text: 
  // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
  // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
  //
  // Eigen is free software; you can redistribute it and/or
  // modify it under the terms of the GNU Lesser General Public
  // License as published by the Free Software Foundation; either
  // version 3 of the License, or (at your option) any later version.
  //
  // Alternatively, you can redistribute it and/or
  // modify it under the terms of the GNU General Public License as
  // published by the Free Software Foundation; either version 2 of
  // the License, or (at your option) any later version.
  //
  // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
  // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
  // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
  // GNU General Public License for more details.
  //
  // You should have received a copy of the GNU Lesser General Public
  // License and a copy of the GNU General Public License along with
  // Eigen. If not, see <http://www.gnu.org/licenses/>.
  
  #ifndef EIGEN_MACROS_H
  #define EIGEN_MACROS_H
  
  #define EIGEN_WORLD_VERSION 3
  #define EIGEN_MAJOR_VERSION 0
  #define EIGEN_MINOR_VERSION 5
  
  #define EIGEN_VERSION_AT_LEAST(x,y,z) (EIGEN_WORLD_VERSION>x || (EIGEN_WORLD_VERSION>=x && \
                                        (EIGEN_MAJOR_VERSION>y || (EIGEN_MAJOR_VERSION>=y && \
                                                                   EIGEN_MINOR_VERSION>=z))))
  #ifdef __GNUC__
    #define EIGEN_GNUC_AT_LEAST(x,y) ((__GNUC__==x && __GNUC_MINOR__>=y) || __GNUC__>x)
  #else
    #define EIGEN_GNUC_AT_LEAST(x,y) 0
  #endif
   
  #ifdef __GNUC__
    #define EIGEN_GNUC_AT_MOST(x,y) ((__GNUC__==x && __GNUC_MINOR__<=y) || __GNUC__<x)
  #else
    #define EIGEN_GNUC_AT_MOST(x,y) 0
  #endif
  
  #if EIGEN_GNUC_AT_MOST(4,3) && !defined(__clang__)
    // see bug 89
    #define EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO 0
  #else
    #define EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO 1
  #endif
  
  #if defined(__GNUC__) && (__GNUC__ <= 3)
  #define EIGEN_GCC3_OR_OLDER 1
  #else
  #define EIGEN_GCC3_OR_OLDER 0
  #endif
  
  // 16 byte alignment is only useful for vectorization. Since it affects the ABI, we need to enable
  // 16 byte alignment on all platforms where vectorization might be enabled. In theory we could always
  // enable alignment, but it can be a cause of problems on some platforms, so we just disable it in
  // certain common platform (compiler+architecture combinations) to avoid these problems.
  // Only static alignment is really problematic (relies on nonstandard compiler extensions that don't
  // work everywhere, for example don't work on GCC/ARM), try to keep heap alignment even
  // when we have to disable static alignment.
  #if defined(__GNUC__) && !(defined(__i386__) || defined(__x86_64__) || defined(__powerpc__) || defined(__ppc__) || defined(__ia64__))
  #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 1
  #else
  #define EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT 0
  #endif
  
  // static alignment is completely disabled with GCC 3, Sun Studio, and QCC/QNX
  #if !EIGEN_GCC_AND_ARCH_DOESNT_WANT_STACK_ALIGNMENT \
   && !EIGEN_GCC3_OR_OLDER \
   && !defined(__SUNPRO_CC) \
   && !defined(__QNXNTO__)
    #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 1
  #else
    #define EIGEN_ARCH_WANTS_STACK_ALIGNMENT 0
  #endif
  
  #ifdef EIGEN_DONT_ALIGN
    #ifndef EIGEN_DONT_ALIGN_STATICALLY
      #define EIGEN_DONT_ALIGN_STATICALLY
    #endif
    #define EIGEN_ALIGN 0
  #else
    #define EIGEN_ALIGN 1
  #endif
  
  // EIGEN_ALIGN_STATICALLY is the true test whether we want to align arrays on the stack or not. It takes into account both the user choice to explicitly disable
  // alignment (EIGEN_DONT_ALIGN_STATICALLY) and the architecture config (EIGEN_ARCH_WANTS_STACK_ALIGNMENT). Henceforth, only EIGEN_ALIGN_STATICALLY should be used.
  #if EIGEN_ARCH_WANTS_STACK_ALIGNMENT && !defined(EIGEN_DONT_ALIGN_STATICALLY)
    #define EIGEN_ALIGN_STATICALLY 1
  #else
    #define EIGEN_ALIGN_STATICALLY 0
    #ifndef EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT
      #define EIGEN_DISABLE_UNALIGNED_ARRAY_ASSERT
    #endif
  #endif
  
  #ifdef EIGEN_DEFAULT_TO_ROW_MAJOR
  #define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION RowMajor
  #else
  #define EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ColMajor
  #endif
  
  #ifndef EIGEN_DEFAULT_DENSE_INDEX_TYPE
  #define EIGEN_DEFAULT_DENSE_INDEX_TYPE std::ptrdiff_t
  #endif
  
  /** Allows to disable some optimizations which might affect the accuracy of the result.
    * Such optimization are enabled by default, and set EIGEN_FAST_MATH to 0 to disable them.
    * They currently include:
    *   - single precision Cwise::sin() and Cwise::cos() when SSE vectorization is enabled.
    */
  #ifndef EIGEN_FAST_MATH
  #define EIGEN_FAST_MATH 1
  #endif
  
  #define EIGEN_DEBUG_VAR(x) std::cerr << #x << " = " << x << std::endl;
  
  // concatenate two tokens
  #define EIGEN_CAT2(a,b) a ## b
  #define EIGEN_CAT(a,b) EIGEN_CAT2(a,b)
  
  // convert a token to a string
  #define EIGEN_MAKESTRING2(a) #a
  #define EIGEN_MAKESTRING(a) EIGEN_MAKESTRING2(a)
  
  #if EIGEN_GNUC_AT_LEAST(4,1) && !defined(__clang__) && !defined(__INTEL_COMPILER)
  #define EIGEN_FLATTEN_ATTRIB __attribute__((flatten))
  #else
  #define EIGEN_FLATTEN_ATTRIB
  #endif
  
  // EIGEN_STRONG_INLINE is a stronger version of the inline, using __forceinline on MSVC,
  // but it still doesn't use GCC's always_inline. This is useful in (common) situations where MSVC needs forceinline
  // but GCC is still doing fine with just inline.
  #if (defined _MSC_VER) || (defined __INTEL_COMPILER)
  #define EIGEN_STRONG_INLINE __forceinline
  #else
  #define EIGEN_STRONG_INLINE inline
  #endif
  
  // EIGEN_ALWAYS_INLINE is the stronget, it has the effect of making the function inline and adding every possible
  // attribute to maximize inlining. This should only be used when really necessary: in particular,
  // it uses __attribute__((always_inline)) on GCC, which most of the time is useless and can severely harm compile times.
  // FIXME with the always_inline attribute,
  // gcc 3.4.x reports the following compilation error:
  //   Eval.h:91: sorry, unimplemented: inlining failed in call to 'const Eigen::Eval<Derived> Eigen::MatrixBase<Scalar, Derived>::eval() const'
  //    : function body not available
  #if EIGEN_GNUC_AT_LEAST(4,0)
  #define EIGEN_ALWAYS_INLINE __attribute__((always_inline)) inline
  #else
  #define EIGEN_ALWAYS_INLINE EIGEN_STRONG_INLINE
  #endif
  
  #if (defined __GNUC__)
  #define EIGEN_DONT_INLINE __attribute__((noinline))
  #elif (defined _MSC_VER)
  #define EIGEN_DONT_INLINE __declspec(noinline)
  #else
  #define EIGEN_DONT_INLINE
  #endif
  
  // this macro allows to get rid of linking errors about multiply defined functions.
  //  - static is not very good because it prevents definitions from different object files to be merged.
  //           So static causes the resulting linked executable to be bloated with multiple copies of the same function.
  //  - inline is not perfect either as it unwantedly hints the compiler toward inlining the function.
  #define EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
  #define EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS inline
  
  #ifdef NDEBUG
  # ifndef EIGEN_NO_DEBUG
  #  define EIGEN_NO_DEBUG
  # endif
  #endif
  
  // eigen_plain_assert is where we implement the workaround for the assert() bug in GCC <= 4.3, see bug 89
  #ifdef EIGEN_NO_DEBUG
    #define eigen_plain_assert(x)
  #else
    #if EIGEN_SAFE_TO_USE_STANDARD_ASSERT_MACRO
      namespace Eigen {
      namespace internal {
      inline bool copy_bool(bool b) { return b; }
      }
      }
      #define eigen_plain_assert(x) assert(x)
    #else
      // work around bug 89
      #include <cstdlib>   // for abort
      #include <iostream>  // for std::cerr
  
      namespace Eigen {
      namespace internal {
      // trivial function copying a bool. Must be EIGEN_DONT_INLINE, so we implement it after including Eigen headers.
      // see bug 89.
      namespace {
      EIGEN_DONT_INLINE bool copy_bool(bool b) { return b; }
      }
      inline void assert_fail(const char *condition, const char *function, const char *file, int line)
      {
        std::cerr << "assertion failed: " << condition << " in function " << function << " at " << file << ":" << line << std::endl;
        abort();
      }
      }
      }
      #define eigen_plain_assert(x) \
        do { \
          if(!Eigen::internal::copy_bool(x)) \
            Eigen::internal::assert_fail(EIGEN_MAKESTRING(x), __PRETTY_FUNCTION__, __FILE__, __LINE__); \
        } while(false)
    #endif
  #endif
  
  // eigen_assert can be overridden
  #ifndef eigen_assert
  #define eigen_assert(x) eigen_plain_assert(x)
  #endif
  
  #ifdef EIGEN_INTERNAL_DEBUGGING
  #define eigen_internal_assert(x) eigen_assert(x)
  #else
  #define eigen_internal_assert(x)
  #endif
  
  #ifdef EIGEN_NO_DEBUG
  #define EIGEN_ONLY_USED_FOR_DEBUG(x) (void)x
  #else
  #define EIGEN_ONLY_USED_FOR_DEBUG(x)
  #endif
  
  #if (defined __GNUC__)
  #define EIGEN_DEPRECATED __attribute__((deprecated))
  #elif (defined _MSC_VER)
  #define EIGEN_DEPRECATED __declspec(deprecated)
  #else
  #define EIGEN_DEPRECATED
  #endif
  
  #if (defined __GNUC__)
  #define EIGEN_UNUSED __attribute__((unused))
  #else
  #define EIGEN_UNUSED
  #endif
  
  // Suppresses 'unused variable' warnings.
  #define EIGEN_UNUSED_VARIABLE(var) (void)var;
  
  #if (defined __GNUC__)
  #define EIGEN_ASM_COMMENT(X)  asm("#" X)
  #else
  #define EIGEN_ASM_COMMENT(X)
  #endif
  
  /* EIGEN_ALIGN_TO_BOUNDARY(n) forces data to be n-byte aligned. This is used to satisfy SIMD requirements.
   * However, we do that EVEN if vectorization (EIGEN_VECTORIZE) is disabled,
   * so that vectorization doesn't affect binary compatibility.
   *
   * If we made alignment depend on whether or not EIGEN_VECTORIZE is defined, it would be impossible to link
   * vectorized and non-vectorized code.
   */
  #if (defined __GNUC__) || (defined __PGI) || (defined __IBMCPP__)
    #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))
  #elif (defined _MSC_VER)
    #define EIGEN_ALIGN_TO_BOUNDARY(n) __declspec(align(n))
  #elif (defined __SUNPRO_CC)
    // FIXME not sure about this one:
    #define EIGEN_ALIGN_TO_BOUNDARY(n) __attribute__((aligned(n)))
  #else
    #error Please tell me what is the equivalent of __attribute__((aligned(n))) for your compiler
  #endif
  
  #define EIGEN_ALIGN16 EIGEN_ALIGN_TO_BOUNDARY(16)
  
  #if EIGEN_ALIGN_STATICALLY
  #define EIGEN_USER_ALIGN_TO_BOUNDARY(n) EIGEN_ALIGN_TO_BOUNDARY(n)
  #define EIGEN_USER_ALIGN16 EIGEN_ALIGN16
  #else
  #define EIGEN_USER_ALIGN_TO_BOUNDARY(n)
  #define EIGEN_USER_ALIGN16
  #endif
  
  #ifdef EIGEN_DONT_USE_RESTRICT_KEYWORD
    #define EIGEN_RESTRICT
  #endif
  #ifndef EIGEN_RESTRICT
    #define EIGEN_RESTRICT __restrict
  #endif
  
  #ifndef EIGEN_STACK_ALLOCATION_LIMIT
  #define EIGEN_STACK_ALLOCATION_LIMIT 20000
  #endif
  
  #ifndef EIGEN_DEFAULT_IO_FORMAT
  #ifdef EIGEN_MAKING_DOCS
  // format used in Eigen's documentation
  // needed to define it here as escaping characters in CMake add_definition's argument seems very problematic.
  #define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat(3, 0, " ", "\n", "", "")
  #else
  #define EIGEN_DEFAULT_IO_FORMAT Eigen::IOFormat()
  #endif
  #endif
  
  // just an empty macro !
  #define EIGEN_EMPTY
  
  #if defined(_MSC_VER) && (!defined(__INTEL_COMPILER))
  #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
    using Base::operator =;
  #else
  #define EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived) \
    using Base::operator =; \
    EIGEN_STRONG_INLINE Derived& operator=(const Derived& other) \
    { \
      Base::operator=(other); \
      return *this; \
    }
  #endif
  
  #define EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Derived) \
    EIGEN_INHERIT_ASSIGNMENT_EQUAL_OPERATOR(Derived)
  
  /**
  * Just a side note. Commenting within defines works only by documenting
  * behind the object (via '!<'). Comments cannot be multi-line and thus
  * we have these extra long lines. What is confusing doxygen over here is
  * that we use '\' and basically have a bunch of typedefs with their
  * documentation in a single line.
  **/
  
  #define EIGEN_GENERIC_PUBLIC_INTERFACE(Derived) \
    typedef typename Eigen::internal::traits<Derived>::Scalar Scalar; /*!< \brief Numeric type, e.g. float, double, int or std::complex<float>. */ \
    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. */ \
    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. */ \
    typedef typename Eigen::internal::nested<Derived>::type Nested; \
    typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \
    typedef typename Eigen::internal::traits<Derived>::Index Index; \
    enum { RowsAtCompileTime = Eigen::internal::traits<Derived>::RowsAtCompileTime, \
          ColsAtCompileTime = Eigen::internal::traits<Derived>::ColsAtCompileTime, \
          Flags = Eigen::internal::traits<Derived>::Flags, \
          CoeffReadCost = Eigen::internal::traits<Derived>::CoeffReadCost, \
          SizeAtCompileTime = Base::SizeAtCompileTime, \
          MaxSizeAtCompileTime = Base::MaxSizeAtCompileTime, \
          IsVectorAtCompileTime = Base::IsVectorAtCompileTime };
  
  
  #define EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \
    typedef typename Eigen::internal::traits<Derived>::Scalar Scalar; /*!< \brief Numeric type, e.g. float, double, int or std::complex<float>. */ \
    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. */ \
    typedef typename Base::PacketScalar PacketScalar; \
    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. */ \
    typedef typename Eigen::internal::nested<Derived>::type Nested; \
    typedef typename Eigen::internal::traits<Derived>::StorageKind StorageKind; \
    typedef typename Eigen::internal::traits<Derived>::Index Index; \
    enum { RowsAtCompileTime = Eigen::internal::traits<Derived>::RowsAtCompileTime, \
          ColsAtCompileTime = Eigen::internal::traits<Derived>::ColsAtCompileTime, \
          MaxRowsAtCompileTime = Eigen::internal::traits<Derived>::MaxRowsAtCompileTime, \
          MaxColsAtCompileTime = Eigen::internal::traits<Derived>::MaxColsAtCompileTime, \
          Flags = Eigen::internal::traits<Derived>::Flags, \
          CoeffReadCost = Eigen::internal::traits<Derived>::CoeffReadCost, \
          SizeAtCompileTime = Base::SizeAtCompileTime, \
          MaxSizeAtCompileTime = Base::MaxSizeAtCompileTime, \
          IsVectorAtCompileTime = Base::IsVectorAtCompileTime }; \
    using Base::derived; \
    using Base::const_cast_derived;
  
  
  #define EIGEN_PLAIN_ENUM_MIN(a,b) (((int)a <= (int)b) ? (int)a : (int)b)
  #define EIGEN_PLAIN_ENUM_MAX(a,b) (((int)a >= (int)b) ? (int)a : (int)b)
  
  // EIGEN_SIZE_MIN_PREFER_DYNAMIC gives the min between compile-time sizes. 0 has absolute priority, followed by 1,
  // followed by Dynamic, followed by other finite values. The reason for giving Dynamic the priority over
  // finite values is that min(3, Dynamic) should be Dynamic, since that could be anything between 0 and 3.
  #define EIGEN_SIZE_MIN_PREFER_DYNAMIC(a,b) (((int)a == 0 || (int)b == 0) ? 0 \
                             : ((int)a == 1 || (int)b == 1) ? 1 \
                             : ((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \
                             : ((int)a <= (int)b) ? (int)a : (int)b)
  
  // EIGEN_SIZE_MIN_PREFER_FIXED is a variant of EIGEN_SIZE_MIN_PREFER_DYNAMIC comparing MaxSizes. The difference is that finite values
  // now have priority over Dynamic, so that min(3, Dynamic) gives 3. Indeed, whatever the actual value is
  // (between 0 and 3), it is not more than 3.
  #define EIGEN_SIZE_MIN_PREFER_FIXED(a,b)  (((int)a == 0 || (int)b == 0) ? 0 \
                             : ((int)a == 1 || (int)b == 1) ? 1 \
                             : ((int)a == Dynamic && (int)b == Dynamic) ? Dynamic \
                             : ((int)a == Dynamic) ? (int)b \
                             : ((int)b == Dynamic) ? (int)a \
                             : ((int)a <= (int)b) ? (int)a : (int)b)
  
  // see EIGEN_SIZE_MIN_PREFER_DYNAMIC. No need for a separate variant for MaxSizes here.
  #define EIGEN_SIZE_MAX(a,b) (((int)a == Dynamic || (int)b == Dynamic) ? Dynamic \
                             : ((int)a >= (int)b) ? (int)a : (int)b)
  
  #define EIGEN_LOGICAL_XOR(a,b) (((a) || (b)) && !((a) && (b)))
  
  #define EIGEN_IMPLIES(a,b) (!(a) || (b))
  
  #define EIGEN_MAKE_CWISE_BINARY_OP(METHOD,FUNCTOR) \
    template<typename OtherDerived> \
    EIGEN_STRONG_INLINE const CwiseBinaryOp<FUNCTOR<Scalar>, const Derived, const OtherDerived> \
    (METHOD)(const EIGEN_CURRENT_STORAGE_BASE_CLASS<OtherDerived> &other) const \
    { \
      return CwiseBinaryOp<FUNCTOR<Scalar>, const Derived, const OtherDerived>(derived(), other.derived()); \
    }
  
  // the expression type of a cwise product
  #define EIGEN_CWISE_PRODUCT_RETURN_TYPE(LHS,RHS) \
      CwiseBinaryOp< \
        internal::scalar_product_op< \
            typename internal::traits<LHS>::Scalar, \
            typename internal::traits<RHS>::Scalar \
        >, \
        const LHS, \
        const RHS \
      >
  
  #endif // EIGEN_MACROS_H
  