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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 #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 {
copy_bool(bool b)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 {
copy_bool(bool b)558     EIGEN_DONT_INLINE bool copy_bool(bool b) { return b; }
559     }
assert_fail(const char * condition,const char * function,const char * file,int line)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 {
ignore_unused_variable(const T &)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