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 7
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 || (EIGEN_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 && (EIGEN_COMP_CLANG || EIGEN_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 #ifndef EIGEN_STRONG_INLINE
491 #if EIGEN_COMP_MSVC || EIGEN_COMP_ICC
492 #define EIGEN_STRONG_INLINE __forceinline
493 #else
494 #define EIGEN_STRONG_INLINE inline
495 #endif
496 #endif
497 
498 // EIGEN_ALWAYS_INLINE is the stronget, it has the effect of making the function inline and adding every possible
499 // attribute to maximize inlining. This should only be used when really necessary: in particular,
500 // it uses __attribute__((always_inline)) on GCC, which most of the time is useless and can severely harm compile times.
501 // FIXME with the always_inline attribute,
502 // gcc 3.4.x and 4.1 reports the following compilation error:
503 //   Eval.h:91: sorry, unimplemented: inlining failed in call to 'const Eigen::Eval<Derived> Eigen::MatrixBase<Scalar, Derived>::eval() const'
504 //    : function body not available
505 //   See also bug 1367
506 #if EIGEN_GNUC_AT_LEAST(4,2)
507 #define EIGEN_ALWAYS_INLINE __attribute__((always_inline)) inline
508 #else
509 #define EIGEN_ALWAYS_INLINE EIGEN_STRONG_INLINE
510 #endif
511 
512 #if EIGEN_COMP_GNUC
513 #define EIGEN_DONT_INLINE __attribute__((noinline))
514 #elif EIGEN_COMP_MSVC
515 #define EIGEN_DONT_INLINE __declspec(noinline)
516 #else
517 #define EIGEN_DONT_INLINE
518 #endif
519 
520 #if EIGEN_COMP_GNUC
521 #define EIGEN_PERMISSIVE_EXPR __extension__
522 #else
523 #define EIGEN_PERMISSIVE_EXPR
524 #endif
525 
526 // this macro allows to get rid of linking errors about multiply defined functions.
527 //  - static is not very good because it prevents definitions from different object files to be merged.
528 //           So static causes the resulting linked executable to be bloated with multiple copies of the same function.
529 //  - inline is not perfect either as it unwantedly hints the compiler toward inlining the function.
530 #define EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
531 #define EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS inline
532 
533 #ifdef NDEBUG
534 # ifndef EIGEN_NO_DEBUG
535 #  define EIGEN_NO_DEBUG
536 # endif
537 #endif
538 
539 // eigen_plain_assert is where we implement the workaround for the assert() bug in GCC <= 4.3, see bug 89
540 #ifdef EIGEN_NO_DEBUG
541   #define eigen_plain_assert(x)
542 #else
543   #if EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO
544     namespace Eigen {
545     namespace internal {
copy_bool(bool b)546     inline bool copy_bool(bool b) { return b; }
547     }
548     }
549     #define eigen_plain_assert(x) assert(x)
550   #else
551     // work around bug 89
552     #include <cstdlib>   // for abort
553     #include <iostream>  // for std::cerr
554 
555     namespace Eigen {
556     namespace internal {
557     // trivial function copying a bool. Must be EIGEN_DONT_INLINE, so we implement it after including Eigen headers.
558     // see bug 89.
559     namespace {
copy_bool(bool b)560     EIGEN_DONT_INLINE bool copy_bool(bool b) { return b; }
561     }
assert_fail(const char * condition,const char * function,const char * file,int line)562     inline void assert_fail(const char *condition, const char *function, const char *file, int line)
563     {
564       std::cerr << "assertion failed: " << condition << " in function " << function << " at " << file << ":" << line << std::endl;
565       abort();
566     }
567     }
568     }
569     #define eigen_plain_assert(x) \
570       do { \
571         if(!Eigen::internal::copy_bool(x)) \
572           Eigen::internal::assert_fail(EIGEN_MAKESTRING(x), __PRETTY_FUNCTION__, __FILE__, __LINE__); \
573       } while(false)
574   #endif
575 #endif
576 
577 // eigen_assert can be overridden
578 #ifndef eigen_assert
579 #define eigen_assert(x) eigen_plain_assert(x)
580 #endif
581 
582 #ifdef EIGEN_INTERNAL_DEBUGGING
583 #define eigen_internal_assert(x) eigen_assert(x)
584 #else
585 #define eigen_internal_assert(x)
586 #endif
587 
588 #ifdef EIGEN_NO_DEBUG
589 #define EIGEN_ONLY_USED_FOR_DEBUG(x) EIGEN_UNUSED_VARIABLE(x)
590 #else
591 #define EIGEN_ONLY_USED_FOR_DEBUG(x)
592 #endif
593 
594 #ifndef EIGEN_NO_DEPRECATED_WARNING
595   #if EIGEN_COMP_GNUC
596     #define EIGEN_DEPRECATED __attribute__((deprecated))
597   #elif EIGEN_COMP_MSVC
598     #define EIGEN_DEPRECATED __declspec(deprecated)
599   #else
600     #define EIGEN_DEPRECATED
601   #endif
602 #else
603   #define EIGEN_DEPRECATED
604 #endif
605 
606 #if EIGEN_COMP_GNUC
607 #define EIGEN_UNUSED __attribute__((unused))
608 #else
609 #define EIGEN_UNUSED
610 #endif
611 
612 // Suppresses 'unused variable' warnings.
613 namespace Eigen {
614   namespace internal {
ignore_unused_variable(const T &)615     template<typename T> EIGEN_DEVICE_FUNC void ignore_unused_variable(const T&) {}
616   }
617 }
618 #define EIGEN_UNUSED_VARIABLE(var) Eigen::internal::ignore_unused_variable(var);
619 
620 #if !defined(EIGEN_ASM_COMMENT)
621   #if EIGEN_COMP_GNUC && (EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM_OR_ARM64)
622     #define EIGEN_ASM_COMMENT(X)  __asm__("#" X)
623   #else
624     #define EIGEN_ASM_COMMENT(X)
625   #endif
626 #endif
627 
628 
629 //------------------------------------------------------------------------------------------
630 // Static and dynamic alignment control
631 //
632 // The main purpose of this section is to define EIGEN_MAX_ALIGN_BYTES and EIGEN_MAX_STATIC_ALIGN_BYTES
633 // as the maximal boundary in bytes on which dynamically and statically allocated data may be alignment respectively.
634 // The values of EIGEN_MAX_ALIGN_BYTES and EIGEN_MAX_STATIC_ALIGN_BYTES can be specified by the user. If not,
635 // a default value is automatically computed based on architecture, compiler, and OS.
636 //
637 // This section also defines macros EIGEN_ALIGN_TO_BOUNDARY(N) and the shortcuts EIGEN_ALIGN{8,16,32,_MAX}
638 // to be used to declare statically aligned buffers.
639 //------------------------------------------------------------------------------------------
640 
641 
642 /* EIGEN_ALIGN_TO_BOUNDARY(n) forces data to be n-byte aligned. This is used to satisfy SIMD requirements.
643  * However, we do that EVEN if vectorization (EIGEN_VECTORIZE) is disabled,
644  * so that vectorization doesn't affect binary compatibility.
645  *
646  * If we made alignment depend on whether or not EIGEN_VECTORIZE is defined, it would be impossible to link
647  * vectorized and non-vectorized code.
648  */
649 #if (defined __CUDACC__)
650   #define EIGEN_ALIGN_TO_BOUNDARY(n) __align__(n)
651 #elif EIGEN_COMP_GNUC || EIGEN_COMP_PGI || EIGEN_COMP_IBM || EIGEN_COMP_ARM
652   #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))
653 #elif EIGEN_COMP_MSVC
654   #define EIGEN_ALIGN_TO_BOUNDARY(n) __declspec(align(n))
655 #elif EIGEN_COMP_SUNCC
656   // FIXME not sure about this one:
657   #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))
658 #else
659   #error Please tell me what is the equivalent of __attribute__((aligned(n))) for your compiler
660 #endif
661 
662 // If the user explicitly disable vectorization, then we also disable alignment
663 #if defined(EIGEN_DONT_VECTORIZE)
664   #define EIGEN_IDEAL_MAX_ALIGN_BYTES 0
665 #elif defined(EIGEN_VECTORIZE_AVX512)
666   // 64 bytes static alignmeent is preferred only if really required
667   #define EIGEN_IDEAL_MAX_ALIGN_BYTES 64
668 #elif defined(__AVX__)
669   // 32 bytes static alignmeent is preferred only if really required
670   #define EIGEN_IDEAL_MAX_ALIGN_BYTES 32
671 #else
672   #define EIGEN_IDEAL_MAX_ALIGN_BYTES 16
673 #endif
674 
675 
676 // EIGEN_MIN_ALIGN_BYTES defines the minimal value for which the notion of explicit alignment makes sense
677 #define EIGEN_MIN_ALIGN_BYTES 16
678 
679 // Defined the boundary (in bytes) on which the data needs to be aligned. Note
680 // that unless EIGEN_ALIGN is defined and not equal to 0, the data may not be
681 // aligned at all regardless of the value of this #define.
682 
683 #if (defined(EIGEN_DONT_ALIGN_STATICALLY) || defined(EIGEN_DONT_ALIGN))  && defined(EIGEN_MAX_STATIC_ALIGN_BYTES) && EIGEN_MAX_STATIC_ALIGN_BYTES>0
684 #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.
685 #endif
686 
687 // EIGEN_DONT_ALIGN_STATICALLY and EIGEN_DONT_ALIGN are deprectated
688 // They imply EIGEN_MAX_STATIC_ALIGN_BYTES=0
689 #if defined(EIGEN_DONT_ALIGN_STATICALLY) || defined(EIGEN_DONT_ALIGN)
690   #ifdef EIGEN_MAX_STATIC_ALIGN_BYTES
691     #undef EIGEN_MAX_STATIC_ALIGN_BYTES
692   #endif
693   #define EIGEN_MAX_STATIC_ALIGN_BYTES 0
694 #endif
695 
696 #ifndef EIGEN_MAX_STATIC_ALIGN_BYTES
697 
698   // Try to automatically guess what is the best default value for EIGEN_MAX_STATIC_ALIGN_BYTES
699 
700   // 16 byte alignment is only useful for vectorization. Since it affects the ABI, we need to enable
701   // 16 byte alignment on all platforms where vectorization might be enabled. In theory we could always
702   // enable alignment, but it can be a cause of problems on some platforms, so we just disable it in
703   // certain common platform (compiler+architecture combinations) to avoid these problems.
704   // Only static alignment is really problematic (relies on nonstandard compiler extensions),
705   // try to keep heap alignment even when we have to disable static alignment.
706   #if EIGEN_COMP_GNUC && !(EIGEN_ARCH_i386_OR_x86_64 || EIGEN_ARCH_ARM_OR_ARM64 || EIGEN_ARCH_PPC || EIGEN_ARCH_IA64)
707   #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 1
708   #elif EIGEN_ARCH_ARM_OR_ARM64 && EIGEN_COMP_GNUC_STRICT && EIGEN_GNUC_AT_MOST(4, 6)
709   // Old versions of GCC on ARM, at least 4.4, were once seen to have buggy static alignment support.
710   // Not sure which version fixed it, hopefully it doesn't affect 4.7, which is still somewhat in use.
711   // 4.8 and newer seem definitely unaffected.
712   #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 1
713   #else
714   #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 0
715   #endif
716 
717   // static alignment is completely disabled with GCC 3, Sun Studio, and QCC/QNX
718   #if !EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT \
719   && !EIGEN_GCC3_OR_OLDER \
720   && !EIGEN_COMP_SUNCC \
721   && !EIGEN_OS_QNX
722     #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 1
723   #else
724     #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 0
725   #endif
726 
727   #if EIGEN_ARCH_WANTS_STACK_ALIGNMENT
728     #define EIGEN_MAX_STATIC_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES
729   #else
730     #define EIGEN_MAX_STATIC_ALIGN_BYTES 0
731   #endif
732 
733 #endif
734 
735 // If EIGEN_MAX_ALIGN_BYTES is defined, then it is considered as an upper bound for EIGEN_MAX_ALIGN_BYTES
736 #if defined(EIGEN_MAX_ALIGN_BYTES) && EIGEN_MAX_ALIGN_BYTES<EIGEN_MAX_STATIC_ALIGN_BYTES
737 #undef EIGEN_MAX_STATIC_ALIGN_BYTES
738 #define EIGEN_MAX_STATIC_ALIGN_BYTES EIGEN_MAX_ALIGN_BYTES
739 #endif
740 
741 #if EIGEN_MAX_STATIC_ALIGN_BYTES==0 && !defined(EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT)
742   #define EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT
743 #endif
744 
745 // At this stage, EIGEN_MAX_STATIC_ALIGN_BYTES>0 is the true test whether we want to align arrays on the stack or not.
746 // It takes into account both the user choice to explicitly enable/disable alignment (by settting EIGEN_MAX_STATIC_ALIGN_BYTES)
747 // and the architecture config (EIGEN_ARCH_WANTS_STACK_ALIGNMENT).
748 // Henceforth, only EIGEN_MAX_STATIC_ALIGN_BYTES should be used.
749 
750 
751 // Shortcuts to EIGEN_ALIGN_TO_BOUNDARY
752 #define EIGEN_ALIGN8  EIGEN_ALIGN_TO_BOUNDARY(8)
753 #define EIGEN_ALIGN16 EIGEN_ALIGN_TO_BOUNDARY(16)
754 #define EIGEN_ALIGN32 EIGEN_ALIGN_TO_BOUNDARY(32)
755 #define EIGEN_ALIGN64 EIGEN_ALIGN_TO_BOUNDARY(64)
756 #if EIGEN_MAX_STATIC_ALIGN_BYTES>0
757 #define EIGEN_ALIGN_MAX EIGEN_ALIGN_TO_BOUNDARY(EIGEN_MAX_STATIC_ALIGN_BYTES)
758 #else
759 #define EIGEN_ALIGN_MAX
760 #endif
761 
762 
763 // Dynamic alignment control
764 
765 #if defined(EIGEN_DONT_ALIGN) && defined(EIGEN_MAX_ALIGN_BYTES) && EIGEN_MAX_ALIGN_BYTES>0
766 #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.
767 #endif
768 
769 #ifdef EIGEN_DONT_ALIGN
770   #ifdef EIGEN_MAX_ALIGN_BYTES
771     #undef EIGEN_MAX_ALIGN_BYTES
772   #endif
773   #define EIGEN_MAX_ALIGN_BYTES 0
774 #elif !defined(EIGEN_MAX_ALIGN_BYTES)
775   #define EIGEN_MAX_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES
776 #endif
777 
778 #if EIGEN_IDEAL_MAX_ALIGN_BYTES > EIGEN_MAX_ALIGN_BYTES
779 #define EIGEN_DEFAULT_ALIGN_BYTES EIGEN_IDEAL_MAX_ALIGN_BYTES
780 #else
781 #define EIGEN_DEFAULT_ALIGN_BYTES EIGEN_MAX_ALIGN_BYTES
782 #endif
783 
784 
785 #ifndef EIGEN_UNALIGNED_VECTORIZE
786 #define EIGEN_UNALIGNED_VECTORIZE 1
787 #endif
788 
789 //----------------------------------------------------------------------
790 
791 
792 #ifdef EIGEN_DONT_USE_RESTRICT_KEYWORD
793   #define EIGEN_RESTRICT
794 #endif
795 #ifndef EIGEN_RESTRICT
796   #define EIGEN_RESTRICT __restrict
797 #endif
798 
799 #ifndef EIGEN_STACK_ALLOCATION_LIMIT
800 // 131072 == 128 KB
801 #define EIGEN_STACK_ALLOCATION_LIMIT 131072
802 #endif
803 
804 #ifndef EIGEN_DEFAULT_IO_FORMAT
805 #ifdef EIGEN_MAKING_DOCS
806 // format used in Eigen's documentation
807 // needed to define it here as escaping characters in CMake add_definition's argument seems very problematic.
808 #define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat(3, 0, " ", "\n", "", "")
809 #else
810 #define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat()
811 #endif
812 #endif
813 
814 // just an empty macro !
815 #define EIGEN_EMPTY
816 
817 #if EIGEN_COMP_MSVC_STRICT && (EIGEN_COMP_MSVC < 1900 || EIGEN_CUDACC_VER>0)
818   // for older MSVC versions, as well as 1900 && CUDA 8, using the base operator is sufficient (cf Bugs 1000, 1324)
819   #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
820     using Base::operator =;
821 #elif EIGEN_COMP_CLANG // workaround clang bug (see http://forum.kde.org/viewtopic.php?f=74&t=102653)
822   #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
823     using Base::operator =; \
824     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) { Base::operator=(other); return *this; } \
825     template <typename OtherDerived> \
826     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other) { Base::operator=(other.derived()); return *this; }
827 #else
828   #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
829     using Base::operator =; \
830     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) \
831     { \
832       Base::operator=(other); \
833       return *this; \
834     }
835 #endif
836 
837 
838 /** \internal
839  * \brief Macro to manually inherit assignment operators.
840  * This is necessary, because the implicitly defined assignment operator gets deleted when a custom operator= is defined.
841  */
842 #define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived) EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived)
843 
844 /**
845 * Just a side note. Commenting within defines works only by documenting
846 * behind the object (via '!<'). Comments cannot be multi-line and thus
847 * we have these extra long lines. What is confusing doxygen over here is
848 * that we use '\' and basically have a bunch of typedefs with their
849 * documentation in a single line.
850 **/
851 
852 #define EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
853   typedef typename Eigen::internal::traits<Derived>::Scalar Scalar; /*!< \brief Numeric type, e.g. float, double, int or std::complex<float>. */ \
854   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. */ \
855   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. */ \
856   typedef typename Eigen::internal::ref_selector<Derived>::type Nested; \
857   typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \
858   typedef typename Eigen::internal::traits<Derived>::StorageIndex StorageIndex; \
859   enum { RowsAtCompileTime = Eigen::internal::traits<Derived>::RowsAtCompileTime, \
860         ColsAtCompileTime = Eigen::internal::traits<Derived>::ColsAtCompileTime, \
861         Flags = Eigen::internal::traits<Derived>::Flags, \
862         SizeAtCompileTime = Base::SizeAtCompileTime, \
863         MaxSizeAtCompileTime = Base::MaxSizeAtCompileTime, \
864         IsVectorAtCompileTime = Base::IsVectorAtCompileTime }; \
865   using Base::derived; \
866   using Base::const_cast_derived;
867 
868 
869 // FIXME Maybe the EIGEN_DENSE_PUBLIC_INTERFACE could be removed as importing PacketScalar is rarely needed
870 #define EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \
871   EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
872   typedef typename Base::PacketScalar PacketScalar;
873 
874 
875 #define EIGEN_PLAIN_ENUM_MIN(a,b) (((int)a <= (int)b) ? (int)a : (int)b)
876 #define EIGEN_PLAIN_ENUM_MAX(a,b) (((int)a >= (int)b) ? (int)a : (int)b)
877 
878 // EIGEN_SIZE_MIN_PREFER_DYNAMIC gives the min between compile-time sizes. 0 has absolute priority, followed by 1,
879 // followed by Dynamic, followed by other finite values. The reason for giving Dynamic the priority over
880 // finite values is that min(3, Dynamic) should be Dynamic, since that could be anything between 0 and 3.
881 #define EIGEN_SIZE_MIN_PREFER_DYNAMIC(a,b) (((int)a == 0 || (int)b == 0) ? 0 \
882                            : ((int)a == 1 || (int)b == 1) ? 1 \
883                            : ((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \
884                            : ((int)a <= (int)b) ? (int)a : (int)b)
885 
886 // EIGEN_SIZE_MIN_PREFER_FIXED is a variant of EIGEN_SIZE_MIN_PREFER_DYNAMIC comparing MaxSizes. The difference is that finite values
887 // now have priority over Dynamic, so that min(3, Dynamic) gives 3. Indeed, whatever the actual value is
888 // (between 0 and 3), it is not more than 3.
889 #define EIGEN_SIZE_MIN_PREFER_FIXED(a,b)  (((int)a == 0 || (int)b == 0) ? 0 \
890                            : ((int)a == 1 || (int)b == 1) ? 1 \
891                            : ((int)a == Dynamic && (int)b == Dynamic) ? Dynamic \
892                            : ((int)a == Dynamic) ? (int)b \
893                            : ((int)b == Dynamic) ? (int)a \
894                            : ((int)a <= (int)b) ? (int)a : (int)b)
895 
896 // see EIGEN_SIZE_MIN_PREFER_DYNAMIC. No need for a separate variant for MaxSizes here.
897 #define EIGEN_SIZE_MAX(a,b) (((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \
898                            : ((int)a >= (int)b) ? (int)a : (int)b)
899 
900 #define EIGEN_LOGICAL_XOR(a,b) (((a) || (b)) && !((a) && (b)))
901 
902 #define EIGEN_IMPLIES(a,b) (!(a) || (b))
903 
904 // the expression type of a standard coefficient wise binary operation
905 #define EIGEN_CWISE_BINARY_RETURN_TYPE(LHS,RHS,OPNAME) \
906     CwiseBinaryOp< \
907       EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)< \
908           typename internal::traits<LHS>::Scalar, \
909           typename internal::traits<RHS>::Scalar \
910       >, \
911       const LHS, \
912       const RHS \
913     >
914 
915 #define EIGEN_MAKE_CWISE_BINARY_OP(METHOD,OPNAME) \
916   template<typename OtherDerived> \
917   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME) \
918   (METHOD)(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
919   { \
920     return EIGEN_CWISE_BINARY_RETURN_TYPE(Derived,OtherDerived,OPNAME)(derived(), other.derived()); \
921   }
922 
923 #define EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,TYPEA,TYPEB) \
924   (Eigen::internal::has_ReturnType<Eigen::ScalarBinaryOpTraits<TYPEA,TYPEB,EIGEN_CAT(EIGEN_CAT(Eigen::internal::scalar_,OPNAME),_op)<TYPEA,TYPEB>  > >::value)
925 
926 #define EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(EXPR,SCALAR,OPNAME) \
927   CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<typename internal::traits<EXPR>::Scalar,SCALAR>, const EXPR, \
928                 const typename internal::plain_constant_type<EXPR,SCALAR>::type>
929 
930 #define EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(SCALAR,EXPR,OPNAME) \
931   CwiseBinaryOp<EIGEN_CAT(EIGEN_CAT(internal::scalar_,OPNAME),_op)<SCALAR,typename internal::traits<EXPR>::Scalar>, \
932                 const typename internal::plain_constant_type<EXPR,SCALAR>::type, const EXPR>
933 
934 // Workaround for MSVC 2010 (see ML thread "patch with compile for for MSVC 2010")
935 #if EIGEN_COMP_MSVC_STRICT<=1600
936 #define EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(X) typename internal::enable_if<true,X>::type
937 #else
938 #define EIGEN_MSVC10_WORKAROUND_BINARYOP_RETURN_TYPE(X) X
939 #endif
940 
941 #define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME) \
942   template <typename T> EIGEN_DEVICE_FUNC inline \
943   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))\
944   (METHOD)(const T& scalar) const { \
945     typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,Scalar,T)>::type PromotedT; \
946     return EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,PromotedT,OPNAME)(derived(), \
947            typename internal::plain_constant_type<Derived,PromotedT>::type(derived().rows(), derived().cols(), internal::scalar_constant_op<PromotedT>(scalar))); \
948   }
949 
950 #define EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
951   template <typename T> EIGEN_DEVICE_FUNC inline friend \
952   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)) \
953   (METHOD)(const T& scalar, const StorageBaseType& matrix) { \
954     typedef typename internal::promote_scalar_arg<Scalar,T,EIGEN_SCALAR_BINARY_SUPPORTED(OPNAME,T,Scalar)>::type PromotedT; \
955     return EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(PromotedT,Derived,OPNAME)( \
956            typename internal::plain_constant_type<Derived,PromotedT>::type(matrix.derived().rows(), matrix.derived().cols(), internal::scalar_constant_op<PromotedT>(scalar)), matrix.derived()); \
957   }
958 
959 #define EIGEN_MAKE_SCALAR_BINARY_OP(METHOD,OPNAME) \
960   EIGEN_MAKE_SCALAR_BINARY_OP_ONTHELEFT(METHOD,OPNAME) \
961   EIGEN_MAKE_SCALAR_BINARY_OP_ONTHERIGHT(METHOD,OPNAME)
962 
963 
964 #ifdef EIGEN_EXCEPTIONS
965 #  define EIGEN_THROW_X(X) throw X
966 #  define EIGEN_THROW throw
967 #  define EIGEN_TRY try
968 #  define EIGEN_CATCH(X) catch (X)
969 #else
970 #  ifdef __CUDA_ARCH__
971 #    define EIGEN_THROW_X(X) asm("trap;")
972 #    define EIGEN_THROW asm("trap;")
973 #  else
974 #    define EIGEN_THROW_X(X) std::abort()
975 #    define EIGEN_THROW std::abort()
976 #  endif
977 #  define EIGEN_TRY if (true)
978 #  define EIGEN_CATCH(X) else
979 #endif
980 
981 
982 #if EIGEN_HAS_CXX11_NOEXCEPT
983 #   define EIGEN_INCLUDE_TYPE_TRAITS
984 #   define EIGEN_NOEXCEPT noexcept
985 #   define EIGEN_NOEXCEPT_IF(x) noexcept(x)
986 #   define EIGEN_NO_THROW noexcept(true)
987 #   define EIGEN_EXCEPTION_SPEC(X) noexcept(false)
988 #else
989 #   define EIGEN_NOEXCEPT
990 #   define EIGEN_NOEXCEPT_IF(x)
991 #   define EIGEN_NO_THROW throw()
992 #   if EIGEN_COMP_MSVC
993       // MSVC does not support exception specifications (warning C4290),
994       // and they are deprecated in c++11 anyway.
995 #     define EIGEN_EXCEPTION_SPEC(X) throw()
996 #   else
997 #     define EIGEN_EXCEPTION_SPEC(X) throw(X)
998 #   endif
999 #endif
1000 
1001 #endif // EIGEN_MACROS_H
1002