Home | History | Annotate | Download | only in util
      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 (at) inria.fr>
      5 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1 (at) 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 #define EIGEN_WORLD_VERSION 3
     15 #define EIGEN_MAJOR_VERSION 3
     16 #define EIGEN_MINOR_VERSION 4
     17 
     18 #define EIGEN_VERSION_AT_LEAST(x,y,z) (EIGEN_WORLD_VERSION>x || (EIGEN_WORLD_VERSION>=x && \
     19                                       (EIGEN_MAJOR_VERSION>y || (EIGEN_MAJOR_VERSION>=y && \
     20                                                                  EIGEN_MINOR_VERSION>=z))))
     21 
     22 // Compiler identification, EIGEN_COMP_*
     23 
     24 /// \internal EIGEN_COMP_GNUC set to 1 for all compilers compatible with GCC
     25 #ifdef __GNUC__
     26   #define EIGEN_COMP_GNUC 1
     27 #else
     28   #define EIGEN_COMP_GNUC 0
     29 #endif
     30 
     31 /// \internal EIGEN_COMP_CLANG set to major+minor version (e.g., 307 for clang 3.7) if the compiler is clang
     32 #if defined(__clang__)
     33   #define EIGEN_COMP_CLANG (__clang_major__*100+__clang_minor__)
     34 #else
     35   #define EIGEN_COMP_CLANG 0
     36 #endif
     37 
     38 
     39 /// \internal EIGEN_COMP_LLVM set to 1 if the compiler backend is llvm
     40 #if defined(__llvm__)
     41   #define EIGEN_COMP_LLVM 1
     42 #else
     43   #define EIGEN_COMP_LLVM 0
     44 #endif
     45 
     46 /// \internal EIGEN_COMP_ICC set to __INTEL_COMPILER if the compiler is Intel compiler, 0 otherwise
     47 #if defined(__INTEL_COMPILER)
     48   #define EIGEN_COMP_ICC __INTEL_COMPILER
     49 #else
     50   #define EIGEN_COMP_ICC 0
     51 #endif
     52 
     53 /// \internal EIGEN_COMP_MINGW set to 1 if the compiler is mingw
     54 #if defined(__MINGW32__)
     55   #define EIGEN_COMP_MINGW 1
     56 #else
     57   #define EIGEN_COMP_MINGW 0
     58 #endif
     59 
     60 /// \internal EIGEN_COMP_SUNCC set to 1 if the compiler is Solaris Studio
     61 #if defined(__SUNPRO_CC)
     62   #define EIGEN_COMP_SUNCC 1
     63 #else
     64   #define EIGEN_COMP_SUNCC 0
     65 #endif
     66 
     67 /// \internal EIGEN_COMP_MSVC set to _MSC_VER if the compiler is Microsoft Visual C++, 0 otherwise.
     68 #if defined(_MSC_VER)
     69   #define EIGEN_COMP_MSVC _MSC_VER
     70 #else
     71   #define EIGEN_COMP_MSVC 0
     72 #endif
     73 
     74 // For the record, here is a table summarizing the possible values for EIGEN_COMP_MSVC:
     75 //  name  ver   MSC_VER
     76 //  2008    9      1500
     77 //  2010   10      1600
     78 //  2012   11      1700
     79 //  2013   12      1800
     80 //  2015   14      1900
     81 //  "15"   15      1900
     82 
     83 /// \internal EIGEN_COMP_MSVC_STRICT set to 1 if the compiler is really Microsoft Visual C++ and not ,e.g., ICC or clang-cl
     84 #if EIGEN_COMP_MSVC && !(EIGEN_COMP_ICC || EIGEN_COMP_LLVM || EIGEN_COMP_CLANG)
     85   #define EIGEN_COMP_MSVC_STRICT _MSC_VER
     86 #else
     87   #define EIGEN_COMP_MSVC_STRICT 0
     88 #endif
     89 
     90 /// \internal EIGEN_COMP_IBM set to 1 if the compiler is IBM XL C++
     91 #if defined(__IBMCPP__) || defined(__xlc__)
     92   #define EIGEN_COMP_IBM 1
     93 #else
     94   #define EIGEN_COMP_IBM 0
     95 #endif
     96 
     97 /// \internal EIGEN_COMP_PGI set to 1 if the compiler is Portland Group Compiler
     98 #if defined(__PGI)
     99   #define EIGEN_COMP_PGI 1
    100 #else
    101   #define EIGEN_COMP_PGI 0
    102 #endif
    103 
    104 /// \internal EIGEN_COMP_ARM set to 1 if the compiler is ARM Compiler
    105 #if defined(__CC_ARM) || defined(__ARMCC_VERSION)
    106   #define EIGEN_COMP_ARM 1
    107 #else
    108   #define EIGEN_COMP_ARM 0
    109 #endif
    110 
    111 /// \internal EIGEN_COMP_ARM set to 1 if the compiler is ARM Compiler
    112 #if defined(__EMSCRIPTEN__)
    113   #define EIGEN_COMP_EMSCRIPTEN 1
    114 #else
    115   #define EIGEN_COMP_EMSCRIPTEN 0
    116 #endif
    117 
    118 
    119 /// \internal EIGEN_GNUC_STRICT set to 1 if the compiler is really GCC and not a compatible compiler (e.g., ICC, clang, mingw, etc.)
    120 #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)
    121   #define EIGEN_COMP_GNUC_STRICT 1
    122 #else
    123   #define EIGEN_COMP_GNUC_STRICT 0
    124 #endif
    125 
    126 
    127 #if EIGEN_COMP_GNUC
    128   #define EIGEN_GNUC_AT_LEAST(x,y) ((__GNUC__==x && __GNUC_MINOR__>=y) || __GNUC__>x)
    129   #define EIGEN_GNUC_AT_MOST(x,y)  ((__GNUC__==x && __GNUC_MINOR__<=y) || __GNUC__<x)
    130   #define EIGEN_GNUC_AT(x,y)       ( __GNUC__==x && __GNUC_MINOR__==y )
    131 #else
    132   #define EIGEN_GNUC_AT_LEAST(x,y) 0
    133   #define EIGEN_GNUC_AT_MOST(x,y)  0
    134   #define EIGEN_GNUC_AT(x,y)       0
    135 #endif
    136 
    137 // FIXME: could probably be removed as we do not support gcc 3.x anymore
    138 #if EIGEN_COMP_GNUC && (__GNUC__ <= 3)
    139 #define EIGEN_GCC3_OR_OLDER 1
    140 #else
    141 #define EIGEN_GCC3_OR_OLDER 0
    142 #endif
    143 
    144 
    145 // Architecture identification, EIGEN_ARCH_*
    146 
    147 #if defined(__x86_64__) || defined(_M_X64) || defined(__amd64)
    148   #define EIGEN_ARCH_x86_64 1
    149 #else
    150   #define EIGEN_ARCH_x86_64 0
    151 #endif
    152 
    153 #if defined(__i386__) || defined(_M_IX86) || defined(_X86_) || defined(__i386)
    154   #define EIGEN_ARCH_i386 1
    155 #else
    156   #define EIGEN_ARCH_i386 0
    157 #endif
    158 
    159 #if EIGEN_ARCH_x86_64 || EIGEN_ARCH_i386
    160   #define EIGEN_ARCH_i386_OR_x86_64 1
    161 #else
    162   #define EIGEN_ARCH_i386_OR_x86_64 0
    163 #endif
    164 
    165 /// \internal EIGEN_ARCH_ARM set to 1 if the architecture is ARM
    166 #if defined(__arm__)
    167   #define EIGEN_ARCH_ARM 1
    168 #else
    169   #define EIGEN_ARCH_ARM 0
    170 #endif
    171 
    172 /// \internal EIGEN_ARCH_ARM64 set to 1 if the architecture is ARM64
    173 #if defined(__aarch64__)
    174   #define EIGEN_ARCH_ARM64 1
    175 #else
    176   #define EIGEN_ARCH_ARM64 0
    177 #endif
    178 
    179 #if EIGEN_ARCH_ARM || EIGEN_ARCH_ARM64
    180   #define EIGEN_ARCH_ARM_OR_ARM64 1
    181 #else
    182   #define EIGEN_ARCH_ARM_OR_ARM64 0
    183 #endif
    184 
    185 /// \internal EIGEN_ARCH_MIPS set to 1 if the architecture is MIPS
    186 #if defined(__mips__) || defined(__mips)
    187   #define EIGEN_ARCH_MIPS 1
    188 #else
    189   #define EIGEN_ARCH_MIPS 0
    190 #endif
    191 
    192 /// \internal EIGEN_ARCH_SPARC set to 1 if the architecture is SPARC
    193 #if defined(__sparc__) || defined(__sparc)
    194   #define EIGEN_ARCH_SPARC 1
    195 #else
    196   #define EIGEN_ARCH_SPARC 0
    197 #endif
    198 
    199 /// \internal EIGEN_ARCH_IA64 set to 1 if the architecture is Intel Itanium
    200 #if defined(__ia64__)
    201   #define EIGEN_ARCH_IA64 1
    202 #else
    203   #define EIGEN_ARCH_IA64 0
    204 #endif
    205 
    206 /// \internal EIGEN_ARCH_PPC set to 1 if the architecture is PowerPC
    207 #if defined(__powerpc__) || defined(__ppc__) || defined(_M_PPC)
    208   #define EIGEN_ARCH_PPC 1
    209 #else
    210   #define EIGEN_ARCH_PPC 0
    211 #endif
    212 
    213 
    214 
    215 // Operating system identification, EIGEN_OS_*
    216 
    217 /// \internal EIGEN_OS_UNIX set to 1 if the OS is a unix variant
    218 #if defined(__unix__) || defined(__unix)
    219   #define EIGEN_OS_UNIX 1
    220 #else
    221   #define EIGEN_OS_UNIX 0
    222 #endif
    223 
    224 /// \internal EIGEN_OS_LINUX set to 1 if the OS is based on Linux kernel
    225 #if defined(__linux__)
    226   #define EIGEN_OS_LINUX 1
    227 #else
    228   #define EIGEN_OS_LINUX 0
    229 #endif
    230 
    231 /// \internal EIGEN_OS_ANDROID set to 1 if the OS is Android
    232 // note: ANDROID is defined when using ndk_build, __ANDROID__ is defined when using a standalone toolchain.
    233 #if defined(__ANDROID__) || defined(ANDROID)
    234   #define EIGEN_OS_ANDROID 1
    235 #else
    236   #define EIGEN_OS_ANDROID 0
    237 #endif
    238 
    239 /// \internal EIGEN_OS_GNULINUX set to 1 if the OS is GNU Linux and not Linux-based OS (e.g., not android)
    240 #if defined(__gnu_linux__) && !(EIGEN_OS_ANDROID)
    241   #define EIGEN_OS_GNULINUX 1
    242 #else
    243   #define EIGEN_OS_GNULINUX 0
    244 #endif
    245 
    246 /// \internal EIGEN_OS_BSD set to 1 if the OS is a BSD variant
    247 #if defined(__FreeBSD__) || defined(__NetBSD__) || defined(__OpenBSD__) || defined(__bsdi__) || defined(__DragonFly__)
    248   #define EIGEN_OS_BSD 1
    249 #else
    250   #define EIGEN_OS_BSD 0
    251 #endif
    252 
    253 /// \internal EIGEN_OS_MAC set to 1 if the OS is MacOS
    254 #if defined(__APPLE__)
    255   #define EIGEN_OS_MAC 1
    256 #else
    257   #define EIGEN_OS_MAC 0
    258 #endif
    259 
    260 /// \internal EIGEN_OS_QNX set to 1 if the OS is QNX
    261 #if defined(__QNX__)
    262   #define EIGEN_OS_QNX 1
    263 #else
    264   #define EIGEN_OS_QNX 0
    265 #endif
    266 
    267 /// \internal EIGEN_OS_WIN set to 1 if the OS is Windows based
    268 #if defined(_WIN32)
    269   #define EIGEN_OS_WIN 1
    270 #else
    271   #define EIGEN_OS_WIN 0
    272 #endif
    273 
    274 /// \internal EIGEN_OS_WIN64 set to 1 if the OS is Windows 64bits
    275 #if defined(_WIN64)
    276   #define EIGEN_OS_WIN64 1
    277 #else
    278   #define EIGEN_OS_WIN64 0
    279 #endif
    280 
    281 /// \internal EIGEN_OS_WINCE set to 1 if the OS is Windows CE
    282 #if defined(_WIN32_WCE)
    283   #define EIGEN_OS_WINCE 1
    284 #else
    285   #define EIGEN_OS_WINCE 0
    286 #endif
    287 
    288 /// \internal EIGEN_OS_CYGWIN set to 1 if the OS is Windows/Cygwin
    289 #if defined(__CYGWIN__)
    290   #define EIGEN_OS_CYGWIN 1
    291 #else
    292   #define EIGEN_OS_CYGWIN 0
    293 #endif
    294 
    295 /// \internal EIGEN_OS_WIN_STRICT set to 1 if the OS is really Windows and not some variants
    296 #if EIGEN_OS_WIN && !( EIGEN_OS_WINCE || EIGEN_OS_CYGWIN )
    297   #define EIGEN_OS_WIN_STRICT 1
    298 #else
    299   #define EIGEN_OS_WIN_STRICT 0
    300 #endif
    301 
    302 /// \internal EIGEN_OS_SUN set to 1 if the OS is SUN
    303 #if (defined(sun) || defined(__sun)) && !(defined(__SVR4) || defined(__svr4__))
    304   #define EIGEN_OS_SUN 1
    305 #else
    306   #define EIGEN_OS_SUN 0
    307 #endif
    308 
    309 /// \internal EIGEN_OS_SOLARIS set to 1 if the OS is Solaris
    310 #if (defined(sun) || defined(__sun)) && (defined(__SVR4) || defined(__svr4__))
    311   #define EIGEN_OS_SOLARIS 1
    312 #else
    313   #define EIGEN_OS_SOLARIS 0
    314 #endif
    315 
    316 
    317 
    318 #if EIGEN_GNUC_AT_MOST(4,3) && !EIGEN_COMP_CLANG
    319   // see bug 89
    320   #define EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO 0
    321 #else
    322   #define EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO 1
    323 #endif
    324 
    325 // This macro can be used to prevent from macro expansion, e.g.:
    326 //   std::max EIGEN_NOT_A_MACRO(a,b)
    327 #define EIGEN_NOT_A_MACRO
    328 
    329 #ifdef EIGEN_DEFAULT_TO_ROW_MAJOR
    330 #define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION Eigen::RowMajor
    331 #else
    332 #define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION Eigen::ColMajor
    333 #endif
    334 
    335 #ifndef EIGEN_DEFAULT_DENSE_INDEX_TYPE
    336 #define EIGEN_DEFAULT_DENSE_INDEX_TYPE std::ptrdiff_t
    337 #endif
    338 
    339 // Cross compiler wrapper around LLVM's __has_builtin
    340 #ifdef __has_builtin
    341 #  define EIGEN_HAS_BUILTIN(x) __has_builtin(x)
    342 #else
    343 #  define EIGEN_HAS_BUILTIN(x) 0
    344 #endif
    345 
    346 // A Clang feature extension to determine compiler features.
    347 // We use it to determine 'cxx_rvalue_references'
    348 #ifndef __has_feature
    349 # define __has_feature(x) 0
    350 #endif
    351 
    352 // Upperbound on the C++ version to use.
    353 // Expected values are 03, 11, 14, 17, etc.
    354 // By default, let's use an arbitrarily large C++ version.
    355 #ifndef EIGEN_MAX_CPP_VER
    356 #define EIGEN_MAX_CPP_VER 99
    357 #endif
    358 
    359 #if EIGEN_MAX_CPP_VER>=11 && (defined(__cplusplus) && (__cplusplus >= 201103L) || EIGEN_COMP_MSVC >= 1900)
    360 #define EIGEN_HAS_CXX11 1
    361 #else
    362 #define EIGEN_HAS_CXX11 0
    363 #endif
    364 
    365 
    366 // Do we support r-value references?
    367 #ifndef EIGEN_HAS_RVALUE_REFERENCES
    368 #if EIGEN_MAX_CPP_VER>=11 && \
    369     (__has_feature(cxx_rvalue_references) || \
    370     (defined(__cplusplus) && __cplusplus >= 201103L) || \
    371     (EIGEN_COMP_MSVC >= 1600))
    372   #define EIGEN_HAS_RVALUE_REFERENCES 1
    373 #else
    374   #define EIGEN_HAS_RVALUE_REFERENCES 0
    375 #endif
    376 #endif
    377 
    378 // Does the compiler support C99?
    379 #ifndef EIGEN_HAS_C99_MATH
    380 #if EIGEN_MAX_CPP_VER>=11 && \
    381     ((defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901))       \
    382   || (defined(__GNUC__) && defined(_GLIBCXX_USE_C99)) \
    383   || (defined(_LIBCPP_VERSION) && !defined(_MSC_VER)))
    384   #define EIGEN_HAS_C99_MATH 1
    385 #else
    386   #define EIGEN_HAS_C99_MATH 0
    387 #endif
    388 #endif
    389 
    390 // Does the compiler support result_of?
    391 #ifndef EIGEN_HAS_STD_RESULT_OF
    392 #if EIGEN_MAX_CPP_VER>=11 && ((__has_feature(cxx_lambdas) || (defined(__cplusplus) && __cplusplus >= 201103L)))
    393 #define EIGEN_HAS_STD_RESULT_OF 1
    394 #else
    395 #define EIGEN_HAS_STD_RESULT_OF 0
    396 #endif
    397 #endif
    398 
    399 // Does the compiler support variadic templates?
    400 #ifndef EIGEN_HAS_VARIADIC_TEMPLATES
    401 #if EIGEN_MAX_CPP_VER>=11 && (__cplusplus > 199711L || EIGEN_COMP_MSVC >= 1900) \
    402   && ( !defined(__NVCC__) || !EIGEN_ARCH_ARM_OR_ARM64 || (defined __CUDACC_VER__ && __CUDACC_VER__ >= 80000) )
    403     // ^^ Disable the use of variadic templates when compiling with versions of nvcc older than 8.0 on ARM devices:
    404     //    this prevents nvcc from crashing when compiling Eigen on Tegra X1
    405 #define EIGEN_HAS_VARIADIC_TEMPLATES 1
    406 #else
    407 #define EIGEN_HAS_VARIADIC_TEMPLATES 0
    408 #endif
    409 #endif
    410 
    411 // Does the compiler fully support const expressions? (as in c++14)
    412 #ifndef EIGEN_HAS_CONSTEXPR
    413 
    414 #ifdef __CUDACC__
    415 // Const expressions are supported provided that c++11 is enabled and we're using either clang or nvcc 7.5 or above
    416 #if EIGEN_MAX_CPP_VER>=14 && (__cplusplus > 199711L && defined(__CUDACC_VER__) && (EIGEN_COMP_CLANG || __CUDACC_VER__ >= 70500))
    417   #define EIGEN_HAS_CONSTEXPR 1
    418 #endif
    419 #elif EIGEN_MAX_CPP_VER>=14 && (__has_feature(cxx_relaxed_constexpr) || (defined(__cplusplus) && __cplusplus >= 201402L) || \
    420   (EIGEN_GNUC_AT_LEAST(4,8) && (__cplusplus > 199711L)))
    421 #define EIGEN_HAS_CONSTEXPR 1
    422 #endif
    423 
    424 #ifndef EIGEN_HAS_CONSTEXPR
    425 #define EIGEN_HAS_CONSTEXPR 0
    426 #endif
    427 
    428 #endif
    429 
    430 // Does the compiler support C++11 math?
    431 // Let's be conservative and enable the default C++11 implementation only if we are sure it exists
    432 #ifndef EIGEN_HAS_CXX11_MATH
    433   #if EIGEN_MAX_CPP_VER>=11 && ((__cplusplus > 201103L) || (__cplusplus >= 201103L) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_MSVC || EIGEN_COMP_ICC)  \
    434       && (EIGEN_ARCH_i386_OR_x86_64) && (EIGEN_OS_GNULINUX || EIGEN_OS_WIN_STRICT || EIGEN_OS_MAC))
    435     #define EIGEN_HAS_CXX11_MATH 1
    436   #else
    437     #define EIGEN_HAS_CXX11_MATH 0
    438   #endif
    439 #endif
    440 
    441 // Does the compiler support proper C++11 containers?
    442 #ifndef EIGEN_HAS_CXX11_CONTAINERS
    443   #if    EIGEN_MAX_CPP_VER>=11 && \
    444          ((__cplusplus > 201103L) \
    445       || ((__cplusplus >= 201103L) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_ICC>=1400)) \
    446       || EIGEN_COMP_MSVC >= 1900)
    447     #define EIGEN_HAS_CXX11_CONTAINERS 1
    448   #else
    449     #define EIGEN_HAS_CXX11_CONTAINERS 0
    450   #endif
    451 #endif
    452 
    453 // Does the compiler support C++11 noexcept?
    454 #ifndef EIGEN_HAS_CXX11_NOEXCEPT
    455   #if    EIGEN_MAX_CPP_VER>=11 && \
    456          (__has_feature(cxx_noexcept) \
    457       || (__cplusplus > 201103L) \
    458       || ((__cplusplus >= 201103L) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_CLANG || EIGEN_COMP_ICC>=1400)) \
    459       || EIGEN_COMP_MSVC >= 1900)
    460     #define EIGEN_HAS_CXX11_NOEXCEPT 1
    461   #else
    462     #define EIGEN_HAS_CXX11_NOEXCEPT 0
    463   #endif
    464 #endif
    465 
    466 /** Allows to disable some optimizations which might affect the accuracy of the result.
    467   * Such optimization are enabled by default, and set EIGEN_FAST_MATH to 0 to disable them.
    468   * They currently include:
    469   *   - single precision ArrayBase::sin() and ArrayBase::cos() for SSE and AVX vectorization.
    470   */
    471 #ifndef EIGEN_FAST_MATH
    472 #define EIGEN_FAST_MATH 1
    473 #endif
    474 
    475 #define EIGEN_DEBUG_VAR(x) std::cerr << #x << " = " << x << std::endl;
    476 
    477 // concatenate two tokens
    478 #define EIGEN_CAT2(a,b) a ## b
    479 #define EIGEN_CAT(a,b) EIGEN_CAT2(a,b)
    480 
    481 #define EIGEN_COMMA ,
    482 
    483 // convert a token to a string
    484 #define EIGEN_MAKESTRING2(a) #a
    485 #define EIGEN_MAKESTRING(a) EIGEN_MAKESTRING2(a)
    486 
    487 // EIGEN_STRONG_INLINE is a stronger version of the inline, using __forceinline on MSVC,
    488 // but it still doesn't use GCC's always_inline. This is useful in (common) situations where MSVC needs forceinline
    489 // but GCC is still doing fine with just inline.
    490 #if EIGEN_COMP_MSVC || EIGEN_COMP_ICC
    491 #define EIGEN_STRONG_INLINE __forceinline
    492 #else
    493 #define EIGEN_STRONG_INLINE inline
    494 #endif
    495 
    496 // EIGEN_ALWAYS_INLINE is the stronget, it has the effect of making the function inline and adding every possible
    497 // attribute to maximize inlining. This should only be used when really necessary: in particular,
    498 // it uses __attribute__((always_inline)) on GCC, which most of the time is useless and can severely harm compile times.
    499 // FIXME with the always_inline attribute,
    500 // gcc 3.4.x and 4.1 reports the following compilation error:
    501 //   Eval.h:91: sorry, unimplemented: inlining failed in call to 'const Eigen::Eval<Derived> Eigen::MatrixBase<Scalar, Derived>::eval() const'
    502 //    : function body not available
    503 //   See also bug 1367
    504 #if EIGEN_GNUC_AT_LEAST(4,2)
    505 #define EIGEN_ALWAYS_INLINE __attribute__((always_inline)) inline
    506 #else
    507 #define EIGEN_ALWAYS_INLINE EIGEN_STRONG_INLINE
    508 #endif
    509 
    510 #if EIGEN_COMP_GNUC
    511 #define EIGEN_DONT_INLINE __attribute__((noinline))
    512 #elif EIGEN_COMP_MSVC
    513 #define EIGEN_DONT_INLINE __declspec(noinline)
    514 #else
    515 #define EIGEN_DONT_INLINE
    516 #endif
    517 
    518 #if EIGEN_COMP_GNUC
    519 #define EIGEN_PERMISSIVE_EXPR __extension__
    520 #else
    521 #define EIGEN_PERMISSIVE_EXPR
    522 #endif
    523 
    524 // this macro allows to get rid of linking errors about multiply defined functions.
    525 //  - static is not very good because it prevents definitions from different object files to be merged.
    526 //           So static causes the resulting linked executable to be bloated with multiple copies of the same function.
    527 //  - inline is not perfect either as it unwantedly hints the compiler toward inlining the function.
    528 #define EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
    529 #define EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS inline
    530 
    531 #ifdef NDEBUG
    532 # ifndef EIGEN_NO_DEBUG
    533 #  define EIGEN_NO_DEBUG
    534 # endif
    535 #endif
    536 
    537 // eigen_plain_assert is where we implement the workaround for the assert() bug in GCC <= 4.3, see bug 89
    538 #ifdef EIGEN_NO_DEBUG
    539   #define eigen_plain_assert(x)
    540 #else
    541   #if EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO
    542     namespace Eigen {
    543     namespace internal {
    544     inline bool copy_bool(bool b) { return b; }
    545     }
    546     }
    547     #define eigen_plain_assert(x) assert(x)
    548   #else
    549     // work around bug 89
    550     #include <cstdlib>   // for abort
    551     #include <iostream>  // for std::cerr
    552 
    553     namespace Eigen {
    554     namespace internal {
    555     // trivial function copying a bool. Must be EIGEN_DONT_INLINE, so we implement it after including Eigen headers.
    556     // see bug 89.
    557     namespace {
    558     EIGEN_DONT_INLINE bool copy_bool(bool b) { return b; }
    559     }
    560     inline void assert_fail(const char *condition, const char *function, const char *file, int line)
    561     {
    562       std::cerr << "assertion failed: " << condition << " in function " << function << " at " << file << ":" << line << std::endl;
    563       abort();
    564     }
    565     }
    566     }
    567     #define eigen_plain_assert(x) \
    568       do { \
    569         if(!Eigen::internal::copy_bool(x)) \
    570           Eigen::internal::assert_fail(EIGEN_MAKESTRING(x), __PRETTY_FUNCTION__, __FILE__, __LINE__); \
    571       } while(false)
    572   #endif
    573 #endif
    574 
    575 // eigen_assert can be overridden
    576 #ifndef eigen_assert
    577 #define eigen_assert(x) eigen_plain_assert(x)
    578 #endif
    579 
    580 #ifdef EIGEN_INTERNAL_DEBUGGING
    581 #define eigen_internal_assert(x) eigen_assert(x)
    582 #else
    583 #define eigen_internal_assert(x)
    584 #endif
    585 
    586 #ifdef EIGEN_NO_DEBUG
    587 #define EIGEN_ONLY_USED_FOR_DEBUG(x) EIGEN_UNUSED_VARIABLE(x)
    588 #else
    589 #define EIGEN_ONLY_USED_FOR_DEBUG(x)
    590 #endif
    591 
    592 #ifndef EIGEN_NO_DEPRECATED_WARNING
    593   #if EIGEN_COMP_GNUC
    594     #define EIGEN_DEPRECATED __attribute__((deprecated))
    595   #elif EIGEN_COMP_MSVC
    596     #define EIGEN_DEPRECATED __declspec(deprecated)
    597   #else
    598     #define EIGEN_DEPRECATED
    599   #endif
    600 #else
    601   #define EIGEN_DEPRECATED
    602 #endif
    603 
    604 #if EIGEN_COMP_GNUC
    605 #define EIGEN_UNUSED __attribute__((unused))
    606 #else
    607 #define EIGEN_UNUSED
    608 #endif
    609 
    610 // Suppresses 'unused variable' warnings.
    611 namespace Eigen {
    612   namespace internal {
    613     template<typename T> EIGEN_DEVICE_FUNC void ignore_unused_variable(const T&) {}
    614   }
    615 }
    616 #define EIGEN_UNUSED_VARIABLE(var) Eigen::internal::ignore_unused_variable(var);
    617 
    618 #if !defined(EIGEN_ASM_COMMENT)
    619   #if EIGEN_COMP_GNUC && (EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM_OR_ARM64)
    620     #define EIGEN_ASM_COMMENT(X)  __asm__("#" X)
    621   #else
    622     #define EIGEN_ASM_COMMENT(X)
    623   #endif
    624 #endif
    625 
    626 
    627 //------------------------------------------------------------------------------------------
    628 // Static and dynamic alignment control
    629 //
    630 // The main purpose of this section is to define EIGEN_MAX_ALIGN_BYTES and EIGEN_MAX_STATIC_ALIGN_BYTES
    631 // as the maximal boundary in bytes on which dynamically and statically allocated data may be alignment respectively.
    632 // The values of EIGEN_MAX_ALIGN_BYTES and EIGEN_MAX_STATIC_ALIGN_BYTES can be specified by the user. If not,
    633 // a default value is automatically computed based on architecture, compiler, and OS.
    634 //
    635 // This section also defines macros EIGEN_ALIGN_TO_BOUNDARY(N) and the shortcuts EIGEN_ALIGN{8,16,32,_MAX}
    636 // to be used to declare statically aligned buffers.
    637 //------------------------------------------------------------------------------------------
    638 
    639 
    640 /* EIGEN_ALIGN_TO_BOUNDARY(n) forces data to be n-byte aligned. This is used to satisfy SIMD requirements.
    641  * However, we do that EVEN if vectorization (EIGEN_VECTORIZE) is disabled,
    642  * so that vectorization doesn't affect binary compatibility.
    643  *
    644  * If we made alignment depend on whether or not EIGEN_VECTORIZE is defined, it would be impossible to link
    645  * vectorized and non-vectorized code.
    646  */
    647 #if (defined __CUDACC__)
    648   #define EIGEN_ALIGN_TO_BOUNDARY(n) __align__(n)
    649 #elif EIGEN_COMP_GNUC || EIGEN_COMP_PGI || EIGEN_COMP_IBM || EIGEN_COMP_ARM
    650   #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))
    651 #elif EIGEN_COMP_MSVC
    652   #define EIGEN_ALIGN_TO_BOUNDARY(n) __declspec(align(n))
    653 #elif EIGEN_COMP_SUNCC
    654   // FIXME not sure about this one:
    655   #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))
    656 #else
    657   #error Please tell me what is the equivalent of __attribute__((aligned(n))) for your compiler
    658 #endif
    659 
    660 // If the user explicitly disable vectorization, then we also disable alignment
    661 #if defined(EIGEN_DONT_VECTORIZE)
    662   #define EIGEN_IDEAL_MAX_ALIGN_BYTES 0
    663 #elif defined(EIGEN_VECTORIZE_AVX512)
    664   // 64 bytes static alignmeent is preferred only if really required
    665   #define EIGEN_IDEAL_MAX_ALIGN_BYTES 64
    666 #elif defined(__AVX__)
    667   // 32 bytes static alignmeent is preferred only if really required
    668   #define EIGEN_IDEAL_MAX_ALIGN_BYTES 32
    669 #else
    670   #define EIGEN_IDEAL_MAX_ALIGN_BYTES 16
    671 #endif
    672 
    673 
    674 // EIGEN_MIN_ALIGN_BYTES defines the minimal value for which the notion of explicit alignment makes sense
    675 #define EIGEN_MIN_ALIGN_BYTES 16
    676 
    677 // Defined the boundary (in bytes) on which the data needs to be aligned. Note
    678 // that unless EIGEN_ALIGN is defined and not equal to 0, the data may not be
    679 // aligned at all regardless of the value of this #define.
    680 
    681 #if (defined(EIGEN_DONT_ALIGN_STATICALLY) || defined(EIGEN_DONT_ALIGN))  && defined(EIGEN_MAX_STATIC_ALIGN_BYTES) && EIGEN_MAX_STATIC_ALIGN_BYTES>0
    682 #error EIGEN_MAX_STATIC_ALIGN_BYTES and EIGEN_DONT_ALIGN[_STATICALLY] are both defined with EIGEN_MAX_STATIC_ALIGN_BYTES!=0. Use EIGEN_MAX_STATIC_ALIGN_BYTES=0 as a synonym of EIGEN_DONT_ALIGN_STATICALLY.
    683 #endif
    684 
    685 // EIGEN_DONT_ALIGN_STATICALLY and EIGEN_DONT_ALIGN are deprectated
    686 // They imply EIGEN_MAX_STATIC_ALIGN_BYTES=0
    687 #if defined(EIGEN_DONT_ALIGN_STATICALLY) || defined(EIGEN_DONT_ALIGN)
    688   #ifdef EIGEN_MAX_STATIC_ALIGN_BYTES
    689     #undef EIGEN_MAX_STATIC_ALIGN_BYTES
    690   #endif
    691   #define EIGEN_MAX_STATIC_ALIGN_BYTES 0
    692 #endif
    693 
    694 #ifndef EIGEN_MAX_STATIC_ALIGN_BYTES
    695 
    696   // Try to automatically guess what is the best default value for EIGEN_MAX_STATIC_ALIGN_BYTES
    697 
    698   // 16 byte alignment is only useful for vectorization. Since it affects the ABI, we need to enable
    699   // 16 byte alignment on all platforms where vectorization might be enabled. In theory we could always
    700   // enable alignment, but it can be a cause of problems on some platforms, so we just disable it in
    701   // certain common platform (compiler+architecture combinations) to avoid these problems.
    702   // Only static alignment is really problematic (relies on nonstandard compiler extensions),
    703   // try to keep heap alignment even when we have to disable static alignment.
    704   #if EIGEN_COMP_GNUC && !(EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM_OR_ARM64 || EIGEN_ARCH_PPC || EIGEN_ARCH_IA64)
    705   #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 1
    706   #elif EIGEN_ARCH_ARM_OR_ARM64 && EIGEN_COMP_GNUC_STRICT && EIGEN_GNUC_AT_MOST(4, 6)
    707   // Old versions of GCC on ARM, at least 4.4, were once seen to have buggy static alignment support.
    708   // Not sure which version fixed it, hopefully it doesn't affect 4.7, which is still somewhat in use.
    709   // 4.8 and newer seem definitely unaffected.
    710   #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 1
    711   #else
    712   #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 0
    713   #endif
    714 
    715   // static alignment is completely disabled with GCC 3, Sun Studio, and QCC/QNX
    716   #if !EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT \
    717   && !EIGEN_GCC3_OR_OLDER \
    718   && !EIGEN_COMP_SUNCC \
    719   && !EIGEN_OS_QNX
    720     #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 1
    721   #else
    722     #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 0
    723   #endif
    724 
    725   #if EIGEN_ARCH_WANTS_STACK_ALIGNMENT
    726     #define EIGEN_MAX_STATIC_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES
    727   #else
    728     #define EIGEN_MAX_STATIC_ALIGN_BYTES 0
    729   #endif
    730 
    731 #endif
    732 
    733 // If EIGEN_MAX_ALIGN_BYTES is defined, then it is considered as an upper bound for EIGEN_MAX_ALIGN_BYTES
    734 #if defined(EIGEN_MAX_ALIGN_BYTES) && EIGEN_MAX_ALIGN_BYTES<EIGEN_MAX_STATIC_ALIGN_BYTES
    735 #undef EIGEN_MAX_STATIC_ALIGN_BYTES
    736 #define EIGEN_MAX_STATIC_ALIGN_BYTES EIGEN_MAX_ALIGN_BYTES
    737 #endif
    738 
    739 #if EIGEN_MAX_STATIC_ALIGN_BYTES==0 && !defined(EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT)
    740   #define EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT
    741 #endif
    742 
    743 // At this stage, EIGEN_MAX_STATIC_ALIGN_BYTES>0 is the true test whether we want to align arrays on the stack or not.
    744 // It takes into account both the user choice to explicitly enable/disable alignment (by settting EIGEN_MAX_STATIC_ALIGN_BYTES)
    745 // and the architecture config (EIGEN_ARCH_WANTS_STACK_ALIGNMENT).
    746 // Henceforth, only EIGEN_MAX_STATIC_ALIGN_BYTES should be used.
    747 
    748 
    749 // Shortcuts to EIGEN_ALIGN_TO_BOUNDARY
    750 #define EIGEN_ALIGN8  EIGEN_ALIGN_TO_BOUNDARY(8)
    751 #define EIGEN_ALIGN16 EIGEN_ALIGN_TO_BOUNDARY(16)
    752 #define EIGEN_ALIGN32 EIGEN_ALIGN_TO_BOUNDARY(32)
    753 #define EIGEN_ALIGN64 EIGEN_ALIGN_TO_BOUNDARY(64)
    754 #if EIGEN_MAX_STATIC_ALIGN_BYTES>0
    755 #define EIGEN_ALIGN_MAX EIGEN_ALIGN_TO_BOUNDARY(EIGEN_MAX_STATIC_ALIGN_BYTES)
    756 #else
    757 #define EIGEN_ALIGN_MAX
    758 #endif
    759 
    760 
    761 // Dynamic alignment control
    762 
    763 #if defined(EIGEN_DONT_ALIGN) && defined(EIGEN_MAX_ALIGN_BYTES) && EIGEN_MAX_ALIGN_BYTES>0
    764 #error EIGEN_MAX_ALIGN_BYTES and EIGEN_DONT_ALIGN are both defined with EIGEN_MAX_ALIGN_BYTES!=0. Use EIGEN_MAX_ALIGN_BYTES=0 as a synonym of EIGEN_DONT_ALIGN.
    765 #endif
    766 
    767 #ifdef EIGEN_DONT_ALIGN
    768   #ifdef EIGEN_MAX_ALIGN_BYTES
    769     #undef EIGEN_MAX_ALIGN_BYTES
    770   #endif
    771   #define EIGEN_MAX_ALIGN_BYTES 0
    772 #elif !defined(EIGEN_MAX_ALIGN_BYTES)
    773   #define EIGEN_MAX_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES
    774 #endif
    775 
    776 #if EIGEN_IDEAL_MAX_ALIGN_BYTES > EIGEN_MAX_ALIGN_BYTES
    777 #define EIGEN_DEFAULT_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES
    778 #else
    779 #define EIGEN_DEFAULT_ALIGN_BYTES EIGEN_MAX_ALIGN_BYTES
    780 #endif
    781 
    782 
    783 #ifndef EIGEN_UNALIGNED_VECTORIZE
    784 #define EIGEN_UNALIGNED_VECTORIZE 1
    785 #endif
    786 
    787 //----------------------------------------------------------------------
    788 
    789 
    790 #ifdef EIGEN_DONT_USE_RESTRICT_KEYWORD
    791   #define EIGEN_RESTRICT
    792 #endif
    793 #ifndef EIGEN_RESTRICT
    794   #define EIGEN_RESTRICT __restrict
    795 #endif
    796 
    797 #ifndef EIGEN_STACK_ALLOCATION_LIMIT
    798 // 131072 == 128 KB
    799 #define EIGEN_STACK_ALLOCATION_LIMIT 131072
    800 #endif
    801 
    802 #ifndef EIGEN_DEFAULT_IO_FORMAT
    803 #ifdef EIGEN_MAKING_DOCS
    804 // format used in Eigen's documentation
    805 // needed to define it here as escaping characters in CMake add_definition's argument seems very problematic.
    806 #define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat(3, 0, " ", "\n", "", "")
    807 #else
    808 #define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat()
    809 #endif
    810 #endif
    811 
    812 // just an empty macro !
    813 #define EIGEN_EMPTY
    814 
    815 #if EIGEN_COMP_MSVC_STRICT && (EIGEN_COMP_MSVC < 1900 ||  defined(__CUDACC_VER__)) // for older MSVC versions, as well as 1900 && CUDA 8, using the base operator is sufficient (cf Bugs 1000, 1324)
    816   #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
    817     using Base::operator =;
    818 #elif EIGEN_COMP_CLANG // workaround clang bug (see http://forum.kde.org/viewtopic.php?f=74&t=102653)
    819   #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
    820     using Base::operator =; \
    821     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) { Base::operator=(other); return *this; } \
    822     template <typename OtherDerived> \
    823     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other) { Base::operator=(other.derived()); return *this; }
    824 #else
    825   #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
    826     using Base::operator =; \
    827     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) \
    828     { \
    829       Base::operator=(other); \
    830       return *this; \
    831     }
    832 #endif
    833 
    834 
    835 /** \internal
    836  * \brief Macro to manually inherit assignment operators.
    837  * This is necessary, because the implicitly defined assignment operator gets deleted when a custom operator= is defined.
    838  */
    839 #define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived) EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived)
    840 
    841 /**
    842 * Just a side note. Commenting within defines works only by documenting
    843 * behind the object (via '!<'). Comments cannot be multi-line and thus
    844 * we have these extra long lines. What is confusing doxygen over here is
    845 * that we use '\' and basically have a bunch of typedefs with their
    846 * documentation in a single line.
    847 **/
    848 
    849 #define EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
    850   typedef typename Eigen::internal::traits<Derived>::Scalar Scalar; /*!< \brief Numeric type, e.g. float, double, int or std::complex<float>. */ \
    851   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. */ \
    852   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. */ \
    853   typedef typename Eigen::internal::ref_selector<Derived>::type Nested; \
    854   typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \
    855   typedef typename Eigen::internal::traits<Derived>::StorageIndex StorageIndex; \
    856   enum { RowsAtCompileTime = Eigen::internal::traits<Derived>::RowsAtCompileTime, \
    857         ColsAtCompileTime = Eigen::internal::traits<Derived>::ColsAtCompileTime, \
    858         Flags = Eigen::internal::traits<Derived>::Flags, \
    859         SizeAtCompileTime = Base::SizeAtCompileTime, \
    860         MaxSizeAtCompileTime = Base::MaxSizeAtCompileTime, \
    861         IsVectorAtCompileTime = Base::IsVectorAtCompileTime }; \
    862   using Base::derived; \
    863   using Base::const_cast_derived;
    864 
    865 
    866 // FIXME Maybe the EIGEN_DENSE_PUBLIC_INTERFACE could be removed as importing PacketScalar is rarely needed
    867 #define EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \
    868   EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
    869   typedef typename Base::PacketScalar PacketScalar;
    870 
    871 
    872 #define EIGEN_PLAIN_ENUM_MIN(a,b) (((int)a <= (int)b) ? (int)a : (int)b)
    873 #define EIGEN_PLAIN_ENUM_MAX(a,b) (((int)a >= (int)b) ? (int)a : (int)b)
    874 
    875 // EIGEN_SIZE_MIN_PREFER_DYNAMIC gives the min between compile-time sizes. 0 has absolute priority, followed by 1,
    876 // followed by Dynamic, followed by other finite values. The reason for giving Dynamic the priority over
    877 // finite values is that min(3, Dynamic) should be Dynamic, since that could be anything between 0 and 3.
    878 #define EIGEN_SIZE_MIN_PREFER_DYNAMIC(a,b) (((int)a == 0 || (int)b == 0) ? 0 \
    879                            : ((int)a == 1 || (int)b == 1) ? 1 \
    880                            : ((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \
    881                            : ((int)a <= (int)b) ? (int)a : (int)b)
    882 
    883 // EIGEN_SIZE_MIN_PREFER_FIXED is a variant of EIGEN_SIZE_MIN_PREFER_DYNAMIC comparing MaxSizes. The difference is that finite values
    884 // now have priority over Dynamic, so that min(3, Dynamic) gives 3. Indeed, whatever the actual value is
    885 // (between 0 and 3), it is not more than 3.
    886 #define EIGEN_SIZE_MIN_PREFER_FIXED(a,b)  (((int)a == 0 || (int)b == 0) ? 0 \
    887                            : ((int)a == 1 || (int)b == 1) ? 1 \
    888                            : ((int)a == Dynamic && (int)b == Dynamic) ? Dynamic \
    889                            : ((int)a == Dynamic) ? (int)b \
    890                            : ((int)b == Dynamic) ? (int)a \
    891                            : ((int)a <= (int)b) ? (int)a : (int)b)
    892 
    893 // see EIGEN_SIZE_MIN_PREFER_DYNAMIC. No need for a separate variant for MaxSizes here.
    894 #define EIGEN_SIZE_MAX(a,b) (((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \
    895                            : ((int)a >= (int)b) ? (int)a : (int)b)
    896 
    897 #define EIGEN_LOGICAL_XOR(a,b) (((a) || (b)) && !((a) && (b)))
    898 
    899 #define EIGEN_IMPLIES(a,b) (!(a) || (b))
    900 
    901 // the expression type of a standard coefficient wise binary operation
    902 #define EIGEN_CWISE_BINARY_RETURN_TYPE(LHS,RHS,OPNAME) \
    903     CwiseBinaryOp< \
    904       EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)< \
    905           typename internal::traits<LHS>::Scalar, \
    906           typename internal::traits<RHS>::Scalar \
    907       >, \
    908       const LHS, \
    909       const RHS \
    910     >
    911 
    912 #define EIGEN_MAKE_CWISE_BINARY_OP(METHOD,OPNAME) \
    913   template<typename OtherDerived> \
    914   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME) \
    915   (METHOD)(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
    916   { \
    917     return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME)(derived(), other.derived()); \
    918   }
    919 
    920 #define EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,TYPEA,TYPEB) \
    921   (Eigen::internal::has_ReturnType<Eigen::ScalarBinaryOpTraits<TYPEA,TYPEB,EIGEN_CAT(EIGEN_CAT(Eigen::internal::scalar_,OPNAME),_op)<TYPEA,TYPEB>  > >::value)
    922 
    923 #define EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(EXPR,SCALAR,OPNAME) \
    924   CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<typename internal::traits<EXPR>::Scalar,SCALAR>, const EXPR, \
    925                 const typename internal::plain_constant_type<EXPR,SCALAR>::type>
    926 
    927 #define EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(SCALAR,EXPR,OPNAME) \
    928   CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<SCALAR,typename internal::traits<EXPR>::Scalar>, \
    929                 const typename internal::plain_constant_type<EXPR,SCALAR>::type, const EXPR>
    930 
    931 // Workaround for MSVC 2010 (see ML thread "patch with compile for for MSVC 2010")
    932 #if EIGEN_COMP_MSVC_STRICT<=1600
    933 #define EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(X) typename internal::enable_if<true,X>::type
    934 #else
    935 #define EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(X) X
    936 #endif
    937 
    938 #define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME) \
    939   template <typename T> EIGEN_DEVICE_FUNC inline \
    940   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))\
    941   (METHOD)(const T& scalar) const { \
    942     typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,Scalar,T)>::type PromotedT; \
    943     return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,PromotedT,OPNAME)(derived(), \
    944            typename internal::plain_constant_type<Derived,PromotedT>::type(derived().rows(), derived().cols(), internal::scalar_constant_op<PromotedT>(scalar))); \
    945   }
    946 
    947 #define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
    948   template <typename T> EIGEN_DEVICE_FUNC inline friend \
    949   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)) \
    950   (METHOD)(const T& scalar, const StorageBaseType& matrix) { \
    951     typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,T,Scalar)>::type PromotedT; \
    952     return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedT,Derived,OPNAME)( \
    953            typename internal::plain_constant_type<Derived,PromotedT>::type(matrix.derived().rows(), matrix.derived().cols(), internal::scalar_constant_op<PromotedT>(scalar)), matrix.derived()); \
    954   }
    955 
    956 #define EIGEN_MAKE_SCALAR_BINARY_OP(METHOD,OPNAME) \
    957   EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
    958   EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME)
    959 
    960 
    961 #ifdef EIGEN_EXCEPTIONS
    962 #  define EIGEN_THROW_X(X) throw X
    963 #  define EIGEN_THROW throw
    964 #  define EIGEN_TRY try
    965 #  define EIGEN_CATCH(X) catch (X)
    966 #else
    967 #  ifdef __CUDA_ARCH__
    968 #    define EIGEN_THROW_X(X) asm("trap;")
    969 #    define EIGEN_THROW asm("trap;")
    970 #  else
    971 #    define EIGEN_THROW_X(X) std::abort()
    972 #    define EIGEN_THROW std::abort()
    973 #  endif
    974 #  define EIGEN_TRY if (true)
    975 #  define EIGEN_CATCH(X) else
    976 #endif
    977 
    978 
    979 #if EIGEN_HAS_CXX11_NOEXCEPT
    980 #   define EIGEN_INCLUDE_TYPE_TRAITS
    981 #   define EIGEN_NOEXCEPT noexcept
    982 #   define EIGEN_NOEXCEPT_IF(x) noexcept(x)
    983 #   define EIGEN_NO_THROW noexcept(true)
    984 #   define EIGEN_EXCEPTION_SPEC(X) noexcept(false)
    985 #else
    986 #   define EIGEN_NOEXCEPT
    987 #   define EIGEN_NOEXCEPT_IF(x)
    988 #   define EIGEN_NO_THROW throw()
    989 #   define EIGEN_EXCEPTION_SPEC(X) throw(X)
    990 #endif
    991 
    992 #endif // EIGEN_MACROS_H
    993