_OP_NAN_PROPAGATION(Type, Func) [](const Type& a, const Type& b) { return Func(a, b); }
+#define EIGEN_BINARY_OP_NAN_PROPAGATION(Type, Func) [](const Type& aa, const Type& bb) { return Func(aa, bb); }
 
 /** \internal \returns the min of \a a and \a b  (coeff-wise).
     If \a a or \b b is NaN, the return value is implementation defined. */
@@ -654,7 +657,8 @@ EIGEN_DEVICE_FUNC inline Packet pmin(const Packet& a, const Packet& b) {
     NaNPropagation determines the NaN propagation semantics. */
 template <int NaNPropagation, typename Packet>
 EIGEN_DEVICE_FUNC inline Packet pmin(const Packet& a, const Packet& b) {
-  return pminmax_impl<NaNPropagation>::run(a, b, EIGEN_BINARY_OP_NAN_PROPAGATION(Packet, (pmin<Packet>)));
+  constexpr bool IsInteger = NumTraits<typename unpacket_traits<Packet>::type>::IsInteger;
+  return pminmax_impl<NaNPropagation, IsInteger>::run(a, b, EIGEN_BINARY_OP_NAN_PROPAGATION(Packet, (pmin<Packet>)));
 }
 
 /** \internal \returns the max of \a a and \a b  (coeff-wise)
@@ -668,7 +672,8 @@ EIGEN_DEVICE_FUNC inline Packet pmax(const Packet& a, const Packet& b) {
     NaNPropagation determines the NaN propagation semantics. */
 template <int NaNPropagation, typename Packet>
 EIGEN_DEVICE_FUNC inline Packet pmax(const Packet& a, const Packet& b) {
-  return pminmax_impl<NaNPropagation>::run(a, b, EIGEN_BINARY_OP_NAN_PROPAGATION(Packet, (pmax<Packet>)));
+  constexpr bool IsInteger = NumTraits<typename unpacket_traits<Packet>::type>::IsInteger;
+  return pminmax_impl<NaNPropagation, IsInteger>::run(a, b, EIGEN_BINARY_OP_NAN_PROPAGATION(Packet, (pmax<Packet>)));
 }
 
 /** \internal \returns the absolute value of \a a */
@@ -873,17 +878,29 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet plset(const typename unpacket_trait
   return a;
 }
 
+template <typename Packet, typename EnableIf = void>
+struct peven_mask_impl {
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet run(const Packet&) {
+    typedef typename unpacket_traits<Packet>::type Scalar;
+    const size_t n = unpacket_traits<Packet>::size;
+    EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) Scalar elements[n];
+    for (size_t i = 0; i < n; ++i) {
+      memset(elements + i, ((i & 1) == 0 ? 0xff : 0), sizeof(Scalar));
+    }
+    return ploadu<Packet>(elements);
+  }
+};
+
+template <typename Scalar>
+struct peven_mask_impl<Scalar, std::enable_if_t<is_scalar<Scalar>::value>> {
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run(const Scalar&) { return Scalar(1); }
+};
+
 /** \internal \returns a packet with constant coefficients \a a, e.g.: (x, 0, x, 0),
      where x is the value of all 1-bits. */
 template <typename Packet>
-EIGEN_DEVICE_FUNC inline Packet peven_mask(const Packet& /*a*/) {
-  typedef typename unpacket_traits<Packet>::type Scalar;
-  const size_t n = unpacket_traits<Packet>::size;
-  EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) Scalar elements[n];
-  for (size_t i = 0; i < n; ++i) {
-    memset(elements + i, ((i & 1) == 0 ? 0xff : 0), sizeof(Scalar));
-  }
-  return ploadu<Packet>(elements);
+EIGEN_DEVICE_FUNC inline Packet peven_mask(const Packet& a) {
+  return peven_mask_impl<Packet>::run(a);
 }
 
 /** \internal copy the packet \a from to \a *to, \a to must be properly aligned */
@@ -1083,8 +1100,13 @@ EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet patanh(const Packet&
 /** \internal \returns the exp of \a a (coeff-wise) */
 template <typename Packet>
 EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pexp(const Packet& a) {
-  EIGEN_USING_STD(exp);
-  return exp(a);
+  return numext::exp(a);
+}
+
+/** \internal \returns the exp2 of \a a (coeff-wise) */
+template <typename Packet>
+EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pexp2(const Packet& a) {
+  return numext::exp2(a);
 }
 
 /** \internal \returns the expm1 of \a a (coeff-wise) */
@@ -1113,7 +1135,7 @@ EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet plog10(const Packet&
   return log10(a);
 }
 
-/** \internal \returns the log10 of \a a (coeff-wise) */
+/** \internal \returns the log2 of \a a (coeff-wise) */
 template <typename Packet>
 EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet plog2(const Packet& a) {
   using Scalar = typename internal::unpacket_traits<Packet>::type;
@@ -1239,26 +1261,46 @@ EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_mul(const
 template <typename Packet>
 EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_min(const Packet& a) {
   typedef typename unpacket_traits<Packet>::type Scalar;
-  return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmin<PropagateFast, Scalar>)));
+  return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmin<Scalar>)));
 }
 
-template <int NaNPropagation, typename Packet>
-EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_min(const Packet& a) {
-  typedef typename unpacket_traits<Packet>::type Scalar;
-  return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmin<NaNPropagation, Scalar>)));
-}
-
-/** \internal \returns the min of the elements of \a a */
+/** \internal \returns the max of the elements of \a a */
 template <typename Packet>
 EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_max(const Packet& a) {
   typedef typename unpacket_traits<Packet>::type Scalar;
-  return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmax<PropagateFast, Scalar>)));
+  return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmax<Scalar>)));
+}
+
+template <int NaNPropagation, typename Packet>
+struct predux_min_max_helper_impl {
+  using Scalar = typename unpacket_traits<Packet>::type;
+  static constexpr bool UsePredux_ = NaNPropagation == PropagateFast || NumTraits<Scalar>::IsInteger;
+  template <bool UsePredux = UsePredux_, std::enable_if_t<!UsePredux, bool> = true>
+  static EIGEN_DEVICE_FUNC inline Scalar run_min(const Packet& a) {
+    return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmin<NaNPropagation, Scalar>)));
+  }
+  template <bool UsePredux = UsePredux_, std::enable_if_t<!UsePredux, bool> = true>
+  static EIGEN_DEVICE_FUNC inline Scalar run_max(const Packet& a) {
+    return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmax<NaNPropagation, Scalar>)));
+  }
+  template <bool UsePredux = UsePredux_, std::enable_if_t<UsePredux, bool> = true>
+  static EIGEN_DEVICE_FUNC inline Scalar run_min(const Packet& a) {
+    return predux_min(a);
+  }
+  template <bool UsePredux = UsePredux_, std::enable_if_t<UsePredux, bool> = true>
+  static EIGEN_DEVICE_FUNC inline Scalar run_max(const Packet& a) {
+    return predux_max(a);
+  }
+};
+
+template <int NaNPropagation, typename Packet>
+EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_min(const Packet& a) {
+  return predux_min_max_helper_impl<NaNPropagation, Packet>::run_min(a);
 }
 
 template <int NaNPropagation, typename Packet>
 EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_max(const Packet& a) {
-  typedef typename unpacket_traits<Packet>::type Scalar;
-  return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmax<NaNPropagation, Scalar>)));
+  return predux_min_max_helper_impl<NaNPropagation, Packet>::run_max(a);
 }
 
 #undef EIGEN_BINARY_OP_NAN_PROPAGATION
@@ -1289,29 +1331,61 @@ EIGEN_DEVICE_FUNC inline bool predux_any(const Packet& a) {
  * The following functions might not have to be overwritten for vectorized types
  ***************************************************************************/
 
-// FMA instructions.
+template <typename Packet, typename EnableIf = void>
+struct pmadd_impl {
+  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet pmadd(const Packet& a, const Packet& b, const Packet& c) {
+    return padd(pmul(a, b), c);
+  }
+  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet pmsub(const Packet& a, const Packet& b, const Packet& c) {
+    return psub(pmul(a, b), c);
+  }
+  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet pnmadd(const Packet& a, const Packet& b, const Packet& c) {
+    return psub(c, pmul(a, b));
+  }
+  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet pnmsub(const Packet& a, const Packet& b, const Packet& c) {
+    return pnegate(pmadd(a, b, c));
+  }
+};
+
+template <typename Scalar>
+struct pmadd_impl<Scalar, std::enable_if_t<is_scalar<Scalar>::value && NumTraits<Scalar>::IsSigned>> {
+  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar pmadd(const Scalar& a, const Scalar& b, const Scalar& c) {
+    return numext::madd<Scalar>(a, b, c);
+  }
+  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar pmsub(const Scalar& a, const Scalar& b, const Scalar& c) {
+    return numext::madd<Scalar>(a, b, Scalar(-c));
+  }
+  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar pnmadd(const Scalar& a, const Scalar& b, const Scalar& c) {
+    return numext::madd<Scalar>(Scalar(-a), b, c);
+  }
+  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Scalar pnmsub(const Scalar& a, const Scalar& b, const Scalar& c) {
+    return -Scalar(numext::madd<Scalar>(a, b, c));
+  }
+};
+
+// Multiply-add instructions.
 /** \internal \returns a * b + c (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC inline Packet pmadd(const Packet& a, const Packet& b, const Packet& c) {
-  return padd(pmul(a, b), c);
+  return pmadd_impl<Packet>::pmadd(a, b, c);
 }
 
 /** \internal \returns a * b - c (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC inline Packet pmsub(const Packet& a, const Packet& b, const Packet& c) {
-  return psub(pmul(a, b), c);
+  return pmadd_impl<Packet>::pmsub(a, b, c);
 }
 
 /** \internal \returns -(a * b) + c (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC inline Packet pnmadd(const Packet& a, const Packet& b, const Packet& c) {
-  return psub(c, pmul(a, b));
+  return pmadd_impl<Packet>::pnmadd(a, b, c);
 }
 
 /** \internal \returns -((a * b + c) (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC inline Packet pnmsub(const Packet& a, const Packet& b, const Packet& c) {
-  return pnegate(pmadd(a, b, c));
+  return pmadd_impl<Packet>::pnmsub(a, b, c);
 }
 
 /** \internal copy a packet with constant coefficient \a a (e.g., [a,a,a,a]) to \a *to. \a to must be 16 bytes aligned
@@ -1520,6 +1594,107 @@ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet pcarg(const Packet& a) {
   return (Packet)pand(result, peven_mask(result));  // atan2 0    atan2 0    ...
 }
 
+/** \internal \returns a packet populated with values in the range [begin, begin + count). Elements
+ * outside this range are not defined. \a *from does not need to be aligned, and can be null if \a count is zero.*/
+template <typename Packet>
+EIGEN_DEVICE_FUNC inline Packet ploaduSegment(const typename unpacket_traits<Packet>::type* from, Index begin,
+                                              Index count) {
+  using Scalar = typename unpacket_traits<Packet>::type;
+  constexpr Index PacketSize = unpacket_traits<Packet>::size;
+  eigen_assert((begin >= 0 && count >= 0 && begin + count <= PacketSize) && "invalid range");
+  Scalar aux[PacketSize] = {};
+  for (Index k = begin; k < begin + count; k++) {
+    aux[k] = from[k];
+  }
+  return ploadu<Packet>(aux);
+}
+
+/** \internal \returns a packet populated with values in the range [begin, begin + count). Elements
+ * outside this range are not defined. \a *from must be aligned, and cannot be null.*/
+template <typename Packet>
+EIGEN_DEVICE_FUNC inline Packet ploadSegment(const typename unpacket_traits<Packet>::type* from, Index begin,
+                                             Index count) {
+  return ploaduSegment<Packet>(from, begin, count);
+}
+
+/** \internal copy the packet \a from in the range [begin, begin + count) to \a *to.
+Elements outside of the range [begin, begin + count) are not defined. \a *to does not need to be aligned, and can be
+null if \a count is zero.*/
+template <typename Scalar, typename Packet>
+EIGEN_DEVICE_FUNC inline void pstoreuSegment(Scalar* to, const Packet& from, Index begin, Index count) {
+  constexpr Index PacketSize = unpacket_traits<Packet>::size;
+  eigen_assert((begin >= 0 && count >= 0 && begin + count <= PacketSize) && "invalid range");
+  Scalar aux[PacketSize];
+  pstoreu<Scalar, Packet>(aux, from);
+  for (Index k = begin; k < begin + count; k++) {
+    to[k] = aux[k];
+  }
+}
+
+/** \internal copy the packet \a from in the range [begin, begin + count) to \a *to.
+Elements outside of the range [begin, begin + count) are not defined. \a *to must be aligned, and cannot be
+null.*/
+template <typename Scalar, typename Packet>
+EIGEN_DEVICE_FUNC inline void pstoreSegment(Scalar* to, const Packet& from, Index begin, Index count) {
+  return pstoreuSegment(to, from, begin, count);
+}
+
+/** \internal \returns a packet populated with values in the range [begin, begin + count). Elements
+ * outside this range are not defined.*/
+template <typename Packet, int Alignment>
+EIGEN_DEVICE_FUNC inline Packet ploadtSegment(const typename unpacket_traits<Packet>::type* from, Index begin,
+                                              Index count) {
+  constexpr int RequiredAlignment = unpacket_traits<Packet>::alignment;
+  if (Alignment >= RequiredAlignment) {
+    return ploadSegment<Packet>(from, begin, count);
+  } else {
+    return ploaduSegment<Packet>(from, begin, count);
+  }
+}
+
+/** \internal copy the packet \a from in the range [begin, begin + count) to \a *to.
+Elements outside of the range [begin, begin + count) are not defined.*/
+template <typename Scalar, typename Packet, int Alignment>
+EIGEN_DEVICE_FUNC inline void pstoretSegment(Scalar* to, const Packet& from, Index begin, Index count) {
+  constexpr int RequiredAlignment = unpacket_traits<Packet>::alignment;
+  if (Alignment >= RequiredAlignment) {
+    pstoreSegment<Scalar, Packet>(to, from, begin, count);
+  } else {
+    pstoreuSegment<Scalar, Packet>(to, from, begin, count);
+  }
+}
+
+#ifndef EIGEN_NO_IO
+
+template <typename Packet>
+class StreamablePacket {
+ public:
+  using Scalar = typename unpacket_traits<Packet>::type;
+  StreamablePacket(const Packet& packet) { pstoreu(v_, packet); }
+
+  friend std::ostream& operator<<(std::ostream& os, const StreamablePacket& packet) {
+    os << "{" << packet.v_[0];
+    for (int i = 1; i < unpacket_traits<Packet>::size; ++i) {
+      os << "," << packet.v_[i];
+    }
+    os << "}";
+    return os;
+  }
+
+ private:
+  Scalar v_[unpacket_traits<Packet>::size];
+};
+
+/**
+ * \internal \returns an intermediary that can be used to ostream packets, e.g. for debugging.
+ */
+template <typename Packet>
+StreamablePacket<Packet> postream(const Packet& packet) {
+  return StreamablePacket<Packet>(packet);
+}
+
+#endif  // EIGEN_NO_IO
+
 }  // end namespace internal
 
 }  // end namespace Eigen

Eigen/src/Core/GlobalFunctions.h

@@ -76,6 +76,7 @@ EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erf, scalar_erf_op, error function,\sa ArrayBas
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erfc, scalar_erfc_op, complement error function,\sa ArrayBase::erfc)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(ndtri, scalar_ndtri_op, inverse normal distribution function,\sa ArrayBase::ndtri)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp, scalar_exp_op, exponential,\sa ArrayBase::exp)
+EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp2, scalar_exp2_op, exponential,\sa ArrayBase::exp2)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(expm1, scalar_expm1_op, exponential of a value minus 1,\sa ArrayBase::expm1)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log, scalar_log_op, natural logarithm,\sa Eigen::log10 DOXCOMMA ArrayBase::log)
 EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log1p, scalar_log1p_op, natural logarithm of 1 plus the value,\sa ArrayBase::log1p)

Eigen/src/Core/IO.h

@@ -68,8 +68,8 @@ struct IOFormat {
     // TODO check if rowPrefix, rowSuffix or rowSeparator contains a newline
     // don't add rowSpacer if columns are not to be aligned
     if ((flags & DontAlignCols)) return;
-    int i = int(matSuffix.length()) - 1;
-    while (i >= 0 && matSuffix[i] != '\n') {
+    int i = int(matPrefix.length()) - 1;
+    while (i >= 0 && matPrefix[i] != '\n') {
       rowSpacer += ' ';
       i--;
     }

Eigen/src/Core/IndexedView.h

@@ -225,14 +225,14 @@ class IndexedViewImpl<XprType, RowIndices, ColIndices, StorageKind, true>
     return this->nestedExpression().data() + row_offset + col_offset;
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const EIGEN_NOEXCEPT {
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept {
     if (traits<Derived>::InnerStrideAtCompileTime != Dynamic) {
       return traits<Derived>::InnerStrideAtCompileTime;
     }
     return innerIncrement() * this->nestedExpression().innerStride();
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const EIGEN_NOEXCEPT {
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept {
     if (traits<Derived>::OuterStrideAtCompileTime != Dynamic) {
       return traits<Derived>::OuterStrideAtCompileTime;
     }
@@ -308,6 +308,12 @@ struct unary_evaluator<IndexedView<ArgType, RowIndices, ColIndices>, IndexBased>
   const XprType& m_xpr;
 };
 
+// Catch assignments to an IndexedView.
+template <typename ArgType, typename RowIndices, typename ColIndices>
+struct evaluator_assume_aliasing<IndexedView<ArgType, RowIndices, ColIndices>> {
+  static const bool value = true;
+};
+
 }  // end namespace internal
 
 }  // end namespace Eigen

Eigen/src/Core/InnerProduct.h

@@ -57,16 +57,20 @@ struct inner_product_assert {
 
 template <typename Func, typename Lhs, typename Rhs>
 struct inner_product_evaluator {
-  static constexpr int LhsFlags = evaluator<Lhs>::Flags, RhsFlags = evaluator<Rhs>::Flags,
-                       SizeAtCompileTime = min_size_prefer_fixed(Lhs::SizeAtCompileTime, Rhs::SizeAtCompileTime),
-                       LhsAlignment = evaluator<Lhs>::Alignment, RhsAlignment = evaluator<Rhs>::Alignment;
+  static constexpr int LhsFlags = evaluator<Lhs>::Flags;
+  static constexpr int RhsFlags = evaluator<Rhs>::Flags;
+  static constexpr int SizeAtCompileTime = size_prefer_fixed(Lhs::SizeAtCompileTime, Rhs::SizeAtCompileTime);
+  static constexpr int MaxSizeAtCompileTime =
+      min_size_prefer_fixed(Lhs::MaxSizeAtCompileTime, Rhs::MaxSizeAtCompileTime);
+  static constexpr int LhsAlignment = evaluator<Lhs>::Alignment;
+  static constexpr int RhsAlignment = evaluator<Rhs>::Alignment;
 
   using Scalar = typename Func::result_type;
   using Packet = typename find_inner_product_packet<Scalar, SizeAtCompileTime>::type;
 
   static constexpr bool Vectorize =
       bool(LhsFlags & RhsFlags & PacketAccessBit) && Func::PacketAccess &&
-      ((SizeAtCompileTime == Dynamic) || (unpacket_traits<Packet>::size <= SizeAtCompileTime));
+      ((MaxSizeAtCompileTime == Dynamic) || (unpacket_traits<Packet>::size <= MaxSizeAtCompileTime));
 
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit inner_product_evaluator(const Lhs& lhs, const Rhs& rhs,
                                                                          Func func = Func())
@@ -85,13 +89,13 @@ struct inner_product_evaluator {
   }
 
   template <typename PacketType, int LhsMode = LhsAlignment, int RhsMode = RhsAlignment>
-  EIGEN_STRONG_INLINE PacketType packet(Index index) const {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index index) const {
     return m_func.packet(m_lhs.template packet<LhsMode, PacketType>(index),
                          m_rhs.template packet<RhsMode, PacketType>(index));
   }
 
   template <typename PacketType, int LhsMode = LhsAlignment, int RhsMode = RhsAlignment>
-  EIGEN_STRONG_INLINE PacketType packet(const PacketType& value, Index index) const {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(const PacketType& value, Index index) const {
     return m_func.packet(value, m_lhs.template packet<LhsMode, PacketType>(index),
                          m_rhs.template packet<RhsMode, PacketType>(index));
   }
@@ -207,8 +211,14 @@ struct scalar_inner_product_op {
   static constexpr bool PacketAccess = false;
 };
 
+// Partial specialization for packet access if and only if
+// LhsScalar == RhsScalar == ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType.
 template <typename Scalar, bool Conj>
-struct scalar_inner_product_op<Scalar, Scalar, Conj> {
+struct scalar_inner_product_op<
+    Scalar,
+    typename std::enable_if<internal::is_same<typename ScalarBinaryOpTraits<Scalar, Scalar>::ReturnType, Scalar>::value,
+                            Scalar>::type,
+    Conj> {
   using result_type = Scalar;
   using conj_helper = conditional_conj<Scalar, Conj>;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(const Scalar& a, const Scalar& b) const {

Eigen/src/Core/Inverse.h

@@ -51,8 +51,8 @@ class Inverse : public InverseImpl<XprType, typename internal::traits<XprType>::
 
   explicit EIGEN_DEVICE_FUNC Inverse(const XprType& xpr) : m_xpr(xpr) {}
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_xpr.cols(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_xpr.rows(); }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_xpr.cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_xpr.rows(); }
 
   EIGEN_DEVICE_FUNC const XprTypeNestedCleaned& nestedExpression() const { return m_xpr; }
 
@@ -92,7 +92,7 @@ struct unary_evaluator<Inverse<ArgType> > : public evaluator<typename Inverse<Ar
 
   enum { Flags = Base::Flags | EvalBeforeNestingBit };
 
-  unary_evaluator(const InverseType& inv_xpr) : m_result(inv_xpr.rows(), inv_xpr.cols()) {
+  EIGEN_DEVICE_FUNC unary_evaluator(const InverseType& inv_xpr) : m_result(inv_xpr.rows(), inv_xpr.cols()) {
     internal::construct_at<Base>(this, m_result);
     internal::call_assignment_no_alias(m_result, inv_xpr);
   }

Eigen/src/Core/Map.h

@@ -102,11 +102,11 @@ class Map : public MapBase<Map<PlainObjectType, MapOptions, StrideType> > {
   typedef PointerType PointerArgType;
   EIGEN_DEVICE_FUNC inline PointerType cast_to_pointer_type(PointerArgType ptr) { return ptr; }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const {
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const {
     return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const {
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const {
     return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer()
            : internal::traits<Map>::OuterStrideAtCompileTime != Dynamic
                ? Index(internal::traits<Map>::OuterStrideAtCompileTime)

Eigen/src/Core/MapBase.h

@@ -84,9 +84,9 @@ class MapBase<Derived, ReadOnlyAccessors> : public internal::dense_xpr_base<Deri
   typedef typename Base::CoeffReturnType CoeffReturnType;
 
   /** \copydoc DenseBase::rows() */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_rows.value(); }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_rows.value(); }
   /** \copydoc DenseBase::cols() */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_cols.value(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_cols.value(); }
 
   /** Returns a pointer to the first coefficient of the matrix or vector.
    *

Eigen/src/Core/MathFunctions.h

@@ -170,8 +170,8 @@ struct imag_ref_default_impl {
 
 template <typename Scalar>
 struct imag_ref_default_impl<Scalar, false> {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Scalar run(Scalar&) { return Scalar(0); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline const Scalar run(const Scalar&) { return Scalar(0); }
+  EIGEN_DEVICE_FUNC constexpr static Scalar run(Scalar&) { return Scalar(0); }
+  EIGEN_DEVICE_FUNC constexpr static const Scalar run(const Scalar&) { return Scalar(0); }
 };
 
 template <typename Scalar>
@@ -182,6 +182,40 @@ struct imag_ref_retval {
   typedef typename NumTraits<Scalar>::Real& type;
 };
 
+}  // namespace internal
+
+namespace numext {
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline internal::add_const_on_value_type_t<EIGEN_MATHFUNC_RETVAL(real_ref, Scalar)> real_ref(
+    const Scalar& x) {
+  return internal::real_ref_impl<Scalar>::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar select(const Scalar& mask, const Scalar& a, const Scalar& b) {
+  return numext::is_exactly_zero(mask) ? b : a;
+}
+
+}  // namespace numext
+
+namespace internal {
+
 /****************************************************************************
  * Implementation of conj                                                 *
  ****************************************************************************/
@@ -221,7 +255,9 @@ template <typename Scalar>
 struct abs2_impl_default<Scalar, true>  // IsComplex
 {
   typedef typename NumTraits<Scalar>::Real RealScalar;
-  EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) { return x.real() * x.real() + x.imag() * x.imag(); }
+  EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) {
+    return numext::real(x) * numext::real(x) + numext::imag(x) * numext::imag(x);
+  }
 };
 
 template <typename Scalar>
@@ -250,16 +286,14 @@ struct sqrt_impl {
 };
 
 // Complex sqrt defined in MathFunctionsImpl.h.
-template <typename T>
-EIGEN_DEVICE_FUNC std::complex<T> complex_sqrt(const std::complex<T>& a_x);
+template <typename ComplexT>
+EIGEN_DEVICE_FUNC ComplexT complex_sqrt(const ComplexT& a_x);
 
 // Custom implementation is faster than `std::sqrt`, works on
 // GPU, and correctly handles special cases (unlike MSVC).
 template <typename T>
 struct sqrt_impl<std::complex<T>> {
-  EIGEN_DEVICE_FUNC static EIGEN_ALWAYS_INLINE std::complex<T> run(const std::complex<T>& x) {
-    return complex_sqrt<T>(x);
-  }
+  EIGEN_DEVICE_FUNC static EIGEN_ALWAYS_INLINE std::complex<T> run(const std::complex<T>& x) { return complex_sqrt(x); }
 };
 
 template <typename Scalar>
@@ -272,13 +306,13 @@ template <typename T>
 struct rsqrt_impl;
 
 // Complex rsqrt defined in MathFunctionsImpl.h.
-template <typename T>
-EIGEN_DEVICE_FUNC std::complex<T> complex_rsqrt(const std::complex<T>& a_x);
+template <typename ComplexT>
+EIGEN_DEVICE_FUNC ComplexT complex_rsqrt(const ComplexT& a_x);
 
 template <typename T>
 struct rsqrt_impl<std::complex<T>> {
   EIGEN_DEVICE_FUNC static EIGEN_ALWAYS_INLINE std::complex<T> run(const std::complex<T>& x) {
-    return complex_rsqrt<T>(x);
+    return complex_rsqrt(x);
   }
 };
 
@@ -299,7 +333,7 @@ struct norm1_default_impl<Scalar, true> {
   typedef typename NumTraits<Scalar>::Real RealScalar;
   EIGEN_DEVICE_FUNC static inline RealScalar run(const Scalar& x) {
     EIGEN_USING_STD(abs);
-    return abs(x.real()) + abs(x.imag());
+    return abs(numext::real(x)) + abs(numext::imag(x));
   }
 };
 
@@ -469,8 +503,8 @@ struct expm1_retval {
  ****************************************************************************/
 
 // Complex log defined in MathFunctionsImpl.h.
-template <typename T>
-EIGEN_DEVICE_FUNC std::complex<T> complex_log(const std::complex<T>& z);
+template <typename ComplexT>
+EIGEN_DEVICE_FUNC ComplexT complex_log(const ComplexT& z);
 
 template <typename Scalar>
 struct log_impl {
@@ -798,8 +832,8 @@ EIGEN_DEVICE_FUNC std::enable_if_t<(std::numeric_limits<T>::has_infinity && !Num
 
 template <typename T>
 EIGEN_DEVICE_FUNC
-    std::enable_if_t<!(std::numeric_limits<T>::has_quiet_NaN || std::numeric_limits<T>::has_signaling_NaN), bool>
-    isnan_impl(const T&) {
+std::enable_if_t<!(std::numeric_limits<T>::has_quiet_NaN || std::numeric_limits<T>::has_signaling_NaN), bool>
+isnan_impl(const T&) {
   return false;
 }
 
@@ -846,7 +880,7 @@ struct sign_impl<Scalar, true, IsInteger> {
     real_type aa = abs(a);
     if (aa == real_type(0)) return Scalar(0);
     aa = real_type(1) / aa;
-    return Scalar(a.real() * aa, a.imag() * aa);
+    return Scalar(numext::real(a) * aa, numext::imag(a) * aa);
   }
 };
 
@@ -907,6 +941,78 @@ struct nearest_integer_impl<Scalar, true> {
   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run_trunc(const Scalar& x) { return x; }
 };
 
+// Extra namespace to prevent leaking std::fma into Eigen::internal.
+namespace has_fma_detail {
+
+template <typename T, typename EnableIf = void>
+struct has_fma_impl : public std::false_type {};
+
+using std::fma;
+
+template <typename T>
+struct has_fma_impl<
+    T, std::enable_if_t<std::is_same<T, decltype(fma(std::declval<T>(), std::declval<T>(), std::declval<T>()))>::value>>
+    : public std::true_type {};
+
+}  // namespace has_fma_detail
+
+template <typename T>
+struct has_fma : public has_fma_detail::has_fma_impl<T> {};
+
+// Default implementation.
+template <typename T, typename Enable = void>
+struct fma_impl {
+  static_assert(has_fma<T>::value, "No function fma(...) for type.  Please provide an implementation.");
+};
+
+// STD or ADL version if it exists.
+template <typename T>
+struct fma_impl<T, std::enable_if_t<has_fma<T>::value>> {
+  static EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T run(const T& a, const T& b, const T& c) {
+    using std::fma;
+    return fma(a, b, c);
+  }
+};
+
+#if defined(EIGEN_GPUCC)
+template <>
+struct has_fma<float> : public true_type {};
+
+template <>
+struct fma_impl<float, void> {
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float run(const float& a, const float& b, const float& c) {
+    return ::fmaf(a, b, c);
+  }
+};
+
+template <>
+struct has_fma<double> : public true_type {};
+
+template <>
+struct fma_impl<double, void> {
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double run(const double& a, const double& b, const double& c) {
+    return ::fma(a, b, c);
+  }
+};
+#endif
+
+// Basic multiply-add.
+template <typename Scalar, typename EnableIf = void>
+struct madd_impl {
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run(const Scalar& x, const Scalar& y, const Scalar& z) {
+    return x * y + z;
+  }
+};
+
+#if EIGEN_SCALAR_MADD_USE_FMA
+template <typename Scalar>
+struct madd_impl<Scalar, std::enable_if_t<has_fma<Scalar>::value>> {
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar run(const Scalar& x, const Scalar& y, const Scalar& z) {
+    return fma_impl<Scalar>::run(x, y, z);
+  }
+};
+#endif
+
 }  // end namespace internal
 
 /****************************************************************************
@@ -1042,27 +1148,6 @@ SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(maxi, fmax)
 
 #endif
 
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x) {
-  return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline internal::add_const_on_value_type_t<EIGEN_MATHFUNC_RETVAL(real_ref, Scalar)> real_ref(
-    const Scalar& x) {
-  return internal::real_ref_impl<Scalar>::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x) {
-  return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x) {
-  return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
-}
-
 template <typename Scalar>
 EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(arg, Scalar) arg(const Scalar& x) {
   return EIGEN_MATHFUNC_IMPL(arg, Scalar)::run(x);
@@ -1248,11 +1333,9 @@ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double trunc(const double& x) {
 // Integer division with rounding up.
 // T is assumed to be an integer type with a>=0, and b>0
 template <typename T>
-EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE EIGEN_CONSTEXPR T div_ceil(T a, T b) {
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE constexpr T div_ceil(T a, T b) {
   using UnsignedT = typename internal::make_unsigned<T>::type;
   EIGEN_STATIC_ASSERT((NumTraits<T>::IsInteger), THIS FUNCTION IS FOR INTEGER TYPES)
-  eigen_assert(a >= 0);
-  eigen_assert(b > 0);
   // Note: explicitly declaring a and b as non-negative values allows the compiler to use better optimizations
   const UnsignedT ua = UnsignedT(a);
   const UnsignedT ub = UnsignedT(b);
@@ -1263,13 +1346,11 @@ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE EIGEN_CONSTEXPR T div_ceil(T a, T b) {
 // Integer round down to nearest power of b
 // T is assumed to be an integer type with a>=0, and b>0
 template <typename T, typename U>
-EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE EIGEN_CONSTEXPR T round_down(T a, U b) {
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE constexpr T round_down(T a, U b) {
   using UnsignedT = typename internal::make_unsigned<T>::type;
   using UnsignedU = typename internal::make_unsigned<U>::type;
   EIGEN_STATIC_ASSERT((NumTraits<T>::IsInteger), THIS FUNCTION IS FOR INTEGER TYPES)
   EIGEN_STATIC_ASSERT((NumTraits<U>::IsInteger), THIS FUNCTION IS FOR INTEGER TYPES)
-  eigen_assert(a >= 0);
-  eigen_assert(b > 0);
   // Note: explicitly declaring a and b as non-negative values allows the compiler to use better optimizations
   const UnsignedT ua = UnsignedT(a);
   const UnsignedU ub = UnsignedU(b);
@@ -1278,8 +1359,7 @@ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE EIGEN_CONSTEXPR T round_down(T a, U b) {
 
 /** Log base 2 for 32 bits positive integers.
  * Conveniently returns 0 for x==0. */
-EIGEN_CONSTEXPR inline int log2(int x) {
-  eigen_assert(x >= 0);
+constexpr int log2(int x) {
   unsigned int v(x);
   constexpr int table[32] = {0, 9,  1,  10, 13, 21, 2,  29, 11, 14, 16, 18, 22, 25, 3, 30,
                              8, 12, 20, 28, 15, 17, 24, 7,  19, 27, 23, 6,  26, 5,  4, 31};
@@ -1317,11 +1397,17 @@ SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(sqrt, sqrt)
 
 /** \returns the cube root of \a x. **/
 template <typename T>
-EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T cbrt(const T& x) {
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::enable_if_t<!NumTraits<T>::IsComplex, T> cbrt(const T& x) {
   EIGEN_USING_STD(cbrt);
   return static_cast<T>(cbrt(x));
 }
 
+template <typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::enable_if_t<NumTraits<T>::IsComplex, T> cbrt(const T& x) {
+  EIGEN_USING_STD(pow);
+  return pow(x, typename NumTraits<T>::Real(1.0 / 3.0));
+}
+
 /** \returns the reciprocal square root of \a x. **/
 template <typename T>
 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T rsqrt(const T& x) {
@@ -1350,17 +1436,17 @@ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double log(const double& x) {
 #endif
 
 template <typename T>
-EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
-    std::enable_if_t<NumTraits<T>::IsSigned || NumTraits<T>::IsComplex, typename NumTraits<T>::Real>
-    abs(const T& x) {
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE std::enable_if_t<NumTraits<T>::IsSigned || NumTraits<T>::IsComplex, typename NumTraits<T>::Real>
+abs(const T& x) {
   EIGEN_USING_STD(abs);
   return abs(x);
 }
 
 template <typename T>
-EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
-    std::enable_if_t<!(NumTraits<T>::IsSigned || NumTraits<T>::IsComplex), typename NumTraits<T>::Real>
-    abs(const T& x) {
+EIGEN_DEVICE_FUNC
+EIGEN_ALWAYS_INLINE std::enable_if_t<!(NumTraits<T>::IsSigned || NumTraits<T>::IsComplex), typename NumTraits<T>::Real>
+abs(const T& x) {
   return x;
 }
 
@@ -1477,6 +1563,63 @@ EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::complex<double> exp(const std::comple
 }
 #endif
 
+template <typename T>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T exp2(const T& x) {
+  EIGEN_USING_STD(exp2);
+  return exp2(x);
+}
+
+// MSVC screws up some edge-cases for std::exp2(complex).
+#ifdef EIGEN_COMP_MSVC
+template <typename RealScalar>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::complex<RealScalar> exp2(const std::complex<RealScalar>& x) {
+  EIGEN_USING_STD(exp);
+  // If z is (x,±∞) (for any finite x), the result is (NaN,NaN) and FE_INVALID is raised.
+  // If z is (x,NaN) (for any finite x), the result is (NaN,NaN) and FE_INVALID may be raised.
+  if ((isfinite)(real_ref(x)) && !(isfinite)(imag_ref(x))) {
+    return std::complex<RealScalar>(NumTraits<RealScalar>::quiet_NaN(), NumTraits<RealScalar>::quiet_NaN());
+  }
+  // If z is (+∞,±∞), the result is (±∞,NaN) and FE_INVALID is raised (the sign of the real part is unspecified)
+  // If z is (+∞,NaN), the result is (±∞,NaN) (the sign of the real part is unspecified)
+  if ((real_ref(x) == NumTraits<RealScalar>::infinity() && !(isfinite)(imag_ref(x)))) {
+    return std::complex<RealScalar>(NumTraits<RealScalar>::infinity(), NumTraits<RealScalar>::quiet_NaN());
+  }
+  return exp2(x);
+}
+#endif
+
+#if defined(SYCL_DEVICE_ONLY)
+SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(exp2, exp2)
+#endif
+
+#if defined(EIGEN_GPUCC)
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float exp2(const float& x) {
+  return ::exp2f(x);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double exp2(const double& x) {
+  return ::exp2(x);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::complex<float> exp2(const std::complex<float>& x) {
+  float com = ::exp2f(x.real());
+  float res_real = com * ::cosf(static_cast<float>(EIGEN_LN2) * x.imag());
+  float res_imag = com * ::sinf(static_cast<float>(EIGEN_LN2) * x.imag());
+  return std::complex<float>(res_real, res_imag);
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE std::complex<double> exp2(const std::complex<double>& x) {
+  double com = ::exp2(x.real());
+  double res_real = com * ::cos(static_cast<double>(EIGEN_LN2) * x.imag());
+  double res_imag = com * ::sin(static_cast<double>(EIGEN_LN2) * x.imag());
+  return std::complex<double>(res_real, res_imag);
+}
+#endif
+
 template <typename Scalar>
 EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(expm1, Scalar) expm1(const Scalar& x) {
   return EIGEN_MATHFUNC_IMPL(expm1, Scalar)::run(x);
@@ -1783,6 +1926,17 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar arithmetic_shift_right(const Scalar
   return bit_cast<Scalar, SignedScalar>(bit_cast<SignedScalar, Scalar>(a) >> n);
 }
 
+template <typename Scalar>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar fma(const Scalar& x, const Scalar& y, const Scalar& z) {
+  return internal::fma_impl<Scalar>::run(x, y, z);
+}
+
+// Multiply-add.
+template <typename Scalar>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar madd(const Scalar& x, const Scalar& y, const Scalar& z) {
+  return internal::madd_impl<Scalar>::run(x, y, z);
+}
+
 }  // end namespace numext
 
 namespace internal {

Eigen/src/Core/MathFunctionsImpl.h

@@ -28,7 +28,7 @@ namespace internal {
    2. If a is zero, approx_a_recip must be infinite with the same sign as a.
    3. If a is infinite, approx_a_recip must be zero with the same sign as a.
 
-   If the preconditions are satisfied, which they are for for the _*_rcp_ps
+   If the preconditions are satisfied, which they are for the _*_rcp_ps
    instructions on x86, the result has a maximum relative error of 2 ulps,
    and correctly handles reciprocals of zero, infinity, and NaN.
 */
@@ -66,7 +66,7 @@ struct generic_reciprocal_newton_step<Packet, 0> {
    2. If a is zero, approx_a_recip must be infinite with the same sign as a.
    3. If a is infinite, approx_a_recip must be zero with the same sign as a.
 
-   If the preconditions are satisfied, which they are for for the _*_rcp_ps
+   If the preconditions are satisfied, which they are for the _*_rcp_ps
    instructions on x86, the result has a maximum relative error of 2 ulps,
    and correctly handles zero, infinity, and NaN. Positive denormals are
    treated as zero.
@@ -76,7 +76,7 @@ struct generic_rsqrt_newton_step {
   static_assert(Steps > 0, "Steps must be at least 1.");
   using Scalar = typename unpacket_traits<Packet>::type;
   EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Packet run(const Packet& a, const Packet& approx_rsqrt) {
-    constexpr Scalar kMinusHalf = Scalar(-1) / Scalar(2);
+    const Scalar kMinusHalf = Scalar(-1) / Scalar(2);
     const Packet cst_minus_half = pset1<Packet>(kMinusHalf);
     const Packet cst_minus_one = pset1<Packet>(Scalar(-1));
 
@@ -116,7 +116,7 @@ struct generic_rsqrt_newton_step<Packet, 0> {
    2. If a is zero, approx_rsqrt must be infinite.
    3. If a is infinite, approx_rsqrt must be zero.
 
-   If the preconditions are satisfied, which they are for for the _*_rsqrt_ps
+   If the preconditions are satisfied, which they are for the _*_rsqrt_ps
    instructions on x86, the result has a maximum relative error of 2 ulps,
    and correctly handles zero and infinity, and NaN. Positive denormal inputs
    are treated as zero.
@@ -171,8 +171,8 @@ struct hypot_impl {
 
 // Generic complex sqrt implementation that correctly handles corner cases
 // according to https://en.cppreference.com/w/cpp/numeric/complex/sqrt
-template <typename T>
-EIGEN_DEVICE_FUNC std::complex<T> complex_sqrt(const std::complex<T>& z) {
+template <typename ComplexT>
+EIGEN_DEVICE_FUNC ComplexT complex_sqrt(const ComplexT& z) {
   // Computes the principal sqrt of the input.
   //
   // For a complex square root of the number x + i*y. We want to find real
@@ -194,21 +194,21 @@ EIGEN_DEVICE_FUNC std::complex<T> complex_sqrt(const std::complex<T>& z) {
   //   if x == 0: u = w, v = sign(y) * w
   //   if x > 0:  u = w, v = y / (2 * w)
   //   if x < 0:  u = |y| / (2 * w), v = sign(y) * w
-
+  using T = typename NumTraits<ComplexT>::Real;
   const T x = numext::real(z);
   const T y = numext::imag(z);
   const T zero = T(0);
   const T w = numext::sqrt(T(0.5) * (numext::abs(x) + numext::hypot(x, y)));
 
-  return (numext::isinf)(y)           ? std::complex<T>(NumTraits<T>::infinity(), y)
-         : numext::is_exactly_zero(x) ? std::complex<T>(w, y < zero ? -w : w)
-         : x > zero                   ? std::complex<T>(w, y / (2 * w))
-                                      : std::complex<T>(numext::abs(y) / (2 * w), y < zero ? -w : w);
+  return (numext::isinf)(y)           ? ComplexT(NumTraits<T>::infinity(), y)
+         : numext::is_exactly_zero(x) ? ComplexT(w, y < zero ? -w : w)
+         : x > zero                   ? ComplexT(w, y / (2 * w))
+                                      : ComplexT(numext::abs(y) / (2 * w), y < zero ? -w : w);
 }
 
 // Generic complex rsqrt implementation.
-template <typename T>
-EIGEN_DEVICE_FUNC std::complex<T> complex_rsqrt(const std::complex<T>& z) {
+template <typename ComplexT>
+EIGEN_DEVICE_FUNC ComplexT complex_rsqrt(const ComplexT& z) {
   // Computes the principal reciprocal sqrt of the input.
   //
   // For a complex reciprocal square root of the number z = x + i*y. We want to
@@ -230,7 +230,7 @@ EIGEN_DEVICE_FUNC std::complex<T> complex_rsqrt(const std::complex<T>& z) {
   //   if x == 0: u = w / |z|, v = -sign(y) * w / |z|
   //   if x > 0:  u = w / |z|, v = -y / (2 * w * |z|)
   //   if x < 0:  u = |y| / (2 * w * |z|), v = -sign(y) * w / |z|
-
+  using T = typename NumTraits<ComplexT>::Real;
   const T x = numext::real(z);
   const T y = numext::imag(z);
   const T zero = T(0);
@@ -239,20 +239,21 @@ EIGEN_DEVICE_FUNC std::complex<T> complex_rsqrt(const std::complex<T>& z) {
   const T w = numext::sqrt(T(0.5) * (numext::abs(x) + abs_z));
   const T woz = w / abs_z;
   // Corner cases consistent with 1/sqrt(z) on gcc/clang.
-  return numext::is_exactly_zero(abs_z) ? std::complex<T>(NumTraits<T>::infinity(), NumTraits<T>::quiet_NaN())
-         : ((numext::isinf)(x) || (numext::isinf)(y)) ? std::complex<T>(zero, zero)
-         : numext::is_exactly_zero(x)                 ? std::complex<T>(woz, y < zero ? woz : -woz)
-         : x > zero                                   ? std::complex<T>(woz, -y / (2 * w * abs_z))
-                    : std::complex<T>(numext::abs(y) / (2 * w * abs_z), y < zero ? woz : -woz);
+  return numext::is_exactly_zero(abs_z)               ? ComplexT(NumTraits<T>::infinity(), NumTraits<T>::quiet_NaN())
+         : ((numext::isinf)(x) || (numext::isinf)(y)) ? ComplexT(zero, zero)
+         : numext::is_exactly_zero(x)                 ? ComplexT(woz, y < zero ? woz : -woz)
+         : x > zero                                   ? ComplexT(woz, -y / (2 * w * abs_z))
+                    : ComplexT(numext::abs(y) / (2 * w * abs_z), y < zero ? woz : -woz);
 }
 
-template <typename T>
-EIGEN_DEVICE_FUNC std::complex<T> complex_log(const std::complex<T>& z) {
+template <typename ComplexT>
+EIGEN_DEVICE_FUNC ComplexT complex_log(const ComplexT& z) {
   // Computes complex log.
+  using T = typename NumTraits<ComplexT>::Real;
   T a = numext::abs(z);
   EIGEN_USING_STD(atan2);
   T b = atan2(z.imag(), z.real());
-  return std::complex<T>(numext::log(a), b);
+  return ComplexT(numext::log(a), b);
 }
 
 }  // end namespace internal

Eigen/src/Core/Matrix.h

@@ -224,8 +224,6 @@ class Matrix : public PlainObjectBase<Matrix<Scalar_, Rows_, Cols_, Options_, Ma
     return Base::_set(other);
   }
 
-  /* Here, doxygen failed to copy the brief information when using \copydoc */
-
   /**
    * \brief Copies the generic expression \a other into *this.
    * \copydetails DenseBase::operator=(const EigenBase<OtherDerived> &other)
@@ -250,22 +248,31 @@ class Matrix : public PlainObjectBase<Matrix<Scalar_, Rows_, Cols_, Options_, Ma
    *
    * \sa resize(Index,Index)
    */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix()
-      : Base(){EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED}
-
-        // FIXME is it still needed
-        EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr explicit Matrix(
-            internal::constructor_without_unaligned_array_assert)
-      : Base(internal::constructor_without_unaligned_array_assert()){EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED}
-
-        EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix(Matrix && other) = default;
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix& operator=(Matrix&& other)
-      EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value) {
+#if defined(EIGEN_INITIALIZE_COEFFS)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix() { EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED }
+#else
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix() = default;
+#endif
+  /** \brief Move constructor */
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix(Matrix&&) = default;
+  /** \brief Moves the matrix into the other one.
+   *
+   */
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix& operator=(Matrix&& other) noexcept(
+      std::is_nothrow_move_assignable<Scalar>::value) {
     Base::operator=(std::move(other));
     return *this;
   }
 
-  /** \copydoc PlainObjectBase(const Scalar&, const Scalar&, const Scalar&,  const Scalar&, const ArgTypes&... args)
+  /** \brief Construct a row of column vector with fixed size from an arbitrary number of coefficients.
+   *
+   * \only_for_vectors
+   *
+   * This constructor is for 1D array or vectors with more than 4 coefficients.
+   *
+   * \warning To construct a column (resp. row) vector of fixed length, the number of values passed to this
+   * constructor must match the the fixed number of rows (resp. columns) of \c *this.
+   *
    *
    * Example: \include Matrix_variadic_ctor_cxx11.cpp
    * Output: \verbinclude Matrix_variadic_ctor_cxx11.out
@@ -279,6 +286,7 @@ class Matrix : public PlainObjectBase<Matrix<Scalar_, Rows_, Cols_, Options_, Ma
 
   /** \brief Constructs a Matrix and initializes it from the coefficients given as initializer-lists grouped by row.
    * \cpp11
+   * \anchor matrix_initializer_list
    *
    * In the general case, the constructor takes a list of rows, each row being represented as a list of coefficients:
    *
@@ -377,7 +385,7 @@ class Matrix : public PlainObjectBase<Matrix<Scalar_, Rows_, Cols_, Options_, Ma
   }
 
   /** \brief Copy constructor */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix(const Matrix& other) = default;
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Matrix(const Matrix&) = default;
 
   /** \brief Copy constructor for generic expressions.
    * \sa MatrixBase::operator=(const EigenBase<OtherDerived>&)
@@ -385,8 +393,8 @@ class Matrix : public PlainObjectBase<Matrix<Scalar_, Rows_, Cols_, Options_, Ma
   template <typename OtherDerived>
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Matrix(const EigenBase<OtherDerived>& other) : Base(other.derived()) {}
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const EIGEN_NOEXCEPT { return 1; }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const EIGEN_NOEXCEPT { return this->innerSize(); }
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return 1; }
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return this->innerSize(); }
 
   /////////// Geometry module ///////////
 

Eigen/src/Core/MatrixBase.h

@@ -112,7 +112,7 @@ class MatrixBase : public DenseBase<Derived> {
                              ConstTransposeReturnType>
       AdjointReturnType;
   /** \internal Return type of eigenvalues() */
-  typedef Matrix<std::complex<RealScalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor>
+  typedef Matrix<internal::make_complex_t<Scalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor>
       EigenvaluesReturnType;
   /** \internal the return type of identity */
   typedef CwiseNullaryOp<internal::scalar_identity_op<Scalar>, PlainObject> IdentityReturnType;
@@ -280,7 +280,7 @@ class MatrixBase : public DenseBase<Derived> {
    * \sa isApprox(), operator!= */
   template <typename OtherDerived>
   EIGEN_DEVICE_FUNC inline bool operator==(const MatrixBase<OtherDerived>& other) const {
-    return cwiseEqual(other).all();
+    return (this->rows() == other.rows()) && (this->cols() == other.cols()) && cwiseEqual(other).all();
   }
 
   /** \returns true if at least one pair of coefficients of \c *this and \a other are not exactly equal to each other.
@@ -289,7 +289,7 @@ class MatrixBase : public DenseBase<Derived> {
    * \sa isApprox(), operator== */
   template <typename OtherDerived>
   EIGEN_DEVICE_FUNC inline bool operator!=(const MatrixBase<OtherDerived>& other) const {
-    return cwiseNotEqual(other).any();
+    return !(*this == other);
   }
 
   NoAlias<Derived, Eigen::MatrixBase> EIGEN_DEVICE_FUNC noalias();
@@ -373,12 +373,14 @@ class MatrixBase : public DenseBase<Derived> {
   template <int Options = 0>
   inline JacobiSVD<PlainObject, Options> jacobiSvd() const;
   template <int Options = 0>
-  EIGEN_DEPRECATED inline JacobiSVD<PlainObject, Options> jacobiSvd(unsigned int computationOptions) const;
+  EIGEN_DEPRECATED_WITH_REASON("Options should be specified using method's template parameter.")
+  inline JacobiSVD<PlainObject, Options> jacobiSvd(unsigned int computationOptions) const;
 
   template <int Options = 0>
   inline BDCSVD<PlainObject, Options> bdcSvd() const;
   template <int Options = 0>
-  EIGEN_DEPRECATED inline BDCSVD<PlainObject, Options> bdcSvd(unsigned int computationOptions) const;
+  EIGEN_DEPRECATED_WITH_REASON("Options should be specified using method's template parameter.")
+  inline BDCSVD<PlainObject, Options> bdcSvd(unsigned int computationOptions) const;
 
   /////////// Geometry module ///////////
 
@@ -391,7 +393,8 @@ class MatrixBase : public DenseBase<Derived> {
 
   EIGEN_DEVICE_FUNC inline PlainObject unitOrthogonal(void) const;
 
-  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline Matrix<Scalar, 3, 1> eulerAngles(Index a0, Index a1, Index a2) const;
+  EIGEN_DEPRECATED_WITH_REASON("Use .canonicalEulerAngles() instead.")
+  EIGEN_DEVICE_FUNC inline Matrix<Scalar, 3, 1> eulerAngles(Index a0, Index a1, Index a2) const;
 
   EIGEN_DEVICE_FUNC inline Matrix<Scalar, 3, 1> canonicalEulerAngles(Index a0, Index a1, Index a2) const;
 
@@ -468,7 +471,7 @@ class MatrixBase : public DenseBase<Derived> {
   EIGEN_MATRIX_FUNCTION(MatrixSquareRootReturnValue, sqrt, square root)
   EIGEN_MATRIX_FUNCTION(MatrixLogarithmReturnValue, log, logarithm)
   EIGEN_MATRIX_FUNCTION_1(MatrixPowerReturnValue, pow, power to \c p, const RealScalar& p)
-  EIGEN_MATRIX_FUNCTION_1(MatrixComplexPowerReturnValue, pow, power to \c p, const std::complex<RealScalar>& p)
+  EIGEN_MATRIX_FUNCTION_1(MatrixComplexPowerReturnValue, pow, power to \c p, const internal::make_complex_t<Scalar>& p)
 
  protected:
   EIGEN_DEFAULT_COPY_CONSTRUCTOR(MatrixBase)

Eigen/src/Core/NestByValue.h

@@ -45,8 +45,8 @@ class NestByValue : public internal::dense_xpr_base<NestByValue<ExpressionType>
 
   EIGEN_DEVICE_FUNC explicit inline NestByValue(const ExpressionType& matrix) : m_expression(matrix) {}
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_expression.rows(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_expression.cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_expression.rows(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_expression.cols(); }
 
   EIGEN_DEVICE_FUNC operator const ExpressionType&() const { return m_expression; }
 

Eigen/src/Core/NumTraits.h

@@ -22,13 +22,13 @@ namespace internal {
 template <typename T, bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
           bool is_integer = NumTraits<T>::IsInteger>
 struct default_digits_impl {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return std::numeric_limits<T>::digits; }
+  EIGEN_DEVICE_FUNC constexpr static int run() { return std::numeric_limits<T>::digits; }
 };
 
 template <typename T>
 struct default_digits_impl<T, false, false>  // Floating point
 {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() {
+  EIGEN_DEVICE_FUNC constexpr static int run() {
     using std::ceil;
     using std::log2;
     typedef typename NumTraits<T>::Real Real;
@@ -39,7 +39,7 @@ struct default_digits_impl<T, false, false>  // Floating point
 template <typename T>
 struct default_digits_impl<T, false, true>  // Integer
 {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return 0; }
+  EIGEN_DEVICE_FUNC constexpr static int run() { return 0; }
 };
 
 // default implementation of digits10(), based on numeric_limits if specialized,
@@ -47,13 +47,13 @@ struct default_digits_impl<T, false, true>  // Integer
 template <typename T, bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
           bool is_integer = NumTraits<T>::IsInteger>
 struct default_digits10_impl {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return std::numeric_limits<T>::digits10; }
+  EIGEN_DEVICE_FUNC constexpr static int run() { return std::numeric_limits<T>::digits10; }
 };
 
 template <typename T>
 struct default_digits10_impl<T, false, false>  // Floating point
 {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() {
+  EIGEN_DEVICE_FUNC constexpr static int run() {
     using std::floor;
     using std::log10;
     typedef typename NumTraits<T>::Real Real;
@@ -64,7 +64,7 @@ struct default_digits10_impl<T, false, false>  // Floating point
 template <typename T>
 struct default_digits10_impl<T, false, true>  // Integer
 {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return 0; }
+  EIGEN_DEVICE_FUNC constexpr static int run() { return 0; }
 };
 
 // default implementation of max_digits10(), based on numeric_limits if specialized,
@@ -72,13 +72,13 @@ struct default_digits10_impl<T, false, true>  // Integer
 template <typename T, bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
           bool is_integer = NumTraits<T>::IsInteger>
 struct default_max_digits10_impl {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return std::numeric_limits<T>::max_digits10; }
+  EIGEN_DEVICE_FUNC constexpr static int run() { return std::numeric_limits<T>::max_digits10; }
 };
 
 template <typename T>
 struct default_max_digits10_impl<T, false, false>  // Floating point
 {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() {
+  EIGEN_DEVICE_FUNC constexpr static int run() {
     using std::ceil;
     using std::log10;
     typedef typename NumTraits<T>::Real Real;
@@ -89,15 +89,28 @@ struct default_max_digits10_impl<T, false, false>  // Floating point
 template <typename T>
 struct default_max_digits10_impl<T, false, true>  // Integer
 {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return 0; }
+  EIGEN_DEVICE_FUNC constexpr static int run() { return 0; }
 };
 
 }  // end namespace internal
 
 namespace numext {
-/** \internal bit-wise cast without changing the underlying bit representation. */
 
-// TODO: Replace by std::bit_cast (available in C++20)
+/** \internal bit-wise cast without changing the underlying bit representation. */
+#if defined(__cpp_lib_bit_cast) && __cpp_lib_bit_cast >= 201806L
+template <typename Tgt, typename Src>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr Tgt bit_cast(const Src& src) {
+  return std::bit_cast<Tgt>(src);
+}
+#elif EIGEN_HAS_BUILTIN(__builtin_bit_cast)
+template <typename Tgt, typename Src>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC constexpr Tgt bit_cast(const Src& src) {
+  EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Src>::value, THIS_TYPE_IS_NOT_SUPPORTED)
+  EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Tgt>::value, THIS_TYPE_IS_NOT_SUPPORTED)
+  EIGEN_STATIC_ASSERT(sizeof(Src) == sizeof(Tgt), THIS_TYPE_IS_NOT_SUPPORTED)
+  return __builtin_bit_cast(Tgt, src);
+}
+#else
 template <typename Tgt, typename Src>
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Tgt bit_cast(const Src& src) {
   // The behaviour of memcpy is not specified for non-trivially copyable types
@@ -113,8 +126,10 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Tgt bit_cast(const Src& src) {
   memcpy(static_cast<void*>(&tgt), static_cast<const void*>(&staged), sizeof(Tgt));
   return tgt;
 }
+#endif
 }  // namespace numext
 
+// clang-format off
 /** \class NumTraits
  * \ingroup Core_Module
  *
@@ -126,48 +141,50 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Tgt bit_cast(const Src& src) {
  *
  * The provided data consists of:
  * \li A typedef \c Real, giving the "real part" type of \a T. If \a T is already real,
- *     then \c Real is just a typedef to \a T. If \a T is \c std::complex<U> then \c Real
+ *     then \c Real is just a typedef to \a T. If \a T is `std::complex<U>` then \c Real
  *     is a typedef to \a U.
  * \li A typedef \c NonInteger, giving the type that should be used for operations producing non-integral values,
  *     such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives
  *     \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to
  *     take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is
  *     only intended as a helper for code that needs to explicitly promote types.
- * \li A typedef \c Literal giving the type to use for numeric literals such as "2" or "0.5". For instance, for \c
- * std::complex<U>, Literal is defined as \c U. Of course, this type must be fully compatible with \a T. In doubt, just
- * use \a T here. \li A typedef \a Nested giving the type to use to nest a value inside of the expression tree. If you
- * don't know what this means, just use \a T here. \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c
- * std::complex type, and to 0 otherwise. \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type
- * such as \c int, and to \c 0 otherwise. \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of
- * the number of CPU cycles needed to by move / add / mul instructions respectively, assuming the data is already stored
- * in CPU registers. Stay vague here. No need to do architecture-specific stuff. If you don't know what this means, just
- * use \c Eigen::HugeCost. \li An enum value \a IsSigned. It is equal to \c 1 if \a T is a signed type and to 0 if \a T
- * is unsigned. \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type
- * \a T must be called, and to 0 if it is safe not to call it. Default is 0 if \a T is an arithmetic type, and 1
- * otherwise. \li An epsilon() function which, unlike <a
- * href="http://en.cppreference.com/w/cpp/types/numeric_limits/epsilon">std::numeric_limits::epsilon()</a>, it returns a
- * \a Real instead of a \a T. \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a
- * default value by the fuzzy comparison operators. \li highest() and lowest() functions returning the highest and
- * lowest possible values respectively. \li digits() function returning the number of radix digits (non-sign digits for
- * integers, mantissa for floating-point). This is the analogue of <a
- * href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits">std::numeric_limits<T>::digits</a> which is used
- * as the default implementation if specialized. \li digits10() function returning the number of decimal digits that can
- * be represented without change. This is the analogue of <a
- * href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits10">std::numeric_limits<T>::digits10</a> which is
- * used as the default implementation if specialized. \li max_digits10() function returning the number of decimal digits
- * required to uniquely represent all distinct values of the type. This is the analogue of <a
- * href="http://en.cppreference.com/w/cpp/types/numeric_limits/max_digits10">std::numeric_limits<T>::max_digits10</a>
+ * \li A typedef \c Literal giving the type to use for numeric literals such as "2" or "0.5". For instance, for
+ *     `std::complex<U>`, Literal is defined as \a U. Of course, this type must be fully compatible with \a T. In doubt,
+ *     just use \a T here.
+ * \li A typedef \c Nested giving the type to use to nest a value inside of the expression tree. If you don't know what
+ *     this means, just use \a T here.
+ * \li An enum value \c IsComplex. It is equal to 1 if \a T is a \c std::complex type, and to 0 otherwise.
+ * \li An enum value \c IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int, and to \c 0 otherwise.
+ * \li Enum values \c ReadCost, \c AddCost and \c MulCost representing a rough estimate of the number of CPU cycles needed to by
+ *     move / add / mul instructions respectively, assuming the data is already stored in CPU registers. Stay vague here.
+ *     No need to do architecture-specific stuff. If you don't know what this means, just use \c Eigen::HugeCost.
+ * \li An enum value \c IsSigned. It is equal to \c 1 if \a T is a signed type and to 0 if \a T is unsigned.
+ * \li An enum value \c RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must be
+ *     called, and to 0 if it is safe not to call it. Default is 0 if \a T is an arithmetic type, and 1 otherwise.
+ * \li An epsilon() function which, unlike <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/epsilon">
+ *     `std::numeric_limits::epsilon()`</a>, it returns a \c Real instead of a \a T.
+ * \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default value by the fuzzy
+ *     comparison operators.
+ * \li highest() and lowest() functions returning the highest and lowest possible values respectively.
+ * \li digits() function returning the number of radix digits (non-sign digits for integers, mantissa for floating-point).
+ *     This is the analogue of <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits">
+ *     `std::numeric_limits<T>::digits`</a> which is used as the default implementation if specialized.
+ * \li digits10() function returning the number of decimal digits that can be represented without change. This is the
+ *     analogue of <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits10">
+ *     `std::numeric_limits<T>::digits10`</a> which is used as the default implementation if specialized.
+ * \li max_digits10() function returning the number of decimal digits required to uniquely represent all distinct values
+ *     of the type. This is the analogue of <a
+ *     href="http://en.cppreference.com/w/cpp/types/numeric_limits/max_digits10">`std::numeric_limits<T>::max_digits10`</a>
  *     which is used as the default implementation if specialized.
  * \li min_exponent() and max_exponent() functions returning the highest and lowest possible values, respectively,
  *     such that the radix raised to the power exponent-1 is a normalized floating-point number.  These are equivalent
- * to <a
- * href="http://en.cppreference.com/w/cpp/types/numeric_limits/min_exponent">std::numeric_limits<T>::min_exponent</a>/
- *     <a
- * href="http://en.cppreference.com/w/cpp/types/numeric_limits/max_exponent">std::numeric_limits<T>::max_exponent</a>.
+ *     to <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/min_exponent">
+ *     `std::numeric_limits<T>::min_exponent`</a>/<a
+ *     href="http://en.cppreference.com/w/cpp/types/numeric_limits/max_exponent">`std::numeric_limits<T>::max_exponent`</a>.
  * \li infinity() function returning a representation of positive infinity, if available.
- * \li quiet_NaN function returning a non-signaling "not-a-number", if available.
+ * \li quiet_NaN() function returning a non-signaling "not-a-number", if available.
  */
-
+// clang-format on
 template <typename T>
 struct GenericNumTraits {
   enum {
@@ -185,32 +202,30 @@ struct GenericNumTraits {
   typedef T Nested;
   typedef T Literal;
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Real epsilon() { return numext::numeric_limits<T>::epsilon(); }
+  EIGEN_DEVICE_FUNC constexpr static Real epsilon() { return numext::numeric_limits<T>::epsilon(); }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int digits10() { return internal::default_digits10_impl<T>::run(); }
+  EIGEN_DEVICE_FUNC constexpr static int digits10() { return internal::default_digits10_impl<T>::run(); }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int max_digits10() {
-    return internal::default_max_digits10_impl<T>::run();
-  }
+  EIGEN_DEVICE_FUNC constexpr static int max_digits10() { return internal::default_max_digits10_impl<T>::run(); }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int digits() { return internal::default_digits_impl<T>::run(); }
+  EIGEN_DEVICE_FUNC constexpr static int digits() { return internal::default_digits_impl<T>::run(); }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int min_exponent() { return numext::numeric_limits<T>::min_exponent; }
+  EIGEN_DEVICE_FUNC constexpr static int min_exponent() { return numext::numeric_limits<T>::min_exponent; }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int max_exponent() { return numext::numeric_limits<T>::max_exponent; }
+  EIGEN_DEVICE_FUNC constexpr static int max_exponent() { return numext::numeric_limits<T>::max_exponent; }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Real dummy_precision() {
+  EIGEN_DEVICE_FUNC constexpr static Real dummy_precision() {
     // make sure to override this for floating-point types
     return Real(0);
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline T highest() { return (numext::numeric_limits<T>::max)(); }
+  EIGEN_DEVICE_FUNC constexpr static T highest() { return (numext::numeric_limits<T>::max)(); }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline T lowest() { return (numext::numeric_limits<T>::lowest)(); }
+  EIGEN_DEVICE_FUNC constexpr static T lowest() { return (numext::numeric_limits<T>::lowest)(); }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline T infinity() { return numext::numeric_limits<T>::infinity(); }
+  EIGEN_DEVICE_FUNC constexpr static T infinity() { return numext::numeric_limits<T>::infinity(); }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline T quiet_NaN() { return numext::numeric_limits<T>::quiet_NaN(); }
+  EIGEN_DEVICE_FUNC constexpr static T quiet_NaN() { return numext::numeric_limits<T>::quiet_NaN(); }
 };
 
 template <typename T>
@@ -218,25 +233,23 @@ struct NumTraits : GenericNumTraits<T> {};
 
 template <>
 struct NumTraits<float> : GenericNumTraits<float> {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline float dummy_precision() { return 1e-5f; }
+  EIGEN_DEVICE_FUNC constexpr static float dummy_precision() { return 1e-5f; }
 };
 
 template <>
 struct NumTraits<double> : GenericNumTraits<double> {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline double dummy_precision() { return 1e-12; }
+  EIGEN_DEVICE_FUNC constexpr static double dummy_precision() { return 1e-12; }
 };
 
 // GPU devices treat `long double` as `double`.
 #ifndef EIGEN_GPU_COMPILE_PHASE
 template <>
 struct NumTraits<long double> : GenericNumTraits<long double> {
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline long double dummy_precision() {
-    return static_cast<long double>(1e-15l);
-  }
+  EIGEN_DEVICE_FUNC constexpr static long double dummy_precision() { return static_cast<long double>(1e-15l); }
 
 #if defined(EIGEN_ARCH_PPC) && (__LDBL_MANT_DIG__ == 106)
   // PowerPC double double causes issues with some values
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline long double epsilon() {
+  EIGEN_DEVICE_FUNC constexpr static long double epsilon() {
     // 2^(-(__LDBL_MANT_DIG__)+1)
     return static_cast<long double>(2.4651903288156618919116517665087e-32l);
   }
@@ -257,10 +270,10 @@ struct NumTraits<std::complex<Real_> > : GenericNumTraits<std::complex<Real_> >
     MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
   };
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int digits10() { return NumTraits<Real>::digits10(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int max_digits10() { return NumTraits<Real>::max_digits10(); }
+  EIGEN_DEVICE_FUNC constexpr static Real epsilon() { return NumTraits<Real>::epsilon(); }
+  EIGEN_DEVICE_FUNC constexpr static Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
+  EIGEN_DEVICE_FUNC constexpr static int digits10() { return NumTraits<Real>::digits10(); }
+  EIGEN_DEVICE_FUNC constexpr static int max_digits10() { return NumTraits<Real>::max_digits10(); }
 };
 
 template <typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
@@ -287,25 +300,19 @@ struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> > {
                                                       : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::MulCost)
   };
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline RealScalar dummy_precision() {
-    return NumTraits<RealScalar>::dummy_precision();
-  }
+  EIGEN_DEVICE_FUNC constexpr static RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
+  EIGEN_DEVICE_FUNC constexpr static RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
 
-  EIGEN_CONSTEXPR
-  static inline int digits10() { return NumTraits<Scalar>::digits10(); }
-  EIGEN_CONSTEXPR
-  static inline int max_digits10() { return NumTraits<Scalar>::max_digits10(); }
+  constexpr static int digits10() { return NumTraits<Scalar>::digits10(); }
+  constexpr static int max_digits10() { return NumTraits<Scalar>::max_digits10(); }
 };
 
 template <>
 struct NumTraits<std::string> : GenericNumTraits<std::string> {
   enum { RequireInitialization = 1, ReadCost = HugeCost, AddCost = HugeCost, MulCost = HugeCost };
 
-  EIGEN_CONSTEXPR
-  static inline int digits10() { return 0; }
-  EIGEN_CONSTEXPR
-  static inline int max_digits10() { return 0; }
+  constexpr static int digits10() { return 0; }
+  constexpr static int max_digits10() { return 0; }
 
  private:
   static inline std::string epsilon();

Eigen/src/Core/PartialReduxEvaluator.h

@@ -103,19 +103,36 @@ struct packetwise_redux_impl<Func, Evaluator, NoUnrolling> {
   EIGEN_DEVICE_FUNC static PacketType run(const Evaluator& eval, const Func& func, Index size) {
     if (size == 0) return packetwise_redux_empty_value<PacketType>(func);
 
-    const Index size4 = (size - 1) & (~3);
+    const Index size4 = 1 + numext::round_down(size - 1, 4);
     PacketType p = eval.template packetByOuterInner<Unaligned, PacketType>(0, 0);
-    Index i = 1;
     // This loop is optimized for instruction pipelining:
     // - each iteration generates two independent instructions
     // - thanks to branch prediction and out-of-order execution we have independent instructions across loops
-    for (; i < size4; i += 4)
+    for (Index i = 1; i < size4; i += 4)
       p = func.packetOp(
           p, func.packetOp(func.packetOp(eval.template packetByOuterInner<Unaligned, PacketType>(i + 0, 0),
                                          eval.template packetByOuterInner<Unaligned, PacketType>(i + 1, 0)),
                            func.packetOp(eval.template packetByOuterInner<Unaligned, PacketType>(i + 2, 0),
                                          eval.template packetByOuterInner<Unaligned, PacketType>(i + 3, 0))));
-    for (; i < size; ++i) p = func.packetOp(p, eval.template packetByOuterInner<Unaligned, PacketType>(i, 0));
+    for (Index i = size4; i < size; ++i)
+      p = func.packetOp(p, eval.template packetByOuterInner<Unaligned, PacketType>(i, 0));
+    return p;
+  }
+};
+
+template <typename Func, typename Evaluator>
+struct packetwise_segment_redux_impl {
+  typedef typename Evaluator::Scalar Scalar;
+  typedef typename redux_traits<Func, Evaluator>::PacketType PacketScalar;
+
+  template <typename PacketType>
+  EIGEN_DEVICE_FUNC static PacketType run(const Evaluator& eval, const Func& func, Index size, Index begin,
+                                          Index count) {
+    if (size == 0) return packetwise_redux_empty_value<PacketType>(func);
+
+    PacketType p = eval.template packetSegmentByOuterInner<Unaligned, PacketType>(0, 0, begin, count);
+    for (Index i = 1; i < size; ++i)
+      p = func.packetOp(p, eval.template packetSegmentByOuterInner<Unaligned, PacketType>(i, 0, begin, count));
     return p;
   }
 };
@@ -174,14 +191,13 @@ struct evaluator<PartialReduxExpr<ArgType, MemberOp, Direction> >
 
   template <int LoadMode, typename PacketType>
   EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC PacketType packet(Index idx) const {
-    enum { PacketSize = internal::unpacket_traits<PacketType>::size };
-    typedef Block<const ArgTypeNestedCleaned, Direction == Vertical ? int(ArgType::RowsAtCompileTime) : int(PacketSize),
-                  Direction == Vertical ? int(PacketSize) : int(ArgType::ColsAtCompileTime), true /* InnerPanel */>
-        PanelType;
-
-    PanelType panel(m_arg, Direction == Vertical ? 0 : idx, Direction == Vertical ? idx : 0,
-                    Direction == Vertical ? m_arg.rows() : Index(PacketSize),
-                    Direction == Vertical ? Index(PacketSize) : m_arg.cols());
+    static constexpr int PacketSize = internal::unpacket_traits<PacketType>::size;
+    static constexpr int PanelRows = Direction == Vertical ? ArgType::RowsAtCompileTime : PacketSize;
+    static constexpr int PanelCols = Direction == Vertical ? PacketSize : ArgType::ColsAtCompileTime;
+    using PanelType = Block<const ArgTypeNestedCleaned, PanelRows, PanelCols, true /* InnerPanel */>;
+    using PanelEvaluator = typename internal::redux_evaluator<PanelType>;
+    using BinaryOp = typename MemberOp::BinaryOp;
+    using Impl = internal::packetwise_redux_impl<BinaryOp, PanelEvaluator>;
 
     // FIXME
     // See bug 1612, currently if PacketSize==1 (i.e. complex<double> with 128bits registers) then the storage-order of
@@ -189,11 +205,39 @@ struct evaluator<PartialReduxExpr<ArgType, MemberOp, Direction> >
     // by pass "vectorization" in this case:
     if (PacketSize == 1) return internal::pset1<PacketType>(coeff(idx));
 
-    typedef typename internal::redux_evaluator<PanelType> PanelEvaluator;
+    Index startRow = Direction == Vertical ? 0 : idx;
+    Index startCol = Direction == Vertical ? idx : 0;
+    Index numRows = Direction == Vertical ? m_arg.rows() : PacketSize;
+    Index numCols = Direction == Vertical ? PacketSize : m_arg.cols();
+
+    PanelType panel(m_arg, startRow, startCol, numRows, numCols);
     PanelEvaluator panel_eval(panel);
-    typedef typename MemberOp::BinaryOp BinaryOp;
-    PacketType p = internal::packetwise_redux_impl<BinaryOp, PanelEvaluator>::template run<PacketType>(
-        panel_eval, m_functor.binaryFunc(), m_arg.outerSize());
+    PacketType p = Impl::template run<PacketType>(panel_eval, m_functor.binaryFunc(), m_arg.outerSize());
+    return p;
+  }
+
+  template <int LoadMode, typename PacketType>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packetSegment(Index i, Index j, Index begin, Index count) const {
+    return packetSegment<LoadMode, PacketType>(Direction == Vertical ? j : i, begin, count);
+  }
+
+  template <int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC PacketType packetSegment(Index idx, Index begin, Index count) const {
+    static constexpr int PanelRows = Direction == Vertical ? ArgType::RowsAtCompileTime : Dynamic;
+    static constexpr int PanelCols = Direction == Vertical ? Dynamic : ArgType::ColsAtCompileTime;
+    using PanelType = Block<const ArgTypeNestedCleaned, PanelRows, PanelCols, true /* InnerPanel */>;
+    using PanelEvaluator = typename internal::redux_evaluator<PanelType>;
+    using BinaryOp = typename MemberOp::BinaryOp;
+    using Impl = internal::packetwise_segment_redux_impl<BinaryOp, PanelEvaluator>;
+
+    Index startRow = Direction == Vertical ? 0 : idx;
+    Index startCol = Direction == Vertical ? idx : 0;
+    Index numRows = Direction == Vertical ? m_arg.rows() : begin + count;
+    Index numCols = Direction == Vertical ? begin + count : m_arg.cols();
+
+    PanelType panel(m_arg, startRow, startCol, numRows, numCols);
+    PanelEvaluator panel_eval(panel);
+    PacketType p = Impl::template run<PacketType>(panel_eval, m_functor.binaryFunc(), m_arg.outerSize(), begin, count);
     return p;
   }
 

Eigen/src/Core/PermutationMatrix.h

@@ -109,6 +109,9 @@ class PermutationBase : public EigenBase<Derived> {
    */
   DenseMatrixType toDenseMatrix() const { return derived(); }
 
+  /** \returns the plain matrix representation of the permutation. */
+  DenseMatrixType eval() const { return toDenseMatrix(); }
+
   /** const version of indices(). */
   const IndicesType& indices() const { return derived().indices(); }
   /** \returns a reference to the stored array representing the permutation. */
@@ -468,17 +471,17 @@ class PermutationWrapper : public PermutationBase<PermutationWrapper<IndicesType
 /** \returns the matrix with the permutation applied to the columns.
  */
 template <typename MatrixDerived, typename PermutationDerived>
-EIGEN_DEVICE_FUNC const Product<MatrixDerived, PermutationDerived, AliasFreeProduct> operator*(
+EIGEN_DEVICE_FUNC const Product<MatrixDerived, PermutationDerived, DefaultProduct> operator*(
     const MatrixBase<MatrixDerived>& matrix, const PermutationBase<PermutationDerived>& permutation) {
-  return Product<MatrixDerived, PermutationDerived, AliasFreeProduct>(matrix.derived(), permutation.derived());
+  return Product<MatrixDerived, PermutationDerived, DefaultProduct>(matrix.derived(), permutation.derived());
 }
 
 /** \returns the matrix with the permutation applied to the rows.
  */
 template <typename PermutationDerived, typename MatrixDerived>
-EIGEN_DEVICE_FUNC const Product<PermutationDerived, MatrixDerived, AliasFreeProduct> operator*(
+EIGEN_DEVICE_FUNC const Product<PermutationDerived, MatrixDerived, DefaultProduct> operator*(
     const PermutationBase<PermutationDerived>& permutation, const MatrixBase<MatrixDerived>& matrix) {
-  return Product<PermutationDerived, MatrixDerived, AliasFreeProduct>(permutation.derived(), matrix.derived());
+  return Product<PermutationDerived, MatrixDerived, DefaultProduct>(permutation.derived(), matrix.derived());
 }
 
 template <typename PermutationType>
@@ -520,16 +523,16 @@ class InverseImpl<PermutationType, PermutationStorage> : public EigenBase<Invers
   /** \returns the matrix with the inverse permutation applied to the columns.
    */
   template <typename OtherDerived>
-  friend const Product<OtherDerived, InverseType, AliasFreeProduct> operator*(const MatrixBase<OtherDerived>& matrix,
-                                                                              const InverseType& trPerm) {
-    return Product<OtherDerived, InverseType, AliasFreeProduct>(matrix.derived(), trPerm.derived());
+  friend const Product<OtherDerived, InverseType, DefaultProduct> operator*(const MatrixBase<OtherDerived>& matrix,
+                                                                            const InverseType& trPerm) {
+    return Product<OtherDerived, InverseType, DefaultProduct>(matrix.derived(), trPerm.derived());
   }
 
   /** \returns the matrix with the inverse permutation applied to the rows.
    */
   template <typename OtherDerived>
-  const Product<InverseType, OtherDerived, AliasFreeProduct> operator*(const MatrixBase<OtherDerived>& matrix) const {
-    return Product<InverseType, OtherDerived, AliasFreeProduct>(derived(), matrix.derived());
+  const Product<InverseType, OtherDerived, DefaultProduct> operator*(const MatrixBase<OtherDerived>& matrix) const {
+    return Product<InverseType, OtherDerived, DefaultProduct>(derived(), matrix.derived());
   }
 };
 

Eigen/src/Core/PlainObjectBase.h

@@ -80,27 +80,6 @@ struct matrix_swap_impl;
 
 }  // end namespace internal
 
-#ifdef EIGEN_PARSED_BY_DOXYGEN
-namespace doxygen {
-
-// This is a workaround to doxygen not being able to understand the inheritance logic
-// when it is hidden by the dense_xpr_base helper struct.
-// Moreover, doxygen fails to include members that are not documented in the declaration body of
-// MatrixBase if we inherits MatrixBase<Matrix<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_> >,
-// this is why we simply inherits MatrixBase, though this does not make sense.
-
-/** This class is just a workaround for Doxygen and it does not not actually exist. */
-template <typename Derived>
-struct dense_xpr_base_dispatcher;
-/** This class is just a workaround for Doxygen and it does not not actually exist. */
-template <typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
-struct dense_xpr_base_dispatcher<Matrix<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>> : public MatrixBase {};
-/** This class is just a workaround for Doxygen and it does not not actually exist. */
-template <typename Scalar_, int Rows_, int Cols_, int Options_, int MaxRows_, int MaxCols_>
-struct dense_xpr_base_dispatcher<Array<Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_>> : public ArrayBase {};
-
-}  // namespace doxygen
-
 /** \class PlainObjectBase
  * \ingroup Core_Module
  * \brief %Dense storage base class for matrices and arrays.
@@ -113,12 +92,7 @@ struct dense_xpr_base_dispatcher<Array<Scalar_, Rows_, Cols_, Options_, MaxRows_
  * \sa \ref TopicClassHierarchy
  */
 template <typename Derived>
-class PlainObjectBase : public doxygen::dense_xpr_base_dispatcher<Derived>
-#else
-template <typename Derived>
-class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
-#endif
-{
+class PlainObjectBase : public internal::dense_xpr_base<Derived>::type {
  public:
   enum { Options = internal::traits<Derived>::Options };
   typedef typename internal::dense_xpr_base<Derived>::type Base;
@@ -188,8 +162,8 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
   EIGEN_DEVICE_FUNC Base& base() { return *static_cast<Base*>(this); }
   EIGEN_DEVICE_FUNC const Base& base() const { return *static_cast<const Base*>(this); }
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_storage.rows(); }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_storage.cols(); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const noexcept { return m_storage.rows(); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const noexcept { return m_storage.cols(); }
 
   /** This is an overloaded version of DenseCoeffsBase<Derived,ReadOnlyAccessors>::coeff(Index,Index) const
    * provided to by-pass the creation of an evaluator of the expression, thus saving compilation efforts.
@@ -324,7 +298,7 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
    *
    * \sa resize(Index,Index), resize(NoChange_t, Index), resize(Index, NoChange_t)
    */
-  EIGEN_DEVICE_FUNC inline constexpr void resize(Index size) {
+  EIGEN_DEVICE_FUNC constexpr void resize(Index size) {
     EIGEN_STATIC_ASSERT_VECTOR_ONLY(PlainObjectBase)
     eigen_assert(((SizeAtCompileTime == Dynamic && (MaxSizeAtCompileTime == Dynamic || size <= MaxSizeAtCompileTime)) ||
                   SizeAtCompileTime == size) &&
@@ -349,7 +323,7 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
    *
    * \sa resize(Index,Index)
    */
-  EIGEN_DEVICE_FUNC inline constexpr void resize(NoChange_t, Index cols) { resize(rows(), cols); }
+  EIGEN_DEVICE_FUNC constexpr void resize(NoChange_t, Index cols) { resize(rows(), cols); }
 
   /** Resizes the matrix, changing only the number of rows. For the parameter of type NoChange_t, just pass the special
    * value \c NoChange as in the example below.
@@ -359,7 +333,7 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
    *
    * \sa resize(Index,Index)
    */
-  EIGEN_DEVICE_FUNC inline constexpr void resize(Index rows, NoChange_t) { resize(rows, cols()); }
+  EIGEN_DEVICE_FUNC constexpr void resize(Index rows, NoChange_t) { resize(rows, cols()); }
 
   /** Resizes \c *this to have the same dimensions as \a other.
    * Takes care of doing all the checking that's needed.
@@ -472,32 +446,19 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
   // Prevent user from trying to instantiate PlainObjectBase objects
   // by making all its constructor protected. See bug 1074.
  protected:
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr PlainObjectBase() : m_storage() {
-    //       EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
-  }
-
-#ifndef EIGEN_PARSED_BY_DOXYGEN
-  // FIXME is it still needed ?
-  /** \internal */
-  EIGEN_DEVICE_FUNC constexpr explicit PlainObjectBase(internal::constructor_without_unaligned_array_assert)
-      : m_storage(internal::constructor_without_unaligned_array_assert()) {
-    // EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
-  }
-#endif
-
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr PlainObjectBase(PlainObjectBase&& other) = default;
-
-  EIGEN_DEVICE_FUNC constexpr PlainObjectBase& operator=(PlainObjectBase&& other) EIGEN_NOEXCEPT {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr PlainObjectBase() = default;
+  /** \brief Move constructor */
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr PlainObjectBase(PlainObjectBase&&) = default;
+  /** \brief Move assignment operator */
+  EIGEN_DEVICE_FUNC constexpr PlainObjectBase& operator=(PlainObjectBase&& other) noexcept {
     m_storage = std::move(other.m_storage);
     return *this;
   }
 
   /** Copy constructor */
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr PlainObjectBase(const PlainObjectBase& other) = default;
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr PlainObjectBase(const PlainObjectBase&) = default;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PlainObjectBase(Index size, Index rows, Index cols)
-      : m_storage(size, rows, cols) {
-    //       EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
-  }
+      : m_storage(size, rows, cols) {}
 
   /** \brief Construct a row of column vector with fixed size from an arbitrary number of coefficients.
    *
@@ -538,7 +499,10 @@ class PlainObjectBase : public internal::dense_xpr_base<Derived>::type
       eigen_assert(list_size == static_cast<size_t>(RowsAtCompileTime) || RowsAtCompileTime == Dynamic);
       resize(list_size, ColsAtCompileTime);
       if (list.begin()->begin() != nullptr) {
-        std::copy(list.begin()->begin(), list.begin()->end(), m_storage.data());
+        Index index = 0;
+        for (const Scalar& e : *list.begin()) {
+          coeffRef(index++) = e;
+        }
       }
     } else {
       eigen_assert(list.size() == static_cast<size_t>(RowsAtCompileTime) || RowsAtCompileTime == Dynamic);

Eigen/src/Core/Product.h

@@ -224,8 +224,8 @@ class Product
                  "if you wanted a coeff-wise or a dot product use the respective explicit functions");
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_lhs.rows(); }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const noexcept { return m_lhs.rows(); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const noexcept { return m_rhs.cols(); }
 
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const LhsNestedCleaned& lhs() const { return m_lhs; }
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const RhsNestedCleaned& rhs() const { return m_rhs; }

Eigen/src/Core/ProductEvaluators.h

@@ -283,7 +283,7 @@ void EIGEN_DEVICE_FUNC outer_product_selector_run(Dst& dst, const Lhs& lhs, cons
 template <typename Lhs, typename Rhs>
 struct generic_product_impl<Lhs, Rhs, DenseShape, DenseShape, OuterProduct> {
   template <typename T>
-  struct is_row_major : std::conditional_t<(int(T::Flags) & RowMajorBit), internal::true_type, internal::false_type> {};
+  struct is_row_major : bool_constant<(int(T::Flags) & RowMajorBit)> {};
   typedef typename Product<Lhs, Rhs>::Scalar Scalar;
 
   // TODO it would be nice to be able to exploit our *_assign_op functors for that purpose
@@ -294,6 +294,7 @@ struct generic_product_impl<Lhs, Rhs, DenseShape, DenseShape, OuterProduct> {
     }
   };
   struct add {
+    /** Add to dst. */
     template <typename Dst, typename Src>
     EIGEN_DEVICE_FUNC void operator()(const Dst& dst, const Src& src) const {
       dst.const_cast_derived() += src;
@@ -305,9 +306,12 @@ struct generic_product_impl<Lhs, Rhs, DenseShape, DenseShape, OuterProduct> {
       dst.const_cast_derived() -= src;
     }
   };
+  /** Scaled add. */
   struct adds {
     Scalar m_scale;
+    /** Constructor */
     explicit adds(const Scalar& s) : m_scale(s) {}
+    /** Scaled add to dst. */
     template <typename Dst, typename Src>
     void EIGEN_DEVICE_FUNC operator()(const Dst& dst, const Src& src) const {
       dst.const_cast_derived() += m_scale * src;
@@ -441,7 +445,7 @@ struct generic_product_impl<Lhs, Rhs, DenseShape, DenseShape, CoeffBasedProductM
 
     eval_dynamic_impl(dst, blas_traits<Lhs>::extract(lhs).template conjugateIf<ConjLhs>(),
                       blas_traits<Rhs>::extract(rhs).template conjugateIf<ConjRhs>(), func, actualAlpha,
-                      std::conditional_t<HasScalarFactor, true_type, false_type>());
+                      bool_constant<HasScalarFactor>());
   }
 
  protected:
@@ -631,6 +635,24 @@ struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, DenseShape,
     return packet<LoadMode, PacketType>(row, col);
   }
 
+  template <int LoadMode, typename PacketType>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const PacketType packetSegment(Index row, Index col, Index begin,
+                                                                       Index count) const {
+    PacketType res;
+    typedef etor_product_packet_impl<bool(int(Flags) & RowMajorBit) ? RowMajor : ColMajor,
+                                     Unroll ? int(InnerSize) : Dynamic, LhsEtorType, RhsEtorType, PacketType, LoadMode>
+        PacketImpl;
+    PacketImpl::run_segment(row, col, m_lhsImpl, m_rhsImpl, m_innerDim, res, begin, count);
+    return res;
+  }
+
+  template <int LoadMode, typename PacketType>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const PacketType packetSegment(Index index, Index begin, Index count) const {
+    const Index row = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime == 1) ? 0 : index;
+    const Index col = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime == 1) ? index : 0;
+    return packetSegment<LoadMode, PacketType>(row, col, begin, count);
+  }
+
  protected:
   add_const_on_value_type_t<LhsNested> m_lhs;
   add_const_on_value_type_t<RhsNested> m_rhs;
@@ -666,6 +688,13 @@ struct etor_product_packet_impl<RowMajor, UnrollingIndex, Lhs, Rhs, Packet, Load
     res = pmadd(pset1<Packet>(lhs.coeff(row, Index(UnrollingIndex - 1))),
                 rhs.template packet<LoadMode, Packet>(Index(UnrollingIndex - 1), col), res);
   }
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run_segment(Index row, Index col, const Lhs& lhs, const Rhs& rhs,
+                                                                Index innerDim, Packet& res, Index begin, Index count) {
+    etor_product_packet_impl<RowMajor, UnrollingIndex - 1, Lhs, Rhs, Packet, LoadMode>::run_segment(
+        row, col, lhs, rhs, innerDim, res, begin, count);
+    res = pmadd(pset1<Packet>(lhs.coeff(row, Index(UnrollingIndex - 1))),
+                rhs.template packetSegment<LoadMode, Packet>(Index(UnrollingIndex - 1), col, begin, count), res);
+  }
 };
 
 template <int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>
@@ -677,6 +706,13 @@ struct etor_product_packet_impl<ColMajor, UnrollingIndex, Lhs, Rhs, Packet, Load
     res = pmadd(lhs.template packet<LoadMode, Packet>(row, Index(UnrollingIndex - 1)),
                 pset1<Packet>(rhs.coeff(Index(UnrollingIndex - 1), col)), res);
   }
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run_segment(Index row, Index col, const Lhs& lhs, const Rhs& rhs,
+                                                                Index innerDim, Packet& res, Index begin, Index count) {
+    etor_product_packet_impl<ColMajor, UnrollingIndex - 1, Lhs, Rhs, Packet, LoadMode>::run_segment(
+        row, col, lhs, rhs, innerDim, res, begin, count);
+    res = pmadd(lhs.template packetSegment<LoadMode, Packet>(row, Index(UnrollingIndex - 1), begin, count),
+                pset1<Packet>(rhs.coeff(Index(UnrollingIndex - 1), col)), res);
+  }
 };
 
 template <typename Lhs, typename Rhs, typename Packet, int LoadMode>
@@ -685,6 +721,12 @@ struct etor_product_packet_impl<RowMajor, 1, Lhs, Rhs, Packet, LoadMode> {
                                                         Index /*innerDim*/, Packet& res) {
     res = pmul(pset1<Packet>(lhs.coeff(row, Index(0))), rhs.template packet<LoadMode, Packet>(Index(0), col));
   }
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run_segment(Index row, Index col, const Lhs& lhs, const Rhs& rhs,
+                                                                Index /*innerDim*/, Packet& res, Index begin,
+                                                                Index count) {
+    res = pmul(pset1<Packet>(lhs.coeff(row, Index(0))),
+               rhs.template packetSegment<LoadMode, Packet>(Index(0), col, begin, count));
+  }
 };
 
 template <typename Lhs, typename Rhs, typename Packet, int LoadMode>
@@ -693,6 +735,12 @@ struct etor_product_packet_impl<ColMajor, 1, Lhs, Rhs, Packet, LoadMode> {
                                                         Index /*innerDim*/, Packet& res) {
     res = pmul(lhs.template packet<LoadMode, Packet>(row, Index(0)), pset1<Packet>(rhs.coeff(Index(0), col)));
   }
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run_segment(Index row, Index col, const Lhs& lhs, const Rhs& rhs,
+                                                                Index /*innerDim*/, Packet& res, Index begin,
+                                                                Index count) {
+    res = pmul(lhs.template packetSegment<LoadMode, Packet>(row, Index(0), begin, count),
+               pset1<Packet>(rhs.coeff(Index(0), col)));
+  }
 };
 
 template <typename Lhs, typename Rhs, typename Packet, int LoadMode>
@@ -701,6 +749,11 @@ struct etor_product_packet_impl<RowMajor, 0, Lhs, Rhs, Packet, LoadMode> {
                                                         const Rhs& /*rhs*/, Index /*innerDim*/, Packet& res) {
     res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
   }
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run_segment(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/,
+                                                                const Rhs& /*rhs*/, Index /*innerDim*/, Packet& res,
+                                                                Index /*begin*/, Index /*count*/) {
+    res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
+  }
 };
 
 template <typename Lhs, typename Rhs, typename Packet, int LoadMode>
@@ -709,6 +762,11 @@ struct etor_product_packet_impl<ColMajor, 0, Lhs, Rhs, Packet, LoadMode> {
                                                         const Rhs& /*rhs*/, Index /*innerDim*/, Packet& res) {
     res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
   }
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run_segment(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/,
+                                                                const Rhs& /*rhs*/, Index /*innerDim*/, Packet& res,
+                                                                Index /*begin*/, Index /*count*/) {
+    res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
+  }
 };
 
 template <typename Lhs, typename Rhs, typename Packet, int LoadMode>
@@ -719,6 +777,13 @@ struct etor_product_packet_impl<RowMajor, Dynamic, Lhs, Rhs, Packet, LoadMode> {
     for (Index i = 0; i < innerDim; ++i)
       res = pmadd(pset1<Packet>(lhs.coeff(row, i)), rhs.template packet<LoadMode, Packet>(i, col), res);
   }
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run_segment(Index row, Index col, const Lhs& lhs, const Rhs& rhs,
+                                                                Index innerDim, Packet& res, Index begin, Index count) {
+    res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
+    for (Index i = 0; i < innerDim; ++i)
+      res = pmadd(pset1<Packet>(lhs.coeff(row, i)), rhs.template packetSegment<LoadMode, Packet>(i, col, begin, count),
+                  res);
+  }
 };
 
 template <typename Lhs, typename Rhs, typename Packet, int LoadMode>
@@ -729,6 +794,13 @@ struct etor_product_packet_impl<ColMajor, Dynamic, Lhs, Rhs, Packet, LoadMode> {
     for (Index i = 0; i < innerDim; ++i)
       res = pmadd(lhs.template packet<LoadMode, Packet>(row, i), pset1<Packet>(rhs.coeff(i, col)), res);
   }
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run_segment(Index row, Index col, const Lhs& lhs, const Rhs& rhs,
+                                                                Index innerDim, Packet& res, Index begin, Index count) {
+    res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
+    for (Index i = 0; i < innerDim; ++i)
+      res = pmadd(lhs.template packetSegment<LoadMode, Packet>(row, i, begin, count), pset1<Packet>(rhs.coeff(i, col)),
+                  res);
+  }
 };
 
 /***************************************************************************
@@ -774,7 +846,7 @@ struct generic_product_impl<Lhs, Rhs, SelfAdjointShape, DenseShape, ProductTag>
 
   template <typename Dest>
   static EIGEN_DEVICE_FUNC void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha) {
-    selfadjoint_product_impl<typename Lhs::MatrixType, Lhs::Mode, false, Rhs, 0, Rhs::IsVectorAtCompileTime>::run(
+    selfadjoint_product_impl<typename Lhs::MatrixType, Lhs::Mode, false, Rhs, 0, Rhs::ColsAtCompileTime == 1>::run(
         dst, lhs.nestedExpression(), rhs, alpha);
   }
 };
@@ -786,7 +858,7 @@ struct generic_product_impl<Lhs, Rhs, DenseShape, SelfAdjointShape, ProductTag>
 
   template <typename Dest>
   static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha) {
-    selfadjoint_product_impl<Lhs, 0, Lhs::IsVectorAtCompileTime, typename Rhs::MatrixType, Rhs::Mode, false>::run(
+    selfadjoint_product_impl<Lhs, 0, Lhs::RowsAtCompileTime == 1, typename Rhs::MatrixType, Rhs::Mode, false>::run(
         dst, lhs, rhs.nestedExpression(), alpha);
   }
 };
@@ -867,6 +939,26 @@ struct diagonal_product_evaluator_base : evaluator_base<Derived> {
                           m_diagImpl.template packet<DiagonalPacketLoadMode, PacketType>(id));
   }
 
+  template <int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE PacketType packet_segment_impl(Index row, Index col, Index id, Index begin, Index count,
+                                                     internal::true_type) const {
+    return internal::pmul(m_matImpl.template packetSegment<LoadMode, PacketType>(row, col, begin, count),
+                          internal::pset1<PacketType>(m_diagImpl.coeff(id)));
+  }
+
+  template <int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE PacketType packet_segment_impl(Index row, Index col, Index id, Index begin, Index count,
+                                                     internal::false_type) const {
+    enum {
+      InnerSize = (MatrixType::Flags & RowMajorBit) ? MatrixType::ColsAtCompileTime : MatrixType::RowsAtCompileTime,
+      DiagonalPacketLoadMode = plain_enum_min(
+          LoadMode,
+          ((InnerSize % 16) == 0) ? int(Aligned16) : int(evaluator<DiagonalType>::Alignment))  // FIXME hardcoded 16!!
+    };
+    return internal::pmul(m_matImpl.template packetSegment<LoadMode, PacketType>(row, col, begin, count),
+                          m_diagImpl.template packetSegment<DiagonalPacketLoadMode, PacketType>(id, begin, count));
+  }
+
   evaluator<DiagonalType> m_diagImpl;
   evaluator<MatrixType> m_matImpl;
 };
@@ -888,7 +980,8 @@ struct product_evaluator<Product<Lhs, Rhs, ProductKind>, ProductTag, DiagonalSha
   typedef typename XprType::PlainObject PlainObject;
   typedef typename Lhs::DiagonalVectorType DiagonalType;
 
-  enum { StorageOrder = Base::StorageOrder_ };
+  static constexpr int StorageOrder = Base::StorageOrder_;
+  using IsRowMajor_t = bool_constant<StorageOrder == RowMajor>;
 
   EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr) : Base(xpr.rhs(), xpr.lhs().diagonal()) {}
 
@@ -901,8 +994,7 @@ struct product_evaluator<Product<Lhs, Rhs, ProductKind>, ProductTag, DiagonalSha
   EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const {
     // FIXME: NVCC used to complain about the template keyword, but we have to check whether this is still the case.
     // See also similar calls below.
-    return this->template packet_impl<LoadMode, PacketType>(
-        row, col, row, std::conditional_t<int(StorageOrder) == RowMajor, internal::true_type, internal::false_type>());
+    return this->template packet_impl<LoadMode, PacketType>(row, col, row, IsRowMajor_t());
   }
 
   template <int LoadMode, typename PacketType>
@@ -910,6 +1002,19 @@ struct product_evaluator<Product<Lhs, Rhs, ProductKind>, ProductTag, DiagonalSha
     return packet<LoadMode, PacketType>(int(StorageOrder) == ColMajor ? idx : 0,
                                         int(StorageOrder) == ColMajor ? 0 : idx);
   }
+
+  template <int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE PacketType packetSegment(Index row, Index col, Index begin, Index count) const {
+    // FIXME: NVCC used to complain about the template keyword, but we have to check whether this is still the case.
+    // See also similar calls below.
+    return this->template packet_segment_impl<LoadMode, PacketType>(row, col, row, begin, count, IsRowMajor_t());
+  }
+
+  template <int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE PacketType packetSegment(Index idx, Index begin, Index count) const {
+    return packetSegment<LoadMode, PacketType>(StorageOrder == ColMajor ? idx : 0, StorageOrder == ColMajor ? 0 : idx,
+                                               begin, count);
+  }
 #endif
 };
 
@@ -929,7 +1034,8 @@ struct product_evaluator<Product<Lhs, Rhs, ProductKind>, ProductTag, DenseShape,
   typedef Product<Lhs, Rhs, ProductKind> XprType;
   typedef typename XprType::PlainObject PlainObject;
 
-  enum { StorageOrder = Base::StorageOrder_ };
+  static constexpr int StorageOrder = Base::StorageOrder_;
+  using IsColMajor_t = bool_constant<StorageOrder == ColMajor>;
 
   EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr) : Base(xpr.lhs(), xpr.rhs().diagonal()) {}
 
@@ -940,14 +1046,23 @@ struct product_evaluator<Product<Lhs, Rhs, ProductKind>, ProductTag, DenseShape,
 #ifndef EIGEN_GPUCC
   template <int LoadMode, typename PacketType>
   EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const {
-    return this->template packet_impl<LoadMode, PacketType>(
-        row, col, col, std::conditional_t<int(StorageOrder) == ColMajor, internal::true_type, internal::false_type>());
+    return this->template packet_impl<LoadMode, PacketType>(row, col, col, IsColMajor_t());
   }
 
   template <int LoadMode, typename PacketType>
   EIGEN_STRONG_INLINE PacketType packet(Index idx) const {
-    return packet<LoadMode, PacketType>(int(StorageOrder) == ColMajor ? idx : 0,
-                                        int(StorageOrder) == ColMajor ? 0 : idx);
+    return packet<LoadMode, PacketType>(StorageOrder == ColMajor ? idx : 0, StorageOrder == ColMajor ? 0 : idx);
+  }
+
+  template <int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE PacketType packetSegment(Index row, Index col, Index begin, Index count) const {
+    return this->template packet_segment_impl<LoadMode, PacketType>(row, col, col, begin, count, IsColMajor_t());
+  }
+
+  template <int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE PacketType packetSegment(Index idx, Index begin, Index count) const {
+    return packetSegment<LoadMode, PacketType>(StorageOrder == ColMajor ? idx : 0, StorageOrder == ColMajor ? 0 : idx,
+                                               begin, count);
   }
 #endif
 };
@@ -1149,6 +1264,22 @@ struct generic_product_impl<Lhs, Rhs, SkewSymmetricShape, SkewSymmetricShape, Pr
   }
 };
 
+template <typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
+struct generic_product_impl<Lhs, Rhs, MatrixShape, HomogeneousShape, ProductTag>
+    : generic_product_impl<Lhs, typename Rhs::PlainObject, MatrixShape, DenseShape, ProductTag> {};
+
+template <typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
+struct generic_product_impl<Lhs, Rhs, HomogeneousShape, MatrixShape, ProductTag>
+    : generic_product_impl<typename Lhs::PlainObject, Rhs, DenseShape, MatrixShape, ProductTag> {};
+
+template <typename Lhs, typename Rhs, int ProductTag>
+struct generic_product_impl<Lhs, Rhs, PermutationShape, HomogeneousShape, ProductTag>
+    : generic_product_impl<Lhs, Rhs, PermutationShape, DenseShape, ProductTag> {};
+
+template <typename Lhs, typename Rhs, int ProductTag>
+struct generic_product_impl<Lhs, Rhs, HomogeneousShape, PermutationShape, ProductTag>
+    : generic_product_impl<Lhs, Rhs, DenseShape, PermutationShape, ProductTag> {};
+
 }  // end namespace internal
 
 }  // end namespace Eigen

Eigen/src/Core/RandomImpl.h

@@ -115,13 +115,14 @@ struct random_float_impl<Scalar, false> {
   }
 };
 
+#if !EIGEN_COMP_NVCC
 // random implementation for long double
 // this specialization is not compatible with double-double scalars
 template <bool Specialize = (sizeof(long double) == 2 * sizeof(uint64_t)) &&
                             ((std::numeric_limits<long double>::digits != (2 * std::numeric_limits<double>::digits)))>
 struct random_longdouble_impl {
   static constexpr int Size = sizeof(long double);
-  static constexpr EIGEN_DEVICE_FUNC inline int mantissaBits() { return NumTraits<long double>::digits() - 1; }
+  static constexpr EIGEN_DEVICE_FUNC int mantissaBits() { return NumTraits<long double>::digits() - 1; }
   static EIGEN_DEVICE_FUNC inline long double run(int numRandomBits) {
     eigen_assert(numRandomBits >= 0 && numRandomBits <= mantissaBits());
     EIGEN_USING_STD(memcpy);
@@ -130,8 +131,15 @@ struct random_longdouble_impl {
     uint64_t randomBits[2];
     long double result = 2.0L;
     memcpy(&randomBits, &result, Size);
+#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
     randomBits[0] |= getRandomBits<uint64_t>(numLowBits);
     randomBits[1] |= getRandomBits<uint64_t>(numHighBits);
+#elif __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
+    randomBits[0] |= getRandomBits<uint64_t>(numHighBits);
+    randomBits[1] |= getRandomBits<uint64_t>(numLowBits);
+#else
+#error Unexpected or undefined __BYTE_ORDER__
+#endif
     memcpy(&result, &randomBits, Size);
     result -= 3.0L;
     return result;
@@ -139,13 +147,14 @@ struct random_longdouble_impl {
 };
 template <>
 struct random_longdouble_impl<false> {
-  static constexpr EIGEN_DEVICE_FUNC inline int mantissaBits() { return NumTraits<double>::digits() - 1; }
+  static constexpr EIGEN_DEVICE_FUNC int mantissaBits() { return NumTraits<double>::digits() - 1; }
   static EIGEN_DEVICE_FUNC inline long double run(int numRandomBits) {
     return static_cast<long double>(random_float_impl<double>::run(numRandomBits));
   }
 };
 template <>
 struct random_float_impl<long double> : random_longdouble_impl<> {};
+#endif
 
 template <typename Scalar>
 struct random_default_impl<Scalar, false, false> {

Eigen/src/Core/RealView.h

@@ -0,0 +1,250 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2025 Charlie Schlosser <cs.schlosser@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REALVIEW_H
+#define EIGEN_REALVIEW_H
+
+// IWYU pragma: private
+#include "./InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+// Vectorized assignment to RealView requires array-oriented access to the real and imaginary components.
+// From https://en.cppreference.com/w/cpp/numeric/complex.html:
+// For any pointer to an element of an array of std::complex<T> named p and any valid array index i,
+// reinterpret_cast<T*>(p)[2 * i] is the real part of the complex number p[i], and
+// reinterpret_cast<T*>(p)[2 * i + 1] is the imaginary part of the complex number p[i].
+
+template <typename ComplexScalar>
+struct complex_array_access : std::false_type {};
+template <>
+struct complex_array_access<std::complex<float>> : std::true_type {};
+template <>
+struct complex_array_access<std::complex<double>> : std::true_type {};
+template <>
+struct complex_array_access<std::complex<long double>> : std::true_type {};
+
+template <typename Xpr>
+struct traits<RealView<Xpr>> : public traits<Xpr> {
+  template <typename T>
+  static constexpr int double_size(T size, bool times_two) {
+    int size_as_int = int(size);
+    if (size_as_int == Dynamic) return Dynamic;
+    return times_two ? (2 * size_as_int) : size_as_int;
+  }
+  using Base = traits<Xpr>;
+  using ComplexScalar = typename Base::Scalar;
+  using Scalar = typename NumTraits<ComplexScalar>::Real;
+  static constexpr int ActualDirectAccessBit = complex_array_access<ComplexScalar>::value ? DirectAccessBit : 0;
+  static constexpr int ActualPacketAccessBit = packet_traits<Scalar>::Vectorizable ? PacketAccessBit : 0;
+  static constexpr int FlagMask =
+      ActualDirectAccessBit | ActualPacketAccessBit | HereditaryBits | LinearAccessBit | LvalueBit;
+  static constexpr int BaseFlags = int(evaluator<Xpr>::Flags) | int(Base::Flags);
+  static constexpr int Flags = BaseFlags & FlagMask;
+  static constexpr bool IsRowMajor = Flags & RowMajorBit;
+  static constexpr int RowsAtCompileTime = double_size(Base::RowsAtCompileTime, !IsRowMajor);
+  static constexpr int ColsAtCompileTime = double_size(Base::ColsAtCompileTime, IsRowMajor);
+  static constexpr int SizeAtCompileTime = size_at_compile_time(RowsAtCompileTime, ColsAtCompileTime);
+  static constexpr int MaxRowsAtCompileTime = double_size(Base::MaxRowsAtCompileTime, !IsRowMajor);
+  static constexpr int MaxColsAtCompileTime = double_size(Base::MaxColsAtCompileTime, IsRowMajor);
+  static constexpr int MaxSizeAtCompileTime = size_at_compile_time(MaxRowsAtCompileTime, MaxColsAtCompileTime);
+  static constexpr int OuterStrideAtCompileTime = double_size(outer_stride_at_compile_time<Xpr>::ret, true);
+  static constexpr int InnerStrideAtCompileTime = inner_stride_at_compile_time<Xpr>::ret;
+};
+
+template <typename Xpr>
+struct evaluator<RealView<Xpr>> : private evaluator<Xpr> {
+  using BaseEvaluator = evaluator<Xpr>;
+  using XprType = RealView<Xpr>;
+  using ExpressionTraits = traits<XprType>;
+  using ComplexScalar = typename ExpressionTraits::ComplexScalar;
+  using ComplexCoeffReturnType = typename BaseEvaluator::CoeffReturnType;
+  using Scalar = typename ExpressionTraits::Scalar;
+
+  static constexpr bool IsRowMajor = ExpressionTraits::IsRowMajor;
+  static constexpr int Flags = ExpressionTraits::Flags;
+  static constexpr int CoeffReadCost = BaseEvaluator::CoeffReadCost;
+  static constexpr int Alignment = BaseEvaluator::Alignment;
+
+  EIGEN_DEVICE_FUNC explicit evaluator(XprType realView) : BaseEvaluator(realView.m_xpr) {}
+
+  template <bool Enable = std::is_reference<ComplexCoeffReturnType>::value, typename = std::enable_if_t<!Enable>>
+  constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index row, Index col) const {
+    ComplexCoeffReturnType cscalar = BaseEvaluator::coeff(IsRowMajor ? row : row / 2, IsRowMajor ? col / 2 : col);
+    Index p = (IsRowMajor ? col : row) & 1;
+    return p ? numext::real(cscalar) : numext::imag(cscalar);
+  }
+
+  template <bool Enable = std::is_reference<ComplexCoeffReturnType>::value, typename = std::enable_if_t<Enable>>
+  constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(Index row, Index col) const {
+    ComplexCoeffReturnType cscalar = BaseEvaluator::coeff(IsRowMajor ? row : row / 2, IsRowMajor ? col / 2 : col);
+    Index p = (IsRowMajor ? col : row) & 1;
+    return reinterpret_cast<const Scalar(&)[2]>(cscalar)[p];
+  }
+
+  constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col) {
+    ComplexScalar& cscalar = BaseEvaluator::coeffRef(IsRowMajor ? row : row / 2, IsRowMajor ? col / 2 : col);
+    Index p = (IsRowMajor ? col : row) & 1;
+    return reinterpret_cast<Scalar(&)[2]>(cscalar)[p];
+  }
+
+  template <bool Enable = std::is_reference<ComplexCoeffReturnType>::value, typename = std::enable_if_t<!Enable>>
+  constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index index) const {
+    ComplexCoeffReturnType cscalar = BaseEvaluator::coeff(index / 2);
+    Index p = index & 1;
+    return p ? numext::real(cscalar) : numext::imag(cscalar);
+  }
+
+  template <bool Enable = std::is_reference<ComplexCoeffReturnType>::value, typename = std::enable_if_t<Enable>>
+  constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar& coeff(Index index) const {
+    ComplexCoeffReturnType cscalar = BaseEvaluator::coeff(index / 2);
+    Index p = index & 1;
+    return reinterpret_cast<const Scalar(&)[2]>(cscalar)[p];
+  }
+
+  constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {
+    ComplexScalar& cscalar = BaseEvaluator::coeffRef(index / 2);
+    Index p = index & 1;
+    return reinterpret_cast<Scalar(&)[2]>(cscalar)[p];
+  }
+
+  template <int LoadMode, typename PacketType>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const {
+    constexpr int RealPacketSize = unpacket_traits<PacketType>::size;
+    using ComplexPacket = typename find_packet_by_size<ComplexScalar, RealPacketSize / 2>::type;
+    EIGEN_STATIC_ASSERT((find_packet_by_size<ComplexScalar, RealPacketSize / 2>::value),
+                        MISSING COMPATIBLE COMPLEX PACKET TYPE)
+    eigen_assert(((IsRowMajor ? col : row) % 2 == 0) && "the inner index must be even");
+
+    Index crow = IsRowMajor ? row : row / 2;
+    Index ccol = IsRowMajor ? col / 2 : col;
+    ComplexPacket cpacket = BaseEvaluator::template packet<LoadMode, ComplexPacket>(crow, ccol);
+    return preinterpret<PacketType, ComplexPacket>(cpacket);
+  }
+
+  template <int LoadMode, typename PacketType>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index index) const {
+    constexpr int RealPacketSize = unpacket_traits<PacketType>::size;
+    using ComplexPacket = typename find_packet_by_size<ComplexScalar, RealPacketSize / 2>::type;
+    EIGEN_STATIC_ASSERT((find_packet_by_size<ComplexScalar, RealPacketSize / 2>::value),
+                        MISSING COMPATIBLE COMPLEX PACKET TYPE)
+    eigen_assert((index % 2 == 0) && "the index must be even");
+
+    Index cindex = index / 2;
+    ComplexPacket cpacket = BaseEvaluator::template packet<LoadMode, ComplexPacket>(cindex);
+    return preinterpret<PacketType, ComplexPacket>(cpacket);
+  }
+
+  template <int LoadMode, typename PacketType>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packetSegment(Index row, Index col, Index begin, Index count) const {
+    constexpr int RealPacketSize = unpacket_traits<PacketType>::size;
+    using ComplexPacket = typename find_packet_by_size<ComplexScalar, RealPacketSize / 2>::type;
+    EIGEN_STATIC_ASSERT((find_packet_by_size<ComplexScalar, RealPacketSize / 2>::value),
+                        MISSING COMPATIBLE COMPLEX PACKET TYPE)
+    eigen_assert(((IsRowMajor ? col : row) % 2 == 0) && "the inner index must be even");
+    eigen_assert((begin % 2 == 0) && (count % 2 == 0) && "begin and count must be even");
+
+    Index crow = IsRowMajor ? row : row / 2;
+    Index ccol = IsRowMajor ? col / 2 : col;
+    Index cbegin = begin / 2;
+    Index ccount = count / 2;
+    ComplexPacket cpacket = BaseEvaluator::template packetSegment<LoadMode, ComplexPacket>(crow, ccol, cbegin, ccount);
+    return preinterpret<PacketType, ComplexPacket>(cpacket);
+  }
+
+  template <int LoadMode, typename PacketType>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packetSegment(Index index, Index begin, Index count) const {
+    constexpr int RealPacketSize = unpacket_traits<PacketType>::size;
+    using ComplexPacket = typename find_packet_by_size<ComplexScalar, RealPacketSize / 2>::type;
+    EIGEN_STATIC_ASSERT((find_packet_by_size<ComplexScalar, RealPacketSize / 2>::value),
+                        MISSING COMPATIBLE COMPLEX PACKET TYPE)
+    eigen_assert((index % 2 == 0) && "the index must be even");
+    eigen_assert((begin % 2 == 0) && (count % 2 == 0) && "begin and count must be even");
+
+    Index cindex = index / 2;
+    Index cbegin = begin / 2;
+    Index ccount = count / 2;
+    ComplexPacket cpacket = BaseEvaluator::template packetSegment<LoadMode, ComplexPacket>(cindex, cbegin, ccount);
+    return preinterpret<PacketType, ComplexPacket>(cpacket);
+  }
+};
+
+}  // namespace internal
+
+template <typename Xpr>
+class RealView : public internal::dense_xpr_base<RealView<Xpr>>::type {
+  using ExpressionTraits = internal::traits<RealView>;
+  EIGEN_STATIC_ASSERT(NumTraits<typename Xpr::Scalar>::IsComplex, SCALAR MUST BE COMPLEX)
+ public:
+  using Scalar = typename ExpressionTraits::Scalar;
+  using Nested = RealView;
+
+  EIGEN_DEVICE_FUNC explicit RealView(Xpr& xpr) : m_xpr(xpr) {}
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return Xpr::IsRowMajor ? m_xpr.rows() : 2 * m_xpr.rows(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return Xpr::IsRowMajor ? 2 * m_xpr.cols() : m_xpr.cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index size() const noexcept { return 2 * m_xpr.size(); }
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_xpr.innerStride(); }
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return 2 * m_xpr.outerStride(); }
+  EIGEN_DEVICE_FUNC void resize(Index rows, Index cols) {
+    m_xpr.resize(Xpr::IsRowMajor ? rows : rows / 2, Xpr::IsRowMajor ? cols / 2 : cols);
+  }
+  EIGEN_DEVICE_FUNC void resize(Index size) { m_xpr.resize(size / 2); }
+  EIGEN_DEVICE_FUNC Scalar* data() { return reinterpret_cast<Scalar*>(m_xpr.data()); }
+  EIGEN_DEVICE_FUNC const Scalar* data() const { return reinterpret_cast<const Scalar*>(m_xpr.data()); }
+
+  EIGEN_DEVICE_FUNC RealView(const RealView&) = default;
+
+  EIGEN_DEVICE_FUNC RealView& operator=(const RealView& other);
+
+  template <typename OtherDerived>
+  EIGEN_DEVICE_FUNC RealView& operator=(const RealView<OtherDerived>& other);
+
+  template <typename OtherDerived>
+  EIGEN_DEVICE_FUNC RealView& operator=(const DenseBase<OtherDerived>& other);
+
+ protected:
+  friend struct internal::evaluator<RealView<Xpr>>;
+  Xpr& m_xpr;
+};
+
+template <typename Xpr>
+EIGEN_DEVICE_FUNC RealView<Xpr>& RealView<Xpr>::operator=(const RealView& other) {
+  internal::call_assignment(*this, other);
+  return *this;
+}
+
+template <typename Xpr>
+template <typename OtherDerived>
+EIGEN_DEVICE_FUNC RealView<Xpr>& RealView<Xpr>::operator=(const RealView<OtherDerived>& other) {
+  internal::call_assignment(*this, other);
+  return *this;
+}
+
+template <typename Xpr>
+template <typename OtherDerived>
+EIGEN_DEVICE_FUNC RealView<Xpr>& RealView<Xpr>::operator=(const DenseBase<OtherDerived>& other) {
+  internal::call_assignment(*this, other.derived());
+  return *this;
+}
+
+template <typename Derived>
+EIGEN_DEVICE_FUNC typename DenseBase<Derived>::RealViewReturnType DenseBase<Derived>::realView() {
+  return RealViewReturnType(derived());
+}
+
+template <typename Derived>
+EIGEN_DEVICE_FUNC typename DenseBase<Derived>::ConstRealViewReturnType DenseBase<Derived>::realView() const {
+  return ConstRealViewReturnType(derived());
+}
+
+}  // namespace Eigen
+
+#endif  // EIGEN_REALVIEW_H

Eigen/src/Core/Redux.h

@@ -414,6 +414,13 @@ class redux_evaluator : public internal::evaluator<XprType_> {
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packetByOuterInner(Index outer, Index inner) const {
     return Base::template packet<LoadMode, PacketType>(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer);
   }
+
+  template <int LoadMode, typename PacketType>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packetSegmentByOuterInner(Index outer, Index inner, Index begin,
+                                                                             Index count) const {
+    return Base::template packetSegment<LoadMode, PacketType>(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer,
+                                                              begin, count);
+  }
 };
 
 }  // end namespace internal

Eigen/src/Core/Ref.h

@@ -73,11 +73,11 @@ class RefBase : public MapBase<Derived> {
   typedef MapBase<Derived> Base;
   EIGEN_DENSE_PUBLIC_INTERFACE(RefBase)
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const {
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const {
     return StrideType::InnerStrideAtCompileTime != 0 ? m_stride.inner() : 1;
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const {
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const {
     return StrideType::OuterStrideAtCompileTime != 0 ? m_stride.outer()
            : IsVectorAtCompileTime                   ? this->size()
            : int(Flags) & RowMajorBit                ? this->cols()
@@ -97,11 +97,11 @@ class RefBase : public MapBase<Derived> {
   typedef Stride<StrideType::OuterStrideAtCompileTime, StrideType::InnerStrideAtCompileTime> StrideBase;
 
   // Resolves inner stride if default 0.
-  static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index resolveInnerStride(Index inner) { return inner == 0 ? 1 : inner; }
+  static EIGEN_DEVICE_FUNC constexpr Index resolveInnerStride(Index inner) { return inner == 0 ? 1 : inner; }
 
   // Resolves outer stride if default 0.
-  static EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index resolveOuterStride(Index inner, Index outer, Index rows, Index cols,
-                                                                    bool isVectorAtCompileTime, bool isRowMajor) {
+  static EIGEN_DEVICE_FUNC constexpr Index resolveOuterStride(Index inner, Index outer, Index rows, Index cols,
+                                                              bool isVectorAtCompileTime, bool isRowMajor) {
     return outer == 0 ? isVectorAtCompileTime ? inner * rows * cols : isRowMajor ? inner * cols : inner * rows : outer;
   }
 

Eigen/src/Core/Replicate.h

@@ -85,8 +85,8 @@ class Replicate : public internal::dense_xpr_base<Replicate<MatrixType, RowFacto
                         THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE)
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const { return m_matrix.rows() * m_rowFactor.value(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const { return m_matrix.cols() * m_colFactor.value(); }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const { return m_matrix.rows() * m_rowFactor.value(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const { return m_matrix.cols() * m_colFactor.value(); }
 
   EIGEN_DEVICE_FUNC const MatrixTypeNested_& nestedExpression() const { return m_matrix; }
 

Eigen/src/Core/Reshaped.h

@@ -215,10 +215,10 @@ class ReshapedImpl_dense<XprType, Rows, Cols, Order, true> : public MapBase<Resh
   EIGEN_DEVICE_FUNC XprType& nestedExpression() { return m_xpr; }
 
   /** \sa MapBase::innerStride() */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const { return m_xpr.innerStride(); }
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const { return m_xpr.innerStride(); }
 
   /** \sa MapBase::outerStride() */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const {
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const {
     return (((Flags & RowMajorBit) == RowMajorBit) ? this->cols() : this->rows()) * m_xpr.innerStride();
   }
 

Eigen/src/Core/ReturnByValue.h

@@ -58,12 +58,8 @@ class ReturnByValue : public internal::dense_xpr_base<ReturnByValue<Derived> >::
   EIGEN_DEVICE_FUNC inline void evalTo(Dest& dst) const {
     static_cast<const Derived*>(this)->evalTo(dst);
   }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT {
-    return static_cast<const Derived*>(this)->rows();
-  }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT {
-    return static_cast<const Derived*>(this)->cols();
-  }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return static_cast<const Derived*>(this)->rows(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return static_cast<const Derived*>(this)->cols(); }
 
 #ifndef EIGEN_PARSED_BY_DOXYGEN
 #define Unusable \

Eigen/src/Core/Reverse.h

@@ -87,8 +87,8 @@ class Reverse : public internal::dense_xpr_base<Reverse<MatrixType, Direction> >
 
   EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Reverse)
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_matrix.rows(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_matrix.cols(); }
 
   EIGEN_DEVICE_FUNC inline Index innerStride() const { return -m_matrix.innerStride(); }
 
@@ -127,19 +127,25 @@ EIGEN_DEVICE_FUNC inline typename DenseBase<Derived>::ReverseReturnType DenseBas
  * \sa VectorwiseOp::reverseInPlace(), reverse() */
 template <typename Derived>
 EIGEN_DEVICE_FUNC inline void DenseBase<Derived>::reverseInPlace() {
+  constexpr int HalfRowsAtCompileTime = RowsAtCompileTime == Dynamic ? Dynamic : RowsAtCompileTime / 2;
+  constexpr int HalfColsAtCompileTime = ColsAtCompileTime == Dynamic ? Dynamic : ColsAtCompileTime / 2;
   if (cols() > rows()) {
     Index half = cols() / 2;
-    leftCols(half).swap(rightCols(half).reverse());
+    this->template leftCols<HalfColsAtCompileTime>(half).swap(
+        this->template rightCols<HalfColsAtCompileTime>(half).reverse());
     if ((cols() % 2) == 1) {
       Index half2 = rows() / 2;
-      col(half).head(half2).swap(col(half).tail(half2).reverse());
+      col(half).template head<HalfRowsAtCompileTime>(half2).swap(
+          col(half).template tail<HalfRowsAtCompileTime>(half2).reverse());
     }
   } else {
     Index half = rows() / 2;
-    topRows(half).swap(bottomRows(half).reverse());
+    this->template topRows<HalfRowsAtCompileTime>(half).swap(
+        this->template bottomRows<HalfRowsAtCompileTime>(half).reverse());
     if ((rows() % 2) == 1) {
       Index half2 = cols() / 2;
-      row(half).head(half2).swap(row(half).tail(half2).reverse());
+      row(half).template head<HalfColsAtCompileTime>(half2).swap(
+          row(half).template tail<HalfColsAtCompileTime>(half2).reverse());
     }
   }
 }

Eigen/src/Core/Select.h

@@ -15,7 +15,7 @@
 
 namespace Eigen {
 
-/** \class Select
+/** \typedef Select
  * \ingroup Core_Module
  *
  * \brief Expression of a coefficient wise version of the C++ ternary operator ?:
@@ -24,73 +24,16 @@ namespace Eigen {
  * \tparam ThenMatrixType the type of the \em then expression
  * \tparam ElseMatrixType the type of the \em else expression
  *
- * This class represents an expression of a coefficient wise version of the C++ ternary operator ?:.
+ * This type represents an expression of a coefficient wise version of the C++ ternary operator ?:.
  * It is the return type of DenseBase::select() and most of the time this is the only way it is used.
  *
  * \sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const
  */
-
-namespace internal {
 template <typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
-struct traits<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> > : traits<ThenMatrixType> {
-  typedef typename traits<ThenMatrixType>::Scalar Scalar;
-  typedef Dense StorageKind;
-  typedef typename traits<ThenMatrixType>::XprKind XprKind;
-  typedef typename ConditionMatrixType::Nested ConditionMatrixNested;
-  typedef typename ThenMatrixType::Nested ThenMatrixNested;
-  typedef typename ElseMatrixType::Nested ElseMatrixNested;
-  enum {
-    RowsAtCompileTime = ConditionMatrixType::RowsAtCompileTime,
-    ColsAtCompileTime = ConditionMatrixType::ColsAtCompileTime,
-    MaxRowsAtCompileTime = ConditionMatrixType::MaxRowsAtCompileTime,
-    MaxColsAtCompileTime = ConditionMatrixType::MaxColsAtCompileTime,
-    Flags = (unsigned int)ThenMatrixType::Flags & ElseMatrixType::Flags & RowMajorBit
-  };
-};
-}  // namespace internal
-
-template <typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
-class Select : public internal::dense_xpr_base<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >::type,
-               internal::no_assignment_operator {
- public:
-  typedef typename internal::dense_xpr_base<Select>::type Base;
-  EIGEN_DENSE_PUBLIC_INTERFACE(Select)
-
-  inline EIGEN_DEVICE_FUNC Select(const ConditionMatrixType& a_conditionMatrix, const ThenMatrixType& a_thenMatrix,
-                                  const ElseMatrixType& a_elseMatrix)
-      : m_condition(a_conditionMatrix), m_then(a_thenMatrix), m_else(a_elseMatrix) {
-    eigen_assert(m_condition.rows() == m_then.rows() && m_condition.rows() == m_else.rows());
-    eigen_assert(m_condition.cols() == m_then.cols() && m_condition.cols() == m_else.cols());
-  }
-
-  inline EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_condition.rows(); }
-  inline EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_condition.cols(); }
-
-  inline EIGEN_DEVICE_FUNC const Scalar coeff(Index i, Index j) const {
-    if (m_condition.coeff(i, j))
-      return m_then.coeff(i, j);
-    else
-      return m_else.coeff(i, j);
-  }
-
-  inline EIGEN_DEVICE_FUNC const Scalar coeff(Index i) const {
-    if (m_condition.coeff(i))
-      return m_then.coeff(i);
-    else
-      return m_else.coeff(i);
-  }
-
-  inline EIGEN_DEVICE_FUNC const ConditionMatrixType& conditionMatrix() const { return m_condition; }
-
-  inline EIGEN_DEVICE_FUNC const ThenMatrixType& thenMatrix() const { return m_then; }
-
-  inline EIGEN_DEVICE_FUNC const ElseMatrixType& elseMatrix() const { return m_else; }
-
- protected:
-  typename ConditionMatrixType::Nested m_condition;
-  typename ThenMatrixType::Nested m_then;
-  typename ElseMatrixType::Nested m_else;
-};
+using Select = CwiseTernaryOp<internal::scalar_boolean_select_op<typename DenseBase<ThenMatrixType>::Scalar,
+                                                                 typename DenseBase<ElseMatrixType>::Scalar,
+                                                                 typename DenseBase<ConditionMatrixType>::Scalar>,
+                              ThenMatrixType, ElseMatrixType, ConditionMatrixType>;
 
 /** \returns a matrix where each coefficient (i,j) is equal to \a thenMatrix(i,j)
  * if \c *this(i,j) != Scalar(0), and \a elseMatrix(i,j) otherwise.
@@ -98,7 +41,7 @@ class Select : public internal::dense_xpr_base<Select<ConditionMatrixType, ThenM
  * Example: \include MatrixBase_select.cpp
  * Output: \verbinclude MatrixBase_select.out
  *
- * \sa DenseBase::bitwiseSelect(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&)
+ * \sa typedef Select
  */
 template <typename Derived>
 template <typename ThenDerived, typename ElseDerived>
@@ -107,15 +50,12 @@ inline EIGEN_DEVICE_FUNC CwiseTernaryOp<
                                        typename DenseBase<Derived>::Scalar>,
     ThenDerived, ElseDerived, Derived>
 DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix, const DenseBase<ElseDerived>& elseMatrix) const {
-  using Op = internal::scalar_boolean_select_op<typename DenseBase<ThenDerived>::Scalar,
-                                                typename DenseBase<ElseDerived>::Scalar, Scalar>;
-  return CwiseTernaryOp<Op, ThenDerived, ElseDerived, Derived>(thenMatrix.derived(), elseMatrix.derived(), derived(),
-                                                               Op());
+  return Select<Derived, ThenDerived, ElseDerived>(thenMatrix.derived(), elseMatrix.derived(), derived());
 }
 /** Version of DenseBase::select(const DenseBase&, const DenseBase&) with
  * the \em else expression being a scalar value.
  *
- * \sa DenseBase::booleanSelect(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
+ * \sa typedef Select
  */
 template <typename Derived>
 template <typename ThenDerived>
@@ -126,15 +66,13 @@ inline EIGEN_DEVICE_FUNC CwiseTernaryOp<
 DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,
                            const typename DenseBase<ThenDerived>::Scalar& elseScalar) const {
   using ElseConstantType = typename DenseBase<ThenDerived>::ConstantReturnType;
-  using Op = internal::scalar_boolean_select_op<typename DenseBase<ThenDerived>::Scalar,
-                                                typename DenseBase<ThenDerived>::Scalar, Scalar>;
-  return CwiseTernaryOp<Op, ThenDerived, ElseConstantType, Derived>(
-      thenMatrix.derived(), ElseConstantType(rows(), cols(), elseScalar), derived(), Op());
+  return Select<Derived, ThenDerived, ElseConstantType>(thenMatrix.derived(),
+                                                        ElseConstantType(rows(), cols(), elseScalar), derived());
 }
 /** Version of DenseBase::select(const DenseBase&, const DenseBase&) with
  * the \em then expression being a scalar value.
  *
- * \sa DenseBase::booleanSelect(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
+ * \sa typedef Select
  */
 template <typename Derived>
 template <typename ElseDerived>
@@ -145,10 +83,8 @@ inline EIGEN_DEVICE_FUNC CwiseTernaryOp<
 DenseBase<Derived>::select(const typename DenseBase<ElseDerived>::Scalar& thenScalar,
                            const DenseBase<ElseDerived>& elseMatrix) const {
   using ThenConstantType = typename DenseBase<ElseDerived>::ConstantReturnType;
-  using Op = internal::scalar_boolean_select_op<typename DenseBase<ElseDerived>::Scalar,
-                                                typename DenseBase<ElseDerived>::Scalar, Scalar>;
-  return CwiseTernaryOp<Op, ThenConstantType, ElseDerived, Derived>(ThenConstantType(rows(), cols(), thenScalar),
-                                                                    elseMatrix.derived(), derived(), Op());
+  return Select<Derived, ThenConstantType, ElseDerived>(ThenConstantType(rows(), cols(), thenScalar),
+                                                        elseMatrix.derived(), derived());
 }
 
 }  // end namespace Eigen

Eigen/src/Core/SelfAdjointView.h

@@ -73,10 +73,10 @@ class SelfAdjointView : public TriangularBase<SelfAdjointView<MatrixType_, UpLo>
 
   EIGEN_DEVICE_FUNC explicit inline SelfAdjointView(MatrixType& matrix) : m_matrix(matrix) {}
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const EIGEN_NOEXCEPT { return m_matrix.outerStride(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const EIGEN_NOEXCEPT { return m_matrix.innerStride(); }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_matrix.rows(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_matrix.cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return m_matrix.outerStride(); }
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return m_matrix.innerStride(); }
 
   /** \sa MatrixBase::coeff()
    * \warning the coordinates must fit into the referenced triangular part

Eigen/src/Core/SelfCwiseBinaryOp.h

@@ -15,33 +15,33 @@
 
 namespace Eigen {
 
-// TODO generalize the scalar type of 'other'
-
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator*=(const Scalar& other) {
-  internal::call_assignment(this->derived(), PlainObject::Constant(rows(), cols(), other),
-                            internal::mul_assign_op<Scalar, Scalar>());
+  using ConstantExpr = typename internal::plain_constant_type<Derived, Scalar>::type;
+  using Op = internal::mul_assign_op<Scalar>;
+  internal::call_assignment(derived(), ConstantExpr(rows(), cols(), other), Op());
   return derived();
 }
 
 template <typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator+=(const Scalar& other) {
-  internal::call_assignment(this->derived(), PlainObject::Constant(rows(), cols(), other),
-                            internal::add_assign_op<Scalar, Scalar>());
-  return derived();
-}
-
-template <typename Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator-=(const Scalar& other) {
-  internal::call_assignment(this->derived(), PlainObject::Constant(rows(), cols(), other),
-                            internal::sub_assign_op<Scalar, Scalar>());
+template <bool Enable, typename>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator*=(const RealScalar& other) {
+  realView() *= other;
   return derived();
 }
 
 template <typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator/=(const Scalar& other) {
-  internal::call_assignment(this->derived(), PlainObject::Constant(rows(), cols(), other),
-                            internal::div_assign_op<Scalar, Scalar>());
+  using ConstantExpr = typename internal::plain_constant_type<Derived, Scalar>::type;
+  using Op = internal::div_assign_op<Scalar>;
+  internal::call_assignment(derived(), ConstantExpr(rows(), cols(), other), Op());
+  return derived();
+}
+
+template <typename Derived>
+template <bool Enable, typename>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator/=(const RealScalar& other) {
+  realView() /= other;
   return derived();
 }
 

Eigen/src/Core/SkewSymmetricMatrix3.h

@@ -66,7 +66,7 @@ class SkewSymmetricBase : public EigenBase<Derived> {
   EIGEN_DEVICE_FUNC DenseMatrixType toDenseMatrix() const { return derived(); }
 
   /** Determinant vanishes */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Scalar determinant() const { return 0; }
+  EIGEN_DEVICE_FUNC constexpr Scalar determinant() const { return 0; }
 
   /** A.transpose() = -A */
   EIGEN_DEVICE_FUNC PlainObject transpose() const { return (-vector()).asSkewSymmetric(); }
@@ -91,9 +91,9 @@ class SkewSymmetricBase : public EigenBase<Derived> {
   EIGEN_DEVICE_FUNC inline SkewSymmetricVectorType& vector() { return derived().vector(); }
 
   /** \returns the number of rows. */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const { return 3; }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const { return 3; }
   /** \returns the number of columns. */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const { return 3; }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const { return 3; }
 
   /** \returns the matrix product of \c *this by the dense matrix, \a matrix */
   template <typename MatrixDerived>
@@ -321,7 +321,7 @@ bool MatrixBase<Derived>::isSkewSymmetric(const RealScalar& prec) const {
   return (this->transpose() + *this).isZero(prec);
 }
 
-/** \returns the matrix product of \c *this by the skew symmetric matrix \skew.
+/** \returns the matrix product of \c *this by the skew symmetric matrix \a skew.
  */
 template <typename Derived>
 template <typename SkewDerived>

Eigen/src/Core/Solve.h

@@ -66,8 +66,8 @@ class Solve : public SolveImpl<Decomposition, RhsType, typename internal::traits
 
   Solve(const Decomposition &dec, const RhsType &rhs) : m_dec(dec), m_rhs(rhs) {}
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_dec.cols(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_dec.cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_rhs.cols(); }
 
   EIGEN_DEVICE_FUNC const Decomposition &dec() const { return m_dec; }
   EIGEN_DEVICE_FUNC const RhsType &rhs() const { return m_rhs; }

Eigen/src/Core/SolveTriangular.h

@@ -216,8 +216,8 @@ struct triangular_solve_retval : public ReturnByValue<triangular_solve_retval<Si
 
   triangular_solve_retval(const TriangularType& tri, const Rhs& rhs) : m_triangularMatrix(tri), m_rhs(rhs) {}
 
-  inline EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_rhs.rows(); }
-  inline EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }
+  constexpr Index rows() const noexcept { return m_rhs.rows(); }
+  constexpr Index cols() const noexcept { return m_rhs.cols(); }
 
   template <typename Dest>
   inline void evalTo(Dest& dst) const {

Eigen/src/Core/SolverBase.h

@@ -78,6 +78,14 @@ class SolverBase : public EigenBase<Derived> {
   template <typename Derived_>
   friend struct internal::solve_assertion;
 
+  ComputationInfo info() const {
+    // CRTP static dispatch: Calls the 'info()' method on the derived class.
+    // Derived must implement 'ComputationInfo info() const'.
+    // If not implemented, name lookup falls back to this base method, causing
+    // infinite recursion (detectable by -Winfinite-recursion).
+    return derived().info();
+  }
+
   enum {
     RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
     ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,

Eigen/src/Core/StlIterators.h

@@ -36,11 +36,11 @@ class indexed_based_stl_iterator_base {
   typedef Index difference_type;
   typedef std::random_access_iterator_tag iterator_category;
 
-  indexed_based_stl_iterator_base() EIGEN_NO_THROW : mp_xpr(0), m_index(0) {}
-  indexed_based_stl_iterator_base(XprType& xpr, Index index) EIGEN_NO_THROW : mp_xpr(&xpr), m_index(index) {}
+  indexed_based_stl_iterator_base() noexcept : mp_xpr(0), m_index(0) {}
+  indexed_based_stl_iterator_base(XprType& xpr, Index index) noexcept : mp_xpr(&xpr), m_index(index) {}
 
-  indexed_based_stl_iterator_base(const non_const_iterator& other) EIGEN_NO_THROW : mp_xpr(other.mp_xpr),
-                                                                                    m_index(other.m_index) {}
+  indexed_based_stl_iterator_base(const non_const_iterator& other) noexcept
+      : mp_xpr(other.mp_xpr), m_index(other.m_index) {}
 
   indexed_based_stl_iterator_base& operator=(const non_const_iterator& other) {
     mp_xpr = other.mp_xpr;
@@ -325,7 +325,7 @@ class pointer_based_stl_iterator {
  public:
   typedef Index difference_type;
   typedef typename XprType::Scalar value_type;
-#if __cplusplus >= 202002L
+#if EIGEN_COMP_CXXVER >= 20 && defined(__cpp_lib_concepts) && __cpp_lib_concepts >= 202002L
   typedef std::conditional_t<XprType::InnerStrideAtCompileTime == 1, std::contiguous_iterator_tag,
                              std::random_access_iterator_tag>
       iterator_category;
@@ -335,15 +335,14 @@ class pointer_based_stl_iterator {
   typedef std::conditional_t<bool(is_lvalue), value_type*, const value_type*> pointer;
   typedef std::conditional_t<bool(is_lvalue), value_type&, const value_type&> reference;
 
-  pointer_based_stl_iterator() EIGEN_NO_THROW : m_ptr(0) {}
-  pointer_based_stl_iterator(XprType& xpr, Index index) EIGEN_NO_THROW : m_incr(xpr.innerStride()) {
+  pointer_based_stl_iterator() noexcept : m_ptr(0) {}
+  pointer_based_stl_iterator(XprType& xpr, Index index) noexcept : m_incr(xpr.innerStride()) {
     m_ptr = xpr.data() + index * m_incr.value();
   }
 
-  pointer_based_stl_iterator(const non_const_iterator& other) EIGEN_NO_THROW : m_ptr(other.m_ptr),
-                                                                               m_incr(other.m_incr) {}
+  pointer_based_stl_iterator(const non_const_iterator& other) noexcept : m_ptr(other.m_ptr), m_incr(other.m_incr) {}
 
-  pointer_based_stl_iterator& operator=(const non_const_iterator& other) EIGEN_NO_THROW {
+  pointer_based_stl_iterator& operator=(const non_const_iterator& other) noexcept {
     m_ptr = other.m_ptr;
     m_incr.setValue(other.m_incr);
     return *this;

Eigen/src/Core/Stride.h

@@ -78,9 +78,9 @@ class Stride {
   }
 
   /** \returns the outer stride */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outer() const { return m_outer.value(); }
+  EIGEN_DEVICE_FUNC constexpr Index outer() const { return m_outer.value(); }
   /** \returns the inner stride */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index inner() const { return m_inner.value(); }
+  EIGEN_DEVICE_FUNC constexpr Index inner() const { return m_inner.value(); }
 
  protected:
   internal::variable_if_dynamic<Index, OuterStrideAtCompileTime> m_outer;

Eigen/src/Core/Swap.h

@@ -65,6 +65,31 @@ class generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT,
     Index col = Base::colIndexByOuterInner(outer, inner);
     assignPacket<StoreMode, LoadMode, PacketType>(row, col);
   }
+
+  template <int StoreMode, int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE void assignPacketSegment(Index row, Index col, Index begin, Index count) {
+    PacketType tmp = m_src.template packetSegment<LoadMode, PacketType>(row, col, begin, count);
+    const_cast<SrcEvaluatorTypeT &>(m_src).template writePacketSegment<LoadMode>(
+        row, col, m_dst.template packetSegment<StoreMode, PacketType>(row, col, begin, count), begin, count);
+    m_dst.template writePacketSegment<StoreMode>(row, col, tmp, begin, count);
+  }
+
+  template <int StoreMode, int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE void assignPacketSegment(Index index, Index begin, Index count) {
+    PacketType tmp = m_src.template packetSegment<LoadMode, PacketType>(index, begin, count);
+    const_cast<SrcEvaluatorTypeT &>(m_src).template writePacketSegment<LoadMode>(
+        index, m_dst.template packetSegment<StoreMode, PacketType>(index, begin, count), begin, count);
+    m_dst.template writePacketSegment<StoreMode>(index, tmp, begin, count);
+  }
+
+  // TODO find a simple way not to have to copy/paste this function from generic_dense_assignment_kernel, by simple I
+  // mean no CRTP (Gael)
+  template <int StoreMode, int LoadMode, typename PacketType>
+  EIGEN_STRONG_INLINE void assignPacketSegmentByOuterInner(Index outer, Index inner, Index begin, Index count) {
+    Index row = Base::rowIndexByOuterInner(outer, inner);
+    Index col = Base::colIndexByOuterInner(outer, inner);
+    assignPacketSegment<StoreMode, LoadMode, PacketType>(row, col, begin, count);
+  }
 };
 
 }  // namespace internal

Eigen/src/Core/Transpose.h

@@ -65,8 +65,8 @@ class Transpose : public TransposeImpl<MatrixType, typename internal::traits<Mat
 
   EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Transpose)
 
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index rows() const noexcept { return m_matrix.cols(); }
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index cols() const noexcept { return m_matrix.rows(); }
 
   /** \returns the nested expression */
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const internal::remove_all_t<MatrixTypeNested>& nestedExpression() const {

Eigen/src/Core/Transpositions.h

@@ -293,9 +293,9 @@ class Transpose<TranspositionsBase<TranspositionsDerived> > {
  public:
   explicit Transpose(const TranspositionType& t) : m_transpositions(t) {}
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index size() const EIGEN_NOEXCEPT { return m_transpositions.size(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_transpositions.size(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_transpositions.size(); }
+  EIGEN_DEVICE_FUNC constexpr Index size() const noexcept { return m_transpositions.size(); }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_transpositions.size(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_transpositions.size(); }
 
   /** \returns the \a matrix with the inverse transpositions applied to the columns.
    */

Eigen/src/Core/TriangularMatrix.h

@@ -58,10 +58,10 @@ class TriangularBase : public EigenBase<Derived> {
     eigen_assert(!((int(Mode) & int(UnitDiag)) && (int(Mode) & int(ZeroDiag))));
   }
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return derived().rows(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return derived().cols(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index outerStride() const EIGEN_NOEXCEPT { return derived().outerStride(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index innerStride() const EIGEN_NOEXCEPT { return derived().innerStride(); }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return derived().rows(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return derived().cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index outerStride() const noexcept { return derived().outerStride(); }
+  EIGEN_DEVICE_FUNC constexpr Index innerStride() const noexcept { return derived().innerStride(); }
 
   // dummy resize function
   EIGEN_DEVICE_FUNC void resize(Index rows, Index cols) {
@@ -194,9 +194,9 @@ class TriangularView
   EIGEN_INHERIT_ASSIGNMENT_OPERATORS(TriangularView)
 
   /** \copydoc EigenBase::rows() */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_matrix.rows(); }
   /** \copydoc EigenBase::cols() */
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_matrix.cols(); }
 
   /** \returns a const reference to the nested expression */
   EIGEN_DEVICE_FUNC const NestedExpression& nestedExpression() const { return m_matrix; }

Eigen/src/Core/VectorwiseOp.h

@@ -36,6 +36,7 @@ template <typename MatrixType, typename MemberOp, int Direction>
 class PartialReduxExpr;
 
 namespace internal {
+
 template <typename MatrixType, typename MemberOp, int Direction>
 struct traits<PartialReduxExpr<MatrixType, MemberOp, Direction> > : traits<MatrixType> {
   typedef typename MemberOp::result_type Scalar;
@@ -63,12 +64,8 @@ class PartialReduxExpr : public internal::dense_xpr_base<PartialReduxExpr<Matrix
   EIGEN_DEVICE_FUNC explicit PartialReduxExpr(const MatrixType& mat, const MemberOp& func = MemberOp())
       : m_matrix(mat), m_functor(func) {}
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT {
-    return (Direction == Vertical ? 1 : m_matrix.rows());
-  }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT {
-    return (Direction == Horizontal ? 1 : m_matrix.cols());
-  }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return (Direction == Vertical ? 1 : m_matrix.rows()); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return (Direction == Horizontal ? 1 : m_matrix.cols()); }
 
   EIGEN_DEVICE_FUNC typename MatrixType::Nested nestedExpression() const { return m_matrix; }
 
@@ -149,6 +146,22 @@ struct member_redux {
   const BinaryOp& binaryFunc() const { return m_functor; }
   const BinaryOp m_functor;
 };
+
+template <typename Scalar>
+struct scalar_replace_zero_with_one_op {
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const Scalar& x) const {
+    return numext::is_exactly_zero(x) ? Scalar(1) : x;
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
+    return pselect(pcmp_eq(x, pzero(x)), pset1<Packet>(Scalar(1)), x);
+  }
+};
+template <typename Scalar>
+struct functor_traits<scalar_replace_zero_with_one_op<Scalar>> {
+  enum { Cost = 1, PacketAccess = packet_traits<Scalar>::HasCmp };
+};
+
 }  // namespace internal
 
 /** \class VectorwiseOp
@@ -193,9 +206,7 @@ class VectorwiseOp {
  public:
   typedef typename ExpressionType::Scalar Scalar;
   typedef typename ExpressionType::RealScalar RealScalar;
-  typedef Eigen::Index Index;  ///< \deprecated since Eigen 3.3
-  typedef typename internal::ref_selector<ExpressionType>::non_const_type ExpressionTypeNested;
-  typedef internal::remove_all_t<ExpressionTypeNested> ExpressionTypeNestedCleaned;
+  typedef internal::remove_all_t<ExpressionType> ExpressionTypeCleaned;
 
   template <template <typename OutScalar, typename InputScalar> class Functor, typename ReturnScalar = Scalar>
   struct ReturnType {
@@ -334,7 +345,7 @@ class VectorwiseOp {
 
   typedef typename ReturnType<internal::member_minCoeff>::Type MinCoeffReturnType;
   typedef typename ReturnType<internal::member_maxCoeff>::Type MaxCoeffReturnType;
-  typedef PartialReduxExpr<const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const ExpressionTypeNestedCleaned>,
+  typedef PartialReduxExpr<const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const ExpressionTypeCleaned>,
                            internal::member_sum<RealScalar, RealScalar>, Direction>
       SquaredNormReturnType;
   typedef CwiseUnaryOp<internal::scalar_sqrt_op<RealScalar>, const SquaredNormReturnType> NormReturnType;
@@ -585,7 +596,7 @@ class VectorwiseOp {
   /** Returns the expression of the sum of the vector \a other to each subvector of \c *this */
   template <typename OtherDerived>
   EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
-      CwiseBinaryOp<internal::scalar_sum_op<Scalar, typename OtherDerived::Scalar>, const ExpressionTypeNestedCleaned,
+      CwiseBinaryOp<internal::scalar_sum_op<Scalar, typename OtherDerived::Scalar>, const ExpressionTypeCleaned,
                     const typename ExtendedType<OtherDerived>::Type>
       operator+(const DenseBase<OtherDerived>& other) const {
     EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
@@ -596,7 +607,7 @@ class VectorwiseOp {
   /** Returns the expression of the difference between each subvector of \c *this and the vector \a other */
   template <typename OtherDerived>
   EIGEN_DEVICE_FUNC CwiseBinaryOp<internal::scalar_difference_op<Scalar, typename OtherDerived::Scalar>,
-                                  const ExpressionTypeNestedCleaned, const typename ExtendedType<OtherDerived>::Type>
+                                  const ExpressionTypeCleaned, const typename ExtendedType<OtherDerived>::Type>
   operator-(const DenseBase<OtherDerived>& other) const {
     EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
     EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
@@ -606,10 +617,9 @@ class VectorwiseOp {
   /** Returns the expression where each subvector is the product of the vector \a other
    * by the corresponding subvector of \c *this */
   template <typename OtherDerived>
-  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
-      CwiseBinaryOp<internal::scalar_product_op<Scalar>, const ExpressionTypeNestedCleaned,
-                    const typename ExtendedType<OtherDerived>::Type> EIGEN_DEVICE_FUNC
-      operator*(const DenseBase<OtherDerived>& other) const {
+  EIGEN_DEVICE_FUNC CwiseBinaryOp<internal::scalar_product_op<Scalar, typename OtherDerived::Scalar>,
+                                  const ExpressionTypeCleaned, const typename ExtendedType<OtherDerived>::Type>
+  operator*(const DenseBase<OtherDerived>& other) const {
     EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
     EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
     EIGEN_STATIC_ASSERT_SAME_XPR_KIND(ExpressionType, OtherDerived)
@@ -619,8 +629,8 @@ class VectorwiseOp {
   /** Returns the expression where each subvector is the quotient of the corresponding
    * subvector of \c *this by the vector \a other */
   template <typename OtherDerived>
-  EIGEN_DEVICE_FUNC CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const ExpressionTypeNestedCleaned,
-                                  const typename ExtendedType<OtherDerived>::Type>
+  EIGEN_DEVICE_FUNC CwiseBinaryOp<internal::scalar_quotient_op<Scalar, typename OtherDerived::Scalar>,
+                                  const ExpressionTypeCleaned, const typename ExtendedType<OtherDerived>::Type>
   operator/(const DenseBase<OtherDerived>& other) const {
     EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
     EIGEN_STATIC_ASSERT_ARRAYXPR(ExpressionType)
@@ -628,18 +638,28 @@ class VectorwiseOp {
     return m_matrix / extendedTo(other.derived());
   }
 
+  using Normalized_NonzeroNormType =
+      CwiseUnaryOp<internal::scalar_replace_zero_with_one_op<Scalar>, const NormReturnType>;
+  using NormalizedReturnType = CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const ExpressionTypeCleaned,
+                                             const typename OppositeExtendedType<Normalized_NonzeroNormType>::Type>;
+
   /** \returns an expression where each column (or row) of the referenced matrix are normalized.
    * The referenced matrix is \b not modified.
+   *
+   * \warning If the input columns (or rows) are too small (i.e., their norm equals to 0), they remain unchanged in the
+   *          resulting expression.
+   *
    * \sa MatrixBase::normalized(), normalize()
    */
-  EIGEN_DEVICE_FUNC CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const ExpressionTypeNestedCleaned,
-                                  const typename OppositeExtendedType<NormReturnType>::Type>
-  normalized() const {
-    return m_matrix.cwiseQuotient(extendedToOpposite(this->norm()));
+  EIGEN_DEVICE_FUNC NormalizedReturnType normalized() const {
+    return m_matrix.cwiseQuotient(extendedToOpposite(Normalized_NonzeroNormType(this->norm())));
   }
 
   /** Normalize in-place each row or columns of the referenced matrix.
-   * \sa MatrixBase::normalize(), normalized()
+   *
+   * \warning If the input columns (or rows) are too small (i.e., their norm equals to 0), they are left unchanged.
+   *
+   * \sa MatrixBase::normalized(), normalize()
    */
   EIGEN_DEVICE_FUNC void normalize() { m_matrix = this->normalized(); }
 
@@ -683,7 +703,7 @@ class VectorwiseOp {
 
  protected:
   EIGEN_DEVICE_FUNC Index redux_length() const { return Direction == Vertical ? m_matrix.rows() : m_matrix.cols(); }
-  ExpressionTypeNested m_matrix;
+  ExpressionType& m_matrix;
 };
 
 // const colwise moved to DenseBase.h due to CUDA compiler bug

Eigen/src/Core/Visitor.h

@@ -25,14 +25,12 @@ struct visitor_impl;
 template <typename Visitor, bool ShortCircuitEvaluation = false>
 struct short_circuit_eval_impl {
   // if short circuit evaluation is not used, do nothing
-  static EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool run(const Visitor&) { return false; }
+  static constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool run(const Visitor&) { return false; }
 };
 template <typename Visitor>
 struct short_circuit_eval_impl<Visitor, true> {
   // if short circuit evaluation is used, check the visitor
-  static EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool run(const Visitor& visitor) {
-    return visitor.done();
-  }
+  static constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool run(const Visitor& visitor) { return visitor.done(); }
 };
 
 // unrolled inner-outer traversal
@@ -296,9 +294,9 @@ class visitor_evaluator {
 
   EIGEN_DEVICE_FUNC explicit visitor_evaluator(const XprType& xpr) : m_evaluator(xpr), m_xpr(xpr) {}
 
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_xpr.rows(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_xpr.cols(); }
-  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index size() const EIGEN_NOEXCEPT { return m_xpr.size(); }
+  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_xpr.rows(); }
+  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_xpr.cols(); }
+  EIGEN_DEVICE_FUNC constexpr Index size() const noexcept { return m_xpr.size(); }
   // outer-inner access
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
     return m_evaluator.coeff(row, col);
@@ -386,173 +384,6 @@ EIGEN_DEVICE_FUNC void DenseBase<Derived>::visit(Visitor& visitor) const {
 
 namespace internal {
 
-/** \internal
- * \brief Base class to implement min and max visitors
- */
-template <typename Derived>
-struct coeff_visitor {
-  // default initialization to avoid countless invalid maybe-uninitialized warnings by gcc
-  EIGEN_DEVICE_FUNC coeff_visitor() : row(-1), col(-1), res(0) {}
-  typedef typename Derived::Scalar Scalar;
-  Index row, col;
-  Scalar res;
-  EIGEN_DEVICE_FUNC inline void init(const Scalar& value, Index i, Index j) {
-    res = value;
-    row = i;
-    col = j;
-  }
-};
-
-template <typename Scalar, int NaNPropagation, bool is_min = true>
-struct minmax_compare {
-  typedef typename packet_traits<Scalar>::type Packet;
-  static EIGEN_DEVICE_FUNC inline bool compare(Scalar a, Scalar b) { return a < b; }
-  static EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& p) { return predux_min<NaNPropagation>(p); }
-};
-
-template <typename Scalar, int NaNPropagation>
-struct minmax_compare<Scalar, NaNPropagation, false> {
-  typedef typename packet_traits<Scalar>::type Packet;
-  static EIGEN_DEVICE_FUNC inline bool compare(Scalar a, Scalar b) { return a > b; }
-  static EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& p) { return predux_max<NaNPropagation>(p); }
-};
-
-// Default implementation used by non-floating types, where we do not
-// need special logic for NaN handling.
-template <typename Derived, bool is_min, int NaNPropagation,
-          bool isInt = NumTraits<typename Derived::Scalar>::IsInteger>
-struct minmax_coeff_visitor : coeff_visitor<Derived> {
-  using Scalar = typename Derived::Scalar;
-  using Packet = typename packet_traits<Scalar>::type;
-  using Comparator = minmax_compare<Scalar, NaNPropagation, is_min>;
-  static constexpr Index PacketSize = packet_traits<Scalar>::size;
-
-  EIGEN_DEVICE_FUNC inline void operator()(const Scalar& value, Index i, Index j) {
-    if (Comparator::compare(value, this->res)) {
-      this->res = value;
-      this->row = i;
-      this->col = j;
-    }
-  }
-  EIGEN_DEVICE_FUNC inline void packet(const Packet& p, Index i, Index j) {
-    Scalar value = Comparator::predux(p);
-    if (Comparator::compare(value, this->res)) {
-      const Packet range = preverse(plset<Packet>(Scalar(1)));
-      Packet mask = pcmp_eq(pset1<Packet>(value), p);
-      Index max_idx = PacketSize - static_cast<Index>(predux_max(pand(range, mask)));
-      this->res = value;
-      this->row = Derived::IsRowMajor ? i : i + max_idx;
-      this->col = Derived::IsRowMajor ? j + max_idx : j;
-    }
-  }
-  EIGEN_DEVICE_FUNC inline void initpacket(const Packet& p, Index i, Index j) {
-    Scalar value = Comparator::predux(p);
-    const Packet range = preverse(plset<Packet>(Scalar(1)));
-    Packet mask = pcmp_eq(pset1<Packet>(value), p);
-    Index max_idx = PacketSize - static_cast<Index>(predux_max(pand(range, mask)));
-    this->res = value;
-    this->row = Derived::IsRowMajor ? i : i + max_idx;
-    this->col = Derived::IsRowMajor ? j + max_idx : j;
-  }
-};
-
-// Suppress NaN. The only case in which we return NaN is if the matrix is all NaN,
-// in which case, row=0, col=0 is returned for the location.
-template <typename Derived, bool is_min>
-struct minmax_coeff_visitor<Derived, is_min, PropagateNumbers, false> : coeff_visitor<Derived> {
-  typedef typename Derived::Scalar Scalar;
-  using Packet = typename packet_traits<Scalar>::type;
-  using Comparator = minmax_compare<Scalar, PropagateNumbers, is_min>;
-
-  EIGEN_DEVICE_FUNC inline void operator()(const Scalar& value, Index i, Index j) {
-    if ((!(numext::isnan)(value) && (numext::isnan)(this->res)) || Comparator::compare(value, this->res)) {
-      this->res = value;
-      this->row = i;
-      this->col = j;
-    }
-  }
-  EIGEN_DEVICE_FUNC inline void packet(const Packet& p, Index i, Index j) {
-    const Index PacketSize = packet_traits<Scalar>::size;
-    Scalar value = Comparator::predux(p);
-    if ((!(numext::isnan)(value) && (numext::isnan)(this->res)) || Comparator::compare(value, this->res)) {
-      const Packet range = preverse(plset<Packet>(Scalar(1)));
-      /* mask will be zero for NaNs, so they will be ignored. */
-      Packet mask = pcmp_eq(pset1<Packet>(value), p);
-      Index max_idx = PacketSize - static_cast<Index>(predux_max(pand(range, mask)));
-      this->res = value;
-      this->row = Derived::IsRowMajor ? i : i + max_idx;
-      this->col = Derived::IsRowMajor ? j + max_idx : j;
-    }
-  }
-  EIGEN_DEVICE_FUNC inline void initpacket(const Packet& p, Index i, Index j) {
-    const Index PacketSize = packet_traits<Scalar>::size;
-    Scalar value = Comparator::predux(p);
-    if ((numext::isnan)(value)) {
-      this->res = value;
-      this->row = 0;
-      this->col = 0;
-      return;
-    }
-    const Packet range = preverse(plset<Packet>(Scalar(1)));
-    /* mask will be zero for NaNs, so they will be ignored. */
-    Packet mask = pcmp_eq(pset1<Packet>(value), p);
-    Index max_idx = PacketSize - static_cast<Index>(predux_max(pand(range, mask)));
-    this->res = value;
-    this->row = Derived::IsRowMajor ? i : i + max_idx;
-    this->col = Derived::IsRowMajor ? j + max_idx : j;
-  }
-};
-
-// Propagate NaNs. If the matrix contains NaN, the location of the first NaN
-// will be returned in row and col.
-template <typename Derived, bool is_min, int NaNPropagation>
-struct minmax_coeff_visitor<Derived, is_min, NaNPropagation, false> : coeff_visitor<Derived> {
-  typedef typename Derived::Scalar Scalar;
-  using Packet = typename packet_traits<Scalar>::type;
-  using Comparator = minmax_compare<Scalar, PropagateNaN, is_min>;
-
-  EIGEN_DEVICE_FUNC inline void operator()(const Scalar& value, Index i, Index j) {
-    const bool value_is_nan = (numext::isnan)(value);
-    if ((value_is_nan && !(numext::isnan)(this->res)) || Comparator::compare(value, this->res)) {
-      this->res = value;
-      this->row = i;
-      this->col = j;
-    }
-  }
-  EIGEN_DEVICE_FUNC inline void packet(const Packet& p, Index i, Index j) {
-    const Index PacketSize = packet_traits<Scalar>::size;
-    Scalar value = Comparator::predux(p);
-    const bool value_is_nan = (numext::isnan)(value);
-    if ((value_is_nan && !(numext::isnan)(this->res)) || Comparator::compare(value, this->res)) {
-      const Packet range = preverse(plset<Packet>(Scalar(1)));
-      // If the value is NaN, pick the first position of a NaN, otherwise pick the first extremal value.
-      Packet mask = value_is_nan ? pnot(pcmp_eq(p, p)) : pcmp_eq(pset1<Packet>(value), p);
-      Index max_idx = PacketSize - static_cast<Index>(predux_max(pand(range, mask)));
-      this->res = value;
-      this->row = Derived::IsRowMajor ? i : i + max_idx;
-      this->col = Derived::IsRowMajor ? j + max_idx : j;
-    }
-  }
-  EIGEN_DEVICE_FUNC inline void initpacket(const Packet& p, Index i, Index j) {
-    const Index PacketSize = packet_traits<Scalar>::size;
-    Scalar value = Comparator::predux(p);
-    const bool value_is_nan = (numext::isnan)(value);
-    const Packet range = preverse(plset<Packet>(Scalar(1)));
-    // If the value is NaN, pick the first position of a NaN, otherwise pick the first extremal value.
-    Packet mask = value_is_nan ? pnot(pcmp_eq(p, p)) : pcmp_eq(pset1<Packet>(value), p);
-    Index max_idx = PacketSize - static_cast<Index>(predux_max(pand(range, mask)));
-    this->res = value;
-    this->row = Derived::IsRowMajor ? i : i + max_idx;
-    this->col = Derived::IsRowMajor ? j + max_idx : j;
-  }
-};
-
-template <typename Derived, bool is_min, int NaNPropagation>
-struct functor_traits<minmax_coeff_visitor<Derived, is_min, NaNPropagation>> {
-  using Scalar = typename Derived::Scalar;
-  enum { Cost = NumTraits<Scalar>::AddCost, LinearAccess = false, PacketAccess = packet_traits<Scalar>::HasCmp };
-};
-
 template <typename Scalar>
 struct all_visitor {
   using result_type = bool;
@@ -632,102 +463,19 @@ struct functor_traits<count_visitor<Scalar>> {
   };
 };
 
+template <typename Derived, bool AlwaysTrue = NumTraits<typename traits<Derived>::Scalar>::IsInteger>
+struct all_finite_impl {
+  static EIGEN_DEVICE_FUNC inline bool run(const Derived& /*derived*/) { return true; }
+};
+#if !defined(__FINITE_MATH_ONLY__) || !(__FINITE_MATH_ONLY__)
+template <typename Derived>
+struct all_finite_impl<Derived, false> {
+  static EIGEN_DEVICE_FUNC inline bool run(const Derived& derived) { return derived.array().isFiniteTyped().all(); }
+};
+#endif
+
 }  // end namespace internal
 
-/** \fn DenseBase<Derived>::minCoeff(IndexType* rowId, IndexType* colId) const
- * \returns the minimum of all coefficients of *this and puts in *row and *col its location.
- *
- * In case \c *this contains NaN, NaNPropagation determines the behavior:
- *   NaNPropagation == PropagateFast : undefined
- *   NaNPropagation == PropagateNaN : result is NaN
- *   NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
- * \warning the matrix must be not empty, otherwise an assertion is triggered.
- *
- * \sa DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visit(), DenseBase::minCoeff()
- */
-template <typename Derived>
-template <int NaNPropagation, typename IndexType>
-EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::minCoeff(IndexType* rowId,
-                                                                                          IndexType* colId) const {
-  eigen_assert(this->rows() > 0 && this->cols() > 0 && "you are using an empty matrix");
-
-  internal::minmax_coeff_visitor<Derived, true, NaNPropagation> minVisitor;
-  this->visit(minVisitor);
-  *rowId = minVisitor.row;
-  if (colId) *colId = minVisitor.col;
-  return minVisitor.res;
-}
-
-/** \returns the minimum of all coefficients of *this and puts in *index its location.
- *
- * In case \c *this contains NaN, NaNPropagation determines the behavior:
- *   NaNPropagation == PropagateFast : undefined
- *   NaNPropagation == PropagateNaN : result is NaN
- *   NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
- * \warning the matrix must be not empty, otherwise an assertion is triggered.
- *
- * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visit(),
- * DenseBase::minCoeff()
- */
-template <typename Derived>
-template <int NaNPropagation, typename IndexType>
-EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::minCoeff(IndexType* index) const {
-  eigen_assert(this->rows() > 0 && this->cols() > 0 && "you are using an empty matrix");
-  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
-
-  internal::minmax_coeff_visitor<Derived, true, NaNPropagation> minVisitor;
-  this->visit(minVisitor);
-  *index = IndexType((RowsAtCompileTime == 1) ? minVisitor.col : minVisitor.row);
-  return minVisitor.res;
-}
-
-/** \fn DenseBase<Derived>::maxCoeff(IndexType* rowId, IndexType* colId) const
- * \returns the maximum of all coefficients of *this and puts in *row and *col its location.
- *
- * In case \c *this contains NaN, NaNPropagation determines the behavior:
- *   NaNPropagation == PropagateFast : undefined
- *   NaNPropagation == PropagateNaN : result is NaN
- *   NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
- * \warning the matrix must be not empty, otherwise an assertion is triggered.
- *
- * \sa DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visit(), DenseBase::maxCoeff()
- */
-template <typename Derived>
-template <int NaNPropagation, typename IndexType>
-EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::maxCoeff(IndexType* rowPtr,
-                                                                                          IndexType* colPtr) const {
-  eigen_assert(this->rows() > 0 && this->cols() > 0 && "you are using an empty matrix");
-
-  internal::minmax_coeff_visitor<Derived, false, NaNPropagation> maxVisitor;
-  this->visit(maxVisitor);
-  *rowPtr = maxVisitor.row;
-  if (colPtr) *colPtr = maxVisitor.col;
-  return maxVisitor.res;
-}
-
-/** \returns the maximum of all coefficients of *this and puts in *index its location.
- *
- * In case \c *this contains NaN, NaNPropagation determines the behavior:
- *   NaNPropagation == PropagateFast : undefined
- *   NaNPropagation == PropagateNaN : result is NaN
- *   NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN
- * \warning the matrix must be not empty, otherwise an assertion is triggered.
- *
- * \sa DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(),
- * DenseBase::maxCoeff()
- */
-template <typename Derived>
-template <int NaNPropagation, typename IndexType>
-EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::maxCoeff(IndexType* index) const {
-  eigen_assert(this->rows() > 0 && this->cols() > 0 && "you are using an empty matrix");
-
-  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
-  internal::minmax_coeff_visitor<Derived, false, NaNPropagation> maxVisitor;
-  this->visit(maxVisitor);
-  *index = (RowsAtCompileTime == 1) ? maxVisitor.col : maxVisitor.row;
-  return maxVisitor.res;
-}
-
 /** \returns true if all coefficients are true
  *
  * Example: \include MatrixBase_all.cpp
@@ -781,7 +529,7 @@ EIGEN_DEVICE_FUNC inline bool DenseBase<Derived>::hasNaN() const {
  */
 template <typename Derived>
 EIGEN_DEVICE_FUNC inline bool DenseBase<Derived>::allFinite() const {
-  return derived().array().isFiniteTyped().all();
+  return internal::all_finite_impl<Derived>::run(derived());
 }
 
 }  // end namespace Eigen

Eigen/src/Core/arch/AVX/Complex.h

@@ -475,19 +475,11 @@ EIGEN_STRONG_INLINE Packet4cf pmsub(const Packet4cf& a, const Packet4cf& b, cons
 }
 template <>
 EIGEN_STRONG_INLINE Packet4cf pnmadd(const Packet4cf& a, const Packet4cf& b, const Packet4cf& c) {
-  __m256 a_odd = _mm256_movehdup_ps(a.v);
-  __m256 a_even = _mm256_moveldup_ps(a.v);
-  __m256 b_swap = _mm256_permute_ps(b.v, _MM_SHUFFLE(2, 3, 0, 1));
-  __m256 result = _mm256_fmaddsub_ps(a_odd, b_swap, _mm256_fmaddsub_ps(a_even, b.v, c.v));
-  return Packet4cf(result);
+  return pnegate(pmsub(a, b, c));
 }
 template <>
 EIGEN_STRONG_INLINE Packet4cf pnmsub(const Packet4cf& a, const Packet4cf& b, const Packet4cf& c) {
-  __m256 a_odd = _mm256_movehdup_ps(a.v);
-  __m256 a_even = _mm256_moveldup_ps(a.v);
-  __m256 b_swap = _mm256_permute_ps(b.v, _MM_SHUFFLE(2, 3, 0, 1));
-  __m256 result = _mm256_fmaddsub_ps(a_odd, b_swap, _mm256_fmsubadd_ps(a_even, b.v, c.v));
-  return Packet4cf(result);
+  return pnegate(pmadd(a, b, c));
 }
 // std::complex<double>
 template <>
@@ -508,21 +500,64 @@ EIGEN_STRONG_INLINE Packet2cd pmsub(const Packet2cd& a, const Packet2cd& b, cons
 }
 template <>
 EIGEN_STRONG_INLINE Packet2cd pnmadd(const Packet2cd& a, const Packet2cd& b, const Packet2cd& c) {
-  __m256d a_odd = _mm256_permute_pd(a.v, 0xF);
-  __m256d a_even = _mm256_movedup_pd(a.v);
-  __m256d b_swap = _mm256_permute_pd(b.v, 0x5);
-  __m256d result = _mm256_fmaddsub_pd(a_odd, b_swap, _mm256_fmaddsub_pd(a_even, b.v, c.v));
-  return Packet2cd(result);
+  return pnegate(pmsub(a, b, c));
 }
 template <>
 EIGEN_STRONG_INLINE Packet2cd pnmsub(const Packet2cd& a, const Packet2cd& b, const Packet2cd& c) {
-  __m256d a_odd = _mm256_permute_pd(a.v, 0xF);
-  __m256d a_even = _mm256_movedup_pd(a.v);
-  __m256d b_swap = _mm256_permute_pd(b.v, 0x5);
-  __m256d result = _mm256_fmaddsub_pd(a_odd, b_swap, _mm256_fmsubadd_pd(a_even, b.v, c.v));
-  return Packet2cd(result);
+  return pnegate(pmadd(a, b, c));
 }
 #endif
+
+/*---------------- load/store segment support ----------------*/
+
+/*---------------- std::complex<float> ----------------*/
+
+template <>
+struct has_packet_segment<Packet2cf> : std::true_type {};
+
+template <>
+struct has_packet_segment<Packet4cf> : std::true_type {};
+
+template <>
+inline Packet2cf ploaduSegment<Packet2cf>(const std::complex<float>* from, Index begin, Index count) {
+  return (Packet2cf)_mm_maskload_ps(&numext::real_ref(*from), segment_mask_2x64(begin, count));
+}
+
+template <>
+inline void pstoreuSegment<std::complex<float>, Packet2cf>(std::complex<float>* to, const Packet2cf& from, Index begin,
+                                                           Index count) {
+  _mm_maskstore_ps(&numext::real_ref(*to), segment_mask_2x64(begin, count), from.v);
+}
+
+template <>
+inline Packet4cf ploaduSegment<Packet4cf>(const std::complex<float>* from, Index begin, Index count) {
+  return (Packet4cf)_mm256_maskload_ps(&numext::real_ref(*from), segment_mask_4x64(begin, count));
+}
+
+template <>
+inline void pstoreuSegment<std::complex<float>, Packet4cf>(std::complex<float>* to, const Packet4cf& from, Index begin,
+                                                           Index count) {
+  _mm256_maskstore_ps(&numext::real_ref(*to), segment_mask_4x64(begin, count), from.v);
+}
+
+/*---------------- std::complex<double> ----------------*/
+
+template <>
+struct has_packet_segment<Packet2cd> : std::true_type {};
+
+template <>
+inline Packet2cd ploaduSegment<Packet2cd>(const std::complex<double>* from, Index begin, Index count) {
+  return (Packet2cd)_mm256_maskload_pd(&numext::real_ref(*from), segment_mask_4x64(2 * begin, 2 * count));
+}
+
+template <>
+inline void pstoreuSegment<std::complex<double>, Packet2cd>(std::complex<double>* to, const Packet2cd& from,
+                                                            Index begin, Index count) {
+  _mm256_maskstore_pd(&numext::real_ref(*to), segment_mask_4x64(2 * begin, 2 * count), from.v);
+}
+
+/*---------------- end load/store segment support ----------------*/
+
 }  // end namespace internal
 
 }  // end namespace Eigen

Eigen/src/Core/arch/AVX/MathFunctions.h

@@ -28,15 +28,13 @@ EIGEN_DOUBLE_PACKET_FUNCTION(log, Packet4d)
 EIGEN_DOUBLE_PACKET_FUNCTION(log2, Packet4d)
 EIGEN_DOUBLE_PACKET_FUNCTION(exp, Packet4d)
 EIGEN_DOUBLE_PACKET_FUNCTION(tanh, Packet4d)
+EIGEN_DOUBLE_PACKET_FUNCTION(cbrt, Packet4d)
 #ifdef EIGEN_VECTORIZE_AVX2
 EIGEN_DOUBLE_PACKET_FUNCTION(sin, Packet4d)
 EIGEN_DOUBLE_PACKET_FUNCTION(cos, Packet4d)
 #endif
-
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_UNUSED Packet4d patan<Packet4d>(const Packet4d& _x) {
-  return generic_patan(_x);
-}
+EIGEN_GENERIC_PACKET_FUNCTION(atan, Packet4d)
+EIGEN_GENERIC_PACKET_FUNCTION(exp2, Packet4d)
 
 // Notice that for newer processors, it is counterproductive to use Newton
 // iteration for square root. In particular, Skylake and Zen2 processors
@@ -99,6 +97,7 @@ EIGEN_STRONG_INLINE Packet8bf pldexp(const Packet8bf& a, const Packet8bf& expone
 
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pcos)
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pexp)
+BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pexp2)
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pexpm1)
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, plog)
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, plog1p)
@@ -108,8 +107,11 @@ BF16_PACKET_FUNCTION(Packet8f, Packet8bf, prsqrt)
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, psin)
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, psqrt)
 BF16_PACKET_FUNCTION(Packet8f, Packet8bf, ptanh)
+
+#ifndef EIGEN_VECTORIZE_AVX512FP16
 F16_PACKET_FUNCTION(Packet8f, Packet8h, pcos)
 F16_PACKET_FUNCTION(Packet8f, Packet8h, pexp)
+F16_PACKET_FUNCTION(Packet8f, Packet8h, pexp2)
 F16_PACKET_FUNCTION(Packet8f, Packet8h, pexpm1)
 F16_PACKET_FUNCTION(Packet8f, Packet8h, plog)
 F16_PACKET_FUNCTION(Packet8f, Packet8h, plog1p)
@@ -119,6 +121,7 @@ F16_PACKET_FUNCTION(Packet8f, Packet8h, prsqrt)
 F16_PACKET_FUNCTION(Packet8f, Packet8h, psin)
 F16_PACKET_FUNCTION(Packet8f, Packet8h, psqrt)
 F16_PACKET_FUNCTION(Packet8f, Packet8h, ptanh)
+#endif
 
 }  // end namespace internal
 

Eigen/src/Core/arch/AVX/PacketMath.h

@@ -118,12 +118,15 @@ struct packet_traits<float> : default_packet_traits {
     HasLog1p = 1,
     HasExpm1 = 1,
     HasExp = 1,
+    HasPow = 1,
     HasNdtri = 1,
     HasBessel = 1,
     HasSqrt = 1,
     HasRsqrt = 1,
+    HasCbrt = 1,
     HasTanh = EIGEN_FAST_MATH,
     HasErf = EIGEN_FAST_MATH,
+    HasErfc = EIGEN_FAST_MATH,
     HasBlend = 1
   };
 };
@@ -144,9 +147,13 @@ struct packet_traits<double> : default_packet_traits {
 #endif
     HasTanh = EIGEN_FAST_MATH,
     HasLog = 1,
+    HasErf = 1,
+    HasErfc = 1,
     HasExp = 1,
+    HasPow = 1,
     HasSqrt = 1,
     HasRsqrt = 1,
+    HasCbrt = 1,
     HasATan = 1,
     HasATanh = 1,
     HasBlend = 1
@@ -649,16 +656,7 @@ template <>
 EIGEN_STRONG_INLINE uint64_t pfirst<Packet4ul>(const Packet4ul& a) {
   return _mm_extract_epi64_0(_mm256_castsi256_si128(a));
 }
-template <>
-EIGEN_STRONG_INLINE int64_t predux<Packet4l>(const Packet4l& a) {
-  __m128i r = _mm_add_epi64(_mm256_castsi256_si128(a), _mm256_extractf128_si256(a, 1));
-  return _mm_extract_epi64_0(r) + _mm_extract_epi64_1(r);
-}
-template <>
-EIGEN_STRONG_INLINE uint64_t predux<Packet4ul>(const Packet4ul& a) {
-  __m128i r = _mm_add_epi64(_mm256_castsi256_si128(a), _mm256_extractf128_si256(a, 1));
-  return numext::bit_cast<uint64_t>(_mm_extract_epi64_0(r) + _mm_extract_epi64_1(r));
-}
+
 #define MM256_SHUFFLE_EPI64(A, B, M) _mm256_shuffle_pd(_mm256_castsi256_pd(A), _mm256_castsi256_pd(B), M)
 EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet4l, 4>& kernel) {
   __m256d T0 = MM256_SHUFFLE_EPI64(kernel.packet[0], kernel.packet[1], 15);
@@ -1826,10 +1824,13 @@ EIGEN_STRONG_INLINE Packet8ui pabs(const Packet8ui& a) {
   return a;
 }
 
+#ifndef EIGEN_VECTORIZE_AVX512FP16
 template <>
 EIGEN_STRONG_INLINE Packet8h psignbit(const Packet8h& a) {
   return _mm_cmpgt_epi16(_mm_setzero_si128(), a);
 }
+#endif  // EIGEN_VECTORIZE_AVX512FP16
+
 template <>
 EIGEN_STRONG_INLINE Packet8bf psignbit(const Packet8bf& a) {
   return _mm_cmpgt_epi16(_mm_setzero_si128(), a);
@@ -1922,20 +1923,19 @@ EIGEN_STRONG_INLINE Packet4d pldexp<Packet4d>(const Packet4d& a, const Packet4d&
 }
 
 template <>
-EIGEN_STRONG_INLINE float predux<Packet8f>(const Packet8f& a) {
-  return predux(Packet4f(_mm_add_ps(_mm256_castps256_ps128(a), _mm256_extractf128_ps(a, 1))));
-}
-template <>
-EIGEN_STRONG_INLINE double predux<Packet4d>(const Packet4d& a) {
-  return predux(Packet2d(_mm_add_pd(_mm256_castpd256_pd128(a), _mm256_extractf128_pd(a, 1))));
-}
-template <>
-EIGEN_STRONG_INLINE int predux<Packet8i>(const Packet8i& a) {
-  return predux(Packet4i(_mm_add_epi32(_mm256_castsi256_si128(a), _mm256_extractf128_si256(a, 1))));
-}
-template <>
-EIGEN_STRONG_INLINE uint32_t predux<Packet8ui>(const Packet8ui& a) {
-  return predux(Packet4ui(_mm_add_epi32(_mm256_castsi256_si128(a), _mm256_extractf128_si256(a, 1))));
+EIGEN_STRONG_INLINE Packet4d pldexp_fast<Packet4d>(const Packet4d& a, const Packet4d& exponent) {
+  // Clamp exponent to [-1024, 1024]
+  const Packet4d min_exponent = pset1<Packet4d>(-1023.0);
+  const Packet4d max_exponent = pset1<Packet4d>(1024.0);
+  const Packet4i e = _mm256_cvtpd_epi32(pmin(pmax(exponent, min_exponent), max_exponent));
+  const Packet4i bias = pset1<Packet4i>(1023);
+
+  // 2^e
+  Packet4i hi = vec4i_swizzle1(padd(e, bias), 0, 2, 1, 3);
+  const Packet4i lo = _mm_slli_epi64(hi, 52);
+  hi = _mm_slli_epi64(_mm_srli_epi64(hi, 32), 52);
+  const Packet4d c = _mm256_castsi256_pd(_mm256_insertf128_si256(_mm256_castsi128_si256(lo), hi, 1));
+  return pmul(a, c);  // a * 2^e
 }
 
 template <>
@@ -1951,65 +1951,6 @@ EIGEN_STRONG_INLINE Packet4ui predux_half_dowto4<Packet8ui>(const Packet8ui& a)
   return _mm_add_epi32(_mm256_castsi256_si128(a), _mm256_extractf128_si256(a, 1));
 }
 
-template <>
-EIGEN_STRONG_INLINE float predux_mul<Packet8f>(const Packet8f& a) {
-  Packet8f tmp;
-  tmp = _mm256_mul_ps(a, _mm256_permute2f128_ps(a, a, 1));
-  tmp = _mm256_mul_ps(tmp, _mm256_shuffle_ps(tmp, tmp, _MM_SHUFFLE(1, 0, 3, 2)));
-  return pfirst(_mm256_mul_ps(tmp, _mm256_shuffle_ps(tmp, tmp, 1)));
-}
-template <>
-EIGEN_STRONG_INLINE double predux_mul<Packet4d>(const Packet4d& a) {
-  Packet4d tmp;
-  tmp = _mm256_mul_pd(a, _mm256_permute2f128_pd(a, a, 1));
-  return pfirst(_mm256_mul_pd(tmp, _mm256_shuffle_pd(tmp, tmp, 1)));
-}
-
-template <>
-EIGEN_STRONG_INLINE float predux_min<Packet8f>(const Packet8f& a) {
-  Packet8f tmp = _mm256_min_ps(a, _mm256_permute2f128_ps(a, a, 1));
-  tmp = _mm256_min_ps(tmp, _mm256_shuffle_ps(tmp, tmp, _MM_SHUFFLE(1, 0, 3, 2)));
-  return pfirst(_mm256_min_ps(tmp, _mm256_shuffle_ps(tmp, tmp, 1)));
-}
-template <>
-EIGEN_STRONG_INLINE double predux_min<Packet4d>(const Packet4d& a) {
-  Packet4d tmp = _mm256_min_pd(a, _mm256_permute2f128_pd(a, a, 1));
-  return pfirst(_mm256_min_pd(tmp, _mm256_shuffle_pd(tmp, tmp, 1)));
-}
-
-template <>
-EIGEN_STRONG_INLINE float predux_max<Packet8f>(const Packet8f& a) {
-  Packet8f tmp = _mm256_max_ps(a, _mm256_permute2f128_ps(a, a, 1));
-  tmp = _mm256_max_ps(tmp, _mm256_shuffle_ps(tmp, tmp, _MM_SHUFFLE(1, 0, 3, 2)));
-  return pfirst(_mm256_max_ps(tmp, _mm256_shuffle_ps(tmp, tmp, 1)));
-}
-
-template <>
-EIGEN_STRONG_INLINE double predux_max<Packet4d>(const Packet4d& a) {
-  Packet4d tmp = _mm256_max_pd(a, _mm256_permute2f128_pd(a, a, 1));
-  return pfirst(_mm256_max_pd(tmp, _mm256_shuffle_pd(tmp, tmp, 1)));
-}
-
-// not needed yet
-// template<> EIGEN_STRONG_INLINE bool predux_all(const Packet8f& x)
-// {
-//   return _mm256_movemask_ps(x)==0xFF;
-// }
-
-template <>
-EIGEN_STRONG_INLINE bool predux_any(const Packet8f& x) {
-  return _mm256_movemask_ps(x) != 0;
-}
-
-template <>
-EIGEN_STRONG_INLINE bool predux_any(const Packet8i& x) {
-  return _mm256_movemask_ps(_mm256_castsi256_ps(x)) != 0;
-}
-template <>
-EIGEN_STRONG_INLINE bool predux_any(const Packet8ui& x) {
-  return _mm256_movemask_ps(_mm256_castsi256_ps(x)) != 0;
-}
-
 EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8f, 8>& kernel) {
   __m256 T0 = _mm256_unpacklo_ps(kernel.packet[0], kernel.packet[1]);
   __m256 T1 = _mm256_unpackhi_ps(kernel.packet[0], kernel.packet[1]);
@@ -2168,7 +2109,6 @@ struct unpacket_traits<Packet8h> {
   };
   typedef Packet8h half;
 };
-#endif
 
 template <>
 EIGEN_STRONG_INLINE Packet8h pset1<Packet8h>(const Eigen::half& from) {
@@ -2311,24 +2251,64 @@ EIGEN_STRONG_INLINE Packet8h ptrunc<Packet8h>(const Packet8h& a) {
   return float2half(ptrunc<Packet8f>(half2float(a)));
 }
 
+template <>
+EIGEN_STRONG_INLINE Packet8h pisinf<Packet8h>(const Packet8h& a) {
+  constexpr uint16_t kInf = ((1 << 5) - 1) << 10;
+  constexpr uint16_t kAbsMask = (1 << 15) - 1;
+  return _mm_cmpeq_epi16(_mm_and_si128(a.m_val, _mm_set1_epi16(kAbsMask)), _mm_set1_epi16(kInf));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pisnan<Packet8h>(const Packet8h& a) {
+  constexpr uint16_t kInf = ((1 << 5) - 1) << 10;
+  constexpr uint16_t kAbsMask = (1 << 15) - 1;
+  return _mm_cmpgt_epi16(_mm_and_si128(a.m_val, _mm_set1_epi16(kAbsMask)), _mm_set1_epi16(kInf));
+}
+
+// convert the sign-magnitude representation to two's complement
+EIGEN_STRONG_INLINE __m128i pmaptosigned(const __m128i& a) {
+  constexpr uint16_t kAbsMask = (1 << 15) - 1;
+  // if 'a' has the sign bit set, clear the sign bit and negate the result as if it were an integer
+  return _mm_sign_epi16(_mm_and_si128(a, _mm_set1_epi16(kAbsMask)), a);
+}
+
+// return true if both `a` and `b` are not NaN
+EIGEN_STRONG_INLINE Packet8h pisordered(const Packet8h& a, const Packet8h& b) {
+  constexpr uint16_t kInf = ((1 << 5) - 1) << 10;
+  constexpr uint16_t kAbsMask = (1 << 15) - 1;
+  __m128i abs_a = _mm_and_si128(a.m_val, _mm_set1_epi16(kAbsMask));
+  __m128i abs_b = _mm_and_si128(b.m_val, _mm_set1_epi16(kAbsMask));
+  // check if both `abs_a <= kInf` and `abs_b <= kInf` by checking if max(abs_a, abs_b) <= kInf
+  // SSE has no `lesser or equal` instruction for integers, but comparing against kInf + 1 accomplishes the same goal
+  return _mm_cmplt_epi16(_mm_max_epu16(abs_a, abs_b), _mm_set1_epi16(kInf + 1));
+}
+
 template <>
 EIGEN_STRONG_INLINE Packet8h pcmp_eq(const Packet8h& a, const Packet8h& b) {
-  return Pack16To8(pcmp_eq(half2float(a), half2float(b)));
+  __m128i isOrdered = pisordered(a, b);
+  __m128i isEqual = _mm_cmpeq_epi16(pmaptosigned(a.m_val), pmaptosigned(b.m_val));
+  return _mm_and_si128(isOrdered, isEqual);
 }
 
 template <>
 EIGEN_STRONG_INLINE Packet8h pcmp_le(const Packet8h& a, const Packet8h& b) {
-  return Pack16To8(pcmp_le(half2float(a), half2float(b)));
+  __m128i isOrdered = pisordered(a, b);
+  __m128i isGreater = _mm_cmpgt_epi16(pmaptosigned(a.m_val), pmaptosigned(b.m_val));
+  return _mm_andnot_si128(isGreater, isOrdered);
 }
 
 template <>
 EIGEN_STRONG_INLINE Packet8h pcmp_lt(const Packet8h& a, const Packet8h& b) {
-  return Pack16To8(pcmp_lt(half2float(a), half2float(b)));
+  __m128i isOrdered = pisordered(a, b);
+  __m128i isLess = _mm_cmplt_epi16(pmaptosigned(a.m_val), pmaptosigned(b.m_val));
+  return _mm_and_si128(isOrdered, isLess);
 }
 
 template <>
 EIGEN_STRONG_INLINE Packet8h pcmp_lt_or_nan(const Packet8h& a, const Packet8h& b) {
-  return Pack16To8(pcmp_lt_or_nan(half2float(a), half2float(b)));
+  __m128i isUnordered = por(pisnan(a), pisnan(b));
+  __m128i isLess = _mm_cmplt_epi16(pmaptosigned(a.m_val), pmaptosigned(b.m_val));
+  return _mm_or_si128(isUnordered, isLess);
 }
 
 template <>
@@ -2367,6 +2347,26 @@ EIGEN_STRONG_INLINE Packet8h pmul<Packet8h>(const Packet8h& a, const Packet8h& b
   return float2half(rf);
 }
 
+template <>
+EIGEN_STRONG_INLINE Packet8h pmadd<Packet8h>(const Packet8h& a, const Packet8h& b, const Packet8h& c) {
+  return float2half(pmadd(half2float(a), half2float(b), half2float(c)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pmsub<Packet8h>(const Packet8h& a, const Packet8h& b, const Packet8h& c) {
+  return float2half(pmsub(half2float(a), half2float(b), half2float(c)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pnmadd<Packet8h>(const Packet8h& a, const Packet8h& b, const Packet8h& c) {
+  return float2half(pnmadd(half2float(a), half2float(b), half2float(c)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8h pnmsub<Packet8h>(const Packet8h& a, const Packet8h& b, const Packet8h& c) {
+  return float2half(pnmsub(half2float(a), half2float(b), half2float(c)));
+}
+
 template <>
 EIGEN_STRONG_INLINE Packet8h pdiv<Packet8h>(const Packet8h& a, const Packet8h& b) {
   Packet8f af = half2float(a);
@@ -2403,36 +2403,6 @@ EIGEN_STRONG_INLINE void pscatter<Eigen::half, Packet8h>(Eigen::half* to, const
   to[stride * 7] = aux[7];
 }
 
-#ifndef EIGEN_VECTORIZE_AVX512FP16
-template <>
-EIGEN_STRONG_INLINE Eigen::half predux<Packet8h>(const Packet8h& a) {
-  Packet8f af = half2float(a);
-  float reduced = predux<Packet8f>(af);
-  return Eigen::half(reduced);
-}
-#endif
-
-template <>
-EIGEN_STRONG_INLINE Eigen::half predux_max<Packet8h>(const Packet8h& a) {
-  Packet8f af = half2float(a);
-  float reduced = predux_max<Packet8f>(af);
-  return Eigen::half(reduced);
-}
-
-template <>
-EIGEN_STRONG_INLINE Eigen::half predux_min<Packet8h>(const Packet8h& a) {
-  Packet8f af = half2float(a);
-  float reduced = predux_min<Packet8f>(af);
-  return Eigen::half(reduced);
-}
-
-template <>
-EIGEN_STRONG_INLINE Eigen::half predux_mul<Packet8h>(const Packet8h& a) {
-  Packet8f af = half2float(a);
-  float reduced = predux_mul<Packet8f>(af);
-  return Eigen::half(reduced);
-}
-
 template <>
 EIGEN_STRONG_INLINE Packet8h preverse(const Packet8h& a) {
   __m128i m = _mm_setr_epi8(14, 15, 12, 13, 10, 11, 8, 9, 6, 7, 4, 5, 2, 3, 0, 1);
@@ -2510,6 +2480,8 @@ EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8h, 4>& kernel) {
   kernel.packet[3] = pload<Packet8h>(out[3]);
 }
 
+#endif
+
 // BFloat16 implementation.
 
 EIGEN_STRONG_INLINE Packet8f Bf16ToF32(const Packet8bf& a) {
@@ -2737,6 +2709,26 @@ EIGEN_STRONG_INLINE Packet8bf pmul<Packet8bf>(const Packet8bf& a, const Packet8b
   return F32ToBf16(pmul<Packet8f>(Bf16ToF32(a), Bf16ToF32(b)));
 }
 
+template <>
+EIGEN_STRONG_INLINE Packet8bf pmadd<Packet8bf>(const Packet8bf& a, const Packet8bf& b, const Packet8bf& c) {
+  return F32ToBf16(pmadd(Bf16ToF32(a), Bf16ToF32(b), Bf16ToF32(c)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8bf pmsub<Packet8bf>(const Packet8bf& a, const Packet8bf& b, const Packet8bf& c) {
+  return F32ToBf16(pmsub(Bf16ToF32(a), Bf16ToF32(b), Bf16ToF32(c)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8bf pnmadd<Packet8bf>(const Packet8bf& a, const Packet8bf& b, const Packet8bf& c) {
+  return F32ToBf16(pnmadd(Bf16ToF32(a), Bf16ToF32(b), Bf16ToF32(c)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8bf pnmsub<Packet8bf>(const Packet8bf& a, const Packet8bf& b, const Packet8bf& c) {
+  return F32ToBf16(pnmsub(Bf16ToF32(a), Bf16ToF32(b), Bf16ToF32(c)));
+}
+
 template <>
 EIGEN_STRONG_INLINE Packet8bf pdiv<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
   return F32ToBf16(pdiv<Packet8f>(Bf16ToF32(a), Bf16ToF32(b)));
@@ -2769,26 +2761,6 @@ EIGEN_STRONG_INLINE void pscatter<bfloat16, Packet8bf>(bfloat16* to, const Packe
   to[stride * 7] = aux[7];
 }
 
-template <>
-EIGEN_STRONG_INLINE bfloat16 predux<Packet8bf>(const Packet8bf& a) {
-  return static_cast<bfloat16>(predux<Packet8f>(Bf16ToF32(a)));
-}
-
-template <>
-EIGEN_STRONG_INLINE bfloat16 predux_max<Packet8bf>(const Packet8bf& a) {
-  return static_cast<bfloat16>(predux_max<Packet8f>(Bf16ToF32(a)));
-}
-
-template <>
-EIGEN_STRONG_INLINE bfloat16 predux_min<Packet8bf>(const Packet8bf& a) {
-  return static_cast<bfloat16>(predux_min<Packet8f>(Bf16ToF32(a)));
-}
-
-template <>
-EIGEN_STRONG_INLINE bfloat16 predux_mul<Packet8bf>(const Packet8bf& a) {
-  return static_cast<bfloat16>(predux_mul<Packet8f>(Bf16ToF32(a)));
-}
-
 template <>
 EIGEN_STRONG_INLINE Packet8bf preverse(const Packet8bf& a) {
   __m128i m = _mm_setr_epi8(14, 15, 12, 13, 10, 11, 8, 9, 6, 7, 4, 5, 2, 3, 0, 1);
@@ -2850,6 +2822,258 @@ EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8bf, 4>& kernel) {
   kernel.packet[3] = _mm_unpackhi_epi32(ab_47, cd_47);
 }
 
+/*---------------- load/store segment support ----------------*/
+
+// returns a mask of 8-bit elements (at most 4) that are all 1's in the range [begin, begin + count) and 0 elsewhere.
+inline __m128i segment_mask_4x8(Index begin, Index count) {
+  eigen_assert(begin >= 0 && begin + count <= 4);
+  long long mask = 1;
+  mask <<= CHAR_BIT * count;
+  mask--;
+  mask <<= CHAR_BIT * begin;
+#if !EIGEN_ARCH_x86_64
+  return _mm_loadl_epi64(reinterpret_cast<const __m128i*>(&mask));
+#else
+  return _mm_cvtsi64_si128(mask);
+#endif
+}
+
+// returns a mask of 8-bit elements (at most 8) that are all 1's in the range [begin, begin + count) and 0 elsewhere.
+inline __m128i segment_mask_8x8(Index begin, Index count) {
+  eigen_assert(begin >= 0 && begin + count <= 8);
+  long long mask = 1;
+  // avoid UB when count == 8
+  mask <<= (CHAR_BIT / 2) * count;
+  mask <<= (CHAR_BIT / 2) * count;
+  mask--;
+  mask <<= CHAR_BIT * begin;
+#if !EIGEN_ARCH_x86_64
+  return _mm_loadl_epi64(reinterpret_cast<const __m128i*>(&mask));
+#else
+  return _mm_cvtsi64_si128(mask);
+#endif
+}
+
+// returns a mask of 32-bit elements (at most 4) that are all 1's in the range [begin, begin + count) and 0 elsewhere.
+inline __m128i segment_mask_4x32(Index begin, Index count) {
+  eigen_assert(begin >= 0 && begin + count <= 4);
+  return _mm_cvtepi8_epi32(segment_mask_4x8(begin, count));
+}
+
+// returns a mask of 64-bit elements (at most 2) that are all 1's in the range [begin, begin + count) and 0 elsewhere.
+inline __m128i segment_mask_2x64(Index begin, Index count) {
+  eigen_assert(begin >= 0 && begin + count <= 2);
+  return _mm_cvtepi8_epi64(segment_mask_4x8(begin, count));
+}
+
+// returns a mask of 32-bit elements (at most 8) that are all 1's in the range [begin, begin + count) and 0 elsewhere.
+inline __m256i segment_mask_8x32(Index begin, Index count) {
+  __m128i mask_epi8 = segment_mask_8x8(begin, count);
+#ifdef EIGEN_VECTORIZE_AVX2
+  __m256i mask_epi32 = _mm256_cvtepi8_epi32(mask_epi8);
+#else
+  __m128i mask_epi32_lo = _mm_cvtepi8_epi32(mask_epi8);
+  __m128i mask_epi32_hi = _mm_cvtepi8_epi32(_mm_srli_epi64(mask_epi8, 32));
+  __m256i mask_epi32 = _mm256_insertf128_si256(_mm256_castsi128_si256(mask_epi32_lo), mask_epi32_hi, 1);
+#endif
+  return mask_epi32;
+}
+
+// returns a mask of 64-bit elements (at most 4) that are all 1's in the range [begin, begin + count) and 0 elsewhere.
+inline __m256i segment_mask_4x64(Index begin, Index count) {
+  __m128i mask_epi8 = segment_mask_4x8(begin, count);
+#ifdef EIGEN_VECTORIZE_AVX2
+  __m256i mask_epi64 = _mm256_cvtepi8_epi64(mask_epi8);
+#else
+  __m128i mask_epi64_lo = _mm_cvtepi8_epi64(mask_epi8);
+  __m128i mask_epi64_hi = _mm_cvtepi8_epi64(_mm_srli_epi64(mask_epi8, 16));
+  __m256i mask_epi64 = _mm256_insertf128_si256(_mm256_castsi128_si256(mask_epi64_lo), mask_epi64_hi, 1);
+#endif
+  return mask_epi64;
+}
+
+/*---------------- float ----------------*/
+
+template <>
+struct has_packet_segment<Packet4f> : std::true_type {};
+
+template <>
+struct has_packet_segment<Packet8f> : std::true_type {};
+
+template <>
+inline Packet4f ploaduSegment<Packet4f>(const float* from, Index begin, Index count) {
+  return _mm_maskload_ps(from, segment_mask_4x32(begin, count));
+}
+
+template <>
+inline void pstoreuSegment<float, Packet4f>(float* to, const Packet4f& from, Index begin, Index count) {
+  _mm_maskstore_ps(to, segment_mask_4x32(begin, count), from);
+}
+
+template <>
+inline Packet8f ploaduSegment<Packet8f>(const float* from, Index begin, Index count) {
+  return _mm256_maskload_ps(from, segment_mask_8x32(begin, count));
+}
+
+template <>
+inline void pstoreuSegment<float, Packet8f>(float* to, const Packet8f& from, Index begin, Index count) {
+  _mm256_maskstore_ps(to, segment_mask_8x32(begin, count), from);
+}
+
+/*---------------- int32 ----------------*/
+
+template <>
+struct has_packet_segment<Packet4i> : std::true_type {};
+
+template <>
+struct has_packet_segment<Packet8i> : std::true_type {};
+
+#ifdef EIGEN_VECTORIZE_AVX2
+
+template <>
+inline Packet4i ploaduSegment<Packet4i>(const int* from, Index begin, Index count) {
+  return _mm_maskload_epi32(from, segment_mask_4x32(begin, count));
+}
+
+template <>
+inline void pstoreuSegment<int, Packet4i>(int* to, const Packet4i& from, Index begin, Index count) {
+  _mm_maskstore_epi32(to, segment_mask_4x32(begin, count), from);
+}
+
+template <>
+inline Packet8i ploaduSegment<Packet8i>(const int* from, Index begin, Index count) {
+  return _mm256_maskload_epi32(from, segment_mask_8x32(begin, count));
+}
+
+template <>
+inline void pstoreuSegment<int, Packet8i>(int* to, const Packet8i& from, Index begin, Index count) {
+  _mm256_maskstore_epi32(to, segment_mask_8x32(begin, count), from);
+}
+
+#else
+
+template <>
+inline Packet4i ploaduSegment<Packet4i>(const int* from, Index begin, Index count) {
+  return _mm_castps_si128(ploaduSegment<Packet4f>(reinterpret_cast<const float*>(from), begin, count));
+}
+
+template <>
+inline void pstoreuSegment<int, Packet4i>(int* to, const Packet4i& from, Index begin, Index count) {
+  pstoreuSegment<float, Packet4f>(reinterpret_cast<float*>(to), _mm_castsi128_ps(from), begin, count);
+}
+
+template <>
+inline Packet8i ploaduSegment<Packet8i>(const int* from, Index begin, Index count) {
+  return _mm256_castps_si256(ploaduSegment<Packet8f>(reinterpret_cast<const float*>(from), begin, count));
+}
+
+template <>
+inline void pstoreuSegment<int, Packet8i>(int* to, const Packet8i& from, Index begin, Index count) {
+  pstoreuSegment<float, Packet8f>(reinterpret_cast<float*>(to), _mm256_castsi256_ps(from), begin, count);
+}
+
+#endif
+
+/*---------------- uint32 ----------------*/
+
+template <>
+struct has_packet_segment<Packet4ui> : std::true_type {};
+
+template <>
+struct has_packet_segment<Packet8ui> : std::true_type {};
+
+template <>
+inline Packet4ui ploaduSegment<Packet4ui>(const uint32_t* from, Index begin, Index count) {
+  return Packet4ui(ploaduSegment<Packet4i>(reinterpret_cast<const int*>(from), begin, count));
+}
+
+template <>
+inline void pstoreuSegment<uint32_t, Packet4ui>(uint32_t* to, const Packet4ui& from, Index begin, Index count) {
+  pstoreuSegment<int, Packet4i>(reinterpret_cast<int*>(to), Packet4i(from), begin, count);
+}
+
+template <>
+inline Packet8ui ploaduSegment<Packet8ui>(const uint32_t* from, Index begin, Index count) {
+  return Packet8ui(ploaduSegment<Packet8i>(reinterpret_cast<const int*>(from), begin, count));
+}
+
+template <>
+inline void pstoreuSegment<uint32_t, Packet8ui>(uint32_t* to, const Packet8ui& from, Index begin, Index count) {
+  pstoreuSegment<int, Packet8i>(reinterpret_cast<int*>(to), Packet8i(from), begin, count);
+}
+
+/*---------------- double ----------------*/
+
+template <>
+struct has_packet_segment<Packet2d> : std::true_type {};
+
+template <>
+struct has_packet_segment<Packet4d> : std::true_type {};
+
+template <>
+inline Packet2d ploaduSegment<Packet2d>(const double* from, Index begin, Index count) {
+  return _mm_maskload_pd(from, segment_mask_2x64(begin, count));
+}
+
+template <>
+inline void pstoreuSegment<double, Packet2d>(double* to, const Packet2d& from, Index begin, Index count) {
+  _mm_maskstore_pd(to, segment_mask_2x64(begin, count), from);
+}
+
+template <>
+inline Packet4d ploaduSegment<Packet4d>(const double* from, Index begin, Index count) {
+  return _mm256_maskload_pd(from, segment_mask_4x64(begin, count));
+}
+
+template <>
+inline void pstoreuSegment<double, Packet4d>(double* to, const Packet4d& from, Index begin, Index count) {
+  _mm256_maskstore_pd(to, segment_mask_4x64(begin, count), from);
+}
+
+#ifdef EIGEN_VECTORIZE_AVX2
+
+/*---------------- int64_t ----------------*/
+
+template <>
+struct has_packet_segment<Packet2l> : std::true_type {};
+
+template <>
+struct has_packet_segment<Packet4l> : std::true_type {};
+
+template <>
+inline Packet2l ploaduSegment<Packet2l>(const int64_t* from, Index begin, Index count) {
+  return _mm_maskload_epi64(reinterpret_cast<const long long*>(from), segment_mask_2x64(begin, count));
+}
+template <>
+inline void pstoreuSegment<int64_t, Packet2l>(int64_t* to, const Packet2l& from, Index begin, Index count) {
+  _mm_maskstore_epi64(reinterpret_cast<long long*>(to), segment_mask_2x64(begin, count), from);
+}
+template <>
+inline Packet4l ploaduSegment<Packet4l>(const int64_t* from, Index begin, Index count) {
+  return _mm256_maskload_epi64(reinterpret_cast<const long long*>(from), segment_mask_4x64(begin, count));
+}
+template <>
+inline void pstoreuSegment<int64_t, Packet4l>(int64_t* to, const Packet4l& from, Index begin, Index count) {
+  _mm256_maskstore_epi64(reinterpret_cast<long long*>(to), segment_mask_4x64(begin, count), from);
+}
+
+/*---------------- uint64_t ----------------*/
+
+template <>
+struct has_packet_segment<Packet4ul> : std::true_type {};
+
+template <>
+inline Packet4ul ploaduSegment<Packet4ul>(const uint64_t* from, Index begin, Index count) {
+  return Packet4ul(ploaduSegment<Packet4l>(reinterpret_cast<const int64_t*>(from), begin, count));
+}
+template <>
+inline void pstoreuSegment<uint64_t, Packet4ul>(uint64_t* to, const Packet4ul& from, Index begin, Index count) {
+  pstoreuSegment<int64_t, Packet4l>(reinterpret_cast<int64_t*>(to), Packet4l(from), begin, count);
+}
+#endif
+
+/*---------------- end load/store segment support ----------------*/
+
 }  // end namespace internal
 
 }  // end namespace Eigen

Eigen/src/Core/arch/AVX/Reductions.h

@@ -0,0 +1,353 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2025 Charlie Schlosser <cs.schlosser@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REDUCTIONS_AVX_H
+#define EIGEN_REDUCTIONS_AVX_H
+
+// IWYU pragma: private
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/* -- -- -- -- -- -- -- -- -- -- -- -- Packet8i -- -- -- -- -- -- -- -- -- -- -- -- */
+
+template <>
+EIGEN_STRONG_INLINE int predux(const Packet8i& a) {
+  Packet4i lo = _mm256_castsi256_si128(a);
+  Packet4i hi = _mm256_extractf128_si256(a, 1);
+  return predux(padd(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE int predux_mul(const Packet8i& a) {
+  Packet4i lo = _mm256_castsi256_si128(a);
+  Packet4i hi = _mm256_extractf128_si256(a, 1);
+  return predux_mul(pmul(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE int predux_min(const Packet8i& a) {
+  Packet4i lo = _mm256_castsi256_si128(a);
+  Packet4i hi = _mm256_extractf128_si256(a, 1);
+  return predux_min(pmin(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE int predux_max(const Packet8i& a) {
+  Packet4i lo = _mm256_castsi256_si128(a);
+  Packet4i hi = _mm256_extractf128_si256(a, 1);
+  return predux_max(pmax(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE bool predux_any(const Packet8i& a) {
+#ifdef EIGEN_VECTORIZE_AVX2
+  return _mm256_movemask_epi8(a) != 0x0;
+#else
+  return _mm256_movemask_ps(_mm256_castsi256_ps(a)) != 0x0;
+#endif
+}
+
+/* -- -- -- -- -- -- -- -- -- -- -- -- Packet8ui -- -- -- -- -- -- -- -- -- -- -- -- */
+
+template <>
+EIGEN_STRONG_INLINE uint32_t predux(const Packet8ui& a) {
+  Packet4ui lo = _mm256_castsi256_si128(a);
+  Packet4ui hi = _mm256_extractf128_si256(a, 1);
+  return predux(padd(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE uint32_t predux_mul(const Packet8ui& a) {
+  Packet4ui lo = _mm256_castsi256_si128(a);
+  Packet4ui hi = _mm256_extractf128_si256(a, 1);
+  return predux_mul(pmul(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE uint32_t predux_min(const Packet8ui& a) {
+  Packet4ui lo = _mm256_castsi256_si128(a);
+  Packet4ui hi = _mm256_extractf128_si256(a, 1);
+  return predux_min(pmin(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE uint32_t predux_max(const Packet8ui& a) {
+  Packet4ui lo = _mm256_castsi256_si128(a);
+  Packet4ui hi = _mm256_extractf128_si256(a, 1);
+  return predux_max(pmax(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE bool predux_any(const Packet8ui& a) {
+#ifdef EIGEN_VECTORIZE_AVX2
+  return _mm256_movemask_epi8(a) != 0x0;
+#else
+  return _mm256_movemask_ps(_mm256_castsi256_ps(a)) != 0x0;
+#endif
+}
+
+#ifdef EIGEN_VECTORIZE_AVX2
+
+/* -- -- -- -- -- -- -- -- -- -- -- -- Packet4l -- -- -- -- -- -- -- -- -- -- -- -- */
+
+template <>
+EIGEN_STRONG_INLINE int64_t predux(const Packet4l& a) {
+  Packet2l lo = _mm256_castsi256_si128(a);
+  Packet2l hi = _mm256_extractf128_si256(a, 1);
+  return predux(padd(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE bool predux_any(const Packet4l& a) {
+  return _mm256_movemask_pd(_mm256_castsi256_pd(a)) != 0x0;
+}
+
+/* -- -- -- -- -- -- -- -- -- -- -- -- Packet4ul -- -- -- -- -- -- -- -- -- -- -- -- */
+
+template <>
+EIGEN_STRONG_INLINE uint64_t predux(const Packet4ul& a) {
+  return static_cast<uint64_t>(predux(Packet4l(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bool predux_any(const Packet4ul& a) {
+  return _mm256_movemask_pd(_mm256_castsi256_pd(a)) != 0x0;
+}
+
+#endif
+
+/* -- -- -- -- -- -- -- -- -- -- -- -- Packet8f -- -- -- -- -- -- -- -- -- -- -- -- */
+
+template <>
+EIGEN_STRONG_INLINE float predux(const Packet8f& a) {
+  Packet4f lo = _mm256_castps256_ps128(a);
+  Packet4f hi = _mm256_extractf128_ps(a, 1);
+  return predux(padd(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_mul(const Packet8f& a) {
+  Packet4f lo = _mm256_castps256_ps128(a);
+  Packet4f hi = _mm256_extractf128_ps(a, 1);
+  return predux_mul(pmul(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_min(const Packet8f& a) {
+  Packet4f lo = _mm256_castps256_ps128(a);
+  Packet4f hi = _mm256_extractf128_ps(a, 1);
+  return predux_min(pmin(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_min<PropagateNumbers>(const Packet8f& a) {
+  Packet4f lo = _mm256_castps256_ps128(a);
+  Packet4f hi = _mm256_extractf128_ps(a, 1);
+  return predux_min<PropagateNumbers>(pmin<PropagateNumbers>(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_min<PropagateNaN>(const Packet8f& a) {
+  Packet4f lo = _mm256_castps256_ps128(a);
+  Packet4f hi = _mm256_extractf128_ps(a, 1);
+  return predux_min<PropagateNaN>(pmin<PropagateNaN>(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_max(const Packet8f& a) {
+  Packet4f lo = _mm256_castps256_ps128(a);
+  Packet4f hi = _mm256_extractf128_ps(a, 1);
+  return predux_max(pmax(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_max<PropagateNumbers>(const Packet8f& a) {
+  Packet4f lo = _mm256_castps256_ps128(a);
+  Packet4f hi = _mm256_extractf128_ps(a, 1);
+  return predux_max<PropagateNumbers>(pmax<PropagateNumbers>(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_max<PropagateNaN>(const Packet8f& a) {
+  Packet4f lo = _mm256_castps256_ps128(a);
+  Packet4f hi = _mm256_extractf128_ps(a, 1);
+  return predux_max<PropagateNaN>(pmax<PropagateNaN>(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE bool predux_any(const Packet8f& a) {
+  return _mm256_movemask_ps(a) != 0x0;
+}
+
+/* -- -- -- -- -- -- -- -- -- -- -- -- Packet4d -- -- -- -- -- -- -- -- -- -- -- -- */
+
+template <>
+EIGEN_STRONG_INLINE double predux(const Packet4d& a) {
+  Packet2d lo = _mm256_castpd256_pd128(a);
+  Packet2d hi = _mm256_extractf128_pd(a, 1);
+  return predux(padd(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux_mul(const Packet4d& a) {
+  Packet2d lo = _mm256_castpd256_pd128(a);
+  Packet2d hi = _mm256_extractf128_pd(a, 1);
+  return predux_mul(pmul(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux_min(const Packet4d& a) {
+  Packet2d lo = _mm256_castpd256_pd128(a);
+  Packet2d hi = _mm256_extractf128_pd(a, 1);
+  return predux_min(pmin(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux_min<PropagateNumbers>(const Packet4d& a) {
+  Packet2d lo = _mm256_castpd256_pd128(a);
+  Packet2d hi = _mm256_extractf128_pd(a, 1);
+  return predux_min<PropagateNumbers>(pmin<PropagateNumbers>(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux_min<PropagateNaN>(const Packet4d& a) {
+  Packet2d lo = _mm256_castpd256_pd128(a);
+  Packet2d hi = _mm256_extractf128_pd(a, 1);
+  return predux_min<PropagateNaN>(pmin<PropagateNaN>(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux_max(const Packet4d& a) {
+  Packet2d lo = _mm256_castpd256_pd128(a);
+  Packet2d hi = _mm256_extractf128_pd(a, 1);
+  return predux_max(pmax(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux_max<PropagateNumbers>(const Packet4d& a) {
+  Packet2d lo = _mm256_castpd256_pd128(a);
+  Packet2d hi = _mm256_extractf128_pd(a, 1);
+  return predux_max<PropagateNumbers>(pmax<PropagateNumbers>(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux_max<PropagateNaN>(const Packet4d& a) {
+  Packet2d lo = _mm256_castpd256_pd128(a);
+  Packet2d hi = _mm256_extractf128_pd(a, 1);
+  return predux_max<PropagateNaN>(pmax<PropagateNaN>(lo, hi));
+}
+
+template <>
+EIGEN_STRONG_INLINE bool predux_any(const Packet4d& a) {
+  return _mm256_movemask_pd(a) != 0x0;
+}
+
+/* -- -- -- -- -- -- -- -- -- -- -- -- Packet8h -- -- -- -- -- -- -- -- -- -- -- -- */
+#ifndef EIGEN_VECTORIZE_AVX512FP16
+
+template <>
+EIGEN_STRONG_INLINE half predux(const Packet8h& a) {
+  return static_cast<half>(predux(half2float(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux_mul(const Packet8h& a) {
+  return static_cast<half>(predux_mul(half2float(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux_min(const Packet8h& a) {
+  return static_cast<half>(predux_min(half2float(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux_min<PropagateNumbers>(const Packet8h& a) {
+  return static_cast<half>(predux_min<PropagateNumbers>(half2float(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux_min<PropagateNaN>(const Packet8h& a) {
+  return static_cast<half>(predux_min<PropagateNaN>(half2float(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux_max(const Packet8h& a) {
+  return static_cast<half>(predux_max(half2float(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux_max<PropagateNumbers>(const Packet8h& a) {
+  return static_cast<half>(predux_max<PropagateNumbers>(half2float(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux_max<PropagateNaN>(const Packet8h& a) {
+  return static_cast<half>(predux_max<PropagateNaN>(half2float(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bool predux_any(const Packet8h& a) {
+  return _mm_movemask_epi8(a) != 0;
+}
+#endif  // EIGEN_VECTORIZE_AVX512FP16
+
+/* -- -- -- -- -- -- -- -- -- -- -- -- Packet8bf -- -- -- -- -- -- -- -- -- -- -- -- */
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux(const Packet8bf& a) {
+  return static_cast<bfloat16>(predux<Packet8f>(Bf16ToF32(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_mul(const Packet8bf& a) {
+  return static_cast<bfloat16>(predux_mul<Packet8f>(Bf16ToF32(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_min(const Packet8bf& a) {
+  return static_cast<bfloat16>(predux_min(Bf16ToF32(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_min<PropagateNumbers>(const Packet8bf& a) {
+  return static_cast<bfloat16>(predux_min<PropagateNumbers>(Bf16ToF32(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_min<PropagateNaN>(const Packet8bf& a) {
+  return static_cast<bfloat16>(predux_min<PropagateNaN>(Bf16ToF32(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_max(const Packet8bf& a) {
+  return static_cast<bfloat16>(predux_max<Packet8f>(Bf16ToF32(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_max<PropagateNumbers>(const Packet8bf& a) {
+  return static_cast<bfloat16>(predux_max<PropagateNumbers>(Bf16ToF32(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_max<PropagateNaN>(const Packet8bf& a) {
+  return static_cast<bfloat16>(predux_max<PropagateNaN>(Bf16ToF32(a)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bool predux_any(const Packet8bf& a) {
+  return _mm_movemask_epi8(a) != 0;
+}
+
+}  // end namespace internal
+}  // end namespace Eigen
+
+#endif  // EIGEN_REDUCTIONS_AVX_H

Eigen/src/Core/arch/AVX/TypeCasting.h

@@ -240,8 +240,8 @@ EIGEN_STRONG_INLINE Packet4d pcast<Packet4l, Packet4d>(const Packet4l& a) {
 #if defined(EIGEN_VECTORIZE_AVX512DQ) && defined(EIGEN_VECTORIZE_AVS512VL)
   return _mm256_cvtepi64_pd(a);
 #else
-  EIGEN_ALIGN16 int64_t aux[4];
-  pstore(aux, a);
+  int64_t aux[4];
+  pstoreu(aux, a);
   return _mm256_set_pd(static_cast<double>(aux[3]), static_cast<double>(aux[2]), static_cast<double>(aux[1]),
                        static_cast<double>(aux[0]));
 #endif
@@ -279,20 +279,22 @@ EIGEN_STRONG_INLINE Packet2l preinterpret<Packet2l, Packet4l>(const Packet4l& a)
 }
 #endif
 
+#ifndef EIGEN_VECTORIZE_AVX512FP16
 template <>
 EIGEN_STRONG_INLINE Packet8f pcast<Packet8h, Packet8f>(const Packet8h& a) {
   return half2float(a);
 }
 
-template <>
-EIGEN_STRONG_INLINE Packet8f pcast<Packet8bf, Packet8f>(const Packet8bf& a) {
-  return Bf16ToF32(a);
-}
-
 template <>
 EIGEN_STRONG_INLINE Packet8h pcast<Packet8f, Packet8h>(const Packet8f& a) {
   return float2half(a);
 }
+#endif
+
+template <>
+EIGEN_STRONG_INLINE Packet8f pcast<Packet8bf, Packet8f>(const Packet8bf& a) {
+  return Bf16ToF32(a);
+}
 
 template <>
 EIGEN_STRONG_INLINE Packet8bf pcast<Packet8f, Packet8bf>(const Packet8f& a) {

Eigen/src/Core/arch/AVX512/MathFunctions.h

@@ -47,16 +47,16 @@ EIGEN_STRONG_INLINE Packet16bf pldexp(const Packet16bf& a, const Packet16bf& exp
 
 #if EIGEN_FAST_MATH
 template <>
-EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f psqrt<Packet16f>(const Packet16f& _x) {
-  return generic_sqrt_newton_step<Packet16f>::run(_x, _mm512_rsqrt14_ps(_x));
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f psqrt<Packet16f>(const Packet16f& x) {
+  return generic_sqrt_newton_step<Packet16f>::run(x, _mm512_rsqrt14_ps(x));
 }
 
 template <>
-EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d psqrt<Packet8d>(const Packet8d& _x) {
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d psqrt<Packet8d>(const Packet8d& x) {
 #ifdef EIGEN_VECTORIZE_AVX512ER
-  return generic_sqrt_newton_step<Packet8d, /*Steps=*/1>::run(_x, _mm512_rsqrt28_pd(_x));
+  return generic_sqrt_newton_step<Packet8d, /*Steps=*/1>::run(x, _mm512_rsqrt28_pd(x));
 #else
-  return generic_sqrt_newton_step<Packet8d, /*Steps=*/2>::run(_x, _mm512_rsqrt14_pd(_x));
+  return generic_sqrt_newton_step<Packet8d, /*Steps=*/2>::run(x, _mm512_rsqrt14_pd(x));
 #endif
 }
 #else
@@ -80,19 +80,19 @@ EIGEN_STRONG_INLINE Packet16f prsqrt<Packet16f>(const Packet16f& x) {
 #elif EIGEN_FAST_MATH
 
 template <>
-EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f prsqrt<Packet16f>(const Packet16f& _x) {
-  return generic_rsqrt_newton_step<Packet16f, /*Steps=*/1>::run(_x, _mm512_rsqrt14_ps(_x));
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet16f prsqrt<Packet16f>(const Packet16f& x) {
+  return generic_rsqrt_newton_step<Packet16f, /*Steps=*/1>::run(x, _mm512_rsqrt14_ps(x));
 }
 #endif
 
 // prsqrt for double.
 #if EIGEN_FAST_MATH
 template <>
-EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d prsqrt<Packet8d>(const Packet8d& _x) {
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet8d prsqrt<Packet8d>(const Packet8d& x) {
 #ifdef EIGEN_VECTORIZE_AVX512ER
-  return generic_rsqrt_newton_step<Packet8d, /*Steps=*/1>::run(_x, _mm512_rsqrt28_pd(_x));
+  return generic_rsqrt_newton_step<Packet8d, /*Steps=*/1>::run(x, _mm512_rsqrt28_pd(x));
 #else
-  return generic_rsqrt_newton_step<Packet8d, /*Steps=*/2>::run(_x, _mm512_rsqrt14_pd(_x));
+  return generic_rsqrt_newton_step<Packet8d, /*Steps=*/2>::run(x, _mm512_rsqrt14_pd(x));
 #endif
 }
 
@@ -108,6 +108,7 @@ EIGEN_STRONG_INLINE Packet16f preciprocal<Packet16f>(const Packet16f& a) {
 
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pcos)
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pexp)
+BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pexp2)
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pexpm1)
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog)
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, plog1p)
@@ -117,8 +118,11 @@ BF16_PACKET_FUNCTION(Packet16f, Packet16bf, prsqrt)
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, psin)
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, psqrt)
 BF16_PACKET_FUNCTION(Packet16f, Packet16bf, ptanh)
+
+#ifndef EIGEN_VECTORIZE_AVX512FP16
 F16_PACKET_FUNCTION(Packet16f, Packet16h, pcos)
 F16_PACKET_FUNCTION(Packet16f, Packet16h, pexp)
+F16_PACKET_FUNCTION(Packet16f, Packet16h, pexp2)
 F16_PACKET_FUNCTION(Packet16f, Packet16h, pexpm1)
 F16_PACKET_FUNCTION(Packet16f, Packet16h, plog)
 F16_PACKET_FUNCTION(Packet16f, Packet16h, plog1p)
@@ -128,6 +132,7 @@ F16_PACKET_FUNCTION(Packet16f, Packet16h, prsqrt)
 F16_PACKET_FUNCTION(Packet16f, Packet16h, psin)
 F16_PACKET_FUNCTION(Packet16f, Packet16h, psqrt)
 F16_PACKET_FUNCTION(Packet16f, Packet16h, ptanh)
+#endif  // EIGEN_VECTORIZE_AVX512FP16
 
 }  // end namespace internal
 

Eigen/src/Core/arch/AVX512/MathFunctionsFP16.h

@@ -0,0 +1,75 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2025 The Eigen Authors.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_MATH_FUNCTIONS_FP16_AVX512_H
+#define EIGEN_MATH_FUNCTIONS_FP16_AVX512_H
+
+// IWYU pragma: private
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+EIGEN_STRONG_INLINE Packet32h combine2Packet16h(const Packet16h& a, const Packet16h& b) {
+  __m512i result = _mm512_castsi256_si512(_mm256_castph_si256(a));
+  result = _mm512_inserti64x4(result, _mm256_castph_si256(b), 1);
+  return _mm512_castsi512_ph(result);
+}
+
+EIGEN_STRONG_INLINE void extract2Packet16h(const Packet32h& x, Packet16h& a, Packet16h& b) {
+  a = _mm256_castsi256_ph(_mm512_castsi512_si256(_mm512_castph_si512(x)));
+  b = _mm256_castsi256_ph(_mm512_extracti64x4_epi64(_mm512_castph_si512(x), 1));
+}
+
+#define _EIGEN_GENERATE_FP16_MATH_FUNCTION(func)                      \
+  template <>                                                         \
+  EIGEN_STRONG_INLINE Packet8h func<Packet8h>(const Packet8h& a) {    \
+    return float2half(func(half2float(a)));                           \
+  }                                                                   \
+                                                                      \
+  template <>                                                         \
+  EIGEN_STRONG_INLINE Packet16h func<Packet16h>(const Packet16h& a) { \
+    return float2half(func(half2float(a)));                           \
+  }                                                                   \
+                                                                      \
+  template <>                                                         \
+  EIGEN_STRONG_INLINE Packet32h func<Packet32h>(const Packet32h& a) { \
+    Packet16h low;                                                    \
+    Packet16h high;                                                   \
+    extract2Packet16h(a, low, high);                                  \
+    return combine2Packet16h(func(low), func(high));                  \
+  }
+
+_EIGEN_GENERATE_FP16_MATH_FUNCTION(psin)
+_EIGEN_GENERATE_FP16_MATH_FUNCTION(pcos)
+_EIGEN_GENERATE_FP16_MATH_FUNCTION(plog)
+_EIGEN_GENERATE_FP16_MATH_FUNCTION(plog2)
+_EIGEN_GENERATE_FP16_MATH_FUNCTION(plog1p)
+_EIGEN_GENERATE_FP16_MATH_FUNCTION(pexp)
+_EIGEN_GENERATE_FP16_MATH_FUNCTION(pexpm1)
+_EIGEN_GENERATE_FP16_MATH_FUNCTION(pexp2)
+_EIGEN_GENERATE_FP16_MATH_FUNCTION(ptanh)
+#undef _EIGEN_GENERATE_FP16_MATH_FUNCTION
+
+// pfrexp
+template <>
+EIGEN_STRONG_INLINE Packet32h pfrexp<Packet32h>(const Packet32h& a, Packet32h& exponent) {
+  return pfrexp_generic(a, exponent);
+}
+
+// pldexp
+template <>
+EIGEN_STRONG_INLINE Packet32h pldexp<Packet32h>(const Packet32h& a, const Packet32h& exponent) {
+  return pldexp_generic(a, exponent);
+}
+
+}  // end namespace internal
+}  // end namespace Eigen
+
+#endif  // EIGEN_MATH_FUNCTIONS_FP16_AVX512_H

Eigen/src/Core/arch/AVX512/PacketMath.h

@@ -40,6 +40,10 @@ typedef eigen_packet_wrapper<__m256i, 1> Packet16h;
 #endif
 typedef eigen_packet_wrapper<__m256i, 2> Packet16bf;
 
+typedef eigen_packet_wrapper<__m512i, 6> Packet32s;
+typedef eigen_packet_wrapper<__m256i, 6> Packet16s;
+typedef eigen_packet_wrapper<__m128i, 6> Packet8s;
+
 template <>
 struct is_arithmetic<__m512> {
   enum { value = true };
@@ -124,15 +128,18 @@ struct packet_traits<float> : default_packet_traits {
     HasATanh = 1,
     HasSqrt = 1,
     HasRsqrt = 1,
+    HasCbrt = 1,
     HasLog = 1,
     HasLog1p = 1,
     HasExpm1 = 1,
     HasNdtri = 1,
     HasBessel = 1,
     HasExp = 1,
+    HasPow = 1,
     HasReciprocal = EIGEN_FAST_MATH,
     HasTanh = EIGEN_FAST_MATH,
     HasErf = EIGEN_FAST_MATH,
+    HasErfc = EIGEN_FAST_MATH,
     HasCmp = 1,
     HasDiv = 1
   };
@@ -148,12 +155,16 @@ struct packet_traits<double> : default_packet_traits {
     HasBlend = 1,
     HasSqrt = 1,
     HasRsqrt = 1,
+    HasCbrt = 1,
     HasSin = EIGEN_FAST_MATH,
     HasCos = EIGEN_FAST_MATH,
     HasLog = 1,
     HasExp = 1,
+    HasPow = 1,
     HasATan = 1,
     HasTanh = EIGEN_FAST_MATH,
+    HasErf = EIGEN_FAST_MATH,
+    HasErfc = EIGEN_FAST_MATH,
     HasATanh = 1,
     HasCmp = 1,
     HasDiv = 1
@@ -245,6 +256,39 @@ struct unpacket_traits<Packet16h> {
 };
 #endif
 
+template <>
+struct unpacket_traits<Packet32s> {
+  typedef numext::int16_t type;
+  typedef Packet16s half;
+  enum {
+    size = 32,
+    alignment = Aligned64,
+    vectorizable = false,
+  };
+};
+
+template <>
+struct unpacket_traits<Packet16s> {
+  typedef numext::int16_t type;
+  typedef Packet8s half;
+  enum {
+    size = 16,
+    alignment = Aligned32,
+    vectorizable = false,
+  };
+};
+
+template <>
+struct unpacket_traits<Packet8s> {
+  typedef numext::int16_t type;
+  typedef Packet8s half;
+  enum {
+    size = 8,
+    alignment = Aligned16,
+    vectorizable = false,
+  };
+};
+
 template <>
 EIGEN_STRONG_INLINE Packet16f pset1<Packet16f>(const float& from) {
   return _mm512_set1_ps(from);
@@ -1332,10 +1376,13 @@ EIGEN_STRONG_INLINE Packet8l pabs(const Packet8l& a) {
   return _mm512_abs_epi64(a);
 }
 
+#ifndef EIGEN_VECTORIZE_AVX512FP16
 template <>
 EIGEN_STRONG_INLINE Packet16h psignbit(const Packet16h& a) {
   return _mm256_srai_epi16(a, 15);
 }
+#endif  // EIGEN_VECTORIZE_AVX512FP16
+
 template <>
 EIGEN_STRONG_INLINE Packet16bf psignbit(const Packet16bf& a) {
   return _mm256_srai_epi16(a, 15);
@@ -1449,40 +1496,6 @@ EIGEN_STRONG_INLINE Packet8d pldexp<Packet8d>(const Packet8d& a, const Packet8d&
   OUTPUT = _mm512_inserti32x4(OUTPUT, _mm256_extractf128_si256(INPUTB, 1), 3);
 #endif
 
-template <>
-EIGEN_STRONG_INLINE float predux<Packet16f>(const Packet16f& a) {
-#ifdef EIGEN_VECTORIZE_AVX512DQ
-  __m256 lane0 = _mm512_extractf32x8_ps(a, 0);
-  __m256 lane1 = _mm512_extractf32x8_ps(a, 1);
-  Packet8f x = _mm256_add_ps(lane0, lane1);
-  return predux<Packet8f>(x);
-#else
-  __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
-  __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
-  __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
-  __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
-  __m128 sum = _mm_add_ps(_mm_add_ps(lane0, lane1), _mm_add_ps(lane2, lane3));
-  return predux<Packet4f>(sum);
-#endif
-}
-template <>
-EIGEN_STRONG_INLINE double predux<Packet8d>(const Packet8d& a) {
-  __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
-  __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
-  __m256d sum = _mm256_add_pd(lane0, lane1);
-  return predux<Packet4d>(sum);
-}
-
-template <>
-EIGEN_STRONG_INLINE int64_t predux<Packet8l>(const Packet8l& a) {
-  return _mm512_reduce_add_epi64(a);
-}
-
-template <>
-EIGEN_STRONG_INLINE int predux<Packet16i>(const Packet16i& a) {
-  return _mm512_reduce_add_epi32(a);
-}
-
 template <>
 EIGEN_STRONG_INLINE Packet8f predux_half_dowto4<Packet16f>(const Packet16f& a) {
 #ifdef EIGEN_VECTORIZE_AVX512DQ
@@ -1529,129 +1542,6 @@ EIGEN_STRONG_INLINE Packet4l predux_half_dowto4<Packet8l>(const Packet8l& a) {
   return _mm256_add_epi64(lane0, lane1);
 }
 
-template <>
-EIGEN_STRONG_INLINE float predux_mul<Packet16f>(const Packet16f& a) {
-// #ifdef EIGEN_VECTORIZE_AVX512DQ
-#if 0
-  Packet8f lane0 = _mm512_extractf32x8_ps(a, 0);
-  Packet8f lane1 = _mm512_extractf32x8_ps(a, 1);
-  Packet8f res = pmul(lane0, lane1);
-  res = pmul(res, _mm256_permute2f128_ps(res, res, 1));
-  res = pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
-  return pfirst(pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
-#else
-  __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
-  __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
-  __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
-  __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
-  __m128 res = pmul(pmul(lane0, lane1), pmul(lane2, lane3));
-  res = pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
-  return pfirst(pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
-#endif
-}
-template <>
-EIGEN_STRONG_INLINE double predux_mul<Packet8d>(const Packet8d& a) {
-  __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
-  __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
-  __m256d res = pmul(lane0, lane1);
-  res = pmul(res, _mm256_permute2f128_pd(res, res, 1));
-  return pfirst(pmul(res, _mm256_shuffle_pd(res, res, 1)));
-}
-template <>
-EIGEN_STRONG_INLINE int predux_mul<Packet16i>(const Packet16i& a) {
-  return _mm512_reduce_mul_epi32(a);
-}
-
-#if EIGEN_COMP_MSVC
-// MSVC's _mm512_reduce_mul_epi64 is borked, at least up to and including 1939.
-//    alignas(64) int64_t data[] = { 1,1,-1,-1,1,-1,-1,-1 };
-//    int64_t out = _mm512_reduce_mul_epi64(_mm512_load_epi64(data));
-// produces garbage: 4294967295.  It seems to happen whenever the output is supposed to be negative.
-// Fall back to a manual approach:
-template <>
-EIGEN_STRONG_INLINE int64_t predux_mul<Packet8l>(const Packet8l& a) {
-  Packet4l lane0 = _mm512_extracti64x4_epi64(a, 0);
-  Packet4l lane1 = _mm512_extracti64x4_epi64(a, 1);
-  Packet4l res = pmul(lane0, lane1);
-  res = pmul(res, Packet4l(_mm256_permute2x128_si256(res, res, 1)));
-  res = pmul(res, Packet4l(_mm256_shuffle_epi32(res, 0xE)));
-  return pfirst(res);
-}
-#else
-template <>
-EIGEN_STRONG_INLINE int64_t predux_mul<Packet8l>(const Packet8l& a) {
-  return _mm512_reduce_mul_epi64(a);
-}
-#endif
-
-template <>
-EIGEN_STRONG_INLINE float predux_min<Packet16f>(const Packet16f& a) {
-  __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
-  __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
-  __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
-  __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
-  __m128 res = _mm_min_ps(_mm_min_ps(lane0, lane1), _mm_min_ps(lane2, lane3));
-  res = _mm_min_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
-  return pfirst(_mm_min_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
-}
-template <>
-EIGEN_STRONG_INLINE double predux_min<Packet8d>(const Packet8d& a) {
-  __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
-  __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
-  __m256d res = _mm256_min_pd(lane0, lane1);
-  res = _mm256_min_pd(res, _mm256_permute2f128_pd(res, res, 1));
-  return pfirst(_mm256_min_pd(res, _mm256_shuffle_pd(res, res, 1)));
-}
-template <>
-EIGEN_STRONG_INLINE int predux_min<Packet16i>(const Packet16i& a) {
-  return _mm512_reduce_min_epi32(a);
-}
-template <>
-EIGEN_STRONG_INLINE int64_t predux_min<Packet8l>(const Packet8l& a) {
-  return _mm512_reduce_min_epi64(a);
-}
-
-template <>
-EIGEN_STRONG_INLINE float predux_max<Packet16f>(const Packet16f& a) {
-  __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
-  __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
-  __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
-  __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
-  __m128 res = _mm_max_ps(_mm_max_ps(lane0, lane1), _mm_max_ps(lane2, lane3));
-  res = _mm_max_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
-  return pfirst(_mm_max_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
-}
-
-template <>
-EIGEN_STRONG_INLINE double predux_max<Packet8d>(const Packet8d& a) {
-  __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
-  __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
-  __m256d res = _mm256_max_pd(lane0, lane1);
-  res = _mm256_max_pd(res, _mm256_permute2f128_pd(res, res, 1));
-  return pfirst(_mm256_max_pd(res, _mm256_shuffle_pd(res, res, 1)));
-}
-template <>
-EIGEN_STRONG_INLINE int predux_max<Packet16i>(const Packet16i& a) {
-  return _mm512_reduce_max_epi32(a);
-}
-template <>
-EIGEN_STRONG_INLINE int64_t predux_max<Packet8l>(const Packet8l& a) {
-  return _mm512_reduce_max_epi64(a);
-}
-
-template <>
-EIGEN_STRONG_INLINE bool predux_any(const Packet16f& x) {
-  Packet16i xi = _mm512_castps_si512(x);
-  __mmask16 tmp = _mm512_test_epi32_mask(xi, xi);
-  return !_mm512_kortestz(tmp, tmp);
-}
-
-template <>
-EIGEN_STRONG_INLINE bool predux_any(const Packet16i& x) {
-  __mmask16 tmp = _mm512_test_epi32_mask(x, x);
-  return !_mm512_kortestz(tmp, tmp);
-}
-
 #define PACK_OUTPUT(OUTPUT, INPUT, INDEX, STRIDE) \
   EIGEN_INSERT_8f_INTO_16f(OUTPUT[INDEX], INPUT[INDEX], INPUT[INDEX + STRIDE]);
 
@@ -2189,6 +2079,7 @@ EIGEN_STRONG_INLINE Packet8d pblend(const Selector<8>& ifPacket, const Packet8d&
 }
 
 // Packet math for Eigen::half
+#ifndef EIGEN_VECTORIZE_AVX512FP16
 template <>
 EIGEN_STRONG_INLINE Packet16h pset1<Packet16h>(const Eigen::half& from) {
   return _mm256_set1_epi16(from.x);
@@ -2213,6 +2104,7 @@ template <>
 EIGEN_STRONG_INLINE void pstore<half>(Eigen::half* to, const Packet16h& from) {
   // (void*) -> workaround clang warning:
   // cast from 'Eigen::half *' to '__m256i *' increases required alignment from 2 to 32
+  EIGEN_DEBUG_ALIGNED_STORE
   _mm256_store_si256((__m256i*)(void*)to, from);
 }
 
@@ -2220,6 +2112,7 @@ template <>
 EIGEN_STRONG_INLINE void pstoreu<half>(Eigen::half* to, const Packet16h& from) {
   // (void*) -> workaround clang warning:
   // cast from 'Eigen::half *' to '__m256i *' increases required alignment from 2 to 32
+  EIGEN_DEBUG_UNALIGNED_STORE
   _mm256_storeu_si256((__m256i*)(void*)to, from);
 }
 
@@ -2359,7 +2252,6 @@ EIGEN_STRONG_INLINE Packet16h pnegate(const Packet16h& a) {
   return _mm256_xor_si256(a, sign_mask);
 }
 
-#ifndef EIGEN_VECTORIZE_AVX512FP16
 template <>
 EIGEN_STRONG_INLINE Packet16h padd<Packet16h>(const Packet16h& a, const Packet16h& b) {
   Packet16f af = half2float(a);
@@ -2393,12 +2285,24 @@ EIGEN_STRONG_INLINE Packet16h pdiv<Packet16h>(const Packet16h& a, const Packet16
 }
 
 template <>
-EIGEN_STRONG_INLINE half predux<Packet16h>(const Packet16h& from) {
-  Packet16f from_float = half2float(from);
-  return half(predux(from_float));
+EIGEN_STRONG_INLINE Packet16h pmadd<Packet16h>(const Packet16h& a, const Packet16h& b, const Packet16h& c) {
+  return float2half(pmadd(half2float(a), half2float(b), half2float(c)));
 }
 
-#endif
+template <>
+EIGEN_STRONG_INLINE Packet16h pmsub<Packet16h>(const Packet16h& a, const Packet16h& b, const Packet16h& c) {
+  return float2half(pmsub(half2float(a), half2float(b), half2float(c)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pnmadd<Packet16h>(const Packet16h& a, const Packet16h& b, const Packet16h& c) {
+  return float2half(pnmadd(half2float(a), half2float(b), half2float(c)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pnmsub<Packet16h>(const Packet16h& a, const Packet16h& b, const Packet16h& c) {
+  return float2half(pnmsub(half2float(a), half2float(b), half2float(c)));
+}
 
 template <>
 EIGEN_STRONG_INLINE Packet8h predux_half_dowto4<Packet16h>(const Packet16h& a) {
@@ -2407,26 +2311,6 @@ EIGEN_STRONG_INLINE Packet8h predux_half_dowto4<Packet16h>(const Packet16h& a) {
   return padd<Packet8h>(lane0, lane1);
 }
 
-template <>
-EIGEN_STRONG_INLINE Eigen::half predux_max<Packet16h>(const Packet16h& a) {
-  Packet16f af = half2float(a);
-  float reduced = predux_max<Packet16f>(af);
-  return Eigen::half(reduced);
-}
-
-template <>
-EIGEN_STRONG_INLINE Eigen::half predux_min<Packet16h>(const Packet16h& a) {
-  Packet16f af = half2float(a);
-  float reduced = predux_min<Packet16f>(af);
-  return Eigen::half(reduced);
-}
-
-template <>
-EIGEN_STRONG_INLINE half predux_mul<Packet16h>(const Packet16h& from) {
-  Packet16f from_float = half2float(from);
-  return half(predux_mul(from_float));
-}
-
 template <>
 EIGEN_STRONG_INLINE Packet16h preverse(const Packet16h& a) {
   __m128i m = _mm_setr_epi8(14, 15, 12, 13, 10, 11, 8, 9, 6, 7, 4, 5, 2, 3, 0, 1);
@@ -2633,6 +2517,8 @@ EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16h, 4>& kernel) {
   kernel.packet[3] = pload<Packet16h>(out[3]);
 }
 
+#endif  // EIGEN_VECTORIZE_AVX512FP16
+
 template <>
 struct is_arithmetic<Packet16bf> {
   enum { value = true };
@@ -2704,11 +2590,13 @@ EIGEN_STRONG_INLINE Packet16bf ploadu<Packet16bf>(const bfloat16* from) {
 
 template <>
 EIGEN_STRONG_INLINE void pstore<bfloat16>(bfloat16* to, const Packet16bf& from) {
+  EIGEN_DEBUG_ALIGNED_STORE
   _mm256_store_si256(reinterpret_cast<__m256i*>(to), from);
 }
 
 template <>
 EIGEN_STRONG_INLINE void pstoreu<bfloat16>(bfloat16* to, const Packet16bf& from) {
+  EIGEN_DEBUG_UNALIGNED_STORE
   _mm256_storeu_si256(reinterpret_cast<__m256i*>(to), from);
 }
 
@@ -2879,7 +2767,27 @@ EIGEN_STRONG_INLINE Packet16bf psub<Packet16bf>(const Packet16bf& a, const Packe
 
 template <>
 EIGEN_STRONG_INLINE Packet16bf pmul<Packet16bf>(const Packet16bf& a, const Packet16bf& b) {
-  return F32ToBf16(pmul<Packet16f>(Bf16ToF32(a), Bf16ToF32(b)));
+  return F32ToBf16(pmul(Bf16ToF32(a), Bf16ToF32(b)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pmadd<Packet16bf>(const Packet16bf& a, const Packet16bf& b, const Packet16bf& c) {
+  return F32ToBf16(pmadd(Bf16ToF32(a), Bf16ToF32(b), Bf16ToF32(c)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pmsub<Packet16bf>(const Packet16bf& a, const Packet16bf& b, const Packet16bf& c) {
+  return F32ToBf16(pmsub(Bf16ToF32(a), Bf16ToF32(b), Bf16ToF32(c)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pnmadd<Packet16bf>(const Packet16bf& a, const Packet16bf& b, const Packet16bf& c) {
+  return F32ToBf16(pnmadd(Bf16ToF32(a), Bf16ToF32(b), Bf16ToF32(c)));
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16bf pnmsub<Packet16bf>(const Packet16bf& a, const Packet16bf& b, const Packet16bf& c) {
+  return F32ToBf16(pnmsub(Bf16ToF32(a), Bf16ToF32(b), Bf16ToF32(c)));
 }
 
 template <>
@@ -2909,26 +2817,6 @@ EIGEN_STRONG_INLINE Packet8bf predux_half_dowto4<Packet16bf>(const Packet16bf& a
   return padd<Packet8bf>(lane0, lane1);
 }
 
-template <>
-EIGEN_STRONG_INLINE bfloat16 predux<Packet16bf>(const Packet16bf& p) {
-  return static_cast<bfloat16>(predux<Packet16f>(Bf16ToF32(p)));
-}
-
-template <>
-EIGEN_STRONG_INLINE bfloat16 predux_mul<Packet16bf>(const Packet16bf& from) {
-  return static_cast<bfloat16>(predux_mul<Packet16f>(Bf16ToF32(from)));
-}
-
-template <>
-EIGEN_STRONG_INLINE bfloat16 predux_min<Packet16bf>(const Packet16bf& from) {
-  return static_cast<bfloat16>(predux_min<Packet16f>(Bf16ToF32(from)));
-}
-
-template <>
-EIGEN_STRONG_INLINE bfloat16 predux_max<Packet16bf>(const Packet16bf& from) {
-  return static_cast<bfloat16>(predux_max<Packet16f>(Bf16ToF32(from)));
-}
-
 template <>
 EIGEN_STRONG_INLINE Packet16bf preverse(const Packet16bf& a) {
   __m256i m = _mm256_setr_epi8(14, 15, 12, 13, 10, 11, 8, 9, 6, 7, 4, 5, 2, 3, 0, 1, 14, 15, 12, 13, 10, 11, 8, 9, 6, 7,
@@ -3085,6 +2973,172 @@ EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16bf, 4>& kernel) {
   kernel.packet[3] = _mm256_permute2x128_si256(abcd_8b, abcd_cf, 0x31);
 }
 
+// Minimal implementation of 16-bit int packets for use in pfrexp, pldexp.
+
+template <>
+EIGEN_STRONG_INLINE Packet32s pset1<Packet32s>(const numext::int16_t& x) {
+  return _mm512_set1_epi16(x);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16s pset1<Packet16s>(const numext::int16_t& x) {
+  return _mm256_set1_epi16(x);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8s pset1<Packet8s>(const numext::int16_t& x) {
+  return _mm_set1_epi16(x);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstore<numext::int16_t, Packet32s>(numext::int16_t* out, const Packet32s& x) {
+  EIGEN_DEBUG_ALIGNED_STORE
+  _mm512_store_epi32(out, x);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstore<numext::int16_t, Packet16s>(numext::int16_t* out, const Packet16s& x) {
+  EIGEN_DEBUG_ALIGNED_STORE
+#if defined(EIGEN_VECTORIZE_AVX512F) && defined(EIGEN_VECTORIZE_AVX512VL)
+  _mm256_store_epi32(out, x);
+#else
+  _mm256_store_si256(reinterpret_cast<__m256i*>(out), x);
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstore<numext::int16_t, Packet8s>(numext::int16_t* out, const Packet8s& x) {
+  EIGEN_DEBUG_ALIGNED_STORE
+#if defined(EIGEN_VECTORIZE_AVX512F) && defined(EIGEN_VECTORIZE_AVX512VL)
+  _mm256_store_epi32(out, x);
+#else
+  _mm_store_si128(reinterpret_cast<__m128i*>(out), x);
+#endif
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstoreu<numext::int16_t, Packet32s>(numext::int16_t* out, const Packet32s& x) {
+  EIGEN_DEBUG_UNALIGNED_STORE
+  _mm512_storeu_epi32(out, x);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstoreu<numext::int16_t, Packet16s>(numext::int16_t* out, const Packet16s& x) {
+  EIGEN_DEBUG_UNALIGNED_STORE
+  _mm256_storeu_epi32(out, x);
+}
+
+template <>
+EIGEN_STRONG_INLINE void pstoreu<numext::int16_t, Packet8s>(numext::int16_t* out, const Packet8s& x) {
+  EIGEN_DEBUG_UNALIGNED_STORE
+  _mm_storeu_epi32(out, x);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet32s padd(const Packet32s& a, const Packet32s& b) {
+  return _mm512_add_epi16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16s padd(const Packet16s& a, const Packet16s& b) {
+  return _mm256_add_epi16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8s padd(const Packet8s& a, const Packet8s& b) {
+  return _mm_add_epi16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet32s psub(const Packet32s& a, const Packet32s& b) {
+  return _mm512_sub_epi16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16s psub(const Packet16s& a, const Packet16s& b) {
+  return _mm256_sub_epi16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8s psub(const Packet8s& a, const Packet8s& b) {
+  return _mm_sub_epi16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet32s pmul(const Packet32s& a, const Packet32s& b) {
+  return _mm512_mullo_epi16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16s pmul(const Packet16s& a, const Packet16s& b) {
+  return _mm256_mullo_epi16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8s pmul(const Packet8s& a, const Packet8s& b) {
+  return _mm_mullo_epi16(a, b);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet32s pnegate(const Packet32s& a) {
+  return _mm512_sub_epi16(_mm512_setzero_si512(), a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16s pnegate(const Packet16s& a) {
+  return _mm256_sub_epi16(_mm256_setzero_si256(), a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8s pnegate(const Packet8s& a) {
+  return _mm_sub_epi16(_mm_setzero_si128(), a);
+}
+
+template <int N>
+EIGEN_STRONG_INLINE Packet32s parithmetic_shift_right(Packet32s a) {
+  return _mm512_srai_epi16(a, N);
+}
+
+template <int N>
+EIGEN_STRONG_INLINE Packet16s parithmetic_shift_right(Packet16s a) {
+  return _mm256_srai_epi16(a, N);
+}
+
+template <int N>
+EIGEN_STRONG_INLINE Packet8s parithmetic_shift_right(Packet8s a) {
+  return _mm_srai_epi16(a, N);
+}
+
+template <int N>
+EIGEN_STRONG_INLINE Packet32s plogical_shift_left(Packet32s a) {
+  return _mm512_slli_epi16(a, N);
+}
+
+template <int N>
+EIGEN_STRONG_INLINE Packet16s plogical_shift_left(Packet16s a) {
+  return _mm256_slli_epi16(a, N);
+}
+
+template <int N>
+EIGEN_STRONG_INLINE Packet8s plogical_shift_left(Packet8s a) {
+  return _mm_slli_epi16(a, N);
+}
+
+template <int N>
+EIGEN_STRONG_INLINE Packet32s plogical_shift_right(Packet32s a) {
+  return _mm512_srli_epi16(a, N);
+}
+
+template <int N>
+EIGEN_STRONG_INLINE Packet16s plogical_shift_right(Packet16s a) {
+  return _mm256_srli_epi16(a, N);
+}
+
+template <int N>
+EIGEN_STRONG_INLINE Packet8s plogical_shift_right(Packet8s a) {
+  return _mm_srli_epi16(a, N);
+}
+
 }  // end namespace internal
 
 }  // end namespace Eigen

Eigen/src/Core/arch/AVX512/Reductions.h

@@ -0,0 +1,297 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2025 Charlie Schlosser <cs.schlosser@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_REDUCTIONS_AVX512_H
+#define EIGEN_REDUCTIONS_AVX512_H
+
+// IWYU pragma: private
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+
+namespace internal {
+
+/* -- -- -- -- -- -- -- -- -- -- -- -- Packet16i -- -- -- -- -- -- -- -- -- -- -- -- */
+
+template <>
+EIGEN_STRONG_INLINE int predux(const Packet16i& a) {
+  return _mm512_reduce_add_epi32(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE int predux_mul(const Packet16i& a) {
+  return _mm512_reduce_mul_epi32(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE int predux_min(const Packet16i& a) {
+  return _mm512_reduce_min_epi32(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE int predux_max(const Packet16i& a) {
+  return _mm512_reduce_max_epi32(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE bool predux_any(const Packet16i& a) {
+  return _mm512_reduce_or_epi32(a) != 0;
+}
+
+/* -- -- -- -- -- -- -- -- -- -- -- -- Packet8l -- -- -- -- -- -- -- -- -- -- -- -- */
+
+template <>
+EIGEN_STRONG_INLINE int64_t predux(const Packet8l& a) {
+  return _mm512_reduce_add_epi64(a);
+}
+
+#if EIGEN_COMP_MSVC
+// MSVC's _mm512_reduce_mul_epi64 is borked, at least up to and including 1939.
+//    alignas(64) int64_t data[] = { 1,1,-1,-1,1,-1,-1,-1 };
+//    int64_t out = _mm512_reduce_mul_epi64(_mm512_load_epi64(data));
+// produces garbage: 4294967295.  It seems to happen whenever the output is supposed to be negative.
+// Fall back to a manual approach:
+template <>
+EIGEN_STRONG_INLINE int64_t predux_mul(const Packet8l& a) {
+  Packet4l lane0 = _mm512_extracti64x4_epi64(a, 0);
+  Packet4l lane1 = _mm512_extracti64x4_epi64(a, 1);
+  return predux_mul(pmul(lane0, lane1));
+}
+#else
+template <>
+EIGEN_STRONG_INLINE int64_t predux_mul<Packet8l>(const Packet8l& a) {
+  return _mm512_reduce_mul_epi64(a);
+}
+#endif
+
+template <>
+EIGEN_STRONG_INLINE int64_t predux_min(const Packet8l& a) {
+  return _mm512_reduce_min_epi64(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE int64_t predux_max(const Packet8l& a) {
+  return _mm512_reduce_max_epi64(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE bool predux_any(const Packet8l& a) {
+  return _mm512_reduce_or_epi64(a) != 0;
+}
+
+/* -- -- -- -- -- -- -- -- -- -- -- -- Packet16f -- -- -- -- -- -- -- -- -- -- -- -- */
+
+template <>
+EIGEN_STRONG_INLINE float predux(const Packet16f& a) {
+  return _mm512_reduce_add_ps(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_mul(const Packet16f& a) {
+  return _mm512_reduce_mul_ps(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_min(const Packet16f& a) {
+  return _mm512_reduce_min_ps(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_min<PropagateNumbers>(const Packet16f& a) {
+  Packet8f lane0 = _mm512_extractf32x8_ps(a, 0);
+  Packet8f lane1 = _mm512_extractf32x8_ps(a, 1);
+  return predux_min<PropagateNumbers>(pmin<PropagateNumbers>(lane0, lane1));
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_min<PropagateNaN>(const Packet16f& a) {
+  Packet8f lane0 = _mm512_extractf32x8_ps(a, 0);
+  Packet8f lane1 = _mm512_extractf32x8_ps(a, 1);
+  return predux_min<PropagateNaN>(pmin<PropagateNaN>(lane0, lane1));
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_max(const Packet16f& a) {
+  return _mm512_reduce_max_ps(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_max<PropagateNumbers>(const Packet16f& a) {
+  Packet8f lane0 = _mm512_extractf32x8_ps(a, 0);
+  Packet8f lane1 = _mm512_extractf32x8_ps(a, 1);
+  return predux_max<PropagateNumbers>(pmax<PropagateNumbers>(lane0, lane1));
+}
+
+template <>
+EIGEN_STRONG_INLINE float predux_max<PropagateNaN>(const Packet16f& a) {
+  Packet8f lane0 = _mm512_extractf32x8_ps(a, 0);
+  Packet8f lane1 = _mm512_extractf32x8_ps(a, 1);
+  return predux_max<PropagateNaN>(pmax<PropagateNaN>(lane0, lane1));
+}
+
+template <>
+EIGEN_STRONG_INLINE bool predux_any(const Packet16f& a) {
+  return _mm512_reduce_or_epi32(_mm512_castps_si512(a)) != 0;
+}
+
+/* -- -- -- -- -- -- -- -- -- -- -- -- Packet8d -- -- -- -- -- -- -- -- -- -- -- -- */
+
+template <>
+EIGEN_STRONG_INLINE double predux(const Packet8d& a) {
+  return _mm512_reduce_add_pd(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux_mul(const Packet8d& a) {
+  return _mm512_reduce_mul_pd(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux_min(const Packet8d& a) {
+  return _mm512_reduce_min_pd(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux_min<PropagateNumbers>(const Packet8d& a) {
+  Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);
+  Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);
+  return predux_min<PropagateNumbers>(pmin<PropagateNumbers>(lane0, lane1));
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux_min<PropagateNaN>(const Packet8d& a) {
+  Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);
+  Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);
+  return predux_min<PropagateNaN>(pmin<PropagateNaN>(lane0, lane1));
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux_max(const Packet8d& a) {
+  return _mm512_reduce_max_pd(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux_max<PropagateNumbers>(const Packet8d& a) {
+  Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);
+  Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);
+  return predux_max<PropagateNumbers>(pmax<PropagateNumbers>(lane0, lane1));
+}
+
+template <>
+EIGEN_STRONG_INLINE double predux_max<PropagateNaN>(const Packet8d& a) {
+  Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);
+  Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);
+  return predux_max<PropagateNaN>(pmax<PropagateNaN>(lane0, lane1));
+}
+
+template <>
+EIGEN_STRONG_INLINE bool predux_any(const Packet8d& a) {
+  return _mm512_reduce_or_epi64(_mm512_castpd_si512(a)) != 0;
+}
+
+#ifndef EIGEN_VECTORIZE_AVX512FP16
+/* -- -- -- -- -- -- -- -- -- -- -- -- Packet16h -- -- -- -- -- -- -- -- -- -- -- -- */
+
+template <>
+EIGEN_STRONG_INLINE half predux(const Packet16h& from) {
+  return half(predux(half2float(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux_mul(const Packet16h& from) {
+  return half(predux_mul(half2float(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux_min(const Packet16h& from) {
+  return half(predux_min(half2float(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux_min<PropagateNumbers>(const Packet16h& from) {
+  return half(predux_min<PropagateNumbers>(half2float(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux_min<PropagateNaN>(const Packet16h& from) {
+  return half(predux_min<PropagateNaN>(half2float(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux_max(const Packet16h& from) {
+  return half(predux_max(half2float(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux_max<PropagateNumbers>(const Packet16h& from) {
+  return half(predux_max<PropagateNumbers>(half2float(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE half predux_max<PropagateNaN>(const Packet16h& from) {
+  return half(predux_max<PropagateNaN>(half2float(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bool predux_any(const Packet16h& a) {
+  return predux_any<Packet8i>(a.m_val);
+}
+#endif
+
+/* -- -- -- -- -- -- -- -- -- -- -- -- Packet16bf -- -- -- -- -- -- -- -- -- -- -- -- */
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux(const Packet16bf& from) {
+  return static_cast<bfloat16>(predux<Packet16f>(Bf16ToF32(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_mul(const Packet16bf& from) {
+  return static_cast<bfloat16>(predux_mul<Packet16f>(Bf16ToF32(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_min(const Packet16bf& from) {
+  return static_cast<bfloat16>(predux_min<Packet16f>(Bf16ToF32(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_min<PropagateNumbers>(const Packet16bf& from) {
+  return static_cast<bfloat16>(predux_min<PropagateNumbers>(Bf16ToF32(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_min<PropagateNaN>(const Packet16bf& from) {
+  return static_cast<bfloat16>(predux_min<PropagateNaN>(Bf16ToF32(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_max(const Packet16bf& from) {
+  return static_cast<bfloat16>(predux_max(Bf16ToF32(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_max<PropagateNumbers>(const Packet16bf& from) {
+  return static_cast<bfloat16>(predux_max<PropagateNumbers>(Bf16ToF32(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bfloat16 predux_max<PropagateNaN>(const Packet16bf& from) {
+  return static_cast<bfloat16>(predux_max<PropagateNaN>(Bf16ToF32(from)));
+}
+
+template <>
+EIGEN_STRONG_INLINE bool predux_any(const Packet16bf& a) {
+  return predux_any<Packet8i>(a.m_val);
+}
+
+}  // end namespace internal
+}  // end namespace Eigen
+
+#endif  // EIGEN_REDUCTIONS_AVX512_H

Eigen/src/Core/arch/AVX512/TrsmUnrolls.inc

@@ -213,11 +213,12 @@ class trans {
   }
 
   /**
-   * Transposes LxunrollN row major block of matrices stored EIGEN_AVX_MAX_NUM_ACC zmm registers to
+   * Transposes LxunrollN row major block of matrices stored `EIGEN_AVX_MAX_NUM_ACC` zmm registers to
    * "unrollN"xL ymm registers to be stored col-major into C.
    *
    *  For 8x48, the 8x48 block (row-major) is stored in zmm as follows:
    *
+   *  ```
    *  row0: zmm0 zmm1 zmm2
    *  row1: zmm3 zmm4 zmm5
    *    .
@@ -231,10 +232,10 @@ class trans {
    *    .
    *    .
    *  row7: zmm14 zmm15
-   *
+   * ```
    *
    * In general we will have {1,2,3} groups of avx registers each of size
-   * EIGEN_AVX_MAX_NUM_ROW. packetIndexOffset is used to select which "block" of
+   * `EIGEN_AVX_MAX_NUM_ROW`. packetIndexOffset is used to select which "block" of
    * avx registers are being transposed.
    */
   template <int64_t unrollN, int64_t packetIndexOffset>

Eigen/src/Core/arch/AVX512/TypeCasting.h

@@ -237,16 +237,12 @@ EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i, Packet16i>(const Packet16i&
   return _mm512_castsi512_si128(a);
 }
 
+#ifndef EIGEN_VECTORIZE_AVX512FP16
 template <>
 EIGEN_STRONG_INLINE Packet8h preinterpret<Packet8h, Packet16h>(const Packet16h& a) {
   return _mm256_castsi256_si128(a);
 }
 
-template <>
-EIGEN_STRONG_INLINE Packet8bf preinterpret<Packet8bf, Packet16bf>(const Packet16bf& a) {
-  return _mm256_castsi256_si128(a);
-}
-
 template <>
 EIGEN_STRONG_INLINE Packet16f pcast<Packet16h, Packet16f>(const Packet16h& a) {
   return half2float(a);
@@ -257,6 +253,13 @@ EIGEN_STRONG_INLINE Packet16h pcast<Packet16f, Packet16h>(const Packet16f& a) {
   return float2half(a);
 }
 
+#endif
+
+template <>
+EIGEN_STRONG_INLINE Packet8bf preinterpret<Packet8bf, Packet16bf>(const Packet16bf& a) {
+  return _mm256_castsi256_si128(a);
+}
+
 template <>
 EIGEN_STRONG_INLINE Packet16f pcast<Packet16bf, Packet16f>(const Packet16bf& a) {
   return Bf16ToF32(a);
@@ -267,68 +270,6 @@ EIGEN_STRONG_INLINE Packet16bf pcast<Packet16f, Packet16bf>(const Packet16f& a)
   return F32ToBf16(a);
 }
 
-#ifdef EIGEN_VECTORIZE_AVX512FP16
-
-template <>
-EIGEN_STRONG_INLINE Packet16h preinterpret<Packet16h, Packet32h>(const Packet32h& a) {
-  return _mm256_castpd_si256(_mm512_extractf64x4_pd(_mm512_castph_pd(a), 0));
-}
-template <>
-EIGEN_STRONG_INLINE Packet8h preinterpret<Packet8h, Packet32h>(const Packet32h& a) {
-  return _mm256_castsi256_si128(preinterpret<Packet16h>(a));
-}
-
-template <>
-EIGEN_STRONG_INLINE Packet16f pcast<Packet32h, Packet16f>(const Packet32h& a) {
-  // Discard second-half of input.
-  Packet16h low = _mm256_castpd_si256(_mm512_extractf64x4_pd(_mm512_castph_pd(a), 0));
-  return _mm512_cvtxph_ps(_mm256_castsi256_ph(low));
-}
-
-template <>
-EIGEN_STRONG_INLINE Packet32h pcast<Packet16f, Packet32h>(const Packet16f& a, const Packet16f& b) {
-  __m512d result = _mm512_undefined_pd();
-  result = _mm512_insertf64x4(
-      result, _mm256_castsi256_pd(_mm512_cvtps_ph(a, _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC)), 0);
-  result = _mm512_insertf64x4(
-      result, _mm256_castsi256_pd(_mm512_cvtps_ph(b, _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC)), 1);
-  return _mm512_castpd_ph(result);
-}
-
-template <>
-EIGEN_STRONG_INLINE Packet8f pcast<Packet16h, Packet8f>(const Packet16h& a) {
-  // Discard second-half of input.
-  Packet8h low = _mm_castps_si128(_mm256_extractf32x4_ps(_mm256_castsi256_ps(a), 0));
-  return _mm256_cvtxph_ps(_mm_castsi128_ph(low));
-}
-
-template <>
-EIGEN_STRONG_INLINE Packet16h pcast<Packet8f, Packet16h>(const Packet8f& a, const Packet8f& b) {
-  __m256d result = _mm256_undefined_pd();
-  result = _mm256_insertf64x2(result,
-                              _mm_castsi128_pd(_mm256_cvtps_ph(a, _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC)), 0);
-  result = _mm256_insertf64x2(result,
-                              _mm_castsi128_pd(_mm256_cvtps_ph(b, _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC)), 1);
-  return _mm256_castpd_si256(result);
-}
-
-template <>
-EIGEN_STRONG_INLINE Packet4f pcast<Packet8h, Packet4f>(const Packet8h& a) {
-  Packet8f full = _mm256_cvtxph_ps(_mm_castsi128_ph(a));
-  // Discard second-half of input.
-  return _mm256_extractf32x4_ps(full, 0);
-}
-
-template <>
-EIGEN_STRONG_INLINE Packet8h pcast<Packet4f, Packet8h>(const Packet4f& a, const Packet4f& b) {
-  __m256 result = _mm256_undefined_ps();
-  result = _mm256_insertf128_ps(result, a, 0);
-  result = _mm256_insertf128_ps(result, b, 1);
-  return _mm256_cvtps_ph(result, _MM_FROUND_TO_NEAREST_INT);
-}
-
-#endif
-
 }  // end namespace internal
 
 }  // end namespace Eigen

Eigen/src/Core/arch/AVX512/TypeCastingFP16.h

@@ -0,0 +1,130 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2025 The Eigen Authors.
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TYPE_CASTING_FP16_AVX512_H
+#define EIGEN_TYPE_CASTING_FP16_AVX512_H
+
+// IWYU pragma: private
+#include "../../InternalHeaderCheck.h"
+
+namespace Eigen {
+namespace internal {
+
+template <>
+EIGEN_STRONG_INLINE Packet32s preinterpret<Packet32s, Packet32h>(const Packet32h& a) {
+  return _mm512_castph_si512(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16s preinterpret<Packet16s, Packet16h>(const Packet16h& a) {
+  return _mm256_castph_si256(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8s preinterpret<Packet8s, Packet8h>(const Packet8h& a) {
+  return _mm_castph_si128(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet32h preinterpret<Packet32h, Packet32s>(const Packet32s& a) {
+  return _mm512_castsi512_ph(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16h preinterpret<Packet16h, Packet16s>(const Packet16s& a) {
+  return _mm256_castsi256_ph(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8h preinterpret<Packet8h, Packet8s>(const Packet8s& a) {
+  return _mm_castsi128_ph(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pcast<Packet16h, Packet16f>(const Packet16h& a) {
+  return half2float(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8f pcast<Packet8h, Packet8f>(const Packet8h& a) {
+  return half2float(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16h pcast<Packet16f, Packet16h>(const Packet16f& a) {
+  return float2half(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8h pcast<Packet8f, Packet8h>(const Packet8f& a) {
+  return float2half(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet16f pcast<Packet32h, Packet16f>(const Packet32h& a) {
+  // Discard second-half of input.
+  Packet16h low = _mm256_castpd_ph(_mm512_extractf64x4_pd(_mm512_castph_pd(a), 0));
+  return _mm512_cvtxph_ps(low);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8f pcast<Packet16h, Packet8f>(const Packet16h& a) {
+  // Discard second-half of input.
+  Packet8h low = _mm_castps_ph(_mm256_extractf32x4_ps(_mm256_castph_ps(a), 0));
+  return _mm256_cvtxph_ps(low);
+}
+template <>
+EIGEN_STRONG_INLINE Packet4f pcast<Packet8h, Packet4f>(const Packet8h& a) {
+  Packet8f full = _mm256_cvtxph_ps(a);
+  // Discard second-half of input.
+  return _mm256_extractf32x4_ps(full, 0);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pcast<Packet16f, Packet32h>(const Packet16f& a, const Packet16f& b) {
+  __m512 result = _mm512_castsi512_ps(_mm512_castsi256_si512(_mm256_castph_si256(_mm512_cvtxps_ph(a))));
+  result = _mm512_insertf32x8(result, _mm256_castph_ps(_mm512_cvtxps_ph(b)), 1);
+  return _mm512_castps_ph(result);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16h pcast<Packet8f, Packet16h>(const Packet8f& a, const Packet8f& b) {
+  __m256 result = _mm256_castsi256_ps(_mm256_castsi128_si256(_mm_castph_si128(_mm256_cvtxps_ph(a))));
+  result = _mm256_insertf32x4(result, _mm_castph_ps(_mm256_cvtxps_ph(b)), 1);
+  return _mm256_castps_ph(result);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8h pcast<Packet4f, Packet8h>(const Packet4f& a, const Packet4f& b) {
+  __m256 result = _mm256_castsi256_ps(_mm256_castsi128_si256(_mm_castps_si128(a)));
+  result = _mm256_insertf128_ps(result, b, 1);
+  return _mm256_cvtxps_ph(result);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet32s pcast<Packet32h, Packet32s>(const Packet32h& a) {
+  return _mm512_cvtph_epi16(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16s pcast<Packet16h, Packet16s>(const Packet16h& a) {
+  return _mm256_cvtph_epi16(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8s pcast<Packet8h, Packet8s>(const Packet8h& a) {
+  return _mm_cvtph_epi16(a);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet32h pcast<Packet32s, Packet32h>(const Packet32s& a) {
+  return _mm512_cvtepi16_ph(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet16h pcast<Packet16s, Packet16h>(const Packet16s& a) {
+  return _mm256_cvtepi16_ph(a);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8h pcast<Packet8s, Packet8h>(const Packet8s& a) {
+  return _mm_cvtepi16_ph(a);
+}
+
+}  // namespace internal
+}  // namespace Eigen
+
+#endif  // EIGEN_TYPE_CASTING_FP16_AVX512_H

Eigen/src/Core/arch/AltiVec/Complex.h

@@ -18,19 +18,28 @@ namespace Eigen {
 
 namespace internal {
 
-static Packet4ui p4ui_CONJ_XOR =
-    vec_mergeh((Packet4ui)p4i_ZERO, (Packet4ui)p4f_MZERO);  //{ 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
+inline Packet4ui p4ui_CONJ_XOR() {
+  return vec_mergeh((Packet4ui)p4i_ZERO, (Packet4ui)p4f_MZERO);  //{ 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
+}
 #ifdef EIGEN_VECTORIZE_VSX
 #if defined(_BIG_ENDIAN)
-static Packet2ul p2ul_CONJ_XOR1 =
-    (Packet2ul)vec_sld((Packet4ui)p2d_MZERO, (Packet4ui)p2l_ZERO, 8);  //{ 0x8000000000000000, 0x0000000000000000 };
-static Packet2ul p2ul_CONJ_XOR2 =
-    (Packet2ul)vec_sld((Packet4ui)p2l_ZERO, (Packet4ui)p2d_MZERO, 8);  //{ 0x8000000000000000, 0x0000000000000000 };
+inline Packet2ul p2ul_CONJ_XOR1() {
+  return (Packet2ul)vec_sld((Packet4ui)p2d_MZERO, (Packet4ui)p2l_ZERO,
+                            8);  //{ 0x8000000000000000, 0x0000000000000000 };
+}
+inline Packet2ul p2ul_CONJ_XOR2() {
+  return (Packet2ul)vec_sld((Packet4ui)p2l_ZERO, (Packet4ui)p2d_MZERO,
+                            8);  //{ 0x8000000000000000, 0x0000000000000000 };
+}
 #else
-static Packet2ul p2ul_CONJ_XOR1 =
-    (Packet2ul)vec_sld((Packet4ui)p2l_ZERO, (Packet4ui)p2d_MZERO, 8);  //{ 0x8000000000000000, 0x0000000000000000 };
-static Packet2ul p2ul_CONJ_XOR2 =
-    (Packet2ul)vec_sld((Packet4ui)p2d_MZERO, (Packet4ui)p2l_ZERO, 8);  //{ 0x8000000000000000, 0x0000000000000000 };
+inline Packet2ul p2ul_CONJ_XOR1() {
+  return (Packet2ul)vec_sld((Packet4ui)p2l_ZERO, (Packet4ui)p2d_MZERO,
+                            8);  //{ 0x8000000000000000, 0x0000000000000000 };
+}
+inline Packet2ul p2ul_CONJ_XOR2() {
+  return (Packet2ul)vec_sld((Packet4ui)p2d_MZERO, (Packet4ui)p2l_ZERO,
+                            8);  //{ 0x8000000000000000, 0x0000000000000000 };
+}
 #endif
 #endif
 
@@ -50,7 +59,7 @@ struct Packet2cf {
     v1 = vec_madd(v1, b.v, p4f_ZERO);
     // multiply a_im * b and get the conjugate result
     v2 = vec_madd(v2, b.v, p4f_ZERO);
-    v2 = reinterpret_cast<Packet4f>(pxor(v2, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR)));
+    v2 = reinterpret_cast<Packet4f>(pxor(v2, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR())));
     // permute back to a proper order
     v2 = vec_perm(v2, v2, p16uc_COMPLEX32_REV);
 
@@ -266,7 +275,7 @@ EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) {
 }
 template <>
 EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a) {
-  return Packet2cf(pxor<Packet4f>(a.v, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR)));
+  return Packet2cf(pxor<Packet4f>(a.v, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR())));
 }
 
 template <>
@@ -399,7 +408,7 @@ struct Packet1cd {
     // multiply a_im * b and get the conjugate result
     v2 = vec_madd(a_im, b.v, p2d_ZERO);
     v2 = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(v2), reinterpret_cast<Packet4ui>(v2), 8));
-    v2 = pxor(v2, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR1));
+    v2 = pxor(v2, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR1()));
 
     return Packet1cd(padd<Packet2d>(v1, v2));
   }
@@ -543,7 +552,7 @@ EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) {
 }
 template <>
 EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a) {
-  return Packet1cd(pxor(a.v, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR2)));
+  return Packet1cd(pxor(a.v, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR2())));
 }
 
 template <>

Eigen/src/Core/arch/AltiVec/MatrixProduct.h

@@ -3155,7 +3155,7 @@ void gemmbfloat16(const DataMapper& res, const bfloat16* indexA, const bfloat16*
 
 #undef MAX_BFLOAT16_ACC_VSX
 
-#include "MatrixVectorProduct.h"
+#include "MatrixVectorProduct.inc"
 
 /************************************
  * ppc64le template specializations *

Eigen/src/Core/arch/AltiVec/PacketMath.h

@@ -185,7 +185,10 @@ struct packet_traits<float> : default_packet_traits {
     HasLog = 1,
     HasExp = 1,
 #ifdef EIGEN_VECTORIZE_VSX
+    HasCmp = 1,
+    HasPow = 1,
     HasSqrt = 1,
+    HasCbrt = 1,
 #if !EIGEN_COMP_CLANG
     HasRsqrt = 1,
 #else
@@ -193,6 +196,7 @@ struct packet_traits<float> : default_packet_traits {
 #endif
     HasTanh = EIGEN_FAST_MATH,
     HasErf = EIGEN_FAST_MATH,
+    HasErfc = EIGEN_FAST_MATH,
 #else
     HasSqrt = 0,
     HasRsqrt = 0,
@@ -423,55 +427,6 @@ struct unpacket_traits<Packet8bf> {
     masked_store_available = false
   };
 };
-inline std::ostream& operator<<(std::ostream& s, const Packet16c& v) {
-  union {
-    Packet16c v;
-    signed char n[16];
-  } vt;
-  vt.v = v;
-  for (int i = 0; i < 16; i++) s << vt.n[i] << ", ";
-  return s;
-}
-
-inline std::ostream& operator<<(std::ostream& s, const Packet16uc& v) {
-  union {
-    Packet16uc v;
-    unsigned char n[16];
-  } vt;
-  vt.v = v;
-  for (int i = 0; i < 16; i++) s << vt.n[i] << ", ";
-  return s;
-}
-
-inline std::ostream& operator<<(std::ostream& s, const Packet4f& v) {
-  union {
-    Packet4f v;
-    float n[4];
-  } vt;
-  vt.v = v;
-  s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
-  return s;
-}
-
-inline std::ostream& operator<<(std::ostream& s, const Packet4i& v) {
-  union {
-    Packet4i v;
-    int n[4];
-  } vt;
-  vt.v = v;
-  s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
-  return s;
-}
-
-inline std::ostream& operator<<(std::ostream& s, const Packet4ui& v) {
-  union {
-    Packet4ui v;
-    unsigned int n[4];
-  } vt;
-  vt.v = v;
-  s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
-  return s;
-}
 
 template <typename Packet>
 EIGEN_STRONG_INLINE Packet pload_common(const __UNPACK_TYPE__(Packet) * from) {
@@ -1513,16 +1468,13 @@ EIGEN_STRONG_INLINE Packet4f print<Packet4f>(const Packet4f& a) {
 
 template <typename Packet>
 EIGEN_STRONG_INLINE Packet ploadu_common(const __UNPACK_TYPE__(Packet) * from) {
-  EIGEN_DEBUG_ALIGNED_LOAD
-#if defined(EIGEN_VECTORIZE_VSX) || !defined(_BIG_ENDIAN)
   EIGEN_DEBUG_UNALIGNED_LOAD
+#if defined(EIGEN_VECTORIZE_VSX)
   return vec_xl(0, const_cast<__UNPACK_TYPE__(Packet)*>(from));
 #else
-  Packet16uc MSQ, LSQ;
-  Packet16uc mask;
-  MSQ = vec_ld(0, (unsigned char*)from);   // most significant quadword
-  LSQ = vec_ld(15, (unsigned char*)from);  // least significant quadword
-  mask = vec_lvsl(0, from);                // create the permute mask
+  Packet16uc MSQ = vec_ld(0, (unsigned char*)from);   // most significant quadword
+  Packet16uc LSQ = vec_ld(15, (unsigned char*)from);  // least significant quadword
+  Packet16uc mask = vec_lvsl(0, from);                // create the permute mask
   // TODO: Add static_cast here
   return (Packet)vec_perm(MSQ, LSQ, mask);  // align the data
 #endif
@@ -1732,7 +1684,7 @@ EIGEN_STRONG_INLINE Packet16uc ploadquad<Packet16uc>(const unsigned char* from)
 template <typename Packet>
 EIGEN_STRONG_INLINE void pstoreu_common(__UNPACK_TYPE__(Packet) * to, const Packet& from) {
   EIGEN_DEBUG_UNALIGNED_STORE
-#if defined(EIGEN_VECTORIZE_VSX) || !defined(_BIG_ENDIAN)
+#if defined(EIGEN_VECTORIZE_VSX)
   vec_xst(from, 0, to);
 #else
   // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
@@ -2068,7 +2020,7 @@ EIGEN_STRONG_INLINE Packet8bf F32ToBf16(Packet4f p4f) {
   input = padd<Packet4ui>(input, rounding_bias);
 
   const EIGEN_DECLARE_CONST_FAST_Packet4ui(nan, 0x7FC00000);
-#ifdef _ARCH_PWR9
+#if defined(_ARCH_PWR9) && defined(EIGEN_VECTORIZE_VSX)
   Packet4bi nan_selector = vec_test_data_class(p4f, __VEC_CLASS_FP_NAN);
   input = vec_sel(input, p4ui_nan, nan_selector);
 
@@ -2115,7 +2067,7 @@ EIGEN_STRONG_INLINE Packet8bf F32ToBf16(Packet4f p4f) {
 /**
  * Pack the high portion of two float Packets into one bfloat16 Packet
  *
- * @param lohi to expect either a low & high OR odd & even order
+ * @tparam lohi to expect either a low & high OR odd & even order
  */
 template <bool lohi>
 EIGEN_ALWAYS_INLINE Packet8bf Bf16PackHigh(Packet4f lo, Packet4f hi) {
@@ -2162,7 +2114,7 @@ EIGEN_ALWAYS_INLINE Packet8bf Bf16PackHigh(Packet4f hi, Packet4f lo) {
 /**
  * Convert and pack two float Packets into one bfloat16 Packet
  *
- * @param lohi to expect either a low & high OR odd & even order
+ * @tparam lohi to expect either a low & high OR odd & even order
  */
 template <bool lohi = true>
 EIGEN_ALWAYS_INLINE Packet8bf F32ToBf16Two(Packet4f lo, Packet4f hi) {
@@ -2177,7 +2129,7 @@ EIGEN_ALWAYS_INLINE Packet8bf F32ToBf16Two(Packet4f lo, Packet4f hi) {
   Packet8bi rounding_bias = vec_cmplt(lsb, p4f2);
   Packet8us input = psub<Packet8us>(p4f, reinterpret_cast<Packet8us>(rounding_bias));
 
-#ifdef _ARCH_PWR9
+#if defined(_ARCH_PWR9) && defined(EIGEN_VECTORIZE_VSX)
   Packet4bi nan_selector_lo = vec_test_data_class(lo, __VEC_CLASS_FP_NAN);
   Packet4bi nan_selector_hi = vec_test_data_class(hi, __VEC_CLASS_FP_NAN);
   Packet8us nan_selector =
@@ -2309,6 +2261,11 @@ EIGEN_STRONG_INLINE Packet8bf pexp<Packet8bf>(const Packet8bf& a) {
   BF16_TO_F32_UNARY_OP_WRAPPER(pexp_float, a);
 }
 
+template <>
+EIGEN_STRONG_INLINE Packet8bf pexp2<Packet8bf>(const Packet8bf& a) {
+  BF16_TO_F32_UNARY_OP_WRAPPER(generic_exp2, a);
+}
+
 template <>
 EIGEN_STRONG_INLINE Packet4f pldexp<Packet4f>(const Packet4f& a, const Packet4f& exponent) {
   return pldexp_generic(a, exponent);
@@ -2381,6 +2338,44 @@ EIGEN_STRONG_INLINE Packet8bf pmadd(const Packet8bf& a, const Packet8bf& b, cons
   return F32ToBf16(pmadd_even, pmadd_odd);
 }
 
+template <>
+EIGEN_STRONG_INLINE Packet8bf pmsub(const Packet8bf& a, const Packet8bf& b, const Packet8bf& c) {
+  Packet4f a_even = Bf16ToF32Even(a);
+  Packet4f a_odd = Bf16ToF32Odd(a);
+  Packet4f b_even = Bf16ToF32Even(b);
+  Packet4f b_odd = Bf16ToF32Odd(b);
+  Packet4f c_even = Bf16ToF32Even(c);
+  Packet4f c_odd = Bf16ToF32Odd(c);
+  Packet4f pmadd_even = pmsub<Packet4f>(a_even, b_even, c_even);
+  Packet4f pmadd_odd = pmsub<Packet4f>(a_odd, b_odd, c_odd);
+  return F32ToBf16(pmadd_even, pmadd_odd);
+}
+template <>
+EIGEN_STRONG_INLINE Packet8bf pnmadd(const Packet8bf& a, const Packet8bf& b, const Packet8bf& c) {
+  Packet4f a_even = Bf16ToF32Even(a);
+  Packet4f a_odd = Bf16ToF32Odd(a);
+  Packet4f b_even = Bf16ToF32Even(b);
+  Packet4f b_odd = Bf16ToF32Odd(b);
+  Packet4f c_even = Bf16ToF32Even(c);
+  Packet4f c_odd = Bf16ToF32Odd(c);
+  Packet4f pmadd_even = pnmadd<Packet4f>(a_even, b_even, c_even);
+  Packet4f pmadd_odd = pnmadd<Packet4f>(a_odd, b_odd, c_odd);
+  return F32ToBf16(pmadd_even, pmadd_odd);
+}
+
+template <>
+EIGEN_STRONG_INLINE Packet8bf pnmsub(const Packet8bf& a, const Packet8bf& b, const Packet8bf& c) {
+  Packet4f a_even = Bf16ToF32Even(a);
+  Packet4f a_odd = Bf16ToF32Odd(a);
+  Packet4f b_even = Bf16ToF32Even(b);
+  Packet4f b_odd = Bf16ToF32Odd(b);
+  Packet4f c_even = Bf16ToF32Even(c);
+  Packet4f c_odd = Bf16ToF32Odd(c);
+  Packet4f pmadd_even = pnmsub<Packet4f>(a_even, b_even, c_even);
+  Packet4f pmadd_odd = pnmsub<Packet4f>(a_odd, b_odd, c_odd);
+  return F32ToBf16(pmadd_even, pmadd_odd);
+}
+
 template <>
 EIGEN_STRONG_INLINE Packet8bf pmin<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
   BF16_TO_F32_BINARY_OP_WRAPPER(pmin<Packet4f>, a, b);
@@ -3177,11 +3172,15 @@ struct packet_traits<double> : default_packet_traits {
     HasSin = EIGEN_FAST_MATH,
     HasCos = EIGEN_FAST_MATH,
     HasTanh = EIGEN_FAST_MATH,
+    HasErf = EIGEN_FAST_MATH,
+    HasErfc = EIGEN_FAST_MATH,
     HasATanh = 1,
     HasATan = 0,
     HasLog = 0,
+    HasCmp = 1,
     HasExp = 1,
     HasSqrt = 1,
+    HasCbrt = 1,
 #if !EIGEN_COMP_CLANG
     HasRsqrt = 1,
 #else
@@ -3392,9 +3391,17 @@ EIGEN_STRONG_INLINE Packet2d pcmp_eq(const Packet2d& a, const Packet2d& b) {
   return reinterpret_cast<Packet2d>(vec_cmpeq(a, b));
 }
 template <>
+#ifdef __POWER8_VECTOR__
 EIGEN_STRONG_INLINE Packet2l pcmp_eq(const Packet2l& a, const Packet2l& b) {
   return reinterpret_cast<Packet2l>(vec_cmpeq(a, b));
 }
+#else
+EIGEN_STRONG_INLINE Packet2l pcmp_eq(const Packet2l& a, const Packet2l& b) {
+  Packet4i halves = reinterpret_cast<Packet4i>(vec_cmpeq(reinterpret_cast<Packet4i>(a), reinterpret_cast<Packet4i>(b)));
+  Packet4i flipped = vec_perm(halves, halves, p16uc_COMPLEX32_REV);
+  return reinterpret_cast<Packet2l>(pand(halves, flipped));
+}
+#endif
 template <>
 EIGEN_STRONG_INLINE Packet2d pcmp_lt_or_nan(const Packet2d& a, const Packet2d& b) {
   Packet2d c = reinterpret_cast<Packet2d>(vec_cmpge(a, b));

Eigen/src/Core/arch/AltiVec/TypeCasting.h

@@ -129,30 +129,20 @@ EIGEN_STRONG_INLINE Packet4f preinterpret<Packet4f, Packet4i>(const Packet4i& a)
 }
 
 #ifdef EIGEN_VECTORIZE_VSX
-// VSX support varies between different compilers and even different
-// versions of the same compiler.  For gcc version >= 4.9.3, we can use
-// vec_cts to efficiently convert Packet2d to Packet2l.  Otherwise, use
-// a slow version that works with older compilers.
-// Update: apparently vec_cts/vec_ctf intrinsics for 64-bit doubles
-// are buggy, https://gcc.gnu.org/bugzilla/show_bug.cgi?id=70963
 template <>
 inline Packet2l pcast<Packet2d, Packet2l>(const Packet2d& x) {
-#if EIGEN_GNUC_STRICT_AT_LEAST(7, 1, 0)
-  return vec_cts(x, 0);  // TODO: check clang version.
-#else
-  double tmp[2];
-  memcpy(tmp, &x, sizeof(tmp));
-  Packet2l l = {static_cast<long long>(tmp[0]), static_cast<long long>(tmp[1])};
-  return l;
-#endif
+  EIGEN_ALIGN_MAX double dtmp[2];
+  pstore(dtmp, x);
+  EIGEN_ALIGN_MAX long long itmp[2] = {static_cast<long long>(dtmp[0]), static_cast<long long>(dtmp[1])};
+  return vec_xl(0, itmp);
 }
 
 template <>
 inline Packet2d pcast<Packet2l, Packet2d>(const Packet2l& x) {
-  unsigned long long tmp[2];
-  memcpy(tmp, &x, sizeof(tmp));
-  Packet2d d = {static_cast<double>(tmp[0]), static_cast<double>(tmp[1])};
-  return d;
+  EIGEN_ALIGN_MAX long long itmp[2];
+  vec_xst(x, 0, itmp);
+  EIGEN_ALIGN_MAX double dtmp[2] = {static_cast<double>(itmp[0]), static_cast<double>(itmp[1])};
+  return pload<Packet2d>(dtmp);
 }
 #endif
 

Eigen/src/Core/arch/Default/BFloat16.h

@@ -613,6 +613,7 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 abs(const bfloat16& a) {
   return numext::bit_cast<bfloat16>(x);
 }
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 exp(const bfloat16& a) { return bfloat16(::expf(float(a))); }
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 exp2(const bfloat16& a) { return bfloat16(::exp2f(float(a))); }
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 expm1(const bfloat16& a) { return bfloat16(numext::expm1(float(a))); }
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 log(const bfloat16& a) { return bfloat16(::logf(float(a))); }
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 log1p(const bfloat16& a) { return bfloat16(numext::log1p(float(a))); }
@@ -672,6 +673,11 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 fmax(const bfloat16& a, const bfl
   return bfloat16(::fmaxf(f1, f2));
 }
 
+EIGEN_DEVICE_FUNC inline bfloat16 fma(const bfloat16& a, const bfloat16& b, const bfloat16& c) {
+  // Emulate FMA via float.
+  return bfloat16(numext::fma(static_cast<float>(a), static_cast<float>(b), static_cast<float>(c)));
+}
+
 #ifndef EIGEN_NO_IO
 EIGEN_ALWAYS_INLINE std::ostream& operator<<(std::ostream& os, const bfloat16& v) {
   os << static_cast<float>(v);
@@ -762,6 +768,37 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC uint16_t bit_cast<uint16_t, Eigen::bfloat1
   return Eigen::bfloat16_impl::raw_bfloat16_as_uint16(src);
 }
 
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 nextafter(const bfloat16& from, const bfloat16& to) {
+  if (numext::isnan EIGEN_NOT_A_MACRO(from)) {
+    return from;
+  }
+  if (numext::isnan EIGEN_NOT_A_MACRO(to)) {
+    return to;
+  }
+  if (from == to) {
+    return to;
+  }
+  uint16_t from_bits = numext::bit_cast<uint16_t>(from);
+  bool from_sign = from_bits >> 15;
+  // Whether we are adjusting toward the infinity with the same sign as from.
+  bool toward_inf = (to > from) == !from_sign;
+  if (toward_inf) {
+    ++from_bits;
+  } else if ((from_bits & 0x7fff) == 0) {
+    // Adjusting away from inf, but from is zero, so just toggle the sign.
+    from_bits ^= 0x8000;
+  } else {
+    --from_bits;
+  }
+  return numext::bit_cast<bfloat16>(from_bits);
+}
+
+// Specialize multiply-add to match packet operations and reduce conversions to/from float.
+template<>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 madd<Eigen::bfloat16>(const Eigen::bfloat16& x, const Eigen::bfloat16& y, const Eigen::bfloat16& z) {
+  return Eigen::bfloat16(static_cast<float>(x) * static_cast<float>(y) + static_cast<float>(z));
+}
+
 }  // namespace numext
 }  // namespace Eigen
 

Eigen/src/Core/arch/Default/GenericPacketMathFunctionsFwd.h

@@ -42,6 +42,26 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Packet pfrexp_generic_get_biased_exponent(
 template <typename Packet>
 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Packet pldexp_generic(const Packet& a, const Packet& exponent);
 
+// Explicitly multiplies
+//    a * (2^e)
+// clamping e to the range
+// [NumTraits<Scalar>::min_exponent()-2, NumTraits<Scalar>::max_exponent()]
+//
+// This is approx 7x faster than pldexp_impl, but will prematurely over/underflow
+// if 2^e doesn't fit into a normal floating-point Scalar.
+//
+// Assumes IEEE floating point format
+template <typename Packet>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Packet pldexp_fast(const Packet& a, const Packet& exponent);
+
+/** \internal \returns cbrt(x) for single precision float */
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pcbrt_float(const Packet& x_in);
+
+/** \internal \returns cbrt(x) for double precision float */
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet pcbrt_double(const Packet& x_in);
+
 /** \internal \returns log(x) for single precision float */
 template <typename Packet>
 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet plog_float(const Packet _x);
@@ -60,15 +80,19 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet plog2_double(const Pa
 
 /** \internal \returns log(1 + x) */
 template <typename Packet>
-Packet generic_plog1p(const Packet& x);
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet generic_log1p(const Packet& x);
 
 /** \internal \returns exp(x)-1 */
 template <typename Packet>
-Packet generic_expm1(const Packet& x);
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet generic_expm1(const Packet& x);
 
 /** \internal \returns atan(x) */
 template <typename Packet>
-EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet generic_patan(const Packet& x);
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet generic_atan(const Packet& x);
+
+/** \internal \returns exp2(x) */
+template <typename Packet>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet generic_exp2(const Packet& x);
 
 /** \internal \returns exp(x) for single precision float */
 template <typename Packet>
@@ -159,44 +183,43 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet generic_round(const Packet& a);
     return p##METHOD##_##SCALAR(_x);                                                              \
   }
 
+// Macros for instantiating these generic functions for different backends.
+#define EIGEN_GENERIC_PACKET_FUNCTION(METHOD, PACKET)                                             \
+  template <>                                                                                     \
+  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_UNUSED PACKET p##METHOD<PACKET>(const PACKET& _x) { \
+    return generic_##METHOD(_x);                                                                  \
+  }
+
 #define EIGEN_FLOAT_PACKET_FUNCTION(METHOD, PACKET) EIGEN_PACKET_FUNCTION(METHOD, float, PACKET)
 #define EIGEN_DOUBLE_PACKET_FUNCTION(METHOD, PACKET) EIGEN_PACKET_FUNCTION(METHOD, double, PACKET)
 
-#define EIGEN_INSTANTIATE_GENERIC_MATH_FUNCS_FLOAT(PACKET)                                     \
-  EIGEN_FLOAT_PACKET_FUNCTION(sin, PACKET)                                                     \
-  EIGEN_FLOAT_PACKET_FUNCTION(cos, PACKET)                                                     \
-  EIGEN_FLOAT_PACKET_FUNCTION(asin, PACKET)                                                    \
-  EIGEN_FLOAT_PACKET_FUNCTION(acos, PACKET)                                                    \
-  EIGEN_FLOAT_PACKET_FUNCTION(tanh, PACKET)                                                    \
-  EIGEN_FLOAT_PACKET_FUNCTION(atanh, PACKET)                                                   \
-  EIGEN_FLOAT_PACKET_FUNCTION(log, PACKET)                                                     \
-  EIGEN_FLOAT_PACKET_FUNCTION(log2, PACKET)                                                    \
-  EIGEN_FLOAT_PACKET_FUNCTION(exp, PACKET)                                                     \
-  template <>                                                                                  \
-  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_UNUSED PACKET pexpm1<PACKET>(const PACKET& _x) { \
-    return generic_expm1(_x);                                                                  \
-  }                                                                                            \
-  template <>                                                                                  \
-  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_UNUSED PACKET plog1p<PACKET>(const PACKET& _x) { \
-    return generic_plog1p(_x);                                                                 \
-  }                                                                                            \
-  template <>                                                                                  \
-  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_UNUSED PACKET patan<PACKET>(const PACKET& _x) {  \
-    return generic_patan(_x);                                                                  \
-  }
+#define EIGEN_INSTANTIATE_GENERIC_MATH_FUNCS_FLOAT(PACKET) \
+  EIGEN_FLOAT_PACKET_FUNCTION(sin, PACKET)                 \
+  EIGEN_FLOAT_PACKET_FUNCTION(cos, PACKET)                 \
+  EIGEN_FLOAT_PACKET_FUNCTION(asin, PACKET)                \
+  EIGEN_FLOAT_PACKET_FUNCTION(acos, PACKET)                \
+  EIGEN_FLOAT_PACKET_FUNCTION(tanh, PACKET)                \
+  EIGEN_FLOAT_PACKET_FUNCTION(atanh, PACKET)               \
+  EIGEN_FLOAT_PACKET_FUNCTION(log, PACKET)                 \
+  EIGEN_FLOAT_PACKET_FUNCTION(log2, PACKET)                \
+  EIGEN_FLOAT_PACKET_FUNCTION(exp, PACKET)                 \
+  EIGEN_FLOAT_PACKET_FUNCTION(cbrt, PACKET)                \
+  EIGEN_GENERIC_PACKET_FUNCTION(expm1, PACKET)             \
+  EIGEN_GENERIC_PACKET_FUNCTION(exp2, PACKET)              \
+  EIGEN_GENERIC_PACKET_FUNCTION(log1p, PACKET)             \
+  EIGEN_GENERIC_PACKET_FUNCTION(atan, PACKET)
 
-#define EIGEN_INSTANTIATE_GENERIC_MATH_FUNCS_DOUBLE(PACKET)                                   \
-  EIGEN_DOUBLE_PACKET_FUNCTION(atanh, PACKET)                                                 \
-  EIGEN_DOUBLE_PACKET_FUNCTION(log, PACKET)                                                   \
-  EIGEN_DOUBLE_PACKET_FUNCTION(sin, PACKET)                                                   \
-  EIGEN_DOUBLE_PACKET_FUNCTION(cos, PACKET)                                                   \
-  EIGEN_DOUBLE_PACKET_FUNCTION(log2, PACKET)                                                  \
-  EIGEN_DOUBLE_PACKET_FUNCTION(exp, PACKET)                                                   \
-  EIGEN_DOUBLE_PACKET_FUNCTION(tanh, PACKET)                                                  \
-  template <>                                                                                 \
-  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_UNUSED PACKET patan<PACKET>(const PACKET& _x) { \
-    return generic_patan(_x);                                                                 \
-  }
+#define EIGEN_INSTANTIATE_GENERIC_MATH_FUNCS_DOUBLE(PACKET) \
+  EIGEN_DOUBLE_PACKET_FUNCTION(atanh, PACKET)               \
+  EIGEN_DOUBLE_PACKET_FUNCTION(log, PACKET)                 \
+  EIGEN_DOUBLE_PACKET_FUNCTION(sin, PACKET)                 \
+  EIGEN_DOUBLE_PACKET_FUNCTION(cos, PACKET)                 \
+  EIGEN_DOUBLE_PACKET_FUNCTION(log2, PACKET)                \
+  EIGEN_DOUBLE_PACKET_FUNCTION(exp, PACKET)                 \
+  EIGEN_DOUBLE_PACKET_FUNCTION(tanh, PACKET)                \
+  EIGEN_DOUBLE_PACKET_FUNCTION(cbrt, PACKET)                \
+  EIGEN_GENERIC_PACKET_FUNCTION(atan, PACKET)               \
+  EIGEN_GENERIC_PACKET_FUNCTION(exp2, PACKET)
 
 }  // end namespace internal
 }  // end namespace Eigen