Macros.h

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@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_MACROS_H
#define EIGEN_MACROS_H
#include "../InternalHeaderCheck.h"
 
//------------------------------------------------------------------------------------------
// Eigen version and basic defaults
//------------------------------------------------------------------------------------------
 
#define EIGEN_WORLD_VERSION 3
#define EIGEN_MAJOR_VERSION 4
#define EIGEN_MINOR_VERSION 90
 
#define EIGEN_VERSION_AT_LEAST(x,y,z) (EIGEN_WORLD_VERSION>x || (EIGEN_WORLD_VERSION>=x && \
                                      (EIGEN_MAJOR_VERSION>y || (EIGEN_MAJOR_VERSION>=y && \
                                                                 EIGEN_MINOR_VERSION>=z))))
 
#ifdef EIGEN_DEFAULT_TO_ROW_MAJOR
#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION Eigen::RowMajor
#else
#define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION Eigen::ColMajor
#endif
 
#ifndef EIGEN_DEFAULT_DENSE_INDEX_TYPE
#define EIGEN_DEFAULT_DENSE_INDEX_TYPE std::ptrdiff_t
#endif
 
// Upperbound on the C++ version to use.
// Expected values are 03, 11, 14, 17, etc.
// By default, let's use an arbitrarily large C++ version.
#ifndef EIGEN_MAX_CPP_VER
#define EIGEN_MAX_CPP_VER 99
#endif
 
#ifndef EIGEN_FAST_MATH
#define EIGEN_FAST_MATH 1
#endif
 
#ifndef EIGEN_STACK_ALLOCATION_LIMIT
// 131072 == 128 KB
#define EIGEN_STACK_ALLOCATION_LIMIT 131072
#endif
 
//------------------------------------------------------------------------------------------
// Compiler identification, EIGEN_COMP_*
//------------------------------------------------------------------------------------------
 
#ifdef __GNUC__
  #define EIGEN_COMP_GNUC (__GNUC__*100+__GNUC_MINOR__*10+__GNUC_PATCHLEVEL__)
#else
  #define EIGEN_COMP_GNUC 0
#endif
 
#if defined(__clang__)
  #define EIGEN_COMP_CLANG (__clang_major__*100+__clang_minor__*10+__clang_patchlevel__)
#else
  #define EIGEN_COMP_CLANG 0
#endif
 
#if defined(__clang__) && defined(__apple_build_version__)
  #define EIGEN_COMP_CLANGAPPLE __apple_build_version__
#else
  #define EIGEN_COMP_CLANGAPPLE 0
#endif
 
#if defined(__castxml__)
  #define EIGEN_COMP_CASTXML 1
#else
  #define EIGEN_COMP_CASTXML 0
#endif
 
#if defined(__llvm__)
  #define EIGEN_COMP_LLVM 1
#else
  #define EIGEN_COMP_LLVM 0
#endif
 
#if defined(__INTEL_COMPILER)
  #define EIGEN_COMP_ICC __INTEL_COMPILER
#else
  #define EIGEN_COMP_ICC 0
#endif
 
#if defined(__INTEL_CLANG_COMPILER)
  #define EIGEN_COMP_CLANGICC __INTEL_CLANG_COMPILER
#else
  #define EIGEN_COMP_CLANGICC 0
#endif
 
#if defined(__MINGW32__)
  #define EIGEN_COMP_MINGW 1
#else
  #define EIGEN_COMP_MINGW 0
#endif
 
#if defined(__SUNPRO_CC)
  #define EIGEN_COMP_SUNCC 1
#else
  #define EIGEN_COMP_SUNCC 0
#endif
 
#if defined(_MSC_VER)
  #define EIGEN_COMP_MSVC _MSC_VER
#else
  #define EIGEN_COMP_MSVC 0
#endif
 
#if defined(__NVCC__)
#if defined(__CUDACC_VER_MAJOR__) && (__CUDACC_VER_MAJOR__ >= 9)
  #define EIGEN_COMP_NVCC  ((__CUDACC_VER_MAJOR__ * 10000) + (__CUDACC_VER_MINOR__ * 100))
#elif defined(__CUDACC_VER__)
  #define EIGEN_COMP_NVCC __CUDACC_VER__
#else
  #error "NVCC did not define compiler version."
#endif
#else
  #define EIGEN_COMP_NVCC 0
#endif
 
// For the record, here is a table summarizing the possible values for EIGEN_COMP_MSVC:
//  name        ver   MSC_VER
//  2015        14      1900
//  "15"        15      1900
//  2017-14.1   15.0    1910
//  2017-14.11  15.3    1911
//  2017-14.12  15.5    1912
//  2017-14.13  15.6    1913
//  2017-14.14  15.7    1914
//  2017        15.8    1915
//  2017        15.9    1916
//  2019 RTW    16.0    1920
 
#if defined(_MSVC_LANG)
  #define EIGEN_COMP_MSVC_LANG _MSVC_LANG
#else
  #define EIGEN_COMP_MSVC_LANG 0
#endif
 
// For the record, here is a table summarizing the possible values for EIGEN_COMP_MSVC_LANG:
// MSVC option                          Standard  MSVC_LANG
// /std:c++14 (default as of VS 2019)   C++14     201402L
// /std:c++17                           C++17     201703L
// /std:c++latest                       >C++17    >201703L
 
#if EIGEN_COMP_MSVC && !(EIGEN_COMP_ICC || EIGEN_COMP_LLVM || EIGEN_COMP_CLANG)
  #define EIGEN_COMP_MSVC_STRICT _MSC_VER
#else
  #define EIGEN_COMP_MSVC_STRICT 0
#endif
 
// XLC   version
// 3.1   0x0301
// 4.5   0x0405
// 5.0   0x0500
// 12.1  0x0C01
#if defined(__IBMCPP__) || defined(__xlc__) || defined(__ibmxl__)
  #define EIGEN_COMP_IBM __xlC__
#else
  #define EIGEN_COMP_IBM 0
#endif
 
#if defined(__PGI)
  #define EIGEN_COMP_PGI (__PGIC__*100+__PGIC_MINOR__)
#else
  #define EIGEN_COMP_PGI 0
#endif
 
#if defined(__CC_ARM) || defined(__ARMCC_VERSION)
  #define EIGEN_COMP_ARM 1
#else
  #define EIGEN_COMP_ARM 0
#endif
 
#if defined(__EMSCRIPTEN__)
  #define EIGEN_COMP_EMSCRIPTEN 1
#else
  #define EIGEN_COMP_EMSCRIPTEN 0
#endif
 
#if defined(__FUJITSU)
  #define EIGEN_COMP_FCC (__FCC_major__*100+__FCC_minor__*10+__FCC_patchlevel__)
#else
  #define EIGEN_COMP_FCC 0
#endif
 
#if defined(__CLANG_FUJITSU)
  #define EIGEN_COMP_CLANGFCC (__FCC_major__*100+__FCC_minor__*10+__FCC_patchlevel__)
#else
  #define EIGEN_COMP_CLANGFCC 0
#endif
 
#if defined(_CRAYC) && !defined(__clang__)
  #define EIGEN_COMP_CPE (_RELEASE_MAJOR*100+_RELEASE_MINOR*10+_RELEASE_PATCHLEVEL)
#else
  #define EIGEN_COMP_CPE 0
#endif
 
#if defined(_CRAYC) && defined(__clang__)
  #define EIGEN_COMP_CLANGCPE (_RELEASE_MAJOR*100+_RELEASE_MINOR*10+_RELEASE_PATCHLEVEL)
#else
  #define EIGEN_COMP_CLANGCPE 0
#endif
 
#if defined(__LCC__) && defined(__MCST__)
  #define EIGEN_COMP_LCC (__LCC__*100+__LCC_MINOR__)
#else
  #define EIGEN_COMP_LCC 0
#endif
 
 
#if EIGEN_COMP_GNUC && !(EIGEN_COMP_CLANG || EIGEN_COMP_ICC || EIGEN_COMP_CLANGICC || EIGEN_COMP_MINGW || EIGEN_COMP_PGI || EIGEN_COMP_IBM || EIGEN_COMP_ARM || EIGEN_COMP_EMSCRIPTEN || EIGEN_COMP_FCC || EIGEN_COMP_CLANGFCC || EIGEN_COMP_CPE || EIGEN_COMP_CLANGCPE || EIGEN_COMP_LCC)
  #define EIGEN_COMP_GNUC_STRICT 1
#else
  #define EIGEN_COMP_GNUC_STRICT 0
#endif
 
// GCC, and compilers that pretend to be it, have different version schemes, so this only makes sense to use with the real GCC.
#if EIGEN_COMP_GNUC_STRICT
  #define EIGEN_GNUC_STRICT_AT_LEAST(x,y,z)  ((__GNUC__ > x) || \
                                              (__GNUC__ == x && __GNUC_MINOR__ > y) || \
                                              (__GNUC__ == x && __GNUC_MINOR__ == y && __GNUC_PATCHLEVEL__ >= z))
  #define EIGEN_GNUC_STRICT_LESS_THAN(x,y,z) ((__GNUC__ < x) || \
                                              (__GNUC__ == x && __GNUC_MINOR__ < y) || \
                                              (__GNUC__ == x && __GNUC_MINOR__ == y && __GNUC_PATCHLEVEL__ < z))
#else
  #define EIGEN_GNUC_STRICT_AT_LEAST(x,y,z)  0
  #define EIGEN_GNUC_STRICT_LESS_THAN(x,y,z) 0
#endif
 
 
 
#if EIGEN_COMP_CLANG && !(EIGEN_COMP_CLANGAPPLE || EIGEN_COMP_CLANGICC || EIGEN_COMP_CLANGFCC || EIGEN_COMP_CLANGCPE)
  #define EIGEN_COMP_CLANG_STRICT 1
#else
  #define EIGEN_COMP_CLANG_STRICT 0
#endif
 
// Clang, and compilers forked from it, have different version schemes, so this only makes sense to use with the real Clang.
#if EIGEN_COMP_CLANG_STRICT
  #define EIGEN_CLANG_STRICT_AT_LEAST(x,y,z)  ((__clang_major__ > x) || \
                                               (__clang_major__ == x && __clang_minor__ > y) || \
                                               (__clang_major__ == x && __clang_minor__ == y && __clang_patchlevel__ >= z))
  #define EIGEN_CLANG_STRICT_LESS_THAN(x,y,z) ((__clang_major__ < x) || \
                                               (__clang_major__ == x && __clang_minor__ < y) || \
                                               (__clang_major__ == x && __clang_minor__ == y && __clang_patchlevel__ < z))
#else
  #define EIGEN_CLANG_STRICT_AT_LEAST(x,y,z)  0
  #define EIGEN_CLANG_STRICT_LESS_THAN(x,y,z) 0
#endif
 
//------------------------------------------------------------------------------------------
// Architecture identification, EIGEN_ARCH_*
//------------------------------------------------------------------------------------------
 
 
#if defined(__x86_64__) || (defined(_M_X64) && !defined(_M_ARM64EC)) || defined(__amd64)
  #define EIGEN_ARCH_x86_64 1
#else
  #define EIGEN_ARCH_x86_64 0
#endif
 
#if defined(__i386__) || defined(_M_IX86) || defined(_X86_) || defined(__i386)
  #define EIGEN_ARCH_i386 1
#else
  #define EIGEN_ARCH_i386 0
#endif
 
#if EIGEN_ARCH_x86_64 || EIGEN_ARCH_i386
  #define EIGEN_ARCH_i386_OR_x86_64 1
#else
  #define EIGEN_ARCH_i386_OR_x86_64 0
#endif
 
#if defined(__arm__)
  #define EIGEN_ARCH_ARM 1
#else
  #define EIGEN_ARCH_ARM 0
#endif
 
#if defined(__aarch64__) || defined(_M_ARM64) || defined(_M_ARM64EC)
  #define EIGEN_ARCH_ARM64 1
#else
  #define EIGEN_ARCH_ARM64 0
#endif
 
#if EIGEN_ARCH_ARM || EIGEN_ARCH_ARM64
  #define EIGEN_ARCH_ARM_OR_ARM64 1
#else
  #define EIGEN_ARCH_ARM_OR_ARM64 0
#endif
 
#if EIGEN_ARCH_ARM_OR_ARM64 && defined(__ARM_ARCH) && __ARM_ARCH >= 8
#define EIGEN_ARCH_ARMV8 1
#else
#define EIGEN_ARCH_ARMV8 0
#endif
 
 
#if EIGEN_ARCH_ARM_OR_ARM64
  #ifndef EIGEN_HAS_ARM64_FP16
    #if defined(__ARM_FP16_FORMAT_IEEE)
      #define EIGEN_HAS_ARM64_FP16 1
    #else
      #define EIGEN_HAS_ARM64_FP16 0
    #endif
  #endif
#endif
 
#if defined(__mips__) || defined(__mips)
  #define EIGEN_ARCH_MIPS 1
#else
  #define EIGEN_ARCH_MIPS 0
#endif
 
#if defined(__sparc__) || defined(__sparc)
  #define EIGEN_ARCH_SPARC 1
#else
  #define EIGEN_ARCH_SPARC 0
#endif
 
#if defined(__ia64__)
  #define EIGEN_ARCH_IA64 1
#else
  #define EIGEN_ARCH_IA64 0
#endif
 
#if defined(__powerpc__) || defined(__ppc__) || defined(_M_PPC) || defined(__POWERPC__)
  #define EIGEN_ARCH_PPC 1
#else
  #define EIGEN_ARCH_PPC 0
#endif
 
 
 
//------------------------------------------------------------------------------------------
// Operating system identification, EIGEN_OS_*
//------------------------------------------------------------------------------------------
 
#if defined(__unix__) || defined(__unix)
  #define EIGEN_OS_UNIX 1
#else
  #define EIGEN_OS_UNIX 0
#endif
 
#if defined(__linux__)
  #define EIGEN_OS_LINUX 1
#else
  #define EIGEN_OS_LINUX 0
#endif
 
// note: ANDROID is defined when using ndk_build, __ANDROID__ is defined when using a standalone toolchain.
#if defined(__ANDROID__) || defined(ANDROID)
  #define EIGEN_OS_ANDROID 1
#else
  #define EIGEN_OS_ANDROID 0
#endif
 
#if defined(__gnu_linux__) && !(EIGEN_OS_ANDROID)
  #define EIGEN_OS_GNULINUX 1
#else
  #define EIGEN_OS_GNULINUX 0
#endif
 
#if defined(__FreeBSD__) || defined(__NetBSD__) || defined(__OpenBSD__) || defined(__bsdi__) || defined(__DragonFly__)
  #define EIGEN_OS_BSD 1
#else
  #define EIGEN_OS_BSD 0
#endif
 
#if defined(__APPLE__)
  #define EIGEN_OS_MAC 1
#else
  #define EIGEN_OS_MAC 0
#endif
 
#if defined(__QNX__)
  #define EIGEN_OS_QNX 1
#else
  #define EIGEN_OS_QNX 0
#endif
 
#if defined(_WIN32)
  #define EIGEN_OS_WIN 1
#else
  #define EIGEN_OS_WIN 0
#endif
 
#if defined(_WIN64)
  #define EIGEN_OS_WIN64 1
#else
  #define EIGEN_OS_WIN64 0
#endif
 
#if defined(_WIN32_WCE)
  #define EIGEN_OS_WINCE 1
#else
  #define EIGEN_OS_WINCE 0
#endif
 
#if defined(__CYGWIN__)
  #define EIGEN_OS_CYGWIN 1
#else
  #define EIGEN_OS_CYGWIN 0
#endif
 
#if EIGEN_OS_WIN && !( EIGEN_OS_WINCE || EIGEN_OS_CYGWIN )
  #define EIGEN_OS_WIN_STRICT 1
#else
  #define EIGEN_OS_WIN_STRICT 0
#endif
 
// compiler  solaris   __SUNPRO_C
// version   studio
// 5.7       10        0x570
// 5.8       11        0x580
// 5.9       12        0x590
// 5.10      12.1      0x5100
// 5.11      12.2      0x5110
// 5.12      12.3      0x5120
#if (defined(sun) || defined(__sun)) && !(defined(__SVR4) || defined(__svr4__))
  #define EIGEN_OS_SUN __SUNPRO_C
#else
  #define EIGEN_OS_SUN 0
#endif
 
#if (defined(sun) || defined(__sun)) && (defined(__SVR4) || defined(__svr4__))
  #define EIGEN_OS_SOLARIS 1
#else
  #define EIGEN_OS_SOLARIS 0
#endif
 
 
//------------------------------------------------------------------------------------------
// Detect GPU compilers and architectures
//------------------------------------------------------------------------------------------
 
// NVCC is not supported as the target platform for HIPCC
// Note that this also makes EIGEN_CUDACC and EIGEN_HIPCC mutually exclusive
#if defined(__NVCC__) && defined(__HIPCC__)
  #error "NVCC as the target platform for HIPCC is currently not supported."
#endif
 
#if defined(__CUDACC__) && !defined(EIGEN_NO_CUDA) && !defined(__SYCL_DEVICE_ONLY__)
  // Means the compiler is either nvcc or clang with CUDA enabled
  #define EIGEN_CUDACC __CUDACC__
#endif
 
#if defined(__CUDA_ARCH__) && !defined(EIGEN_NO_CUDA) && !defined(__SYCL_DEVICE_ONLY__)
  // Means we are generating code for the device
  #define EIGEN_CUDA_ARCH __CUDA_ARCH__
#endif
 
#if defined(EIGEN_CUDACC)
#include <cuda.h>
  #define EIGEN_CUDA_SDK_VER (CUDA_VERSION * 10)
#else
  #define EIGEN_CUDA_SDK_VER 0
#endif
 
#if defined(__HIPCC__) && !defined(EIGEN_NO_HIP) && !defined(__SYCL_DEVICE_ONLY__)
  // Means the compiler is HIPCC (analogous to EIGEN_CUDACC, but for HIP)
  #define EIGEN_HIPCC __HIPCC__
 
  // We need to include hip_runtime.h here because it pulls in
  // ++ hip_common.h which contains the define for  __HIP_DEVICE_COMPILE__
  // ++ host_defines.h which contains the defines for the __host__ and __device__ macros
  #include <hip/hip_runtime.h>
 
  #if defined(__HIP_DEVICE_COMPILE__) && !defined(__SYCL_DEVICE_ONLY__)
    // analogous to EIGEN_CUDA_ARCH, but for HIP
    #define EIGEN_HIP_DEVICE_COMPILE __HIP_DEVICE_COMPILE__
  #endif
 
  // For HIP (ROCm 3.5 and higher), we need to explicitly set the launch_bounds attribute
  // value to 1024. The compiler assigns a default value of 256 when the attribute is not
  // specified. This results in failures on the HIP platform, for cases when a GPU kernel
  // without an explicit launch_bounds attribute is called with a threads_per_block value
  // greater than 256.
  //
  // This is a regression in functioanlity and is expected to be fixed within the next
  // couple of ROCm releases (compiler will go back to using 1024 value as the default)
  //
  // In the meantime, we will use a "only enabled for HIP" macro to set the launch_bounds
  // attribute.
 
  #define EIGEN_HIP_LAUNCH_BOUNDS_1024 __launch_bounds__(1024)
 
#endif
 
#if !defined(EIGEN_HIP_LAUNCH_BOUNDS_1024)
#define EIGEN_HIP_LAUNCH_BOUNDS_1024
#endif // !defined(EIGEN_HIP_LAUNCH_BOUNDS_1024)
 
// Unify CUDA/HIPCC
 
#if defined(EIGEN_CUDACC) || defined(EIGEN_HIPCC)
//
// If either EIGEN_CUDACC or EIGEN_HIPCC is defined, then define EIGEN_GPUCC
//
#define EIGEN_GPUCC
//
// EIGEN_HIPCC implies the HIP compiler and is used to tweak Eigen code for use in HIP kernels
// EIGEN_CUDACC implies the CUDA compiler and is used to tweak Eigen code for use in CUDA kernels
//
// In most cases the same tweaks are required to the Eigen code to enable in both the HIP and CUDA kernels.
// For those cases, the corresponding code should be guarded with
//      #if defined(EIGEN_GPUCC)
// instead of
//      #if defined(EIGEN_CUDACC) || defined(EIGEN_HIPCC)
//
// For cases where the tweak is specific to HIP, the code should be guarded with
//      #if defined(EIGEN_HIPCC)
//
// For cases where the tweak is specific to CUDA, the code should be guarded with
//      #if defined(EIGEN_CUDACC)
//
#endif
 
#if defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIP_DEVICE_COMPILE)
//
// If either EIGEN_CUDA_ARCH or EIGEN_HIP_DEVICE_COMPILE is defined, then define EIGEN_GPU_COMPILE_PHASE
//
#define EIGEN_GPU_COMPILE_PHASE
//
// GPU compilers (HIPCC, NVCC) typically do two passes over the source code,
//   + one to compile the source for the "host" (ie CPU)
//   + another to compile the source for the "device" (ie. GPU)
//
// Code that needs to enabled only during the either the "host" or "device" compilation phase
// needs to be guarded with a macro that indicates the current compilation phase
//
// EIGEN_HIP_DEVICE_COMPILE implies the device compilation phase in HIP
// EIGEN_CUDA_ARCH implies the device compilation phase in CUDA
//
// In most cases, the "host" / "device" specific code is the same for both HIP and CUDA
// For those cases, the code should be guarded with
//       #if defined(EIGEN_GPU_COMPILE_PHASE)
// instead of
//       #if defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIP_DEVICE_COMPILE)
//
// For cases where the tweak is specific to HIP, the code should be guarded with
//      #if defined(EIGEN_HIP_DEVICE_COMPILE)
//
// For cases where the tweak is specific to CUDA, the code should be guarded with
//      #if defined(EIGEN_CUDA_ARCH)
//
#endif
 
#if EIGEN_ARCH_ARM_OR_ARM64
  #ifndef EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
    // Clang only supports FP16 on aarch64, and not all intrinsics are available
    // on A32 anyways even in GCC (e.g. vdiv_f16, vsqrt_f16).
    #if EIGEN_ARCH_ARM64 && defined(__ARM_FEATURE_FP16_VECTOR_ARITHMETIC) && !defined(EIGEN_GPU_COMPILE_PHASE)
      #define EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC 1
    #else
      #define EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC 0
    #endif
  #endif
#endif
 
#if EIGEN_ARCH_ARM_OR_ARM64
  #ifndef EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC
    // Clang only supports FP16 on aarch64, and not all intrinsics are available
    // on A32 anyways, even in GCC (e.g. vceqh_f16).
    #if EIGEN_ARCH_ARM64 && defined(__ARM_FEATURE_FP16_SCALAR_ARITHMETIC) && !defined(EIGEN_GPU_COMPILE_PHASE)
      #define EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC 1
    #endif
  #endif
#endif
 
#if defined(EIGEN_USE_SYCL) && defined(__SYCL_DEVICE_ONLY__)
// EIGEN_USE_SYCL is a user-defined macro while __SYCL_DEVICE_ONLY__ is a compiler-defined macro.
// In most cases we want to check if both macros are defined which can be done using the define below.
#define SYCL_DEVICE_ONLY
#endif
 
//------------------------------------------------------------------------------------------
// Detect Compiler/Architecture/OS specific features
//------------------------------------------------------------------------------------------
 
// Cross compiler wrapper around LLVM's __has_builtin
#ifdef __has_builtin
#  define EIGEN_HAS_BUILTIN(x) __has_builtin(x)
#else
#  define EIGEN_HAS_BUILTIN(x) 0
#endif
 
// A Clang feature extension to determine compiler features.
// We use it to determine 'cxx_rvalue_references'
#ifndef __has_feature
# define __has_feature(x) 0
#endif
 
// The macro EIGEN_CPLUSPLUS is a replacement for __cplusplus/_MSVC_LANG that
// works for both platforms, indicating the C++ standard version number.
//
// With MSVC, without defining /Zc:__cplusplus, the __cplusplus macro will
// report 199711L regardless of the language standard specified via /std.
// We need to rely on _MSVC_LANG instead, which is only available after
// VS2015.3.
#if EIGEN_COMP_MSVC_LANG > 0
#define EIGEN_CPLUSPLUS EIGEN_COMP_MSVC_LANG
#elif EIGEN_COMP_MSVC >= 1900
#define EIGEN_CPLUSPLUS 201103L
#elif defined(__cplusplus)
#define EIGEN_CPLUSPLUS __cplusplus
#else
#define EIGEN_CPLUSPLUS 0
#endif
 
// The macro EIGEN_COMP_CXXVER defines the c++ version expected by the compiler.
// For instance, if compiling with gcc and -std=c++17, then EIGEN_COMP_CXXVER
// is defined to 17.
#if EIGEN_CPLUSPLUS >= 202002L
  #define EIGEN_COMP_CXXVER 20
#elif EIGEN_CPLUSPLUS >= 201703L
  #define EIGEN_COMP_CXXVER 17
#elif EIGEN_CPLUSPLUS >= 201402L
  #define EIGEN_COMP_CXXVER 14
#elif EIGEN_CPLUSPLUS >= 201103L
  #define EIGEN_COMP_CXXVER 11
#else
  #define EIGEN_COMP_CXXVER 03
#endif
 
 
// The macros EIGEN_HAS_CXX?? defines a rough estimate of available c++ features
// but in practice we should not rely on them but rather on the availability of
// individual features as defined later.
// This is why there is no EIGEN_HAS_CXX17.
#if EIGEN_MAX_CPP_VER < 14 || EIGEN_COMP_CXXVER < 14 || \
  (EIGEN_COMP_MSVC && EIGEN_COMP_MSVC < 1900) || \
  (EIGEN_COMP_ICC && EIGEN_COMP_ICC < 1500) || \
  (EIGEN_COMP_NVCC && EIGEN_COMP_NVCC < 80000) || \
  (EIGEN_COMP_CLANG_STRICT && EIGEN_COMP_CLANG < 390) || \
  (EIGEN_COMP_CLANGAPPLE && EIGEN_COMP_CLANGAPPLE < 9000000) || \
  (EIGEN_COMP_GNUC_STRICT && EIGEN_COMP_GNUC < 510)
#error This compiler appears to be too old to be supported by Eigen
#endif
 
// Does the compiler support C99?
// Need to include <cmath> to make sure _GLIBCXX_USE_C99 gets defined
#include <cmath>
#ifndef EIGEN_HAS_C99_MATH
#if ((defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901))       \
  || (defined(__GNUC__) && defined(_GLIBCXX_USE_C99)) \
  || (defined(_LIBCPP_VERSION) && !defined(_MSC_VER)) \
  || (EIGEN_COMP_MSVC) || defined(SYCL_DEVICE_ONLY))
  #define EIGEN_HAS_C99_MATH 1
#else
  #define EIGEN_HAS_C99_MATH 0
#endif
#endif
 
// Does the compiler support std::hash?
#ifndef EIGEN_HAS_STD_HASH
// The std::hash struct is defined in C++11 but is not labelled as a __device__
// function and is not constexpr, so cannot be used on device.
#if !defined(EIGEN_GPU_COMPILE_PHASE)
#define EIGEN_HAS_STD_HASH 1
#else
#define EIGEN_HAS_STD_HASH 0
#endif
#endif  // EIGEN_HAS_STD_HASH
 
#ifndef EIGEN_HAS_STD_INVOKE_RESULT
#if EIGEN_MAX_CPP_VER >= 17 && EIGEN_COMP_CXXVER >= 17
#define EIGEN_HAS_STD_INVOKE_RESULT 1
#else
#define EIGEN_HAS_STD_INVOKE_RESULT 0
#endif
#endif
 
#define EIGEN_CONSTEXPR constexpr
 
// NOTE: the required Apple's clang version is very conservative
//       and it could be that XCode 9 works just fine.
// NOTE: the MSVC version is based on https://en.cppreference.com/w/cpp/compiler_support
//       and not tested.
// NOTE: Intel C++ Compiler Classic (icc) Version 19.0 and later supports dynamic allocation
//       for over-aligned data, but not in a manner that is compatible with Eigen.
//       See https://gitlab.com/libeigen/eigen/-/issues/2575
#ifndef EIGEN_HAS_CXX17_OVERALIGN
#if EIGEN_MAX_CPP_VER>=17 && EIGEN_COMP_CXXVER>=17 && (                 \
           (EIGEN_COMP_MSVC >= 1912)                                    \
        || (EIGEN_GNUC_STRICT_AT_LEAST(7,0,0))                          \
        || (EIGEN_CLANG_STRICT_AT_LEAST(5,0,0))                         \
        || (EIGEN_COMP_CLANGAPPLE && EIGEN_COMP_CLANGAPPLE >= 10000000) \
      ) && !EIGEN_COMP_ICC
#define EIGEN_HAS_CXX17_OVERALIGN 1
#else
#define EIGEN_HAS_CXX17_OVERALIGN 0
#endif
#endif
 
#if defined(EIGEN_CUDACC)
  // While available already with c++11, this is useful mostly starting with c++14 and relaxed constexpr rules
  #if defined(__NVCC__)
    // nvcc considers constexpr functions as __host__ __device__ with the option --expt-relaxed-constexpr
    #ifdef __CUDACC_RELAXED_CONSTEXPR__
      #define EIGEN_CONSTEXPR_ARE_DEVICE_FUNC
    #endif
  #elif defined(__clang__) && defined(__CUDA__) && __has_feature(cxx_relaxed_constexpr)
    // clang++ always considers constexpr functions as implicitly __host__ __device__
    #define EIGEN_CONSTEXPR_ARE_DEVICE_FUNC
  #endif
#endif
 
// Does the compiler support the __int128 and __uint128_t extensions for 128-bit
// integer arithmetic?
//
// Clang and GCC define __SIZEOF_INT128__ when these extensions are supported,
// but we avoid using them in certain cases:
//
// * Building using Clang for Windows, where the Clang runtime library has
//   128-bit support only on LP64 architectures, but Windows is LLP64.
#ifndef EIGEN_HAS_BUILTIN_INT128
#if defined(__SIZEOF_INT128__) && !(EIGEN_OS_WIN && EIGEN_COMP_CLANG)
#define EIGEN_HAS_BUILTIN_INT128 1
#else
#define EIGEN_HAS_BUILTIN_INT128 0
#endif
#endif
 
//------------------------------------------------------------------------------------------
// Preprocessor programming helpers
//------------------------------------------------------------------------------------------
 
// This macro can be used to prevent from macro expansion, e.g.:
//   std::max EIGEN_NOT_A_MACRO(a,b)
#define EIGEN_NOT_A_MACRO
 
#define EIGEN_DEBUG_VAR(x) std::cerr << #x << " = " << x << std::endl;
 
// concatenate two tokens
#define EIGEN_CAT2(a,b) a ## b
#define EIGEN_CAT(a,b) EIGEN_CAT2(a,b)
 
#define EIGEN_COMMA ,
 
// convert a token to a string
#define EIGEN_MAKESTRING2(a) #a
#define EIGEN_MAKESTRING(a) EIGEN_MAKESTRING2(a)
 
// EIGEN_STRONG_INLINE is a stronger version of the inline, using __forceinline on MSVC,
// but it still doesn't use GCC's always_inline. This is useful in (common) situations where MSVC needs forceinline
// but GCC is still doing fine with just inline.
#ifndef EIGEN_STRONG_INLINE
#if (EIGEN_COMP_MSVC || EIGEN_COMP_ICC) && !defined(EIGEN_GPUCC)
#define EIGEN_STRONG_INLINE __forceinline
#else
#define EIGEN_STRONG_INLINE inline
#endif
#endif
 
// EIGEN_ALWAYS_INLINE is the strongest, it has the effect of making the function inline and adding every possible
// attribute to maximize inlining. This should only be used when really necessary: in particular,
// it uses __attribute__((always_inline)) on GCC, which most of the time is useless and can severely harm compile times.
// FIXME with the always_inline attribute,
#if EIGEN_COMP_GNUC && !defined(SYCL_DEVICE_ONLY)
#define EIGEN_ALWAYS_INLINE __attribute__((always_inline)) inline
#else
#define EIGEN_ALWAYS_INLINE EIGEN_STRONG_INLINE
#endif
 
#if EIGEN_COMP_GNUC
#define EIGEN_DONT_INLINE __attribute__((noinline))
#elif EIGEN_COMP_MSVC
#define EIGEN_DONT_INLINE __declspec(noinline)
#else
#define EIGEN_DONT_INLINE
#endif
 
#if EIGEN_COMP_GNUC
#define EIGEN_PERMISSIVE_EXPR __extension__
#else
#define EIGEN_PERMISSIVE_EXPR
#endif
 
// GPU stuff
 
// Disable some features when compiling with GPU compilers (SYCL/HIPCC)
#if defined(SYCL_DEVICE_ONLY) || defined(EIGEN_HIP_DEVICE_COMPILE)
  // Do not try asserts on device code
  #ifndef EIGEN_NO_DEBUG
  #define EIGEN_NO_DEBUG
  #endif
 
  #ifdef EIGEN_INTERNAL_DEBUGGING
  #undef EIGEN_INTERNAL_DEBUGGING
  #endif
#endif
 
// No exceptions on device.
#if defined(SYCL_DEVICE_ONLY) || defined(EIGEN_GPU_COMPILE_PHASE)
  #ifdef EIGEN_EXCEPTIONS
  #undef EIGEN_EXCEPTIONS
  #endif
#endif
 
#if defined(SYCL_DEVICE_ONLY)
  #ifndef EIGEN_DONT_VECTORIZE
    #define EIGEN_DONT_VECTORIZE
  #endif
  #define EIGEN_DEVICE_FUNC __attribute__((flatten)) __attribute__((always_inline))
// All functions callable from CUDA/HIP code must be qualified with __device__
#elif defined(EIGEN_GPUCC)
    #define EIGEN_DEVICE_FUNC __host__ __device__
#else
  #define EIGEN_DEVICE_FUNC
#endif
 
 
// this macro allows to get rid of linking errors about multiply defined functions.
//  - static is not very good because it prevents definitions from different object files to be merged.
//           So static causes the resulting linked executable to be bloated with multiple copies of the same function.
//  - inline is not perfect either as it unwantedly hints the compiler toward inlining the function.
#define EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC
#define EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC inline
 
#ifdef NDEBUG
# ifndef EIGEN_NO_DEBUG
#  define EIGEN_NO_DEBUG
# endif
#endif
 
// eigen_assert can be overridden
#ifndef eigen_assert
#define eigen_assert(x) eigen_plain_assert(x)
#endif
 
#ifdef EIGEN_INTERNAL_DEBUGGING
#define eigen_internal_assert(x) eigen_assert(x)
#else
#define eigen_internal_assert(x) ((void)0)
#endif
 
#if defined(EIGEN_NO_DEBUG) || (defined(EIGEN_GPU_COMPILE_PHASE) && defined(EIGEN_NO_DEBUG_GPU))
#define EIGEN_ONLY_USED_FOR_DEBUG(x) EIGEN_UNUSED_VARIABLE(x)
#else
#define EIGEN_ONLY_USED_FOR_DEBUG(x)
#endif
 
#ifndef EIGEN_NO_DEPRECATED_WARNING
  #if EIGEN_COMP_GNUC
    #define EIGEN_DEPRECATED __attribute__((deprecated))
  #elif EIGEN_COMP_MSVC
    #define EIGEN_DEPRECATED __declspec(deprecated)
  #else
    #define EIGEN_DEPRECATED
  #endif
#else
  #define EIGEN_DEPRECATED
#endif
 
#if EIGEN_COMP_GNUC
#define EIGEN_UNUSED __attribute__((unused))
#else
#define EIGEN_UNUSED
#endif
 
#if EIGEN_COMP_GNUC
  #define EIGEN_PRAGMA(tokens) _Pragma(#tokens)
  #define EIGEN_DIAGNOSTICS(tokens) EIGEN_PRAGMA(GCC diagnostic tokens)
  #define EIGEN_DIAGNOSTICS_OFF(msc, gcc) EIGEN_DIAGNOSTICS(gcc)
#elif EIGEN_COMP_MSVC
  #define EIGEN_PRAGMA(tokens) __pragma(tokens)
  #define EIGEN_DIAGNOSTICS(tokens) EIGEN_PRAGMA(warning(tokens))
  #define EIGEN_DIAGNOSTICS_OFF(msc, gcc) EIGEN_DIAGNOSTICS(msc)
#else
  #define EIGEN_PRAGMA(tokens)
  #define EIGEN_DIAGNOSTICS(tokens)
  #define EIGEN_DIAGNOSTICS_OFF(msc, gcc)
#endif
 
#define EIGEN_DISABLE_DEPRECATED_WARNING EIGEN_DIAGNOSTICS_OFF(disable : 4996, ignored "-Wdeprecated-declarations")
 
// Suppresses 'unused variable' warnings.
namespace Eigen {
  namespace internal {
    template<typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr void ignore_unused_variable(const T&) {}
  }
}
#define EIGEN_UNUSED_VARIABLE(var) Eigen::internal::ignore_unused_variable(var);
 
#if !defined(EIGEN_ASM_COMMENT)
  #if EIGEN_COMP_GNUC && (EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM_OR_ARM64)
    #define EIGEN_ASM_COMMENT(X)  __asm__("#" X)
  #else
    #define EIGEN_ASM_COMMENT(X)
  #endif
#endif
 
 
// Acts as a barrier preventing operations involving `X` from crossing. This
// occurs, for example, in the fast rounding trick where a magic constant is
// added then subtracted, which is otherwise compiled away with -ffast-math.
//
// See bug 1674
#if !defined(EIGEN_OPTIMIZATION_BARRIER)
  #if EIGEN_COMP_GNUC
    // According to https://gcc.gnu.org/onlinedocs/gcc/Constraints.html:
    //   X: Any operand whatsoever.
    //   r: A register operand is allowed provided that it is in a general
    //      register.
    //   g: Any register, memory or immediate integer operand is allowed, except
    //      for registers that are not general registers.
    //   w: (AArch32/AArch64) Floating point register, Advanced SIMD vector
    //      register or SVE vector register.
    //   x: (SSE) Any SSE register.
    //      (AArch64) Like w, but restricted to registers 0 to 15 inclusive.
    //   v: (PowerPC) An Altivec vector register.
    //   wa:(PowerPC) A VSX register.
    //
    // "X" (uppercase) should work for all cases, though this seems to fail for
    // some versions of GCC for arm/aarch64 with
    //   "error: inconsistent operand constraints in an 'asm'"
    // Clang x86_64/arm/aarch64 seems to require "g" to support both scalars and
    // vectors, otherwise
    //   "error: non-trivial scalar-to-vector conversion, possible invalid
    //    constraint for vector type"
    //
    // GCC for ppc64le generates an internal compiler error with x/X/g.
    // GCC for AVX generates an internal compiler error with X.
    //
    // Tested on icc/gcc/clang for sse, avx, avx2, avx512dq
    //           gcc for arm, aarch64,
    //           gcc for ppc64le,
    // both vectors and scalars.
    //
    // Note that this is restricted to plain types - this will not work
    // directly for std::complex<T>, Eigen::half, Eigen::bfloat16. For these,
    // you will need to apply to the underlying POD type.
    #if EIGEN_ARCH_PPC && EIGEN_COMP_GNUC_STRICT
      // This seems to be broken on clang. Packet4f is loaded into a single
      //   register rather than a vector, zeroing out some entries. Integer
      //   types also generate a compile error.
      #if EIGEN_OS_MAC
        // General, Altivec for Apple (VSX were added in ISA v2.06):
        #define EIGEN_OPTIMIZATION_BARRIER(X)  __asm__  ("" : "+r,v" (X));
      #else
        // General, Altivec, VSX otherwise:
        #define EIGEN_OPTIMIZATION_BARRIER(X)  __asm__  ("" : "+r,v,wa" (X));
      #endif
    #elif EIGEN_ARCH_ARM_OR_ARM64
      #ifdef __ARM_FP
        // General, VFP or NEON.
        // Clang doesn't like "r",
        //    error: non-trivial scalar-to-vector conversion, possible invalid
        //           constraint for vector typ
        #define EIGEN_OPTIMIZATION_BARRIER(X)  __asm__  ("" : "+g,w" (X));
      #else
        // Arm without VFP or NEON.
        // "w" constraint will not compile.
        #define EIGEN_OPTIMIZATION_BARRIER(X)  __asm__  ("" : "+g" (X));
      #endif
    #elif EIGEN_ARCH_i386_OR_x86_64
      // General, SSE.
      #define EIGEN_OPTIMIZATION_BARRIER(X)  __asm__  ("" : "+g,x" (X));
    #else
      // Not implemented for other architectures.
      #define EIGEN_OPTIMIZATION_BARRIER(X)
    #endif
  #else
    // Not implemented for other compilers.
    #define EIGEN_OPTIMIZATION_BARRIER(X)
  #endif
#endif
 
#if EIGEN_COMP_MSVC
  // NOTE MSVC often gives C4127 warnings with compiletime if statements. See bug 1362.
  // This workaround is ugly, but it does the job.
#  define EIGEN_CONST_CONDITIONAL(cond)  (void)0, cond
#else
#  define EIGEN_CONST_CONDITIONAL(cond)  cond
#endif
 
#ifdef EIGEN_DONT_USE_RESTRICT_KEYWORD
  #define EIGEN_RESTRICT
#endif
#ifndef EIGEN_RESTRICT
  #define EIGEN_RESTRICT __restrict
#endif
 
 
#ifndef EIGEN_DEFAULT_IO_FORMAT
#ifdef EIGEN_MAKING_DOCS
// format used in Eigen's documentation
// needed to define it here as escaping characters in CMake add_definition's argument seems very problematic.
#define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat(3, 0, " ", "\n", "", "")
#else
#define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat()
#endif
#endif
 
// just an empty macro !
#define EIGEN_EMPTY
 
 
// When compiling CUDA/HIP device code with NVCC or HIPCC
// pull in math functions from the global namespace.
// In host mode, and when device code is compiled with clang,
// use the std versions.
#if (defined(EIGEN_CUDA_ARCH) && defined(__NVCC__)) || defined(EIGEN_HIP_DEVICE_COMPILE)
  #define EIGEN_USING_STD(FUNC) using ::FUNC;
#else
  #define EIGEN_USING_STD(FUNC) using std::FUNC;
#endif
 
#if EIGEN_COMP_MSVC_STRICT && EIGEN_COMP_NVCC
  // Wwhen compiling with NVCC, using the base operator is necessary,
  //   otherwise we get duplicate definition errors
  // For later MSVC versions, we require explicit operator= definition, otherwise we get
  //   use of implicitly deleted operator errors.
  // (cf Bugs 920, 1000, 1324, 2291)
  #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
    using Base::operator =;
#elif EIGEN_COMP_CLANG // workaround clang bug (see http://forum.kde.org/viewtopic.php?f=74&t=102653)
  #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
    using Base::operator =; \
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) { Base::operator=(other); return *this; } \
    template <typename OtherDerived> \
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other) { Base::operator=(other.derived()); return *this; }
#else
  #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
    using Base::operator =; \
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) \
    { \
      Base::operator=(other); \
      return *this; \
    }
#endif
 
 
#define EIGEN_DEFAULT_COPY_CONSTRUCTOR(CLASS) EIGEN_DEVICE_FUNC CLASS(const CLASS&) = default;
 
 
 
#define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived)  \
    EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
    EIGEN_DEFAULT_COPY_CONSTRUCTOR(Derived)
 
#define EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(Derived)  \
    EIGEN_DEVICE_FUNC Derived() = default; \
    EIGEN_DEVICE_FUNC ~Derived() = default;
 
 
 
 
 
#define EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
  typedef typename Eigen::internal::traits<Derived>::Scalar Scalar;  \
  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;  \
  typedef typename Base::CoeffReturnType CoeffReturnType;  \
  typedef typename Eigen::internal::ref_selector<Derived>::type Nested; \
  typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \
  typedef typename Eigen::internal::traits<Derived>::StorageIndex StorageIndex; \
  enum CompileTimeTraits \
      { RowsAtCompileTime = Eigen::internal::traits<Derived>::RowsAtCompileTime, \
        ColsAtCompileTime = Eigen::internal::traits<Derived>::ColsAtCompileTime, \
        Flags = Eigen::internal::traits<Derived>::Flags, \
        SizeAtCompileTime = Base::SizeAtCompileTime, \
        MaxSizeAtCompileTime = Base::MaxSizeAtCompileTime, \
        IsVectorAtCompileTime = Base::IsVectorAtCompileTime }; \
  using Base::derived; \
  using Base::const_cast_derived;
 
 
// FIXME Maybe the EIGEN_DENSE_PUBLIC_INTERFACE could be removed as importing PacketScalar is rarely needed
#define EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \
  EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
  typedef typename Base::PacketScalar PacketScalar;
 
 
#if EIGEN_HAS_BUILTIN(__builtin_expect) || EIGEN_COMP_GNUC
#define EIGEN_PREDICT_FALSE(x) (__builtin_expect(x, false))
#define EIGEN_PREDICT_TRUE(x) (__builtin_expect(false || (x), true))
#else
#define EIGEN_PREDICT_FALSE(x) (x)
#define EIGEN_PREDICT_TRUE(x) (x)
#endif
 
// the expression type of a standard coefficient wise binary operation
#define EIGEN_CWISE_BINARY_RETURN_TYPE(LHS,RHS,OPNAME) \
    CwiseBinaryOp< \
      EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)< \
          typename internal::traits<LHS>::Scalar, \
          typename internal::traits<RHS>::Scalar \
      >, \
      const LHS, \
      const RHS \
    >
 
#define EIGEN_MAKE_CWISE_BINARY_OP(METHOD,OPNAME) \
  template<typename OtherDerived> \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME) \
  (METHOD)(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
  { \
    return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME)(derived(), other.derived()); \
  }
 
#define EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,TYPEA,TYPEB) \
  (Eigen::internal::has_ReturnType<Eigen::ScalarBinaryOpTraits<TYPEA,TYPEB,EIGEN_CAT(EIGEN_CAT(Eigen::internal::scalar_,OPNAME),_op)<TYPEA,TYPEB>  > >::value)
 
#define EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(EXPR,SCALAR,OPNAME) \
  CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<typename internal::traits<EXPR>::Scalar,SCALAR>, const EXPR, \
                const typename internal::plain_constant_type<EXPR,SCALAR>::type>
 
#define EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(SCALAR,EXPR,OPNAME) \
  CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<SCALAR,typename internal::traits<EXPR>::Scalar>, \
                const typename internal::plain_constant_type<EXPR,SCALAR>::type, const EXPR>
 
#define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME) \
  template <typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
  const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,Scalar,T)>::type,OPNAME)\
  (METHOD)(const T& scalar) const { \
    typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,Scalar,T)>::type PromotedT; \
    return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,PromotedT,OPNAME)(derived(), \
           typename internal::plain_constant_type<Derived,PromotedT>::type(derived().rows(), derived().cols(), internal::scalar_constant_op<PromotedT>(scalar))); \
  }
 
#define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
  template <typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend \
  const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(typename internal::promote_scalar_arg<Scalar EIGEN_COMMA T EIGEN_COMMA EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,T,Scalar)>::type,Derived,OPNAME) \
  (METHOD)(const T& scalar, const StorageBaseType& matrix) { \
    typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,T,Scalar)>::type PromotedT; \
    return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedT,Derived,OPNAME)( \
           typename internal::plain_constant_type<Derived,PromotedT>::type(matrix.derived().rows(), matrix.derived().cols(), internal::scalar_constant_op<PromotedT>(scalar)), matrix.derived()); \
  }
 
#define EIGEN_MAKE_SCALAR_BINARY_OP(METHOD,OPNAME) \
  EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
  EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME)
 
 
#if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(EIGEN_CUDA_ARCH) && !defined(EIGEN_EXCEPTIONS) && !defined(EIGEN_USE_SYCL) && !defined(EIGEN_HIP_DEVICE_COMPILE)
  #define EIGEN_EXCEPTIONS
#endif
 
 
#ifdef EIGEN_EXCEPTIONS
#  define EIGEN_THROW_X(X) throw X
#  define EIGEN_THROW throw
#  define EIGEN_TRY try
#  define EIGEN_CATCH(X) catch (X)
#else
#  if defined(EIGEN_CUDA_ARCH)
#    define EIGEN_THROW_X(X) asm("trap;")
#    define EIGEN_THROW asm("trap;")
#  elif defined(EIGEN_HIP_DEVICE_COMPILE)
#    define EIGEN_THROW_X(X) asm("s_trap 0")
#    define EIGEN_THROW asm("s_trap 0")
#  else
#    define EIGEN_THROW_X(X) std::abort()
#    define EIGEN_THROW std::abort()
#  endif
#  define EIGEN_TRY if (true)
#  define EIGEN_CATCH(X) else
#endif
 
 
#define EIGEN_NOEXCEPT noexcept
#define EIGEN_NOEXCEPT_IF(x) noexcept(x)
#define EIGEN_NO_THROW noexcept(true)
#define EIGEN_EXCEPTION_SPEC(X) noexcept(false)
 
 
// The all function is used to enable a variadic version of eigen_assert which can take a parameter pack as its input.
namespace Eigen {
namespace internal {
 
EIGEN_DEVICE_FUNC inline bool all(){ return true; }
 
template<typename T, typename ...Ts>
EIGEN_DEVICE_FUNC bool all(T t, Ts ... ts){ return t && all(ts...); }
 
}
}
 
// provide override and final specifiers if they are available:
#define EIGEN_OVERRIDE override
#define EIGEN_FINAL final
 
// Wrapping #pragma unroll in a macro since it is required for SYCL
#if defined(SYCL_DEVICE_ONLY)
  #if defined(_MSC_VER)
    #define EIGEN_UNROLL_LOOP __pragma(unroll)
  #else
    #define EIGEN_UNROLL_LOOP _Pragma("unroll")
  #endif
#else
  #define EIGEN_UNROLL_LOOP
#endif
 
// Notice: Use this macro with caution. The code in the if body should still
// compile with C++14.
#if defined(EIGEN_HAS_CXX17_IFCONSTEXPR)
#define EIGEN_IF_CONSTEXPR(X) if constexpr (X)
#else
#define EIGEN_IF_CONSTEXPR(X) if (X)
#endif
 
#endif // EIGEN_MACROS_H