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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_META_H
+#define EIGEN_META_H
+
+#if defined(EIGEN_GPU_COMPILE_PHASE)
+
+ #include <cfloat>
+
+ #if defined(EIGEN_CUDA_ARCH)
+ #include <math_constants.h>
+ #endif
+
+ #if defined(EIGEN_HIP_DEVICE_COMPILE)
+ #include "Eigen/src/Core/arch/HIP/hcc/math_constants.h"
+ #endif
+
+#endif
+
+// Recent versions of ICC require <cstdint> for pointer types below.
+#define EIGEN_ICC_NEEDS_CSTDINT (EIGEN_COMP_ICC>=1600 && EIGEN_COMP_CXXVER >= 11)
+
+// Define portable (u)int{32,64} types
+#if EIGEN_HAS_CXX11 || EIGEN_ICC_NEEDS_CSTDINT
+#include <cstdint>
+namespace Eigen {
+namespace numext {
+typedef std::uint8_t uint8_t;
+typedef std::int8_t int8_t;
+typedef std::uint16_t uint16_t;
+typedef std::int16_t int16_t;
+typedef std::uint32_t uint32_t;
+typedef std::int32_t int32_t;
+typedef std::uint64_t uint64_t;
+typedef std::int64_t int64_t;
+}
+}
+#else
+// Without c++11, all compilers able to compile Eigen also
+// provide the C99 stdint.h header file.
+#include <stdint.h>
+namespace Eigen {
+namespace numext {
+typedef ::uint8_t uint8_t;
+typedef ::int8_t int8_t;
+typedef ::uint16_t uint16_t;
+typedef ::int16_t int16_t;
+typedef ::uint32_t uint32_t;
+typedef ::int32_t int32_t;
+typedef ::uint64_t uint64_t;
+typedef ::int64_t int64_t;
+}
+}
+#endif
+
+namespace Eigen {
+
+typedef EIGEN_DEFAULT_DENSE_INDEX_TYPE DenseIndex;
+
+/**
+ * \brief The Index type as used for the API.
+ * \details To change this, \c \#define the preprocessor symbol \c EIGEN_DEFAULT_DENSE_INDEX_TYPE.
+ * \sa \blank \ref TopicPreprocessorDirectives, StorageIndex.
+ */
+
+typedef EIGEN_DEFAULT_DENSE_INDEX_TYPE Index;
+
+namespace internal {
+
+/** \internal
+ * \file Meta.h
+ * This file contains generic metaprogramming classes which are not specifically related to Eigen.
+ * \note In case you wonder, yes we're aware that Boost already provides all these features,
+ * we however don't want to add a dependency to Boost.
+ */
+
+// Only recent versions of ICC complain about using ptrdiff_t to hold pointers,
+// and older versions do not provide *intptr_t types.
+#if EIGEN_ICC_NEEDS_CSTDINT
+typedef std::intptr_t IntPtr;
+typedef std::uintptr_t UIntPtr;
+#else
+typedef std::ptrdiff_t IntPtr;
+typedef std::size_t UIntPtr;
+#endif
+#undef EIGEN_ICC_NEEDS_CSTDINT
+
+struct true_type { enum { value = 1 }; };
+struct false_type { enum { value = 0 }; };
+
+template<bool Condition>
+struct bool_constant;
+
+template<>
+struct bool_constant<true> : true_type {};
+
+template<>
+struct bool_constant<false> : false_type {};
+
+template<bool Condition, typename Then, typename Else>
+struct conditional { typedef Then type; };
+
+template<typename Then, typename Else>
+struct conditional <false, Then, Else> { typedef Else type; };
+
+template<typename T> struct remove_reference { typedef T type; };
+template<typename T> struct remove_reference<T&> { typedef T type; };
+
+template<typename T> struct remove_pointer { typedef T type; };
+template<typename T> struct remove_pointer<T*> { typedef T type; };
+template<typename T> struct remove_pointer<T*const> { typedef T type; };
+
+template <class T> struct remove_const { typedef T type; };
+template <class T> struct remove_const<const T> { typedef T type; };
+template <class T> struct remove_const<const T[]> { typedef T type[]; };
+template <class T, unsigned int Size> struct remove_const<const T[Size]> { typedef T type[Size]; };
+
+template<typename T> struct remove_all { typedef T type; };
+template<typename T> struct remove_all<const T> { typedef typename remove_all<T>::type type; };
+template<typename T> struct remove_all<T const&> { typedef typename remove_all<T>::type type; };
+template<typename T> struct remove_all<T&> { typedef typename remove_all<T>::type type; };
+template<typename T> struct remove_all<T const*> { typedef typename remove_all<T>::type type; };
+template<typename T> struct remove_all<T*> { typedef typename remove_all<T>::type type; };
+
+template<typename T> struct is_arithmetic { enum { value = false }; };
+template<> struct is_arithmetic<float> { enum { value = true }; };
+template<> struct is_arithmetic<double> { enum { value = true }; };
+template<> struct is_arithmetic<long double> { enum { value = true }; };
+template<> struct is_arithmetic<bool> { enum { value = true }; };
+template<> struct is_arithmetic<char> { enum { value = true }; };
+template<> struct is_arithmetic<signed char> { enum { value = true }; };
+template<> struct is_arithmetic<unsigned char> { enum { value = true }; };
+template<> struct is_arithmetic<signed short> { enum { value = true }; };
+template<> struct is_arithmetic<unsigned short>{ enum { value = true }; };
+template<> struct is_arithmetic<signed int> { enum { value = true }; };
+template<> struct is_arithmetic<unsigned int> { enum { value = true }; };
+template<> struct is_arithmetic<signed long> { enum { value = true }; };
+template<> struct is_arithmetic<unsigned long> { enum { value = true }; };
+
+template<typename T, typename U> struct is_same { enum { value = 0 }; };
+template<typename T> struct is_same<T,T> { enum { value = 1 }; };
+
+template< class T >
+struct is_void : is_same<void, typename remove_const<T>::type> {};
+
+#if EIGEN_HAS_CXX11
+template<> struct is_arithmetic<signed long long> { enum { value = true }; };
+template<> struct is_arithmetic<unsigned long long> { enum { value = true }; };
+using std::is_integral;
+#else
+template<typename T> struct is_integral { enum { value = false }; };
+template<> struct is_integral<bool> { enum { value = true }; };
+template<> struct is_integral<char> { enum { value = true }; };
+template<> struct is_integral<signed char> { enum { value = true }; };
+template<> struct is_integral<unsigned char> { enum { value = true }; };
+template<> struct is_integral<signed short> { enum { value = true }; };
+template<> struct is_integral<unsigned short> { enum { value = true }; };
+template<> struct is_integral<signed int> { enum { value = true }; };
+template<> struct is_integral<unsigned int> { enum { value = true }; };
+template<> struct is_integral<signed long> { enum { value = true }; };
+template<> struct is_integral<unsigned long> { enum { value = true }; };
+#if EIGEN_COMP_MSVC
+template<> struct is_integral<signed __int64> { enum { value = true }; };
+template<> struct is_integral<unsigned __int64> { enum { value = true }; };
+#endif
+#endif
+
+#if EIGEN_HAS_CXX11
+using std::make_unsigned;
+#else
+// TODO: Possibly improve this implementation of make_unsigned.
+// It is currently used only by
+// template<typename Scalar> struct random_default_impl<Scalar, false, true>.
+template<typename> struct make_unsigned;
+template<> struct make_unsigned<char> { typedef unsigned char type; };
+template<> struct make_unsigned<signed char> { typedef unsigned char type; };
+template<> struct make_unsigned<unsigned char> { typedef unsigned char type; };
+template<> struct make_unsigned<signed short> { typedef unsigned short type; };
+template<> struct make_unsigned<unsigned short> { typedef unsigned short type; };
+template<> struct make_unsigned<signed int> { typedef unsigned int type; };
+template<> struct make_unsigned<unsigned int> { typedef unsigned int type; };
+template<> struct make_unsigned<signed long> { typedef unsigned long type; };
+template<> struct make_unsigned<unsigned long> { typedef unsigned long type; };
+#if EIGEN_COMP_MSVC
+template<> struct make_unsigned<signed __int64> { typedef unsigned __int64 type; };
+template<> struct make_unsigned<unsigned __int64> { typedef unsigned __int64 type; };
+#endif
+
+// Some platforms define int64_t as `long long` even for C++03, where
+// `long long` is not guaranteed by the standard. In this case we are missing
+// the definition for make_unsigned. If we just define it, we run into issues
+// where `long long` doesn't exist in some compilers for C++03. We therefore add
+// the specialization for these platforms only.
+#if EIGEN_OS_MAC || EIGEN_COMP_MINGW
+template<> struct make_unsigned<unsigned long long> { typedef unsigned long long type; };
+template<> struct make_unsigned<long long> { typedef unsigned long long type; };
+#endif
+#endif
+
+template <typename T> struct add_const { typedef const T type; };
+template <typename T> struct add_const<T&> { typedef T& type; };
+
+template <typename T> struct is_const { enum { value = 0 }; };
+template <typename T> struct is_const<T const> { enum { value = 1 }; };
+
+template<typename T> struct add_const_on_value_type { typedef const T type; };
+template<typename T> struct add_const_on_value_type<T&> { typedef T const& type; };
+template<typename T> struct add_const_on_value_type<T*> { typedef T const* type; };
+template<typename T> struct add_const_on_value_type<T* const> { typedef T const* const type; };
+template<typename T> struct add_const_on_value_type<T const* const> { typedef T const* const type; };
+
+#if EIGEN_HAS_CXX11
+
+using std::is_convertible;
+
+#else
+
+template<typename From, typename To>
+struct is_convertible_impl
+{
+private:
+ struct any_conversion
+ {
+ template <typename T> any_conversion(const volatile T&);
+ template <typename T> any_conversion(T&);
+ };
+ struct yes {int a[1];};
+ struct no {int a[2];};
+
+ template<typename T>
+ static yes test(T, int);
+
+ template<typename T>
+ static no test(any_conversion, ...);
+
+public:
+ static typename internal::remove_reference<From>::type* ms_from;
+#ifdef __INTEL_COMPILER
+ #pragma warning push
+ #pragma warning ( disable : 2259 )
+#endif
+ enum { value = sizeof(test<To>(*ms_from, 0))==sizeof(yes) };
+#ifdef __INTEL_COMPILER
+ #pragma warning pop
+#endif
+};
+
+template<typename From, typename To>
+struct is_convertible
+{
+ enum { value = is_convertible_impl<From,To>::value };
+};
+
+template<typename T>
+struct is_convertible<T,T&> { enum { value = false }; };
+
+template<typename T>
+struct is_convertible<const T,const T&> { enum { value = true }; };
+
+#endif
+
+/** \internal Allows to enable/disable an overload
+ * according to a compile time condition.
+ */
+template<bool Condition, typename T=void> struct enable_if;
+
+template<typename T> struct enable_if<true,T>
+{ typedef T type; };
+
+#if defined(EIGEN_GPU_COMPILE_PHASE) && !EIGEN_HAS_CXX11
+#if !defined(__FLT_EPSILON__)
+#define __FLT_EPSILON__ FLT_EPSILON
+#define __DBL_EPSILON__ DBL_EPSILON
+#endif
+
+namespace device {
+
+template<typename T> struct numeric_limits
+{
+ EIGEN_DEVICE_FUNC
+ static EIGEN_CONSTEXPR T epsilon() { return 0; }
+ static T (max)() { assert(false && "Highest not supported for this type"); }
+ static T (min)() { assert(false && "Lowest not supported for this type"); }
+ static T infinity() { assert(false && "Infinity not supported for this type"); }
+ static T quiet_NaN() { assert(false && "quiet_NaN not supported for this type"); }
+};
+template<> struct numeric_limits<float>
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static float epsilon() { return __FLT_EPSILON__; }
+ EIGEN_DEVICE_FUNC
+ static float (max)() {
+ #if defined(EIGEN_CUDA_ARCH)
+ return CUDART_MAX_NORMAL_F;
+ #else
+ return HIPRT_MAX_NORMAL_F;
+ #endif
+ }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static float (min)() { return FLT_MIN; }
+ EIGEN_DEVICE_FUNC
+ static float infinity() {
+ #if defined(EIGEN_CUDA_ARCH)
+ return CUDART_INF_F;
+ #else
+ return HIPRT_INF_F;
+ #endif
+ }
+ EIGEN_DEVICE_FUNC
+ static float quiet_NaN() {
+ #if defined(EIGEN_CUDA_ARCH)
+ return CUDART_NAN_F;
+ #else
+ return HIPRT_NAN_F;
+ #endif
+ }
+};
+template<> struct numeric_limits<double>
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static double epsilon() { return __DBL_EPSILON__; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static double (max)() { return DBL_MAX; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static double (min)() { return DBL_MIN; }
+ EIGEN_DEVICE_FUNC
+ static double infinity() {
+ #if defined(EIGEN_CUDA_ARCH)
+ return CUDART_INF;
+ #else
+ return HIPRT_INF;
+ #endif
+ }
+ EIGEN_DEVICE_FUNC
+ static double quiet_NaN() {
+ #if defined(EIGEN_CUDA_ARCH)
+ return CUDART_NAN;
+ #else
+ return HIPRT_NAN;
+ #endif
+ }
+};
+template<> struct numeric_limits<int>
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static int epsilon() { return 0; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static int (max)() { return INT_MAX; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static int (min)() { return INT_MIN; }
+};
+template<> struct numeric_limits<unsigned int>
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static unsigned int epsilon() { return 0; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static unsigned int (max)() { return UINT_MAX; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static unsigned int (min)() { return 0; }
+};
+template<> struct numeric_limits<long>
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static long epsilon() { return 0; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static long (max)() { return LONG_MAX; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static long (min)() { return LONG_MIN; }
+};
+template<> struct numeric_limits<unsigned long>
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static unsigned long epsilon() { return 0; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static unsigned long (max)() { return ULONG_MAX; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static unsigned long (min)() { return 0; }
+};
+template<> struct numeric_limits<long long>
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static long long epsilon() { return 0; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static long long (max)() { return LLONG_MAX; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static long long (min)() { return LLONG_MIN; }
+};
+template<> struct numeric_limits<unsigned long long>
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static unsigned long long epsilon() { return 0; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static unsigned long long (max)() { return ULLONG_MAX; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static unsigned long long (min)() { return 0; }
+};
+template<> struct numeric_limits<bool>
+{
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static bool epsilon() { return false; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static bool (max)() { return true; }
+ EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+ static bool (min)() { return false; }
+};
+
+}
+
+#endif // defined(EIGEN_GPU_COMPILE_PHASE) && !EIGEN_HAS_CXX11
+
+/** \internal
+ * A base class do disable default copy ctor and copy assignment operator.
+ */
+class noncopyable
+{
+ EIGEN_DEVICE_FUNC noncopyable(const noncopyable&);
+ EIGEN_DEVICE_FUNC const noncopyable& operator=(const noncopyable&);
+protected:
+ EIGEN_DEVICE_FUNC noncopyable() {}
+ EIGEN_DEVICE_FUNC ~noncopyable() {}
+};
+
+/** \internal
+ * Provides access to the number of elements in the object of as a compile-time constant expression.
+ * It "returns" Eigen::Dynamic if the size cannot be resolved at compile-time (default).
+ *
+ * Similar to std::tuple_size, but more general.
+ *
+ * It currently supports:
+ * - any types T defining T::SizeAtCompileTime
+ * - plain C arrays as T[N]
+ * - std::array (c++11)
+ * - some internal types such as SingleRange and AllRange
+ *
+ * The second template parameter eases SFINAE-based specializations.
+ */
+template<typename T, typename EnableIf = void> struct array_size {
+ enum { value = Dynamic };
+};
+
+template<typename T> struct array_size<T,typename internal::enable_if<((T::SizeAtCompileTime&0)==0)>::type> {
+ enum { value = T::SizeAtCompileTime };
+};
+
+template<typename T, int N> struct array_size<const T (&)[N]> {
+ enum { value = N };
+};
+template<typename T, int N> struct array_size<T (&)[N]> {
+ enum { value = N };
+};
+
+#if EIGEN_HAS_CXX11
+template<typename T, std::size_t N> struct array_size<const std::array<T,N> > {
+ enum { value = N };
+};
+template<typename T, std::size_t N> struct array_size<std::array<T,N> > {
+ enum { value = N };
+};
+#endif
+
+/** \internal
+ * Analogue of the std::size free function.
+ * It returns the size of the container or view \a x of type \c T
+ *
+ * It currently supports:
+ * - any types T defining a member T::size() const
+ * - plain C arrays as T[N]
+ *
+ */
+template<typename T>
+EIGEN_CONSTEXPR Index size(const T& x) { return x.size(); }
+
+template<typename T,std::size_t N>
+EIGEN_CONSTEXPR Index size(const T (&) [N]) { return N; }
+
+/** \internal
+ * Convenient struct to get the result type of a nullary, unary, binary, or
+ * ternary functor.
+ *
+ * Pre C++11:
+ * Supports both a Func::result_type member and templated
+ * Func::result<Func(ArgTypes...)>::type member.
+ *
+ * If none of these members is provided, then the type of the first
+ * argument is returned.
+ *
+ * Post C++11:
+ * This uses std::result_of. However, note the `type` member removes
+ * const and converts references/pointers to their corresponding value type.
+ */
+#if EIGEN_HAS_STD_INVOKE_RESULT
+template<typename T> struct result_of;
+
+template<typename F, typename... ArgTypes>
+struct result_of<F(ArgTypes...)> {
+ typedef typename std::invoke_result<F, ArgTypes...>::type type1;
+ typedef typename remove_all<type1>::type type;
+};
+#elif EIGEN_HAS_STD_RESULT_OF
+template<typename T> struct result_of {
+ typedef typename std::result_of<T>::type type1;
+ typedef typename remove_all<type1>::type type;
+};
+#else
+template<typename T> struct result_of { };
+
+struct has_none {int a[1];};
+struct has_std_result_type {int a[2];};
+struct has_tr1_result {int a[3];};
+
+template<typename Func, int SizeOf>
+struct nullary_result_of_select {};
+
+template<typename Func>
+struct nullary_result_of_select<Func, sizeof(has_std_result_type)> {typedef typename Func::result_type type;};
+
+template<typename Func>
+struct nullary_result_of_select<Func, sizeof(has_tr1_result)> {typedef typename Func::template result<Func()>::type type;};
+
+template<typename Func>
+struct result_of<Func()> {
+ template<typename T>
+ static has_std_result_type testFunctor(T const *, typename T::result_type const * = 0);
+ template<typename T>
+ static has_tr1_result testFunctor(T const *, typename T::template result<T()>::type const * = 0);
+ static has_none testFunctor(...);
+
+ // note that the following indirection is needed for gcc-3.3
+ enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
+ typedef typename nullary_result_of_select<Func, FunctorType>::type type;
+};
+
+template<typename Func, typename ArgType, int SizeOf=sizeof(has_none)>
+struct unary_result_of_select {typedef typename internal::remove_all<ArgType>::type type;};
+
+template<typename Func, typename ArgType>
+struct unary_result_of_select<Func, ArgType, sizeof(has_std_result_type)> {typedef typename Func::result_type type;};
+
+template<typename Func, typename ArgType>
+struct unary_result_of_select<Func, ArgType, sizeof(has_tr1_result)> {typedef typename Func::template result<Func(ArgType)>::type type;};
+
+template<typename Func, typename ArgType>
+struct result_of<Func(ArgType)> {
+ template<typename T>
+ static has_std_result_type testFunctor(T const *, typename T::result_type const * = 0);
+ template<typename T>
+ static has_tr1_result testFunctor(T const *, typename T::template result<T(ArgType)>::type const * = 0);
+ static has_none testFunctor(...);
+
+ // note that the following indirection is needed for gcc-3.3
+ enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
+ typedef typename unary_result_of_select<Func, ArgType, FunctorType>::type type;
+};
+
+template<typename Func, typename ArgType0, typename ArgType1, int SizeOf=sizeof(has_none)>
+struct binary_result_of_select {typedef typename internal::remove_all<ArgType0>::type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1>
+struct binary_result_of_select<Func, ArgType0, ArgType1, sizeof(has_std_result_type)>
+{typedef typename Func::result_type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1>
+struct binary_result_of_select<Func, ArgType0, ArgType1, sizeof(has_tr1_result)>
+{typedef typename Func::template result<Func(ArgType0,ArgType1)>::type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1>
+struct result_of<Func(ArgType0,ArgType1)> {
+ template<typename T>
+ static has_std_result_type testFunctor(T const *, typename T::result_type const * = 0);
+ template<typename T>
+ static has_tr1_result testFunctor(T const *, typename T::template result<T(ArgType0,ArgType1)>::type const * = 0);
+ static has_none testFunctor(...);
+
+ // note that the following indirection is needed for gcc-3.3
+ enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
+ typedef typename binary_result_of_select<Func, ArgType0, ArgType1, FunctorType>::type type;
+};
+
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2, int SizeOf=sizeof(has_none)>
+struct ternary_result_of_select {typedef typename internal::remove_all<ArgType0>::type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>
+struct ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, sizeof(has_std_result_type)>
+{typedef typename Func::result_type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>
+struct ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, sizeof(has_tr1_result)>
+{typedef typename Func::template result<Func(ArgType0,ArgType1,ArgType2)>::type type;};
+
+template<typename Func, typename ArgType0, typename ArgType1, typename ArgType2>
+struct result_of<Func(ArgType0,ArgType1,ArgType2)> {
+ template<typename T>
+ static has_std_result_type testFunctor(T const *, typename T::result_type const * = 0);
+ template<typename T>
+ static has_tr1_result testFunctor(T const *, typename T::template result<T(ArgType0,ArgType1,ArgType2)>::type const * = 0);
+ static has_none testFunctor(...);
+
+ // note that the following indirection is needed for gcc-3.3
+ enum {FunctorType = sizeof(testFunctor(static_cast<Func*>(0)))};
+ typedef typename ternary_result_of_select<Func, ArgType0, ArgType1, ArgType2, FunctorType>::type type;
+};
+
+#endif
+
+#if EIGEN_HAS_STD_INVOKE_RESULT
+template<typename F, typename... ArgTypes>
+struct invoke_result {
+ typedef typename std::invoke_result<F, ArgTypes...>::type type1;
+ typedef typename remove_all<type1>::type type;
+};
+#elif EIGEN_HAS_CXX11
+template<typename F, typename... ArgTypes>
+struct invoke_result {
+ typedef typename result_of<F(ArgTypes...)>::type type1;
+ typedef typename remove_all<type1>::type type;
+};
+#else
+template<typename F, typename ArgType0 = void, typename ArgType1 = void, typename ArgType2 = void>
+struct invoke_result {
+ typedef typename result_of<F(ArgType0, ArgType1, ArgType2)>::type type1;
+ typedef typename remove_all<type1>::type type;
+};
+
+template<typename F>
+struct invoke_result<F, void, void, void> {
+ typedef typename result_of<F()>::type type1;
+ typedef typename remove_all<type1>::type type;
+};
+
+template<typename F, typename ArgType0>
+struct invoke_result<F, ArgType0, void, void> {
+ typedef typename result_of<F(ArgType0)>::type type1;
+ typedef typename remove_all<type1>::type type;
+};
+
+template<typename F, typename ArgType0, typename ArgType1>
+struct invoke_result<F, ArgType0, ArgType1, void> {
+ typedef typename result_of<F(ArgType0, ArgType1)>::type type1;
+ typedef typename remove_all<type1>::type type;
+};
+#endif
+
+struct meta_yes { char a[1]; };
+struct meta_no { char a[2]; };
+
+// Check whether T::ReturnType does exist
+template <typename T>
+struct has_ReturnType
+{
+ template <typename C> static meta_yes testFunctor(C const *, typename C::ReturnType const * = 0);
+ template <typename C> static meta_no testFunctor(...);
+
+ enum { value = sizeof(testFunctor<T>(static_cast<T*>(0))) == sizeof(meta_yes) };
+};
+
+template<typename T> const T* return_ptr();
+
+template <typename T, typename IndexType=Index>
+struct has_nullary_operator
+{
+ template <typename C> static meta_yes testFunctor(C const *,typename enable_if<(sizeof(return_ptr<C>()->operator()())>0)>::type * = 0);
+ static meta_no testFunctor(...);
+
+ enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };
+};
+
+template <typename T, typename IndexType=Index>
+struct has_unary_operator
+{
+ template <typename C> static meta_yes testFunctor(C const *,typename enable_if<(sizeof(return_ptr<C>()->operator()(IndexType(0)))>0)>::type * = 0);
+ static meta_no testFunctor(...);
+
+ enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };
+};
+
+template <typename T, typename IndexType=Index>
+struct has_binary_operator
+{
+ template <typename C> static meta_yes testFunctor(C const *,typename enable_if<(sizeof(return_ptr<C>()->operator()(IndexType(0),IndexType(0)))>0)>::type * = 0);
+ static meta_no testFunctor(...);
+
+ enum { value = sizeof(testFunctor(static_cast<T*>(0))) == sizeof(meta_yes) };
+};
+
+/** \internal In short, it computes int(sqrt(\a Y)) with \a Y an integer.
+ * Usage example: \code meta_sqrt<1023>::ret \endcode
+ */
+template<int Y,
+ int InfX = 0,
+ int SupX = ((Y==1) ? 1 : Y/2),
+ bool Done = ((SupX-InfX)<=1 ? true : ((SupX*SupX <= Y) && ((SupX+1)*(SupX+1) > Y))) >
+ // use ?: instead of || just to shut up a stupid gcc 4.3 warning
+class meta_sqrt
+{
+ enum {
+ MidX = (InfX+SupX)/2,
+ TakeInf = MidX*MidX > Y ? 1 : 0,
+ NewInf = int(TakeInf) ? InfX : int(MidX),
+ NewSup = int(TakeInf) ? int(MidX) : SupX
+ };
+ public:
+ enum { ret = meta_sqrt<Y,NewInf,NewSup>::ret };
+};
+
+template<int Y, int InfX, int SupX>
+class meta_sqrt<Y, InfX, SupX, true> { public: enum { ret = (SupX*SupX <= Y) ? SupX : InfX }; };
+
+
+/** \internal Computes the least common multiple of two positive integer A and B
+ * at compile-time.
+ */
+template<int A, int B, int K=1, bool Done = ((A*K)%B)==0, bool Big=(A>=B)>
+struct meta_least_common_multiple
+{
+ enum { ret = meta_least_common_multiple<A,B,K+1>::ret };
+};
+template<int A, int B, int K, bool Done>
+struct meta_least_common_multiple<A,B,K,Done,false>
+{
+ enum { ret = meta_least_common_multiple<B,A,K>::ret };
+};
+template<int A, int B, int K>
+struct meta_least_common_multiple<A,B,K,true,true>
+{
+ enum { ret = A*K };
+};
+
+
+/** \internal determines whether the product of two numeric types is allowed and what the return type is */
+template<typename T, typename U> struct scalar_product_traits
+{
+ enum { Defined = 0 };
+};
+
+// FIXME quick workaround around current limitation of result_of
+// template<typename Scalar, typename ArgType0, typename ArgType1>
+// struct result_of<scalar_product_op<Scalar>(ArgType0,ArgType1)> {
+// typedef typename scalar_product_traits<typename remove_all<ArgType0>::type, typename remove_all<ArgType1>::type>::ReturnType type;
+// };
+
+/** \internal Obtains a POD type suitable to use as storage for an object of a size
+ * of at most Len bytes, aligned as specified by \c Align.
+ */
+template<unsigned Len, unsigned Align>
+struct aligned_storage {
+ struct type {
+ EIGEN_ALIGN_TO_BOUNDARY(Align) unsigned char data[Len];
+ };
+};
+
+} // end namespace internal
+
+namespace numext {
+
+#if defined(EIGEN_GPU_COMPILE_PHASE)
+template<typename T> EIGEN_DEVICE_FUNC void swap(T &a, T &b) { T tmp = b; b = a; a = tmp; }
+#else
+template<typename T> EIGEN_STRONG_INLINE void swap(T &a, T &b) { std::swap(a,b); }
+#endif
+
+#if defined(EIGEN_GPU_COMPILE_PHASE) && !EIGEN_HAS_CXX11
+using internal::device::numeric_limits;
+#else
+using std::numeric_limits;
+#endif
+
+// Integer division with rounding up.
+// T is assumed to be an integer type with a>=0, and b>0
+template<typename T>
+EIGEN_DEVICE_FUNC
+T div_ceil(const T &a, const T &b)
+{
+ return (a+b-1) / b;
+}
+
+// The aim of the following functions is to bypass -Wfloat-equal warnings
+// when we really want a strict equality comparison on floating points.
+template<typename X, typename Y> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+bool equal_strict(const X& x,const Y& y) { return x == y; }
+
+#if !defined(EIGEN_GPU_COMPILE_PHASE) || (!defined(EIGEN_CUDA_ARCH) && defined(EIGEN_CONSTEXPR_ARE_DEVICE_FUNC))
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+bool equal_strict(const float& x,const float& y) { return std::equal_to<float>()(x,y); }
+
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+bool equal_strict(const double& x,const double& y) { return std::equal_to<double>()(x,y); }
+#endif
+
+template<typename X, typename Y> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+bool not_equal_strict(const X& x,const Y& y) { return x != y; }
+
+#if !defined(EIGEN_GPU_COMPILE_PHASE) || (!defined(EIGEN_CUDA_ARCH) && defined(EIGEN_CONSTEXPR_ARE_DEVICE_FUNC))
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+bool not_equal_strict(const float& x,const float& y) { return std::not_equal_to<float>()(x,y); }
+
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
+bool not_equal_strict(const double& x,const double& y) { return std::not_equal_to<double>()(x,y); }
+#endif
+
+} // end namespace numext
+
+} // end namespace Eigen
+
+#endif // EIGEN_META_H