cart-elc

Source code for CART-ELC
git clone git://git.laack.co/cart-elc.git
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Macros.h (52909B)


      1 // This file is part of Eigen, a lightweight C++ template library
      2 // for linear algebra.
      3 //
      4 // Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
      5 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
      6 //
      7 // This Source Code Form is subject to the terms of the Mozilla
      8 // Public License v. 2.0. If a copy of the MPL was not distributed
      9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
     10 
     11 #ifndef EIGEN_MACROS_H
     12 #define EIGEN_MACROS_H
     13 
     14 //------------------------------------------------------------------------------------------
     15 // Eigen version and basic defaults
     16 //------------------------------------------------------------------------------------------
     17 
     18 #define EIGEN_WORLD_VERSION 3
     19 #define EIGEN_MAJOR_VERSION 4
     20 #define EIGEN_MINOR_VERSION 0
     21 
     22 #define EIGEN_VERSION_AT_LEAST(x,y,z) (EIGEN_WORLD_VERSION>x || (EIGEN_WORLD_VERSION>=x && \
     23                                       (EIGEN_MAJOR_VERSION>y || (EIGEN_MAJOR_VERSION>=y && \
     24                                                                  EIGEN_MINOR_VERSION>=z))))
     25 
     26 #ifdef EIGEN_DEFAULT_TO_ROW_MAJOR
     27 #define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION Eigen::RowMajor
     28 #else
     29 #define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION Eigen::ColMajor
     30 #endif
     31 
     32 #ifndef EIGEN_DEFAULT_DENSE_INDEX_TYPE
     33 #define EIGEN_DEFAULT_DENSE_INDEX_TYPE std::ptrdiff_t
     34 #endif
     35 
     36 // Upperbound on the C++ version to use.
     37 // Expected values are 03, 11, 14, 17, etc.
     38 // By default, let's use an arbitrarily large C++ version.
     39 #ifndef EIGEN_MAX_CPP_VER
     40 #define EIGEN_MAX_CPP_VER 99
     41 #endif
     42 
     43 /** Allows to disable some optimizations which might affect the accuracy of the result.
     44   * Such optimization are enabled by default, and set EIGEN_FAST_MATH to 0 to disable them.
     45   * They currently include:
     46   *   - single precision ArrayBase::sin() and ArrayBase::cos() for SSE and AVX vectorization.
     47   */
     48 #ifndef EIGEN_FAST_MATH
     49 #define EIGEN_FAST_MATH 1
     50 #endif
     51 
     52 #ifndef EIGEN_STACK_ALLOCATION_LIMIT
     53 // 131072 == 128 KB
     54 #define EIGEN_STACK_ALLOCATION_LIMIT 131072
     55 #endif
     56 
     57 //------------------------------------------------------------------------------------------
     58 // Compiler identification, EIGEN_COMP_*
     59 //------------------------------------------------------------------------------------------
     60 
     61 /// \internal EIGEN_COMP_GNUC set to 1 for all compilers compatible with GCC
     62 #ifdef __GNUC__
     63   #define EIGEN_COMP_GNUC (__GNUC__*10+__GNUC_MINOR__)
     64 #else
     65   #define EIGEN_COMP_GNUC 0
     66 #endif
     67 
     68 /// \internal EIGEN_COMP_CLANG set to major+minor version (e.g., 307 for clang 3.7) if the compiler is clang
     69 #if defined(__clang__)
     70   #define EIGEN_COMP_CLANG (__clang_major__*100+__clang_minor__)
     71 #else
     72   #define EIGEN_COMP_CLANG 0
     73 #endif
     74 
     75 /// \internal EIGEN_COMP_CASTXML set to 1 if being preprocessed by CastXML
     76 #if defined(__castxml__)
     77   #define EIGEN_COMP_CASTXML 1
     78 #else
     79   #define EIGEN_COMP_CASTXML 0
     80 #endif
     81 
     82 /// \internal EIGEN_COMP_LLVM set to 1 if the compiler backend is llvm
     83 #if defined(__llvm__)
     84   #define EIGEN_COMP_LLVM 1
     85 #else
     86   #define EIGEN_COMP_LLVM 0
     87 #endif
     88 
     89 /// \internal EIGEN_COMP_ICC set to __INTEL_COMPILER if the compiler is Intel compiler, 0 otherwise
     90 #if defined(__INTEL_COMPILER)
     91   #define EIGEN_COMP_ICC __INTEL_COMPILER
     92 #else
     93   #define EIGEN_COMP_ICC 0
     94 #endif
     95 
     96 /// \internal EIGEN_COMP_MINGW set to 1 if the compiler is mingw
     97 #if defined(__MINGW32__)
     98   #define EIGEN_COMP_MINGW 1
     99 #else
    100   #define EIGEN_COMP_MINGW 0
    101 #endif
    102 
    103 /// \internal EIGEN_COMP_SUNCC set to 1 if the compiler is Solaris Studio
    104 #if defined(__SUNPRO_CC)
    105   #define EIGEN_COMP_SUNCC 1
    106 #else
    107   #define EIGEN_COMP_SUNCC 0
    108 #endif
    109 
    110 /// \internal EIGEN_COMP_MSVC set to _MSC_VER if the compiler is Microsoft Visual C++, 0 otherwise.
    111 #if defined(_MSC_VER)
    112   #define EIGEN_COMP_MSVC _MSC_VER
    113 #else
    114   #define EIGEN_COMP_MSVC 0
    115 #endif
    116 
    117 #if defined(__NVCC__)
    118 #if defined(__CUDACC_VER_MAJOR__) && (__CUDACC_VER_MAJOR__ >= 9)
    119   #define EIGEN_COMP_NVCC  ((__CUDACC_VER_MAJOR__ * 10000) + (__CUDACC_VER_MINOR__ * 100))
    120 #elif defined(__CUDACC_VER__)
    121   #define EIGEN_COMP_NVCC __CUDACC_VER__
    122 #else
    123   #error "NVCC did not define compiler version."
    124 #endif
    125 #else
    126   #define EIGEN_COMP_NVCC 0
    127 #endif
    128 
    129 // For the record, here is a table summarizing the possible values for EIGEN_COMP_MSVC:
    130 //  name        ver   MSC_VER
    131 //  2008         9      1500
    132 //  2010        10      1600
    133 //  2012        11      1700
    134 //  2013        12      1800
    135 //  2015        14      1900
    136 //  "15"        15      1900
    137 //  2017-14.1   15.0    1910
    138 //  2017-14.11  15.3    1911
    139 //  2017-14.12  15.5    1912
    140 //  2017-14.13  15.6    1913
    141 //  2017-14.14  15.7    1914
    142 
    143 /// \internal EIGEN_COMP_MSVC_LANG set to _MSVC_LANG if the compiler is Microsoft Visual C++, 0 otherwise.
    144 #if defined(_MSVC_LANG)
    145   #define EIGEN_COMP_MSVC_LANG _MSVC_LANG
    146 #else
    147   #define EIGEN_COMP_MSVC_LANG 0
    148 #endif
    149 
    150 // For the record, here is a table summarizing the possible values for EIGEN_COMP_MSVC_LANG:
    151 // MSVC option                          Standard  MSVC_LANG
    152 // /std:c++14 (default as of VS 2019)   C++14     201402L
    153 // /std:c++17                           C++17     201703L
    154 // /std:c++latest                       >C++17    >201703L
    155 
    156 /// \internal EIGEN_COMP_MSVC_STRICT set to 1 if the compiler is really Microsoft Visual C++ and not ,e.g., ICC or clang-cl
    157 #if EIGEN_COMP_MSVC && !(EIGEN_COMP_ICC || EIGEN_COMP_LLVM || EIGEN_COMP_CLANG)
    158   #define EIGEN_COMP_MSVC_STRICT _MSC_VER
    159 #else
    160   #define EIGEN_COMP_MSVC_STRICT 0
    161 #endif
    162 
    163 /// \internal EIGEN_COMP_IBM set to xlc version if the compiler is IBM XL C++
    164 // XLC   version
    165 // 3.1   0x0301
    166 // 4.5   0x0405
    167 // 5.0   0x0500
    168 // 12.1  0x0C01
    169 #if defined(__IBMCPP__) || defined(__xlc__) || defined(__ibmxl__)
    170   #define EIGEN_COMP_IBM __xlC__
    171 #else
    172   #define EIGEN_COMP_IBM 0
    173 #endif
    174 
    175 /// \internal EIGEN_COMP_PGI set to PGI version if the compiler is Portland Group Compiler
    176 #if defined(__PGI)
    177   #define EIGEN_COMP_PGI (__PGIC__*100+__PGIC_MINOR__)
    178 #else
    179   #define EIGEN_COMP_PGI 0
    180 #endif
    181 
    182 /// \internal EIGEN_COMP_ARM set to 1 if the compiler is ARM Compiler
    183 #if defined(__CC_ARM) || defined(__ARMCC_VERSION)
    184   #define EIGEN_COMP_ARM 1
    185 #else
    186   #define EIGEN_COMP_ARM 0
    187 #endif
    188 
    189 /// \internal EIGEN_COMP_EMSCRIPTEN set to 1 if the compiler is Emscripten Compiler
    190 #if defined(__EMSCRIPTEN__)
    191   #define EIGEN_COMP_EMSCRIPTEN 1
    192 #else
    193   #define EIGEN_COMP_EMSCRIPTEN 0
    194 #endif
    195 
    196 
    197 /// \internal EIGEN_GNUC_STRICT set to 1 if the compiler is really GCC and not a compatible compiler (e.g., ICC, clang, mingw, etc.)
    198 #if EIGEN_COMP_GNUC && !(EIGEN_COMP_CLANG || EIGEN_COMP_ICC || EIGEN_COMP_MINGW || EIGEN_COMP_PGI || EIGEN_COMP_IBM || EIGEN_COMP_ARM || EIGEN_COMP_EMSCRIPTEN)
    199   #define EIGEN_COMP_GNUC_STRICT 1
    200 #else
    201   #define EIGEN_COMP_GNUC_STRICT 0
    202 #endif
    203 
    204 
    205 #if EIGEN_COMP_GNUC
    206   #define EIGEN_GNUC_AT_LEAST(x,y) ((__GNUC__==x && __GNUC_MINOR__>=y) || __GNUC__>x)
    207   #define EIGEN_GNUC_AT_MOST(x,y)  ((__GNUC__==x && __GNUC_MINOR__<=y) || __GNUC__<x)
    208   #define EIGEN_GNUC_AT(x,y)       ( __GNUC__==x && __GNUC_MINOR__==y )
    209 #else
    210   #define EIGEN_GNUC_AT_LEAST(x,y) 0
    211   #define EIGEN_GNUC_AT_MOST(x,y)  0
    212   #define EIGEN_GNUC_AT(x,y)       0
    213 #endif
    214 
    215 // FIXME: could probably be removed as we do not support gcc 3.x anymore
    216 #if EIGEN_COMP_GNUC && (__GNUC__ <= 3)
    217 #define EIGEN_GCC3_OR_OLDER 1
    218 #else
    219 #define EIGEN_GCC3_OR_OLDER 0
    220 #endif
    221 
    222 
    223 
    224 //------------------------------------------------------------------------------------------
    225 // Architecture identification, EIGEN_ARCH_*
    226 //------------------------------------------------------------------------------------------
    227 
    228 
    229 #if defined(__x86_64__) || (defined(_M_X64) && !defined(_M_ARM64EC)) || defined(__amd64)
    230   #define EIGEN_ARCH_x86_64 1
    231 #else
    232   #define EIGEN_ARCH_x86_64 0
    233 #endif
    234 
    235 #if defined(__i386__) || defined(_M_IX86) || defined(_X86_) || defined(__i386)
    236   #define EIGEN_ARCH_i386 1
    237 #else
    238   #define EIGEN_ARCH_i386 0
    239 #endif
    240 
    241 #if EIGEN_ARCH_x86_64 || EIGEN_ARCH_i386
    242   #define EIGEN_ARCH_i386_OR_x86_64 1
    243 #else
    244   #define EIGEN_ARCH_i386_OR_x86_64 0
    245 #endif
    246 
    247 /// \internal EIGEN_ARCH_ARM set to 1 if the architecture is ARM
    248 #if defined(__arm__)
    249   #define EIGEN_ARCH_ARM 1
    250 #else
    251   #define EIGEN_ARCH_ARM 0
    252 #endif
    253 
    254 /// \internal EIGEN_ARCH_ARM64 set to 1 if the architecture is ARM64
    255 #if defined(__aarch64__) || defined(_M_ARM64) || defined(_M_ARM64EC)
    256   #define EIGEN_ARCH_ARM64 1
    257 #else
    258   #define EIGEN_ARCH_ARM64 0
    259 #endif
    260 
    261 /// \internal EIGEN_ARCH_ARM_OR_ARM64 set to 1 if the architecture is ARM or ARM64
    262 #if EIGEN_ARCH_ARM || EIGEN_ARCH_ARM64
    263   #define EIGEN_ARCH_ARM_OR_ARM64 1
    264 #else
    265   #define EIGEN_ARCH_ARM_OR_ARM64 0
    266 #endif
    267 
    268 /// \internal EIGEN_ARCH_ARMV8 set to 1 if the architecture is armv8 or greater.
    269 #if EIGEN_ARCH_ARM_OR_ARM64 && defined(__ARM_ARCH) && __ARM_ARCH >= 8
    270 #define EIGEN_ARCH_ARMV8 1
    271 #else
    272 #define EIGEN_ARCH_ARMV8 0
    273 #endif
    274 
    275 
    276 /// \internal EIGEN_HAS_ARM64_FP16 set to 1 if the architecture provides an IEEE
    277 /// compliant Arm fp16 type
    278 #if EIGEN_ARCH_ARM64
    279   #ifndef EIGEN_HAS_ARM64_FP16
    280     #if defined(__ARM_FP16_FORMAT_IEEE)
    281       #define EIGEN_HAS_ARM64_FP16 1
    282     #else
    283       #define EIGEN_HAS_ARM64_FP16 0
    284     #endif
    285   #endif
    286 #endif
    287 
    288 /// \internal EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC set to 1 if the architecture
    289 /// supports Neon vector intrinsics for fp16.
    290 #if EIGEN_ARCH_ARM64
    291   #ifndef EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
    292     #if defined(__ARM_FEATURE_FP16_VECTOR_ARITHMETIC)
    293       #define EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC 1
    294     #else
    295       #define EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC 0
    296     #endif
    297   #endif
    298 #endif
    299 
    300 /// \internal EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC set to 1 if the architecture
    301 /// supports Neon scalar intrinsics for fp16.
    302 #if EIGEN_ARCH_ARM64
    303   #ifndef EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC
    304     #if defined(__ARM_FEATURE_FP16_SCALAR_ARITHMETIC)
    305       #define EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC 1
    306     #endif
    307   #endif
    308 #endif
    309 
    310 /// \internal EIGEN_ARCH_MIPS set to 1 if the architecture is MIPS
    311 #if defined(__mips__) || defined(__mips)
    312   #define EIGEN_ARCH_MIPS 1
    313 #else
    314   #define EIGEN_ARCH_MIPS 0
    315 #endif
    316 
    317 /// \internal EIGEN_ARCH_SPARC set to 1 if the architecture is SPARC
    318 #if defined(__sparc__) || defined(__sparc)
    319   #define EIGEN_ARCH_SPARC 1
    320 #else
    321   #define EIGEN_ARCH_SPARC 0
    322 #endif
    323 
    324 /// \internal EIGEN_ARCH_IA64 set to 1 if the architecture is Intel Itanium
    325 #if defined(__ia64__)
    326   #define EIGEN_ARCH_IA64 1
    327 #else
    328   #define EIGEN_ARCH_IA64 0
    329 #endif
    330 
    331 /// \internal EIGEN_ARCH_PPC set to 1 if the architecture is PowerPC
    332 #if defined(__powerpc__) || defined(__ppc__) || defined(_M_PPC)
    333   #define EIGEN_ARCH_PPC 1
    334 #else
    335   #define EIGEN_ARCH_PPC 0
    336 #endif
    337 
    338 
    339 
    340 //------------------------------------------------------------------------------------------
    341 // Operating system identification, EIGEN_OS_*
    342 //------------------------------------------------------------------------------------------
    343 
    344 /// \internal EIGEN_OS_UNIX set to 1 if the OS is a unix variant
    345 #if defined(__unix__) || defined(__unix)
    346   #define EIGEN_OS_UNIX 1
    347 #else
    348   #define EIGEN_OS_UNIX 0
    349 #endif
    350 
    351 /// \internal EIGEN_OS_LINUX set to 1 if the OS is based on Linux kernel
    352 #if defined(__linux__)
    353   #define EIGEN_OS_LINUX 1
    354 #else
    355   #define EIGEN_OS_LINUX 0
    356 #endif
    357 
    358 /// \internal EIGEN_OS_ANDROID set to 1 if the OS is Android
    359 // note: ANDROID is defined when using ndk_build, __ANDROID__ is defined when using a standalone toolchain.
    360 #if defined(__ANDROID__) || defined(ANDROID)
    361   #define EIGEN_OS_ANDROID 1
    362 #else
    363   #define EIGEN_OS_ANDROID 0
    364 #endif
    365 
    366 /// \internal EIGEN_OS_GNULINUX set to 1 if the OS is GNU Linux and not Linux-based OS (e.g., not android)
    367 #if defined(__gnu_linux__) && !(EIGEN_OS_ANDROID)
    368   #define EIGEN_OS_GNULINUX 1
    369 #else
    370   #define EIGEN_OS_GNULINUX 0
    371 #endif
    372 
    373 /// \internal EIGEN_OS_BSD set to 1 if the OS is a BSD variant
    374 #if defined(__FreeBSD__) || defined(__NetBSD__) || defined(__OpenBSD__) || defined(__bsdi__) || defined(__DragonFly__)
    375   #define EIGEN_OS_BSD 1
    376 #else
    377   #define EIGEN_OS_BSD 0
    378 #endif
    379 
    380 /// \internal EIGEN_OS_MAC set to 1 if the OS is MacOS
    381 #if defined(__APPLE__)
    382   #define EIGEN_OS_MAC 1
    383 #else
    384   #define EIGEN_OS_MAC 0
    385 #endif
    386 
    387 /// \internal EIGEN_OS_QNX set to 1 if the OS is QNX
    388 #if defined(__QNX__)
    389   #define EIGEN_OS_QNX 1
    390 #else
    391   #define EIGEN_OS_QNX 0
    392 #endif
    393 
    394 /// \internal EIGEN_OS_WIN set to 1 if the OS is Windows based
    395 #if defined(_WIN32)
    396   #define EIGEN_OS_WIN 1
    397 #else
    398   #define EIGEN_OS_WIN 0
    399 #endif
    400 
    401 /// \internal EIGEN_OS_WIN64 set to 1 if the OS is Windows 64bits
    402 #if defined(_WIN64)
    403   #define EIGEN_OS_WIN64 1
    404 #else
    405   #define EIGEN_OS_WIN64 0
    406 #endif
    407 
    408 /// \internal EIGEN_OS_WINCE set to 1 if the OS is Windows CE
    409 #if defined(_WIN32_WCE)
    410   #define EIGEN_OS_WINCE 1
    411 #else
    412   #define EIGEN_OS_WINCE 0
    413 #endif
    414 
    415 /// \internal EIGEN_OS_CYGWIN set to 1 if the OS is Windows/Cygwin
    416 #if defined(__CYGWIN__)
    417   #define EIGEN_OS_CYGWIN 1
    418 #else
    419   #define EIGEN_OS_CYGWIN 0
    420 #endif
    421 
    422 /// \internal EIGEN_OS_WIN_STRICT set to 1 if the OS is really Windows and not some variants
    423 #if EIGEN_OS_WIN && !( EIGEN_OS_WINCE || EIGEN_OS_CYGWIN )
    424   #define EIGEN_OS_WIN_STRICT 1
    425 #else
    426   #define EIGEN_OS_WIN_STRICT 0
    427 #endif
    428 
    429 /// \internal EIGEN_OS_SUN set to __SUNPRO_C if the OS is SUN
    430 // compiler  solaris   __SUNPRO_C
    431 // version   studio
    432 // 5.7       10        0x570
    433 // 5.8       11        0x580
    434 // 5.9       12        0x590
    435 // 5.10	     12.1      0x5100
    436 // 5.11	     12.2      0x5110
    437 // 5.12	     12.3      0x5120
    438 #if (defined(sun) || defined(__sun)) && !(defined(__SVR4) || defined(__svr4__))
    439   #define EIGEN_OS_SUN __SUNPRO_C
    440 #else
    441   #define EIGEN_OS_SUN 0
    442 #endif
    443 
    444 /// \internal EIGEN_OS_SOLARIS set to 1 if the OS is Solaris
    445 #if (defined(sun) || defined(__sun)) && (defined(__SVR4) || defined(__svr4__))
    446   #define EIGEN_OS_SOLARIS 1
    447 #else
    448   #define EIGEN_OS_SOLARIS 0
    449 #endif
    450 
    451 
    452 //------------------------------------------------------------------------------------------
    453 // Detect GPU compilers and architectures
    454 //------------------------------------------------------------------------------------------
    455 
    456 // NVCC is not supported as the target platform for HIPCC
    457 // Note that this also makes EIGEN_CUDACC and EIGEN_HIPCC mutually exclusive
    458 #if defined(__NVCC__) && defined(__HIPCC__)
    459   #error "NVCC as the target platform for HIPCC is currently not supported."
    460 #endif
    461 
    462 #if defined(__CUDACC__) && !defined(EIGEN_NO_CUDA)
    463   // Means the compiler is either nvcc or clang with CUDA enabled
    464   #define EIGEN_CUDACC __CUDACC__
    465 #endif
    466 
    467 #if defined(__CUDA_ARCH__) && !defined(EIGEN_NO_CUDA)
    468   // Means we are generating code for the device
    469   #define EIGEN_CUDA_ARCH __CUDA_ARCH__
    470 #endif
    471 
    472 #if defined(EIGEN_CUDACC)
    473 #include <cuda.h>
    474   #define EIGEN_CUDA_SDK_VER (CUDA_VERSION * 10)
    475 #else
    476   #define EIGEN_CUDA_SDK_VER 0
    477 #endif
    478 
    479 #if defined(__HIPCC__) && !defined(EIGEN_NO_HIP)
    480   // Means the compiler is HIPCC (analogous to EIGEN_CUDACC, but for HIP)
    481   #define EIGEN_HIPCC __HIPCC__
    482 
    483   // We need to include hip_runtime.h here because it pulls in
    484   // ++ hip_common.h which contains the define for  __HIP_DEVICE_COMPILE__
    485   // ++ host_defines.h which contains the defines for the __host__ and __device__ macros
    486   #include <hip/hip_runtime.h>
    487 
    488   #if defined(__HIP_DEVICE_COMPILE__)
    489     // analogous to EIGEN_CUDA_ARCH, but for HIP
    490     #define EIGEN_HIP_DEVICE_COMPILE __HIP_DEVICE_COMPILE__
    491   #endif
    492 
    493   // For HIP (ROCm 3.5 and higher), we need to explicitly set the launch_bounds attribute
    494   // value to 1024. The compiler assigns a default value of 256 when the attribute is not
    495   // specified. This results in failures on the HIP platform, for cases when a GPU kernel
    496   // without an explicit launch_bounds attribute is called with a threads_per_block value
    497   // greater than 256.
    498   //
    499   // This is a regression in functioanlity and is expected to be fixed within the next
    500   // couple of ROCm releases (compiler will go back to using 1024 value as the default)
    501   //
    502   // In the meantime, we will use a "only enabled for HIP" macro to set the launch_bounds
    503   // attribute.
    504 
    505   #define EIGEN_HIP_LAUNCH_BOUNDS_1024 __launch_bounds__(1024)
    506 
    507 #endif
    508 
    509 #if !defined(EIGEN_HIP_LAUNCH_BOUNDS_1024)
    510 #define EIGEN_HIP_LAUNCH_BOUNDS_1024
    511 #endif // !defined(EIGEN_HIP_LAUNCH_BOUNDS_1024)
    512 
    513 // Unify CUDA/HIPCC
    514 
    515 #if defined(EIGEN_CUDACC) || defined(EIGEN_HIPCC)
    516 //
    517 // If either EIGEN_CUDACC or EIGEN_HIPCC is defined, then define EIGEN_GPUCC
    518 //
    519 #define EIGEN_GPUCC
    520 //
    521 // EIGEN_HIPCC implies the HIP compiler and is used to tweak Eigen code for use in HIP kernels
    522 // EIGEN_CUDACC implies the CUDA compiler and is used to tweak Eigen code for use in CUDA kernels
    523 //
    524 // In most cases the same tweaks are required to the Eigen code to enable in both the HIP and CUDA kernels.
    525 // For those cases, the corresponding code should be guarded with
    526 //      #if defined(EIGEN_GPUCC)
    527 // instead of
    528 //      #if defined(EIGEN_CUDACC) || defined(EIGEN_HIPCC)
    529 //
    530 // For cases where the tweak is specific to HIP, the code should be guarded with
    531 //      #if defined(EIGEN_HIPCC)
    532 //
    533 // For cases where the tweak is specific to CUDA, the code should be guarded with
    534 //      #if defined(EIGEN_CUDACC)
    535 //
    536 #endif
    537 
    538 #if defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIP_DEVICE_COMPILE)
    539 //
    540 // If either EIGEN_CUDA_ARCH or EIGEN_HIP_DEVICE_COMPILE is defined, then define EIGEN_GPU_COMPILE_PHASE
    541 //
    542 #define EIGEN_GPU_COMPILE_PHASE
    543 //
    544 // GPU compilers (HIPCC, NVCC) typically do two passes over the source code,
    545 //   + one to compile the source for the "host" (ie CPU)
    546 //   + another to compile the source for the "device" (ie. GPU)
    547 //
    548 // Code that needs to enabled only during the either the "host" or "device" compilation phase
    549 // needs to be guarded with a macro that indicates the current compilation phase
    550 //
    551 // EIGEN_HIP_DEVICE_COMPILE implies the device compilation phase in HIP
    552 // EIGEN_CUDA_ARCH implies the device compilation phase in CUDA
    553 //
    554 // In most cases, the "host" / "device" specific code is the same for both HIP and CUDA
    555 // For those cases, the code should be guarded with
    556 //       #if defined(EIGEN_GPU_COMPILE_PHASE)
    557 // instead of
    558 //       #if defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIP_DEVICE_COMPILE)
    559 //
    560 // For cases where the tweak is specific to HIP, the code should be guarded with
    561 //      #if defined(EIGEN_HIP_DEVICE_COMPILE)
    562 //
    563 // For cases where the tweak is specific to CUDA, the code should be guarded with
    564 //      #if defined(EIGEN_CUDA_ARCH)
    565 //
    566 #endif
    567 
    568 #if defined(EIGEN_USE_SYCL) && defined(__SYCL_DEVICE_ONLY__)
    569 // EIGEN_USE_SYCL is a user-defined macro while __SYCL_DEVICE_ONLY__ is a compiler-defined macro.
    570 // In most cases we want to check if both macros are defined which can be done using the define below.
    571 #define SYCL_DEVICE_ONLY
    572 #endif
    573 
    574 //------------------------------------------------------------------------------------------
    575 // Detect Compiler/Architecture/OS specific features
    576 //------------------------------------------------------------------------------------------
    577 
    578 #if EIGEN_GNUC_AT_MOST(4,3) && !EIGEN_COMP_CLANG
    579   // see bug 89
    580   #define EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO 0
    581 #else
    582   #define EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO 1
    583 #endif
    584 
    585 // Cross compiler wrapper around LLVM's __has_builtin
    586 #ifdef __has_builtin
    587 #  define EIGEN_HAS_BUILTIN(x) __has_builtin(x)
    588 #else
    589 #  define EIGEN_HAS_BUILTIN(x) 0
    590 #endif
    591 
    592 // A Clang feature extension to determine compiler features.
    593 // We use it to determine 'cxx_rvalue_references'
    594 #ifndef __has_feature
    595 # define __has_feature(x) 0
    596 #endif
    597 
    598 // Some old compilers do not support template specializations like:
    599 // template<typename T,int N> void foo(const T x[N]);
    600 #if !(   EIGEN_COMP_CLANG && (   (EIGEN_COMP_CLANG<309)                                                       \
    601                               || (defined(__apple_build_version__) && (__apple_build_version__ < 9000000)))  \
    602       || EIGEN_COMP_GNUC_STRICT && EIGEN_COMP_GNUC<49)
    603 #define EIGEN_HAS_STATIC_ARRAY_TEMPLATE 1
    604 #else
    605 #define EIGEN_HAS_STATIC_ARRAY_TEMPLATE 0
    606 #endif
    607 
    608 // The macro EIGEN_CPLUSPLUS is a replacement for __cplusplus/_MSVC_LANG that
    609 // works for both platforms, indicating the C++ standard version number.
    610 //
    611 // With MSVC, without defining /Zc:__cplusplus, the __cplusplus macro will
    612 // report 199711L regardless of the language standard specified via /std.
    613 // We need to rely on _MSVC_LANG instead, which is only available after
    614 // VS2015.3.
    615 #if EIGEN_COMP_MSVC_LANG > 0
    616 #define EIGEN_CPLUSPLUS EIGEN_COMP_MSVC_LANG
    617 #elif EIGEN_COMP_MSVC >= 1900
    618 #define EIGEN_CPLUSPLUS 201103L
    619 #elif defined(__cplusplus)
    620 #define EIGEN_CPLUSPLUS __cplusplus
    621 #else
    622 #define EIGEN_CPLUSPLUS 0
    623 #endif
    624 
    625 // The macro EIGEN_COMP_CXXVER defines the c++ verson expected by the compiler.
    626 // For instance, if compiling with gcc and -std=c++17, then EIGEN_COMP_CXXVER
    627 // is defined to 17.
    628 #if EIGEN_CPLUSPLUS > 201703L
    629   #define EIGEN_COMP_CXXVER 20
    630 #elif EIGEN_CPLUSPLUS > 201402L
    631   #define EIGEN_COMP_CXXVER 17
    632 #elif EIGEN_CPLUSPLUS > 201103L
    633   #define EIGEN_COMP_CXXVER 14
    634 #elif EIGEN_CPLUSPLUS >= 201103L
    635   #define EIGEN_COMP_CXXVER 11
    636 #else
    637   #define EIGEN_COMP_CXXVER 03
    638 #endif
    639 
    640 #ifndef EIGEN_HAS_CXX14_VARIABLE_TEMPLATES
    641   #if defined(__cpp_variable_templates) && __cpp_variable_templates >= 201304 && EIGEN_MAX_CPP_VER>=14
    642     #define EIGEN_HAS_CXX14_VARIABLE_TEMPLATES 1
    643   #else
    644     #define EIGEN_HAS_CXX14_VARIABLE_TEMPLATES 0
    645   #endif
    646 #endif
    647 
    648 
    649 // The macros EIGEN_HAS_CXX?? defines a rough estimate of available c++ features
    650 // but in practice we should not rely on them but rather on the availabilty of
    651 // individual features as defined later.
    652 // This is why there is no EIGEN_HAS_CXX17.
    653 // FIXME: get rid of EIGEN_HAS_CXX14 and maybe even EIGEN_HAS_CXX11.
    654 #if EIGEN_MAX_CPP_VER>=11 && EIGEN_COMP_CXXVER>=11
    655 #define EIGEN_HAS_CXX11 1
    656 #else
    657 #define EIGEN_HAS_CXX11 0
    658 #endif
    659 
    660 #if EIGEN_MAX_CPP_VER>=14 && EIGEN_COMP_CXXVER>=14
    661 #define EIGEN_HAS_CXX14 1
    662 #else
    663 #define EIGEN_HAS_CXX14 0
    664 #endif
    665 
    666 // Do we support r-value references?
    667 #ifndef EIGEN_HAS_RVALUE_REFERENCES
    668 #if EIGEN_MAX_CPP_VER>=11 && \
    669     (__has_feature(cxx_rvalue_references) || \
    670      (EIGEN_COMP_CXXVER >= 11) || (EIGEN_COMP_MSVC >= 1600))
    671   #define EIGEN_HAS_RVALUE_REFERENCES 1
    672 #else
    673   #define EIGEN_HAS_RVALUE_REFERENCES 0
    674 #endif
    675 #endif
    676 
    677 // Does the compiler support C99?
    678 // Need to include <cmath> to make sure _GLIBCXX_USE_C99 gets defined
    679 #include <cmath>
    680 #ifndef EIGEN_HAS_C99_MATH
    681 #if EIGEN_MAX_CPP_VER>=11 && \
    682     ((defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901))       \
    683   || (defined(__GNUC__) && defined(_GLIBCXX_USE_C99)) \
    684   || (defined(_LIBCPP_VERSION) && !defined(_MSC_VER)) \
    685   || (EIGEN_COMP_MSVC >= 1900) || defined(SYCL_DEVICE_ONLY))
    686   #define EIGEN_HAS_C99_MATH 1
    687 #else
    688   #define EIGEN_HAS_C99_MATH 0
    689 #endif
    690 #endif
    691 
    692 // Does the compiler support result_of?
    693 // result_of was deprecated in c++17 and removed in c++ 20
    694 #ifndef EIGEN_HAS_STD_RESULT_OF
    695 #if EIGEN_HAS_CXX11 && EIGEN_COMP_CXXVER < 17
    696 #define EIGEN_HAS_STD_RESULT_OF 1
    697 #else
    698 #define EIGEN_HAS_STD_RESULT_OF 0
    699 #endif
    700 #endif
    701 
    702 // Does the compiler support std::hash?
    703 #ifndef EIGEN_HAS_STD_HASH
    704 // The std::hash struct is defined in C++11 but is not labelled as a __device__
    705 // function and is not constexpr, so cannot be used on device.
    706 #if EIGEN_HAS_CXX11 && !defined(EIGEN_GPU_COMPILE_PHASE)
    707 #define EIGEN_HAS_STD_HASH 1
    708 #else
    709 #define EIGEN_HAS_STD_HASH 0
    710 #endif
    711 #endif  // EIGEN_HAS_STD_HASH
    712 
    713 #ifndef EIGEN_HAS_STD_INVOKE_RESULT
    714 #if EIGEN_MAX_CPP_VER >= 17 && EIGEN_COMP_CXXVER >= 17
    715 #define EIGEN_HAS_STD_INVOKE_RESULT 1
    716 #else
    717 #define EIGEN_HAS_STD_INVOKE_RESULT 0
    718 #endif
    719 #endif
    720 
    721 #ifndef EIGEN_HAS_ALIGNAS
    722 #if EIGEN_MAX_CPP_VER>=11 && EIGEN_HAS_CXX11 &&   \
    723       (     __has_feature(cxx_alignas)            \
    724         ||  EIGEN_HAS_CXX14                       \
    725         || (EIGEN_COMP_MSVC >= 1800)              \
    726         || (EIGEN_GNUC_AT_LEAST(4,8))             \
    727         || (EIGEN_COMP_CLANG>=305)                \
    728         || (EIGEN_COMP_ICC>=1500)                 \
    729         || (EIGEN_COMP_PGI>=1500)                 \
    730         || (EIGEN_COMP_SUNCC>=0x5130))
    731 #define EIGEN_HAS_ALIGNAS 1
    732 #else
    733 #define EIGEN_HAS_ALIGNAS 0
    734 #endif
    735 #endif
    736 
    737 // Does the compiler support type_traits?
    738 // - full support of type traits was added only to GCC 5.1.0.
    739 // - 20150626 corresponds to the last release of 4.x libstdc++
    740 #ifndef EIGEN_HAS_TYPE_TRAITS
    741 #if EIGEN_MAX_CPP_VER>=11 && (EIGEN_HAS_CXX11 || EIGEN_COMP_MSVC >= 1700) \
    742   && ((!EIGEN_COMP_GNUC_STRICT) || EIGEN_GNUC_AT_LEAST(5, 1)) \
    743   && ((!defined(__GLIBCXX__))   || __GLIBCXX__ > 20150626)
    744 #define EIGEN_HAS_TYPE_TRAITS 1
    745 #define EIGEN_INCLUDE_TYPE_TRAITS
    746 #else
    747 #define EIGEN_HAS_TYPE_TRAITS 0
    748 #endif
    749 #endif
    750 
    751 // Does the compiler support variadic templates?
    752 #ifndef EIGEN_HAS_VARIADIC_TEMPLATES
    753 #if EIGEN_MAX_CPP_VER>=11 && (EIGEN_COMP_CXXVER >= 11) \
    754   && (!defined(__NVCC__) || !EIGEN_ARCH_ARM_OR_ARM64 || (EIGEN_COMP_NVCC >= 80000) )
    755     // ^^ Disable the use of variadic templates when compiling with versions of nvcc older than 8.0 on ARM devices:
    756     //    this prevents nvcc from crashing when compiling Eigen on Tegra X1
    757 #define EIGEN_HAS_VARIADIC_TEMPLATES 1
    758 #elif  EIGEN_MAX_CPP_VER>=11 && (EIGEN_COMP_CXXVER >= 11) && defined(SYCL_DEVICE_ONLY)
    759 #define EIGEN_HAS_VARIADIC_TEMPLATES 1
    760 #else
    761 #define EIGEN_HAS_VARIADIC_TEMPLATES 0
    762 #endif
    763 #endif
    764 
    765 // Does the compiler fully support const expressions? (as in c++14)
    766 #ifndef EIGEN_HAS_CONSTEXPR
    767   #if defined(EIGEN_CUDACC)
    768   // Const expressions are supported provided that c++11 is enabled and we're using either clang or nvcc 7.5 or above
    769     #if EIGEN_MAX_CPP_VER>=14 && (EIGEN_COMP_CXXVER >= 11 && (EIGEN_COMP_CLANG || EIGEN_COMP_NVCC >= 70500))
    770       #define EIGEN_HAS_CONSTEXPR 1
    771     #endif
    772   #elif EIGEN_MAX_CPP_VER>=14 && (__has_feature(cxx_relaxed_constexpr) || (EIGEN_COMP_CXXVER >= 14) || \
    773     (EIGEN_GNUC_AT_LEAST(4,8) && (EIGEN_COMP_CXXVER >= 11)) || \
    774     (EIGEN_COMP_CLANG >= 306 && (EIGEN_COMP_CXXVER >= 11)))
    775     #define EIGEN_HAS_CONSTEXPR 1
    776   #endif
    777 
    778   #ifndef EIGEN_HAS_CONSTEXPR
    779     #define EIGEN_HAS_CONSTEXPR 0
    780   #endif
    781 
    782 #endif // EIGEN_HAS_CONSTEXPR
    783 
    784 #if EIGEN_HAS_CONSTEXPR
    785 #define EIGEN_CONSTEXPR constexpr
    786 #else
    787 #define EIGEN_CONSTEXPR
    788 #endif
    789 
    790 // Does the compiler support C++11 math?
    791 // Let's be conservative and enable the default C++11 implementation only if we are sure it exists
    792 #ifndef EIGEN_HAS_CXX11_MATH
    793   #if EIGEN_MAX_CPP_VER>=11 && ((EIGEN_COMP_CXXVER > 11) || (EIGEN_COMP_CXXVER == 11) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_MSVC || EIGEN_COMP_ICC)  \
    794       && (EIGEN_ARCH_i386_OR_x86_64) && (EIGEN_OS_GNULINUX || EIGEN_OS_WIN_STRICT || EIGEN_OS_MAC))
    795     #define EIGEN_HAS_CXX11_MATH 1
    796   #else
    797     #define EIGEN_HAS_CXX11_MATH 0
    798   #endif
    799 #endif
    800 
    801 // Does the compiler support proper C++11 containers?
    802 #ifndef EIGEN_HAS_CXX11_CONTAINERS
    803   #if    EIGEN_MAX_CPP_VER>=11 && \
    804          ((EIGEN_COMP_CXXVER > 11) \
    805       || ((EIGEN_COMP_CXXVER == 11) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_MSVC || EIGEN_COMP_ICC>=1400)))
    806     #define EIGEN_HAS_CXX11_CONTAINERS 1
    807   #else
    808     #define EIGEN_HAS_CXX11_CONTAINERS 0
    809   #endif
    810 #endif
    811 
    812 // Does the compiler support C++11 noexcept?
    813 #ifndef EIGEN_HAS_CXX11_NOEXCEPT
    814   #if    EIGEN_MAX_CPP_VER>=11 && \
    815          (__has_feature(cxx_noexcept) \
    816       || (EIGEN_COMP_CXXVER > 11) \
    817       || ((EIGEN_COMP_CXXVER == 11) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_MSVC || EIGEN_COMP_ICC>=1400)))
    818     #define EIGEN_HAS_CXX11_NOEXCEPT 1
    819   #else
    820     #define EIGEN_HAS_CXX11_NOEXCEPT 0
    821   #endif
    822 #endif
    823 
    824 #ifndef EIGEN_HAS_CXX11_ATOMIC
    825   #if    EIGEN_MAX_CPP_VER>=11 && \
    826          (__has_feature(cxx_atomic) \
    827       || (EIGEN_COMP_CXXVER > 11) \
    828       || ((EIGEN_COMP_CXXVER == 11) && (EIGEN_COMP_MSVC==0 || EIGEN_COMP_MSVC >= 1700)))
    829     #define EIGEN_HAS_CXX11_ATOMIC 1
    830   #else
    831     #define EIGEN_HAS_CXX11_ATOMIC 0
    832   #endif
    833 #endif
    834 
    835 #ifndef EIGEN_HAS_CXX11_OVERRIDE_FINAL
    836   #if    EIGEN_MAX_CPP_VER>=11 && \
    837        (EIGEN_COMP_CXXVER >= 11 || EIGEN_COMP_MSVC >= 1700)
    838     #define EIGEN_HAS_CXX11_OVERRIDE_FINAL 1
    839   #else
    840     #define EIGEN_HAS_CXX11_OVERRIDE_FINAL 0
    841   #endif
    842 #endif
    843 
    844 // NOTE: the required Apple's clang version is very conservative
    845 //       and it could be that XCode 9 works just fine.
    846 // NOTE: the MSVC version is based on https://en.cppreference.com/w/cpp/compiler_support
    847 //       and not tested.
    848 #ifndef EIGEN_HAS_CXX17_OVERALIGN
    849 #if EIGEN_MAX_CPP_VER>=17 && EIGEN_COMP_CXXVER>=17 && (                                 \
    850            (EIGEN_COMP_MSVC >= 1912)                                                    \
    851         || (EIGEN_GNUC_AT_LEAST(7,0))                                                   \
    852         || ((!defined(__apple_build_version__)) && (EIGEN_COMP_CLANG>=500))             \
    853         || (( defined(__apple_build_version__)) && (__apple_build_version__>=10000000)) \
    854       )
    855 #define EIGEN_HAS_CXX17_OVERALIGN 1
    856 #else
    857 #define EIGEN_HAS_CXX17_OVERALIGN 0
    858 #endif
    859 #endif
    860 
    861 #if defined(EIGEN_CUDACC) && EIGEN_HAS_CONSTEXPR
    862   // While available already with c++11, this is useful mostly starting with c++14 and relaxed constexpr rules
    863   #if defined(__NVCC__)
    864     // nvcc considers constexpr functions as __host__ __device__ with the option --expt-relaxed-constexpr
    865     #ifdef __CUDACC_RELAXED_CONSTEXPR__
    866       #define EIGEN_CONSTEXPR_ARE_DEVICE_FUNC
    867     #endif
    868   #elif defined(__clang__) && defined(__CUDA__) && __has_feature(cxx_relaxed_constexpr)
    869     // clang++ always considers constexpr functions as implicitly __host__ __device__
    870     #define EIGEN_CONSTEXPR_ARE_DEVICE_FUNC
    871   #endif
    872 #endif
    873 
    874 // Does the compiler support the __int128 and __uint128_t extensions for 128-bit
    875 // integer arithmetic?
    876 //
    877 // Clang and GCC define __SIZEOF_INT128__ when these extensions are supported,
    878 // but we avoid using them in certain cases:
    879 //
    880 // * Building using Clang for Windows, where the Clang runtime library has
    881 //   128-bit support only on LP64 architectures, but Windows is LLP64.
    882 #ifndef EIGEN_HAS_BUILTIN_INT128
    883 #if defined(__SIZEOF_INT128__) && !(EIGEN_OS_WIN && EIGEN_COMP_CLANG)
    884 #define EIGEN_HAS_BUILTIN_INT128 1
    885 #else
    886 #define EIGEN_HAS_BUILTIN_INT128 0
    887 #endif
    888 #endif
    889 
    890 //------------------------------------------------------------------------------------------
    891 // Preprocessor programming helpers
    892 //------------------------------------------------------------------------------------------
    893 
    894 // This macro can be used to prevent from macro expansion, e.g.:
    895 //   std::max EIGEN_NOT_A_MACRO(a,b)
    896 #define EIGEN_NOT_A_MACRO
    897 
    898 #define EIGEN_DEBUG_VAR(x) std::cerr << #x << " = " << x << std::endl;
    899 
    900 // concatenate two tokens
    901 #define EIGEN_CAT2(a,b) a ## b
    902 #define EIGEN_CAT(a,b) EIGEN_CAT2(a,b)
    903 
    904 #define EIGEN_COMMA ,
    905 
    906 // convert a token to a string
    907 #define EIGEN_MAKESTRING2(a) #a
    908 #define EIGEN_MAKESTRING(a) EIGEN_MAKESTRING2(a)
    909 
    910 // EIGEN_STRONG_INLINE is a stronger version of the inline, using __forceinline on MSVC,
    911 // but it still doesn't use GCC's always_inline. This is useful in (common) situations where MSVC needs forceinline
    912 // but GCC is still doing fine with just inline.
    913 #ifndef EIGEN_STRONG_INLINE
    914 #if (EIGEN_COMP_MSVC || EIGEN_COMP_ICC) && !defined(EIGEN_GPUCC)
    915 #define EIGEN_STRONG_INLINE __forceinline
    916 #else
    917 #define EIGEN_STRONG_INLINE inline
    918 #endif
    919 #endif
    920 
    921 // EIGEN_ALWAYS_INLINE is the stronget, it has the effect of making the function inline and adding every possible
    922 // attribute to maximize inlining. This should only be used when really necessary: in particular,
    923 // it uses __attribute__((always_inline)) on GCC, which most of the time is useless and can severely harm compile times.
    924 // FIXME with the always_inline attribute,
    925 // gcc 3.4.x and 4.1 reports the following compilation error:
    926 //   Eval.h:91: sorry, unimplemented: inlining failed in call to 'const Eigen::Eval<Derived> Eigen::MatrixBase<Scalar, Derived>::eval() const'
    927 //    : function body not available
    928 //   See also bug 1367
    929 #if EIGEN_GNUC_AT_LEAST(4,2) && !defined(SYCL_DEVICE_ONLY)
    930 #define EIGEN_ALWAYS_INLINE __attribute__((always_inline)) inline
    931 #else
    932 #define EIGEN_ALWAYS_INLINE EIGEN_STRONG_INLINE
    933 #endif
    934 
    935 #if EIGEN_COMP_GNUC
    936 #define EIGEN_DONT_INLINE __attribute__((noinline))
    937 #elif EIGEN_COMP_MSVC
    938 #define EIGEN_DONT_INLINE __declspec(noinline)
    939 #else
    940 #define EIGEN_DONT_INLINE
    941 #endif
    942 
    943 #if EIGEN_COMP_GNUC
    944 #define EIGEN_PERMISSIVE_EXPR __extension__
    945 #else
    946 #define EIGEN_PERMISSIVE_EXPR
    947 #endif
    948 
    949 // GPU stuff
    950 
    951 // Disable some features when compiling with GPU compilers (NVCC/clang-cuda/SYCL/HIPCC)
    952 #if defined(EIGEN_CUDACC) || defined(SYCL_DEVICE_ONLY) || defined(EIGEN_HIPCC)
    953   // Do not try asserts on device code
    954   #ifndef EIGEN_NO_DEBUG
    955   #define EIGEN_NO_DEBUG
    956   #endif
    957 
    958   #ifdef EIGEN_INTERNAL_DEBUGGING
    959   #undef EIGEN_INTERNAL_DEBUGGING
    960   #endif
    961 
    962   #ifdef EIGEN_EXCEPTIONS
    963   #undef EIGEN_EXCEPTIONS
    964   #endif
    965 #endif
    966 
    967 #if defined(SYCL_DEVICE_ONLY)
    968   #ifndef EIGEN_DONT_VECTORIZE
    969     #define EIGEN_DONT_VECTORIZE
    970   #endif
    971   #define EIGEN_DEVICE_FUNC __attribute__((flatten)) __attribute__((always_inline))
    972 // All functions callable from CUDA/HIP code must be qualified with __device__
    973 #elif defined(EIGEN_GPUCC)
    974     #define EIGEN_DEVICE_FUNC __host__ __device__
    975 #else
    976   #define EIGEN_DEVICE_FUNC
    977 #endif
    978 
    979 
    980 // this macro allows to get rid of linking errors about multiply defined functions.
    981 //  - static is not very good because it prevents definitions from different object files to be merged.
    982 //           So static causes the resulting linked executable to be bloated with multiple copies of the same function.
    983 //  - inline is not perfect either as it unwantedly hints the compiler toward inlining the function.
    984 #define EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC
    985 #define EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC inline
    986 
    987 #ifdef NDEBUG
    988 # ifndef EIGEN_NO_DEBUG
    989 #  define EIGEN_NO_DEBUG
    990 # endif
    991 #endif
    992 
    993 // eigen_plain_assert is where we implement the workaround for the assert() bug in GCC <= 4.3, see bug 89
    994 #ifdef EIGEN_NO_DEBUG
    995   #ifdef SYCL_DEVICE_ONLY // used to silence the warning on SYCL device
    996     #define eigen_plain_assert(x) EIGEN_UNUSED_VARIABLE(x)
    997   #else
    998     #define eigen_plain_assert(x)
    999   #endif
   1000 #else
   1001   #if EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO
   1002     namespace Eigen {
   1003     namespace internal {
   1004     inline bool copy_bool(bool b) { return b; }
   1005     }
   1006     }
   1007     #define eigen_plain_assert(x) assert(x)
   1008   #else
   1009     // work around bug 89
   1010     #include <cstdlib>   // for abort
   1011     #include <iostream>  // for std::cerr
   1012 
   1013     namespace Eigen {
   1014     namespace internal {
   1015     // trivial function copying a bool. Must be EIGEN_DONT_INLINE, so we implement it after including Eigen headers.
   1016     // see bug 89.
   1017     namespace {
   1018     EIGEN_DONT_INLINE bool copy_bool(bool b) { return b; }
   1019     }
   1020     inline void assert_fail(const char *condition, const char *function, const char *file, int line)
   1021     {
   1022       std::cerr << "assertion failed: " << condition << " in function " << function << " at " << file << ":" << line << std::endl;
   1023       abort();
   1024     }
   1025     }
   1026     }
   1027     #define eigen_plain_assert(x) \
   1028       do { \
   1029         if(!Eigen::internal::copy_bool(x)) \
   1030           Eigen::internal::assert_fail(EIGEN_MAKESTRING(x), __PRETTY_FUNCTION__, __FILE__, __LINE__); \
   1031       } while(false)
   1032   #endif
   1033 #endif
   1034 
   1035 // eigen_assert can be overridden
   1036 #ifndef eigen_assert
   1037 #define eigen_assert(x) eigen_plain_assert(x)
   1038 #endif
   1039 
   1040 #ifdef EIGEN_INTERNAL_DEBUGGING
   1041 #define eigen_internal_assert(x) eigen_assert(x)
   1042 #else
   1043 #define eigen_internal_assert(x)
   1044 #endif
   1045 
   1046 #ifdef EIGEN_NO_DEBUG
   1047 #define EIGEN_ONLY_USED_FOR_DEBUG(x) EIGEN_UNUSED_VARIABLE(x)
   1048 #else
   1049 #define EIGEN_ONLY_USED_FOR_DEBUG(x)
   1050 #endif
   1051 
   1052 #ifndef EIGEN_NO_DEPRECATED_WARNING
   1053   #if EIGEN_COMP_GNUC
   1054     #define EIGEN_DEPRECATED __attribute__((deprecated))
   1055   #elif EIGEN_COMP_MSVC
   1056     #define EIGEN_DEPRECATED __declspec(deprecated)
   1057   #else
   1058     #define EIGEN_DEPRECATED
   1059   #endif
   1060 #else
   1061   #define EIGEN_DEPRECATED
   1062 #endif
   1063 
   1064 #if EIGEN_COMP_GNUC
   1065 #define EIGEN_UNUSED __attribute__((unused))
   1066 #else
   1067 #define EIGEN_UNUSED
   1068 #endif
   1069 
   1070 // Suppresses 'unused variable' warnings.
   1071 namespace Eigen {
   1072   namespace internal {
   1073     template<typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ignore_unused_variable(const T&) {}
   1074   }
   1075 }
   1076 #define EIGEN_UNUSED_VARIABLE(var) Eigen::internal::ignore_unused_variable(var);
   1077 
   1078 #if !defined(EIGEN_ASM_COMMENT)
   1079   #if EIGEN_COMP_GNUC && (EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM_OR_ARM64)
   1080     #define EIGEN_ASM_COMMENT(X)  __asm__("#" X)
   1081   #else
   1082     #define EIGEN_ASM_COMMENT(X)
   1083   #endif
   1084 #endif
   1085 
   1086 
   1087 // Acts as a barrier preventing operations involving `X` from crossing. This
   1088 // occurs, for example, in the fast rounding trick where a magic constant is
   1089 // added then subtracted, which is otherwise compiled away with -ffast-math.
   1090 //
   1091 // See bug 1674
   1092 #if !defined(EIGEN_OPTIMIZATION_BARRIER)
   1093   #if EIGEN_COMP_GNUC
   1094     // According to https://gcc.gnu.org/onlinedocs/gcc/Constraints.html:
   1095     //   X: Any operand whatsoever.
   1096     //   r: A register operand is allowed provided that it is in a general
   1097     //      register.
   1098     //   g: Any register, memory or immediate integer operand is allowed, except
   1099     //      for registers that are not general registers.
   1100     //   w: (AArch32/AArch64) Floating point register, Advanced SIMD vector
   1101     //      register or SVE vector register.
   1102     //   x: (SSE) Any SSE register.
   1103     //      (AArch64) Like w, but restricted to registers 0 to 15 inclusive.
   1104     //   v: (PowerPC) An Altivec vector register.
   1105     //   wa:(PowerPC) A VSX register.
   1106     //
   1107     // "X" (uppercase) should work for all cases, though this seems to fail for
   1108     // some versions of GCC for arm/aarch64 with
   1109     //   "error: inconsistent operand constraints in an 'asm'"
   1110     // Clang x86_64/arm/aarch64 seems to require "g" to support both scalars and
   1111     // vectors, otherwise
   1112     //   "error: non-trivial scalar-to-vector conversion, possible invalid
   1113     //    constraint for vector type"
   1114     //
   1115     // GCC for ppc64le generates an internal compiler error with x/X/g.
   1116     // GCC for AVX generates an internal compiler error with X.
   1117     //
   1118     // Tested on icc/gcc/clang for sse, avx, avx2, avx512dq
   1119     //           gcc for arm, aarch64,
   1120     //           gcc for ppc64le,
   1121     // both vectors and scalars.
   1122     //
   1123     // Note that this is restricted to plain types - this will not work
   1124     // directly for std::complex<T>, Eigen::half, Eigen::bfloat16. For these,
   1125     // you will need to apply to the underlying POD type.
   1126     #if EIGEN_ARCH_PPC && EIGEN_COMP_GNUC_STRICT
   1127       // This seems to be broken on clang.  Packet4f is loaded into a single
   1128       //   register rather than a vector, zeroing out some entries.  Integer
   1129       //   types also generate a compile error.
   1130       // General, Altivec, VSX.
   1131       #define EIGEN_OPTIMIZATION_BARRIER(X)  __asm__  ("" : "+r,v,wa" (X));
   1132     #elif EIGEN_ARCH_ARM_OR_ARM64
   1133       // General, NEON.
   1134       #define EIGEN_OPTIMIZATION_BARRIER(X)  __asm__  ("" : "+g,w" (X));
   1135     #elif EIGEN_ARCH_i386_OR_x86_64
   1136       // General, SSE.
   1137       #define EIGEN_OPTIMIZATION_BARRIER(X)  __asm__  ("" : "+g,x" (X));
   1138     #else
   1139       // Not implemented for other architectures.
   1140       #define EIGEN_OPTIMIZATION_BARRIER(X)
   1141     #endif
   1142   #else
   1143     // Not implemented for other compilers.
   1144     #define EIGEN_OPTIMIZATION_BARRIER(X)
   1145   #endif
   1146 #endif
   1147 
   1148 #if EIGEN_COMP_MSVC
   1149   // NOTE MSVC often gives C4127 warnings with compiletime if statements. See bug 1362.
   1150   // This workaround is ugly, but it does the job.
   1151 #  define EIGEN_CONST_CONDITIONAL(cond)  (void)0, cond
   1152 #else
   1153 #  define EIGEN_CONST_CONDITIONAL(cond)  cond
   1154 #endif
   1155 
   1156 #ifdef EIGEN_DONT_USE_RESTRICT_KEYWORD
   1157   #define EIGEN_RESTRICT
   1158 #endif
   1159 #ifndef EIGEN_RESTRICT
   1160   #define EIGEN_RESTRICT __restrict
   1161 #endif
   1162 
   1163 
   1164 #ifndef EIGEN_DEFAULT_IO_FORMAT
   1165 #ifdef EIGEN_MAKING_DOCS
   1166 // format used in Eigen's documentation
   1167 // needed to define it here as escaping characters in CMake add_definition's argument seems very problematic.
   1168 #define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat(3, 0, " ", "\n", "", "")
   1169 #else
   1170 #define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat()
   1171 #endif
   1172 #endif
   1173 
   1174 // just an empty macro !
   1175 #define EIGEN_EMPTY
   1176 
   1177 
   1178 // When compiling CUDA/HIP device code with NVCC or HIPCC
   1179 // pull in math functions from the global namespace.
   1180 // In host mode, and when device code is compiled with clang,
   1181 // use the std versions.
   1182 #if (defined(EIGEN_CUDA_ARCH) && defined(__NVCC__)) || defined(EIGEN_HIP_DEVICE_COMPILE)
   1183   #define EIGEN_USING_STD(FUNC) using ::FUNC;
   1184 #else
   1185   #define EIGEN_USING_STD(FUNC) using std::FUNC;
   1186 #endif
   1187 
   1188 #if EIGEN_COMP_MSVC_STRICT && (EIGEN_COMP_MSVC < 1900 || (EIGEN_COMP_MSVC == 1900 && EIGEN_COMP_NVCC))
   1189   // For older MSVC versions, as well as 1900 && CUDA 8, using the base operator is necessary,
   1190   //   otherwise we get duplicate definition errors
   1191   // For later MSVC versions, we require explicit operator= definition, otherwise we get
   1192   //   use of implicitly deleted operator errors.
   1193   // (cf Bugs 920, 1000, 1324, 2291)
   1194   #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
   1195     using Base::operator =;
   1196 #elif EIGEN_COMP_CLANG // workaround clang bug (see http://forum.kde.org/viewtopic.php?f=74&t=102653)
   1197   #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
   1198     using Base::operator =; \
   1199     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) { Base::operator=(other); return *this; } \
   1200     template <typename OtherDerived> \
   1201     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other) { Base::operator=(other.derived()); return *this; }
   1202 #else
   1203   #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
   1204     using Base::operator =; \
   1205     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) \
   1206     { \
   1207       Base::operator=(other); \
   1208       return *this; \
   1209     }
   1210 #endif
   1211 
   1212 
   1213 /**
   1214  * \internal
   1215  * \brief Macro to explicitly define the default copy constructor.
   1216  * This is necessary, because the implicit definition is deprecated if the copy-assignment is overridden.
   1217  */
   1218 #if EIGEN_HAS_CXX11
   1219 #define EIGEN_DEFAULT_COPY_CONSTRUCTOR(CLASS) CLASS(const CLASS&) = default;
   1220 #else
   1221 #define EIGEN_DEFAULT_COPY_CONSTRUCTOR(CLASS)
   1222 #endif
   1223 
   1224 
   1225 
   1226 /** \internal
   1227  * \brief Macro to manually inherit assignment operators.
   1228  * This is necessary, because the implicitly defined assignment operator gets deleted when a custom operator= is defined.
   1229  * With C++11 or later this also default-implements the copy-constructor
   1230  */
   1231 #define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived)  \
   1232     EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
   1233     EIGEN_DEFAULT_COPY_CONSTRUCTOR(Derived)
   1234 
   1235 /** \internal
   1236  * \brief Macro to manually define default constructors and destructors.
   1237  * This is necessary when the copy constructor is re-defined.
   1238  * For empty helper classes this should usually be protected, to avoid accidentally creating empty objects.
   1239  *
   1240  * Hiding the default destructor lead to problems in C++03 mode together with boost::multiprecision
   1241  */
   1242 #if EIGEN_HAS_CXX11
   1243 #define EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(Derived)  \
   1244     Derived() = default; \
   1245     ~Derived() = default;
   1246 #else
   1247 #define EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(Derived)  \
   1248     Derived() {}; \
   1249     /* ~Derived() {}; */
   1250 #endif
   1251 
   1252 
   1253 
   1254 
   1255 
   1256 /**
   1257 * Just a side note. Commenting within defines works only by documenting
   1258 * behind the object (via '!<'). Comments cannot be multi-line and thus
   1259 * we have these extra long lines. What is confusing doxygen over here is
   1260 * that we use '\' and basically have a bunch of typedefs with their
   1261 * documentation in a single line.
   1262 **/
   1263 
   1264 #define EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
   1265   typedef typename Eigen::internal::traits<Derived>::Scalar Scalar; /*!< \brief Numeric type, e.g. float, double, int or std::complex<float>. */ \
   1266   typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; /*!< \brief The underlying numeric type for composed scalar types. \details In cases where Scalar is e.g. std::complex<T>, T were corresponding to RealScalar. */ \
   1267   typedef typename Base::CoeffReturnType CoeffReturnType; /*!< \brief The return type for coefficient access. \details Depending on whether the object allows direct coefficient access (e.g. for a MatrixXd), this type is either 'const Scalar&' or simply 'Scalar' for objects that do not allow direct coefficient access. */ \
   1268   typedef typename Eigen::internal::ref_selector<Derived>::type Nested; \
   1269   typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \
   1270   typedef typename Eigen::internal::traits<Derived>::StorageIndex StorageIndex; \
   1271   enum CompileTimeTraits \
   1272       { RowsAtCompileTime = Eigen::internal::traits<Derived>::RowsAtCompileTime, \
   1273         ColsAtCompileTime = Eigen::internal::traits<Derived>::ColsAtCompileTime, \
   1274         Flags = Eigen::internal::traits<Derived>::Flags, \
   1275         SizeAtCompileTime = Base::SizeAtCompileTime, \
   1276         MaxSizeAtCompileTime = Base::MaxSizeAtCompileTime, \
   1277         IsVectorAtCompileTime = Base::IsVectorAtCompileTime }; \
   1278   using Base::derived; \
   1279   using Base::const_cast_derived;
   1280 
   1281 
   1282 // FIXME Maybe the EIGEN_DENSE_PUBLIC_INTERFACE could be removed as importing PacketScalar is rarely needed
   1283 #define EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \
   1284   EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
   1285   typedef typename Base::PacketScalar PacketScalar;
   1286 
   1287 
   1288 #define EIGEN_PLAIN_ENUM_MIN(a,b) (((int)a <= (int)b) ? (int)a : (int)b)
   1289 #define EIGEN_PLAIN_ENUM_MAX(a,b) (((int)a >= (int)b) ? (int)a : (int)b)
   1290 
   1291 // EIGEN_SIZE_MIN_PREFER_DYNAMIC gives the min between compile-time sizes. 0 has absolute priority, followed by 1,
   1292 // followed by Dynamic, followed by other finite values. The reason for giving Dynamic the priority over
   1293 // finite values is that min(3, Dynamic) should be Dynamic, since that could be anything between 0 and 3.
   1294 #define EIGEN_SIZE_MIN_PREFER_DYNAMIC(a,b) (((int)a == 0 || (int)b == 0) ? 0 \
   1295                            : ((int)a == 1 || (int)b == 1) ? 1 \
   1296                            : ((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \
   1297                            : ((int)a <= (int)b) ? (int)a : (int)b)
   1298 
   1299 // EIGEN_SIZE_MIN_PREFER_FIXED is a variant of EIGEN_SIZE_MIN_PREFER_DYNAMIC comparing MaxSizes. The difference is that finite values
   1300 // now have priority over Dynamic, so that min(3, Dynamic) gives 3. Indeed, whatever the actual value is
   1301 // (between 0 and 3), it is not more than 3.
   1302 #define EIGEN_SIZE_MIN_PREFER_FIXED(a,b)  (((int)a == 0 || (int)b == 0) ? 0 \
   1303                            : ((int)a == 1 || (int)b == 1) ? 1 \
   1304                            : ((int)a == Dynamic && (int)b == Dynamic) ? Dynamic \
   1305                            : ((int)a == Dynamic) ? (int)b \
   1306                            : ((int)b == Dynamic) ? (int)a \
   1307                            : ((int)a <= (int)b) ? (int)a : (int)b)
   1308 
   1309 // see EIGEN_SIZE_MIN_PREFER_DYNAMIC. No need for a separate variant for MaxSizes here.
   1310 #define EIGEN_SIZE_MAX(a,b) (((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \
   1311                            : ((int)a >= (int)b) ? (int)a : (int)b)
   1312 
   1313 #define EIGEN_LOGICAL_XOR(a,b) (((a) || (b)) && !((a) && (b)))
   1314 
   1315 #define EIGEN_IMPLIES(a,b) (!(a) || (b))
   1316 
   1317 #if EIGEN_HAS_BUILTIN(__builtin_expect) || EIGEN_COMP_GNUC
   1318 #define EIGEN_PREDICT_FALSE(x) (__builtin_expect(x, false))
   1319 #define EIGEN_PREDICT_TRUE(x) (__builtin_expect(false || (x), true))
   1320 #else
   1321 #define EIGEN_PREDICT_FALSE(x) (x)
   1322 #define EIGEN_PREDICT_TRUE(x) (x)
   1323 #endif
   1324 
   1325 // the expression type of a standard coefficient wise binary operation
   1326 #define EIGEN_CWISE_BINARY_RETURN_TYPE(LHS,RHS,OPNAME) \
   1327     CwiseBinaryOp< \
   1328       EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)< \
   1329           typename internal::traits<LHS>::Scalar, \
   1330           typename internal::traits<RHS>::Scalar \
   1331       >, \
   1332       const LHS, \
   1333       const RHS \
   1334     >
   1335 
   1336 #define EIGEN_MAKE_CWISE_BINARY_OP(METHOD,OPNAME) \
   1337   template<typename OtherDerived> \
   1338   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME) \
   1339   (METHOD)(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
   1340   { \
   1341     return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME)(derived(), other.derived()); \
   1342   }
   1343 
   1344 #define EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,TYPEA,TYPEB) \
   1345   (Eigen::internal::has_ReturnType<Eigen::ScalarBinaryOpTraits<TYPEA,TYPEB,EIGEN_CAT(EIGEN_CAT(Eigen::internal::scalar_,OPNAME),_op)<TYPEA,TYPEB>  > >::value)
   1346 
   1347 #define EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(EXPR,SCALAR,OPNAME) \
   1348   CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<typename internal::traits<EXPR>::Scalar,SCALAR>, const EXPR, \
   1349                 const typename internal::plain_constant_type<EXPR,SCALAR>::type>
   1350 
   1351 #define EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(SCALAR,EXPR,OPNAME) \
   1352   CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<SCALAR,typename internal::traits<EXPR>::Scalar>, \
   1353                 const typename internal::plain_constant_type<EXPR,SCALAR>::type, const EXPR>
   1354 
   1355 // Workaround for MSVC 2010 (see ML thread "patch with compile for for MSVC 2010")
   1356 #if EIGEN_COMP_MSVC_STRICT && (EIGEN_COMP_MSVC_STRICT<=1600)
   1357 #define EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(X) typename internal::enable_if<true,X>::type
   1358 #else
   1359 #define EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(X) X
   1360 #endif
   1361 
   1362 #define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME) \
   1363   template <typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
   1364   EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(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))\
   1365   (METHOD)(const T& scalar) const { \
   1366     typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,Scalar,T)>::type PromotedT; \
   1367     return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,PromotedT,OPNAME)(derived(), \
   1368            typename internal::plain_constant_type<Derived,PromotedT>::type(derived().rows(), derived().cols(), internal::scalar_constant_op<PromotedT>(scalar))); \
   1369   }
   1370 
   1371 #define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
   1372   template <typename T> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE friend \
   1373   EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(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)) \
   1374   (METHOD)(const T& scalar, const StorageBaseType& matrix) { \
   1375     typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,T,Scalar)>::type PromotedT; \
   1376     return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedT,Derived,OPNAME)( \
   1377            typename internal::plain_constant_type<Derived,PromotedT>::type(matrix.derived().rows(), matrix.derived().cols(), internal::scalar_constant_op<PromotedT>(scalar)), matrix.derived()); \
   1378   }
   1379 
   1380 #define EIGEN_MAKE_SCALAR_BINARY_OP(METHOD,OPNAME) \
   1381   EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
   1382   EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME)
   1383 
   1384 
   1385 #if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(EIGEN_CUDA_ARCH) && !defined(EIGEN_EXCEPTIONS) && !defined(EIGEN_USE_SYCL) && !defined(EIGEN_HIP_DEVICE_COMPILE)
   1386   #define EIGEN_EXCEPTIONS
   1387 #endif
   1388 
   1389 
   1390 #ifdef EIGEN_EXCEPTIONS
   1391 #  define EIGEN_THROW_X(X) throw X
   1392 #  define EIGEN_THROW throw
   1393 #  define EIGEN_TRY try
   1394 #  define EIGEN_CATCH(X) catch (X)
   1395 #else
   1396 #  if defined(EIGEN_CUDA_ARCH)
   1397 #    define EIGEN_THROW_X(X) asm("trap;")
   1398 #    define EIGEN_THROW asm("trap;")
   1399 #  elif defined(EIGEN_HIP_DEVICE_COMPILE)
   1400 #    define EIGEN_THROW_X(X) asm("s_trap 0")
   1401 #    define EIGEN_THROW asm("s_trap 0")
   1402 #  else
   1403 #    define EIGEN_THROW_X(X) std::abort()
   1404 #    define EIGEN_THROW std::abort()
   1405 #  endif
   1406 #  define EIGEN_TRY if (true)
   1407 #  define EIGEN_CATCH(X) else
   1408 #endif
   1409 
   1410 
   1411 #if EIGEN_HAS_CXX11_NOEXCEPT
   1412 #   define EIGEN_INCLUDE_TYPE_TRAITS
   1413 #   define EIGEN_NOEXCEPT noexcept
   1414 #   define EIGEN_NOEXCEPT_IF(x) noexcept(x)
   1415 #   define EIGEN_NO_THROW noexcept(true)
   1416 #   define EIGEN_EXCEPTION_SPEC(X) noexcept(false)
   1417 #else
   1418 #   define EIGEN_NOEXCEPT
   1419 #   define EIGEN_NOEXCEPT_IF(x)
   1420 #   define EIGEN_NO_THROW throw()
   1421 #   if EIGEN_COMP_MSVC || EIGEN_COMP_CXXVER>=17
   1422       // MSVC does not support exception specifications (warning C4290),
   1423       // and they are deprecated in c++11 anyway. This is even an error in c++17.
   1424 #     define EIGEN_EXCEPTION_SPEC(X) throw()
   1425 #   else
   1426 #     define EIGEN_EXCEPTION_SPEC(X) throw(X)
   1427 #   endif
   1428 #endif
   1429 
   1430 #if EIGEN_HAS_VARIADIC_TEMPLATES
   1431 // The all function is used to enable a variadic version of eigen_assert which can take a parameter pack as its input.
   1432 namespace Eigen {
   1433 namespace internal {
   1434 
   1435 inline bool all(){ return true; }
   1436 
   1437 template<typename T, typename ...Ts>
   1438 bool all(T t, Ts ... ts){ return t && all(ts...); }
   1439 
   1440 }
   1441 }
   1442 #endif
   1443 
   1444 #if EIGEN_HAS_CXX11_OVERRIDE_FINAL
   1445 // provide override and final specifiers if they are available:
   1446 #   define EIGEN_OVERRIDE override
   1447 #   define EIGEN_FINAL final
   1448 #else
   1449 #   define EIGEN_OVERRIDE
   1450 #   define EIGEN_FINAL
   1451 #endif
   1452 
   1453 // Wrapping #pragma unroll in a macro since it is required for SYCL
   1454 #if defined(SYCL_DEVICE_ONLY)
   1455   #if defined(_MSC_VER)
   1456     #define EIGEN_UNROLL_LOOP __pragma(unroll)
   1457   #else
   1458     #define EIGEN_UNROLL_LOOP _Pragma("unroll")
   1459   #endif
   1460 #else
   1461   #define EIGEN_UNROLL_LOOP
   1462 #endif
   1463 
   1464 #endif // EIGEN_MACROS_H